TY - JOUR

T1 - A Tool for Analysis of Existence of Equilibria and Voltage Stability in Power Systems with Constant Power Loads

AU - Matveev, Alexey S.

AU - MacHado, Juan E.

AU - Ortega, Romeo

AU - Schiffer, Johannes

AU - Pyrkin, Anton

N1 - Funding Information: Manuscript received March 8, 2019; revised June 25, 2019 and October 23, 2019; accepted January 2, 2020. Date of publication January 9, 2020; date of current version October 21, 2020. This work was supported in part by the Government of Russian Federation under Grant GOSZADANIE 2.8878.2017/8.9, Grant 08-08, and in part by the National Natural Science Foundation of China under Grant 61473183 and Grant U1509211. The work of J. E. Machado was supported by the Mexican Government through the National Council of Science and Technology (CONACyT). Recommended by Associate Editor Y. Le Gor-rec. (Corresponding author: Romeo Ortega.) A. S. Matveev is with the Department of Mathematics and Mechanics, Saint Petersburg State University, St. Petersburg 198504, Russia (e-mail: almat1712@yahoo.com). Publisher Copyright: © 2020 IEEE. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/11

Y1 - 2020/11

N2 - It is well known that constant power loads in power systems have a destabilizing effect. Their growing presence in modern installations significantly aggravates this issue, hence, motivating the development of new methods to analyze their effect in ac and dc power systems. Formally, this problem can be cast as the analysis of solutions of a set of nonlinear algebraic equations of the form f(x)=0, where f: Rn → Rn, to which we associate the differential equation ˙x=f(x). By invoking advanced concepts of dynamical systems theory and effectively exploiting its monotonicity, the following properties are established: First, prove that, if there are equilibria, there is a distinguished one that is stable and attractive, and give conditions such that it is unique. Second, give a simple online procedure to decide whether equilibria exist or not and to compute the distinguished one. Third, prove that the method is also applicable for the case when the parameters of the system are not exactly known. It is shown how the proposed tool can be applied to the analysis of long-term voltage stability in ac power systems, and to the study of existence of equilibria of multiterminal high-voltage dc systems and dc microgrids.

AB - It is well known that constant power loads in power systems have a destabilizing effect. Their growing presence in modern installations significantly aggravates this issue, hence, motivating the development of new methods to analyze their effect in ac and dc power systems. Formally, this problem can be cast as the analysis of solutions of a set of nonlinear algebraic equations of the form f(x)=0, where f: Rn → Rn, to which we associate the differential equation ˙x=f(x). By invoking advanced concepts of dynamical systems theory and effectively exploiting its monotonicity, the following properties are established: First, prove that, if there are equilibria, there is a distinguished one that is stable and attractive, and give conditions such that it is unique. Second, give a simple online procedure to decide whether equilibria exist or not and to compute the distinguished one. Third, prove that the method is also applicable for the case when the parameters of the system are not exactly known. It is shown how the proposed tool can be applied to the analysis of long-term voltage stability in ac power systems, and to the study of existence of equilibria of multiterminal high-voltage dc systems and dc microgrids.

KW - Constant power loads (CPLs)

KW - existence of equilibria

KW - power systems

KW - voltage-stability

UR - http://www.scopus.com/inward/record.url?scp=85095701957&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/c2621cd4-66bb-3d55-a768-e32c24f58e41/

U2 - 10.1109/TAC.2020.2965028

DO - 10.1109/TAC.2020.2965028

M3 - Article

AN - SCOPUS:85095701957

VL - 65

SP - 4726

EP - 4740

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 11

M1 - 8954769

ER -