Optimal Reactive Power Dispatch Research Articles

A Fractional-Order Archimedean Spiral Moth–Flame Optimization Strategy to Solve Optimal Power Flows

This research utilizes the innovative fractional-order Archimedean spiral moth–flame optimization (FO-AMFO) technique to address the issues of the optimal reactive power dispatch (ORPD) problem. The formulated fitness function aims to minimize power losses and determine the ideal flow of reactive power for the IEEE 30- and 57-bus test systems. The extensive functions of the fractional evolutionary computing strategy are utilized to address the minimization problem of ORPD. This involves determining the control variables, such as VAR compensators, bus voltages, and the tap setting of the transformers. The effective incorporation of reactive compensation devices into traditional power grids has greatly reduced power losses; however, it has resulted in an increase in the complexity of optimization problems. A comparison of the findings indicates that swarming fractional intelligence using FO-AMFO surpassed the state-of-the-art competitors in terms of minimizing power losses.

Series and shunt FACTS controllers based optimal reactive power dispatch

Optimal reactive power dispatch involves the determination and management of reactive power resources in a power system to maintain voltage stability, improve power transfer capability, and minimize system losses. Reactive power is essential for maintaining voltage levels within acceptable limits and ensuring the reliable operation of electrical networks. The whale optimization algorithm (WOA) has been proposed to obtain the optimal location of flexible alternating current transmission system (FACTS) components. The efficacy of WOA is tested using conventional IEEE 14 and 30 bus test systems. Static var compensator (SVC) is used as shunt and the thyristor-controlled series capacitor (TCSC) as a series FACTS controller. The analysis is carried out for both the systems with and without FACTS controllers. Optimization techniques are applied to select the optimal control parameters. The suggested strategy is compared to other contemporary techniques such as particle swarm optimization (PSO) and grey wolf optimization (GWO). At various loading situations, the WOA-based technique outperforms other two techniques.

Optimal Reactive Power Dispatch problem integrating probabilistic model of wind power for uncertainties in load using JAYA algorithm

The optimal reactive power dispatch (ORPD) is a method for optimising power system engineering to reduce power loss and voltage deviation. This work addresses the ORPD problem considering load uncertainty, where load is varied in ten different instances. The optimal conditions have been determined for the system with minimum power loss and minimum total voltage deviations for different loading instances. The problem has also been integrated with the probabilistic nature of wind power, calculated using the Weibull Probability Distribution Function (WPDF). The aim is to obtain the optimal values of wind power using the WPDF for two separate cases: overestimation and underestimation, integrate these power individually, and minimise both the power loss and voltage deviation for the ten different loading scenarios. This hybrid wind power integrated ORPD problem, considering load uncertainty, has been tested on the IEEE 30 and IEEE 57 bus systems using the JAYA algorithm and other optimisation techniques. This tuning-parameter-free JAYA algorithm has obtained the best solutions for power loss of 1.8641 MW and TVD of 0.123 p.u. for the overestimated wind power integration at the IEEE 30 bus system at 100% loading compared to the other algorithms. It also acquired the best power loss and TVD solutions of 1.9144 MW and 0.1245 p.u., respectively, for the underestimated wind power at the same bus system for 100% loading with the highest convergence rate. The overall study establishes the JAYA algorithm as a superior optimising technique for solving this hybrid ORPD problem compared to the other techniques.

A mini review on optimal reactive power dispatch incorporating renewable energy sources and flexible alternating current transmission system

AbstractThe electrical power system (EPS) has been heavily stressed due to high load demand. It operates close to the total capacity limits, resulting in voltage instability that can lead to voltage collapse. In this regard, incorporating flexible alternating current transmission system (FACTS) devices and renewable energy sources (RESs) to obtain the optimum values of the generator voltage, reactive compensation, and transformer tab in optimal reactive power dispatch (ORPD) is essential in increasing the reliability and safety of the system. ORPD involves discrete and continuous variables, which are nonlinear, noncontinuous, non-convex, and complex problems. The objective functions of ORPD are reduction in active power loss (Ploss), voltage deviation, and voltage profile enhancement. This paper presents a recent advancement of the ORPD problem, mathematical formulation of the objectives function, and a summary of various metaheuristic optimization methods (single and hybrid) used to solve the ORPD problems. The hybrid method combines two or more methods to improve the demerits of one method to obtain a quality solution to a problem. This review covered incorporating FACTS devices and RESs used in solving the ORPD problem to reduce the active Ploss and improve the voltage profile in the EPS. The benefits of FACTS devices and RESs are also discussed. Also, various metaheuristic algorithms (single, modified, and hybrid) employed to solve the ORPD problem were discussed. The future direction for researchers in this field was provided to give insight into the applicability and performance. Overall, this research explores different techniques used in solving ORPD problems from the optimization point of view to incorporating RESs and FACTS devices to obtain quality solutions. Some existing methods do not guarantee an optimum solution, but incorporating RESs and FACTS devices will help attain the best solution to the problem for better power system operation to improve system reliability and voltage profile. Based on the review journal, it can be concluded that hybrid techniques offer efficient quality solutions to the ORPD problem.

