A Grid Status Analysis Method with Large-Scale Wind Power Access Using Big Data

Abstract

Targeting the problem of the power grid facing greater risks with the connection of large-scale wind power, a method for power grid state analysis using big data is proposed. First, based on the big data, the wind power matrix and the branch power matrix are each constructed. Second, for the wind energy matrix, the eigenvalue index in the complex domain and the spectral density index in the real domain are constructed based on the circular law and the M-P law, respectively, to describe the variation of wind energy. Then, based on the concept of entropy and the M-P law, the index for describing the variation of the branch power is constructed. Finally, in order to analyze the real-time status of the grid connected to large-scale wind power, the proposed index is combined with the sliding time window. The simulation results based on the enhanced IEEE-33 bus system show that the proposed method can perform real-time analysis on the grid state of large-scale wind power connection from different perspectives, and its sensitivity is good.

1. Introduction

At present, the world’s petroleum energy is becoming increasingly scarce, and the problem of carbon emissions is becoming more and more serious. Under this background, the large-scale construction of the wind power base is of great significance to the adjustment of the energy structure, energy conservation and emission reduction [1]. However, the large-scale centralized access to wind power also increases the possibility of the power grid going black [2]. Therefore, a comprehensive and accurate grid condition analysis is conducive to controlling the operation of the grid under large-scale access.

Now, for a single power system, the literature [3,4,5] proposes a power grid state evaluation method based on entropy theory and points out that the load rate and network structure of the line are important factors affecting the power grid state evolution. The literature [6] combines the above two factors and considers the distribution balance of load rate and proposes a comprehensive evaluation method of a self-organized critical state of the power grid based on joint weighted entropy. However, the load rate zoning is greatly affected by human factors and the evaluation results are uncertain. For the power grid with large-scale wind power centralized access, the literature [7] constructs network topology entropy and power flow entropy based on entropy theory and analyzes the power grid state from the perspective of the influence of wind power fluctuation on power flow entropy. Additionally, for the above-mentioned situations, the literature [8] takes weighted power flow entropy, network topology entropy, wind wave dynamic entropy and other entropy physical indexes as inputs and constructs the mapping relationship between key physical quantity indexes and the power grid state through neural networks. However, it requires a large number of training samples, and the generalization of machine learning methods is poor, so its application in practice is limited.

Random matrix theory (RMT) is a mathematical statistical method based on big data. It analyzes the big data matrix from the perspective of feature distribution to avoid information loss due to dimension reduction or feature extraction. It has achieved good application results in data-driven power grid situation awareness [9], transient stability analysis [10], power grid weak point identification [11], power consumption behavior analysis [12] and power grid state analysis, which verifies the effectiveness of random matrix theory in power grid state analysis.

Therefore, based on the random matrix theory and making full use of the big data of power grid measurement, a power grid state evaluation method including the power grid state analysis method of large-scale wind power centralized access is proposed in this paper. The contributions of this paper are as follows:

(1)

Based on the ring law and M-P law, the evaluation indexes of wind power change level in the complex domain and real domain are constructed, respectively. The comprehensive index of wind power change rate is constructed by combining the two.

(2)

Based on the concept of entropy and M-P law, the state evaluation index of the power network is constructed to represent the power change level of the branch.

(3)

Based on the synthesis of the wind power change index and branch power change index, the power grid state analysis index under large-scale wind power access is constructed. Combining the proposed index with the sliding time window, the real-time state analysis of the power grid connected with large-scale wind power is carried out from different angles.

2. Random Matrix Theory

Random matrix theory is a high-dimensional mathematical statistical method. It analyzes the correlation degree of the whole system from the perspective of probability and can reflect the operating state of the system from the global perspective.

2.1. Sample Covariance Matrix and Empirical Spectrum Distribution

For a matrix Y with dimension N and sample number T, the sample covariance matrix M of the matrix is:

$$\mathit{M}=\frac{1}{\mathit{T}}\mathit{Y}{\mathit{Y}}^{*}$$

(1)

where ${\mathit{Y}}^{*}$ is the complex conjugate transposition of $\mathit{Y}$. In the analysis of large-dimensional data, the analysis quantity in many multivariate statistics can be expressed as the function of the empirical spectrum distribution of the sample covariance, and so the sample covariance is widely used in the random matrix.

