Representation of transformers in switching surge studies

Abstract

A Transformer representation suitable for switching surge analysis is derived in terms of 'primitive' inductance and capacitance matrices. Connection matrices are used to account for all types of winding connections. Frequency dependance of elements is considered. The transmission line is formulated on a frequency basis, and the earth return path is represented by Carson's formula. Series and shunt compensation are also included with the line. The cable is similarly formulated. The problem is solved in the frequency plane using the Fourier Transform, and then transformed back into the time domain. Modal analysis is used for both transmission line and cable two port admittance matrix formulation. Energisation on both low voltage as well as high voltage sides of the source side transformer are considered for transformer feeders. A few comparisons with field test oscillograms are given to validate the formulation of the problem. Voltage non-linearities when surge divertors are present are considered using a step response of the linear system and Duhamel's integral, together with the Newton-Raphson iterative technique for both single phase and three operation. Finally, the Newton-Raphson algorithm is further extended to take into account the magnetic non-linearity of the transformer 'core. Flux coupling between phases during saturation is calculated based on the instantaneous reluctance values of the individual limbs and the leakage air path.