Multi-objective Optimal Power Flow Problem Research Articles

Dynamic switched crowding-based multi-objective particle swarm optimization algorithm for solving multi-objective AC-DC optimal power flow problem

In this paper, the multi-objective AC-DC optimal power flow (MO/AC-DC OPF) problem in the presence of renewable energy sources (RESs), flexible AC transmission system (FACTS) devices and multi-terminal direct current (MTDC) systems is introduced for the first time. Conflicting objective functions and the high complexity of the objective and constraint spaces are the main challenges in finding optimal solutions for MO/AC-DC OPF. To overcome these challenges, twelve different versions of the dynamic switched crowding-based multi-objective particle swarm optimization (DSC-MOPSO) algorithm are introduced in this paper. Studies on multimodal optimization problems have shown that all DSC-MOPSO versions have better performance metrics than the MOPSO algorithm. Using the developed DSC-MOPSO and its strong competitors, the Pareto-optimal solution sets of the MO/AC-DC OPF problem are investigated. In these investigations, the performances of the algorithms are tested for the minimization of dual and triple objectives such as fuel cost, voltage level deviation, emission and power loss in a modified IEEE 30-bus power grid. According to the simulation results, the proposed DSC-MOPSO achieved an improvement in fuel cost between 0.02 % and 5.05 % and a reduction in active power loss between 0.44 % and 30.74 % compared to its competitors. The Hypervolume (HV) performance metric was used to evaluate the Pareto-front coverage performance of DSC-MOPSO and other optimizers. The results from nine case studies of the MO/AC-DC OPF were statistically analyzed by the Friedman test according to the 1/HV metric. According to the Friedman test results, the rankings of DSC-MOPSO and MOMA are 1.984 and 3.079, respectively, ranking first and second among all competitors. Finally, in this study, feasible solutions for MO/AC-DC OPF problem are identified for the first time and the stability of competitive algorithms in finding these solutions is analyzed for the first time. The success rates and search times of DSC-MOPSO and MOMA algorithms in finding feasible solutions for MO/AC-DC OPF are 91.01 % (30.641 s) and 82.01 % (46.038 s), respectively.

Two-stage coevolutionary constrained multi-objective optimization algorithm for solving optimal power flow problems with wind power and FACTS devices

As a large amount of wind energy is integrated into the grid, the randomness it brings poses a challenge to modern power systems. The application of Flexible AC Transmission Systems (FACTS) in the grid is becoming more and more common, and it is necessary to consider how to choose suitable equipment in the appropriate locations. In this paper, a multi-objective optimal power flow (MOOPF) model with wind farms and FACTS devices is established. The Weibull probability density function is used to establish the wind speed model, and the cost problem brought by wind power is considered. The locations and ratings of thyristor-controlled series compensators, thyristor-controlled phase shifters, and static VAR compensators are added to the system as control variables. In addition, the constraints on the prohibited operating areas of thermal power generators and the valve point effect are also considered. Coevolutionary constrained multi-objective optimization algorithm (CCMO) is an advanced technology, and this paper improves it and names it two-stage coevolutionary constrained multi-objective optimization algorithm (TSCCMO). The proposed algorithm uses the constraint violation value as an additional objective function in the sub-population environmental selection process, and integrates a neighborhood selection strategy into the mating selection process. The population evolution process is divided into two stages, in the first stage the two populations cooperate weakly, and in the second stage the two populations will have strong cooperation. TSCCMO is used to solve this complex constrained MOOPF problem, and its results are compared and analyzed with CCMO, NSGA–II–CDP, C3M, and PPS. The comprehensive performance of TSCCMO is the best among the 6 cases.

Multi-objective RIME algorithm-based techno economic analysis for security constraints load dispatch and power flow including uncertainties model of hybrid power systems

