Bi-level generator start-up sequence optimization model for power system restoration considering the DoS attack

• The power generation of generators considering the DoS attack in the power system restoration process is investigated for the first time. • A bi-level optimization model of the GSUS against the DoS attack is proposed to determine the optimal time instant of the attack and the optimal GSUS scheme. • To improve the computational efficiency, the upper-level and lower-level models are reformulated as mixed-integer linear programming ones. The reasonable generator start-up sequence (GSUS) strategy is beneficial to increasing the energy capacity of power systems after a blackout. Since the decision-making strategies of power systems are highly dependent on the cyber system, the denial of service (DoS) attack, as the most common type of cyber attacks, may prevent the generators from being re-started at their desired time and degrade performance of the optimal GSUS strategy in the power system restoration process, which has not been studied in the existing methods. To fill this gap, a bi-level GSUS optimization strategy against the DoS attack is proposed in this work. First, the effects of the DoS attack on the power generation of generators are analyzed and quantified by the generation energy loss. Then, a bi-level optimization model for the GSUS is proposed considering the DoS attack, where the upper-level model, referred to as the attacker model, aims to maximize the energy loss to prolong the restoration of generators by optimizing the time instant of the attack, while the lower-level model, referred to as the defender model, aims to maximize the energy generation by adjusting the optimal GSUS strategy in the restoration process. Both the upper-level and lower-level models are reformulated as mixed-integer linear programing problems, which can be efficiently solved by commercial solvers. Finally, the IEEE 39-bus power system and an actual power system in China are employed to verify the effectiveness of the proposed model.