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 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.     

Optimal Allocation of Distributed Generation and Shunt Capacitors for the Reduction of Total Voltage Deviation and Total Line Loss in Radial Distribution Systems Using Binary Collective Animal Behavior Optimization Algorithm

This article presents a novel binary collective animal behavior algorithm to solve the problem of optimal allotment of distributed generation sets and shunt capacitors in radial distribution systems. Simultaneous sizing and placement of distributed generation units and shunt capacitors in distribution systems is a very complex optimization task, because it is a problem of combinatorial analysis with mixed-integer and binary variables and hard restrictions. With the objective of optimal allotment of shunt capacitor banks and distributed generations, a binary collective animal behavior algorithm optimizes the total line loss, or the total voltage deviation separately in a distribution system, by optimally and simultaneously allocating capacitor banks and distributed generations of optimal ratings, considering the topology of a radial distribution network. The binary collective animal behavior algorithm is applied on various balanced IEEE radial distribution networks. The results are compared to those of a conventional binary particle swarm optimization algorithm to establish the optimization superiority of binary collective animal behavior algorithm.     

电容器实时优化投切的最优匹配注入流法

为了提出一种用于电网无功补偿优化的通用的、规范化的解析算法，该文从回路分析法和电路叠加定理等电路的基本原理出发，导出了一个崭新的概念——最优匹配注入流。基于最优匹配注入流，开发出一个用于优化电容器投切的高效算法。该算法可应用于输电网和配电网的电容器优化中，也可应用于发电机和电容器共同参与的电网无功优化。文中提出的算法可对系统有功损耗进行优化的同时消除支路负载越限。整个计算过程包含若干次潮流计算和最优匹配注入流的计算，因而计算效率很高。该算法不仅可以直接应用于电网规划，而且满足实时控制的要求。该文还把电容器优化投切这类组合优化问题转换为一系列的递推电路问题，为求解该类问题提供了一种新的思考方法。另外，最优匹配注入流也可以应用于电容器的安装地点和容量选择的优化问题。     

Optimal Placement and Sizing of Inverter-Based Distributed Generation Units and Shunt Capacitors in Distorted Distribution Systems Using a Hybrid Phasor Particle Swarm Optimization and Gravitational Search Algorithm

Abstract

In this paper, a novel hybrid population-based meta-heuristic algorithm, called the hybrid Phasor Particle Swarm Optimization and Gravitational Search Algorithm (PPSOGSA), is proposed to solve the problem of optimal placement and sizing of inverter-based distributed generation (DG) units and shunt capacitors in radial distribution systems with linear and non-linear loads. The objective of the problem is reduction of active power losses considering constraints of the fundamental frequency active and reactive power balance, RMS voltage, and total harmonic distortion of voltage (THD_V) at each bus of the network, as well as the branch flow constraints. The performance of the PPSOGSA-based approach is evaluated on the standard IEEE 33- and 69-bus test systems under sinusoidal and non-sinusoidal operating conditions. Compared to the original PPSO and GSA and other algorithms commonly used in the optimal sitting and sizing problem of DG units and shunt capacitors, it is found that the proposed algorithm has yielded better results.     

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.     

Stability region and radius in electric power systems under sustained random perturbations

Two concepts are proposed to characterize the behavior of stochastic systems under sustained random perturbations in time: Using Lyapunov exponents we define the region where an electric power system can be operated under random perturbations without losing stability; and we characterize the maximum perturbation size that a system can sustain. The proposed methodology is applied to international test systems of nine and thirty-nine buses.     

A Multi-objective Shuffled Bat algorithm for optimal placement and sizing of multi distributed generations with different load models

In this paper a new and efficient hybrid multi-objective optimization algorithm is proposed for optimal placement and sizing of the Distributed generations (DGs) in radial distribution systems. A Multi-objective Shuffled Bat algorithm is proposed to evaluate the impact of DG placement and sizing for an optimal improvement of the distribution system with different load models. In this study, the ideal sizes and locations of DG units are found by considering the power losses, cost and voltage deviation as objective functions to minimize. Furthermore, the study is verified with voltage dependent load models like industrial, residential, commercial and mixed load models. The feasibility of the proposed technique is verified with the 33 bus distribution network and also the qualitative comparisons against a well-known technique, known as Non-dominated Sorting Genetic Algorithm II (NSGA-II) is done and results are presented.     

