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     

Iterative bad-data suppression applied to state estimators based on the augmented matrix method

The augmented matrix method for power system state estimation combines simple conception, good numerical behavior and computational efficiency. Concerning bad-data processing, however, the method presents a difficulty: the calculation of normalized residuals is not straightforward, so that the implementation of conventional bad-data identification procedures may become complicated.

This paper presents a technique for bad-data processing based on weighted residuals and a nonquadratic cost function to circumvent that problem. The weighted residuals are immediately available from the proposed formulation for the augmented matrix method. The non-quadratic cost function is piecewise quadratic-constant and the break points are varied through the iterations to allow proper bad-data identification. The application of a diakoptical technique avoids the need for costly refactorizations of the augmented matrix. The results from simulation studies carried out with the IEEE 14-bus and 30-bus test systems are presented.     

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.     

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。     

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.     

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.     

Robust dynamic state estimation of power systems based onM-Estimation and realistic modeling of system dynamics

This paper presents a new scheme of dynamic state estimation, utilizing a statistical approach called the M-Estimation to resolve the filtering problem robustly. In the prediction step, realistic treatment of system dynamics based on nodal analysis produces an efficient state prediction method. The proposed Robust Realistic Dynamic State Estimation (RRDSE) has been tested on 5-bus, 14-bus, and 30-bus test systems and the results are presented. The error analysis presented reveals the superiority of the proposed RRDSE particularly when the system measurements are under bad-data condition     

Diakoptic State Estimation Using Phasor Measurement Units

This paper presents a diakoptic-based distributed state estimation (SE) algorithm suitable for large-scale power systems. In the proposed approach the large-scale power system is divided into a certain number of subsystems by removing tie line measurements. Based on diakoptic theory, the SE problem is then partitioned into a number of subproblems which are solved for each subsystem using local computational resources. In subsequent steps, the intermediate subsystem SE solutions are sent to a central computer for completing the state estimation process by taking the tie line measurements into consideration. Phasor measurement units are used to make each subproblem solvable and to coordinate the voltage angles of each subsystem SE solution. Test results on the IEEE 14-bus test bed and IEEE 118-bus test bed are provided.      

An integer-arithmetic algorithm for observability analysis of systems with SCADA and PMU measurements

This paper presents an efficient numerical method for observability analysis of systems including both conventional (SCADA) measurements and synchronized phasor (PMU) measurements, using integer preserving Gaussian elimination of integer coefficient matrices. The observable islands are identified in a noniterative manner, by performing backward substitutions on the integer triangular factors of the integer gain matrix. Multiple placement of conventional and phasor measurements for a system that is found to be unobservable is done by a direct method, using the integer triangular factors of a Gram matrix associated with a reduced size Jacobian matrix. Since all computations performed are exact, no round-off error, numerical instability, or zero identification problems occur. The IEEE 14-bus system is used to illustrate the steps of the proposed method. Test results for the IEEE 300-bus and the FRCC 3949-bus systems are provided to demonstrate the features of the proposed algorithms.     

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。     

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。     

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.      

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.     

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     

基于正交变换与置信域的量测方差估计与权重设置算法

在状态估计实际应用中,量测方差获取和权重设置存在一定的困难。伴随状态估计运算量越来越繁重,现有量测方差估计算法的收敛性无法得到保证。为此提出了一种基于正交变换与置信域的量测方差估计和权重设置算法。利用正交变换降低迭代系数矩阵条件数,提高量测方差估计的数值稳定性;根据正交变换的化简结果,结合拉格朗日乘子法,建立新的量测方差估计模型;对于迭代过程的中间数据,采用置信域作为目标函数的约束,确保每次估计结果落在置信区间内;最后,通过IEEE 14/30/118标准系统算例证明了该算法的有效性。     

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.     

基于负荷电流的配电网非量测负荷估计

提出了一种基于负荷电流的抗差估计算法用于修正10kv配电网非量测负荷。该算法将配电网中的功率量测变换为电流量测，实现了雅可比矩阵常数化，负荷电流实虚部解耦求解。并采用了权值随残差变化的权函数，从而较大程度上抑制了伪量测中坏数据对估计结果的不良影响。文中还给出了IEEE33节点配电系统的计算结果。结果表明，该算法能够有效地修正伪量测数据，使其准确度达到或接近实际量测值的准确度。     

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。     

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.     

新息图拓扑可观测性及不良数据可辨识性分析

新息图状态估计在拓扑结构获取和不良数据辨识方面与一般状态估计差异较大。文中研究了新息图状态估计拓扑结构可观测性、量测数据的相关性、不良数据的可检测性和可辨识性问题。由获得连支推算新息的必要条件确定拓扑结构可观测性;利用新息差向量的表现特征分析不良数据可检测性和可辨识性,最后给出了较优的辨识连支不良数据的顺序。对该算法的分析及IEEE30节点系统算例表明,新息图状态估计中不良数据可辨识性可进行定性分析,其辨识不正常事件的能力强,量测冗余度要求较低。