Optimisation methods for electric power system operations

Economically efficient and contingency-reliable operations in electric power systems are vital for modern society, with optimisation-based decision support systems serving as instrumental tools. This thesis focuses on advancing solution methods for the AC Optimal Power Flow (OPF) and AC Optimal Transmission Switching (OTS) problems, both fundamental to power system operations. The first part of this thesis explores mixed-integer linear programming (MILP) approaches for the OPF and OTS problems. Extensive computational experiments are conducted to investigate the advantages and disadvantages of a widely used MILP method for the OTS problem. Building upon these insights, a new MILP-based approach for the OTS problem is proposed, with computational experiments demonstrating its effectiveness under a special operating condition. Additionally, a piecewise linear relaxation of the OPF problem utilising state-of-the-art mixed-integer programming techniques is introduced, with computational experiments illustrating its effectiveness under certain operating conditions. The second part explores convex conic optimisation methods for the AC OPF problem and mixed-integer convex conic optimisation approaches for the AC OTS problem. Two classes of valid inequalities are developed to strengthen an existing convex conic relaxation of the AC OPF problem. Moreover, one of these classes of valid inequalities is adapted to improve an existing mixed-integer second-order conic programming relaxation of the OTS problem, further strengthened by polyhedral results to mitigate computational challenges. Computational experiments demonstrate the effectiveness of the proposed approaches for both the AC OPF and AC OTS problems.