A hybrid method for the optimal reactive power dispatch and the control of voltagesin an electrical energy network

A hybrid method for the optimal reactive power dispatch and the control of voltagesin an electrical energy network

A novel solution for the optimal reactive power dispatch problem using an artificial neural network integrated with the firefly optimization algorithm

This article applies a novel intelligence technique to solve power system issues faced daily. Compensation for reactive power is a significant issue faced by power system operators in research. The solution can be obtained by handling a multi-objective task and multiconstraints by reducing the active power loss and minimizing the voltage deviation at the load end. The novelty of the research focuses on integrating artificial neural network techniques with the firefly algorithm, a novel optimization algorithm for attaining an objective function. The Levenberg–Marquardt back-propagation algorithm is most suited for proper tuning of the control variables. The objective of this research can be attained by appropriately tuning the control variables connected with the IEEE test bus systems, which helps to maximally improve the voltage profile. Existing research studies have focused on reactive power management, which is attained by solving optimal reactive power flow problems employing nature-inspired approach techniques such as the symbiotic organism search algorithm, the cuckoo search algorithm, the black hole algorithm, the krill herd algorithm, and whale optimization. The evolving strategy, the firefly algorithm (FFA), minimizes the multiconstraint functions more competently and effectively than any conventional algorithm. To showcase the strength of the firefly algorithm incorporating AI, it is examined on standard IEEE test bus systems, namely, the 14-, 30-, and 58-bus networks. The obtained results quantify the effectiveness of the proposed methodology, that is, the artificial intelligence technique implementing the firefly algorithm gives better results than conventional methods.

Scenario-Based Approach to Solve Optimal Reactive Power Dispatch Problem with Integration of Solar Energy Using Modified Ant Line Optimizer

Scenario-Based Approach to Solve Optimal Reactive Power Dispatch Problem with Integration of Solar Energy Using Modified Ant Line Optimizer

Hybrid particle swarm and sea horse optimization algorithm-based optimal reactive power dispatch of power systems comprising electric vehicles

The reliability and effectiveness of today's electrical grids rely heavily on optimal reactive power dispatch (ORPD). The ORPD problem gets more challenging to resolve in the setting of ever-increasingly dynamic and complex systems. To handle the ORPD while also considering the existence of electric vehicles, this research introduces a novel technique: the Hybrid Particle Swarm Optimization and Sea Horse Optimization (PSOSHO) algorithm. Byreducing both active power loss and voltage variation, the proposed PSOSHO approach aims at improving the efficiency and reliability of the power grid. Simulation studies on reference power grids, including the IEEE 30-bus and IEEE 57-bus networks, verified its efficacy. Existing metaheuristic optimization techniques are compared using the same restrictions, governing parameters, and data. The results show that the PSOSHO method is trustworthy and effective in resolving the ORPD problem. One of the most pressing issues facing today's electricity grids is how to accommodate the growing number of electric vehicles. Real data on electric vehicles are incorporated in the analyses to obtain a realistic study. The suggested PSOSHO algorithm is a significant step forward in this area, providing a reliable and effective answer to the problem of optimum reactive power dispatch and helping to ensure the long-term viability of power systems in the age of electromobility.

