Convolutional neural network ‐ based power system frequency security assessment

Weak inertia characteristics of power systems with high penetrations of renewables have become a prominent problem for frequency security. To solve this problem, a convolutional neural network (CNN) ‐ based deep learning approach is applied to realize rapid frequency security assessment (FSA). First, the time series frequency security feature is autonomously mined from the wide ‐ area measurement data to serve as the input data. By doing so, the complex construction process of frequency security feature quantity is avoided. A deep learning structure is then used to establish a non ‐ linear mapping relationship between time series features and frequency security indicators to realize end ‐ to ‐ end power system frequency security prediction. Next, the evaluation accuracy of the proposed approach is optimized by tuning the key parameters in the CNN ‐ based evaluation model. Through data measurement error analysis and a wind penetration sensitivity study, the anti ‐ interference performance of the proposed evaluation model is demonstrated. Finally, the effectiveness of the CNN ‐ based FSA is verified by case studies of a modified 16 ‐ machine 68 ‐ node system and the China Southern Power Grid.


| INTRODUCTION
In China, with installations of large-scale renewable generators, DC transmission systems, and other power electronic equipment [1][2][3], the dynamic characteristics of power system frequency, voltage, and power angle are becoming increasingly complicated [4][5][6][7][8]. This seriously threatens the operating security of the power grid. As an important reference for evaluating the anti-interference ability of a system, the security of system frequency can be comprehensively evaluated according to the maximum frequency, rate of change of frequency, and quasi-steady state frequency when an active power disturbance occurs [9,10]. However, since power electronic equipment can intensify the high-dimensional non-linear features of the system, it is usually difficult to obtain an accurate expression of system frequency after a disturbance. Thus, developing an accurate frequency security assessment (FSA) method is of great significance [11].
Currently, FSA methods can be divided mainly into two types: time-domain simulation [12,13] and machine learningbased approaches [14][15][16]. Time-domain simulation obtains the system frequency curves by solving high-dimensional nonlinear algebraic and differential equations after the active power disturbance. It then calculates the evaluation index to assess system frequency security. For example, the reference [12] uses time-domain simulation to calculate the quasi-steady state frequency of a power system and evaluate frequency security. However, power system frequency cannot be quantitatively described in this way. On the basis of analyzing the impacts of different frequency drop depths, the reference characterizes the accumulation area of different drop depths by weighting factors and then quantitatively describes the extent of the frequency response under the active power disturbance [13]. However, due to the highly non-linear features of the system (e.g. renewable generation output fluctuation, flexible DC system dynamic characteristics, and multitype disturbances), it is difficult to address the data combination explosion problem caused by multiple uncertainties using a time-domain simulation. In contrast, machine learning-based methods have the advantages of being model-free and highly accurate and thus are widely used in the areas of wind power prediction, information network security situation forecasting, and transient stability assessment. Reference [14] uses a single-layer extreme learning machine algorithm with one hidden layer for power system frequency security margin assessment. Reference [15] predicts the minimum frequency after a grid disturbance by a support vector machine regression model. The accuracy of the model is verified by the test system and the actual power grid. From the literature review, it is concluded that machine learning has higher accuracy and is promising for the online application of FSA.
Even though existing machine learning methods can effectively assess system frequency security, there are still problems, such as frequency security feature construction [16,17] and model construction [18][19][20], that need to be solved. In terms of feature construction, the 'three-segment' feature construction method [17] is generally used, which contains part of the time dimension information (the steadystate moment, initial moment of fault, and ultimate moment of fault). However, it is difficult to capture the overall time dimension information of the system operation, which restricts its potential to improve FSA accuracy. In terms of model construction, reference [18] proposes an artificial neural network (ANN)-based frequency dynamic assessment method to realize FSA effectively. Reference [19] first predicts a minimum frequency value through the linear frequency response model, then modifies it to improve the prediction accuracy by using a neural network. Reference [20] attempts to predict the maximum frequency after a disturbance in the islanding system by using a backpropagation neural network method to realize effective maximum frequency prediction. However, the abovementioned single-layer learning approaches are restricted by data processing capabilities and generalization capabilities. They suffer from high dimensionality, low accuracy, and other problems in large-scale systems. As an important branch of the machine learning method, the convolutional neural network (CNN) [21][22][23], driven by wide-area measurement data, uses self-learning to learn the characteristics of wide-area measurement data during the whole process of a disturbance. It constructs a deep learning framework with a multiple-hiddenlayers learning framework with multiple layers hidden by model training. The CNNs algorithm has been widely used in wind power forecasting [22], small-signal stability assessment [23], power transformer fault diagnosis [24,25] etc. However, there is still a lack of research in CNN-based FSA. Given the advantages of self-learning and multilayer structured learning, the CNN provides a perfect alternative choice. This paper considers self-learning and multi-layer structure learning model and CNN-based deep learning technique is applied to realize FSA. The main contributions of this paper are as follows: (1) The time series frequency security feature is autonomously mined from the wide-area measurement data to serve as the input data to avoid the complex construction process of frequency security feature quantity. (2) CNN is applied to realize end-to-end power system frequency security prediction, which significantly improves the evaluation accuracy of the proposed algorithm.
The remainder of this paper is organized as follows. Section 2 describes the principle of FSA. Section 3 develops the CNN based frequency security evaluation. Case studies with a modified 16-machine 68-node system and the China Southern Power Grid (CSG) are presented in Section 4 to demonstrate the effectiveness of the proposed method. Finally, the conclusions are drawn in Section 5.

