Generic multidimensional economic environmental operation of power systems using equilibrium optimization algorithm

The economic emission load dispatch (EELD) problem is one of the main challenges to power system operators due to the complexity of the interconnected power systems and the non-linear characteristics of the objective functions (OFs). Therefore, the EELD problem has attracted significant attention in the electric power system because it has important objectives. Thus, this paper proposes the equilibrium optimization algorithm (EOA) to solve the EELD problem in electrical power systems by minimizing the total fuel cost and emissions, considering system and operational constraints. The OFs are optimized with and without considering valve point effects (VPE) and transmission system loss. The multi-OF, which aims to optimize these objectives simultaneously, is considered. In the proposed EOA, agents are particles and concentrations that express the solution and position, respectively. The proposed EOA is evaluated and tested on different-sized standard test systems having 10, 20, 40, and 80 generation units through several case studies. The numerical results obtained by the proposed EOA are compared with other optimization techniques such as grey wolf optimization, particle swarm optimization (PSO), differential evolution algorithm, and other optimization techniques in the literature. To show the reliability of the proposed algorithm for solving the considered OFs on a large-scale power system with and without considering different practical constraints such as VPE, ramp-rate limits (RRL), and prohibited operating zones (POZs) of generating units, the proposed EOA is evaluated and tested on the 140-unit test system. Also, the proposed multi-objective EOA (MOEOA) successfully acquires the Pareto optimal front to find the best compromise solution between the considered OFs. Also, the statistical analysis and the Wilcoxon signed rank test between the EOA and other optimization techniques for solving the EELD problem are performed. From numerical results, the total fuel cost obtained without considering VPE using the proposed EOA is reduced by 0.1414%, 0.1295%, 0.6864%, 5.8441% than the results of PSO, with maximum savings of 150 $/hr, 78 $/hr, 820 $/hr, and 14,730 $/hr for 10, 20, 40, and 80 units, respectively. The total fuel cost considering VPE is reduced by 0.0753%, 0.2536%, 2.8891%, and 3.6186% than the base case with maximum savings of 80 $/hr, 158 $/hr, 3610 $/hr, 9230 $/hr for 10, 20, 40, and 80 units, respectively. The total emission is reduced by 1.7483%, 12.8673%, and 7.5948% from the base case for 10, 40, and 80 units, respectively. For the 140-unit test system, the total fuel cost without and with considering VPE, RRL, and POZs is reduced by 6.4203% and 7.2394%, than the results of PSO with maximum savings of 107,200 $/hr and 126,400 $/hr. The total emission is reduced by 2.5688% from the base case. The comparative studies show the superiority of the EOA for the economic/environmental operation of the power system by solving the EELD problem with more accuracy and efficiency, especially as the system size increases.