Analytical Study of the Impacts of Stochastic Load Fluctuation on the Dynamic Voltage Stability Margin Using Bifurcation Theory

TL;DR

This study investigates how stochastic load fluctuations affect power system voltage stability, revealing the trade-off between fluctuation intensity and load variation speed using bifurcation theory and simulations.

Contribution

It uncovers the impact of load fluctuation parameters on voltage stability margin and introduces a novel analysis of their trade-off using stochastic differential equations.

Findings

Larger fluctuation intensity reduces stability margin.

Slower load variation speed decreases stability margin.

Trade-off between fluctuation intensity and load variation speed affects stability.

Abstract

This paper studies the impacts of stochastic load fluctuations, namely the fluctuation intensity and the load power variation speed, on power system dynamic voltage stability. Additionally, the trade-off relationship between the two parameters is revealed, which provides important insights regarding the potential of using energy storage to maintain voltage stability under high uncertainty. To this end, Stochastic Differential-Algebraic Equations (SDAEs) are used to model the stochastic load variation; bifurcation analysis is carried out to explain the influence of stochasticity. Numerical study and Monte Carlo simulations on the IEEE 14-bus system demonstrate that a larger fluctuation intensity or a slower load power variation speed may lead to a smaller voltage stability margin. To the best of authors' knowledge, this work uncovers the impacts of the time evolution property of the driving parameters, i.e., the load power variation speed and its trade off effect with the fluctuation intensity on the size of the dynamic voltage stability margin.