| PRINCIPLE OF FREQUENCY SECURITY EVALUATION
When an active power disturbance occurs during normal system operation, system frequency deviation can be described by the following first-order ODE [26]: where H [MWs/Hz] is the inertia of the system after generation loss, Δf(t) is the frequency deviation of the system, D [1/Hz] is the damping coefficient of the load, P D [MW] is the power system load level, and ΔP g,s (t) [MW] describes the additional power provided by the generator g or storage s following the generation loss ΔP L [MW]. Figure 1 shows the dynamic frequency-response curve. As shown in Figure 1, f ex , f ss , and R F , are the extrema of frequency, quasi-steady state frequency, and rate of change of frequency. They can be used as three important indices to determine whether system frequency is secure after an active power disturbance. Therefore, the system frequency security status is determined by whether f ex , R F , and f ss would trigger the action of system frequency protection and cause cutting machine/load shedding. The details are explained as follows: (1) The high-frequency cutting machine: if the maximum frequency is higher than the start-up frequency of the high-frequency cutting machine, system frequency is insecure. (2) Under frequency load shedding: if the minimum frequency is lower than the start-up frequency under frequency load shedding, the system frequency is unsecured. (3) Frequency change rate protection: if the absolute value of R F exceeds the start-up frequency of the frequency change rate protection device, such as |R F | > R F,max , the system frequency is insecure. (4) Do not trigger frequency protection if the frequency is between f min and f max , and |R F | < R F,max , as the system frequency is secure.
The time-domain simulation is the most common method to determine system frequency security. It constructs a frequency-response model of a multimachine power system and simulates the frequency change curve under different active power disturbance circumstances. Because of disadvantages of time-domain simulation, such as a large amount of calculation, long operational time etc., it is difficult to address the data combination explosion problem caused by multiple uncertainties.

| CNN-BASED FREQUENCY SECURITY EVALUATION
The CNN-based power system FSA is divided into three parts: input and output variables selection, offline training, and online evaluation.

