A novel analytical methodology for estimating high-frequency lumped model inductances and series capacitance of transformer winding: an indirect measurement procedure

In this article, a new analytical method is introduced to effectively estimate the self-inductance, mutual inductances, and series capacitance of transformer windings. The approach uses FR data collected at the winding terminals with the neutral open test. It applies an analytical formula that converts the sum of the inverse squares of both short-circuit and open-circuit natural frequencies, derived from the FR curve, into a polynomial function. These formulas are based on a lumped, mutually coupled equivalent model of the winding, with relationships expressed as a polynomial function connected by a factor relating the inductances, generalized to an N-1 degree for the N-th section of the model. By solving this polynomial, all winding inductance values can be accurately estimated, enabling the determination of the series capacitance. Notably, this method relies solely on measurements of the FR curve, ground capacitance, and equivalent inductance, providing an indirect yet highly efficient way to determine all parameters of the lumped mutually coupled equivalent model. This technique has been rigorously validated through experimental frequency response measurements on two air-core insulated windings, producing remarkably precise results that demonstrate its effectiveness in the field of frequency modeling.