CN111900731B - A PMU-based Power System State Estimation Performance Evaluation Method - Google Patents

Abstract

The invention relates to a PMU-based power system state estimation performance evaluation method, which specifically includes: actually measuring the measured value S _m of the observed object through the PMU of the power system, obtaining the state estimated value S _se of S _m , and comparing S _m and S _se Input the trained classification model, obtain the classification accuracy and label value, and calculate the state estimation performance evaluation index. The training process is: obtain the measurement error data set X of the observed object through the power system simulation platform, normalize X and calculate Probability Density Function of X

Obtain S _t through the power system simulation platform, superimpose S _t and

Obtain S _m , obtain the state estimation value S _se of each S _m , α _m is set to 0 or 1, and use S _t , S _m , S _se and α _m to train the classification model. Compared with the prior art, the present invention has the advantages of high accuracy, simple operation and labor saving.

Description

A PMU-based Power System State Estimation Performance Evaluation Method

technical field

The invention relates to a power system state estimation performance evaluation technology, in particular to a PMU-based power system state estimation performance evaluation method.

Background technique

The power system state estimation performance evaluation method is a key technology for power system operation and control. It can measure key information such as the accuracy of the state estimation result. An accurate and reasonable state estimation result can ensure the correct operation and control of the power system. With the integration of large amounts of renewable energy into the grid, complex transmission networks and diverse loads, the way the power system operates is changing rapidly. The linear state estimation based on phasor measurement unit (PMU) can better reflect the current state of the system. However, the PMU error is a key issue that affects the accuracy of linear state estimation. In practical research, it is usually considered that the PMU error obeys a Gaussian distribution. However, there are many factors that affect the accuracy of PMU measurement data, mainly including the amplitude error and phase angle error of the voltage transformer and the current transformer, the transmission error of the cable channel and the synchronization clock error. Therefore, the PMU error should follow a more complex distribution. At the same time, in the actual power system, neither the true value of the PMU measurement point nor the real state of the power system can be obtained, so the state estimation performance in the actual power system is difficult to evaluate.

At present, the main indicator for evaluating the performance of state estimation is the pass rate η, which is defined as:

Among them, m is the measurement quantity, ri is the measurement residual of the measurement point _i , and ε _i is the threshold;

However, the pass rate depends on the threshold ε _i for distinguishing whether it is qualified or not. ε _i is a constant set according to engineering experience, and there is no actual theoretical basis;

At the same time, there are also studies using the concept of cross-entropy in information theory as the evaluation standard of state estimation performance, but it only reflects the relationship between the measured value and the estimated value, and does not involve the real state of the power system.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a PMU-based power system state estimation performance evaluation method in order to overcome the above-mentioned defects in the prior art, which has high accuracy, simple and convenient operation, and saves manpower.

The object of the present invention can be realized through the following technical solutions:

A PMU-based power system state estimation performance evaluation method, specifically:

The measurement values S _m of n ₂ observation objects are actually measured by the n ₂ PMUs of the power system, and the observation objects include one or more of voltage amplitude, voltage phase angle, current amplitude and current phase angle, Obtain the state estimation value S _se of each S _m through state estimation, input the n ₂ groups of S _m and S _se correspondingly to the n ₂ groups of trained classification models, and use the S _m and S _se given by the n ₂ classification models to divide Standard, correspondingly obtain n ₂ marked values α _m , calculate the state estimation performance evaluation index λ, and the calculation formula is:

Among them, p _mi and α _mi are the ith classification accuracy p _m and the label value α _m respectively, and the calculation formula of the p _m is:

Among them, n _r and n _f are the number of correct classifications and the number of incorrect classifications after the classification model is trained;

Wherein, the training process of the described n ₂ groups of classification models is:

通过电力系统仿真平台获取n₂组观测对象真值S_t，通过叠加S_t和

理论求得n₂组S_m，通过状态估计获取各个S_m的状态估计值S_se，判断每组S_t、S_m和S_se是否满足判断公式，若满足则对应生成值为1的标记值α_m，否则生成值为0的α_m，所述的判断公式如下：The measurement error data set X of the observed object is obtained through the PMU of the power system simulation platform. In order to facilitate analysis and comparison, the X is normalized and the probability density function of X is calculated.

