CN105699804A

CN105699804A - Big data fault detection and positioning method for power distribution network

Info

Publication number: CN105699804A
Application number: CN201610045643.7A
Authority: CN
Inventors: 孙晓颖; 刘国红; 陈若男; 陈建; 于海洋; 温艳鑫
Original assignee: Jilin University
Current assignee: Jilin University
Priority date: 2016-01-22
Filing date: 2016-01-22
Publication date: 2016-06-22
Anticipated expiration: 2036-01-22
Also published as: CN105699804B

Abstract

The invention provides a method for detecting and locating big data faults in a distribution network, which belongs to the field of smart grids. This method uses the synchronized phasor measurement unit PMU to receive the voltage sampling data of the distribution network, preprocesses the voltage received by each PMU and constructs the receiving matrix, and uses the random matrix theory to obtain the unbiased estimate of the covariance matrix of the received data. Decompose the covariance matrix to obtain the corresponding principal components, apply the principal component analysis to calculate the linear regression coefficient, apply the coefficient to calculate the relative approximation error, compare the relative approximation error and the threshold value, and realize the fault detection and location of the distribution network. The method proposed by the invention overcomes the problem of biased traditional covariance matrix estimation under multiple PMU measurements, and can realize real-time detection and location of distribution network faults.

Description

A big data fault detection and location method for distribution network

技术领域technical field

本发明属于智能电网领域，具体涉及一种配电网大数据故障检测与定位方法。The invention belongs to the field of smart grids, and in particular relates to a method for detecting and locating big data faults in distribution networks.

背景技术Background technique

配电网是向最终用户供电的网络，是电力系统发电、输电、配电、用电中向用户供电的主要环节。配电网处于电力系统的末端，地域分布广、电网规模大、设备种类多、网络连接多样、运行方式多变等使其运行状态分析具有一定的困难和复杂性。在智能电网系统中，随着同步测量装置(PhasorMeasurementUnit,PMU)广泛使用，电网运行数据的实时处理问题引起了广泛关注。The distribution network is a network that supplies power to end users, and is the main link in power generation, transmission, distribution, and consumption of power systems to supply power to users. The distribution network is at the end of the power system, and its wide geographical distribution, large-scale power grid, various types of equipment, various network connections, and variable operation modes make the analysis of its operating status difficult and complex. In the smart grid system, with the widespread use of the synchronous measurement unit (PhasorMeasurementUnit, PMU), the real-time processing of grid operation data has attracted widespread attention.

应用同步测量装置数据分析电网的监测、监测和控制已经取得显著进展。Lyapunov指数的电压相量被利用来监视短期电压稳定的稳定性，利用离散傅里叶变换可以实现PMU的自适应技术传输线路故障检测和定位，此外，应用相量角度测量和系统拓扑结构可实现配电网故障检测。Significant progress has been made in the monitoring, monitoring and control of power grids using data analysis from synchronized measuring devices. The voltage phasor of the Lyapunov exponent is exploited to monitor the stability of the short-term voltage stability, the adaptive technique of the PMU can be realized by using the discrete Fourier transform to detect and locate the transmission line fault, moreover, the application of the phasor angle measurement and the system topology can realize Distribution network fault detection.

从研究的角度来看，同步测量相量的大型部署带来的一个主要问题是接收数据矩阵维数的增加，即PMU数目和采样点数以不变的比例系数同时趋于无穷大。在现有的基于空间相关性的配电网故障检测与定位方法中，其关键步骤是计算接收数据的协方差矩阵的无偏估计。传统的计算协方差矩阵的方法基于最大似然这一思想，将样本协方差矩阵作为真实协方差矩阵的无偏估计值，然而，这一计算方法的适用条件是PMU数目较小，且样本数远远大于PMU数目。当将上述传统的基于最大似然估计的协方差矩阵计算方法直接应用到大规模部署的PMU测量装置时，将出现较大的估计偏差，导致相应的算法性能明显下降。From a research point of view, a major problem brought about by the large-scale deployment of synchrometric phasors is the increase in the dimension of the received data matrix, that is, the number of PMUs and the number of sampling points tend to infinity at the same time with a constant scaling factor. In the existing distribution network fault detection and location methods based on spatial correlation, the key step is to calculate the unbiased estimate of the covariance matrix of the received data. The traditional method of calculating the covariance matrix is based on the idea of maximum likelihood, and the sample covariance matrix is used as an unbiased estimate of the real covariance matrix. However, the applicable condition of this calculation method is that the number of PMUs is small and the number of samples Much larger than the number of PMUs. When the above-mentioned traditional method of covariance matrix calculation based on maximum likelihood estimation is directly applied to a large-scale deployment of PMU measurement devices, large estimation deviations will occur, resulting in a significant decrease in the performance of the corresponding algorithm.

