Bi-level mixed-integer linear programming algorithm for evaluating the impact of load-redistribution attacks on Volt-VAR optimization in high- and medium-voltage distribution systems

Abstract The increasing integration of distributed generators into distribution systems (DSs) poses significant challenges to the stable operation and cyber-physical security of integrated high- and medium-voltage distribution system (HMVDS), leaving Volt-VAR optimization (VVO) vulnerable to load-redistribution attacks. This study focused on VVO in an HMVDS subject to the load-redistribution attack. The VVO under load-redistribution attack was formulated as a single-leader-multi-follower bi-level mixed-integer linear programming (BMILP) model that captured the interaction between the attacker and DS operators. The attacker in the upper level aimed to maximize voltage deviations and load curtailment through load-redistribution attack, while the DS operators aimed to minimize the voltage deviations in the lower levels. A relaxation-based bi-level reformulation and decomposition algorithm was designed to solve the BMILP model through replacing each mixed-integer linear programming lower-level problem with multiple linear programming lower-level problems, and using nonnegative relaxation variables and penalty functions to ensure equivalence. Finally, case studies on a constructed HMVDS and a real-world HMVDS were conducted to illustrate the impact of load-redistribution attacks on VVO and verify the effectiveness of the proposed methods.