Obtain the true value S _t of n ₂ groups of observation objects through the power system simulation platform, and by stacking S _t and

Theoretically obtain n ₂ groups of S _m , obtain the state estimated value S _se of each S _m through state estimation, and judge whether each group of S _t , S _m and S _se satisfies the judgment formula, and if so, the corresponding mark value with a value of 1 is generated α _m , otherwise α _m with a value of 0 is generated, and the judgment formula is as follows:

|Si _m -Si _t |>|Si _se -Si _t |

where Si _m , Si _t and Si _se are the i-th group S _m , S _t and S _se , respectively;

Taking n ₂ groups of S _t , S _m , S _se and α _m as training data, the classification model is trained, and n ₂ classification models are obtained correspondingly.

Further, the classification model includes an SVM model, a binary tree model or a neural network model, and the kernel function for training the classification model is a Gaussian kernel function.

Further, the acquisition process of the described measurement error data set X is:

The measured value S _m of the observation object is measured by the PMU on the node of the power system simulation platform, the S _t of the node on the power system simulation platform is inquired through the simulation software, and the measurement error is obtained by calculating the difference between S _m and S _t . The group measurement incorrectly constitutes an X.

Further, the formula of the described normalization processing is:

为第j个归一化后的测量误差，E(X)为X的期望，var(X)为X的方差，x_j为X中的第j个测量误差。in,

is the jth normalized measurement error, E(X) is the expectation of X, var(X) is the variance of X, and x _j is the jth measurement error in X.

的计算公式如下：Further, the said

The calculation formula is as follows:

Among them, K is the Gaussian kernel function, h is the kernel density estimation window width, x _j is the jth observation data in X, and n ₁ is the number of samples of X;

The calculation formula of the kernel density estimation window width h is:

的精度，如果h取值过小，会导致

起伏大且不连续，误差大。Among them, σ is the standard deviation of X, R is the interquartile range of X, and N is the number of observations in X. If the value of h is too large, or decrease

precision, if the value of h is too small, it will cause

The fluctuation is large and discontinuous, and the error is large.

Further, the described state estimation algorithm can reduce the measurement error and increase the accuracy and availability of the measurement data. Its basic idea is based on the weighted least squares method to solve an optimization problem:

stS _m =H(S _t )+w

Among them, H is the measurement equation, the H establishes the relationship between S _m and S _t , w is the measurement error, W is the weight matrix, the W is the diagonal sparse matrix, and the diagonal elements are the corresponding measurement The inverse of the error variance.

Compared with the prior art, the present invention has the following beneficial effects:

(1) The present invention obtains the error characteristics of the PMU measurement data through the power system simulation platform, then superimposes the error characteristics on the true value of the observation object, theoretically calculates the measurement value of the observation object, forms the training data of the classification model, and finally at a new time The object measurement values and corresponding state estimates of each node of the power system are obtained on the cross-section, and several groups of classification models are input and trained. Finally, the state estimation performance evaluation index λ is calculated, and the topology analysis is carried out in combination with the power system simulation platform and machine learning training. It solves the problem of the unknowability of the real state of the power system, and the evaluation results are more objective and accurate. At the same time, it does not require a large number of on-site measured data of the power system, which is easy to operate, saves manpower and material resources, and reduces costs;

(2) The present invention can adopt the SVM model, the binary tree model or the neural network model as the classification model, and has a wide application range.

Description of drawings

FIG. 1 is a flow chart of the method of the present invention.

