Optimal Power Flow Problem Research Articles

Development and Analysis of Optimization Algorithm for Demand-Side Management Considering Optimal Generation Scheduling and Power Flow in Grid-Connected AC/DC Microgrid

The world energy sector is experiencing many challenges, such as maintaining a demand–supply balance with continuous increases in demand, reliability issues, and environmental concerns. Distributed energy resources (DERs) that use renewable energy sources (RESs) have become more prevalent due to environmental challenges and the depletion of fossil fuel reserves. An increased penetration of RESs in a microgrid system facilitates the establishment of a local independent system. However, these systems, due to the uncertainties of RESs, still encounter major issues, like increased operating costs or operating constraint violations, optimal power management, etc. To solve these issues, this paper proposes a stochastic programming model to minimize the total operating cost and emissions and improve the operational reliability with the help of a generalized normal distribution optimization (GNDO). A day-ahead demand response is scheduled, aiming to shift loads to enhance RES utilization efficiency. Demand-side management (DSM) with RESs is utilized, and battery energy storage systems in low-voltage and medium-voltage microgrids are shown. Mathematical formulations of each element in the microgrids were performed. Optimal and consumer-friendly solutions were found for all the cases. Environmental concerns based on the amount of harmful emissions were also analyzed. The importance of demand response is demonstrated vividly. The aim is to optimize energy consumption and achieve optimum cost of operation via DSM, considering several security constraints. A comparative analysis of operating costs, emission values, and the voltage deviation was carried out to prove and justify their potential to solve the optimal scheduling and power flow problem in AC/DC microgrids.

Integrating renewable energy and V2G uncertainty into optimal power flow: A gradient bald eagle search optimization algorithm with local escaping operator

AbstractHere, a new approach is proposed for solving the optimal power flow (OPF) problem in transmission networks using a Gradient Bald Eagle Search Algorithm (GBES) with a Local Escaping Operator (LEO). The method takes into account uncertainty of the renewable energy sources (wind energy and photovoltaic systems) and Vehicle‐to‐Grid (V2G) in the stochastic OPF problem. To improve the efficiency of the proposed technique and enhance its local exploitation capability, the LEO method's selection features are utilized. Monte Carlo methods are employed to estimate the generation costs of the renewable sources and PEVs and study their feasibility. The uncertainty of the renewable sources and PEVs is represented by Weibull, lognormal, and normal probability distribution functions (PDFs). The GBES approach is experimentally compared with well‐known meta‐heuristics using twenty‐three different test functions, and the results indicate its superiority over BES and other recently developed algorithms. Furthermore, the proposed method's effectiveness is evaluated using IEEE 30‐bus test system under various scenarios, and the simulation results demonstrate that it can effectively address OPF issues considering renewable energy sources and V2G, providing superior optimal solutions compared to other algorithms.

A high-performance democratic political algorithm for solving multi-objective optimal power flow problem

The optimal power flow (OPF) is one of the most noticeable and integral tools in the power system operation and control and aims to obtain the most economical combination of power plants to exactly serve the total demand of the system without any load shedding or islanding through adjusting control variables to meet operational, economic, and environmental constraints. To achieve this goal, the successful implementation of an expeditious and reliable optimization algorithm is crucial. To solve this issue, this research proposes an enhanced democratic political algorithm (DPA), which can effectively solve multi-objective optimum power flow problems. The proposed method is a version of the democratic political optimization algorithm in which the search capability of this method to cover the borders of the Pareto frontier is enhanced. For the sake of practicality, the objectives with innate differences such as total emission, active power loss, and fuel cost are selected. Due to the practical limitations in real power systems, additional restrictions including valve-point effect, multi-fuel characteristics, and forbidden operational zones, are also considered. The proposed approach is tested and validated on IEEE 57-bus and IEEE 118-bus systems with different case studies. Simulation results are analyzed and compared with two popular and commonly used multi-objective-evolutionary algorithms namely, non-dominated sorting genetic algorithm II (NSGA-II) and the multi-objective particle swarm optimization (MOPSO) on the problem. The study results illustrate the effectiveness of the proposed method in handling different scales, non-convex, and multi-objective optimization problems.

