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The fundamental objective of economic load dispatch is to operate the available generating units such that the needed load demand satisfies the lowest generation cost and also complies with the various constraints. With proper power system operation planning using optimized generation limits, it is possible to reduce the cost of power generation. To fulfill the needs of such objectives, proper planning and economic load dispatch can help to plan the operation of the electrical power system. To optimize the economic load dispatch problems, various classical and new evolutionary optimization approaches have been used in research articles. Classical optimization techniques are outdated due to many limitations and are also unable to provide a global solution to the ELD problem. This work uses a new variant of particle swarm optimization techniques called modified particle swarm optimization, which is effective and efficient at finding optimum solutions for single as well as multi-objective economic load dispatch problems. The proposed MPSO is used to solve single and multi-objective problems. This work considers constraints like power balance and power generation limits. The proposed techniques are tested for three different case studies of ELD and EELD problems. (1) The first case is tested using the data of 13 generating unit systems along with the valve point loading effect; (2) the second case is tested using 15 generating unit systems along with the ramp rate limits; and (3) the third case is tested using the economic emission dispatch (EELD) as a multi-objective problem for 6 generating unit systems. The outcomes of the suggested procedures are contrasted with those of alternative optimization methods. The results show that the suggested strategy is efficient and produces superior optimization outcomes than existing optimization techniques.

Operation scheduling in electric power grids is one of the most practical optimization problems as it sets a target for the efficient management of the electric power supply and demand. Advancement of a method to solve this issue is crucially required, especially in microgrids. This is because the operational capability of microgrids is generally lower than that of conventional bulk power grids, and therefore, it is extremely important to develop an appropriate, coordinated operation schedule of the microgrid components. Although various techniques have been developed to solve the problem, there is no established solution. The authors propose a problem framework and a solution method that finds the optimal operation schedule of the microgrid components considering the uncertainty in the available data. In the authors’ proposal, the objective function of the target problem is formulated as the expected cost of the microgrid’s operations. Since the risk of imbalance in the power supply and demand is evaluated as a part of the objective function, the necessary operational reserve power is automatically calculated. The usefulness of the proposed problem framework and its solution method was verified through numerical simulations and the results are discussed.

This paper proposes a novel nature-inspired optimization algorithm called the Fox optimizer (FOX) which mimics the foraging behavior of foxes in nature when hunting preys. The algorithm is based on techniques for measuring the distance between the fox and its prey to execute an efficient jump. After presenting the mathematical models and the algorithm of FOX, five classical benchmark functions and CEC2019 benchmark test functions are used to evaluate it’s performance. The FOX algorithm is also compared against the Dragonfly optimization Algorithm (DA), Particle Swarm Optimization (PSO), Fitness Dependent Optimizer (FDO), Grey Wolf Optimization (GWO), Whale Optimization Algorithm (WOA), Chimp Optimization Algorithm (ChOA), Butterfly Optimization Algorithm (BOA) and Genetic Algorithm (GA). The results indicate that FOX outperforms the above-mentioned algorithms. Subsequently, the Wilcoxon rank-sum test is used to ensure that FOX is better than the comparative algorithms in statistically significant manner. Additionally, parameter sensitivity analysis is conducted to show different exploratory and exploitative behaviors in FOX. The paper also employs FOX to solve engineering problems, such as pressure vessel design, and it is also used to solve electrical power generation: economic load dispatch problems. The FOX has achieved better results in terms of optimizing the problems against GWO, PSO, WOA, and FDO.

Economic Load Dispatch (ELD) is a complicated and demanding problem for power engineers. ELD relates to the minimization of the economic cost of production, thereby allocating the produced power by each unit in the most possible economic manner. In recent years, emphasis has been laid on minimization of emissions, in addition to cost, resulting in the Combined Economic and Emission Dispatch (CEED) problem. The solutions of the ELD and CEED problems are mostly dominated by metaheuristics. The performance of the Chameleon Swarm Algorithm (CSA) for solving the ELD problem was tested in this work. CSA mimics the hunting and food searching mechanism of chameleons. This algorithm takes into account the dynamics of food hunting of the chameleon on trees, deserts, and near swamps. The performance of the aforementioned algorithm was compared with a number of advanced algorithms in solving the ELD and CEED problems, such as Sine Cosine Algorithm (SCA), Grey Wolf Optimization (GWO), and Earth Worm Algorithm (EWA). The simulated results established the efficacy of the proposed CSA algorithm. The power mismatch factor is the main item in ELD problems. The best value of this factor must tend to nearly zero. The CSA algorithm achieves the best power mismatch values of 3.16×10−13, 4.16×10−12 and 1.28×10−12 for demand loads of 700, 1000, and 1200 MW, respectively, of the ELD problem. The CSA algorithm achieves the best power mismatch values of 6.41×10−13 , 8.92×10−13 and 1.68×10−12 for demand loads of 700, 1000, and 1200 MW, respectively, of the CEED problem. Thus, the CSA algorithm was found to be superior to the algorithms compared in this work.

