Multi-objective Optimal Power Flow Problem Research Articles

Optimal power flow using krill herd algorithm

In this article, an efficient optimization procedure based on herding behavior of krill individuals, krill herd algorithm (KHA), for the solution of multi-objective optimal power flow (OPF) with the objective of fuel cost minimization, voltage deviation minimization and voltage stability improvement is proposed. This algorithm is based on the effect of the influence of a teacher on the output of learners in a class. The proposed KHA approach is carried out on the standard IEEE 30-bus, IEEE 57-bus and IEEE 118-bus systems to solve different single and multi-objective OPF problems. Simulation results of the proposed approach are compared to differential evolution (DE), modified DE (MDE), multi-objective DE (MODE), evolving ant direction DE (EADDE), particle swarm optimization (PSO), improved genetic algorithm (IGA), gradient method, biogeography-based optimization (BBO), PSO with inertia weight approach (PSOIWA), PSO with constriction factor approach (PSOCFA), real-coded GA (RGA), artificial bee colony (ABC), general passive congregation PSO (GPAC), local passive congregation PSO (LPAC), coordinated aggregation (CA), interior point method (IPM) and quantum-inspired evolutionary algorithm (QEA). The comparison demonstrates the superiority of the proposed approach and confirms its potential to solve multi-objective OPF problems. Copyright © 2014 John Wiley & Sons, Ltd.

Fuzzy Multi-Objective Optimal Power Flow Using Genetic Algorithms Applied to Algerian Electrical Network

This paper presents a mathematical model for solving Multi-Objective Optimal Power Flow problem considering uncertainties modeled by fuzzy numbers aecting three objective functions given by total generation cost, total gas emission and voltage profle index. The presented resolution approach is based on Genetic Algorithm (GA), where the parameters of this algorithm are determined and optimized after many tests of execution. A model for analyzing trade-off between profit and security constraint is developed. The probabilities of crossover and mutation optimized for GA parameters, dedicated to the presented approach are used to demonstrate a performance and effectiveness of the algorithm compared to other approaches mentioned in this paper. The mathematic model is applied in the Algerian electrical network for 59-bus test system.

A modified teaching–learning based optimization for multi-objective optimal power flow problem

In this paper, a modified teaching–learning based optimization algorithm is analyzed to solve the multi-objective optimal power flow problem considering the total fuel cost and total emission of the units. The modified phase of the optimization algorithm utilizes a self-adapting wavelet mutation strategy. Moreover, a fuzzy clustering technique is proposed to avoid extremely large repository size besides a smart population selection for the next iteration. These techniques make the algorithm searching a larger space to find the optimal solutions while speed of the convergence remains good. The IEEE 30-Bus and 57-Bus systems are used to illustrate performance of the proposed algorithm and results are compared with those in literatures. It is verified that the proposed approach has better performance over other techniques.

A Solution to Multi Objective Optimal Power Flow Using Hybrid Cultural-Based Differential Evolution

This paper presents a hybrid Cultural-based Differential Evolution for solving a multi-objective Optimal Power Flow (OPF) in support of power system operation and control . The multi-objective OPF was formulated for tackling with total generation cost and environmental impacts simultaneously. The proposed method was applied to the standard IEEE 30-bus test system. The results show that solving the multi-objective OPF problem by the Cultural-based Differential Evolution is more effective than other swarm intelligence methods in the literature.

Hybrid Ant Optimization System for Multiobjective Optimal Power Flow Problem under Fuzziness

In this paper, a new hybrid optimization system is presented. Our approach integrates the merits of both ant colony optimization and steady state genetic algorithm and it has two characteristic features. Firstly, Since there is instabilities in the global market and the rapid fluctuations of prices, a fuzzy representation of the optimal power flow problem has been defined, where the input data involve many parameters whose possible values may be assigned by the expert. Secondly, by enhancing ant colony optimization through steady state genetic algorithm, a strong robustness and more effectively algorithm was created. Also, stable Pareto set of solutions has been detected, where in a practical sense only Pareto optimal solutions that are stable are of interest since there are always uncertainties associated with efficiency data. Moreover to help the decision maker DM to extract the best compromise solution from a finite set of alternatives a TOPSIS (Technique for Order Performance by Similarity to Ideal Solution) method is adopted. It is based upon simultaneous minimization of distance from an ideal point (IP) and maximization of distance from a nadir point (NP). The results on the standard IEEE systems demonstrate the capabilities of the proposed approach to generate true and well-distributed Pareto optimal nondominated solutions of the multiobjective OPF.

