WO2023241327A1 - 一种最大特征向量电网异常定位方法 - Google Patents

一种最大特征向量电网异常定位方法 Download PDF

Info

Publication number
WO2023241327A1
WO2023241327A1 PCT/CN2023/096037 CN2023096037W WO2023241327A1 WO 2023241327 A1 WO2023241327 A1 WO 2023241327A1 CN 2023096037 W CN2023096037 W CN 2023096037W WO 2023241327 A1 WO2023241327 A1 WO 2023241327A1
Authority
WO
WIPO (PCT)
Prior art keywords
matrix
power grid
abnormal
max
node
Prior art date
Application number
PCT/CN2023/096037
Other languages
English (en)
French (fr)
Inventor
杨朝辉
吴定会
费佳杰
杨宇辉
钱加兵
张娟
Original Assignee
无锡隆玛科技股份有限公司
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by 无锡隆玛科技股份有限公司 filed Critical 无锡隆玛科技股份有限公司
Publication of WO2023241327A1 publication Critical patent/WO2023241327A1/zh

Links

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08—Locating faults in cables, transmission lines, or networks
    • G01R31/088—Aspects of digital computing
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
    • Y04S10/52—Outage or fault management, e.g. fault detection or location

Definitions

  • the invention belongs to the technical field of power grid fault diagnosis, and specifically relates to a method for locating power grid anomalies based on the maximum eigenvector of a sample covariance matrix.
  • Current power grid anomaly positioning methods mainly include model-driven methods and data-driven methods.
  • the model-driven method has problems such as complex modeling and difficult solution;
  • the data-driven method is more suitable for analyzing and processing power data, effectively improving the speed and accuracy of power grid anomaly positioning.
  • the current data-driven method is mainly based on the random matrix theory.
  • statistical analysis of eigenvalues and eigenvectors reveals the characteristics of the system from a macro perspective.
  • Abnormal location is achieved by analyzing the status matrix composed of power grid status data.
  • the elements of the sample covariance matrix S are independent and identically distributed random variables, and the element sizes of their eigenvectors are close to each other; conversely, when the system is abnormal, the matrix elements show a certain correlation, and accordingly, the eigenvectors
  • the elements of will change significantly, the randomness of the system is destroyed, and the elements of the sample covariance matrix S no longer satisfy the random matrix theory.
  • power grid abnormal node locating methods based on random matrix theory are divided into two categories. Specifically, power grid abnormal node locating based on augmented matrix to construct an augmented matrix of each node; power grid abnormal node based on sample covariance matrix eigenvectors. Positioning, constructing the abnormal positioning indicator and the node number of the corresponding largest element.
  • the above anomaly positioning method based on the augmented matrix can reduce the scope of the anomaly area, but the process of constructing the node augmented matrix is complex and the calculation time is long, so the analysis efficiency of this type of method needs to be improved.
  • the anomaly positioning method based on the sample covariance matrix eigenvector has the advantages of high analysis efficiency and fast calculation speed, and is of great significance to improving the accuracy of the power grid anomaly positioning method.
  • the present invention proposes an abnormal node positioning method based on the maximum eigenvector of the sample covariance matrix, which effectively improves the accuracy of abnormal positioning.
  • the power grid abnormal positioning method provided by the present invention includes the following steps:
  • Step 1 Select sample nodes from the power grid status data collected by the wide-area measurement unit, and construct the data source matrix X S ;
  • Step 2 Collect the status data at the abnormality detection time t F and T W -1 moments thereafter, and construct a window matrix X, where T W is the number of columns of the window matrix X;
  • Step 3 Perform data processing on matrix X to obtain a standard non-Hermitian matrix
  • Step 4 Perform eigendecomposition: calculate matrix The sample covariance matrix S and its maximum eigenvector v max ;
  • Step 5 Construct the abnormal positioning index based on the maximum feature vector v max , perform feature amplification processing on the elements in the abnormal positioning index, and obtain the improved abnormal positioning index l max . Compare and analyze the element values of l max , and output the number of the abnormal node.
  • N is the number of variables in the selected system
  • x 1 (t) represents a column vector composed of the measurement data of the first variable
