Solution to unit commitment problem using Lagrangian relaxation and Mendel's GA method

Abstract

Phenomenal increase in load and cost of electricity has raised many challenges ranging from security of the system to the economics of generation. For economic operation of power system, the solution to Unit Commitment problem is necessary. Unit Commitment aims to schedule the generation to meet the load demands at the most economical rate for the next few hours. It decides that which unit should be operated in that particular period of study and which should not. On time horizon basis, it can be varied from few hours to one week. In this paper, the solution to unit commitment problem is achieved using Lagrangian relaxation and modified Mendel's GA approach for standard 10 unit system for 24 hours with 1-hour time interval. The Lagrangian Relaxation (LR) method provides a good optimal solution but it sometimes suffers from numerical convergence and problems related to solution quality. The proposed Lagrangian Relaxation and Mendel's Genetic Algorithms (LRMGA) include Mendel's Genetic Algorithm into Lagrangian Relaxation method to update the Lagrangian multipliers and improve the performance in solving problems like Unit Commitment (UC) problem. Results so obtained are compared with those obtained with various other methods. Solutions obtained show better convergence and highly optimal solution by LRMGA.