Multi-objective Optimal Reactive Power Dispatch Research Articles

Multiobjective Optimal Reactive Power Dispatch Considering Voltage Stability Using Shuffled Frog Leaping Algorithm

This study addresses a shuffled frog leaping algorithm for solving the multi-objective reactive power dispatch problem in a power system. Optimal Reactive Power Dispatch (ORPD) is formulated as a nonlinear, multi-modal and mixed-variable problem. The intended technique is based on the minimization of the real power loss, minimization of voltage deviation and maximization of the voltage stability margin. Generator voltages, capacitor banks and tap positions of tap changing transformers are used as optimization variables of this problem. A memetic meta-heuristic named as shuffled frog-leaping algorithm is intended to solve multi-objective optimal reactive power dispatch problems considering voltage stability margin and voltage deviation. The Shuffled Frog-Leaping Algorithm (SFLA) is a population-based cooperative search metaphor inspired by natural memetics. The algorithm contains elements of local search and global information exchange. The most important benefit of this algorithm is higher speed of convergence to a better solution. The intended method is applied to ORPD problem on IEEE 57 bus power systems and compared with two versions of differential evolutionary algorithm. The simulation results show the effectiveness of the intended method.

An enhanced firefly algorithm to multi-objective optimal active/reactive power dispatch with uncertainties consideration

Abstract This paper presents an enhanced firefly algorithm for solving multi-objective optimal active and reactive power dispatch problems with load and wind generation uncertainties. The optimal dispatches of active and reactive power were considered simultaneously. In reactive power dispatch, the load tap changer positions of transformers, the reactive power injection of capacitors, and the voltages of slack bus and PV buses are controlled to reduce the transmission line losses and the voltage deviations of load buses. In active power dispatch, economic dispatch including losses is used to obtain the active power outputs of thermal generating units and to decrease the fuel costs. The proposed algorithm was based on a firefly algorithm, the formula and parameters of which were updated and modified, and a mutation strategy and local random search were used to enhance the exploration and search capabilities of the algorithm. The IEEE 30-bus system was used to demonstrate the effectiveness of the proposed method for solving multi-objective optimal active and reactive power dispatch problems while considering uncertainties. The results of the proposed method were compared with the results of other algorithms. The results showed that the proposed method achieved a more favorable solution than the other algorithms.

Chaotic improved PSO-based multi-objective optimization for minimization of power losses and L index in power systems

Multi-objective optimal reactive power dispatch (MOORPD) seeks to not only minimize power losses, but also improve the stability of power system simultaneously. In this paper, the static voltage stability enhancement is achieved through incorporating L index in MOORPD problem. Chaotic improved PSO-based multi-objective optimization (MOCIPSO) and improved PSO-based multi-objective optimization (MOIPSO) approaches are proposed for solving complex multi-objective, mixed integer nonlinear problems such as minimization of power losses and L index in power systems simultaneously. In MOCIPSO and MOIPSO based optimization approaches, crossover operator is proposed to enhance PSO diversity and improve their global searching capability, and for MOCIPSO based optimization approach, chaotic sequences based on logistic map instead of random sequences is introduced to PSO for enhancing exploitation capability. In the two approaches, constrain-prior Pareto-dominance method (CPM) is proposed to meet the inequality constraints on state variables, the sorting and crowding distance methods are considered to maintain a well distributed Pareto optimal solutions, and moreover, fuzzy set theory is employed to extract the best compromise solution over the Pareto optimal curve. The proposed approaches have been examined and tested in the IEEE 30 bus and the IEEE 57 bus power systems. The performances of MOCIPSO, MOIPSO, and multi-objective PSO (MOPSO) approaches are compared with respect to multi-objective performance measures. The simulation results are promising and confirm the ability of MOCIPSO and MOIPSO approaches for generating lower power losses and smaller L index than MOPSO method.