  • x (t) represents a column composed of the measurement data of N variables vector.
  • the construction process of the window matrix in step 2 is as follows : using a sliding time window with a width of T W to process the data source matrix This builds the window matrix X.
  • step three uses the constructed window matrix to normalize the row changes of the state data through equation (2) to obtain an N ⁇ T w non-Hermitian matrix.
  • x i,j represents the elements of the window matrix X, is the row vector of the window matrix X; is a matrix row vector; ⁇ ( xi ) is the mean of the row vector of the matrix X, and ⁇ ( xi ) is the standard deviation of the row vector of the window matrix X; is a matrix mean of row vector, is a matrix The standard deviation of the row vector.
  • the eigendecomposition process of step 4 is as follows: According to the constructed non-Hermitian matrix, the sample covariance matrix S is calculated according to Equation (3):
  • T w is the number of columns of the window matrix X; further, the maximum eigenvector v max of the matrix S is obtained through eigendecomposition.
  • l iS is the i-th element of the abnormal positioning index l S before feature amplification processing
  • l i is the i-th element of the abnormal positioning index l max after feature amplification processing
  • l m is the maximum element value of l S
  • l dif is the difference between the maximum element value and the second maximum value of l S.
  • the abnormal node determination method based on the abnormal positioning index l max is as follows:
  • the topology of the system can be combined to increase the significantly larger and non-adjacent elements in l max
  • the element is determined to be an abnormal element, and its corresponding node number is the number of the abnormal node.
  • the present invention uses the maximum eigenvector method to achieve the purpose of abnormal location by analyzing the distribution of eigenvector elements.
  • the present invention directly calculates the sample covariance matrix within the fault period to avoid the problem of matrix duplication. Compared with the spectral deviation method Abnormal positioning is achieved through matrix copying and splicing, which takes less time and improves computing efficiency.
  • the elements corresponding to the abnormal node and its adjacent nodes may be close in size. After feature amplification processing, the elements corresponding to the abnormal node will be significantly larger than other elements.
  • the element distribution of the maximum eigenvector in the maximum eigenvector method in the present invention is more stable, is not easily affected by the randomness of noise, and has high anomaly positioning accuracy.
  • the abnormal positioning method of the present invention has more accurate abnormal positioning, and the positioning is less time-consuming, and can quickly and accurately locate abnormal nodes in the power grid.
  • Figure 1 is a flow chart of the anomaly positioning method proposed by the present invention.
  • Figure 2 shows the topology structure diagram of the IEEE39 node system.
  • Figure 3 is a simulation diagram of abnormal positioning under simple faults using the present invention.
  • Figure 4 is a simulation diagram of the minimum eigenvector method for abnormal location under simple faults.
  • Figure 5 is a simulation diagram of abnormal positioning under simple faults using the spectral deviation method.
  • Figure 6 shows the anomaly positioning results of the minimum eigenvector method.
  • the present invention generally includes the following steps:
  • Step 1 Collect power grid status data in real time, select sample nodes, and construct a data source matrix X S based on the measurement data;
  • Step 2 Use a sliding time window to collect status data at the abnormality detection time t F and TW -1 moments thereafter to construct a window matrix X.
  • the abnormality detection time t F means that the system detects an abnormal situation in the power grid at time t F . But the system cannot determine where the exception occurred.
  • Step 3 Standardize the window matrix X to obtain a standard non-Hermitian matrix
  • Step 4 Calculate the matrix The sample covariance matrix S and its maximum eigenvector v max .
  • Step 5 Calculate the abnormal positioning index l max , compare and analyze the element values of l max , and output the number of the node corresponding to the largest element.
  • the power grid status data includes bus voltage amplitude and phase angle, branch current, active power and reactive power injected by the generator, etc. Different status data can be selected to build a data matrix after analyzing the demand. Each status data was analyzed separately. In the experiment, simple faults and multiple faults can be set up for simulation analysis. According to the analysis requirements, the measurement data of the bus voltage is selected as the sample node.
