AU2020327340B2 - Method for evaluating state estimation performance of power system based on PMU - Google Patents
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Abstract
The present disclosure relates to a method for evaluating state estimation performance of a
power system based on a phasor measurement unit (PMU). The method is specifically: actually
obtaining an observed object measurement value S. through measurement by using a PMU of
a power system; obtaining a state estimation value se of Sm; inputting Sm and se into a
trained classification model, to obtain a classification accuracy and a tag value; and calculating a
state estimation performance evaluation index. A training process is: obtaining a measurement
error data set X of an observed object through a power system simulation platform;
normalizing X ; calculating a probability density function (x) of X ; obtaining St
through the power system simulation platform; obtaining Sm by superimposing St and using
f(x); obtaining a state estimation value se of each Sm, where am is 0 or 1; and training
the classification model by using St, Sm, se and am. Compared with the prior art, the
present disclosure has advantages of high accuracy, easy operation, and labor saving.
Description
[0001] The present disclosure relates to a technology for evaluating state estimation performance of a power system, and in particular, to a method for evaluating state estimation performance of a power system based on a phasor measurement unit (PMU).
[0002] The method for evaluating state estimation performance of a power system is a key technology for operation and control of the power system, and can measure key information such as accuracy of a state estimation result. An accurate and appropriate state estimation result can ensure correct operation and control of the power system. As a large quantity of renewable energy sources are grid-connected, a power transmission network is complex, and the load is diversified, an operation mode of the power system changes rapidly. Linear state estimation based on a PMU can better reflect a current state of the system. However, a PMU error is a key problem that affects accuracy of the linear state estimation. In actual research, it is usually considered that the PMU error is subject to Gaussian distribution. However, there are many factors that affect accuracy of PMU measurement data, mainly an amplitude error and a phase angle error of a voltage transformer and a current transformer, a cable channel transmission error, and a synchronization clock error. Therefore, the PMU error should be subject to a more complex distribution. In addition, in an actual power system, none of a truth value of a PMU measurement point and an actual state of the power system can be obtained. Therefore, state estimation performance in the actual power system is difficult to evaluate.
[0003] Currently, a main indicator for evaluating the state estimation performance is a pass rate 7 , which is defined as:
1 rn r7 -Y a,*100%
[0004] m
[0005] >
[00061 where M is a measurement quantity, I is a measurement residual of a measurement point i, and Ci is a threshold.
[0007] However, the pass rate depends on the threshold for distinguishing pass or fail, and Ci is a constant set according to engineering experience and has no actual theoretical basis.
[0008] In addition, there are studies using a concept of cross entropy in the information theory as an evaluation criterion for state estimation performance, but it reflects only a relationship between a measurement value and an estimated value and does not relate to the actual state of the power system. SUMMARY
[0009] An objective of the present disclosure is to provide a method for evaluating state estimation performance of a power system based on a PMU with advantages of high accuracy, easy operation, and labor saving, to overcome the foregoing disadvantages in the prior art.
[0010] The objective of the present disclosure can be achieved by using the following technical solution:
[0011] A method for evaluating state estimation performance of a power system based on a PMU is specifically:
[0012] actually obtaining n2 observed object measurement values S, through measurement by using n2 PMUs of a power system, where an observed object includes one or more of a voltage amplitude, a voltage phase angle, a current amplitude, and a current phase angle; obtaining a state estimation value Se, of each S, through state estimation; separately and correspondingly inputting n2 groups of S. and n2 groups of Ss, into n2 trained classification models, to correspondingly obtain n2 tag values a, by using classification criteria of S. and Se, provided by the n 2 classification models; calculating a state estimation performance evaluation index X, and determining the state of the power system according to the state estimation performance evaluation index X to control the power system, where a calculation formula is:
Z(piai)
[0013] n2
[0014] where Pmi and ami are respectively an ith classification accuracy Pm and an ithtag value a, and a calculation formula of Pm is:
_ n,
[0015] nr +n
n n
[0016] where r and f are respectively a classification correctness quantity and a classification error quantity after the classification models are trained;
[0017] where a training process of the n2 classification models is:
[0018] obtaining a measurement error data set X of an observed object by using a PMU of a power system simulation platform; for ease of analysis and comparison, normalizing X; calculating a probability density function (x) of X ; obtaining n2 groups of observed S n object truth values St through the power system simulation platform; obtaining 2 groups of Sm by superimposing St and using a f(x) theory; obtaining the state estimation value of each Sm through state estimation; determining whether each group of St, Sm, and satisfies a determining formula; and if yes, correspondingly generating a tag value am with a value of 1; otherwise, generating am with a value of 0, where the determining formula is as follows:
[0019] 1Si -St11S - t1
[00201 where Sim, Sit, and S se are respectively an ith group of Sm ,an ith group of St, and an ith group of ,se;and
[0021] training the classification models by using n2 groups of St, Sm, Ese, and am as training data, to correspondingly obtain n2 classification models.
