Power System Optimization Problems Research Articles

Boston Consulting Group Matrix-Based Equilibrium Optimizer for Numerical Optimization and Dynamic Economic Dispatch

Numerous optimization problems exist in the design and operation of power systems, critical for efficient energy use, cost minimization, and system stability. With increasing energy demand and diversifying energy structures, these problems grow increasingly complex. Metaheuristic algorithms have been highlighted for their flexibility and effectiveness in addressing such complex problems. To further explore the theoretical support of metaheuristic algorithms for optimization problems in power systems, this paper proposes a novel algorithm, the Boston Consulting Group Matrix-based Equilibrium Optimizer (BCGEO), which integrates the Equilibrium Optimizer (EO) with the classic economic decision-making model, the Boston Consulting Group Matrix. This matrix is utilized to construct a model for evaluating the potential of individuals, aiding in the rational allocation of computational resources, thereby achieving a better balance between exploration and exploitation. In comparative experiments across various dimensions on CEC2017, the BCGEO demonstrated superior search performance over its peers. Furthermore, in dynamic economic dispatch, the BCGEO has shown strong optimization capabilities and potential in power system optimization problems. Additionally, the experimental results in the spacecraft trajectory optimization problem suggest its potential for broader application across various fields.

Optimizing FACTS Device Placement Using the Fata Morgana Algorithm: A Cost and Power Loss Minimization Approach in Uncertain Load Scenario-Based Systems

Today, reliable power delivery and increasing demand are important issues in modern power systems. Flexible Alternating Current Transmission Systems (FACTS) devices are used to control transmission line parameters to increase power transfer and stability. Nevertheless, the problem of determining the optimal placement and sizing of these devices is still challenging, as the placement and sizing of the devices affects generation costs, power losses, voltage stability, and system reliability. This study proposes the Fata Morgana Algorithm (FATA), an optimization algorithm inspired by the natural process of mirage formation to optimize placement and sizing of FACTS devices in an IEEE 30 bus system with wind turbine integration. The FATA algorithm is evaluated against recently developed and improved optimization techniques, such as rime-ice formation phenomenon based Improved RIME (IRIME) Algorithm, Newton–Raphson-Based Optimization (NRBO), Resistance Capacitance Algorithm (RCA), Krill Optimization Algorithm (KOA), and Grey Wolf Optimizer (GWO), across multiple optimization objectives: reduction in generation cost, reduction in power loss and combined generation cost plus power loss, termed as Gross cost function. Results obtained show that FATA consistently outperforms the other algorithms in terms of convergence and solution quality, offering a robust approach to solving single objective optimization problems. FATA theoretically provides a good balance between exploration and exploitation, and produces better global solutions. It practically increases power system efficiency by lowering operational costs and losses and improving stability. Results indicate that the FATA algorithm produced minimum generation cost of 807.0405 $/h, which is 0.088–0.426% less than the competing algorithms. It also reduced power losses to 5.5917 MW, which is 1.095–6.781% less than other methods. For gross cost minimization, the FATA algorithm achieved a minimum gross cost of 1366.3727 $/h, which is 0.4799% better than the next best algorithm and 3.2261% better than the worst. The results also show that FATA is robust in solving complex optimization problems in power systems, and it provides significant improvements in run time and convergence efficiency. The main advantage for readers is that FATA provides a reliable and efficient way to optimize power systems. Future work could also investigate the application of FATA in real time, as well as in larger power networks with more renewable energy sources.

Investigating Intelligent Forecasting and Optimization in Electrical Power Systems: A Comprehensive Review of Techniques and Applications

Electrical power systems are the lifeblood of modern civilization, providing the essential energy infrastructure that powers our homes, industries, and technologies. As our world increasingly relies on electricity, and modern power systems incorporate renewable energy sources, the challenges have become more complex, necessitating advanced forecasting and optimization to ensure effective operation and sustainability. This review paper provides a comprehensive overview of electrical power systems and delves into the crucial roles that forecasting and optimization play in ensuring future sustainability. The paper examines various forecasting methodologies from traditional statistical approaches to advanced machine learning techniques, and it explores the challenges and importance of renewable energy forecasting. Additionally, the paper offers an in-depth look at various optimization problems in power systems including economic dispatch, unit commitment, optimal power flow, and network reconfiguration. Classical optimization methods and newer approaches such as meta-heuristic algorithms and artificial intelligence-based techniques are discussed. Furthermore, the review paper examines the integration of forecasting and optimization, demonstrating how accurate forecasts can enhance the effectiveness of optimization algorithms. This review serves as a reference for electrical engineers developing sophisticated forecasting and optimization techniques, leading to changing consumer behaviors, addressing environmental concerns, and ensuring a reliable, efficient, and sustainable energy future.

