A new numerical algorithm to check the observability and bad-data processing ability of the metering scheme

This paper provides a unified approach for the optimization of measurements placements employed for power system online monitoring through state estimation. The proposed methodology, which can be suitable for the mixed measure system, preserves state estimation observability and bad-data processing capability by employing numerical algorithms for observability checking, critical measurements and critical couple identification. First, node injection radix measurements and measurement categories are defined. According to the above definitions, the coefficient matrix can be solved. The analysis on the column vectors of the coefficient matrix can determine each measurement classification. Furthermore, the numbers of each measurement class contains can determine bad-data processing capability. The observability can be checked by the type number of measurements. The proposed method is illustrated with the IEEE39-bus system and the IEEE118-bus system. Results from the case studies are presented to demonstrate that the approach adequately fulfills the desired properties related to observability, bad-data processing, cost, and robustness.     

基于量测函数向量线性相关的网络可观测性分析

提出了一种新的数值算法,该算法通过分析量测函数向量之间的线性相关性,首先定义节点注入基量测,然后求用节点注入基量测函数向量线性表示的系数矩阵,再用冗余量测中部分量测对应系数矩阵中的相应行组成新矩阵,然后将该新矩阵简化后并通过求其秩来判断网络的可观测性。文中以某地区220 kV电网为实际背景进行了可观测性判断分析,结果表明该方法有效可行,满足实际应用的要求。     

Placement of Synchronized Measurements for Power System Observability

This paper presents a method for the use of synchronized measurements for complete observability of a power system. The placement of phasor measurement units (PMUs), utilizing time-synchronized measurements of voltage and current phasors, is studied in this paper. An integer quadratic programming approach is used to minimize the total number of PMUs required, and to maximize the measurement redundancy at the power system buses. Existing conventional measurements can also be accommodated in the proposed PMU placement method. Complete observability of the system is ensured under normal operating conditions as well as under the outage of a single transmission line or a single PMU. Simulation results on the IEEE 14-bus, 30-bus, 57-bus, and 118-bus test systems as well as on a 298-bus test system are presented in this paper.      

Optimal placement of PMUs to maintain network observability using a modified BPSO algorithm

This paper presents a novel approach to optimal placement of Phasor Measurement Units (PMUs) for state estimation. At first, an optimal measurement set is determined to achieve full network observability during normal conditions, i.e. no PMU failure or transmission line outage. Then, in order to consider contingency conditions, the derived scheme in normal conditions is modified to maintain network observability after any PMU loss or a single transmission line outage. Observability analysis is carried out using topological observability rules. A new rule is added that can decrease the number of required PMUs for complete system observability. A modified Binary Particle Swarm Optimization (BPSO) algorithm is used as an optimization tool to obtain the minimal number of PMUs and their corresponding locations while satisfying associated constraint. Numerical results on different IEEE test systems are presented to demonstrate the effectiveness of the proposed approach.     

An efficient algebraic approach to observability analysis in state estimation

An efficient and compact algebraic approach to state estimation observability is proposed. It is based on transferring rows to columns and vice versa in the Jacobian measurement matrix. The proposed methodology provides a unified approach to observability checking, critical measurement identification, determination of observable islands, and selection of pseudo-measurements to restore observability. Additionally, the observability information obtained from a given set of measurements can provide directly the observability obtained from any subset of measurements of the given set. Several examples are used to illustrate the capabilities of the proposed methodology, and results from a large case study are presented to demonstrate the appropriate computational behavior of the proposed algorithms. Finally, some conclusions are drawn.     

Optimal meter placement for maintaining observability during singlebranch outages

This paper presents a method for designing measurement systems, that will not only make the systems observable, but also will maintain observability against loss of network branches. A linear programming based solution is proposed for choosing a measurement configuration that will make the system fully observable. Subsequently, a systematic method of appending a minimum number of additional measurements to ensure full observability against branch outages, is described. Contingencies considered in this paper relate to the loss of any single branch. However, the method can be extended to the case of multiple contingencies, provided the cost of adding more meters is financially justifiable. Numerical examples illustrating the proposed method, are given in the paper     

