Optimal Reactive Power Dispatch Problem Research Articles

An effective gradient jellyfish search algorithm for optimal reactive power dispatch in electrical networks

AbstractAn effective optimization technique, called gradient jellyfish search optimizer (GJSO), is introduced here to address the optimal reactive power dispatch (ORPD) issue in electric networks. The ORPD problem is a complex non‐linear optimization issue involving integrated variables, aimed at achieving safe and cost‐effective operation of the system by determining optimal values for generator voltage, tap changers of transformers, and reactive power compensation. The performance of the original JSO technique is enhanced by integrating the local escaping operator into the GJSO approach. The effectiveness of the GJSO methodology is evaluated via comparison with two existing methodologies: the original jellyfish search optimizer and the equilibrium optimizer. Jellyfish search optimizer is a meta‐heuristic optimization algorithm inspired by the movement of jellyfish in the water, while equilibrium optimizer draws inspiration from game theory and equilibrium concepts. Simulations were conducted using typical IEEE‐30 bus and IEEE‐57 bus systems to validate the performance of the GJSO methodology. Two versions of the objective function are examined: minimizing line power loss and minimizing total voltage deviations at the buses. The simulation results demonstrated that the GJSO algorithm exhibited superior performance in terms of accuracy and stability compared to the standard jellyfish search optimizer and equilibrium optimizer algorithms.

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.

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 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

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.

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.

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.

A Novel Adaptive Manta-Ray Foraging Optimization for Stochastic ORPD Considering Uncertainties of Wind Power and Load Demand

The optimal control of reactive powers in electrical systems can improve a system’s performance and security; this can be provided by the optimal reactive power dispatch (ORPD). Under the high penetration of renewable energy resources (RERs) such as wind turbines (WTs), the ORPD problem solution has become a challenging and complex task due to the fluctuations and uncertainties of generated power from WTs. In this regard, this paper solved the conventional ORPD and the stochastic ORPD (SORPD) at uncertainties of the generated power from WTs and the load demand. An Adaptive Manta-Ray Foraging Optimization (AMRFO) was presented based on three modifications, including the fitness distance balance selection (FDB), Quasi Oppositional based learning (QOBL), and an adaptive Levy Flight (ALF). The ORPD and SORPD were solved to reduce the power loss (PLoss) and the total expected PLoss (TEPL), the voltage deviations (VD) and the total expected VD (TEVD). The normal and Weibull probability density functions (PDFs), along with the scenario reduction method and the Monte Carlo simulation (MCS), were utilized for uncertainty representations. The performance and validity of the suggested AMRFO were compared to other optimizers, including SCSO, WOA, DO, AHA, and the conventional MRFO on the IEEE 30-bus system and standard benchmark functions. These simulation results confirm the supremacy of the suggested AMRFO for the ORPD and SORPD solution compared to the other reported techniques.

Using the Whale Optimization Algorithm to Solve the Optimal Reactive Power Dispatch Problem

The optimal reactive power dispatch (ORPD) is a complex, optimal non-meritorious control issue with continuous and discontinuous control variables. This article exhibits a whale optimization algorithm (WOA) motivated by the whale’s bubble-net hunting tactic to resolve ORPD. The intention is to comply with certain constraints to promote the voltage transmission quality by adequately altering the parameters. The WOA not only equalizes exploitation and exploration to maximize the overall performance and eliminate search stagnation but also has remarkable sustainability and robustness to accomplish superior convergence speed and computation accuracy. The WOA is contrasted with MFO, BA, GOA, GWO, MDWA, SMA, SPBO and SSA by diminishing the fitness value to highlight the superiority and stability. The experimental results reveal that WOA exhibits a superior convergence level and computation precision to accomplish the minimum active power loss and superior control variables.

Enhanced transient search optimization algorithm-based optimal reactive power dispatch including electric vehicles

Optimal reactive power dispatch (ORPD) in electrical networks is essential for the secure and stable operation of the entire power system; it also significantly impacts the economic situation. However, the solution of ORPD is highly complex while considering the multiple variables, time-varying characteristics, dynamic loads such as electric vehicles, and operational constraints. The ORPD problem is classified as a non-linear, non-convex complex problem. Thus, a robust optimization technique should be utilized to solve the ORPD. This paper presents a novel Enhanced Transient Search Optimization (ETSO) technique for the optimal solution of the ORPD problem by integrating electric vehicles (EVs). The proposed ETSO implemented for the optimal solution of ORPD consequently minimize the active power loss and voltage deviation at the load buses. The proposed method is tested and verified on the IEEE 30-bus, the IEEE-57 bus, and IEEE 118-bus systems. The simulation results show the robustness and efficiency of the proposed ETSO optimization in solving the ORPD problem by evaluating and comparing it with other well-established metaheuristic optimization methods under the same system data, control variables, and constraints. Statistical features of the proposed ETSO algorithm and the results obtained led to an improvement in the performance of the power systems.

