Development and application of equilibrium optimizer for optimal power flow calculation of power system

Abstract

This paper proposes an enhanced version of Equilibrium Optimizer (EO) called (EEO) for solving global optimization and the optimal power flow (OPF) problems. The proposed EEO algorithm includes a new performance reinforcement strategy with the Lévy Flight mechanism. The algorithm addresses the shortcomings of the original Equilibrium Optimizer (EO) and aims to provide better solutions (than those provided by EO) to global optimization problems, especially OPF problems. The proposed EEO efficiency was confirmed by comparing its results on the ten functions of the CEC’20 test suite, to those of other algorithms, including high-performance algorithms, i.e., CMA-ES, IMODE, AGSK and LSHADE_cnEpSin. Moreover, the statistical significance of these results was validated by the Wilcoxon’s rank-sum test. After that, the proposed EEO was applied to solve the the OPF problem. The OPF is formulated as a nonlinear optimization problem with conflicting objectives and subjected to both equality and inequality constraints. The performance of this technique is deliberated and evaluated on the standard IEEE 30-bus test system for different objectives. The obtained results of the proposed EEO algorithm is compared to the original EO algorithm and those obtained using other techniques mentioned in the literature. These Simulation results revealed that the proposed algorithm provides better optimized solutions than 20 published methods and results as well as the original EO algorithm. The EEO superiority was demonstrated through six different cases, that involved the minimization of different objectives: fuel cost, fuel cost with valve-point loading effect, emission, total active power losses, voltage deviation, and voltage instability. Also, the comparison results indicate that EEO algorithm can provide a robust, high-quality feasible solutions for different OPF problems.

An enhanced hunter‐prey optimization for optimal power flow with FACTS devices and wind power integration

“…In the field of power systems, the optimal power flow (OPF) problem using thermal power generators has been extensively studied, with several meta-heuristic algorithms being applied. These include the moth swarm algorithm (MSA) [23], white sharks algorithm (WSA) [24], an improved Remora Optimization Algorithm (IROA) [25], an enhanced Remora Optimization Algorithm (ROA) [26], an enhanced multi-objective Quasi-reflected Jellyfish search algorithm (MOQRJFS) [27], an improved adaptive differential evolution (DE) [28], enhanced equilibrium optimizer (EEO) [29], a hybrid evolutionary algorithm combining particle swarm optimization (PSO) and crow search algorithm (CSA) applied to the distribution portion of IEEE 30-bus ring and IEEE 69-bus distribution network [30], successive history-based adaptive differential evolutionary (SHADE) algorithm [31], Enhanced slime mould algorithm (ESMA) [32], a new version of the salp swarm algorithm (SSA) [33], a multi-regional OPF considering load and generation variability using marine predators algorithm (MPA) [34], a multi-objective evolutionary algorithm with constraint handling technique based on non-dominated sorting [35], Hybrid Gradient-Based Optimizer with Moth Flame Optimization Algorithm (GBOMFO) [36], an enhanced MSA (EMSA) based on quasi-opposition based learning [37], an orthogonal learning FIGURE 3 Basic structure and model of TCSC [58]. [58].…”

“…In the field of power systems, the optimal power flow (OPF) problem using thermal power generators has been extensively studied, with several meta‐heuristic algorithms being applied. These include the moth swarm algorithm (MSA) [23], white sharks algorithm (WSA) [24], an improved Remora Optimization Algorithm (IROA) [25], an enhanced Remora Optimization Algorithm (ROA) [26], an enhanced multi‐objective Quasi‐reflected Jellyfish search algorithm (MOQRJFS) [27], an improved adaptive differential evolution (DE) [28], enhanced equilibrium optimizer (EEO) [29], a hybrid evolutionary algorithm combining particle swarm optimization (PSO) and crow search algorithm (CSA) applied to the distribution portion of IEEE 30‐bus ring and IEEE 69‐bus distribution network [30], successive history‐based adaptive differential evolutionary (SHADE) algorithm [31], Enhanced slime mould algorithm (ESMA) [32], a new version of the salp swarm algorithm (SSA) [33], a multi‐regional OPF considering load and generation variability using marine predators algorithm (MPA) [34], a multi‐objective evolutionary algorithm with constraint handling technique based on non‐dominated sorting [35], Hybrid Gradient‐Based Optimizer with Moth Flame Optimization Algorithm (GBOMFO) [36], an enhanced MSA (EMSA) based on quasi‐opposition based learning [37], an orthogonal learning Bird swarm algorithm [38], a chaotic equilibrium optimization (CEO) [39], modified Rao‐2 algorithm [40], the delicate flower pollination algorithm (DFPA) [41], the levy spiral flight equilibrium optimizer (LSFEO) [42], the teaching‐learning‐studying‐based optimizer (TLSBO) [43], the boundary assigned animal migration optimization (BA‐AMO) [44], an adaptive Quasi‐oppositional differential migrated biogeography‐based optimization (AQODMBBO) [45], the chaotic Bonobo optimizer (CBO) [46], and the social spider optimization (SSO) [47]. Furthermore, a gravitational search algorithm (GSA) was used in a study to compare the optimal performance of static VAR compensator (SVC) in voltage stability enhancement problems [48].…”

Optimal power flow analysis considering renewable energy resources uncertainty based on an improved wild horse optimizer

“…To address these issues, numerous heuristic optimization techniques were proposed through the last years. These intended to reach a best solution for the power network without adjusting the standard cost function such as Teaching-Learning-Based Optimization (TLBO) algorithm [10], chaotic Bonobo optimizer (CBO) [4], Modified Jaya Algorithm (MJYAY) [11], enhanced equilibrium optimizer (EEO) [12], Hybrid Firefly Bat technique with the constraints-prior object-fuzzy sorting (HFBA-COFS) algorithm [13], Rao-3 algorithm [14], Enhanced Slime Mould Algorithm (ESMA) [15], Mathematical distribution coyote optimization algorithm with crossover operator (MDCOA) [16], ensembled successive history adaptive differential evolutionary algorithm [17], White Sharks Algorithm (WSA) [18], and a Gaussian Bare-Bones Levy-Flight Firefly Algorithm [19]. Research in this domain indicates that each study has attempted to propose an algorithm that can outperform prior techniques.…”

Application of new power flow calculation in ship power system

“…In this paper, the Newton method is used to analyze the ship power system, build the relevant mathematical model and analyze its stability [5] . Based on the power flow calculation method, the steadystate performance analysis has great and far-reaching significance for improving its performance and improving the stability and reliability.…”