Stability Assessment of Power Systems Based on a Robust Sum-of-Squares Optimization Approach
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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 single-machine-infinite-bus system, we demonstrate the application of the method in this paper.