  • Step 1 The IEEE39 node network includes a total of 39 buses.
  • Step 2 The process of constructing the window matrix X includes:
  • the data is processed in real time using a sliding window model. Select the width of the sliding time window to be TW .
  • the window will move backward by one sampling point at each sampling time.
  • T W is the width of the sliding time window.
  • T W is usually selected in the range of tens to hundreds to approximately make the initial conditions satisfy the random matrix assumption. In the experiment, we suggested that the selection range of T W is 50 ⁇ T W ⁇ 200.
  • T W 100 is selected, and the window matrix X is obtained as follows:
  • Step 3 Standardize the state data of the window matrix X constructed in Step 2 to obtain a non-Hermitian matrix
  • x i,j represents the elements of the window matrix X, is the row vector of the window matrix X; represents matrix Elements, is a matrix row vector; ⁇ ( xi ) is the mean of the row vector of the matrix X, and ⁇ ( xi ) is the standard deviation of the row vector of the window matrix X; is a matrix mean of row vector , is a matrix The standard deviation of the row vector.
  • T W is the number of columns of the window matrix X, that is, the width of the sliding time window.
  • l iS is the element corresponding to the i-th node of the power grid in the abnormal positioning index
  • e i is an N ⁇ 1-dimensional unit vector, and only the i-th node The element is 1
  • v max, i is the i-th element of v max ;
  • means taking the absolute value;
  • ⁇ > means the inner product of the vector.
  • l iS is the i-th element of the abnormal positioning index l S before feature amplification processing
  • l i is the i-th element of the abnormal positioning index l max after feature amplification processing
  • l m is the maximum element value of l S
  • l dif is the difference between the maximum value and the second largest value of the element of l S.
  • the abnormal node determination based on the abnormal positioning index l max is to find whether there are any significantly increased elements in l max :
  • the topology of the system can be combined to increase the significantly larger and non-adjacent elements in l max
  • the element is determined to be an abnormal element, and its corresponding node number is the number of the abnormal node.
  • l max When there are multiple non-adjacent elements in l max that are 3 times or more than other elements, it indicates that multiple nodes in the power grid have failed. Combined with the topology of the system, l max is 3 times or more than other elements and Elements that are topologically non-adjacent are determined as abnormal elements.
  • a simple fault is set up in the experimental power grid model below, and the method proposed by the present invention is compared with the minimum eigenvector method and the spectral deviation method to verify the effectiveness of the abnormal positioning method. .
  • the spectral deviation of the sample covariance matrix corresponding to the augmented matrix composed of the voltage of node 9 is the largest, which indicates that the anomaly occurs at node 9, which is consistent with the actual situation, that is, all three methods can be located.
  • Abnormal node the spectral deviation of the sample covariance matrix corresponding to the augmented matrix composed of the voltage of node 9 is the largest, which indicates that the anomaly occurs at node 9, which is consistent with the actual situation, that is, all three methods can be located.
  • the minimum eigenvector method has unstable positioning due to the unstable distribution of the minimum eigenvector elements.
  • the value of node No. 16 of the abnormal positioning index is larger, indicating that an abnormality occurs at node No. 16, which is inconsistent with the actual setting of node No. 9 as a fault node.
  • the element distribution of the maximum eigenvector has high stability, is less affected by white noise, and has higher anomaly positioning accuracy; the spectral deviation anomaly positioning method based on the augmented matrix achieves anomaly
  • the positioning accuracy is close to 100%, but compared with the maximum eigenvector method, the operation takes a long time, about 35 times that of the eigenvector method.
  • the matrix dimension increases, the calculation time of spectral deviation will continue to increase, and the calculation time will be significantly greater than that of the eigenvector method.

