Capacitor placement of distribution systems using particle swarm optimization approaches

Capacitor placement plays an important role in distribution system planning and operation. In distribution systems of electrical energy, banks of capacitors are widely installed to compensate the reactive power, reduce the energy loss in system, voltage profile improvement, and feeder capacity release. The capacitor placement problem is a combinatorial optimization problem having an objective function composed of power losses and capacitor installation costs subject to bus voltage constraints. Recently, many approaches have been proposed to solve the capacitor placement problem as a mixed integer programming problem. This paper presents a new capacitor placement method which employs particle swarm optimization (PSO) approaches with operators based on Gaussian and Cauchy probability distribution functions and also in chaotic sequences for a given load pattern of distribution systems. The proposed approaches are demonstrated by two examples of application. Simulation results show that the proposed method can achieve an optimal solution as the exhaustive search can but with much less computational time.     

基于交流支路电气剖分思想的配电网电容器优化投切方法

基于交流支路电气剖分思想,提出了一种配电网电容器的优化投切方法。对某一网络状态,电气剖分方法可以把配电网剖分成从变电站根节点到负荷节点的链式剖分子网络,将配电网的电容器优化投切问题转化成求剖分子网络的网损最小值问题。在满足电压约束的前提下,该快速求解方法直接采用物理寻优方式求得电容器的投切分量,使剖分子网络的功率损耗最小,并通过对各投切点的容量分量进行累加归整,得到了原系统各投切点的投切容量。IEEE 69节点系统的计算结果表明,该方法在保证得到优良解的前提下具有收敛快、效率高的特点,为解决大型配电网的电容器优化投切问题提供了新的思路和方法。     

Optimal allocation of capacitor banks in radial distribution systems for minimization of real power loss and maximization of network savings using bio-inspired optimization algorithms

In this paper, two new algorithms are implemented to solve optimal placement of capacitors in radial distribution systems in two ways that is, optimal placement of fixed size of capacitor banks (Variable Locations Fixed Capacitor banks-VLFQ) and optimal sizing and placement of capacitors (Variable Locations Variable sizing of Capacitors-VLVQ) for real power loss minimization and network savings maximization. The two bio-inspired algorithms Bat Algorithm (BA) and Cuckoo Search (CS): search for all possible locations in the system along with the different sizes of capacitors, in which the optimal sizes of capacitor are chosen to be standard sizes that are available in the market. To check the feasibility, the proposed algorithms are applied on standard 34 and 85 bus radial distribution systems. And the results are compared with results of other methods like Particle Swarm Optimization (PSO), Harmonic Search (HS), Genetic Algorithm (GA), Artificial Bee Colony (ABC), Teaching Learning Based Optimization (TLBO) and Plant Growth Simulation Algorithm (PGSA), as available in the literature. The proposed approaches are capable of producing high-quality solutions with good performance of convergence. The entire simulation has been developed in MATLAB R2010a software.     

基于遗传-模拟退火算法的配电网电容器优化配置

随着配电网规模的不断扩大,传统的依照经验配置电容器的方法日显其局限性,具体表现在电容器容量配置得不足或过剩,更严重的情况是部分电容器需要投入时由于局部电压的限制而不能投入.将遗传-模拟退火算法用于解决配电网电容器优化配置问题,建立了相应的数学模型,目标函数为配电网有功网损费用、电容器的购置及安装费用总和最小,该算法将电容器的安装位置及安装容量离散化,并在初始方案种群产生和群体进化策略两方面对该算法作了改进,对一个30节点配电网的电容器优化配置结果表明了遗传-模拟退火算法的合理性和可行性.     

