Integration of Distributed Generation in Power Networks Considering Constraints on Discrete Size of Distributed Generation Units

Abstract—An optimization algorithm based on a novel discrete particle swarm optimization technique is proposed in this article for optimal sizing and location of distributed generation in a power distribution network. The proposed algorithm considers distributed generation size and location as discrete variables substantially reducing the search space and, consequently, computational requirements of the optimization problem. The proposed algorithm treats the generator sizes as real discrete variables with uneven step sizes that reflect the sizes of commercially available generators, meaning that it can handle a mixed search space of integer (generator location), discrete (generator sizes), and continuous (reactive power output) variables while substantially reducing the search space and, consequently, computational burden of the optimization problem. The validity of the proposed discrete particle swarm optimization algorithm is tested on a standard 69-bus benchmark distribution network with four different test cases. Two optimization scenarios are considered for each test case: a single objective optimization study where network real power loss is minimized and a multi-objective study in which network voltages are also considered. The proposed algorithm is shown to be effective in finding the optimal or near-optimal solution to the problem at a fraction of the computational cost associated with other algorithms.     

一种分布式电源选址定容的两阶段优化规划方法

针对预先未给定分布式电源(distributed generator,DG)待选接入点的DG选址定容规划,提出了一种以配电网运行成本最小为目标的两阶段优化规划方法:第一阶段,建立了一个基于权系数的DG选址模型,并运用有效集法进行求解,筛选出一组DG待选接入点组合;第二阶段,提出了一种动态混沌粒子群算法来求解第一阶段所得出的待选DG节点的定容问题,并将最优规划结果值返回给第一阶段,从而确定出DG最优的接入节点和接入容量。最后通过美国PGE 69节点系统验证了所提模型的可行性以及方法的有效性。     

满足静态电压稳定增强要求的发电机最佳调整方法

为增强电力系统的静态电压稳定性,同时最大限度地减小运行人员的操作工作量,提出了一种综合经济性和静态电压稳定性的发电机最佳调整模型。该模型以发电机参与调整台数最少和发电成本最小为目标,约束条件包括系统负荷裕度满足设定提升要求和电力系统安全运行要求。该问题的数学本质是一个多目标非线性混合整数规划问题。为实现上述问题的求解,首先以线性灵敏度方法快速估算所需调整出力的发电机,求解控制数量最少的整数规划问题。然后以发电成本最小为目标,利用线性规划法求解各台发电机的调整出力值。最后在IEEE39节点算例和IEEE118节点算例进行仿真验证,结果表明所提模型与求解方法能很好地解决系统的静态电压稳定性增强控制问题。     

Security constrained optimal power flow considering detailed generator model by a new robust differential evolution algorithm

This paper presents a new multiobjective model, including two objective functions of generation cost and voltage stability margin, for optimal power flow (OPF) problem. Moreover, the proposed OPF formulation contains a detailed generator model including active/reactive power generation limits, valve loading effects, multiple fuel options and prohibited operating zones of units. Furthermore, security constraints, including bus voltage limits and branch flow limits in both steady state and post-contingency state of credible contingencies, are also taken into account in the proposed formulation. To solve this OPF problem a novel robust differential evolution algorithm (RDEA) owning a new recombination operator is presented. The proposed RDEA has a minimum number of adjustable parameters. Besides, a new constraint handling method is also presented, which enhances the efficiency of the RDEA to search the solution space. To show the efficiency and advantages of the proposed solution method, it is applied to several test systems having complex solution spaces and compared with several of the most recently published approaches.     

Application of pattern search method to power system security constrained economic dispatch with non-smooth cost function

Direct search methods are evolutionary algorithms used to solve optimization problems. (DS) methods do not require any information about the gradient of the objective function at hand while searching for an optimum solution. One of such methods is Pattern Search (PS) algorithm. This paper presents a new approach based on a constrained pattern search algorithm to solve a security constrained power system economic dispatch problem (SCED) with non-smooth cost function. Operation of power systems demands a high degree of security to keep the system satisfactorily operating when subjected to disturbances, while and at the same time it is required to pay attention to the economic aspects. Pattern recognition technique is used first to assess dynamic security. Linear classifiers that determine the stability of electric power system are presented and added to other system stability and operational constraints. The problem is formulated as a constrained optimization problem in a way that insures a secure-economic system operation. Pattern search method is then applied to solve the constrained optimization formulation. In particular, the method is tested using three different test systems. Simulation results of the proposed approach are compared with those reported in literature. The outcome is very encouraging and proves that pattern search (PS) is very applicable for solving security constrained power system economic dispatch problem (SCED). In addition, valve-point effect loading and total system losses are considered to further investigate the potential of the PS technique. Based on the results, it can be concluded that the PS has demonstrated ability in handling highly nonlinear discontinuous non-smooth cost function of the SCED.     

