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。     

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 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.     

State estimation and bad data processing for systems including PMU and SCADA measurements

Conventional state estimators (SE) are based on real-time measurements, consisting of bus voltages and active and reactive power flows and injections, and estimate the voltage phasors of the network buses. Until recently, these measurements were obtained only through SCADA. With the advent of GPS synchronized measurements obtained by phasor measurement units (PMU), effective techniques are required to incorporate the extremely accurate PMU measurements into state estimation, in order to improve its performance and observability. This paper develops a non-linear weighted least squares estimator by modeling the current phasor measurements either in rectangular or in polar coordinates and compares the two approaches. Any numerical problems arised at flat start or for lightly loaded lines, are resolved. The error amplification, due to the current phasor measurement transformation from polar into rectangular coordinates, is also investigated. The normalized residual test is used to effectively identify any bad data in the conventional and phasor measurements. The proposed techniques are tested with the IEEE 14-bus system.     

Optimal PMU placement for power system state estimation with random component outages

Phasor measurement units (PMUs) provide globally synchronized measurements of voltage and current phasors in real-time and at a high sampling rate. Hence, they permit improving the state estimation performance in power systems. In this paper we propose a novel method for optimal PMU placement in a power system suffering from random component outages (RCOs). In the proposed method, for a given RCO model, the optimal PMU locations are chosen to minimize the state estimation error covariance. We consider both static and dynamic state estimation. To reduce the complexity, the search for the optimal PMU locations is constrained to the set of locations guaranteeing topological observability. We present numerical results showing the application and scalability of our method using the IEEE 9-bus, 14-bus, 39-bus and 118-bus systems.     

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.     

Weak bus-constrained PMU placement for complete observability of a connected power network considering voltage stability indices

Phasor measurement units (PMUs) are preferred for installation at weak buses in a power network. Therefore, the weak buses need to be located and the strategic locations of PMUs identified to ensure network observability. Thus, the primary aim of this work is to identify the placements of the maximum number of PMUs installed at the weak buses in the electrical network. The voltage collapse proximity indicator, line stability index, fast voltage stability index, and a new voltage stability indicator utilizing load flow measurement are used to determine the weak buses. A novel deterministic methodology based on a binary-integer linear programming model is then proposed to determine the optimal locations of PMUs. The effect of a single PMU outage considering the weak buses is also demonstrated. The effectiveness of the developed approach is tested and validated on the standard IEEE 14-, 118-, 300-, and New England 39-bus systems. The obtained results are also compared to those using different weak bus methodologies.     

An Independent Component Analysis Approach for Wide-Area Monitoring of Power System Disturbances

Abstract

Wide-area power system monitoring based on phasor measurement units allows collecting a set of physical variables for evaluating the system security and stability, as well as for detecting power system disturbances. However, trends, noise and non-Gaussian distribution in measurements are important challenges for carrying out the detection, localization and visualization of power system disturbances. In this paper, a methodology that combines independent component analysis with statistical indices for detecting and visualizing anomalous dynamic events from wide-area measurements is proposed. From the statistical indices, two charts are also proposed to provide a better understanding of the system disturbances. Finally, a set of simulated data obtained from a transient stability model of the New England/New York test system is used to demonstrate the effectiveness of the proposed technique.     

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.     

配电网状态估计的全局灵敏度分析及应用

在配电网状态估计中,量测装置配置不齐全,通常引入伪量测来满足系统的可观性要求。考虑到量测数据有一定的误差以及伪量测与真实值之间可能存在偏差,配电网状态估计的量测和伪量测存在不确定性,这会影响配电网状态估计的准确性。文中提出了配电网状态估计的全局灵敏度分析方法,辨识影响状态估计精度的关键(伪)量测不确定性因素及其位置;利用稀疏多项式混沌展开计算全局灵敏度指标,以提高全局灵敏度分析的计算效率;建立了基于不确定性因素重要性排序的量测装置布点方法。采用IEEE 33节点配电网进行仿真,通过与常用方法进行比较,验证了所提方法的有效性。该方法克服了传统状态估计灵敏度分析方法的不足,能有效评估(伪)量测不确定性因素的交互作用对状态估计的影响;此外,基于全局灵敏度分析的量测装置布点方法能显著提高配电网状态估计精度。     

