Abstract Ensuring frequency stability in interconnected power systems is challenging due to continuous load variations and fluctuations in tie-line power. This study focuses on designing and optimizing controllers for Automatic Generation Control (AGC) of a two-area power system to achieve zero-frequency deviation under dynamic load conditions. Five different controllers—PID (Proportional-Integral-Derivative), PIDn, FOPID (Fractional Order PID), TID (Tilt-Integral-Derivative), and PIDA—were tested. Their parameters were optimized using seven advanced metaheuristic algorithms: Artificial Rabbit Optimization, Chernobyl Disaster Optimizer (CDO), Modified Chernobyl Disaster Optimizer (mCDO), Golden Jackal Optimization, Honey Badger Algorithm, Mont-Flame Optimization, and Spider Wasp Optimizer. A total of 35 simulation studies were conducted, and performance was evaluated using the Integral of Time-Weighted Absolute Error (ITAE) metric Among the tested controllers, the FOPID-mCDO combination achieved the lowest ITAE value (0.320684), a settling time of 3.6 s, and minimal overshoot (0.0083 Hz) and undershoot (− 0.1480 Hz). Compared to conventional PID controllers, this configuration reduced settling time by 10% and improved frequency stability under dynamic load variations. The proposed mCDO algorithm, which integrates neighborhood–global and wandering search strategies to enhance the exploration–exploitation balance of the original CDO, outperformed the standard CDO by enabling faster convergence and more precise parameter tuning. The findings indicate that the FOPID-mCDO combination is a promising approach for automatic generation control in multi-area power systems.

Abstract In this paper, an optimization algorithm called supercell thunderstorm algorithm (STA) is proposed. STA draws inspiration from the strategies employed by storms, such as spiral motion, tornado formation, and the jet stream. It is a computational algorithm specifically designed to simulate and model the behavior of supercell thunderstorms. These storms are known for their rotating updrafts, strong wind shear, and potential for generating tornadoes. The optimization procedures of the STA algorithm are based on three distinct approaches: exploring a divergent search space using spiral motion, exploiting a convergent search space through tornado formation, and navigating through the search space with the aid of the jet stream. To evaluate the effectiveness of the proposed STA algorithm in achieving optimal solutions for various optimization problems, a series of test sequences were conducted. Initially, the algorithm was tested on a set of 23 well-established functions. Subsequently, the algorithm’s performance was assessed on more complex problems, including ten CEC2019 test functions, in the second experimental sequence. Finally, the algorithm was applied to five real-world engineering problems to validate its effectiveness. The experimental results of the STA algorithm were compared to those of contemporary metaheuristic methods. The analysis clearly demonstrates that the developed STA algorithm outperforms other methods in terms of performance.

Data-driven optimal power flow (OPF) approach has been a research focus in recent years. However, the current data-driven OPF approaches face the following difficulties: 1) the data-driven solutions may have large deviations and are not trustable, facing out-of-distribution (OOD) samples and 2) it is hard to judge whether the solutions of the data-driven approach can be trusted. To handle these problems, this article first improves the generalization ability of the data-driven OPF method by embedding the inherent pattern of the OPF solution into the data-driven learning process. As an optimization problem, the OPF solution has certain fixed patterns that are not influenced by the distribution of samples. For example, the load balance constraints should always be satisfied. This leads to an inherent requirement of output vectors, which can be utilized to guide the learning process of the data-driven OPF method. Second, an adaptability judging method based on the decoder neural network is proposed to determine whether the data-driven OPF approach can produce trustable solutions. By measuring the decoding error from latent features to input features, the adaptability of neural networks for input samples could be accurately judged. According to extensive results on various systems, the proposed method can improve the calculation accuracy of OOD data by an average of 30.19% compared with state-of-the-art methods. With the adaptability judgment method, the accuracy of the data-driven approach can achieve higher than 98% for OOD data, whereas the accuracy of other methods ranges from 34.08% to 94.50% on the same set of OOD test data.