Grey Wolf Optimizer (GWO) is a recently developed meta-heuristic search algorithm inspired by grey wolves (Canis lupus), which simulate the social stratum and hunting mechanism of grey wolves in nature and based on three main steps of hunting: searching for prey, encircling prey and attacking prey. This paper presents the application of GWO algorithm for the solution of non-convex and dynamic economic load dispatch problem (ELDP) of electric power system. The performance of GWO is tested for ELDP of small-, medium- and large-scale power systems, and the results are verified by a comparative study with lambda iteration method, Particle Swarm Optimization algorithm, Genetic Algorithm, Biogeography-Based Optimization, Differential Evolution algorithm, pattern search algorithm, NN-EPSO, FEP, CEP, IFEP and MFEP. Comparative results show that the GWO algorithm is able to provide very competitive results compared to other well-known conventional, heuristics and meta-heuristics search algorithms.

The economic load dispatch (eld) problem strives to optimize the division of total power demand among the power generators under specified constraints. It is solved by scheduling the generating units of a power plant that meet the load demand with minimum generation cost while satisfying various equality and inequality constraints. Achieving global optimal points is considered difficult due to the involvement of a non-linear objective function and large search domain. The slime mould algorithm (SMA) was recently proposed to solve complex problems. Its convergence rate and capability of capturing optimal global solutions are pretty satisfactory. In this paper, a chaotic number-based slime mould algorithm (CSMA) is suggested for ELD problems the first time. Five test cases with different power demands have been considered to compare the performance of the proposed approach against SMA, salp swarm algorithm (SSA), moth flame optimizer (MFO), grey wolf optimizer (GWO), biogeography based optimizer (BBO), grasshopper optimization algorithm (GOA), multi-verse optimizer (MVO) on 6, 13, 15, 40, and 140 generators ELD problems. The experimental results show that the proposed algorithm reduces the total generation cost significantly. CSMA outperformed SMA in all test cases that justify the effectiveness of chaotic sequences used in the proposed work. Further, three statistical tests have been conducted to justify the competitiveness of the suggested approach.

The osprey optimization algorithm (OOA) is a new metaheuristic motivated by the strategy of hunting fish in seas. In this study, the OOA is applied to solve one of the main items in a power system called economic load dispatch (ELD). The ELD has two types. The first type takes into consideration the minimization of the cost of fuel consumption, this type is called ELD. The second type takes into consideration the cost of fuel consumption and the cost of emission, this type is called combined emission and economic dispatch (CEED). The performance of the OOA is compared against several techniques to evaluate its reliability. These methods include elephant herding optimization (EHO), the rime-ice algorithm (RIME), the tunicate swarm algorithm (TSA), and the slime mould algorithm (SMA) for the same case study. Also, the OOA is compared with other techniques in the literature, such as an artificial bee colony (ABO), the sine cosine algorithm (SCA), the moth search algorithm (MSA), the chimp optimization algorithm (ChOA), and monarch butterfly optimization (MBO). Power mismatch is the main item used in the evaluation of the OOA with all of these methods. There are six cases used in this work: 6 units for the ELD problem at three different loads, and 6 units for the CEED problem at three different loads. Evaluation of the techniques was performed for 30 various runs based on measuring the standard deviation, minimum fitness function, and maximum mean values. The superiority of the OOA is achieved according to the obtained results for the ELD and CEED compared to all competitor algorithms.

In the revolution of green energy development, microgrids with renewable energy sources such as solar, wind and fuel cells are becoming a popular and effective way of controlling and managing these sources. On the other hand, owing to the intermittency and wide range of dynamic responses of renewable energy sources, battery energy-storage systems have become an integral feature of microgrids. Intelligent energy management and battery sizing are essential requirements in the microgrids to ensure the optimal use of the renewable sources and reduce conventional fuel utilization in such complex systems. This paper presents a novel approach to meet these requirements by using the grey wolf optimization (GWO) technique. The proposed algorithm is implemented for different scenarios, and the numerical simulation results are compared with other optimization methods including the genetic algorithm (GA), particle swarm optimization (PSO), the Bat algorithm (BA), and the improved bat algorithm (IBA). The proposed method (GWO) shows outstanding results and superior performance compared with other algorithms in terms of solution quality and computational efficiency. The numerical results show that the GWO with a smart utilization of battery energy storage (BES) helped to minimize the operational costs of microgrid by 33.185% in comparison with GA, PSO, BA and IBA.

This article proposes the use of a leader white shark optimizer (LWSO) with the aim of improving the exploitation of the conventional white shark optimizer (WSO) and solving the economic operation-based load dispatch (ELD) problem. The ELD problem is a crucial aspect of power system operation, involving the allocation of power generation resources to meet the demand while minimizing operational costs. The proposed approach aims to enhance the performance and efficiency of the WSO by introducing a leadership mechanism within the optimization process, which aids in more effectively navigating the complex ELD solution space. The LWSO achieves increased exploitation by utilizing a leader-based mutation selection throughout each generation of white sharks. The efficacy of the proposed algorithm is tested on 13 engineer benchmarks non-convex optimization problems from CEC 2020 and compared with recent metaheuristic algorithms such as dung beetle optimizer (DBO), conventional WSO, fox optimizer (FOX), and moth-flame optimization (MFO) algorithms. The LWSO is also used to address the ELD problem in different case studies (6 units, 10 units, 11 units, and 40 units), with 20 separate runs using the proposed LWSO and other competitive algorithms being statistically assessed to demonstrate its effectiveness. The results show that the LWSO outperforms other metaheuristic algorithms, achieving the best solution for the benchmarks and the minimum fuel cost for the ELD problem. Additionally, statistical tests are conducted to validate the competitiveness of the LWSO algorithm.