A comparative study of evolutionary algorithms and particle swarm optimization approaches for constrained multi-objective optimization problems

Many real-world optimization problems contain multiple conflicting objectives as well as additional problem constraints. These problems are referred to as constrained multi-objective optimization problems (CMOPs). Many meta-heuristics for solving CMOPs, called constrained multi-objective meta-heuristics (CMOMHs) have been introduced in the literature, including those using particle swarm optimization (PSO)(Kennedy and Eberhart, 1995), genetic algorithms (GAs)(Man et al., 1996), and differential evolution (DE)(Storn and Price, 1997). CMOMHs can be grouped into four different classes: classic CMOMHs, co-evolutionary approaches, multi-stage approaches, and multi-tasking approaches. An extensive comparative study of twenty different CMOMHs on a wide variety of test problems, including real-world CMOPs in the fields of science and engineering, is conducted. A multi-swarm PSO approach called constrained multi-guide particle swarm optimization (ConMGPSO) is introduced and compared to the best-performing previous approaches according to the comparative study. The performance of each algorithm was found to be problem dependent, however the best overall approaches were ConMGPSO, paired-offspring constrained evolutionary algorithm (POCEA)(He et al., 2021), adaptive non-dominated sorting genetic algorithm III (A-NSGA-III)(Jain and Deb, 2014), and constrained multi-objective framework using Q-learning and evolutionary multi-tasking (CMOQLMT)(Ming and Gong, 2023). ConMGPSO and POCEA had the best performance on the CF benchmark set, which contains examples of bi-objective and tri-objective CMOPs with disconnected CPOFs. The CMOQLMT approach had the best performance on the DAS-CMOP benchmark set, which contain additional difficulty in terms of feasibility-, convergence-, and diversity-hardness. For the selected real-world CMOPs, A-NSGA-III had the best performance overall. ConMGPSO was shown to have the best performance on the process, design, and synthesis problems, and had competitive performance for the power system optimization problems.

A hybrid quantum–classical algorithm for mixed-integer optimization in power systems

Mixed Integer Linear Programming (MILP) can be considered the backbone of the modern power system optimization process, with a large application spectrum, from Unit Commitment and Optimal Transmission Switching to verifying Neural Networks for power system applications. The main issue of these formulations is the computational complexity of the solution algorithms, as they are considered NP-Hard problems. Quantum computing has been tested as a potential solution towards reducing the computational burden imposed by these problems, providing promising results, motivating the can be used to speedup the solution of MILPs. In this work, we present a general framework for solving power system optimization problems with a Quantum Computer (QC), which leverages mathematical tools and QCs’ sampling ability to provide accelerated solutions. Our guiding applications are the optimal transmission switching and the verification of neural networks trained to solve a DC Optimal Power Flow. Specifically, using an accelerated version of Benders Decomposition , we split a given MILP into an Integer Master Problem and a linear Subproblem and solve it through a hybrid “quantum–classical” approach, getting the best of both worlds. We provide 2 use cases, and benchmark the developed framework against other classical and hybrid methodologies, to demonstrate the opportunities and challenges of hybrid quantum–classical algorithms for power system mixed integer optimization problems.

Optimal power dispatch in hybrid power system for medium- and large-scale practical power systems using self-adaptive bonobo optimizer algorithm

