A Symbolic Expression for Computing the Driving Point Impedance and Pole-Zero-Gain of a Transformer from its Winding Parameters

Ladder networks are commonly used to study transformer windings for issues like partial discharges, winding deformations, and surge phenomena. The Driving Point Impedance (DPI) is a commonly studied parameter as it can be measured at the terminals and has alternating poles and zeros. Calculating DPI is usually done through state space modelling, but there is no direct formula available for a generalized transformer winding. In this study, a symbolic expression for computing the DPI function and its pole-zero gain directly from the impedance parameters is proposed. However, the calculation involves computing the inverse of the characteristic polynomial [sI − A] with a symbolic variable ‘s’, which is challenging. The problem is solved by breaking down the system matrix (A) using a block matrix inversion algorithm. Simulation results for a six-section ladder network of a transformer winding are presented to validate the proposed expressions.