Detailed ways

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and provides a detailed implementation manner and a specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

A PMU-based power system state estimation performance evaluation method, as shown in Figure 1, is as follows:

包含了PMU测量误差分布特性，通过电力系统仿真平台获取n₂组观测对象真值S_t，通过叠加S_t和

理论求得n₂组S_m，通过状态估计获取各个S_m的状态估计值S_se，判断每组S_t、S_m和S_se是否满足判断公式，若满足则对应生成值为1的标记值α_m，否则生成值为0的α_m，判断公式如下：There are n ₂ monitoring nodes on the power system, and each monitoring node is equipped with a PMU. The measurement error data set X of the observation object is obtained through the PMU of the power system simulation platform, and the data set is normalized and calculated. Probability Density Function of X

Including the distribution characteristics of PMU measurement error, the true value S t of n ₂ groups of observation objects is obtained through the power system simulation platform, and the true value S _t of n 2 groups of observation objects is obtained by stacking S _t and

Theoretically obtain n ₂ groups of S _m , obtain the state estimated value S _se of each S _m through state estimation, and judge whether each group of S _t , S _m and S _se satisfies the judgment formula, and if so, the corresponding mark value with a value of 1 is generated α _m , otherwise α _m with a value of 0 is generated, and the judgment formula is as follows:

|Si _m -Si _t |>|Si _se -Si _t |

where Si _m , Si _t and Si _se are respectively S _m , S _t and S _se of the i-th node;

Since it is impossible to obtain the true value of the observed object of the actual power system, n ₂ groups of S _t , S _m , S _se and α _m are used as training data to perform SVM training, and the training kernel function is a Gaussian kernel function, corresponding to n ₂ A trained SVM model;

On the time section that needs to be evaluated, n ₂ PMUs of the power system actually measure the measured value S _m of n ₂ observation objects, and the observation objects are voltage amplitude and voltage phase angle, that is, S _m includes the measured value of voltage amplitude and voltage The phase angle measurement value, obtain the state estimated value S _se of each S _m through the state estimation, input the n ₂ groups of S _m and S _se correspondingly to the n ₂ groups of trained classification models, and use the S given by the n ₂ classification models. _m and S _se are divided into standards, corresponding to n ₂ marked values α _m are obtained, and the state estimation performance evaluation index λ is calculated. The calculation formula is:

Among them, p _mi and α _mi are the ith classification accuracy p _m and the label value α _m respectively, and the calculation formula of p _m is:

Among them, n _r and n _f are the number of correct classifications and the number of incorrect classifications after the classification model is trained;

The 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:

stS _m =H(S _t )+w

Among them, H is the measurement equation, establishing the relationship between S _m and S _t , w is the measurement error, W is the weight matrix, which is a diagonal sparse matrix, and the diagonal elements are the reciprocal of the corresponding measurement error variance.

The acquisition process of the measurement error dataset X is:

The measured value S _m of the observation object is measured by the PMU on the node of the power system simulation platform, the S _t of the node on the power system simulation platform is inquired through the simulation software, and the measurement error is obtained by calculating the difference between S _m and S _t . The group measurement incorrectly constitutes an X.

The formula for normalization is:

为第j个归一化后的测量误差，E(X)为X的期望，var(X)为X的方差，x_j为X中的第j个测量误差。in,

is the jth normalized measurement error, E(X) is the expectation of X, var(X) is the variance of X, and x _j is the jth measurement error in X.

的计算公式如下：

The calculation formula is as follows:

Among them, K is the Gaussian kernel function, h is the kernel density estimation window width, x _j is the jth observation data in X, and n ₁ is the number of samples of X;

The calculation formula of the kernel density estimation window width h is:

的精度，如果h取值过小，会导致

起伏大且不连续，误差大。where σ is the standard deviation of X, R is the interquartile range of X, and N is the number of observations in X. If the value of h is too large, or decrease

precision, if the value of h is too small, it will cause

The fluctuation is large and discontinuous, and the error is large.

This embodiment proposes a PMU-based power system state estimation performance evaluation method. First, the error characteristics of the PMU measurement data are obtained through the power system simulation platform, and then the error characteristics are superimposed on the true value of the observation object, and the measurement of the observation object is theoretically calculated. value, constitute the training data of the SVM model, and finally obtain the object measurement value and the corresponding state estimation value of each node of the power system on the new time section, and input and train several groups of SVM models, and finally calculate the state estimation performance evaluation index λ , does not require a large amount of field measured data of the power system, and combines the power system simulation platform and machine learning training for topology analysis, and the evaluation results are more objective and accurate.

