Security-Constrained Unit Commitment for AC-DC Grids With Generation and Load Uncertainty

Abstract

The uncertainties in renewable generators and load demand make it a challenge for system operators to execute the security-constrained unit commitment (SCUC) program in an ac-dc grid. The SCUC is a nonlinear mixed-integer optimization problem due to the power flow equations, constraints imposed by the ac-dc converters, and the binary variables associated with the generators’ on/off state. In this paper, we study the SCUC problem in ac-dc grids with generation and load uncertainty. We introduce the concept of conditional value-at-risk to limit the risk of deviations in the load demand and renewable generation. We relax the binary variables and introduce a $l_1$ -norm regularization term to the objective function, and then use convex relaxation techniques to transform the problem into a semidefinite program (SDP). We develop an algorithm based on the iterative reweighted $l_1$ -norm approximation that involves solving a sequence of SDPs. Simulations are performed on an IEEE 30-bus test system. Results show that the proposed algorithm returns a solution within 2% gap from the global optimal solution for the underlying test system. When compared with the multi-stage algorithm in the literature, our algorithm has a lower running time and returns a solution with a smaller gap from the global optimal solution.