The empirical spectrum distribution function is as follows:

$$F^M(x)=\frac{1}{p}{\displaystyle \sum _{i=1}^{p}I\left\{{\lambda }_i^M\le x\right\}},x\in R$$

(2)

where $F^{\mathit{M}}(x)$ is the empirical spectrum distribution function; $p$ is the number of eigenvalues; ${\lambda }_i^{\mathit{M}}$ is the i-th eigenvalue of matrix M; $I\{\cdot \}$ is an indicative function.

When the elements of a high-dimensional random matrix are all independent identically distributed (IID) random variables, we call the limit of the empirical spectral distribution as the limit spectral distribution. Furthermore, when the mean value is 0 and the variance is ${\sigma }^2$, the limit spectrum distribution of the sample covariance matrix of the random matrix converges to the following formula with a probability of 1:

$$f_c(\lambda )=\{{}_{{}_{0\begin{array}{ccc},& & \end{array}}{\begin{array}{ccc}& & \end{array}}_{others}}^{\frac{1}{2\pi c\lambda {\sigma }^2}\overline{)(b-\lambda )(\lambda -a)},a\le \lambda \le b}$$

(3)

where $a={\sigma }^2\sqrt{1-c^2},b={\sigma }^2\sqrt{1+c^2}$, and where $c=\mathrm{p}/n$ and ${\sigma }^2$ is the variance. This is the M-P law with parameters c and ${\sigma }^2$, which is a statistical property of high-dimensional matrices.

The M-P law analyzes the correlation within the data from the perspective of the limit spectrum distribution. When the data inside the high-dimensional matrix conforms to the independent identity distribution condition and there is no correlation between the elements in the matrix, the limit spectrum distribution of the matrix will be consistent with the M-P law. On the contrary, when the data in the matrix do not conform to the condition of independent identity distribution and there is correlation within the data, the limit spectral distribution will deviate from the M-P law. Figure 1 is an M-P law diagram corresponding to a random matrix of 80 × 200, where red is the spectral distribution result estimated with the Gaussian kernel, and blue is the M-P law.

2.2. The Ring Law

The torus law describes how much the data deviates from the randomness in the random matrix.

Let matrix $\mathit{Y}=\left\{x_{ij}\right\}$ be non-Hermitian random matrix of order $N\times T$. It satisfies $N,T\to \infty ,N/T\in \left(0,1\right)$. In addition, each element in the matrix satisfies the independent identity distribution (IID) with a mean of 0 and a variance of 1. Let the singular value equivalent matrix of $\mathit{Y}$ be $\widehat{\mathit{Y}}$, then the empirical spectral distribution of the covariance matrix of $\widehat{\mathit{Y}}$ almost always converges to the one ring theorem, and its probability density is:

$$f({\lambda }_i)=\{{}_{0,\begin{array}{ccc}& & others\end{array}}^{\frac{1}{\pi c}{\left|{\lambda }_i\right|}^{-2},\begin{array}{cc}& \end{array}{(1-c)}^{1/2}\le \left|{\lambda }_i\right|\le 1}$$

(4)

where ${\lambda }_i$ is the characteristic value of $\widehat{\mathit{Y}}$. The ring theorem states that if the elements of $\mathit{Y}$ satisfy the independent and identical distribution, the eigenvalues of the covariance of $\mathit{Y}$ will be distributed in the ring with the outer ring radius of 1 and the inner ring radius of $(1-c{)}^{{}_{1/2}}$. Otherwise, if there is correlation within the system, some eigenvalues will converge to the center of the ring. The stronger the correlation, the stronger the degree of convergence to the center.

2.3. Average Spectral Radius

The randomness of a single eigenvalue of a matrix cannot reflect the randomness of the matrix. The mean spectral radius (MSR) is a linear statistical measure that can be used to reflect the statistical characteristics of the eigenvalues. It is the average of the distances between all eigenvalues on the complex plane and the center point.

$$\mathrm{M}\mathrm{S}\mathrm{R}=\frac{1}{N}{\displaystyle \sum _{i=1}^N\left|{\lambda }_i\right|}$$

(5)

where N is the number of eigenvalues, and the number of eigenvalues is the same as the dimension of $\mathit{Y}$.

3. Data Model Construction and Data Processing

3.1. State Analysis Matrix Construction and Preprocessing Method

In this paper, the power of each wind turbine and the power of each branch are used to construct the state analysis matrix, then the data characteristics are extracted from it. Lastly, we analyze the state change in the power grid with large-scale wind power access.

