基于MO-APSO的含风电场电力系统动态环境经济调度

为综合考虑碳排放权交易对风火联供模式的影响,基于节能减排、发电效益、机组运行3个方面约束条件,引入碳排放权交易成本函数,构建了考虑发电成本、碳交易成本、环境成本的风火联供系统多目标动态环境经济调度(DEED)模型。提出一种多目标自适应粒子群优化(MO-APSO)算法求解该DEED问题。根据寻优过程中粒子当前的适应度函数值,对惯性权重及学习因子进行自适应修正,进一步改善早熟的缺陷,增强全局搜索能力。含风电场的10机电力系统仿真结果表明:所提方法能同时优化成本和排放这2个冲突的目标,且获得了比其他算法更为宽广和均匀的Pareto前沿,有效降低了联供系统的碳排放量及综合运行成本。     

基于节点概率可观性的PMU多目标优化配置

针对相量测量单元(phasor measurement unit, PMU)的多目标优化配置(multi-objective optimal PMU placement, MOPP)问题,提出一种计及节点概率可观性的MOPP模型。从节点可观的角度,考虑PMU及线路的故障概率,计算节点失去可观性的概率。在进行PMU的优化配置时,同时考虑PMU安装数量最少和各节点失去可观性的平均概率最小2个优化目标,采用基于快速非支配排序策略的多目标生物地理学优化(multi-objective biogeography-based optimization, MOBBO)算法进行求解得到Pareto解集,并利用模糊决策理论得到最优折衷解。IEEE 14和57节点系统的大量仿真结果表明,所提方法可以在MOPP中差异化计及PMU以及支路故障概率的影响,与非支配排序遗传算法相比,MOBBO在求解MOPP模型中能够得到更为逼近Pareto前沿的解,提供更佳的决策参考方案。     

电力系统无功优化多目标处理与算法改进

电力系统无功优化属于典型的多目标非线性复杂优化问题,求解非常困难。近年来,众多智能优化算法应用于该问题,其中粒子群优化(Particle Swarm Optimization,PSO)算法最具代表性;但PSO算法性能仍有待提高,如可能陷入局部极值。提出一种多策略融合粒子群优化(Particle Swarm Optimization with Multi-Strategy Integration,MSI-PSO)算法,对速度更新公式引入选择操作,分阶段加速因子调整和惯性权重动态调整,以平衡粒子局部搜索与全局探索能力;同时,随机选取部分性能差的粒子,将其速度更新公式中的个体认知部分修改为社会认知部分,以提高算法搜索精度和收敛速度。建立以系统网络损耗最小和系统电压稳定裕度最大为目标的无功优化仿真模型,分别考虑加权法、隶属度函数法和Pareto法实施多目标处理。针对IEEE30节点测试系统进行仿真实验,结果表明,和其他几种改进PSO算法以及基于pareto最优解集PSO算法进行对比,所提MSI-PSO算法具有更好的性能,能够有效求解电力系统多目标无功优化问题。     

基于改进多目标蜉蝣算法的配网电池储能系统最优选址定容

电池储能系统(BESSs)在配电网的选址定容是保证BESSs和配电网经济可靠运行的关键。基于此,提出了一种配电网BESSs最优选址定容方法。首先,采用C-均值聚类算法对全年的负荷曲线和风、光出力曲线进行典型日聚类。进而,以BESSs日均综合成本、电压波动和负荷波动最小为目标,建立了配电网BESSs最优选址定容的多目标优化模型。为获得BESSs等决策变量的Pareto最优解集,设计了改进的多目标蜉蝣算法(MMOMA)进行求解。为实现三个目标的最佳权衡,采用改进理想点决策(IIPBD)方法对Pareto最优解集进行折中决策。最后,利用扩展的IEEE33节点配电系统进行仿真测试,以验证所提方法的有效性。仿真结果表明,与另外两种传统多目标优化算法相比：所提MMOMA获得的Pareto前沿分布更广、更均匀;IIPBD方法获得的折中决策方案有效实现了BESSs投资成本的最小化,同时能显著降低配电网的电压波动和负荷波动。     

基于柔性直流互联的多微网集成聚合运行优化及分析

为解决多微网集成聚合控制与运行管理问题,提出一种多微网柔性直流互联方案及多目标优化调度方法。首先介绍了多微网柔性直流互联结构和电压源型变流器(VSC)模型。然后,以微网中电压波动最小和系统网损最小为优化目标,综合考虑交流系统、直流系统和VSC的运行约束,提出了基于柔性直流互联多微网的多目标优化模型。最后,采用改进非劣排序多目标遗传算法(NSGA-Ⅱ)和交直流混合潮流算法对多目标优化模型进行求解,得到帕累托(Pareto)最优解集,针对Pareto最优解集中解的数量大的问题,提出采用模糊聚类法对Pareto最优解集进行筛选,得到最终优化调度方案。对算例进行了仿真分析,结果表明所提模型和算法能够有效抑制微网电压的波动,进而提高可再生能源的渗透率,同时保证系统的经济运行。     

