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.     

遗传算法在电力系统无功优化中的应用

在利用遗传算法求解电力系统的无功优化问题，在优化编码和变异概率取值两个方面进行了研究，进一步推动了遗传算法在实际系统优化问题中的应用。在电力系统无功优化这个具有多局部极小值的寻优方面，把遗传算法所求得的无功优化结果和传统的基于梯度寻优方向的非线性规划法所得的优化结果进行比较，指出了遗传算法在处理非连续的和非平滑的函数寻优方面优于传统的寻优方法，具备全局寻优的能力。     

Optimal clustering of power networks using genetic algorithms

This paper presents a new method for optimal network decomposition based on genetic algorithms (GAs). GAs present a powerful, globally oriented optimization method which exploits the mechanism of natural genetics, working on populations of candidate solutions in an effort to reach optima or near optima. Test results on IEEE standard networks are given and compared with those using simulated annealing. The genetic algorithm approach is found to produce significantly better solutions.     

配电网络重构的研究

总结了求解配电网重构的各种方法。指出由于组合数学的特性,数学优化理论不适用于配电网重构;基于模拟退火方法的配电网重构算法可以获得全局最优解,但存在算法依赖参数和计算量大的缺点;基于人工神经网络的算法,其精度取决于样本,获得完整样本困难,而且训练样本的时间较长;遗传算法的很多特点适于求解配电网重构的问题,如果能结合配电网重构的特点对算法收敛性进一步研究,提高其速度,则将在配电网重构中得到更好的应用;模糊数学和专家系统必须依赖于其他技术的发展;最优流模式和基于开关交换的算法不能保证得到全局最优解,但与启发式规则结合后,可以较快地得到满意的结果,是目前解决配电网重构的有效算法。     

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.      

区域电力系统最优备用容量模型与算法

建立实现备用容量最小的区域互联电力系统最优备用容量数学模型,推算多区域互联电力系统的联络线功率增量方程,以及区域互联电力系统频率偏差与区域备用容量的关系表达式。针对问题的具体特点,运用自适应免疫遗传算法对该模型进行求解,充分考虑频率偏差、负荷的随机波动以及区域互联系统运行的各种可靠安全约束,分别对独立的电力系统以及通过交直流联络线互联组成的区域电力系统进行仿真计算,可得到一天中24个时段的弹性备用容量。独立电力系统的算例表明：随着电力系统规模的扩大以及装机容量的逐步增大,最优备用容量占最大负荷的比例会逐步减小,可以减小0.395%~9.366%。对区域互联系统的算例表明：当区域系统互联时可以在一定程度上减小区域系统的备用容量,互联区域系统比各个独立系统的备用容量要减少1.036%~1.858%,节约了互联区域电力系统的成本,在一定程度上提高了区域互联系统运行的经济性。实例计算结果验证了所提模型的合理性、所提方法的可行性。     

A New Affine Arithmetic-Based Optimal Network Reconfiguration to Minimize Losses in a Distribution System Considering Uncertainty Using Binary Particle Swarm Optimization

Abstract

In the present work, Binary Particle Swarm Optimization (BPSO) based optimal re-configuration for balanced and unbalanced radial distribution networks using Affine Arithmetic (AA), with uncertainty in generation and load, is proposed to minimize the system losses. An expression for three phase real affine power loss is derived with partial deviations of real power loss in lines with respect to power injections in other buses and also with respect to power injections in other phases in case of unbalanced distribution systems. The major contribution of the present work is the application of AA based optimal network reconfiguration, to both balanced and unbalanced radial distribution networks with uncertainty. The proposed method is tested on IEEE 16, 33, 85 and 119 bus balanced distribution systems and an unbalanced 123 bus system with Distributed Generation (DG) connected at some buses. The optimal loss intervals obtained by the proposed method are compared with that obtained by Interval Arithmetic (IA) and Monte Carlo (MC) simulations based methods. The simulation results show that proposed AA based analysis gives an optimal reconfiguration, for both balanced and unbalanced radial distribution systems with uncertainty as compared to existing IA based method.     

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.     

