Improved Fitness-Dependent Optimizer for Solving Economic Load Dispatch Problem

Abstract

Economic load dispatch depicts a fundamental role in the operation of power systems, as it decreases the environmental load, minimizes the operating cost, and preserves energy resources. The optimal solution to economic load dispatch problems and various constraints can be obtained by evolving several evolutionary and swarm-based algorithms. The major drawback to swarm-based algorithms is premature convergence towards an optimal solution. Fitness-dependent optimizer is a novel optimization algorithm stimulated by the decision-making and reproductive process of bee swarming. Fitness-dependent optimizer (FDO) examines the search spaces based on the searching approach of particle swarm optimization. To calculate the pace, the fitness function is utilized to generate weights that direct the search agents in the phases of exploitation and exploration. In this research, the authors have used a fitness-dependent optimizer to solve the economic load dispatch problem by reducing fuel cost, emission allocation, and transmission loss. Moreover, the authors have enhanced a novel variant of the fitness-dependent optimizer, which incorporates novel population initialization techniques and dynamically employed sine maps to select the weight factor for the fitness-dependent optimizer. The enhanced population initialization approach incorporates a quasi-random Sabol sequence to generate the initial solution in the multidimensional search space. A standard 24-unit system is employed for experimental evaluation with different power demands. The empirical results obtained using the enhanced variant of the fitness-dependent optimizer demonstrate superior performance in terms of low transmission loss, low fuel cost, and low emission allocation compared to the conventional fitness-dependent optimizer. The experimental study obtained 7.94E-12, the lowest transmission loss using the enhanced fitness-dependent optimizer. Correspondingly, various standard estimations are used to prove the stability of the fitness-dependent optimizer in phases of exploitation and exploration.

Figure 1

Honey bee anatomy [17].

Figure 2

Bee swarming process cycle [17].

Figure 3

Population initialization with random number generator following the uniform sequence.

Figure 4

Population initialization with Sobol sequence following the random distribution.

Figure 5

Flowchart for the enhanced FDO algorithm along with ELD application.

Figure 6

Convergence comparison (optimal allocation emission) of FDO with the enhanced variant of FDO on the first 6 thermal units with 100 epochs and different power demands.

Figure 7

Convergence comparison (transmission loss) of FDO with the enhanced variant of FDO on the 24 thermal units with 100 epochs and different power demands.

Figure 8

Convergence comparison (transmission loss) of FDO with the enhanced variant of FDO on the 24 thermal units with 200 epochs and different power demands.

Figure 9

One-way ANOVA test comparison (optimal allocation emission) of FDO with the enhanced variant of FDO on the 24 thermal units with 100 epochs and different power demands.

Figure 10

One-way ANOVA test comparison (optimal allocation emission) of FDO with the enhanced variant of FDO on the 24 thermal units with 200 epochs and different power demands.