This article introduces a modified version of the Artificial Ecosystem Optimization (AEO) algorithm, called Long-term Memory Component AEO (LMAEO), for optimizing the reconfiguration of radial distribution networks. The LMAEO algorithm incorporates a long-term memory component, enabling individuals in the population to make decisions based on past experiences. This integration of long-term memory allows the algorithm to explore a wider range of potential solutions during the optimization process, potentially leading to improved performance and better exploration of the solution space. To verify the effectiveness and superiority of the LMAEO technique, it is compared with the conventional AEO algorithm and other well-known algorithms using seven benchmark functions. The proposed LMAEO algorithm successfully addresses the reconfiguration of distribution systems considering reliability for the modified 12-bus, 33-bus and 69-bus IEEE test systems. Leveraging the strengths of AEO and the long-term memory component, the LMAEO algorithm achieves efficient solutions for this problem. To assess the performance of the proposed LMAEO, a comparison is made with the original AEO algorithm. The results demonstrate that the LMAEO technique surpasses the AEO optimizer in terms of optimal reconfiguration of distribution systems jointly considering reliability, system losses and voltage deviations.

Abstract In areas where conventional energy sources are unavailable, alternative energy technologies play a crucial role in generating electricity. These technologies offer various benefits, such as reliable energy supply, environmental sustainability, and employment opportunities in rural regions. This study focuses on the development of a novel optimization algorithm called the modified firebug swarm algorithm (mFSO). Its objective is to determine the optimal size of an integrated renewable power system for supplying electricity to a specific remote site in Dehiba town, located in the eastern province of Tataouine, Tunisia. The proposed configuration for the standalone hybrid system involves PV/biomass/battery, and three objective functions are considered: minimizing the total energy cost (COE), reducing the loss of power supply probability (LPSP), and managing excess energy (EXC). The effectiveness of the modified algorithm is evaluated using various tests, including the Wilcoxon test, boxplot analysis, and the ten benchmark functions of the CEC2020 benchmark. Comparative analysis between the mFSO and widely used algorithms like the original Firebug Swarm Optimization (FSO), Slime Mold Algorithm (SMA), and Seagull Optimization Algorithm (SOA) demonstrates that the proposed mFSO technique is efficient and effective in solving the design problem, surpassing other optimization algorithms.

Abstract 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.

Abstract The interest in incorporating environmentally friendly and renewable sources of energy, like photovoltaic (PV) technology, into electricity grids has grown significantly. These sources offer benefits, such as reduced power losses and improved voltage stability. To optimize these advantages, it is essential to determine optimal placement and management of these energy resources. This paper proposes an Improved RUNge–Kutta optimizer (IRUN) for allocating PV-based distributed generations (DGs) and Battery Energy Storage (BES) in distribution networks. IRUN utilizes three strategies to avoid local optima and enhance exploration and exploitation phases: a non-linear operator for smoother transitions, a Chaotic Local Search for thorough exploration, and diverse solution updates for refinement. The efficacy of IRUN is evaluated using 10 benchmark functions from the CEC’20 test suite, followed by statistical analysis. Next, IRUN is used to optimize the allocation of PVDG and BES to minimize energy losses in two standard IEEE distribution networks. The optimization problem is divided into two stages. In the first stage, the optimal size and the location of PV systems are calculated to meet peak load demand. In the second stage, considering time-varying load demand and intermittent PV generation, effective energy management of BES is employed. The effectiveness of IRUN is compared against the original RUN and other well-known optimization algorithms through simulation results. The comprehensive analysis demonstrates that IRUN outperforms the compared algorithms, making it a leading solution for optimizing PV distributed generation and BES allocation in distribution networks and the results show that the energy loss reduction reaches 63.54% and 68.19% when using PVand BES in IEEE 33-bus and IEEE 69 bus respectively.

Abstract In this study, an improved bald eagle search optimization algorithm (IBES) is utilized to develop home energy management systems for smart homes. This research is crucial for energy field researchers who are interested in optimizing energy consumption. The primary objective is to optimally manage load demand, reduce the average peak ratio, lower electricity bills, and enhance user comfort. To accomplish this goal, the load conversion strategy is used to coordinate household appliances and manage the home power system effectively. This approach aims to minimize peak–average ratios and electricity costs while ensuring consumer convenience. To minimize electricity bills, the study schedules the consumer’s daily activities based on actual time and next day’s energy demand. Furthermore, a fitness criterion is used to balance the load between off-peak and on-peak hours. The scheduler is designed to achieve an optimal device on/off state that minimizes device waiting time by coordinating household appliances in real time. To address the background problem of real-time rescheduling, dynamic programming is employed. The study evaluates the modified algorithm’s performance using three pricing strategies: critical peak pricing, real-time pricing, and time of use. The modified IBES technique is utilized to achieve the specified objectives of minimizing the electricity bill, reducing the peak–average ratio, and enhancing user convenience.