此外，同步相量测量单元的大规模使用还将明显导致接收数据量的增加，增加了分析数据空间相关性的难度，从数学角度分析，当配电网中出现故障时，必然导致数据空间相关性发生变化，因此，在PMU数目较多的条件下，探索降低接收数据的维度，提升分析数据空间相关性的有效性，是有待解决的另一个问题。In addition, the large-scale use of synchrophasor measurement units will obviously lead to an increase in the amount of received data, which increases the difficulty of analyzing the spatial correlation of data. From a mathematical point of view, when a fault occurs in the distribution network, it will inevitably lead to spatial correlation of data. Therefore, under the condition of a large number of PMUs, it is another problem to be solved to explore and reduce the dimension of the received data and improve the effectiveness of analyzing the spatial correlation of the data.

随机矩阵理论是研究在矩阵的维数和样本数同时趋于无穷时，协方差矩阵的精确估计方法、特征值与特征向量的分布特性等的有效数学工具。本发明所提出的方法在充分分析随机矩阵理论的基础上，研究出适用于多PMU测量下下的电压接收数据的协方差矩阵的无偏估计方法，病讲主成分分析应用到配电网电压故障检测与定位中，以提升算法的实时性和有效性。Random matrix theory is an effective mathematical tool to study the precise estimation method of covariance matrix, the distribution characteristics of eigenvalues and eigenvectors when the dimension of the matrix and the number of samples tend to infinity at the same time. The method proposed in the present invention, on the basis of fully analyzing the random matrix theory, develops an unbiased estimation method for the covariance matrix of the voltage receiving data under multi-PMU measurement, and applies principal component analysis to the distribution network voltage Fault detection and location to improve the real-time and effectiveness of the algorithm.

发明内容Contents of the invention

本发明提供了一种配电网大数据故障检测与定位方法。用于解决在PMU数目较多的情况下，接收数据协方差矩阵估计不准确，数据维数增加限制算法实用性、难以对配电网故障进行实时诊断和定位的问题。The invention provides a big data fault detection and location method of distribution network. It is used to solve the problems that in the case of a large number of PMUs, the estimation of the covariance matrix of the received data is inaccurate, the increase of the data dimension limits the practicability of the algorithm, and it is difficult to diagnose and locate the faults of the distribution network in real time.

本发明采取的方案是，包含如下步骤：The scheme that the present invention takes is, comprises the following steps:

(1)根据配电网拓扑结构布放PMU，形成配电网大数据测量装置；(1) Arrange PMUs according to the topological structure of the distribution network to form a big data measurement device for the distribution network;

(2)应用步骤(1)中的测量装置接收配电网电压数据；(2) The measuring device in the application step (1) receives the distribution network voltage data;

(3)对接收的电压数据进行预处理；(3) Preprocessing the received voltage data;

(4)应用预处理后的数据构造数据接收矩阵；(4) Applying the preprocessed data to construct a data receiving matrix;

(5)应用随机矩阵理论计算数据接收矩阵的协方差矩阵的无偏估计；(5) Apply random matrix theory to calculate the unbiased estimate of the covariance matrix of the data receiving matrix;

(6)对协方差矩阵的无偏估计进行特征值分解，提取相应的主成分；(6) Decompose the eigenvalues of the unbiased estimate of the covariance matrix, and extract the corresponding principal components;

(7)应用主成分分析计算线性回归系数；(7) Apply principal component analysis to calculate the linear regression coefficient;

(8)应用线性回归系数计算相对近似误差；(8) Applying the linear regression coefficient to calculate the relative approximation error;

(9)对比相对近似误差与门限值的大小，实现配电网故障检测与定位。(9) Comparing the relative approximation error and the threshold value to realize the detection and location of distribution network faults.

上述方法中描述的接收数据预处理过程主要为计算接收的电压数据的均值，以此为基础从接收数据中减去均值；The received data preprocessing process described in the above method is mainly to calculate the average value of the received voltage data, and subtract the average value from the received data on this basis;

本发明所述步骤(4)构造数据接收矩阵，其具体构造方法为每一个PMU接收的数据构成接收矩阵的列，每一时刻的采样数据构成接收矩阵的行，假设PMU个数为N，对N路PMU数据进行M次采样，第i(i＝0,...,N)个PMU接收到的电压采样数据表示为其中上标T为矩阵的转置，则接收数据矩阵为Y_M×N:＝[y⁽¹⁾,.y⁽²⁾,..,y^(N-1),y^(N)]。Step (4) of the present invention constructs the data reception matrix, and its specific construction method is that the data that each PMU receives constitutes the row of the reception matrix, and the sampling data at each moment constitutes the row of the reception matrix, assuming that the number of PMUs is N, for N channels of PMU data are sampled M times, and the voltage sampling data received by the i (i=0,...,N)th PMU is expressed as Wherein the superscript T is the transposition of the matrix, then the received data matrix is Y _M×N :=[y ⁽¹⁾ ,.y ⁽²⁾ ,..,y ^(N-1) ,y ^(N) ].

