A Fast and Scalable Iterative Solution of a Socio‐Economic Security‐Constrained Optimal Power Flow With Two‐Stage Post‐Contingency Control

ABSTRACT Power systems must accommodate faster‐growing demand and energy production at a rate that exceeds the pace of new grid infrastructure development. Moving from the deterministic ‘N‐1’ security criterion to a probabilistic security criterion in security‐constrained optimal power flow (SCOPF) can safely increase the power transfer capability of power systems. However, this has been computationally intractable for large power systems when including corrective actions. In this paper, a fast and scalable iterative methodology for solving the SCOPF problem is proposed using problem decomposition and the inverse matrix modification lemma (IMML). The proposed probabilistic corrective‐SCOPF formulation tackles system operational security planning by combining previous research with considerations of short‐term and long‐term post‐contingency limits, probability of branch outages, and preventive and corrective actions. Using two post‐contingency states and contingency probabilities, the SCOPF could provide improved system security at a lower cost when compared to the SCOPF with only preventive actions, for example, the typical ‘N‐1’ formulation. Additional security is ensured using a post‐contingency load‐shedding limit constraint based on system operator policy. The bearing idea in the proposed solution methodology is to relax the problem and then iteratively add constraints as and when they are violated, resulting in a solution that satisfies all constraints in the original problem. Solving the post‐contingency power flow using the IMML with bus voltage angles was found to be up to four orders of magnitude faster than doing the same using a high‐performance sparse matrix solver (KLU) with power transfer distribution factors. The proposed methodology is applied to a range of test systems containing up to 10,000 buses with a computational time of up to 3375 s for 12,706 branch contingencies. Calculating the contingency power flows takes 1.3% of the total solution time using the proposed methodology, by exploiting the IMML.