Spectral and Modal Methods for Studying Stability and Control of Electric Power Systems
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Spectral and Modal Methods for Studying Stability and Control of Electric Power Systems N. I. Voropai∗,a , I. I. Golub∗,b , D. N. Efimov∗,c , A. B. Iskakov∗∗,d , and I. B. Yadykin∗∗,e ∗
Melentiev Energy Systems Institute, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia ∗∗ Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia e-mail: a [email protected], b [email protected], c efi[email protected], d [email protected], e [email protected] Received August 2, 2019 Revised February 29, 2020 Accepted May 25, 2020
Abstract—The paper provides an overview of spectral and modal analysis methods for studying the stability of electric power systems (EPSs) and their control. Consideration is given to theoretical grounds of the methods and to the experience of their application for detecting the heterogeneity of the systems’ structure, identifying the coherency of generators’ motion, simplifying the mathematical model of the dynamics of EPSs, assessing their small-signal stability, and selecting the control actions to ensure it. The analysis of sub-Gramians for studying the EPS stability and other new directions in the development of the modal approach are discussed. Keywords: electric power systems, spectral analysis, modal analysis, stability assessment, control, model order reduction, sub-Gramians DOI: 10.1134/S000511792010001X
1. INTRODUCTION Electric power systems (EPSs) are human-made sophisticated technological facilities that include thousands of power generators interconnected for joint operation in an electric network; their rotors under normal conditions rotate at the same (synchronous) angular speed. The EPS stability under small and large disturbances has been and remains one of the most focal problems since the moment of constructing the first electric power system. This problem is especially significant for the sizeable present-day EPSs due to the emergence of new factors, such as irregular generation by renewable power sources, demand response of consumers, use of efficiently controlled devices based on power electronics in the electric network and among consumers. All these factors considerably deteriorate the properties of EPSs in terms of their stability. Furthermore, due to heterogeneity of the network structure, there remain bottlenecks (cutsets or groups of ties of the same directions with limited transfer capability), especially in the weakened network structure in post-emergency and maintenance conditions of large EPSs. The heterogeneity of the network structure stems from the presence in it of subsystems with strong internal ties and weak ties and buses between these subsystems (see Section 3). More extensive use of distributed generation units in EPSs, including the units based on renewable energy with low rotor inertia and the units connected to the network via back-to-back blocks, aggravates the situation as they reduce the system’s inertia and raise the risk of its stability loss. Violation of the stability of a complex system can lead to the cas
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