N-1 reliable unit commitment via progressive hedging

Progressive hedging is a scenario-based decomposition method that can be applied to solve the stochastic unit commitment problem. Progressive hedging is not guaranteed to converge to the global optimal solution since unit commitment involves integer variables. Slow convergence rates and cyclic behaviors have been previously observed in practice. Hedging is conventionally performed on the unit commitment status variables. In this paper, several hedging methods are proposed to improve progressive hedging for the N-1 (single contingency) stochastic unit commitment problem. In particular, hedging on the start-up and shutdown variables is proposed and tested in this paper. The performance of the progressive hedging is rather sensitive to the choice in the penalty factors. Thus, several strategies for choosing the penalty factors are evaluated for the cases when using the unit commitment status variables versus using the start-up and shutdown binary variables as the hedging mechanisms. Finally, a hybrid approach using both progressive hedging and an extensive form stochastic programming formulation is implemented in order to obtain a set of feasible unit commitment solutions and compare different hedging methods.