Topology-Aware Graph Neural Networks for Learning Feasible and Adaptive AC-OPF Solutions

Solving the optimal power flow (OPF) problem is a fundamental task to ensure the system efficiency and reliability in real-time electricity grid operations. We develop a new topology-informed graph neural network (GNN) approach for predicting the optimal solutions of real-time ac-OPF problem. To incorporate grid topology to the NN model, the proposed GNN-for-OPF framework innovatively exploits the locality property of locational marginal prices and voltage magnitude. Furthermore, we develop a physics-aware (ac-)flow feasibility regularization approach for general OPF learning. The advantages of our proposed designs include reduced model complexity, improved generalizability and feasibility guarantees. By providing the analytical understanding on the graph subspace stability under grid topology contingency, we show the proposed GNN can quickly adapt to varying grid topology by an efficient re-training strategy. Numerical tests on various test systems of different sizes have validated the prediction accuracy, improved flow feasibility, and topology adaptivity capability of our proposed GNN-based learning framework.

An Online Joint Optimization–Estimation Architecture for Distribution Networks

In this article, we propose an optimal joint optimization–estimation architecture for distribution networks, which jointly solves the optimal power flow (OPF) problem and static state estimation (SE) problem through an online gradient-based feedback algorithm. The main objective is to enable a fast and timely interaction between the OPF decisions and state estimators with limited sensor measurements. First, convergence and optimality of the proposed algorithm are analytically established. Then, the proposed gradient-based algorithm is modified by introducing statistical information of the inherent estimation and linearization errors for an improved and robust performance of the online OPF decisions. Overall, the proposed method eliminates the traditional separation of operation and monitoring, where optimization and estimation usually operate at distinct layers and different time scales. Hence, it enables a computationally affordable, efficient, and robust online operational framework for distribution networks under time-varying settings.

Embedding Dependencies Between Wind Farms in Distributionally Robust Optimal Power Flow

The increasing share of renewables in the electricity generation mix comes along with an increasing uncertainty in power supply. In the recent years, distributionally robust optimization has gained significant interest due to its ability to make informed decisions under uncertainty, which are robust to misrepresentations of the distributional information (e.g., from probabilistic forecasts). This is achieved by introducing an ambiguity set that describes the potential deviations from an empirical distribution of all uncertain parameters. However, this set typically overlooks the inherent dependencies of uncertainty, e.g., spatial dependencies of weather-dependent energy sources. This paper goes beyond the state-of-the-art models by embedding such dependencies within the definition of ambiguity set. In particular, we propose a new copula-based ambiguity set which is tailored to capture any type of dependencies. The resulting problem is reformulated as a conic program which is kept generic such that it can be applied to any decision-making problem under uncertainty in power systems. Given the Optimal Power Flow (OPF) problem as one of the main potential applications, we illustrate the performance of our proposed distributionally robust model applied to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i)</i> a DC-OPF problem for a meshed transmission system and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii)</i> an AC-OPF problem using <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LinDistFlow</i> approximation for a radial distribution system.

CoLinFlow: An Iterative Solution Approach for the Scenario-Based AC OPF in Active Meshed Distribution Grids With Batteries

Distribution grids are characterized by an increased installation of renewable energy sources (RESs) and of batteries. Both the uncertainty of RESs and the controllability of batteries should be considered when optimizing their operation. This leads to large-scale, non-convex Optimal Power Flow (OPF) problems. Existing solution approaches either refer to radial grids or do not work under uncertainty. However, many Distribution System Operators operate their grids in meshed topologies. In this paper, CoLinFlow, an efficient solution approach for a scenario-based AC OPF in meshed balanced three-phase distribution grids with intermittent RESs and controllable batteries is proposed. First, a particular power flow form in rectangular coordinates that is accurate for meshed grids is applied. Then, Generalized Linearized Power Flow (GLPF), a novel linearization of the power flow equations based on replacing non-linear terms with constants is developed. Based on GLPF, we design CoLinFlow, a heuristic iterative scheme that at each iteration solves a convex OPF and updates GLPF until convergence. The solution of CoLinFlow at convergence is proven to be feasible with respect to the original non-convex OPF and convergence is reached after very few iterations. Also, it is shown that CoLinFlow achieves almost the same optimal objective as Ipopt, while being faster.