Optimal Reactive Power Dispatch of Power System using Improved Harmony Search Algorithm

This paper presents improved harmony search algorithm (IHSA) to solve multi-objective optimal reactive power dispatch (ORPD) problem by minimizing active power loss,voltage deviation and voltage stability index. To acclerate the convergence speed and to enhance the solution quality dynamic pitch adjusting rate and variable band width are incorporated in orginal harmony search algorithm (HSA). In this work IHSA is used to find the settings of control variables such as generator voltages, tap positions of tap changing transformers and amount of VAR injection. The proposed IHSA is implemented on IEEE 30 and 57 bus systems and the results are compared with other computational intelligence-based techniques such as particle swarm optimization (PSO) and differential evolution (DE). A comparison of simulation results reveals the effectiveness of proposed algorithm over other well established population based optimization techniques.

Solution of multi-objective optimal reactive power dispatch using pareto optimality particle swarm optimization method

For Multi-Objective Optimal Reactive Power Dispatch (MORPD), a new approach is proposed as a simultaneous minimization of the active power transmission loss, the bus voltage deviation and the voltage stability index of a power system are obtained. Optimal settings of continuous and discrete control variables (e.g., generator voltages, tap positions of tap changing transformers and the number of shunt reactive compensation devices to be switched) are determined. MORPD is solved using Particle Swarm Optimization (PSO). Also, Pareto Optimality PSO (POPSO) is proposed to improve the performance of the multi-objective optimization task defined with competing and non-commensurable objectives. The decision maker requires to manage a representative Pareto-optimal set provided by imposition of a hierarchical clustering algorithm. The proposed approach was tested using IEEE 30-bus and IEEE 118-bus test systems. When simulation results are compared with several commonly used algorithms, they indicate better performance and good potential for their efficient applications in solving MORPD problems.

Strength Pareto Multigroup Search Optimizer for Multiobjective Optimal Reactive Power Dispatch

Multiobjective optimal reactive power dispatch (MORD) is a highly constrained nonlinear nondifferential multimodal Pareto optimization problem with a mixture of continuous and discrete variables. This paper presents a novel strength Pareto multigroup search optimizer (SPMGSO) for solving this challenging problem. In the proposed algorithm, a number of enhancement mechanisms, such as ring-migration synergistic cooperation, crowding entropy constraint treatment, and chaotic logistic dispersion, were developed to effectively strengthen the diversity and distribution of the resulting nondominated front (NDF). The final best compromise solution is then extracted from the NDF using a hierarchical clustering and an equilibria-based multicriteria decision-making scheme. In addition, the multicore processing was introduced to parallelize the multigroup search so as to greatly improve the execution speed of the algorithm. Computational studies on the benchmark IEEE 30-bus and 162-bus power systems have confirmed the superior performance and improvement of the proposed algorithm for solving this Pareto problem, and demonstrated its applicability and capability to cope with the high-dimensional MORD problems with multiple operational objectives.

Multiobjective Optimal Reactive Power Dispatch and Voltage Control: A New Opposition-Based Self-Adaptive Modified Gravitational Search Algorithm

This paper presents a novel opposition-based self-adaptive modified gravitational search algorithm (OSAMGSA) for optimal reactive power dispatch and voltage control in power-system operation. The problem is formulated as a mixed integer, nonlinear optimization problem, which has both continuous and discrete control variables. In order to achieve the optimal value of loss, voltage deviation, and voltage stability index, it is necessary to find the optimal value of control variables such as the tap positions of tap changing transformers, generator voltages, and compensation capacitor. Therefore, this complicated problem needs to be solved by an accurate optimization algorithm. This paper solves the aforementioned problem by using the gravitational search algorithm (GSA), which is one of the novel optimization algorithms based on the gravity law and mass interactions. To improve the efficiency of this algorithm, the tuning of its parameters is accomplished using random generation, and by applying the self-adaptive parameter tuning scheme. Also, the proposed OSAMGSA of this paper employs the opposition-based population initialization and self-adaptive probabilistic learning approach for generation jumping and escaping from local optima. Since the proposed problem is a multiobjective optimization problem incorporating several solutions instead of one, we applied the Pareto optimal solution method in order to find all Pareto optimal solutions. Moreover, the fuzzy decision method is used for obtaining the best compromise solution between them.