In recent times, the landscape of power systems has undergone significant evolution, particularly with the integration of diverse renewable energy sources (RESs). This advancement presents an invaluable opportunity to enhance energy efficiency in the modern power grid, primarily by bolstering the role of stochastic RESs. The challenge lies in the optimal power flow (OPF), a multifaceted and non-linear optimization challenge that grows more complex with the inclusion of stochastic RESs that aims to optimize the allocation of power system resources to minimize the operational cost while maintaining the stability and security of the system. Addressing this, the current study introduces an innovative optimization approach, the Multi-Objective RIME (MORIME) algorithm. Drawing inspiration from the physical phenomenon of rime-ice, called the RIME, the MORIME seeks to effectively tackle OPF issues. This algorithm enhances solution accuracy by smartly dividing with non-dominated sorting and crowding distance mechanism. The proposed OPF model incorporates three types of RESs: solar photovoltaic, wind and small-scale hydropower units. While uncertainties in wind speed and solar irradiation are managed through Monte Carlo simulations, the small hydro unit is considered a constant power source. The efficacy of the MORIME algorithm is tested on IEEE 30 bus systems and results indicate that the MORIME method identifies the optimal solution for the multi-objective OPF problem while satisfying the power system constraints, thereby proving its effectiveness and superiority over MOWOA, MOGWO, MOALO, MOMRFO and MOAGDE in terms of Hyper Volume (HV) and reciprocal of Pareto Sets Proximity (1/PSP) metrices. The MORIME source code is available at: https://github.com/kanak02/MORIME

A solution to multi Objective Stochastic Optimal Power Flow problem using mutualism and elite strategy based Pelican Optimization Algorithm

Wind Energy is rapidly growing into one of the most popular energy options for power generation. However, the unpredictability of wind necessitates the employment of a distribution function when describing the wind environment. In the depiction of wind speeds, the two significant parameters of the Weibull distribution, such as the scale parameter and the shape parameter are often utilized. Therefore, it is essential to choose the most appropriate approach for estimating these parameters. Furthermore, the uncertainty in delegated power from variable wind speeds makes system management challenging. In this paper, the Weibull distribution parameters were determined using the Pelican Optimization Algorithm (POA). POA has gained extensive popularity among the research community and is currently used to address a wide range of optimization problems. However, the exploration and exploitation are not properly balanced in this algorithm. To overcome this problem a novel hybrid algorithm namely Mutualism phase based POA (MPOA) is proposed with the help of mutualism phase of Symbiotic Organisms Search (SOS) algorithm. To demonstrate the efficacy and robustness MPOA is applied on multi-objective Optimal Power Flow (MO-OPF) problems. For this study IEEE 30 bus standard system and modified IEEE 30 bus system consisting of two wind farms are taken. The purpose of this work is to examine the impact of changing the Weibull parameters, reverse and penalty cost coefficients on the overall generation cost while considering all the security aspects.

Optimal stochastic power flow using enhanced multi-objective mayfly algorithm

For the classical multi-objective optimal power flow (MOOPF) problem, only traditional thermal power generators are used in power systems. However, there is an increasing interest in renewable energy sources and the MOOPF problem using wind and solar energy has been raised to replace part of the thermal generators in the system with wind turbines and solar photovoltaics (PV) generators. The optimization objectives of MOOPF with renewable energy sources vary with the study case. They are mainly a combination of 2–4 objectives from fuel cost, emissions, power loss and voltage deviation (VD). In addition, reasonable prediction of renewable power is a major difficulty due to the discontinuous, disordered and unstable nature of renewable energy. In this paper, the Weibull probability distribution function (PDF) and lognormal PDF are applied to evaluate the available wind and available solar power, respectively. In this paper, an enhanced multi-objective mayfly algorithm (NSMA-SF) based on non-dominated sorting and the superiority of feasible solutions is implemented to tackle the MOOPF problem with wind and solar energy. The algorithm NSMA-SF is applied to the modified IEEE-30 and standard IEEE-57 bus test systems. The simulation results are analyzed and compared with the recently reported MOOPF results.

Optimizing dynamic economic dispatch through an enhanced Cheetah-inspired algorithm for integrated renewable energy and demand-side management

This study presents the Enhanced Cheetah Optimizer Algorithm (ECOA) designed to tackle the intricate real-world challenges of dynamic economic dispatch (DED). These complexities encompass demand-side management (DSM), integration of non-conventional energy sources, and the utilization of pumped-storage hydroelectric units. Acknowledging the variability of solar and wind energy sources and the existence of a pumped-storage hydroelectric system, this study integrates a solar-wind-thermal energy system. The DSM program not only enhances power grid security but also lowers operational costs. The research addresses the DED problem with and without DSM implementation to analyze its impact. Demonstrating effectiveness on two test systems, the suggested method's efficacy is showcased. The recommended method's simulation results have been compared to those obtained using Cheetah Optimizer Algorithm (COA) and Grey Wolf Optimizer. The optimization results indicate that, for both the 10-unit and 20-unit systems, the proposed ECOA algorithm achieves savings of 0.24% and 0.43%, respectively, in operation costs when Dynamic Economic Dispatch is conducted with Demand-Side Management (DSM). This underscores the advantageous capability of DSM in minimizing costs and enhancing the economic efficiency of the power systems. Our ECOA has greater adaptability and reliability, making it a promising solution for addressing multi-objective energy management difficulties within microgrids, particularly when demand response mechanisms are incorporated. Furthermore, the suggested ECOA has the ability to elucidate the multi-objective dynamic optimal power flow problem in IEEE standard test systems, particularly when electric vehicles and renewable energy sources are integrated.

