Optimization of Power System Operation: Approximations, Relaxations, and Decomposition

With higher penetration of renewable generation and market liberalization, operating points of electric power systems become increasingly variable and less predictable. To ensure economically efficient and secure operation of such systems, fast and robust optimization algorithms are required. Despite considerable research efforts, the development of these algorithms remains a challenge due to the nonlinearity and high dimensionality of system models. This dissertation focuses on the optimal power flow (OPF) problem, which is at the heart of techniques used in power system operation and planning. As this problem is non-convex and highly nonlinear, modern solvers cannot always find its locally optimal or even feasible point. To address this issue, an approximation of the OPF problem is proposed that helps reduce its complexity without compromising the solution quality. Moreover, the obtained solution is guaranteed to be physically meaningful. Next, this work presents several computationally efficient techniques for strengthening convex relaxations of the OPF problem. A tighter relaxation helps provide a better estimate of a globally optimal solution of the original problem and recover a physically meaningful operating point. Lastly, this work presents several approaches to incorporating risk-based security indices in the OPF problem. To reduce the computational burden of solving the resulting problems, decomposition algorithms are employed. The proposed techniques were tested on grids of various sizes. The results demonstrate that these techniques can potentially help improve optimization tools used in power system operation