Distributed Predictive Secondary Control With Soft Constraints for Optimal Dispatch in Hybrid AC/DC Microgrids

Hybrid AC/DC microgrids (H-MGs) are a prominent solution for integrating distributed generation and modern AC and DC loads. However, controlling these systems is challenging as multiple electrical variables need to be controlled and coordinated. To provide flexibility to the control system, these variables can be regulated to specific values or within secure bands. This paper proposes a set of distributed model predictive control schemes for the secondary control level to control certain variables to specific values and other variables within secure pre-defined bands into H-MGs. Specifically, optimal dispatch of active and reactive power is achieved while frequency and voltages are regulated within secure bands in H-MGs. Dynamic models of AC generators, DC generators and interlinking converters along with their novel multi-objective cost functions are developed in constrained distributed predictive optimisation problems to simultaneously achieve the aforementioned objectives via information sharing. Extensive simulation work validates the performance of this proposal.

An enhanced arithmetic optimization algorithm for optimal control of reactive power

AbstractIn this article, an enhanced arithmetic optimization algorithm (EAOA) is utilized to resolve the optimal reactive power dispatch problem (ORPD) of power plants, which is a non‐linear, non‐smooth, complex optimization problem. Typically, it is formulated as a constrained optimal power flow problem. This paper utilizes the gamma distribution to generate initial random solutions, which improves the accuracy of the arithmetic optimization algorithm (AOA). The original mode of deviation of math optimizer accelerated (MOA) is replaced with the improved pattern of change in the prey's energy in Harris Hawk Optimization (HHO), which creates a superior balance between the exploration and exploitation of AOA. This paper implements logarithmic and exponential operators in place of division and multiplication operators, which improves the exploration ability of AOA and also utilizes the gamma distribution in the generation of random numbers, which are essential for the selection of operators in both search phase which enlarges the search area and improves the global optimum solution. A parametric analysis is performed on 10 benchmark functions for nine possible values before selecting the algorithm's initial parameters. A comparative statistical analysis along with Friedman's test is carried out on 23 benchmark functions to test the overall performance as compared to Sine‐Cosine Algorithm (SCA), Swarm‐Salp Algorithm, Grey Wolf Optimization (GWO), and basic Arithmetic Optimization Algorithm (AOA). EAOA is applied to the IEEE 57 bus system for optimal reactive power control. EAOA reports a significant reduction in a power loss of 23.2 MW, which is 18.596% smaller than the system's base case power loss of 28.5 MW as compared to Artificial Bee Colony (ABC), Firefly Algorithm (FA), Bat‐inspired Algorithm (BAT), Cuckoo Search Algorithm (CSA), and Modified Ant Lion Algorithm (MALO) which reports a reduction in a power loss of 14.73%, 15.43%, 15.43%, 16.14%, and 16.14% respectively. EAOA reduces the TVD to 0.76 pu, compared to ABC, FA, BAT, CSA, and MALO, which minimizes the TVD to 0.84, 0.82, 0.88, 0.82, and 0.79, respectively. This proves that EAOA performs better in resolving ORCP problems regarding the quality of solutions and convergence. A detailed comparative statistical analysis of EAOA with CSA, BAT, and WOA (Whale Optimization Algorithm) is conducted in terms of Probability Distribution Functions (PDF) and Cumulative Distribution Functions (CDF), along with the Wilcoxson sign rank test, which proves that EAOA gives the solution with a higher degree of precision.

Optimal Reactive Power Dispatch problem using exchange market based Butterfly Optimization Algorithm

The Butterfly Optimization Algorithm (BOA) is a swarm-based optimization technique which takes its inspiration from the butterflies’ foraging activity. BOA has gained extensive popularity among the research community and is now utilized to tackle a variety of optimization challenges. However, literatures suggest that its exploration and exploitation are not properly balanced. To overcome this problem, BOA is fused with the crossover of Exchange Market Algorithm (EMA) and with non-uniform mutation. In this paper, enhanced BOA (EBOA) is used for solving the Optimal Reactive Power Dispatch (ORPD) problems. ORPD is traditionally a power system optimization tool that regulates control variables such as Generator bus Voltage, tap settings of tap-changing transformers, and VAR output of compensating devices in order to reduce real power loss, improve voltage deviation, and increase voltage stability. The suggested technique is evaluated using the IEEE 30 bus standard test system, IEEE 118 bus standard test system and Indian 62 bus system. To determine the efficacy of the algorithm, the findings from BOA and EBOA are compared to those produced by other researchers and published in the literature. From the results it can be observed that the proposed algorithm is able to reduce the active power loss by 22%, voltage deviation by 91.6% and L-Index by 42.02 % from their corresponding initial value for IEEE 30 bus system. Similar results can be seen from other test system also. The proposed algorithm is also tested in solving benchmark problems. The simulated results confirm the efficiency and robustness of the algorithm for solving ORPD problems.

