Efficient Sampling and Sensitivity Analysis of Rare Transient Instability Events via Subset Simulation

TL;DR

The paper addresses the challenge of estimating rare transient instability events in power systems under high uncertainty. It introduces a subset simulation framework to efficiently estimate small TI probabilities and to perform sample-based sensitivity analysis, enabling identification of critical uncertain inputs and targeted mitigation. Through a WSCC 9-bus case with wind farms, the approach demonstrates superior efficiency over direct Monte Carlo and reveals that increasing a specific load’s power can markedly enhance system robustness. The work provides practical insights for probabilistic transient stability assessment and proposes a data-driven path toward mitigation strategies and future surrogate-based improvements.

Abstract

Assessing the risk of low-probability high-impact transient instability (TI) events is crucial for ensuring robust and stable power system operation under high uncertainty. However, direct Monte Carlo (DMC) simulation for rare TI event sampling is computationally intensive. This paper proposes a subset simulation-based method for efficient small TI probability estimation, rare TI events sampling, and subsequent sensitivity analysis. Numerical studies on the modified WSCC 9-bus system demonstrate the efficiency of the proposed method over DMC. Additionally, targeted stability enhancement strategies are designed to eliminate rare TI events and enhance the system's robustness to specific transient faults.

Figures (6)

• Figure 1: Illustration of transient rotor angle stability and fault clearing time (FCT). Trajectories exhibiting the largest rotor angle difference are highlighted in black. The fault-on periods with different FCTs are highlighted in red. A large FCT can render the system transient unstable.
• Figure 2: Illustration of the SubSim-based small TI probability estimation process. The details for each step can be found in Algorithm \ref{['alg:SubSim_algorithmn']}.
• Figure 3: Summary of the proposed sample-based sensitivity analysis method.
• Figure 4: WSCC 3-machine 9-bus system with two wind farms. The blue circles mark the conventional synchronous generators. The green circles indicate the WTGs and the numbers inside the circle represent bus generator indices. The green arrows represent uncertain loads.
• Figure 5: Unconditional \ref{['eq:IntervalP']} and conditional \ref{['eq:IntervalP_F']} marginal interval probability of the independent random inputs estimated by SubSim. The unconditional probabilities are around $1\%$ due to the percentile-based interval division. A conditional probability significantly exceeding $1\%$ implies a potential contribution of the corresponding input to the rare TI events.