A novel codification for meta-heuristic techniques used in distribution network reconfiguration

In this paper, a new codification is proposed for various meta-heuristic techniques to solve the reconfiguration problem of distribution networks. The full potential of meta-heuristic algorithms can be exploited by their efficient codification using some engineering knowledge base. The distribution system reconfiguration problems are non-differentiable, mixed integer and highly complex combinatorial in nature. In addition, the radiality constraint typically increases the intricacy of the meta-heuristic evolutionary algorithms. The proposed codification is based upon the fundamentals of graph theory which not only restricts the search space but also avoids tedious mesh checks. The proposed codification is computationally efficient and guarantees to generate only feasible radial topologies all times. The proposed method has been tested on three different test distribution systems and the results are promising.     

Optimal reconfiguration of distribution systems with representation of uncertainties through interval analysis

The present work presents an approach for optimal reconfiguration of electrical distribution systems (EDS) to minimize energy losses considering uncertainties in the load demand and in the wind based distributed generation (DG). The optimization algorithm applied to solve the reconfiguration problem is based on the bio-inspired metaheuristic Artificial Immune Systems (AIS). An interval power flow model is used to obtain an interval energy loss from the representation of the uncertainties. The interval loss is used to guide the AIS algorithm through the search space. Network and operational constraints as the radiality and connectivity of the network as well as different load levels are considered. Well-known test systems are used to assess the impact of the uncertainties representation in the reconfiguration problem.     

Distribution system reconfiguration for loss minimization using modified bacterial foraging optimization algorithm

In this paper the network reconfiguration problem is formulated as non-linear objective optimization problem. The proposed solution to this problem is framed as a non-linear combinatorial optimization problem and status of switches is non-differentiable which is solved using modified bacterial foraging algorithm, the algorithm is modified for better convergence. The modified bacterial foraging algorithm is described in a general context and then applied specifically to the network reconfiguration problem. This program was tested on 16 bus, 33 bus & 69 bus test systems. The test results proved that the efficiency of modified bacterial foraging algorithm is better than other existing methodology.     

Reconfiguration of distribution networks to minimize loss and disruption costs using genetic algorithms

In this paper a computational implementation of an evolutionary algorithm (EA) is shown in order to tackle the problem of reconfiguring radial distribution systems. The developed module considers power quality indices such as long duration interruptions and customer process disruptions due to voltage sags, by using the Monte Carlo simulation method. Power quality costs are modeled into the mathematical problem formulation, which are added to the cost of network losses. As for the EA codification proposed, a decimal representation is used. The EA operators, namely selection, recombination and mutation, which are considered for the reconfiguration algorithm, are herein analyzed. A number of selection procedures are analyzed, namely tournament, elitism and a mixed technique using both elitism and tournament. The recombination operator was developed by considering a chromosome structure representation that maps the network branches and system radiality, and another structure that takes into account the network topology and feasibility of network operation to exchange genetic material. The topologies regarding the initial population are randomly produced so as radial configurations are produced through the Prim and Kruskal algorithms that rapidly build minimum spanning trees.     

配电网重构的逐级开关状态互换法

配电网重构是一个多目标、多约束、离散的非线性组合优化问题。根据配电网的特点,结合开关交换原理和网络构建算法,提出了开关状态互换的概念,并对其实现优化的原理进行了详细分析,表明可以收敛到最优解。利用启发信息简化寻优途径,在求解过程中运用禁忌思想,避免不必要的重复计算,大大加快收敛速度。将配电网供电恢复和优化重构统一考虑,并考虑了电容器的投切,为运行人员提供满足系统电压、容量和拓扑约束的配电网运行结构和开关操作列表,构建了配电网的优化运行方式。算例表明该算法是有效的。     

最小化运行费用的时变重构全局优化算法

该文提出了一种以运行费用最小为目标的时变重构全局优化算法。将时变重构问题分解为多个静态重构子问题，使用核心模式遗传最短路算法(CSGSA)分别求解每个子问题，得出候选放射状网络结构，并使用动态规划，根据各子问题的结果求解全局最优的时变重构策略。算法还对开关操作次数约束进行了处理，使之不影响动态规划的全局最优性。所提算法是配电网络实时调度，规划和离线分析的有效工具。     