基于CAMOCS算法的多目标无功优化

针对传统算法在求解多目标函数上存在局限性问题,在标准多目标布谷鸟搜索(Multi-objective Cuckoo Search,MOCS)算法的基础上,采用Kent混沌映射生成多样性初始解,并自适应改变算法的搜索步长,结合多目标Pareto最优解概念,提出一种混沌自适应多目标布谷鸟搜索(Chaotic Adaptive Multi-objective Cuckoo Search,CAMOCS)算法,并利用该算法对所建立的多目标无功优化模型进行求解,最后在IEEE 14节点系统算例仿真验证了所提方法的有效性和可行性。     

决策空间自组织多模态多目标鲸鱼优化算法研究

针对当前多模态多目标优化算法在获得Pareto解集的完整性、收敛性方面的不足，提出了一种决策空间自组织多模态多目标鲸鱼优化算法(MMO＿SOM＿WOA)。首先将鲸鱼优化算法首次用于求解多模态多目标问题，通过鲸鱼优化算法本身的随机性提高寻找Pareto解集完整性的能力。其次将自组织映射网络与鲸鱼优化算法相结合，迭代开始时为鲸鱼优化算法建立良好的邻域。最后使用精英反向学习策略初始化种群和非支配排序机制获得均匀且完整的解。通过与当前5种经典算法在多模态多目标优化问题上进行仿真对比，结果表明MMO＿SOM＿WOA算法兼顾Pareto解集的多样性和Pareto解的完整性，收敛速度和收敛精度均得到提升具有较高的性能，有效解决多模态多目标优化问题。     

含风电的高维多目标安全约束机组组合问题求解方法

建立了最小化系统总运行费用、总网损、总购电费用和污染气体排放量4个目标的含风电场、储能电站和抽水蓄能电站的多目标安全约束机组组合模型。采用凸松弛法将安全约束机组组合的混合整数非线性规划模型转化为混合整数凸规划模型以降低模型求解的计算复杂度,并提出求解四目标优化问题Pareto前沿的方法。首先采用Spearman相关系数法选出一个次优目标,利用ε-约束法将四目标优化问题转化为一系列三目标优化问题;再根据规格化法平面约束法求解每个三目标优化问题的完整Pareto前沿曲面,从而得到三维空间中四目标优化问题的Pareto前沿曲面簇。通过对修改IEEE9节点系统和某实际电网的计算结果表明,所提出的模型和算法能够快速有效地获得四目标优化问题的均匀分布Pareto最优解集。     

基于绿色证书交易机制的含风电场电力系统动态环境经济调度

为了促进风电消纳以及提高电力系统的经济性,构建基于绿色证书交易机制的含风电场电力系统多目标动态环境经济调度（DEED）模型,提出一种基于反向学习混沌搜索的OLCS-MOEA/D算法的DEED调度求解方法。首先,采用广义反向学习初始化种群提高种群多样性,并引入基于Logistic映射的混沌搜索算法以增强算法局部搜索能力。然后,为了验证算法的性能,采用标准测试函数F1—F7进行测试,同时将该算法对模型进行求解,获得了比其他算法范围更广和分布均匀的Pareto解集前沿。最后,对基于绿色证书交易机制的动态环境经济调度与传统动态环境经济调度进行结果对比分析,通过仿真算例验证该模型和算法的有效性和优越性。     

基于免疫进化细菌觅食算法的多目标无功优化

为了更好地解决电力系统多目标无功优化问题,分析了当前多目标无功优化算法存在的缺陷,提出了一种基于免疫进化的改进多目标细菌觅食优化算法。该算法求得的Pareto最优解分布均匀,收敛性和鲁棒性好。IEEE14,IEEE30节点测试系统的算例结果表明所提的算法在多目标无功优化中具有良好的效果,为各目标之间的权衡分析提供了有效工具,是一种求解多目标无功优化问题的有效方法。     

Optimal location and setting of SVC and TCSC devices using non-dominated sorting particle swarm optimization