Shunt capacitor placement in radial distribution networks considering switching transients decision making approach

This paper provides a new approach in decision making process for shunt capacitor placement in distribution networks. The main core of the evaluation process is a multi-objective framework to allocate the capacitor banks. The power loss and the total harmonic distortion (THD) are the objective functions of the system under study in a long-term planning horizon. In order to select the executive plan introduced by using a multi-objective model, transient switching overvoltages have been considered. As the size and location of shunt capacitors may result in unacceptable overvoltages, the proposed technical decision making framework can be applied to avoid corresponding damages. In this paper, an iterative conventional power flow technique is introduced. This technique can be applied to evaluate THD for distribution networks as well as other power flow based objectives, such as power losses calculation and voltage stability assessment. The presented framework is a two stage one where at the first stage, a non-dominated sorting genetic algorithm (NSGA-II) augmented with a local search technique is used in order to solve the addressed multi-objective optimization problem. Then, at the second stage, a decision making support technique is applied to determine the best solution from the obtained Pareto front. In order to evaluate the effectiveness of the proposed method, two benchmarks are addressed in this paper. The first test system is a 9-bus distribution network and the second one is an 85-bus large scale distribution network. The simulation results show that the presented method is satisfactory and consistent with the expectation.     

Optimal capacitor placement in a radial distribution system using Plant Growth Simulation Algorithm

This paper presents a new and efficient approach for capacitor placement in radial distribution systems that determine the optimal locations and size of capacitor with an objective of improving the voltage profile and reduction of power loss. The solution methodology has two parts: in part one the loss sensitivity factors are used to select the candidate locations for the capacitor placement and in part two a new algorithm that employs Plant Growth Simulation Algorithm (PGSA) is used to estimate the optimal size of capacitors at the optimal buses determined in part one. The main advantage of the proposed method is that it does not require any external control parameters. The other advantage is that it handles the objective function and the constraints separately, avoiding the trouble to determine the barrier factors. The proposed method is applied to 10, 34, and 85-bus radial distribution systems. The solutions obtained by the proposed method are compared with other methods. The proposed method has outperformed the other methods in terms of the quality of solution.     

An efficient hybrid method for solving the optimal sitting and sizing problem of DG and shunt capacitor banks simultaneously based on imperialist competitive algorithm and genetic algorithm

Nowadays due to development of distribution systems and increase in electricity demand, the use of distributed generation (DG) sources and capacitors banks in parallel are increased. Determining the installation location and capacity are two significant factors affecting network loss reduction and improving network performance. This paper, proposes an efficient hybrid method based on Imperialist Competitive Algorithm (ICA) and genetic algorithm (GA) which can greatly envisaged with problems for optimal placement and sizing of DG sources and capacitor banks simultaneously. The objective function is power loss reduction, improving system voltage profile, increasing voltage stability index, load balancing and transmission and distribution relief capacity for both utilities and the customers.The proposed method is implemented on IEEE 33 bus and 69 bus radial distribution systems and the results are compared with GA/Particle swarm optimization (PSO) method. Test results show that the proposed method is more effective and has higher capability in finding optimum solutions.     

Bacterial foraging solution based fuzzy logic decision for optimal capacitor allocation in radial distribution system

This paper proposes a novel methodology for the optimal location and sizing of shunt capacitors in radial distribution systems. This method is based on a fuzzy decision making which using a new evolutionary method. The capacitor placement optimization problem includes: minimizing the cost of peak power, reducing energy loss and improving voltage profile. The installation node is selected by the fuzzy reasoning supported by the fuzzy set theory in a step by step procedure. Also an evolutionary algorithm known as bacteria foraging algorithm (BFA) is utilized in solving the objective multivariable optimization problem and the optimal node for capacitor placement is determined. The proposed approach is applied to 34-bus distribution system as a test study and the results are compared with previous method. The results show that this method provides more economic solution by reducing power losses, energy loss, total required capacitive compensation and show a good improvement in nodes voltage to be in the requested range. Comparison between the proposed method in this paper and similar methods in other research works shows the effectiveness of the proposed method for solving optimum capacitor planning problem.     

配电网电容器优化投切的改进模型及算法

配电网电容器优化投切的目的是在实时运行阶段有效降低电网的有功损耗,同时避免电容器过多投切造成损毁。文章研究了考虑投切次数限制的配电网电容器优化投切问题,针对现有静态模型的局限性和动态模型的复杂性,提出了目标函数中计及投切代价的优化模型,将全局动态优化问题解耦为分段静态优化问题,在有效控制电容器投切次数的基础上大大缩减了解空间的规模。针对此模型,采用改进粒子群优化算法进行求解。算例分析表明文中的模型和方法在实用性、可行性和计算速度等方面均有良好表现。     

