Elimination of Mutual Inductances from the State-Space Model of a Transformer Winding’s Ladder Network Using Eigen Decomposition

Mutual inductances exist between different sections of a transformer winding’s ladder network due to the interaction of the magnetic field between the two corresponding sections carrying different currents. Precise estimation of mutual inductances is critical because any error in its determination will deviate the simulated frequency response of the winding, resulting in incorrect transformer diagnostic. Mutual inductance can be estimated from transformer design details using analytical formulae or finite element analysis. It can also be estimated by fitting the measured and estimated driving point impedances with non-linear optimization techniques. However, none of the techniques available guarantee a unique, physically realisable, and accurate solution. This paper proposes an eigen decomposition-based method for elimination of the mutual coupling between coils and the transformed decoupled state-space model is obtained without affecting the frequency response signature of the transformer. To demonstrate the efficacy of the estimated transformed decoupled state-space model, simulation results of a six-section ladder network are presented.