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.     

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.     

基于分块QR分解的一种状态估计算法

文中提出了一种基于分块QR分解的状态估计方法。该方法把虚拟测量处理为等式约束，避免了由于权因子分散而导致的数值病态问题。在每次迭代中，通过对两个分块矩阵的QR分解和一个稀疏三角线性方程组的求解，实现了系数矩阵的三角分解。与带有约束的正规方程(NE/C)法相比，不但消除了Jacobian矩阵叉乘造成的信息损失，而且保证了分解的数值稳定性。稀疏QR分解采用了基于Givens变换的方法并利用最小度列排序和变主元消元策略。减少注入元素的数目，提高了状态估计的计算效率。试验系统的仿真结果表明了该方法具有良好的数值稳定性和鲁棒性，而且有较高的计算效率，可以满足在线状态估计的要求。     

超大规模电网快速状态估计的实现方法

随着一体化互联大电网全局分析决策中心的建设,对实时状态估计计算速度提出了更高要求。采用多线程并行计算技术实现了快速分解状态估计信息矩阵的快速计算,在稀疏矩阵节点优化编号及其因子分解过程中采用标准模板库关联容器存储稀疏矩阵。基于新一代调控系统验证环境和实际电网拼接模型算例进行了验证。结果表明：在超大规模电网状态估计中,采用多线程并行计算信息矩阵及其因子分解具有较高的加速比,结合基于关联容器的稀疏矩阵存储格式,能够有效提升编程效率和程序品质以及状态估计的计算效率。     

Sparse vector method improvements via minimum inverse fill-inordering

A practical ordering algorithm to enhance sparse vector methods without sacrificing the sparsity of the table of factors is presented. The proposed algorithm locally minimizes the number of new nonzero elements in the inverse of the lower triangular matrix during the factorization process. Two refined versions which can usually give the shortest length on factorization path of single and/or composite singletons are provided. Test results from previously published ordering algorithms based on minimum fill-in are also presented for comparison. The performance of applications to power system state estimation is evaluated. It is shown that the proposed ordering algorithm is a very effective strategy for the improvement of sparse vector methods     

A unified approach to robust meter placement against loss ofmeasurements and branch outages

This paper presents a systematic procedure by which measurement systems can be optimally upgraded. The proposed procedure yields a measurement configuration that can withstand any single branch outage or loss of single measurement, without losing network observability. It is a numerical method based on the measurement Jacobian and sparse triangular factorization, making its implementation easy in existing state estimators. It can be used off-line in planning and meter placement studies or it can be implemented as part of the on-line observability analysis function. Details of the procedure are presented using numerical examples     

稀疏技术在电力系统状态估计中的应用

研究了电力系统状态估计中稀疏技术的应用方法。首先根据因子矩阵和消去树，讨论了稀疏向量法。然后基于给定的稀疏矩阵存储方法和符号因子化技术，提出了一种采用稀疏向量法进行LDLT分解的算法，最后结合量测残差方差计算给出了两种应用稀疏技术计算的方法。算法的有效性在IEEE 118和IEEE 300系统上得到了验证。     

KLU稀疏直接求解器在状态估计中的应用

稀疏矩阵及稀疏线性方程组求解已成为大规模电网状态估计计算效率的瓶颈,阐释了基于BTF和Gilbert-Peierls算法的稀疏矩阵直接求解器KLU（Clark Kent LU）,并将其嵌入到智能调度技术支持系统中生产运行的状态估计程序功能。首先在计算得到雅可比矩阵的基础上基于OpenMP并行化技术快速求解信息矩阵;然后使用KLU求解器进行信息矩阵的因子表符号分析和数值分解;最后在状态估计计算过程中使用KLU求解器求解线性方程组,从而提高大规模电网状态估计的计算效率。通过省中心、分中心、模型数据中心D5000的状态估计实际应用,证明了该方法的有效性和实用性。     

电力系统无功综合优化的线性规划内点法

本文采用原对偶路径跟踪法直接求解无功综合优化问题的非标准形式的线性规划模型。通过消去松驰变量和部分拉格朗日乘子变量,使得在每步迭代中求解的线性方程组的系数矩阵为对称稀疏矩阵,可用三角分解法有效求解。实际系统的计算结果表明,当系统的约束条件和变量数目增加时,此算法的迭代次数变化较少。     

