Generic algorithm to calculate Jacobian matrix used for ladder network parameters identification and winding fault diagnosis

Abstract

Ladder network parameters identification of transformer winding based on frequency response analysis data is crucial to winding fault diagnosis. In the authors’ previous study, the Gauss–Newton iteration algorithm (GNIA) had been proposed to efficiently identify the network parameters. The core in GNIA is the Jacobian matrix, composed of derivative of frequency response function (FRF) to network components. This study proposes a generic algorithm to calculate this Jacobian matrix. Two key problems concerning the algorithm are solved elaborately. The first problem is the method for derivative calculation toward an arbitrary FRF based on adjoint network method (ANM). The other issue is the mathematical model construction of double ladder network and its adjoint network toward different FRFs to obtain all network branch voltages and currents, which are required in the derivative calculation by ANM. This generic algorithm can efficiently and effectively calculate the Jacobian matrix, which can be applied on ladder network parameters identification and winding fault diagnosis.