本发明所述步骤(5)应用随机矩阵理论计算接收电压数据矩阵的协方差矩阵的无偏估计，其具体过程是在OAS估计中，通过权衡低偏差和低方差得到估计函数定义如下：Step (5) of the present invention applies random matrix theory to calculate the unbiased estimate of the covariance matrix of the received voltage data matrix, and its specific process is to obtain the estimated function by weighing low deviation and low variance in OAS estimation It is defined as follows:

$\begin{matrix} \underset{p p}{min min} & E E. {{| | | | \overset{~ ~}{Σ Σ} - - {R R}_{Y Y} | | {| |}_{F f}^{22}}} \end{matrix}$

其中：E为数学期望，以及Where: E is the mathematical expectation, and

$\overset{~ ~}{Σ Σ} = = ((11 - - p p)) {\overset{~ ~}{R R}}_{Y Y} + + p p \overset{~ ~}{U u}$

其中的样本协方差矩阵，p为收缩因子，用于减小均方误差，通常在0与1之间取值，收缩目标U定义如下：in The sample covariance matrix of , p is the shrinkage factor, used to reduce the mean square error, usually takes a value between 0 and 1, and the shrinkage target U is defined as follows:

$\overset{~ ~}{U u} = = \frac{T T r r (({\overset{~ ~}{R R}}_{Y Y}))}{N N} I I$

式中Tr为矩阵的迹，I为N维单位矩阵，假设各个样本之间为独立同分布，则In the formula, Tr is the trace of the matrix, I is the N-dimensional unit matrix, assuming that the samples are independent and identically distributed, then

${p p}_{p p} = = \frac{((11 - - \frac{22}{N N})) T T r r (({R R}_{Y Y}^{22})) + + {Tr Tr}^{22} (({R R}_{Y Y}))}{((M m + + 11 - - \frac{22}{N N})) T T r r (({R R}_{Y Y}^{22})) + + ((11 - - \frac{M m}{N N})) {Tr Tr}^{22} (({R R}_{Y Y}))}$

R_Y为真实协方差矩阵，在实际应用中，直接求解真实协方差矩阵R_Y是不可行的，通过OAS估计对上式进行迭代，得到近似协方差矩阵首次迭代时使用R_Y的一个初始假设值，p₀可以取0到1之间的任意值，之后通过不断迭代对求得的协方差矩阵进行修正，直到迭代收敛：R _Y is the real covariance matrix. In practical applications, it is not feasible to directly solve the real covariance matrix R _Y. The above formula is iterated through OAS estimation to obtain an approximate covariance matrix An initial hypothetical value of _RY is used in the first iteration, p ₀ can take any value between 0 and 1, and then modify the obtained covariance matrix through continuous iteration until the iteration converges:

${p p}_{i i + + 11} = = \frac{((11 - - \frac{22}{N N})) T T r r (({\overset{~ ~}{Σ Σ}}_{i i} {\overset{~ ~}{R R}}_{Y Y})) + + {Tr Tr}^{22} (({\overset{~ ~}{Σ Σ}}_{i i}))}{((M m + + 11 - - \frac{22}{N N})) T T r r (({\overset{~ ~}{Σ Σ}}_{i i} {\overset{~ ~}{R R}}_{Y Y})) + + ((11 - - \frac{M m}{N N})) {Tr Tr}^{22} (({\overset{~ ~}{Σ Σ}}_{i i}))}$

${\overset{~ ~}{Σ Σ}}_{i i + + 11} = = ((11 - - {p p}_{i i + + 11})) {\overset{~ ~}{R R}}_{Y Y} + + {p p}_{i i + + 11} \overset{~ ~}{U u}$

当上式收敛时，可以得到p_OAS When the above formula converges, we can get p _OAS

${p p}_{O o A A S S} = = m m i i n no {{\frac{((11 - - \frac{22}{N N})) T T r r (({\overset{~ ~}{R R}}_{Y Y}^{22})) + + {Tr Tr}^{22} (({\overset{~ ~}{R R}}_{Y Y}))}{((M m + + 11 - - \frac{22}{N N})) [[T T r r (({\overset{~ ~}{R R}}_{Y Y}^{22})) - - \frac{{Tr Tr}^{22} (({\overset{~ ~}{R R}}_{Y Y}))}{N N}]]},, 11}}$

利用得到的p_OAS得到最终估计出的协方差矩阵的无偏估计为Use the resulting p _OAS to get an unbiased estimate of the final estimated covariance matrix for

${\overset{^^}{R R}}_{Y Y} = = ((11 - - {p p}_{O o A A S S})) {\overset{~ ~}{R R}}_{Y Y} + + {p p}_{O o A A S S} \overset{~ ~}{U u} . .$

本发明所述步骤(6)中提取主成分，其过程是对协方差矩阵的无偏估计进行特征值分解Extract principal component in step (6) of the present invention, its process is the unbiased estimate to covariance matrix Do eigenvalue decomposition

$\frac{11}{M m} {\overset{^^}{R R}}_{Y Y} {α α}_{j j} = = {l l}_{j j} {α α}_{j j},, j j = = 11,, 22,, ... ...,, N N$

其中为协方差矩阵无偏估计的N个特征值，为与特征值对应的N个特征向量；in unbiased estimate for the covariance matrix The N eigenvalues of is the N eigenvectors corresponding to the eigenvalues;

将的N个特征值进行降序排列，其对应的特征向量随特征值排序；将τ设置为方差阈值，利用累计方差贡献率选择出刚好满足的前L个特征向量，构造L维主成分PCm。Will The N eigenvalues of the eigenvalues are sorted in descending order, and the corresponding eigenvectors are sorted with the eigenvalues; set τ as the variance threshold, and use the cumulative variance contribution rate to select the one that just satisfies The first L eigenvectors of , construct the L-dimensional principal component PCm.