Landscapes

  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Mathematical Physics (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Locating Faults (AREA)

Abstract

一种最大特征向量电网异常定位方法，其步骤包括选取样本节点，构建数据源矩阵；采集异常检出时刻及其后T W-1个时刻的状态数据，构建窗口矩阵；对窗口矩阵进行数据处理，得到标准非Hermitian矩阵；计算非Hermitian矩阵的样本协方差矩阵S并求取矩阵S的最大特征向量；计算异常定位指标，对异常定位指标中的元素做特征放大处理，得到改进的异常定位指标l max，比较分析l max的元素值，输出异常节点的编号。本方法使最大特征向量的元素分布更稳定，不易被噪声影响，有着较高的定位精度。此外，本方法直接计算故障时段内的样本协方差矩阵，避免出现矩阵复制的问题，缩短了计算耗时，提高了运算效率。

Description

一种最大特征向量电网异常定位方法 技术领域
本发明属于电网故障诊断技术领域，具体涉及一种样本协方差矩阵最大特征向量的电网异常定位方法。
背景技术
电网在工作时，容易因外部环境及内部结构的影响发生故障。在检测到电网异常之后，及时对异常节点进行定位并排除能够保障电网的安全稳定运行，可以防止故障进一步扩大，减少故障对电网的安全威胁，对工业生产和人民生活的安全有着重要意义。
现在的电网异常定位方法主要包括模型驱动法和数据驱动法。其中，模型驱动法存在建模复杂、求解困难等问题；数据驱动法更适用于分析处理电力数据，有效提高电网异常定位的速度与精度。
目前数据驱动法主要以随机矩阵理论为基础，通过集成历史数据和实时数据到矩阵中，统计分析特征值和特征向量，从宏观角度揭示系统的特性。通过分析由电网状态数据构成的状态矩阵实现异常定位。当电网状态正常时，样本协方差矩阵S的元素为独立同分布的随机变量，其特征向量的元素大小接近；反之，当系统出现异常时，矩阵元素呈现一定的相关性，相应的，特征向量的元素会发生显著变化，系统的随机性被破坏，样本协方差矩阵S的元素不再满足随机矩阵理论。
现有的基于随机矩阵理论的电网异常节点定位方法分为两类，具体的，基于增广矩阵的电网异常节点定位，构建各个节点的增广矩阵；基于样本协方差矩阵特征向量的电网异常节点定位，构建异常定位指标及其所对应最大元素的节点编号。以上基于增广矩阵的异常定位方法能够缩小异常区域范围，但构建节点增广矩阵的过程复杂、运算时间长，因此该类方法的分析效率有待提高。相较于基于增广矩阵的异常定位方法，基于样本协方差矩阵特征向量的异常定位方法具有分析效率高、计算速度快的优点，对提高电网异常定位方法的精度具有重要意义。
发明内容
为了实现对异常节点的快速定位，并提高异常定位的精度，本发明基于样本协方差矩阵的最大特征向量提出了一种异常节点定位方法，有效提高了异常定位的精度。
为了实现上述目的，本发明提供的电网异常定位方法包括以下步骤：
步骤一：从广域测量单元采集的电网状态数据中，选取样本节点，构造数据源矩阵XS；
步骤二：采集异常检出时刻tF及其后TW-1个时刻的状态数据，构建窗口矩阵X，其中TW为窗口矩阵X的列数；
步骤三：对矩阵X进行数据处理，得到标准非Hermitian矩阵
步骤四：进行特征分解：计算矩阵的样本协方差矩阵S及其最大特征向量vmax；
步骤五：根据最大特征向量vmax构建异常定位指标，对异常定位指标中的元素做特征放大处理，得到改进的异常定位指标lmax，比较分析lmax的元素值，输出异常节点的编号。
具体的，步骤一中按照时间顺序将所有采样时刻的样本节点数据排列，则可以完成下述数据源矩阵的构建：
x(t)＝[x1(t),x2(t),…,xN(t)]T       (1)
其中，N为选取系统的变量的个数，x1(t)表示第一个变量的量测数据构成的列向量，依次类推，x(t)表示N个变量的量测数据构成的一个列向量。
具体的，步骤二的窗口矩阵的构建过程为：采用宽度为TW的滑动时间窗处理数据源矩阵XS，截取异常检出时刻tF及其后TW-1个时刻的状态数据，以此构建窗口矩阵X。
具体的，步骤三根据所构建的窗口矩阵，通过式(2)将状态数据进行行变化标准化，得到N×Tw的非Hermitian矩阵
