Fault location observability analysis and optimal meter placement based on voltage measurements

Various transmission line fault location algorithms have been proposed in the past depending on measurements available. These methods evince that if a sufficient number of meters are placed in a power network to record the fault measurements, then the fault location can be reliably estimated. A relevant question to ask may be: how many meters are sufficient in order to derive a reliable and unique fault location estimate for a given network? This paper addresses this question by defining and performing the fault location observability analysis. An optimal meter placement scheme is proposed for determining the optimal locations to place meters so as to make the system observable while minimizing the required number of meters to reduce costs. The proposed method is especially useful for power networks where digital relays have not yet been widely adopted and measuring devices such as digital fault recorders are deployed for monitoring purposes. A sample power network has been employed to illustrate the proposed method.     

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     

基于可观测性分析的计及DG不确定性配电网表计优化配置

提出一种基于可观测性分析的计及分布式电源(DG)出力不确定性的配电网表计优化配置算法。首先,对含DG配电网的可观测性进行了分析,得到表计配置原则,通过网络分割算法分割网络加权树进行表计配置;然后,对满足可观测性要求的表计配置方案进行优化,采用拉丁超立方抽样技术对DG出力不确定性进行处理,得到使量测系统表计数目最少和负荷均衡度最大的配置方案;最后,通过对14节点配电网络和IEEE 33节点系统进行测试计算,验证了所提算法的有效性。     

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。     

A simple factorization-based observability analysis and meter placement method

A simple factorization-based observability analysis and meter placement method is presented in this paper. Measurement Jacobian matrix is extended to include non-existing branch flow measurements so that observable islands are identified simultaneously when extra candidate measurements are placed to make the network observable if initially the system is unobservable. The method is described in detail along with numerical examples, which illustrates its effectiveness.     

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     

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.     

线性相关环及其在电力系统可观察性分析中的应用

在分析测量向量间线性相关的基础上提出了线性相关环的概念,介绍了将线性相关环用于可观察性判断,以提高在线应用实时性的具体方法,如对Ｈ矩阵直接分解,大节点合并法及将数值法与拓扑法相结合的方法,同时将线性相关环用于解决后备重数,择优布置测量等问题。     

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.     

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。     

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.     

电网谐波状态估计中的可观性分析

谐波状态估计的一个难点,在于量测数目通常小于状态量数目,导致量测—状态方程欠定,系统不完全可观。针对该问题,进行了3个方面的研究:首先,结合数学分析和实际电网分析,从减少状态量的角度,实现方程由欠定变为恰定或超定,在保证系统状态完全可观的前提下,大大减少量测设备的数目;其次,将奇异值分解法(SVD)应用在系统可观部分的判断和计算中;然后,针对可观性分析中传统代数方法不足,结合矩阵条件数,提出一种实用的线性无关排序法,并将该方法用于指导不可观系统量测设备的调整和添加,实现系统良好的可观性。最后以菏泽—仿山220kV—110kV—35kV配电系统为例,对SVD和线性无关排序法进行说明,验证了方法的可行性。     

Transmission network fault location observability with minimal PMU placement

This paper presents a concept of fault-location observability and a new fault-location scheme for transmission networks based on synchronized phasor measurement units (PMUs). Using the proposed scheme, minimal PMUs are installed in existing power transmission networks so that the fault, if it occurs, can be located correctly in the network. The scheme combines the fault-location algorithm and the fault-side selector. Extensive simulation results verify the proposed scheme.     

电力系统PMU最优配置数字规划算法

随着相量量测装置(PMU)硬件技术的逐渐成熟和高速通信网络的发展,PMU在电力系统中的状态估计、动态监测和稳定控制等方面得到了广泛应用.为达到系统完全可观,在所有的节点上均装设PMU既不可能也没有必要.文中提出一种基于系统拓扑可观性理论的数字规划算法,利用PMU和系统提供的状态信息,最大限度地对网络拓扑约束方程式进行了简化,以配置PMU数目最小为目标,形成了PMU最优配置问题,并采用禁忌搜索算法求解该问题.其突出优点是利用了系统混合测量集数据,即不仅考虑了PMU实测数据,同时计及了可用的潮流数据.在IEEE14节点和IEEE 118节点系统的仿真结果表明,与常规的PMU最优配置算法相比,所提出的数字规划算法可以实现安装较少数量的PMU而整个系统可观的目标.     

Power system observability with minimal phasor measurementplacement

The placement of a minimal set of phasor measurement units (PMUs) so as to make the system measurement model observable, and thereby linear, is investigated. A PMU placed at a bus measures the voltage as well as all the current phasors at that bus, requiring the extension of the topological observability theory. In particular, the concept of spanning tree is extended to that of spanning measurement subgraph with an actual or a pseudomeasurement assigned to each of its branches. The minimal PMU set is found through a dual search algorithm which uses both a modified bisecting search and a simulated-annealing-based method. The former fixes the number of PMUs while the latter looks for a placement set that leads to an observable network for a fixed number of PMUs. In order to accelerate the procedure, an initial PMU placement is provided by a graph-theoretic procedure which builds a spanning measurement subgraph according to a depth-first search. From computer simulation results for various test systems it appears that only one fourth to one third of the system buses need to be provided with PMUs in order to make the system observable     

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.     

Harmonic source location and meter placement optimization by impedance network approach

The level of harmonic distortion on modern power systems is a concern as more non-linear devices are used in energy conversion. Therefore, locating the harmonic source is important to identify and to take appropriate actions for eliminating the distortion. Also meter placement is a crucial part of harmonic location problem. The placement approach should both provide limited number of meter locations and overcome misallocation of the source because of the difficulty in obtaining correct network impedances. Consequently, a harmonic source location method by using impedance network approach with a new optimal meter placement algorithm (OMPA) is proposed in this paper. The validation of OMPA for different levels of harmonic impedance errors is performed using Monte Carlo technique and the effectiveness of the algorithm is shown by using IEEE 30-bus test system.     

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.      

电力系统拓朴可观测性和量测量配置的辅助分析

本文提出了一种简便、有效的电力系统可观测性和量测量配置的计算机辅助分析算法。相应的辅助分析软件可以为电力系统调度中心的工作人员在进行电网量测量的合理配置,或者为在远动装置检修、更新时进行量测量的调整补充,提供辅助分析的手段。该方法可以从在线实时数据库获得系统结构,开关状态和量测系统信息,通过网络结线分析和网络可观测生成树分析网络可观测性,保证电力系统状态估计软件的正常运行。     

配电网谐波量测装置最优配置方法

为满足油田节能减排与工艺调整要求,变频器等非线性电力电子设备的应用日益广泛,油田配电网谐波污染日趋严重。谐波在线监测系统为测量和分析油田配电网谐波分布特征奠定了基础;但受应用经济性约束,谐波量测终端安装数量有限,有必要对其安装位置进行优化。本文综合考虑谐波状态估计可观测度与冗余度,提出了一种量测终端优化定址方法。采用谐波状态估计可观性逻辑判断法,利用节点关联矩阵计算不同谐波量测终端配置方案下系统可观测度与冗余度;在保证系统可观测度最大的前提下,以冗余度最大为目标优化量测终端安装位置。实现在终端数量有限的情况下提高油田配电网谐波状态估计的可观测度与精度,建模仿真结果证明了该方法的有效性。