[0022] Further, the classification model includes an SVM model, a binary tree model, or a neural network model, and a kernel function for training the classification model is a Gaussian kernel function.
[0023] Further, a process of obtaining the measurement error data set X is:
[0024] obtaining the observed object measurement value m through measurement by using the PMU on a node of the power system simulation platform; querying ' of the node on the power system simulation platform by using simulation software; obtaining a measurement error by calculating a difference between Sm and St; and forming X by using several groups of measurement errors.
[0025] Further, a formula of the normalization is:
x;-E(X)
[0026] j var(X)
[0027] where /i is a jth normalized measurement error, E(X) is an expectation of X, var(X) is a variance of X, and Xj is a jth measurement error in X.
[0028] Further, a calculation formula of(x) is as follows:
f(x)=-- 1 K( x-x'1
[0029] nih j h
[0030] where K is a Gaussian kernel function, h is a kernel density estimation window width, X. is jth observation data in X, and ni is a sample quantity of X.
[0031] A calculation formula of the kernel density estimation window width h is:
h = min{u, }R 1.06 * N
[0032] 1.34
[0033] where 0~ is a standard deviation of X,R is an interquartile range of X,andNisan amount of observation data in X.Ifavalueof h is extremely large, accuracy of (x) is reduced. If a value of h is extremely small, f(x) is caused to fluctuate greatly and be discontinuous, resulting in large errors.
[0034] Further, the state estimation algorithm can reduce measurement errors, increase accuracy and availability of measurement data, and its basic idea is based on the weighted least squares method to solve an optimization problem:
Se = arg min[S. - H (S,)] T W[S, - H(S,)] S,
[00351 s.t. S, H(S)+w
[0036] where H is a measurement equation and H establishes a relationship between Sm and St, W is a measurement error, W is a weight matrix and W is a diagonal sparse matrix, and a diagonal element is a reciprocal of a variance of a corresponding measurement error.
[0037] Compared with the prior art, the present disclosure has the following beneficial effects:
[0038] (1) According to the present disclosure, an error characteristic of PMU measurement data is obtained through a power system simulation platform; then the error characteristic is superimposed on an observed object truth value, to theoretically calculate an observed object measurement value and training data that forms a classification model; an object measurement value and a corresponding state estimation value of each node of a power system are obtained in a new time section and are input into several groups of trained classification models; and finally a state estimation performance evaluation index X is calculated. Topology analysis combined with the power system simulation platform and machine learning training resolves a problem of unknowability of a real state of the power system, and an evaluation result is more objective and accurate, without requiring a large amount of field actual measurement data of the power system. This is easy to operate, saves manpower and material resources, and reduces costs.
[0039] (2) The present disclosure can use an SVM model, a binary tree model, or a neural network model as a classification model, and therefore can be widely applied.
[0040] FIG. 1 is a flowchart of a method according to the present disclosure.
[0041] The present disclosure is described in detail below with reference to the accompanying drawings and a specific embodiment. This embodiment is implemented on the premise of the technical solution of the present disclosure and provides the detailed implementations and specific operation processes, but the protection scope of the present disclosure is not limited to the following embodiment.
[0042] As shown in FIG. 1, a method for evaluating state estimation performance of a power system based on a PMU is specifically as follows:
[0043] The power system is provided with n2 monitoring nodes, and each monitoring node is provided with a PMU. The method includes: obtaining a measurement error data set X of an observed object by using a PMU of a power system simulation platform; normalizing the data set; calculating a probability density function f(x) of X , where f(x) includes a PMU measurement error distribution feature; obtaining n2 groups of observed object truth values St through the power system simulation platform; obtaining n2 groups of - by superimposing
St and using a f(x) theory; obtaining the state estimation value of each Sm through state estimation; determining whether each group of S, S, and satisfies a determining formula; and if yes, correspondingly generating a tag value am with a value of 1; otherwise, generating am with a value of 0. The determining formula is as follows:
10044] Sim- 1 -se 1
[00451 where Sim, Sit, and S se are respectively Sm, St, and e of an ith node.
