Long-term security-constrained unit commitment: hybrid Dantzig-Wolfe decomposition and subgradient approach

The solution of a long-term security-constrained unit commitment (SCUC) problem, which often spans several months to a year, may consider multiple long-term fuel and emission constraints in addition to operating constraints embedded in short-term SCUC. The size and the complexity of long-term SCUC are often beyond reasonable computing time and resources. Hence, Lagrangian relaxation is applied in this paper to manage coupling constraints over the entire period. Based on dual relaxation, the large-scale optimization problem is decomposed into many tractable short-term SCUC subproblems without long-term fuel and emission constraints. The resource penalty prices are linking signals for the coordination of subproblems. The short-term SCUC may be solved by any numerical optimization methods, including mixed integer programming and Lagrangian relaxation. A hybrid subgradient and Dantzig-Wolfe decomposition approach is presented for managing Lagrangian multipliers in the large-scale dual optimization of long-term SCUC problem. The proposed hybrid approach is a tradeoff between calculation speed and accuracy of the long-term SCUC solution. A modified IEEE 118-bus system is analyzed to exhibit the effectiveness of the proposed approach.