# Model Reduction by Hermite Polynomials and Genetic Algorithm

Volume 9, Issue 3, pp 188-202
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### Authors

Hasan Nasiri Soloklo - Department of Electrical Engineering, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran. Omid Nail - Department of Electrical Engineering, Saghez branch, Islamic Azad university, Saghez, Iran. Malihe M. Farsangi - Electrical Engineering Department, Shahid Bahonar University of Kerman.

### Abstract

The present paper attempts to develop order reduction methods where the suggested reduction model consists of two phases. First, full order system is expanded by Hermite polynomials, then a set of parameters in a fixed structure are determined, whose values define the reduced order system. The values are obtained using Genetic Algorithm (GA) by minimizing the errors between the l first coefficients of Hermite polynomials expansion of full and reduced systems. To satisfy the stability, Routh criterion is used as constraints in optimization problem. To present the ability of the proposed method, three test systems are reduced. The results obtained are compared with other existing techniques. The results obtained show the accuracy and efficiency of the proposed method.

### Keywords

• Hermite polynomials
• genetic algorithm
• Routh array
• order reduction
• stability constraints.

•  93C05
•  93D05
•  93B20
•  92D99
•  93A15

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