A bad data identification method for linear programming stateestimation

The author presents a bad-data identification procedure for linear programming (LP) power system static state estimation. LP state estimators minimize the weighted sum of the absolute values of the measurement residuals. The proposed procedure first detects the bad data using the measurement residuals of those measurements rejected by the LP estimator. Then the bad measurement is identified and eliminated by estimating the measurement errors of the zero residual measurements. The residuals obtained from this second estimation step are made use of for this purpose. In order to minimize the computational burden during the elimination cycles, a fast way of eliminating measurements through weight changing is also presented. The performance of the proposed procedure is tested and the results are presented, using AEP's 14, 30, 57 and 118     

小干扰稳定性分析中一种关键特征值计算的稀疏实现

该文提出了一种大规模电力系统小干扰稳定性分析中基于稀疏技术的关键特征值求解方法。该方法借助于Cayley变换，将关键特征值计算变为主特征值的计算，导出了基于稀疏增广状态矩阵的幂法迭代公式，并利用稀疏2×2分块矩阵及稀疏三角分解技术实现了该方法。2个示例系统的计算结果验证了算法的正确性和有效性。该方法不但可用于低频振荡抑制中控制器参数的协调优化，而且其中使用的多种基本技术也可以推广到基于子空间法求取部分关键特征值的各种迭代计算中。     

大电网动态无功优化的快速解耦算法

建立电网的完整动态无功优化模型是一个计及设备动作次数约束并考虑变量离散化特性的非线性混合整数规划问题。由于其修正方程系数矩阵具有可分块结构特点,对此系数矩阵采用块矩阵解耦求解,能够在一定程度上解决大电网计算时的＂维数灾＂问题。上述计算的关键点是对修正方程系数矩阵的计算存储及对系数矩阵进行三角分解结果的计算存储,对此提出对系数矩阵进行两次三角分解的方法,大大地降低大电网计算的数据存储量。以一个实际的14节点供电系统、某省级538节点系统和IEEE 118节点系统作为算例,计算结果表明,所提出的算法能有效地解决大电网的动态无功优化＂维数灾＂问题。     

Fast calculation using parallel processing and pipeline processing in power system analysis

This paper presents an application of parallel processing and pipeline processing to power system analysis. The system matrix is transformed to a bordered block diagonal form (BBDF) matrix for effective utilization of the processors. After LU factorization, subnetworks organize sparse matrices and the boundary network organizes a full matrix. First, a parallel processing technique is used to calculate subnetworks. Then, as pipeline processing is applied, inverse matrix of the boundary network is multiplied. The proposed method is made operational on a parallel computing system including a pipeline processor. A consideration on the transient stability analysis using the proposed method also is presented at the end of this paper.     

Topology error identification using normalized Lagrange multipliers

This paper introduces a method for topology error identification based on the use of normalized Lagrange multipliers. The proposed methodology models circuit breakers as network switching branches whose statuses are treated as operational constraints in the state estimation problem. The corresponding Lagrange multipliers are then normalized and used as a tool for topology error identification, in the same fashion as measurement normalized residuals are conventionally employed for analog bad data processing. Results of tests performed with the proposed algorithm for different types of topology errors are reported     

STEKF协同残差归一化的感应电机转速辨识方法

为了提高感应电机无速度传感器矢量控制系统的性能,提出了一种强跟踪扩展卡尔曼滤波(STEKF)协同残差归一化(NR)的自适应转速估计方法。通过将渐消因子引入到状态预测协方差矩阵中,实时在线调整增益矩阵,强迫输出残差序列保持相互正交。同时,通过对残差进行归一化处理,自适应地调节渐消因子,消除由残差本身数值差异引起的信息不对称。该文提出的方法提高了系统模型对于实际系统以及外部环境变化的适应性,有效降低了估计误差,满足对于低速的估计要求。对基于STEKF协同残差归一化观测器的感应电机无速度传感器矢量控制系统进行了实验验证,实验结果证明了算法的正确性和有效性。     

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。     

一种改进的Hachtel状态估计方法

电力系统状态估计常用加权最小二乘(W LS)法处理,这种方法中量测权值的悬殊和大量的注入量测会导致信息矩阵出现病态问题,降低算法的收敛性。综合带约束的正规方程(NE/C)法和海克特(H ach te l)法数值稳定性好的优点,把量测量合理分类构建信息矩阵,并采用分块稀疏矩阵技术,形成了一种计算速度快、数值稳定性好的状态估计新算法。理论和算例分析验证了该算法的有效性。     

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.     

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.     

A sensitivity analysis method to compute the residual covariance matrix

In state estimation, the covariance matrix of residuals is used to compute the normalized residuals and to detect erroneous measurements. This paper describes a method based on sensitivity analysis that allows computing the residual covariance matrix. The proposed method is estimator-independent, i.e., it is suitable for most solution approaches based on mathematical programming procedures. Several case studies illustrate the technique proposed. Relevant conclusions are finally drawn.