The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make many modifications and changes according to the concept of the present invention without creative efforts. Therefore, all technical solutions that can be obtained by those skilled in the art through logical analysis, reasoning or limited experiments on the basis of the prior art according to the concept of the present invention shall fall within the protection scope determined by the claims.

Claims (10)

1. a power system state estimation performance evaluation method based on PMU, is characterized in that, is specifically: The n ₂ measured values S _m of the observation objects are actually measured by the n ₂ PMUs of the power system, the state estimated value S _se of each S _m is obtained through the state estimation, and the n ₂ groups of S _m and S _se are respectively corresponding to the input of the n ₂ groups For the trained classification model, n ₂ label values α _m are obtained correspondingly, and the state estimation performance evaluation index λ is calculated. The calculation formula is:

Among them, p _mi and α _mi are the ith classification accuracy p _m and the label value α _m respectively, and the calculation formula of the p _m is:

Among them, n _r and n _f are the number of correct classifications and the number of incorrect classifications after the classification model is trained; Wherein, the training process of the described n ₂ groups of classification models is: Obtain the measurement error data set X of the observed object through the PMU of the power system simulation platform, normalize X, and calculate the probability density function of X

Obtain the true value S _t of n ₂ groups of observation objects through the power system simulation platform, and by stacking S _t and

Theoretically obtain n ₂ groups of S _m , obtain the state estimated value S _se of each S _m through state estimation, and judge whether each group of S _t , S _m and S _se satisfies the judgment formula, and if so, the corresponding mark value with a value of 1 is generated α _m , otherwise α _m with a value of 0 is generated, and the judgment formula is as follows: |Si _m -Si _t |>|Si _se -Si _t | where Si _m , Si _t and Si _se are the i-th group S _m , S _t and S _se , respectively; Use n ₂ groups of S _t , S _m , S _se and α _m for classification model training, and correspondingly obtain n ₂ classification models. 2. A PMU-based power system state estimation performance evaluation method according to claim 1, wherein the calculation formula of the state estimation is:

stS _m =H(S _t )+w Among them, H is the measurement equation, w is the measurement error, and W is the weight matrix. 3. A PMU-based power system state estimation performance evaluation method according to claim 1, wherein the

The calculation formula is as follows:

Among them, K is the kernel density function, h is the kernel density estimation window width, x _j is the jth observation data in X, and n ₁ is the number of samples of X. 4. A PMU-based power system state estimation performance evaluation method according to claim 3, wherein the calculation formula of the kernel density estimation window width h is:

where σ is the standard deviation of X, R is the interquartile range of X, and N is the number of observations in X. 5 . The PMU-based power system state estimation performance evaluation method according to claim 3 , wherein the K is a Gaussian kernel function. 6 . 6 . The PMU-based power system state estimation performance evaluation method according to claim 1 , wherein the observation object comprises one of voltage amplitude, voltage phase angle, current amplitude and current phase angle. 7 . one or more. 7 . The PMU-based power system state estimation performance evaluation method according to claim 1 , wherein the kernel function for training the classification model is a Gaussian kernel function. 8 . 8. A PMU-based power system state estimation performance evaluation method according to claim 1, wherein the acquisition process of the measurement error data set X is: The measurement value S _m of the observation object is measured by the PMU of the power system simulation platform, the true value S _t of the observation object is inquired through the power system simulation platform, and the measurement error is obtained by calculating the difference between S _m and S _t , which is composed of several groups of measurement errors X. 9. A PMU-based power system state estimation performance evaluation method according to claim 1, wherein the normalization processing formula is:

in,

is the jth normalized measurement error, E(X) is the expectation of X, var(X) is the variance of X, and x _j is the jth measurement error in X. 10 . The PMU-based power system state estimation performance evaluation method according to claim 1 , wherein the classification model comprises an SVM model, a binary tree model or a neural network model. 11 .

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