Multi-objective Optimal Power Flow Problem Research Articles

Single and Multi-Objective Optimal Power Flow Based on Hunger Games Search with Pareto Concept Optimization

In this study, a new meta-heuristic optimization method inspired by the behavioral choices of animals and hunger-driven activities, called hunger games search (HGS), is suggested to solve and formulate the single- and multi-objective optimal power flow problem in power systems. The main aim of this study is to optimize the objective functions, which are total fuel cost of generator, active power losses in transmission lines, total emission issued by fossil-fueled thermal units, voltage deviation at PQ bus, and voltage stability index. The proposed HGS approach is optimal and easy, avoids stagnation in local optima, and can solve multi-constrained objectives. Various single-and multi-objective (conflicting) functions were proposed simultaneously to solve OPF problems. The proposed algorithm (HGS) was developed to solve the multi-objective function, called the multi-objective hunger game search (MOHGS), by incorporating the proposed optimization (HGS) with Pareto optimization. The fuzzy membership theory is the function responsible to extract the best compromise solution from non-dominated solutions. The crowding distance is the strategies carried out to determine and ordering the Pareto non-dominated set. Two standard tests (IEEE 30 bus and IEEE 57 bus systems) are the power systems that were applied to investigate the performance of the proposed approaches (HGS and MOHGS) for solving single and multiple objective functions with 25 studied cases using MATLAB software. The numerical results obtained by the proposed approaches (HGS and MOHGS) were compared to other optimization algorithms in the literature. The numerical results confirmed the efficiency and superiority of the proposed approaches by achieving an optimal solution and giving the faster convergence characteristics in single objective functions and extracting the best compromise solution and well-distributed Pareto front solutions in multi-objective functions.

A Slime Mould Algorithm Programming for Solving Single and Multi-Objective Optimal Power Flow Problems with Pareto Front Approach: A Case Study of the Iraqi Super Grid High Voltage

Optimal power flow (OPF) represents one of the most important issues in the electrical power system for energy management, planning, and operation via finding optimal control variables with satisfying the equality and inequality constraints. Several optimization methods have been proposed to solve OPF problems, but there is still a need to achieve optimum performance. A Slime Mould Algorithm (SMA) is one of the new stochastic optimization methods inspired by the behaviour of the oscillation mode of slime mould in nature. The proposed algorithm is characterized as easy, simple, efficient, avoiding stagnation in the local optima and moving toward the optimal solution. Different frameworks have been applied to achieve single and conflicting multi-objective functions simultaneously (Bi, Tri, Quad, and Quinta objective functions) for solving OPF problems. These objective functions are total fuel cost of generation units, real power loss on transmission lines, total emission issued by fossil-fuelled thermal units, voltage deviation at load bus, and voltage stability index of the whole system. The proposed algorithm SMA has been developed by incorporating it with Pareto concept optimization to generate a new approach, named the Multi-Objective Slime Mould Algorithm (MOSMS), to solve multi-objective optimal power flow (MOOPF) problems. Fuzzy set theory and crowding distance are the proposed strategies to obtain the best compromise solution and rank and reduce a set of non-dominated solutions, respectively. To investigate the performance of the proposed algorithm, two standard IEEE test systems (IEEE 30 bus IEEE 57 bus systems) and a practical system (Iraqi Super Grid High Voltage 400 kV) were tested with 29 case studies based on MATLAB software. The optimal results obtained by the proposed approach (SMA) were compared with other algorithms mentioned in the literature. These results confirm the ability of SMA to provide better solutions to achieve the optimal control variables.