式中，表示矩阵的元素，i＝1,2,…,N，N为选取系统的变量的个数，j＝1,2,…,TW；xi,j表示窗口矩阵X的元素，为窗口矩阵X的行向量；为矩阵的行向量；μ(xi)为矩阵X行向量的均值，σ(xi)为窗口矩阵X行向量的标准差；为矩阵行向量的均值，为矩阵行向量的标准差。
具体的，步骤四的特征分解过程为：根据构建的非Hermitian矩阵，按照式(3)求取样本协方差矩阵S：
其中表示的共轭转置矩阵，Tw为窗口矩阵X的列数；进一步通过特征分解得到矩阵S的最大特征向量vmax。
步骤五根据步骤四矩阵S的最大特征向量vmax构建异常定位指标lS＝(l1S,l2S,…,liS)，其元素表达式如式(4)所示：
liS＝|<vmax,i,ei>|      (4)
其中，i为电网的节点编号，i＝1,2,…,N，N为选取系统的变量的个数，liS为电网第i个节点在异常定位指标中对应的元素；ei为N×1维的单位向量，仅有第i个元素为1；vmax,i为vmax的第i个元素；|·|表示取绝对值；<·>表示向量内积；经过式(4)的处理，liS均为大于零的实数。
当电网节点数较多或故障特征不明显时，相邻节点对应的liS大小接近；为了准确定位异常节点，根据式(5)对liS做特征放大处理，得到改进的异常定位指标lmax＝(l1,l2,…,li)，
其中，liS为特征放大处理前的异常定位指标lS的第i个元素，li为特征放大处理后的异常定位指标lmax的第i个元素；lm为lS的元素最大值，ldif为lS的元素最大值与第二大值的差值。
基于异常定位指标lmax的异常节点判定方法如下：
1)当lmax中仅有一个元素明显大于其他元素时，表明电网仅有一个节点发生故障，且该异常元素对应的节点编号即为异常节点的编号；
2)当lmax中有多个不相邻元素明显大于其他元素时，表明电网有多个节点发生故障，此时可以结合系统的拓扑结构，将lmax中明显增大且拓扑不相邻的元素确定为异常元素，其对应的节点编号即为异常节点的编号。
本发明的有益效果是：
1、本发明利用最大特征向量方法通过分析特征向量元素分布情况来达到异常定位的目的，本发明直接计算故障时段内的样本协方差矩阵，避免出现矩阵复制的问题，相较于谱偏离度方法通过矩阵复制及拼接实现异常定位，运算耗时少，提高了运算效率。
2、在未经特征放大处理前，异常节点及其邻近节点对应的元素可能存在大小接近的情况，经过特征放大处理，异常节点对应的元素将明显大于其他元素。
3、相较于最小特征向量法，本发明中的最大特征向量法中的最大特征向量的元素分布的稳定性更高，不易受到噪声随机性的影响，具有较高的异常定位精度。
因此，本发明的异常定位方法具有较准确的异常定位，且定位耗时少，能够快速、准确地做到电网异常节点定位。
附图说明
图1为本发明提出的异常定位方法的流程图。
图2为IEEE39节点系统拓扑结构图。
图3为采用本发明在简单故障下异常定位的仿真图。
图4为最小特征向量方法在简单故障下异常定位的仿真图。
图5为谱偏离度方法在简单故障下异常定位的仿真图。
图6为最小特征向量方法的异常定位结果。
具体实施方式
下面将结合附图和具体实施例对本发明进一步详细描述。
如图1所示，本发明总体包括以下步骤：
步骤一：实时采集电网状态数据，选取样本节点，基于量测数据构造数据源矩阵XS；
步骤二：采用滑动时间窗采集异常检出时刻tF及其后TW-1个时刻的状态数据，以此构建窗口矩阵X。异常检出时刻tF指系统检测到在tF时刻出现电网异常情况。但系统无法确定发生异常的位置。
步骤三：对窗口矩阵X进行标准化处理，得到标准非Hermitian矩阵
步骤四：计算矩阵的样本协方差矩阵S及其最大特征向量vmax。
步骤五：计算异常定位指标lmax，比较分析lmax的元素值，输出的最大元素对应的节点的编号。
以下通过图2所示的IEEE39节点系统进行仿真分析，详细说明本发明提出的基于协方差矩阵最大特征向量的电网异常定位方法。电网状态数据包括有母线电压幅值和相角、支路电流、发电机注入有功功率和无功功率等，可以分析需求后选择不同的状态数据来构建数据矩阵。每种状态数据单独进行分析。实验中，可以设置简单故障和多重故障进行仿真分析。根据分析需求，选取母线电压的量测数据作为样本节点。
步骤一：IEEE39节点网络共包括39条母线。以每一条母线的电压为测量状态变量进行采样，即N＝39。在采样时刻t，N个变量的量测数据可以构成一个列向量：
x(t)＝[x1(t),x2(t),…,xN(t)]T    (1)
例如：

