A Distributed State Estimator Utilizing Synchronized Phasor Measurements

With the creation of balancing authorities by the North American Reliability Council that span large portions of the North American interconnection, and stringent requirements for real time monitoring of power system evolution, faster and more accurate state estimation algorithms that can efficiently handle systems of very large sizes are needed in the present environment. This paper presents a distributed state estimation algorithm suitable for large-scale power systems. Synchronized phasor measurements are applied to aggregate the voltage phase angles of each decomposed subsystem in the distributed state estimation solution. The aggregated state estimation solution is obtained from the distributed solution using a sensitivity analysis based update at chosen boundary buses. Placement of synchronized phasor measurements in the decomposed subsystems is also investigated in this paper. Test results on the IEEE 118-bus test bed are provided     

基于一致性理论的多区域电力系统分布式状态估计

随着电网规模不断扩大,传统集中式状态估计方法的数据通信与存储任务重、计算量大,难以满足现代电力系统状态估计需求。在计及系统状态估计非线性的基础上,将电力系统划分为若干个不重叠的子区域,并利用拉格朗日乘子法对状态估计方程进行解耦,建立电力系统多区域非线性状态估计模型。基于一致性理论建立全分布式状态估计方法对模型进行求解,该方法无需状态估计控制中心,只需各子区域交换一致性变量和边界节点的状态变量信息,各子区域便可平行独立地计算本地状态变量估计值,较集中式状态估计均衡了通信及计算负担。IEEE 14节点系统仿真结果验证了所提分布式状态估计方法的有效性。     

Decentralized unscented Kalman filter based on a consensus algorithm for multi-area dynamic state estimation in power systems

A decentralized unscented Kalman filter (UKF) method based on a consensus algorithm for multi-area power system dynamic state estimation is presented in this paper. The overall system is split into a certain number of non-overlapping areas. Firstly, each area executes its own dynamic state estimation based on local measurements by using the UKF. Next, the consensus algorithm is required to perform only local communications between neighboring areas to diffuse local state information. Finally, according to the global state information obtained by the consensus algorithm, the UKF is run again for each area. Its performance is compared with the distributed UKF without consensus algorithm on the IEEE 14-bus and 118-bus systems. The low communication requirements and high estimation accuracy of the decentralized UKF make it an alternative solution to the multi-area power system dynamic state estimation.     

基于联络线扩展区域分解协调的分布式并行状态估计

为适应互联电网日益复杂的结构形式和分层分区管理模式,采用联络线分区解耦方式对互联系统进行分布式状态估计计算。考虑到估计计算精度与计算效率的均衡,提出了一种将联络线扩展区域状态估计和灵敏度矩阵协调算法结合的分布式状态估计算法。设计分布式状态估计整体思路,一方面,在实现联络线分区解耦的前提下,完成分区层各子区独立状态估计计算和灵敏度矩阵求解,利用子区计算时机动态构建协调层联络线估计区域并完成并行状态估计计算;另一方面,根据协调层下发的联络线估计值和灵敏度矩阵,分区层各子区并行实现边界估计值不匹配量的协调修正计算。最后,通过IEEE 118节点、IEEE 30节点和实际互联电网的模拟仿真,验证上述算法实现分布式状态估计计算的优越性。仿真结果表明,采用该算法进行分布式估计计算,既具有较高的估计精度、收敛速度和计算效率,又可实现并行独立计算,避免集中式状态估计计算规模大、无法解决局部不可观测或不收敛的瓶颈问题。     

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.     

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.     