Optimal power flow for distribution networks using gravitational search algorithm

This paper presents a gravitational search algorithm (GSA)-based approach to solve the optimal power flow (OPF) problem in a distribution network with distributed generation (DG) units. The OPF problem is formulated as a nonlinear optimization problem with equality and inequality constraints, where optimal control settings in case of fuel cost minimization of DG units, power loss minimization in the distribution network, and finally simultaneous minimization of the fuel cost and power loss are obtained. The proposed approach is tested on an 11-node test system and on a modified IEEE 34-node test system. Simulation results obtained from the proposed GSA approach are compared with that obtained using a genetic algorithm approach. The results show the effectiveness and robustness of the proposed GSA approach.     

Optimization of distributed generation systems using a new discrete PSO and OPF

Many methods have been applied to achieve optimal site and size of distributed generation systems. This paper introduces a new hybrid method, which employs discrete particle swarm optimization and optimal power flow to overcome this shortcoming. The main technical constraints are imposed for utilities, which could apply this approach to search the best sites to connect distributed generation systems in a distribution network choosing among a large number of potential combinations. A fair comparison between the proposed algorithm and other methods is performed. For such goal, convergence curves of objective function versus number of iterations are computed. The proposed algorithm reaches a better solution than Genetic Algorithms considering similar number of evaluations.     

Optimal distributed generation location and size using a modified teaching–learning based optimization algorithm

In this paper, a method which employs a Modified Teaching–Learning Based Optimization (MTLBO) algorithm is proposed to determine the optimal placement and size of Distributed Generation (DG) units in distribution systems. For the sake of clarity, and without loss of generality, the objective function considered is to minimize total electrical power losses, although the problem can be easily configured as multi-objective (other objective functions can be considered at the same time), where the optimal location of DG systems, along with their sizes, are simultaneously obtained. The optimal DG site and size problem is modeled as a mixed integer nonlinear programming problem. Evolutionary methods are used by researchers to solve this problem because of their independence from type of the objective function and constraints. Recently, a new evolutionary method called Teaching–Learning Based Optimization (TLBO) algorithm has been presented, which is modified and used in this paper to find the best sites to connect DG systems in a distribution network, choosing among a large number of potential combinations. A comparison between the proposed algorithm and a brute force method is performed. Besides this, it has also been carried out a comparison using several results available in other articles published by others authors. Numerical results for two test distribution systems have been presented in order to show the effectiveness of the proposed approach.     

Multi-objective Optimization Approach for Optimal Distributed Generation Sizing and Placement

Abstract—This article describes a multi-objective optimization method to solve the optimal distributed generation sizing and placement. The optimization problem considers two objectives: minimizing the total real power losses of the network and minimizing the overall distributed generation installation cost. The objectives are combined into a scalar objective optimization problem by using weighted sum method. Both objective functions and equality and inequality constraints are formulated as a non-linear program and solved by a sequential quadratic programming deterministic technique. The multi-objective optimization method gives several answers instead of a single (unique) one. These answers are optimal, and the designer (decision maker) can select the proper solution according to subjective preferences. These optimum results are known as the Pareto front. A fuzzy decision-making procedure for order preference is used for finding the best compromise solution from the set of Pareto solutions. The proposed method is tested using a 15-bus radial distribution system to show its applicability. A comparative study is performed to evaluate two cases—a single distributed generation unit installation and a multiple distributed generation installation—ending by a comparative study of the two cases.     

Optimal Load Flow in Hydro-Thermal Systems: Computational Experience with Newton's Method

ABSTRACT

In this paper the problem of optimal load flow in a hydro-thermal electric power system is considered. It is assumed that the hydro generation resources are energy limited. As a result, a dynamic optimization problem involving the daily schedule of the system is encountered. The scheduling problem requires the solution of a large scale set of nonlinear simultaneous equations. In this paper Newton's method is used to solve the scheduling problem. The algorithm has been successfully tested with five test systems varying in size from a 5 bus system to a 57 bus system. Results of the computational experience are summarized in this paper.     

