Stability Assessment of Power Systems Based on a Robust Sum-of-Squares Optimization Approach

Abstract

Secure operation of the evolving power systems, characterised by more renewable energy sources and increasingly variable consumption, will require enhanced monitoring and more automatic control actions. One example is the need for fast detection and control actions to avoid loss of synchronism or grid islanding caused by transient instability. In this paper, we present a method suitable for on-line transient stability assessment of power systems, based on Lyapunov's second method for stability analysis of dynamical systems. The method uses Sum-Of-Squares optimization to algorithmically construct a Polynomial Lyapunov Function and estimate the Region-Of-Attraction for a given stable operating state. The main benefit of the method is that it obviates the painstaking process of finding a suitable Lyapunov function. Our approach includes a robust handling of the truncation error in the Taylor series expansion of the system model, and thereby ensures that the estimate of the region of attraction around an operating point is inside the actual region of attraction. Using a singlemachine-infinite-bus system, we demonstrate the application of the method in this paper.

Maximal Positively Invariant Set Determination for Transient Stability Assessment in Power Systems

“…Indeed, a ROA provides the set of acceptable (post-fault) conditions of a dynamic system which are known to reach a given target set in a specified time. They can be obtained through the construction of polynomial Lyapunov functions [3], [4], as well as using the notion of occupation measures and Lasserre's hierarchy [5], [6]. As long as the dynamics of the system is polynomial, both formulations yield a moment-sum-of-squares (SOS) optimization program that can be efficiently solved by semi-definite programming (SDP), a particular class of efficient convex optimization tools.…”