3.1.1. Wind Power Matrix

It is assumed that there are $p$ nodes in the power grid connected with wind turbines, and each measuring point has a power value at the sampling time $t_i$. Then, the power values of all measuring points can form a time vector $x(t_i)$, as shown in Equation (6):

$$x(t_i)=[x_{1t_i},x_{2t_i}\dots x_{p{t}_i}]$$

(6)

For the N sampling results, all time vectors are combined to form a high-dimensional data matrix X with a size of $p\times n$:

$$\mathit{X}=\left[\begin{array}{cccc}{x}_{11}& x_{12}& \dots & x_{1n}\\ x_{21}& x_{22}& \dots & x_{2n}\\ ⋮& \dots & \dots & \dots \\ x_{p1}& x_{p2}& \dots & x_{pn}\end{array}\right]$$

(7)

From Equation (7), each line of $\mathit{X}$ is the same measurement point, and each column is the same sampling time.

3.1.2. Wind Power Matrix

Suppose there are $q$ branches in the power grid and each branch has a power value at the sampling time $t_i$. Then, the power values of all branches can form a time vector $y(t_i)$. For n sampling results, the branch power matrix $\mathit{Z}$ is the same as the structure of matrix $\mathit{X}$, as shown in Formula (8):

$${\mathit{Z}}_{q\times n}=\left[\begin{array}{cccc}{z}_{11}& z_{12}& \dots & z_{1n}\\ z_{21}& z_{22}& \dots & z_{2n}\\ ⋮& \dots & \dots & \dots \\ z_{q1}& z_{q2}& \dots & z_{qn}\end{array}\right]$$

(8)

3.2. State Matrix Preprocessing Method

Normalize $\mathit{X}$ according to Formula (9) to obtain a normalization matrix $\tilde{\mathit{X}}$ with a mean value of 0 and a variance of 1:

$$\begin{array}{c}{\tilde{X}}_i=(X_i-\mu (X_i))/\sigma (X_i),\\ i=1,2,\dots p\end{array}$$

(9)

where $\mu (X_i)$ and $\sigma (X_i)$, respectively, represent the mean and variance of $X_i$, and $X_i$ is the i-th line of $\mathit{X}$.

In the same way, the normalized matrix $\tilde{\mathit{Z}}$ can be obtained.

In large-dimensional data analysis, many multivariate statistical analysis quantities can be expressed as empirical spectral distribution functions of sample covariance. Therefore, the covariance matrices of $\tilde{\mathit{X}}$ and $\tilde{\mathit{Z}}$ can be obtained, respectively, and on this basis, the state of the power grid with large-scale wind power centralized access can be analyzed by applying the random matrix theory.

4. Power Grid State Analysis under Large-Scale Wind Power Connection

4.1. Power Grid State Evaluation Index Based on Wind Power Matrix

4.1.1. Wind Power Change Level Index Based on Ring Law

Under large-scale wind power connection, the output change of the wind turbine will affect the state of the power grid. Specifically, the power change in the wind turbine will cause the change in the power flow distribution of the power grid, and then cause the change in the state of the power grid.

The ring law points out that when there are only white noise, small disturbances and measurement errors in the system, the data distribution of the system will show a statistical random characteristic. When the data satisfy the independent identity distribution, the singular eigenvalues of the state matrix of the system will be distributed in the ring with the inner ring radius of ${\left(1-c\right)}^{1/2}$ and the outer ring radius of 1 on the complex plane. On the contrary, when there are signal sources (events) in the system, this randomness will be broken, and the data will no longer meet the condition of independent and identical distribution, and the singular eigenvalues will fall into the inner loop. The higher the degree of deviation of the elements in the matrix from the independent uniform distribution, the higher the degree of convergence of the eigenvalues to the center of the circle. The singular eigenvalue analysis of the wind power matrix $\tilde{\mathit{X}}$ is carried out. When the power of the large-scale connected wind turbines in the power grid changes little, the singular value of the covariance matrix corresponding to x will be distributed between the inner and outer rings, and the average spectral radius (MSR) is between the inner ring radius and 1. On the contrary, when the overall power of the wind turbine changes, whether there is an overall increase or decrease, the singular value of the covariance matrix corresponding to x will fall into the inner loop. Moreover, the greater the power change, the greater the degree of convergence of singular values to the center of the circle, and the smaller the value of MSR. Therefore, MSR can be used to construct an index to characterize the change level in wind power.