Optimal reactive power dispatch using quasi-oppositional teaching learning based optimization

This paper presents a newly developed teaching learning based optimization (TLBO) algorithm to solve multi-objective optimal reactive power dispatch (ORPD) problem by minimizing real power loss, voltage deviation and voltage stability index. To accelerate the convergence speed and to improve solution quality quasi-opposition based learning (QOBL) concept is incorporated in original TLBO algorithm. The proposed TLBO and quasi-oppositional TLBO (QOTLBO) approaches are implemented on standard IEEE 30-bus and IEEE 118-bus test systems. Results demonstrate superiority in terms of solution quality of the proposed QOTLBO approach over original TLBO and other optimization techniques and confirm its potential to solve the ORPD problem.

Adaptive multiple evolutionary algorithms search for multi-objective optimal reactive power dispatch

SUMMARY Multi-objective evolutionary algorithm (MOEA) based on Pareto optimality has emerged as an important approach for optimal reactive power dispatch (ORPD) problem. However, because of the deficiency of adopting evolution operators with single search characteristics, existing MOEA for multi-objective ORPD (MORPD) often fails to maintain universal and robust performance in different phases of optimization process. On the basis of running multiple algorithms simultaneously and adaptive selection strategy, this paper proposes a new optimal method for MORPD. Firstly, an algorithm candidate pool containing four different algorithms is constructed through the analysis of characteristics of state-of-the-art MOEA while considering the rules of consistency and complementarity. Then, during the optimizing search, the quantity of offspring individuals generated by each candidate algorithm at different stages of optimization process is determined adaptively by learning from its previous experience in generating promising solutions. The proposed method is tested on the IEEE 30-bus system; its computing performance is compared with existing popular MOEAs from the point of view of Pareto fronts, outer solutions and C measure. Experimental results show that the new method can obtain better performance of convergence during the entire optimization process. Copyright © 2013 John Wiley & Sons, Ltd.

有考虑负载不确定性的多目标最佳虚功率调度

由于传统的最佳虚功率调度都是将负载需求假设为已知的固定值，以求得负载在确定状态下的最佳解，但实际的负载需求含有不确定性。为了使调度结果更适用于实际情形，本文探讨考虑负载不确定性的多目标最佳虚功率调度问题。此外，本文提出以增强型萤火虫演算法(Enhanced Firefly Algorithm, EFA)应用于此问题，增强型萤火虫演算法是将原萤火虫演算法的更新式作改良且修改参数并加入突变机制，以增强演算法的开采与搜索能力，并加快收敛速度且不易陷入局部解。另外，本文使用模糊理论建立模糊归属函数，以解决多目标不同性质及目标函数“越小越好”这种不明确语意的问题。为了验证本文所使用的方法对于考虑负载不确定性的多目标最佳虚功率调度问题的有效性，本文使用IEEE57-Bus系统作为测试系统，并与其它演算法作比较。实验结果证实本文所提出的方法确实可以获得较好的结果。 In traditional optimal reactive power dispatch problem, the optimal solution is found under the condition that the load demands are assumed to be known and fixed, but the practical load demands have uncertainty. This paper investigates the multi-objective optimal reactive power dispatch with considering load uncertainty to make the dispatch results more suitable for real situation. In this paper, an enhanced firefly algorithm is presented to solve the problem. Enhanced firefly algorithm is based on firefly algorithm that the update formula and parameters are modified and the mutation strategy is utilized to enhance the capabilities of exploring and searching. So the proposed algorithm can converge fast and the solution can avoid trapping in local minimum. Furthermore, in order to deal with the multi-objective problem and the ambiguous linguistic expression such as “as little as possible”, the fuzzy theory is employed to establish the fuzzy membership functions. To demonstrate the effectiveness of the proposed method for solving multi-objective optimal reactive power dispatch with considering load uncertainty problem, the IEEE 57-Bus system has been applied to the reactive power dispatching and the results of the proposed method are compared with those of other algorithms. The results show that the proposed method can get better solution.

