A techno-economic study of a pump storage hydropower system for ultra-deep level mines applied to Driefontein No. 9 Shaft DM Steenekamp orcid.org 0000-0001-7081-6118 Dissertation submitted in fulfilment of the requirements for the degree Master of Engineering in Mechanical Engineering at the North-West University Supervisor: Prof Chris Storm Graduation May 2018 Student number: 21649103 ii ABSTRACT The energy required for mineral recovery is a major operational cost and strategic focus for the global mining sector. Power disruptions result in loss of production throughput and deceased profitability. Therefore, mines are required to review their power sources to ensure the sustainability and viability of their operations. In the South African region, the recent electricity tariff increases have had a major effect on energy-intensive users and subsequently significantly impacted investor decisions. The business case for alternative energy sources, which include renewable energy sources, has become far more compelling in the current economic climate. However, renewable energy is characterised by an intermittent supply, but with the selection of an appropriate storage mechanism, power variability can be mitigated and the system‟s flexibility is enhanced. Only pumped storage hydropower is capable of meeting the anticipated technological and economic constraints with regard to storage capacity. High energy recovery has been recorded for energy recovery systems in deep level shafts. More than 50 turbines with a combined capacity of over 65 MW have been installed underground in various mines in South Africa. The use of current mine infrastructure of existing deep level mine shafts for underground pumped hydro-electric storage (UPHES) systems reduces the initial system capital cost and the depths of a potential network of tunnels provides potential hydraulic heads exceeding 1000 m. Driefontein No. 9 Shaft, a sub-shaft system consisting of a main shaft with shaft diameter 9.15 m and a shaft depth of 2 095 m, has been under care and maintenance for several years. The shaft is fully equipped with a dedicated production winder, dual-purpose production and men/material winder, shaft steelwork, electrical and communication cabling, various pipe columns and main haulages connecting the main shaft to the sub-vertical and ventilation shaft. A concept UPHES system model was produced in Excel and populated with the Driefontein No. 9 Shaft system parameters. The UPHES system configuration consists of a lower reservoir and pump station on 24 level, 2 095 m below datum (BD), a mid-shaft reservoir and pump chamber in mid-shaft - 1 050 m BD and a upper reservoir on intermediate pump chamber level, -150 m BD. The turbine chamber is also located on 24 level. Various assumptions are made, which include operational assumptions, such as when pumps are operational and when turbines are operational and system assumptions, which pertain to the general system components and their associated capacities. The UPHES system model was verified by using a simulation model developed in Engineering Equation Solver (EES). Unlike the Excel model, the EES simulation allows the pump and generating schedules to be varied for weekdays, Saturdays and Sundays. Therefore, the system was optimised using the EES simulation. The first priority for optimising the EES simulation model was to reduce the return on investment (ROI) as it is required that the asset investment is returned in the shortest time possible for the mine to benefit from the system‟s energy saving potential. Therefore, in order to optimise the utilisation of iii existing infrastructure and lower capital costs, the costs dependent on the system output parameters were optimised along with the output parameters. The largest energy savings are achieved by maximising the number of hours of generating electricity during periods in which a peak tariff is charged and maximising the number of hours pumped only in periods in which off-peak tariffs are charged. This strategy maximises the number of hours during the day in which the maximum differential cost between tariffs is charged. Strategically scheduled pump and generating schedules are required to achieve the optimal system energy saving. An optimisation matrix was used to evaluate the pumping and generating schedules and the effect thereof on the number of pumps required per pump chamber, lower reservoir capacity, capital expenditure (CAPEX), electricity savings and ROI. It was determined that a break-even point exists at which the electricity cost savings are negatively affected by a decreased differential between the higher and lower tariff charged, because the cost of power consumed due to pumping cannot be recovered when energy is generated with the turbine. It was determined that if the percentage differential between peak and off-peak tariffs in the low demand season reaches 64% (off-peak tariff as a percentage of the peak tariff) or higher, the system no longer displays any electricity cost savings. Also, the percentage differential between the high demand season standard and peak tariff for the current 2016/2017 Megaflex tariff structure is 188% (standard tariff as a percentage of the off-peak tariff). The break-even point for the high demand season standard and peak tariff differential was calculated as 157% (standard tariff as a percentage of the off- peak tariff), therefore if the percentage differential reaches 157% or lower, the system no longer displays any electricity cost savings. The findings described above were applied to the EES simulation and subsequently the optimal and most suitable option was selected for the Driefontein No. 9 Shaft UPHES system. The maximum trim off the electricity cost is given in the table below: Description Unit Total Annual total power cost – original system ZAR [RM] 72 350 987 Annual total power cost – UPHES system ZAR [RM] 66 835 000 Annual electricity cost savings ZAR [RM] 6 001 000 ROI Years 5.0 Total system electricity cost trim (% of original power required) 7.63% In order to validate the EES simulation, operational data of the energy recovery system installed at the Driefontein No. 5 Shaft were used. At the Driefontein No. 5 Shaft, the potential energy of the water in the chilled water shaft column is converted to mechanical energy by the turbine located 1 680 m below surface. The turbine system was retrofitted to the existing system and high energy recovery has been recorded for this installation. The turbine has the capacity to generate 4.6 MW. When the power calculated with the UPHES model is measured against the Driefontein No. 5 Shaft test data, the UPHES model power calculated is 1.05% lower than the power generated by the Driefontein No. 5 Shaft turbine. The EES simulation was subsequently validated. iv KEYWORDS Pumped hydroelectric storage, PHES, underground pumped hydroelectric storage, UPHES, energy storage, Eskom Megaflex, tariffs, ultra-deep, mines, energy, recovery, optimised custom UPHES system, schedule, capital cost estimate, CAPEX. ______________________________ v ACKNOWLEDGEMENTS Thanks be to our Lord, Jesus Christ, who was, and is, and is to come. For creating this world, and all in it, with the greatest wisdom of all. Thank you for extending the same wisdom to us and giving us the knowledge perfectly suited to be able to glorify Your Holy Name. 22 “The Lord brought me (wisdom) forth as the first of his works, before his deeds of old; 23 I (wisdom) was formed long ages ago, at the very beginning, when the world came to be. 24 When there were no watery depths, I was given birth, when there were no springs overflowing with water; 25 before the mountains were settled in place, before the hills, I was given birth, 26 before he made the world or its fields or any of the dust of the earth. 27 I was there when he set the heavens in place, when he marked out the horizon on the face of the deep, 28 when he established the clouds above and fixed securely the fountains of the deep, 29 when he gave the sea its boundary so the waters would not overstep his command, and when he marked out the foundations of the earth. 30 Then I was constantly at his side. I was filled with delight day after day, rejoicing always in his presence, 31 rejoicing in his whole world and delighting in mankind. Amen ______________________________ vi CONTENTS DECLARATION........................................................................................................................................i ABSTRACT.....................................................................................................................................….....ii KEYWORDS………….............................................................................................................................iv ACKNOWLEDGEMENTS..... ..................................................................................................................v CONTENTS…….....................................................................................................................................vi LIST OF TABLES…….............................................................................................................................x LIST OF FIGURES................................................................................................................................xii GLOSSARY OF TERMS.......................................................................................................................xiv NOMENCLATURE….............................................................................................................................xv TECHNICAL UNITS…...........................................................................................................................xvi 1 INTRODUCTION ....................................................................................................... 1-1 1.1 BACKGROUND .......................................................................................................................... 1-1 1.2 PROBLEM STATEMENT ........................................................................................................... 1-2 1.3 OBJECTIVE ................................................................................................................................ 1-2 1.4 RESEARCH METHODOLOGY AND EXPERIMENTAL PROCEDURE ..................................... 1-3 1.5 SCOPE AND LIMITS OF THE STUDY ....................................................................................... 1-3 1.6 DISSERTATION STRUCTURE .................................................................................................. 1-4 2 LITERATURE STUDY ............................................................................................... 2-5 2.1 INTRODUCTION ........................................................................................................................ 2-5 2.2 ENERGY AND MINES ................................................................................................................ 2-5 2.2.1 Cost of Energy ...................................................................................................................... 2-6 2.2.2 Eskom Tariff Increases ......................................................................................................... 2-8 2.2.3 Energy Saving Initiatives ...................................................................................................... 2-8 2.3 RENEWABLE ENERGY AND MINES ........................................................................................ 2-8 2.3.1 What is Renewable Energy? ................................................................................................ 2-9 2.3.2 Renewable Energy in South Africa ...................................................................................... 2-9 2.3.3 Cost of Renewable Energy ................................................................................................. 2-10 2.3.4 Photovoltaic Plants ............................................................................................................. 2-11 vii 2.3.5 Storage of Renewable Energy ........................................................................................... 2-12 2.4 UNDERGROUND PUMPED HYDROELECTRIC ENERGY STORAGE .................................. 2-13 2.4.1 Recovery of the Energy of Water Going Down Mine Shafts .............................................. 2-13 2.4.2 Concept of UPHES Plants .................................................................................................. 2-14 2.4.3 UPHES generation potential .............................................................................................. 2-14 2.4.4 System storage efficiency .................................................................................................. 2-14 2.4.5 Economics of a UPHES system ......................................................................................... 2-15 2.4.6 Use of existing mine infrastructure ..................................................................................... 2-15 2.4.7 Subsurface construction ..................................................................................................... 2-15 2.4.8 Main System Components ................................................................................................. 2-16 2.4.8.1 Pumps and turbines ........................................................................................................... 2-16 2.4.8.2 Turbines .............................................................................................................................. 2-17 2.4.8.3 Pumps ................................................................................................................................ 2-18 2.4.8.4 Upper and lower reservoirs ................................................................................................ 2-19 2.4.8.5 Emergency storage capacity and pumps ........................................................................... 2-19 2.4.8.6 Access shaft and pipe column ............................................................................................ 2-19 2.5 TREATING THE ROOT CAUSE OF ACID MINE DRAINAGE .................................................. 2-20 2.6 RISKS ASSOCIATED WITH UPHES ........................................................................................ 2-21 2.7 STATUTORY REQUIREMENTS .............................................................................................. 2-22 2.8 CONCLUSION .......................................................................................................................... 2-23 3 TECHNICAL BACKGROUND ................................................................................. 3-24 3.1 DRIEFONTEIN GOLD MINE .................................................................................................... 3-24 3.2 GEOLOGICAL CONDITIONS ................................................................................................... 3-24 3.3 DRIEFONTEIN NO. 9 SHAFT ................................................................................................... 3-25 3.4 SHAFT INFRASTRUCTURE .................................................................................................... 3-27 3.4.1 Pelton Turbine .................................................................................................................... 3-27 3.4.1.1 Driefontein No. 5 shaft Pelton turbine efficiency ................................................................ 3-27 3.4.1.2 System discharge rate to net head ratio ............................................................................ 3-27 3.4.2 Existing Chilled Water Column ........................................................................................... 3-28 3.4.3 Existing Chilled Water Column Pipe Schedules ................................................................. 3-28 3.4.4 Dewatering Pumps ............................................................................................................. 3-29 3.4.5 Upper, Mid-Shaft and Lower Reservoirs ............................................................................ 3-29 viii 4 UPHES SYSTEM MODEL ...................................................................................... 4-31 4.1 SYSTEM CONFIGURATION .................................................................................................... 4-31 4.1.1 Master UPHES System Model ........................................................................................... 4-31 4.1.2 Pipe Pressure Calculations ................................................................................................ 4-31 4.1.3 CAPEX Model..................................................................................................................... 4-31 4.2 TYPICAL POD .......................................................................................................................... 4-33 4.3 MEGAFLEX TARIFFS .............................................................................................................. 4-34 4.4 ASSUMPTIONS ........................................................................................................................ 4-35 4.5 INPUT PARAMETERS ............................................................................................................. 4-35 4.6 PIPE PRESSURE CALCULATIONS ........................................................................................ 4-36 4.6.1 Pipe Pressure Rating Calculations ..................................................................................... 4-37 4.6.2 Limiting Flow Rate .............................................................................................................. 4-38 4.7 CAPITAL COST MODEL .......................................................................................................... 4-40 4.7.1 Basis of Estimate ................................................................................................................ 4-40 4.7.2 Bill of Quantities.................................................................................................................. 4-40 4.7.3 Bill of Quantities – UPHES System: Driefontein No. 9 Shaft ............................................. 4-43 4.8 RESULTS ................................................................................................................................. 4-44 4.8.1 UPHES System Generating Capacity ................................................................................ 4-44 4.8.1.1 Instantaneous UPHES system generating capacity........................................................... 4-44 4.8.1.2 Power generated during peak tariff periods only ................................................................ 4-44 4.8.1.3 Power generated during peak and standard tariff periods ................................................. 4-46 4.8.2 Electricity Cost Savings ...................................................................................................... 4-48 4.8.3 Return on Investment ......................................................................................................... 4-49 5 EES MODEL ........................................................................................................... 5-50 5.1 SIMULATION INPUT PARAMETERS ...................................................................................... 5-50 5.2 SIMULATION OUTPUT PARAMETERS .................................................................................. 5-51 5.3 VERIFICATION ......................................................................................................................... 5-52 5.3.1 Simulation Results .............................................................................................................. 5-52 5.3.1.1 Power generated during peak tariff periods only ................................................................ 5-52 5.3.1.2 Power generated during peak and standard tariff periods ................................................. 5-53 5.3.1.3 Evaluation of simulation results .......................................................................................... 5-53 ix 5.4 SYSTEM OPTIMISATION ........................................................................................................ 5-54 5.4.1 Optimal Generating Schedules .......................................................................................... 5-54 5.4.2 Optimal Pumping Schedules .............................................................................................. 5-56 5.4.3 Tariff Differential Break-Even Point .................................................................................... 5-58 5.4.4 Optimised UPHES System for Driefontein No. 9 Shaft ...................................................... 5-61 6 MODEL VALIDATION ............................................................................................. 6-63 6.1 DRIEFONTEIN NO. 5 SHAFT ENERGY RECOVERY SYSTEM .............................................. 6-63 6.1.1 Layout and Operation ......................................................................................................... 6-64 6.1.2 Trips and Alarms ................................................................................................................ 6-65 6.2 TEST DATA .............................................................................................................................. 6-65 6.3 DATA EVALUATION................................................................................................................. 6-68 6.4 UPHES MODEL VALIDATION ................................................................................................. 6-69 7 CONCLUSION AND RECOMMENDATIONS .......................................................... 7-71 REFERENCES AND BIBLIOGRAPHY ............................................................................ 7-73 REFERENCES ................................................................................................................................... 7-73 BIBLIOGRAPHY ................................................................................................................................. 7-76 APPENDICES .................................................................................................................. 7-79 ______________________________ x LIST OF TABLES TABLE 2-1: TYPICAL MEGAFLEX STRUCTURE ANTICIPATED FOR A MINE ................................................................................. 2-7 TABLE 2-2: MOST USED STORAGE TECHNOLOGIES IN RENEWABLE ENERGY SYSTEMS ............................................................. 2-13 TABLE 2-3: WATER PUMPED FROM THE WORKINGS AT MINES ON THE WEST WITS LINE ........................................................ 2-21 TABLE 3-1: DRIEFONTEIN NO. 9 SHAFT COMPLEX INFORMATION ..................................................................................... 3-25 TABLE 3-2: DRIEFONTEIN NO. 5 SHAFT PELTON TURBINE TECHNICAL DESIGN DATA .............................................................. 3-27 TABLE 3-3: DRIEFONTEIN NO. 5 SHAFT PELTON TURBINE EFFICIENCIES .............................................................................. 3-27 TABLE 3-4: CHILLED WATER SHAFT PIPING DESIGN INPUT PARAMETERS .............................................................................. 3-28 TABLE 4-1: 2015/2016 MEGAFLEX TARIFF STRUCTURE USED IN THE MODEL ..................................................................... 4-34 TABLE 4-2: MODEL INPUT PARAMETERS ...................................................................................................................... 4-36 TABLE 4-3: SHAFT PIPING PRESSURES .......................................................................................................................... 4-37 TABLE 4-4: PEAK PIPE PRESSURE AND SELECTED PIPE SCHEDULE BETWEEN BD 0.00 M AND BD - 698.3 M .............................. 4-38 TABLE 4-5: PEAK PIPE PRESSURE AND SELECTED PIPE SCHEDULE BETWEEN BD - 698.30 M TO BD - 1 396.6 M ........................ 4-38 TABLE 4-6: PEAK PIPE PRESSURE AND SELECTED PIPE SCHEDULE BETWEEN BD -698.30 M TO BD - 1 396.6 M ......................... 4-38 TABLE 4-7: PEAK PIPE PRESSURE BD 0.00 M TO BD- 698.3 M AT LIMITING VELOCITY ......................................................... 4-39 TABLE 4-8: PEAK PIPE PRESSURE BD - 698.30 M TO BD - 1 396.6 M AT LIMITING VELOCITY ................................................ 4-39 TABLE 4-9: PEAK PIPE PRESSURE BD -1 396.6 M TO BD – 2 095 M AT LIMITING VELOCITY .................................................. 4-39 TABLE 4-10: CAPITAL COST MODEL INPUT PARAMETERS ................................................................................................. 4-40 TABLE 4-11: GENERATING DURING PEAK TARIFF PERIODS ONLY – SYSTEM PARAMETERS ........................................................ 4-44 TABLE 4-12: GENERATING DURING PEAK AND STANDARD TARIFF PERIODS – SYSTEM PARAMETERS .......................................... 4-46 TABLE 4-13: GENERATING DURING PEAK TARIFF PERIODS ONLY – TRIM .............................................................................. 4-48 TABLE 4-14: GENERATING DURING PEAK AND STANDARD TARIFF PERIODS – TRIM ................................................................ 4-48 TABLE 4-15: ROI ASSUMING A TARIFF INCREASE OF 8% PA ............................................................................................. 4-49 TABLE 5-1: EES SIMULATION MODEL INPUT PARAMETERS ............................................................................................... 5-50 TABLE 5-2: EES SIMULATION MODEL OUTPUT PARAMETERS ............................................................................................ 5-51 TABLE 5-3: GENERATING DURING PEAK TARIFF PERIODS ONLY, EES SIMULATION RESULTS ..................................................... 5-52 TABLE 5-4: GENERATING DURING PEAK AND STANDARD TARIFF PERIODS, EES SIMULATION RESULTS ........................................ 5-53 TABLE 5-5: OPTIMISATION EVALUATION MATRIX – OPTION 1 TO 9 ................................................................................... 5-56 TABLE 5-6: OPTIMISATION EVALUATION MATRIX – OPTION 3 TO 9, 10 .............................................................................. 5-58 xi TABLE 5-7: TARIFF DIFFERENTIAL BREAK-EVEN POINT FOR LOW DEMAND SEASONS ............................................................. 5-59 TABLE 5-8: TARIFF DIFFERENTIAL BREAK-EVEN POINT FOR HIGH DEMAND SEASONS ............................................................. 5-60 TABLE 5-9: OPTIMISED UPHES SYSTEM EES SIMULATION RESULTS .................................................................................. 5-61 TABLE 6-1: DRIEFONTEIN NO. 5 SHAFT SYSTEM OPERATING PARAMETERS ......................................................................... 6-64 TABLE 6-2: DRIEFONTEIN NO. 5 SHAFT SYSTEM OPERATING PARAMETERS DURING DATA COLLECTION ..................................... 6-65 TABLE 6-3: MODEL INPUT PARAMETERS ...................................................................................................................... 6-69 TABLE 6-4: MODEL OUTPUT PARAMETERS ................................................................................................................... 6-69 TABLE 7-1: OPTIMISED DRIEFONTEIN NO. 9 SHAFT UPHES SYSTEM – TRIM ...................................................................... 7-72 ______________________________ xii LIST OF FIGURES FIGURE 2-1: ELECTRICITY CONSUMPTION BREAKDOWN (GOLDFIELDS, 2011) ..................................................................... 2-6 FIGURE 2-2: TARIFFS AND CHARGES BOOKLET 2013/14 (ESKOM, 2013) ............................................................................ 2-6 FIGURE 2-3: REIPPPP TENDER OUTCOME – AVERAGE POWER TARIFFS .............................................................................. 2-10 FIGURE 2-4: AVERAGE ESKOM TARIFFS VERSUS UTILITY–SCALE RENEWABLE ENERGY TARIFFS (ESKOM, 2016) ........................... 2-11 FIGURE 2-5: POWER GENERATION FACTOR .................................................................................................................. 2-11 FIGURE 2-6: TYPICAL POD LOAD PROFILE .................................................................................................................... 2-12 FIGURE 2-7: PELTON TURBINE MANUFACTURED AT VOITH IN GERMANY (VOITH, 2015)....................................................... 2-16 FIGURE 2-8: APPLICATION RANGE FOR PELTON TURBINES (VOITH, 2015) .......................................................................... 2-17 FIGURE 2-9: TURBINE EFFICIENCY FOR 2, 4 AND 6 NEEDLE OPERATION AT STANISHOUS POWERHOUSE (ROBERTS ET AL., 2011) ... 2-18 FIGURE 2-10: MULTISTAGE CLEAR WATER PUMPS’ PERFORMANCE RANGE (SULZER, 2015) .................................................. 2-18 FIGURE 2-11: CROSS-SECTION OF A SHAFT WITH TWO PIPE COLUMNS (WINDE ET AL., 2017) ................................................ 2-20 FIGURE 2-12: WATER FROM THE INRUSH OVERFLOWING INTO NO. 4 SHAFT ...................................................................... 2-22 FIGURE 3-1: LOCATION OF THE DRIEFONTEIN GOLD MINE (GOLDFIELDS, 2009) .................................................................. 3-24 FIGURE 3-2: GEOLOGICAL CONDITIONS AT THE DRIEFONTEIN GOLD MINE (WINDE EL AL, 2017 ) ............................................ 3-25 FIGURE 3-3: DRIEFONTEIN NO. 9 SHAFT COMPLEX LAYOUT (SATELLITE VIEW) ..................................................................... 3-26 FIGURE 3-4: SHAFT INFRASTRUCTURE DIAGRAM ............................................................................................................ 3-26 FIGURE 3-5: TYPICAL HAULAGE CROSS-SECTION ............................................................................................................ 3-30 FIGURE 4-1: UPHES SYSTEM CONFIGURATION ............................................................................................................. 4-32 FIGURE 4-2: TYPICAL POD DURING LOW DEMAND SEASON ............................................................................................. 4-33 FIGURE 4-3: TYPICAL POD DURING HIGH DEMAND SEASON ............................................................................................ 4-33 FIGURE 4-4: POD LOAD PROFILE – POWER GENERATED DURING PEAK TARIFF PERIODS ONLY .................................................. 4-45 FIGURE 4-5: DAILY ENERGY COST PROFILE – POWER GENERATED DURING PEAK TARIFF PERIODS ONLY ...................................... 4-45 FIGURE 4-6: POD LOAD PROFILE – POWER GENERATED DURING PEAK AND STANDARD TARIFF PERIODS .................................... 4-47 FIGURE 4-7: DAILY ENERGY COST PROFILE – POWER GENERATED DURING PEAK AND STANDARD TARIFF PERIODS ........................ 4-47 FIGURE 4-8: ROI (ASSUMING AN 8% PA TARIFF INCREASE) ............................................................................................. 4-49 FIGURE 5-1: LOAD AND COST PROFILE VERSUS TIME (WEEKDAYS)..................................................................................... 5-55 FIGURE 5-2: LOAD AND COST PROFILE VS TIME (SATURDAYS) ........................................................................................... 5-55 FIGURE 5-3: LOAD AND COST PROFILE VERSUS TIME (SUNDAYS) ....................................................................................... 5-55 xiii FIGURE 5-4: LOAD AND COST PROFILE VERSUS TIME (WEEKDAYS) OPTION 3, 9 AND 10 ........................................................ 5-57 FIGURE 5-5: LOAD AND COST PROFILE VERSUS TIME (SATURDAYS) OPTION 3, 10 AND 11 ..................................................... 5-57 FIGURE 5-6: LOAD AND COST PROFILE VERSUS TIME (SUNDAYS) OPTION 3, 10 AND 11 ........................................................ 5-57 FIGURE 5-7: OPTIMISED LOAD AND COST PROFILE VERSUS TIME (WEEKDAYS) ..................................................................... 5-62 FIGURE 5-8: OPTIMISED LOAD AND COST PROFILE VERSUS TIME (SATURDAYS) .................................................................... 5-62 FIGURE 5-9: OPTIMISED LOAD AND COST PROFILE VERSUS TIME (SUNDAYS) ....................................................................... 5-62 FIGURE 6-1: DRIEFONTEIN NO. 5 SHAFT TURBINE ......................................................................................................... 6-63 FIGURE 6-2: DRIEFONTEIN NO. 5 SHAFT TURBINE BYPASS LINE AND LUBRICATION ............................................................... 6-64 FIGURE 6-3: DRIEFONTEIN NO. 5 SHAFT TURBINE TRIPS AND ALARMS ............................................................................... 6-65 FIGURE 6-4: TURBINE MONITORING SCREEN ................................................................................................................. 6-66 FIGURE 6-5: TURBINE TEST DATA DATED 27 JANUARY 2014 ........................................................................................... 6-67 FIGURE 6-6: DATA EVALUATION – ACTUAL AND THEORETICAL POWER VERSUS TIME ............................................................. 6-68 FIGURE 6-7: DATA EVALUATION – ACTUAL POWER (BLACK), THEORETICAL POWER (BLUE) AND DISCHARGE RATE TO NET HEAD RATIO (RED) VERSUS FLOW RATE ................................................................................................................................. 6-69 FIGURE 6-8: VALIDATION ......................................................................................................................................... 