| Input and output variable selection
Offline fault calculations are performed in the power system simulation software PSD-BPA under different load disturbance levels, generator outputs, wind penetration levels, and other circumstances. With the help of the system's spatiotemporal big data properties, the time-series bus voltage magnitude, and phase angle, the active and reactive line power flows can be used as input variables with unit power regulation, inertia time constant, switch state, spinning reserve level, and damping coefficient taken as input variables. This gives the fault sample data both time and space properties to improve the evaluation accuracy rate. Based on the system frequency at the transient simulation, f ex and f ss can be used as variable output and are shown in Table 1. The proposed CNN-based FSA method must read the measurement information within a short time after disturbance, so it is difficult for CNN to achieve R F prediction. At the same time, the frequency protection device can calculate R F based on the instantaneous data after the disturbance, so it is not used as variable output.

| Data normalization
The range and dimension of time-series data obtained from PSD-BPA (i.e. bus voltage magnitude and phase angle) are different. In the polar coordinate system formed by the voltage amplitude and phase angle, when the voltage vector rotates around the origin and passes the polar axis, the value of the voltage phase angle can jump from either 180°to −180°or from −180°to 180°, which will affect the measured results. For example, Figure 2 shows the bus voltage magnitude and phase angle in the modified 16-machine 68-node system when active power is suddenly reduced to 729 MW.
It is necessary to conduct a pretreatment for the original fault sample data based on the wide-area measurement. Currently, normalization and standardization are commonly used methods for preconditioning. However, it does not apply to time-series input data. Therefore, the bus voltage magnitude and phase angle are transformed into the form of real and imaginary voltage to normalize their dimensions and the value ranges in this work. This method can realize the normalization of measurement data, which the complete data of the system has reserved: where U and θ are the respective voltage magnitude and phase angle, and U R and U I are the respective real and imaginary voltages. Once the real and imaginary parts of the voltage are converted by Equation (3), the influence of the initial state bias of the time series samples is avoided, so the input samples have the same distribution: where U R (0), U I (0), P(0) and Q(0) are respectively the real and imaginary parts of the voltage, active power, and reactive power vector at the initial time, U R (t), U I (t), P(t) and Q(t) are respectively the real and imaginary parts of the voltage and the active and reactive power vector at time t, U R_rv (t), U I_rv (t),

| Data integration
According to the temporal characteristics of the system simulation curve, the high-dimension fault sample matrix considering time distribution is constructed as the CNN input data. At time t, the real and imaginary parts of the voltage of the l-th busbar are UR l(t) and UI l(t), respectively, and the active and reactive power are P l (t) and Q l (t), respectively, where t = 1, 2, … , T, and T is the length of the time window for data sampling, l = 1, 2,…, L, and L is the total number of busbars. Then the time-series feature of the l-th busbar is represented by ; U I_rv l ð1Þ; P rv l ð1Þ; Q rv l ð1Þ⋯; When the time-series features of all busbars are extended to high-dimension sample X that contains the information of key busbars, the matrix dimension is 5 + L � 4T = W: Suppose Xm n is the n-th sample of the m-th system operating state, and then from Equation (5), we further extend it to a multisystem operating state high-dimension sample G containing the information of key busbars: where m = 1, 2, …, M, M is the sum of the system operating states, and To unify the input data format, the high-dimension time sample matrix of the CNN needs to be reconstructed and imported as a colour picture. This work uses the extrema of frequency and quasisteady-state frequency as output variables to obtain the output variable matrix Y Z�k : where k = 2 is the number of output variables, representing there are two output variables and the number of channels is 2, ym k � n is the data corresponding to the m � N + n row of the k-th output.

| Training the CNN-based system frequency security evaluation model
The CNN is a deep learning network that focuses on convolution operations. The 'end-to-end' characteristic of CNN is the main difference with traditional machine learning methods. Users only need to input the system measurement data for frequency security prediction and there is no need to participate in feature extraction, dimension lifting, and other intermediate data processing. Therefore, it is more applicable for analyzing data with complex data structure or deep information which people cannot easily extract data features. CNN is composed of an input layer, a convolution layer, a pooling layer, and a fully connected layer. Figure 3 shows a typical CNN model.