基于相量量测的电力系统谐波状态估计算法的研究

基于相量量测单元的电力系统谐波状态估计技术,可选取电力网络的节点谐波电压为状态量,支路电流、节点注入电流和节点电压相量为量测量,从而使谐波状态方程成为线性方程.本文根据这个特点,再结合量测方案的不同情况,提出了在冗余量测和基本量测时,采用便于工程实际应用的乔累斯基算法来求解线性谐波状态方程,其计算量只是高斯消元法的一半,且不用考虑选主元,大大减少了计算的时间;在量测矩阵欠定时,采用奇异值分解算法,不仅可以为欠定的状态方程提供稳定的最小二乘解,而且该算法本身具有可观性分析的功能,不需要采用其它算法进行可观性分析,从而极大地简化了谐波状态估计分析的难度.最后通过仿真程序验证了这两种算法在谐波状态估计求解问题中的有效性和可靠性.     

Observability analysis and bad data processing for state estimationwith equality constraints

A factorization-based observability analysis and the normalized residual-based bad-data processing have been carried out for state estimation using the normal equation approach. The observability analysis is conducted during the process of triangular factorization of the gain matrix. The normalized residuals are calculated using the sparse inverse of the gain matrix. The method of Lagrange multipliers is applied to handle state estimation with equality constraints arising from zero injections, because of its better numerical robustness. The method uses a different coefficient matrix in place of the gain matrix at each iteration. The factorization-based observability analysis and normalized residual-based bad-data processing are extended to state estimation with equality constraints. It is shown that the observability analysis can be carried out in the triangular factorization of the coefficient matrix, and the normalized residuals can be calculated using the sparse inverse of this matrix. Test results are presented     

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。     

基于表计配置的配电网可观测性分析

给出了一种配电网可观测性分析的定义，即使用典型负荷模式描述负荷变化规律，且每个负荷用户被赋予不同的表征指标，在变化的网络结构下，支路上优先配置最小数目的功率量测表计，利用量测方程求解典型负荷模式，从而获得各节点负荷，配电网可观测；有效的网络分割方法分割期望网络结构的加权树来优化表计配置，使得在量测方程可解的前提下，量测区域用户的指标均衡。算例进行了可观测分析和表计配置的测试。所提出的可观测分析思路能够折衷考虑经济性和运行需要，而表计配置也为配电网自动化改造提供一个思路。     

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.     

Method of identifying weak transmission network stabilityboundaries

Methods of determining weak transmission stability boundaries are developed based on the strong controllability and observability properties of power systems. This theory has been previously applied to a dynamical model of the generators and network. It was established previously that the network and generator states associated with a cluster of generator and load buses surrounded by weak transmission boundaries are strongly controllable and observable for a single measurement and control at generators or load buses in that bus cluster. Such a bus cluster is called the control area. Two methods of determining control areas, where strong controllability and observability hold, are developed. Both methods attempt to determine weak transmission stability boundaries that encircle control areas. The groups of generators identified as belonging to each control area is identical to the groups of coherent generators determined using a RMS coherency measure evaluated for the set of all inertial load flow contingencies     

Numerical observability analysis based on network graph theory

This paper presents a numerical method for topological observability analysis of a measured power system. By floating-point operations on the echelon form of a rectangular test matrix, which is based on network graph properties, observability and maximal observable islands are determined. A minimal set of pseudo measurements, which make an unobservable network barely observable, is selected in a noniterative manner. The existing numerical methods are based on the number of zero pivots that may appear during the factorization of the measurement Jacobian or the gain matrix. Due to round-off errors, the zero pivots may be misclassified. The problem becomes more severe when the number of injection measurements is large, resulting in a great disparity of values in Jacobian or gain matrix. In the proposed method, the test matrix consists of +/-1 values, it is numerically better conditioned and zero pivots are identified more accurately. By topological processing of the flow measured branches and by removing the redundant injection measured nodes that are incident only to flow measured branches or branches which form loops with flow measured branches, a reduced test matrix is created with fewer nonzero elements than the Jacobian or the gain matrix, resulting in less computational effort. The method details are illustrated by various test systems.     