6-70 ______________________________ xiv GLOSSARY OF TERMS Chilled water Water cooled by refrigeration plants and used for underground cooling purposes Generating schedules A schedule with time allocated to generating electricity with the turbine within a 24-hour cycle Life of mine The number of years that the mine is expected to be productively operated Pilot calculation Model calculation using low demand season or high demand season tariffs charged Pumping schedules A schedule with time allocated to pumping water to the upper reservoir within a 24-hour cycle Shaft column Piping installed in the shaft; includes the shaft dewatering column and the turbine feed column Trim Term used to describe the reduction in the total electricity costs ______________________________ xv NOMENCLATURE AMD Acid Mine Drainage ASME American Society of Material/Mechanical Engineers ASTM American Society for Testing and Materials B.Eng. Baccalaureus in Engineering BD Below Datum, ground elevation is at 0 m BD CAPEX Capital Expenditure DoE Department of Energy DSM Demand Side Management EES Engineering Equation Solver. Computer program used in cycle design and optimisation in this project. FWR Far West Rand HDS High Demand Season ID Internal diameter IPC Intermediate Pump Chamber IRP National Integrated Resources Plan LDS Low Demand Season NB Nominal Bore (pipe specification) NWU North-West University PA Per Annum PHES Pumped Hydro Electric Storage POD Point of Distribution PV Photovoltaic REA Renewable Energy Advisors REIPPPP Renewable Energy Independent Power Producer Procurement Programme ROI Return on Investment SCH Schedule (pipe specification) TOU Time of Use UPHES Underground Pumped Hydro Electric Storage U/G Underground ______________________________ xvi TECHNICAL UNITS kPa Kilopascals kW Kilowatts kWh Kilowatt-hour GWh Gigawatt-hour %VAR Percentage variation Hydraulic efficiency Pump efficiency Turbine efficiency h Effective head c/kWh Cents per kilowatt-hour kg/(ms) Fluid dynamic viscosity, kilogram per second kg/m 3 Fluid density, kilogram per cubic metre kV Kilovolt l Litres l/s Litres per second m Metre m/s 2 Metre per second squared m 3 Cubic metre MR Million rand MWh Megawatt-hour NB Nominal bore (pipe diameter) Nm Newton-metre R System discharge rate to net head ratio R/kVA Rand per kilovolt-ampere Rpm Rotations per minute ZAR South African rand ______________________________ 1-1 1 INTRODUCTION 1.1 BACKGROUND The energy required for mining and beneficiation is a key cost driver amounting to between 18% and 20% of the operational cost of mines. Energy is a major operational cost and therefore a strategic focus for the mining sector today. The South African national grid, supplied by the public utility provider, Eskom, has been under strain since 2007. Between 2012 and 2015, infrastructure failure, maintenance backlogs and failure to bring new generating capacity online as planned resulted in load shedding, the impact of which affected economic growth negatively. Furthermore, although South Africa‟s tariff prices are ranked 10 th most expensive out of 18 countries surveyed in a 2016 Energy Market Survey conducted by NUS Consulting, they also displayed the second biggest jump behind Belgium‟s 9.9% increase (Writer, 2015). Tariff price hikes are constantly under South African media scrutiny and remain a controversial matter. In South Africa, the majority of mining operations are entirely tied into the grid and electricity costs charged by Eskom are structured according to the Megaflex tariff structure. In 2016 the off-peak and peak tariffs charged during the high demand season (June to August) was 44.10 c/kWh and 268.06 c/kWh respectively (Eskom, 2016). The peak and off-peak tariffs increased at an approved 8% per annum since July 2014 until the end of June 2018. In June 2017, Moneyweb reported to have viewed an undisclosed confidential draft submitted by Eskom for comment to National Treasury proposing an increase of 19.9% for the year 2018/2019 (Slabbert, 2017). Mines must therefore consider alternative energy sources because it is strategically imperative for the sustainability of their operations. The business case for alternative energy sources has consequently become far more compelling as renewable energy is an alternative to conventional sources of energy. However, the sustainability of renewable energy is hampered by a characteristic intermitted supply. With the selection of an appropriate storage mechanism, power variations can be mitigated and system flexibility enhanced. Only pumped hydroelectric storage (PHES) supplies high amounts of power for significantly long periods and is capable of producing the quantum of energy required by mining operations. PHES is used to store energy in the form of potential energy. Water is pumped from a lower reservoir during periods when off-peak tariffs are charged to an upper reservoir. During peak tariff charge periods, electricity is generated by turbines converting this potential energy into electrical power. Traditionally a PHES system is applied to take advantage of the difference between a peak and off- peak tariff. Electricity generated by the water flowing through the turbine fed from the upper reservoir is sold back to the grid, during periods in which the peak tariff is charged. A PHES system requires either a very large body of water or large variation in height. Ultra-deep level gold mines provide large variations in head since their depths typically exceed 1 000 m. Furthermore, 1-2 the infrastructure to support great volumes of water is created by the underground excavations made to access the ore body. The use of ultra-deep level South African mines for underground pumped hydroelectric storage (UPHES) systems can therefore possibly have great economic potential. UPHES not only provides a solution to the issue encountered with regard to storing renewable energy, but also to the tariff increases threatening the sustainability of mining operations in South Africa. Mines that have reached the end of life of mine have been or are in the process of being decommissioned. These mines are normally flooded, all entries are sealed and the site is secured. In some cases, mines are placed under care and maintenance, because of trepidations about profitability. Vertical shafts placed under care and maintenance are maintained in so far as is necessary to allow the shaft to be used for possible future operations by the current or future owner. An opportunity is presented in both cases: equip the shaft with a UPHES system. Not only can the existing shaft infrastructure be used to reduce the capital costs and gain schedule advantages, but electricity can be generated in sufficient quantities and returned to the grid in periods in which peak tariffs are charged. There is therefore an opportunity to capitalise on decommissioned mines and mines placed under care and maintenance, in South Africa. If proven technologically feasible, as has already been proven from experience with similar systems, the system can be implemented at Driefontein No. 9 Shaft. Driefontein No. 9 Shaft, a sub-shaft system consisting of a main shaft with shaft diameter 9.15 m and a shaft depth of 2 095 m, has been under care and maintenance for several years. The shaft is fully equipped with a dedicated production winder, dual purpose production and men/material winder, shaft steelwork, electrical cables, communication cables, various pipe columns and main haulages on 21, 21.5, 22, 23 and 24 level connecting the main shaft to the sub-vertical and ventilation shaft. The opportunity has been identified to install a UPHES system in this shaft. 1.2 PROBLEM STATEMENT There is no existing techno-economic study for a UPHES system, customised to suit the Driefontein No. 9 Shaft infrastructure, to evaluate the feasibility for implementation of this identified opportunity. 1.3 OBJECTIVE This study endeavours to evaluate a custom UPHES system for possible implementation at the Driefontein No. 9 Shaft by: (1) Developing a concept UPHES model to evaluate:  Pumping and turbine generating efficiencies  Peak- and off-peak tariff structures (for generating and pumping)  Capital expenditure (CAPEX)  Calculation of return on investment (ROI) (2) Verifying the concept model (3) Simulating a UPHES system for the Driefontein No. 9 Shaft with the verified model 1-3 (4) Validating the simulated UPHES system with actual operational data from a similar installation. Furthermore, the study will endeavour to identify the limitations of the UPHES system applied to ultra- deep level gold mines and give special consideration to the laws and regulations that govern the safe operation of mines in South Africa. 1.4 RESEARCH METHODOLOGY AND EXPERIMENTAL PROCEDURE The methodology to evaluate a custom UPHES system applied to ultra-deep level gold mines will consist of: (1) A literature survey to determine what existing technology is available (2) Development of a concept UPHES model by using Excel. The model must consist of:  Principal input and output  Off-peak, standard and peak-tariff structure values  Summer season pilot calculation  Winter season pilot calculation  Pipe pressure calculation sheets (linked externally to the principal input and output sheets), for the feed to the turbine and water pumped to the upper reservoir  CAPEX model  Return on investment (ROI) (3) Population of the concept UPHES model with real component parameters of the Driefontein No. 9 Shaft (4) Verification of the custom system UPHES model with the Engineering Equations Solver (EES) program (5) Evaluation of the verified, optimised and custom system model and investigation of optimisation opportunities by considering:  Reducing capital costs by using existing infrastructure  Optimal generation schedules to optimise electricity savings and ROI  Optimal pumping schedules to optimise electricity savings and ROI  Determination of the break-even point with regard to the Eskom tariff differential  Energy and overall system efficiency implication  Optimum efficiency (6) Validation of the Driefontein No. 9 Shaft UPHES system model with actual test data from the Driefontein No. 5 Shaft UPHES system (7) Investigation of the legacy of the Driefontein No. 9 Shaft as a future community asset (8) Derivation of a conclusion and formulation of recommendations from the results. 1.5 SCOPE AND LIMITS OF THE STUDY • UPHES with Pelton wheel turbine(s) (not Francis and Kaplan turbines) • Only on custom system development and plant is used for validation 1-4 • Only RSA/Eskom tariff structure and local CAPEX • Only RSA laws and regulations 1.6 DISSERTATION STRUCTURE The dissertation consists of seven chapters. Each chapter follows the research methodology described in section 1.4. In summary, this dissertation consists of:  Chapter 1: The background, problem statement, study objective, research methodology listed in points, the scope and limitations of the study  Chapter 2: Literature survey considering similar studies and suitable technology available in UPHES systems  Chapter 3: Technical background of Driefontein No. 9 Shaft and the available shaft infrastructure  Chapter 4: Concept UPHES model on Excel, as well as the Driefontein No. 9 Shaft model populated with real component parameters  Chapter 5: EES model with verification of the Driefontein No. 9 Shaft model and model optimisation  Chapter 6: Validation of the Diefontein No. 9 Shaft UPHES system model with actual test data from the Driefontein No. 5 Shaft UPHES system  Chapter 7: Conclusions and recommendations. ______________________________ 2-5 2 LITERATURE STUDY 2.1 INTRODUCTION The focus of the global mining sector is productivity and increased profits. Energy has become a major operational cost and strategic focus for the African mining sector due to power disruptions causing major operational issues, loss of production throughput and therefore deceased profitability. The challenge however is not limited to disruptions, but also concerns energy price increases. Mines are therefore required to review their power options to ensure the sustainability and viability of their operations, whether their operations are locally tied to the grid or self-generating in remote locations. This study commences with an investigation to establish the relationship between energy and mines and then broadly reviews challenges currently faced in the mining sector. Various energy-saving initiatives have been implemented with the purpose of reducing energy consumption by using energy- efficient equipment or simply by means of managing energy demand in order to shift loads to periods when peak tariffs are not charged. This may solve some of the issues discussed in this investigation, but not the issue of infrastructure constraints, i.e. energy supply constraints and power disruptions. During the Renewables and Mining Summit in July 2015, mining leaders responsible for decisions on power for operations stressed that these energy constraints had strengthened the business case for renewable energy as a suitable alternative source, especially for mines that are required to curtail production because of supply constraints (Baker, 2015). However, intermittent supply is a characteristic of renewable energy sources such as solar power and wind power. Current storage technologies above 10 MWh are restricted to batteries, compressed air and pumped storage hydropower (Pickard, 2009). Only pumped storage hydropower supplies high volumes of power for significantly long periods in which renewable energy, such as solar and wind power, cannot be generated. In the case of ultra-deep level mine operations, systems for recovering the potential energy of water flowing down the production shafts have been successfully implemented. During the shaft‟s production life, chilled water is piped underground in shaft columns for refrigeration purposes and in the process the water‟s potential energy is recovered. Because of the success of the current energy recovery systems, various economic studies have been conducted to determine the feasibility of applying these system principles to develop the concept of UPHES. 2.2 ENERGY AND MINES South African mining operations consume approximately 15% to 20% of the electricity generated at coal-powered and hydroelectric plants by the national energy provider, Eskom. Gold mines account for 47% of the mining industry‟s power, platinum mines consume 33% and all other mines the remaining 20% (Eskom, 2016). 2-6 Energy consumption is directly related to the depth of the mineral reserve mined. Gold mines are generally deeper owing to the depth at which the gold deposits are located. Electricity demand increases with an increase in mine depth because approximately 48% of energy consumed is for ventilation, pumping and refrigeration purposes (Goldfields, 2011). The chart below shows a typical breakdown of energy consumption for major equipment in deep level mining operations: FIGURE 2-1: Electricity consumption breakdown (Goldfields, 2011) In 2013, the Southern African Power Pool region lacked 2 131 MW of generating capacity (SAPP, 2013). Of the 300 000 GWh demanded in 2013, the national energy provider, Eskom, was able to generate just over 232 000 GWh. After the commissioning of Madupi Unit 6 and synchronisation of the Ingula Units 3 and 4 in 2016, the power utility was able to generate only 239 000 GWh of the 400 000 GWh demand forecast for 2016. 2.2.1 Cost of Energy The Megaflex costing structure is used to determine the time of use (TOU) electricity tariff for mines, which are grouped with urban customers with a notified maximum demand of greater than 1 MVA capable of shifting load. Charges included in this costing structure include three TOU periods, namely peak, standard and off-peak (Eskom, 2013). The TOU periods defined by Eskom are illustrated in Figure 2-2: Figure 2-2: Tariffs and charges booklet 2013/14 (Eskom, 2013) 2-7 Notwithstanding the above electricity charge, the following charges are also included:  Access charges associated with the distribution network  Transmission network charges based on voltage and length of the transmission zone  Affordability subsidy charges applied to the total active energy purchased  Reliability charges based on the voltage of the supply  Service charges based on the monthly utilised capacity  Network demand charges based on electricity demand on the network  Electrification and rural subsidy charge, which is applied to the total active energy measured at the point of distribution (POD)  Reactive energy charge supplied in excess of 30% (0,96 power factor or less) of the kWh recorded during the peak and standard periods  Administration charges based on the monthly utilised capacity of each POD. Table 2-1 shows the urban tariffs based on the Megaflex structure for a typical mine of which the supply network is rated between 500 V and 66 kV and of which the transmission line is no longer than 300 km. Mines are typically categorised as key customers, who are charged higher service and administration charges than consumers using less than 1 MVA. Table 2-1: Typical Megaflex structure anticipated for a mine U n it E s k o m t a ri ff 2 0 1 3 /2 0 1 4 * E s k o m t a ri ff 2 0 1 4 /2 0 1 5 * * E s k o m t a ri ff 2 0 1 5 /2 0 1 6 * ** E s k o m t a ri ff 2 0 1 6 /2 0 1 7 * ** * E s k o m t a ri ff 2 0 1 7 /2 0 1 8 * ** ** Low-demand season (September – May) Peak (c/kWh) [c/kWh] 65.68 70.93 79.93 87.44 89.36 Standard (c/kWh) [c/kWh] 45.20 48.82 55.02 60.19 61.51 Off peak (c/kWh) [c/kWh] 28.68 30.97 34.90 38.18 39.02 High-demand season (June – August) Peak (c/kWh) [c/kWh] 201.33 217.44 245.03 268.06 273.96 Standard (c/kWh) [c/kWh] 60.99 65.87 74.23 81.21 83.00 Off peak (c/kWh) [c/kWh] 33.12 35.77 40.31 44.10 45.07 Network Access Charge (NAC) [R/kVA] 10.67 11.52 12.45 13.44 14.52 Transmission Network Charge (TNC) [R/kVA] 5.35 5.78 6.51 7.12 7.28 NAC and TNC [R/kVA] 16.02 17.30 18.96 20.56 21.80 Affordability Subsidy Charge [c/kWh] 2.07 2.24 2.44 2.65 2.87 Reliability Service Charge [c/kWh] 0.26 0.28 0.32 0.35 0.36 Combined Affordability & Reliability Charge [c/kWh] 2.33 2.52 2.76 3.00 3.23 Network Demand [R/kVA] 20.23 21.85 24.62 26.93 27.52 Electrification & Rural Network Subsidy Charge [c/kWh] 5.20 5.62 6.33 7.90 7.08 Service Charge [R/day/account] 2616.1 2825.3 3183.9 3483.2 3559.8 Administration Charge [R/day/POD] 83.55 90.23 101.68 111.24 113.69 Reactive Energy Charge [c/kVArh] 9.40 10.15 11.44 12.52 12.80 * Eskom (2013), ** Eskom (2014), ***Eskom (2015), **** Eskom (2016 (2)), ***** Eskom (2017) 2-8 2.2.2 Eskom Tariff Increases On 28 February 2013, the National Energy Regulator of South Africa approved an annual 8% price increase in Eskom‟s tariffs for the period 2013/14 to 2017/18 (Eskom, 2015), as shown in Table 2-1. Media groups have reported that this tariff increase was not enough to ensure Eskom‟s sustainability. Nevertheless, according to an Energy Market Survey conducted by NUS Consulting, South Africa‟s tariff prices still remain 10 th most expensive out of 18 countries surveyed, but displayed the second biggest jump behind Belgium‟s 9.9% increase (Writer, 2015). In a study conducted by Boonzaier et al., a model of where and when tipping points are breached with regard to rapidly rising electricity tariffs was created and used to determine its effect on sector and company level. The study found that for energy-intensive users, rapid increases in electricity tariffs will have an impact on investor decisions with regard to cutting costs, implementation of energy efficiency measures, closing parts of their operations, moving plants to other countries and investing in other sectors (Boonzaaier et al., 2013). In June 2017 Moneyweb reported having viewed an undisclosed confidential draft submitted by Eskom for comment to National Treasury proposing an increase of 19.9% (Slabbert, 2017). 2.2.3 Energy Saving Initiatives Various energy saving initiatives have been deployed by many, if not all mining operations, with the intention of lowering the electricity bill without negatively affecting production and mineral recovery rates. These energy saving initiatives, termed demand side management, are aimed at either shifting loads during periods in which peak tariffs are charged or reducing the quantity of electricity consumed by installing energy-efficient equipment (Pelzer et al. 2008). Measures implemented at many South African mining operations to lower energy consumption include the use of variable speed drives, energy-efficient lighting and improving the efficiency of heating, cooling, ventilation and air-conditioning systems. Furthermore, because dewatering systems contribute to more than 6% of the 36 937 MW electricity peak in South Africa, pumping cycles are optimised to reduce the pumping requirements during peak tariff periods by using real-time energy management systems. Savings of up to 596 MW have been recorded subsequent to the implementation of 202 energy-saving initiatives in South African mines, contributing 19% of the savings accumulated in the mining, commercial, agriculture and residential sectors (Etzinger, 2012). 2.3 RENEWABLE ENERGY AND MINES The business case for alternative energy sources has become far more compelling in the current economic climate. Renewable energy is an alternative to the conventional sources of energy for both grid-tied and off-grid mining operations. These renewable energy sources make a compelling case, given the significant challenges faced (Baker, 2015). 2-9 Akram Elhenawy, global mining key accounts manager from the mechanised mining forerunners Caterpillar, stressed this point during the Renewable and Mining Summit in 2015, stating that in response to diminishing concerns about reliability, investment in the renewable energy market has increased, which reflects better understanding of the benefits of integrated renewable energy solutions (Elhenaway et al., 2015). In South Africa, the mining sector questioned the reliability of renewable energy for many years, having been content with the supply from Eskom, the sole provider of electricity to the South African electricity grid. Eskom CEO Brian Danes suggested in a statement made in 2014 that state-owned Eskom‟s reluctance to react to the growth of electricity demand after the decision to not pursue increasing the generating capacity of the national grid in 1998, had caused the problem of reliability to shift from renewable energy sources to the once resolute supply. 2.3.1 What is Renewable Energy? Renewable energy refers to a source of energy that cannot expire or become depleted and is therefore sustainable. There are only two primary sources of renewable energy, which have an impact on the earth, i.e. gravitation and nuclear power (Pickard et al. 2009): 1) The nuclear source naturally emanates from nuclear fusion reactions of the sun and the nuclear decay within the earth. The effects of heat radiation can be harnessed with chemical- based conversion methods or mechanical methods capturing the effects of the induced pressure differentials. These methods are also used today to harness the effects of deep terrestrial fission reactions that produce geothermal resources. The secondary source emanating from this primary source is therefore solar, wind and geothermal renewable energy sources. 2) The second primary source of renewable energy is the earth‟s gravitational force arising from the earth-moon interaction, transferred to the seas to produce the tides. Human-mediated harnessing of the earth‟s gravitational power source is either by wave energy converters or by converting the potential energy from water flowing from a higher to a lower elevation. Therefore, the secondary sources emanating from this primary source are hydropower and ocean energy. It must be noted that human-mediated nuclear processes, such as controlled fission or fusion, are viewed as a sustainable source but not a renewable source of energy. This is because the fuel used to generate energy is diminished and cannot be used again in the same process. 2.3.2 Renewable Energy in South Africa Renewable energy has gained momentum globally owing to sustainability and energy security concerns. This global shift has resulted in cheaper renewable energy technologies, government policy support and procurement programmes. 2-10 In order to encourage investment and develop socio-economic and environmentally sustainable growth in South Africa, the Renewable Energy Independent Power Producer Procurement Programme (REIPPPP) was developed and implemented by the South African Department of Energy (DoE). International investors view the sunshine and wind throughout the year, as well as the large open tracts of land in South Africa, as huge potential for investment in renewable energy projects. Projects covered by the programme are onshore wind, solar photovoltaic (PV), concentrated solar power, landfill mass, small hydropower and biogas. 2.3.3 Cost of Renewable Energy The South African national government uses the bidding process facilitated by the REIPPPP to procure renewable energy generation capacity in line with the National Integrated Resources Plan (IRP) for electricity 2010 – 2030. The first four bid windows of the REIPPPP for solar PV and wind are summarised by Bischof-Niemz et al. (2016) in Figure 2-3. Figure 2-3: REIPPPP tender outcome – average power tariffs The tariffs offered by utility scale solar PV and wind energy in South Africa, shown in Figure 2-4, are falling below the 1 R/kWh mark. In comparison, the tariff charged by Eskom is expected to increase above this mark. Decreases in the tariffs from renewable energy technologies are a result of increases in the global renewable energy generation capacity (GreenCape, 2017). Renewable Energy Advisors (REA) suggested in 2013 that the cost of renewable energy technology has decreased in the past two years. Further to the decrease in the cost of the technology, tax incentives are also now available and assist reducing the system ROI (Sola, 2013). 2-11 Figure 2-4: Average Eskom tariffs versus utility–scale renewable energy tariffs (Eskom, 2016) While renewables such as PV plants and wind turbines are capable of lowering the consumption of fuel to power large generators in off-grid mining operations in the range of 30% to 70%, the use of these renewable resources are hampered by their characteristic intermitted supply. 2.3.4 Photovoltaic Plants Some sectors of the renewable energy market, such as solar power, have developed rapidly to the extent where it has reached price parody with regard to industrial loads. This has been achieved because of the possibility of storing energy in lead-acid and sodium-sulphur batteries, but is limited to 10 MWh (Pickard et al, 2009). Therefore, global mining and renewable energy sectors focus their attention mainly on driving the solutions associated with the effects of the first primary source of renewable energy: solar radiation. In 2015, Sibanye Gold, the largest gold mining house in South Africa, announced plans to build a PV solar plant with an installed capacity of 150 MW by 2017 (Wallington, 2016). The plant is expected to provide approximately 30% and 10% of their peak and total operational power requirements respectively. The generating capacity of such a PV plant is limited to the surface area available for the erection of the solar panels and can essentially only convert radiation energy to electricity when these panels are exposed to the sun‟s rays. This means that a power-generating factor exists that can reflect the energy-generating capacity of a PV plant at any given time, as is illustrated in Figure 2-5 (Ma, 2014). Figure 2-5: Power generation factor 0 0.2 0.4 0.6 0.8 1 0 :3 0 1 :3 0 2 :3 0 3 :3 0 4 :3 0 5 :3 0 6 :3 0 7 :3 0 8 :3 0 9 :3 0 1 0 :3 0 1 1 :3 0 1 2 :3 0 1 3 :3 0 1 4 :3 0 1 5 :3 0 1 6 :3 0 1 7 :3 0 1 8 :3 0 1 9 :3 0 2 0 :3 0 2 1 :3 0 2 2 :3 0 2 3 :3 0 2-12 Matching the potential energy that can be harvested from solar radiation to a POD load profile can become rather complicated. Ideally the energy produced should be applied to the periods in which the load profile peaks, especially periods when electricity is charged at a peak tariff. Figure 2-6 shows a POD load profile for a typical operational shaft with the power generating factor overlain. Figure 2-6: Typical POD load profile The excess energy generated that is not used instantaneously must therefore be stored. The means for doing this must be capable of storing vast quantities, as is evident from the 150 MW PV plant envisioned by Sibanye Gold and variations in a typical load profile. 2.3.5 Storage of Renewable Energy With the selection of an appropriate storage mechanism, power variations can be mitigated and system flexibility can be enhanced. Studies considering strategies for storing energy of input power provided by intermitted resources have demonstrated that only a few options are feasible, considering the current and future predicted technological capabilities. In a study conducted by Amrouche et al., various renewable energy storage methods are investigated and the most frequently used technologies and their associated efficiencies are listed as follows: 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 10000 11000 12000 13000 14000 15000 16000 17000 18000 19000 20000 0 :3 0 1 :3 0 2 :3 0 3 :3 0 4 :3 0 5 :3 0 6 :3 0 7 :3 0 8 :3 0 9 :3 0 1 0 :3 0 1 1 :3 0 1 2 :3 0 1 3 :3 0 1 4 :3 0 1 5 :3 0 1 6 :3 0 1 7 :3 0 1 8 :3 0 1 9 :3 0 2 0 :3 0 2 1 :3 0 2 2 :3 0 2 3 :3 0 P o w e r g e n e ra ti o n f a c to r k W h TYPICAL OPERATING MINE POD LOAD PROFILE Standard tarrif charges Peak tarrif charges Photovoltaic generation factor Power from supplier 2-13 Table 2-2: Most used storage technologies in renewable energy systems Energy Storage Method Technologies Time Scale Efficiency [%] Electrochemical Batteries Medium (minutes) 90 - 95 Flow batteries storage Medium (hour) 75 - 80 Hydrogen (HES) Hydrogen Long 65 - 75 Mechanical Flywheel energy storage Short (seconds) 80 - 90 Pumped hydro energy storage Long (hours) 70 - 85 Compressed air energy storage Long (hours) 64 - 75 Electrical Super capacitor energy storage Short (seconds) 90 - 98 Electromagnetic Superconducting magnetic energy storage Short (seconds) 90 - 99 Thermal Thermal Medium 80 - 90 Current storage technologies above 10 MWh are restricted to lead-acid and sodium-sulphur batteries, compressed air and pumped storage hydropower. Only pumped storage hydropower supplies high values of power for significantly long periods, capable of producing 1000 MWh (Montero et al. 2015). Pumped storage hydropower has therefore been identified in these studies to be capable of meeting the anticipated technological and economic constraints (Pickard et al. 2009). It can be expected that pumped hydro storage technology will advance in order to meet the demand. 2.4 UNDERGROUND PUMPED HYDROELECTRIC ENERGY STORAGE 2.4.1 Recovery of the Energy of Water Going Down Mine Shafts In South Africa, deep level mining operations make use of large cooling systems to reduce underground ambient temperatures to conditions conducive to a healthy work environment as regulated by the Mine Health and Safety Act 29 of 1996 and Minerals Act 50 of 1991. These systems comprise one or more central refrigeration plants located on surface. Chilled water is distributed to underground heat-exchanging systems via one or multiple shaft columns to working levels of up to 3 000 m below surface. The implication of surface-located refrigeration plants is the rise in the temperature of chilled water resulting from the dissipation of pipe friction into thermal energy. Whillier (1977) suggests that the rise in temperature is approximately 2.33˚C per 1000 m shaft depth. The increase in temperature adversely affects the temperature of cooled air circulated at the mining face. If the water were passed through a turbine at the bottom of the shaft, the water would return to the ambient pressure under constant entropy conditions, therefore more than halving the rise in temperature. The potential energy of the water in the shaft column is converted to mechanical energy in the turbine, therefore recovering a part of the energy required to pump the water back to surface. 2-14 High energy recovery has been recorded for many of these types of energy recovery systems over a wide capacity range of differential heads. More than 50 turbines with a combined capacity of over 65 MW have been installed underground in various mines in South Africa (Karanitsch, 2010). 2.4.2 Concept of UPHES Plants PHES refers to a system in which electric power is used to pump water to a reservoir, located at a height above a lower reservoir. In the upper reservoir the water is stored until there is a shortage of electrical power. Water from the upper reservoir is then gravity-fed through a turbine converting the gravitational potential energy into electrical power, thereby ensuring grid stability. The use of the potential head created in mine shafts for the storage of energy is not a new concept. A UPHES system refers to a PSHP system of which all system power-generating components are underground, specifically applied to deep level mines. Fessenden (1917) patented a “system of storing power” underground and suggested that one horse power hour of energy may be stored for every cubic yard of water content of the lower reservoir in a mine shaft, for which a shaft depth of 1200 feet would be sufficient. 2.4.3 UPHES generation potential The feasibility of a UPHES system must consider the amount of energy that can be generated. The parameters determining the energy that can potentially be generated by a UPHES system are shown in Equation 1: where the volume of water in the upper reservoir is given in cubic metres ( , water density in kilograms per cubic metre ( ), gravitational acceleration ( and distance between the upper and lower reservoir in metres ( . The electrical power ( ) generated in Megawatt is determined by taking into consideration the turbine efficiency ( ) and the period in hours in which the turbine is used to generate electricity ( ): . 2.4.4 System storage efficiency The system storage efficiency of conventional pumped hydroelectric storage systems varies in practice between 70% and 80%, with some claiming 87% (Rehman et al., 2015). Losses are attributed to pipe friction, turbulence and heat loss. The storage efficiency ( ) of a UPHES system can be determined by Equation 1: . 2-15 2.4.5 Economics of a UPHES system The basic principle of a UPHES system is applied to take advantage of the Megaflex tariff structure. The Megaflex tariff structure, discussed in section 2.2.1, consists of peak, standard and off-peak tariffs. In low and high demand seasons, the off-peak tariff is 56% and 17% of the peak tariff charged respectively. Water is therefore pumped to the upper reservoir during the period in which off-peak tariffs are charged, and allowed to flow to the lower reservoir through the turbine to generate electricity during periods in which peak tariffs are charged. The power generated is then sold back to the grid, at a lower price than sold by Eskom. All PHES systems are net consumers of energy and therefore not independent sources of power. They are therefore conventionally used as:  Storage systems for conventional power plants (coal, oil, gas or nuclear)  Storage of energy generated by renewable energy plants (solar and wind)  Energy input during peak demand periods. Therefore a PHES or UPHES system is only economically viable if the difference between the peak and off-peak tariff can account for the efficiency related additional energy required from Eskom (Winde, Kaiser & Erasmus, 2017). 2.4.6 Use of existing mine infrastructure The main advantage of using existing mine infrastructure is not only the reduction in construction costs due to the largest excavation component already existing, but also the depths at which a potential network of tunnels exists, providing potential heads exceeding 1000 m and more. Montero et al. (2015) conducted a study to analyse various aspects of using the existing mine infrastructure of the Prosper-Haniel mine in Germany for the development of a UPHES system. The underground tunnel network envisioned as the lower reservoir can hold approximately 600 000 m 3 at a potential head of 600 to 1000 m. 2.4.7 Subsurface construction Traditionally only certain parts of PHES plants are situated underground. Turbines are placed in subsurface caverns to protect the landscape and other aesthetics. The first combination of a PHES plant with a subsurface cavern for water was put into operation in Austria in 2006 with the expansion of the Nassfeld plant. The expansion of the plant was inundated with various technical, landscape- related and legal implications, leading to the establishment of a subsurface pipe system. After six months of construction, 160 000 m 3 was excavated to construct a 1950 m tunnel. The cost of excavation and support of the surrounding rock was exorbitant and the expansion project amounted to 13 MЄ (Tschernutter, 2010). In Italy, Austrian energy provider KELAG AG studied an entirely subsurface PHES to be built into a mountain. Water from an upper cavern was planned to flow to a cavern 900 m lower and the plant 2-16 would have an installed capacity of 250 MW. The upper and lower reservoirs were to be excavated caverns 0.6 Mm 3 in volume. The investment costs were estimated at 300 MЄ. Protests and subsequent negative public relations effectively caused the project to be abandoned (Madlener et al., 2013). The use of UPHES has the added advantage that the construction is not topographically restricted to sites where above-ground upper and lower reservoirs can be placed together because the lower reservoir can be excavated from the subterranean rock almost anywhere immediately above the upper reservoir (Montero, 2015). Goldisthal, one of the largest PSHP plants in Germany, has both upper and lower reservoirs located on surface, while the generator, turbine and transformers are built into a cavern in a mountain. Around 152 000 m 3 and 32 000 m 3 had to be excavated for the turbine house and entry tunnel respectively (Heiland et al., 2013). The building of the upper reservoir on the hilltop required removal of the peak, which raised great aesthetic and ecological concerns, eliciting serious protest from the local community and nature protection groups. 