按照时间顺序将各个采样时刻的量测数据构成的列向量排列，则可构成数据源矩阵：
XS＝(x(1),x(2),…,x(t),…)     (2)
例如：
步骤二构建窗口矩阵X的过程包括：
对数据采用滑动窗口模型进行实时处理。选取滑动时间窗口宽度为TW，窗口会在每一次采样时间向后移动一个采样点，则窗口中包含当前时刻t＝tF的数据以及随后TW-1个历史时刻的数据。对应的状态变量组成的时刻的窗口矩阵如式(3)所示：
X(t)＝(x(t-TW+1),x(t-TW+2),…,x(t))     (3)
其中：TW为滑动时间窗的宽度。TW通常选取范围为几十到几百，近似使初始条件满足随机矩阵假设。实验中我们建议的TW选取范围为50≤TW≤200。
实施例中选取TW＝100，得到窗口矩阵X如下：
步骤三对步骤二所构建的窗口矩阵X进行状态数据标准化处理，得到非Hermitian矩阵
利用式(4)对窗口矩阵X进行逐行变换，得到标准非Hermitian矩阵
式中，i＝1,2,…,N，j＝1,2,…,TW；xi,j表示窗口矩阵X的元素，为窗口矩阵X的行向量；表示矩阵的元素，为矩阵的行向量；μ(xi)为矩阵X行向量的均值，σ(xi)为窗口矩阵X行向量的标准差；为矩阵行向量的均值， 为矩阵行向量的标准差。
步骤四中矩阵的样本协方差矩阵S由式(5)求得：
其中表示的共轭转置，TW为窗口矩阵X的列数，即滑动时间窗的宽度。
然后，通过特征分解计算样本协方差矩阵S的最大特征向量vmax。
步骤五中，根据步骤四选取矩阵S的最大特征向量vmax构建异常定位指标lS＝(l1S,l2S,…,liS)，其元素表达式如式(6)所示：
liS＝|<vmax,i,ei>|       (6)
其中，i＝1,2,…,N为电网的节点编号，liS为电网第i个节点在异常定位指标中对应的元素；ei为N×1维的单位向量，仅有第i个元素为1；vmax,i为vmax的第i个元素；|·|表示取绝对值；<·>表示向量内积。经过式(6)的处理，liS均为大于零的实数。
因为当电网节点数较多或故障特征不明显时，相邻节点对应的liS大小接近，所以难以确定异常节点。为了准确定位异常节点，根据式(7)对liS做特征放大处理，得到改进的异常定位指标lmax＝(l1,l2,…,li)
其中，liS为特征放大处理前的异常定位指标lS的第i个元素，li为特征放大处理后的异常定位指标lmax的第i个元素；lm为lS的元素最大值，ldif为lS的元素最大值与第二大值的差值，当矩阵XS确定后，lm和ldif均为定值。
基于异常定位指标lmax的异常节点判定即是寻找lmax中有无明显增大的元素：
1)当lmax中仅有一个元素明显大于其他元素时，表明电网仅有一个节点发生故障，且该异常元素对应的节点编号即为异常节点的编号；
2)当lmax中有多个不相邻元素明显大于其他元素时，表明电网有多个节点发生故障，此时可以结合系统的拓扑结构，将lmax中明显增大且拓扑不相邻的元素确定为异常元素，其对应的节点编号即为异常节点的编号。
具体在实验中，我们设定判定方法如下：
1)当lmax中仅有一个元素为其他元素的3倍或以上时，判定电网仅有一个节点发生故障；
2)当lmax中有多个不相邻元素为其他元素的3倍或以上时，表明电网有多个节点发生故障，结合系统的拓扑结构，将lmax中为其他元素3倍或以上且拓扑不相邻的元素判定为异常元素。
为了验证本发明提出的异常定位方法的有效性，以下对实验电网模型设置简单故障，将本发明提出的方法与最小特征向量方法和谱偏离度方法进行对比分析，验证此异常定位方法的有效性。
针对简单故障，假设检测到电网在三种方法在tF＝503时刻出现异常，采用本发明所述的异常定位方法，采集t＝503～602时刻的状态数据进行异常节点定位的分析，设置9号节点为异常节点，异常类型为三相短路接地。该故障下的三种异常定位结果如图3、图4、图5所示。由图可知，在tF＝503时刻电网出现异常，系统随机性被破坏，最大特征向量和最小特征向量方法中，异常定位指标的9号元素的数值大于其他元素，因此判定异常节点编号为9，与实际相符。在谱偏离度方法中，由9号节点电压构成的增广矩阵对应的样本协方差矩阵的谱偏离度最大，这表明异常发生在9号节点，与实际情况相符，即三种方法均可定位异常节点。
然而在实际应用中，由于白噪声具有随机性，即使保持信噪比不变，由于最小特征向量元素分布不稳定，最小特征向量方法存在定位不准确的情况，如图6所示，在最小特征向量方法中，异常定位指标的16号节点的数值较大，表明16号节点发生异常，与实际设置9号节点为故障节点不符。
在相同信噪比下，针对每种方法各进行10000次仿真实验，统计了各个方法的异常定位精度和平均运算耗时，如表1所示。
表1
由表1可以看出，相对于最小特征向量方法，最大特征向量的元素分布稳定度高，受白噪声影响小，异常定位精度较高；基于增广矩阵实现的谱偏离度异常定位方法，异常定位精度接近100％，但对比其与最大特征向量方法，运算耗时长，约为特征向量方法的35倍。进一步，若矩阵维度增大，谱偏离度的运算耗时会持续增加，运算耗时将显著大于特征向量方法。
以上的实施例仅用于说明本发明，而并非作为对本发明的限定，所应用的对象不限于IEEE39节点网络，所设置的异常类型不限于三相短路接地，只要在本发明的范围内，对上述实施实例的变化、变型都将落在本发明的权利要求书范围内。