Multiple objective optimization based on particle swarm algorithm for MMC-MTDC system

Multi-terminal high voltage DC (MTDC) network is an effective technology to integrate large-scale offshore wind energy sources into conventional AC grids and improve the stability and flexibility of the power system. In this paper, firstly, an analytical model of a general applicable MTDC system integrated with several isolated AC grids is established. Then, an improved AC-DC power flow algorithm is used to eliminate the additional DC slack bus or droop bus iteration (SBI/DBI) step of the conventional AC-DC sequential power flow. A multi-objective optimal power flow (MOPF) algorithm is proposed to minimize two optimization targets, i.e., overall active power loss and generation costs of the system. To increase the degree of freedom, adaptive droop control is used in the proposed optimization algorithm in which the voltage references and droop coefficients of the modular multilevel converters (MMCs) are control variables. A multiple objective particle swarm optimization (MOPSO) method is applied to solve the MOPF problem and achieve the Pareto front. A technique for order of preference by similarity to ideal solution (TOPSIS) is incorporated in the decision analysis section and helps the decision maker to identify the best compromise solution.

Multi-objective optimal power flow based gray wolf optimization method

Introduction. One of predominant problems in energy systems is the economic operation of electric energy generating systems. In this paper, one a new evolutionary optimization approach, based on the behavior of meta-heuristic called grey wolf optimization is applied to solve the single and multi-objective optimal power flow and emission index problems. Problem. The optimal power flow are non-linear and non-convex very constrained optimization problems. Goal is to minimize an objective function necessary for a best balance between the energy production and its consumption, which is presented as a nonlinear function, taking into account of the equality and inequality constraints. Methodology. The grey wolf optimization algorithm is a nature inspired comprehensive optimization method, used to determine the optimal values of the continuous and discrete control variables. Practical value. The effectiveness and robustness of the proposed method have been examined and tested on the standard IEEE 30-bus test system with multi-objective optimization problem. The results of proposed method have been compared and validated with hose known references published recently. Originality. The results are promising and show the effectiveness and robustness of proposed approach.

Multi-objective ACOPF using distributed gradient dynamics

This paper proposes a distributed gradient dynamics approach for solving Multi-Objective AC Optimal Power Flow (MO-ACOPF) problem. The fuel cost, environmental pollution, and network loss are considered as objective functions. The non-convex MO-ACOPF problem is reformulated as a gradient dynamical system. We derive condition under which the equilibrium point of the proposed gradient dynamical system is the saddle point of the MO-ACOPF Lagrangian function. We propose a distributed solution algorithm for derived MO-ACOPF gradient dynamical system. In the distributed solution algorithm, each bus in the power network is assumed as a local agent, which only uses information from its neighbor agents to compute optimal operating points. We prove convergence of our distributed algorithm to the equilibrium point of the MO-ACOPF gradient dynamical system (and accordingly to the primal and dual optimum of original MO-ACOPF). Accordingly, our proposed approach has the following main advantages: (a) it is a distributed and decentralized algorithm and accordingly it needs less computational time as compared to the centralized model, (b) it has the proof of convergence to the global optimal solution, and (c) it is suitable for varying loads in power networks. The simulation results based on standard IEEE 14-, 30- ,39-, 57-, 118- and 300-bus test systems in different scenarios are carefully studied. The proposed distributed gradient dynamics provides the best results compared to the relevant literature as illustrated by simulation results.

Wind farm incorporated optimal power flow solutions through multi-objective horse herd optimization with a novel constraint handling technique

Optimal power flow plays an important role in integrating wind power into electric power networks. Because of its complexities, standard formulae are insufficient for the present scenario. Therefore, the multi-objective optimal power flow problems for wind farm incorporated power systems have been explored in this paper. The objectives are to minimize the generation costs, pollutant emissions, power losses, and voltage deviations. This paper proposes the development of a multi-objective meta-heuristic horse herd optimization for solving multi-objective optimal power flow problems. For this, a decomposition concept is introduced to the proposed algorithm leading to decomposition based multi-objective horse herd optimization algorithm. The constraint handling techniques in the previous papers have been found to be inefficient for optimal power flow problems. Therefore, a novel constraint handling technique is proposed in this paper to effectively control the variables out of bounds. In order to validate the performance and suitability of the proposed algorithm, seven case studies are examined. The algorithm is tested on wind farm incorporated IEEE-30, IEEE-57, and IEEE-118 bus test systems to demonstrate the efficiency in solving multi-objective optimal power flow problem for various problem sizes. The experimental results are demonstrating the efficiency of the proposed algorithm in solving complex optimization problems of various scales with multiple objectives.

