A Frank–Wolfe Progressive Hedging Algorithm for Improved Lower Bounds in Stochastic SCUC

Abstract

The instantaneous penetration of renewable generation, such as wind and solar generation, reaches over 50% in certain balancing areas in the United States. These generation resources are inherently characterized by uncertainties and variabilities in their output. Stochastic security-constrained unit commitment (S-SCUC) using a progressive hedging algorithm (PHA) has been utilized to schedule the generation resources under uncertainties. However, dual bounds obtained in the PHA are sensitive to the penalty factor chosen, and the convergence of the PHA is problematic due to the existence of integer decisions. In this paper, we apply a novel Frank-Wolfe-based simplicial decomposition method in conjunction with the PHA (FW-PHA) to improve the quality of dual bounds and the convergence characteristics in solving the S-SCUC. The numerical tests are carried out on the IEEE RTS-96 and IEEE 118-bus systems. The numerical results show the effectiveness of the proposed FW-PHA-based S-SCUC. In comparison with the traditional PHA, the proposed algorithm converges to a tighter dual bound and is robust to any penalty factor selected.

Keywords

• Augmented Lagrangian relaxation
• Frank-Wolfe method
• lower bound
• progressive hedging
• and stochastic unit commitment