Computationally efficient methods for solving optimal power flow problems by exploiting supplementary information

Motivated by the important role of electrical energy in the quality of life in cities, the electric power flow management, scheduling, and optimization is a critical task, especially in large-scale power systems. The power flow equations as the heart of power system operation translate the power injections and voltages steady-state relationship. The nonlinearity of the power flow equations makes the optimal power flow (OPF) problem a nonconvex NP-hard optimization problem which usually has multiple optima. The complexity of the OPF problem increases significantly as the size of the power system increases, so obtaining an optimal solution for an OPF problem within a reasonable time is one of the main challenges in the optimization of the power system research area. Therefore, a variety of deterministic and non-deterministic techniques have been applied to OPF problems over the last 50 years of research on power networks. Although the mature deterministic algorithms are usually able to quickly find a solution, most of them do not guarantee global optimality of the obtained solution and they may get trapped in any local optima and no additional information is provided regarding the solution. Certifiably obtaining a globally optimal solution is important for certain applications of OPF problems. In this thesis, firstly, a meta-heuristic optimization approach, called fully informed water cycle algorithm (FIWCA), is proposed with the idea of exchanging global and local information among the individuals in the populations with the goal of achieving a reasonable solution within a smaller number of iterations and shorter time, and also avoiding trapping in any local optima. Many global optimization techniques, such as semidefinite programming (SDP), compute an optimality gap that compares the achievable objective value corresponding to a feasible point from a local solution algorithm with an objective value bound from a convex relaxation technique. Rather than the traditional practice of completely separating the local solution and convex relaxation computations, this thesis next proposes a method that exploits information from a local solution to speed up the computation of an objective value bound using a SDP relaxation. The improvement in computational tractability comes with the trade-off of reduced tightness for the resulting objective value bound. Recent development in power industry leads to a more complicated optimization problem to solve. The conventional way of solving static OPF problem is unsuitable for power networks, especially at the distribution level, having renewable energy sources (RES), energy storage systems (ESS) and flexible loads (FL) owing to the time-coupled and stochastic dynamics. On the other hand, convex relaxation approaches are not suitable for distribution grids owing to their high line resistance. This thesis next proposes a computationally efficient approach for solving receding horizon control (RHC) based Alternating Current OPF problems in energy grids having intermittent renewable energy generation, storage devices and flexible loads. The proposed method decomposes the solution into two stages. A Direct Current OPF (DCOPF) problem is solved using an RHC approach at the first stage by embedding forecasts on renewable generation and demand. A single-period ACOPF to optimize both line-losses and operating cost is solved at the second stage with the storage and flexible loads fixed at the optimal values computed in the first stage. In addition, hot-start is provided to the second stage optimization problem using the generation schedule computed at the first stage.Doctor of Philosoph