2.4.8 Main System Components 2.4.8.1 Pumps and turbines The study conducted by Winde et al. (2017) suggests the use of one of two options:  Option 1: Combined pump-turbine unit (reversible Francis turbine)  Option 2: Pelton turbine. The combined pump-turbine can pump water to heads of up to approximately 800 m, which restricts the system‟s potential head and is therefore not suitable for ultra-deep shafts (Winde et al., 2017). The Pelton turbine (an impulse type water turbine) is suitable for heads exceeding 1000 m. A German manufacturer manufactured a Pelton turbine capable of generating electricity as an hydraulic head of 1 220 m in 2008 and installed it at Akkoy II, Turkey (Voith, 2015). Figure 2-7: Pelton turbine manufactured at Voith in Germany (Voith, 2015) 2-17 2.4.8.2 Turbines The following formulae are used (Gupta et al., 2016) for determining the theoretical power input in Watts ( the actual output power in Watts ( and the hydraulic efficiency ( : . The application range of standard and special application Pelton turbines manufactured by Voith is shown in Figure 2-8: Figure 2-8: Application range for Pelton turbines (Voith, 2015) The Pelton runner typically operates in atmospheric pressure with one to six jets of water through needle nozzels impinging tangentially on the runner. The function of the needle nozzle is to regulate the flow of water to the runner. The needle jet is regulated by the governor via mechanical- or electric hydraulic controls. The shape of the needle nozzle is designed for rapid acceleration at the exit end and for assuring a uniform water jet at all the openings. The needle valve/nozzle assembly is placed as close to the runner as possible to avoid the jet spreading due to air friction (HAP, 2012). Pelton turbines with multi-needles are among the most efficient designs of hydroelectric turbines. The Pelton turbine used at the Stanislaus powerhouse in California, commissioned since 1963, which has a nameplate rating of 113 000 hp at 1 525 ft hydrauluic head, and generator nameplate rating of 91 MW, 91 MVA, 0.9 power factor at 13.8 kV, is operated with six nozzles (Roberts & Nunnelly, 2011). The efficiency of the turbine at Stanislaus is shown in Figure 2-9: 2-18 Figure 2-9: Turbine efficiency for 2, 4 and 6 needle operation at Stanishous powerhouse (Roberts et al., 2011) 2.4.8.3 Pumps Multistage clear water pumps are used for high volume and high lift applications at gold mines. The quality of the water is clear or slightly polluted with abrasive particles. These pumps are therefore particularly fitting for mine dewatering. Heads of between 120 and 1 800 m can be pumped at capacities between 130 and 1 000 m 3 /h, as shown in Figure 2-10: Figure 2-10: Multistage clear water pumps’ performance range (Sulzer, 2015) 2-19 2.4.8.4 Upper and lower reservoirs Winde et al. (2017) suggest that the upper and lower reservoirs be constructed by using existing mine haulages and tunnels. Main haulages, developed from the shaft stations, are about 5 m wide by 3 m high in typical South African gold mines. Reef cross-cuts connecting the main haulages to reef drive are on average 180 m long, 3 m wide and 3 m high. These cross-cuts and main haulages canbe used to construct underground reservoirs by simply constructing dam walls. The quartzite walls are sufficiently inert and will therefore not adversely affect water quality. 2.4.8.5 Emergency storage capacity and pumps Winde et al. (2017) further suggest that a number of levels below the lower reservoir be kept available for emergency storage capacity. The emergency storage volume must be sufficient to accommodate the entire volume of the circulating system, including a buffering capacity to accommodate additional water egress; 1 Mm 3 is suggested to be a sufficient buffering capacity. Furthermore, submersible pumps must be provided to dewater the emergency storage excavations (Winde et al. 2017) 2.4.8.6 Access shaft and pipe column The shaft, connecting the surface and underground workings, equipped with shaft steelwork, conveyance guides, man riding conveyances, electrical cables, instrumentation cables, communication cables and pipe columns, will be used as is. Ventilation of the mine is also routed through the shaft (upcast/downcast configuration). Winde et al. (2017) note that the shaft diameter must be able to accommodate the size of equipment required to be transported in the shaft during construction of the UPHES system. It is also important to note that the winders must be able to accommodate the mass of the equipment to be transported. The pipe size required for feeding water to the turbine to accommodate the required flow rate is dependent on the required generation capacity of the system. The generation capacity is linked to the storage capacity of the upper and lower reservoir. The system contemplated by Wilde et al. (2017) assumes a hypothetical storage volume of 1 Mm 3 used to generate power for four hours per day. This would require a flow rate through the turbine of 70 m 3 /s. To accommodate this flow rate in a pipe, the pipe‟s inner diameter would have to be 2.5 m with a flow velocity of 14.2 m/s. In order to reduce the losses attributed to turbulence and friction, it is suggested that two pipes be installed, as shown in Figure 2-11. The use of 2.5 m diameter pipes would be a very costly to manufacture and install. Winde et al. (2017) suggest that a 5 m raisebored shaft be considered. Such constructions have been used in conventional PHES systems, for example at Goldisthal, Germany. 2-20 . Figure 2-11: Cross-section of a shaft with two pipe columns (Winde et al., 2017) 2.5 TREATING THE ROOT CAUSE OF ACID MINE DRAINAGE The excavations required to access ore bodies such as the shaft excavation, development of the main haulages and eventually access to the reef horizon is a major constituent of capital cost of the shaft. After the ore body has been mined, these excavations are abandoned and flooded after decommissioning the shaft. The oxidisation of the sulphides contained in mined ore and waste in the water creates highly acidic and polluted water, eventually emerging from these flooded mines, known as acid mine drainage (AMD). The largest groundwater resource in South Africa, located above the gold reefs in the Far West Rand (FWR), is held by karstified dolomites supporting a range of high-yielding karst springs (Schrader & Winde, 2015). Flooding of some of the already decommissioned mines has occurred because of the egress of groundwater and lack of proper management and planning, the result of which is AMD draining into the environment in and around Johannesburg. The cost of addressing these issues has been estimated at R10 billion, which involves decanting AMD, but not treating the root cause. An estimated total volume of 130 million litres per day will be treated and potentially an additional 200 million litres per day once the other mines in the FWR are decommissioned (Kolver, 2014). In a study conducted by Winde, Kaiser and Erasmus (2017), the viability of using deep level gold mines on the FWR was considered. The study suggests that current and future decommissioned mines can be kept from becoming sources of AMD by using an open UPHES system. The continuous ingress of fissure water is balanced in an open UPHES system by cleaning and discharging excess 2-21 water on surface. The decommissioned mine, which would have been viewed as a long-term liability, can be converted to an asset storing energy and providing clean water (Winde, Kaiser & Erasmus, 2017). Winde et al. (2017) further suggest that the economic viability of the UPHES system should not be based only on the profitability of energy generation, but also on the system‟s potential regarding integration into a system for treating the root cause of AMD. 2.6 RISKS ASSOCIATED WITH UPHES In studies conducted by Eskom from 1997 to 2006 the use of a High Head Underground Pumped Storage (HHUPS) system in deep level gold mine shafts was investigated (Winde et al., 2017). The project was generally found to be feasible, but was not implemented owing to concerns about sterilising the ore reserves. The study excluded underground excavations that are overlain by karst aquifers in the FWR as they were seen as too risky. Specific reasons for the risk were not mentioned. However, in contrast to the exclusions of this study, in a study conducted by Winde and Stoch (2011) the large water resources and large excavations were considered integral assets for the implementation of UPHES (Stoch and Winde, 2011). Perhaps the risks are those associated with the immensity of these aquifers. In a research article by Cousens and Garrett (1969) investigating the infamous flood at the West Driefontein Mine in October 1968, an uncontrolled inrush estimated at 322 Ml/day of fissure water was found to have entered the mine. The flood continued unabated for 23 days before it was stemmed. The tremendous efforts and organisation that made it possible to bring the situation under control, thus preventing the loss of the mine, were unprecedented. The source of the massive water quantities were the high-yielding karst springs held by karstified dolomites located above the gold reefs on the FWR. In Table 2-3 an indication is given of the dewatering capacity and the maximum water quantities pumped at the West Driefontein Mine as well as surrounding mines during 1968. Figure 2-11 shows the water from the inrush overflowing into the mine‟s shaft. Table 2-3: Water pumped from the workings at mines on the West Wits line Operation Pumping position, October 1968 Maximum quantities pumped Available pumping capacity [Ml/day] Water pumped to surface [Ml/day] Rate [Ml/day] Period [year] Doornfontein 26 11 13 1960 West Driefontein 238 64 121 1963 Libanon 34 11 11 1968 Venterspost 76 36 47 1961 2-22 Figure 2-12: Water from the inrush overflowing into No. 4 Shaft 2.7 STATUTORY REQUIREMENTS Chapter 13.1(1) of the Mine Health and Safety Act of 1996 Regulations states that the employer must prevent employees from being trapped in any underground excavation by providing, were practical to do so, a means of secondary egress from every underground working place. These two exits must be connected to separate means of egress to the surface. If it is not practical to provide the second exit, other reasonable measures must be implemented as determined by the mine‟s risk assessment, to prevent people from being trapped in an underground excavation. Therefore, if considering a UPHES for any shaft system, a second means of egress must be considered. In some cases the hoists can be considered as an alternative practical means of egress to surface, provided that the provisions of Minerals Act, Regulation 6.5.2.1 are complied with. The regulation states that ladders may not be provided if two winding plants of adequate capacity are immediately available. These two winding plants must be powered from two independent power sources, which can be either a complete ring circuit or duplicate supply power lines. 2-23 2.8 CONCLUSION The literature study indicates that the recent electricity tariff increases in South Africa have had a major effect on energy-intensive users. Rapid increases in electricity tariffs will have an impact on investor decisions such as cutting costs, implementation of energy efficiency measures, closing parts of their mining operations, moving plants to other countries and investing in other sectors. The business case for alternative energy sources, which include renewable energy sources, has become far more compelling in the current economic climate. The South African mining sector, which for many years had been content with the national supplier, Eskom, is now considering alternative energy. In order to encourage investment and developing socio-economic and environmentally sustainable growth in South Africa, the REIPPPP was developed and implemented by the South African DoE. International investors view South Africa as having huge potential for investment in renewable energy projects. Projects covered by the programme are onshore wind, solar PV, concentrated solar power, landfill mass, small hydropower and biogas. Renewable energy is characterised by an intermittent supply, but with the selection of an appropriate storage mechanism, power variations can be mitigated and system flexibility can be enhanced. Studies considering strategies for storing energy obtained from input power provided by intermittent resources have demonstrated that only pumped storage hydropower is capable of meeting the anticipated technological and economic constraints with regard to storage capacity. Further to the storage aspect of renewable energy, high energy recovery has been recorded for energy recovery systems in deep level shafts. These systems resemble underground pumped hydro- electric storage and differ only in that the systems are retrofitted to existing chilled water columns and refrigeration circuits. The use of existing mine infrastructure of existing deep level mine shafts is two-fold in that the initial system capital cost is significantly reduced and the depths at which a potential network of tunnels exists provides potential heads exceeding 1000 m. Furthermore, it is suggested that current and future decommissioned mines can be kept from becoming sources of AMD by using an open UPHES system where the continuous ingress of fissure water is balanced by cleaning and discharging of excess water. A decommissioned mine, which would have been viewed as a long-term liability, can be converted to an asset storing energy and providing clean water. ______________________________ 3-24 3 TECHNICAL BACKGROUND 3.1 DRIEFONTEIN GOLD MINE The Driefontein gold mine is located in the FWR goldfields, situated in the geographically unique and world-renowned Witwatersrand Basin, one of the most significant gold deposits in mining history. The operations are well-established, shallow to ultra-deep level gold mines accessed through eight shaft systems. The various shafts extend to depths between 600 and 3 000 m below surface. Five shafts consist of sub-vertical shaft systems and two of tertiary shaft systems. Figure 3-1: Location of the Driefontein gold mine (Goldfields, 2009) 3.2 GEOLOGICAL CONDITIONS The Driefontein gold mine is located on the Kaap Vaal Craton, an old, stable and comparatively thick basement having a low thermal gradient that keeps rock temperatures at manageable levels, even at great depths (Winde et al., 2017). The location of the shafts at the Driefontein gold mine is important, as it provides geotechnical and tectonic stability for UPHES. Another important fact is that the hard rock formations are covered by dolomite, which over millions of years have dissolved through chemical dissolution, resulting in underground cavities connected by fractures, fissures, faults and slots. These form the high-ingress zone, shown in Figure 3-1, and are hydraulically interconnected to the overlaying aquifer. The lower no-ingress zone is isolated from water egress (Winde et al., 2017). 3-25 Figure 3-2: Geological conditions at the Driefontein gold mine (Winde el al, 2017 ) 3.3 DRIEFONTEIN NO. 9 SHAFT The Driefontein No. 9 Shaft consists of a production shaft and ventilation shaft. The ventilation shaft is located approximately 120 m to the south of the production shaft. The detail of the shaft complex is given in Table 3-1 and the site layout is shown in Figure 3-3. The shaft system is illustrated diagrammatically illustrated in Figure 3-4. Table 3-1: Driefontein No. 9 Shaft complex information Major Infrastructure Description Production shaft Shaft diameter 9 150 mm, shaft depth 2 095 m (24 level) Ventilation shaft Shaft diameter 7 000 mm, shaft depth 2 883 m (40 level) Production shaft, production winder Blair multi-rope (BMR) winder, skip-and-skip arrangement, payload 22.5 t per skip Production shaft, dual purpose winder Double drum, 12 tonne skips and three deck cages Ventilation shaft Kibble and stage winders (on site) 3-26 Figure 3-3: Driefontein No. 9 Shaft complex layout (satellite view) Figure 3-4: Shaft infrastructure diagram 3-27 3.4 SHAFT INFRASTRUCTURE 3.4.1 Pelton Turbine The Pelton turbine used in the simulation model is based on the Pelton turbine used for recovering energy from the chilled water column installed in the No. 5 Shaft. The technical design data of this Pelton turbine are given in Table 3-2: Table 3-2: Driefontein No. 5 Shaft Pelton turbine technical design data Description Unit Value Turbine type [-] Pelton Turbine Number of jets [-] 2 Speed [rpm] 3 000 Net head [m] 1 680 Minimum head [m] 1 620 Rated discharge [l/s] 320 Discharge rate to net head ratio [-] 0.19 Turbine output [kW] 4 625 3.4.1.1 Driefontein No. 5 shaft Pelton turbine efficiency The efficiencies of the Pelton turbine used at Driefontein No. 5 Shaft are given in Table 3-3. The system was designed to be operated with a maximum of 2 water jets with the runner in a vertical position. Table 3-3: Driefontein No. 5 Shaft Pelton turbine efficiencies Percentage of the rated discharge Efficiency Comments 100% rated discharge 87.7% 2 jets in operation 75% rated discharge 88.2% 2 jets in operation 50% rated discharge 88.0% 1 jet in operation 25% rated discharge 86.4% 1 jet in operation 3.4.1.2 System discharge rate to net head ratio The manufacturer recommends that the turbine must not be operated with a discharge of 15% below the rated discharge to prevent damage to the runner and jets. Operating the turbine below the minimum head can damage the runner as well. In principle the Pelton turbine must be operated within the discharge rate to net head ratio. 3-28 Therefore, to suit a discharge rate to net head ratio of 1.9, and at a net head of approximately 1 945 m, the discharge rate to net head ratio for the UPHES system at Driefontein No. 9 Shaft should be approximately 370 l/s. 3.4.2 Existing Chilled Water Column Two options must be considered to determine if the existing chilled water column can be used for water flowing downward toward the turbine, or pumped to the upper reservoir. The two options are:  Option 1: Use of the existing chilled water column for water flowing downward to the turbine, and use of a new dedicated dewatering column for dewatering purposes  Option 2: Use of the current chilled water column for dewatering purposes, and use of a new dedicated column for feeding water to the turbine. The use of the existing pipe column for the purpose of pumping water from the lower reservoir to the upper reservoir is possible, provided that the periods in which water is pumped to the upper reservoir and periods in which power is generated do not overlap. However, a break in the shaft column feeding the turbine would decrease the maximum head achieved, which would affect the generating capacity of the system. Also, the maximum head that a Sulzer multistage clear water pump with 11 stages can pump is 1 800 m (friction losses included). Therefore it is necessary to tee the shaft column in mid shaft to connect the mid-shaft pump station. The same is required at IPC level. The second option of installing a dedicated dewatering column would only be necessary if the chilled water column cannot be used as the column feeding the turbine. The suitability of the existing chilled water column is discussed in subsequent sections. 3.4.3 Existing Chilled Water Column Pipe Schedules The chilled water column installed at Driefontein No. 9 Shaft extends from a surface cold water dam to EL -2 907 BD. The design flow rate is 200 l/s. More information on the column is not available. To determine the suitability of the column with regard to either a flow down the column to the turbine or use as a pump column, the pipe design to feasibility level is required to determine suitable pipe thickness (schedule). These schedules are then assumed to correspond to the existing chilled water column. The following input parameters are used to determine the pipe schedule(s): Table 3-4: Chilled water shaft piping design input parameters Description Value Units Reference Density of water 998 kg/m 3 Assumed clean water Dynamic viscosity of water 1.30E-03 kg/(ms) @ 10 °C (Munson et al., 2010) Pipe roughness 0.00015 m For galvanised steel pipe Gravitational constant 9.81 m/s 2 3-29 Description Value Units Reference Pipe diameter 350 NB Pipe outer diameter 355.6 NB Pipe inner diameter Specification 1 317.5 mm ASTM 106 - Grade B Pipe wall thickness Specification 1 19.05 mm Schedule 80 Pipe inner diameter Specification 2 300.02 mm ASTM 106 - Grade B Pipe wall thickness Specification 2 27.79 mm Schedule 120 Pipe inner diameter Specification 3 280.18 mm ASTM 106 - Grade B Pipe wall thickness Specification 3 37.71 mm Schedule 160 Bulk modulus of water 2068 MPa Bulk modulus of steel 206000 MPa Volumetric flow rate 200 ℓ/s Velocity Spec 1 2.53 m/s Velocity Spec 2 2.83 m/s Velocity Spec 3 3.24 m/s Surface elevation 0 m Spec break 1 elevation -698.3 m Spec break 2 elevation -698.3 m Pump elevation -2095.0 m Pipe length 1 698.3 m Pipe length 2 698.3 m Pipe length 3 698.3 m Total pipe length 2095.0 m 3.4.4 Dewatering Pumps It is assumed that the Driefontein No. 9 Shaft is equipped with eight dewatering pumps, whether located on site or sourced from neighbouring shafts. The number of pumps available greatly affects the system capital cost. 3.4.5 Upper, Mid-Shaft and Lower Reservoirs The lower reservoir of the UPHES system envisioned for the Driefontein No. 9 Shaft will be constructed by using the existing haulages connecting the main shaft to the sub-vertical shaft. The water will be contained by constructing dam walls. Water levels will be monitored with a float switch. A redundant secondary level monitor will be required and used to compare the float switch reading. A redundant level monitoring system will ensure that accurate dam levels are observed at all times. 3-30 The main haulage developments towards the sub shaft is sufficient to accommodate between 1 Ml and 10 Ml. The lower reservoir capacity therefore does not limit the UPHES system capacity. Although the length of the haulages and chambers on IPC and mid-shaft may not be sufficient for the storage capacities required, the upper reservoir and mid-shaft reservoir can be developed from the existing infrastructure and extended to suit the capacity required. Main haulages, developed from the shaft stations, are typically about 3.5 m wide by 3 m high, as shown in Figure 3-5. A 100 m long haulage would therefore be able to store approximately 1 050 m 3 of water, therefore 1 Ml. Figure 3-5: Typical haulage cross-section The technical background provided in this chapter provides information to sufficient detail for understanding the UPHES system model and parameters. The next chapter discusses the UPHES concept system developed for the purposes of determining the system‟s energy generating capacity and electricity cost savings. ______________________________ 4-31 4 UPHES SYSTEM MODEL 4.1 SYSTEM CONFIGURATION The UPHES system model configuration consists of the following components:  Upper reservoir located on IPC level (-150 m BD)  Mid-shaft reservoir and mid-shaft pump station located in mid-shaft (- 1 050 m BD)  Lower reservoir, lower pump chamber and turbine chamber located on the lower reservoir level (- 2095 m BD). The lower reservoir level is located approximately 60 m above shaft bottom  Dewatering shaft column connecting the lower reservoir to the mid-shaft reservoir  Dewatering shaft column connecting the mid-shaft reservoir to the upper reservoir  Water feed column connecting the upper reservoir to the lower reservoir The system model output parameters are generated using the various calculation sheets described in the sub-sections to follow. The system configuration shown in Figure 4-1. 4.1.1 Master UPHES System Model The master UPHES system model considers system input parameters such as the load profile anticipated for a typical deep level shaft system, the Megaflex tariff structure for summer seasons (LDS) and winter seasons (HDS) and the fundamental system parameters. The operational and system assumptions regarding these input parameters are defined in Section 4.4. Refer to Appendix I for the master UPHES system model and pipe pressure calculations. 4.1.2 Pipe Pressure Calculations Pipe pressure calculation checks are conducted for the piping delivering water to the turbine and the piping required for the water pumped between the lower reservoir, mid-shaft reservoir and upper reservoir. The calculated flow rate turbine is an input to the model, and the flow rates required to dewater the lower reservoir is an output parameter, fed into the pressure calculation check for the dewatering column. 4.1.3 CAPEX Model The CAPEX model considers all infrastructure required for the UPHES system, including the shaft construction. The CAPEX model uses the output parameters from the master calculation to determine the estimated quantities. The CAPEX model is later modified to suit the Driefontein No. 9 Shaft by taking into account the current infrastructure and existing equipment available for use. 4-32 Figure 4-1: UPHES system configuration 4-33 4.2 TYPICAL POD A typical load profile for a single POD, shown in Figure 4-1 and Figure 4-2, was sourced from the Energy Management Department at Sibanye Gold. This single POD supplies electricity to a mine producing between 40 and 60 ktpm. The load profile is shown in combination with the periods in which off-peak (green), peak (red) and standard tariffs (yellow) are charged based on the Megaflex costing structure discussed in section 2.2.1 during LDS and HDS. Figure 4-2: Typical POD during low demand season Figure 4-3: Typical POD during high demand season 4-34 4.3 MEGAFLEX TARIFFS The Megaflex tariff structure differs from the weekday structure on Saturday and Sunday, as can be seen from Figure 2-2 in section 2.2.1. The Megaflex tariffs used in the model are based on the tariffs published for the 2015/2016 financial year: Table 4-1: 2015/2016 Megaflex tariff structure used in the model Time of day LOW DEMAND SEASON TARIFF (SEPTEMBER - MAY) Cost/kWh (VAT Incl.) HIGH DEMAND SEASON TARIFF (JUNE - AUGUST) Cost/kWh (VAT Incl.) 24 hr cycle Weekday Saturday Sunday Weekday Saturday Sunday 00:00 39.79 39.79 39.79 45.95 45.95 45.95 01:00 39.79 39.79 39.79 45.95 45.95 45.95 02:00 39.79 39.79 39.79 45.95 45.95 45.95 03:00 39.79 39.79 39.79 45.95 45.95 45.95 04:00 39.79 39.79 39.79 45.95 45.95 45.95 05:00 39.79 39.79 39.79 45.95 45.95 45.95 06:00 62.72 39.11 39.79 279.33 45.95 45.95 07:00 91.12 62.72 39.79 279.33 84.62 45.95 08:00 91.12 62.72 39.79 279.33 84.62 45.95 09:00 91.12 62.72 39.79 84.62 84.62 45.95 10:00 62.72 62.72 39.79 84.62 84.62 45.95 11:00 62.72 62.72 39.79 84.62 84.62 45.95 12:00 62.72 39.79 39.79 84.62 45.95 45.95 13:00 62.72 39.79 39.79 84.62 45.95 45.95 14:00 62.72 39.79 39.79 84.62 45.95 45.95 15:00 62.72 39.79 39.79 84.62 45.95 45.95 16:00 62.72 39.79 39.79 84.62 45.95 45.95 17:00 62.72 39.79 39.79 279.33 45.95 45.95 18:00 91.12 62.72 39.79 279.33 84.62 45.95 19:00 91.12 62.72 39.79 84.62 84.62 45.95 20:00 62.72 39.79 39.79 84.62 45.95 45.95 21:00 62.72 39.79 39.79 84.62 45.95 45.95 22:00 39.79 39.79 39.79 45.95 45.95 45.95 23:00 39.79 39.79 39.79 45.95 45.95 45.95 4-35 4.4 ASSUMPTIONS Various operational and system assumptions are made in the Excel model. The operational assumptions include operational system parameters, such as when pumps are operational and when turbines are operational. System assumptions include assumptions pertaining to the general system components and their associated capacities: The operational assumptions include the following:  Water is only pumped from the lower reservoir to the upper reservoir during off-peak tariff periods.  Power is only generated during standard and peak tariff periods. The following system assumptions are made and are based on the technical background as detailed in section 3:  The existing chilled water column serves as the shaft pump column.  Shaft water column dimensions are as determined in section 3.4.2.4: o 350 NB, SCH 80, surface to BD – 298.3 m o 350 NB, SCH 120, BD – 298.3 m to BD – 1 396.6 m o 350 NB, SCH 160, BD – 1 396.6 m to BD – 2 095.0 m.  A new turbine column will be installed next to the existing chilled water column.  The water flows down the existing pipe column at 370 l/s to satisfy the turbine discharge rate to net head ratio (refer to section 3.4.1.1).  Unlimited storage capacity is available in the upper, mid-shaft and lower reservoirs, as discussed in section 3.4.4. 4.5 INPUT PARAMETERS The input parameters of the model are given in Table 4-2. These input parameters are based on the UPHES system envisioned for the Driefontein No. 9 Shaft. The shaft dewatering arrangement will consist of a pump station on 24 level, -2 095 m BD, and another located mid-shaft, -1 050 BD. Water collected in the lower reservoir, located on 24 level, is pumped to mid-shaft. From mid-shaft, water is pumped to IPC level, (-150 BD) into the upper reservoir. A water balance determines the volume of water to be pumped from the dam on IPC level in order to keep the UPHES system in balance. Water ingress from outside the UPHES system is estimated to not exceed 4 l/s. The model determines the required capacity of the upper and lower reservoirs, as well as the number of pumps required in order to dewater the lower reservoir in the time available. Excess water pumped to the upper reservoir is pumped to the surface collection dams for treatment at the AMD treatment plant. 4-36 Table 4-2: Model input parameters UPHES INPUT PARAMETERS Description Unit Value Comments Water density [kg/m 3 ] 998 Assumed approximately constant Gravitational acceleration [m/s 2 ] 9.81 Assumed approximately constant Number of turbines [-] 1 Turbine flow rate [l/s] 369.55 Refer to Section 3.4.1 Discharge rate/net head [-] 0.19 Refer to Section 3.4.1 Turbine efficiency [%] 91 Refer to Section 3.4.1 Pumping rate (single pump) [l/s] 55.56 Refer to Section 3.4.3 Pump efficiency [%] 89 Refer to Section 3.4.3 IPC top (- 150 BD) [m] 150 Upper reservoir Mid-shaft (- 1 050 BD) [m] 1050 Mid-shaft pump chamber and reservoir 24 lvl (- 2 095 m BD) [m] 2095 Turbine, pump chamber and lower reservoir Number of off-peak hours (low / high demand seasons) [hrs] 8 Number of hours available for pumping water to the upper reservoir 4.6 PIPE PRESSURE CALCULATIONS Based on the flow rates, preliminary pipe lengths and pipe diameters in Table 3-1, the pipe pressures are determined as shown in Table 4-3. Pipe pressures are determined with the Darcy equations; Darcy friction factors are calculated using the Colebrook iteration for turbulent flow and static pressure changes (Munson et al., 2010): ( ) The static pressure change is: The total pipe pressure is therefore: . All pipes are assumed to be hot dip galvanised and therefore the absolute surface roughness of the pipe is taken as 0.15 mm. 4-37 Table 4-3: Shaft piping pressures In le t p re s s u re [k P a ] P ip e l e n g th [ m ] F lo w v e lo c it y [m /s ] ID [m ] R e y n o ld s n u m b e r F ri c ti o n f a c to r F ri c ti o n l o s s [k P a ] C h a n g e i n h e ig h t [m ] T o ta l p ip e p re s s u re [ k P a ] O u tl e t p re s s u re [k P a ] 0.0 698.3 3.24 0.280 6.98E+05 0.0176 253.890 698.3 7091 7090.8 7090.8 698.3 2.83 0.300 6.52E+05 0.0175 178.492 698.3 7015 14106.3 14106.3 698.3 2.53 0.318 6.16E+05 0.0173 133.410 698.3 6970 21076.6 4.6.1 Pipe Pressure Rating Calculations As per ASME B31.3, the following equations and parameters are used to determine the maximum allowable gauge pressure of the pipe column given in Table 4-4: ( ( where , , , , , , , 4-38 Table 4-4: Peak pipe pressure and selected pipe schedule between BD 0.00 m and BD - 698.3 m Description Value Units Reference Pipe outer diameter 355.6 mm ASTM 106 - Grade B Stress value of material 183 MPa ASME B31.3 Table A1 + 33% for transient flow condition Weld joint strength 1 - ASME B31.3 Table 302.3.5 ASME quality factor 1.00 - ASME B31.3 Table A-B1 ASME coefficient 0.4 - ASME B31.3 Table 304.1.1 Pipe specification wall thickness 19.1 mm Sum of mechanical allowances 4.4 mm 2 mm (corrosion),12.5% (mill tolerance) Pressure design wall thickness 14.7 mm Design gauge pressure 15 647.7 kPa Peak pressure 11 332.5 kPa 72% of design gauge pressure Table 4-5: Peak pipe pressure and selected pipe schedule between BD - 698.30 m to BD - 1 396.6 m Description Value Units Reference Pipe specification wall thickness 27.8 mm Sum of mechanical allowances 5.5 mm 2 mm (corrosion),12.5% (mill tolerance) Pressure design wall thickness 22.3 mm Design gauge pressure 24 236.8 kPa Peak pressure 18 169.5 kPa 75% of design gauge pressure Table 4-6: Peak pipe pressure and selected pipe schedule between BD -698.30 m to BD - 1 396.6 m Description Value Units Reference Pipe specification wall thickness 37.7 mm Sum of mechanical allowances 6.7 mm 2 mm (corrosion),12.5% (mill tolerance) Pressure design wall thickness 31.0 mm Design gauge pressure 34 370.5 kPa Peak pressure 25 006.4 kPa 73% of design gauge pressure 4.6.2 Limiting Flow Rate Whillier et al. (1977) published various guidelines for the effective design of gravity-fed water systems. The limiting velocity of a vertical shaft pipe column occurs when the frictional head loss is 1 m of water per metre length of pipe. Standard pipe lengths are used for shaft piping, either 6 m or 9 m lengths. 4-39 If the maximum limiting velocity is determined by using these criteria and assuming 9 m pipe lengths, the resultant flow rate is 405.58 l/s. The limiting pipe flow rate is 9% above the turbine flow rate required to satisfy a 1.9 discharge rate to net head ratio. At a flow rate of 369.6 l/s, the peak pressure in the pipe column from surface to BD -698.3 m is 3% below the design gauge pressure at the maximum limiting velocity. Although the resulting friction head loss is 0.832 m per pipe length, which is acceptable in terms of the guidelines suggested by Whillier et al. (1977), a safety margin of 3% is not acceptable. Therefore, the existing chilled water column will be used as a shaft pump column and a new suitable shaft turbine column must be installed. The resulting peak pipe pressures are given in the tables below: Table 4-7: Peak pipe pressure BD 0.00 m to BD- 698.3 m at limiting velocity Description Value Units Reference Design gauge pressure 15 647.7 kPa Peak pressure 15 143.7 kPa 97% of design gauge pressure Table 4-8: Peak pipe pressure BD - 698.30 m to BD - 1 396.6 m at limiting velocity Description Value Units Reference Design gauge pressure 24 236.8 kPa Peak pressure 21 980.6 kPa 91% of design gauge pressure Table 4-9: Peak pipe pressure BD -1 396.6 m to BD – 2 095 m at limiting velocity Description Value Units Reference Design gauge pressure 34 370.5 kPa Peak pressure 28 817.6 kPa 84% of design gauge pressure 4-40 4.7 CAPITAL COST MODEL 4.7.1 Basis of Estimate The capital cost estimate is based on the supply and installation rate of all the equipment and infrastructure required for a complete UPHES system. The total cost of the equipment can only be established once the system output parameters are known. Output parameters such as the storage capacity of each reservoir, number of pumps required per pump chamber and number of dewatering columns required are determined from the master calculation. The model uses the output of the simulation to determine the quantities of equipment required to determine the approximate UPHES system capital cost. The CAPEX model is structured in packages, namely winding plant, headgear, shaft development, shaft infrastructure, station development, off-shaft development, pump chambers and turbine chamber. The CAPEX model is structured to not exclude the current infrastructure in order to give an indicative cost of a new system. The capital cost estimate is built on a +30%, -15% accuracy and uses a 17% contingency value based on the level of accuracy associated with each system component in the capital cost estimate. 