本发明所述步骤(7)中计算线性回归系数，其方法是将矩阵Y_M×N在L维主成分子空间进行投影，得到矩阵YYCalculate the linear regression coefficient in the step (7) of the present invention, its method is that matrix Y _{M * N} is carried out projection in L dimension principal component subspace, obtains matrix YY

YY＝Y·PCmYY＝Y·PCm

${Y Y}_{B B} : : = = [[{y the y}_{b b}^{11},, {y the y}_{b b}^{22},, ... ...,, {y the y}_{b b}^{S S}]] &Element; &Element; {R R}^{M m \times \times S S}$

其中S<L，y_b满足Where S<L, y _b satisfies

$c c o o s the s θ θ = = (({y the y}_{b b}^{i i} \cdot &Center Dot; {y the y}_{b b}^{j j})) / / ((| | {y the y}_{b b}^{i i} | | \cdot \cdot | | {y the y}_{b b}^{j j} | |)) \approx \approx 00,, i i,, j j = = 11,, 22,, ... ...,, S S$

利用Y_B表示yⁱ，其中yⁱ∈Y_M×N且则线性回归系数vⁱ满足Use Y _B to denote y ⁱ , where y ⁱ ∈ Y _M×N and Then the linear regression coefficient v ⁱ satisfies

${y the y}^{i i} \approx \approx {Σ Σ}_{j j = = 11}^{m m} {v v}_{j j}^{i i} \cdot \cdot {y the y}_{b b}^{j j} = = {Y Y}_{B B} \cdot \cdot {v v}^{i i}$

进一步可得线性回归系数vⁱ Further linear regression coefficient v ⁱ can be obtained

${v v}^{i i} = = {(({Y Y}_{B B}^{T T} {Y Y}_{B B}))}^{- - 11} {Y Y}_{B B}^{T T} {y the y}^{i i}$

其中上标-1为矩阵的逆。where the superscript -1 is the inverse of the matrix.

本发明所述步骤(8)中计算相对近似误差，其方法是假设检测阶段近似的第n(n＝1,2,…,N-S)个PMU在t时刻的数据为 Calculating the relative approximation error in the step (8) of the present invention, its method is to assume that the data of the nth (n=1, 2,..., NS) PMU that detects stage approximation at time t is

$\overset{~ ~}{x x} {((t t))}^{n no} : : = = \overset{~ ~}{{Y Y}_{B B}} ((t t)) \cdot \cdot {v v}^{i i}$

式中为在t时刻计算得到的Y_B，将近似得到的与t时刻的实际电压采样数据z(t)ⁿ做差，得到绝对近似误差 In the formula is the Y _B calculated at time t, and the approximate Make a difference with the actual voltage sampling data z(t) ⁿ at time t to get the absolute approximate error

$\overset{^^}{e e} {((t t))}^{n no} = = \overset{~ ~}{x x} {((t t))}^{n no} - - z z {((t t))}^{n no}$

由于在电力系统中，故障发生时变量的变化幅度不是很大，所以是非常小的，这导致不能准确地判断出故障是否发生，为避免这一问题，因此将除以训练阶段对应PMU的的平均值er_s ⁿ，可以将故障时刻的近似误差数据放大，做到相对近似误差r(t)ⁿ Because in the power system, the variable range is not very large when a fault occurs, so is very small, which makes it impossible to accurately determine whether a fault has occurred. To avoid this problem, the Divided by the training phase corresponding to the PMU The average value of er _s ⁿ can amplify the approximate error data at the time of the fault, so that the relative approximate error r(t) ⁿ

$r r {((t t))}^{n no} = = \frac{\overset{^^}{e e} {((t t))}^{n no}}{{er er}_{s the s}^{n no}} \times \times 100100 % %$

本发明所述步骤(9)中实现配电网故障检测与定位，其方法是通过历史事故的PMU数据，确定一个阈值η，当In step (9) of the present invention, realize distribution network fault detection and location, its method is to determine a threshold value n by the PMU data of historical accident, when

|r(t)ⁿ|≥η|r(t) ⁿ |≥η

时，可判定故障发生，t为故障时间，即表征对故障的检测，n为故障PMU，表征对故障的定位。When , it can be determined that a fault occurs, t is the fault time, which represents the detection of the fault, and n is the faulty PMU, which represents the location of the fault.

