CN111900731B - PMU-based power system state estimation performance evaluation method - Google Patents

PMU-based power system state estimation performance evaluation method Download PDF

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CN111900731B
CN111900731B CN202010746249.2A CN202010746249A CN111900731B CN 111900731 B CN111900731 B CN 111900731B CN 202010746249 A CN202010746249 A CN 202010746249A CN 111900731 B CN111900731 B CN 111900731B
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谢伟
陆超
宋文超
华斌
方陈
林俊杰
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State Grid Shanghai Electric Power Co Ltd
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Abstract

The invention relates to a PMU-based power system state estimation performance evaluation method, which specifically comprises the following steps: actual measurement of measurement value S of observation object by PMU of power systemmObtaining SmState estimation value S ofseWill SmAnd SseInputting a trained classification model to obtain classification accuracy and a marking value and calculating a state estimation performance evaluation index, wherein the training process comprises the following steps: obtaining a measurement error data set X of an observed object through a power system simulation platform, carrying out normalization processing on the X and calculating a probability density function of the X
Figure DDA0002608452500000011
Obtaining S through a power system simulation platformtBy superposition of StAnd
Figure DDA0002608452500000012
to obtain SmObtaining each SmState estimation value S ofse，αmTaking 0 or 1, using St、Sm、SseAnd alphamAnd training a classification model. Compared with the prior art, the method has the advantages of high accuracy, simplicity and convenience in operation, labor saving and the like.

Description

PMU-based power system state estimation performance evaluation method
Technical Field
The invention relates to a technology for evaluating the state estimation performance of a force system, in particular to a method for evaluating the state estimation performance of a power system based on a PMU.
Background
The evaluation method for the state estimation performance of the power system is a key technology for operation and control of the power system, can measure key information such as precision of a state estimation result, and the like, and can ensure correct operation and control of the power system by an accurate and reasonable state estimation result. With the integration of a large amount of renewable energy, the complexity of a power transmission network, the diversification of loads, and the rapid change of the operation mode of a power system. A Phasor Measurement Unit (PMU) based linear state estimation may better reflect the current state of the system. PMU errors, however, are a critical issue affecting the accuracy of the linearity state estimation. In practical studies, PMU errors are generally considered to follow a gaussian distribution. However, there are many factors that affect the accuracy of PMU measurement data, and there are mainly amplitude errors and phase angle errors of the voltage transformer and the current transformer, transmission errors of the cable channel, and synchronous clock errors. Therefore, the PMU error should follow a more complex distribution. Meanwhile, in an actual power system, a real value of a PMU measurement point and a real state of the power system are not available, so that the state estimation performance in the actual power system is difficult to evaluate.
Currently, the main index for evaluating the state estimation performance is the yield η, which is defined as:
Figure GDA0003075769330000011
Figure GDA0003075769330000012
wherein m is a measurement quantity, riThe measurement residual error of the measurement point i is epsiloniIs a threshold value;
but the yield depends on a threshold epsilon for discriminating between passing and failingi，εiThe constant is set according to engineering experience, and no practical theoretical basis exists;
meanwhile, research utilizes the concept of cross entropy in the information theory as a state estimation performance evaluation standard, but the method only reflects the relation between a measured value and an estimated value and does not relate to the real state of the power system.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides the PMU-based power system state estimation performance evaluation method which is high in accuracy, simple and convenient to operate and labor-saving.