4.7.2 Bill of Quantities The rolled-up bill of quantities (showing the anticipated cost of each of the sub-sectioned items in each package) is shown in Table 4-10: Table 4-10: Capital cost model input parameters CAPITAL COST ESTIMATE 2016 WBS ITEM EQUIPMENT RATE [ZAR/unit] COMMENTS Winding Plant 1 Men/material winder 31 015 166.00 Includes mechanical, electrical and control equipment, as well as ropes, rope attachments, conveyances, winder foundations and winder building 2 Auxiliary winder 23 261 374.50 Includes mechanical, electrical and control equipment, as well as ropes, rope attachments, conveyances, winder foundations and winder building Headgear 3 A-frame headgear 37 958 026.00 140 t headgear assumed suitable for the required duty (during sinking operations and permanent condition), including leg foundations and headgear equipment (sheaves and tipping chutes) 4-41 CAPITAL COST ESTIMATE 2016 WBS ITEM EQUIPMENT RATE [ZAR/unit] COMMENTS 4 Collar construction and backfill 7 504 650.95 Includes collar excavation, concrete lining, mass concrete fill and backfill as required Shaft Development 5 Shaft development (blind sink) 360 000/m 342 000/m 318 000/m Main pre-sink and line Main sink (slow sink and line) Main sink (to shaft bottom) Shaft Infrastructure 6 Shaft steelwork 1 179 000/m Includes supply and install rate for fixed guides, buntons and inserts 7 350 NB, SCH 80 10 097.30 Turbine feed column – 9 m lengths, flanged pipes (number determined by considering number of turbine columns including additional pump columns required) 8 350 NB, SCH 120 12 337.19 9 350 NB, SCH 160 13 864.49 10 Bends, fittings, pipe brackets TBD Based on 5% of the total pipe supply cost 11 Valves TBD Based on 10% of the total pipe supply cost 12 Pipe installation TBD Based on 40% of the total pipe supply cost 13 Shaft cables and communication cables 1 039 775.30 Supply rate for 2 300 m (scale to suit shaft depth) 14 Shaft cables and communication cables 216 585.85 Installation rate for 2 300 m (scale to suit shaft depth) Station Development 15 Station development 6 189 909.00 Off-Station Development 16 Excavation: Upper reservoir 2 800.00/m 3 Per metre rate (cross section 3.5 m x3.0 m) 17 Construction: Upper reservoir 50 000.00 Supply and construction rate per dam wall 18 Excavation: Lower reservoir 2 800.00/m 3 Per metre rate (cross section 3.5 m x3.0 m) 19 Construction: Lower reservoir 50 000.00 Supply and construction rate per dam wall 20 Excavation: Mid-shaft reservoir 2 800.00/m 3 Per metre rate (cross section 3.5 m x3.0 m) 21 Construction: Mid- shaft reservoir 50 000.00 Supply and construction rate per dam wall 4-42 CAPITAL COST ESTIMATE 2016 WBS ITEM EQUIPMENT RATE [ZAR/unit] COMMENTS Pump Chambers 22 Clear Water Pumps 3 134 883.23 Supply and installation cost per unit, includes commissioning 23 Pumps electrical, control and instrumentation (C&I) equipment 275 129.55 Supply cost of C&I per unit 24 Pumps electrical, control and instrumentation equipment 173 611.63 Installation cost of C&I per unit 25 Pump station construction 305 417.38 Typical large pump station construction (incl. steelwork) length: 50 m, width 6.5 m, height 6.8 m 26 Pump station excavation 2 800.00/m 3 Typical large pump station excavation, (incl. supports) length: 50 m, width 6.5 m, height 6.8 m 27 Pump station overhead crane 368 000.00 Includes supply, installation and commissioning Turbine Chamber 28 Turbine 4 630 500.00 Per unit supply and installation rate 29 Turbine electrical, control and instrumentation equipment 1 100.518.20 Per unit supply rate only 30 Turbine electrical, control and instrumentation equipment 694 446.51 Per unit installation and commissioning rate 31 Turbine chamber construction 353 558.79 Medium sized chamber construction (incl. steelwork) length: 25 m, width 6.5 m, height 6.8 m 32 Turbine chamber excavation 2 800.00/m 3 Medium sized chamber excavation, (incl. supports) length: 25 m, width 6.5 m, height 6.8 m 4-43 4.7.3 Bill of Quantities – UPHES System: Driefontein No. 9 Shaft The bill of quantities was updated by considering the existing infrastructure at the Driefontein No.9 Shaft. The following items are excluded from the CAPEX model in accordance with the existing infrastructure of the Driefontein No. 9 Shaft:  Winding plant  Headgear, including equipment installed in the headgear such as deflection sheaves  Shaft development  Station development  Off-station development (mid-shaft station development and the 24 level station development)  Shaft steelwork (buntons, conveyance guides and pipe brackets). Allowance is made for the supply and installation of the following additional items:  Turbine feed column from IPC to 24 level, including pipe routing and valves in the pump and turbine chambers  Upper reservoir excavation and construction of dam walls  Mid-shaft storage reservoir and construction of a dam wall  Construction of dam walls for the lower reservoir  Supply, installation and commissioning of additional pumps as required (excluding the pumps already installed)  Excavation and construction of the pump chamber on the mid-shaft level  Supply and installation of electric overhead travelling cranes for the 24 level pump chamber and mid-shaft pump chamber  Excavation and construction of the turbine chamber on 24 level  Supply, installation and commissioning of one turbine. 4-44 4.8 RESULTS 4.8.1 UPHES System Generating Capacity This section shows the resulting system generation capacity regarding:  Instantaneous turbine power generation capacity  Generation capacity during peak tariff periods and the resulting system parameters  Generation capacity during peak and standard tariff periods and the resulting system parameters. 4.8.1.1 Instantaneous UPHES system generating capacity The instantaneous energy generation capacity of the turbine is given by the equations and parameters detailed in section 2.4.2.1. With a total effective head of 1 945 m, the turbine is theoretically capable of instantaneously generating 6.40 MW at a flow rate of 369.55 l/s. 4.8.1.2 Power generated during peak tariff periods only Applying the generating capacity of the turbine during peak tariff periods results in generating power for five hours a day, during both LDS and HDS. The theoretical power generated amounts to 32.02 MWh/day. Table 4-11 shows the resulting system parameters such as the total amount of water in the lower reservoir, number of multistage clear water pumps required to dewater the lower reservoir and the total electrical power required to pump the water to the upper reservoir. Figure 4-4 and Figure 4-5 show the POD load profile and weekday cost profile resulting from generating only during peak tariff periods. Table 4-11: Generating during peak tariff periods only – system parameters Description Unit Value No. of hours operated [hrs] 5 Effective head [m] 1945 Theoretical power generated [MW] 6.40 Theoretical electrical power generated [MWh] 32.02 Volume of water in the lower reservoir [Ml] 6.65 No. of multistage clear water pumps required in mid-shaft and IPC lvl [-] 5 Total water pumped to upper reservoir [Ml] 8.0 Power required to pump water to mid-shaft per pump [MW] 3.391 Power required to pump water to IPC per pump [MW] 2.901 Total power required [MW] 6.291 Total electrical power required [MWh] 50.33 Hours required to fill up upper reservoir [hrs] 8 4-45 Figure 4-4: POD load profile – power generated during peak tariff periods only Figure 4-5: Daily energy cost profile – power generated during peak tariff periods only 4-46 4.8.1.3 Power generated during peak and standard tariff periods Applying the generating capacity of the turbine during peak and standard tariff periods results in generating power for 16 hours a day, during both LDS and HDS. Fourteen pumps are then required to pump water from the lower reservoir to the upper reservoir, triple the requirement indicated in the previous section. The theoretical power generated amounts to 102.46 MWh/day. Table 4-12 shows the resulting system parameters, such as the total amount of water in the lower reservoir, number of multistage clear water pumps required to dewater the lower reservoir and the total electrical power required to pump the water to the upper reservoir. Figure 4-6 and Figure 4-7 show the POD load profile and weekday cost profile resulting from generating only during peak and standard tariff periods. Table 4-12: Generating during peak and standard tariff periods – system parameters Description Unit Value No. of hours operated [hrs] 16 Effective head [m] 1945 Theoretical power generated [MW] 6.40 Theoretical electrical power generated [MWh] 102.46 Volume of water in the lower reservoir [Ml] 21.29 No. of multistage clear water pumps required in mid-shaft and IPC lvl [-] 14 Total water pumped to upper reservoir [Ml] 22.4 Power required to pump water to mid shaft per pump [MW] 9.494 Power required to pump water to IPC per pump [MW] 8.122 Total power required [MW] 17.62 Total electrical power required [MWh] 140.93 Hours required to fill up upper reservoir [hrs] 8 4-47 Figure 4-6: POD load profile – power generated during peak and standard tariff periods Figure 4-7: Daily energy cost profile – power generated during peak and standard tariff periods 4-48 4.8.2 Electricity Cost Savings The resulting electricity cost savings with regard to peak tariff period power generation vs. peak/standard tariff period power generation is 5.52 MR and 7.50 MR per annum respectively. In both cases more electricity is required to power the pumps to pump water to the upper reservoir during off-peak periods. The additional power required is shown as a percentage of the original power requirement in Table 4-13 and Table 4-14. Table 4-13: Generating during peak tariff periods only – trim Description Unit LDS HDS Total ANNUAL POWER REQUIREMENTS AND COSTS – ORIGINAL WEEKDAY POD PROFILE TOTAL POWER REQ. [kW] 84 558 911 28 496 043 113 054 954 TOTAL POWER COST ZAR [RM] 46 042 378 26 308 609 72 350 987 ANNUAL POWER REQUIREMENTS AND COSTS – UPHES SYSTEM WEEKDAY POD PROFILE TOTAL POWER REQ. [kW] 89 558 069 30 180 741 119 738 810 TOTAL POWER COST ZAR [RM] 44 636 869 22 196 306 66 833 175 ADDITIONAL POWER REQ. [kW] 4 999 158 1 684 698 6 683 856 SAVINGS ZAR [RM] 1 405 509 4 112 303 5 517 812 EXTRA POWER REQUIRED (% OF INITIAL POWER REQ.) 5.91% TOTAL SYSYTEM POWER COST TRIM (% OF INITIAL POWER REQ.) 7.63% Table 4-14: Generating during peak and standard tariff periods – trim Description Unit LDS HDS Total ANNUAL POWER REQUIREMENTS AND COSTS – ORIGINAL WEEKDAY POD PROFILE TOTAL POWER REQ. [kW] 84 558 911 28 496 043 113 054 954 TOTAL POWER COST ZAR [RM] 46 042 378 26 308 609 72 350 987 ANNUAL POWER REQUIREMENTS AND COSTS – UPHES SYSTEM WEEKDAY POD PROFILE TOTAL POWER REQ. [kW] 95 060 111 32 034 909 127 095 020 TOTAL POWER COST ZAR [RM] 43 686 740 21 166 288 64 853 028 ADDITIONAL POWER REQ. [kW] 10 501 200 3 538 866 14 040 066 SAVINGS ZAR [RM] 2 355 639 5 142 321 7 497 960 EXTRA POWER REQ. PA (% OF INITIAL POWER REQ.) 12.42% TOTAL SYSYTEM POWER COST TRIM PA (% OF INITIAL POWER REQ.) 10.36% 4-49 4.8.3 Return on Investment The theoretical ROI is determined by assuming an increase in the Eskom Megaflex tariff structure of approximately 8% per annum. The ROI for each option is given in Table 4-15 and shown in Figure 4-8 and Figure 4-9: Table 4-15: ROI assuming a tariff increase of 8% pa System Description ROI (years) UPHES system configured to generate power during peak tariff charges only 5.5 UPHES system configured to generate power during peak and standard tariff charges 12 Figure 4-8: ROI (assuming an 8% pa tariff increase) The UPHES system model developed provides all the required output parameters in order to evaluate a UPHES system. The next chapter discusses the detail of the development of the EES model, evaluation of the results generated and subsequent verification of the UPHES system model. ______________________________ 5-50 5 EES MODEL The UPHES system is simulated the using EES program. The system configuration detailed in Figure 4-1 is used along with the following input parameters:  Typical POD load profile, as detailed in Section 4.1  2016/2017 Megaflex tariff structure, as stipulated in Section 4.3  System assumptions in accordance with the assumptions made in Section 4.4  CAPEX model customised to exclude existing infrastructure at the Driefontein No. 9 Shaft as defined in Section 4.7  System input parameters in accordance with the system configuration as defined Section 4.5. Parametric tables are used to input the Megaflex tariff structure, POD load profile and pumping and generating schedules. 5.1 SIMULATION INPUT PARAMETERS The following input parameters are used: Table 5-1: EES simulation model input parameters Description Unit Value Comments Primary Input Parameters Water density rho_water [kg/m 3 ] 998 Gravitational acceleration g [m/s 2 ] 9.81 Number of turbines S_TURBINE [-] 1 Turbine flow rate V_TURBINE [l/s] 369.55 Discharge rate/net head R_DISCHARGE_HEAD [-] 0.19 Turbine efficiency eta_TURBINE [%] 91 Pumping rate V_PUMP [l/s] 55.56 Single pump Pump efficiency eta_PUMP [%] 89 Pipe friction factor f [-] 0.0174 Pipe diameter D_i_PIPE [mm] 248.18 Turbine feed No. of pumps required* S_PUMPS_MANUAL [-] 5 (System installed capacity 32 MWh) No. of pumps required* S_PUMPS_MANUAL [-] 14 (System installed capacity 102.5 MWh) UPHES System Elevations IPC level H_1_IPC_9 [m] 150 Upper reservoir Mid-shaft H_2_MID_SHAFT_9 [m] 1050 Mid-shaft reservoir 24 level H_3_24LVL_9 [m] 2095 Lower reservoir Operational Input Parameters No. of hours pumping HRS_PUMPS [hrs] 8 (System installed capacity 32 MWh) 5-51 Description Unit Value Comments No. of hours pumping HRS_PUMPS [hrs] 8 (System installed capacity 102.5 MWh) No. of hours generating HRS_TURBINE [hrs] 5 (System installed capacity 32 MWh) No. of hours generating HRS_TURBINE [hrs] 16 (System installed capacity 102.5 MWh) * The number of pumps used to facilitate a healthy water balance is a manual input parameter emanating from the calculated number of pumps required 5.2 SIMULATION OUTPUT PARAMETERS The following output parameters are generated: Table 5-2: EES simulation model output parameters Description Unit Primary Output Parameters System generation capacity P_ACTUAL [kW] System generation capacity P_TURBINE_MWh [MWh] Effective head H_EFFECTIVE [m] Approximate pipe friction (24 level to mid-shaft) H_3_FRICTION [m] Approximate pipe friction (mid-shaft to IPC level) H_2_FRICTION [m] Water velocity (pump column) VEL_UP [m/s] Upper reservoir volume VOL_UPPER_RESERVOIR [Ml] Number of pumps required S_PUMPS [No] Lower reservoir volume VOL_LOWER_RESERVOIR [Ml] Power required (24 level pumps) P_PUMPS_24LVL_9 [MW] Power required (mid-shaft pumps) P_PUMPS_MID_SHAFT_9 [MW] Total power required for pumping P_PUMPS_MWh [MW] Megaflex Tariff Structure Duration – off-peak tariffs charged during weekdays D_WEEKDAY_OFF_PEAK [No] Duration – standard tariffs charged during weekdays D_WEEKDAY_STANDARD [No] Duration – peak tariffs charged during weekdays D_WEEKDAY_PEAK [No] Duration – off-peak tariffs charged on Saturdays D_SATURDAY_OFF_PEAK [No] Duration – standard tariffs charged on Saturdays D_SATURDAY_STANDARD [No] Duration – peak tariffs charged on Saturdays D_SATURDAY_PEAK [No] Duration – off-peak tariffs charged on Sundays D_SUNDAY_OFF_PEAK [No] Duration – standard tariffs charged on Sundays D_SUNDAY_STANDARD [No] Duration – peak tariffs charged on Sundays D_SUNDAY_PEAK [No] Annual percentage tariff increase ESKOM [%] Load Profile and Electricity Cost Original load profile POD_USAGE_PA [kWh] 5-52 Description Unit Cost of the POD electricity consumed ZAR_POD_USAGE_PA [MR] Load profile of the UPHES system POD_USAGE_PA_UPHES [kWh] Cost of POD electricity consumed ZAR_POD_USAGE_PA [MR] Electricity cost savings SAVINGS [MR] System CAPEX (Refer to Section 4.7) CAPEX – winding plant PACKAGE_1 [MR] CAPEX – headframe and auxiliary equipment PACKAGE_2 [MR] CAPEX – shaft development PACKAGE_3 [MR] CAPEX – shaft infrastructure PACKAGE_4 [MR] CAPEX – station development PACKAGE_5 [MR] CAPEX – off-station development PACKAGE_6 [MR] CAPEX – pumps PACKAGE_7 [MR] CAPEX – turbines PACKAGE_8 [MR] 5.3 VERIFICATION The model is used to simulate the UPHES system applied to the Driefontein No. 9 Shaft. The results of both system operational conditions were generated, namely:  Power generated during peak tariff periods only  Power generated during peak and standard tariff periods. The EES simulation model results used as verification models are included in Appendix II. 5.3.1 Simulation Results 5.3.1.1 Power generated during peak tariff periods only Results were generated using the EES simulation model applied to the Driefontein No. 9 Shaft for power generated during peak tariff periods only. These results compare with the results generated with the UPHES system modelled in Excel as follows: Table 5-3: Generating during peak tariff periods only, EES simulation results Description Unit UPHES Excel model results UPHES EES simulation results % VAR Effective head [m] 1945 1945 0.00 Theoretical power generated [MW] 6.400 6.404 -0.06 Theoretical electrical power generated [MWh] 32.02 32.02 0.00 Number of pumps required [-] 5 4.157 (5) 0.00 Upper reservoir volume [Ml] 8.0 8.001 -0.01 Lower reservoir volume [Ml] 6.65 6.652 -0.03 5-53 Description Unit UPHES Excel model results UPHES EES simulation results % VAR Power required to pump water to mid shaft [MW] 3.391 3.379 0.35 Power required to pump water to IPC [MW] 2.901 2.912 -0.38 Total electrical power required [MWh] 50.33 50.33 0.00 Total power required per annum - UPHES [MWh] 119.7 119.7 0.00 Total power cost per annum - UPHES [MR] 66.83 66.83 0.00 Total UPHES system CAPEX [MR] 44.29 44.36 -0.16 Electricity cost savings [MR] 5.518 5.518 0.00 ROI [years] 5 (+6 months) 5 to 6 N/A 5.3.1.2 Power generated during peak and standard tariff periods Results were generated using the EES simulation model applied to the Driefontein No. 9 Shaft for power generated during peak and standard tariff periods. These results compare with the results generated with the UPHES system modelled in Excel as follows: Table 5-4: generating during peak and standard tariff periods, EES simulation results Description Unit UPHES Excel model results UPHES EES simulation results % VAR Effective head [m] 1945 1945 0.00 Theoretical power generated [MW] 6.40 6.404 -0.06 Theoretical electrical power generated [MWh] 102.46 102.5 -0.04 Number of pumps required [-] 14 13.3 (14) 0.00 Upper reservoir volume [Ml] 22.4 22.4 0.00 Lower reservoir volume [Ml] 21.29 21.29 0.00 Power required to pump water to mid-shaft [MW] 9.494 9.462 0.34 Power required to pump water to IPC [MW] 8.122 8.153 -0.38 Total electrical power required [MWh] 140.93 140.9 0.02 Total power required per annum - UPHES [MWh] 127.1 127.1 0.00 Total power cost per annum - UPHES [MR] 64.85 64.90 -0.08 Total UPHES system CAPEX [MR] 162.64 162.9 -0.16 Electricity cost savings [MR] 7.498 7.534 -0.48 ROI [years] 12 (+1 month) 12 to 13 N/A 5.3.1.3 Evaluation of simulation results The variance between the results generated with the Excel model and the EES simulation is given in Table 5-3 and Table 5-4. The EES simulation model generated results with negligible variance from the results generated by the Excel model. The system is therefore validated by using the EES simulation. 5-54 5.4 SYSTEM OPTIMISATION In order to optimise the UPHES simulation model, the first priority must be to reduce the ROI. Although a large system is preferred when the UPHES system is considered as a legacy asset, larger systems will require larger capital investments. It is a requirement that the asset investment is returned in the shortest time possible for the mine to benefit from the system‟s energy saving potential. The option of generating power during periods in which peak and off-peak tariffs are charged requires a large capital investment, which can only be recovered after 12 to 13 years, whereas the option of generating power during periods when peak tariff are charged requires a capital investment that can be recovered within five to six years. The latter option is therefore selected as the „go forward‟ option for optimisation. The major contributors to the capital cost estimate are the cost of underground reservoir excavation and the supply, installation and commissioning of additional pumps. These costs are dependent on the system output parameters and can be optimised along with the output parameters. The cost for turbine supply, installation and commissioning and the additional shaft column to be installed for the turbine feed cannot be reduced, as this is a fixed system requirement. In order to reduce the capital investment, the existing infrastructure must be used optimally and if possible, to the extent that additional equipment is not required. The available pumps at the Driefontein shaft are the primary constraint because the excavations and construction of underground reservoirs are a function of the system‟s generation capacity. The number of hours spent generating electricity during periods in which a peak tariff is charged determines the amount of water transferred to the lower reservoir. The greatest energy savings are achieved by maximising the number of hours generating electricity during periods in which a peak tariff is charged and maximising the number of hours pumped only in periods in which off-peak tariffs are charged. This strategy maximises the number of hours during the day in which the maximum differential cost between tariffs are charged. Strategically scheduled pump and generating schedules are required to achieve the optimal system energy saving. The system is therefore optimised if the number of pumps can be kept to the number currently available (eight pumps), electricity is generated at all hours available in the periods when peak tariffs are charged and the water balance can be maintained by utilising periods when off-peak tariffs are charged during weekends. 5.4.1 Optimal Generating Schedules The load and cost profiles of the first option presented are shown in Figure 5-1, Figure 5-2 and Figure 5-3 for both LDSs and HDSs. These cost and load profiles are generated based on the option of generating electricity during periods in which peak tariffs are charged as per the Excel model. The pump and generation schedules are identical and applied to weekdays, Saturdays and Sundays: 5-55 Figure 5-1: Load and cost profile versus time (Weekdays) Figure 5-2: Load and cost profile vs time (Saturdays) Figure 5-3: Load and cost profile versus time (Sundays) Unlike the Excel model, the EES simulation allows the pump and generating schedules to be varied for weekdays, Saturdays and Sundays. An optimisation matrix is used to evaluate the pumping and generating schedules and their effect on the number of pumps required per pump chamber, lower reservoir capacity, CAPEX, electricity savings and ROI. The number of pumps required per pump chamber and lower reservoir capacity is a major cost contributor and is therefore included in the evaluation. 5-56 Table 5-5: Optimisation evaluation matrix – option 1 to 9 O P T IO N W E E K D A Y ( L D S ) S A T U R D A Y ( L D S ) S U N D A Y ( L D S ) W E E K D A Y ( H D S ) S A T U R D A Y ( H D S ) S U N D A Y ( H D S ) G E N E R A T IO N S C H E D U L E W E E K D A Y [ H R S ] P U M P IN G S C H E D U L E W E E K D A Y S H R S ] P U M P IN G S C H E D U L E S A T U R D A Y [ H R S ] P U M P IN G S C H E D U L E S U N D A Y [ H R S ] P U M P S P E R P U M P C H A M B E R [ N o ] L O W E R R E S E R V O IR C A P A C IT Y [ M l] C A P E X [ M R ] S A V IN G S [ M R ] R O I [Y E A R S ] 1 • • • • • • 5 8 8 8 5 6.652 44.361 5.518 5.5 2 • • • • 5 8 8 5 6.652 44.361 5.935 5.1 3 • • 5 8 5 6.652 44.361 5.946 5.0 4 • (5) □ (1) • (5) □ (1) 6 8 8 8 5 7.982 49.25 6.242 5.3 5 • (5) □ (2) • (5) □ (2) 7 8 8 8 6 9.313 61.33 8.134 5.2 6 • (5) • (5) 5 9 9 9 4 6.652 37.71 4.702 5.4 7 • (5) □ (1) • (5) □ (1) 6 9 9 9 5 7.982 49.25 4.383 7.3 8 • (5) □ (1) • (5) □ (1) 6 8 5 7.982 49.25 4.199 7.6 9 • (4) • (4) 4 8 4 5.322 32.28 3.959 5.5 ● Generating during peak tariffs (no. of hours) □ Generating during standard tariffs (no. of hours) Option 3 presents the best electricity savings and ROI. It is therefore selected as the „go forward‟ option for optimisation of pumping schedules. 5.4.2 Optimal Pumping Schedules The pump schedules must be configured to allow sufficient dewatering of the lower reservoir to maintain a water balance in accordance with the lower reservoir storage capacity. The number of pumps in each pump chamber can be reduced to the number currently available in an effort to reduce the capital cost of the system by scheduling pumping on Saturdays and Sundays. However, to maintain the system‟s water balance, additional storage capacity in the lower reservoir is required to store the water that is not pumped to the upper reservoir on weekdays. The additional capacity infers additional excavation and construction costs for the lower reservoir, thus increasing the system‟s capital cost. 5-57 Options 9 and 10 consider rescheduling one and two hours of pumping on weekdays to Saturdays. The capacity of the lower reservoir is increased by a factor of 0.625 for every hour rescheduled to Saturdays or Sundays. The load and cost profiles are shown in Figure 5-4, Figure 5-5 and Figure 5-6 for both LDS and HDS. Figure 5-4: Load and cost profile versus time (Weekdays) option 3, 9 and 10 Figure 5-5: Load and cost profile versus time (Saturdays) option 3, 10 and 11 Figure 5-6: Load and cost profile versus time (Sundays) option 3, 10 and 11 5-58 The optimisation matrix is used to evaluate the effect of rescheduling pump schedules to Saturdays on the number of pumps required per pump chamber, lower reservoir capacity, CAPEX, electricity savings and ROI. Table 5-6: Optimisation evaluation matrix – option 3 to 9, 10 O P T IO N W E E K D A Y ( L D S ) S A T U R D A Y ( L D S ) S U N D A Y ( L D S ) W E E K D A Y ( H D S ) S A T U R D A Y ( H D S ) S U N D A Y ( H D S ) G E N E R A T IO N S C H E D U L E W E E K D A Y [ H R S ] P U M P IN G S C H E D U L E W E E K D A Y H R S ] P U M P IN G S C H E D U L E S A T U R D A Y [ H R S ] P U M P IN G S C H E D U L E S U N D A Y [ H R S ] P U M P S P E R P U M P C H A M B E R [ N o ] L O W E R R E S E R V O IR C A P A C IT Y [ M l] C A P E X [ M R ] S A V IN G S [ M R ] R O I [Y E A R S ] 3 • (5) • (5) 5 8 5 6.652 44.361 5.946 5.0 10 • (5) • (5) 5 7 5 4 10.81 59.64 5.946 6.6 11 • (5) • (5) 5 6 10 4 21.62 99.37 5.946 10 ● Generating during peak tariffs (no. of hours) □ Generating during standard tariffs (no. of hours) The capital cost of the system increases by 34.4% for every hour rescheduled to Saturdays. Option 3 continues to present the best electricity savings and ROI. It is therefore selected as the „go forward‟ option for evaluation of the effect of tariff differentials on the electricity cost savings. 5.4.3 Tariff Differential Break-Even Point When evaluating option 1 with the EES model, it is found that the electricity cost savings are reduced when the system is applied on Saturdays and Sundays. A break-even point therefore exists during which the electricity cost savings is negatively affected by a decreased differential between the higher and lower tariff charged because the cost of power consumption due to pumping cannot be recovered when energy is generated with the turbine. The cost differential between the LDS off-peak and peak tariff for the current 2016/2017 Megaflex tariff structure is 44% (off-peak tariff as a percentage of the peak tariff). With this differential cost the electricity savings is R 8 994.51 for weekdays. If the percentage differential reaches 64%, the system no longer displays any electricity cost savings. The percentage differential between the standard and peak tariff for the current 2016/2017 Megaflex tariff structure is 69%, 5% above the break-even point. Table 5-6 shows the tariff differential break-even point calculation results: 5-59 TABLE 5-7: Tariff differential break-even point for low demand seasons LOW DEMAND SEASON ESKOM Megaflex tariff structure (LDS) Rate [c/kWh] % of peak tariff % of current peak tariff Peak tariff 91.1 100% 100% Off-peak tariff 57.9548373 64% 44% Standard tariff 62.72235 69% 69% Load [kWh] LDS Tariff [c/kWh] Turbine [kWh] Pumps [kWh] Residual load [kWh] Power cost [ZAR] Savings [ZAR] 1 13 059.4 58.0 6291.3 19 350.7 11 214.67241 -3646.12999 2 14 204.5 58.0 6291.3 20 495.8 11 878.30166 -3646.12999 3 15 449.0 58.0 6291.3 21 740.3 12 599.5728 -3646.12999 4 15 409.3 58.0 6291.3 21 700.6 12 576.56473 -3646.12999 5 15 008.0 58.0 6291.3 21 299.3 12 343.99196 -3646.12999 6 14 907.6 58.0 6291.3 21 198.9 12 285.80531 -3646.12999 7 14 338.8 62.7 14 338.8 8 993.632322 0 8 12 834.0 91.1 6403.7 6 430.3 5 857.96602 5833.80798 9 11 820.0 91.1 6403.7 5 416.3 4 934.21202 5833.80798 10 11 018.0 91.1 6403.7 4 614.3 4 203.59002 5833.80798 11 10 935.0 62.7 10 935.0 6 858.688973 0 12 11 229.0 62.7 11 229.0 7 043.092682 0 13 11 717.0 62.7 11 717.0 7 349.17775 0 14 12 771.0 62.7 12 771.0 8 010.271319 0 15 12 771.0 62.7 12 771.0 8 010.271319 0 16 13 055.0 62.7 13 055.0 8 188.402793 0 17 12 798.0 62.7 12 798.0 8 027.206353 0 18 12 536.0 62.7 12 536.0 7 862.873796 0 19 12 377.1 91.1 6403.7 5 973.3 5 441.69368 5833.80798 20 12 128.0 91.1 6403.7 5 724.3 5 214.80002 5833.80798 21 12 015.0 62.7 12 015.0 7 536.090353 0 22 12 152.0 62.7 12 152.0 7 622.019972 0 23 12 573.0 58.0 6291.3 18 864.3 10 932.79168 -3646.12999 24 12 673.0 58.0 6291.3 18 964.3 10 990.74651 -3646.12999 Total electricity cost savings 0.00 The cost differential between the HDS off-peak and peak tariff for the current 2016/2017 Megaflex tariff structure is 16% (off-peak tariff as a percentage of the peak tariff). With this differential cost the electricity saving is R66 943.68 for weekdays. Similarly, if the percentage differential reaches 64%, the system no longer displays any electricity cost savings. The percentage differential between the HDS standard and peak tariff for the current 2016/2017 Megaflex tariff structure is 188% (standard tariff as a percentage of the off-peak tariff). The break-even 5-60 point in this case was calculated as 157%, therefore if the percentage differential reaches 157% or lower, the system no longer displays any electricity cost savings. Table 5-7 shows the tariff differential break-even point calculation results for HDS Saturdays: TABLE 5-8: Tariff differential break-even point for high demand seasons HIGH DEMAND SEASON ESKOM Megaflex tariff structure (HDS) Rate [c/kWh] % of off-peak tariff % of current peak tariff Peak tariff 279.33 100% Off-peak tariff 44.6928 16% Standard tariff 70.25322 157% 30% Load [kWh] HDS Tariff [c/kWh] Turbine [kWh] Pumps [kWh] Residual load [kWh] Power cost [ZAR] Savings [ZAR] 1 13 059.4 44.7 6291.3 19 350.7 8 648.374061 -2811.77148 2 14 204.5 44.7 6291.3 20 495.8 9 160.142375 -2811.77148 3 15 449.0 44.7 6291.3 21 740.3 9 716.362148 -2811.77148 4 15 409.3 44.7 6291.3 21 700.6 9 698.619107 -2811.77148 5 15 008.0 44.7 6291.3 21 299.3 9 519.2669 -2811.77148 6 14 907.6 44.7 6291.3 21 198.9 9 474.395329 -2811.77148 7 14 338.8 44.7 14 338.8 6 408.411206 0 8 12 834.0 70.3 6403.7 6 430.3 4 517.46422 4498.834362 9 11 820.0 70.3 6403.7 5 416.3 3 805.096543 4498.834362 10 11 018.0 70.3 6403.7 4 614.3 3 241.665699 4498.834362 11 10 935.0 70.3 10 935.0 7 682.189886 0 12 11 229.0 70.3 11 229.0 7 888.73436 0 13 11 717.0 44.7 11 717.0 5 236.655376 0 14 12 771.0 44.7 12 771.0 5 707.717488 0 15 12 771.0 44.7 12 771.0 5 707.717488 0 16 13 055.0 44.7 13 055.0 5 834.64504 0 17 12 798.0 44.7 12 798.0 5 719.784544 0 18 12 536.0 44.7 12 536.0 5 602.689408 0 19 12 377.1 70.3 6403.7 5 973.3 4 196.449145 4498.834362 20 12 128.0 70.3 6403.7 5 724.3 4 021.476469 4498.834362 21 12 015.0 44.7 12 015.0 5 369.83992 0 22 12 152.0 44.7 12 152.0 5 431.069056 0 23 12 573.0 44.7 6291.3 18 864.3 8 430.99722 -2811.77148 24 12 673.0 44.7 6291.3 18 964.3 8 475.69002 -2811.77148 Total electricity cost savings 0.00 5-61 5.4.4 Optimised UPHES System for Driefontein No. 9 Shaft The findings of Section 5.4.3 are applied to Option 3. The output parameters of the EES simulation are given in Table 5-9. The load and cost profiles are shown in Figure 5-7, Figure 5-8 and Figure 5-9 for both LDSs and HDSs. Table 5-9: Optimised UPHES system EES simulation results Description Unit Optimised UPHES EES simulation results Effective head [m] 1945 Theoretical power generated [MW] 6.404 Theoretical electrical power generated [MWh] 32.02 Number of pumps required [-] 4.157 (5) Upper reservoir volume [Ml] 8.001 Lower reservoir volume [Ml] 6.652 Power required to pump water to mid-shaft [MW] 3.379 Power required to pump water to IPC [MW] 2.912 Total electrical power required [MWh] 50.33 Total UPHES system CAPEX [MR] 44.36 Electricity cost savings [MR] 6.001 ROI [years] 5 The UPHES system model for the Driefontein No. 9 Shaft is optimised and verified. The next chapter discusses the detail of validating the results by comparing the system operational data from the energy recovery system at the Driefontein No. 5 Shaft. 