Chance-Constrained Optimization-Based Unbalanced Optimal Power Flow for Radial Distribution Networks

Optimal power flow (OPF) is an important tool for active management of distribution networks with renewable energy generation (REG). It is better to treat REG as stochastic variables in the distribution network OPF. In addition, distribution networks are unbalanced in nature. Thus, in this paper, a chance constrained optimization-based multiobjective OPF model is formulated to consider the forecast errors of REG in the short-term operation of radial unbalanced distribution networks. In the model, expected total active power losses of distribution lines, expected overload risk and voltage violation risk with respect to N-1 contingencies are minimized, and inequality constraints in the normal state are satisfied with a predefined probability level. Thus, the profitability and security can be balanced in the presence of stochastic REG. The proposed multiobjective OPF problem is solved by the multiobjective group search optimization and the two-point estimate method. Simulation results show that distribution network economy and postcontingency performance deteriorate with increased penetration level of REG, and the penetration level has a greater impact than the forecast errors of REG.

Artificial bee colony algorithm for solving multi-objective optimal power flow problem

This paper presents a new and efficient method for solving optimal power flow (OPF) problem in electric power systems. In the proposed approach, artificial bee colony (ABC) algorithm is employed as the main optimizer for optimal adjustments of the power system control variables of the OPF problem. The control variables involve both continuous and discrete variables. Different objective functions such as convex and non-convex fuel costs, total active power loss, voltage profile improvement, voltage stability enhancement and total emission cost are chosen for this highly constrained nonlinear non-convex optimization problem. The validity and effectiveness of the proposed method is tested with the IEEE 9-bus system, IEEE 30-bus system and IEEE 57-bus system, and the test results are compared with the results found by other heuristic methods reported in the literature recently. The simulation results obtained show that the proposed ABC algorithm provides accurate solutions for any type of the objective functions.

Comprehensive Learning Particle Swarm Optimization (CLPSO) for Multi-objective Optimal Power Flow

The Optimal Power Flow (OPF) problem has been widely used in power system operation and planning for determining electricity prices and amount of emission. This paper presents a Comprehensive Learning Particle Swarm Optimization (CLPSO) algorithm to solve the highly constrained multi-objective OPF involving conflicting objectives, considering fuel cost and emission level functions. The proposed technique has been carried out on IEEE 30-bus test system. The results demonstrate the capability of the proposed CLPSO approach to generate well-distributed Pareto optimal non-dominated solutions of multi-objective OPF problem. The results show that the approaches developed are feasible and efficient.

Comprehensive Learning Particle Swarm Optimization (CLPSO) for Multi-objective Optimal Power Flow

The Optimal Power Flow (OPF) problem has been widely used in power system operation and planning for determining electricity prices and amount of emission. This paper presents a Comprehensive Learning Particle Swarm Optimization (CLPSO) algorithm to solve the highly constrained multi-objective OPF involving conflicting objectives, considering fuel cost and emission level functions. The proposed technique has been carried out on IEEE 30-bus test system. The results demonstrate the capability of the proposed CLPSO approach to generate well-distributed Pareto optimal non-dominated solutions of multi-objective OPF problem. The results show that the approaches developed are feasible and efficient.

Solving multi-objective optimal power flow problem considering wind-STATCOM using differential evolution

In this paper, a simple strategy based differential evolution was proposed for solving the problem of multi-objective environmental optimal power flow considering a hybrid model (Wind-Shunt-FACTS). The DE algorithm optimized simultaneously a combined vector control based active power of wind sources and reactive power of multi STATCOM exchanged with the electrical power system to minimize fuel cost and emissions. The proposed strategy was examined and applied to the standard IEEE 30-bus with smooth cost function to solve the problem of security environmental economic dispatch considering multi distributed hybrid model based wind and STATCOM controllers. In addition, the proposed approach was validated on a large practical electrical power system 40 generating units considering valve point effect. Simulation results demonstrate that choosing the installation of multi type of FACTS devices in coordination with many distributed wind sources is a vital research area.

