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.     

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.     

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.     

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.     

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.     

Optimal reactive power dispatch using self-adaptive real coded genetic algorithm

In this paper, self-adaptive real coded genetic algorithm (SARGA) is used as one of the techniques to solve optimal reactive power dispatch (ORPD) problem. The self-adaptation in real coded genetic algorithm (RGA) is introduced by applying the simulated binary crossover (SBX) operator. The binary tournament selection and polynomial mutation are also introduced in real coded genetic algorithm. The problem formulation involves continuous (generator voltages), discrete (transformer tap ratios) and binary (var sources) decision variables. The stochastic based SARGA approach can handle all types of decision variables and produce near optimal solutions. The IEEE 14- and 30-bus systems were used as test systems to demonstrate the applicability and efficiency of the proposed method. The performance of the proposed method is compared with evolutionary programming (EP) and previous approaches reported in the literature. The results show that SARGA solves the ORPD problem efficiently.     

基于一种不可行内点法的电力系统无功优化

在应用内点法进行线性规划时,尚不能保证它的全面收敛性。提出了一种新的算法来求解无功线性优化问题。利用潮流雅可比矩阵直接变换求取灵敏度系数,建立无功优化线性规划模型,同时采用一种不可行内点算法来直接求解该问题。IEEE 14节点、30节点、57节点系统的计算结果表明,该算法能有效求解无功优化线性规划问题,同时在初始点的选择上不要求从内点启动,迭代收敛次数稳定,对计算系统的规模不敏感。     

基于内点法和改进遗传算法的无功优化组合策略

提出了一种求解无功优化问题的组合策略,该策略将无功优化问题分解为连续优化和离散优化2个子问题,分别用预测–校正内点法和改进遗传算法进行求解。考虑到实际电网在进行无功优化控制时,发电机是主要的调节手段,先不考虑离散变量的约束,采用预测–校正内点法优化连续变量;然后保持连续变量不变,用改进遗传算法优化离散变量;再返回到连续优化阶段,如此交替求解。当出现相邻的连续优化阶段和离散优化阶段网损变化的差值小于设定值时,停止优化。IEEE14、30、57、118节点系统的仿真结果表明,该策略比其它组合算法在收敛性和计算效率上更具优越性。     

伪并行遗传算法在无功优化中的应用

在无功优化中，应用矩阵奇异值分解理论，引入了静态电压稳定裕度最大化目标和并行遗传算法思想，提出了用于无功优化的伪并行遗传算法。该算法在一定程度上避免了常规遗传算法容易出现的“早熟”现象，收敛速度也有一定提高。对Ward＆Hale 6节点和IEEE 14节点系统进行了测试，计算结果表明，本文所提模型和算法是合理可行的。     

Impact of the penetration of distributed generation on optimal reactive power dispatch

Optimal reactive power dispatch (ORPD) is a complex and non-linear problem, and is one of the sub-problems of optimal power flow (OPF) in a power system. ORPD is formulated as a single-objective problem to minimize the active power loss in a transmission system. In this work, power from distributed generation (DG) is integrated into a conventional power system and the ORPD problem is solved to minimize transmission line power loss. It proves that the application of DG not only contributes to power loss minimization and improvement of system stability but also reduces energy consumption from the conventional sources. A recently proposed meta-heuristic algorithm known as the JAYA algorithm is applied to the standard IEEE 14, 30, 57 and 118 bus systems to solve the newly developed ORPD problem with the incorporation of DG. The simulation results prove the superiority of the JAYA algorithm over others. The respective optimal values of DG power that should be injected into the four IEEE test systems to obtain the minimum transmission line power losses are also provided.     

基于IBBDE算法的交直流混联系统无功优化

随着高压直流输电工程(HVDC)投产规模持续增长,交直流混联电网的格局初步形成,给传统电网无功优化带来挑战。文中提出一种改进骨干差分进化算法(Improved Bare-bones Differential Evolution,IBBDE)求解交直流混联系统无功优化问题。在骨干差分进化算法的基础上,IBBDE算法采用广义反向学习初始化种群和自适应调整交叉概率的改进措施以提升种群的全局寻优能力。以含HVDC的IEEE 30节点系统为算例进行分析,结果表明,与差分进化算法和骨干差分进化算法相比,所提IBBDE算法可获得更优的无功优化效果,且寻优稳定性更好。     