Multiobjective Optimal Power Flow Using Multiobjective Search Group Algorithm

This paper proposes a new multi-objective method that efficiently solves the multi-objective optimal power flow (MOOPF) problem in power systems. The objective of solving the MOOPF problem is to concurrently optimize the fuel cost, emissions, and active power loss. The proposed multi-objective search group algorithm (MOSGA) is an effective method that combines the merits of the original search group algorithm with fast nondominated sorting, crowding distance, and archive selection strategies to acquire a nondominated set in a single run. The MOSGA is employed on IEEE 30-bus and 57-bus systems to validate its robustness and efficiency. It was found that implementing MOSGA to solve the MOOPF significantly enhanced the performance of power systems in terms of economic, environmental, and technical benefits. As for Case 6, the fuel cost, emissions, and active power loss were reduced by 16.5707%, 52.0605%, and 60.9443%, respectively. The simulation results were analyzed and compared with those of previously reported studies based on the best individual solutions, compromise solutions, and performance indicators. The comparative results confirmed the potential and advantage of MOSGA when solving the MOOPF problem efficiently and MOSGA had high-quality optimal solutions.

Solvability region of AC–DC power systems with volatile renewable energy sources

The high voltage direct current (HVDC) is widely incorporated into today’s AC power grids. It is a key technology to address the issues for large power transmission and power flow control. However, the HVDC may influence the consumption-ability of systems for renewable energy sources (RES). This paper studies the solvability region in the AC–DC system with HVDC under the volatile RES generation and system operation constraints. The set of all admissible injection patterns of RES is termed dispatchable region, which is depicted by the Pareto frontier of multi-objective optimization problems. An adopted ε-constraints method is used to solve the multi-objective optimal power flow problem. Cases study on an adopted IEEE-30 bus system are provided to analyze the impaction of HVDC control strategies and parameters.

Optimization of Optimal Power Flow Problem Using Multi-Objective Manta Ray Foraging Optimizer

Finding a feasible solution set for optimization problems in conflict with objective functions poses significant challenges. Moreover, in such problems, the level of complexity may increase depending on the geometry of the objective and decision spaces. The most effective methods in solving multi-objective problems having high levels of complexity are search algorithms using the Pareto-based archiving approach. Recently, the crowding distance approach has been used to improve the performance of the Pareto-based archiving method. This article presents research conducted on the development of a method that can find the optimum solution set for a multi-objective optimal power flow (MOOPF) problem whose objective functions are in conflict. For this purpose, a powerful and effective method was developed using the Pareto archiving approach based on crowding distance. The performance of the developed method was tested on twenty-four benchmark problems of different types and difficulty levels and compared with competing algorithms. The data obtained from the experimental trials and four different performance metrics were analyzed using statistical test methods. Analysis results showed that the proposed method yielded a competitive performance on different types of multi-objective optimization problems and was able to find the best solutions in the literature for the real-world MOOPF problem.

EWOA-OPF: Effective Whale Optimization Algorithm to Solve Optimal Power Flow Problem

The optimal power flow (OPF) is a vital tool for optimizing the control parameters of a power system by considering the desired objective functions subject to system constraints. Metaheuristic algorithms have been proven to be well-suited for solving complex optimization problems. The whale optimization algorithm (WOA) is one of the well-regarded metaheuristics that is widely used to solve different optimization problems. Despite the use of WOA in different fields of application as OPF, its effectiveness is decreased as the dimension size of the test system is increased. Therefore, in this paper, an effective whale optimization algorithm for solving optimal power flow problems (EWOA-OPF) is proposed. The main goal of this enhancement is to improve the exploration ability and maintain a proper balance between the exploration and exploitation of the canonical WOA. In the proposed algorithm, the movement strategy of whales is enhanced by introducing two new movement strategies: (1) encircling the prey using Levy motion and (2) searching for prey using Brownian motion that cooperate with canonical bubble-net attacking. To validate the proposed EWOA-OPF algorithm, a comparison among six well-known optimization algorithms is established to solve the OPF problem. All algorithms are used to optimize single- and multi-objective functions of the OPF under the system constraints. Standard IEEE 6-bus, IEEE 14-bus, IEEE 30-bus, and IEEE 118-bus test systems are used to evaluate the proposed EWOA-OPF and comparative algorithms for solving the OPF problem in diverse power system scale sizes. The comparison of results proves that the EWOA-OPF is able to solve single- and multi-objective OPF problems with better solutions than other comparative algorithms.