Grey Wolf Optimizer Algorithm for Multi-Objective Optimal Power Flow

This article introduces the Grey Wolf Optimizer (GWO) algorithm, a novel method aimed at tackling the challenges posed by the multi-objective Optimal Power Flow (OPF) problem. Drawing inspiration from the foraging behavior of grey wolves, GWO stands apart from traditional approaches by enhancing initial solutions without relying on gradient data collection from the objective function. In the domain of power system optimization, the OPF problem is widely acknowledged, involving constraints related to generator parameters, valve-point loading, reactive power, and active power. The proposed GWO technique is applied to IEEE 14-bus and 30-bus power systems, targeting four case objectives: minimizing cost with quadratic cost function, minimizing cost with inclusion of valve point, minimizing power loss, and minimizing both cost and losses simultaneously. For the IEEE-14 bus system, which requires meeting a power demand of 259 MW, GWO yields optimal costs of 827.0056 $hr, 833.4691 $hr, 1083.2410 $hr, and 852.2255 $hr across the four cases. Similarly, for the IEEE-30 bus system aiming to satisfy a demand of 283.4 MW, GWO achieves optimal costs of 801.8623 $hr, 825.9321 $hr, 1028.6309 $hr, and 850.4794 $hr for the respective cases. These optimal results are then compared with existing research outcomes, highlighting the efficiency and cost-effectiveness of the GWO algorithm when juxtaposed with alternative methods for solving the OPF problem.

Environmental–Economic Analysis of Multi-Node Community Microgrid Operation in Normal and Abnormal Conditions—A Case Study of Indonesia

This paper presents a comprehensive analysis of the operation management of a multi-node community microgrid (MG), emphasizing power flow constraints and the integration of photovoltaic (PV) and battery systems. This study formulates MG operation management as a multi-objective optimal power flow problem, aiming to minimize costs (maximize profits) and emissions simultaneously. The multi-objective particle swarm optimization (MPSO) method is employed to tackle this complex optimization challenge, yielding a Pareto optimal front that represents the trade-offs between these conflicting objectives. In addition to the normative operation scenarios, this research investigates the robustness of the MG system in the face of abnormal situations. These abnormal scenarios include damage to the PV system, sudden increases in the MG load, and the loss of connection to the main electricity grid. This study focuses on Lombok Island, Indonesia as a practical case study, acknowledging the ongoing efforts to implement the community MG concept in this region. It is observed that when the access to the electricity grid is limited, the energy not served (ENS) increases to 2.88 MWh. During the fault scenario in which there is a 20% increase in the hourly load of each MG, a total of 4.5 MWh ENS is obtained. It is concluded that a resilient operation management system is required to ensure a consistent and reliable energy supply in community MGs in the face of disruptions.

Optimal site and size of FACTS devices with the integration of uncertain wind generation on a solution of stochastic multi-objective optimal power flow problem

To reduce the Carbon footprint and reduce emissions from the globe, the world has kicked-off to leave reliance of fossil fuels and generate electrical energy from renewable energy sources. The MOOPF problem is becoming more complex, and the number of decision variables is increasing, with the introduction of power electronics-based Flexible AC Transmission Systems (FACTS) devices. These power system components can all be used to increase controllability, effectiveness, stability, and sustainability. The added uncertainty and variability that FACTS devices and wind generation provide to the power system makes it challenging to find the right solution to MOOPF issues. In order to determine the best combination of control and state variables for the MOOPF problem, this paper develops three cases of competing objective functions. These cases include minimizing the total cost of power produced as well as over- and underestimating the cost of wind generation, emission rate, and the cost of power loss caused by transmission lines. In the case studies, power system optimization is done while dealing with both fixed and variable load scenarios. The proposed algorithm was tested on three different cases with different objective functions. The algorithm achieved an expected cost of $833.014/h and an emission rate of conventional thermal generators of 0.665 t/h in the case 1. In Case 2, the algorithm obtained a minimum cost of $731.419/h for active power generation and a cost of power loss is 124.498 $/h for energy loss. In Case 3, three objective functions were minimized simultaneously, leading to costs of $806.6/h for emissions, 0.647 t/h, and $214.9/h for power loss.

