Searching for the shortest path to voltage instability boundary: From Euclidean space to algebraic manifold

Abstract

Voltage instability is one of the main causes of power system blackouts. This paper focuses on finding the shortest path to the boundary of the singularity-induced voltage instability problem. Instead of using the Euclidean distance, we propose to use the arc length of the path on the network constraint manifold. This formulation is further converted into an optimal control framework to solve for the shortest path on the manifold. We rigorously show that the global solution of the proposed problem formulation always ends on the correct singular boundary. However, the traditional Euclidean distance formulation does not achieve this crucial topological property, thus, can lead to a wrong voltage collapse direction and/or a very conservative estimation of the stability margin. Numerical simulations are firstly performed on a low-dimensional example to fully visualize the algebraic manifold, the singular submanifold, and the optima for both problem formulations. Then, a larger 39-bus example is investigated in three different cases for both formulations. The results validate our theoretical statements that our proposed formulation always identifies the shortest path towards the correct voltage instability boundary. A broad range of potential applications using the proposed method are further discussed.