Abstract Many real-world problems demand optimization, minimization of costs and maximization of profits, and meta-heuristic algorithms have proficiently proved their ability to achieve optimum results. This study proposes an alternative algorithm of Lévy Flight Distribution (LFD) by integrating Opposition-based learning (OBL) operator, termed LFD-OBL, for resolving intrinsic drawbacks of the canonical LFD. The proposed approach adopts OBL operator for catering search stagnancy to ensure faster convergence rate. We validate the usefulness of our approach through IEEE CEC’20 test suite, and compare results with original LFD and several other counterparts such as Moth-flame optimization, whale optimization algorithm, grasshopper optimisation algorithm, thermal exchange optimization, sine-cosine algorithm, artificial ecosystem-based optimization, Henry gas solubility optimization, and Harris’ hawks optimization. To further validate the efficiency of LFD-OBL, we apply it on parameters optimization of Solar Cell based on the Three-Diode Photovoltaic model. The qualitative and quantitative results of all the experiments performed in this study suggest superiority of the proposed method.

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.

Abstract The integration of demand response programs (DRPs) into the energy management (EM) system of microgrids (MGs) helps in improving the load characteristics by allowing consumers to interoperate for achieving techno-economic advantages. In this paper, an improved algorithm is called LINFO is proposed for modifying search ability of the original weIghted meaN oF vectOrs (INFO) algorithm as well as avoiding its weaknesses like trapping in a local optima. The improved algorithm's efficiency is confirmed by comparing its results with those obtained by the original INFO and other optimization techniques using different standard benchmark test functions. Moreover, this improved algorithm and the original version are applied for solving the EM problem with the aim of optimizing the operation cost of the MGs in the presence DRPs. They are used to solve day-ahead EM problem for optimal operation of renewable energy resources, the optimal generation from a conventional diesel engines (DEs); taking into account the participation of customers in DRP for minimizing MG operating cost, which includes the cost of DEs fuel and the power transactions cost with the main grid. To demonstrate the efficacy of the proposed LINFO, simulation results are compared with the results of well-known and newly developed optimization techniques.

Abstract The concept of interconnected multi-microgrids (MMGs) is presented as a promising solution for the improvement in the operation, control, and economic performance of the distribution networks. The energy management of the MMGs is a strenuous and challenging task, especially with the integration of renewable energy resources (RERs) and variation in the loading due to the intermittency of these resources and the stochastic nature of the load demand. In this regard, the energy management of the MMGs is optimized with optimal inclusion of a hybrid system consisting of a photovoltaic (PV) and a wind turbine (WT)-based distributed generation (DGs) under uncertainties of the generated powers and the load variation. A modified Capuchin Search Algorithm (MCapSA) is presented and applied for the energy management of the MMGs. The MCapSA is based on enhancing the searching abilities of the standard Capuchin Search Algorithm (CapSA) using three improvement strategies including the quasi-oppositional-based learning (QOBL), the random movement-based Levy flight distribution, and the exploitation mechanism of the prairie dogs in the prairie dog optimization (PDO). The optimized function is a multi-objective function that comprises of the cost and the voltage deviation reduction along with stability enhancement. The effectiveness of the proposed technique is verified on standard benchmark functions and the obtained results. Then, the proposed method is used for energy management of IEEE 33-bus and 69-bus MMGs at uncertainties conation. The results depict that the energy management with inclusion of WTs and PVs using the proposed technique can reduce the cost and summation of the VD by 46.41% and 62.54%, and the VSI is enhanced by 15.1406% for the first MMG. Likewise, for the second MMG, the cost and summation of the VD are reduced by 44.19% and 39.70%, and the VSI is enhanced by 4.49%.