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.     

多负荷水平下的配电网无功优化规划方法

针对目前多负荷水平无功优化方法计算相对复杂,实用难度较大等不足,提出了结合免疫算法和最优覆盖理论的配网无功优化规划的新方法。该方法通过改进的免疫算法,在最大负荷水平下获得无功最优补偿点和总补偿容量;运用聚类分析思想处理历史负荷数据,简化和统一数据量;根据最优覆盖原理,考虑折算生成各补偿点的无功需求概率分布曲线,以降损和提高电容利用率为目标,最终实现各补偿点的电容分组配置。实际配网应用中的良好效果,充分验证了所提方法计算便捷,配置实用的优点。     

Optimal siting and sizing of distributed generation accompanied by reconfiguration of distribution networks for maximum loss reduction by using a new UVDA-based heuristic method

A great number of methods have been proposed for distributed generation (DG) placement in distribution networks to minimize the power loss of Medium Voltage (MV) lines. However, very few researches have been done for network configuration in parallel with the DG siting and sizing for the maximum system loss reduction. In this paper, a heuristic method based on “uniform voltage distribution based constructive reconfiguration algorithm” (UVDA) is proposed for the simultaneous reconfiguration and DG siting and sizing. The results obtained from the application of the proposed method on two well-known distribution networks and a real network clearly verify the robustness of the contributed technique. The simulation results demonstrate that the proposed approach is able to find the best solution of the problem found so far. Also, the presented method is applicable to real large-scale distribution systems to find the optimal solution in a very short period of time.     

Optimal allocation of capacitors in unbalanced multi-converter distribution systems: A comparison of some fast techniques based on genetic algorithms

Genetic algorithms (GAs) are widely used for optimal allocation of capacitors in distribution systems. When dealing with large-scale systems, such as in case of unbalanced multi-converter distribution systems, these algorithms can require significant computational efforts, which reduce their effectiveness. In order to reduce processing time for GAs and simultaneously maintain adequate levels of accuracy, methods based on the reduction of the search space of GAs or based on micro-genetic algorithms have been proposed. These methods generally guarantee good solutions with acceptable levels of computational effort. In this paper, some fast, GA-based methods are compared and applied for solving the problem of optimal sizing and siting of capacitors in unbalanced multi-converter distribution systems. The algorithms have been implemented and tested on the unbalanced IEEE 34-bus test distribution system, and their performances have been compared with the performance of the simple genetic algorithm technique.     

Optimal placement and sizing of distributed generators and shunt capacitors for power loss minimization in radial distribution networks using hybrid heuristic search optimization technique

This paper attempts to minimize power losses in radial distribution networks and facilitates an enhancement in bus voltage profile by determining optimal locations, optimally sized distributed generators and shunt capacitors by hybrid Harmony Search Algorithm approach. To overcome the drawback of premature and slow convergence of Harmony Search Algorithm (HSA) over multi model fitness landscape, the Particle Artificial Bee Colony algorithm (PABC) is utilized to enhance the harmony memory vector. In the first approach, the formulation echoes the determination of loss sensitivity factor to decide the sensitive nodes and thereafter decides on the optimal rating through the use of hybrid Algorithm. The second approach encircles the role of hybrid Algorithm to search for both the optimal candidate nodes and sizing of compensating devices by significant increase in loss reduction with the former approach. The procedure travels to examine the robustness of the proposed hybrid approach on 33 and 119 node test systems and the result outcomes are compared with the other techniques existing in the literature. The simulation results reveal the efficiency of the proposed hybrid algorithm in obtaining optimal solution for simultaneous placement of distributed generators and shunt capacitors in distribution networks.     