考虑环网检测的配电网拓扑重构遗传算法

提出了一种基于遗传算法的配电网自动优化重构方法。由于配电网拓扑约束的限制(连通辐射状网络),遗传算法在解决配电网重构问题过程中,可能产生大量不可行解。针对该问题,首先提出了一种快速"环网和孤立节点"检测算法,可检测进化过程中产生的解是否满足配电网拓扑约束的要求;其次,提出了一种基于拓扑搜索的初始种群自动形成算法,该算法除可用于初始种群的形成外,还可用于生成新的解以替代遗传进化过程中产生的不可行解。为了提高遗传算法的收敛性能,提出了一种定向变异的遗传算子,该算子不仅可保证经变异运算后产生的个体满足配电网拓扑约束的要求,而且可保证该个体为本次变异操作可产生的最优解。该算法的提出提高了遗传算法解决重构问题的自动化程度和收敛性能。以IEEE 33节点、PGE 69节点和119节点系统为例对方法进行了测试,验证了该方法的有效性。     

计及分布式电源接入的配电网重构

分布式电源的接入使得配电网重构需要考虑更多的安全因素。基于配电网支路潮流模型,建立以重构周期内网络有功损最低,以满足分布式电源接入下网络运行安全为约束的配电网重构。为有效求解该重构数学模型,利用凸松弛方法将原问题中二次项进行松弛,使之形成混合整数二阶锥规划形式,从而可利用YALMIP商业软件进行高效求解。最后,通过改进的IEEE 33节点测试系统进行仿真分析,并与现有基于粒子群算法及启发式算法的配电网重构方法进行对比,结果表明基于凸优化技术的重构结果不仅能够有效避免算法陷于局部最优,而且稳定性好、计算效率高。     

Path-based distribution network modeling: application to reconfiguration for loss reduction

This paper is devoted to efficiently modeling the connectivity of distribution networks, which are structurally meshed but radially operated. A new approach, based on the "path-to-node" concept, is presented, allowing both topological and electrical constraints to be algebraically formulated before the actual radial configuration is determined. In order to illustrate the possibilities of the proposed framework, the problem of network reconfiguration for power loss reduction is considered. Two different optimization algorithms-one resorting to a genetic algorithm and the other solving a conventional mixed-integer linear problem-are fully developed. The validity and effectiveness of the path-based distribution network modeling are demonstrated on different test systems.     

蚁群算法在配电网重构的应用

配电网络重构是一个非常复杂的大规模组合优化问题。蚁群算法作为一种现代启发式寻优技术,适合于求解组合优化问题,其主要特点是正反馈、分布式计算、易与其它算法结合以及富于建设性贪婪启发式搜索。对配电网络从图论拓扑结构上进行分析,将配网重构问题转化为求图的生成树问题,并以破圈法为基础得到快速而有效地求解图的生成树的方法。在应用蚁群算法求解配网重构问题时,通过首支路选择随机化和取消蚁群算法常用的启发值的方法,扩大算法搜索范围,使算法可以跳出局部最优化陷阱,改善算法的搜索效果。对IEEE 69网络的算例表明,该方法能以较少的计算量和较大的概率收敛于全局最优解。     

An efficient heuristic algorithm for reconfiguration based on branch power flows direction

This paper presents a meshed algorithm for optimal reconfiguration of distribution systems. In the reconfiguration problem, the final objective is to reach a radial network that optimizes some function like the network losses. Many algorithms start from a radial network where a switch closure is complemented by opening of another switch to ensure a radial network. These radial algorithms have an inherent inconvenient, that is, the final solution depends on the initial radial network selected. Other group of algorithms initially represent the distribution network as a meshed network and then open switches until a radial system is obtained. In this paper, to avoid the above aforementioned inconvenient of radial algorithms, a meshed algorithm is used. Furthermore, taking into account that breakpoint nodes are defined as the nodes where the branch power flows converge, the contribution of this paper is to provide a method for solving the problem when multiple loops are considered using an approach based on the breakpoint nodes, since it is complicated to associate each breakpoint node with its corresponding loop. On the other hand, one of the drawbacks of the reconfiguration problem is the need to solve a great number of power flow computations for calculating the losses in each stage of the algorithm. The algorithm proposed has the property that reduces the number of power flows. By this way, the execution time of the algorithm is improved. Besides, it is not necessary to check the network connectivity at each step of the procedure. To prove the effectiveness of the proposed algorithm several test systems have been used, achieving good results.     