The purpose of the invention can be realized by the following technical scheme:
a PMU-based power system state estimation performance evaluation method specifically comprises the following steps:
n through the power system2Actual measurement of n by each PMU2Measured value S of each observed objectmThe observation object comprises one or more of voltage amplitude, voltage phase angle, current amplitude and current phase angle, and each S is obtained through state estimationmState estimation value S ofseN is to be2Group SmAnd SseRespectively correspond to input n2Grouping the trained classification models using n2S given by a classification modelmAnd SseDividing the standard to obtain n2A mark value alphamAnd calculating a state estimation performance evaluation index lambda, wherein the calculation formula is as follows:
Figure GDA0003075769330000021
wherein p ismiAnd alphamiRespectively the ith classification accuracy pmAnd a mark value alphamSaid p ismThe calculation formula of (2) is as follows:
Figure GDA0003075769330000022
wherein n isrAnd nfRespectively carrying out correct quantity and wrong quantity of classification on the classification model after training;
wherein, said n2The training process of the group classification model is as follows:
obtaining a measurement error data set X of an observed object by a PMU of a power system simulation platform, normalizing the X for convenient analysis and comparison, and calculating a probability density function of the X
Figure GDA0003075769330000023
Obtaining n through a power system simulation platform2Group Observation truth StBy superimposing StAnd
Figure GDA0003075769330000024
theoretical solution of n2Group SmObtaining respective S by state estimationmState estimation value S ofseJudging each group St、SmAnd SseWhether the judgment formula is satisfied, if so, the marking value alpha with the corresponding generation value of 1 is generatedmOtherwise, generate α with value 0mThe judgment formula is as follows:
|Sim-Sit|＞|Sise-Sit|
wherein Si ism、SitAnd SiseAre respectively the ith group Sm、StAnd Sse；
N is to be2Group St、Sm、SseAnd alphamAs training data, performing classification model training to correspondingly obtain n2And (4) classifying the models.
Further, the classification model comprises an SVM model, a binary tree model or a neural network model, and the kernel function of the training classification model is a Gaussian kernel function.
Further, the acquisition process of the measurement error data set X is as follows:
measuring a measurement value S of an observation object through PMU on a node of a power system simulation platformmQuerying nodes on a simulation platform of an electrical power system by simulation softwareStBy calculating SmAnd StThe difference value of (A) is used to obtain the measurement error, and X is formed by a plurality of groups of measurement errors.
Further, the formula of the normalization process is as follows:
Figure GDA0003075769330000031
wherein the content of the first and second substances,
Figure GDA0003075769330000032
is the j normalized measurement error, E (X) is the expectation of X, var (X) is the variance of X, XjIs the jth measurement error in X.
Further, the
Figure GDA0003075769330000033
The calculation formula of (a) is as follows:
Figure GDA0003075769330000034
where K is the Gaussian kernel function, h is the kernel density estimation window width, xjFor the jth observation in X, n1Number of samples of X;
the calculation formula of the kernel density estimation window width h is as follows:
Figure GDA0003075769330000035
wherein, sigma is the standard deviation of X, R is the four-quadrant spacing of X, N is the number of observed data in X, if h is too large, or decrease
Figure GDA0003075769330000036
If h is too small, this will result in
Figure GDA0003075769330000037
Large and discontinuous undulations and errorsIs large.
Furthermore, the state estimation algorithm can reduce the measurement error and increase the accuracy and the availability of the measured data, and the basic idea is based on a weighted least square method to solve an optimization problem:
Figure GDA0003075769330000038
s.t.Sm＝H(St)+w
wherein H is a measurement equation, and the H establishes SmAnd StW is a measurement error, W is a weight matrix, W is a diagonal sparse matrix, and diagonal elements are inverses of variances of the corresponding measurement errors.