5-62 Figure 5-7: Optimised load and cost profile versus time (Weekdays) Figure 5-8: Optimised load and cost profile versus time (Saturdays) Figure 5-9: Optimised load and cost profile versus time (Sundays) ______________________________ 6-63 6 MODEL VALIDATION 6.1 DRIEFONTEIN NO. 5 SHAFT ENERGY RECOVERY SYSTEM In Section 2.4.1 of the literature study, reference is made to energy recovery systems in South African deep level mining operations. Like these systems, in the energy recovery system at the Driefontein No. 5 Shaft potential energy is recovered from the chilled water flowing down the shaft columns. The shaft refrigeration circuit consists of a central refrigeration plant located on surface. Chilled water is distributed to underground heat-exchanging systems via a single shaft column to working levels 1 680 m below surface. The potential energy of the water in the shaft column is converted to mechanical energy by the turbine, therefore recovering a part of the energy required to pump return water back to the surface. The turbine system was retrofitted to the existing system and high energy recovery has been recorded for this installation ever since. The turbine has the capacity to generate 4 625 kW. The turbine installation at Driefontein No. 5 Shaft is shown in Figure 6-1: Figure 6-1: Driefontein No. 5 Shaft turbine 6-64 6.1.1 Layout and Operation The turbine is located on 22 level. Water from the central refrigeration plant located on surface, with an average temperature of 4°C, is piped underground via a dedicated chilled water column. A dam, located on 20 level, is used to store the water from the turbine outlet to a maximum capacity of 95% before shutting down the turbine. The system operating parameters are shown in Table 6-1: Table 6-1: Driefontein No. 5 Shaft system operating parameters Operating parameter Unit Value Pressure at turbine inlet MPa 15 to 17.5 Flow rate at turbine inlet l/s 334.7 Velocity flow m/s 5.2 Motor speed rpm 3 000 to 3 020 Power kW 4 660 Turbine oil bearing temperature °C T_1 = 37.5 and T_2 = 46.4 Motor oil bearing temperature °C T_1 = 35.8 and T_2 = 38.4 Lubricating oil is constantly circulated through the system to avoid high operating temperatures. Two oil tanks are installed, one for normal duty and the other serving as an auxiliary tank. An oil pump and reticulation circuit is used to circulate the oil continuously. A jet deflector pump is used to deflect the jet when the turbine is turned off suddenly or during start-up. The system inlet pressure is constantly monitored and set to trip and direct the chilled water to bypass the turbine and discharge into the 20 level dam (open end) in the event of excessive column pressures. A high-level schematic of the bypass line and lubrication circulation is shown in Figure 6-2: Figure 6-2: Driefontein No. 5 Shaft turbine bypass line and lubrication 6-65 6.1.2 Trips and Alarms The instrumentation used to monitor the turbine and generator during operation is shown in Figure 6-3: Figure 6-3: Driefontein No. 5 Shaft turbine trips and alarms 6.2 TEST DATA Test data were collected from the Supervisory Control and Data Acquisition system on 27 January 2014. The data are shown in Figure 6-5 at the end of this section. During data collection the actual system parameters observed were as follows: Table 6-2: Driefontein No. 5 Shaft system operating parameters during data collection Description Unit Actual Alarm Trip Turbine Monitoring System Turbine under Speed rpm 3 003.4 2 860 2 850 Turbine over Speed rpm 3 003.4 3 180 3 200 D.E. Vibration mm/s 1.2 12 15 DE Bearing Temperature °C 43.5 70 80 NDE Bearing Temperature °C 58.4 85 90 Flow l/s 331.7 Pressure kPa 15.0 Generator Monitoring System Red Winding Temperature °C 39.8 110 120 Blue Winding Temperature °C 40.1 110 120 White Winding Temperature °C 45.4 110 120 6-66 Description Unit Actual Alarm Trip DE Bearing Temperature °C 44.5 70 80 NDE Bearing Temperature °C 44.3 70 80 Power kW 4465.2 Lubrication Checks Generator: D.E Bearing Flow Healthy Generator: N.D.E Bearing Flow Healthy Turbine: D.E Bearing Flow Healthy Turbine: N.D.E Bearing Flow Healthy Oil Tank: Oil Level Flow Healthy Figure 6-4: Turbine monitoring screen 6-67 F ig u re 6 -5 : T u rb in e t e s t d a ta d a te d 2 7 J a n u a ry 2 0 1 4 6-68 6.3 DATA EVALUATION The test data were evaluated using EES and the following equations:  Theoretical power ( in Watts where the water density ( ) in kg/m 3 , gravitational acceleration ( ) in m/s2, flow rate ( ) in m3/s and the distance between the upper and lower reservoir ( ) in m:  Actual output power ( in Watts where the turbine speed ( ) in rpm and torque ( ) in Nm:  Hydraulic efficiency ( : . The actual power (black) and theoretical power (blue) generated are plotted over 16.7 minutes (1000 seconds), as shown in Figure 6-6. The average hydraulic efficiency is 1.17. The actual power and theoretical power are also evaluated against the flow rate measured and plotted in Figure 6-7. The discharge rate to net head ratio is also calculated and the results overlain on the power vs. flow rate graph. Figure 6-6: Data evaluation – actual and theoretical power versus time 6-69 Figure 6-7: Data evaluation – actual power (black), theoretical power (blue) and discharge rate to net head ratio (red) versus flow rate 6.4 UPHES MODEL VALIDATION The system parameters of the Driefontein No. 5 Shaft were inserted into the UPHES model and the output parameters were generated. Table 6-3 and Table 6-4 show the input and output parameters: Table 6-3: Model input parameters Description Unit Value Comments Water density [kg/m 3 ] 998 Assumed approximately constant (ρ(293 K)) Gravitational acceleration [m/s 2 ] 9.81 Assumed approximately constant Number of turbines [-] 1 Turbine flow rate [l/s] 334.7 Discharge rate/net head [-] 0.20 Ratio exceeds 0.19 Turbine efficiency [%] 85.47 Shaft depth [m] 1680 Location of turbine (22 level) Table 6-4: Model output parameters Description Unit Value Comments Theoretical power generated [MW] 4.71 6-70 If the power calculated with the UPHES model is measured against the test data, the UPHES model power calculated is 1.05% lower than the power generated by the Driefontein No. 5 Shaft turbine. Therefore, considering the small difference in the values measured and calculated, the UPHES model is validated. Refer to Appendix IV for the EES validation model. Figure 6-8: Validation ______________________________ 334.7 4760 7-71 7 CONCLUSION AND RECOMMENDATIONS The concept UPHES system model was produced in Excel and populated with the Driefontein No. 9 Shaft system parameters as per the UPHES system configuration envisioned for the Driefontein No. 9 Shaft. The shaft dewatering arrangement will consist of a pump station on 24 level, -2 095 m BD, and another located in mid-shaft, -1 050 BD. Water collected in the lower reservoir, located on 24 level, is pumped to mid-shaft. From mid-shaft, water is pumped to IPC level, (-150 BD) into the upper reservoir. Various operational and system assumptions are made in the Excel model. The operational assumptions included operational system parameters, such as when pumps are operational and when turbines are operational. System assumptions include assumptions pertaining to the general system components and their associated capacities. A flow rate of 369.6 l/s was selected, which is based on the guidelines suggested by Whillier et al. (1977), with an acceptable safety margin. The existing chilled water column will therefore be used as a shaft pump column and a new suitable shaft turbine column must be installed Pipe pressure calculation checks were conducted for the shaft pipe columns required for the water transferred between the lower reservoir, mid-shaft reservoir and the upper reservoir. Results were generated for determining the system generation capacity during peak tariff periods only and the generation capacity during peak and standard tariff periods. The resulting output parameters were validated using an EES simulation model. In order to optimise the UPHES simulation model, it was established that the first priority must be to reduce the ROI because it is required that the asset investment is returned in the shortest time possible for the mine to benefit from the system‟s energy-saving potential. The option of generating power during periods in which peak and off-peak tariffs are charged requires a large capital investment, which can only be recovered after 12 to 13 years. This option was subsequently eliminated. In contrast, the option of generating power during periods when peak tariff are charged requires a capital investment that can be recovered within five to six years. This option was therefore selected for optimisation. In order to optimise the utilisation of existing infrastructure, and therefore lower capital costs, the costs dependent on the system output parameters were optimised along with the output parameters, i.e. number of pumps required per pump chamber and underground reservoir capacity. The cost of turbine supply, installation and commissioning and the additional shaft column to be installed for the turbine feed cannot be reduced, as this is a fixed system requirement. The greatest energy savings are achieved by maximising the number of hours of generating electricity during periods in which a peak tariff is charged and maximising the number of hours pumped only in 7-72 periods in which off-peak tariffs are charged. This strategy maximises the number of hours during the day in which the maximum differential cost between tariffs are charged. Strategically scheduled pump and generating schedules are required to achieve the optimal system energy saving. Unlike the Excel model, the EES simulation allows the pump and generating schedules to be varied on weekdays, Saturdays and Sundays. An optimisation matrix was used to evaluate the pumping and generating schedules and the effect thereof on the number of pumps required per pump chamber, lower reservoir capacity, CAPEX, electricity savings and ROI. The pump schedules were configured to allow sufficient dewatering of the lower reservoir to maintain a water balance in accordance with the lower reservoir storage capacity and an effort was made to reduce the number of pumps required per pump chamber by rescheduling weekday pumping requirements over Saturdays or Sundays. However, to maintain the system water balance, additional storage capacity in the lower reservoir is required to store the water that is not pumped to the upper reservoir on weekdays. The additional capacity infers additional excavation and construction costs for the lower reservoir, thus increasing the system capital cost. The cost differential between the LDS off-peak and peak tariff for the current 2016/2017 Megaflex tariff structure is 44% (off-peak tariff as a percentage of the peak tariff). The cost differential between the HDS off-peak and peak tariff for the current 2016/2017 Megaflex tariff structure is 16% (off-peak tariff as a percentage of the peak tariff). It was determined that if the percentage differential reaches 64% or higher, the system no longer displays any electricity cost savings. The percentage differential between the HDS standard and peak tariff for the current 2016/2017 Megaflex tariff structure is 188% (standard tariff as a percentage of the off-peak tariff). The break-even point in this case was calculated as 157%; therefore if the percentage differential reaches 157% or lower, the system no longer displays any electricity cost savings. The findings described above were applied to the EES simulation. This option was subsequently selected as the optimal and most suitable option for the Driefontein No. 9 Shaft UPHES system. 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Bischof-Niemz, T. & Fourie, R., 2016, „Cost of new generators in South Africa – Comparative analysis based on recent IPP announcements‟, viewed 22 October 2016, at http://www.ee.co.za/wp- content/uploads/2016/10/New_Power_Generators_RSA-CSIR-14Oct2016.pdf 7-77 Cronimet / THEnergy Study, 2015, Solar projects, energy efficiency and load shifting for an optimized energy management in the mining industry, viewed on 8 October 2016, at http://www.crm- ps.com/upload/files/2015SEPT_Study_EnergyEfficiency.pdf Deloitte, 2016, Tracking the trends 2016 – the top 10 issues mining companies will face in the coming year, viewed on 24 October 2016, at https://www2.deloitte.com/content/dam/Deloitte /global/Documents/Energy-and-Resources/gx-er-tracking-the-trends-2016.pdf Eberhard, A., Kolker, J. & Leigland, J., 2014, „South Africa‟s Renewable Energy IPP Procurement Program: Success Factors and Lessons‟, viewed 18 September 2016 at http://www.gsb.uct.ac.za/files/ppiafreport.pdf Energy Intelligence n.d., REIPPPP: All you need to know, viewed 30 September 2016, at http://www.energyintelligence.co.za/reippp-all-you-need-to-know/ Eskom Holdings SOC Ltd, 2014, Integrated Report 2014, viewed 18 September 2016, at http://integratedreport.eskom.co.za/pdf/fullintegrated.pdf Eskom Holdings SOC Ltd, 2015, Integrated Report, 2015, viewed 18 September 2016, at http://www.eskom.co.za/IR2015/Documents/EskomIR2015single.pdf Eskom Holdings SOC Ltd, 2016, Integrated Report, 2016, viewed 19 September 2016, at http://www.eskom.co.za/IR2016/Documents/Eskom_integrated_report_2016.pdf Faku, D., (2014), Mining industry needs to improve its profit margins – PWC, viewed 24 October 2016, at https://www.pressreader.com/south-africa/the-star-early edition/20141112/282046210388304 Hasan, A., Twala, B., Ouahada, K. & Marwala, T., 2014, „Energy usage optimization in South African mines‟, Archive of Mining Sciences, Vol. 59 (2014), p. 53-69 Ibrahim, H., Ilinca, A. & Perron, J., 2008, „Energy storage systems – characteristics and comparisons‟, Renewable and Sustainable Energy Reviews 12, pp. 1221-1250 Klumpp, F., 2016, „Comparison of pumped hydro, hydrogen storage and compressed air energy storage for integrating high shares of renewable energies – Potential, cost-comparison and ranking‟, Journal of Energy Storage, pp. 119-128 SAPP (Southern African Power Pool), 2016, „Annual Report 2016‟, viewed 23 September 2016, at http://www.sapp.co.zw/docs/SAPP%20ANNUAL%20REPORT%202016.pdf Slabbert, A., (2017), Eskom tariff shocker in store for 2018?, viewed 14 January 2017, at https://techcentral.co.za/eskom-tariff-shocker-in-store-for-2018/71108/ Sola Future Energy n.d., Real cost of solar energy is cheaper than new coal, viewed 23 September 2016, at http://www.solafuture.co.za/news/real-cost-of-solar-energy-is-cheaper-than-new-coal 7-78 Yang, C. & Jackson, R.B., 2011, „Opportunities and barriers to pumped-hydro energy storage in the United States‟, Renewable and Sustainable Energy Reviews 15, pp. 839-944 Zakeri, B. & Syri, S., 2015, „Electrical energy storage systems: A comparative life cycle cost analysis‟, Renewable and Sustainable Energy Reviews 42, pp. 569-596 7-79 APPENDICES I. Master UPHES system model and pipe pressure calculations II. EES Verification Model III. EES Optimised Model IV. EES Validation Model MASTER UPHES CALCULATION REV 0 01 SEPTEMBER 2017 Unit Value Comments Water density [kg/m3] 998 Gravitational acceleration [m/s2] 9.81 No. of turbines [-] 1 Turbine flow rate [l/s] 369.55 Discharge rate / net head [-] 0.19 Max. ratio = 0.19 Feed to turbine (flow rate) [l/s] 369.6 Chilled water pipe diameter (NB 350, SCH 160) @ 2095 m BD [mm] 284.18 Turbine efficiency [%] 91 Pumping rate (single pump) [l/s] 55.56 Pump efficiency [%] 89 IPC top (- 150 BD) [m] 150 Mid shaft (- 1 050 BD) [m] 1050 24 lvl (- 2 095 m BD) [m] 2095 Location of turbines No. of hours operated (peak) [hrs] 5 Effective head [m] 1945 Theoretical power generated [MW] 6.40 Theoretical electrical power generated [MWh] 32.02 Volume of water in the lower reservoir [Ml] 6.65 No. of multistage clear water pumps required [-] 4.15744 No. of multistage clear water pumps required in mid shaft [-] 5 No. of multistage clear water pumps required on IPC [-] 5 Total water pumped in 0.5hrs [Ml] 0.5 Total water pumped to upper reservoir [Ml] 8 Check Total pumping rate [l/s] 277.8 Power required to pump water to mid shaft per pump [MW] 3.391 Power required to pump water to IPC per pump [MW] 2.901 Total power required [MW] 6.29133 Total electrical power required [MWh] 50.3306 Hours required to fill up upper reservoir [hrs] 8 Check Max. off peak hours available [hrs] 8 No. of dewatering columns required [-] 2 OUTPUT PARAMETERS UPHES INPUT PARAMETERS INPUT PAGE 1 MASTER UPHES CALCULATION REV 0 01 SEPTEMBER 2017 Pilot PEAK TARIFF CHARGED (LDS) 1000000000 1000000000 1000000000 STANDARD TARIFF CHARGED (LDS) 1000000000 1000000000 1000000000 1000000000 1000000000 OFF-PEAK TARIFF CHARGED (LDS) 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 2000000000 2000000000 1000000000 1000000000 1000000000 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 2 2 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 Electricity from Eskom (without UPHES) 0:30 1:00 1:30 2:00 2:30 3:00 3:30 4:00 4:30 5:00 5:30 6:00 6:30 7:00 7:30 8:00 8:30 Weekday 13059.38 13059.38 14204.46 14204.46 15449 15449 15409.3 15409.3 15008 15008 14907.6 14907.6 14338.8 14338.8 12834 12834 11820 Saturday 13059.38 13059.38 14204.46 14204.46 15449 15449 15409.3 15409.3 15008 15008 14907.6 14907.6 14338.8 14338.8 12834 12834 11820 Sunday 13059.38 13059.38 14204.46 14204.46 15449 15449 15409.3 15409.3 15008 15008 14907.6 14907.6 14338.8 14338.8 12834 12834 11820 Power cost (without UPHES) [ZAR] 5196.327302 5196.327302 8909.037312 8909.037312 14077.1288 14077.1288 14040.95416 14040.95416 13675.2896 13675.2896 13583.80512 13583.80512 13065.51456 13065.51456 11694.3408 11694.3408 10770.384 WEEKDAY Power generated (peak - LDS) [kW] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6403.740923 6403.740923 6403.740923 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 Electrical power generated (peak - LDS) [kWh] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6403.740923 6403.740923 6403.740923 Pumps running [No] 5 5 5 5 5 5 5 5 5 5 5 5 Water pumped in period [Ml] 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0 0 0 0 0 Total volume of water pumped to upper reservoir [Ml] 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7 7 Electrical power required to pump water to upper reservoir [kW] 6291.33 6291.33 6291.33 6291.33 6291.33 6291.33 6291.33 6291.33 6291.33 6291.33 6291.33 6291.33 0.00 0.00 0.00 0.00 0.00 Percentage of POD load reduced [%] 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 100% 100% 108% Percentage of POD load reduced [%] 48% 48% 44% 44% 41% 41% 41% 41% 42% 42% 42% 42% 0% 0% 0% 0% 0% Electricty from Eskom (with UPHES) - LDS [kWh] 19350.71 19350.71 20495.79 20495.79 21740.33 21740.33 21700.63 21700.63 21299.33 21299.33 21198.93 21198.93 14338.80 14338.80 6430.26 6430.26 5416.26 Power cost UPHES @ peak [ZAR] 7699.65 7699.65 12854.96 12854.96 19809.79 19809.79 19773.61 19773.61 19407.95 19407.95 19316.46 19316.46 13065.51 13065.51 5859.25 5859.25 4935.30 WD (LDS) Sat (LDS) Sun (LDS) WD (LDS)* Sat (LDS)* Sun (LDS)* Weekday (LDS) Saturday (LDS) Sunday (LDS) Weekday (LDS)* Saturday (LDS)* Sunday (LDS)* 13,059 13,059 13,059 19,350.710 19,350.710 19,351 R 5,196.3273 R 5,196.3273 R 5,196.3273 R 7,699.6475 R 7,699.6475 R 7,699.6475 14,204 14,204 14,204 20,495.790 20,495.790 20,496 R 5,651.9546 R 5,651.9546 R 5,651.9546 R 8,155.2748 R 8,155.2748 R 8,155.2748 15,449 15,449 15,449 21,740.330 21,740.330 21,740 R 6,147.1571 R 6,147.1571 R 6,147.1571 R 8,650.4773 R 8,650.4773 R 8,650.4773 15,409 15,409 15,409 21,700.630 21,700.630 21,701 R 6,131.3605 R 6,131.3605 R 6,131.3605 R 8,634.6806 R 8,634.6806 R 8,634.6806 15,008 15,008 15,008 21,299.330 21,299.330 21,299 R 5,971.6832 R 5,971.6832 R 5,971.6832 R 8,475.0034 R 8,475.0034 R 8,475.0034 14,908 14,908 14,908 21,198.930 21,198.930 21,199 R 5,931.7340 R 5,931.7340 R 5,931.7340 R 8,435.0542 R 8,435.0542 R 8,435.0542 14,339 14,339 14,339 14,338.800 14,338.800 14,339 R 8,993.2954 R 5,705.4085 R 5,705.4085 R 8,993.2954 R 5,705.4085 R 5,705.4085 12,834 12,834 12,834 6,430.259 6,430.259 6,430 R 11,694.3408 R 8,049.4848 R 5,106.6486 R 5,859.2521 R 4,033.0585 R 2,558.6001 11,820 11,820 11,820 5,416.259 5,416.259 5,416 R 10,770.3840 R 7,413.5040 R 4,703.1780 R 4,935.2953 R 3,397.0777 R 2,155.1295 11,018 11,018 11,018 4,614.259 4,614.259 4,614 R 10,039.6016 R 6,910.4896 R 4,384.0622 R 4,204.5129 R 2,894.0633 R 1,836.0137 10,935 10,935 10,935 10,935.000 10,935.000 10,935 R 6,858.4320 R 6,858.4320 R 4,351.0365 R 6,858.4320 R 6,858.4320 R 4,351.0365 11,229 11,229 11,229 11,229.000 11,229.000 11,229 R 7,042.8288 R 7,042.8288 R 4,468.0191 R 7,042.8288 R 7,042.8288 R 4,468.0191 11,717 11,717 11,717 11,717.000 11,717.000 11,717 R 7,348.9024 R 4,662.1943 R 4,662.1943 R 7,348.9024 R 4,662.1943 R 4,662.1943 12,771 12,771 12,771 12,771.000 12,771.000 12,771 R 8,009.9712 R 5,081.5809 R 5,081.5809 R 8,009.9712 R 5,081.5809 R 5,081.5809 13,055 13,055 13,055 13,055.000 13,055.000 13,055 R 8,188.0960 R 5,194.5845 R 5,194.5845 R 8,188.0960 R 5,194.5845 R 5,194.5845 12,798 12,798 12,798 12,798.000 12,798.000 12,798 R 8,026.9056 R 5,092.3242 R 5,092.3242 R 8,026.9056 R 5,092.3242 R 5,092.3242 12,536 12,536 12,536 12,536.000 12,536.000 12,536 R 7,862.5792 R 4,988.0744 R 4,988.0744 R 7,862.5792 R 4,988.0744 R 4,988.0744 12,377 12,377 12,377 12,377.060 12,377.060 12,377 R 7,762.8920 R 4,924.8322 R 4,924.8322 R 7,762.8920 R 4,924.8322 R 4,924.8322 12,128 12,128 12,128 5,724.259 5,724.259 5,724 R 11,051.0336 R 7,606.6816 R 4,825.7312 R 5,215.9449 R 3,590.2553 R 2,277.6827 12,015 12,015 12,015 5,611.259 5,611.259 5,611 R 10,948.0680 R 7,535.8080 R 4,780.7685 R 5,112.9793 R 3,519.3817 R 2,232.7200 12,152 12,152 12,152 12,152.000 12,152.000 12,152 R 7,621.7344 R 4,835.2808 R 4,835.2808 R 7,621.7344 R 4,835.2808 R 4,835.2808 12,573 12,573 12,573 12,573.000 12,573.000 12,573 R 7,885.7856 R 5,002.7967 R 5,002.7967 R 7,885.7856 R 5,002.7967 R 5,002.7967 12,732 12,732 12,732 19,023.330 19,023.330 19,023 R 5,066.0628 R 5,066.0628 R 5,066.0628 R 7,569.3830 R 7,569.3830 R 7,569.3830 12,673 12,673 12,673 18,964.330 18,964.330 18,964 R 5,042.5867 R 5,042.5867 R 5,042.5867 R 7,545.9069 R 7,545.9069 R 7,545.9069 57,611,566 14,248,022 12,699,324 61,017,585 15,090,370.580 13,450,113 RM 34.455 RM 6.534 RM 5.053 R 32.7536 R 6.5314 R 5.3518 Total 84,558,911 kW/LDS Total 89,558,069 kW/LDS RM 46.042 RM 44.637 0.000 c/kWh 0.000 c/kWh Savings R 1.41 8% Current Annual Energy Profile (LDS) Hydro Annual Energy Profile (LDS) Current Annual Cost (RM) HydroSystem Annual Cost (RM) 5000 10000 15000 20000 25000 30000 0 : 3 0 1 : 0 0 1 : 3 0 2 : 0 0 2 : 3 0 3 : 0 0 3 : 3 0 4 : 0 0 4 : 3 0 5 : 0 0 5 : 3 0 6 : 0 0 6 : 3 0 7 : 0 0 7 : 3 0 8 : 0 0 8 : 3 0 9 : 0 0 9 : 3 0 1 0 : 0 0 1 0 : 3 0 1 1 : 0 0 1 1 : 3 0 1 2 : 0 0 1 2 : 3 0 1 3 : 0 0 1 3 : 3 0 1 4 : 0 0 1 4 : 3 0 1 5 : 0 0 1 5 : 3 0 1 6 : 0 0 1 6 : 3 0 1 7 : 0 0 1 7 : 3 0 1 8 : 0 0 1 8 : 3 0 1 9 : 0 0 1 9 : 3 0 2 0 : 0 0 2 0 : 3 0 2 1 : 0 0 2 1 : 3 0 2 2 : 0 0 2 2 : 3 0 2 3 : 0 0 2 3 : 3 0 0 : 0 0 k W h SINGLE POD LOAD PROFILE ‐ LDS OFF‐PEAK TARIFF CHARGED (LDS) PEAK TARIFF CHARGED (LDS) STANDARD TARIFF CHARGED (LDS) Electricity from Eskom (without UPHES) Electricty from Eskom (with UPHES) ‐ LDS Calculation LDS PAGE 1 OF 3 MASTER UPHES CALCULATION REV 0 01 SEPTEMBER 2017 PEAK STAN OFF- Elect Wee Satu Sund Powe WEEK Powe Elect Pum Wate Tota Elect Perc Perc Elect Powe 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 9:00 9:30 10:00 10:30 11:00 11:30 12:00 12:30 13:00 13:30 14:00 14:30 15:00 15:30 16:00 16:30 17:00 17:30 18:00 11820 11018 11018 10935 10935 11229 11229 11717 11717 12771 12771 13055 13055 12798 12798 12536 12536 12377.06 12377.06 11820 11018 11018 10935 10935 11229 11229 11717 11717 12771 12771 13055 13055 12798 12798 12536 12536 12377.06 12377.06 11820 11018 11018 10935 10935 11229 11229 11717 11717 12771 12771 13055 13055 12798 12798 12536 12536 12377.06 12377.06 10770.384 10039.6016 10039.6016 9963.972 9963.972 10231.8648 10231.8648 10676.5304 10676.5304 11636.9352 11636.9352 11895.716 11895.716 11661.5376 11661.5376 11422.8032 11422.8032 11277.97707 11277.97707 6403.740923 6403.740923 6403.740923 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6403.740923 6403.740923 6403.740923 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 108% 116% 116% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 5416.26 4614.26 4614.26 10935.00 10935.00 11229.00 11229.00 11717.00 11717.00 12771.00 12771.00 13055.00 13055.00 12798.00 12798.00 12536.00 12536.00 12377.06 12377.06 4935.30 4204.51 4204.51 9963.97 9963.97 10231.86 10231.86 10676.53 10676.53 11636.94 11636.94 11895.72 11895.72 11661.54 11661.54 11422.80 11422.80 11277.98 11277.98 LOW DEMAND SEASON 5000 10000 15000 20000 25000 30000 0 : 3 0 1 : 0 0 1 : 3 0 2 : 0 0 2 : 3 0 3 : 0 0 3 : 3 0 4 : 0 0 4 : 3 0 5 : 0 0 5 : 3 0 6 : 0 0 6 : 3 0 7 : 0 0 7 : 3 0 8 : 0 0 8 : 3 0 9 : 0 0 9 : 3 0 1 0 : 0 0 1 0 : 3 0 1 1 : 0 0 1 1 : 3 0 1 2 : 0 0 1 2 : 3 0 1 3 : 0 0 1 3 : 3 0 1 4 : 0 0 1 4 : 3 0 1 5 : 0 0 1 5 : 3 0 1 6 : 0 0 1 6 : 3 0 1 7 : 0 0 1 7 : 3 0 1 8 : 0 0 1 8 : 3 0 1 9 : 0 0 1 9 : 3 0 2 0 : 0 0 2 0 : 3 0 2 1 : 0 0 2 1 : 3 0 2 2 : 0 0 2 2 : 3 0 2 3 : 0 0 2 3 : 3 0 0 : 0 0 k W h POD LOAD PROFILE ‐ POWER GENERATED DURING PEAK TARIFF PERIODS ONLY Electricity from Eskom (without UPHES) Electricty from Eskom (with UPHES) ‐ LDS Electricty from Eskom (with UPHES) ‐ HDS Calculation LDS PAGE 2 OF 3 MASTER UPHES CALCULATION REV 0 01 SEPTEMBER 2017 PEAK STAN OFF- Elect Wee Satu Sund Powe WEEK Powe Elect Pum Wate Tota Elect Perc Perc Elect Powe 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 2 2 2 2 1 1 1 1 0 0 0 0 18 18 19 19 20 20 21 21 22 22 23 23 18:30 19:00 19:30 20:00 20:30 21:00 21:30 22:00 22:30 23:00 23:30 0:00 12128 12128 12015 12015 12152 12152 12573 12573 12732 12732 12673 12673 12128 12128 12015 12015 12152 12152 12573 12573 12732 12732 12673 12673 12128 12128 12015 12015 12152 12152 12573 12573 12732 12732 12673 12673 11051.0336 11051.0336 10948.068 10948.068 11072.9024 11072.9024 11456.5176 11456.5176 11601.3984 11601.3984 11547.6376 11547.6376 542,994.55ZAR 6403.740923 6403.740923 6403.740923 6403.740923 0 0 0 0 0 0 0 0 32,019 1 1 1 1 0 0 0 0 0 0 0 0 6403.740923 6403.740923 6403.740923 6403.740923 0 0 0 0 0 0 0 0 5 5 5 5 0 0 0 0 0 0 0 0 0.5 0.5 0.5 0.5 0.5 1 1.5 2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 6291.33 6291.33 6291.33 6291.33 100,661 106% 106% 107% 107% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 49% 49% 50% 50% 5724.26 5724.26 5611.26 5611.26 12152.00 12152.00 12573.00 12573.00 19023.33 19023.33 18964.33 18964.33 5215.94 5215.94 5112.98 5112.98 11072.90 11072.90 11456.52 11456.52 17334.06 17334.06 17280.30 17280.30 566,334.07ZAR 104.29830% Calculation LDS PAGE 3 OF 3 MASTER UPHES CALCULATION REV 0 01 SEPTEMBER 2017 Pilot PEAK TARIFF CHARGED (HDS) 1000000000 1000000000 1000000000 1000000000 STANDARD TARIFF CHARGED (HDS) 1000000000 1000000000 1000000000 1000000000 OFF-PEAK TARIFF CHARGED (HDS) 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 Electricty from Eskom (without UPHES) 0:30 1:00 1:30 2:00 2:30 3:00 3:30 4:00 4:30 5:00 5:30 6:00 6:30 7:00 7:30 8:00 Weekday 13059.38 13059.38 14204.46 14204.46 15449 15449 15409.3 15409.3 15008 15008 14907.6 14907.6 14338.8 14338.8 12834 12834 Saturday 13059.38 13059.38 14204.46 14204.46 15449 15449 15409.3 15409.3 15008 15008 14907.6 14907.6 14338.8 14338.8 12834 12834 Sunday 13059.38 13059.38 14204.46 14204.46 15449 15449 15409.3 15409.3 15008 15008 14907.6 14907.6 14338.8 14338.8 12834 12834 Power cost (without UPHES) [ZAR] 5196.327302 5196.327302 8909.037312 8909.037312 14077.1288 14077.1288 14040.95416 14040.95416 13675.2896 13675.2896 13583.80512 13583.80512 13065.51456 13065.51456 11694.3408 11694.3408 WEEKDAY Power generated (peak - HDS) [kW] 0 0 0 0 0 0 0 0 0 0 0 0 6403.740923 6403.740923 6403.740923 6403.740923 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 Electrical power generated (peak - HDS) [kWh] 0 0 0 0 0 0 0 0 0 0 0 0 6403.740923 6403.740923 6403.740923 6403.740923 Pumps running [No] 5 5 5 5 5 5 5 5 5 5 5 5 Water pumped in period [Ml] 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0 0 0 0 Total volume of water pumped to upper reservoir [Ml] 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7 7 Electrical power required to pump water to upper reservo[kWh] 6291.33 6291.33 6291.33 6291.33 6291.33 6291.33 6291.33 6291.33 6291.33 6291.33 6291.33 6291.33 0.00 0.00 0.00 0.00 Percentage of POD load reduced [%] 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 89% 89% 100% 100% Percentage of POD load reduced [%] 48% 48% 44% 44% 41% 41% 41% 41% 42% 42% 42% 42% 0% 0% 0% 0% Electricty from Eskom (with UPHES) - HDS [kWh] 19350.71 19350.71 20495.79 20495.79 21740.33 21740.33 21700.63 21700.63 21299.33 21299.33 21198.93 21198.93 7935.06 7935.06 6430.26 6430.26 Power cost UPHES @ peak [ZAR] 7699.65 7699.65 12854.96 12854.96 19809.79 19809.79 19773.61 19773.61 19407.95 19407.95 19316.46 19316.46 7230.43 7230.43 5859.25 5859.25 WD (HDS) Sat (HDS) Sun (HDS) WD (HDS)* Sat (HDS)* Sun (HDS)* Weekday (HDS) Saturday (HDS) Sunday (HDS) Weekday (HDS)* Saturday (HDS)* Sunday (HDS)* 13,059 13,059 13,059 19,351 19,351 19,351 R 6,000.7851 R 6,000.7851 R 6,000.7851 R 8,891.6512 R 8,891.6512 R 8,891.6512 14,204 14,204 14,204 20,496 20,496 20,496 R 6,526.9494 R 6,526.9494 R 6,526.9494 R 9,417.8154 R 9,417.8154 R 9,417.8154 15,449 15,449 15,449 21,740 21,740 21,740 R 7,098.8155 R 7,098.8155 R 7,098.8155 R 9,989.6816 R 9,989.6816 R 9,989.6816 15,409 15,409 15,409 21,701 21,701 21,701 R 7,080.5734 R 7,080.5734 R 7,080.5734 R 9,971.4394 R 9,971.4394 R 9,971.4394 15,008 15,008 15,008 21,299 21,299 21,299 R 6,896.1760 R 6,896.1760 R 6,896.1760 R 9,787.0421 R 9,787.0421 R 9,787.0421 14,908 14,908 14,908 21,199 21,199 21,199 R 6,850.0422 R 6,850.0422 R 6,850.0422 R 9,740.9083 R 9,740.9083 R 9,740.9083 14,339 14,339 14,339 7,935 7,935 7,935 R 40,052.5700 R 6,588.6786 R 6,588.6786 R 22,165.0005 R 3,646.1596 R 3,646.1596 12,834 12,834 12,834 6,430 6,430 6,430 R 35,849.2122 R 10,860.1308 R 5,897.2230 R 17,961.6427 R 5,441.2852 R 2,954.7040 11,820 11,820 11,820 5,416 5,416 5,416 R 33,016.8060 R 10,002.0840 R 5,431.2900 R 15,129.2365 R 4,583.2384 R 2,488.7710 11,018 11,018 11,018 11,018 11,018 11,018 R 9,323.4316 R 9,323.4316 R 5,062.7710 R 9,323.4316 R 9,323.4316 R 5,062.7710 10,935 10,935 10,935 10,935 10,935 10,935 R 9,253.1970 R 9,253.1970 R 5,024.6325 R 9,253.1970 R 9,253.1970 R 5,024.6325 11,229 11,229 11,229 11,229 11,229 11,229 R 9,501.9798 R 9,501.9798 R 5,159.7255 R 9,501.9798 R 9,501.9798 R 5,159.7255 11,717 11,717 11,717 11,717 11,717 11,717 R 9,914.9254 R 5,383.9615 R 5,383.9615 R 9,914.9254 R 5,383.9615 R 5,383.9615 12,771 12,771 12,771 12,771 12,771 12,771 R 10,806.8202 R 5,868.2745 R 5,868.2745 R 10,806.8202 R 5,868.2745 R 5,868.2745 13,055 13,055 13,055 13,055 13,055 13,055 R 11,047.1410 R 5,998.7725 R 5,998.7725 R 11,047.1410 R 5,998.7725 R 5,998.7725 12,798 12,798 12,798 12,798 12,798 12,798 R 10,829.6676 R 5,880.6810 R 5,880.6810 R 10,829.6676 R 5,880.6810 R 5,880.6810 12,536 12,536 12,536 12,536 12,536 12,536 R 10,607.9632 R 5,760.2920 R 5,760.2920 R 10,607.9632 R 5,760.2920 R 5,760.2920 12,377 12,377 12,377 5,973 5,973 5,973 R 34,572.8417 R 5,687.2591 R 5,687.2591 R 16,685.2722 R 2,744.7401 R 2,744.7401 12,128 12,128 12,128 5,724 5,724 5,724 R 33,877.1424 R 10,262.7136 R 5,572.8160 R 15,989.5729 R 4,843.8680 R 2,630.2970 12,015 12,015 12,015 12,015 12,015 12,015 R 10,167.0930 R 10,167.0930 R 5,520.8925 R 10,167.0930 R 10,167.0930 R 5,520.8925 12,152 12,152 12,152 12,152 12,152 12,152 R 10,283.0224 R 5,583.8440 R 5,583.8440 R 10,283.0224 R 5,583.8440 R 5,583.8440 12,573 12,573 12,573 12,573 12,573 12,573 R 10,639.2726 R 5,777.2935 R 5,777.2935 R 10,639.2726 R 5,777.2935 R 5,777.2935 12,732 12,732 12,732 19,023 19,023 19,023 R 5,850.3540 R 5,850.3540 R 5,850.3540 R 8,741.2201 R 8,741.2201 R 8,741.2201 12,673 12,673 12,673 18,964 18,964 18,964 R 5,823.2435 R 5,823.2435 R 5,823.2435 R 8,714.1096 R 8,714.1096 R 8,714.1096 19,823,334 4,336,354 4,336,354 20,995,298 4,592,721 4,592,721 RM 21.880 RM 2.436 RM 1.993 R 17.6358 R 2.4502 R 2.1104 Total 28,496,043 kW/LDS Total 30,180,741 kW/LDS RM 26.309 RM 22.196 0.000 c/kWh 0.000 c/kWh Savings R 4.11 20% Current Annual Energy Profile (LDS) Hydro Annual Energy Profile (LDS) Current Annual Cost (RM) HydroSystem Annual Cost (RM) 5000 10000 15000 20000 25000 30000 0 : 3 0 1 : 0 0 1 : 3 0 2 : 0 0 2 : 3 0 3 : 0 0 3 : 3 0 4 : 0 0 4 : 3 0 5 : 0 0 5 : 3 0 6 : 0 0 6 : 3 0 7 : 0 0 7 : 3 0 8 : 0 0 8 : 3 0 9 : 0 0 9 : 3 0 1 0 : 0 0 1 0 : 3 0 1 1 : 0 0 1 1 : 3 0 1 2 : 0 0 1 2 : 3 0 1 3 : 0 0 1 3 : 3 0 1 4 : 0 0 1 4 : 3 0 1 5 : 0 0 1 5 : 3 0 1 6 : 0 0 1 6 : 3 0 1 7 : 0 0 1 7 : 3 0 1 8 : 0 0 1 8 : 3 0 1 9 : 0 0 1 9 : 3 0 2 0 : 0 0 2 0 : 3 0 2 1 : 0 0 2 1 : 3 0 k W h SINGLE POD LOAD PROFILE ‐ HDS OFF‐PEAK TARIFF CHARGED (HDS) PEAK TARIFF CHARGED (HDS) STANDARD TARIFF CHARGED (HDS) Electricty from Eskom (without UPHES) Electricty from Eskom UPHES system calc REV K peak generation repaired PAGE 1 OF 3 MASTER UPHES CALCULATION REV 0 01 SEPTEMBER 2017 PEA STAN OFF- Elec Wee Satu Sund Pow WEE Pow Elec Pum Wat Tota Elec Perc Perc Elec Pow 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 8:30 9:00 9:30 10:00 10:30 11:00 11:30 12:00 12:30 13:00 13:30 14:00 14:30 15:00 15:30 16:00 16:30 17:00 17:30 11820 11820 11018 11018 10935 10935 11229 11229 11717 11717 12771 12771 13055 13055 12798 12798 12536 12536 12377.06 11820 11820 11018 11018 10935 10935 11229 11229 11717 11717 12771 12771 13055 13055 12798 12798 12536 12536 12377.06 11820 11820 11018 11018 10935 10935 11229 11229 11717 11717 12771 12771 13055 13055 12798 12798 12536 12536 12377.06 10770.384 10770.384 10039.6016 10039.6016 9963.972 9963.972 10231.8648 10231.8648 10676.5304 10676.5304 11636.9352 11636.9352 11895.716 11895.716 11661.5376 11661.5376 11422.8032 11422.8032 11277.97707 6403.740923 6403.740923 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6403.740923 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 6403.740923 6403.740923 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6403.740923 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 108% 108% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 103% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 5416.26 5416.26 11018.00 11018.00 10935.00 10935.00 11229.00 11229.00 11717.00 11717.00 12771.00 12771.00 13055.00 13055.00 12798.00 12798.00 12536.00 12536.00 5973.32 4935.30 4935.30 10039.60 10039.60 9963.97 9963.97 10231.86 10231.86 10676.53 10676.53 11636.94 11636.94 11895.72 11895.72 11661.54 11661.54 11422.80 11422.80 5442.89 HIGH DEMAND SEASON 2 2 : 0 0 2 2 : 3 0 2 3 : 0 0 2 3 : 3 0 0 : 0 0  (with UPHES) ‐ HDS 5000 10000 15000 20000 25000 30000 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 k W h Electricty from Esko UPHES system calc REV K peak generation repaired PAGE 2 OF 3 MASTER UPHES CALCULATION REV 0 01 SEPTEMBER 2017 PEA STAN OFF- Elec Wee Satu Sund Pow WEE Pow Elec Pum Wat Tota Elec Perc Perc Elec Pow 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 2 2 2 1 1 1 1 1 1 0 0 0 0 17 18 18 19 19 20 20 21 21 22 22 23 23 18:00 18:30 19:00 19:30 20:00 20:30 21:00 21:30 22:00 22:30 23:00 23:30 0:00 12377.06 12128 12128 12015 12015 12152 12152 12573 12573 12732 12732 12673 12673 12377.06 12128 12128 12015 12015 12152 12152 12573 12573 12732 12732 12673 12673 12377.06 12128 12128 12015 12015 12152 12152 12573 12573 12732 12732 12673 12673 11277.97707 11051.0336 11051.0336 10948.068 10948.068 11072.9024 11072.9024 11456.5176 11456.5176 11601.3984 11601.3984 11547.6376 11547.6376 6403.740923 6403.740923 6403.740923 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 6403.740923 6403.740923 6403.740923 0 0 0 0 0 0 0 0 0 0 5 5 5 5 0 0 0 0 0 0 0 0 0 0.5 0.5 0.5 0.5 0.5 1 1.5 2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 6291.33 6291.33 6291.33 6291.33 103% 106% 106% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 49% 49% 50% 50% 5973.32 5724.26 5724.26 12015.00 12015.00 12152.00 12152.00 12573.00 12573.00 19023.33 19023.33 18964.33 18964.33 5442.89 5215.94 5215.94 10948.07 10948.07 11072.90 11072.90 11456.52 11456.52 17334.06 17334.06 17280.30 17280.30 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 SINGLE POD LOAD PROFILE ‐ HDS om (without UPHES) Electricty from Eskom (with UPHES) ‐ HDS UPHES system calc REV K peak generation repaired PAGE 3 OF 3 MASTER UPHES CALCULATION REV 0 01 SEPTEMBER 2017 UNIT LDS HDS TOTAL TOTAL POWER REQ. [kW] 84,558,911 28,496,043 113,054,954 TOTAL POWER COST ZAR [RM] 46,042,378 26,308,609 72,350,987 TOTAL POWER REQ. [kW] 89,558,069 30,180,741 119,738,810 TOTAL POWER COST ZAR [RM] 44,636,869 22,196,306 66,833,175 ADDITIONAL POWER REQUIRED [kW] 4,999,158 1,684,698 6,683,856 SAVINGS ZAR [RM] 1,405,509 4,112,303 5,517,812 5.91% 7.63% UPHES SYSTEM POD PROFILE - COST PER YEAR ORIGINAL POD PROFILE - COST PER YEAR EXTRA POWER REQUIRED (% OF INITIAL POWER REQUIREMENT) TOTAL SYSYTEM POWER COST TRIM (% OF INITIAL POWER REQUIREMENT) 