Incorporating renewable energy sources (RESs) introduces a notable amount of uncertainty in the optimal planning and operation of electrical power grids. Under these circumstances, this paper proposes the application of a recently introduced metaheuristic optimization technique to solve the stochastic optimal power flow (OPF) problem involving wind and solar power sources. The self-adaptive bonobo optimizer (SaBO) is used to minimize three distinct objective functions: (i) Total generation cost (TGC) minimization, including both thermal and wind/solar generation costs, (ii) Power loss minimization, (iii) Combined generation cost and emissions effect minimization. The costs associated with the stochastic generation of wind and solar power included direct costs, reserves and penalty costs from the overestimation and underestimation of available wind and solar power, respectively. The performance of the proposed algorithm is evaluated on two power systems: the modified IEEE 30-bus and the Algerian DZA 114-bus test systems. To demonstrate the efficacy of the SaBO, the obtained results have been compared with those obtained from the Kepler optimization algorithm (KOA) and other recently published optimizers under the same case studies and constraints. The comparative results clearly show the superiority of the SaBO algorithm over all other well-known optimization algorithms provided in the literature for solving the OPF problem. This is evidenced by minimizing total generation costs of 781.2363 $/h for the modified IEEE 30-bus and 16,706.1630 $/h for the Algerian DZA-114-bus system. Furthermore, the integration of RES led to a notable 2.33% and 11.67% reduction in total generation cost for the IEEE 30-bus and Algerian DZA 114-bus systems, respectively, compared to their initial configurations without RESs. The promising findings highlight the powerful of the optimizer to solve non-linear and complex optimization problems in power systems.

Embedded Real-Swarm Evolutionary Programming Technique for Intelligent Load Curtailment Strategy

Some traditional optimization techniques are inaccurate and failed to reach their optimal solutions since the solutions normally stuck at local optimal. Thus, any optimization technique cannot be generalized as a reliable optimizer since some optimization techniques are unique to solve optimization problems. This may also occur in power system optimization problem. Load curtailment is one of the important issues in power systems since its approach can help control the power system loss. In general, it is termed as loss minimization so that the delivery of electricity to the consumers can be smoothened. This paper proposes a new optimization technique, Embedded Real Swarm Evolutionary Programming (ERSEP) for identify contingencies occurrence in power system. ERSEP is the integration of real mutation swarm operator with the traditional evolutionary programming (EP) which aims to produce better results in terms of achieving lower optimal solution. Comparative studies were conducted to observe the advantages of ERSEP over the traditional. Results exhibited that the proposed ERSEP outperformed the traditional EP in achieving lower optimal solution validated on IEEE 30-Bus Reliability Test System (RTS). Significant results deduced from this study revealed that total transmission loss reduction worth 52.83% was achieved by EP, 54.09% solved by PSO and 74.09% by ERSEP in Case 1 for chosen load condition. In Case 2, ERSEP maintains to achieve the highest loss reduction worth 54.97%, while EP achieved 51.03% and PSO achieved 52.98% loss reduction. ERSEP maintains to achieve highest loss reduction worth 61.63%, while EP achieved 51.03% and PSO achieved 52.98% loss reduction. This implies that ERSEP is superior in all cases to reach the lowest minimized transmission loss.

Learning-assisted optimization for transmission switching

The design of new strategies that exploit methods from machine learning to facilitate the resolution of challenging and large-scale mathematical optimization problems has recently become an avenue of prolific and promising research. In this paper, we propose a novel learning procedure to assist in the solution of a well-known computationally difficult optimization problem in power systems: The Direct Current Optimal Transmission Switching (DC-OTS) problem. The DC-OTS problem consists in finding the configuration of the power network that results in the cheapest dispatch of the power generating units. With the increasing variability in the operating conditions of power grids, the DC-OTS problem has lately sparked renewed interest, because operational strategies that include topological network changes have proved to be effective and efficient in helping maintain the balance between generation and demand. The DC-OTS problem includes a set of binaries that determine the on/off status of the switchable transmission lines. Therefore, it takes the form of a mixed-integer program, which is NP-hard in general. In this paper, we propose an approach to tackle the DC-OTS problem that leverages known solutions to past instances of the problem to speed up the mixed-integer optimization of a new unseen model. Although our approach does not offer optimality guarantees, a series of numerical experiments run on a real-life power system dataset show that it features a very high success rate in identifying the optimal grid topology (especially when compared to alternative competing heuristics), while rendering remarkable speed-up factors.

