A FAST ALGORITHM FOR THE SEMI-DEFINITE RELAXATION OF THE STATE ESTIMATION PROBLEM IN POWER GRIDS - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Industrial and Management Optimization Année : 2019

A FAST ALGORITHM FOR THE SEMI-DEFINITE RELAXATION OF THE STATE ESTIMATION PROBLEM IN POWER GRIDS

Résumé

State estimation in power grids is a crucial step for monitoring and control tasks. It was shown that the state estimation problem can be solved using a convex relaxation based on semi-definite programming. In the present paper, we propose a fast algorithm for solving this relaxation. Our approach uses the Bürer Monteiro factorisation in a special way that solves the problem on the sphere and estimates the scale in a Gauss-Seidel fashion. Simulation results confirm the promising behaviour of the method. 1. Introduction. Power networks have been a topic of extensive recent studies, both from an engineering and an applied mathematical viewpoint. The main problems addressed in Power Networks engineering come from the need to control and monitor large and sometimes very large grids. The problem of estimating the state, i.e. the voltage at each bus, is one of the most basic problems in the field. One of the major difficulties with the state estimation problem is that it is a non convex polynomial least-squares optimisation problem. Fortunately, several recent works have addressed this issue. In this paper, we leverage the structure of the problem in order to provide an efficient method based on the breakthrough results of Bürer and Monteiro [8] and the recent discoveries around matrix least-squares problems [29].
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Dates et versions

hal-02515906 , version 1 (25-03-2020)

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Stephane Chretien, Paul Clarkson. A FAST ALGORITHM FOR THE SEMI-DEFINITE RELAXATION OF THE STATE ESTIMATION PROBLEM IN POWER GRIDS. Journal of Industrial and Management Optimization, 2019, 16, pp.431 - 443. ⟨10.3934/jimo.2018161⟩. ⟨hal-02515906⟩
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