Claims (9)

  1. 一种最大特征向量电网异常定位方法，其特征是，包括以下步骤：
    步骤一：从广域测量单元采集的电网状态数据中，选取样本节点，构造数据源矩阵XS；
    步骤二：采集异常检出时刻tF及其后TW-1个时刻的状态数据，构建窗口矩阵X，其中TW为窗口矩阵X的列数；
    步骤三：对矩阵X进行数据处理，得到标准非Hermitian矩阵
    步骤四：进行特征分解：计算矩阵的样本协方差矩阵S及其最大特征向量vmax；
    步骤五：根据最大特征向量vmax构建异常定位指标，对异常定位指标中的元素做特征放大处理，得到改进的异常定位指标lmax，比较分析lmax的元素值，输出异常节点的编号。
  2. 如权利要求1所述的最大特征向量电网异常定位方法，其特征是，步骤一中按照时间顺序将所有采样时刻的样本节点数据排列，则可以完成下述数据源矩阵的构建：
    x(t)＝[x1(t),x2(t),…,xN(t)]T  (1)
    其中，N为选取系统的变量的个数，x1(t)表示第一个变量的量测数据构成的列向量，依次类推，x(t)表示N个变量的量测数据构成的一个列向量。
  3. 如权利要求2所述的最大特征向量电网异常定位方法，其特征是，步骤二的窗口矩阵的构建过程为：采用宽度为TW的滑动时间窗处理数据源矩阵XS，截取异常检出时刻tF及其后TW-1个时刻的状态数据，以此构建窗口矩阵X。
  4. 如权利要求1所述的最大特征向量电网异常定位方法，其特征是，TW的取值范围为50≤TW≤200。
  5. 如权利要求3所述的最大特征向量电网异常定位方法，其特征是，步骤三根据所构建的窗口矩阵，通过式(2)将状态数据进行行变化标准化，得到N×Tw的非Hermitian矩阵
    式中，表示矩阵的元素，i＝1,2,…,N，N为选取系统的变量的个数，j＝1,2,…,TW；xi,j表示窗口矩阵X的元素，为窗口矩阵X的行向量；为矩阵的行向量；μ(xi)为矩阵X行向量的均值，σ(xi)为窗口矩阵X行向量的标准差；为矩阵行向量的均值，为矩阵行向量的标准差。
  6. 如权利要求1所述的最大特征向量电网异常定位方法，其特征是，步骤四的特征分解过程为：根据构建的非Hermitian矩阵，按照式(3)求取样本协方差矩阵S：
    其中表示的共轭转置矩阵，Tw为窗口矩阵X的列数；进一步通过特征分解得到矩阵S的 最大特征向量vmax。
  7. 如权利要求6所述的最大特征向量电网异常定位方法，其特征是，步骤五根据步骤四矩阵S的最大特征向量vmax构建异常定位指标lS＝(l1S,l2S,…,liS)，其元素表达式如式(4)所示：
    liS＝|<vmax,i,ei>|  (4)
    其中，i为电网的节点编号，i＝1,2,…,N，N为选取系统的变量的个数，liS为电网第i个节点在异常定位指标中对应的元素；ei为N×1维的单位向量，仅有第i个元素为1；vmax,i为vmax的第i个元素；|·|表示取绝对值；<·>表示向量内积；经过式(4)的处理，liS均为大于零的实数。
  8. 如权利要求7所述的最大特征向量电网异常定位方法，其特征是，当电网节点数较多或故障特征不明显时，相邻节点对应的liS大小接近；为了准确定位异常节点，根据式(5)对liS做特征放大处理，得到改进的异常定位指标lmax＝(l1,l2,…,li)，
    其中，liS为特征放大处理前的异常定位指标lS的第i个元素，li为特征放大处理后的异常定位指标lmax的第i个元素；lm为lS的元素最大值，ldif为lS的元素最大值与第二大值的差值。
  9. 如权利要求8所述的最大特征向量电网异常定位方法，其特征是，基于异常定位指标lmax的异常节点判定方法如下：
    1)当lmax中仅有一个元素是其他元素的3倍或以上时，表明电网仅有一个节点发生故障，且该异常元素对应的节点编号即为异常节点的编号；
    2)当lmax中有多个不相邻元素是其他元素的3倍或以上时，表明电网有多个节点发生故障，此时结合系统的拓扑结构，将lmax中是其他元素三倍或以上且拓扑不相邻的元素确定为异常元素，其对应的节点编号即为异常节点的编号。
PCT/CN2023/096037 2022-06-14 2023-05-24 一种最大特征向量电网异常定位方法 WO2023241327A1 (zh)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
CN202210667135.8A CN115032502A (zh) 2022-06-14 2022-06-14 一种最大特征向量电网异常定位方法
CN202210667135.8 2022-06-14

Publications (1)

Publication Number Publication Date
WO2023241327A1 true WO2023241327A1 (zh) 2023-12-21

Family

ID=83125072

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/CN2023/096037 WO2023241327A1 (zh) 2022-06-14 2023-05-24 一种最大特征向量电网异常定位方法

Country Status (2)

Country Link
CN (1) CN115032502A (zh)
WO (1) WO2023241327A1 (zh)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115032502A (zh) * 2022-06-14 2022-09-09 无锡隆玛科技股份有限公司 一种最大特征向量电网异常定位方法

Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20130176174A1 (en) * 2012-01-10 2013-07-11 Ramesh Annavajjala Method and System for Estimating Time of Arrival of Signals Using Maximum Eigenvalue Detection
JP2013242151A (ja) * 2012-05-17 2013-12-05 Mitsubishi Electric Corp Ｄｂｆ信号処理装置およびその処理方法
CN106932686A (zh) * 2017-03-21 2017-07-07 国网上海市电力公司 基于最大最小特征值法的电网异常快速检测方法
CN108196165A (zh) * 2018-01-09 2018-06-22 贵州大学 基于样本协方差矩阵最大特征值的电网异常状态检测方法
CN109657613A (zh) * 2018-12-19 2019-04-19 贵州大学 基于幂法和并行计算技术的大规模电网异常负荷识别方法
CN114062850A (zh) * 2021-11-17 2022-02-18 江南大学 一种双阈值电网早期故障检测方法
US20220060220A1 (en) * 2020-08-21 2022-02-24 Nokia Technologies Oy Regularization of covariance matrix and eigenvalue decomposition in a mimo system
CN114116832A (zh) * 2021-11-04 2022-03-01 广西电网有限责任公司桂林供电局 一种基于数据驱动的配电网异常识别方法
CN115032502A (zh) * 2022-06-14 2022-09-09 无锡隆玛科技股份有限公司 一种最大特征向量电网异常定位方法

Patent Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20130176174A1 (en) * 2012-01-10 2013-07-11 Ramesh Annavajjala Method and System for Estimating Time of Arrival of Signals Using Maximum Eigenvalue Detection
JP2013242151A (ja) * 2012-05-17 2013-12-05 Mitsubishi Electric Corp Ｄｂｆ信号処理装置およびその処理方法
CN106932686A (zh) * 2017-03-21 2017-07-07 国网上海市电力公司 基于最大最小特征值法的电网异常快速检测方法
CN108196165A (zh) * 2018-01-09 2018-06-22 贵州大学 基于样本协方差矩阵最大特征值的电网异常状态检测方法
CN109657613A (zh) * 2018-12-19 2019-04-19 贵州大学 基于幂法和并行计算技术的大规模电网异常负荷识别方法
US20220060220A1 (en) * 2020-08-21 2022-02-24 Nokia Technologies Oy Regularization of covariance matrix and eigenvalue decomposition in a mimo system
CN114116832A (zh) * 2021-11-04 2022-03-01 广西电网有限责任公司桂林供电局 一种基于数据驱动的配电网异常识别方法
CN114062850A (zh) * 2021-11-17 2022-02-18 江南大学 一种双阈值电网早期故障检测方法
CN115032502A (zh) * 2022-06-14 2022-09-09 无锡隆玛科技股份有限公司 一种最大特征向量电网异常定位方法

Also Published As

Publication number Publication date
CN115032502A (zh) 2022-09-09

Similar Documents

Publication Publication Date Title
Gao et al. A physically inspired data-driven model for electricity theft detection with smart meter data
CN109193650B (zh) 一种基于高维随机矩阵理论的电网薄弱点评估方法
WO2023241326A1 (zh) 基于样本协方差矩阵最大特征值变化率的电网异常检测方法
WO2023241327A1 (zh) 一种最大特征向量电网异常定位方法
CN109061387A (zh) 一种基于圆环定理的电网异常状态判别方法
CN112485747A (zh) 一种电容式电压互感器误差状态评估方法
CN112504511A (zh) 一种发电机定子温度监测方法、装置及介质
CN114062850A (zh) 一种双阈值电网早期故障检测方法
CN110632455A (zh) 一种基于配网同步量测大数据的故障检测定位方法
CN111007351A (zh) 一种基于高维随机矩阵特征根检测的配网异常检测方法
CN107607342B (zh) 空调机房设备群的健康能效检测方法
Wu et al. Analysis of electricity stealing based on user electricity characteristics of electricity information collection system
Zhou et al. Fault locating and severity assessment for power distribution systems based on elasticity network topology mapping
CN110018417A (zh) 基于径向杂散磁通检测的电机故障诊断方法、系统及介质
CN116736212B (zh) 一种互感器运行误差在线监测及计量方法
CN111507374A (zh) 一种基于随机矩阵理论的电网海量数据异常检测方法
CN111273126A (zh) 一种配电网拓扑快速感知方法
CN111046331A (zh) 一种基于信号异常的健康监控方法
Zhang et al. Detection and identification of bad data based on neural network and k-means clustering
CN109684749A (zh) 一种考虑运行特性的光伏电站等值建模方法
CN116151656A (zh) 一种基于大维矩阵谱分析的配电网薄弱性评估方法
CN113298133B (zh) 超临界机组锅炉爆管故障诊断方法
Deng et al. A fractional hilbert transform order optimization algorithm based DE for bearing health monitoring
CN118332321B (zh) 一种基于事件数据驱动的风电场阻抗获取方法及装置
Han et al. Efficient Abnormal Load Identification in Large-Scale Power System employing Rayleigh Quotient Method and Parallel Computing Techniques

Legal Events

Date Code Title Description
121 Ep: the epo has been informed by wipo that ep was designated in this application

Ref document number: 23822897

Country of ref document: EP

Kind code of ref document: A1