基于相量量测的等式约束二阶段状态估计模型

利用PMU的量测信息实现系统的动态可观测,考虑PMU数据刷新时间快的特点,在R.F.Nuqui的动态监测模型的基础上建立了适合静态估计的基于等式约束二阶段估计模型。该模型将PMU和SCADA的量测数据共同用于非线性估计,采用零注入节点功率作为等式约束条件来提高估计精度,然后对非线性估计的结果和PMU的支路电流相量进行线性估计。模拟了当系统某节点负荷持续变化时,利用等效导纳法对非线性区域节点状态量进行估计,最后采用IEEE 14和57节点系统算例对提出的模型进行了验证。     

Analysis of confidence bounds in power system state estimation with uncertainty in both measurements and parameters

A method for uncertainty analysis in power system state estimation is proposed. The uncertainty is expressed in both measurements and network parameters. Uncertainties in both measurements and parameters are known and bounded. The problem is formulated as a constrained non-linear optimization problem. To find the tightest possible upper and lower bounds of any state variable, the problem is solved by sequential quadratic programming (SQP) techniques. When applied to the 6-bus, IEEE 14-bus and IEEE 30-bus networks, the proposed method shows reliability and accuracy in estimating the uncertainty bounds in power system state estimation. In addition, assessment of time performance is carried out to demonstrate that the proposed method is suitable for either an on-line or an off-line application.     

Distributed agent-based state estimation considering controlled coordination layer

The buses involved in re-estimation is fixed in the traditional distributed state estimation. On the one hand, if only the boundary buses were re-estimated, will lead to a high power mismatch in a short or low impedance transmission line. On the other hand, if all the buses were re-estimated again, will lead to unnecessary computational burden. To solve this problem, this paper presents a new distributed agent-based state estimation that considers controlled coordination layer. Each local agent of a subsystem is in charge of the state estimation of its own system. The global sensitivity agent is responsible for the sensitivity analysis of the entire system. The boundary bus aggregation agent determines the range of coordination layer to be re-estimated according to the state estimation deviation of each boundary bus defined in this paper. Furthermore, the observability analysis judgment theorem of the overlapped DSE and the topology analysis suitable for the bad data of boundary region are investigated. The proposed method is illustrated with the IEEE 14-bus system, and the test results for the IEEE 118-bus system are provided.     

结合模糊综合评判与决策的电力系统状态估计

针对电力系统状态估计中各种类型量测数据精度对状态估计结果有重要影响的问题,在基本加权最小二乘法估计的基础上,结合模糊综合评判与决策中的层次分析法(Analytic Hierarchy Process,AHP)讨论了一种改进权值确定方法的加权最小二乘法。它是将电力系统状态估计分解为量测值与估计值的差值平方最小(目标)、不同类型的量测值(准则)、各类型量测值相对精度的大小(方案)等层次,在此基础上进行定性和定量分析。通过IEEE 14-bus、IEEE 30-bus和IEEE 57-bus的标准算例进行仿真分析,证明层次分析法确定权值的加权最小二乘法能够有效地计算出电力系统的状态估计值。通过和基本加权最小二乘法进行比较,证明了该方法的优越性和实用性。     

考虑新能源不确定性的互联电网交换功率鲁棒优化模型

高比例新能源及其不确定性增加了多区域交流互联系统交换功率控制的难度,为保证区域间联络线传输功率的协调分布及其波动相对均衡,提出了一种考虑互联电网外特性的交换功率稳定控制模型。考虑互联系统自动发电控制(AGC)参与因子与联络线潮流分布的关联关系,推导并构建了互联系统AGC下的潮流模型。进而,以联络线功率波动幅值最小为目标函数,建立了基于鲁棒优化的区域交换功率稳定控制模型,并提出了一种基于松弛法的协同演化算法对该模型进行求解。以双IEEE 14节点和IEEE 118节点测试系统为例进行仿真分析,将无优化与鲁棒优化计算结果进行对比,结果表明鲁棒优化可以有效应对新能源随机出力的影响,对于外特性的稳定性具有明显改善效果,并验证了所提算法的有效性和实用性。     

Tie-line constrained distributed state estimation

This paper presents an implementable distributed state estimation method for online analysis of power systems having multiple, geographically separated areas. Distributed state estimation apart from giving a faster solution, also improves the condition number of the resultant gain matrices. The method proposed here uses the conventional WLS estimator (Gauss-Newton method) with equality constraints forcing the tie line flows as calculated by the adjacent areas to be equal. Based on the topology of the network, the system is partitioned into multiple areas and a processor is assigned to each of these areas for solving the local state estimation problem. Simulations carried out on the IEEE 14, 30 and 118 bus systems show good convergence properties and improvement on the condition number of the gain matrices when compared with centralized algorithms.     