Ant Colony Optimization Approach Based Genetic Algorithms for Multiobjective Optimal Power Flow Problem under Fuzziness

In this paper, a new optimization system based genetic algorithm is presented. Our approach integrates the merits of both ant colony optimization and genetic algorithm and it has two characteristic features. Firstly, since there is instabilities in the global market, implications of global financial crisis and the rapid fluctuations of prices, a fuzzy representation of the optimal power flow problem has been defined, where the input data involve many parameters whose possible values may be assigned by the expert. Secondly, by enhancing ant colony optimization through genetic algorithm, a strong robustness and more effectively algorithm was created. Also, stable Pareto set of solutions has been detected, where in a practical sense only Pareto optimal solutions that are stable are of interest since there are always uncertainties associated with efficiency data. The results on the standard IEEE systems demonstrate the capabilities of the proposed approach to generate true and well-distributed Pareto optimal nondominated solutions of the multiobjective OPF.

MULTI-OBJECTIVE ADAPTIVE CLONAL SELECTION ALGORITHM FOR SOLVING OPF WITH WECS AND LOAD UNCERTAINTY

In this paper a solution to multi-objective optimal power flow (OPF) problem using an adaptive clonal selection algorithm (ACSA) with the incorporation of wind energy conversion system (WECS) is presented.

Distributed multi-step Q(λ) learning for Optimal Power Flow of large-scale power grids

This paper presents a novel distributed multi-step Q(λ) learning algorithm (DQ(λ)L) based on multi-agent system for solving large-scale multi-objective OPF problem. It does not require any manipulation to the conventional mathematical Optimal Power Flow (OPF) model. Large-scale power system is first partitioned to subsystems and each subsystem is managed by an agent. Each agent adopts the standard multi-step Q(λ) learning algorithm to pursue its own objectives independently and approaches to the global optimal through cooperation and coordination among agents. The proposed DQ(λ)L has been thoroughly studied and tested on the IEEE 9-bus and 118-bus systems. Case studies demonstrated that DQ(λ)L is a feasible and effective for solving multi-objective OPF problem in large-scale complex power grid.

Solution of multi-objective optimal power flow using gravitational search algorithm

This article presents application of an efficient and reliable heuristic technique inspired by swarm behaviours in nature namely, gravitational search algorithm (GSA) for solution of multi-objective optimal power flow (OPF) problems. GSA is based on the Newton's law of gravity and mass interactions. In the proposed algorithm, the searcher agents are a collection of masses that interact with each other using laws of gravity and motion of Newton. In order to investigate the performance of the proposed scheme, multi-objective OPF problems are solved. A standard 26-bus and IEEE 118-bus systems with three different individual objectives, namely fuel cost minimisation, active power loss minimisation and voltage deviation minimisation, are considered. In multi-objective problem formulation fuel cost and loss; fuel cost and voltage deviation; fuel cost, loss and voltage deviation are minimised simultaneously. Results obtained by GSA are compared with mixed integer particle swarm optimisation, evolutionary programming, genetic algorithm and biogeography-based optimisation. The results show that the new GSA algorithm outperforms the other techniques in terms of convergence speed and global search ability.

Application of Multi-Objective Teaching Learning based Optimization Algorithm to Optimal Power Flow Problem

This paper presents a non-domination based sorting multiobjective teaching-learning-based optimization algorithm, for solving the optimal power flow (OPF) problem. The OPF problem is a nonlinear constrained multi-objective optimization problem where the fuel cost, Transmission losses and L-index are to be minimized. Since the problem is treated as a true multi-objective optimization problem, different trade-off solutions are provided. The decision maker has an option to choose a solution among the different trade-off solutions provided in the pareto-optimal front. The standard IEEE 30-bus test system is used and the results show the effectiveness of MOTLBO and confirm its potential to solve the multi-objective OPF problem. Simulation results clearly show that the proposed method is able to produce true and well distributed Pareto optimal solutions for multiobjective OPF problem and the comparison with the results reported in the literature demonstrates the superiority of the proposed approach and confirms its potential to solve the multi-objective OPF problem.

Improved particle swarm optimisation for multi-objective optimal power flow considering the cost, loss, emission and voltage stability index

The study presents an improved particle swarm optimisation (IPSO) method for the multi-objective optimal power flow (OPF) problem. The proposed multi-objective OPF considers the cost, loss, voltage stability and emission impacts as the objective functions. A fuzzy decision-based mechanism is used to select the best compromise solution of Pareto set obtained by the proposed algorithm. Furthermore, to improve the quality of the solution, particularly to avoid being trapped in local optima, this study presents an IPSO that profits from chaos queues and self-adaptive concepts to adjust the particle swarm optimisation (PSO) parameters. Also, a new mutation is applied to increase the search ability of the proposed algorithm. The 30-bus IEEE test system is presented to illustrate the application of the proposed problem. The obtained results are compared with those in the literatures and the superiority of the proposed approach over other methods is demonstrated.

