考虑系统完全可观测性的PMU最优配置方法

基于电力系统线性量测模型，研究了引入相量测量单元（PMU）相关量测集后的增广关联矩阵的电力系统可观测性拓扑分析方法，以保证系统结构完全可观测性和最大量测数据冗余度为约束，以配置PMU数目最小为目标，形成了PMU最优配置问题，并应用禁忌搜索（TS）方法求解该问题，保证了全局寻优。算例表明，该方法准确可靠、有效可行。     

基于图论的电力系统PMU布点优化算法

基于最小支配集理论和电力系统线性量测模型，提出了可观测节点集合、WAMS可观测矩阵两个概念以及一种新的节点可观测性计算规则。以保证系统的完全可观测性和以系统图的最小支配集为搜索范围构成约束条件, 以电力系统状态完全可观测和相量测量装置（PMU）配置数目最小为目标,形成了PMU配置优化问题。并应用禁忌搜索(TS)方法求解该问题,保证了全局寻优。最后采用 IEEE 14、30、57 、118节点系统和新英格兰 39 节点系统对该方法进行了验证,仿真结果表明该方法的有效性和可行性。     

基于01整数规划的多目标最优PMU配置算法

针对目前缺乏多目标PMU配置方法,提出了一种基于线性01规划的多目标优化配置算法。并在此基础上导出了三种特殊模型,分别处理系统在正常运行方式下完全可观测的PMU布点问题,在线路N-1故障时系统仍可观测的PMU布点问题及在PMU N-1故障时系统仍可观测的PMU布点问题。该方法的突出特点在于能够同时将以上三种布点需求使用统一的形式同时处理,并且最终的布点方案在保证PMU数目最少或保证配置PMU所需费用最少的基础上获得了最高的测量冗余度。通过IEEE30、IEEE 57、IEEE118节点系统布点验证了该方法的有效性和灵活性。     

基于01整数规划的多目标最优PMU配置算法

针对目前缺乏多目标PMU配置方法,提出了一种基于线性01规划的多目标优化配置算法.并在此基础上导出了三种特殊模型,分别处理系统在正常运行方式下完全可观测的PMU布点问题,在线路N-1故障时系统仍可观测的PMU布点问题及在PMU N-1故障时系统仍可观测的PMU布点问题.该方法的突出特点在于能够同时将以上三种布点需求使用统一的形式同时处理,并且最终的布点方案在保证PMU数目最少或保证配置PMU所需费用最少的基础上获得了最高的测量冗余度.通过IEEE30、IEEE 57、IEEE118节点系统布点验证了该方法的有效性和灵活性.     

船舶电力系统相量测量单元多目标优化配置问题

为实现船舶电力系统潮流方程直接可解,同时保证相量测量单元(PMU)配置数目最少和N-1电压相量可解冗余度最高,提出了船舶电力系统PMU多目标优化配置方法。首先根据船舶电力系统不同工况下潮流方程的特点,分析得到PMU配置方案是否满足不同工况下潮流方程直接可解的判断方法;在此基础上,着重考虑最大运行工况下PMU配置数目最少和N-1电压相量可解冗余度最高的要求,建立了PMU多目标优化配置模型,并采用量子遗传优化算法对模型进行求解。以24节点典型船舶电力系统为例对所提方法进行了说明和验证,结果表明,该方法可实现全局多目标寻优,从而找到准确而完整的Pareto最优前沿。得到的PMU优化配置方案可为船舶电力系统配置PMU提供参考。     

考虑高风险连锁故障的PMU配置方法

针对连锁故障会导致广域测量系统(WAMS)丧失对电力系统完全可观测能力的问题,提出了一种考虑高风险连锁故障的最优相量测量单元(PMU)配置方法.首先使用隐性故障模型和风险理论对电力系统的连锁故障进行模拟仿真和统计分析,从而对系统中的高风险连锁故障进行辨识;进而通过最优PMU配置保证在单一高风险连锁故障发生的情况下WAMS能够保持对电网的完全可观测.以IEEE 39节点系统为例进行了PMU配置和分析,实验结果表明该方法在经济性和鲁棒性之间能够取得较好的平衡.     

一种改进的相量测量装置最优配置方法

以电力系统状态完全可观测和相量测量装置(PMU)配置数目最小为目标,提出了一种改进的PMU最优配置方法.将启发式方法和模拟退火方法有效结合以确保得到最优解,提高了基于启发式方法的初始PMU配置方案的质量,通过改进配置模型缩小了模拟退火方法的寻优范围,从而提高了求解速度.还提出了一种基于节点邻接矩阵的快速可观测性分析方法.最后采用IEEE 14、IEEE 30、IEEE 118节点系统和新英格兰39节点系统对该方法进行了验证.     