Improved Harmony Algorithm and Power Loss Index for optimal locations and sizing of capacitors in radial distribution systems

In this paper, an Improved Harmony Algorithm (IHA) is proposed for optimal allocations and sizing of capacitors in various distribution systems. Initially, Power Loss Index (PLI) is introduced to get the highest candidate buses for installing capacitors. Then, the proposed IHA is employed to decide the most optimal locations of capacitors and their sizing from the elected buses by PLI. The objective function is designed to reduce the total cost and losses and consequently, to increase the net saving per year. The proposed algorithm is tested on three different radial distribution systems. The obtained results via the proposed algorithm are compared with others to highlight its benefits. Moreover, the results are introduced to verify the effectiveness of the suggested algorithm under different loading conditions.     

Improved Harmony Algorithm for optimal locations and sizing of capacitors in radial distribution systems

In this paper, an Improved Harmony Algorithm (IHA) is proposed for optimal allocations and sizing of capacitors in various distribution systems. First the most candidate buses for installing capacitors are suggested using Loss Sensitivity Factors (LSF) and Voltage Stability Index (VSI). Then the proposed IHA is employed to deduce the size of capacitors and their locations from the elected buses. The objective function is designed to reduce the total cost and consequently, to increase the net saving per year. The proposed algorithm is tested on 85 and 118 bus radial distribution systems. The obtained results via the proposed algorithm are compared with others to highlight their benefits. Moreover, the results are introduced to verify the effectiveness of the suggested algorithm to minimize the losses and total cost and to enhance the voltage profiles and net saving for various distribution systems and different loading conditions.     

Optimal Power Flow using Glowworm Swarm Optimization

An important objective of the Optimal Power Flow (OPF) problem is to minimize the generation cost and keep the power outputs of generators, bus voltages, bus shunt reactors/capacitors and transformer tap settings in their secure limits. Solving this OPF problem using classical methods suffer from the disadvantages of highly limited capability to solve the practical large scale power system problems. To overcome the inherent limitations of conventional optimization techniques, Swarm Intelligence (SI) methods have been developed. However, the environmental concern, dictate the minimization of emissions of the thermal plants. Individually, if one objective is optimized, other objective is compromised. Hence, Multi-Objective Optimal Power Flow (MO-OPF) problem has been formulated in this paper. Swarm Intelligence methods, such as Particle Swarm Optimization (PSO) and Glowworm Swarm Optimization (GSO) have been used to solve the OPF problem with generation cost and emission minimizations as objective functions. The effectiveness of the proposed algorithms are tested on IEEE 30 bus and practical Indian 75 bus systems for cost minimization as objective function, and IEEE 30 bus test system for minimization of cost and emission as objectives. The results obtained from both the networks, the PSO and GSO are compared with each other based on different parameters.     

运用遗传算法选择性消除多电平逆变器新拓扑中的谐波

目前,传统的PWM技术和选择性谐波消除问题得到了广泛研究。提出运用遗传算法来选择性消除多电平逆变器新拓扑中的谐波。新拓扑与传统结构相比较有减少开关数量的优势,并且可以把输出电平的数量扩展到任何值,该系统减轻了执行机构的复杂性,缩短了计算时间。对于每一个被要求消除的谐波,如果最优开关切换角存在,搜索过程中,遗传算法都可以找到一组最佳开关切换角。模拟仿真和实验结果都验证了新拓扑适合于不同电平数量的逆变器和不同次数的谐波消除。     

Swarm intelligence based algorithms for reactive power planning with Flexible AC transmission system devices

In the proposed work, authors have applied swarm intelligence based algorithms for the effective Co-ordination of Flexible AC transmission system (FACTS) devices with other existing Var sources present in the network. IEEE 30 and IEEE 57 bus systems are taken as standard test systems. SPSO (Simple Particle Swarm Optimization) and other two swarm based intelligence approaches like APSO (Adaptive Particle Swarm Optimization) and EPSO (Evolutionary Particle Swarm Optimization) are used for the optimal setting of the Var sources and FACTS devices. The result obtained with the proposed approach is compared with the result found by the conventional RPP (Reactive power planning) approach where shunt capacitors, transformer tap setting arrangements and reactive generations of generators are used as planning variables. It is observed that reactive power planning with FACTS devices yields much better result in terms of reducing active power loss and total operating cost of the system even considering the investment costs of FACTS devices.     

Flower Pollination Algorithm and Loss Sensitivity Factors for optimal sizing and placement of capacitors in radial distribution systems

In this paper, Flower Pollination Algorithm (FPA) is proposed for optimal allocations and sizing of capacitors in various distribution systems. First the most candidate buses for installing capacitors are suggested using Loss Sensitivity Factors (LSF). Then the proposed FPA is employed to deduce the locations of capacitors and their sizing from the elected buses. The proposed algorithm is tested on 10, 33 and 69 bus radial distribution systems. The obtained results via the proposed algorithm are compared with others to highlight the benefits of the proposed algorithm in reducing total cost and maximizing the net saving. Moreover, the results are introduced to verify the effectiveness of the proposed algorithm to enhance the voltage profiles for various distribution systems.     

