Physics-Based Thermal Model of Shunt Reactors

While holding several constructive similarities with power transformers, shunt reactors' thermal behavior differs significantly from transformers. Yet, the most common approach is to estimate the temperature distribution of shunt reactors using the same thermal model developed for power transformers. While adjusting some of the empirical coefficients of the model may lead to minimizing the deviations in the predicted temperatures, due to the exponential nature of the solid insulation life consumption, small deviations in the hottest spot temperature may represent several years or decades of difference in the expected lifespan. A physics-based thermal model was included in the IEEE C57.91 in the 80s, traditionally referred to as the “Annex G” model. Rather than using time constants and exponential functions to predict the temperature gradients under different loading conditions, the model utilizes a model similar to a Runge-Kutta method, on a sequential calculation procedure based on an initial value, using small enough time steps. For each time step, equations are used to calculate the heat generated and dissipated by the different elements of the transformer, estimating the temperature variation for the average winding and the hotspot region. Considering the differences in the variation of losses and heat dissipation as a function of the system voltage, the so-called “Annex G” model was adapted for shunt reactors. A comparison of the results with measurements and results from other models is presented in this article.