A hybrid method of lagrangian relaxation and genetic algorithm for solving UC problem

Unit commitment (UC) is a very important issue of generation scheduling in electric power systems. A hybrid method combining the adaptive Lagrangian relaxation (ALR) and Genetic Algorithm (GA) is presented in this paper. By using Lagrangian multipliers to relax system-wide demand and reserve constraints, the UC problem is decomposed and converted into a two-level optimization problem. The low-level problems solve the optimal commitment of single unit, and GA is used. The probabilities of crossover and mutation are adaptively changed for each generation. In this way, the prematurity can be avoided. The high-level problems optimize the Lagrangian multipliers, and the adaptive updating of the multipliers is adopted. The oscillations of dual gap are reduced by using adaptive updating of the Lagrangian multipliers. Numerical results show that the feature of easy implementation, better convergence, and highly near-optimal solution to the UC problem can be achieved by the method. It is more robust and adaptive than the traditional methods.