An improved algorithm of finding steady‐state solutions for AC machines

Abstract

Purpose

The purpose of this paper is to reduce issues arising when computing steady‐state solutions for AC machine models using the harmonic balance method.

Design/methodology/approach

Generally, currents at steady‐states of AC machines are described by periodic or quasi‐periodic time functions, which Fourier spectra are determined by an infinite set of algebraic equations obtained from a harmonic balance method. To solve them, after reducing to finite dimensions, an iterative algorithm is developed in this paper. It bases on the LU decomposition of an infinite matrix representing the inductance matrix of an AC machine. Since that decomposition is done separately, due to a band type form of this matrix, the equation set determining the Fourier spectra of currents is solved recurrently.

Findings

An algorithm for the LU decomposition of an infinite matrix representing the inductance matrix of an AC machine and an iterative algorithm for determining AC machine steady‐state currents in a recursive manner.

Research limitations/implications

The approach is limited to solving of so‐called “circuital” models of AC voltage supplied machines. The approach breaks the large dimension barrier when solving steady‐state equations for AC machines.

Practical implications

Reducing computer requirements in terms of computer memory, workload and computing time to determine a steady‐state solution for AC machines.

Originality/value

A separation of the LU decomposition of an infinite matrix representing the inductance matrix in AC machine steady‐state model from the solution method.

Citation

Sobczyk, T. (2010), "An improved algorithm of finding steady‐state solutions for AC machines", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 29 No. 3, pp. 773-788. https://doi.org/10.1108/03321641011028305