本发明的优点是：The advantages of the present invention are:

(1)本发明所提方法研究了随机矩阵理论中多种协方差矩阵无偏估计的计算方法，通过对比分析将OAS重构方法引入到配电网大数据处理中，克服了传统样本协方差矩阵计算方法估计偏差较大的问题，提升了相应算法的适用性；(1) The method proposed in the present invention studies the calculation methods of various covariance matrix unbiased estimates in the random matrix theory, and introduces the OAS reconstruction method into the distribution network big data processing through comparative analysis, which overcomes the traditional sample covariance The problem of large estimation deviation of the matrix calculation method improves the applicability of the corresponding algorithm;

(2)本发明所提方法在获得接收数据协方差矩阵无偏估计值的基础上，应用主成分分析降低接收数据的维数，提升了配电网电压空间相关性分析的有效性以及相应算法的计算有效性；(2) On the basis of obtaining the unbiased estimated value of the covariance matrix of the received data, the proposed method of the present invention applies principal component analysis to reduce the dimension of the received data, and improves the validity of the distribution network voltage spatial correlation analysis and the corresponding algorithm The computational validity of

(3)本发明所提方法将相对近似误差作为评价配电网电压空间相关性变化的标准，通过比较相对近似误差与门限值的关系确定配电网故障是否发生以及发生的时刻和位置，可实现电压故障的实时检测与定位。(3) The method proposed in the present invention regards the relative approximation error as the standard for evaluating the spatial correlation change of the distribution network voltage, and determines whether the distribution network fault occurs and the time and position of the occurrence by comparing the relationship between the relative approximation error and the threshold value, Real-time detection and location of voltage faults can be realized.

附图说明Description of drawings

图1是本发明所采用的配电网电压数据测量装置示意图；Fig. 1 is a schematic diagram of a distribution network voltage data measuring device adopted in the present invention;

图2是本发明的流程图；Fig. 2 is a flow chart of the present invention;

图3是IEEE39节点系统图；Fig. 3 is a diagram of IEEE39 node system;

图4是特征值贡献比选择结果图；Fig. 4 is the selection result diagram of eigenvalue contribution ratio;

图5是配电网电压故障检测结果图；Fig. 5 is a diagram of the detection result of the distribution network voltage fault;

图6是配电网电压故障定位结果图。Figure 6 is a diagram of the distribution network voltage fault location results.

具体实施方式detailed description

包括下列步骤：Include the following steps:

(1)：根据配电网拓扑结构布放PMU，形成配电网大数据测量装置；(1): Arrange PMUs according to the topological structure of the distribution network to form a big data measurement device for the distribution network;

依据配电网拓扑结构布放PMU，所形成的测量装置如图1所示，其特点是PMU均匀布放在整个配电网；The PMUs are laid out according to the topological structure of the distribution network, and the resulting measurement device is shown in Figure 1, and its characteristic is that the PMUs are evenly placed in the entire distribution network;

(2)：应用步骤(1)中的测量装置接收配电网电压数据；(2): The measuring device in the application step (1) receives the distribution network voltage data;

在所需检测区域安放PMU装置，用来分别接收各个区域的PMU数据，将得到的原始数据输送到本地相位数据集中器中，之后把各个本地数据集中器的数据汇总，输送到公司数据集中器，并进行存储；Place the PMU device in the required detection area to receive the PMU data of each area respectively, and send the obtained raw data to the local phase data concentrator, and then aggregate the data of each local data concentrator and send it to the company data concentrator , and store it;

(3)：对接收数据进行预处理；(3): Preprocessing the received data;

计算接收的电压数据u的均值v，以此为基础从接收数据中减去均值，获得预处理后的电压数据y＝u-v；Calculate the average value v of the received voltage data u, and subtract the average value from the received data on this basis to obtain the preprocessed voltage data y=u-v;

(4)：应用预处理后的数据构造数据接收矩阵；(4): apply the preprocessed data to construct a data receiving matrix;

每一个PMU接收的数据构成接收矩阵的列，每一时刻的采样数据构成接收矩阵的行，假设PMU个数为N，对N路PMU数据进行M次采样，第i(i＝0,...,N)个PMU接收到的电压采样数据表示为其中上标T为矩阵的转置，则接收数据矩阵为Y_M×N:＝[y⁽¹⁾,.y⁽²⁾,..,y^(N-1),y^(N)]；The data received by each PMU constitutes the columns of the receiving matrix, and the sampled data at each moment constitutes the rows of the receiving matrix. Assuming that the number of PMUs is N, the data of N channels of PMUs are sampled M times, and the i (i=0,... ., N) The voltage sampling data received by the PMUs is expressed as Wherein the superscript T is the transposition of the matrix, then the received data matrix is Y _M×N :=[y ⁽¹⁾ ,.y ⁽²⁾ ,..,y ^(N-1) ,y ^(N) ];

(5)：应用随机矩阵理论计算数据接收矩阵的协方差矩阵的无偏估计；(5): Apply random matrix theory to calculate the unbiased estimate of the covariance matrix of the data receiving matrix;

在OAS估计中，通过权衡低偏差和低方差得到估计函数定义如下：In OAS estimation, the estimated function is obtained by balancing low bias and low variance It is defined as follows:

