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. INDEX TERMS Augmented Lagrangian relaxation, Frank-Wolfe method, lower bound, progressive hedging, and stochastic unit commitment.

Tractable Stochastic Unit Commitment for Large Systems During Predictable Hazards

“…In this segment, all the network variables are calculated, not just the previously selected ones. For example, in power flow calculation, equations (18) and (19) are changed to (27) and (28), respectively.…”

“…The literature on modeling N-k generation outage scenarios completely abstracts from the complexities of transmission network and power flow calculations [17]- [19]. There is also a vast body of literature focusing on uncertainties regarding the error in the prediction of power injection by renewable energy resources [20]- [28]. There are a few studies on the modeling of uncertain equipment failures in the transmission network.…”

Improved Lagrangian relaxation generation decision-support in presence of electric vehicles

“…However, in such pool of possible solutions, few have received the industry approval on large-scale UC implementation. Nevertheless, the most appreciated techniques include priority listing (PL), dynamic programming (DP), Lagrangian relaxation (LR), and mixed integer programming (MIP) [13][14][15][16][17][18][19][20].…”

“…In this sense, CSA finds the best update for the Lagrangian multiplier at each iteration. As a consequence, the executional performance of the UC-LR can be improved and unnecessary commitment of the units is avoided [6][7][8][15][16][17][18][19][20][21][22].…”

“…As a remedy, stochastic search algorithm such as genetic algorithm (GA), particle swarm optimization (PSO) can provide stochastic way of non-linear optimization which is inspired by biologically advancement in the nature. The advantages of such techniques was cited in many technical literatures especially for complex mathematical equations for a nonlinear problem is a formidable task [15,16,[19][20][21][22][23].…”