Multi-objective optimal reactive power dispatch considering voltage stability in power systems using HFMOEA

This paper proposes a new hybrid fuzzy multi-objective evolutionary algorithm (HFMOEA) based approach for solving complex multi-objective, mixed integer nonlinear problems such as optimal reactive power dispatch considering voltage stability (ORPD-VS). In HFMOEA based optimization approach, the two parameters like crossover probability (PC) and mutation probability (PM) are varied dynamically through the output of a fuzzy logic controller. The fuzzy logic controller is designed on the basis of expert knowledge to enhance the overall stochastic search capability for generating better pareto-optimal solution. Two detailed case studies are presented: Firstly, the performance of HFMOEA is tested on five benchmark test problems such as ZDT1, ZDT2, ZDT3, ZDT4 and ZDT6 as suggested by Zitzler, Deb and Thiele; Secondly, HFMOEA is applied to multi-objective ORPD-VS problem. In both the case studies, the optimization results obtained from HFMOEA are analysed and compared with the same obtained from two versions of elitist non-dominated sorting genetic algorithms such as NSGA-II and MNSGA-II in terms of various performance metrics. The simulation results are promising and confirm the ability of HFMOEA for generating better pareto-optimal fronts with superior convergence and diversity.

Gravitational Search Algorithm Based Optimal Reactive Power Dispatch for Voltage Stability Enhancement

In this article, an efficient and reliable optimization procedure based on the behaviors of swarm in nature, namely the gravitational search algorithm, is proposed for solving multi-objective optimal reactive power dispatch problems, which minimizes transmission loss while maintaining the quality of voltages. The gravitational search algorithm is based on Newton's law of gravity and interaction of masses. In the proposed algorithm, the searcher agents which are a collection of masses interact with each other using Newton's laws of gravity and motion. In order to investigate the performance of the proposed scheme, multi-objective optimal reactive power dispatch problems are solved. This new gravitational search algorithm method is tested on IEEE 57-bus and IEEE 118-bus power systems. Results obtained by the gravitational search algorithm are compared with two versions of genetic algorithms, three versions of differential evolution algorithms, four versions of particle swarm optimization algorithms and the seeker optimization algorithm It is observed from the test results that the proposed gravitational search algorithm approach converges to better solutions much faster than the earlier reported approaches.

Solving multiobjective optimal reactive power dispatch using modified NSGA-II

This paper addresses an application of modified NSGA-II (MNSGA-II) by incorporating controlled elitism and dynamic crowding distance (DCD) strategies in NSGA-II to multiobjective optimal reactive power dispatch (ORPD) problem by minimizing real power loss and maximizing the system voltage stability. To validate the Pareto-front obtained using MNSGA-II, reference Pareto-front is generated using multiple runs of single objective optimization with weighted sum of objectives. For simulation purposes, IEEE 30 and IEEE 118 bus test systems are considered. The performance of MNSGA-II, NSGA-II and multiobjective particle swarm optimization (MOPSO) approaches are compared with respect to multiobjective performance measures. TOPSIS technique is applied on obtained non-dominated solutions to determine best compromise solution (BCS). Karush–Kuhn–Tucker (KKT) conditions are also applied on the obtained non-dominated solutions to substantiate a claim on optimality. Simulation results are quite promising and the MNSGA-II performs better than NSGA-II in maintaining diversity and authenticates its potential to solve multiobjective ORPD effectively.

Non-dominated sorting genetic algorithm-II for robust multi-objective optimal reactive power dispatch

The concept of robust optimal solution is incorporated into multi-objective optimal reactive power dispatch (MORPD) for the consideration of uncertain load perturbations during system operations. Robust MORPD searches for solutions that are immune to parameter drifts and load changes. It uses information of load-increase directions to promote the stability of optimal solutions in the presence of load perturbations. Non-dominated sorting genetic algorithm-II (NSGA-II) is adopted to search for the robust Pareto solutions on a standard IEEE 118-bus system. The simulation validated the effectiveness of NSGA-II for robust MORPD. NSGA-II obtained Pareto solutions over the trade-off surface. The experimental results also indicated that the robust Pareto solutions are comparatively less sensitive to load perturbations in their neighbourhoods and can maintain their objective values against uncertain load perturbations. Robust MORPD can provide optimal solutions with a higher degree of stability in the face of perturbations and can be more practical in reactive power optimisation of the real-time operation systems.