MMC功率运行区域分析及环流切换控制策略

通过对模块化多电平换流器(MMC)动态特性和控制机理的分析,提出基于系统容量、电容电压波动阈值以及最大瞬时调制比的功率运行区域确定方法,并通过该方法对环流抑制和环流注入控制策略在不同子模块电容配置下的功率运行区域进行了比较分析。该方法可以优化子模块电容参数选取,避免过度冗余设计。此外,提出基于电压预测的环流控制器,使在不同工作点下可根据分析结果直接进行最优环流控制模式切换。对某单一桥臂子模块数为20的MMC系统进行仿真研究,结果验证了所提功率运行区域分析方法及其环流切换控制策略的正确性和有效性。     

Optimal capacitor placements in distribution systems. I. A newformulation and the overall problem

A novel formulation of the general capacitor placement problem taking into consideration practical aspects of capacitors, the load constraints, and the operational constraints at different load levels is presented. This formulation is a combinatorial optimization problem with a nondifferentiable objective function. A solution methodology based on an optimization technique (simulated annealing) is proposed to determine the locations where capacitors are to be installed, the types and sizes of capacitors to be installed, and the control settings of these capacitors at different load levels. The solution methodology can offer the global optimal solution for the general capacitor placement problem     

配电网变电站并列运行三绕组变压器无功补偿的经济分析

配电网变电站三绕组变压器的无功补偿大多数是在低压侧安装并联运行的单组或多组电容器,传统上电容器投入与否或投入几组是根据变压器电源侧的功率因数大小来控制。这种控制方法的缺点是:仅考虑功率因数提高减少了变压器损耗的因素,而忽视了投入电容器介质损耗增大的因素。讨论了配电网两台三绕组变压器中压侧分列低压侧并列运行时,并联无功补偿电容器的经济运行;根据变压器损耗与电容器介质损耗之和最小的原则分析计算投切电容器组的临界负载,发现在某些条件下提高功率因数不仅不节电反而浪费电量;并在此基础上提出判断电容器经济运行的方法:最后举例说明了经济运行的节电效果。     

Optimal shunt capacitor allocation by fuzzy dynamic programming

A new approach using fuzzy dynamic programming to decide the optimal location and size of compensation shunt capacitors for distribution systems with harmonic distortion is proposed. To decide the optimal capacitor placement, a fuzzy dynamic programming model in which the real power loss, voltage deviation, and harmonic distortion are all expressed in fuzzy set notation is developed. The problem is formulated as a fuzzy dynamic programming of the minimization of real power loss and capacitor cost under the constraints of voltage limits and total harmonic distortion. A simple algorithm that is based on the fuzzy set is proposed to determine an optimal solution. This algorithm greatly reduces the effort of finding the optimal location via an exhaustive search. A practical distribution system is selected for computer simulation to test the efficiency of the proposed fuzzy dynamic programming method. It is found that the system loss and harmonic distortion can be reduced very effectively by this proposed algorithm.     

主馈线和分支线路相结合的配电网无功补偿

针对配电网负荷多变的特点,提出采用电容器对10kV配电网进行无功补偿时,采用分支线路末端配电变压器低压侧和主馈线相结合的优化补偿方式。以系统有功网损、电容器的安置费用加权最小为目标函数。根据配电网辐射状树形分布特征,首先在分支线路末端以提高线路功率因数确定电容器的补偿容量及其类型,然后在主馈线上依无功负荷的分布情况再确定电容器补偿的最佳位置和容量。潮流计算采用配电网广泛使用的前推回代法。最后,以实际电网为例,说明了该算法的可行性和优越性。     

Oppositional krill herd algorithm for optimal location of capacitor with reconfiguration in radial distribution system

The delivery of power from sources to the consumer points is always accompanied of power losses. Basically, active losses in distribution systems can be reduced by optimal reconfigurations of the network. Optimal capacitor allocation problem in reconfigured distribution network is a challenge of researchers for several decades. This paper presents a computationally efficient methodology namely, krill herd (KH) algorithm to find optimal location of capacitor and optimal reconfiguration in order to minimize real power loss of radial distribution systems. Moreover, the opposition based learning (OBL) concept is integrated with KH algorithm for improving the convergence speed and simulation results. In order to show the usefulness and supremacy, the conventional KH and proposed oppositional KH (OKH) algorithms are tested on 33-bus and 69-bus radial distribution networks. The simulation results of the proposed methods are compared with fuzzy multi-objective approach and non dominated sorting genetic algorithm (NSGA). The solution results show that OKH technique could generate better quality solutions and better convergence characteristics than those obtained by conventional KH algorithm and other existing optimization techniques available in the literature. Results also show the robustness of the proposed methodology to solve reconfigured distribution network (RDN) problems.     