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.

A multi-objective thermal exchange optimization model for solving optimal power flow problems in hybrid power systems

This study addresses the challenges associated with optimal power flow (OPF) management in hybrid power systems incorporating diverse energy sources, particularly focusing on the unpredictability of renewable energy sources (RESs). A novel analytics approach is introduced using Multi-Objective Thermal Exchange Optimization (MOTEO). MOTEO is based on modeling energy transfer grounded on Newton’s Law of Cooling. The model integrates innovative non-dominated sorting and crowing distance strategies to effectively solve the multi-objective optimization problem. The proposed hybrid OPF model incorporates four primary types of energy resources: thermal, wind, solar, and small-hydro, offering a holistic approach to power management in hybrid systems. Our model’s practical applicability and efficiency are validated through rigorous testing on a modified IEEE 30-Bus system, benchmarked against other contemporary optimization methodologies. The results demonstrate that the MOTEO model successfully identifies optimal solutions for the multi-objective optimal power flow (MOOPF) problem while maintaining compliance with stringent power system constraints. This novel contribution enhances the field of analytics by providing a robust and efficient model to handle the complex problem of OPF in hybrid systems, thereby ensuring increased system reliability.

Biparty multiobjective optimal power flow: The problem definition and an evolutionary approach

The multiobjective optimal power flow (MOOPF) problem consists of adjusting the generator power and the voltage state of each node within the feasible range in the process of power transmission and, finally of achieving the objectives of optimizing the cost, loss and stability, etc. In the MOOPF, two key decision makers are usually involved, which are the power generation sector and the transmission sector. Thus, it is more suitable to model an MOOPF as a biparty multiobjective optimal power flow (BPMOOPF) problem. However, so far, there is no work on treating and solving the MOOPF problem from the perspective of biparty multiobjective optimization. In this paper, we propose the definition of the BPMOOPF problem as well as a novel evolutionary biparty multiobjective optimization algorithm for solving the BPMOOPF problem, which we call BPMOOPF-EA. Our experimental results show that, compared two state-of-the-art algorithms (C-MOEA/D and A-NSGA-III), our proposed BPMOOPF-EA has a better performance when solving the BPMOOPF problem.

Multi-objective pathfinder algorithm for multi-objective optimal power flow problem with random renewable energy sources: wind, photovoltaic and tidal

In this paper, the multi-objective optimal power flow (MOOPF) problem optimization objectives focus on four optimization objectives: generation cost, emission, real power loss and voltage deviation (VD). Three renewable energy sources with successful industrial applications, including wind energy, solar energy, and tidal energy are introduced. Renewable energy supply is uncertain, so Weibull distribution probability, lognormal probability and Gumbel probability are used to calculate the instability and intermittency of wind energy, solar energy and tidal energy, respectively. The inclusion of four energy supplies on the IEEE-30 test system and the consideration of renewable energy reserves and penalty cost calculation improve the realism of the model. In order to obtain the control parameters that minimize the four optimization objectives, a named multi-objective pathfinder algorithm (MOPFA) based on elite dominance and crowding distance was proposed to solve this multi-objective optimization problem. Simulation results show the feasibility of the model, and MOPFA can get more evenly distributed Pareto front and provide more diverse solutions. A compromise solution was selected by the fuzzy decision system. Comparison with the recently published literature also shows that the proposed model can effectively reduce emissions and other indicators. In addition, the statistical test results show that MOPFA's multi-objective optimization performance ranks first. In solving this complex optimization problem, results show the MOPFA is superior to other multi-objective algorithms in optimization accuracy and speed.