Abstract Integrating distributed generations (DGs) into the radial distribution system (RDS) are becoming more crucial to capture the benefits of these DGs. However, the non-optimal integration of renewable DGs and shunt capacitors may lead to several operational challenges in distribution systems, including high energy losses, poor voltage quality, reverse power flow, and lower voltage stability. Therefore, in this paper, the multi-objective optimization problem is expressed with precisely selected three conflicting goals, incorporating the reduction in both power loss and voltage deviation and improvement of voltage stability. A new index for voltage deviation called root mean square voltage is suggested. The proposed multi-objective problems are addressed using two freshly metaheuristic techniques for optimal sitting and sizing multiple SCs and renewable DGs with unity and optimally power factors into RDS, presuming several voltage-dependent load models. These optimization techniques are the multi-objective thermal exchange optimization (MOTEO) and the multi-objective Lichtenberg algorithm (MOLA), which are regarded as being physics-inspired techniques. The MOLA is inspired by the physical phenomena of lightning storms and Lichtenberg figures (LF), while the MOTEO is developed based on the concept of Newtonian cooling law. The MOLA as a hybrid algorithm differs from many in the literature since it combines the population and trajectory-based search approaches. Further, the developed methodology is implemented on the IEEE 69-bus distribution network during several optimization scenarios, such as bi- and tri-objective problems. The fetched simulation outcomes confirmed the superiority of the MOTEO algorithm in achieving accurate non-dominated solutions with fewer outliers and standard deviation among all studied metrics.

Abstract This paper provides a novel, unique, and improved optimization algorithm called the modified Orca Predation Algorithm (mOPA). The mOPA is based on the original Orca Predation Algorithm (OPA), which combines two enhancing strategies: Lévy flight and opposition-based learning. The mOPA method is proposed to enhance search efficiency and avoid the limitations of the original OPA. This mOPA method sets up to solve the global optimization issues. Additionally, its effectiveness is compared with various well-known metaheuristic methods, and the CEC’20 test suite challenges are used to illustrate how well the mOPA performs. Case analysis demonstrates that the proposed mOPA method outperforms the benchmark regarding computational speed and yields substantially higher performance than other methods. The mOPA is applied to ensure that all load demand is met with high reliability and the lowest energy cost of an isolated hybrid system. The optimal size of this hybrid system is determined through simulation and analysis in order to service a tiny distant location in Egypt while reducing costs. Photovoltaic panels, biomass gasifier, and fuel cell units compose the majority of this hybrid system’s configuration. To confirm the mOPA technique’s superiority, its outcomes have been compared with the original OPA and other well-known metaheuristic algorithms.

Abstract Solving the energy management (EM) problem in microgrids with the incorporation of demand response programs helps in achieving technical and economic advantages and enhancing the load curve characteristics. The EM problem, with its large number of constraints, is considered as a nonlinear optimization problem. Artificial rabbits optimization has an exceptional performance, however there is no single algorithm can solve all engineering problem. So, this paper proposes a modified version of artificial rabbits optimization algorithm, called QARO, by quantum mechanics based on Monte Carlo method to determine the optimal scheduling for MG resources effectively. The main objective is minimization of the daily operating cost with the maximization of MG operator (MGO) benefit. The operating cost includes the conventional diesel generator operating cost and the cost of power transactions with the grid. The performance of the proposed algorithm is assessed using different standard benchmark test functions. A ranking order for the test function based on the average value and Tied rank technique, Wilcoxon's rank test based on median value, and Anova Kruskal–Wallis test showed that QARO achieved best results on the most functions and outperforms all other compared technique. The obtained results of the proposed QARO are compared with those obtained by employing well-known and newly-developed algorithms. Moreover, the proposed QARO is used to solve two case studies of day-ahead EM problem in MG, then the obtained results are also compared with other well-known optimization techniques, the results demonstrate the effectiveness of QARO in reducing the operating cost and maximization the MGO benefit.