Simultaneous placement of distributed generation and capacitors in distribution networks considering voltage stability index

With regard to widespread use of distributed generation in distribution network, its technical impacts in distribution network should be thoroughly analyzed. In this paper simultaneous placement of distributed generation (DG) and capacitor is considered in radial distribution network with different load levels. The objectives of the problem are reduction of active and reactive power loss, reduction of energy loss and improvement of voltage profile. Also effect of capacitor and DG on voltage stability improvement has been considered in the objective function. Memetic algorithm is used to find optimal solutions. This algorithm is combinatorial form of local search and genetic algorithm. The performance of the proposed method is assessed on a test distribution network.     

10kV配电网电容器的优化配置规划决策

配电网电容器优化配置规划决策系统从降损节能、改善电能质量的角度,侧重依据电网实际运行状态,利用智能分组算法,保证在各种运行条件下都能对电网无功补偿、电压调节提供最优的补偿容量组合;并针对当前的无功补偿投资预算,给出经济效益最佳的配置方案组合。配电网电容器优化配置规划决策系统科学、合理地解决了配电网电容器的补偿容量、补偿地点和补偿分组问题,算例及分析表明了该分组算法应用于配电网电容器优化配置的有效性和实用性。     

主动配电网储能系统的多目标优化配置

储能系统在平滑间歇式能源功率波动、削峰填谷、改善电压质量以及提供灵活的功率调节等方面都发挥了巨大的作用。主动配电网能否实现对间歇性可再生能源进行完整消纳以及网络优化运行,在很大程度上依赖于主动配电网的储能系统配置是否合理。文中从削峰填谷能力、电压质量以及功率主动调节能力3个方面建立主动配电网储能系统的多目标优化配置模型,并使用带权极小模理想点法求解该多目标优化问题,避免求解多目标规划问题复杂的Pareto前端曲面,简化了问题求解的复杂度。最后,通过算例验证了所提模型及其求解方法的有效性。     

配电网无功补偿的动态优化算法

配电网无功补偿动态优化的目的是在考虑负荷变化和电容器操作次数约束的条件下,求得各节点电容器的最优动作时间和投入容量。该文将动态优化问题描述为变约束优化问题,并提出一种求解算法。算法先将动态优化问题分解为一系列单节点电容器动态优化子问题,然后通过迭代求解一系列子问题的方式得到整个动态优化问题的最优解。由于给出的单节点电容器动态优化子问题的求解算法可以在变约束条件下搜索到子问题的最优解,而且在迭代求解过程中电容器的投入容量和动作时问都可以得到修正,因此使整个动态优化问题能得到更好的优化结果。算例表明,提出的算法是可行和有效的。     

基于有效生成初始种群的配电网无功规划优化遗传算法

现有遗传算法用于配电网无功规划优化时,初始种群的产生一般是在人为设定补偿点个数及其补偿组数的条件下进行,这使初始种群包含很大比例的无效解,并导致解空间太大而造成寻优速度缓慢和效率不高。基于一般遗传算法,根据节点优化编号和辐射状配电网特点,提出了一种既有序又随机的方法。该方法可动态确定各节点无功补偿的组数上限及初始补偿组数,可按优化编号由大到小的顺序对补偿点进行无功补偿,且后补偿时的最大补偿组数自动考虑了先前补偿电容器的影响,同时每个补偿点组数的选择是在0和最大补偿组数之间随机产生的。这种方法克服了现有靠经验人工事先设置合理补偿节点总数及各补偿节点组数上限的困难,并使由此生成的初始种群包含尽可能多的可行解。另外,对可能在一个节点补偿多组标准电容器的问题提出了一种辅助的有效实用方法。IEEE33节点系统和多个实际算例的计算结果表明,上述方法用于求解无功规划优化问题可提高计算精度和速度。