[0046] Because an actual observed object truth value of the power system cannot be obtained, n2 groups of St, Sm, se, and am are used as training data for SVM training. A kernel
function for the training is a Gaussian kernel function. n2 trained SVM models are obtained correspondingly.
[0047] In a time section in which evaluation is required, n2 observed object measurement values Sm are actually obtained through measurement by using n2 PMUs of the power system, where observed objects are a voltage amplitude and a voltage phase angle, that is, Sm includes a voltage amplitude measurement value and a voltage phase angle measurement value. A state estimation value of each Sm is obtained through state estimation. n2 groups of SM and n2 groups of are separately and correspondingly input into n2 trained classification models, to correspondingly obtain n2 tag values am by using classification criteria of Sm and se provided by the n2 classification models. A state estimation performance evaluation index X is calculated, and a calculation formula is:
(pm am,)
[0048] n2
[0049] where Pmi and ami are respectively an ith classification accuracy Pm and an ithtag value am, and a calculation formula of Pm is:
_ n,
[0050] nr +n
[0051] where nr and n. are respectively a classification correctness quantity and a classification error quantity after the classification models are trained.
[0052] A calculation process of the state estimation is an optimization solution process based on the weighted least squares method, and the calculation formula is as follows:
Ss = arg min[S. - H(S,)] T W[S, - H(S,)] S,
[0053] s.t. S, H(S,)+w
[0054] where H is a measurement equation and establishes a relationship between Sm and St, w is a measurement error, W is a weight matrix and is a diagonal sparse matrix, and a diagonal element is a reciprocal of a variance of a corresponding measurement error.
[0055] A process of obtaining the measurement error data set X is:
[0056] obtaining the observed object measurement value - through measurement by using the PMU on a node of the power system simulation platform; querying S of the node on the power system simulation platform by using simulation software; obtaining a measurement error by calculating a difference between Sm and St; and forming X by using several groups of measurement errors.
[0057] A formula of the normalization is:
x;-E(X)
[0058] var(X)
[0059] where is a jth normalized measurement error, E(X) is an expectation of X, var(X) is a variance of X, and Xi is a jth measurement error in X.
[0060] A calculation formula of f(x) isasfollows:
f (x)= 1 K( xK(-) j
[0061] nih . h
[0062] where K is a Gaussian kernel function, h is a kernel density estimation window width, Xj is jth observation data in X, and ni is a sample quantity of X.
[0063] A calculation formula of the kernel density estimation window width h is:
2 h = min{u,R }*1.06 * N-
[0064] 1.34
[0065] where 0~ is a standard deviation of X , R is an interquartile range of X , and N is an amount of observation data in X. If a value of h is extremely large, accuracy of f(x) is reduced. If a value of h is extremely small, f(x) is caused to fluctuate greatly and be discontinuous, resulting in large errors.
[0066] This embodiment provides a method for evaluating state estimation performance of a power system based on a PMU. In the method, an error characteristic of PMU measurement data is first obtained through a power system simulation platform. Then, the error characteristic is superimposed on an observed object truth value, to theoretically calculate an observed object measurement value and training data that forms an SVM model. An object measurement value and a corresponding state estimation value of each node of a power system are obtained in a new time section and are input into several groups of trained SVM models. Finally, a state estimation performance evaluation index Xis calculated. There is no need for a large amount of field actual measurement data of the power system, and topology analysis is performed in combination with the power system simulation platform and machine learning training. Therefore, an evaluation result is more objective and accurate.
[0067] The preferred specific embodiment of the present disclosure is described in detail above. It should be understood that a person of ordinary skill in the art can make various modifications and variations according to the concept of the present disclosure without creative efforts. Therefore, all technical solutions that can be obtained by a person skilled in the art based on the prior art through logical analysis, deduction, or limited experiments according to the concept of the present disclosure shall fall within the protection scope defined by the appended claims.
[0068] The reference to any prior art in this specification is not, and should not be taken as, an acknowledgement or any form of suggestion that such prior art forms part of the common general knowledge.
[0069] It will be understood that the terms "comprise" and "include" and any of their derivatives (e.g. comprises, comprising, includes, including) as used in this specification, and the claims that follow, is to be taken to be inclusive of features to which the term refers, and is not meant to exclude the presence of any additional features unless otherwise stated or implied.