基于改进粒子群优化算法的电力市场下的无功优化

在厂网分开、竞价上网的市场模式下综合考虑电力系统安全约束，建立了以有功网损和无功费用最小为目标函数并包含各种运行约束条件的电力系统无功优化数学模型。应用改进粒子群优化算法求解该无功优化模型，并结合动态调整罚函数法将无功优化问题转化成无约束求极值问题，从而有效地提高了改进粒子群优化算法的全局收敛能力和计算精度，使电网公司取得了最大经济效益。以IEEE30节点系统为例进行了仿真计算，结果表明了本文采用的无功优化模型和算法的正确性、适用性和较好的经济性。     

基于鲸鱼优化算法的无功优化调度

针对目前电力系统中的无功优化问题尚缺乏一种能兼顾求解的高效性与全局搜索最优性的方法,本文将一种新的启发式算法--鲸鱼优化算法(WOA)运用到电网无功优化调度中,以系统有功功率损耗最低为目标函数,通过引入惩罚函数建立无功优化模型,对IEEE-14节点系统与IEEE-30节点系统进行仿真,并利用单因素方差分析法(One-way ANOVA)将所得结果与之前的粒子群优化算法(PSO)及引入加速度系数的时变粒子群优化(PSO-TVAC)进行比较,研究表明WOA算法在迭代次数、搜索能力及收敛问题上的潜力,并证明了在解决电力系统无功优化问题上的鲁棒性和有效性,同时也为解决非线性约束问题提供了新途径。     

考虑拓扑影响的风电场无功优化策略研究

双馈风电机组(DFIG)机群的拓扑结构对风电场无功优化有较大影响。分析了DFIG的无功出力极限,将DFIG作为风电场连续无功源,计及风电场有载调压变压器分接头设置对DFIG机端电压的影响。以风电场内部有功损耗最小为优化目标建立风电场无功优化模型。最后,以丹麦HornsRev1离岸风电场为例,采用粒子群优化算法对所建立的无功优化模型进行求解。仿真结果验证了所提优化控制策略的安全性和经济性。     

Optimal VAR control for improvements in voltage profiles and for real power loss minimization using Biogeography Based Optimization

In this paper, a Biogeography Based Optimization (BBO) technique is introduced to solve multi-constrained optimal reactive power flow (ORPF) problem in power system. ORPF is a multi-objective nonlinear optimization problem that minimizes the bus voltage deviation and real power loss. The feasibility of the proposed algorithm is demonstrated for IEEE 30-bus system and IEEE 118-bus system. A comparison of simulation results reveals optimization efficacy of the proposed scheme over other well established population based optimization techniques like conventional particle swarm optimization (PSO), general passive congregation PSO (GPAC), local passive congregation PSO (LPAC), coordinated aggregation (CA) and interior point based OPF (IP-OPF).     

多目标无功优化的向量评价自适应免疫粒子群算法

为了克服粒子群算法在高维复杂问题寻优时容易陷入局部搜索的现象,提出了一种自适应免疫粒子群算法。该算法利用引入免疫系统的免疫信息处理机制和自动调整动量系数的自适应因子,从整体上达到系统的最佳控制方案。并将基于目标向量的个体评价方法与自适应免疫粒子群算法相结合,提出了基于向量评价的自适应免疫粒子群算法(vector evaluated adaptive immune particle swarm optimization,VEAIPSO)来解决多目标无功优化问题。通过引入静态电压稳定指标,建立了以系统有功损耗最小、节点电压偏移量最小及静态电压稳定裕度最大为目标的多目标无功优化模型。IEEE30和IEEE118节点系统算例仿真结果表明,该算法能有效地解决多目标无功优化问题,并具有良好的收敛稳定性和较高的寻优精度。     

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。     

基于自适应模糊粒子群算法的电力系统无功优化研究

针对传统粒子群算法搜索精度低和易早熟的缺点,提出了一种自适应模糊粒子群算法(AFPSO)对电力系统进行无功优化.该算法对惯性权重进行非线性的调整,有效地提高了算法的收敛速度和精度,并对位置的更新采用模糊控制,较好地解决了粒子群易早熟的问题.将该算法应用于无功优化问题中,在IEEE-30节点系统上进行测试,证明了AFPSO算法的有效性和优越性.     

基于免疫算法的多目标无功优化

在详细分析无功优化约束条件和目标函数以及研究无功优化免疫算法中抗体产生及其编码和解码的基础上,针对目前无功优化目标函数大多是基于权重系数基础多目标函数的组合,提出了基于免疫算法的多目标无功优化算法, 即用整体亲和力和部分亲和力概念来表示抗体对抗原的亲和程度,然后通过分别计算抗体的局部和整体亲和力来对抗体进行排序,依据此顺序选择抗体进行克隆、交叉变异等操作,并反复进行以求取系统无功优化的Pareto解集。对 IEEE14节点系统和IEEE118节点系统进行了多次无功优化计算,结果表明了该算法的有效性。