Multi-objective Optimal Power Flow Research Articles

Improved mountain gazelle optimizer based interactive distributed strategy to solving large scale OPF

This paper focuses on solving the multi-objective optimal power flow of large-scale power systems under critical loading margin stability with accuracy using a novel improved mountain gazelle optimizer (IMGO)-based flexible distributed strategy. Multi-shunt compensator-based flexible alternative current transmission systems (FACTS), such as SVC and STATCOM devices, are integrated at specified locations to exchange reactive power with the network. Several metaheuristic methods can solve the standard OPF related to small and medium test systems. However, by considering large-scale electric systems based on FACTS devices and renewable energy and by considering the operation under loading margin stability, the majority of these techniques fail to achieve a near-global solution because of the high dimension and nonlinearity of the problem to be solved. This study proposes the Multi-Objective OPF-Based Distributed Strategy (MO-OPFDS), a new planning strategy that optimizes individually and simultaneously various objective functions, in particular the total power loss (T∆P), and the total voltage deviation (T∆V). Standard MGO search is enhanced by automatically balancing exploration and exploitation throughout the search. The robustness of the proposed variant was validated on a large electric test system, the IEEE 118-Bus, and on the Algerian Network 114-Bus under normal conditions and at critical loading margin stability. The obtained results compared with several recent techniques clearly confirm the high performance of the proposed method in terms of solution accuracy and convergence behavior.

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.

Optimal power flow research of AC–DC hybrid grid with multiple energy routers

AC/DC hybrid grids are the future development trends of grids, and energy routers (ERs) can play key roles in controlling power flow, realizing the regulation of electric energy and improving power quality in the grids. At present, there have been many studies on the structure and control strategy of ERs, but only a few studies are on the power flow distribution and optimization of AC/DC hybrid grids with ERs. To enhance the efficacy of ERs in system-wide regulation and operational optimization, a multi-objective optimal power flow model is formulated for AC–DC hybrid systems with multiple ERs. In order to make ERs play a better role in overall regulation and operation optimization, the multi-objective optimal power flow model of AC–DC hybrid system with multi-ERS is established based on Newton–Raphson method (NR) and alternating iteration method with power consumption and voltage deviation as optimization objectives. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) is used to optimize the model, and a smoother Pareto solution set is obtained compared with multi-objective particle swarm optimization (MOPSO). Then, fuzzy membership method is used to make compromise decision on the Pareto solution set to obtain the optimal compromise solution. Simulation and analysis on an enhanced IEEE 69 bus system verifies the validity of the model. In addition, the results obtained from the compromise solution are compared with the optimization results of MOPF obtained by MOPSO and that of single-objective power flow (SOPF) obtained by Particle Swarm Algorithm (PSO) in the same system. It is proved that the optimization model established can achieve the optimization objectives of reducing voltage deviation and power loss simultaneously to improve the overall performance of the system and optimize the operation state of the system.

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.

Cooperative optimal operation of hybrid energy integrated system considering multi‐objective dragonfly algorithm

AbstractTo meet the recent energy demand, hybrid energy systems (HESs) play an important role in providing more stable power as well as backup power to the grid. It is always preferable for the power system network to be operated in a secure, dependable, stable, and cost‐effective manner. The optimal power flow (OPF) problem is used to determine the ideal power system network control parameter settings. The majority of the OPF problem, fuel cost reduction is treated as an objective function, but the environmental impact of the generating is ignored. Both fuel expense and emission are treated as objective functions of the work in this case. This research describes a solution for multi‐objective optimal power flow (MOOPF) with a HES integrated conventional power system. HES in this work is made up of a wind park and a compressed air energy storage system (CAES). In this case, locational marginal pricing (LMP) is employed to determine the best location of HES in the power system. To achieve the goals of this work, the multi‐objective dragonfly algorithm (MODA) is used. The IEEE 30 bus system is used to evaluate the MODA. The MODA method findings are validated against other well‐known optimization algorithms such as the multi‐objective ant colony system (MOACS) algorithm, multi‐objective enhanced self‐adaptive differential evolution (MOESDE) algorithm, modified multi‐objective evolutionary algorithm‐based decomposition (MOEA/D), multi‐objective particle swarm algorithm (MOPOSO), and non‐dominated sorting genetic algorithm (NSGA‐II).

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.

Individual and collective objectives in an energy community with network constraints

The issue at play is to facilitate the deployment of renewable energy sources by coordinating privately owned batteries to also support local power systems. Battery systems most often exclusively answer the individual objective of their owner (e.g., a reduction in the energy bill). This study intends to explore whether both paradigms, (i) minimizing individual costs and (ii) mitigating network constraints, are achievable for individual battery systems, and if not, what trade-offs are available. Most studies in the literature take a subjective stand in their valuation of individual costs versus grid constraints. A set of Pareto optimal solutions is explored to provide a full picture of the aforementioned trade-off. As such, a novel Multi-Objective Optimal Power Flow (MOOPF) algorithm is developed to solve a convexified battery control problem. Results show the ability of the proposed methodology to provide a frame of reference to compare online battery controllers, e.g., if a controller can exploit synergies between individual and collective objectives or not. Further, and for the proposed scenario, local energy communities provide a strictly better set of Pareto optimal solutions than individually operated systems.