其中：E为数学期望，以及Where: E is the mathematical expectation, and

其中为Y_M×N的样本协方差矩阵，p为收缩因子，用于减小均方误差，通常在0与1之间取值。收缩目标U定义如下：in is the sample covariance matrix of Y _M×N , and p is the shrinkage factor, which is used to reduce the mean square error, and usually takes a value between 0 and 1. The contraction target U is defined as follows:

$\overset{~ ~}{U u} = = \frac{T T r r (({\overset{~ ~}{R R}}_{Y Y}))}{N N} I I$

${\overset{^^}{R R}}_{Y Y} = = ((11 - - {p p}_{O o A A S S})) {\overset{~ ~}{R R}}_{Y Y} + + {p p}_{O o A A S S} \overset{~ ~}{U u}$

(6)：对协方差矩阵进行特征值分解，提取相应的主成分；(6): Decompose the eigenvalues of the covariance matrix and extract the corresponding principal components;

对协方差矩阵的无偏估计进行特征值分解Unbiased Estimation of the Covariance Matrix Do eigenvalue decomposition

将的N个特征值进行降序排列，其对应的特征向量随特征值排序；将τ设置为方差阈值，利用累计方差贡献率选择出刚好满足的前L个特征向量，构造L维主成分PCm；Will The N eigenvalues of the eigenvalues are sorted in descending order, and the corresponding eigenvectors are sorted with the eigenvalues; set τ as the variance threshold, and use the cumulative variance contribution rate to select the one that just satisfies The first L eigenvectors of , construct the L-dimensional principal component PCm;

(7)：应用主成分分析计算线性回归系数；(7): Applying principal component analysis to calculate linear regression coefficients;

将矩阵Y_M×N在L维主成分子空间进行投影，得到矩阵YYProject the matrix Y _M×N in the L-dimensional principal component subspace to obtain the matrix YY

YY＝Y·PCmYY＝Y·PCm

其中S<L，y_b满足Where S<L, y _b satisfies

${y the y}^{i i} \approx \approx {Σ Σ}_{j j = = 11}^{m m} {v v}_{j j}^{i i} \cdot &Center Dot; {y the y}_{b b}^{j j} = = {Y Y}_{B B} \cdot &Center Dot; {v v}^{i i}$

其中上标-1为矩阵的逆；where the superscript -1 is the inverse of the matrix;

(8)：应用线性回归系数计算相对近似误差；(8): Applying the linear regression coefficient to calculate the relative approximation error;

假设检测阶段近似的第n(n＝1,2,…,N-S)个PMU在t时刻的数据为 Assume that the data of the nth (n=1,2,...,NS) PMU approximated in the detection stage at time t is

由于在电力系统中，故障发生时变量的变化幅度不是很大，所以是非常小的，这导致不能准确地判断出故障是否发生。为避免这一问题，因此将除以训练阶段对应PMU的的平均值er_s ⁿ，可以将故障时刻的近似误差数据放大，做到相对近似误差r(t)ⁿ Because in the power system, the variable range is not very large when a fault occurs, so is very small, which makes it impossible to accurately determine whether a fault has occurred. To avoid this problem, the Divided by the training phase corresponding to the PMU The average value of er _s ⁿ can amplify the approximate error data at the time of the fault, so that the relative approximate error r(t) ⁿ

(9)：对比相对近似误差与门限值的大小，实现配电网故障检测与定位，(9): Comparing the size of the relative approximation error and the threshold value, to realize the fault detection and location of the distribution network,

通过历史事故的PMU数据，确定一个阈值η，当Through the PMU data of historical accidents, determine a threshold η, when

|r(t)ⁿ|≥η|r(t) ⁿ |≥η

下面通过一些实验数据分析本发明所提出的配电网大数据故障诊断与定位方法的性能。仿真实验1和仿真实验2所采用的仿真软件为MATLAB软件。The performance of the distribution network big data fault diagnosis and location method proposed by the present invention is analyzed below through some experimental data. The simulation software used in simulation experiment 1 and simulation experiment 2 is MATLAB software.

