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.     

Multi-objective optimal reactive power dispatch using multi-objective differential evolution

This paper presents multi-objective differential evolution (MODE) to solve multi-objective optimal reactive power dispatch (MORPD) problem by minimizing active power transmission loss and voltage deviation and maximizing voltage stability while varying control variables such as generator terminal voltages, transformer taps and reactive power output of shunt VAR compensators. MODE has been tested on IEEE 30-bus, 57-bus and 118-bus systems. Numerical results for these three test systems have been compared with those acquired from strength pareto evolutionary algorithm 2 (SPEA 2).     

Optimal VAR control for real power loss minimization using differential evolution algorithm

Differential evolution algorithm (DEA) is an efficient and powerful population-based stochastic search technique for solving optimization problems over continuous space, which has been proved to be a promising evolutionary algorithm for solving the ORPD problem and many engineering problems. However, the success of DEA in solving a specific problem crucially depends on appropriately choosing trial vector generation strategies (mutation strategies) and their associated control parameter values. This paper presents a differential evolution technique with various trial vector generation strategies based on optimal reactive power dispatch for real power loss minimization in power system. The proposed methodology determines control variable settings such as generator terminal voltages, tap positions and the number of shunts compensator to be switched, for real power loss minimization in the transmission systems. The DE method has been examined and tested on the IEEE 14-bus, 30-bus and the equivalent Algerian electric 114-bus power system. The obtained results are compared with two other methods, namely, interior point method (IPM), Particle Swarm Optimization (PSO) and other methods in the literature. The comparison study demonstrates the potential of the proposed approach and shows its effectiveness and robustness to solve the ORPD problem.     

Optimal reactive power dispatch based on harmony search algorithm

This paper presents a harmony search algorithm for optimal reactive power dispatch (ORPD) problem. Optimal reactive power dispatch is a mixed integer, nonlinear optimization problem which includes both continuous and discrete control variables. The proposed algorithm is used to find the settings of control variables such as generator voltages, tap positions of tap changing transformers and the amount of reactive compensation devices to optimize a certain object. The objects are power transmission loss, voltage stability and voltage profile which are optimized separately. In the presented method, the inequality constraints are handled by penalty coefficients. The study is implemented on IEEE 30 and 57-bus systems and the results are compared with other evolutionary programs such as simple genetic algorithm (SGA) and particle swarm optimization (PSO) which have been used in the last decade and also other algorithms that have been developed in the recent years.     

Network loss minimization with voltage security using differential evolution

This paper presents a differential evolution (DE) based optimal power flow (OPF) for reactive power dispatch in power system planning studies. DE is a simple population-based search algorithm for global optimization and has a minimum number of control parameters. The problem is formulated as a mixed integer non-linear optimization problem taking into account both continuous and discrete control variables. The proposed method determines control variable settings such as generator voltages (continuous), tap positions (discrete) and the number of shunt reactive compensation devices to be switched (discrete) for real power loss minimization in the transmission system using DE algorithm. Most of the evolutionary algorithm applications to optimization problems apply penalty function approach to handle the inequality constraints, involving penalty coefficients. The correct combination of these coefficients can be determined only by a trial and error basis. In the proposed approach, the inequality constraints are handled by penalty parameterless scheme. Voltage security margin was evaluated using continuation power flow (CPF), to ensure the feasibility of the optimal control variable setting. The suitability of the method was tested on IEEE 14 and IEEE RTS 24-bus systems and results compared with sequential quadratic programming (SQP) method. The DE provides near global solutions comparable to that obtained using SQP.     

Optimal power flow using differential evolution algorithm

This paper presents an efficient and reliable evolutionary-based approach to solve the optimal power flow (OPF) problem. The proposed approach employs differential evolution algorithm for optimal settings of OPF problem control variables. The proposed approach is examined and tested on the standard IEEE 30-bus test system with different objectives that reflect fuel cost minimization, voltage profile improvement, and voltage stability enhancement. The proposed approach results are compared with the results reported in the literature. The results show the effectiveness and robustness of the proposed approach.     

Optimal power flow using differential evolution algorithm

This paper presents an evolutionary-based approach to solve the optimal power flow (OPF) problem. The proposed approach employs differential evolution (DE) algorithm for optimal settings of OPF control variables. The proposed approach is examined and tested on the standard IEEE 30-bus test system with different objective functions that reflect fuel cost minimization, voltage profile improvement, and voltage stability enhancement. In addition, non-smooth piecewise quadratic cost function has been considered. The simulation results of the proposed approach are compared to those reported in the literature. The results demonstrate the potential of the proposed approach and show its effectiveness and robustness to solve the OPF problem for the systems considered.     