基于动态规划算法的PMU优化配置

以电力系统状态完全可观测和PMU配置数目最小为目标,提出基于动态规划算法的PMU优化配置方案。选择PMU配置位置为动态规划的状态,PMU台数为动态规划的阶段数,从而实现动态规划计算。通过预处理准则、对称性准则、优胜劣汰准则提高了计算效率。用文中方法对IEEE 14和IEEE 39节点系统进行了PMU配置。与其他文献方法对比表明了该算法的正确性与优越性。     

基于免疫BPSO算法与拓扑可观性的PMU最优配置

以电力系统状态完全可观测和相量测量单元PMU配置数目最小为优化目标,基于PMU的功能特点和电力网络的拓扑结构信息,形成快速且通用的电网拓扑可观测性判别方法,并设计了一种结合免疫系统信息处理机制的二进制粒子群优化算法对目标函数进行求解,该算法综合了粒子群优化算法简单快速和免疫系统种群多样性的优点,明显改善了进化后期算法的收敛性能和全局寻优能力.最后通过对IEEE14和新英格兰39母线系统进行PMU优化配置仿真及量测冗余性分析,验证了本文方法的有效性和优越性.     

用于负荷侧强迫振荡监测的PMU优化配置

针对电力系统周期性负荷扰动引发的强迫振荡问题,提出了一种应用于负荷侧强迫振荡监测问题的相量测量单元(phasor measurement unit,PMU)优化配置方法。通过分析冲击负荷典型特征得出PMU监测策略,缩小监测范围以保证PMU配置的经济性;建立二分类逻辑树来进行PMU优化配置分析,并利用网络连通算法和网络拓扑辨识来获取进行PMU优化配置所需的网络中变电站编号、PMU配置状态及网络中各节点连接情况等数字化信息。该方法保证了PMU配置的经济性与负荷侧强迫振荡的监控,最后通过示例验证了该方法的可行性。     

Optimal PMU placement method for complete topological and numerical observability of power system

This paper presents a new method of optimal PMU placement (OPP) for complete power system observability. A two-stage PMU placement method is proposed, where stage-1 finds out the minimum number of PMUs required to make the power system topologically observable and stage-2 is proposed to check if the resulted PMU placement (from stage-1) leads to a full ranked measurement Jacobian. In case the PMUs placed, ensuring topological observability in stage-1, do not lead to the Jacobian of full rank, a sequential elimination algorithm (SEA) is proposed in stage-2 to find the optimal locations of additional PMUs, required to be placed to make the system numerically observable as well. The proposed method is tested on three systems and the results are compared with three other topological observability based PMU placement methods. The simulation results ensure the complete system observability and also demonstrate the need of using stage-2 analysis along with the topological observability based PMU placement methods.     

ILP-based multistage placement of PMUs with dynamic monitoring constraints

This paper addresses two aspects of the optimal Phasor Measurement Unit (PMU) placement problem. Firstly, an ILP (Integer Linear Programing) model for the optimal multistage placement of PMUs is proposed. The approach finds the number of PMUs and its placement in separate stages, while maximizing the system observability at each period of time. The model takes into account: the available budget per stage, the power system expansion along with the multistage PMU placement, redundancy in the PMU placement against the failure of a PMU or its communication links, user defined time constraints for PMU allocation, and the zero-injection effect. Secondly, it is proposed a methodology to identify buses to be observed for dynamic stability monitoring. Two criteria, which are inter-area observability and intra-area observability, have been considered. The methodology identifies coherent groups in large power systems by using a new technique based on graph theory. The technique requires neither full stability studies nor a predefined number of groups. Also, a centrality criterion is used to select a bus for monitoring each coherent area and supervise inter-area oscillations. Then, PMUs are located to ensure complete observability inside each area (intra-area monitoring). Methodology is applied on the 14-bus test system, the 57-bus test system with expansion plans, and the 16-machine 68 bus test system. Results indicate that the optimization model finds the optimal number of PMUs when the PMU placement by stages is required, while the observability at each stage is maximized. Additionally, it is shown that expansion plans and particular requirements of observability can be considered in the model without increasing the number of required PMUs, and the zero-injection effect, which reduces the number of PMUs, can be considered in the model.     

基于改进粒子群算法的PMU装置数量增加过程中的最优配置方法

针对现有电力系统相量测量装置(PMU)在系统中的最优配置问题,进一步考虑了系统发展过程中PMU数量增加的最优配置问题。以电力系统线性量测模型为基础,通过拓扑分析方法,以全系统可观为约束,以系统最大冗余度为目标,并使用改进的粒子群算法进行计算,实现PMU数量增加过程中的最优配置。通过算例证明了算法的有效可靠。     

Optimal placement of PMUs with limited number of channels for complete topological observability of power systems under various contingencies

In optimal PMU placement problem, a common assumption is that each PMU installed at a bus can measure the voltage phasor of the installed bus and the current phasors of all lines incident to the bus. However, available PMUs have limited number of channels and cannot measure the current phasors of all their incident lines. The aim of this paper is to recognize the effect of channel capacity of PMUs on their optimal placement for complete power system observability. Initially, the conventional full observability of power networks is formulated. Next, a modified algorithm based on integer linear programming model for the optimal placement of these types of PMUs is presented. The proposed formulation is also extended for assuring complete observability under different contingencies such as single PMU loss and single line outage. Moreover, the problem of combination of PMUs with different number of channels and varying costs in optimal PMU placement is investigated. Since the proposed optimization formulation is regarded to be a multiple-solution one, total measurement redundancy index is evaluated and the solution with the highest redundancy index is selected as the optimal solution. The proposed formulation is applied to several IEEE standard test systems and compared with the existing techniques.     

