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### Genetic Lagrangian Relaxation Selection Method for the Solution of Unit Commitment Problem

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DOI: https://doi.org/10.15866/irea.v7i2.17022

#### Abstract

The units' commitment problem is considered as the selection of units to be placed in operation, and the load distribution among them. The solution of these problems can be solved by using optimization problems, with a general objective of minimizing the system operating costs subject to demand and operating constraints. This optimization problem is formulated as mathematical programming problems. The commitment uses Lagrange multiplier method of the available units so as to limit the search range for economical and satisfactory commitment schedules based on an iterative technique used and the progression from one iteration to the next is based on an extrapolation technique in which the last two successive values of the incremental cost are employed to estimate the next value. This paper presents the solution of these problems by modifying Lagrange multiplier method to provide efficient solutions for formulating the unit commitment problem over periods of up to 24 hours. The unit commitment problem is solved by using the genetic algorithm tuning of the Lagrangian multiplier λ. The main function of the Unit Commitment takes into consideration the spinning reserve, start-up cost for each unit is dependent on the amount of time the unit has been shutdown prior to start-up. A variety of spinning reserve requirement is observed and the operation of individual units must satisfy the specified minimum up and minimum downtimes constraints. The proposed modification and presents the test results on a benchmark system comprising 10 generators. The solution method is applied to test power systems. The mathematical algorithm for the solution of the specified problem is presented and the results of the computed studies reflect the robustness of the modified algorithm in solving the unit commitment problem compared with the conventional method.

#### Keywords

Unit Commitment; Lagrangian Relaxation; Optimization Problems; Equality Constraints; Non-Equality Constraints; Incremental Cost; Spinning Reserve; Start-Up; Genetic Algorithm

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