A multitree approach for global solution of ACOPF problems using piecewise outer approximations. (9th June 2018) - Liu, Jianfeng; Bynum, Michael; Castillo, Anya; Watson, Jean-Paul; Laird, Carl D.
Highlights: An outer-approximation approach for global solution of ACOPF is proposed. This approach relies on piecewise relaxations based on SOCP formulations of ACOPF. The piecewise OA approach can solve ACOPF test problems to global optimality. The approach is applicable to MINLPs with nonlinear AC power flow equations. Abstract: Electricity markets rely on the rapid solution of the optimal power flow (OPF) problem to determine generator power levels and set nodal prices. Traditionally, the OPF problem has been formulated using linearized, approximate models, ignoring nonlinear alternating current (AC) physics. These approaches do not guarantee global optimality or even feasibility in the real ACOPF problem. We introduce an outer-approximation approach to solve the ACOPF problem to global optimality based on alternating solution of upper- and lower-bounding problems. The lower-bounding problem is a piecewise relaxation based on strong second-order cone relaxations of the ACOPF, and these piecewise relaxations are selectively refined at each major iteration through increased variable domain partitioning. Our approach is able to efficiently solve all but one of the test cases considered to an optimality gap below 0.1%. Furthermore, this approach opens the door for global solution of MINLP problems with AC power flow equations.