Data-Driven Nonparametric Probabilistic Optimal Power Flow: An Integrated Probabilistic Forecasting and Analysis Methodology

With large-scale integration of renewable energy such as wind power, probabilistic analysis of optimal power flow becomes crucial for the decision-making of power systems. This paper proposes a novel data-driven integrated probabilistic forecasting and analysis (IPFA) methodology for the nonparametric probabilistic optimal power flow (N-POPF), which internalizes the probabilistic forecasting and nonparametric distributional description forms into uncertainty analysis. The proposed IPFA methodology fully utilizes the uncertainty analysis method to guide the model-free nonparametric probabilistic forecasting of wind power, and then conducts the N-POPF analysis effectively based on the uncertainty information contained in historical data. A comprehensive uncertainty evaluation criterion based on point estimate method and differential entropy is proposed to assess both the inherent uncertainty and uncertainty influence of input random variables. Then a model-free multivariate probabilistic forecasting method is established to directly support the solving of N-POPF problems with similar historical measurements. Finally, with deterministic optimal power flow problems corresponding to the selected historical samples, a weighted combination approach for the power flow results is developed to derive the quantiles of the output random variables. Comprehensive experiments on IEEE 24-bus and 118-bus test systems validate the superiority of the proposed IPFA methodology in estimation accuracy and computational efficiency.

Evaluation of Economic Impact of Renewable Energy Sources in Multi-period Optimal Operation of Power Systems

Abstract: In order to operate the electrical network economically and effectively, generation from various sources must be appropriately scheduled. Integrated systems are more common today because of the increase in the cost of fossil fuels and the technological advancements made in the field of renewable energy Resources. To be able to determine the best settings, the optimal power flow problem is posed with all relevant system characteristics, including generator outputs. The network might include conventional fossil fuel generators and renewable energy sources like wind power generators and solar photovoltaic. The classic problem of optimal power flow is a complex non-linear problem with non-linear constraints. In this research, it is suggested how thermal plants with wind and solar integration operate economically using General Algebraic Modeling System (GAMS) software's which has used Non-linear programming to resolve the Dynamic Economic Dispatch (DED) which is a part of optimal power flow problem. The impact of wind and solar integration on the cost-effective operation of thermal units while taking into considering IEEE-24 bus test system has been researched. In this paper, the reduction of a thermal plant's fuel consumption with the integration of wind and solar power is the primary focus of study.

Multi‐objective optimal power flow using grasshopper optimization algorithm

SummaryThis paper introduces grasshopper optimization algorithm to efficiently prove its superiority in the optimal power flow problem. To demonstrate the efficiency of the proposed algorithm, it is implemented on the standard IEEE 30‐bus, IEEE 57‐bus, and IEEE 118‐bus test systems with different objectives that reveal presentation indices of the power system. Twelve different cases, in single and multi‐objective optimization space, are considered on different curves of fuel cost, environmental pollution emission, voltage profile, and active power loss. The simulation results obtained from grasshopper optimization algorithm techniques are compared to other new evolutionary optimization methods surfaced in the current state‐of‐the‐art literature. It is revealed that the proposed approach secures better consequence over the other newly originated popular optimization techniques and reflects its improved quality solutions and faster convergence speed. The results obtained in this work demonstrate that the grasshopper optimization algorithm method can successfully be applied to solve the non‐linear problems connected to power systems.