4.1.2. Wind Power Change Level Index Based on M-P Law

The M-P law states that when the elements in the matrix conform to the independent identical distribution condition, the spectral distribution corresponding to the covariance matrix will converge to the M-P law. When the elements in the matrix deviate from the independent uniform distribution condition, the spectral distribution corresponding to the covariance matrix will also deviate from the M-P law. As described in Section 4.1.1, if the wind power matrix X is subjected to spectral analysis, the degree to which the spectral distribution deviates from the M-P law indicates the degree to which the wind power changes.

In this paper, the probability density similarity index of spectral distribution is constructed with reference to document [13,14]. Let the spectral distribution function of the standard M-P law be $f_1(x),x\in [c_1,d_1]$, and the spectral distribution function corresponding to the wind power matrix be $f_2(x),x\in [c_2,d_2]$. Define the difference degree V between the two functions as:

$$v={\displaystyle {\int }_c^d{\left|f_1(x)-f_2(x)\right|}^n} \mathrm{d}x$$

(10)

where $c=\min \left(c_1,c_2\right)$, $d=\max \left(d_1,d_2\right)$ and n is the order. For the finite dimensional wind power matrix, there is a discrete form of Formula (10), as shown in Formula (11).

$$V=\frac{1}{N}{\displaystyle \sum _{i=1}^N{\left|f_1(ki)-f_2(ki)\right|}^n}$$

(11)

where $k=(d-c)/N$.

The smaller v and V, the closer $f_1(x)$ and $f_2(x)$ are, the smaller the change in wind power. On the contrary, the greater the difference between $f_1(x)$ and $f_2(x)$, the greater the change in wind power.

4.1.3. Comprehensive Index of Wind Power Change Rate

Based on the indicators in Section 3.1.1 and Section 3.1.2, this section synthesizes the two indicators. Thus, the change in wind power in the grid connected with large-scale wind power is comprehensively described from a more comprehensive perspective. The constructed indicators are shown in Formula (12):

$$W=MSR+c/V$$

(12)

where C is a constant. Then, when the wind power in the power grid does not change significantly, the singular value corresponding to the wind power matrix is distributed between the inner and outer rings, and the MSR is also between the radius of the inner and outer rings, and the value is relatively large. At the same time, the spectral distribution obtained based on wind power is similar to the M-P law. If V is small, the comprehensive index w of wind power change rate is large. On the contrary, a large wind power change rate will cause the odd-5-odd value corresponding to the wind power matrix to drop to the center of the circle, and the MSR is small. The deviation between the spectral distribution obtained based on wind power and M-P law is large. If V is large, W is small.

4.2. Power Grid Status Evaluation Index Based on Branch Power Matrix

The change in wind power or the abnormal state of the power grid (such as grounding fault, load abnormality, etc.) will cause the redistribution of power flow in the power grid. Therefore, in this section, based on the branch power matrix, the M-P law and entropy theory are used to construct the power grid state evaluation index that represents the branch power change.

The definition of entropy [15] is:

$$H=-C{\displaystyle \sum _{i=1}^{q}p\left({\omega }_i\right)}\ln p\left({\omega }_i\right)$$

(13)

where C is a constant, $l$ is the number of states and $p\left({\omega }_i\right)(i=1,\dots ,l)$ is the state occurrence probability. Entropy represents the disorder degree of the system. The larger its value, the greater the disorder degree of the system.

Among them, the calculation method of $p\left({\omega }_i\right)$ is referred to [16,17]. That is, calculate the covariance matrix of the branch power matrix Z, and then calculate the contribution rate of each branch power to the anomaly based on the M-P law. The details are as follows:

$$p\left({\omega }_i\right)=\frac{{\displaystyle \sum _{{\lambda }_k>b}{\lambda }_k{W}_{ik}^2}}{{\displaystyle \sum _{{\lambda }_k>b}{\lambda }_k}}$$

(14)

where ${\lambda }_k$ is the k-th eigenvalue of the covariance matrix of the branch power matrix, $W_{ik}$ represents the i-th element of the eigenvector $W_k$ corresponding to the k-th eigenvalue and b is the value calculated according to the size of the branch power matrix in Equation (3).

Then, $p\left({\omega }_i\right)$ represents the contribution rate of the i-th branch to the abnormal state of the power grid, and H represents the abnormal level of the whole power grid from the perspective of entropy. Additionally, the smaller and more uniform the change in branch power, the smaller the corresponding entropy index H. On the contrary, the larger the side path rate of each branch and the more uneven the change in each branch, the larger the corresponding entropy index H.