A Dynamic Framework for Multiobjective Mixed-Integer Optimal Power Flow Analyses

This paper proposes a reliable and computationally efficient framework for solving multiobjective mixed-integer Optimal Power Flow problems. The main idea is to apply the interior point theory and the goal-attainment method to recast a generic OPF problem with both real and integer decision variables by an equivalent scalar optimization problem with equality constraints. Then, thanks to the adoption of the Lyapunov theory, an asymptotically stable dynamic system is designed such that its equilibrium points coincide with the stationary points of the Lagrangian function of the equivalent problem. Thanks to this approach, the OPF solutions can be promptly and reliably obtained by solving a set of ordinary differential equations, rather than using an iterative Newton-based scheme, which can fail to converge due to several numerical issues. Detailed numerical results are presented and discussed in order to prove the effectiveness of the proposed framework in solving real world problems.

TSO-DSO Coordination Schemes to Facilitate Distributed Resources Integration

The incorporation of renewable energy into power systems poses serious challenges to the transmission and distribution power system operators (TSOs and DSOs). To fully leverage these resources there is a need for a new market design with improved coordination between TSOs and DSOs. In this paper we propose two coordination schemes between TSOs and DSOs: one centralised and another decentralised that facilitate the integration of distributed based generation; minimise operational cost; relieve congestion; and promote a sustainable system. In order to achieve this, we approximate the power equations with linearised equations so that the resulting optimal power flows (OPFs) in both the TSO and DSO become convex optimisation problems. In the resulting decentralised scheme, the TSO and DSO collaborate to optimally allocate all resources in the system. In particular, we propose an iterative bi-level optimisation technique where the upper level is the TSO that solves its own OPF and determines the locational marginal prices at substations. We demonstrate numerically that the algorithm converges to a near optimal solution. We study the interaction of TSOs and DSOs and the existence of any conflicting objectives with the centralised scheme. More specifically, we approximate the Pareto front of the multi-objective optimal power flow problem where the entire system, i.e., transmission and distribution systems, is modelled. The proposed ideas are illustrated through a five bus transmission system connected with distribution systems, represented by the IEEE 33 and 69 bus feeders.

Multi-Objective Optimal Power Flow Problems Based on Slime Mould Algorithm

Solving the optimal power flow problems (OPF) is an important step in optimally dispatching the generation with the considered objective functions. A single-objective function is inadequate for modern power systems, required high-performance generation, so the problem becomes multi-objective optimal power flow (MOOPF). Although the MOOPF problem has been widely solved by many algorithms, new solutions are still required to obtain better performance of generation. Slime mould algorithm (SMA) is a recently proposed metaheuristic algorithm that has been applied to solve several optimization problems in different fields, except the MOOPF problem, while it outperforms various algorithms. Thus, this paper proposes solving MOOPF problems based on SMA considering cost, emission, and transmission line loss as part of the objective functions in a power system. The IEEE 30-, 57-, and 118-bus systems are used to investigate the performance of the SMA on solving MOOPF problems. The objective values generated by SMA are compared with those of other algorithms in the literature. The simulation results show that SMA provides better solutions than many other algorithms in the literature, and the Pareto fronts presenting multi-objective solutions can be efficiently obtained.