Economic and environmental dispatch of power systems: Minimising CO2 emissions by integrating renewable energy sources

This paper analyses the impact of the integration of renewable energy sources on the economic and environmental operation of power systems (PS). The models of renewable energy sources, as well as the generation cost function and Carbon Dioxide (CO2) emissions are integrated in an Optimal Power Flow (OPF) formulation in order to obtain a non-linear multi-objective optimisation model, which considers economic and environmental aspects. This OPF model, having integrated the models of renewable energy sources, allows to evaluate the impact that these energy sources have on the minimisation of generation cost and CO2 emissions. In this work, the multi-objective OPF problem is solved using weighting factors for the two functions considered in the global objective function. Several case studies are carried out to evaluate the effect of the integration of renewable energy sources on the economic and environmental operation of power systems. The results of the case studies show that renewable energy sources reduce generation cost and CO2 emissions.

A distributed approach for solving AC–DC multi-objective OPF problem

This paper first proposes an optimization model for Multi-Objective Optimal Power Flow (MO-OPF) problem in AC–DC networks. The considered objective functions are the fuel cost, active power losses, and environmental emission. The AC and DC power flow equations, the converter operating limits, the voltage magnitude limits, and line capacity limits are considered in the proposed AC–DC MO-OPF model. Then an equivalent Gradient Dynamical System (GDS) for the AC–DC MO-OPF model is derived. Each equilibrium point of this GDS is a Karush–Kuhn–Tucker (KKT) point of the original AC–DC MO-OPF model. In Theorem 1, we derive condition under which this KKT point is a saddle point of the original AC–DC MO-OPF problem. The equivalent GDS has the property that it can be solved using a distributed solution algorithm. Every bus in the AC–DC power grid is considered as a local agent in the proposed distributed GDS algorithm, which only obtains information only from its neighbors. In Theorem 2, we prove that proposed distributed approach is locally convergent to the saddle point of the original AC–DC MO-OPF problem. To show the performance of our distributed approach to solve our developed AC–DC MO-OPF model, the simulation results based on several test systems are provided.

Solving Optimal Power Flow Problem via Improved Constrained Adaptive Differential Evolution

The optimal power flow problem is one of the most widely used problems in power system optimizations, which are multi-modal, non-linear, and constrained optimization problems. Effective constrained optimization methods can be considered in tackling the optimal power flow problems. In this paper, an ϵ-constrained method-based adaptive differential evolution is proposed to solve the optimal power flow problems. The ϵ-constrained method is improved to tackle the constraints, and a p-best selection method based on the constraint violation is implemented in the adaptive differential evolution. The single and multi-objective optimal power flow problems on the IEEE 30-bus test system are used to verify the effectiveness of the proposed and improved εadaptive differential evolution algorithm. The comparison between state-of-the-art algorithms illustrate the effectiveness of the proposed and improved εadaptive differential evolution algorithm. The proposed algorithm demonstrates improvements in nine out of ten cases.

Multi-Objective Optimal Power Flow Solutions Using Improved Multi-Objective Mayfly Algorithm (IMOMA)

This paper realizes the implementation of Improved Multi-objective Mayfly Algorithm (IMOMA) for getting optimal solutions related to optimal power flow problem with smooth and nonsmooth fuel cost coefficients. It is performed by considering Simulated Binary Crossover, polynomial mutation and dynamic crowding distance in the existing Multi-objective Mayfly Algorithm. The optimal power flow problem is formulated as a Multi-objective Optimization Problem that consists of different objective functions, viz. fuel cost with/ without valve point loading effect, active power losses, voltage deviation and voltage stability. The performance of Improved Multi-objective Mayfly Algorithm is interpreted in terms of the present Multi-objective Mayfly Algorithm and Nondominated Sorting Genetic Algorithm-II. The algorithms are applied under different operating scenarios of the IEEE 30-bus test system, 62-bus Indian utility system and IEEE 118-bus test system with different combinations of objective functions. The obtained Pareto fronts achieved through the implementation of Improved Multi-objective Mayfly Algorithm, Multi-objective Mayfly Algorithm and Nondominated Sorting Genetic Algorithm-II are compared with the reference Pareto front attained by using weighted sum method based on the Covariance Matrix-adapted Evolution Strategy method. The performances of these algorithms are individually analyzed and validated by considering the performance metrics such as convergence, divergence, generational distance, inverted generational distance, minimum spacing, spread and spacing. The best compromising solution is achieved by implementing the Technique for Order of Preference by Similarity to Ideal Solution method. The overall result has shown the effectiveness of Improved Multi-objective Mayfly Algorithm for solving multi-objective optimal power flow problem.