Solution of optimal reactive power dispatch of power systems using hybrid particle swarm optimization and imperialist competitive algorithms

Management of reactive power resources is essential for secure and stable operation of power systems in the standpoint of voltage stability. In power systems, the purpose of optimal reactive power dispatch (ORPD) problem is to identify optimal values of control variables to minimize the objective function considering the constraints. The most popular objective functions in ORPD problem are the total transmission line loss and total voltage deviation (TVD). This paper proposes a hybrid approach based on imperialist competitive algorithm (ICA) and particle swarm optimization (PSO) to find the solution of optimal reactive power dispatch (ORPD) of power systems. The proposed hybrid method is implemented on standard IEEE 57-bus and IEEE 118-bus test systems. The obtained results show that the proposed hybrid approach is more effective and has higher capability in finding better solutions in comparison to ICA and PSO methods.     

Environmental/economic power dispatch problem using multi-objective differential evolution algorithm

This paper presents a multi-objective differential evolution (MODE) algorithm for environmental/economic power dispatch (EED) problem. The EED problem is formulated as a nonlinear constrained multi-objective problem with competing and non-commensurable objectives of fuel cost, emission and system loss. The proposed MODE approach adopts an external elitist archive to retain non-dominated solutions found during the evolutionary process. In order to preserve the diversity of Pareto optimality, a crowding entropy diversity measure tactic is proposed. The crowding entropy strategy is able to measure the crowding degree of the solutions more accurately. In addition, fuzzy set theory is employed to extract the best compromise solution. Several optimization runs of the proposed approach have been carried out on the IEEE 30- and 118-bus test system. The results demonstrate the capability of the proposed MODE approach to generate well-distributed Pareto optimal non-dominated solutions of multi-objective EED problem. The comparison with reported results of other MOEAs reveals the superiority of the proposed MODE approach and confirms its potential for solving other power systems multi-objective optimization problems.     

Differential evolution algorithm for optimal reactive power dispatch

Reactive power dispatch (RPD) is one of the important tasks in the operation and control of power system. This paper presents an efficient and reliable evolutionary-based approach to solve the RPD problem. The proposed approach employs differential evolution (DE) algorithm for optimal settings of RPD control variables. The proposed approach is examined and tested on the standard IEEE 30-bus test system with different objectives that reflect power losses minimization, voltage profile improvement, and voltage stability enhancement. The simulation results of the proposed approach are compared to those reported in the literature. The results demonstrate the potential of the proposed approach and show its effectiveness and robustness to solve the RPD problem.     

A two-point estimate method for uncertainty modeling in multi-objective optimal reactive power dispatch problem

Due to nonlinear and discrete variables and constraints, optimal reactive power dispatch (ORPD) is a complex optimization problem in power systems. In this paper, the purpose is to solve multi objective ORPD (MO-ORPD) problem considering bus voltage limits, the limits of branches power flow, generators voltages, transformers tap changers and the amount of compensation on weak buses. The objectives of this paper are real power losses and voltage deviations from their corresponding nominal values, which are conflicting objectives. Because of the stochastic behavior of loads, the MO-ORPD problem requires a probabilistic approach. Hence, in this paper, a two-point estimate method (TPEM) is proposed to model the load uncertainty in MO-ORPD problem. Moreover, the proposed method is compared with some other methods such as deterministic approaches and Monte Carlo simulations (MCS). The obtained results approve the efficiency of the proposed methodology. The proposed models are implemented and solved using GAMS optimization package and verified using IEEE 14-bus and IEEE 30-bus standard test systems.     

基于差异进化和PC集群的并行无功优化

提出了一种在线求解电力系统无功优化问题的方法。该方法基于新的差异进化（DE）算法和并行计算技术,在PC集群上实现优化。IEEE118节点系统的算例表明：DE算法尽管简单,但可快速收敛到近似最优解;采用并行差异进化和适当规模的PC集群,可大大缩短电力系统无功优化的计算时间,使之满足在线应用的需要。     

Reactive power dispatch considering voltage stability with seeker optimization algorithm

Optimal reactive power dispatch (ORPD) has a growing impact on secure and economical operation of power systems. This issue is well known as a non-linear, multi-modal and multi-objective optimization problem where global optimization techniques are required in order to avoid local minima. In the last decades, computation intelligence-based techniques such as genetic algorithms (GAs), differential evolution (DE) algorithms and particle swarm optimization (PSO) algorithms, etc., have often been used for this aim. In this work, a seeker optimization algorithm (SOA) based method is proposed for ORPD considering static voltage stability and voltage deviation. The SOA is based on the concept of simulating the act of human searching where search direction is based on the empirical gradient by evaluating the response to the position changes and step length is based on uncertainty reasoning by using a simple Fuzzy rule. The algorithm's performance is studied with comparisons of two versions of GAs, three versions of DE algorithms and four versions of PSO algorithms on the IEEE 57 and 118-bus power systems. The simulation results show that the proposed approach performed better than the other listed algorithms and can be efficiently used for the ORPD problem.     