Multi-Objective Optimal Power Flow in Islanded Microgrids with Solar PV Generation by NLTV-MOPSO

Optimal operation in islanded microgrids is one of most fundamental and prominent non-linear optimization problems investigated with new/different objective(s) with respect to the adaptable system constraints concerning to effective power dispatch. This paper presents a novel optimization method with distinct goals for optimal dispatch of both real and reactive powers from Distributed Generations (DGs) in islanded microgrids. The proposed method implements it by optimal tuning of droop parameters in dispatchable DGs, towards optimal dispatch strategy of each DG in the microgrid. The objectives considered are generation cost, emission, and diversity in voltage profile from unity. A new variant in Multi-Objective Particle Swarm Optimization (MOPSO) with Non-Linear Time Variation (NLTV) feature collectively referred to as NLTV-MOPSO has been proposed to solve the formulated problem. The uniqueness in proposed MOPSO are NLTV and modified mutation strategy in exploiting entire search space; there from a single optimal solution is obtained from Pareto by fuzzification. The effectiveness of proposed method with/without solar PV along with energy storage is verified with other MOPSO based algorithms. Also the simulation results for plug-and-play capability were tested effectively in proposed method. The results show the adaptability and performance of the proposed method for considered multi-objective optimal power flow problem in islanded microgrid.

Research on Novel Whale Algorithm for Multi-objective Optimal Power Flow Problem

To solve the non-differentiable optimal power flow (OPF) problems while satisfying various operational constrains, a multi-objective novel whale optimization algorithm (MONWOA) is proposed. MONWOA algorithm can overcome the premature-convergence of standard whale optimization algorithm. A Pareto-dominant approach with constrains (PDA) is employed to guarantee no violations of various inequality constraints on state variables. MONWOA algorithm is applied to optimize fuel cost, emission, active power loss and fuel cost (with value-point loadings). The bi-objective and tri-objective trials are implemented on IEEE30-bus system and the IEEE57-bus system. A large number of experimental results obtained by MONWOA and MOPSO algorithms, demonstrate that MONWOA has the definite competitive advantages to obtain uniform distribution Pareto front set (PFs), high-quality Pareto optimal solution (POS) and search for the best compromise solution (BCS) in solving MOOPF problem.

Comfort loss associated with automated demand response for multi-objective optimal power flow

This paper proposes a formulation to estimate user comfort loss associated with the automated demand response (ADR) in the multi-objective optimal power flow (MOOPF). It is hypothesized that the proposed method is capable of finding a trade-off among generation cost, ADR, and emission in MOOPF. Then, a numerical simulation is conducted to assess its capability. Generally, maintaining supply–demand balance in electrical power systems (EPSs) is tremendously difficult in tropical climates such as Iran with extreme heatwaves (EHWs). Besides EHWs, increasing user participation is another challenge for load management. Therefore, researchers and utilities are highly motivated to decrease peak to valley distance in these situations. For this purpose, ADR is a promising approach to increase user participation and shape the load. To increase ADR, we need to minimize user comfort loss of participating in load management programs. So far, however, there has been little discussion about considering comfort loss in the MOOPF problem. Therefore, enumerating comfort loss in the IEEE 30-bus test system with integrated HAN systems is investigated using numerical simulation. The proposed formulation considers flexibility and priority of each appliance in ADR. The MOEA/D-SF algorithm which has demonstrated superiority in solving MOOPF is utilized in this simulation. In conclusion, the results approve the hypothesis and demonstrate improved benefits for aggregators, users and utilities. The salient contribution of this research is the proposed comfort loss function that facilitates ADR and increases user participation.