| Input layer
The input layer is the matrix corresponding to the system frequency security prediction samples. Each row of the matrix represents the vector corresponding to a certain prediction sample of the frequency. The row and column are respectively the numbers of samples and sampling points, which can be used as the input layer. The number of the channel represents the number of the output variables.

| Convolution layer
The input feature is extracted by the convolution layer through a convolution operation and selects multiple convolution kernels based on actual conditions. Every convolution kernel performs a convolution operation with the input layer data of the upper layer to obtain the corresponding feature and is used as the input for the next layer. The convolutional method is a common processing method for image processing. The convolution kernel is a linear operation for two-dimensional input data. After the activation function is added, as shown in Equation (8): where h ij is the j-th column and i-th row element of the output matrix, the matrix dimension is I � J, i = 1, 2,…, I, j = 1, 2,…, J, φ cd is the d-th column and c-th row element of the convolution kernel, and the matrix dimension is C � D. G i+c,j+d is the ( j + d )-th column and (i + c)-th row element of the input matrix, b and f are respectively the deviation variable and the activation function.

| Pooling layer
Since the convolution layer performs a convolution operation to the original input data, it contains a large number of features. However, these features cannot be directly used in the next layer due to the high computational burden. However, pooling the layers can enable the operation of polymerization statistics on features to realize data dimension reduction.
Pooling is a down-sampling method, which divides the input into several non-overlapping areas, and takes the average of each area (average pooling), as calculated by where S 1 and S 2 are respectively the row and column dimensions of the pooling area, E ab is the a-th row, b-th The basic framework of convolutional neural network WANG ET AL.
column element of the output matrix after pooling, and the dimension is (I/S 1 ) (J/S 2 ), where a = 0, 1,…, I/S 1 − 1, b = 0, 1,…, J/S 2 − 1, h aS 1 þi;bS 2 þj is the aS 1 + i-th row and bS 2 + j-th column element of the output matrix. After pooling the output data obtained by the convolution operation, the matrix dimension is reduced to 1/(S 1 S 2 ) of its original size, which significantly decreases the matrix dimension and the amount of calculation but improves the robustness of the model.

| Fully connected layer
The fully connected layer expands the two-dimensional output data of the last layer into one-dimensional data. It maps learnt features onto the output. The fully connected layer is described as follows: where e i is i-th input variables, ω = [ω 1 , ω 2 ,…, ω i ,…, ω n ] is the connection weight, and μ and o are respectively the deviation variable and output.

| Process assessment of system frequency security
The flowchart of the CNN-based FSA is shown in Figure 4. It contains two parts: (1) offline system frequency security evaluation model training and (2) online system frequency security evaluation.

| Offline training
First, the big data sample set is constructed by the data from a historical database and offline transient simulation. Then the data sample set is randomly divided into two subsets for CNNbased FSA model training and testing. After setting reasonable convolutional kernel parameters and a convolution layer number, the FSA model is trained by the training set and then tested by the testing set.

| Online evaluation
System FSA or predicted power disturbance events can be determined according to grid operational characteristics. Once a disturbance happens, the measurement data is taken as the input and then normalized. An offline trained CNN model is used to operate system frequency security evaluation. Then, reverse normalization on the output data is conducted to obtain the frequency index value of the disturbance events. Finally, the frequency security of the disturbance events is comprehensively evaluated to determine whether the protection device should be activated.

| FSA and prediction performance index
In this work, the mean absolute percentage error (MAPE) is used to evaluate the prediction accuracy of the system frequency, which is the MAPE of the actual and prediction value of the system frequency: where y i andŷ i are respectively the frequency index actual value and prediction value of the i-th sample, and N is the number of test sample. The frequency assessment accuracy rate, secure case evaluation accuracy rate, and insecure case evaluation accuracy rate are used to evaluate the FSA performance: where E AC is the frequency assessment accuracy rate, E AC1 and E AC2 are respectively the secure and insecure case evaluation accuracy rates, N TP and N FP are respectively the number of power system frequency security samples that evaluated as secure and insecure, and N TN and N FN are respectively the number of power system frequency insecure samples that evaluated as secured and insecure samples.