Least Squares Regression Based Ant Lion Optimizer to Solve Optimal Reactive Power and Economic Load Dispatch Problems

Least Squares Regression Based Ant Lion Optimizer to Solve Optimal Reactive Power and Economic Load Dispatch Problems

Solution to the deterministic and stochastic Optimal Reactive Power Dispatch by integration of solar, wind-hydro powers using Modified Artificial Hummingbird Algorithm

In electrical power networks, the optimal reactive power dispatch (ORPD) problem is essential to the system studies to perform reliable and secure operations by maintaining the control variable within their permissible limits. An electric network consisting of thermal generators has been studied widely for optimal power dispatch problems. Increasing renewable energy resources (RERs) penetration into the electric power grid required power flow studies while integrating these resources. It is a strenuous task to incorporate renewable energy resources into the ORPD problem due to the stochastic nature of RERs. This paper solved the stochastic optimal reactive power dispatch (ORPD) problem considering the uncertainties of renewable resources such as; solar PV, wind turbine, and hydropower generation systems. The time-varying load demand and the power generated from the renewable energy resources are represented using the normal, the lognormal, the Weibull, and the Gumbel probability density function (PDFs). Then, the Monte Carlo simulations reduction of scenarios-based technique is applied to generate a suitable number of scenarios. The second contribution presents an efficient version of the Artificial Hummingbird Algorithm (MAHA) for solving the Stochastic and Non-Stochastic ORPD. The proposed MAHA is based on the levy flight motion and the distance bandwidth motion around the best solution to enhance the exploration and exploitation behavior of the traditional AHA to avoid trapping into the local minima. The proposed algorithm is validated and tested on the IEEE 30-bus system for active power loss reduction, voltage profile improvement, and voltage stability enhancement. The results showed the effectiveness and superiority of the proposed MAHA for solving the ORPD problem compared to the well-known conventional algorithms such as AHA, GWO, SCA, DO, BWO and other state-of-the-art algorithms.

Ingenuity of Shannon entropy-based fractional order hybrid swarming strategy to solve optimal power flows

An important issue for researchers looking into the effectiveness of power distribution systems is the Optimal Reactive-Power Dispatch (ORPD) problem, which aims to reduce real power line losses. Numerous techniques have been created with the express purpose of improving upon the optimization method's performance in tuning operational variables and exploring it through the estimation of results. Using entropy evolution (EE) and fractional calculus (FC) concepts, the research presents a novel method that is implemented in the hybrid meta-heuristic computational paradigm of Moth Flame Optimization (MFO) and Particle Swarm Optimization (PSO) algorithms for the ORPD problem. These techniques were incorporated into the MFO-PSO algorithm to enhance its memory effect, robustness, and stability. This was done to address the MFO-PSO vulnerability. ORPD problem using the IEEE-57 bus and IEEE-118 bus standards are used to test the novel Entropy design MFO and Fractional-order PSO algorithms as (EMFO-FPSO). The superiority of the proposed EMFO-FPSO algorithm has been demonstrated through a comparative analysis study with well-known optimizer solvers from the literature.

Improved PSO with Disturbance Term for Solving ORPD Problem in Power Systems

The essential purpose of an energy system is to provide electricity to its loads effectively and economically, as well as safely and reliably. Therefore, the solutions to the problems of Optimal Power Flow (OPF) and Optimal Reactive Power Dispatch (ORPD) to enable the efficient employment of various energy distributions should be found. Our work focuses on the ORPD issue; it can be formulated as a non-linear constraint and with single or multiple objectives optimization problems. Minimizing total losses is one of the main objective functions to solve the ORPD problem. This paper presents the use of an improved particle swarm optimization -with a disturbance term- (called PSO-DT) algorithm, to find the solution of ORPD in the standard IEEE 30-bus power system for reducing electrical power transmission losses. The obtained results demonstrate that the proposed method is more efficient and has a more extraordinary ability to get better solutions compared to the basic PSO method.