Analytical adaptive distributed multi-objective optimization algorithm for optimal power flow problems

The convergence speed of analytic distributed multi-objective optimization algorithms should be higher when solving distributed multi-objective optimization algorithms. An adaptive operation is introduced into the only analytic distributed multi-objective optimization algorithm, which is an interchange objective value method. Therefore, an adaptive interchange objective value method is proposed for distributed multi-objective optimization problems. The proposed adaptive interchange objective value method updates the reward coefficients of a basic analytical distributed multi-objective optimization algorithm in the iteration process of solving distributed multi-objective optimization problems. The adaptive interchange objective value method obtains multiple satisfy optimal objectives for multiple subsidiary distributed multi-objective optimization problems security and quickly. To verify the feasibility and effectiveness of the adaptive interchange objective value method for the analytical distributed multi-objective optimization problems, the analytical distributed multi-objective optimal power flow problems under IEEE 118-bus, IEEE 300-bus power system and the medium part of the European system with 1472-bus test system are simulated. The numerical simulation results under these three cases show that the proposed adaptive interchange objective value method can obtain multiple distributed objectives for analytical distributed multi-objective optimal power flow problems security and quickly.

A novel hybrid self-adaptive heuristic algorithm to handle single- and multi-objective optimal power flow problems

The optimal power flow (OPF) is a key tool in the planning and operation of power systems, and aims to optimize the operational costs involved in the production and transport of energy by adjusting control variables to meet operational, economic, and environmental constraints. To achieve this goal, a successful implementation of an expeditious and reliable optimization algorithm is crucial. To this end, this paper proposes and scrutinizes a novel fuzzy adaptive hybrid configuration oriented to a joint self-adaptive particle swarm optimization (SPSO) and differential evolution algorithms, namely FAHSPSO-DE, to address the multi-objective OPF (MOOPF) problem. For the sake of practicality, the objectives with innate differences such as total fuel cost, active power losses, and the emission are selected. Due to the practical limitations in real power systems, additional restrictions, including valve-point effect, multi-fuel characteristic, and prohibited operating zones, are also taken into account. In order to validate the performance of the proposed approach, ten various benchmark functions are examined, while three IEEE standard systems such as IEEE 30-, 57-, and 118-bus test systems are employed to demonstrate the performance and suitability of the proposed approach in solving the OPF problem expeditiously. Results have been compared with those in the literature and show the effectiveness of our proposal in handling different scales, multi-objective, and non-convex optimization problems.

Solution of Optimal Power Flow Using Non-Dominated Sorting Multi Objective Based Hybrid Firefly and Particle Swarm Optimization Algorithm

In this paper, a multi-objective hybrid firefly and particle swarm optimization (MOHFPSO) was proposed for different multi-objective optimal power flow (MOOPF) problems. Optimal power flow (OPF) was formulated as a non-linear problem with various objectives and constraints. Pareto optimal front was obtained by using non-dominated sorting and crowding distance methods. Finally, an optimal compromised solution was selected from the Pareto optimal set by applying an ideal distance minimization method. The efficiency of the proposed MOHFPSO technique was tested on standard IEEE 30-bus and IEEE 57-bus test systems with various conflicting objectives. Simulation results were also compared with non-dominated sorting based multi-objective particle swarm optimization (MOPSO) and different optimization algorithms reported in the current literature. The achieved results revealed the potential of the proposed algorithm for MOOPF problems.

Non-interactive approach to solve multi-objective optimal power flow problem

The purpose of this research work is to solve the multi-objective optimal power flow (MO-OPF) problem using non-interactive approach. In this approach, the decision maker (DM) is not involved; however, the prior preference information is available to the DM. A satisficing function is offered to take care of the conflict between non-commensurable objectives, and the multi-objective problem is reformulated as a scalar optimization problem. This approach reduces the computation work involved for generating the Pareto front and for selecting the best satisficing solution. To attain the satisficing solutions, a hybrid optimization technique is applied, which integrates invasive weed optimization (IWO) with Powell’s pattern search (PPS) method. The IWO algorithm, utilized as the stochastic search technique, takes inspiration from the ability of weeds to adopt the environmental changes. Being a conjugate-based local search technique, the PPS method exhibits admirable exploitation search capability that further improves the solution provided by the IWO technique. The effectiveness of the proposed solution approach is confirmed by applying it to the three standard test systems, and the comparison is carried out with the well-established algorithms. Further, t test confirms the robustness of the proposed solution approach.