A novel model reduction approach for linear time-invariant systems via enhanced PSO-DV algorithm and improved MPPA method

Abstract

In this article, the combination of stochastic search and conventional approaches are used to develop an optimal frequency-domain model order reduction method for determining the stable and accurate reduced-order model for the stable large-scale linear time-invariant systems. The method uses the enhanced particle swarm optimization with differentially perturbed velocity algorithm to determine the denominator polynomial coefficients of the reduced-order model, whereas the numerator polynomial coefficients of the reduced-order model are determined by using an improved multi-point Padé approximation method. The method generates an optimum reduced-order model by minimizing an objective function [Formula: see text], which is formulated using two functions. The first function, [Formula: see text], evaluates the measure of integral squared error between the step responses of the original system and the reduced-order model. And the second function evaluates the measure of retention of full impulse response energy of the original system in the reduced-order model. Therefore, by minimizing the objective function ‘ E’, the proposed method is guaranteed for preserving passivity, stability and the accuracy of the original higher order system in the reduced-order model. The proposed method is extended to the linear time-invariant multi-input multi-output system. In this case, an optimal reduced-order model is determined by minimizing a single objective function [Formula: see text], which is formulated by linear scalarizing of all the objective function [Formula: see text] components. The method is popular for preserving stability, passivity and accuracy of the original system in the reduced-order model. The validation of the method is shown by applying to a sixth-order single-input single-output hydropower system model as well as to the seventh-order two-area multi-input multi-output power system model. The comparison of the simulation results of integral squared error and impulse response energy values of the reduced-order models demonstrates the dominance of the proposed method than the existing reduction methods available in the literature.