Linearization Method for Large-Scale Hydro-Thermal Security-Constrained Unit Commitment

Security-constrained unit commitment (SCUC) is one of the most fundamental optimization problems in power systems. The objective of SCUC is to minimize the operating cost while respecting both system-wide and generator-specific constraints. It leads to a large-scale and mixed-integer programming (MIP) model with a large number of binary decision variables which is difficult to solve. This paper, based on the convex hull theory of single-unit, proposes a linearization method for the hydro-thermal SCUC problem with decoupled thermal units and variable-head hydro units. Then, the strategy of embedding two types of convex hulls in a multi-unit commitment and the heuristic method of constructing a feasible solution are designed, by which the multi-UC is approximated from large-scale mixed-integer programming to linear programming that can be solved in polynomial time. Finally, we theoretically prove that the optimal solution of the proposed LP model is always better than that of the Lagrangian Relaxation model. Numerical experiments on several large-scale test systems demonstrate the effectiveness and efficiency of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper proposes a linear programming model for the SCUC problem by lifting up to a higher-dimensional space. It realizes an important innovation in reducing the computational complexity of SCUC from the perspective of linearization. The proposed method can be well applied to large-scale long-term unit commitment problems. To better use this method, the following two properties should be highlighted: 1) the error of the proposed method is less than the Lagrangian relaxation method and decreases with the increasing system scales and 2) the computational efficiency of the proposed method is 10-100 times faster than that of the MIP model. We have tested many practical power systems and find that the error of the proposed LP model is usually very small compared with the precise MIP while the computational performance is significantly improved. In some practical cases, the decision makers usually do not want to find the precise optimal solution while only an approximation under a fast speed, because the boundary condition is imprecise. The proposed method is useful. Besides, for the cases that need the precise optimal solution, the proposed method can provide a high-quality initial solution for the MIP model to accelerate the convergence.

An application of Gorilla troops optimizer in solving the problem of economic load dispatch considering valve point loading effect

Economic load dispatch (ELD) is one of the fundamental and important optimization problems in an electrical power system. The goal of the ELD problem is to minimize the overall cost of fuel used by generators while satisfying the different constraints like power balance limitations, operational capacity limits, ramp-rate limits, and prohibited operating zones and valve point loading effect (VPLE). The paper introduces a novel optimization technique, termed Gorilla Troop Optimization (GTO), inspired by the mimic’s behavior of gorilla troops, for solving the Economic Load Dispatch (ELD) Problem. The ELD Problem is assessed both with and without the valve-point effect, considering best, average, and worst fuel costs in dollars per hour ($/hr). The proposed GTO is applied to four different case studies to find the best global solution. The effectiveness of the GTO is evaluated using four distinct IEEE unit systems, including the IEEE 3-unit, 6-unit, 10-unit, and 40-unit test systems. From the simulation results, it has been realized that GTO show superior results as compared to other algorithms in terms of the total fuel cost minimization, convergence speed, and computation time to achieve the global optimal solution in all the case studies.

Code and Data Repository for Decomposable Formulation of Transmission Constraints for Decentralized Power Systems Optimization

One of the most complicating factors in decentralized solution methods for a broad range of power system optimization problems is the modeling of power flow equations. Existing formulations for direct current (DC) power flows either have limited scalability or are very dense and unstructured, making them unsuitable for large-scale decentralized studies. In this work, we present a novel sparsified variant of the injection shift factors formulation, which has a decomposable block-diagonal structure and scales well for large systems. We also propose a decentralized solution method, based on alternating direction multiplier method (ADMM), that efficiently handle transmission line outages in N-1 security requirements. Benchmarks on Multi-Zonal Security-Constrained Unit Commitment problems show that the proposed formulation and algorithm can reliably and efficiently solve interconnection-level test systems, with up to 6,515 buses, with no convergence or numerical issues.

Simulation tools for FACTS devices optimization problems in electrical power systems

&lt;p&gt;Technological advancements and ongoing scientific research have significantly contributed to addressing challenges within electrical networks. The emergence of FACTS (Flexible AC Transmission Systems) devices has introduced new opportunities for enhancing the safety and efficiency of these networks. A key focus for researchers in this domain has been optimizing FACTS devices, particularly in terms of identifying the most suitable locations, sizes, and types of controllers within electrical systems. The advent of simulation software has played a crucial role in the evolution of electrical and electronics engineering. Both offline and real-time simulation tools have gained traction in recent years, proving essential for the effective management of power systems and FACTS controllers. In this paper, we present a comprehensive overview of modeling, classification, and simulation-based approaches to various optimization challenges associated with FACTS controllers. We examined a range of simulation platforms, including MATLAB/Simulink, PSAT, EMTDC/PSC etc., assessing their effectiveness in evaluating the performance of optimized FACTS controllers and their dynamic interactions within power networks.&lt;/p&gt;

