An Extended Stochastic Region of Attraction Estimation Method for Power Systems Under Stochastic Sustained Disturbances

Stochastic sustained disturbances (SSDs) in renewable energy output impact power system transient stability. This study addresses the dynamic performance of power systems under SSDs using Lévy-driven stochastic differential algebraic equations (LDSDAEs). The stochastic region of attraction for LDSDAEs is divided into a stable region and a probabilistically stable region, collectively termed the extended stochastic region of attraction (ESRA). Traditional methods for estimating the deterministic region of attraction (RA) are inadequate. To address this issue, this study proposes an estimation method for the ESRA of LDSDAEs based on escape probability. We first derive an integro-differential equation for escape probabilities of initial system states near the attractor of LDSDAEs. We then explore the connection between escape probability and ESRA. Finally, we propose a wavelet basis functions-based extended projection method to solve the integro-differential equation, providing an analytical expression for escape probabilities and thus determining the ESRA. Case studies on the modified IEEE 39- and 118-bus systems demonstrate the proposed method's high computational accuracy and efficiency for power systems under Lévy disturbances.