DC Optimal Power Flow Formulation and Solution Using QuadProgJ∗

Nonlinear AC Optimal Power Flow (OPF) problems are commonly approximated by linearized DC OPF problems to obtain real power solutions for restructured wholesale power markets. We first present a standard DC OPF problem, which has the numerically desirable form of a strictly convex quadratic programming (SCQP) problem when voltage angles are eliminated by substitution. We next augment this standard DC OPF problem in a physically meaningful way, still retaining an SCQP form, so that solution values for voltage angles and locational marginal prices are directly obtained along with real power injections and branch flows. We then show how this augmented DC OPF problem can be solved using QuadProgJ, an open-source Java SCQP solver newly developed by the authors that implements the well-known dual active-set SCQP algorithm by Goldfarb and Idnani (1983). To demonstrate the accuracy of QuadProgJ, comparative results are reported for a well-known suite of numerical QP test cases with up to 1500 decision variables plus constraints. Detailed QuadProgJ results are also reported for 3-node and 5-node DC OPF test cases taken from power systems texts and ISO-NE/PJM training manuals.