Solving corrective risk-based security-constrained optimal power flow with Lagrangian relaxation and Benders decomposition

• An efficient decomposition based algorithm is developed to solve the corrective risk-based SCOPF problem.
• The risk is a probabilistic index that is a function of conditions under normal and all contingencies.
• A combined use of Lagrangian relaxation and Benders decomposition can solve the problem efficiently.
• The proposed approach is tested on the IEEE 30-bus system and on the ISO New England bulk system.

This paper presents an efficient decomposition based algorithm to solve the corrective risk-based security-constrained optimal power flow (CRB-SCOPF) problem. The mathematical formulation was proposed imposing, in addition to the traditional post-contingency corrective constraints, constraints related to both circuit risk and system risk. Solving the CRB-SCOPF model is difficult since the risk index is a function of conditions under normal and all contingencies, and thus it greatly increases the dimension of the optimization problem. The proposed approach applies Lagrangian relaxation to the system risk constraints and then applies Benders decomposition to the remaining Lagrangian subproblem. The proposed approach is tested on the IEEE 30-bus system and on the ISO New England bulk system.