Multi-Objective Approach for Reconfiguration of Distribution Systems with Distributed Generations

This paper presents a fuzzy multi-objective based heuristic algorithm for network reconfiguration of distribution systems considering distributed generations (DGs). The objectives of reduction of real power loss, branch current carrying capacity limit, maximum and minimum voltage constraints, and feeder load balancing are considered for performance enhancement of the distribution system. Since these objectives are non-commensurable and difficult to solve simultaneously using conventional approaches, they are converted into fuzzy domain and a fuzzy multi-objective function is formulated. A sensitivity analysis based on voltage profile improvement and real power loss reduction is used for obtaining optimal locations of DGs and genetic algorithm is used for optimal sizing of DGs. The proposed reconfiguration algorithm is implemented in two stages, initially in the first stage without incorporating DGs and in the second stage incorporating DGs for obtaining an optimal distribution system network reconfiguration. The advantage of the proposed method is demonstrated through a seventy node four feeders and a sixteen node three feeders distribution systems.     

基于混合整数二次锥规划方法的含分布式电源配电网优化重构方法

含分布式电源(DG)的配电网重构问题属于NP难问题,数学规划是寻求该类问题求解方法的一个良好途径。提出了一个种含DG配电网优化重构的混合整数二次锥规划模型,并使用具有多项式时间复杂性的内点算法进行求解。考虑了开关状态,不同类型DG的投切、出力状态,将其作为优化变量;使用线性加权和法将配电网运行费用、可再生能源损失统一为综合费用,作为规划的目标函数;将潮流约束进行变换并合理松弛为二次锥约束,最终建立了混合整数二次锥规划模型。最后通过算例证明了求解相同优化重构问题时该方法较已有方法得出结果更优,以综合费用最小为目标时得出的结果同时有利于可再生能源消纳、降低网损和减少费用。     

提升分布式电源接纳能力的配电网三相鲁棒动态重构

不可控分布式电源(UDG)给主动配电网带来了显著的功率波动和不确定性。为消纳更多的UDG,主动配电网的拓扑结构应随系统的运行工况动态灵活配置。此外,由于配电系统的负荷通常是三相不平衡的,实际应用中也需要计及网络三相不平衡的重构模型。对此,基于自适应二阶段鲁棒优化方法,提出了一种三相不平衡配电网的动态重构方法。其中,第一阶段为在考虑的整个重构超前时段内优化网络的拓扑,以减少日常的开关费用并保持网络的辐射状结构。第二阶段为基于给定的网络拓扑和UDG出力不确定集合,通过执行三相动态最优潮流来最小化系统最坏情况下的运行成本。所提二阶段鲁棒动态重构模型可采用列与约束生成算法进行求解,并且线性三相潮流模型的采用,使主问题与子问题均可建模为混合整数线性规划问题。通过对修改的IEEE 34节点及IEEE 123节点系统的测试计算,验证了所提方法的有效性。     

Optimal Spinning Reserve Allocation with Full AC Network Constraints Via a Nonlinear Interior Point Method

An effective optimal spinning reserve allocation (OSRA) method is proposed in this paper using Optimal Power Flow (OPF). It enables optimal allocation of spinning reserve and load curtailment incorporating full AC network constraints and dynamic restriction on generation such as ramp-rate constraints. A Primal-Dual Interior Point (PDIP) method, which can efficiently handle both equality constraints and inequality constraints, is employed to solve the formulated dynamic OPF problem. In this model, spinning reserve and load curtailment constraints impose an interdependency between the generation output of units which usually are separable in conventional Newton OPF. A decomposition algorithm is therefore derived to handle the interdependency so that the constraint matrix of generation and that of network can be handled separately by slightly changing the entries of Hessian matrix. Therefore, the proposed method is not only still able to utilize the elegant super sparsity technique of Newton method, but also eliminates its ineffective binding active set determination procedure. Furthermore, the influences of spinning reserve on spot price (SP) are also discussed. A shift effect is observed.     