Incorporating photovoltaic inverter capability into stochastic optimal reactive power dispatch through an enhanced artificial gorilla troops optimizer

AbstractThis study addresses the challenging task of solving optimal reactive power dispatch (ORPD) while incorporating renewable energy resources (RERs), considering their stochastic and time‐varying nature. Specifically, the focus is on solving the stochastic optimal reactive power dispatch (SORPD) problem, taking into account uncertainties in load demand and generated power, as well as the reactive power generation capability of photovoltaic (PV) systems. To tackle this problem, an enhanced Artificial Gorilla Troops Optimizer (EGTO) is proposed, which utilizes multiple strategies. The objective is to minimize power loss and improve voltage profile and system stability under uncertain conditions. The algorithm is applied and tested on the IEEE 30‐bus system, both with and without the STATCOM functionality of the PV system. A comparison is conducted against other well‐known optimization algorithms. The results demonstrate the significant improvement achieved by incorporating the PV unit. The inclusion of the PV system leads to reduced expected power losses, voltage deviations, and improved voltage stability. Specifically, without and with the STATCOM functionality, the expected power loss decreases from 5.9218 MW at the base case to 1.1419 MW and 1.1197 MW, respectively. Similarly, the expected voltage deviation decreases from 1.9320 p.u. to 0.0909 p.u. and 0.0893 p.u., respectively, and the expected voltage stability decreases from 0.1336 p.u. to 0.07199 p.u. and 0.07142 p.u., respectively.

Multi-Area and Multi-Period Optimal Reactive Power Dispatch in Electric Power Systems

Factors such as persistent demand growth, expansion project delays, and the rising adoption of renewable energy sources highlight the importance of operating power systems within safe operational margins. The optimal reactive power dispatch (ORPD) seeks to find operating points that allow greater flexibility in reactive power reserves, thus ensuring the safe operation of power systems. The main contribution of this paper is a multi-area and multi-period ORPD (MA-MP-ORPD) model, which seeks the minimization of the voltage deviation in pilot nodes, the reactive power deviation of shunt elements, and the total reactive power generated, all taking into account the operational constraints for each area. The MA-MP-ORPD was implemented in the Python programming language using the Pyomo library; furthermore, the BONMIN solver was employed to solve this mixed-integer nonlinear programming problem. The problem was formulated from the standpoint of the system operator; therefore, it minimizes the variations of critical variables from the desired operative values; furthermore, the number of maneuvers of the reactive compensation elements was also minimized to preserve their lifetimes. The results obtained on IEEE test systems of 39 and 57 buses validated its applicability and effectiveness. The proposed approach allowed obtaining increases in the reactive power reserves of up to 59% and 62% for the 39- and 57-bus test systems, respectively, while ensuring acceptable operation values of the critical variables.

A Methodology to Evaluate Reactive Power Reserves Scarcity During the Energy Transition

The lack of reserves for reactive power production and absorption is an envisioned, still basically unexplored, threat to the voltage profile adequacy and thereby secure operation of transmission grids during the energy transition toward renewable-dominated power production. This paper proposes a novel, generic, comprehensive, and realistic methodology to identify when this issue of reactive power reserves (RPRs) scarcity during plausible scenarios of the energy transition would become severe. The computational core of the proposed methodology comprises four different AC security-constrained optimal power flow (SCOPF) problems: one conventional, two tailored ones that assess the RPRs scarcity in production and absorption modes, respectively, and an optimal reactive power dispatch. The methodology is versatile, offering the possibility to assess RPRs in different timescales, ranging from day-ahead short-term operation to years-ahead long-term operation, and considering appropriate renewable energy production forecasts and day-dependent load profiles. The proposed methodology can serve as a decision support tool for the transmission system operator (TSO), allowing to plug and play different plausible energy transition scenarios (e.g., differing in terms of sequence and timing of: phased out power plants as well as location, type, and size of renewable energy sources deployed) and ultimately informing the TSO about the timing where RPRs become insufficient to maintain security. Without loss of generality, the value of the proposed methodology is extensively demonstrated in a 60-bus Nordic32 system, considering 52 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N-1$</tex-math></inline-formula> line and generator contingencies, while the tractability of AC SCOPF problems is assessed in a 1,203-bus system.