仿真实验：本实验用以分析特征值的贡献比以及所提方法的有效性，实验过程中采用IEEE39节点模型产生的电压数据形成接收数据矩阵，起节点系统图如图3所示，该模型中假设第9个PMU和第30个PMU为故障位置，故障发生时间为分别为第235个采样点和第274个采样点，特征值贡献币比的仿真结果如图4所示，配电网电压故障检测与定位结果分别如图5和图6所示，分析图4可知，应用39维的数据矩阵进行故障检测与故障定位时，可选择10个主特征值所对应的特征向量作为主成分，分析图5可知，所提出的方法在采样点标号分别为235和274点的相对近似误差明显大于其他采样点，即实现了电压故障的实时检测；分析图6可知，在第9个PMU和第30个PMU时，所提方法计算的相对近似误差明显高于其他PMU，即可实现对电压故障的准确定位。Simulation experiment: This experiment is used to analyze the contribution ratio of eigenvalues and the effectiveness of the proposed method. During the experiment, the voltage data generated by the IEEE39 node model is used to form the receiving data matrix. The starting node system diagram is shown in Figure 3. In this model Assuming that the 9th PMU and the 30th PMU are the fault locations, and the fault occurrence time is the 235th sampling point and the 274th sampling point respectively, the simulation results of the eigenvalue contribution ratio are shown in Figure 4, the distribution network voltage The results of fault detection and location are shown in Fig. 5 and Fig. 6 respectively. Analyzing Fig. 4, it can be seen that when using a 39-dimensional data matrix for fault detection and fault location, the eigenvectors corresponding to the 10 main eigenvalues can be selected as the principal components. Analyzing Figure 5, we can see that the relative approximation errors of the proposed method at the sampling points labeled 235 and 274 are significantly larger than other sampling points, that is, real-time detection of voltage faults is realized; analyzing Figure 6, we can see that at the ninth PMU and the When there are 30 PMUs, the relative approximation error calculated by the proposed method is significantly higher than that of other PMUs, and the accurate location of voltage faults can be realized.

Claims

1. A distribution network big data fault detection and location method, is characterized in that comprising the following steps:

(1) Arrange PMUs according to the topological structure of the distribution network to form a big data measurement device for the distribution network;

(2) The measuring device in the application step (1) receives the distribution network voltage data;

(3) Preprocessing the received voltage data;

(4) Applying the preprocessed data to construct a data receiving matrix;

(5) Apply random matrix theory to calculate the unbiased estimate of the covariance matrix of the data receiving matrix;

(6) Decompose the eigenvalues of the unbiased estimate of the covariance matrix, and extract the corresponding principal components;

(7) Apply principal component analysis to calculate the linear regression coefficient;

(8) Applying the linear regression coefficient to calculate the relative approximation error;

(9) Comparing the relative approximation error and the threshold value to realize the detection and location of distribution network faults.

2. according to claim 1, a kind of distribution network big data fault detection and location method is characterized in that: the concrete construction method of step (4) constructing data reception matrix is the row that the data that each PMU receives constitutes reception matrix, The sampling data at each moment constitutes the row of the receiving matrix. Assuming that the number of PMUs is N, the data of N PMUs is sampled M times, and the voltage sampling data received by the i (i=0,...,N) PMU Expressed as Where the superscript T is the transpose of the matrix, then the received data matrix is

Y_{m \times N} : = [{the y}^{(1)}, . {the y}^{(2)}, .., {the y}^{(N - 1)}, {the y}^{(N)}] .

3. A kind of distribution network big data fault detection and localization method according to claim 1, is characterized in that: the specific process of step (5) is in OAS estimation, obtains estimation function by weighing low deviation and low variance It is defined as follows:

\begin{matrix} \underset{p p}{m m i i n no} & E E. {{| | | | \overset{~ ~}{Σ Σ} - - {R R}_{Y Y} | | {| |}_{F f}^{22}}} \end{matrix}

Where: E is the mathematical expectation, and

\overset{~ ~}{Σ Σ} = = ((11 - - p p)) {\overset{~ ~}{R R}}_{Y Y} + + p p \overset{~ ~}{U u}

in is the sample covariance matrix of Y _M×N , and p is the shrinkage factor, which is used to reduce the mean square error, and usually takes a value between 0 and 1. The contraction target U is defined as follows:

\overset{~ ~}{U u} = = \frac{T T r r (({\overset{~ ~}{R R}}_{Y Y}))}{N N} I I

In the formula, Tr is the trace of the matrix, I is the N-dimensional unit matrix, assuming that the samples are independent and identically distributed, then

{p p}_{p p} = = \frac{((11 - - \frac{22}{N N})) T T r r (({R R}_{Y Y}^{22})) + + {Tr Tr}^{22} (({R R}_{Y Y}))}{((M m + + 11 - - \frac{22}{N N})) T T r r (({R R}_{Y Y}^{22})) + + ((11 - - \frac{M m}{N N})) {Tr Tr}^{22} (({R R}_{Y Y}))}

R _Y is the real covariance matrix. In practical applications, it is not feasible to directly solve the real covariance matrix R _Y. The above formula is iterated through OAS estimation to obtain an approximate covariance matrix An initial hypothetical value of _RY is used in the first iteration, p ₀ can take any value between 0 and 1, and then modify the obtained covariance matrix through continuous iteration until the iteration converges:

{p p}_{i i + + 11} = = \frac{((11 - - \frac{22}{N N})) T T r r (({\overset{~ ~}{Σ Σ}}_{i i} {\overset{~ ~}{R R}}_{Y Y})) + + {Tr Tr}^{22} (({\overset{~ ~}{Σ Σ}}_{i i}))}{((M m + + 11 - - \frac{22}{N N})) T T r r (({\overset{~ ~}{Σ Σ}}_{i i} {\overset{~ ~}{R R}}_{Y Y})) + + ((11 - - \frac{M m}{N N})) {Tr Tr}^{22} (({\overset{~ ~}{Σ Σ}}_{i i}))}

