Contingency analysis via SDP relaxations of the OPF problem

We aim to solve the OPF problem by defining contingency scenarios involved in the optimization problem by means of a SDP relaxation. Contingency scenarios are performed for the IEEE 39-bus system. Contingency analyses are performed by generation and line losses. Contingency scenarios are considered to be possible events. These events may be single contingencies, such as a generation unit failures or transmission line failures, or they may be double contingencies. Transmission line contingencies occur with the loss of critical lines of the transmission grid on the system. After single or multiple contingencies occur, it is required to shed some load, drop or trip the generation, or trip transmission lines for maintaining secure grid operations. In our contingency scenarios, we basically determine the appropriate amount of load to be shed. The SDP based OPF problem is tested for feasible transactions and generation dispatches in the system. if such action is feasible, the global optimal solution of the SDP-based OPF problem is guaranteed. In addition, the impact of worst-case contingency is examined for our test system. The amount of load shedding required is thus obtained.