Abstract
This paper presents an algorithm estimating the regions of attraction of power systems based on the Lyapunov function approach where a sublevel set of a Lyapunov function for a target system is used as the estimate. In particular, we focus here on the algorithm based on sum of squares (SOS) programming, which has been recently proposed, and aim to develop a simpler algorithm for the practical use. For this aim, we present an algorithm overcoming the difficulty of the SOS programming problem addressed in the existing study, i.e., the bilinear constraints, in a simpler way. In the proposed algorithm, two SOS programming problems are iteratively solved, and the number of the problems solved at each iteration is reduced to half of that in the existing algorithm. In addition, we theoretically analyze the proposed algorithm, and show the convergence under certain conditions. The performance of our algorithm is demonstrated by numerical examples.
Highlights
Stability analysis of power systems has been a major topic in the field of power engineering
From Theorem 1, the proposed algorithm works as long as there exists a solution to the SOSP1 at k = 1, and it converges if the region of attraction (ROA) is bounded
This paper has considered an algorithm estimating the ROA of a given power system by using sum of squares (SOS) programming
Summary
Stability analysis of power systems has been a major topic in the field of power engineering. A promising method to solve this problem is the Lyapunov function approach, i.e., to find a Lyapunov function for a target system and use the sublevel set as an estimate of the ROA. The algorithm is composed of two loops, and we have to iteratively solve four different types of SOS programming problems in a loop Such complexity is undesirable for the users because the time and effort spent to understand and implement the algorithm increase. We guarantee that there exist solutions to the two SOS programming problems solved at each iteration, and show that the algorithm converges under certain conditions. This provides a theoretical guarantee for the proposed algorithm
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