On Analytical Estimation of Inductances in Equivalent Ladder Network Model of a Homogeneous Transformer Winding Using FRA Data

The determination of ladder-network model parameters for transformer winding holds paramount significance in validating the design constraints of the transformer winding, with a particular emphasis on facilitating thorough analysis of its impulse behaviour. As these parameters cannot be measured directly, the majority of studies documented in the literature rely on iterative optimization techniques for estimation, and as of now, no analytical solution has been reported and implemented. To address this concern, this paper introduces an analytical approach for estimating unknown self and mutual inductances in equivalent ladder-network model of a homogeneous transformer winding, employing frequency response measurement. For this purpose, the method derived necessary linear and non-linear equations of unknown inductances pertaining to the coupled ladder-network model of the winding. The solution is directly obtained utilizing essential peak and trough frequencies extracted from three measured admittance magnitude responses along with series and ground capacitances determined separately. The practicality of the method has been verified using experimental results on three different transformer windings including one with iron-core. For improved precision, the estimated inductance values were fine-tuned further using conventional optimization technique. Results indeed demonstrate the practicality as well as efficacy of the method.