考虑提高系统无功备用容量的无功优化调度

充裕的无功备用容量是保证系统电压稳定的一个重要因素，因此在日常无功优化调度过程中考虑提高系统的无功备用容量是防止电压失稳的重要手段之一。文章在分析发电机备用容量数学模型的基础上，定义了基于电压稳定的系统无功备用容量的计算公式，提出了考虑增大无功备用容量、减少网络损耗以及减小电压偏移的多目标无功优化调度算法。并将该算法应用于IEEE 30节点系统，证明了所定义的基于电压稳定的系统无功备用容量计算公式的正确性及提高备用容量的无功优化调度算法的可行性。     

电力系统无功优化的多智能体粒子群优化算法

无功优化是电力系统实现电压和无功功率最优控制和调度的基础,提出了一种全新的优化算法一多智能体粒子群优化算法来求解此类优化问题。该算法结合multi-agent系统和粒子群优化技术,构造了一个格子环境,所有Agent都固定在格子环境中。每一个Agent相当于粒子群优化算法中的一个粒子,它们通过与其邻居的竞争、合作和自学习操作,并且吸收了粒子群优化算法的进化机理,能够更快地、更精确地收敛到全局最优解。在IEEE30节点系统上进行校验,并与其它方法比较,结果表明,提出的算法具有质量高的解、收敛特性好、运行速度快的突出优点。     

Differential evolution algorithm for emission constrained economic power dispatch problem

In this paper, a differential evolution (DE) algorithm is developed to solve emission constrained economic power dispatch (ECEPD) problem. Traditionally electric power systems are operated in such a way that the total fuel cost is minimized regardless of emissions produced. With increased requirements for environmental protection, alternative strategies are required. The proposed algorithm attempts to reduce the production of atmospheric emissions such as sulfur oxides and nitrogen oxides, caused by the operation of fossil-fueled thermal generation. Such reduction is achieved by including emissions as a constraint in the objective of the overall dispatching problem. A simple constraint approach to handle the system constraints is proposed. The performance of the proposed algorithm is tested on standard IEEE 30-bus system and is compared with conventional methods. The results obtained demonstrate the effectiveness of the proposed algorithm for solving the emission constrained economic power dispatch problem.     

改进差分进化算法在电力系统无功优化中的应用

针对电力系统无功优化具有非线性、多控制变量、多约束条件、连续变量和离散变量混杂的特点,提出了一种改进的差分进化算法。该算法根据进化学习过程中积累的经验,利用优良群体引导变异的方向,同时提取优良群体各维元素的信息,以优良群体信息指导个体每一维变量的交叉操作。IEEE 30节点系统算例表明,所提算法较基本差分进化算法和粒子群算法,收敛速度快、计算精度高、稳定性好、能有效地求解电力系统无功优化问题。     

Seeker Optimization Algorithm for Optimal Reactive Power Dispatch

Optimal reactive power dispatch problem in power systems has thrown a growing influence on secure and economical operation of power systems. However, this issue is well known as a nonlinear, multimodal and mixed-variable problem. In the last decades, computation intelligence-based techniques, such as genetic algorithms (GAs), differential evolution (DE) algorithms and particle swarm optimization (PSO) algorithms, etc., have often been used for this aim. In this work, a seeker optimization algorithm (SOA)-based reactive power dispatch method is proposed. The SOA is based on the concept of simulating the act of human searching, where the search direction is based on the empirical gradient by evaluating the response to the position changes and the step length is based on uncertainty reasoning by using a simple Fuzzy rule. In this study, the algorithm's performance is evaluated on benchmark function optimization. Then, the SOA is applied to optimal reactive power dispatch on standard IEEE 57- and 118-bus power systems, and compared with conventional nonlinear programming method, two versions of GAs, three versions of DE algorithms and four versions of PSO algorithms. The simulation results show that the proposed approach is superior to the other listed algorithms and can be efficiently used for optimal reactive power dispatch.      

邻域拓扑粒子群优化算法在电力系统无功优化中的应用

提出了一种基于邻域拓扑粒子群优化算法(NTPSO)的大规模电力系统无功优化新算法。该算法在概念上比标准PSO算法更精确,认为每个粒子是受它邻域范围内最优粒子的影响。研究了当前流行的五种邻域拓扑结构得到五种邻域拓扑粒子群优化算法,其中包括已在一系列标准函数上测试过的比其它拓扑效果更好的Square拓扑。文中应用这五种NTPSO分别对IEEE30节点系统和IEEE57节点系统进行了无功优化的仿真计算,结果表明基于Square拓扑的NTPSO算法的优化效果最好,为求解大规模电力系统无功优化问题提供了新的思路。     

基于NW小世界的量子进化算法在无功优化中的研究

针对量子进化算法的早熟问题,提出了一种适于电力系统无功优化的NW（newman-watts）小世界量子进化算法。该算法引入了NW小世界网络模型,以一种新颖的随机加边方式动态改变种群个体的邻域拓扑结构,从而保证了整个优化过程中的种群多样性,提高了算法的全局搜索能力。应用该算法对IEEE-14节点和IEEE-57节点系统进行无功优化的仿真分析,结果表明,NW小世界量子进化算法在电网无功优化计算中具有较强的全局寻优能力和较高的收敛精度。