0 5,000 10,000 15,000 20,000 25,000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 kW h 24 hour cycle DAILY ENERGY PROFILE NORMAL WEEKDAY VS. LDS & HDS WITH UPHES* WD (LDS) WD (LDS)* WD (HDS) WD (HDS)* R 0.0000 R 5,000.0000 R 10,000.0000 R 15,000.0000 R 20,000.0000 R 25,000.0000 R 30,000.0000 R 35,000.0000 R 40,000.0000 R 45,000.0000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 ZA R  24 hour cycle DAILY ENERGY COST PROFILE NORMAL WEEKDAY VS. LDS & HDS WITH UPHES* Weekday (LDS) Weekday (LDS)* Weekday (HDS) Weekday (HDS)* OUTPUT PAGE 1 OF 1 MASTER UPHES CALCULATION REV 0 01 SEPTEMBER 2017 TOTAL SYSTEM COST 44,289,974.97ZAR SAVINGS (SYSTEM INSTALLED CAPACITY 32 MWh) MEGAFLEX TARIFF INCREASE ROI VALUE (SYSTEM INSTALLED CAPACITY 32 MWh) YEAR 1 5,517,812.48ZAR 8% 38,772,162.49ZAR 1 YEAR 2 5,959,237.48ZAR 8% 32,812,925.01ZAR 1 YEAR 3 6,435,976.48ZAR 8% 26,376,948.53ZAR 1 YEAR 4 6,950,854.60ZAR 8% 19,426,093.94ZAR 1 YEAR 5 7,506,922.96ZAR 8% 11,919,170.98ZAR 1 YEAR 6 8,107,476.80ZAR 8% 3,811,694.18ZAR 1 YEAR 7 8,756,074.94ZAR 8% (4,944,380.77)ZAR 0.44 Months 5.44 Years ROI CALCULATION  ZAR (10,000,000.00)  ZAR (5,000,000.00)  ZAR ‐  ZAR 5,000,000.00  ZAR 10,000,000.00  ZAR 15,000,000.00  ZAR 20,000,000.00  ZAR 25,000,000.00  ZAR 30,000,000.00  ZAR 35,000,000.00  ZAR 40,000,000.00  ZAR 45,000,000.00 0 1 2 3 4 5 6 7 8 SA VI N GS  /  S YS TE M  R O I [ ZA R[ YEARS ROI ROI VALUE (SYSTEM INSTALLED CAPACITY 32 MWh) SAVINGS (SYSTEM INSTALLED CAPACITY 32 MWh) ROI PAGE 1 OF 1 MASTER UPHES CALCULATION REV 0 01 SEPTEMBER 2017 Unit Value Comments Water density [kg/m3] 998 Gravitational acceleration [m/s2] 9.81 No. of turbines [-] 1 Turbine flow rate [l/s] 369.55 Discharge rate / net head [-] 0.19 Max. ratio = 0.19 Feed to turbine (flow rate) [l/s] 369.6 Chilled water pipe diameter (NB 350, SCH 160) @ 2095 m BD [mm] 284.18 Turbine efficiency [%] 91 Pumping rate (single pump) [l/s] 55.56 Pump efficiency [%] 89 IPC top (- 150 BD) [m] 150 Mid shaft (- 1 050 BD) [m] 1050 24 lvl (- 2 095 m BD) [m] 2095 Location of turbines No. of hours operated (peak) [hrs] 16 Effective head [m] 1945 Theoretical power generated [MW] 6.40 Theoretical electrical power generated [MWh] 102.46 Volume of water in the lower reservoir [Ml] 21.29 No. of multistage clear water pumps required [-] 13.3038 No. of multistage clear water pumps required in mid shaft [-] 14 No. of multistage clear water pumps required on IPC [-] 14 Total water pumped in 0.5hrs [Ml] 1.4 Total water pumped to upper reservoir [Ml] 22.4 Check Total pumping rate [l/s] 777.8 Power required to pump water to mid shaft per pump [MW] 9.494 Power required to pump water to IPC per pump [MW] 8.122 Total power required [MW] 17.6157 Total electrical power required [MWh] 140.926 Hours required to fill up upper reservoir [hrs] 8 Check Max. off peak hours available [hrs] 8 No. of dewatering columns required [-] 2 OUTPUT PARAMETERS UPHES INPUT PARAMETERS INPUT PAGE 1 OF 1 MASTER UPHES CALCULATION REV 0 01 SEPTEMBER 2017 Pilot PEAK TARIFF CHARGED (LDS) 1000000000 1000000000 1000000000 1000000000 1000000000 STANDARD TARIFF CHARGED (LDS) 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 OFF-PEAK TARIFF CHARGED (LDS) 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 2000000000 2000000000 1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 2 2 2 2 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 Electricity from Eskom (without UPHES) 0:30 1:00 1:30 2:00 2:30 3:00 3:30 4:00 4:30 5:00 5:30 6:00 6:30 7:00 7:30 8:00 8:30 9:00 9:30 Weekday 13059.38 13059.38 14204.46 14204.46 15449 15449 15409.3 15409.3 15008 15008 14907.6 14907.6 14338.8 14338.8 12834 12834 11820 11820 11018 Saturday 13059.38 13059.38 14204.46 14204.46 15449 15449 15409.3 15409.3 15008 15008 14907.6 14907.6 14338.8 14338.8 12834 12834 11820 11820 11018 Sunday 13059.38 13059.38 14204.46 14204.46 15449 15449 15409.3 15409.3 15008 15008 14907.6 14907.6 14338.8 14338.8 12834 12834 11820 11820 11018 Power cost (without UPHES) [ZAR] 5196.327302 5196.327302 8909.037312 8909.037312 14077.1288 14077.1288 14040.95416 14040.95416 13675.2896 13675.2896 13583.80512 13583.80512 13065.51456 13065.51456 11694.3408 11694.3408 10770.384 10770.384 10039.6016 WEEKDAY Power generated (peak - LDS) [kW] 0 0 0 0 0 0 0 0 0 0 0 0 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 Electrical power generated (peak - LDS) [kWh] 0 0 0 0 0 0 0 0 0 0 0 0 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 Pumps running [No] 14 14 14 14 14 14 14 14 14 14 14 14 Water pumped in period [Ml] 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 0 0 0 0 0 0 0 Total volume of water pumped to upper reservoir [Ml] 7 8.4 9.8 11.2 12.6 14 15.4 16.8 18.2 19.6 21 22.4 Electrical power required to pump water to upper reservoir [kW] 17615.72 17615.72 17615.72 17615.72 17615.72 17615.72 17615.72 17615.72 17615.72 17615.72 17615.72 17615.72 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Percentage of POD load reduced [%] 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 89% 89% 100% 100% 108% 108% 116% Percentage of POD load reduced [%] 135% 135% 124% 124% 114% 114% 114% 114% 117% 117% 118% 118% 0% 0% 0% 0% 0% 0% 0% Electricty from Eskom (with UPHES) - LDS [kWh] 30675.10 30675.10 31820.18 31820.18 33064.72 33064.72 33025.02 33025.02 32623.72 32623.72 32523.32 32523.32 7935.06 7935.06 6430.26 6430.26 5416.26 5416.26 4614.26 Power cost UPHES @ peak [ZAR] 12205.62 12205.62 19957.62 19957.62 30128.58 30128.58 30092.40 30092.40 29726.74 29726.74 29635.25 29635.25 7230.43 7230.43 5859.25 5859.25 4935.30 4935.30 4204.51 WD (LDS) Sat (LDS) Sun (LDS) WD (LDS)* Sat (LDS)* Sun (LDS)* Weekday (LDS) Saturday (LDS) Sunday (LDS) Weekday (LDS)* Saturday (LDS)* Sunday (LDS)* 13,059 13,059 13,059 30,675.104 30,675.104 30,675 R 5,196.3273 R 5,196.3273 R 5,196.3273 R 12,205.6237 R 12,205.6237 R 12,205.6237 14,204 14,204 14,204 31,820.184 31,820.184 31,820 R 5,651.9546 R 5,651.9546 R 5,651.9546 R 12,661.2511 R 12,661.2511 R 12,661.2511 15,449 15,449 15,449 33,064.724 33,064.724 33,065 R 6,147.1571 R 6,147.1571 R 6,147.1571 R 13,156.4535 R 13,156.4535 R 13,156.4535 15,409 15,409 15,409 33,025.024 33,025.024 33,025 R 6,131.3605 R 6,131.3605 R 6,131.3605 R 13,140.6569 R 13,140.6569 R 13,140.6569 15,008 15,008 15,008 32,623.724 32,623.724 32,624 R 5,971.6832 R 5,971.6832 R 5,971.6832 R 12,980.9796 R 12,980.9796 R 12,980.9796 14,908 14,908 14,908 32,523.324 32,523.324 32,523 R 5,931.7340 R 5,931.7340 R 5,931.7340 R 12,941.0305 R 12,941.0305 R 12,941.0305 14,339 14,339 14,339 7,935.059 7,935.059 7,935 R 8,993.2954 R 5,705.4085 R 5,705.4085 R 4,976.8691 R 3,157.3600 R 3,157.3600 12,834 12,834 12,834 6,430.259 6,430.259 6,430 R 11,694.3408 R 8,049.4848 R 5,106.6486 R 5,859.2521 R 4,033.0585 R 2,558.6001 11,820 11,820 11,820 5,416.259 5,416.259 5,416 R 10,770.3840 R 7,413.5040 R 4,703.1780 R 4,935.2953 R 3,397.0777 R 2,155.1295 11,018 11,018 11,018 4,614.259 4,614.259 4,614 R 10,039.6016 R 6,910.4896 R 4,384.0622 R 4,204.5129 R 2,894.0633 R 1,836.0137 10,935 10,935 10,935 4,531.259 4,531.259 4,531 R 6,858.4320 R 6,858.4320 R 4,351.0365 R 2,842.0057 R 2,842.0057 R 1,802.9880 11,229 11,229 11,229 4,825.259 4,825.259 4,825 R 7,042.8288 R 7,042.8288 R 4,468.0191 R 3,026.4025 R 3,026.4025 R 1,919.9706 11,717 11,717 11,717 5,313.259 5,313.259 5,313 R 7,348.9024 R 4,662.1943 R 4,662.1943 R 3,332.4761 R 2,114.1458 R 2,114.1458 12,771 12,771 12,771 6,367.259 6,367.259 6,367 R 8,009.9712 R 5,081.5809 R 5,081.5809 R 3,993.5449 R 2,533.5324 R 2,533.5324 13,055 13,055 13,055 6,651.259 6,651.259 6,651 R 8,188.0960 R 5,194.5845 R 5,194.5845 R 4,171.6697 R 2,646.5360 R 2,646.5360 12,798 12,798 12,798 6,394.259 6,394.259 6,394 R 8,026.9056 R 5,092.3242 R 5,092.3242 R 4,010.4793 R 2,544.2757 R 2,544.2757 12,536 12,536 12,536 6,132.259 6,132.259 6,132 R 7,862.5792 R 4,988.0744 R 4,988.0744 R 3,846.1529 R 2,440.0259 R 2,440.0259 12,377 12,377 12,377 5,973.319 5,973.319 5,973 R 7,762.8920 R 4,924.8322 R 4,924.8322 R 3,746.4657 R 2,376.7837 R 2,376.7837 12,128 12,128 12,128 5,724.259 5,724.259 5,724 R 11,051.0336 R 7,606.6816 R 4,825.7312 R 5,215.9449 R 3,590.2553 R 2,277.6827 12,015 12,015 12,015 5,611.259 5,611.259 5,611 R 10,948.0680 R 7,535.8080 R 4,780.7685 R 5,112.9793 R 3,519.3817 R 2,232.7200 12,152 12,152 12,152 5,748.259 5,748.259 5,748 R 7,621.7344 R 4,835.2808 R 4,835.2808 R 3,605.3081 R 2,287.2323 R 2,287.2323 12,573 12,573 12,573 6,169.259 6,169.259 6,169 R 7,885.7856 R 5,002.7967 R 5,002.7967 R 3,869.3593 R 2,454.7482 R 2,454.7482 12,732 12,732 12,732 30,347.724 30,347.724 30,348 R 5,066.0628 R 5,066.0628 R 5,066.0628 R 12,075.3592 R 12,075.3592 R 12,075.3592 12,673 12,673 12,673 30,288.724 30,288.724 30,289 R 5,042.5867 R 5,042.5867 R 5,042.5867 R 12,051.8831 R 12,051.8831 R 12,051.8831 57,611,566 14,248,022 12,699,324 64,766,229 16,017,454.579 14,276,427 RM 34.455 RM 6.534 RM 5.053 R 31.2409 R 6.7652 R 5.6806 Total 84,558,911 kW/LDS Total 95,060,111 kW/LDS RM 46.042 RM 43.687 0.000 c/kWh 0.000 c/kWh Savings R 2.36 16% Current Annual Energy Profile (LDS) Hydro Annual Energy Profile (LDS) Current Annual Cost (RM) HydroSystem Annual Cost (RM) 5000 10000 15000 20000 25000 30000 0 : 3 0 1 : 0 0 1 : 3 0 2 : 0 0 2 : 3 0 3 : 0 0 3 : 3 0 4 : 0 0 4 : 3 0 5 : 0 0 5 : 3 0 6 : 0 0 6 : 3 0 7 : 0 0 7 : 3 0 8 : 0 0 8 : 3 0 9 : 0 0 9 : 3 0 1 0 : 0 0 1 0 : 3 0 1 1 : 0 0 1 1 : 3 0 1 2 : 0 0 1 2 : 3 0 1 3 : 0 0 1 3 : 3 0 1 4 : 0 0 1 4 : 3 0 1 5 : 0 0 1 5 : 3 0 1 6 : 0 0 1 6 : 3 0 1 7 : 0 0 1 7 : 3 0 1 8 : 0 0 1 8 : 3 0 1 9 : 0 0 1 9 : 3 0 2 0 : 0 0 2 0 : 3 0 2 1 : 0 0 2 1 : 3 0 2 2 : 0 0 2 2 : 3 0 2 3 : 0 0 2 3 : 3 0 0 : 0 0 k W h SINGLE POD LOAD PROFILE ‐ LDS OFF‐PEAK TARIFF CHARGED (LDS) PEAK TARIFF CHARGED (LDS) STANDARD TARIFF CHARGED (LDS) Electricity from Eskom (without UPHES) Electricty from Eskom (with UPHES) ‐ LDS Calculation LDS PAGE 1 OF 3 MASTER UPHES CALCULATION REV 0 01 SEPTEMBER 2017 PEAK STAN OFF-P Electr Week Satur Sund Powe WEEK Powe Electr Pump Wate Total Electr Perce Perce Electr Powe 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 10:00 10:30 11:00 11:30 12:00 12:30 13:00 13:30 14:00 14:30 15:00 15:30 16:00 16:30 17:00 17:30 18:00 18:30 19:00 19:30 20:00 11018 10935 10935 11229 11229 11717 11717 12771 12771 13055 13055 12798 12798 12536 12536 12377.06 12377.06 12128 12128 12015 12015 11018 10935 10935 11229 11229 11717 11717 12771 12771 13055 13055 12798 12798 12536 12536 12377.06 12377.06 12128 12128 12015 12015 11018 10935 10935 11229 11229 11717 11717 12771 12771 13055 13055 12798 12798 12536 12536 12377.06 12377.06 12128 12128 12015 12015 10039.6016 9963.972 9963.972 10231.8648 10231.8648 10676.5304 10676.5304 11636.9352 11636.9352 11895.716 11895.716 11661.5376 11661.5376 11422.8032 11422.8032 11277.97707 11277.97707 11051.0336 11051.0336 10948.068 10948.068 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 116% 117% 117% 114% 114% 109% 109% 100% 100% 98% 98% 100% 100% 102% 102% 103% 103% 106% 106% 107% 107% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 4614.26 4531.26 4531.26 4825.26 4825.26 5313.26 5313.26 6367.26 6367.26 6651.26 6651.26 6394.26 6394.26 6132.26 6132.26 5973.32 5973.32 5724.26 5724.26 5611.26 5611.26 4204.51 4128.88 4128.88 4396.78 4396.78 4841.44 4841.44 5801.85 5801.85 6060.63 6060.63 5826.45 5826.45 5587.71 5587.71 5442.89 5442.89 5215.94 5215.94 5112.98 5112.98 LOW DEMAND SEASON 5000 10000 15000 20000 25000 30000 0 : 3 0 1 : 0 0 1 : 3 0 2 : 0 0 2 : 3 0 3 : 0 0 3 : 3 0 4 : 0 0 4 : 3 0 5 : 0 0 5 : 3 0 6 : 0 0 6 : 3 0 7 : 0 0 7 : 3 0 8 : 0 0 8 : 3 0 9 : 0 0 9 : 3 0 1 0 : 0 0 1 0 : 3 0 1 1 : 0 0 1 1 : 3 0 1 2 : 0 0 1 2 : 3 0 1 3 : 0 0 1 3 : 3 0 1 4 : 0 0 1 4 : 3 0 1 5 : 0 0 1 5 : 3 0 1 6 : 0 0 1 6 : 3 0 1 7 : 0 0 1 7 : 3 0 1 8 : 0 0 1 8 : 3 0 1 9 : 0 0 1 9 : 3 0 2 0 : 0 0 2 0 : 3 0 2 1 : 0 0 2 1 : 3 0 2 2 : 0 0 2 2 3 0 k W h POD LOAD PROFILE ‐ POWER GENERATED DURING PEAK TARIFF PERIODS ONLY Electricity from Eskom (without UPHES) Electricty from Eskom (with UPHES) ‐ LDS Electricty from Eskom (with UPHES) ‐ Calculation LDS PAGE 2 OF 3 MASTER UPHES CALCULATION REV 0 01 SEPTEMBER 2017 PEAK STAN OFF-P Electr Week Satur Sund Powe WEEK Powe Electr Pump Wate Total Electr Perce Perce Electr Powe 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1 1 1 1 0 0 0 0 20 20 21 21 22 22 23 23 20:30 21:00 21:30 22:00 22:30 23:00 23:30 0:00 12152 12152 12573 12573 12732 12732 12673 12673 12152 12152 12573 12573 12732 12732 12673 12673 12152 12152 12573 12573 12732 12732 12673 12673 11072.9024 11072.9024 11456.5176 11456.5176 11601.3984 11601.3984 11547.6376 11547.6376 542,994.55ZAR 6403.740923 6403.740923 6403.740923 6403.740923 0 0 0 0 102,460 1 1 1 1 0 0 0 0 6403.740923 6403.740923 6403.740923 6403.740923 0 0 0 0 14 14 14 14 0 0 0 0 1.4 1.4 1.4 1.4 1.4 2.8 4.2 5.6 0.00 0.00 0.00 0.00 17615.72 17615.72 17615.72 17615.72 281,852 105% 105% 102% 102% 0% 0% 0% 0% 0% 0% 0% 0% 138% 138% 139% 139% 5748.26 5748.26 6169.26 6169.26 30347.72 30347.72 30288.72 30288.72 5237.81 5237.81 5621.43 5621.43 27652.85 27652.85 27599.08 27599.08 585,004.84ZAR 107.73678% 2 2 : 3 0 2 3 : 0 0 2 3 : 3 0 0 : 0 0 HDS Calculation LDS PAGE 3 OF 3 MASTER UPHES CALCULATION REV 0 01 SEPTEMBER 2017 Pilot PEAK TARIFF CHARGED (HDS) 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 STANDARD TARIFF CHARGED (HDS) 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 OFF-PEAK TARIFF CHARGED (HDS) 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 Electricty from Eskom (without UPHES) 0:30 1:00 1:30 2:00 2:30 3:00 3:30 4:00 4:30 5:00 5:30 6:00 6:30 7:00 7:30 8:00 8:30 9:00 Weekday 13059.38 13059.38 14204.46 14204.46 15449 15449 15409.3 15409.3 15008 15008 14907.6 14907.6 14338.8 14338.8 12834 12834 11820 11820 Saturday 13059.38 13059.38 14204.46 14204.46 15449 15449 15409.3 15409.3 15008 15008 14907.6 14907.6 14338.8 14338.8 12834 12834 11820 11820 Sunday 13059.38 13059.38 14204.46 14204.46 15449 15449 15409.3 15409.3 15008 15008 14907.6 14907.6 14338.8 14338.8 12834 12834 11820 11820 Power cost (without UPHES) [ZAR] 5196.327302 5196.327302 8909.037312 8909.037312 14077.1288 14077.1288 14040.95416 14040.95416 13675.2896 13675.2896 13583.80512 13583.80512 13065.51456 13065.51456 11694.3408 11694.3408 10770.384 10770.384 WEEKDAY Power generated (peak - HDS) [kW] 0 0 0 0 0 0 0 0 0 0 0 0 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 Electrical power generated (peak - HDS) [kWh] 0 0 0 0 0 0 0 0 0 0 0 0 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 Pumps running [No] 14 14 14 14 14 14 14 14 14 14 14 14 Water pumped in period [Ml] 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 0 0 0 0 0 0 Total volume of water pumped to upper reservoir [Ml] 7 8.4 9.8 11.2 12.6 14 15.4 16.8 18.2 19.6 21 22.4 Electrical power required to pump water to upper reservo [kWh] 17615.72 17615.72 17615.72 17615.72 17615.72 17615.72 17615.72 17615.72 17615.72 17615.72 17615.72 17615.72 0.00 0.00 0.00 0.00 0.00 0.00 Percentage of POD load reduced [%] 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 89% 89% 100% 100% 108% 108% Percentage of POD load reduced [%] 135% 135% 124% 124% 114% 114% 114% 114% 117% 117% 118% 118% 0% 0% 0% 0% 0% 0% Electricty from Eskom (with UPHES) - HDS [kWh] 30675.10 30675.10 31820.18 31820.18 33064.72 33064.72 33025.02 33025.02 32623.72 32623.72 32523.32 32523.32 7935.06 7935.06 6430.26 6430.26 5416.26 5416.26 Power cost UPHES @ peak [ZAR] 12205.62 12205.62 19957.62 19957.62 30128.58 30128.58 30092.40 30092.40 29726.74 29726.74 29635.25 29635.25 7230.43 7230.43 5859.25 5859.25 4935.30 4935.30 WD (HDS) Sat (HDS) Sun (HDS) WD (HDS)* Sat (HDS)* Sun (HDS)* Weekday (HDS) Saturday (HDS) Sunday (HDS) Weekday (HDS)* Saturday (HDS)* Sunday (HDS)* 13,059 13,059 13,059 30,675 30,675 30,675 R 6,000.7851 R 6,000.7851 R 6,000.7851 R 14,095.2101 R 14,095.2101 R 14,095.2101 14,204 14,204 14,204 31,820 31,820 31,820 R 6,526.9494 R 6,526.9494 R 6,526.9494 R 14,621.3744 R 14,621.3744 R 14,621.3744 15,449 15,449 15,449 33,065 33,065 33,065 R 7,098.8155 R 7,098.8155 R 7,098.8155 R 15,193.2405 R 15,193.2405 R 15,193.2405 15,409 15,409 15,409 33,025 33,025 33,025 R 7,080.5734 R 7,080.5734 R 7,080.5734 R 15,174.9984 R 15,174.9984 R 15,174.9984 15,008 15,008 15,008 32,624 32,624 32,624 R 6,896.1760 R 6,896.1760 R 6,896.1760 R 14,990.6010 R 14,990.6010 R 14,990.6010 14,908 14,908 14,908 32,523 32,523 32,523 R 6,850.0422 R 6,850.0422 R 6,850.0422 R 14,944.4672 R 14,944.4672 R 14,944.4672 14,339 14,339 14,339 7,935 7,935 7,935 R 40,052.5700 R 6,588.6786 R 6,588.6786 R 22,165.0005 R 3,646.1596 R 3,646.1596 12,834 12,834 12,834 6,430 6,430 6,430 R 35,849.2122 R 10,860.1308 R 5,897.2230 R 17,961.6427 R 5,441.2852 R 2,954.7040 11,820 11,820 11,820 5,416 5,416 5,416 R 33,016.8060 R 10,002.0840 R 5,431.2900 R 15,129.2365 R 4,583.2384 R 2,488.7710 11,018 11,018 11,018 4,614 4,614 4,614 R 9,323.4316 R 9,323.4316 R 5,062.7710 R 3,904.5860 R 3,904.5860 R 2,120.2520 10,935 10,935 10,935 4,531 4,531 4,531 R 9,253.1970 R 9,253.1970 R 5,024.6325 R 3,834.3514 R 3,834.3514 R 2,082.1135 11,229 11,229 11,229 4,825 4,825 4,825 R 9,501.9798 R 9,501.9798 R 5,159.7255 R 4,083.1342 R 4,083.1342 R 2,217.2065 11,717 11,717 11,717 5,313 5,313 5,313 R 9,914.9254 R 5,383.9615 R 5,383.9615 R 4,496.0798 R 2,441.4425 R 2,441.4425 12,771 12,771 12,771 6,367 6,367 6,367 R 10,806.8202 R 5,868.2745 R 5,868.2745 R 5,387.9746 R 2,925.7555 R 2,925.7555 13,055 13,055 13,055 6,651 6,651 6,651 R 11,047.1410 R 5,998.7725 R 5,998.7725 R 5,628.2954 R 3,056.2535 R 3,056.2535 12,798 12,798 12,798 6,394 6,394 6,394 R 10,829.6676 R 5,880.6810 R 5,880.6810 R 5,410.8220 R 2,938.1620 R 2,938.1620 12,536 12,536 12,536 6,132 6,132 6,132 R 10,607.9632 R 5,760.2920 R 5,760.2920 R 5,189.1176 R 2,817.7730 R 2,817.7730 12,377 12,377 12,377 5,973 5,973 5,973 R 34,572.8417 R 5,687.2591 R 5,687.2591 R 16,685.2722 R 2,744.7401 R 2,744.7401 12,128 12,128 12,128 5,724 5,724 5,724 R 33,877.1424 R 10,262.7136 R 5,572.8160 R 15,989.5729 R 4,843.8680 R 2,630.2970 12,015 12,015 12,015 5,611 5,611 5,611 R 10,167.0930 R 10,167.0930 R 5,520.8925 R 4,748.2474 R 4,748.2474 R 2,578.3735 12,152 12,152 12,152 5,748 5,748 5,748 R 10,283.0224 R 5,583.8440 R 5,583.8440 R 4,864.1768 R 2,641.3250 R 2,641.3250 12,573 12,573 12,573 6,169 6,169 6,169 R 10,639.2726 R 5,777.2935 R 5,777.2935 R 5,220.4270 R 2,834.7745 R 2,834.7745 12,732 12,732 12,732 30,348 30,348 30,348 R 5,850.3540 R 5,850.3540 R 5,850.3540 R 13,944.7790 R 13,944.7790 R 13,944.7790 12,673 12,673 12,673 30,289 30,289 30,289 R 5,823.2435 R 5,823.2435 R 5,823.2435 R 13,917.6685 R 13,917.6685 R 13,917.6685 19,823,334 4,336,354 4,336,354 22,285,154 4,874,877 4,874,877 RM 21.880 RM 2.436 RM 1.993 R 16.4851 R 2.4411 R 2.2400 Total 28,496,043 kW/LDS Total 32,034,909 kW/LDS RM 26.309 RM 21.166 0.000 c/kWh 0.000 c/kWh Savings R 5.14 28% Current Annual Energy Profile (LDS) Hydro Annual Energy Profile (LDS) Current Annual Cost (RM) HydroSystem Annual Cost (RM) 5000 10000 15000 20000 25000 30000 0 : 3 0 1 : 0 0 1 : 3 0 2 : 0 0 2 : 3 0 3 : 0 0 3 : 3 0 4 : 0 0 4 : 3 0 5 : 0 0 5 : 3 0 6 : 0 0 6 : 3 0 7 : 0 0 7 : 3 0 8 : 0 0 8 : 3 0 9 : 0 0 9 : 3 0 1 0 : 0 0 1 0 : 3 0 1 1 : 0 0 1 1 : 3 0 1 2 : 0 0 1 2 : 3 0 1 3 : 0 0 1 3 : 3 0 1 4 : 0 0 1 4 : 3 0 1 5 : 0 0 1 5 : 3 0 1 6 : 0 0 1 6 : 3 0 1 7 : 0 0 1 7 : 3 0 1 8 : 0 0 1 8 : 3 0 1 9 : 0 0 1 9 : 3 0 2 0 : 0 0 2 0 : 3 0 2 1 : 0 0 2 1 : 3 0 2 2 : 0 0 2 2 : 3 0 2 3 : 0 0 2 3 : 3 0 0 : 0 0 k W h SINGLE POD LOAD PROFILE ‐ HDS OFF‐PEAK TARIFF CHARGED (HDS) PEAK TARIFF CHARGED (HDS) STANDARD TARIFF CHARGED (HDS) Electricty from Eskom (without UPHES) Electricty from Eskom (with UPHES) ‐ HDS Calculation HDS PAGE 1 OF 3 MASTER UPHES CALCULATION REV 0 01 SEPTEMBER 2017 PEAK STAN OFF- Elect Wee Satu Sund Pow WEEK Pow Elect Pum Wate Tota Elect Perc Perc Elect Pow 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 9:30 10:00 10:30 11:00 11:30 12:00 12:30 13:00 13:30 14:00 14:30 15:00 15:30 16:00 16:30 17:00 17:30 18:00 18:30 19:00 19:30 11018 11018 10935 10935 11229 11229 11717 11717 12771 12771 13055 13055 12798 12798 12536 12536 12377.06 12377.06 12128 12128 12015 11018 11018 10935 10935 11229 11229 11717 11717 12771 12771 13055 13055 12798 12798 12536 12536 12377.06 12377.06 12128 12128 12015 11018 11018 10935 10935 11229 11229 11717 11717 12771 12771 13055 13055 12798 12798 12536 12536 12377.06 12377.06 12128 12128 12015 10039.6016 10039.6016 9963.972 9963.972 10231.8648 10231.8648 10676.5304 10676.5304 11636.9352 11636.9352 11895.716 11895.716 11661.5376 11661.5376 11422.8032 11422.8032 11277.97707 11277.97707 11051.0336 11051.0336 10948.068 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 116% 116% 117% 117% 114% 114% 109% 109% 100% 100% 98% 98% 100% 100% 102% 102% 103% 103% 106% 106% 107% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 4614.26 4614.26 4531.26 4531.26 4825.26 4825.26 5313.26 5313.26 6367.26 6367.26 6651.26 6651.26 6394.26 6394.26 6132.26 6132.26 5973.32 5973.32 5724.26 5724.26 5611.26 4204.51 4204.51 4128.88 4128.88 4396.78 4396.78 4841.44 4841.44 5801.85 5801.85 6060.63 6060.63 5826.45 5826.45 5587.71 5587.71 5442.89 5442.89 5215.94 5215.94 5112.98 HIGH DEMAND SEASON 5000 10000 15000 20000 25000 30000 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 0 : 0 0 k W h SINGLE POD LOAD PROFILE ‐ LDS Electricty from Eskom (without UPHES) Electricty from Eskom (with UPHES) ‐ HDS Calculation HDS PAGE 2 OF 3 MASTER UPHES CALCULATION REV 0 01 SEPTEMBER 2017 PEAK STAN OFF- Elect Wee Satu Sund Pow WEEK Pow Elect Pum Wate Tota Elect Perc Perc Elect Pow 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1 1 1 1 1 0 0 0 0 19 20 20 21 21 22 22 23 23 20:00 20:30 21:00 21:30 22:00 22:30 23:00 23:30 0:00 12015 12152 12152 12573 12573 12732 12732 12673 12673 12015 12152 12152 12573 12573 12732 12732 12673 12673 12015 12152 12152 12573 12573 12732 12732 12673 12673 10948.068 11072.9024 11072.9024 11456.5176 11456.5176 11601.3984 11601.3984 11547.6376 11547.6376 542,994.55ZAR 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 0 0 0 0 102,460 1 1 1 1 1 0 0 0 0 6403.740923 6403.740923 6403.740923 6403.740923 6403.740923 0 0 0 0 14 14 14 14 0 0 0 0 0 1.4 1.4 1.4 1.4 1.4 2.8 4.2 5.6 0.00 0.00 0.00 0.00 0.00 17615.72 17615.72 17615.72 17615.72 281,852 107% 105% 105% 102% 102% 0% 0% 0% 0% 0% 0% 0% 0% 0% 138% 138% 139% 139% 5611.26 5748.26 5748.26 6169.26 6169.26 30347.72 30347.72 30288.72 30288.72 5112.98 5237.81 5237.81 5621.43 5621.43 27652.85 27652.85 27599.08 27599.08 585,004.84ZAR 107.73678% Calculation HDS PAGE 3 OF 3 MASTER UPHES CALCULATION REV 0 01 SEPTEMBER 2017 UNIT LDS HDS TOTAL TOTAL POWER REQ. [kW] 84,558,911 28,496,043 113,054,954 TOTAL POWER COST ZAR [RM] 46,042,378 26,308,609 72,350,987 TOTAL POWER REQ. [kW] 95,060,111 32,034,909 127,095,020 TOTAL POWER COST ZAR [RM] 43,686,740 21,166,288 64,853,028 ADDITIONAL POWER REQUIRED [kW] 10,501,200 3,538,866 14,040,066 SAVINGS ZAR [RM] 2,355,639 5,142,321 7,497,960 12.42% 10.36% UPHES SYSTEM POD PROFILE - COST PER YEAR ORIGINAL POD PROFILE - COST PER YEAR EXTRA POWER REQUIRED (% OF INITIAL POWER REQUIREMENT) TOTAL SYSYTEM POWER COST TRIM (% OF INITIAL POWER REQUIREMENT) 0 5,000 10,000 15,000 20,000 25,000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 kW h 24 hour cycle DAILY ENERGY PROFILE NORMAL WEEKDAY VS. LDS & HDS WITH UPHES* WD (LDS) WD (LDS)* WD (HDS) WD (HDS)* R 0.0000 R 5,000.0000 R 10,000.0000 R 15,000.0000 R 20,000.0000 R 25,000.0000 R 30,000.0000 R 35,000.0000 R 40,000.0000 R 45,000.0000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 ZA R  24 hour cycle DAILY ENERGY COST PROFILE NORMAL WEEKDAY VS. LDS & HDS WITH UPHES* Weekday (LDS) Weekday (LDS)* Weekday (HDS) Weekday (HDS)* OUTPUT PAGE 1 OF 1 MASTER UPHES CALCULATION REV 0 01 SEPTEMBER 2017 TOTAL SYSTEM COST 162,638,420.91ZAR SAVINGS (SYSTEM INSTALLED CAPACITY 102.5 MWh) MEGAFLEX TARIFF INCREASE ACCUMULATIVE MEGAFLEX TARIFF INCREASE ROI VALUE (SYSTEM INSTALLED CAPACITY 102.5 MWh) YEAR 1 7,497,959.73ZAR 8% 8% 155,140,461.18ZAR 1 YEAR 2 8,097,796.50ZAR 8% 9% 147,042,664.68ZAR 1 YEAR 3 8,745,620.22ZAR 8% 9% 138,297,044.46ZAR 1 YEAR 4 9,445,269.84ZAR 8% 10% 128,851,774.61ZAR 1 YEAR 5 10,200,891.43ZAR 8% 11% 118,650,883.18ZAR 1 YEAR 6 11,016,962.74ZAR 8% 12% 107,633,920.44ZAR 1 YEAR 7 11,898,319.76ZAR 8% 13% 95,735,600.68ZAR 1 YEAR 8 12,850,185.34ZAR 8% 14% 82,885,415.33ZAR 1 YEAR 9 13,878,200.17ZAR 8% 15% 69,007,215.16ZAR 1 YEAR 10 14,988,456.19ZAR 8% 16% 54,018,758.98ZAR 1 YEAR 11 16,187,532.68ZAR 8% 17% 37,831,226.30ZAR 1 YEAR 12 17,482,535.29ZAR 8% 19% 20,348,691.00ZAR 1 YEAR 13 18,881,138.12ZAR 8% 20% 1,467,552.88ZAR 1.08 Months YEAR 14 20,391,629.17ZAR 8% 22% (18,924,076.28)ZAR 13.08 Years ROI CALCULATION 0% 5% 10% 15% 20% 25% ZAR (40,000,000.00) ZAR (20,000,000.00) ZAR - ZAR 20,000,000.00 ZAR 40,000,000.00 ZAR 60,000,000.00 ZAR 80,000,000.00 ZAR 100,000,000.00 ZAR 120,000,000.00 ZAR 140,000,000.00 ZAR 160,000,000.00 ZAR 180,000,000.00 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 M EG AF LE X TA R IF F IN C R EA SE S (A C C U M U LA TI VE ) SA VI N G S / S YS TE M R O I [ ZA R [ YEARS ROI ROI VALUE (SYSTEM INSTALLED CAPACITY 102.5 MWh) SAVINGS (SYSTEM INSTALLED CAPACITY 102.5 MWh) ROI VALUE (SYSTEM INSTALLED CAPACITY 32 MWh) SAVINGS (SYSTEM INSTALLED CAPACITY 32 MWh) ACCUMULATIVE MEGAFLEX TARIFF INCREASE ROI PAGE 1 OF 1 File:F:\UPHES SYSTEM EES\UPHES VERIFICATION MODEL REV D PEAK CAPEX.EES 8/24/2017 7:22:32 PM Page 1 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa {PROGRAM OPERATIONAL STEPS (1) INSERT ALL INPUT PARAMETERS, SOLVE PRINCIPAL OUTPUT PARAMETERS (2) REMOVE COMMENT BRACKETS FROM LOAD AND ELECTRICITY COST CALCULATIONS, SOLVE PARAMETRIC TABLE (3) REPLACE THE COMMENT BRACKETS TO THE LOAD AND ELECTRICITY COST CALCULATIONS AFTER SOLVING THE PRAMETRIC TABLE, REMOVE THE COMMENT BRACKETS FROM THE ELECTRICITY SAVINGS SECTION, CLICK SOLVE} {INPUT PARAMETERS} rho_water = 998 [kg/m3] g = 9.81 [m/s2] S_TURBINE = 1 [-] {NUMBER TURBINES} V_TURBINE = 369.55 [l/s] R_DISCHARGE_HEAD = V_TURBINE/H_EFFECTIVE eta_TURBINE = 0.91 V_PUMP = 55.56 [l/s] eta_PUMP = 0.89 f = 0.0174 {PIPE FRICTION FACTOR ASSUMED} D_i_PIPE = 284.18 [mm] {OPERATIONAL INPUT PARAMETERS} HRS_PUMP = 8 [hrs] HRS_TURBINE = 5 [hrs] {ELEVATIONS} H_1_IPC_9 = 150 [m] H_2_MID_SHAFT_9 = 1050 [m] H_3_24LVL_9 = 2095 [m] {SYSTEM OPERATIONAL FORMULAS} P_ACTUAL = rho_water*g*(H_EFFECTIVE)*(V_TURBINE/1000)*eta_TURBINE/1000 H_EFFECTIVE = (H_3_24LVL_9-H_1_IPC_9) P_TURBINE_MWh = (P_ACTUAL* HRS_TURBINE)/1000 VOL_LOWER_RESERVOIR = V_TURBINE*(HRS_TURBINE*60*60)/1000000 S_PUMPS = (VOL_LOWER_RESERVOIR*1000000)/(V_PUMP*60*60)/HRS_PUMP VOL_UPPER_RESERVOIR = (S_PUMPS_MANUAL_INPUT*V_PUMP*HRS_PUMP*60*60)/1000000 P_PUMPS_24LVL_9 = ((rho_water*g*(H_3_24LVL_9-H_2_MID_SHAFT_9+H_3_FRICTION)*(V_PUMP/1000))/ eta_PUMP)*S_PUMPS_MANUAL_INPUT/1000000 P_PUMPS_MID_SHAFT_9 = ((rho_water*g*(H_2_MID_SHAFT_9-H_1_IPC_9+H_2_FRICTION)*(V_PUMP/1000))/ eta_PUMP)*S_PUMPS_MANUAL_INPUT/1000000 P_PUMPS_MWh = (P_PUMPS_24LVL_9+P_PUMPS_MID_SHAFT_9)*HRS_PUMP H_3_FRICTION = (f*(H_3_24LVL_9-H_2_MID_SHAFT_9 +50)*VEL_UP^2)/(2*g*(D_i_PIPE/1000)) H_2_FRICTION = (f*(H_2_MID_SHAFT_9-H_1_IPC_9 +50)*VEL_UP^2)/(2*g*(D_i_PIPE/1000)) VEL_UP = 4.22 {((V_PUMP/1000)*S_PUMPS_MANUAL_INPUT)/(pi*(D_i_PIPE/1000))} {MANUAL INPUT (1)} S_PUMPS_MANUAL_INPUT = 5 {MEGAFLEX TARIFF STRUCTURE - INPUT 2016/2017} {TIME_INTERVAL = 1 [HRS]} {POD_USAGE = 20000 [Wh]} {T_WEEKDAY_LDS = 68.19 [c/kWh] T_SATURDAY_LDS = 68.19 [c/kWh] T_SUNDAY_LDS = 68.19 [c/kWh] T_WEEKDAY_HDS = 68.19 [c/kWh] T_SATURDAY_HDS = 68.19 [c/kWh] T_SUNDAY_HDS = 68.19 [c/kWh]} T_LDS_OFF_PEAK = 68.19 [c/kWh] T_LDS_STANDARD = 107.49 [c/kWh] T_LDS_PEAK = 156.16 [c/kWh] File:F:\UPHES SYSTEM EES\UPHES VERIFICATION MODEL REV D PEAK CAPEX.EES 8/24/2017 7:22:32 PM Page 2 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa T_HDS_OFF_PEAK = 78.75 [c/kWh] T_HDS_STANDARD = 145.02 [c/kWh] T_HDS_PEAK = 478.72 [c/kWh] D_WEEKDAY_OFF_PEAK = 8 D_WEEKDAY_STANDARD = 11 D_WEEKDAY_PEAK = 5 D_LDS_WEEKDAY_TARIFF = 186 D_LDS_SATURDAY_TARIFF = 46 D_LDS_SUNDAY_TARIFF = 41 D_HDS_WEEKDAY_TARIFF = 64 D_HDS_SATURDAY_TARIFF = 14 D_HDS_SUNDAY_TARIFF = 14 ESKOM = 1.05^0 {ASSUMED MEGAFLEX TARIFF INCREASE} {LOAD AND ELECTRICITY COST CALCULATIONS} {WEEKDAY} {POD_USAGE_UPHES_LDS = (P_ACTUAL)*P_1_LDS POD_USAGE_PUMPS_LDS = (P_PUMPS_24LVL_9*1000+P_PUMPS_MID_SHAFT_9*1000)*P_2_LDS POD_USAGE_TOTAL_LDS = POD_USAGE - POD_USAGE_UPHES_LDS + POD_USAGE_PUMPS_LDS ZAR_POD_USAGE_WEEKDAY_LDS = POD_USAGE*T_WEEKDAY_LDS/100*ESKOM ZAR_POD_USAGE_WD_LDS_UPHES = POD_USAGE_TOTAL_LDS*T_WEEKDAY_LDS/100*ESKOM POD_USAGE_UPHES_HDS = (P_ACTUAL)*P_1_HDS POD_USAGE_PUMPS_HDS = (P_PUMPS_24LVL_9*1000+P_PUMPS_MID_SHAFT_9*1000)*P_2_HDS POD_USAGE_TOTAL_HDS = POD_USAGE - POD_USAGE_UPHES_HDS + POD_USAGE_PUMPS_HDS ZAR_POD_USAGE_WEEKDAY_HDS = POD_USAGE*T_WEEKDAY_HDS/100*ESKOM ZAR_POD_USAGE_WD_HDS_UPHES = POD_USAGE_TOTAL_HDS*T_WEEKDAY_HDS/100*ESKOM {SATURDAY} POD_USAGE_UPHES_LDS_SAT = (P_ACTUAL)*P_1_LDS_SAT POD_USAGE_PUMPS_LDS_SAT = (P_PUMPS_24LVL_9*1000+P_PUMPS_MID_SHAFT_9*1000)*P_2_LDS_SAT POD_USAGE_TOTAL_LDS_SAT = POD_USAGE - POD_USAGE_UPHES_LDS_SAT + POD_USA GE_PUMPS_LDS_SAT ZAR_POD_USAGE_SAT_LDS = POD_USAGE*T_SATURDAY_LDS/100*ESKOM ZAR_POD_USAGE_SAT_LDS_UPHES = POD_USAGE_TOTAL_LDS_SAT*T_SATURDAY_LDS/100*ESKOM POD_USAGE_UPHES_HDS_SAT = (P_ACTUAL)*P_1_HDS_SAT POD_USAGE_PUMPS_HDS_SAT = (P_PUMPS_24LVL_9*1000+P_PUMPS_MID_SHAFT_9*1000)*P_2_HDS_SAT POD_USAGE_TOTAL_HDS_SAT = POD_USAGE - POD_USAGE_UPHES_HDS_SAT + POD_US AGE_PUMPS_HDS_SAT ZAR_POD_USAGE_SAT_HDS = POD_USAGE*T_SATURDAY_HDS/100*ESKOM ZAR_POD_USAGE_SAT_HDS_UPHES = POD_USAGE_TOTAL_HDS_SAT*T_SATURDAY_HDS/100*ESKOM {SUNDAY} POD_USAGE_UPHES_LDS_SUN = (P_ACTUAL)*P_1_LDS_SUN POD_USAGE_PUMPS_LDS_SUN = (P_PUMPS_24LVL_9*1000+P_PUMPS_MID_SHAFT_9*1000)*P_2_LDS_SUN POD_USAGE_TOTAL_LDS_SUN = POD_USAGE - POD_USAGE_UPHES_LDS_SUN + POD_US AGE_PUMPS_LDS_SUN ZAR_POD_USAGE_SUN_LDS = POD_USAGE*T_SUNDAY_LDS/100*ESKOM ZAR_POD_USAGE_SUN_LDS_UPHES = POD_USAGE_TOTAL_LDS_SUN*T_SUNDAY_LDS/100*ESKOM POD_USAGE_UPHES_HDS_SUN = (P_ACTUAL)*P_1_HDS_SUN POD_USAGE_PUMPS_HDS_SUN = (P_PUMPS_24LVL_9*1000+P_PUMPS_MID_SHAFT_9*1000)*P_2_HDS_SUN POD_USAGE_TOTAL_HDS_SUN = POD_USAGE - POD_USAGE_UPHES_HDS_SUN + POD_US AGE_PUMPS_HDS_SUN ZAR_POD_USAGE_SUN_HDS = POD_USAGE*T_SUNDAY_HDS/100*ESKOM ZAR_POD_USAGE_SUN_HDS_UPHES = POD_USAGE_TOTAL_HDS_SUN*T_SUNDAY_HDS/100*ESKOM} {ELECTRICITY SAVINGS} POD_USAGE_PA = (sumparametric('Table 1', 'POD_USAGE')*D_LDS_WEEKDAY_TARIFF+sumparametric('Table 1', ' File:F:\UPHES SYSTEM EES\UPHES VERIFICATION MODEL REV D PEAK CAPEX.EES 8/24/2017 7:22:32 PM Page 3 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa POD_USAGE')*D_HDS_WEEKDAY_TARIFF+sumparametric('Table 1', 'POD_USAGE')*D_LDS_SATURDAY_TARIFF+ sumparametric('Table 1', 'POD_USAGE')*D_HDS_SATURDAY_TARIFF+sumparametric('Table 1', 'POD_USAGE')* D_LDS_SUNDAY_TARIFF+sumparametric('Table 1', 'POD_USAGE')*D_HDS_SUNDAY_TARIFF)/1000000 ZAR_POD_USAGE_PA = (sumparametric('Table 1', 'ZAR_POD_USAGE_WEEKDAY_LDS')*D_LDS _WEEKDAY_TARIFF+sumparametric('Table 1', 'ZAR_POD_USAGE_WEEKDAY_HDS')*D_HDS_WEEKDAY_TARIFF+ sumparametric('Table 1', 'ZAR_POD_USAGE_SAT_LDS')*D_LDS_SATURDAY_TARIFF + sumparametric('Table 1', ' ZAR_POD_USAGE_SAT_HDS')*D_HDS_SATURDAY_TARIFF+SUMPARAMETRIC('Table 1', 'ZAR _POD_USAGE_SUN_LDS')*D_LDS_SUNDAY_TARIFF+SUMPARAMETRIC('Table 1', 'ZAR_POD_USAGE_SUN_HDS') *D_HDS_SUNDAY_TARIFF)/1000000 POD_USAGE_PA_UPHES_LDS= (sumparametric('Table 1', 'POD_USAGE_TOTAL_LDS')*D_LDS_WEEKDAY_TARIFF + sumparametric('Table 1', 'POD_USAGE_TOTAL_LDS_SAT')*D_LDS_SATURDAY_TARIFF+ sumparametric('Table 1', ' POD_USAGE_TOTAL_LDS_SUN')*D_LDS_SUNDAY_TARIFF + sumparametric('Table 1', 'POD_USAGE_TOTAL_HDS') *D_HDS_WEEKDAY_TARIFF+sumparametric('Table 1', 'POD_USAGE_TOTAL_HDS_SAT')*D_HDS _SATURDAY_TARIFF+sumparametric('Table 1', 'POD_USAGE_TOTAL_HDS_SUN')*D_HDS_SUNDAY_TARIFF)/ 1000000 ZAR_POD_USAGE_PA_UPHES = (sumparametric('Table 1', 'ZAR_POD_USAGE_WD_LDS_UPHES')* D_LDS_WEEKDAY_TARIFF+sumparametric('Table 1', 'ZAR_POD_USAGE_WD_HDS_UPHES')*D _HDS_WEEKDAY_TARIFF+sumparametric('Table 1', 'ZAR_POD_USAGE_SAT_LDS_UPHES')*D_ LDS_SATURDAY_TARIFF + sumparametric('Table 1', 'ZAR_POD_USAGE_SAT_HDS_UPHES')*D_ HDS_SATURDAY_TARIFF+SUMPARAMETRIC('Table 1', 'ZAR_POD_USAGE_SUN_LDS_UPHES')* D_LDS_SUNDAY_TARIFF+SUMPARAMETRIC('Table 1', 'ZAR_POD_USAGE_SUN_HDS_UPHES')* D_HDS_SUNDAY_TARIFF)/1000000 SAVINGS = ZAR_POD_USAGE_PA - ZAR_POD_USAGE_PA_UPHES {ESTIMATED CAPEX - CONSIDERATION GIVEN TO EXISTING INFRASTRUCTURE} PACKAGE_1 = 0 {WINDING PLANT} PACKAGE_2 = 0 {HEADGEAR} PACKAGE_3 = 0 {SHAFT DEVELOPMENT} PACKAGE_4_A = (10097.30*(H_EFFECTIVE/3/9))+(12337.19*(H_EFFECTIVE/3/9))+(13864.49*(H_EFFECTIVE/3/9)) {SHAFT PIPE COLUMN - TURBINE FEED} PACKAGE_4_B = PACKAGE_4_A*0.05+PACKAGE_4_A*0.1+PACKAGE_4_A*0.4+(1039775.30*(H_3_24LVL_9/2300))+ (216585.85*(H_3_24LVL_9/2300)) {SHAFT INFRASTRUCTURE} PACKAGE_4 = PACKAGE_4_A + PACKAGE_4_B PACKAGE_5 = 0 {STATION DEVELOPMENT} PACKAGE_6_UPPER_RES = 2800*(VOL_LOWER_RESERVOIR*1.15*1000)+50000*((VOL_LOWER_RESERVOIR* 1.15)/3) PACKAGE_6_MID_RES = 2800*(VOL_LOWER_RESERVOIR*0.15*1000)+50000*1 PACKAGE_6_LOWER_RES = 50000*(VOL_LOWER_RESERVOIR/3) {ONLY DAM WALLS} PACKAGE_6 = PACKAGE_6_UPPER_RES + PACKAGE_6_LOWER_RES + PACKAGE_6_MID_RES {RESERVOIRS} PACKAGE_7 = ((3134883.23+275129.55+173611.63)*(S_PUMPS_MANUAL_INPUT*2-8))+(305417.38+2800*8*( S_PUMPS_MANUAL_INPUT-4))+368000*2 {PUMP CHAMBERS - ASSUME SUPPLY OF ALL PUMPS} PACKAGE_8 = (4630500+1100518.20+694446.51) {SUPPLY COST OF ONE TURBINE, SWITCHGEAR AND GENERATOR} TOTAL_CAPEX = (PACKAGE_1 + PACKAGE_2 + PACKAGE_3 + PACKAGE_4 + PACKAGE_5 + PACKAGE_6 + PACKAGE_7 + PACKAGE_8)/1000000 Parametric Table: Table 1 TIMEINTERVAL TWEEKDAY,LDS TSATURDAY,LDS TSUNDAY,LDS TWEEKDAY,HDS TSATURDAY,HDS [hrs] [c/kWh] [c/kWh] [c/kWh] [c/kWh] [c/kWh] Run 1 0 39.79 39.79 39.79 45.95 45.95 Run 2 1 39.79 39.79 39.79 45.95 45.95 Run 3 2 39.79 39.79 39.79 45.95 45.95 Run 4 3 39.79 39.79 39.79 45.95 45.95 Run 5 4 39.79 39.79 39.79 45.95 45.95 Run 6 5 39.79 39.79 39.79 45.95 45.95 File:F:\UPHES SYSTEM EES\UPHES VERIFICATION MODEL REV D PEAK CAPEX.EES 8/24/2017 7:22:32 PM Page 4 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa Parametric Table: Table 1 TIMEINTERVAL TWEEKDAY,LDS TSATURDAY,LDS TSUNDAY,LDS TWEEKDAY,HDS TSATURDAY,HDS [hrs] [c/kWh] [c/kWh] [c/kWh] [c/kWh] [c/kWh] Run 7 6 62.72 39.79 39.79 279.3 45.95 Run 8 7 91.12 62.72 39.79 279.3 84.62 Run 9 8 91.12 62.72 39.79 279.3 84.62 Run 10 9 91.12 62.72 39.79 84.62 84.62 Run 11 10 62.72 62.72 39.79 84.62 84.62 Run 12 11 62.72 62.72 39.79 84.62 84.62 Run 13 12 62.72 39.79 39.79 84.62 45.95 Run 14 13 62.72 39.79 39.79 84.62 45.95 Run 15 14 62.72 39.79 39.79 84.62 45.95 Run 16 15 62.72 39.79 39.79 84.62 45.95 Run 17 16 62.72 39.79 39.79 84.62 45.95 Run 18 17 62.72 39.79 39.79 279.3 45.95 Run 19 18 91.12 62.72 39.79 279.3 84.62 Run 20 19 91.12 62.72 39.79 84.62 84.62 Run 21 20 62.72 39.79 39.79 84.62 45.95 Run 22 21 62.72 39.79 39.79 84.62 45.95 Run 23 22 39.79 39.79 39.79 45.95 45.95 Run 24 23 39.79 39.79 39.79 45.95 45.95 Parametric Table: Table 1 TSUNDAY,HDS PODUSAGE P1,LDS P2,LDS P1,LDS,SAT P2,LDS,SAT P1,LDS,SUN P2,LDS,SUN [c/kWh] [kWh] [WD] [WD] [SAT] [SAT] [SUN] [SUN] Run 1 45.95 13059 0 1 0 1 0 1 Run 2 45.95 14204 0 1 0 1 0 1 Run 3 45.95 15449 0 1 0 1 0 1 Run 4 45.95 15409 0 1 0 1 0 1 Run 5 45.95 15008 0 1 0 1 0 1 Run 6 45.95 14908 0 1 0 1 0 1 Run 7 45.95 14339 0 0 0 0 0 0 Run 8 45.95 12834 1 0 1 0 1 0 Run 9 45.95 11820 1 0 1 0 1 0 Run 10 45.95 11018 1 0 1 0 1 0 Run 11 45.95 10935 0 0 0 0 0 0 Run 12 45.95 11229 0 0 0 0 0 0 Run 13 45.95 11717 0 0 0 0 0 0 Run 14 45.95 12771 0 0 0 0 0 0 Run 15 45.95 13055 0 0 0 0 0 0 Run 16 45.95 12798 0 0 0 0 0 0 Run 17 45.95 12536 0 0 0 0 0 0 Run 18 45.95 12377 0 0 0 0 0 0 Run 19 45.95 12128 1 0 1 0 1 0 Run 20 45.95 12015 1 0 1 0 1 0 Run 21 45.95 12152 0 0 0 0 0 0 Run 22 45.95 12573 0 0 0 0 0 0 Run 23 45.95 12732 0 1 0 1 0 1 Run 24 45.95 12673 0 1 0 1 0 1 Parametric