Vulnerability analysis of power system under uncertain cyber-physical attacks based on stochastic bi-level optimization

Coordinated cyber-physical attacks on power systems have become increasingly prevalent, highlighting the need to explore the interactions between cyber attacks targeting relay protection and physical attacks on electrical equipment. However, existing research has yet not adequately addressed the uncertainty associated with the success probability of such attacks. This paper proposes a vulnerability analysis method of power transmission system under uncertain cyber-physical attacks based on stochastic bi-level optimization. An analytical model is developed to characterize the relationships among attack target selection, attack success/failure scenarios, and scenarios probabilities. Based on this analytical model, a stochastic bi-level optimization-based vulnerability identification model is proposed, which incorporates the success probabilities of cyber attacks and the comprehensive loss across different scenarios. Through dual decomposition and two linearization methods, the original bi-level nonlinear model is transformed into a single-level mixed-integer linear programming problem to improve the solution performance. A case study finally validates that the introduction of attack success probability parameters may lead to new attack patterns. The proposed method provides valuable insights into the attack strategies of adversaries with varying levels of capability, thereby offering a foundation for the development of effective defensive strategies.