A quantified multi-stage optimization method for resource allocation of electric grid defense planning

Implicit enumeration (IE) and Column-and-Constraint Generation (CCG) are two commonly used methods to solve the tri-level resource allocation of electric grid defense planning problem. However, there exist deficiencies in computational efficiency or problem adaptability when these two methods are used. To overcome these drawbacks, we proposed a quantified multi-stage optimization (QMO) method that attains superior defense strategies with moderate computational effort. The traditional tri-level problem is first transformed into a quantified attacker's programming (QAP) and a quantified defender's programming (QDP) model, and then solved with introduced multi-stage optimization framework. Numerical case studies have been carried out on IEEE 118-bus test system. By combining with the IE method, we find that the proposed IE-QMO method can obtain a better solution without being trapped in a local optimum. Results validate that the proposed method reveals better adaptability in large-scale problems without expanding the scale of the to-be-solved problems. Moreover, we introduce comprehensive defense priorities of transmission lines based on the proposed method to help system planner making line hardening decisions.