Optimal Reactive Power Dispatch in ADNs using DRL and the Impact of Its Various Settings and Environmental Changes.

Modern active distribution networks (ADNs) witness increasing complexities that require efforts in control practices, including optimal reactive power dispatch (ORPD). Deep reinforcement learning (DRL) is proposed to manage the network's reactive power by coordinating different resources, including distributed energy resources, to enhance performance. However, there is a lack of studies examining DRL elements' performance sensitivity. To this end, in this paper we examine the impact of various DRL reward representations and hyperparameters on the agent's learning performance when solving the ORPD problem for ADNs. We assess the agent's performance regarding accuracy and training time metrics, as well as critic estimate measures. Furthermore, different environmental changes are examined to study the DRL model's scalability by including other resources. Results show that compared to other representations, the complementary reward function exhibits improved performance in terms of power loss minimization and convergence time by 10-15% and 14-18%, respectively. Also, adequate agent performance is observed to be neighboring the best-suited value of each hyperparameter for the studied problem. In addition, scalability analysis depicts that increasing the number of possible action combinations in the action space by approximately nine times results in 1.7 times increase in the training time.

Equilibrium Optimizer Algorithm for Optimal Reactive Power Dispatch

Optimal Reactive Power Dispatch (ORPD) is a significant research area in terms of maintaining the reliability and safety of the power system and operating it more economically. ORPD problem can be formed from a variety of perspectives including the minimization of the active power losses and voltage deviation, and improving the voltage stability performance. The majority of methods so as to deal with ORPD problem is meta-heuristic techniques because of the complex, non-linear and non-convex nature of the problem. In this paper, a new physic-based meta-heuristic algorithm, Equilibrium Optimizer (EO), is proposed for ORPD problem to reach the optimal settings of control variables such as voltage magnitudes in PV buses, tap positions of transformers and reactive power support of shunt devices. The introduced algorithm is evaluated on IEEE 30-bus test system by using various objectives, and a comparison of the implemented method to other optimization techniques described in the literature is utilized to assess its efficacy. Simulation results and statistical indicators demonstrate that the EO algorithm validates its computational efficacy and robustness in handling the ORPD problem.

Optimal Reactive Power Dispatch in Electric Transmission Systems Using the Multi-Agent Model with Volt-VAR Control

The optimal dispatch of reactive power is a fundamental task in the operational planning of electrical power systems. This task aims to minimize active power losses and improve voltage levels within the electrical power system. This paper presents the application of the particle swarm optimization methodology to achieve optimal reactive power dispatch. The methodology’s performance is demonstrated by its high processing speed and the results obtained through a comprehensive global search for reactive power dispatch. Additionally, experimental results confirm the algorithm’s effectiveness in optimizing the objective function across different case studies, highlighting its ability to achieve optimal reactive power dispatch. This study represents a significant advancement in the field of power system optimization and provides a useful tool for managing and controlling these systems.

A Grey Wolf Optimization Algorithm-Based Optimal Reactive Power Dispatch with Wind-Integrated Power Systems