Table: Table 1 P1,HDS P2,HDS P1,HDS,SAT P2,HDS,SAT P1,HDS,SUN P2,HDS,SUN PODUSAGE,UPHES,LDS [WD] [WD] [SAT] [SAT] [SUN] [SUN] [kWh] Run 1 0 1 0 1 0 1 0 Run 2 0 1 0 1 0 1 0 Run 3 0 1 0 1 0 1 0 File:F:\UPHES SYSTEM EES\UPHES VERIFICATION MODEL REV D PEAK CAPEX.EES 8/24/2017 7:22:32 PM Page 5 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa Parametric Table: Table 1 P1,HDS P2,HDS P1,HDS,SAT P2,HDS,SAT P1,HDS,SUN P2,HDS,SUN PODUSAGE,UPHES,LDS [WD] [WD] [SAT] [SAT] [SUN] [SUN] [kWh] Run 4 0 1 0 1 0 1 0 Run 5 0 1 0 1 0 1 0 Run 6 0 1 0 1 0 1 0 Run 7 1 0 1 0 1 0 0 Run 8 1 0 1 0 1 0 6404 Run 9 1 0 1 0 1 0 6404 Run 10 0 0 0 0 0 0 6404 Run 11 0 0 0 0 0 0 0 Run 12 0 0 0 0 0 0 0 Run 13 0 0 0 0 0 0 0 Run 14 0 0 0 0 0 0 0 Run 15 0 0 0 0 0 0 0 Run 16 0 0 0 0 0 0 0 Run 17 0 0 0 0 0 0 0 Run 18 1 0 1 0 1 0 0 Run 19 1 0 1 0 1 0 6404 Run 20 0 0 0 0 0 0 6404 Run 21 0 0 0 0 0 0 0 Run 22 0 0 0 0 0 0 0 Run 23 0 1 0 1 0 1 0 Run 24 0 1 0 1 0 1 0 Parametric Table: Table 1 PODUSAGE,PUMPS,LDS PODUSAGE,TOTAL,LDS ZARPOD,USAGE,WEEKDAY,LDS ZARPOD,USAGE,WD,LDS,UPHES [kWh] [kWh] [ZAR] [ZAR] Run 1 6291 19350 5196 7700 Run 2 6291 20496 5652 8155 Run 3 6291 21740 6147 8650 Run 4 6291 21700 6131 8634 Run 5 6291 21299 5972 8475 Run 6 6291 21199 5932 8435 Run 7 0 14339 8993 8993 Run 8 0 6430 11694 5859 Run 9 0 5416 10770 4935 Run 10 0 4614 10040 4205 Run 11 0 10935 6858 6858 Run 12 0 11229 7043 7043 Run 13 0 11717 7349 7349 Run 14 0 12771 8010 8010 Run 15 0 13055 8188 8188 Run 16 0 12798 8027 8027 Run 17 0 12536 7863 7863 Run 18 0 12377 7763 7763 Run 19 0 5724 11051 5216 Run 20 0 5611 10948 5113 Run 21 0 12152 7622 7622 Run 22 0 12573 7886 7886 Run 23 6291 19023 5066 7569 Run 24 6291 18964 5043 7546 Parametric Table: Table 1 PODUSAGE,PUMPS,HDS PODUSAGE,UPHES,HDS PODUSAGE,TOTAL,HDS ZARPOD,USAGE,WEEKDAY,HDS [kWh] [kWh] [kWh] [ZAR] File:F:\UPHES SYSTEM EES\UPHES VERIFICATION MODEL REV D PEAK CAPEX.EES 8/24/2017 7:22:32 PM Page 6 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa Parametric Table: Table 1 PODUSAGE,PUMPS,HDS PODUSAGE,UPHES,HDS PODUSAGE,TOTAL,HDS ZARPOD,USAGE,WEEKDAY,HDS [kWh] [kWh] [kWh] [ZAR] Run 1 6291 0 19350 6001 Run 2 6291 0 20496 6527 Run 3 6291 0 21740 7099 Run 4 6291 0 21700 7080 Run 5 6291 0 21299 6896 Run 6 6291 0 21199 6850 Run 7 0 6404 7935 40053 Run 8 0 6404 6430 35849 Run 9 0 6404 5416 33017 Run 10 0 0 11018 9323 Run 11 0 0 10935 9253 Run 12 0 0 11229 9502 Run 13 0 0 11717 9915 Run 14 0 0 12771 10807 Run 15 0 0 13055 11047 Run 16 0 0 12798 10830 Run 17 0 0 12536 10608 Run 18 0 6404 5973 34573 Run 19 0 6404 5724 33877 Run 20 0 0 12015 10167 Run 21 0 0 12152 10283 Run 22 0 0 12573 10639 Run 23 6291 0 19023 5850 Run 24 6291 0 18964 5823 Parametric Table: Table 1 ZARPOD,USAGE,WD,HDS,UPHES PODUSAGE,UPHES,LDS,SAT PODUSAGE,PUMPS,LDS,SAT [ZAR] [kWh] [kWh] Run 1 8892 0 6291 Run 2 9418 0 6291 Run 3 9990 0 6291 Run 4 9971 0 6291 Run 5 9787 0 6291 Run 6 9741 0 6291 Run 7 22165 0 0 Run 8 17962 6404 0 Run 9 15129 6404 0 Run 10 9323 6404 0 Run 11 9253 0 0 Run 12 9502 0 0 Run 13 9915 0 0 Run 14 10807 0 0 Run 15 11047 0 0 Run 16 10830 0 0 Run 17 10608 0 0 Run 18 16685 0 0 Run 19 15990 6404 0 Run 20 10167 6404 0 Run 21 10283 0 0 Run 22 10639 0 0 Run 23 8741 0 6291 Run 24 8714 0 6291 Parametric Table: Table 1 File:F:\UPHES SYSTEM EES\UPHES VERIFICATION MODEL REV D PEAK CAPEX.EES 8/24/2017 7:22:32 PM Page 7 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa PODUSAGE,TOTAL,LDS,SAT ZARPOD,USAGE,SAT,LDS ZARPOD,USAGE,SAT,LDS,UPHES PODUSAGE,UPHES,HDS,SAT [kWh] [ZAR] [ZAR] [kWh] Run 1 19350 5196 7700 0 Run 2 20496 5652 8155 0 Run 3 21740 6147 8650 0 Run 4 21700 6131 8634 0 Run 5 21299 5972 8475 0 Run 6 21199 5932 8435 0 Run 7 14339 5705 5705 6404 Run 8 6430 8049 4033 6404 Run 9 5416 7414 3397 6404 Run 10 4614 6910 2894 0 Run 11 10935 6858 6858 0 Run 12 11229 7043 7043 0 Run 13 11717 4662 4662 0 Run 14 12771 5082 5082 0 Run 15 13055 5195 5195 0 Run 16 12798 5092 5092 0 Run 17 12536 4988 4988 0 Run 18 12377 4925 4925 6404 Run 19 5724 7607 3590 6404 Run 20 5611 7536 3519 0 Run 21 12152 4835 4835 0 Run 22 12573 5003 5003 0 Run 23 19023 5066 7569 0 Run 24 18964 5043 7546 0 Parametric Table: Table 1 PODUSAGE,PUMPS,HDS,SAT PODUSAGE,TOTAL,HDS,SAT ZARPOD,USAGE,SAT,HDS [kWh] [kWh] [ZAR] Run 1 6291 19350 6001 Run 2 6291 20496 6527 Run 3 6291 21740 7099 Run 4 6291 21700 7080 Run 5 6291 21299 6896 Run 6 6291 21199 6850 Run 7 0 7935 6589 Run 8 0 6430 10860 Run 9 0 5416 10002 Run 10 0 11018 9323 Run 11 0 10935 9253 Run 12 0 11229 9502 Run 13 0 11717 5384 Run 14 0 12771 5868 Run 15 0 13055 5999 Run 16 0 12798 5881 Run 17 0 12536 5760 Run 18 0 5973 5687 Run 19 0 5724 10263 Run 20 0 12015 10167 Run 21 0 12152 5584 Run 22 0 12573 5777 Run 23 6291 19023 5850 Run 24 6291 18964 5823 Parametric Table: Table 1 ZARPOD,USAGE,SAT,HDS,UPHES PODUSAGE,UPHES,LDS,SUN PODUSAGE,PUMPS,LDS,SUN File:F:\UPHES SYSTEM EES\UPHES VERIFICATION MODEL REV D PEAK CAPEX.EES 8/24/2017 7:22:33 PM Page 8 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa [ZAR] [kWh] [kWh] Run 1 8892 0 6291 Run 2 9418 0 6291 Run 3 9990 0 6291 Run 4 9971 0 6291 Run 5 9787 0 6291 Run 6 9741 0 6291 Run 7 3646 0 0 Run 8 5441 6404 0 Run 9 4583 6404 0 Run 10 9323 6404 0 Run 11 9253 0 0 Run 12 9502 0 0 Run 13 5384 0 0 Run 14 5868 0 0 Run 15 5999 0 0 Run 16 5881 0 0 Run 17 5760 0 0 Run 18 2745 0 0 Run 19 4844 6404 0 Run 20 10167 6404 0 Run 21 5584 0 0 Run 22 5777 0 0 Run 23 8741 0 6291 Run 24 8714 0 6291 Parametric Table: Table 1 PODUSAGE,TOTAL,LDS,SUN ZARPOD,USAGE,SUN,LDS ZARPOD,USAGE,SUN,LDS,UPHES [kWh] [ZAR] [ZAR] Run 1 19350 5196 7700 Run 2 20496 5652 8155 Run 3 21740 6147 8650 Run 4 21700 6131 8634 Run 5 21299 5972 8475 Run 6 21199 5932 8435 Run 7 14339 5705 5705 Run 8 6430 5107 2559 Run 9 5416 4703 2155 Run 10 4614 4384 1836 Run 11 10935 4351 4351 Run 12 11229 4468 4468 Run 13 11717 4662 4662 Run 14 12771 5082 5082 Run 15 13055 5195 5195 Run 16 12798 5092 5092 Run 17 12536 4988 4988 Run 18 12377 4925 4925 Run 19 5724 4826 2278 Run 20 5611 4781 2233 Run 21 12152 4835 4835 Run 22 12573 5003 5003 Run 23 19023 5066 7569 Run 24 18964 5043 7546 Parametric Table: Table 1 PODUSAGE,UPHES,HDS,SUN PODUSAGE,PUMPS,HDS,SUN PODUSAGE,TOTAL,HDS,SUN ZARPOD,USAGE,SUN,HDS [kWh] [kWh] [kWh] [ZAR] File:F:\UPHES SYSTEM EES\UPHES VERIFICATION MODEL REV D PEAK CAPEX.EES 8/24/2017 7:22:33 PM Page 9 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa Run 1 0 6291 19350 6001 Run 2 0 6291 20496 6527 Run 3 0 6291 21740 7099 Run 4 0 6291 21700 7080 Run 5 0 6291 21299 6896 Run 6 0 6291 21199 6850 Run 7 6404 0 7935 6589 Run 8 6404 0 6430 5897 Run 9 6404 0 5416 5431 Run 10 0 0 11018 5063 Run 11 0 0 10935 5025 Run 12 0 0 11229 5160 Run 13 0 0 11717 5384 Run 14 0 0 12771 5868 Run 15 0 0 13055 5999 Run 16 0 0 12798 5881 Run 17 0 0 12536 5760 Run 18 6404 0 5973 5687 Run 19 6404 0 5724 5573 Run 20 0 0 12015 5521 Run 21 0 0 12152 5584 Run 22 0 0 12573 5777 Run 23 0 6291 19023 5850 Run 24 0 6291 18964 5823 Parametric Table: Table 1 ZARPOD,USAGE,SUN,HDS,UPHES [ZAR] Run 1 8892 Run 2 9418 Run 3 9990 Run 4 9971 Run 5 9787 Run 6 9741 Run 7 3646 Run 8 2955 Run 9 2489 Run 10 5063 Run 11 5025 Run 12 5160 Run 13 5384 Run 14 5868 Run 15 5999 Run 16 5881 Run 17 5760 Run 18 2745 Run 19 2630 Run 20 5521 Run 21 5584 Run 22 5777 Run 23 8741 Run 24 8714 File:F:\UPHES SYSTEM EES\UPHES VERIFICATION MODEL REV D PEAK CAPEX.EES 8/24/2017 7:22:33 PM Page 10 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa Parametric Table: Table 2 VTURBINE RDISCHARGE,HEAD PACTUAL [l/s] [-] [kW] Run 1 200 0.1028 3466 Run 2 212.5 0.1093 3682 Run 3 225 0.1157 3899 Run 4 237.5 0.1221 4116 Run 5 250 0.1285 4332 Run 6 262.5 0.135 4549 Run 7 275 0.1414 4765 Run 8 287.5 0.1478 4982 Run 9 300 0.1542 5199 Run 10 312.5 0.1607 5415 Run 11 325 0.1671 5632 Run 12 337.5 0.1735 5848 Run 13 350 0.1799 6065 Run 14 362.5 0.1864 6282 Run 15 375 0.1928 6498 Run 16 387.5 0.1992 6715 Run 17 400 0.2057 6931 Run 18 412.5 0.2121 7148 Run 19 425 0.2185 7365 Run 20 437.5 0.2249 7581 Run 21 450 0.2314 7798 Run 22 462.5 0.2378 8014 Run 23 475 0.2442 8231 Run 24 487.5 0.2506 8448 Run 25 500 0.2571 8664 0 5 10 15 20 25 0 5000 10000 15000 20000 25000 5000 10000 15000 20000 25000 TIMEINTERVAL [hrs] PO D P O W ER C O N SU M ED [k W h] EL EC TR IC IT Y C O ST [ ZA R ] File:F:\UPHES SYSTEM EES\UPHES VERIFICATION MODEL REV D PEAK CAPEX.EES 8/24/2017 7:22:33 PM Page 11 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa 0 5 10 15 20 25 0 5000 10000 15000 20000 25000 0 10000 20000 30000 40000 50000 60000 70000 TIMEINTERVAL [hrs] PO D P O W ER C O N SU M ED [k W h] EL EC TR IC IT Y C O ST [Z A R ] 0 5 10 15 20 25 0 5000 10000 15000 20000 25000 4000 6000 8000 10000 12000 14000 16000 TIMEINTERVAL [hrs] PO D P O W ER C O N SU M ED [k W h] EL EC TR IC IT Y C O ST [Z A R ] File:F:\UPHES SYSTEM EES\UPHES VERIFICATION MODEL REV D PEAK CAPEX.EES 8/24/2017 7:22:33 PM Page 12 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa 0 5 10 15 20 25 5000 10000 15000 20000 25000 5000 10000 15000 20000 25000 TIMEINTERVAL [hrs] PO D P O W ER C O N SU M ED [k W h] EL EC TR IC IT Y C O ST [Z A R ] 0 5 10 15 20 25 0 5000 10000 15000 20000 25000 2000 4000 6000 8000 10000 12000 14000 16000 TIMEINTERVAL [hrs] PO D P O W ER C O N SU M ED [k W h] EL EC TR IC IT Y C O ST [Z A R ] File:F:\UPHES SYSTEM EES\UPHES VERIFICATION MODEL REV D PEAK CAPEX.EES 8/24/2017 7:22:33 PM Page 13 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa 0 5 10 15 20 25 5000 10000 15000 20000 25000 4000 6000 8000 10000 12000 14000 16000 18000 TIMEINTERVAL [hrs] PO D P O W ER C O N SU M ED [k W h} EL EC TR IC IT Y C O ST [Z A R ] 200 300 400 500 3000 4000 5000 6000 7000 8000 9000 0.1 0.15 0.2 0.25 0.3 VTURBINE [l/s] P A C TU A L [k W ] R D IS C H A R G E, H EA D [ -] File:UPHES VERIFICATION MODEL REV D PEAK & STANDARD CAPEX.EES 8/24/2017 7:31:12 PM Page 1 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa {PROGRAM OPERATIONAL STEPS (1) INSERT ALL INPUT PARAMETERS, SOLVE PRINCIPAL OUTPUT PARAMETERS (2) REMOVE COMMENT BRACKETS FROM LOAD AND ELECTRICITY COST CALCULATIONS, SOLVE PARAMETRIC TABLE (3) REPLACE THE COMMENT BRACKETS TO THE LOAD AND ELECTRICITY COST CALCULATIONS AFTER SOLVING THE PRAMETRIC TABLE, REMOVE THE COMMENT BRACKETS FROM THE ELECTRICITY SAVINGS SECTION, CLICK SOLVE} {INPUT PARAMETERS} rho_water = 998 [kg/m3] g = 9.81 [m/s2] S_TURBINE = 1 [-] {NUMBER TURBINES} V_TURBINE = 369.55 [l/s] R_DISCHARGE_HEAD = V_TURBINE/H_EFFECTIVE eta_TURBINE = 0.91 V_PUMP = 55.56 [l/s] eta_PUMP = 0.89 f = 0.0174 {PIPE FRICTION FACTOR ASSUMED} D_i_PIPE = 284.18 [mm] {OPERATIONAL INPUT PARAMETERS} HRS_PUMP = 8 [hrs] HRS_TURBINE = 16 [hrs] {ELEVATIONS} H_1_IPC_9 = 150 [m] H_2_MID_SHAFT_9 = 1050 [m] H_3_24LVL_9 = 2095 [m] {SYSTEM OPERATIONAL FORMULAS} P_ACTUAL = rho_water*g*(H_EFFECTIVE)*(V_TURBINE/1000)*eta_TURBINE/1000 H_EFFECTIVE = (H_3_24LVL_9-H_1_IPC_9) P_TURBINE_MWh = (P_ACTUAL* HRS_TURBINE)/1000 VOL_LOWER_RESERVOIR = V_TURBINE*(HRS_TURBINE*60*60)/1000000 S_PUMPS = (VOL_LOWER_RESERVOIR*1000000)/(V_PUMP*60*60)/HRS_PUMP VOL_UPPER_RESERVOIR = (S_PUMPS_MANUAL_INPUT*V_PUMP*HRS_PUMP*60*60)/1000000 P_PUMPS_24LVL_9 = ((rho_water*g*(H_3_24LVL_9-H_2_MID_SHAFT_9+H_3_FRICTION)*(V_PUMP/1000))/ eta_PUMP)*S_PUMPS_MANUAL_INPUT/1000000 P_PUMPS_MID_SHAFT_9 = ((rho_water*g*(H_2_MID_SHAFT_9-H_1_IPC_9+H_2_FRICTION)*(V_PUMP/1000))/ eta_PUMP)*S_PUMPS_MANUAL_INPUT/1000000 P_PUMPS_MWh = (P_PUMPS_24LVL_9+P_PUMPS_MID_SHAFT_9)*HRS_PUMP H_3_FRICTION = (f*(H_3_24LVL_9-H_2_MID_SHAFT_9 +50)*VEL_UP^2)/(2*g*(D_i_PIPE/1000)) H_2_FRICTION = (f*(H_2_MID_SHAFT_9-H_1_IPC_9 +50)*VEL_UP^2)/(2*g*(D_i_PIPE/1000)) VEL_UP = 4.22 {((V_PUMP/1000)*S_PUMPS_MANUAL_INPUT)/(pi*(D_i_PIPE/1000))} {MANUAL INPUT (1)} S_PUMPS_MANUAL_INPUT = 14 {MEGAFLEX TARIFF STRUCTURE - INPUT 2016/2017} {TIME_INTERVAL = 1 [HRS]} {POD_USAGE = 20000 [Wh]} {T_WEEKDAY_LDS = 68.19 [c/kWh] T_SATURDAY_LDS = 68.19 [c/kWh] T_SUNDAY_LDS = 68.19 [c/kWh] T_WEEKDAY_HDS = 68.19 [c/kWh] T_SATURDAY_HDS = 68.19 [c/kWh] T_SUNDAY_HDS = 68.19 [c/kWh]} T_LDS_OFF_PEAK = 68.19 [c/kWh] T_LDS_STANDARD = 107.49 [c/kWh] T_LDS_PEAK = 156.16 [c/kWh] File:UPHES VERIFICATION MODEL REV D PEAK & STANDARD CAPEX.EES 8/24/2017 7:31:12 PM Page 2 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa T_HDS_OFF_PEAK = 78.75 [c/kWh] T_HDS_STANDARD = 145.02 [c/kWh] T_HDS_PEAK = 478.72 [c/kWh] D_WEEKDAY_OFF_PEAK = 8 D_WEEKDAY_STANDARD = 11 D_WEEKDAY_PEAK = 5 D_LDS_WEEKDAY_TARIFF = 186 D_LDS_SATURDAY_TARIFF = 46 D_LDS_SUNDAY_TARIFF = 41 D_HDS_WEEKDAY_TARIFF = 64 D_HDS_SATURDAY_TARIFF = 14 D_HDS_SUNDAY_TARIFF = 14 ESKOM = 1.08^0 {ASSUMED MEGAFLEX TARIFF INCREASE} {LOAD AND ELECTRICITY COST CALCULATIONS} {WEEKDAY} {POD_USAGE_UPHES_LDS = (P_ACTUAL)*P_1_LDS POD_USAGE_PUMPS_LDS = (P_PUMPS_24LVL_9*1000+P_PUMPS_MID_SHAFT_9*1000)*P_2_LDS POD_USAGE_TOTAL_LDS = POD_USAGE - POD_USAGE_UPHES_LDS + POD_USAGE_PUMPS_LDS ZAR_POD_USAGE_WEEKDAY_LDS = POD_USAGE*T_WEEKDAY_LDS/100*ESKOM ZAR_POD_USAGE_WD_LDS_UPHES = POD_USAGE_TOTAL_LDS*T_WEEKDAY_LDS/100*ESKOM POD_USAGE_UPHES_HDS = (P_ACTUAL)*P_1_HDS POD_USAGE_PUMPS_HDS = (P_PUMPS_24LVL_9*1000+P_PUMPS_MID_SHAFT_9*1000)*P_2_HDS POD_USAGE_TOTAL_HDS = POD_USAGE - POD_USAGE_UPHES_HDS + POD_USAGE_PUMPS_HDS ZAR_POD_USAGE_WEEKDAY_HDS = POD_USAGE*T_WEEKDAY_HDS/100*ESKOM ZAR_POD_USAGE_WD_HDS_UPHES = POD_USAGE_TOTAL_HDS*T_WEEKDAY_HDS/100*ESKOM {SATURDAY} POD_USAGE_UPHES_LDS_SAT = (P_ACTUAL)*P_1_LDS_SAT POD_USAGE_PUMPS_LDS_SAT = (P_PUMPS_24LVL_9*1000+P_PUMPS_MID_SHAFT_9*1000)*P_2_LDS_SAT POD_USAGE_TOTAL_LDS_SAT = POD_USAGE - POD_USAGE_UPHES_LDS_SAT + POD_USA GE_PUMPS_LDS_SAT ZAR_POD_USAGE_SAT_LDS = POD_USAGE*T_SATURDAY_LDS/100*ESKOM ZAR_POD_USAGE_SAT_LDS_UPHES = POD_USAGE_TOTAL_LDS_SAT*T_SATURDAY_LDS/100*ESKOM POD_USAGE_UPHES_HDS_SAT = (P_ACTUAL)*P_1_HDS_SAT POD_USAGE_PUMPS_HDS_SAT = (P_PUMPS_24LVL_9*1000+P_PUMPS_MID_SHAFT_9*1000)*P_2_HDS_SAT POD_USAGE_TOTAL_HDS_SAT = POD_USAGE - POD_USAGE_UPHES_HDS_SAT + POD_US AGE_PUMPS_HDS_SAT ZAR_POD_USAGE_SAT_HDS = POD_USAGE*T_SATURDAY_HDS/100*ESKOM ZAR_POD_USAGE_SAT_HDS_UPHES = POD_USAGE_TOTAL_HDS_SAT*T_SATURDAY_HDS/100*ESKOM {SUNDAY} POD_USAGE_UPHES_LDS_SUN = (P_ACTUAL)*P_1_LDS_SUN POD_USAGE_PUMPS_LDS_SUN = (P_PUMPS_24LVL_9*1000+P_PUMPS_MID_SHAFT_9*1000)*P_2_LDS_SUN POD_USAGE_TOTAL_LDS_SUN = POD_USAGE - POD_USAGE_UPHES_LDS_SUN + POD_US AGE_PUMPS_LDS_SUN ZAR_POD_USAGE_SUN_LDS = POD_USAGE*T_SUNDAY_LDS/100*ESKOM ZAR_POD_USAGE_SUN_LDS_UPHES = POD_USAGE_TOTAL_LDS_SUN*T_SUNDAY_LDS/100*ESKOM POD_USAGE_UPHES_HDS_SUN = (P_ACTUAL)*P_1_HDS_SUN POD_USAGE_PUMPS_HDS_SUN = (P_PUMPS_24LVL_9*1000+P_PUMPS_MID_SHAFT_9*1000)*P_2_HDS_SUN POD_USAGE_TOTAL_HDS_SUN = POD_USAGE - POD_USAGE_UPHES_HDS_SUN + POD_US AGE_PUMPS_HDS_SUN ZAR_POD_USAGE_SUN_HDS = POD_USAGE*T_SUNDAY_HDS/100*ESKOM ZAR_POD_USAGE_SUN_HDS_UPHES = POD_USAGE_TOTAL_HDS_SUN*T_SUNDAY_HDS/100*ESKOM} {ELECTRICITY SAVINGS} POD_USAGE_PA = (sumparametric('Table 1', 'POD_USAGE')*D_LDS_WEEKDAY_TARIFF+sumparametric('Table 1', ' File:UPHES VERIFICATION MODEL REV D PEAK & STANDARD CAPEX.EES 8/24/2017 7:31:12 PM Page 3 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa POD_USAGE')*D_HDS_WEEKDAY_TARIFF+sumparametric('Table 1', 'POD_USAGE')*D_LDS_SATURDAY_TARIFF+ sumparametric('Table 1', 'POD_USAGE')*D_HDS_SATURDAY_TARIFF+sumparametric('Table 1', 'POD_USAGE')* D_LDS_SUNDAY_TARIFF+sumparametric('Table 1', 'POD_USAGE')*D_HDS_SUNDAY_TARIFF)/1000000 ZAR_POD_USAGE_PA = (sumparametric('Table 1', 'ZAR_POD_USAGE_WEEKDAY_LDS')*D_LDS _WEEKDAY_TARIFF+sumparametric('Table 1', 'ZAR_POD_USAGE_WEEKDAY_HDS')*D_HDS_WEEKDAY_TARIFF+ sumparametric('Table 1', 'ZAR_POD_USAGE_SAT_LDS')*D_LDS_SATURDAY_TARIFF + sumparametric('Table 1', ' ZAR_POD_USAGE_SAT_HDS')*D_HDS_SATURDAY_TARIFF+SUMPARAMETRIC('Table 1', 'ZAR _POD_USAGE_SUN_LDS')*D_LDS_SUNDAY_TARIFF+SUMPARAMETRIC('Table 1', 'ZAR_POD_USAGE_SUN_HDS') *D_HDS_SUNDAY_TARIFF)/1000000 POD_USAGE_PA_UPHES_LDS= (sumparametric('Table 1', 'POD_USAGE_TOTAL_LDS')*D_LDS_WEEKDAY_TARIFF + sumparametric('Table 1', 'POD_USAGE_TOTAL_LDS_SAT')*D_LDS_SATURDAY_TARIFF+ sumparametric('Table 1', ' POD_USAGE_TOTAL_LDS_SUN')*D_LDS_SUNDAY_TARIFF + sumparametric('Table 1', 'POD_USAGE_TOTAL_HDS') *D_HDS_WEEKDAY_TARIFF+sumparametric('Table 1', 'POD_USAGE_TOTAL_HDS_SAT')*D_HDS _SATURDAY_TARIFF+sumparametric('Table 1', 'POD_USAGE_TOTAL_HDS_SUN')*D_HDS_SUNDAY_TARIFF)/ 1000000 ZAR_POD_USAGE_PA_UPHES = (sumparametric('Table 1', 'ZAR_POD_USAGE_WD_LDS_UPHES')* D_LDS_WEEKDAY_TARIFF+sumparametric('Table 1', 'ZAR_POD_USAGE_WD_HDS_UPHES')*D _HDS_WEEKDAY_TARIFF+sumparametric('Table 1', 'ZAR_POD_USAGE_SAT_LDS_UPHES')*D_ LDS_SATURDAY_TARIFF + sumparametric('Table 1', 'ZAR_POD_USAGE_SAT_HDS_UPHES')*D_ HDS_SATURDAY_TARIFF+SUMPARAMETRIC('Table 1', 'ZAR_POD_USAGE_SUN_LDS_UPHES')* D_LDS_SUNDAY_TARIFF+SUMPARAMETRIC('Table 1', 'ZAR_POD_USAGE_SUN_HDS_UPHES')* D_HDS_SUNDAY_TARIFF)/1000000 SAVINGS = ZAR_POD_USAGE_PA - ZAR_POD_USAGE_PA_UPHES {ESTIMATED CAPEX - CONSIDERATION GIVEN TO EXISTING INFRASTRUCTURE} PACKAGE_1 = 0 {WINDING PLANT} PACKAGE_2 = 0 {HEADGEAR} PACKAGE_3 = 0 {SHAFT DEVELOPMENT} PACKAGE_4_A = (10097.30*(H_EFFECTIVE/3/9))+(12337.19*(H_EFFECTIVE/3/9))+(13864.49*(H_EFFECTIVE/3/9)) {SHAFT PIPE COLUMN - TURBINE FEED} PACKAGE_4_B = PACKAGE_4_A*0.05+PACKAGE_4_A*0.1+PACKAGE_4_A*0.4+(1039775.30*(H_3_24LVL_9/2300))+ (216585.85*(H_3_24LVL_9/2300)) {SHAFT INFRASTRUCTURE} PACKAGE_4 = PACKAGE_4_A + PACKAGE_4_B PACKAGE_5 = 0 {STATION DEVELOPMENT} PACKAGE_6_UPPER_RES = 2800*(VOL_LOWER_RESERVOIR*1.15*1000)+50000*((VOL_LOWER_RESERVOIR* 1.15)/3) PACKAGE_6_MID_RES = 2800*(VOL_LOWER_RESERVOIR*0.15*1000)+50000*1 PACKAGE_6_LOWER_RES = 50000*(VOL_LOWER_RESERVOIR/3) {ONLY DAM WALLS} PACKAGE_6 = PACKAGE_6_UPPER_RES + PACKAGE_6_LOWER_RES + PACKAGE_6_MID_RES {RESERVOIRS} PACKAGE_7 = ((3134883.23+275129.55+173611.63)*(S_PUMPS_MANUAL_INPUT*2-8))+(305417.38+2800*8*( S_PUMPS_MANUAL_INPUT-4))+368000*2 {PUMP CHAMBERS - ASSUME SUPPLY OF ALL PUMPS} PACKAGE_8 = (4630500+1100518.20+694446.51) {SUPPLY COST OF ONE TURBINE, SWITCHGEAR AND GENERATOR} TOTAL_CAPEX = (PACKAGE_1 + PACKAGE_2 + PACKAGE_3 + PACKAGE_4 + PACKAGE_5 + PACKAGE_6 + PACKAGE_7 + PACKAGE_8)/1000000 water = 998 [kg/m3] g = 9.81 [m/s2] STURBINE = 1 [-] VTURBINE = 369.55 [l/s] RDISCHARGE,HEAD = VTURBINE HEFFECTIVE File:UPHES VERIFICATION MODEL REV D PEAK & STANDARD CAPEX.EES 8/24/2017 7:31:13 PM Page 4 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa TURBINE = 0.91 VPUMP = 55.56 [l/s] PUMP = 0.89 f = 0.0174 Di,PIPE = 284.18 [mm] HRSPUMP = 8 [hrs] HRSTURBINE = 16 [hrs] H1,IPC,9 = 150 [m] H2,MID,SHAFT,9 = 1050 [m] H3,24LVL,9 = 2095 [m] PACTUAL = water · g · HEFFECTIVE · VTURBINE 1000 · TURBINE 1000 HEFFECTIVE = H3,24LVL,9 – H1,IPC,9 PTURBINE,MWh = PACTUAL · HRSTURBINE 1000 VOLLOWER,RESERVOIR = VTURBINE · HRSTURBINE · 60 · 60 1000000 SPUMPS = VOLLOWER,RESERVOIR · 1000000 VPUMP · 60 · 60 · HRSPUMP VOLUPPER,RESERVOIR = SPUMPS,MANUAL,INPUT · VPUMP · HRSPUMP · 60 · 60 1000000 PPUMPS,24LVL,9 = water · g · H3,24LVL,9 – H2,MID,SHAFT,9 + H3,FRICTION · VPUMP 1000 PUMP · SPUMPS,MANUAL,INPUT 1000000 PPUMPS,MID,SHAFT,9 = water · g · H2,MID,SHAFT,9 – H1,IPC,9 + H2,FRICTION · VPUMP 1000 PUMP · SPUMPS,MANUAL,INPUT 1000000 PPUMPS,MWh = PPUMPS,24LVL,9 + PPUMPS,MID,SHAFT,9 · HRSPUMP H3,FRICTION = f · H3,24LVL,9 – H2,MID,SHAFT,9 + 50 · VELUP 2 2 · g · Di,PIPE 1000 H2,FRICTION = f · H2,MID,SHAFT,9 – H1,IPC,9 + 50 · VELUP 2 2 · g · Di,PIPE 1000 VELUP = 4.22 SPUMPS,MANUAL,INPUT = 14 File:UPHES VERIFICATION MODEL REV D PEAK & STANDARD CAPEX.EES 8/24/2017 7:31:13 PM Page 5 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa TLDS,OFF,PEAK = 68.19 [c/kWh] TLDS,STANDARD = 107.49 [c/kWh] TLDS,PEAK = 156.16 [c/kWh] THDS,OFF,PEAK = 78.75 [c/kWh] THDS,STANDARD = 145.02 [c/kWh] THDS,PEAK = 478.72 [c/kWh] DWEEKDAY,OFF,PEAK = 8 DWEEKDAY,STANDARD = 11 DWEEKDAY,PEAK = 5 DLDS,WEEKDAY,TARIFF = 186 DLDS,SATURDAY,TARIFF = 46 DLDS,SUNDAY,TARIFF = 41 DHDS,WEEKDAY,TARIFF = 64 DHDS,SATURDAY,TARIFF = 14 DHDS,SUNDAY,TARIFF = 14 ESKOM = 1.08 0 PODUSAGE,PA = SumParametric 'Table 1' , 'PODUSAGE' · DLDS,WEEKDAY,TARIFF + SumParametric 'Table 1' , 'PODUSAGE' 1000000 ZARPOD,USAGE,PA = SumParametric 'Table 1' , 'ZARPOD,USAGE,WEEKDAY,LDS' · DLDS,WEEKDAY,TARIFF + SumParametric 1000000 PODUSAGE,PA,UPHES,LDS = SumParametric 'Table 1' , 'PODUSAGE,TOTAL,LDS' · DLDS,WEEKDAY,TARIFF + SumParametric 'Ta 1000000 ZARPOD,USAGE,PA,UPHES = SumParametric 'Table 1' , 'ZARPOD,USAGE,WD,LDS,UPHES' · DLDS,WEEKDAY,TARIFF + SumParam 1000000 SAVINGS = ZARPOD,USAGE,PA – ZARPOD,USAGE,PA,UPHES PACKAGE1 = 0 PACKAGE2 = 0 PACKAGE3 = 0 File:UPHES VERIFICATION MODEL REV D PEAK & STANDARD CAPEX.EES 8/24/2017 7:31:13 PM Page 6 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa PACKAGE4,A = 10097.3 · HEFFECTIVE 3 · 9 + 12337.19 · HEFFECTIVE 3 · 9 + 13864.49 · HEFFECTIVE 3 · 9 PACKAGE4,B = PACKAGE4,A · 0.05 + PACKAGE4,A · 0.1 + PACKAGE4,A · 0.4 + 1.03978 x 10 6 · H3,24LVL,9 2300 + 216585.85 · H3,24LVL,9 2300 PACKAGE4 = PACKAGE4,A + PACKAGE4,B PACKAGE5 = 0 PACKAGE6,UPPER,RES = 2800 · VOLLOWER,RESERVOIR · 1.15 · 1000 + 50000 · VOLLOWER,RESERVOIR · 1.15 3 PACKAGE6,MID,RES = 2800 · VOLLOWER,RESERVOIR · 0.15 · 1000 + 50000 · 1 PACKAGE6,LOWER,RES = 50000 · VOLLOWER,RESERVOIR 3 PACKAGE6 = PACKAGE6,UPPER,RES + PACKAGE6,LOWER,RES + PACKAGE6,MID,RES PACKAGE7 = 3.13488 x 10 6 + 275129.55 + 173611.63 · SPUMPS,MANUAL,INPUT · 2 – 8 + 305417.38 + 2800 · 8 · SPUMPS,MANUAL,INPUT – 4 + 368000 · 2 PACKAGE8 = 4.6305 x 10 6 + 1.10052 x 10 6 + 694446.51 TOTALCAPEX = PACKAGE1 + PACKAGE2 + PACKAGE3 + PACKAGE4 + PACKAGE5 + PACKAGE6 + PACKAGE7 + PACKAG 1000000 SOLUTION Unit Settings: SI C kPa kJ mass deg DHDS,SATURDAY,TARIFF = 14 [-] DHDS,SUNDAY,TARIFF = 14 [-] DHDS,WEEKDAY,TARIFF = 64 [-] Di,PIPE = 284.2 [mm] DLDS,SATURDAY,TARIFF = 46 [-] DLDS,SUNDAY,TARIFF = 41 [-] DLDS,WEEKDAY,TARIFF = 186 [-] DWEEKDAY,OFF,PEAK = 8 [-] DWEEKDAY,PEAK = 5 [-] DWEEKDAY,STANDARD = 11 [-] ESKOM = 1 PUMP = 0.89 [-] TURBINE = 0.91 [-] f = 0.0174 [-] g = 9.81 [m/s2] HRSPUMP = 8 [hrs] HRSTURBINE = 16 [hrs] H1,IPC,9 = 150 [m] H2,FRICTION = 52.8 [m] H2,MID,SHAFT,9 = 1050 [m] H3,24LVL,9 = 2095 [m] File:UPHES VERIFICATION MODEL REV D PEAK & STANDARD CAPEX.EES 8/24/2017 7:31:14 PM Page 7 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa H3,FRICTION = 60.85 HEFFECTIVE = 1945 [m] PACKAGE1 = 0 PACKAGE2 = 0 PACKAGE3 = 0 PACKAGE4 = 5.197E+06 PACKAGE4,A = 2.615E+06 PACKAGE4,B = 2.583E+06 PACKAGE5 = 0 PACKAGE6 = 7.829E+07 PACKAGE6,LOWER,RES = 354768 PACKAGE6,MID,RES = 8.990E+06 PACKAGE6,UPPER,RES = 6.895E+07 PACKAGE7 = 7.294E+07 PACKAGE8 = 6.425E+06 PODUSAGE,PA = 113.1 [MWh] PODUSAGE,PA,UPHES,LDS = 127.1 PACTUAL = 6404 [kW] PPUMPS,24LVL,9 = 9.462 [MW] PPUMPS,MID,SHAFT,9 = 8.153 [MW] PPUMPS,MWh = 140.9 [MWh] PTURBINE,MWh = 102.5 [MWh] water = 998 [kg/m3] RDISCHARGE,HEAD = 0.19 [-] SAVINGS = 7.534 [MR] SPUMPS = 13.3 [No] SPUMPS,MANUAL,INPUT = 14 [No] STURBINE = 1 [-] TOTALCAPEX = 162.9 THDS,OFF,PEAK = 78.75 [c/kWh] THDS,PEAK = 478.7 [c/kWh] THDS,STANDARD = 145 [c/kWh] TLDS,OFF,PEAK = 68.19 [c/kWh] TLDS,PEAK = 156.2 [c/kWh] TLDS,STANDARD = 107.5 [c/kWh] VELUP = 4.22 [m/s] VOLLOWER,RESERVOIR = 21.29 [ML] VOLUPPER,RESERVOIR = 22.4 [ML] VPUMP = 55.56 [l/s] VTURBINE = 369.6 [l/s] ZARPOD,USAGE,PA = 72.43 [MR] ZARPOD,USAGE,PA,UPHES = 64.9 [MR] 19 potential unit problems were detected. Parametric Table: Table 1 TIMEINTERVAL TWEEKDAY,LDS TSATURDAY,LDS TSUNDAY,LDS TWEEKDAY,HDS TSATURDAY,HDS [hrs] [c/kWh] [c/kWh] [c/kWh] [c/kWh] [c/kWh] Run 1 0 39.79 39.79 39.79 45.95 45.95 Run 2 1 39.79 39.79 39.79 45.95 45.95 Run 3 2 39.79 39.79 39.79 45.95 45.95 Run 4 3 39.79 39.79 39.79 45.95 45.95 Run 5 4 39.79 39.79 39.79 45.95 45.95 Run 6 5 39.79 39.79 39.79 45.95 45.95 Run 7 6 62.72 39.79 39.79 279.3 84.62 Run 8 7 91.12 62.72 39.79 279.3 84.62 Run 9 8 91.12 62.72 39.79 279.3 84.62 File:UPHES VERIFICATION MODEL REV D PEAK & STANDARD CAPEX.EES 8/24/2017 7:31:14 PM Page 8 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa Parametric Table: Table 1 TIMEINTERVAL TWEEKDAY,LDS TSATURDAY,LDS TSUNDAY,LDS TWEEKDAY,HDS TSATURDAY,HDS [hrs] [c/kWh] [c/kWh] [c/kWh] [c/kWh] [c/kWh] Run 10 9 91.12 62.72 39.79 84.62 84.62 Run 11 10 62.72 62.72 39.79 84.62 84.62 Run 12 11 62.72 62.72 39.79 84.62 45.95 Run 13 12 62.72 39.79 39.79 84.62 45.95 Run 14 13 62.72 39.79 39.79 84.62 45.95 Run 15 14 62.72 39.79 39.79 84.62 45.95 Run 16 15 62.72 39.79 39.79 84.62 45.95 Run 17 16 62.72 39.79 39.79 84.62 45.95 Run 18 17 62.72 39.79 39.79 279.3 84.62 Run 19 18 91.12 62.72 39.79 279.3 84.62 Run 20 19 91.12 62.72 39.79 84.62 84.62 Run 21 20 62.72 39.79 39.79 84.62 45.95 Run 22 21 62.72 39.79 39.79 84.62 45.95 Run 23 22 39.79 39.79 39.79 45.95 45.95 Run 24 23 39.79 39.79 39.79 45.95 45.95 Parametric Table: Table 1 TSUNDAY,HDS PODUSAGE P1,LDS P2,LDS P1,LDS,SAT P2,LDS,SAT P1,LDS,SUN P2,LDS,SUN [c/kWh] [kWh] [WD] [WD] [SAT] [SAT] [SUN] [SUN] Run 1 45.95 13059 0 1 0 1 0 1 Run 2 45.95 14204 0 1 0 1 0 1 Run 3 45.95 15449 0 1 0 1 0 1 Run 4 45.95 15409 0 1 0 1 0 1 Run 5 45.95 15008 0 1 0 1 0 1 Run 6 45.95 14908 0 1 0 1 0 1 Run 7 45.95 14339 1 0 1 0 1 0 Run 8 45.95 12834 1 0 1 0 1 0 Run 9 45.95 11820 1 0 1 0 1 0 Run 10 45.95 11018 1 0 1 0 1 0 Run 11 45.95 10935 1 0 1 0 1 0 Run 12 45.95 11229 1 0 1 0 1 0 Run 13 45.95 11717 1 0 1 0 1 0 Run 14 45.95 12771 1 0 1 0 1 0 Run 15 45.95 13055 1 0 1 0 1 0 Run 16 45.95 12798 1 0 1 0 1 0 Run 17 45.95 12536 1 0 1 0 1 0 Run 18 45.95 12377 1 0 1 0 1 0 Run 19 45.95 12128 1 0 1 0 1 0 Run 20 45.95 12015 1 0 1 0 1 0 Run 21 45.95 12152 1 0 1 0 1 0 Run 22 45.95 12573 1 0 1 0 1 0 Run 23 45.95 12732 0 1 0 1 0 1 Run 24 45.95 12673 0 1 0 1 0 1 Parametric Table: Table 1 P1,HDS P2,HDS P1,HDS,SAT P2,HDS,SAT P1,HDS,SUN P2,HDS,SUN PODUSAGE,UPHES,LDS [WD] [WD] [SAT] [SAT] [SUN] [SUN] [kWh] Run 1 0 1 0 1 0 1 0 Run 2 0 1 0 1 0 1 0 Run 3 0 1 0 1 0 1 0 Run 4 0 1 0 1 0 1 0 Run 5 0 1 0 1 0 1 0 Run 6 0 1 0 1 0 1 0 File:UPHES VERIFICATION MODEL REV D PEAK & STANDARD CAPEX.EES 8/24/2017 7:31:14 PM Page 9 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa Parametric Table: Table 1 P1,HDS P2,HDS P1,HDS,SAT P2,HDS,SAT P1,HDS,SUN P2,HDS,SUN PODUSAGE,UPHES,LDS [WD] [WD] [SAT] [SAT] [SUN] [SUN] [kWh] Run 7 1 0 1 0 1 0 6404 Run 8 1 0 1 0 1 0 6404 Run 9 1 0 1 0 1 0 6404 Run 10 1 0 1 0 1 0 6404 Run 11 1 0 1 0 1 0 6404 Run 12 1 0 1 0 1 0 6404 Run 13 1 0 1 0 1 0 6404 Run 14 1 0 1 0 1 0 6404 Run 15 1 0 1 0 1 0 6404 Run 16 1 0 1 0 1 0 6404 Run 17 1 0 1 0 1 0 6404 Run 18 1 0 1 0 1 0 6404 Run 19 1 0 1 0 1 0 6404 Run 20 1 0 1 0 1 0 6404 Run 21 1 0 1 0 1 0 6404 Run 22 1 0 1 0 1 0 6404 Run 23 0 1 0 1 0 1 0 Run 24 0 1 0 1 0 1 0 Parametric Table: Table 1 PODUSAGE,PUMPS,LDS PODUSAGE,TOTAL,LDS ZARPOD,USAGE,WEEKDAY,LDS ZARPOD,USAGE,WD,LDS,UPHES [kWh] [kWh] [ZAR] [ZAR] Run 1 17615 30674 5196 12205 Run 2 17615 31819 5652 12661 Run 3 17615 33064 6147 13156 Run 4 17615 33024 6131 13140 Run 5 17615 32623 5972 12981 Run 6 17615 32523 5932 12941 Run 7 0 7935 8993 4977 Run 8 0 6430 11694 5859 Run 9 0 5416 10770 4935 Run 10 0 4614 10040 4205 Run 11 0 4531 6858 2842 Run 12 0 4825 7043 3026 Run 13 0 5313 7349 3332 Run 14 0 6367 8010 3994 Run 15 0 6651 8188 4172 Run 16 0 6394 8027 4010 Run 17 0 6132 7863 3846 Run 18 0 5973 7763 3746 Run 19 0 5724 11051 5216 Run 20 0 5611 10948 5113 Run 21 0 5748 7622 3605 Run 22 0 6169 7886 3869 Run 23 17615 30347 5066 12075 Run 24 17615 30288 5043 12052 Parametric Table: Table 1 PODUSAGE,PUMPS,HDS PODUSAGE,UPHES,HDS PODUSAGE,TOTAL,HDS ZARPOD,USAGE,WEEKDAY,HDS [kWh] [kWh] [kWh] [ZAR] Run 1 17615 0 30674 6001 Run 2 17615 0 31819 6527 Run 3 17615 0 33064 7099 File:UPHES VERIFICATION MODEL REV D PEAK & STANDARD CAPEX.EES 8/24/2017 7:31:15 PM Page 10 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa Parametric Table: Table 1 PODUSAGE,PUMPS,HDS PODUSAGE,UPHES,HDS PODUSAGE,TOTAL,HDS ZARPOD,USAGE,WEEKDAY,HDS [kWh] [kWh] [kWh] [ZAR] Run 4 17615 0 33024 7080 Run 5 17615 0 32623 6896 Run 6 17615 0 32523 6850 Run 7 0 6404 7935 40053 Run 8 0 6404 6430 35849 Run 9 0 6404 5416 33017 Run 10 0 6404 4614 9323 Run 11 0 6404 4531 9253 Run 12 0 6404 4825 9502 Run 13 0 6404 5313 9915 Run 14 0 6404 6367 10807 Run 15 0 6404 6651 11047 Run 16 0 6404 6394 10830 Run 17 0 6404 6132 10608 Run 18 0 6404 5973 34573 Run 19 0 6404 5724 33877 Run 20 0 6404 5611 10167 Run 21 0 6404 5748 10283 Run 22 0 6404 6169 10639 Run 23 17615 0 30347 5850 Run 24 17615 0 30288 5823 Parametric Table: Table 1 ZARPOD,USAGE,WD,HDS,UPHES PODUSAGE,UPHES,LDS,SAT PODUSAGE,PUMPS,LDS,SAT [ZAR] [kWh] [kWh] Run 1 14095 0 17615 Run 2 14621 0 17615 Run 3 15193 0 17615 Run 4 15175 0 17615 Run 5 14990 0 17615 Run 6 14944 0 17615 Run 7 22165 6404 0 Run 8 17962 6404 0 Run 9 15129 6404 0 Run 10 3905 6404 0 Run 11 3834 6404 0 Run 12 4083 6404 0 Run 13 4496 6404 0 Run 14 5388 6404 0 Run 15 5628 6404 0 Run 16 5411 6404 0 Run 17 5189 6404 0 Run 18 16685 6404 0 Run 19 15990 6404 0 Run 20 4748 6404 0 Run 21 4864 6404 0 Run 22 5220 6404 0 Run 23 13944 0 17615 Run 24 13917 0 17615 Parametric Table: Table 1 PODUSAGE,TOTAL,LDS,SAT ZARPOD,USAGE,SAT,LDS ZARPOD,USAGE,SAT,LDS,UPHES PODUSAGE,UPHES,HDS,SAT [kWh] [ZAR] [ZAR] [kWh] File:UPHES VERIFICATION MODEL REV D PEAK & STANDARD CAPEX.EES 8/24/2017 7:31:15 PM Page 11 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa Parametric Table: Table 1 PODUSAGE,TOTAL,LDS,SAT ZARPOD,USAGE,SAT,LDS ZARPOD,USAGE,SAT,LDS,UPHES PODUSAGE,UPHES,HDS,SAT [kWh] [ZAR] [ZAR] [kWh] Run 1 30674 5196 12205 0 Run 2 31819 5652 12661 0 Run 3 33064 6147 13156 0 Run 4 33024 6131 13140 0 Run 5 32623 5972 12981 0 Run 6 32523 5932 12941 0 Run 7 7935 5705 3157 6404 Run 8 6430 8049 4033 6404 Run 9 5416 7414 3397 6404 Run 10 4614 6910 2894 6404 Run 11 4531 6858 2842 6404 Run 12 4825 7043 3026 6404 Run 13 5313 4662 2114 6404 Run 14 6367 5082 2534 6404 Run 15 6651 5195 2647 6404 Run 16 6394 5092 2544 6404 Run 17 6132 4988 2440 6404 Run 18 5973 4925 2377 6404 Run 19 5724 7607 3590 6404 Run 20 5611 7536 3519 6404 Run 21 5748 4835 2287 6404 Run 22 6169 5003 2455 6404 Run 23 30347 5066 12075 0 Run 24 30288 5043 12052 0 Parametric Table: Table 1 PODUSAGE,PUMPS,HDS,SAT PODUSAGE,TOTAL,HDS,SAT ZARPOD,USAGE,SAT,HDS [kWh] [kWh] [ZAR] Run 1 17615 30674 6001 Run 2 17615 31819 6527 Run 3 17615 33064 7099 Run 4 17615 33024 7080 Run 5 17615 32623 6896 Run 6 17615 32523 6850 Run 7 0 7935 12133 Run 8 0 6430 10860 Run 9 0 5416 10002 Run 10 0 4614 9323 Run 11 0 4531 9253 Run 12 0 4825 5160 Run 13 0 5313 5384 Run 14 0 6367 5868 Run 15 0 6651 5999 Run 16 0 6394 5881 Run 17 0 6132 5760 Run 18 0 5973 10473 Run 19 0 5724 10263 Run 20 0 5611 10167 Run 21 0 5748 5584 Run 22 0 6169 5777 Run 23 17615 30347 5850 Run 24 17615 30288 5823 Parametric Table: Table 1 File:UPHES VERIFICATION MODEL REV D PEAK & STANDARD CAPEX.EES 8/24/2017 7:31:15 PM Page 12 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa ZARPOD,USAGE,SAT,HDS,UPHES PODUSAGE,UPHES,LDS,SUN PODUSAGE,PUMPS,LDS,SUN [ZAR] [kWh] [kWh] Run 1 14095 0 17615 Run 2 14621 0 17615 Run 3 15193 0 17615 Run 4 15175 0 17615 Run 5 14990 0 17615 Run 6 14944 0 17615 Run 7 6715 6404 0 Run 8 5441 6404 0 Run 9 4583 6404 0 Run 10 3905 6404 0 Run 11 3834 6404 0 Run 12 2217 6404 0 Run 13 2441 6404 0 Run 14 2926 6404 0 Run 15 3056 6404 0 Run 16 2938 6404 0 Run 17 2818 6404 0 Run 18 5055 6404 0 Run 19 4844 6404 0 Run 20 4748 6404 0 Run 21 2641 6404 0 Run 22 2835 6404 0 Run 23 13944 0 17615 Run 24 13917 0 17615 Parametric Table: Table 1 PODUSAGE,TOTAL,LDS,SUN ZARPOD,USAGE,SUN,LDS ZARPOD,USAGE,SUN,LDS,UPHES [kWh] [ZAR] [ZAR] Run 1 30674 5196 12205 Run 2 31819 5652 12661 Run 3 33064 6147 13156 Run 4 33024 6131 13140 Run 5 32623 5972 12981 Run 6 32523 5932 12941 Run 7 7935 5705 3157 Run 8 6430 5107 2559 Run 9 5416 4703 2155 Run 10 4614 4384 1836 Run 11 4531 4351 1803 Run 12 4825 4468 1920 Run 13 5313 4662 2114 Run 14 6367 5082 2534 Run 15 6651 5195 2647 Run 16 6394 5092 2544 Run 17 6132 4988 2440 Run 18 5973 4925 2377 Run 19 5724 4826 2278 Run 20 5611 4781 2233 Run 21 5748 4835 2287 Run 22 6169 5003 2455 Run 23 30347 5066 12075 Run 24 30288 5043 12052 Parametric Table: Table 1 PODUSAGE,UPHES,HDS,SUN PODUSAGE,PUMPS,HDS,SUN PODUSAGE,TOTAL,HDS,SUN ZARPOD,USAGE,SUN,HDS File:UPHES VERIFICATION MODEL REV D PEAK & STANDARD CAPEX.EES 8/24/2017 7:31:15 PM Page 13 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa [kWh] [kWh] [kWh] [ZAR] Run 1 0 17615 30674 6001 Run 2 0 17615 31819 6527 Run 3 0 17615 33064 7099 Run 4 0 17615 33024 7080 Run 5 0 17615 32623 6896 Run 6 0 17615 32523 6850 Run 7 6404 0 7935 6589 Run 8 6404 0 6430 5897 Run 9 6404 0 5416 5431 Run 10 6404 0 4614 5063 Run 11 6404 0 4531 5025 Run 12 6404 0 4825 5160 Run 13 6404 0 5313 5384 Run 14 6404 0 6367 5868 Run 15 6404 0 6651 5999 Run 16 6404 0 6394 5881 Run 17 6404 0 6132 5760 Run 18 6404 0 5973 5687 Run 19 6404 0 5724 5573 Run 20 6404 0 5611 5521 Run 21 6404 0 5748 5584 Run 22 6404 0 6169 5777 Run 23 0 17615 30347 5850 Run 24 0 17615 30288 5823 Parametric Table: Table 1 ZARPOD,USAGE,SUN,HDS,UPHES [ZAR] Run 1 14095 Run 2 14621 Run 3 15193 Run 4 15175 Run 5 14990 Run 6 14944 Run 7 3646 Run 8 2955 Run 9 2489 Run 10 2120 Run 11 2082 Run 12 2217 Run 13 2441 Run 14 2926 Run 15 3056 Run 16 2938 Run 17 2818 Run 18 2745 Run 19 2630 Run 20 2578 Run 21 2641 Run 22 2835 Run 23 13944 Run 24 13917 File:UPHES VERIFICATION MODEL REV D PEAK & STANDARD CAPEX.EES 8/24/2017 7:31:15 PM Page 14 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa Parametric Table: Table 2 VTURBINE RDISCHARGE,HEAD PACTUAL [l/s] [-] [kW] Run 1 200 0.1028 3466 Run 2 212.5 0.1093 3682 Run 3 225 0.1157 3899 Run 4 237.5 0.1221 4116 Run 5 250 0.1285 4332 Run 6 262.5 0.135 4549 Run 7 275 0.1414 4765 Run 8 287.5 0.1478 4982 Run 9 300 0.1542 5199 Run 10 312.5 0.1607 5415 Run 11 325 0.1671 5632 Run 12 337.5 0.1735 5848 Run 13 350 0.1799 6065 Run 14 362.5 0.1864 6282 Run 15 375 0.1928 6498 Run 16 387.5 0.1992 6715 Run 17 400 0.2057 6931 Run 18 412.5 0.2121 7148 Run 19 425 0.2185 7365 Run 20 437.5 0.2249 7581 Run 21 450 0.2314 7798 Run 22 462.5 0.2378 8014 Run 23 475 0.2442 8231 Run 24 487.5 0.2506 8448 Run 25 500 0.2571 8664 0 5 10 15 20 25 0 5000 10000 15000 20000 25000 30000 35000 2000 4000 6000 8000 10000 12000 14000 TIMEINTERVAL [hrs] PO D P O W ER C O N SU M ED [k W h] EL EC TR IC IT Y C O ST [ ZA R ] File:UPHES VERIFICATION MODEL REV D PEAK & STANDARD CAPEX.EES 8/24/2017 7:31:15 PM Page 15 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa 0 5 10 15 20 25 0 5000 10000 15000 20000 25000 0 10000 20000 30000 40000 50000 60000 70000 TIMEINTERVAL [hrs] PO D P O W ER C O N SU M ED [k W h] EL EC TR IC IT Y C O ST [Z A R ] 0 5 10 15 20 25 0 5000 10000 15000 20000 25000 4000 6000 8000 10000 12000 14000 16000 TIMEINTERVAL [hrs] PO D P O W ER C O N SU M ED [k W h] EL EC TR IC IT Y C O ST [Z A R ] File:UPHES VERIFICATION MODEL REV D PEAK & STANDARD CAPEX.EES 8/24/2017 7:31:16 PM Page 16 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa 0 5 10 15 20 25 5000 10000 15000 20000 25000 5000 10000 15000 20000 25000 TIMEINTERVAL [hrs] PO D P O W ER C O N SU M ED [k W h] EL EC TR IC IT Y C O ST [Z A R ] 0 5 10 15 20 25 0 5000 10000 15000 20000 25000 2000 4000 6000 8000 10000 12000 14000 16000 TIMEINTERVAL [hrs] PO D P O W ER C O N SU M ED [k W h] EL EC TR IC IT Y C O ST [Z A R ] File:UPHES VERIFICATION MODEL REV D PEAK & STANDARD CAPEX.EES 8/24/2017 7:31:16 PM Page 17 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa 0 5 10 15 20 25 5000 10000 15000 20000 25000 4000 6000 8000 10000 12000 14000 16000 18000 TIMEINTERVAL [hrs] PO D P O W ER C O N SU M ED [k W h} EL EC TR IC IT Y C O ST [Z A R ] 200 300 400 500 3000 4000 5000 6000 7000 8000 9000 0.1 0.15 0.2 0.25 0.3 VTURBINE [l/s] P A C TU A L [k W ] R D IS C H A R G E, H EA D [ -] File:F:\UPHES SYSTEM EES\UPHES DFT 9 SHAFT REV H FINAL OPTIMISED.EES 8/27/2017 3:20:29 PM Page 1 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa {PROGRAM OPERATIONAL STEPS (1) INSERT ALL INPUT PARAMETERS, SOLVE PRINCIPAL OUTPUT PARAMETERS (2) REMOVE COMMENT BRACKETS FROM LOAD AND ELECTRICITY COST CALCULATIONS, SOLVE PARAMETRIC TABLE (3) REPLACE THE COMMENT BRACKETS TO THE LOAD AND ELECTRICITY COST CALCULATIONS AFTER SOLVING THE PRAMETRIC