4.3. Comprehensive Indicators of Power Grid Status under Large-Scale Wind Power Access

Under the large-scale access of wind power, the power change in wind power and the power change in each branch in the power grid reflect the state of the whole power grid. Therefore, this section synthesizes the indicators mentioned in Section 4.1 and Section 4.2 to construct the power grid status analysis indicators under large-scale wind power access, as shown in Formula (15):

$$S=W/H$$

(15)

As mentioned above, the more stable the grid state of large-scale wind power access, the greater the s value. On the contrary, the greater the change in wind power, the greater the degree of abnormality and the smaller the s value.

4.4. Description of Power Grid State Trajectory Based on Sliding Time Window

Combining the state evaluation index of the power grid with the sliding time window can evaluate the state of the power grid and depict the operation track of the power grid in real time. When the power grid structure is determined, the number of fans P and the number of branches Q of the power grid are also determined. The value of n is determined by $c_1=p/n\in \left(0,1\right)$ and $c_2=q/n\in \left(0,1\right)$ where n is the width of the time window.

Among the N columns of sampling values, there is one column of current time data and $n-1$ column of historical data. Let the step size of the sliding time window be 1, that is, one column of historical data is moved out and one column of data at the current time is moved in at each sampling time.

With the movement of time, in each sliding time window, the power grid state evaluation index based on the wind power matrix, the power grid state evaluation index based on the branch power matrix and the comprehensive power grid state index under the large-scale wind power access are calculated, respectively, and the response is analyzed.

5. Example Analysis

In this paper, based on reference [18], the 33 node distribution system was improved to verify the effectiveness of the method proposed in this paper, as shown in Figure 2. Among them, the line parameters of the original system remain unchanged, so that the upper limit of the active output of the wind turbine was 0.6 MW, and the range of the reactive output was −0.02~0.06 Mvar. We installed 10 groups of fans at node 10 and 10 groups of fans at node 24. In the process of simulation verification, this paper built the model based on PSASP. When the wind speed increases and single-phase grounding occurs at node 6, the proposed indexes were analyzed. The simulation sampling frequency was 100 Hz and the simulation duration was 5S.

The change in wind speed will cause the change in wind turbine output, and the change in wind turbine output will affect the change in power flow distribution in the power grid, thus causing the change in the power grid state. This section assumes that the wind speed slowly increases from 6 to 10 m/s. The change in wind speed during simulation is shown in Figure 3. That is, at 0–1 s, the wind speed is maintained at about 6 m/s; at 1–3 s, the wind speed increases linearly to 10 m/s; at 3–5 s, the wind speed is kept at 10 m/s. This paper was based on the above simulation. We collected the corresponding wind power output data and branch power data, constructed the corresponding wind power matrix and branch power matrix and analyzed the power grid status.

5.1. Analysis of Power Grid Status Evaluation Index Based on Wind Power Matrix

This section uses the power data of 10 wind turbines at node 10 and 10 wind turbines at node 24 in the simulation stage to construct a wind power matrix with dimension of 20. Let the width of the sliding time window be n = 50 based on $c_1=p/n\in \left(0,1\right)$. The width of the sliding time window in the branch power matrix is also 50. Figure 4 shows the wind power change level index based on the ring law and the wind power change level index based on the M-P law and the comprehensive index of the wind power change rate. Among them, C = 1 in the comprehensive index of the wind power change rate. (The weight preference of MSR and V can be selected according to the actual situation.) Since the sliding time window width is taken as n = 50, the values of various indicators start from t = 0.5.

As shown in Figure 4a, MSR can accurately reflect the change level in wind power. At t = 0–1 s, MSR remained at about 0.9 and was relatively stable in the process. It correctly shows the situation that the wind power changes slightly. When t = 1.01 s, MSR drops obviously. Furthermore, in the stage of t = 1.01–4 s, MSR is in a vibrating state, which corresponds to the wind speed gradually increasing in this stage. It is worth noting that the wind speed remains at 10 m/s from t = 3 s, but the MSR does not start to recover to a relatively stable state until t = 4 s. It shows that the wind speed change at this stage has a great impact on the wind power output. Although the wind speed has been maintained at about 10/s in the stage of t = 3–4 s, the changes in power flow and wind power caused by the changes in wind speed continue until t = 4 s.

The index V describes the variation level of wind power in the grid from the angle of the deviation degree between the spectral distribution and the M-P law. As shown in Figure 4b, when t = 0.5–1, the value of V is kept at about 0.01, because at this stage, the wind speed is kept at 6 m/s, the wind power is kept at a certain level with little change and the value and distribution of the constructed wind power matrix do not change much. Therefore, the corresponding spectral distribution is close to the M-P law, so the V value is small. Starting from t = 1.07 s, the value of V increases abruptly and oscillates, which accurately reflects the change process in wind power level.

