Lagrangian relaxation combined with differential evolution algorithm for unit commitment problem

In this paper, a technique of combining Lagrangian relaxation (LR) with a differential evolution algorithm (DEA) method (LR-DEA) is proposed for solving unit commitment (UC) problem of thermal power plants. The merits of DEA method are parallel search and optimization capabilities. The unit commitment problem is formulated as the minimization of a performance index, which is sum of objectives (fuel cost, start-up cost) and several equality and inequality constraints (power balance, generator limits, spinning reserve, minimum up/down time). The efficiency and effectiveness of the proposed technique is initially demonstrated via the analysis of 10-unit test system. A detailed comparative study among the conventional LR, genetic algorithm (GA), evolutionary programming (EP), a hybrid of Lagrangian relaxation and genetic algorithm (LRGA), ant colony search algorithm (ACSA), and the proposed method is presented. From the experimental results, the proposed method has high accuracy of solution achievement, stable convergence characteristics, simple implementation and satisfactory computational time.