Scalable Unit Commitment with AC Power Flow via Semidefinite Programming Relaxation

Ramtin Madani, Alper Atamturk and Ali Davoudi. “Scalable Unit Commitment with AC Power Flow via Semidefinite Programming Relaxation“. BCOL Research Report 17.03, IEOR, University of California-Berkeley.

Abstract: Determining the most economic strategies for supply and transmission of electricity is a daunting computational challenge. The amount of effort to optimize the schedule of generating units and route of power, can grow exponentially with the number of decision variables. Practical approaches to this problem involve legacy approximations and ad-hoc heuristics that may undermine the efficiency and reliability of power system operations, that are ever growing in scale and complexity. Therefore, developing powerful optimization methods for detailed power system scheduling is critical to the realization of smart grids and has received significant attention recently. In this paper, we propose a computational method, which is capable of solving large-scale power system scheduling problems with thousands of generating units, while accurately incorporating the nonlinear equations that govern the flow of electricity on the grid. We design a polynomial-time solvable third-order semidefinite programming (TSDP) relaxation, with the aim of finding a near globally optimal solution for the unit commitment problem with AC power flow constraints. The proposed method is demonstrated on large-scale benchmark instances from real-world European grid data, for which provably optimal or near-optimal solutions are obtained.