{\overset{~ ~}{Σ Σ}}_{i i + + 11} = = ((11 - - {p p}_{i i + + 11})) {\overset{~ ~}{R R}}_{Y Y} + + {p p}_{i i + + 11} \overset{~ ~}{U u}

When the above formula converges, we can get p _OAS

{p p}_{O o A A S S} = = m m i i n no {{\frac{((11 - - \frac{22}{N N})) T T r r (({\overset{~ ~}{R R}}_{Y Y}^{22})) + + {Tr Tr}^{22} (({\overset{~ ~}{R R}}_{Y Y}))}{((M m + + 11 - - \frac{22}{N N})) [[T T r r (({\overset{~ ~}{R R}}_{Y Y}^{22})) - - \frac{{Tr Tr}^{22} (({\overset{~ ~}{R R}}_{Y Y}))}{N N}]]},, 11}}

Use the resulting p _OAS to get an unbiased estimate of the final estimated covariance matrix for:

{\overset{^^}{R R}}_{Y Y} = = ((11 - - {p p}_{O o A A S S})) {\overset{~ ~}{R R}}_{Y Y} + + {p p}_{O o A A S S} \overset{~ ~}{U u} . .

4. according to claim 1 a kind of distribution network big data fault detection and localization method, it is characterized in that: the process of extracting principal components in the described step (6) is the unbiased estimation to covariance matrix Perform an eigenvalue decomposition:

\frac{11}{M m} {\overset{^^}{R R}}_{Y Y} {α α}_{j j} = = {l l}_{j j} {α α}_{j j},, j j = = 11,, 22,, ... ...,, N N

in unbiased estimate for the covariance matrix The N eigenvalues of is the N eigenvectors corresponding to the eigenvalues;

Will The N eigenvalues of the eigenvalues are sorted in descending order, and the corresponding eigenvectors are sorted with the eigenvalues; set τ as the variance threshold, and use the cumulative variance contribution rate to select the one that just satisfies The first L eigenvectors of , construct the L-dimensional principal component PCm;.

5. a kind of distribution network big data fault detection and location method according to claim 1, is characterized in that: the method for calculating linear regression coefficient in the described step (7) is to matrix Y _{M * N} in L dimension main component The molecular space is projected to obtain the matrix YY:

YY＝Y·PCm

{Y Y}_{B B} : : = = [[{y the y}_{b b}^{11},, {y the y}_{b b}^{22},, ... ...,, {y the y}_{b b}^{S S}]] &Element; &Element; {R R}^{M m \times \times S S}

Where S<L, y _b satisfies:

c c o o s the s θ θ = = (({y the y}_{b b}^{i i} \cdot \cdot {y the y}_{b b}^{j j})) / / ((| | {y the y}_{b b}^{i i} | | \cdot \cdot | | {y the y}_{b b}^{j j} | |)) \approx \approx 00,, i i,, j j = = 11,, 22,, ... ...,, S S

Use Y _B to denote y ⁱ , where y ⁱ ∈ Y _M×N and Then the linear regression coefficient v ⁱ satisfies:

{y the y}^{i i} \approx \approx {Σ Σ}_{j j = = 11}^{m m} {v v}_{j j}^{i i} \cdot &Center Dot; {y the y}_{b b}^{j j} = = {Y Y}_{B B} \cdot \cdot {v v}^{i i}

Further linear regression coefficient v ⁱ can be obtained:

{v v}^{i i} = = {(({Y Y}_{B B}^{T T} {Y Y}_{B B}))}^{- - 11} {Y Y}_{B B}^{T T} {y the y}^{i i}

where the superscript -1 is the inverse of the matrix.

6. According to claim 1, a method for detecting and locating big data faults in a distribution network is characterized in that: the method for calculating the relative approximation error in the step (8) is to assume that the nth (n=1 ,2,…,NS) PMU data at time t is

\overset{~ ~}{x x} {((t t))}^{n no} : : = = \overset{~ ~}{{Y Y}_{B B}} ((t t)) \cdot \cdot {v v}^{i i}

In the formula is the Y _B calculated at time t, and the approximate Make a difference with the actual voltage sampling data z(t) ⁿ at time t to get the absolute approximate error

\overset{^^}{e e} {((t t))}^{n no} = = \overset{~ ~}{x x} {((t t))}^{n no} - - z z {((t t))}^{n no}

Will Divided by the training phase corresponding to the PMU average of The approximation error data at the fault moment can be amplified to achieve a relative approximation error r(t) ⁿ

r r {((t t))}^{n no} = = \frac{\overset{^^}{e e} {((t t))}^{n no}}{{er er}_{s the s}^{n no}} \times \times 100100 % % . .

7. according to claim 1, a kind of distribution network big data fault detection and location method is characterized in that: in the described step (9), the method for realizing distribution network fault detection and location is by the PMU data of historical accidents, Determine a threshold η, when

|r(t) ⁿ |≥η

When , it can be determined that a fault occurs, t is the fault time, which represents the detection of the fault, and n is the faulty PMU, which represents the location of the fault.