Analysis and Prediction of Electric Power System’s Stability Based on Virtual State Estimators

Natalia Bakhtadze,Igor Yadikin

doi:10.3390/math9243194

Natalia Bakhtadze, Igor Yadikin

Open Access

https://doi.org/10.3390/math9243194

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Journal: Mathematics	Publication Date: Dec 10, 2021
Citations: 3	License type: CC BY 4.0

Affiliation: V. A. Trapeznikov Institute of Control Sciences

Abstract

The stability of bilinear systems is investigated using spectral techniques such as selective modal analysis. Predictive models of bilinear systems based on inductive knowledge extracted by big data mining techniques are applied with associative search of statistical patterns. A method and an algorithm for the elementwise solution of the generalized matrix Lyapunov equation are developed for discrete bilinear systems. The method is based on calculating the sequence of values of a fixed element of the solution matrix, which depends on the product of the eigenvalues of the dynamics matrix of the linear part and the elements of the nonlinearity matrixes. A sufficient condition for the convergence of all sequences is obtained, which is also a BIBO (bounded input bounded output) systems stability condition for the bilinear system.

Highlights

Stability estimators are increasingly used in mode planning and supervisory control in present day electric power systems (EPS) [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]
Research methods for bilinear systems have been actively developed over recent decades [2,3,4,5,20,21,24,25,26,27,28]
The method is based on calculating the sequence of values of a fixed element of the solution matrix, which depends on the product of the eigenvalues of the dynamics matrix of the linear part and the elements of the nonlinearity matrixes

Summary

Introduction

Stability estimators (soft sensors) are increasingly used in mode planning and supervisory control in present day electric power systems (EPS) [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]. Due to the growing popularity of distributed generation and renewable energy sources (RES) in EPS, its operation modes may approach the stability limits. It is, necessary to improve both predictive modeling techniques and the methods of analysis and preventive control for small deviation modes, and for essentially nonlinear ones [14,20,21,22,23]. Spectral methods of stability analysis, in particular, selective modal analysis, are widely used in the design and operation of EPS [16,18,22,23]

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Conclusion