改进二进制粒子群优化算法在配电网络重构中的应用

配电网络重构是一个非常复杂的大规模组合优化问题。网络重构中,能否得到有效解,即保证辐射状网络,是一个很关键的问题。对电网拓扑进行简化,配合破圈法更新粒子,得到100％的有效解,大大提高了计算速度。提出一种应用于配电网络重构的改进二进制粒子群优化算法,并结合禁忌搜索算法,使PSO算法跳出局部最优化陷阱,改善了算法的搜索效果,加快了寻优速度。最后对IEEE 69节点系统进行计算,并与相关文献结果进行对比,表明本文改进算法具有快速、高效的全局寻优能力。     

基于Tabu搜索的配电网络重构算法

配电网络重构是一个非常复杂的、大规模的组合优化问题。该文提出了一种非常有效的、鲁棒性很好的算法来求解正常运行条件下配电网络的重构问题,以减少网络中的能量损失费用。该算法基于Tabu搜索方法(TS)。作为现代启发式方法家族中的重要一员,Tabu搜索方法是近几年来发展起来的用于求解组合最优问题的一种通用算法。文中详细阐述了用于配电网络重构问题时Tabu搜索方法中各成员的设计。为了证明该文方法的可行性和有效性,还研究了3个不同规模的IEEE测试网络的重构问题。结果表明,该文提出的方法是一种非常有效的方法。     

基于改进环网编码法的配电网辐射性判别方法

配电网辐射性约束是配电网优化问题中的一个重要约束,但目前用于判断配电网辐射性的方法都较为复杂,限制了相关问题的求解效率。为解决这一问题,文中从图论的角度出发,对配电网拓扑结构中可能出现的孤岛和环路的特征进行了分析,提出了配电网满足辐射性的充要条件。进一步将其与元启发式算法中常用的环网编码法结合,并对环网编码法进行了改进,提出了环路法与割集法两种可用于检测配电网辐射性以及修正不可行解的方法。将提出的方法应用到配电网重构问题中,并基于IEEE 33节点系统,通过对不同辐射性检验方法的计算结果和计算效率的对比,证明了方法的正确性与高效性。     

市场环境下输配电系统一体化分布式交易优化方法

随着可再生能源的高渗透率接入和主动配电网的规模化发展,系统之间对于能量交易和灵活性资源共享的需求迫切。文中基于广义主从分解协调方法,将一体化输配电市场分解为输电系统批发市场主问题和多个配电系统零售市场子问题,并建立了基于混合整数线性规划的考虑备用需求约束的输电网络模型和基于混合整数二阶锥规划的适用于网络重构的配电网络模型,同时提出了适用于输配电市场一体化问题的分布式优化的分解协调方法,可有效降低市场的购电成本。在模型中模拟了配电系统运营商进行策略性报价意愿的约束,且配电网系统采用的网络重构模型能有效地精细化网损和模拟远程开关控制,提高市场的流动性。基于库恩-塔克(KKT)条件从理论上证明了该模型和方法的最优性,并通过算例证明了方法的有效性。     

基于蚁群最优的配电网络重构算法

配电网络重构是一个非常复杂的大规模组合优化问题。本文提出了一种新颖的基于蚁群最优的算法来求解正常运行条件下的配电网络重构问题,以达到损失最小,蚁群最优算法法（Ant Colony Optimization,简称ACO算法）是一种新型通用内启发式算法。在求解组合最优问题上,ACO算法已被证明是非常有效的。ACO算法本质上是一个多代理系统,在这个系统中单个代理之间的交互导致了整个蚁群的复杂行为。这种方法的主要特征是正反馈,分布式计算以及富有建设性的贪婪启发式搜索的运用,为了证明本文提出的算法的可行性和有效笥,我们研究了两个算例系统,并给出了计算结果,结论表明,本文提出的算法是相当有希望的。