An Improved MOEA/D Algorithm for the Solution of the Multi-Objective Optimal Power Flow Problem

The optimal power flow (OPF) is an important tool for the secure and economic operation of the power system. It attracts many researchers to pay close attention. Many algorithms are used to solve the OPF problem. The decomposition-based multi-objective algorithm (MOEA/D) is one of them. However, the effectiveness of the algorithm decreases as the size of the power system increases. Therefore, an improved MOEA/D (IMOEA/D) is proposed in this paper to solve the OPF problem. The main goal of IMOEA/D is to speed up the convergence of the algorithm and increase species diversity. To achieve this goal, three improvement strategies are introduced. Firstly, the competition strategy between the barnacle optimization algorithm and differential evolution algorithm is adopted to overcome the reduced species diversity. Secondly, an adaptive mutation strategy is employed to enhance species diversity at the latter stage of iteration. Finally, the selective candidate with similarity selection is used to balance the exploration and exploitation capabilities of the proposed algorithm. Simulation experiments are performed on IEEE 30-bus and IEEE 57-bus test systems. The obtained results show that the above three measures can effectively improve the diversity of the population, and also demonstrate the competitiveness and effectiveness of the proposed algorithm for the OPF problem.

MMKE: Multi-trial vector-based monkey king evolution algorithm and its applications for engineering optimization problems.

Monkey king evolution (MKE) is a population-based differential evolutionary algorithm in which the single evolution strategy and the control parameter affect the convergence and the balance between exploration and exploitation. Since evolution strategies have a considerable impact on the performance of algorithms, collaborating multiple strategies can significantly enhance the abilities of algorithms. This is our motivation to propose a multi-trial vector-based monkey king evolution algorithm named MMKE. It introduces novel best-history trial vector producer (BTVP) and random trial vector producer (RTVP) that can effectively collaborate with canonical MKE (MKE-TVP) using a multi-trial vector approach to tackle various real-world optimization problems with diverse challenges. It is expected that the proposed MMKE can improve the global search capability, strike a balance between exploration and exploitation, and prevent the original MKE algorithm from converging prematurely during the optimization process. The performance of the MMKE was assessed using CEC 2018 test functions, and the results were compared with eight metaheuristic algorithms. As a result of the experiments, it is demonstrated that the MMKE algorithm is capable of producing competitive and superior results in terms of accuracy and convergence rate in comparison to comparative algorithms. Additionally, the Friedman test was used to examine the gained experimental results statistically, proving that MMKE is significantly superior to comparative algorithms. Furthermore, four real-world engineering design problems and the optimal power flow (OPF) problem for the IEEE 30-bus system are optimized to demonstrate MMKE's real applicability. The results showed that MMKE can effectively handle the difficulties associated with engineering problems and is able to solve single and multi-objective OPF problems with better solutions than comparative algorithms.

A Many-Objective Marine Predators Algorithm for Solving Many-Objective Optimal Power Flow Problem

Since the increases in electricity demand, environmental awareness, and power reliability requirements, solutions of single-objective optimal power flow (OPF) and multi-objective OPF (MOOPF) (two or three objectives) problems are inadequate for modern power system management and operation. Solutions to the many-objective OPF (more than three objectives) problems are necessary to meet modern power-system requirements, and an efficient optimization algorithm is needed to solve the problems. This paper presents a many-objective marine predators algorithm (MaMPA) for solving single-objective OPF (SOOPF), multi-objective OPF (MOOPF), and many-objective OPF (MaOPF) problems as this algorithm has been widely used to solve other different problems with many successes, except for MaOPF problems. The marine predators algorithm (MPA) itself cannot solve multi- or many-objective optimization problems, so the non-dominated sorting, crowding mechanism, and leader mechanism are applied to the MPA in this work. The considered objective functions include cost, emission, transmission loss, and voltage stability index (VSI), and the IEEE 30- and 118-bus systems are tested to evaluate the algorithm performance. The results of the SOOPF problem provided by MaMPA are found to be better than various algorithms in the literature where the provided cost of MaMPA is more than that of the compared algorithms for more than 1000 USD/h in the IEEE 118-bus system. The statistical results of MaMPA are investigated and express very high consistency with a very low standard deviation. The Pareto fronts and best-compromised solutions generated by MaMPA for MOOPF and MaOPF problems are compared with various algorithms based on the hypervolume indicator and show superiority over the compared algorithms, especially in the large system. The best-compromised solution of MaMPA for the MaOPF problem is found to be greater than the compared algorithms around 4.30 to 85.23% for the considered objectives in the IEEE 118-bus system.