Misocp-based solution approaches to the unit commitment problem with AC power flows

Official URL: https://risc01.sabanciuniv.edu/record=b2579562_(Table of contents)

Unit Commitment (UC) and Optimal Power Flow (OPF) are fundamental problems in short-term electrical power systems planning. Generally, the UC problem is solved to determine the commitment status of generators. Then, the OPF problem is solved to determine the power generation levels of committed generators. Instead of solving these problems in a serial manner, solving the UC problem and the OPF problem with AC power flows simultaneously as a mixed-integer nonlinear program (MINLP) can yield better results, but there is only a limited number of studies in the literature utilizing such an approach. Adopting this approach, we develop a base algorithm, in which we solve a mixedinteger second order conic program (MISOCP) relaxation of the UC problem with AC power flows. Then, we solve the multiperiod OPF (MOPF) problem by a local solver, where commitment statuses from the first step are fixed to find a feasible solution to the original MINLP. The second step yields a feasible solution to the original problem. We then assess the quality of the feasible solution by using the lower bound obtained from the first step. In order to obtain better lower bounds, we add some valid inequalities that are originally developed for the OPF problem to the base algorithm, which we call enhanced algorithm. For the problem instances with small number of buses, the base and the enhanced algorithms are able to provide small optimality gaps for the problem. However, it takes a long time to solve the MISOCP problem in larger instances. In order to solve the larger instances, we adopt a Lagrangian decomposition method. With the addition of the mentioned valid inequalities, the quality of the lower bound of the Lagrangian subproblems are improved. Thanks to this decomposition method, we obtain feasible solutions to the problem instances that the other algorithms are not able to provide feasible solutions within a reasonable time limit.