Optimal Probabilistic Allocation of Photovoltaic Distributed Generation: Proposing a Scenario-Based Stochastic Programming Model

The recent developments in the design, planning, and operation of distribution systems indicate the need for a modern integrated infrastructure in which participants are managed through the perceptions of a utility company in an economic network (e.g., energy loss reduction, restoration, etc.). The penetration of distributed generation units in power systems are growing due to their significant influence on the key attributes of power systems. As a result, the placement, type, and size of distributed generations have an essential role in reducing power loss and lowering costs. Power loss minimization, investment and cost reduction, and voltage profile improvement combine to form a conceivable goal function for distributed generation allocation in a constrained optimization problem, and they require a complex procedure to control them in the most appropriate way while satisfying network constraints. Such a complex decision-making procedure can be solved by adjusting the dynamic optimal power flow problem to the associated network. The purpose of the present work is to handle the distributed generation allocation problem for photovoltaic units, attempting to reduce energy and investment costs while accounting for generation unpredictability as well as load fluctuation. The problem is analyzed under various scenarios of solar radiation through a stochastic programming technique because of the intense uncertainty of solar energy resources. The formulation of photovoltaic distributed generation allocation is represented as a mixed-integer second-order conic programming problem. The IEEE 33-bus and real-world 136-bus distribution systems are tested. The findings illustrate the efficacy of the proposed mathematical model and the role of appropriate distributed generation allocation.

Gaussian bare-bones Levy circulatory system-based optimization for power flow in the presence of renewable units

The Optimal Power Flow (OPF) is a vital issue in electrical networks to ensure the economical and safe operation to transfer electrical energy that is very complex, non-linear, and limited. In the electrical networks with Renewable Energy Sources (RES), the OPF problem is a much more complex and constrained optimization problem because incorporating the intermittent nature of RESs, including Wind Turbine (WT) and Photovoltaic (PV), which have been used in this article, and OPF is often used to optimize various problems. In this research, an effort has been made to modify and improve the performance of a new algorithm named Circulatory System-Based Optimization (CSBO) to a more powerful algorithm for complex OPF problems, and the result of this research was to present a more effective and powerful algorithm named Gaussian Bare-bones Levy CSBO (GBLCSBO). CSBO mimics the mating behavior of the circulatory system in the body. The IEEE 30-bus and 118-bus test networks are adopted to validate the capability of the suggested approach in minimizing four objectives, which include the total generation cost, voltage deviation, power loss, and pollution emission.Finally, to know the performance and strength of GBLCSBO for solving various OPF problems, several new powerful algorithms include Seagull Optimization Algorithm (SOA), Teaching-Learning-Based Optimization (TLBO), Gray Wolf Optimizer (GWO), Multi-Verse Optimizer (MVO) have been used to compare with GBLCSBO. Also, the CEC 2017 test functions were used to measure the performance of GBLCSBO in a broader range of optimization problems.The optimization results in both topics of OPF problems and various test functions compared with various algorithms showed that GBLCSBO is both strong and robust and has a suitable and comparative performance in a wide range of different optimization problems such as OPF. According to the obtained results, the GBLCSBO demonstrates high potential in solving OPF problems.

Optimal Power Flow of Power System with Static VAR Compensator using Moth Flame Optimization with Locational Marginal Price

The determination of a generation unit's locational marginal price (LMP), which depends on our understanding of transmission line capacity and optimal power flow (OPF) based on reality, is crucial to evaluating the performance of the unit and determining its profit. Minimising the total cost of the generators will lower the price of electricity on the market. Since power flow equations are nonlinear, numerical and repetition-based approaches should be used to solve them. The equations in this paper are solved using a Moth Flame Optimization (MFO), and to enhance the performance of the MFO in its structure, for simultaneous calculations of power passing through in transmission lines so that by learning about the capacity of transmission lines, in addition to the optimal power flow becoming a reality, the price of electricity is determined using uniform market pricing, or LMP method. The FACTS device used for the problem is Static Var Compensator (SVC). Finally, values for bus voltages, line losses, power injected to buses, power travelling via lines, total generating costs, and generator profits would be included in the output of the proposed MFO algorithm. Additionally, the results of testing the proposed methodology on the IEEE 30-BUS network reveal improvements on the OPF problem.

