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.
Highlights
In the Electric Reliability Council of Texas (ERCOT), installed wind capacity grew from a little over 100 MW in 2000 to over 22,000 MW by the end of 2018 [1]
Motivated by a combined Frank-Wolfe and progressive hedging algorithm (PHA) (FW-PHA) algorithm [17], we apply it for the first time to the Stochastic security-constrained unit commitment (S-SCUC) problem by proposing an improved approach to obtain the Lagrangian dual solution
The deterministic extensive form of the S-SCUC with a moderate number of scenarios can result in a computational burden that quickly exceeds the capability of any current state of the art MIP solver
Summary
In the Electric Reliability Council of Texas (ERCOT), installed wind capacity grew from a little over 100 MW in 2000 to over 22,000 MW by the end of 2018 [1]. Motivated by a combined Frank-Wolfe and PHA (FW-PHA) algorithm [17], we apply it for the first time to the S-SCUC problem by proposing an improved approach to obtain the Lagrangian dual solution. Since the set Ks is non-convex due to the existence of integer variables in the SCUC problem, the PHA may be solved using a heuristic approach and its algorithmic convergence is not guaranteed. The deterministic extensive form of the S-SCUC with a moderate number of scenarios can result in a computational burden that quickly exceeds the capability of any current state of the art MIP solver This is the main reason why the decomposition-based algorithms (e.g., Bender decomposition, Lagrangian relaxation, etc.) are proposed to solve it iteratively. Given the fact that Ks is non-convex, we apply a novel Frank-Wolfe based simplicial decomposition approach [17] to tackle this barrier
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