Contraction Region Analysis for Power Systems

This work is fully devoted to contraction theory-based analysis of stability. We discuss the contraction region and contraction metric that define for the power system model. The classical model of power system is contracting with respect to the proposed metric. The stability of nonlinear power system is proved by studying the properties of its Jacobian matrix. We demonstrate the necessary conditions for the existence of contraction for underlying the proposed power system model. The results of our simulations show that the contraction region exists. All eigenvalues of the Jacobian matrix are simulated to capture the behavior of a two-machine power system.