Keeping the bus voltage within acceptable limits depends on dispatching reactive power. Power quality improves as a result of creating an effective power flow system, which also helps to reduce power loss. Therefore, optimal reactive power dispatch (ORPD) studies aim at designing appropriate system configurations to enable a reliable operation of power systems. Establishment of such a configuration is handled through control variables in power systems. Various control variables, such as adjusting generator bus voltages, transformer tap locations, and switchable shunt capacitor sizes, are utilized to achieve this objective. Additionally, the integration of wind power can greatly impact power quality and mitigate power loss. In this study, the Grey Wolf Optimization (GWO) approach was applied to the ORPD issue for the first time to discover the best placement of newly installed wind power in the power system while taking into account tap changer settings, shunt capacitor sizes, and generated power levels. The main objective was to determine optimal wind placement to minimize power loss and voltage deviation, while maintaining control variables within specified limits. On the basis of IEEE 30-bus and IEEE 118-bus systems, the performance of the proposed method was investigated. The results demonstrated the superiority of GWO in multiple scenarios. In IEEE-30, GWO outperformed the PSO, GA, ABC, OGSA, HBMO, and HFA methods, reducing total loss by 10.36%, 18.03%, 9.19%, 7.13%, 5.23%, and 7.73%, respectively, and voltage deviation by 68.00%, 1.59%, 36.34%, 41.97%, 46.29%, and 71.08%, respectively. In wind integration scenarios, GWO achieved the simultaneous reduction of power loss and voltage deviation. In IEEE-118, GWO outperformed the ABC, PSO, GSA, and CFA methods, reducing power loss by approximately 19.91%, 16.83%, 14.09%, and 4.36%, respectively, and voltage deviation by 8.50%, 14.15%, 16.19%, and 7.17%, respectively. These promising results highlighted the potential of the GWO algorithm to facilitate the integration of renewable energy sources, and its role in promoting sustainable energy solutions. In addition, this study conducted an analysis to investigate site-specific wind placement by using the Weibull distribution function and commercial wind turbines.

Stochastic Multi-Objective Optimal Reactive Power Dispatch with the Integration of Wind and Solar Generation

The exponential growth of unpredictable renewable power production sources in the power grid results in difficult-to-regulate reactive power. The ultimate goal of optimal reactive power dispatch (ORPD) is to find the optimal voltage level of all the generators, the transformer tap ratio, and the MVAR injection of shunt VAR compensators (SVC). More realistically, the ORPD problem is a nonlinear multi-objective optimization problem. Therefore, in this paper, the multi-objective ORPD problem is formulated and solved considering the simultaneous minimization of the active power loss, voltage deviation, emission, and the operating cost of renewable and thermal generators. Usually, renewable power generators such as wind and solar are uncertain; therefore, Weibull and lognormal probability distribution functions are considered to model wind and solar power, respectively. Due to the unavailability and uncertainty of wind and solar power, appropriate PDFs have been used to generate 1000 scenarios with the help of Monte Carlo simulation techniques. Practically, it is not possible to solve the problem considering all the scenarios. Therefore, the scenario reduction technique based on the distance metric is applied to select the 24 representative scenarios to reduce the size of the problem. Moreover, the efficient non-dominated sorting genetic algorithm II-based bidirectional co-evolutionary algorithm (BiCo), along with the constraint domination principle, is adopted to solve the multi-objective ORPD problem. Furthermore, a modified IEEE standard 30-bus system is employed to show the performance and superiority of the proposed algorithm. Simulation results indicate that the proposed algorithm finds uniformly distributed and near-global final non-dominated solutions compared to the recently available state-of-the-art multi-objective algorithms in the literature.

Jaya-AEO: An Innovative Hybrid Optimizer for Reactive Power Dispatch Optimization in Power Systems

In the domain of electric power systems, ensuring stable voltage and efficient transmission is crucial. Optimal reactive power dispatch (ORPD) is a vital step toward improving system stability, enhancing economic feasibility, and increasing overall efficiency. Various optimization techniques are employed to minimize real power loss and voltage deviation in the network. This article proposes a hybrid algorithm called Enhanced Jaya and Artificial Ecosystem-Based Optimization (EJAEO) to address the ORPD problem. The algorithm aims to determine the optimal values of variables such as reactive compensation, generators’ voltages, and transformers’ tape ratio. Two single objective functions are tested on standard IEEE 30-Bus and IEEE 57-Bus systems, and the suggested modification of the Artificial Ecosystem-Based Optimization (AEO) improves population effectiveness in achieving optimal solutions. The simulation findings of the EJAEO algorithm demonstrated its superiority over three recent algorithms (AEO), Turbulent Flow of Water-Based Optimization, and Jaya algorithm), as well as certain previously published ORPD methods used for the same problem. In the case of the IEEE 30-Bus system, the proposed EJAEO algorithm achieved the best results in terms of power losses (4.944805) and voltage deviation (0.121196). Similarly, in the IEEE 57-Bus system, our EJAEO algorithm outperformed others, yielding the lowest power losses (23.33052) and voltage deviation (0.579286). The EJAEO algorithm outperforms other algorithms in terms of accuracy, speed of convergence, and robustness. These findings highlight the potential of EJAEO as a promising technique for solving the ORPD problem in power systems.