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.      

A novel hybrid state estimator for including synchronized phasor measurements

State estimator is crucial for on-line power system monitoring, analysis and control. With the increasing use of synchronized phasor measurement units (PMU) in power grids, how to utilize phasor measurements to improve the precision of state estimator becomes imperative. Since there are lots of traditional measurements in SCADA system and it is hard for phasor measurements to replace them in the near future, the best way is to develop hybrid state estimator which includes both phasor and traditional measurements to get better behavior. In this paper, a novel state estimator for including voltage phasors, branch current phasors and traditional measurements is proposed. The detailed model and how to calculate covariance matrix of PMU measurements are described in detail. New England 39-bus system and IEEE 118-bus system are used as test systems and the simulation results demonstrate that the proposed state estimation algorithm improves the precision greatly and gets better behavior as compared with other state estimators with or without phasor measurements.     

Multi area state estimation using synchronized phasor measurements

This paper investigates the problem of state estimation in very large power systems, which may contain several control areas. An estimation approach which coordinates locally obtained decentralized estimates while improving bad data processing capability at the area boundaries is presented. Each area is held responsible for maintaining a sufficiently redundant measurement set to allow bad data processing among its internal measurements. It is assumed that synchronized phasor measurements from different area buses are available in addition to the conventional measurements provided by the substation remote terminal units. The estimator is implemented and tested using different measurement configurations for the IEEE 118-bus test system and the 4520-bus ERCOT 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.     

Voltage stability monitoring of power systems using reduced network and artificial neural network

This paper presents network reduction based methodologies to monitor voltage stability of power systems using limited number of measurements. In a multi-area power system, artificial neural networks (ANNs) are used to estimate the loading margin of the overall system, based on measurements from the internal area only. Information regarding the important measurements from the external areas is considered in measurement transformation through the network reduction process, to enhance the estimation accuracy of the ANNs. A Z-score based bad or missing data processing algorithm is implemented to make the methodologies robust. To account for changing operating conditions, adaptive training of the ANNs is also suggested. The proposed methods are successfully implemented on IEEE 14-bus and 118-bus test systems.     

计及PMU的电力系统状态估计混合模型的研究

在等效电流量测变换状态估计模型的基础上引入旋转变换,实现方程的实、虚部严格解耦,并建立一种非线性估计和线性估计相结合的混合状态估计模型:首先把PMU节点的状态量测值以及PMU相关节点的状态推算值作为估计值进行非线性估计,然后再利用非线性估计结果和PMU量测进行线性估计。该模型可以充分利用PMU的量测,提高状态估计收敛速度,同时可以进一步利用PMU量测来提高估计精度,所需的存储量较小,具有较好的工程应用前景。最后采用IEEE14和IEEE30节点系统对该模型进行了验证。     

Hierarchical static state estimation in a large-scale electric power system: Estimation error analysis

This paper discusses the hierarchical state estimation method for a large-scale power system from the point of view of the estimation error. It is shown that the error is bounded and depends on the number of subsystems comprising the power system, on the subsystem state estimation errors, on the number of measured lines coupling individual subsystems, and on the kind of power flow measurements from those lines used in the calculations. Theoretical considerations are illustrated by use of numerical results.     

改进的基于复数域标幺化的快速解耦状态估计算法

当前基于复数域标幺化的配电网快速解耦状态估计算法仍存在部分支路阻抗比绝对值较大影响算法收敛性能的问题。针对该问题,提出了改进的基于复数域标幺化的快速解耦状态估计算法。在电压和功率的基准值中引入相角进行复数域标幺化,并对标幺化后阻抗比绝对值较大的支路进行串联补偿。该串联补偿方法通过给予待补偿支路1个附加电抗以减小支路阻抗比,同时串联1条虚拟支路以消除附加电抗对支路参数的影响,而最优补偿电抗的取值由各支路阻抗比绝对值的均值决定。分别在IEEE 33节点的对称配电系统和IEEE 13、123节点的不对称配电系统中对改进的基于复数域标幺化的快速解耦状态估计算法进行测试与分析。