兼顾元件权重和发电机同调性的山东电网PMU布点方法

在稳定计算的基础上，对于相量测量单元(phasor measurement unit，PMU)最优配置问题，进行了可观性权重设置和机组同调性分析。首先把逐点法与穷举法结合到一起形成了一种新的静态可观性改进算法，并引入了元件权重的概念来区分对不同设备可观性要求的程度；然后考虑了发电机同调性的影响，以可观性布点为基础，形成了动态可观性的布点；最后根据山东电网2006年夏季大方式的稳定计算结果，结合可观性和发电机同调性，提出了一种分阶段实施的有效PMU布点方法。     

基于改进自适应遗传算法的系统可观测PMU最优配置

以电力系统配置同步相量测量单元（PMU）个数最少、系统有最大测量冗余度为目标，全网可观测为约束，提出PMU最优配置模型，同时针对实际电网中存在某些重要节点已经初步安装PMU或者必须安装PMU的情况，提出了特殊约束条件，并给出了相应的求解算法。在此基础上，用改进自适应遗传算法求解此模型，保证全局最优。对某省49节点电网进行的计算表明，改进的自适应遗传算法收敛到全局最优解的概率优于传统的遗传算法和自适应遗传算法，更适用于工程实际。     

Optimal allocation of phasor measurement unit for full observability of the connected power network

This paper presents binary particle swarm optimization (BPSO) technique for the optimal allocation of phasor measurement units (PMUs) for the entire observability of connected power network. Phasor measurement units are considered as one of the most important measuring devices in the prospect of connected power network. PMUs function may be incorporated to the wide-area connected power networks for monitoring and controlling purposes. The optimal PMU placement (OPP) problem provides reference to the assurance of the minimal number of PMUs and their analogous locations for observability of the entire connected power networks. Binary particle swarm optimization (BPSO) algorithm is developed for the solution of OPP problem. The efficacy and robustness of the proposed method has been tested on the IEEE 14-bus, IEEE 30-bus, New England 39-bus, IEEE 57-bus, IEEE 118-bus and Northern Regional Power Grid (NRPG) 246-bus test system. The results obtained by proposed approach are compared with other standard methods and it is observed that this BPSO based placement of phasor measurement units is found to be the best among all other techniques discussed.     

Minimizing the number of PMUs and their optimal placement in power systems

This paper presents a new method for minimizing the number of PMUs and their optimal placement in power systems. The proposed method provides suitable constraints for power systems with two adjacent injection measurements (IMs). In addition, suitable constraints for considering the connection of two buses to each other and to an injection bus are proposed. The proposed constraints result in a reduction in the number of PMUs even though the system topological observability is complete. Existing conventional measurements are also considered. First, the number of PMUs is minimized in such a way that the system topological observability is complete. Then the optimal placement is done to maximize the measurements redundancy. The resulting phased to be installed in multiple stages. The optimal number of PMUs that ensure system topological observability under failure of a PMU or a line is also simulated. Simulations are performed on IEEE 30, 57 and 118 bus test systems by binary integer programming. The results show that the number of PMUs is equal to or less than the corresponding results of recently published papers, while the system topological observability is complete, and measurement redundancy is increased.     

用免疫BPSO算法和N-1原则多目标优化配置PMU

为了在满足全网的完全可观测的前提下实现PMU安装投入的性价比最高,通过理论分析得出判断电网节点拓扑可观测的依据,并提出以N-1可靠性检验原则对PMU配置方案进行冗余性检验,由此以全网完全可观测、PMU数目最少和N-1量测冗余度最高为目标建立了PMU多目标优化配置数学模型,并设计了一种结合免疫系统信息处理机制的二进制粒子群优化算法对模型进行求解。该算法综合了粒子群优化算法简单快速和免疫系统种群多样性的优点,明显改善了进化后期算法的收敛性能和全局寻优能力。对新英格兰39母线系统进行PMU多目标优化配置仿真及量测冗余性分析的结果表明,该法对PMU配置方案的量测可靠性及其所需PMU数量进行综合评价可方便快捷地得到性价比最优的方案,较之普通的PMU单目标优化配置方法更为合理和灵活。