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In this paper, we study unit commitment (UC) problems considering theuncertainty of load and wind power generation. UC problem is formulated as achance-constrained two-stage stochastic programming problem where the chanceconstraint is used to restrict the probability of load imbalance. In additionto the conventional mixed integer linear programming formulation using Big-M,we present the bilinear mixed integer formulation of chance constraint, andthen derive its linear counterpart using McCormick linearization method. Then,we develop a bilinear variant of Benders decomposition method, which is aneasy-to-implement algorithm, to solve the resulting large-scale linearcounterpart. Our results on typical IEEE systems demonstrate that (i) thebilinear mixed integer programming formula-tion is stronger than theconventional one; (ii) the proposed Benders decomposition algorithm isgenerally an order of magnitude faster than using a professional solver todirectly compute both linear and bilinear chance-constrained UC models.

Chance-Constrained Two-Stage Unit Commitment under Uncertain Load and Wind Power Output Using Bilinear Benders Decomposition