基于有功无功联合调整的动态潮流

提出了一种新型潮流算法,可同时考虑无功功率的区域平衡以及系统负荷变化所产生的净加速功率,并通过有功和无功的联合调整以获得更合理的潮流结果。计算过程取消了常规潮流算法定义的节点类型,使所有节点均参加有功和无功迭代,避免了人为确定节点类型对潮流分布的不良影响。最后通过IEEE30节点系统将所提算法与常规潮流算法、动态潮流算法进行了比较,结果表明所提算法能够改善系统的有功和无功功率分布。     

A parallel distributed computing framework for Newton–Raphson load flow analysis of large interconnected power systems

This paper proposes a simple parallel and distributed computing framework for the conventional Newton–Raphson load flow (NRLF) solution of large interconnected power systems. The proposed approach is based on message-passing distributed-memory architecture with separate workstations, and involves the piecewise analysis of power systems utilizing the network tearing procedure. The NRLF solution method, applied to each torn system at the selected buses, employs the matrix inversion lemma consisting of the factorization, forward elimination and back substitution procedures. The computational requirements of the state-of-the art parallel algorithm to obtain the correction vector involved in the back substitution procedure is reduced with the proposed approach in which the back substitution is carried out in parallel taking into account the split buses, rather than the order in which the forward elimination is performed. The investigations are carried out on the IEEE 118 bus standard test system in a Redhat Linux based 100 Mbps Ethernet LAN environment. The investigations reveal that the proposed method is significantly faster than the conventional NRLF and also the NRLF based on the state-of-the-art parallel algorithm, and thus finds potential applications for the real-time load flow solution of both regulated and deregulated power systems distributed over large geographical areas.     

Quasi-Oppositional Swine Influenza Model Based Optimization with Quarantine for optimal allocation of DG in radial distribution network

Optimal allocation of Distributed Generations (DGs) is one of the major problems of distribution utilities. Optimum locations and sizes of DG sources have profoundly created impact on system losses, voltage profile, and voltage stability of a distribution network. In this paper Quasi-Oppositional Swine Influenza Model Based Optimization with Quarantine (QOSIMBO-Q) has been applied to solve a multi-objective function for optimal allocation and sizing of DGs in distribution systems. The objective is to minimize network power losses, achieve better voltage regulation and improve the voltage stability within the frame-work of the system operation and security constraints in radial distribution systems. The limitation of SIMBO-Q algorithm is that it takes large number of iterations to obtain optimum solution in large scale real systems. To overcome this limitation and to improve computational efficiency, quasi-opposition based learning (QOBL) concept is introduced in basic SIMBO-Q algorithm. The proposed QOSIMBO-Q algorithm has been applied to 33-bus and 69-bus radial distribution systems and results are compared with other evolutionary techniques like Genetic Algorithm (GA), Particle Swarm Optimization (PSO), combined GA/PSO, Teaching Learning Based Optimization (TLBO) and Quasi-Oppositional Teaching Learning Based Optimization (QOTLBO). Numerical studies represent the effectiveness and out-performance of the proposed QOSIMBO-Q algorithm.     

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.     

Optimal capacitor placement in distorted distribution networks with different load models using Penalty Free Genetic Algorithm

Genetic Algorithm with special constraint handling procedure is proposed for the discrete optimization problem of capacitor placement and sizing in distribution system for cost reduction and power quality improvement. We use gene encoding that enables simple integer representation of possible different number of capacitors of various standard sizes to be placed on a bus. A pair-wise comparison in tournament selection operator is used so that it does not require any penalty parameter tuning, thus avoiding the most difficult aspect of the selection of appropriate penalty parameters.Proposed Penalty Free Genetic Algorithm (PFGA) is tested on 18-bus, 69-bus and 141-bus systems and the obtained results are better than the results from other methods. Simulations with different load models are also performed. It is shown that load models where active and reactive loads are voltage dependent, such as residential, commercial and industrial, constant Z and constant I model lead to completely different solutions. Therefore, careful load modeling should be put in place in order to obtain more realistic picture of the total savings.     

基于改进蚁群算法的分布式电源容量优化配置

以实现配电网经济成本最低和环境污染最小为目的,设计了基于改进蚁群算法的分布式电源容量优化配置方法。首先,考虑节点环境不同因素搭建含多类分布式电源的配电网综合运行模型,明确了系统运行约束以及功率约束;其次,通过对信息素进行约束提出了改进型蚁群算法,以提高蚁群算法的收敛精度以及速度;之后,设计了基于改进型蚁群算法的配电网容量优化配置流程;最后,在Matlab平台上实现了中压配电网系统的容量优化以及选址,与相关案例结果对比分析验证了所提出方法的有效性。