电力系统状态估计可观测性分析中关于量测岛合并的理论分析

分析了电网量测岛的特点和可观测性的概念。在此基础上，根据电路理论中的两个基本性质，得出了量测岛内最多只含一个复电压未知状态量的基本结论，并由此给出了量测岛间合并的理论依据。出了简化网络分析的目的，提出了内网等值和节点分裂这两个合并分析时的基本处理手段，为新的可观测性拓扑算法的提出做了理论上的准备，文中所提量测岛合并的理论依据得到了实际系统的验证。     

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.     

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。     

Power System Harmonic State Estimation and Observability Analysis via Sparsity Maximization

Harmonic state estimation (HSE) is used to locate harmonic sources and estimate harmonic distributions in power transmission networks. When only a limited number of harmonic meters are available, existing HSE methods have limited effectiveness due to observability problems. This paper describes a new system-wide harmonic state estimator that can reliably identify harmonic sources using fewer meters than unknown state variables. Note there are only a small number of simultaneous harmonic sources among the suspicious buses. Traditional observability analysis is extended to general underdetermined estimation when considering the sparsity of state variables. It is shown that the underdetermined HSE can become observable with proper measurement arrangements by applying the sparsity of state variables. The HSE is formulated as a constrained sparsity maximization problem based on L1-norm minimization. It can be solved efficiently by an equivalent linear programming. Numerical experiments are conducted in the IEEE 14-bus power system to test the proposed method. The underdetermined system contains nine meters and 13 suspicious buses. The results show that the proposed sparsity maximization approach can reliably identify harmonic sources in the presence of measurement noises, model parameter deviations, and small nonzero injections     

电力系统割集空间静态电压稳定域的可视化及实现

安全域的可视化可以提高电力系统的可观测性,帮助调度人员快速估计系统当前的安全状态,针对应采取的预防性措施做出正确的预断。介绍了静态电压稳定域可视化系统的理论与数值仿真依据,以及在河南电网调度通信中心能量管理系统(EMS)上的可视化软件的开发情况。该软件包以定时获取SCADA实时量测数据为基础,快速计算关键断面在割集功率空间中的潮流传输极限边界,并采用OpenGL 3D图形开发技术首次实现了电力系统稳定域在EMS上的可视化,为运行调度人员提供了系统电压稳定性测度的直观显示。由于避免了大规模的连续潮流计算,每个计算周期在几秒至几分钟内(由网络规模大小决定)即可完成,因此在线电压稳定性监视功能得以实现。软件包在Digital UNIX操作平台上开发,对多种UNIX系统具有很好的兼容性和可移植性,为在新一代EMS中嵌入该功能模块奠定了良好的基础。     

The Observability Problem in Traffic Models: Algebraic and Topological Methods

This paper deals with the problem of observability of traffic networks, understanding as such the problem of identifying which is the subset of the origin-destination (OD)-pair and link flows that can be calculated based on a subset of observed OD-pair and link flows, and related problems. A modified topological version of an existing algebraic method for solving observability problems is given. The method is based on a step-by-step procedure, allowing us to update the information once each item of information (OD-pair or link flow) becomes available. In particular, three different observability problems are stated and solved using the proposed methodology, which is illustrated by its application to the Nguyen-Dupuis network and compared with the algebraic version. The topological version is much faster, uses much less memory, and presents no rounding errors or zero test problems but identifies fewer observable flows.     

计及系统可观测性的网络化简与黑启动分区方案制定

基于相量测量单元的广域相量测量系统能够实时反映电网的动态变化,其测量信息的实时性将有助于系统恢复安全快速进行,为大停电后的系统恢复带来新的机遇。首先,将黑启动分区方案优化问题和广域相量测量系统结合起来,建立了考虑系统可观测性的黑启动分区整数线性规划模型。该模型除满足分区功率平衡、分区连通性、特殊支路开断约束以及分区最小规模限制这些基本约束外,还将全网可观测和联络节点可观测2种可观性要求分别转化成线性约束纳入其中。其次,利用可观测度为0以及部分可观测度为1的节点对拓扑图进行简化,降低了优化模型决策空间的规模,进而提高了计算效率。IEEE 118系统算例结果验证了所提模型和系统简化方法的有效性,同时也进一步表明模型的可扩展性。