The specific wind power change level indicators MSR and V can be found as follows:

(1)

MSR suddenly decreased from t = 1.01 s, while V suddenly increased from t = 1.07 s, indicating that the sensitivity of MSR is greater than V. MSR has a continuous value decreasing process during the change in wind speed, while V is similar to the level when the wind power does not change in some periods, such as t = 2.5–3.2 s and t > 3.77 s.

(2)

MSR and V have certain correspondence. In addition to sensitivity, both of them fluctuate near the change in wind speed (if MSR is a significant drop and V is a significant increase). Both of them exhibit oscillation at the stage of increasing wind speed and recovered to the level of wind speed of 4 m/s in the later stage of simulation.

The indicator w combines MSR and V to describe the change level in wind power from a comprehensive perspective. That is, when t = 0.07 s, the index began to drop significantly, and it showed a relatively volatile situation in the next stage. It is further explained that the change in wind speed causes the change in wind power, and the change does not stop because of the stopping of the change in wind speed but causes the change in power flow of the power grid and further causes the change in the output of the wind turbine.

5.2. Analysis of Power Grid Status Evaluation Index Based on Branch Power Matrix

In this section, the branch power matrix was constructed with the branch power of 43 branches in the IEEE-33 node, and the width of the sliding time window was n = 50 based on $c_2=q/n\in \left(0,1\right)$. Figure 5 is the entropy index based on this paper.

As shown in Figure 5, the proposed entropy index combines the concept of entropy with the high-dimensional random matrix theory, and correctly reflects the change in branch power in the process of wind speed change. When t = 0–1.07 s, the index H remains around 0. This is because at this stage, the wind speed change rate is small, the power flow distribution of the power grid is also small, the power change in each branch is small and the power change distribution is relatively uniform (that is, the power change in each branch is small). At the stage of t = 1.07–3.95 s, the change in wind speed causes the change in wind power, and then causes the change in power flow of the power grid, so that the branch power changes. From t = 3.96–4.37 s, the entropy index gradually decreases to 0, and then increases from t = 4.38 s, which indicates that at the stage of t = 3.96–5 s, the change in wind power makes the state of the power grid change.

In order to further verify the reaction ability of the entropy index proposed in this paper to the change in branch power, Figure 6 describes the change in entropy of each branch power in the whole simulation process (i.e., Equation (14)). It can be seen from Figure 6 that during the period of 0–1 s, the change entropy of the power of each branch is almost zero, which corresponds to the relatively stable wind speed and power grid state at this stage.

5.3. Comprehensive Index Analysis of Power Grid Status under Large-Scale Wind Power Access

Based on the calculation results in Section 4.1 and Section 4.2, this section analyzes the comprehensive indicators of power grid status under large-scale wind power access, and the results are shown in Figure 7.

The comprehensive index s proposed in this paper can accurately reflect the change in the power grid state when large-scale wind power is connected. At the stage of t = 0.5–1.1 s and t > 3.9 s, the value of index s is large, which corresponds to the wind speed with a small change rate. At the stage of t = 1.1–3.9 s, the index s is kept at a small value, which corresponds to the wind speed that changed in this stage. It can be seen that the comprehensive index takes into account the changes in wind power and branch power at the same time and describes the power grid status under large-scale wind power access from a more comprehensive perspective.

6. Conclusions

In this paper, the wind power matrix and branch power matrix are, respectively, constructed based on the measured big data, and the corresponding indexes are constructed to analyze the power grid state of large-scale wind power access. The results demonstrated that the proposed indexes can analyze the state of the power grid under large-scale wind power access from different angles. In the application process, the appropriate indexes can be selected according to the needs. Meanwhile, all the indexes have good sensitivity. The wind speed change set in this paper started from t = 1.01 s, and the proposed index changed significantly from 1.1 s at the latest, and the delay time was 0.09 s, which verifies the sensitivity of the proposed index. Combining the proposed index with a sliding time window allows the real-time state analysis of the power grid under large-scale wind power access to be performed.

The work of this paper provides support for power grid state analysis under large-scale wind power access. The follow-up work will further consider the factors affecting the power grid status under large-scale wind power access and construct more comprehensive power grid status analysis indicators to provide decision support for operators.