Dimension Estimation of Transformer Windings Based on Frequency Response Measurement

Frequency response of a transformer winding is a powerful tool to determine the parameters of fast transient models in case that the internal structure and design documents are not available. One method to determine the model parameters is to estimate the geometric dimensions of the winding and calculating the parameters of the model based on the estimated dimensions and existing analytical formulas. In the current paper, dimension estimation of a transformer winding to estimate the parameters of a detailed RCLM model for fast transient analysis is converted to an optimization problem. The resulting model is called transient gray box model. The gray box model of the transformers' windings is used for analysis of internal behavior of a winding when a transformer's factory documentation is not accessible. Particle swarm optimization algorithm is used to minimize a proper cost function to achieve the best overall fitting between measured and calculated frequency response of the winding in a range of 10 kHz to 1 MHz. Several tests are conducted on a non-interleaved double disk winding to evaluate the precision of the model. In addition to the terminal frequency response measurement, internal frequency response of the winding are measured. Comparison between simulation results and both measured internal and external voltage waveforms, confirm that determining the RCLM model parameters based on estimation of winding dimension is a reliable and applicable method to study the transformer winding behavior.