Compared with the prior art, the invention has the following beneficial effects:
(1) according to the method, the error characteristic of PMU measurement data is obtained through a power system simulation platform, the error characteristic is superposed on a true value of an observation object, a measurement value of the observation object is calculated theoretically to form training data of a classification model, finally, an object measurement value and a corresponding state estimation value of each node of a power system are obtained on a new time section, a plurality of groups of trained models are input, and finally, a state estimation performance evaluation index lambda is calculated;
(2) the invention can adopt SVM model, binary tree model or neural network model as classification model, and has wide application range.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
A method for evaluating state estimation performance of a power system based on a PMU, as shown in fig. 1, specifically includes:
n is arranged on the power system2Each monitoring node is provided with a PMU, a measurement error data set X of an observed object is obtained through the PMU of the power system simulation platform, normalization processing is carried out on the data set, and the probability density function of the X is calculated
Figure GDA0003075769330000041
Figure GDA0003075769330000042
The method comprises the steps of obtaining n through a power system simulation platform by virtue of PMU measurement error distribution characteristics2Group Observation truth StBy superimposing StAnd
Figure GDA0003075769330000043
theoretical solution of n2Group SmObtaining respective S by state estimationmState estimation value S ofseJudging each group St、SmAnd SseWhether the judgment formula is satisfied, if so, the marking value alpha with the corresponding generation value of 1 is generatedmOtherwise, generate α with value 0mThe judgment formula is as follows:
|Sim-Sit|＞|Sise-Sit|
wherein Si ism、SitAnd SiseS of the ith nodem、StAnd Sse；
N is a value obtained by subtracting the true value of the observation target from the true value of the observation target2Group St、Sm、SseAnd alphamPerforming SVM training as training data, wherein the kernel function of the training is a Gaussian kernel function, and correspondingly obtaining n2A trained SVM model;
by electric power systems in time sections to be evaluatedn2Actual measurement of n by each PMU2Measured value S of each observed objectmThe observed objects are the voltage amplitude and the voltage phase angle, i.e. SmIncluding voltage amplitude measurements and voltage phase angle measurements, each S is obtained by state estimationmState estimation value S ofseN is to be2Group SmAnd SseRespectively correspond to input n2Grouping the trained classification models using n2S given by a classification modelmAnd SseDividing the standard to obtain n2A mark value alphamAnd calculating a state estimation performance evaluation index lambda, wherein the calculation formula is as follows:
Figure GDA0003075769330000051
wherein p ismiAnd alphamiRespectively the ith classification accuracy pmAnd a mark value alpham，pmThe calculation formula of (2) is as follows:
Figure GDA0003075769330000052
wherein n isrAnd nfRespectively carrying out correct quantity and wrong quantity of classification on the classification model after training;
the calculation process of the state estimation is an optimization solving process based on a weighted least square method, and the calculation formula is as follows:
Figure GDA0003075769330000053
s.t.Sm＝H(St)+w
wherein H is a measurement equation, and S is establishedmAnd StW is the measurement error, W is the weight matrix, which is a diagonal sparse matrix, and the diagonal elements are the reciprocal of the variance of the corresponding measurement error.
The acquisition process of the measurement error data set X is:
measuring a measurement value S of an observation object through PMU on a node of a power system simulation platformmQuerying S of nodes on the simulation platform of the power system through simulation softwaretBy calculating SmAnd StThe difference value of (A) is used to obtain the measurement error, and X is formed by a plurality of groups of measurement errors.
The formula of the normalization process is:
Figure GDA0003075769330000054
wherein the content of the first and second substances,
Figure GDA0003075769330000055
is the j normalized measurement error, E (X) is the expectation of X, var (X) is the variance of X, XjIs the jth measurement error in X.
Figure GDA0003075769330000056
The calculation formula of (a) is as follows:
Figure GDA0003075769330000057
where K is the Gaussian kernel function, h is the kernel density estimation window width, xjFor the jth observation in X, n1Number of samples of X;
the calculation formula of the kernel density estimation window width h is as follows:
Figure GDA0003075769330000058
wherein, sigma is the standard deviation of X, R is the four-quadrant spacing of X, N is the number of observed data in X, if h is too large, or decrease
Figure GDA0003075769330000059
If h is too small, this will result in
Figure GDA00030757693300000510
The fluctuation is large and discontinuous, and the error is large.