TABLE, REMOVE THE COMMENT BRACKETS FROM THE ELECTRICITY SAVINGS SECTION, CLICK SOLVE} {INPUT PARAMETERS} rho_water = 998 [kg/m3] g = 9.81 [m/s2] S_TURBINE = 1 [-] {NUMBER TURBINES} V_TURBINE = 369.55 [l/s] R_DISCHARGE_HEAD = V_TURBINE/H_EFFECTIVE eta_TURBINE = 0.91 V_PUMP = 55.56 [l/s] eta_PUMP = 0.89 f = 0.0174 {PIPE FRICTION FACTOR ASSUMED} D_i_PIPE = 284.18 [mm] {OPERATIONAL INPUT PARAMETERS} HRS_PUMP = 8 [hrs] HRS_TURBINE = 5 [hrs] {ELEVATIONS} H_1_IPC_9 = 150 [m] H_2_MID_SHAFT_9 = 1050 [m] H_3_24LVL_9 = 2095 [m] {SYSTEM OPERATIONAL FORMULAS} P_ACTUAL = rho_water*g*(H_EFFECTIVE)*(V_TURBINE/1000)*eta_TURBINE/1000 H_EFFECTIVE = (H_3_24LVL_9-H_1_IPC_9) P_TURBINE_MWh = (P_ACTUAL* HRS_TURBINE)/1000 VOL_LOWER_RESERVOIR = V_TURBINE*(HRS_TURBINE*60*60)/1000000 S_PUMPS = (VOL_LOWER_RESERVOIR*1000000)/(V_PUMP*60*60)/HRS_PUMP VOL_UPPER_RESERVOIR = (S_PUMPS_MANUAL_INPUT*V_PUMP*HRS_PUMP*60*60)/1000000 P_PUMPS_24LVL_9 = ((rho_water*g*(H_3_24LVL_9-H_2_MID_SHAFT_9+H_3_FRICTION)*(V_PUMP/1000))/ eta_PUMP)*S_PUMPS_MANUAL_INPUT/1000000 P_PUMPS_MID_SHAFT_9 = ((rho_water*g*(H_2_MID_SHAFT_9-H_1_IPC_9+H_2_FRICTION)*(V_PUMP/1000))/ eta_PUMP)*S_PUMPS_MANUAL_INPUT/1000000 P_PUMPS_MWh = (P_PUMPS_24LVL_9+P_PUMPS_MID_SHAFT_9)*HRS_PUMP H_3_FRICTION = (f*(H_3_24LVL_9-H_2_MID_SHAFT_9 +50)*VEL_UP^2)/(2*g*(D_i_PIPE/1000)) H_2_FRICTION = (f*(H_2_MID_SHAFT_9-H_1_IPC_9 +50)*VEL_UP^2)/(2*g*(D_i_PIPE/1000)) VEL_UP = 4.22 {((V_PUMP/1000)*S_PUMPS_MANUAL_INPUT)/(pi*(D_i_PIPE/1000))} {MANUAL INPUT (1)} S_PUMPS_MANUAL_INPUT = 5 {MEGAFLEX TARIFF STRUCTURE - INPUT 2016/2017} {TIME_INTERVAL = 1 [HRS]} {POD_USAGE = 20000 [Wh]} {T_WEEKDAY_LDS = 68.19 [c/kWh] T_SATURDAY_LDS = 68.19 [c/kWh] T_SUNDAY_LDS = 68.19 [c/kWh] T_WEEKDAY_HDS = 68.19 [c/kWh] T_SATURDAY_HDS = 68.19 [c/kWh] T_SUNDAY_HDS = 68.19 [c/kWh]} T_LDS_OFF_PEAK = 68.19 [c/kWh] T_LDS_STANDARD = 107.49 [c/kWh] T_LDS_PEAK = 156.16 [c/kWh] File:F:\UPHES SYSTEM EES\UPHES DFT 9 SHAFT REV H FINAL OPTIMISED.EES 8/27/2017 3:20:29 PM Page 2 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa T_HDS_OFF_PEAK = 78.75 [c/kWh] T_HDS_STANDARD = 145.02 [c/kWh] T_HDS_PEAK = 478.72 [c/kWh] D_WEEKDAY_OFF_PEAK = 8 D_WEEKDAY_STANDARD = 11 D_WEEKDAY_PEAK = 5 D_LDS_WEEKDAY_TARIFF = 186 D_LDS_SATURDAY_TARIFF = 46 D_LDS_SUNDAY_TARIFF = 41 D_HDS_WEEKDAY_TARIFF = 64 D_HDS_SATURDAY_TARIFF = 14 D_HDS_SUNDAY_TARIFF = 14 ESKOM = 1.05^0 {ASSUMED MEGAFLEX TARIFF INCREASE} {LOAD AND ELECTRICITY COST CALCULATIONS} {WEEKDAY} {POD_USAGE_UPHES_LDS = (P_ACTUAL)*P_1_LDS POD_USAGE_PUMPS_LDS = (P_PUMPS_24LVL_9*1000+P_PUMPS_MID_SHAFT_9*1000)*P_2_LDS POD_USAGE_TOTAL_LDS = POD_USAGE - POD_USAGE_UPHES_LDS + POD_USAGE_PUMPS_LDS ZAR_POD_USAGE_WEEKDAY_LDS = POD_USAGE*T_WEEKDAY_LDS/100*ESKOM ZAR_POD_USAGE_WD_LDS_UPHES = POD_USAGE_TOTAL_LDS*T_WEEKDAY_LDS/100*ESKOM POD_USAGE_UPHES_HDS = (P_ACTUAL)*P_1_HDS POD_USAGE_PUMPS_HDS = (P_PUMPS_24LVL_9*1000+P_PUMPS_MID_SHAFT_9*1000)*P_2_HDS POD_USAGE_TOTAL_HDS = POD_USAGE - POD_USAGE_UPHES_HDS + POD_USAGE_PUMPS_HDS ZAR_POD_USAGE_WEEKDAY_HDS = POD_USAGE*T_WEEKDAY_HDS/100*ESKOM ZAR_POD_USAGE_WD_HDS_UPHES = POD_USAGE_TOTAL_HDS*T_WEEKDAY_HDS/100*ESKOM {SATURDAY} POD_USAGE_UPHES_LDS_SAT = (P_ACTUAL)*P_1_LDS_SAT POD_USAGE_PUMPS_LDS_SAT = (P_PUMPS_24LVL_9*1000+P_PUMPS_MID_SHAFT_9*1000)*P_2_LDS_SAT POD_USAGE_TOTAL_LDS_SAT = POD_USAGE - POD_USAGE_UPHES_LDS_SAT + POD_USA GE_PUMPS_LDS_SAT ZAR_POD_USAGE_SAT_LDS = POD_USAGE*T_SATURDAY_LDS/100*ESKOM ZAR_POD_USAGE_SAT_LDS_UPHES = POD_USAGE_TOTAL_LDS_SAT*T_SATURDAY_LDS/100*ESKOM POD_USAGE_UPHES_HDS_SAT = (P_ACTUAL)*P_1_HDS_SAT POD_USAGE_PUMPS_HDS_SAT = (P_PUMPS_24LVL_9*1000+P_PUMPS_MID_SHAFT_9*1000)*P_2_HDS_SAT POD_USAGE_TOTAL_HDS_SAT = POD_USAGE - POD_USAGE_UPHES_HDS_SAT + POD_US AGE_PUMPS_HDS_SAT ZAR_POD_USAGE_SAT_HDS = POD_USAGE*T_SATURDAY_HDS/100*ESKOM ZAR_POD_USAGE_SAT_HDS_UPHES = POD_USAGE_TOTAL_HDS_SAT*T_SATURDAY_HDS/100*ESKOM {SUNDAY} POD_USAGE_UPHES_LDS_SUN = (P_ACTUAL)*P_1_LDS_SUN POD_USAGE_PUMPS_LDS_SUN = (P_PUMPS_24LVL_9*1000+P_PUMPS_MID_SHAFT_9*1000)*P_2_LDS_SUN POD_USAGE_TOTAL_LDS_SUN = POD_USAGE - POD_USAGE_UPHES_LDS_SUN + POD_US AGE_PUMPS_LDS_SUN ZAR_POD_USAGE_SUN_LDS = POD_USAGE*T_SUNDAY_LDS/100*ESKOM ZAR_POD_USAGE_SUN_LDS_UPHES = POD_USAGE_TOTAL_LDS_SUN*T_SUNDAY_LDS/100*ESKOM POD_USAGE_UPHES_HDS_SUN = (P_ACTUAL)*P_1_HDS_SUN POD_USAGE_PUMPS_HDS_SUN = (P_PUMPS_24LVL_9*1000+P_PUMPS_MID_SHAFT_9*1000)*P_2_HDS_SUN POD_USAGE_TOTAL_HDS_SUN = POD_USAGE - POD_USAGE_UPHES_HDS_SUN + POD_US AGE_PUMPS_HDS_SUN ZAR_POD_USAGE_SUN_HDS = POD_USAGE*T_SUNDAY_HDS/100*ESKOM ZAR_POD_USAGE_SUN_HDS_UPHES = POD_USAGE_TOTAL_HDS_SUN*T_SUNDAY_HDS/100*ESKOM} {ELECTRICITY SAVINGS} POD_USAGE_PA = (sumparametric('Table 1', 'POD_USAGE')*D_LDS_WEEKDAY_TARIFF+sumparametric('Table 1', ' File:F:\UPHES SYSTEM EES\UPHES DFT 9 SHAFT REV H FINAL OPTIMISED.EES 8/27/2017 3:20:29 PM Page 3 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa POD_USAGE')*D_HDS_WEEKDAY_TARIFF+sumparametric('Table 1', 'POD_USAGE')*D_LDS_SATURDAY_TARIFF+ sumparametric('Table 1', 'POD_USAGE')*D_HDS_SATURDAY_TARIFF+sumparametric('Table 1', 'POD_USAGE')* D_LDS_SUNDAY_TARIFF+sumparametric('Table 1', 'POD_USAGE')*D_HDS_SUNDAY_TARIFF)/1000000 ZAR_POD_USAGE_PA = (sumparametric('Table 1', 'ZAR_POD_USAGE_WEEKDAY_LDS')*D_LDS _WEEKDAY_TARIFF+sumparametric('Table 1', 'ZAR_POD_USAGE_WEEKDAY_HDS')*D_HDS_WEEKDAY_TARIFF+ sumparametric('Table 1', 'ZAR_POD_USAGE_SAT_LDS')*D_LDS_SATURDAY_TARIFF + sumparametric('Table 1', ' ZAR_POD_USAGE_SAT_HDS')*D_HDS_SATURDAY_TARIFF+SUMPARAMETRIC('Table 1', 'ZAR _POD_USAGE_SUN_LDS')*D_LDS_SUNDAY_TARIFF+SUMPARAMETRIC('Table 1', 'ZAR_POD_USAGE_SUN_HDS') *D_HDS_SUNDAY_TARIFF)/1000000 POD_USAGE_PA_UPHES_LDS= (sumparametric('Table 1', 'POD_USAGE_TOTAL_LDS')*D_LDS_WEEKDAY_TARIFF + sumparametric('Table 1', 'POD_USAGE_TOTAL_LDS_SAT')*D_LDS_SATURDAY_TARIFF+ sumparametric('Table 1', ' POD_USAGE_TOTAL_LDS_SUN')*D_LDS_SUNDAY_TARIFF + sumparametric('Table 1', 'POD_USAGE_TOTAL_HDS') *D_HDS_WEEKDAY_TARIFF+sumparametric('Table 1', 'POD_USAGE_TOTAL_HDS_SAT')*D_HDS _SATURDAY_TARIFF+sumparametric('Table 1', 'POD_USAGE_TOTAL_HDS_SUN')*D_HDS_SUNDAY_TARIFF)/ 1000000 ZAR_POD_USAGE_PA_UPHES = (sumparametric('Table 1', 'ZAR_POD_USAGE_WD_LDS_UPHES')* D_LDS_WEEKDAY_TARIFF+sumparametric('Table 1', 'ZAR_POD_USAGE_WD_HDS_UPHES')*D _HDS_WEEKDAY_TARIFF+sumparametric('Table 1', 'ZAR_POD_USAGE_SAT_LDS_UPHES')*D_ LDS_SATURDAY_TARIFF + sumparametric('Table 1', 'ZAR_POD_USAGE_SAT_HDS_UPHES')*D_ HDS_SATURDAY_TARIFF+SUMPARAMETRIC('Table 1', 'ZAR_POD_USAGE_SUN_LDS_UPHES')* D_LDS_SUNDAY_TARIFF+SUMPARAMETRIC('Table 1', 'ZAR_POD_USAGE_SUN_HDS_UPHES')* D_HDS_SUNDAY_TARIFF)/1000000 SAVINGS = ZAR_POD_USAGE_PA - ZAR_POD_USAGE_PA_UPHES {ESTIMATED CAPEX - CONSIDERATION GIVEN TO EXISTING INFRASTRUCTURE} PACKAGE_1 = 0 {WINDING PLANT} PACKAGE_2 = 0 {HEADGEAR} PACKAGE_3 = 0 {SHAFT DEVELOPMENT} PACKAGE_4_A = (10097.30*(H_EFFECTIVE/3/9))+(12337.19*(H_EFFECTIVE/3/9))+(13864.49*(H_EFFECTIVE/3/9)) {SHAFT PIPE COLUMN - TURBINE FEED} PACKAGE_4_B = PACKAGE_4_A*0.05+PACKAGE_4_A*0.1+PACKAGE_4_A*0.4+(1039775.30*(H_3_24LVL_9/2300))+ (216585.85*(H_3_24LVL_9/2300)) {SHAFT INFRASTRUCTURE} PACKAGE_4 = PACKAGE_4_A + PACKAGE_4_B PACKAGE_5 = 0 {STATION DEVELOPMENT} PACKAGE_6_UPPER_RES = 2800*(VOL_LOWER_RESERVOIR*1.15*1000)+50000*((VOL_LOWER_RESERVOIR* 1.15)/3) PACKAGE_6_MID_RES = 2800*(VOL_LOWER_RESERVOIR*0.15*1000)+50000*1 PACKAGE_6_LOWER_RES = 50000*(VOL_LOWER_RESERVOIR/3) {ONLY DAM WALLS} PACKAGE_6 = PACKAGE_6_UPPER_RES + PACKAGE_6_LOWER_RES + PACKAGE_6_MID_RES {RESERVOIRS} PACKAGE_7 = ((3134883.23+275129.55+173611.63)*(S_PUMPS_MANUAL_INPUT*2-8))+(305417.38+2800*8*( S_PUMPS_MANUAL_INPUT-4))+368000*2 {PUMP CHAMBERS - ASSUME SUPPLY OF ALL PUMPS} PACKAGE_8 = (4630500+1100518.20+694446.51) {SUPPLY COST OF ONE TURBINE, SWITCHGEAR AND GENERATOR} TOTAL_CAPEX = (PACKAGE_1 + PACKAGE_2 + PACKAGE_3 + PACKAGE_4 + PACKAGE_5 + PACKAGE_6 + PACKAGE_7 + PACKAGE_8)/1000000 water = 998 [kg/m3] g = 9.81 [m/s2] STURBINE = 1 [-] VTURBINE = 369.55 [l/s] RDISCHARGE,HEAD = VTURBINE HEFFECTIVE File:F:\UPHES SYSTEM EES\UPHES DFT 9 SHAFT REV H FINAL OPTIMISED.EES 8/27/2017 3:20:29 PM Page 4 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa TURBINE = 0.91 VPUMP = 55.56 [l/s] PUMP = 0.89 f = 0.0174 Di,PIPE = 284.18 [mm] HRSPUMP = 8 [hrs] HRSTURBINE = 5 [hrs] H1,IPC,9 = 150 [m] H2,MID,SHAFT,9 = 1050 [m] H3,24LVL,9 = 2095 [m] PACTUAL = water · g · HEFFECTIVE · VTURBINE 1000 · TURBINE 1000 HEFFECTIVE = H3,24LVL,9 – H1,IPC,9 PTURBINE,MWh = PACTUAL · HRSTURBINE 1000 VOLLOWER,RESERVOIR = VTURBINE · HRSTURBINE · 60 · 60 1000000 SPUMPS = VOLLOWER,RESERVOIR · 1000000 VPUMP · 60 · 60 · HRSPUMP VOLUPPER,RESERVOIR = SPUMPS,MANUAL,INPUT · VPUMP · HRSPUMP · 60 · 60 1000000 PPUMPS,24LVL,9 = water · g · H3,24LVL,9 – H2,MID,SHAFT,9 + H3,FRICTION · VPUMP 1000 PUMP · SPUMPS,MANUAL,INPUT 1000000 PPUMPS,MID,SHAFT,9 = water · g · H2,MID,SHAFT,9 – H1,IPC,9 + H2,FRICTION · VPUMP 1000 PUMP · SPUMPS,MANUAL,INPUT 1000000 PPUMPS,MWh = PPUMPS,24LVL,9 + PPUMPS,MID,SHAFT,9 · HRSPUMP H3,FRICTION = f · H3,24LVL,9 – H2,MID,SHAFT,9 + 50 · VELUP 2 2 · g · Di,PIPE 1000 H2,FRICTION = f · H2,MID,SHAFT,9 – H1,IPC,9 + 50 · VELUP 2 2 · g · Di,PIPE 1000 VELUP = 4.22 SPUMPS,MANUAL,INPUT = 5 File:F:\UPHES SYSTEM EES\UPHES DFT 9 SHAFT REV H FINAL OPTIMISED.EES 8/27/2017 3:20:30 PM Page 5 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa TLDS,OFF,PEAK = 68.19 [c/kWh] TLDS,STANDARD = 107.49 [c/kWh] TLDS,PEAK = 156.16 [c/kWh] THDS,OFF,PEAK = 78.75 [c/kWh] THDS,STANDARD = 145.02 [c/kWh] THDS,PEAK = 478.72 [c/kWh] DWEEKDAY,OFF,PEAK = 8 DWEEKDAY,STANDARD = 11 DWEEKDAY,PEAK = 5 DLDS,WEEKDAY,TARIFF = 186 DLDS,SATURDAY,TARIFF = 46 DLDS,SUNDAY,TARIFF = 41 DHDS,WEEKDAY,TARIFF = 64 DHDS,SATURDAY,TARIFF = 14 DHDS,SUNDAY,TARIFF = 14 ESKOM = 1.05 0 PODUSAGE,PA = SumParametric 'Table 1' , 'PODUSAGE' · DLDS,WEEKDAY,TARIFF + SumParametric 'Table 1' , 'PODUSAGE' 1000000 ZARPOD,USAGE,PA = SumParametric 'Table 1' , 'ZARPOD,USAGE,WEEKDAY,LDS' · DLDS,WEEKDAY,TARIFF + SumParametric 1000000 PODUSAGE,PA,UPHES,LDS = SumParametric 'Table 1' , 'PODUSAGE,TOTAL,LDS' · DLDS,WEEKDAY,TARIFF + SumParametric 'Ta 1000000 ZARPOD,USAGE,PA,UPHES = SumParametric 'Table 1' , 'ZARPOD,USAGE,WD,LDS,UPHES' · DLDS,WEEKDAY,TARIFF + SumParam 1000000 SAVINGS = ZARPOD,USAGE,PA – ZARPOD,USAGE,PA,UPHES PACKAGE1 = 0 PACKAGE2 = 0 PACKAGE3 = 0 File:F:\UPHES SYSTEM EES\UPHES DFT 9 SHAFT REV H FINAL OPTIMISED.EES 8/27/2017 3:20:30 PM Page 6 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa PACKAGE4,A = 10097.3 · HEFFECTIVE 3 · 9 + 12337.19 · HEFFECTIVE 3 · 9 + 13864.49 · HEFFECTIVE 3 · 9 PACKAGE4,B = PACKAGE4,A · 0.05 + PACKAGE4,A · 0.1 + PACKAGE4,A · 0.4 + 1.03978 x 10 6 · H3,24LVL,9 2300 + 216585.85 · H3,24LVL,9 2300 PACKAGE4 = PACKAGE4,A + PACKAGE4,B PACKAGE5 = 0 PACKAGE6,UPPER,RES = 2800 · VOLLOWER,RESERVOIR · 1.15 · 1000 + 50000 · VOLLOWER,RESERVOIR · 1.15 3 PACKAGE6,MID,RES = 2800 · VOLLOWER,RESERVOIR · 0.15 · 1000 + 50000 · 1 PACKAGE6,LOWER,RES = 50000 · VOLLOWER,RESERVOIR 3 PACKAGE6 = PACKAGE6,UPPER,RES + PACKAGE6,LOWER,RES + PACKAGE6,MID,RES PACKAGE7 = 3.13488 x 10 6 + 275129.55 + 173611.63 · SPUMPS,MANUAL,INPUT · 2 – 8 + 305417.38 + 2800 · 8 · SPUMPS,MANUAL,INPUT – 4 + 368000 · 2 PACKAGE8 = 4.6305 x 10 6 + 1.10052 x 10 6 + 694446.51 TOTALCAPEX = PACKAGE1 + PACKAGE2 + PACKAGE3 + PACKAGE4 + PACKAGE5 + PACKAGE6 + PACKAGE7 + PACKAG 1000000 SOLUTION Unit Settings: SI C kPa kJ mass deg DHDS,SATURDAY,TARIFF = 14 [-] DHDS,SUNDAY,TARIFF = 14 [-] DHDS,WEEKDAY,TARIFF = 64 [-] Di,PIPE = 284.2 [mm] DLDS,SATURDAY,TARIFF = 46 [-] DLDS,SUNDAY,TARIFF = 41 [-] DLDS,WEEKDAY,TARIFF = 186 [-] DWEEKDAY,OFF,PEAK = 8 [-] DWEEKDAY,PEAK = 5 [-] DWEEKDAY,STANDARD = 11 [-] ESKOM = 1 PUMP = 0.89 [-] TURBINE = 0.91 [-] f = 0.0174 [-] g = 9.81 [m/s2] HRSPUMP = 8 [hrs] HRSTURBINE = 5 [hrs] H1,IPC,9 = 150 [m] H2,FRICTION = 52.8 [m] H2,MID,SHAFT,9 = 1050 [m] H3,24LVL,9 = 2095 [m] File:F:\UPHES SYSTEM EES\UPHES DFT 9 SHAFT REV H FINAL OPTIMISED.EES 8/27/2017 3:20:31 PM Page 7 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa H3,FRICTION = 60.85 HEFFECTIVE = 1945 [m] PACKAGE1 = 0 PACKAGE2 = 0 PACKAGE3 = 0 PACKAGE4 = 5.197E+06 PACKAGE4,A = 2.615E+06 PACKAGE4,B = 2.583E+06 PACKAGE5 = 0 PACKAGE6 = 2.450E+07 PACKAGE6,LOWER,RES = 110865 PACKAGE6,MID,RES = 2.844E+06 PACKAGE6,UPPER,RES = 2.155E+07 PACKAGE7 = 8.231E+06 PACKAGE8 = 6.425E+06 PODUSAGE,PA = 113.1 [MWh] PODUSAGE,PA,UPHES,LDS = 117.9 [MWH] PACTUAL = 6404 [kW] PPUMPS,24LVL,9 = 3.379 [MW] PPUMPS,MID,SHAFT,9 = 2.912 [MW] PPUMPS,MWh = 50.33 [MWh] PTURBINE,MWh = 32.02 [MWh] water = 998 [kg/m3] RDISCHARGE,HEAD = 0.19 [-] SAVINGS = 6.001 [MR] SPUMPS = 4.157 [No] SPUMPS,MANUAL,INPUT = 5 [No] STURBINE = 1 [-] TOTALCAPEX = 44.36 [MR] THDS,OFF,PEAK = 78.75 [c/kWh] THDS,PEAK = 478.7 [c/kWh] THDS,STANDARD = 145 [c/kWh] TLDS,OFF,PEAK = 68.19 [c/kWh] TLDS,PEAK = 156.2 [c/kWh] TLDS,STANDARD = 107.5 [c/kWh] VELUP = 4.22 [m/s] VOLLOWER,RESERVOIR = 6.652 [ML] VOLUPPER,RESERVOIR = 8.001 [ML] VPUMP = 55.56 [l/s] VTURBINE = 369.6 [l/s] ZARPOD,USAGE,PA = 72.35 [MR] ZARPOD,USAGE,PA,UPHES = 66.35 [MR] 20 potential unit problems were detected. Parametric Table: Table 1 TIMEINTERVAL TWEEKDAY,LDS TSATURDAY,LDS TSUNDAY,LDS TWEEKDAY,HDS TSATURDAY,HDS [hrs] [c/kWh] [c/kWh] [c/kWh] [c/kWh] [c/kWh] Run 1 0 39.79 39.79 39.79 45.95 45.95 Run 2 1 39.79 39.79 39.79 45.95 45.95 Run 3 2 39.79 39.79 39.79 45.95 45.95 Run 4 3 39.79 39.79 39.79 45.95 45.95 Run 5 4 39.79 39.79 39.79 45.95 45.95 Run 6 5 39.79 39.79 39.79 45.95 45.95 Run 7 6 62.72 39.79 39.79 279.3 45.95 Run 8 7 91.12 62.72 39.79 279.3 84.62 Run 9 8 91.12 62.72 39.79 279.3 84.62 File:F:\UPHES SYSTEM EES\UPHES DFT 9 SHAFT REV H FINAL OPTIMISED.EES 8/27/2017 3:20:31 PM Page 8 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa Parametric Table: Table 1 TIMEINTERVAL TWEEKDAY,LDS TSATURDAY,LDS TSUNDAY,LDS TWEEKDAY,HDS TSATURDAY,HDS [hrs] [c/kWh] [c/kWh] [c/kWh] [c/kWh] [c/kWh] Run 10 9 91.12 62.72 39.79 84.62 84.62 Run 11 10 62.72 62.72 39.79 84.62 84.62 Run 12 11 62.72 62.72 39.79 84.62 84.62 Run 13 12 62.72 39.79 39.79 84.62 45.95 Run 14 13 62.72 39.79 39.79 84.62 45.95 Run 15 14 62.72 39.79 39.79 84.62 45.95 Run 16 15 62.72 39.79 39.79 84.62 45.95 Run 17 16 62.72 39.79 39.79 84.62 45.95 Run 18 17 62.72 39.79 39.79 279.3 45.95 Run 19 18 91.12 62.72 39.79 279.3 84.62 Run 20 19 91.12 62.72 39.79 84.62 84.62 Run 21 20 62.72 39.79 39.79 84.62 45.95 Run 22 21 62.72 39.79 39.79 84.62 45.95 Run 23 22 39.79 39.79 39.79 45.95 45.95 Run 24 23 39.79 39.79 39.79 45.95 45.95 Parametric Table: Table 1 TSUNDAY,HDS PODUSAGE P1,LDS P2,LDS P1,LDS,SAT P2,LDS,SAT P1,LDS,SUN P2,LDS,SUN [c/kWh] [kWh] [WD] [WD] [SAT] [SAT] [SUN] [SUN] Run 1 45.95 13059 0 1 0 0 0 0 Run 2 45.95 14204 0 1 0 0 0 0 Run 3 45.95 15449 0 1 0 0 0 0 Run 4 45.95 15409 0 1 0 0 0 0 Run 5 45.95 15008 0 1 0 0 0 0 Run 6 45.95 14908 0 1 0 0 0 0 Run 7 45.95 14339 0 0 0 0 0 0 Run 8 45.95 12834 1 0 0 0 0 0 Run 9 45.95 11820 1 0 0 0 0 0 Run 10 45.95 11018 1 0 0 0 0 0 Run 11 45.95 10935 0 0 0 0 0 0 Run 12 45.95 11229 0 0 0 0 0 0 Run 13 45.95 11717 0 0 0 0 0 0 Run 14 45.95 12771 0 0 0 0 0 0 Run 15 45.95 13055 0 0 0 0 0 0 Run 16 45.95 12798 0 0 0 0 0 0 Run 17 45.95 12536 0 0 0 0 0 0 Run 18 45.95 12377 0 0 0 0 0 0 Run 19 45.95 12128 1 0 0 0 0 0 Run 20 45.95 12015 1 0 0 0 0 0 Run 21 45.95 12152 0 0 0 0 0 0 Run 22 45.95 12573 0 0 0 0 0 0 Run 23 45.95 12732 0 1 0 0 0 0 Run 24 45.95 12673 0 1 0 0 0 0 Parametric Table: Table 1 P1,HDS P2,HDS P1,HDS,SAT P2,HDS,SAT P1,HDS,SUN P2,HDS,SUN PODUSAGE,UPHES,LDS [WD] [WD] [SAT] [SAT] [SUN] [SUN] [kWh] Run 1 0 1 0 1 0 0 0 Run 2 0 1 0 1 0 0 0 Run 3 0 1 0 1 0 0 0 Run 4 0 1 0 1 0 0 0 Run 5 0 1 0 1 0 0 0 Run 6 0 1 0 1 0 0 0 File:F:\UPHES SYSTEM EES\UPHES DFT 9 SHAFT REV H FINAL OPTIMISED.EES 8/27/2017 3:20:31 PM Page 9 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa Parametric Table: Table 1 P1,HDS P2,HDS P1,HDS,SAT P2,HDS,SAT P1,HDS,SUN P2,HDS,SUN PODUSAGE,UPHES,LDS [WD] [WD] [SAT] [SAT] [SUN] [SUN] [kWh] Run 7 1 0 0 1 0 0 0 Run 8 1 0 1 0 0 0 6404 Run 9 1 0 1 0 0 0 6404 Run 10 0 0 1 0 0 0 6404 Run 11 0 0 1 0 0 0 0 Run 12 0 0 1 0 0 0 0 Run 13 0 0 0 0 0 0 0 Run 14 0 0 0 0 0 0 0 Run 15 0 0 0 0 0 0 0 Run 16 0 0 0 0 0 0 0 Run 17 0 0 0 0 0 0 0 Run 18 1 0 0 0 0 0 0 Run 19 1 0 0 0 0 0 6404 Run 20 0 0 0 0 0 0 6404 Run 21 0 0 0 0 0 0 0 Run 22 0 0 0 0 0 0 0 Run 23 0 1 0 0 0 0 0 Run 24 0 1 0 1 0 0 0 Parametric Table: Table 1 PODUSAGE,PUMPS,LDS PODUSAGE,TOTAL,LDS ZARPOD,USAGE,WEEKDAY,LDS ZARPOD,USAGE,WD,LDS,UPHES [kWh] [kWh] [ZAR] [ZAR] Run 1 6291 19350 5196 7700 Run 2 6291 20496 5652 8155 Run 3 6291 21740 6147 8650 Run 4 6291 21700 6131 8634 Run 5 6291 21299 5972 8475 Run 6 6291 21199 5932 8435 Run 7 0 14339 8993 8993 Run 8 0 6430 11694 5859 Run 9 0 5416 10770 4935 Run 10 0 4614 10040 4205 Run 11 0 10935 6858 6858 Run 12 0 11229 7043 7043 Run 13 0 11717 7349 7349 Run 14 0 12771 8010 8010 Run 15 0 13055 8188 8188 Run 16 0 12798 8027 8027 Run 17 0 12536 7863 7863 Run 18 0 12377 7763 7763 Run 19 0 5724 11051 5216 Run 20 0 5611 10948 5113 Run 21 0 12152 7622 7622 Run 22 0 12573 7886 7886 Run 23 6291 19023 5066 7569 Run 24 6291 18964 5043 7546 Parametric Table: Table 1 PODUSAGE,PUMPS,HDS PODUSAGE,UPHES,HDS PODUSAGE,TOTAL,HDS ZARPOD,USAGE,WEEKDAY,HDS [kWh] [kWh] [kWh] [ZAR] Run 1 6291 0 19350 6001 Run 2 6291 0 20496 6527 Run 3 6291 0 21740 7099 File:F:\UPHES SYSTEM EES\UPHES DFT 9 SHAFT REV H FINAL OPTIMISED.EES 8/27/2017 3:20:32 PM Page 10 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa Parametric Table: Table 1 PODUSAGE,PUMPS,HDS PODUSAGE,UPHES,HDS PODUSAGE,TOTAL,HDS ZARPOD,USAGE,WEEKDAY,HDS [kWh] [kWh] [kWh] [ZAR] Run 4 6291 0 21700 7080 Run 5 6291 0 21299 6896 Run 6 6291 0 21199 6850 Run 7 0 6404 7935 40053 Run 8 0 6404 6430 35849 Run 9 0 6404 5416 33017 Run 10 0 0 11018 9323 Run 11 0 0 10935 9253 Run 12 0 0 11229 9502 Run 13 0 0 11717 9915 Run 14 0 0 12771 10807 Run 15 0 0 13055 11047 Run 16 0 0 12798 10830 Run 17 0 0 12536 10608 Run 18 0 6404 5973 34573 Run 19 0 6404 5724 33877 Run 20 0 0 12015 10167 Run 21 0 0 12152 10283 Run 22 0 0 12573 10639 Run 23 6291 0 19023 5850 Run 24 6291 0 18964 5823 Parametric Table: Table 1 ZARPOD,USAGE,WD,HDS,UPHES PODUSAGE,UPHES,LDS,SAT PODUSAGE,PUMPS,LDS,SAT [ZAR] [kWh] [kWh] Run 1 8892 0 0 Run 2 9418 0 0 Run 3 9990 0 0 Run 4 9971 0 0 Run 5 9787 0 0 Run 6 9741 0 0 Run 7 22165 0 0 Run 8 17962 0 0 Run 9 15129 0 0 Run 10 9323 0 0 Run 11 9253 0 0 Run 12 9502 0 0 Run 13 9915 0 0 Run 14 10807 0 0 Run 15 11047 0 0 Run 16 10830 0 0 Run 17 10608 0 0 Run 18 16685 0 0 Run 19 15990 0 0 Run 20 10167 0 0 Run 21 10283 0 0 Run 22 10639 0 0 Run 23 8741 0 0 Run 24 8714 0 0 Parametric Table: Table 1 PODUSAGE,TOTAL,LDS,SAT ZARPOD,USAGE,SAT,LDS ZARPOD,USAGE,SAT,LDS,UPHES PODUSAGE,UPHES,HDS,SAT [kWh] [ZAR] [ZAR] [kWh] File:F:\UPHES SYSTEM EES\UPHES DFT 9 SHAFT REV H FINAL OPTIMISED.EES 8/27/2017 3:20:32 PM Page 11 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa Parametric Table: Table 1 PODUSAGE,TOTAL,LDS,SAT ZARPOD,USAGE,SAT,LDS ZARPOD,USAGE,SAT,LDS,UPHES PODUSAGE,UPHES,HDS,SAT [kWh] [ZAR] [ZAR] [kWh] Run 1 13059 5196 5196 0 Run 2 14204 5652 5652 0 Run 3 15449 6147 6147 0 Run 4 15409 6131 6131 0 Run 5 15008 5972 5972 0 Run 6 14908 5932 5932 0 Run 7 14339 5705 5705 0 Run 8 12834 8049 8049 6404 Run 9 11820 7414 7414 6404 Run 10 11018 6910 6910 6404 Run 11 10935 6858 6858 6404 Run 12 11229 7043 7043 6404 Run 13 11717 4662 4662 0 Run 14 12771 5082 5082 0 Run 15 13055 5195 5195 0 Run 16 12798 5092 5092 0 Run 17 12536 4988 4988 0 Run 18 12377 4925 4925 0 Run 19 12128 7607 7607 0 Run 20 12015 7536 7536 0 Run 21 12152 4835 4835 0 Run 22 12573 5003 5003 0 Run 23 12732 5066 5066 0 Run 24 12673 5043 5043 0 Parametric Table: Table 1 PODUSAGE,PUMPS,HDS,SAT PODUSAGE,TOTAL,HDS,SAT ZARPOD,USAGE,SAT,HDS [kWh] [kWh] [ZAR] Run 1 6291 19350 6001 Run 2 6291 20496 6527 Run 3 6291 21740 7099 Run 4 6291 21700 7080 Run 5 6291 21299 6896 Run 6 6291 21199 6850 Run 7 6291 20630 6589 Run 8 0 6430 10860 Run 9 0 5416 10002 Run 10 0 4614 9323 Run 11 0 4531 9253 Run 12 0 4825 9502 Run 13 0 11717 5384 Run 14 0 12771 5868 Run 15 0 13055 5999 Run 16 0 12798 5881 Run 17 0 12536 5760 Run 18 0 12377 5687 Run 19 0 12128 10263 Run 20 0 12015 10167 Run 21 0 12152 5584 Run 22 0 12573 5777 Run 23 0 12732 5850 Run 24 6291 18964 5823 Parametric Table: Table 1 File:F:\UPHES SYSTEM EES\UPHES DFT 9 SHAFT REV H FINAL OPTIMISED.EES 8/27/2017 3:20:32 PM Page 12 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa ZARPOD,USAGE,SAT,HDS,UPHES PODUSAGE,UPHES,LDS,SUN PODUSAGE,PUMPS,LDS,SUN [ZAR] [kWh] [kWh] Run 1 8892 0 0 Run 2 9418 0 0 Run 3 9990 0 0 Run 4 9971 0 0 Run 5 9787 0 0 Run 6 9741 0 0 Run 7 9479 0 0 Run 8 5441 0 0 Run 9 4583 0 0 Run 10 3905 0 0 Run 11 3834 0 0 Run 12 4083 0 0 Run 13 5384 0 0 Run 14 5868 0 0 Run 15 5999 0 0 Run 16 5881 0 0 Run 17 5760 0 0 Run 18 5687 0 0 Run 19 10263 0 0 Run 20 10167 0 0 Run 21 5584 0 0 Run 22 5777 0 0 Run 23 5850 0 0 Run 24 8714 0 0 Parametric Table: Table 1 PODUSAGE,TOTAL,LDS,SUN ZARPOD,USAGE,SUN,LDS ZARPOD,USAGE,SUN,LDS,UPHES [kWh] [ZAR] [ZAR] Run 1 13059 5196 5196 Run 2 14204 5652 5652 Run 3 15449 6147 6147 Run 4 15409 6131 6131 Run 5 15008 5972 5972 Run 6 14908 5932 5932 Run 7 14339 5705 5705 Run 8 12834 5107 5107 Run 9 11820 4703 4703 Run 10 11018 4384 4384 Run 11 10935 4351 4351 Run 12 11229 4468 4468 Run 13 11717 4662 4662 Run 14 12771 5082 5082 Run 15 13055 5195 5195 Run 16 12798 5092 5092 Run 17 12536 4988 4988 Run 18 12377 4925 4925 Run 19 12128 4826 4826 Run 20 12015 4781 4781 Run 21 12152 4835 4835 Run 22 12573 5003 5003 Run 23 12732 5066 5066 Run 24 12673 5043 5043 Parametric Table: Table 1 PODUSAGE,UPHES,HDS,SUN PODUSAGE,PUMPS,HDS,SUN PODUSAGE,TOTAL,HDS,SUN ZARPOD,USAGE,SUN,HDS File:F:\UPHES SYSTEM EES\UPHES DFT 9 SHAFT REV H FINAL OPTIMISED.EES 8/27/2017 3:20:32 PM Page 13 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa [kWh] [kWh] [kWh] [ZAR] Run 1 0 0 13059 6001 Run 2 0 0 14204 6527 Run 3 0 0 15449 7099 Run 4 0 0 15409 7080 Run 5 0 0 15008 6896 Run 6 0 0 14908 6850 Run 7 0 0 14339 6589 Run 8 0 0 12834 5897 Run 9 0 0 11820 5431 Run 10 0 0 11018 5063 Run 11 0 0 10935 5025 Run 12 0 0 11229 5160 Run 13 0 0 11717 5384 Run 14 0 0 12771 5868 Run 15 0 0 13055 5999 Run 16 0 0 12798 5881 Run 17 0 0 12536 5760 Run 18 0 0 12377 5687 Run 19 0 0 12128 5573 Run 20 0 0 12015 5521 Run 21 0 0 12152 5584 Run 22 0 0 12573 5777 Run 23 0 0 12732 5850 Run 24 0 0 12673 5823 Parametric Table: Table 1 ZARPOD,USAGE,SUN,HDS,UPHES [ZAR] Run 1 6001 Run 2 6527 Run 3 7099 Run 4 7080 Run 5 6896 Run 6 6850 Run 7 6589 Run 8 5897 Run 9 5431 Run 10 5063 Run 11 5025 Run 12 5160 Run 13 5384 Run 14 5868 Run 15 5999 Run 16 5881 Run 17 5760 Run 18 5687 Run 19 5573 Run 20 5521 Run 21 5584 Run 22 5777 Run 23 5850 Run 24 5823 File:F:\UPHES SYSTEM EES\UPHES DFT 9 SHAFT REV H FINAL OPTIMISED.EES 8/27/2017 3:20:32 PM Page 14 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa Parametric Table: Table 2 VTURBINE RDISCHARGE,HEAD PACTUAL [l/s] [-] [kW] Run 1 200 0.1028 3466 Run 2 212.5 0.1093 3682 Run 3 225 0.1157 3899 Run 4 237.5 0.1221 4116 Run 5 250 0.1285 4332 Run 6 262.5 0.135 4549 Run 7 275 0.1414 4765 Run 8 287.5 0.1478 4982 Run 9 300 0.1542 5199 Run 10 312.5 0.1607 5415 Run 11 325 0.1671 5632 Run 12 337.5 0.1735 5848 Run 13 350 0.1799 6065 Run 14 362.5 0.1864 6282 Run 15 375 0.1928 6498 Run 16 387.5 0.1992 6715 Run 17 400 0.2057 6931 Run 18 412.5 0.2121 7148 Run 19 425 0.2185 7365 Run 20 437.5 0.2249 7581 Run 21 450 0.2314 7798 Run 22 462.5 0.2378 8014 Run 23 475 0.2442 8231 Run 24 487.5 0.2506 8448 Run 25 500 0.2571 8664 0 5 10 15 20 25 0 5000 10000 15000 20000 25000 0 2000 4000 6000 8000 10000 12000 TIMEINTERVAL [hrs] PO D P O W ER C O N SU M ED [k W h] EL EC TR IC IT Y C O ST [ ZA R ] File:F:\UPHES SYSTEM EES\UPHES DFT 9 SHAFT REV H FINAL OPTIMISED.EES 8/27/2017 3:20:32 PM Page 15 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa 0 5 10 15 20 25 0 5000 10000 15000 20000 25000 0 4000 8000 12000 16000 20000 24000 28000 32000 36000 40000 44000 48000 TIMEINTERVAL [hrs] PO D P O W ER C O N SU M ED [k W h] EL EC TR IC IT Y C O ST [Z A R ] 0 5 10 15 20 25 0 5000 10000 15000 20000 25000 0 2x103 4x103 6x103 8x103 TIMEINTERVAL [hrs] PO D P O W ER C O N SU M ED [k W h] EL EC TR IC IT Y C O ST [Z A R ] File:F:\UPHES SYSTEM EES\UPHES DFT 9 SHAFT REV H FINAL OPTIMISED.EES 8/27/2017 3:20:33 PM Page 16 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa 0 5 10 15 20 25 0 5000 10000 15000 20000 25000 0 2000 4000 6000 8000 10000 12000 TIMEINTERVAL [hrs] PO D P O W ER C O N SU M ED [k W h] EL EC TR IC IT Y C O ST [Z A R ] 0 5 10 15 20 25 0 5000 10000 15000 20000 25000 0 2000 4000 6000 8000 10000 12000 TIMEINTERVAL [hrs] PO D P O W ER C O N SU M ED [k W h] EL EC TR IC IT Y C O ST [Z A R ] File:F:\UPHES SYSTEM EES\UPHES DFT 9 SHAFT REV H FINAL OPTIMISED.EES 8/27/2017 3:20:33 PM Page 17 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa 0 5 10 15 20 25 0 5000 10000 15000 20000 25000 0 2000 4000 6000 8000 10000 12000 TIMEINTERVAL [hrs] PO D P O W ER C O N SU M ED [k W h} EL EC TR IC IT Y C O ST [Z A R ] 200 300 400 500 3000 4000 5000 6000 7000 8000 9000 0.1 0.15 0.2 0.25 0.3 VTURBINE [l/s] P A C TU A L [k W ] R D IS C H A R G E, H EA D [ -] File:F:\UPHES SYSTEM EES\Validation_D5_Test_Data.EES 8/24/2017 3:31:02 PM Page 1 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa {INPUT PARAMETERS} rho_water = 1000 [kg/m3] g = 9.81 [m/s2] {DFT NO. 5 SHAFT INPUT PARAMETERS} L_0_BD_5 = 0 [m] {UPPER RESERVOIR ELEVATION - 5 SHAFT} L_1_BD_5 = 840 [m] {MID-SHAFT ELEVATION - 5 SHAFT} L_2_BD_5 = 1680 [m] {LOWER RESERVOIR ELEVATION - 5 SHAFT} {DFT NO. 5 SHAFT DATA} P_ACTUAL = (2*pi*N_TURBINE*T_TURBINE)/60/1000*S_FEED {N_TURBINE = 3000 [rpm]} {P_ACTUAL = 4625 [kW]} {V_TURBINE = 320 [l/s]} {S_FEED = 1 [-]} eta_H = P_THEORETICAL/P_ACTUAL P_THEORETICAL = rho_water*g*L_2_BD_5*(V_TURBINE/1000)/1000 P_ACTUAL_CALCULATED = eta_DATA_SHEET*P_THEORETICAL {DFT NO. 9 SHAFT INPUT PARAMETERS} L_0_BD_9 = 150 [m] {UPPER RESERVOIR ELEVATION - 9 SHAFT} L_1_BD_9 = 1000 [m] {MID-SHAFT ELEVATION - 9 SHAFT} L_2_BD_9 = 2095 [m] {LOWER RESERVOIR ELEVATION - 9 SHAFT} P_THEORETICAL_9 = rho_water*g*(L_2_BD_9-L_0_BD_9)*(V_TURBINE/1000)/1000 eta_DATA_SHEET = 0.877 [-] P_ACTUAL_9/P_THEORETICAL_9 = eta_DATA_SHEET RATIO_SYSTEM = V_TURBINE/L_2_BD_5 {DISCHARGE RATE TO NET HEAD RATIO} {TIME = 0 [MIN]} water = 1000 [kg/m3] g = 9.81 [m/s2] L0,BD,5 = 0 [m] L1,BD,5 = 840 [m] L2,BD,5 = 1680 [m] PACTUAL = 2 ·  · NTURBINE · TTURBINE 60 · 1000 · SFEED H = PTHEORETICAL PACTUAL PTHEORETICAL = water · g · L2,BD,5 · VTURBINE 1000 · 1000 PACTUAL,CALCULATED = DATA,SHEET · PTHEORETICAL File:F:\UPHES SYSTEM EES\Validation_D5_Test_Data.EES 8/24/2017 3:31:02 PM Page 2 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa L0,BD,9 = 150 [m] L1,BD,9 = 1000 [m] L2,BD,9 = 2095 [m] PTHEORETICAL,9 = water · g · L2,BD,9 – L0,BD,9 · VTURBINE 1000 · 1000 DATA,SHEET = 0.877 [-] PACTUAL,9 PTHEORETICAL,9 = DATA,SHEET RATIOSYSTEM = VTURBINE L2,BD,5 Parametric Table: DFT NO. 5 SHAFT TEST DATA TIME NTURBINE PACTUAL SFEED VTURBINE TTURBINE PTHEORETICAL H [MIN] [rpm] [kW] [-] [l/s] [Nm] [kW] [-] Run 1 10 3006 4616 100 331 Run 2 20 3000 4650 100 332 148 5472 1.177 Run 3 30 2995 4642 100 332 148 5472 1.179 Run 4 40 3008 4628 100 332 146.9 5472 1.182 Run 5 50 3006 4622 95 332 154.6 5472 1.184 Run 6 60 2997 3967 65 275 194.5 4532 1.142 Run 7 70 2992 4652 100 330 148.5 5439 1.169 Run 8 80 2999 4645 100 333 147.9 5488 1.182 Run 9 90 2994 4675 100 332 149.1 5472 1.17 Run 10 100 2999 4662 100 332 148.4 5472 1.174 Run 11 110 3008 4638 100 332 147.2 5472 1.18 Run 12 120 2999 4653 100 334 148.2 5505 1.183 Run 13 130 3002 4666 95 332 156.2 5472 1.173 Run 14 140 3001 4664 85 332 174.6 5472 1.173 Run 15 150 3001 4472 75 312 189.7 5142 1.15 Run 16 160 2999 4283 70 295 194.8 4862 1.135 Run 17 170 2998 4005 65 278 196.3 4582 1.144 Run 18 180 2997 4005 65 278 196.3 4582 1.144 Run 19 190 3000 3989 65 278 195.3 4582 1.149 Run 20 200 2999 3994 65 275 195.7 4532 1.135 Run 21 210 3011 4642 100 333 147.2 5488 1.182 Run 22 220 3013 4612 100 331 146.2 5455 1.183 Run 23 230 2998 4659 100 333 148.4 5488 1.178 Run 24 240 3008 4655 100 333 147.8 5488 1.179 Run 25 250 2991 4639 100 334 148.1 5505 1.187 Run 26 260 2989 4614 100 332 147.4 5472 1.186 Run 27 270 3002 4267 70 296 193.9 4878 1.143 Run 28 280 3011 4712 100 332 149.4 5472 1.161 Run 29 290 2996 4697 100 333 149.7 5488 1.168 Run 30 300 3010 4678 100 332 148.4 5472 1.17 Run 31 310 2997 4678 100 334 149.1 5505 1.177 Run 32 320 3011 4691 100 332 148.8 5472 1.166 Run 33 330 3000 4688 100 333 149.2 5488 1.171 Run 34 340 3011 4708 95 334 157.2 5505 1.169 Run 35 350 3003 4678 90 333 165.3 5488 1.173 File:F:\UPHES SYSTEM EES\Validation_D5_Test_Data.EES 8/24/2017 3:31:03 PM Page 3 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa Parametric Table: DFT NO. 5 SHAFT TEST DATA TIME NTURBINE PACTUAL SFEED VTURBINE TTURBINE PTHEORETICAL H [MIN] [rpm] [kW] [-] [l/s] [Nm] [kW] [-] Run 36 360 3006 4581 80 326 181.9 5373 1.173 Run 37 370 2996 4016 65 277 196.9 4565 1.137 Run 38 380 2999 4684 100 333 149.1 5488 1.172 Run 39 390 3000 4688 100 334 149.2 5505 1.174 Run 40 400 3002 4656 100 336 148.1 5538 1.189 Run 41 410 3009 4675 100 337 148.4 5554 1.188 Run 42 420 3007 4698 100 337 149.2 5554 1.182 Run 43 430 3002 4677 100 335 148.8 5521 1.18 Run 44 440 2997 4661 100 337 148.5 5554 1.192 Run 45 450 3006 4638 90 336 163.7 5538 1.194 Run 46 460 3004 4750 100 335 151 5521 1.162 Run 47 470 3000 4716 100 335 150.1 5521 1.171 Run 48 480 3008 4697 100 334 149.1 5505 1.172 Run 49 490 3001 4648 100 336 147.9 5538 1.191 Run 50 500 3001 4639 100 338 147.6 5571 1.201 Run 51 510 2998 4620 100 337 147.2 5554 1.202 Run 52 520 3012 4630 100 337 146.8 5554 1.2 Run 53 530 3007 4658 95 334 155.7 5505 1.182 Run 54 540 3009 4677 85 334 174.6 5505 1.177 Run 55 550 3000 4472 75 313 189.8 5158 1.154 Run 56 560 3002 4309 70 299 195.8 4928 1.144 Run 57 570 2990 4047 65 281 198.8 4631 1.144 Run 58 580 3002 4034 65 282 197.4 4648 1.152 Run 59 590 3000 4589 100 334 146.1 5505 1.2 Run 60 600 2995 4723 100 337 150.6 5554 1.176 Run 61 610 3003 4664 100 337 148.3 5554 1.191 Run 62 620 3000 4673 100 335 148.7 5521 1.181 Run 63 630 3006 4638 100 334 147.3 5505 1.187 Run 64 640 3000 4662 100 334 148.4 5505 1.181 Run 65 650 2995 4686 95 334 157.3 5505 1.175 Run 66 660 3003 4275 70 297 194.2 4895 1.145 Run 67 670 3002 4731 100 337 150.5 5554 1.174 Run 68 680 3008 4669 100 335 148.2 5521 1.182 Run 69 690 2997 4686 100 333 149.3 5488 1.171 Run 70 700 3002 4683 100 335 149 5521 1.179 Run 71 710 2994 4686 95 335 157.3 5521 1.178 Run 72 720 3001 4558 80 331 181.3 5455 1.197 Run 73 730 3006 4014 65 278 196.2 4582 1.141 Run 74 740 3003 4711 100 336 149.8 5538 1.175 Run 75 750 3008 4681 100 336 148.6 5538 1.183 Run 76 760 2997 4677 95 333 156.9 5488 1.173 Run 77 770 3002 4664 85 334 174.5 5505 1.18 Run 78 780 2997 4483 75 316 190.5 5208 1.162 Run 79 790 3006 4300 70 298 195.1 4911 1.142 Run 80 800 3002 4780 100 335 152.1 5521 1.155 Run 81 810 3002 4734 100 334 150.6 5505 1.163 Run 82 820 3000 4733 100 333 150.7 5488 1.16 Run 83 830 2996 4498 75 315 191.2 5191 1.154 Run 84 840 3009 4769 100 335 151.3 5521 1.158 Run 85 850 3000 4708 100 336 149.9 5538 1.176 Run 86 860 3000 4650 100 336 148 5538 1.191 Run 87 870 3008 4666 100 334 148.1 5505 1.18 Run 88 880 3013 4680 100 334 148.3 5505 1.176 Run 89 890 3003 4706 100 334 149.6 5505 1.17 Run 90 900 3010 4442 75 309 187.9 5093 1.146 File:F:\UPHES SYSTEM EES\Validation_D5_Test_Data.EES 8/24/2017 3:31:03 PM Page 4 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa Parametric Table: DFT NO. 5 SHAFT TEST DATA TIME NTURBINE PACTUAL SFEED VTURBINE TTURBINE PTHEORETICAL H [MIN] [rpm] [kW] [-] [l/s] [Nm] [kW] [-] Run 91 910 3007 4761 100 336 151.2 5538 1.163 Run 92 920 2996 4686 100 336 149.4 5538 1.182 Run 93 930 2997 4666 100 334 148.7 5505 1.18 Run 94 940 3008 4644 100 336 147.4 5538 1.192 Run 95 950 3001 4645 100 335 147.8 5521 1.189 Run 96 960 3002 4675 100 334 148.7 5505 1.177 Run 97 970 3008 4675 90 333 164.9 5488 1.174 Run 98 980 2994 4553 80 330 181.5 5439 1.195 Run 99 990 3003 4495 75 317 190.6 5224 1.162 Parametric Table: DFT NO. 5 SHAFT TEST DATA PACTUAL,CALCULATED RATIOSYSTEM PTHEORETICAL,9 PACTUAL,9 [kW] [kW] [kW] Run 1 Run 2 4799 0.1976 6335 5556 Run 3 4799 0.1976 6335 5556 Run 4 4799 0.1976 6335 5556 Run 5 4799 0.1976 6335 5556 Run 6 3975 0.1637 5247 4602 Run 7 4770 0.1964 6297 5522 Run 8 4813 0.1982 6354 5572 Run 9 4799 0.1976 6335 5556 Run 10 4799 0.1976 6335 5556 Run 11 4799 0.1976 6335 5556 Run 12 4828 0.1988 6373 5589 Run 13 4799 0.1976 6335 5556 Run 14 4799 0.1976 6335 5556 Run 15 4510 0.1857 5953 5221 Run 16 4264 0.1756 5629 4936 Run 17 4018 0.1655 5304 4652 Run 18 4018 0.1655 5304 4652 Run 19 4018 0.1655 5304 4652 Run 20 3975 0.1637 5247 4602 Run 21 4813 0.1982 6354 5572 Run 22 4784 0.197 6316 5539 Run 23 4813 0.1982 6354 5572 Run 24 4813 0.1982 6354 5572 Run 25 4828 0.1988 6373 5589 Run 26 4799 0.1976 6335 5556 Run 27 4278 0.1762 5648 4953 Run 28 4799 0.1976 6335 5556 Run 29 4813 0.1982 6354 5572 Run 30 4799 0.1976 6335 5556 Run 31 4828 0.1988 6373 5589 Run 32 4799 0.1976 6335 5556 Run 33 4813 0.1982 6354 5572 Run 34 4828 0.1988 6373 5589 Run 35 4813 0.1982 6354 5572 Run 36 4712 0.194 6220 5455 Run 37 4004 0.1649 5285 4635 Run 38 4813 0.1982 6354 5572 Run 39 4828 0.1988 6373 5589 Run 40 4856 0.2 6411 5622 Run 41 4871 0.2006 6430 5639 File:F:\UPHES SYSTEM EES\Validation_D5_Test_Data.EES 8/24/2017 3:31:04 PM Page 5 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa Parametric Table: DFT NO. 5 SHAFT TEST DATA PACTUAL,CALCULATED RATIOSYSTEM PTHEORETICAL,9 PACTUAL,9 [kW] [kW] [kW] Run 42 4871 0.2006 6430 5639 Run 43 4842 0.1994 6392 5606 Run 44 4871 0.2006 6430 5639 Run 45 4856 0.2 6411 5622 Run 46 4842 0.1994 6392 5606 Run 47 4842 0.1994 6392 5606 Run 48 4828 0.1988 6373 5589 Run 49 4856 0.2 6411 5622 Run 50 4885 0.2012 6449 5656 Run 51 4871 0.2006 6430 5639 Run 52 4871 0.2006 6430 5639 Run 53 4828 0.1988 6373 5589 Run 54 4828 0.1988 6373 5589 Run 55 4524 0.1863 5972 5238 Run 56 4322 0.178 5705 5003 Run 57 4061 0.1673 5362 4702 Run 58 4076 0.1679 5381 4719 Run 59 4828 0.1988 6373 5589 Run 60 4871 0.2006 6430 5639 Run 61 4871 0.2006 6430 5639 Run 62 4842 0.1994 6392 5606 Run 63 4828 0.1988 6373 5589 Run 64 4828 0.1988 6373 5589 Run 65 4828 0.1988 6373 5589 Run 66 4293 0.1768 5667 4970 Run 67 4871 0.2006 6430 5639 Run 68 4842 0.1994 6392 5606 Run 69 4813 0.1982 6354 5572 Run 70 4842 0.1994 6392 5606 Run 71 4842 0.1994 6392 5606 Run 72 4784 0.197 6316 5539 Run 73 4018 0.1655 5304 4652 Run 74 4856 0.2 6411 5622 Run 75 4856 0.2 6411 5622 Run 76 4813 0.1982 6354 5572 Run 77 4828 0.1988 6373 5589 Run 78 4567 0.1881 6029 5288 Run 79 4307 0.1774 5686 4987 Run 80 4842 0.1994 6392 5606 Run 81 4828 0.1988 6373 5589 Run 82 4813 0.1982 6354 5572 Run 83 4553 0.1875 6010 5271 Run 84 4842 0.1994 6392 5606 Run 85 4856 0.2 6411 5622 Run 86 4856 0.2 6411 5622 Run 87 4828 0.1988 6373 5589 Run 88 4828 0.1988 6373 5589 Run 89 4828 0.1988 6373 5589 Run 90 4466 0.1839 5896 5171 Run 91 4856 0.2 6411 5622 Run 92 4856 0.2 6411 5622 Run 93 4828 0.1988 6373 5589 Run 94 4856 0.2 6411 5622 Run 95 4842 0.1994 6392 5606 Run 96 4828 0.1988 6373 5589 File:F:\UPHES SYSTEM EES\Validation_D5_Test_Data.EES 8/24/2017 3:31:04 PM Page 6 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa Parametric Table: DFT NO. 5 SHAFT TEST DATA PACTUAL,CALCULATED RATIOSYSTEM PTHEORETICAL,9 PACTUAL,9 [kW] [kW] [kW] Run 97 4813 0.1982 6354 5572 Run 98 4770 0.1964 6297 5522 Run 99 4582 0.1887 6049 5305 270 280 290 300 310 320 330 340 4000 4200 4400 4600 4800 5000 0.17 0.18 0.19 0.2 0.21 VTURBINE [l/s] P A C TU A L [k W ] R A TI O SY ST EM File:F:\UPHES SYSTEM EES\Validation_D5_Test_Data.EES 8/24/2017 3:31:04 PM Page 7 EES Ver. 10.107: #2413: Mechanical & Nuclear Engineering, North-West University, Potchefstroom, South Africa 0 100 200 300 400 500 600 700 800 900 1000 3800 4000 4200 4400 4600 4800 5000 5200 5400 5600 5800 6000 TIME [min] P A C TU A L [k W ]