| CASE STUDIES
In this section, the accuracy and effectiveness of the proposed method are tested in a modified 16-machine 68-node system and the CSG.

| The modified 16-machine 68-node system
This test system has five regions, where regions 1, 2, and 3 are equivalent systems and regions 4 and 5 are, respectively, the New York and New England systems, as shown in Figure 5.
The modified system has 18 generators in total, including 16 synchronous generators and 2 wind farms. To simulate the impact of wind penetration on system frequency, the wind turbines are connected to nodes 66 and 68. Moreover, lines 41-42 are replaced by a VSC-HVDC line for power transmission between regions. The generator is a sixth-order model, and the excitation system model is IEEE-DC1. The load model is WECC, and the total load is 18,233 MW. The model and control parameters of wind power and VSC-HVDC can be referred to in the reference [27,28].
The power system simulation software PSD-BPA is used to conduct transient simulations under different load disturbance, generator power outputs, and wind penetration levels. The transient simulation generates 12,600 samples to form the sample set, including 6820 secure cases, 5737 insecure cases, and 43 critical cases. Among them, 8400 samples are randomly selected to train the FSA model, while the performance of the model is tested using the remaining samples. The activation criterion of the frequency protection device is f > f max , f < f min , |R F | > R F,max , and |R F | < R F,max . Otherwise, the protection device would not be activated where f max = 51 Hz, f min = 49 Hz, and R F,max = 1 Hz/s.

| FSA accuracy analysis
The accuracy of the CNN-based FSA can be evaluated from the system frequency prediction error and the MAPE. The number of CNN convolution layers is seven, and the wind penetration level is 5%. The sample distribution of CNNbased FSA is shown in Table 2.
As shown in Table 2, the sample proportion of the extrema of frequency and quasi-steady state frequency are respectively 92.76% and 95.63% under 0.05 Hz of frequency prediction error. The values of the MAPE are 0.0356% and 0.0392%, respectively. Therefore, it is concluded that the CNN-based FSA model has high prediction accuracy.
To further verify the accuracy of the CNN-based FSA, ANN, decision tree (DT), and kernel ridge regression (KRR) algorithms are also applied to evaluate frequency security using the same sample set. The MAPE and evaluation accuracies for the four artificial intelligence algorithms are shown in Table 3.
As shown in Table 3, the MAPE of the CNN-based FSA is the smallest. Compared with other prediction methods, CNN has a higher prediction accuracy. In contrast, the MAPE values of the ANN, DT, and KRR algorithms are respectively 9.32, 8.17, and 1.33 times that of CNN at the extremum of frequency. Meanwhile, the E AC1 and E AC2 of CNN are respectively 100% and 99.79% at the extremum of frequency, which is higher than for the other three methods. The E AC of CNN is 99.91%, which is higher than for ANN, DT, and KRR by 2.91%, 1.77%, and 0.38%. The high accuracy of CNN has also been verified under quasi-steady state frequency. The main reason for this is that CNN constructs a deep learning framework with a multi-hidden-layer learning framework with multiple layers hidden by model training. It is applied to realize end-to-end FSA, which significantly improves accuracy. Therefore, it is summarized that the CNN-based FSA has a high system frequency prediction and assessment accuracy rate.

