Thermal Unit Commitment Solution Using an Improved Lagrangian Relaxation

An improved Lagrangian relaxation (LR) solution to the thermal unit commitment problem (UCP) is proposed in this paper. The algorithm is characterized by: (1) a new Matlab function to determine the optimal path of the dual problem, (2) new initialization procedure of Lagrangian multipliers, based on both unit and time interval classification, (3) a flexible adjustment of Lagrangian multipliers, and (4) a dynamic search for uncertain stage scheduling, using a Lagrangian relaxation dynamic programming method (LR-DP). After the LR best feasible solution is reached, and when identical or similar units exist, a unit decommitment is used to adjust the solution. The proposed algorithm is tested and compared to conventional Lagrangian relaxation (LR), genetic algorithm (GA), evolutionary programming (EP), Lagrangian relaxation and genetic algorithm (LRGA), and genetic algorithm based on unit characteristic classification (GAUC) on systems with the number of generating units in the range of 10 to 100. The total system production cost of the proposed algorithm is less than the others especially for the larger number of generating units. Computational time was found to increase almost linearly with system size, which is favorable for large-scale implementation.