基于改进粒子群算法的配电网分布式电源规划

合理地对分布式电源进行选址和定容对于实现配电网网损最小是至关重要的.应用改进粒子群优化算法进行配电网分布式电源(DG)规划,并结合罚函数法将DG规划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.对69节点和33节点配电测试系统进行仿真计算,结果表明了论文采用的DG规划模型和改进粒子群优化算法的正确性和适用性.     

基于改进粒子群算法的配电网分布式电源规划

合理地对分布式电源进行选址和定容对于实现配电网网损最小是至关重要的。应用改进粒子群优化算法进行配电网分布式电源（DG）规划,并结合罚函数法将DG规划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。对69节点和33节点配电测试系统进行仿真计算,结果表明了论文采用的DG规划模型和改进粒子群优化算法的正确性和适用性。     

新电改背景下产业园区供电系统容量优化配置方法

产业园区作为新一轮电力体制改革的重要试点,利用分布式新能源发电来替代传统的集中式供电模式是其供电系统发展的重要趋势之一。开展了产业园区供电系统规划中分布式电源/储能系统优化配置问题的研究,重点研究了多能互补、源—储—荷协调互动和基于日前分时电价的需求侧响应对于容量优化配置方案的影响。为了表征多能互补特性,提出了分布式电源供电电量不足比和分布式电源供电不足小时数比两个指标。在需求侧响应建模时,针对利用电力需求弹性矩阵建模存在着电量转移不平衡及需求侧过度响应等问题,提出了改进的需求侧响应模型。在此基础上,建立了以总费用最小为优化目标的产业园区供电系统分布式电源/储能系统优化配置模型,并利用遗传算法与模式搜索算法相结合的组合型智能算法对优化配置模型进行求解,最后利用典型算例对提出的优化配置方法进行了分析验证。     

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.     

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.     

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.     

改进PSO算法和Lagrange乘数法应用于短期发电计划

电力系统短期发电计划研究是一个离散、复杂、多维的非线性整数规划问题,求解非常困难。采用改进的粒子群(particle swarm optimization,PSO)算法通过线性改变权重因子,连续变量离散化,以及增加第二最优项用于求解最优机组组合问题;拉格朗日乘数法适合于多维函数在约束条件下的求解极值问题,用于求解各机组在各时段的经济出力。方法的可行性通过10机系统中检验。仿真结果表明,该方法能够求得高质量解,减少机组运行费用,具有有效性和可行性。     

Self-adaptive evolutionary programming and its application to multi-objective optimal operation of power systems

This paper proposes a new algorithm to solve multi-objective optimal operation of power systems problem. The algorithm is based on combination of general evolutionary programming and random search technique. The algorithm includes two important procedures. First, a new pattern of mutation is developed in this paper. Secondly, the developed mutation operator is self-adaptive during optimization. Furthermore, in a multi-objective optimal operation study four objectives (cost of generation with valve point loading, transmission losses, environmental pollution and steady-state security regions) are considered for optimization, and an ideal point method is used to solve the problem. The proposed algorithm is tested on the IEEE six-bus and 30-bus systems. Numerical results and comparison demonstrate that the new method not only can deal agilely with constraints, but also can reduce the CPU time and prevent the search from being in local optima.     

HSA based solution to the UC problem

Unit-commitment (UC) as a complicated problem needs powerful methods to solve. This paper presents the use of harmony search algorithm (HSA), a recently developed meta-heuristic algorithm, in order to obtain optimal solution for the UC problem. The proposed algorithm has simple implementation and provides optimal solutions in a reasonable time. The method is tested using small and large scale test cases in the literature. Numerical results show that the proposed algorithm can find better solutions in comparison with conventional methods and it is an efficient way to solve UC problems especially in large-scale power systems.     

分布式电源选址定容优化算法

通过分析分布式电源对配电网规划的影响,提出一种带惯性权重的粒子群算法,对配电网规划中分布式电源的选址和定容进行优化.首先,建立了综合目标模型,包括由分布式电源的投资运行费用、网损费用及购电费用构成的归一化目标函数,由出力限制等构成的约束条件,然后,利用Matlab仿真工具对所提算法进行了实现,仿真结果表明,本算法全局搜...