A tool for the evaluation and selection of state estimatormeasurement schemes

This paper describes an approach for evaluating and selecting the measurement scheme for power system state estimation. The approach utilizes a computer package which has been developed for analyzing all the power system state estimation related functions. In the proposed approach the measurement configuration is selected so that the following criteria are met: measurement system observability and reliability, bad data detectability and identifiability, state estimation accuracy. The necessary algorithms to analyze the above criteria are described     

A reduced model for power system observability: analysis andrestoration

An algorithm for observability analysis and restoration in power system state estimation is presented. The problem of P-δ, Q-V and complete observability is addressed. In the proposed algorithm, groups of buses are represented by supernodes and the problem of observability analysis and restoration is examined with a reduced network. The proposed algorithm is easily implemented and it is independent of the state estimation solution algorithm. In case of unobservability, the proposed methodology identifies directly the maximal islands and determines the number and the placement of the required pseudomeasurements for observability restoration. Results from several test cases are presented     

A state estimation approach for fault location in transmission lines considering data acquisition errors and non-synchronized records

The performance of algorithms for fault location is directly related to the accuracy of its input data. Thus, factors such as errors in the line parameters, failures in synchronization of oscillographic records and errors in measurements of voltage and current can significantly influence the accuracy of algorithms that use bad data to indicate the faults location. This paper presents a methodology for fault location based on the theory of state estimation in order to determine the location of faults more accurately by considering realistic systematic errors that may be present in measurements of voltage and current. The methodology developed is innovative because, besides calculating the most likely fault distance obtained from measurement errors, the variance associated with the distance found is also determined, using the errors theory. The obtained results are relevant to show that the proposed estimation approach works even adopting realistic variances. Moreover, the fault location brings performance gains compared to a traditional algorithm, available in the literature.     

配电系统关键量测解耦快速辨识及鲁棒量测优化配置

对配电系统实时运行状态的准确感知离不开状态估计,状态估计的正常运行与量测系统状况紧密相关。文中提出了一种针对三相不平衡配电系统的关键量测和关键量测组解耦快速辨识的新方法,该方法实现了关键量测和关键量测组辨识的解耦和非迭代:一方面,辨识过程仅需进行有功功率部分的状态估计,极大降低了计算规模;另一方面,整个计算过程无需迭代,并给出了相应的严格理论证明。此外,建立了配电系统三相m~(-1)鲁棒量测优化配置模型,以保证任一量测缺失时网络仍然可观测。将所提方法和模型应用于改进的IEEE 37节点算例进行测试,计算结果显示关键量测解耦快速辨识方法的辨识速度远快于解耦前,鲁棒量测优化配置显著降低了配电系统不可观测的风险。     

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.     

Generalized State Estimation of Flexible AC Power Systems Considering Wind Generators and Primary Frequency Control

This paper proposes a practical approach to incorporate the mathematical models of both fixed-speed and variable-speed wind turbine generators, automatic load frequency controls as well as voltage magnitude and frequency dependent loads into a weighted least squares-based state estimation algorithm suitable for the analysis of flexible alternating current (AC) transmission systems. As opposed to conventional static state estimators, where the inclusion of these electric components has been neglected so far, the proposed approach permits the determination of the steady state operation of a power system in the event of a supply-demand unbalance by estimating the magnitude of the frequency deviation from its nominal value. The state estimation is based on measurements related to those that should be obtained by a supervisory control and data acquisition (SCADA) system and phasor measurement units. For the purpose of this paper, the set of values associated with SCADA measurements (nodal power injections, power flows, and voltage magnitudes) and phasor measurement unit (PMU) measurements (voltage and current phasors) are generated from a power flow analysis of the network under study. Lastly, numerical simulations are reported to demonstrate the effectiveness of the proposed approach.     

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.     

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.