Claims (10)
1. A method for evaluating state estimation performance of a power system based on a phasor measurement unit (PMU), wherein the method is specifically:
actually obtaining n2 observed object measurement values Sm through measurement by using n2 PMUs of a power system; obtaining a state estimation value Sse of each Sn through state estimation; separately and correspondingly inputting n2 groups of Sr and n2 groups of Sse into n2 trained classification models, to correspondingly obtain n2 tag values am; calculating a state estimation performance evaluation index X, and determining the state of
the power system according to the state estimation performance evaluation index X to control the power system,
wherein a calculation formula is:
Z(Pmiami) n2
wherein Pni and ani are respectively an ith classification accuracy Pm and an itag value a., and a calculation formula of Pm is:
n p,, =rn n, +n,.
wherein nr and nf are respectively a classification correctness quantity and a classification error quantity after the classification models are trained,
wherein a training process of the n2 classification models is:
obtaining a measurement error data set X of an observed object by using a PMU of a power system simulation platform; normalizing X, calculating a probability density function n S f(x) of X; obtaining n2 groups of observed object truth values t through the power system simulation platform; obtaining n2 groups of Sm by superimposing S and using a f(x) theory; obtaining the state estimation value Sse of each Sm through state estimation; determining whether each group of S', S ,-, and S se satisfies a determining formula; and if yes, correspondingly generating a tag value an with a value of 1; otherwise, generating a, with a value of 0, wherein the determining formula is as follows:
| Sim - Si, |>| Sie - Si, |
wherein Sin, Sit, and Sse are respectively an ith group of S , an ith group of St, and an ith group of se; and
training the classification models by using n2 groups of St, Sm , Sse, and am, to correspondingly obtain n2 classification models.
2. The method for evaluating state estimation performance of a power system based on a PMU according to claim 1, wherein a calculation formula of the state estimation is:
Se arg min[S, - H(S, )]TW[S, - H(S,)] St s.t. Sm, = H(S,)+ w
wherein H is a measurement equation, W is a measurement error, and W is a weight matrix.
3. The method for evaluating state estimation performance of a power system based on a PMU according to claim 1, wherein a calculation formula of f(x) is as follows:
1 x -x f(x) - K( ') ni h, h
wherein K is a kernel density function, h is a kernel density estimation window width, is jth observation data in X, and ni is a sample quantity of X.
4. The method for evaluating state estimation performance of a power system based on a PMU according to claim 3, wherein a calculation formula of the kernel density estimation window width h is:
h = min{o, R *1.06* N-°2 1.34
wherein (~ is a standard deviation of X, R is an interquartile range of X, and N is an amount of observation data in X.
5. The method for evaluating state estimation performance of a power system based on a PMU according to claim 3, wherein K is a Gaussian kernel function.
6. The method for evaluating state estimation performance of a power system based on a PMU according to claim 1, wherein the observed object comprises one or more of a voltage amplitude, a voltage phase angle, a current amplitude, and a current phase angle.
7. The method for evaluating state estimation performance of a power system based on a PMU according to claim 1, wherein a kernel function for training the classification model is a Gaussian kernel function.
8. The method for evaluating state estimation performance of a power system based on a PMU according to claim 1, wherein a process of obtaining the measurement error data set X is:
obtaining the observed object measurement value S through measurement by using the PMU of the power system simulation platform; querying the observed object truth value St through the power system simulation platform; obtaining a measurement error by calculating a difference between S" and St; and forming X by using several groups of measurement errors.
9. The method for evaluating state estimation performance of a power system based on a PMU according to claim 1, wherein a formula of the normalization is:
X; - E(X)
var(X)
wherein i is a jth normalized measurement error, E(X) is an expectation of X, var(X) is a variance of X, and x' is a jth measurement error in X.
10. The method for evaluating state estimation performance of a power system based on a PMU according to claim 1, wherein the classification model comprises an SVM model, a binary tree model, or a neural network model.
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| CN110705887A (en) * | 2019-10-10 | 2020-01-17 | 国网湖北省电力有限公司计量中心 | Low-voltage transformer area operation state comprehensive evaluation method based on neural network model |
| CN111900731B (en) * | 2020-07-29 | 2021-10-08 | 国网上海市电力公司 | PMU-based power system state estimation performance evaluation method |
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