In this paper, a new method for optimal locating multi-type FACTS devices in order to optimize multi-objective voltage stability problem is presented. The proposed methodology is based on a new variant of particle swarm optimization (PSO) specialized in multi-objective optimization problem known as non-dominated sorting particle swarm optimization (NSPSO). The crowding distance technique is used to maintain the Pareto front size at the chosen limit, without destroying its characteristics. To aid the decision maker choosing the best compromise solution from the Pareto front, the fuzzy-based mechanism is employed for this task. NSPSO is used to find the optimal location and setting of two types of FACTS namely: Thyristor controlled series compensator (TCSC) and static var compensator (SVC) that maximize static voltage stability margin (SVSM), reduce real power losses (RPL), and load voltage deviation (LVD). The optimization is carried out on two and three objective functions for various FACTS combinations considering. For ensure the robustness of the proposed method and gives a practical sense of our study, N − 1 contingency analysis and the stress of power system is considered in the optimization process. The thermal limits of lines and voltage limits of load buses are considered as the security constraints. The proposed method is validated on IEEE 30-bus and realistic Algerian 114-bus power system. The simulation results are compared with those obtained by particle swarm optimization (PSO) and non-dominated sorting genetic algorithms (NSGA-II). The comparisons show the effectiveness of the proposed NSPSO to solve the multi-objective optimization problem and capture Pareto optimal solutions with satisfactory diversity characteristics.     

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.     

含高比例风光新能源电网的多目标无功优化算法

为适应新能源大量接入电网的趋势,基于不同时刻的风速、光照强度、温度等气象条件信息,评估出风光新能源的无功调节容量,搭建了含高比例风光新能源参与调控的电网多目标无功优化模型。为快速获得电网中变压器分接头档位调节、无功补偿设备投切、传统发电机组电压调节以及风光的无功输出等控制措施的帕累托最优解集,采用寻优性能高效的多目标樽海鞘群算法（multi-objective salp swarm algorithm, MSSA）进行无功优化求解。为更客观找出电网线损、电压偏差、静态电压稳定裕度等不同目标之间的折中解,采用改进的理想点法进行多目标最优解集决策。最后,利用扩展的IEEE标准9节点和39节点算例进行仿真分析,并引入传统多目标智能优化算法来进行比较验证。仿真结果表明：与其他2种传统多目标智能优化算法相比,所提算法获得的帕累托前沿分布更广、更均匀;利用改进理想点法进行决策之后,可有效降低电网的线损和电压偏差,同时提高了电网的静态电压稳定裕度。     

Multi-objective harmony search algorithm for optimal power flow problem

This paper proposes a multi-objective harmony search (MOHS) algorithm for optimal power flow (OPF) problem. OPF problem is formulated as a non-linear constrained multi-objective optimization problem where different objectives and various constraints have been considered into the formulation. Fast elitist non-dominated sorting and crowding distance have been used to find and manage the Pareto optimal front. Finally, a fuzzy based mechanism has been used to select a compromise solution from the Pareto set. The proposed MOHS algorithm has been tested on IEEE 30 bus system with different objectives. Simulation results are also compared with fast non-dominated sorting genetic algorithm (NSGA-II) method. It is clear from the comparison that the proposed method is able to generate true and well distributed Pareto optimal solutions for OPF problem.     

多目标混合进化算法及其在经济调度中的应用

鉴于环境保护的要求,对于经济调度问题,需同时考虑环境要求、发电费用等多个目标。提出一种基于进化规划(evolutionary programming,EP)和粒子群优(particle swarm optimization,PSO)的多目标混合进化算法(multi-objective evolutionary programming and particle swarm optimization,MOEPPSO),MOEPPSO采用了EP的变异操作,用来抑制PSO的快速收敛所带来的种群早熟问题,而PSO的记忆、协作能力则弥补了EP收敛速度慢的缺点。此外,MOEPPSO应用自适应网格算法对外部库中的Pareto解集进行调整,对一个30节点IEEE系统进行计算,结果显示MOEPPSO在获得最优Pareto解集、降低计算复杂度、提高收敛效率等方面具有很强的优越性。     

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.     

Single and Multi-objective Optimal Power Flow Using Grey Wolf Optimizer and Differential Evolution Algorithms

This article applies the grey wolf optimizer and differential evolution (DE) algorithms to solve the optimal power flow (OPF) problem. Both algorithms are used to optimize single objective functions sequentially under the system constraints. Then, the DE algorithm is utilized to solve multi-objective OPF problems. The indicator of the static line stability index is incorporated into the OPF problem. The fuzzy-based Pareto front method is tested to find the best compromise point of multi-objective functions. The proposed algorithms are used to determine the optimal values of the continuous and discrete control variables. These algorithms are applied to the standard IEEE 30-bus and 118-bus systems with different scenarios. The simulation results are investigated and analyzed. The achieved results show the effectiveness of the proposed algorithms in comparison with the other recent heuristic algorithms in the literature.