Solving optimal power flow problems via a constrained many-objective co-evolutionary algorithm

The optimal power flow problem in power systems is characterized by a number of complex objectives and constraints, which aim to optimize the total fuel cost, emissions, active power loss, voltage magnitude deviation, and other metrics simultaneously. These conflicting objectives and strict constraints challenge existing optimizers in balancing between active power and reactive power, along with good trade-offs among many metrics. To address these difficulties, this paper develops a co-evolutionary algorithm to solve the constrained many-objective optimization problem of optimal power flow, which evolves three populations with different selection strategies. These populations are evolved towards different parts of the huge objective space divided by large infeasible regions, and the cooperation between them renders assistance to the search for feasible and Pareto-optimal solutions. According to the experimental results on benchmark problems and the IEEE 30-bus, IEEE 57-bus, and IEEE 118-bus systems, the proposed algorithm is superior over peer algorithms in solving constrained many-objective optimization problems, especially the optimal power flow problems.

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 power flow with distributed energy sources using whale optimization algorithm

&lt;span lang="EN-US"&gt;Renewable energy generation is increasingly attractive since it is &lt;br /&gt; non-polluting and viable. Recently, the technical and economic performance of power system networks has been enhanced by integrating renewable energy sources (RES). This work focuses on the size of solar and wind production by replacing the thermal generation to decrease cost and losses on a big electrical power system. The Weibull and Lognormal probability density functions are used to calculate the deliverable power of wind and solar energy, to be integrated into the power system. Due to the uncertain and intermittent conditions of these sources, their integration complicates the optimal power flow problem. This paper proposes an optimal power flow (OPF) using the whale optimization algorithm (WOA), to solve for the stochastic wind and solar power integrated power system. In this paper, the ideal capacity of RES along with thermal generators has been determined by considering total generation cost as an objective function. The proposed methodology is tested on the IEEE-30 system to ensure its usefulness. Obtained results show the effectiveness of WOA when compared with other algorithms like non-dominated sorting genetic algorithm (NSGA-II), grey wolf optimization (GWO) and particle swarm optimization-GWO (PSO-GWO).&lt;/span&gt;

A second-order conic approximation to solving the optimal power flow problem in bipolar DC networks while considering a high penetration of distributed energy resources

This article presents an optimal power flow (OPF) formulation based on the branch flow model for bipolar DC grids with asymmetric loading. The proposal considers the power injection formulation of the OPF to obtain the branch flow model equations that allow solving the power flow problem in bipolar DC networks. Furthermore, a nonlinear programming (NLP) optimization model is deduced and transformed into a second-order conic programming one, which involves convex optimization and guarantees a global optimum for the relaxed model, the uniqueness of this solution, and fast convergence. Finally, an approximation based on balanced operation is proposed to simplify the OPF. Several case studies in two test systems composed of 21 and 85 nodes with a bipolar structure demonstrate that the proposal is accurate, fast, and close to the exact solution of the NLP model when compared with competitive literature reports. All optimization models were implemented in the Python language.

Comparative Analysis of the Particle Swarm Optimization and Primal-Dual Interior-Point Algorithms for Transmission System Volt/VAR Optimization in Rectangular Voltage Coordinates

Optimal power flow (OPF) is one of the most widely studied problems in the field of operations research, as it applies to the optimal and efficient operation of the electric power system. Both the problem formulation and solution techniques have attracted significant research interest over the decades. A wide range of OPF problems have been formulated to cater for the various operational objectives of the power system and are mainly expressed either in polar or rectangular voltage coordinates. Many different solution techniques falling into the two main categories of classical/deterministic optimization and heuristic/non-deterministic optimization techniques have been explored in the literature. This study considers the Volt/VAR optimization (VVO) variant of the OPF problem formulated in rectangular voltage coordinates, which is something of a departure from the majority of the studies, which tend to use the polar coordinate formulation. The heuristic particle swarm optimization (PSO) and the classical primal-dual interior-point method (PDIPM) are applied to the solution of the VVO problem and a comparative analysis of the relative performance of the two algorithms for this problem is presented. Four case studies based on the 6-bus, IEEE 14-bus, 30-bus, and 118-bus test systems are presented. The comparative performance analysis reveals that the two algorithms have complementary strengths, when evaluated on the basis of the solution quality and computational efficiency. Particularly, the PSO algorithm achieves greater power loss minimization, whereas the PDIPM exhibits greater speed of convergence (and, thus, better computational efficiency) relative to the PSO algorithm, particularly for higher-dimensional problems. An additional distinguishing characteristic of the proposed solution is that it incorporates the Newton–Raphson load flow computation, also formulated in rectangular voltage coordinates, which adds to the efficiency and effectiveness of the presented solution method.