Cogeneration systems planning using structured genetic algorithms

This paper proposes a new approach to plan cogeneration systems, that of distributed energy systems. The proposed approach uses structured genetic algorithms. Cogeneration systems planning provides optimal allocation of cogeneration systems, a layout of the pipeline network structure for distributing heat energy between cogeneration systems and demand areas, and optimal heat and electric energy supply to meet the energy demands. The planning is formalized as a combinatorial optimization problem with minimizing cost of energy supply as its objectives. The traditional solution method is based on mathematical programming methods. But it is difficult to get an optimal solution as the number of areas increases because of combinatorial explosion and nonlinearity. This paper describes a new method to solve the cogeneration systems planning based on genetic algorithms. The solution of the cogeneration systems planning problem has a network structure. The proposed method applies structured genetic algorithms whose genotype has a tree structure to represent a network structure. The characteristics of the proposed method are analyzed by applying the new method to empirical data of the area around station K. © 1997 Scripta Technica, Inc. Electr Eng Jpn 119(2): 26–35, 1997     

A recursive power flow method for radial distribution networks: Analysis,solvability and convergence

A new Recursive Power Flow (RPF) algorithm for balanced/unbalanced radial distribution systems is proposed in this paper. Four generalized constant matrixes, that are calculated based on the graph theory, are used to obtain the power flow solution. These matrixes completely describe topology of a distribution system and models of its elements. In this method, each branch of a distribution system is considered as a bipolar. The method is able to consider detailed model of the elements. Solvability and convergence properties of the method have been mathematically presented. The method has been studied on the standard 16, 33 and 69-bus balanced distribution systems. In addition, this method is tested on 4 and 13-bus unbalanced standard distribution systems. Also, the method is tested on a 1337-bus real distribution system in Lorestan Electrical Power Distribution Company, Iran. The simulation results demonstrate the accuracy, computational efficiency and robustness of the proposed method.     

A Multi-objective Optimization for Sizing and Placement of Voltage-controlled Distributed Generation Using Supervised Big Bang–Big Crunch Method

Abstract—This article presents an efficient multi-objective optimization approach based on the supervised big bang–big crunch method for optimal planning of dispatchable distributed generator. The proposed approach aims to enhance the system performance indices by optimal sizing and placement of distributed generators connected to balanced/unbalanced distribution networks. The distributed generation units in the proposed algorithms are modeled as a voltage-controlled node with the flexibility to be converted to a constant power node in the case of reactive power limit violation. The proposed algorithm is implemented in the MATLAB (The MathWorks, Natick, Massachusetts, USA) environment, and the simulation studies are performed on IEEE 69-bus and IEEE 123-node distribution test systems. Validation of the proposed method is done by comparing the results with published results obtained from other competing methods, and the consequent discussions prove the effectiveness of the proposed approach.     

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 three-phase power flow method for real-time distribution systemanalysis

This paper presents a three-phase power flow solution method for real-time analysis of primary distribution systems. This method is a direct extension of the compensation-based power flow method for weakly meshed distribution systems from single phase to three-phase, with the emphasis on modeling of dispersed generation (PV nodes), unbalanced and distributed loads, and voltage regulators and shunt capacitors with automatic local tap controls. The method proposed here is capable of addressing these modeling challenges while still maintaining a high execution speed required for real-time application in distribution automation systems. The paper also includes test results from the application of a computer program developed based on the proposed method to large primary electric distribution systems     

改进的相分量法求解电力系统复杂故障新算法

针对基于对称分量法的传统故障分析方法求解复杂故障尤其是参数不对称电力系统复杂故障时,序网连接复杂、难以求解的问题,提出了一种基于多端口理论与优化的相分量系统网络模型求解具有不对称参数的电力系统复杂故障的新算法。该方法利用矩阵的对角化变换对传统相分量法进行优化,以减小计算量,并与多端口理论相结合,推导出一种既适用于各种类型简单故障,又适用于多重复故障计算的计算机通用数学模型。模型简单实用,通用性强。对比编程计算结果与EMTPE仿真结果,证明该算法准确有效。