A variegated GWO algorithm implementation in emerging power systems optimization problems

This paper proposes a novel hybrid algorithm which is mathematically modelled by amalgamating the superior features of recently developed Grey Wolf Optimizer (GWO), Sine Cosine Algorithm (SCA), and Crow Search Algorithm (CSA). Researchers have already implemented the aforementioned three algorithms and obtained superior quality results for solving diverse optimization problems. The novel hybrid Variegated GWO Algorithm (VGWO) developed in this proposed research work is initially realized and validated for solving IEEE CEC-C06 2019 benchmark functions. Thereafter, the proposed VGWO is utilized as an optimization tool to solve three emerging and complex power system optimization problems which includes energy management of microgrid systems operated in both islanded and grid-connected mode, dynamic economic emission dispatch and reactive power planning (RPP) problem. A comparative analysis of the proposed VGWO approach with other established metaheuristics is undertaken for each optimization problem. Numerical results show that the novel hybrid VGWO algorithm outperformed an ample number of optimization techniques in providing better quality solutions. The proposed hybrid algorithm yielded a 36.93% reduction in active power loss and 36.80% reduction in operating cost with respect to base case condition for RPP problem. Likewise while solving microgrid energy management problems 9–30% savings was realized in the generation cost compared to the ones mentioned in literature. The capability of handling many complex constraints within a minimum amount of computational time to provide consistently best solutions prioritize the proposed hybrid algorithm among its kinds. Statistical analysis validates the authenticity and viability of the proposed algorithm.

Optimization of Artificial Intelligence Algorithm based on Neural Network in Complex System

The purpose of this paper is to discuss the application of AI (Artificial Intelligence) algorithm with NN (Neural Network) in complex system optimization. Therefore, this paper takes the optimization of power system as the research object and designs a hybrid NN model. The model can effectively extract features from historical power data and predict future power demand and supply. At the same time, the NN model is optimized by genetic algorithm. The algorithm can efficiently search the optimal solution in a large solution space and has the ability to deal with multi-objective optimization problems. Finally, it is verified by experiments. By using test data sets to evaluate the model, it is found that the algorithm in this paper has high accuracy and applicability in dealing with power system optimization problems. At the same time, the model can effectively reduce the cost of power generation and improve the stability of the system. These achievements provide new ideas and methods for future complex system optimization, and provide useful reference for promoting the development and application of AI technology. In order to provide some guidance for practical application.

An Advanced High Dimensional Power System of Optimization Problems Algorithm

New Evolutionary Algorithm-based for High-Dimensional Power System Optimization Problems and Modern power system optimization problems face growing challenges as there are numerous decision variables and unbiased functions. Multi-objective evolutionary algorithms (MOEAs) basically are popularly applied for solving and dealing with such complicated problems in substantial power systems that have several objective functions. However, customary MOEAs works appropriately when the number of objective features comes to be less than three. Generally, the effectiveness of MOEAs begins to decrease apparently with an increase in the number of unbiased functions. This study is devoted to applying an authentic gradable evolutionary algorithm for the purpose of solving power system optimization issues which manifest numerous objective functions. In particular, this seeks an algorithm based upon NSGA-II algorithm dedicated for an efficient solution of multi-objective optimization problems. Here, we attempt to modify NSGA-II algorithm to effectively solve many target optimization problems. A novel effective grouping method is applied in the proposed algorithm in similar to the non-dominant grouping method of NSGA-II algorithm to accelerate decision convergence action in POF. The recommended algorithm is compared with modern numerous objective optimization algorithms following three test problems. The findings reveal that as the number of unbiased functions is noticeably large, the algorithm that we propose is significantly superior to other algorithms.

Black Widow Optimization for Power System Load Frequency Control: A Comparative Study

This research paper mainly engrossed on developing a suitable novel tuning methodology named Black Widow Optimization (BWO) Algorithm for power system optimization problems. Load Frequency Control (LFC) and Automatic Voltage Regulator (AVR), two of the most important control systems in the power system arena, are employed as test systems to assess the efficiency of the suggested BWO approach. Various analyses, such as transient analysis, are employed to evaluate the efficiency of the suggested BWO approach in LFC and AVR systems. robustness analysis and convergence analysis. The significant performance measures of test system such as output power of each generating unit, maximum peak, settling time, steady state error, rise time and voltage/frequency deviations of the frequency and voltage responses are considered for the comparison purposes. The comparative analysis clearly demonstrates that the proposed novel tuning methodology provides better transient performances subjected to Step Load Perturbations (SLP), Variable Load Perturbations (VLP), and robustness performances under a wide range of load and parameter changes ranging from -50% to +50%. The convergence analysis of BWO algorithm also performed in LFC and AVR test systems and results better convergence characteristics with minimal convergence time as well as least fitness value is obtained with the BWO algorithm.