ALGORITMO DE BUSCA DISPERSA PARA RESOLUÇÃO DE PROBLEMAS DE OTIMIZAÇÃO DISCRETOS E CONTÍNUOS

Optimization problems are very complex to be solved, as they can present multiple optimal solutions and, in certain cases, only a globally optimal solution. The mathematical formulation of these problems is composed of continuous and discrete variables with linear and nonlinear functions. The solution of these problems by mathematical modeling through solvers may not converge to a feasible solution or may demand much computational time, when many variables are considered. Thus, using metaheuristics to solve these problems is desirable according to the literature. The scatter search (SS) metaheuristic algorithm has been highlighted in the literature as an excellent combinatorial optimization algorithm for dealing with quality and diversity solutions. This work aims to present two methods using the SS algorithm to solve problems with continuous and discrete variables. Therefore, the SS algorithm is implemented to solve the traveling salesperson problem (TSP), which is a problem that contains only discrete variables, and also, another version of SS is implemented to solve the optimal power flow (OPF) problem, which has continuous and discrete variables. Two instances of the TSP and three instances of the OPF problem were used. The results show that the SS solves both problems efficiently and presents better results in some cases than the solutions of the same problems using classical mathematical models through solvers. It is concluded that implementing the SS algorithm does not require much effort and that good results can be achieved for solving optimization problems with variables of any nature.

An effective solution to the optimal power flow problem using meta-heuristic algorithms

Financial loss in power systems is an emerging problem that needs to be resolved. To tackle the mentioned problem, energy generated from various generation sources in the power network needs proper scheduling. In order to determine the best settings for the control variables, this study formulates and solves an optimal power flow (OPF) problem. In the proposed work, the bird swarm algorithm (BSA), JAYA, and a hybrid of both algorithms, termed as HJBSA, are used for obtaining the settings of optimum variables. We perform simulations by considering the constraints of voltage stability and line capacity, and generated reactive and active power. In addition, the used algorithms solve the problem of OPF and minimize carbon emission generated from thermal systems, fuel cost, voltage deviations, and losses in generation of active power. The suggested approach is evaluated by putting it into use on two separate IEEE testing systems, one with 30 buses and the other with 57 buses. The simulation results show that for the 30-bus system, the minimization in cost by HJBSA, JAYA, and BSA is 860.54 $/h, 862.31, $/h and 900.01 $/h, respectively, while for the 57-bus system, it is 5506.9 $/h, 6237.4, $/h and 7245.6 $/h for HJBSA, JAYA, and BSA, respectively. Similarly, for the 30-bus system, the power loss by HJBSA, JAYA, and BSA is 9.542 MW, 10.102 MW, and 11.427 MW, respectively, while for the 57-bus system, the value of power loss is 13.473 MW, 20.552, MW and 18.638 MW for HJBSA, JAYA, and BSA, respectively. Moreover, HJBSA, JAYA, and BSA cause reduction in carbon emissions by 4.394 ton/h, 4.524, ton/h and 4.401 ton/h, respectively, with the 30-bus system. With the 57-bus system, HJBSA, JAYA, and BSA cause reduction in carbon emissions by 26.429 ton/h, 27.014, ton/h and 28.568 ton/h, respectively. The results show the outperformance of HJBSA.