A New Method for the Calculation of Subtransmission and Distribution System Transients Based on the FFT

Abstract

A new method for the calculation of subtransmission and distribution system voltages is proposed. The method is appropriate for the calculation of bus voltage transients due to the operation of large industrial loads: in this sense, the method is for power quality calculations. In particular, the method may be used for load currents which are electronically switched. The method is based on the Fourier transform of Ohm's law Vi(?)=Zij(?Ij(?) where Zij is the transfer impedeance between the busses i and j which are the busses at which the voltage transient is to be calculated and the bus at which high load currents occur, respectively. The Fourier transform is valid for most types of power system transients of practical interest, and this transform may be readily approximated by the fast Fourier transform (FFT). The FFT is a computationally efficient transform which is widely used in communications engineering and certain other areas. In this paper, a new method is described for the calculation of Zij(?). The method is based on a decoupling procedure whereby the power network is decomposed into two circuits. One of these circuits is composed of resistive and inductive elements, and the other is composed of conductive and capacitive elements. The former is a series network which has frequency dependence given by R + j?L and the latter is a shunt network with the admittance characteristic G + j?C. An interesting matrix version of the parallel impedance formula is developed and used to find Zij,(?).