The embodiment provides a PMU-based power system state estimation performance evaluation method, which includes the steps of firstly obtaining error characteristics of PMU measurement data through a power system simulation platform, then superposing the error characteristics on an observation object true value, theoretically calculating observation object measurement values to form training data of an SVM model, finally obtaining object measurement values and corresponding state estimation values of all nodes of a power system on a new time section, inputting a plurality of trained SVM models, and finally calculating a state estimation performance evaluation index lambda.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims (10)

1. A PMU-based power system state estimation performance evaluation method is characterized by comprising the following steps:
n through the power system2Actual measurement of n by each PMU2Measured value S of each observed objectmObtaining respective S by state estimationmState estimation value S ofseN is to be2Group SmAnd SseRespectively correspond to input n2The trained classification models are combined, and n is obtained correspondingly2A mark value alphamAnd calculating a state estimation performance evaluation index lambda, wherein the calculation formula is as follows:
Figure FDA0003075769320000011
wherein p ismiAnd alphamiRespectively the ith classification accuracy pmAnd a mark value alphamSaid p ismThe calculation formula of (2) is as follows:
Figure FDA0003075769320000012
wherein n isrAnd nfRespectively carrying out correct quantity and wrong quantity of classification on the classification model after training;
wherein, said n2The training process of the group classification model is as follows:
obtaining a measurement error data set X of an observed object through a PMU of a power system simulation platform, carrying out normalization processing on the X, and calculating a probability density function of the X
Figure FDA0003075769320000013
Obtaining n through a power system simulation platform2Group Observation truth StBy superimposing StAnd
Figure FDA0003075769320000014
theoretical solution of n2Group SmObtaining respective S by state estimationmState estimation value S ofseJudging each group St、SmAnd SseWhether the judgment formula is satisfied, if so, the marking value alpha with the corresponding generation value of 1 is generatedmOtherwise, generate α with value 0mThe judgment formula is as follows:
|Sim-Sit|＞|Sise-Sit|
wherein Si ism、SitAnd SiseAre respectively the ith group Sm、StAnd Sse；
Using n2Group St、Sm、SseAnd alphamCarrying out classification model training to correspondingly obtain n2And (4) classifying the models.
2. The PMU-based power system state estimation performance evaluation method according to claim 1, characterized in that the state estimation calculation formula is:
Figure FDA0003075769320000015
s.t.Sm＝H(St)+w
wherein, H is the measurement equation, W is the measurement error, and W is the weight matrix.
3. The PMU-based power system state estimation performance evaluation method according to claim 1, characterized in that the method includes
Figure FDA0003075769320000016
The calculation formula of (a) is as follows:
Figure FDA0003075769320000021
where K is the kernel density function, h is the kernel density estimation window width, xjFor the jth observation in X, n1Number of samples of X.
4. The PMU-based power system state estimation performance evaluation method according to claim 3, characterized in that the calculation formula of the kernel density estimation window width h is:
Figure FDA0003075769320000022
where σ is the standard deviation of X, R is the four-bit distance of X, and N is the number of observed data in X.
5. The PMU-based power system state estimation performance evaluation method of claim 3, characterized in that K is a Gaussian kernel function.
6. The PMU-based power system state estimation performance evaluation method of claim 1, wherein the observed object includes one or more of a voltage magnitude, a voltage phase angle, a current magnitude, and a current phase angle.
7. The PMU-based power system state estimation performance evaluation method of claim 1, characterized in that the kernel function of the training classification model is a Gaussian kernel function.
8. The PMU-based power system state estimation performance evaluation method according to claim 1, wherein the measurement error dataset X is obtained by:
PMU through electric power system simulation platform measures observation object measured value SmInquiring the true value S of the observation object through the power system simulation platformtBy calculating SmAnd StThe difference value of (A) is used to obtain the measurement error, and X is formed by a plurality of groups of measurement errors.
9. The PMU-based power system state estimation performance evaluation method according to claim 1, characterized in that the formula of the normalization process is:
Figure FDA0003075769320000023
wherein the content of the first and second substances,
Figure FDA0003075769320000024
is the j normalized measurement error, E (X) is the expectation of X, var (X) is the variance of X, XjIs the jth measurement error in X.
10. The PMU-based power system state estimation performance evaluation method according to claim 1, characterized in that the classification model includes an SVM model, a binary tree model or a neural network model.
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