A Critical Escape Probability Formulation for Enhancing the Transient Stability of Power Systems with System Parameter Design

arXiv (Cornell University)

Abstract

For the enhancement of the transient stability of power systems, the key is to define a quantitative optimization formulation with system parameters as decision variables. In this paper, we model the disturbances by Gaussian noise and define a metric named Critical Escape Probability (CREP) based on the invariant probability measure of a linearised stochastic processes. CREP characterizes the probability of the state escaping from a critical set. CREP involves all the system parameters and reflects the size of the basin of attraction of the nonlinear systems. An optimization framework that minimizes CREP with the system parameters as decision variablesis is presented. Simulations show that the mean first hitting time when the state hits the boundary of the critical set, that is often used to describe the stability of nonlinear systems, is dramatically increased by minimizing CREP. This indicates that the transient stability of the system is effectively enhanced. It also shown that suppressing the state fluctuations only is insufficient for enhancing the transient stability. In addition, the famous Braess' paradox which also exists in power systems is revisited. Surprisingly, it turned out that the paradoxes identified by the traditional metric may not exist according to CREP. This new metric opens a new avenue for the transient stability analysis of future power systems integrated with large amounts of renewable energy.

Authors 5

1. Xian Wu

   Shandong University

   Affiliation as printed

   School of Mathematics , Shandong University , Jinan , 250100 , P. R. China

2. Kaihua Xi

   Shandong University

   Affiliation as printed

   School of Mathematics , Shandong University , Jinan , 250100 , P. R. China

3. Aijie Cheng

   Shandong University

   Affiliation as printed

   School of Mathematics , Shandong University , Jinan , 250100 , P. R. China

4. Chenghui Zhang

   Shandong University

   Affiliation as printed

   School of Control Science and Engineering , Shandong University , Jinan , 250061 , P. R. China

5. Hai Xiang Lin Aachen Institute of Environmental Sciences (CML)

   Leiden University · Delft University of Technology

   Affiliation as printed

   Delft Institute of Applied Mathematics , Delft University of Technology , Delft , 2628 CD , The Netherlands

   Institute of Environmental Sciences (CML) , Leiden University , Leiden 2333 CC , The Netherlands