Robust contingency-constrained load restoration method for transmission systems considering modified SOCP formulation of power flow

A proper load restoration method can speed up the load restoration phase and reduce the outage losses of power systems after natural disasters. Existing research assumes that transmission lines would not trip again in the load restoration phase, which is not always acceptable, especially in the outage scenario due to natural disasters. Besides, the feasibility of the load restoration scheme relies on an exact mathematical model of the load restoration problem, while the existing second-order cone programming (SOCP) based model is not suitable for transmission power systems due to the lack of voltage angle related arctangent constraints. To address these two main drawbacks in existing research on load restoration, a robust contingency-constrained load restoration model (CCLRM) for transmission systems considering the modified SOCP formulation of power flow is proposed with the objective of reducing the outage losses taking the worst contingency into account. To identify the worst contingency for the CCLRM, a bi-level worst contingency identification model (WOCIM) is proposed and reformulated into a single-level model by employing the duality theory to make the WOCIM solvable. The non-linear voltage angle related arctangent constraints in the modified SOCP based power flow expression in both models are studied and reformulated into the convex ones based on the convex envelope theory, thereby enhancing the accuracy of the presented models. Case studies on the IEEE 30-bus power system and IEEE 118-bus power system are conducted to illustrate the effectiveness of the proposed method.