Optimal power flow solutions through multi-objective programming

Despite the progress achieved in the development of optimal power flow (OPF) programs, most of the solution techniques reported in the literature suffer from the difficulty of dealing with objective functions of different natures at the same time. However, the need for alternative power network solutions during the planning of a power system operation requires the optimization of several performance indexes simultaneously. In this study, attention is focused on the modelling and solution of a parameterized multi-objective OPF problem. The proposed OPF model combines two classical multi-objective optimization approaches, the weighted sum and the constraint methods, through a parameterization scheme to manipulate the objective functions. This parameterization allows relaxation of the constraints imposed to handle the performance indexes, to facilitate the convergence of the iterative process. The resulting optimization problem, which ultimately is a mono-objective optimization problem, is solved through the nonlinear version of the predictor–corrector interior point method. The IEEE 24-bus test system was used to obtain the numerical results of the computational simulation.

Application of Multi Objective Technique to Incorporate UPFC in Optimal Power Flow using Modified Bacterial Foraging Technique

A modified bacterial foraging technique is applied to solve the multi-objective optimal power flow problem with unified power flow controller (UPFC). The introduction of UPFC in power system improves the stability and it is one of the crucial factors for effective modern power systems. Effective means for controlling and improving power flow is done by installing fast reacting devices such as a Unified Power Flow Controller (UPFC).The application of modified bacterial foraging technique is applied to find optimal location of unified power flow controller to achieve solution of optimal power flow and this problem is formulated by multi-objective optimization using bacterial foraging technique. The optimal power flow problem is used to minimize the overall cost functions, which include the total active and reactive production cost function of the generators and installation cost of UPFCs and also the OPF constraints are generators, transmission lines and UPFCs limits are included. Modified Bacterial foraging algorithm and multi-objective optimization technique is applied to the problem with use of controllable UPFC devices is proposed. The specified power flow control constraints due to the use of UPFC devices are included in the OPF problem in addition to these normal conventional constraints. The sensitivity analysis is carried out for the location of UPFC devices. This provides an enhanced economic solution with the use of controllable of UPFC devices. Simulations are performed modified IEEE 4 bus and IEEE 30 bus system for optimal location of UPFC and the results obtained are encouraging and will be useful in electrical restructuring.

A modified shuffle frog leaping algorithm for multi-objective optimal power flow

This paper presents an efficient and reliable evolutionary-based approach to solve the Optimal Power Flow (OPF) problem by considering the emission issue. The OPF problem has been widely used in power system operation and planning for determining electricity prices. Therefore, the conventional optimal power flow cannot meet the environmental protection requirements, because it only considers generation cost minimization. The multi-objective optimal power flow considers economical and emission issues. By adding the emission objective in the optimal power flow problem, this problem become more complicated than before and it needs to be solved with an accurate algorithm. This paper proposes an algorithm based on the Shuffle Frog Leaping Algorithm (SLFA) to solve the multi-objective OPF problem. Furthermore, this paper presents a modified SLFA called MSLFA algorithm which profits from a mutation in order to reduce the processing time and improve the quality of solutions, particularly to avoid being trapped in local optima. The IEEE 30-bus test system is presented to illustrate the application of the proposed problem.

Application of NSGA-II in Solving Multiobjective Optimal Power Flow

This paper is an application of NSGA-II for solving multiobjective optimal power flow problems in power systems. Objective functions considered in this work are conventional quadratic cost and emission along with highly non-linear features like cost curve with valve point loading and cubic emission function etc. In addition, more than two objectives are optimized simultaneously. The problem is formulated as mixed integer one with both continuous and discrete control variables. The performance of the proposed algorithm has been tested on three different IEEE test systems. Results for the test system-1 have been validated with the reported works. The comparison is done with the classical weighted sum method for IEEE-30 bus system and further experimentation is done on two other test cases such as IEEE-57 bus and IEEE-118 bus systems. The results demonstrate the effectiveness of the proposed approach for finding the Power System optimal solutions even when more than two confl icting objectives are considered simultaneously.