Enhanced coati optimization algorithm-based optimal power flow including renewable energy uncertainties and electric vehicles

Power systems now face new issues due to incorporating electric vehicles (EVs) and renewable energy resources (RERs). This paper proposes a novel Enhanced Coati Optimization Algorithm (ECOA) for obtaining the optimal solution of the probabilistic optimal power flow (POPF) problems. The ECOA is a metaheuristic optimization algorithm that is robust and efficient for solving complex problems. It is used to tackle the OPF problem, which considers the stochastic characteristics of RERs. Moreover, EVs are included in the presented power systems in this paper. The novel approach is tested and verified on the IEEE-57 and IEEE-118 networks. The effectiveness of the proposed method is demonstrated by making a comparison with other metaheuristic-based methods. To obtain a practical study, real data of wind speed, solar irradiance, and electric vehicles profile are incorporated in the dynamic analyses. The simulation results show that the ECOA is robust and efficient for solving the OPF problem. It can also improve the performance of power systems with RESs and EVs. The findings of this research demonstrate that the suggested approach is promising for power system optimization problems, including RERs and EVs.

Reconfiguration of Distribution Network based DG and Capacitors using Grey Wolf Algorithm for Power Loss Reduction

Network reconfiguration is one of the methods used for power loss reduction in distribution network by altering the close/open position of Tie/Sectionalizing switches without interruption of power to all loads. The other methods used are placing of distribution generators and connecting capacitors. The best results are obtained when all the three are used simultaneously using grey wolf algorithm which is a recent evolutionary algorithm which gives the place of connection and values of capacitor and distribution generators along with sectionalizing switches which are to be opened. This algorithm was implemented for a standard 33 and 69 bus distribution system in a MATLAB environment for comparing with other algorithms with constraints. This algorithm has good exploration (new search) and exploitation (thorough local search) potential for application in many power system optimization problems.

Optimal allocation of distributed generation for power flow enhancement in distribution network

AbstractThis article articulates the enhancement of voltage profiles in transmission systems by reducing the voltage deviation and system power losses. Electric power flows uniformly throughout Regional Distribution Networks in the power grid station, resulting in low voltage consistency, significant voltage dips and power losses in the distribution network, highlighting high R/X ratios even with a heavy load or power failure issues, despite installing distributed generation in the radial distribution system for enhancing voltage profile in the grid network. The meta‐heuristic optimization algorithm plays a vital role in determining optimal location of DG for attaining the objective of research. In the practical network, a single objective optimization strategy cannot be employed to solve of power system optimization problems of all kinds. Hence multi‐objective function needs to be addressed. The prime task of this research is to investigate and allocate an optimal location to connect the Distributed Generation, with evaluation of the best DG configuration, with minimized power losses and improved voltage profile of the distribution network using the Hummingbird Optimization Algorithm. A standard IEEE 37‐bus Radial Distribution system is employed as the test bus system to test the performance and effectiveness of the optimization technique. To show the stiffness of the proposed algorithm the results are compared with various optimization approaches that employ similar objective functions.

Golden Jackal Algorithm for Optimal Size and Location of Distributed Generation in Unbalanced Distribution Networks

The Golden Jackal Optimization algorithm (GJO) is used in this study to address the problem of optimal placement and sizing of single and multiple distributed generators (DGs) on the IEEE123 test system. The proposed approach attempts to minimize the total power loss of the system while respecting the voltage and power limits. The GJO algorithm is a new meta-heuristic algorithm inspired by the behavior of the golden jackal in the wild. The GJO algorithm is used to find the ideal location and sizing of DGs, and the results are compared with those obtained by other meta-heuristic techniques. According to the simulation results, the GJO method outperforms other metaheuristic algorithms in terms of problem-solving, while satisfying all constraints of the system. The proposed approach also demonstrates the effectiveness of the GJO algorithm in the solution of complex optimization problems in power systems