A double decomposition based coevolutionary algorithm for distributed multi-objective OPF solution

Due to the vast and complex nature of the power systems, the study of distributed solution to multi-objective OPF (MO-OPF) problem is vital. However, the existing distributed MO-OPF approaches are based on mathematical programming techniques. The tedious repetition of algorithmic executions is inevitable. Moreover, they can hardly solve the non-differential problem. In this paper, the coevolutionary multi-objective evolutionary algorithm (MOEA), combining the idea of decomposition, is introduced to solve the distributed MO-OPF problem. The decomposition first occurs on decision variables. After segmenting, multiple subpopulations can coevolve in a distributed manner under the support of a new proposed distributed fitness evaluation method. Further, an objective decomposition (OBD) method is applied to the proposed distributed MO-OPF approach. The problem is decomposed again based on objective functions. By this OBD method, the fitness assignment problem is effectively alleviated and a more extensively covered pareto front can be obtained. The experimental results on two systems of different scales first show the effectiveness of the proposed distributed approach and then demonstrate the excellence of the OBD method in large-scale system.

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.

Multi-objective random-fuzzy optimal power flow of transmission-distribution interaction considering security region constraints

Multi-objective random-fuzzy optimal power flow of transmission-distribution interaction considering security region constraints

Multi-objective optimal power flow of thermal-wind-solar power system using an adaptive geometry estimation based multi-objective differential evolution

Sustainable energy is a key component of sustainable development. The current grid can be supplied by fossil fuel generators and renewable energy sources (RESs)-based generators, such as solar photovoltaic (PV) and wind power generators. In an electrical network, power generation from several sources must be optimally coordinated to ensure efficient and economical operation. However, the intermittent and uncertain nature of RESs complicate the operation of power systems. In this study, an adaptive geometry estimation-based multi-objective differential evolution (AGE-MODE) method is proposed for multi-objective optimal power flow in a hybrid power system of thermal, wind, and solar energy sources (MOOPF-TWS). In the proposed approach, wind and solar PV power outputs are predicted based on Weibull and lognormal probability distribution functions, respectively. Therefore, the generation costs for solar and wind power can be divided into direct costs, penalty costs for underestimation, and reserve costs for overestimation. Furthermore, the emissions, voltage deviation, and real power loss are considered in particular cases. AGE-MODE is applied to modified IEEE 30-bus and 57-bus systems, where different case studies are simulated with combinations of two-, three-, and four-objective optimizations in MOOPF-TWS problems. Comparisons between AGE-MODE and other recently developed multi-objective methods demonstrate its effectiveness in resolving MOOPF-TWS problems, particularly for cases with more than two objectives.

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 Optimal Power Flow Using a Modified Weighted Teaching-Learning Based Optimization Algorithm

The optimal power flow (OPF) problem is one of the most popular and important issues that researchers need to solve in power systems. In this study, a modified weighted teaching-learning-based optimization (WTLBO) algorithm was designed and implemented for the OPF problem, regarding the teaching-learning-based optimization (TLBO) algorithm, which is one of the meta-heuristic algorithms. To demonstrate the effectiveness of TLBO and developed WTLBO algorithms in OPF solutions, six different single/multi-objective functions consisting of targets, such as fuel cost, total active power losses, and voltage deviation were tested on standard IEEE 30 and 57 bus systems. Multi-objective functions were transformed into a single objective function using the weighted sum method. Analysis results were compared with different optimization algorithms used in the literature. When the developed WTLBO algorithm is compared according to the single/multi-objective functions in OPF solutions, it has been proven that it performs better than the original TLBO algorithm and other algorithms in the literature. As a result of the analysis, according to the TLBO algorithm, in the IEEE 30 bus power system, in the proposed WTLBO algorithm, a decrease of 0.05% in the total fuel cost, 2.20% in active power losses, and 13.37% in voltage deviation are observed.

Multi-objective Optimal Power Flow Employing a Hybrid Sine Cosine–Grey Wolf Optimizer

Multi-objective Optimal Power Flow Employing a Hybrid Sine Cosine–Grey Wolf Optimizer

Multi-Objective Optimal Power Flow Incorporating Flexible Alternating Current Transmission Systems: Application of a Wavelet-Oriented Evolutionary Algorithm

This article presents a meta-heuristic hybrid algorithm to solve multi-objective optimal power flow (MOOPF) taking into account multi-fuel constraint. Four different objective functions, which comprise total generation cost, emission, real power transmission losses, and voltage deviation, are simultaneously considered in the proposed MOOPF. Furthermore, two types of flexible alternating current transmission system (FACTS) devices are utilized including thyristor controlled series compensator (TCSC) and unified power flow controller (UPFC). Considering all of the aspects referred to above makes the traditional OPF problem more complicated; hence, it is necessary to approach the problem by a powerful optimization algorithm. Toward this end, this article develops a hybrid algorithm oriented to shuffled frog leaping algorithm (SFLA) and particle swarm optimization (PSO), called hybrid wavelet mutation (WM) based SFLA-wavelet mutation based PSO (HWM2SFLA-PSO). Obtained results validate the effectiveness of the proposed hybrid algorithm in solving different forms of the OPF problem on IEEE test systems compared to those available in the literature. Moreover, the comparison substantiates the superiority of the proposed HWM2SFLA-PSO algorithm in terms of execution time, quality of solution as well as preventing from convergence to local optima, to name but three.