An investigation into the occurrence of ferroresonance in small distribution transformers in South Africa

Abstract

In 2019, an article published by Geldenhuys and Padayachee reported unexpected overvoltages during the commissioning phase of distribution transformers. Consequently, resonance was reported as the cause of overvoltages on the secondary winding when the expected voltage was 0 V. Recent changes to the SANS 780 standard mandated a reduction in distribution transformer core losses, which made the overvoltages even worse. Geldenhuys and Padayachee claim to have only scratched the surface of the problem. A hypothesis was developed that the unexpected overvoltages could be caused by ferroresonance and a research study was launched to investigate the resonance phenomenon found in 32 kVA, 22/0.4 kV distribution transformers complying with the new SANS 780 standard of 2019. Ferroresonance is a nonlinear form of resonance involving a saturable inductor and a capacitor. Ferroresonance was first identified and described in 1914. Consequently, a vast amount of resources is available on the topic. Despite extensive studies in this field, ferroresonance is still poorly understood in the scientific community. This work provides a lengthy critical review of the literature on this topic. The literature on ferroresonance proves that the initiation of ferroresonance is strongly dependent on a wide variety of factors. One of these is remnant flux. The remnant flux dependence makes the modelling of ferroresonance particularly difficult. Accurate ferroresonance studies require a detailed hysteresis model which can store remnant flux upon de-energization. Consequently this work also contains a detailed study on hysteresis, which could be a study all on its own. The most prominent hysteresis models from this study are the Jiles-Atherton, Preisach and Tellinen models. The Tellinen model is the most elementary of these models and its implementation is straightforward. The Preisach model is the most complex and also the most accurate. The Jiles-Atherton model is most often used in literature since it is less involved than the Preisach model while still retaining the ability to model minor loops and remnant flux. Chapter 3 develops Tellinen and Jiles-Atherton hysteresis models and replicates results found in the literature. An important outcome in the study of ferroresonance proves that the π-transformer model is superior to the traditional T-model for the modelling of ferroresonance. Chapter 3 of this report replicates results found in literature and builds on the π-model to develop an accurate representation of the transformer being studied. The π-model is developed even further by considering not only the standard Open-Circuit (OC) and Short-Circuit (SC) transformer tests, but also the Sweep Frequency Response Analysis (SFRA) of the transformer. The SFRA allows the user to define a parallel capacitance across the magnetization branch of the transformer model,

which significantly improves its frequency behaviour up to 10 kHz. These capacitances are typically neglected for a lack of transformer design data. Chapter 3 also contains a detailed discussion on the use of peak vs Root Mean Squared (RMS) data points for simulation and the effect that high harmonic content can have on the modelling of a nonlinear inductor. Despite replicating hysteretic results in the literature, neither the Tellinen model nor the Jiles-Atherton model could accurately represent the transformer being studied. High harmonic content during the OC test presented numerous hurdles which could not be overcome. Numerical errors limited the use of the Tellinen model, while parameter determination was problematic for the Jiles-Atherton model. This is despite the use of Particle Swarm Optimization (PSO) to determine the 5 parameters of the Jiles-Atherton model. The developed π-model is used in Chapter 4 and Chapter 5 to conduct switching studies of the single-phase transformer in a power system. The overvoltages reported by Geldenhuys and Padayachee are replicated and independent studies show that the transformer is susceptible to ferroresonance. Bifurcation diagrams are used to investigate the effect of a variation in parameters on the ferroresonance of the transformer. However, simulations prove beyond doubt that ferroresonance is not the cause of the overvoltages in the power system. Two main reasons can be provided for this conclusion: 1) low line-to-ground voltage during single-phase switching and 2) low internal capacitance of the transformer. Chapter 5 proceeds to discuss three different mitigation strategies to reduce the overvoltages initiated by single-phase switching. The report concludes by making recommendations for future improvements, such as alternative cost functions for the PSO algorithm. This will allow hysteresis and remnant flux to also be taken into consideration. Several appendices provide proofs of errors in literature, MATLAB code, simulation data points and an article presented by the author at the 2021 South African Universities Power Engineering Conference.