| The impact of model parameters on FSA
The CNN model parameters have a great impact on the accuracy rate of FSA. We focus here on studying the impacts of convolution kernel size (CKS) and the number of convolution layers. The wind penetration ratio rate is set to 5%, and the extremum of frequency is taken as an example to analyze variation of the frequency prediction and assessment accuracy rate. First, with seven convolution layers, the evaluation and prediction results of different convolution kernel are shown in Figure 6.
As shown in Figure 6, the MAPE is 0.056% when the CKS is 5 � 5. The MAPE values are respectively 2.04 and 1.18 times that of the CKS when it is 5 � 5, 3 � 3, and 7 � 7. Meanwhile, when the CKS is 5 � 5, the E AC is 99.91%, which is 0.14% and 0.50% improved over the cases where the CKS is 3 � 3 and 7 � 7. The reason for the evaluation accuracy change is that the number of output features is determined by the CKS. As the CKS decreases, the number of estimation data becomes smaller. The evaluation accuracy of the large convolution kernel can be improved by a superposition calculation of multiple small convolution kernels. The number of model parameters and estimation complexity can be reduced under conditions of constant connectivity. Therefore, it is difficult to operate an accurate presentation on output features if the convolution kernel is too small. To maximize the evaluation and prediction properties of system frequency, multiple 5 � 5 CKSs are used for convolution operation.
The impacts of CNN convolution layer numbers on prediction accuracy and the assessment accuracy rate at the extremum of frequency are then analyzed. The MAPE and the evaluation accuracy for different convolutional layers are shown in Table 4.
As shown in Table 4, the MAPE gradually decreases as the convolution layers increase. The MAPE reaches a minimum of 0.0356% with seven convolution layers. The MAPE value of a single convolution layer is 3.13 times that of the case with seven convolution layers. Meanwhile, the E AC , E AC1 , and E AC2 are respectively 99.91%, 100%, and 99.79% with seven convolution layers. The accuracy is improved by 0.98%, 0.39%, and 1.72% compared with the case with only one convolution layer. If the number of convolution layers is increased to eight, the complexity of the convolutional layer will increase and cause an overfitting phenomenon, and the prediction accuracy will decrease. Therefore, the prediction and assessment accuracy rates are highest with seven convolution layers. The convolution layers of CNN are reasonably selected, which can ensure the prediction accuracy rate of FSA. With one and seven convolution layers, the CNN-based system frequency prediction errors are as shown in Figure 7.
As shown in Figure 7, the one-convolution layer power system frequency prediction error is centrally distributed in the range of 0-0.008 p.u. with poor frequency prediction accuracy. The power system frequency prediction error is centrally distributed in the range of 0-0.00249 p.u. when the number of convolution layers is increased to seven. At this time, the system frequency prediction accuracy can be effectively improved.

| The impact of wind penetration on FSA
To investigate the impact of different wind penetration levels on frequency security evaluation, a comparative analysis of the MAPE and evaluation accuracy rate of the system frequency is conducted, covering the wind penetration levels of 0%, 5%, 10%, and 15% at the extremum of frequency, as shown in Table 5.
It can be observed from Table 5 that as the wind penetration level increases from 0% to 15%, the MAPE of the system frequency under different wind penetration levels remains small, and the secure and insecure system frequency case evaluation accuracy is higher than 99.24% and 99.34%, respectively. The main reason for this is that the time series frequency security feature at different wind penetration levels is autonomously mined from the wide-area measurement data to serve as the input data. Therefore, the CNN-based approach has good adaptability, and wind penetration has little influence on the FSA accuracy rate. Further, the system frequency under different operating conditions is analyzed, as shown in Table 6. At this time, the active power disturbance is set to a sudden decrease of 1200 MW in load to observe system frequency index changes under different wind penetration ratios and system inertia.
From Table 6, it can be observed that as the wind penetration increases from 0% to 15%, the output power of thermal power generating units gradually decreases, and the system rotational inertia decreases from 18,408 MW/s to 15,468 MW/s. When the wind penetration ratio reaches 10% and higher, the low inertia characteristic of the power system becomes prominent, and the extremum of frequency higher than 51 Hz is obtained after the active power disturbance. The high-frequency cutting machine action is then triggered. Figure 8 shows different system frequency change curves. Under various wind power penetration rates and system inertia, it is observed that F I G U R E 6 MAPE and evaluation accuracy for various convolution kernel sizes. MAPE, mean absolute percentage error

