Scalable Security Investment Methods for Voltage Stability of Power Systems

We develop investment approaches to secure electric power systems against load attacks that may cause voltage instability. The attacker attempts to alter the reactive power setpoints of the loads covertly and intelligently to reduce the voltage stability margin of the grid. The defender, or the system operator, aims to compensate for this reduction by retuning the reactive power dispatch of control devices such as shunt capacitor banks. The question is: how much financial investment should the attacker and the defender plan for to succeed in their respective objectives? To address this question, we formulate a cost-based Stackelberg game, where the defender is aware of the attacker's budget, and a robust-defense sequential algorithm for the realistic case when the defender is not fully informed about the attacker's resources. We demonstrate that these methods operate reliably under time-varying load uncertainties. To provide scalability to large-scale power system models, we develop a genetic algorithm where both players evolve their candidate solutions in opposite directions simultaneously. Finally, the proposed methods are validated using IEEE prototype models, demonstrating that reliable and robust defense is feasible unless the defender's resources are severely limited relative to the attacker's resources.