A Fast Penalty-Based Gauss-Seidel Method for Stochastic Unit Commitment With Uncertain Load and Wind Generation

Abstract

Stochastic network-constrained unit commitment (S-NCUC) can be used to manage the uncertainty of an increasing penetration level of renewable energy effectively. However, the drawbacks of the progressive hedging algorithm (PHA) based solutions are that they are not provably convergent due to the non-convexity of S-NCUC. Additionally, the solution obtained is usually fractional-valued (non-binary) and therefore not readily implementable. In this paper, we apply a novel Penalty-Based Gauss-Seidel (PBGS) algorithm in solving S-NCUC using an exact augmented Lagrangian representation with proven convergence. To improve the computational efficiency of the PBGS, we further propose an accelerating technique with rigorous proof to skip solving scenarios when certain conditions are met during iterations. We numerically validate the proposed algorithms on the IEEE 118-bus system and a practically-sized ERCOT-like system, both with variable wind generation. Numerical results demonstrate the efficacy of the proposed algorithms in yielding high-quality S-NCUC solutions. The merits of the proposed algorithms are also revealed in comparison with PHA and extensive-form (EF) based mixed-integer programming solutions.

Keywords

• Exact augmented Lagrangian
• Frank-Wolfe algorithm
• Gauss-Seidel method
• mixed-integer programming
• progressive hedging algorithm
• stochastic programming