| Anti-interference of frequency security evaluation
In this section, interference signals are added to the input data to simulate the measurement error of wide-area measurement data. When there is no interference signal, the system frequency prediction accuracy of the CNN and the ANN are as shown in Figure 9.
The anti-interference ability of the CNN for system frequency security evaluation is analyzed when the mean values of interference signals are 0.0001, 0.001, and 0.01, respectively. Multiple system frequency security evaluations are performed to obtain the mean value of the MAPE and evaluation accuracy rate, as shown in Tables 7 and 8.
From Table 7, it is observed that when the mean value of the interference signals is 0.0001, the mean value of MAPE for the CNN-based FSA is 0.04076%. In contrast, the mean value of the MAPE for the ANN-based FSA is 9.47 times that of the CNN-based FSA. When the mean values of the interference signals are 0.001 and 0.01, the prediction performance of the CNN is still better than that of ANN because the time series frequency security feature is autonomously mined from the wide-area measurement data to serve as the input data to avoid complex construction process of frequency security feature quantity. Therefore, the proposed CNN-based FSA method is robust towards interference signals.
As shown in Table 8, when the mean value of the interference signal is 0.0001, the mean value of the CNN system frequency E AC is 99.56%. Meanwhile, the E AC of the ANN is higher than that of the CNN. When the mean value of the interference signals is 0.001 and 0.01, the evaluation accuracy of the CNN-based FSA is still better than that of the ANNbased FSA. This indicates that under different interference signals, the evaluation accuracy rate of the CNN-based FSA is better than it is for the ANN-based FSA. In conclusion, the CNN-based FSA has better anti-interference ability than the ANN-based FSA. The accuracy rates of the extrema of frequency and quasisteady state frequency are shown in Figure 11.
It can be observed from Figure 11 that the system E AC of the extremum of frequency is 99.16%, which is less than the E AC values of the quasi-steady state frequency. The E AC2 rate of the extremum of frequency is 97.51%, which is an improvement of 0.64% compared with the case of quasisteady-state frequency. The E AC2 of the extremum of frequency is 100%, which is a 0.42% improvement over the cases of the quasi-steady state frequency. Therefore, the CNN-based approach maintains a high evaluation accuracy rate in a practical grid.
Further, we conduct a comparative analysis of the frequency evaluation accuracy of the ANN, DT, KRR, and CNN at the extremum of frequency. The number of convolution layers is seven, as shown in Table 9.
Since the data dimension of the actual system is too large for the ANN to conduct security evaluation, only results of the CNN, DT, and KRR are provided in this work. Table 9 shows that the E AC1 of CNN at the extremum of frequency is 100%, which is the same as that of DT and KRR. The E AC2 of the CNN is 97.51%, which is improved by 7.51% and 5.31% compared with DT and KRR. Meanwhile, the E AC of the CNN is 99.16%, which is still higher than the DT and KRR classifiers. Therefore, the effectiveness and accuracy of the proposed method in CSG system frequency security evaluation are validated.

| CONCLUSION
A CNN-based deep learning approach is proposed to realize rapid FSA. Compared with existing machine learning methods, such as the ANN, DT, and KRR, the CNN can self-extract features from wide-area measurement data and avoid the feature-construction difficulties of traditional machine learning methods with a higher frequency prediction and evaluation accuracy rate. From the accuracy analysis of CNN, it is concluded that the CNN has a higher evaluation accuracy when the convolutional kernel size is 5 � 5 and the number of convolution layers is seven, and wind penetration has little influence on the FSA accuracy rate. Further, the CNN-based FSA has better anti-interference ability than traditional classifiers, such as ANN, so it can provide a more reliable reference. In this regard, the output of CNN-based FSA could be used as an input signal for a frequency security control system that protects and controls the power system under emergency conditions. The validity of the CNN-based FSA is verified in a CSG system.