Abstract This paper introduces a multi-objective variant of the marine predators algorithm (MPA) called the multi-objective improved marine predators algorithm (MOIMPA), which incorporates concepts from Quantum theory. By leveraging Quantum theory, the MOIMPA aims to enhance the MPA’s ability to balance between exploration and exploitation and find optimal solutions. The algorithm utilizes a concept inspired by the Schrödinger wave function to determine the position of particles in the search space. This modification improves both exploration and exploitation, resulting in enhanced performance. Additionally, the proposed MOIMPA incorporates the Pareto dominance mechanism. It stores non-dominated Pareto optimal solutions in a repository and employs a roulette wheel strategy to select solutions from the repository, considering their coverage. To evaluate the effectiveness and efficiency of MOIMPA, tests are conducted on various benchmark functions, including ZDT and DTLZ, as well as using the evolutionary computation 2009 (CEC’09) test suite. The algorithm is also evaluated on engineering design problems. A comparison is made between the proposed multi-objective approach and other well-known evolutionary optimization methods, such as MOMPA, multi-objective ant lion optimizer, and multi-objective multi-verse optimization. The statistical results demonstrate the robustness of the MOIMPA approach, as measured by metrics like inverted generational distance, generalized distance, spacing, and delta. Furthermore, qualitative experimental results confirm that MOIMPA provides highly accurate approximations of the true Pareto fronts.

Abstract In order to assure accurate modelling, this study presents a new technique for appropriately modelling and simulating a proton exchange membrane fuel cell (PEMFC) system. The PEMFC is a cleaner and more sustainable energy source as compared to fossil fuels. The fundamental idea is to minimize the sum of squared error (SSE) between the estimated and measured output voltage for the Ballard Mark V model in order to identify the model parameters of PEMFC stacks as efficiently as possible using a newly developed meta-heuristic called enhanced efficient optimization algorithm (EINFO). The proposed optimizer is considered an enhanced version of the original INFO algorithm. By balancing the exploration and exploitation phases better, the EINFO algorithm is intended to improve the performance of the original INFO approach and prevent local optima. The new method was tested on 23 benchmark functions and compared to the original INFO algorithm as well as other recently evolved optimizers. The algorithm is examined and compared with some literature meta-heuristics, including the particle swarm optimization, sine cosine algorithm, dragonfly algorithm, atom search optimization, Harris hawks optimization, and efficient optimization algorithm, using 50 independent runs, in terms of convergence speed and least SSE. When compared to other methods, the final findings show that, the suggested technique achieves the fastest convergence speed.

Abstract Due to the rapid development of photovoltaic (PV) system and spreading of its application, the accuracy of modeling of solar cells, as the main and basic element of PV systems, is gaining relevance. In this paper, an Enhanced Harris Hawk Optimization Algorithm (EHHO) is proposed and applied for estimating the required parameters of different PV models in an effective and accurate way. Harris Hawk Algorithm (HHO) is based on Hawks ways in hunting and catching their preys. The HHO utilizes two phases including exploration and exploitation. The main purpose of proposed enhancement is to improve the second phase of HHO. This enhancement is performed on the exploration phase by fluctuating toward or outward the best optimal solution using sine and cosine functions. Both conventional and proposed algorithms are applied for single, double and triple diode PV models. In order to test the applicability and robustness of proposed algorithm, it is applied for estimating the parameters of different real PV systems and compared with other recent optimization algorithms. The results show that the proposed EHHO is more accurate than conventional HHO and other algorithms.

This paper presents an efficient analytical technique to identify the optimal location and sizing of the distributed generation (DG) and shunt capacitor (SC) into a radial distribution system (RDS). The main objective of allocating DG and SC is to reduce the power losses which leads to improve the overall voltage profile with considering equality and inequality constraints. The DGs and SCs are placed at the bus that gives minimum power loss, while the optimal size is determined using the analytical technique. Moreover, a load variation with 50%, 100%, and 150% respected to the base case is studied to show the efficiency of proposed algorithm. Overall case studies are carried out using IEEE 69-bus RDS and the obtained results are compared with other optimization techniques used in the same manner.

SSSC is an important member of Flexible AC transmission Systems (FACTS) device family. It is considered to be a superior series FACTS device, as it has the ability to control the flow of both active and reactive power in a transmission line. Therefore, it is important to have a model for this device to facilitate studies involving it. This paper presents a simple SSSC model in NEPLAN power system analysis software, where it mainly depends on power injection method. This model is developed so that it can be utilized in studies concerned with SSSC in NEPLAN software, as the software suffers a lack of such a model. This model is tested on the standard IEEE 30 bus and IEEE 14-bus systems in different conditions to ensure its performance, quality in various load flow calculations and effectivity in NEPLAN software.