Regulated Two-Dimensional Deep Convolutional Neural Network-Based Power Quality Classifier for Microgrid

Abstract

Due to the penetration of renewable energy and load variation in the microgrid, the diagnosis of power quality disturbances (PQD) is important to the operation stability and safety of the microgrid system. Once the power imbalance is present between the generation and the load demand, the fundamental frequency would deviate from the nominal value. As a result, the performance of the power quality classifier based on the neural network would be deteriorated since the deviation of fundamental frequency is not taken into account. In this paper, the regulated two-dimensional (2D) deep convolutional neural network (CNN)-based approach for PQD classification is proposed. In the data preprocessing stage, the IEC-based synchronizer is introduced to detect the deviation of fundamental frequency. In this way, the 2D grayscale image serving as the input of the deep CNN classifier can be accurately regulated. The obtained 2D image can effectively preserve information and waveform characteristics of the PQD signal. The experiment is implemented with datasets containing 14 different categories of PQD. According to this result, it is revealed that the regulated 2D deep CNN can improve the effectiveness of PQD classification in a real-time manner. Furthermore, the proposed method outperforms the methods in previous studies according to the field verification.

1. Introduction

With the high penetration of renewable energy and widespread usage of power-electronic loads, the operation stability of the microgrid would be deteriorated due to the power quality disturbances (PQD). For the grid-connected mode, the voltage-type PQD of the power grid would interfere with the operation of the microgrid [1]. The current-type PQD is significant to the microgrid in the islanded mode due to the nonlinear loads in the power system [2]. The emergence of PQD would lead to the malfunction or inefficiency of electricity equipment in the microgrid. Therefore, identification and detection of PQD are indispensable to the system reliability and security. In recent years, intelligent approaches based on deep learning have been applied for the classification of PQD. Among numerous intelligent approaches, the convolutional neural network (CNN) is one of the effective structures and is widely employed in the PQD classification work [3].

The one-dimensional (1D) CNN for PQD classification has been implemented in the literature [4,5,6,7,8]. These studies are focused on the improvement of the classification performance in the over-fitting problem [4], modification of the process in the feature extraction of PQD [5,6], and proposal of the hybrid classification model [7]. To deal with the issues related to computational burden and the complexity of the classification model, the advanced data compression technique in the data preprocessing is proposed in [8]. However, a lot of PQD information would disappear due to the compression process.

Due to the learning capability for the diversity and complexity of image features, the CNN method is applied for the classification of two-dimensional (2D) images [9]. If one would apply the CNN for the classification of PQD, which is a 1D signal, the data preprocessing process is required to convert the 1D power signal to the 2D image. Since more PQD information can be included in the 2D image than that in the 1D signal, many image conversion techniques have been carried out in recent years [10,11,12,13,14,15,16,17]. Fast discrete curvelet transform is employed in [10] to extract the feature image of PQD. In [11], the signal-waveform image is directly utilized for the training the PQD classifier. The space phasor diagram is applied in [12,13,14] for the transformation of the sag signal into the PQD image. In the studies of [15,16,17], an image transformation matrix is proposed, where the sampling points of the PQD signal are rearranged in the matrix and then converted into the grayscale image. However, some important features are completely lost in the transformation of [12,13,14]. Once the fundamental frequency is deviated from the nominal value, the rearrangement of the image transformation matrix in [15,16,17] would lead to classification inaccuracy. This is because the time positions of PQD would be deteriorated due to the variation of fundamental frequency.

In this paper, a regulated 2D deep CNN-based power quality classifier is proposed to enhance the identification performance. In Section 2.1, the mathematical models of classical PQD discussed in this paper are introduced. The IEC-based synchronizer is developed in the preprocessing stage to estimate the deviation of fundamental frequency of the microgrid in Section 2.2. Then, the 2D grayscale image for the training of the deep CNN classifier is regulated in Section 2.3 with the obtained fundamental frequency, where the PQD information can be accurately preserved. After the PQD training with the structure of deep CNN mentioned in Section 2.4, the power quality classifier is ready for the disturbance identification. To examine the performance of PQD classification, the results of training and evaluation phases and field experiments with the proposed and compared classifiers are presented in Section 3.

2. Proposed Regulated 2D Deep CNN-Based Power Quality Classifier

The proposed regulated 2D deep CNN-based power quality classifier can be divided into three stages: signal synchronization (SS), image regulation (IR), and disturbance classification (DC). In the SS stage, the deviated fundamental frequency can be obtained with the synchronizer based on IEC Std. 61000-4-7. Then, the obtained fundamental frequency would be used to split the PQD signal correctly and regulate the 2D grayscale image matrix in the IR stage. The regulated feature image would then be processed in the DC stage to perform the PQD identification. The solution procedure of proposed power quality classifier is depicted in Figure 1. In the following, first, the mathematical models for the generation of PQD training data are introduced. Furthermore, the proposed approach to implement the IEC-based synchronizer and image regulation is presented. Then, the structure of the applied deep CNN model is introduced.

2.1. Mathematical Model of PQD

To provide sufficient and diverse PQD data, the mathematical models with the parameter variations in IEEE Std. 1159 were employed to generate the synthetic PQD for the training of the power quality classifier in this section [18]. As listed in

Table 1. Mathematical models and parameter constraints of PQD.

PQD	Category	Mathematical Model	Parameter Constraints
Normal	C01	$s\left(t\right)=A\left[1\pm \alpha \left(u\left(t-t_1\right)-u\left(t-t_2\right)\right)\right]sin\left(\omega t\right)$	$\alpha \le 0.1$$, T\le t_2-t_1\le 10T$$, \omega =2\pi f$
Sag	C02	$s\left(t\right)=A\left[1-\alpha \left(u\left(t-t_1\right)-u\left(t-t_2\right)\right)\right]sin\left(\omega t\right)$	$0.1\le \alpha \le 0.9$$, T\le t_2-t_1\le 10T$
Swell	C03	$s\left(t\right)=A\left[1+\alpha \left(u\left(t-t_1\right)-u\left(t-t_2\right)\right)\right]sin\left(\omega t\right)$	$0.1\le \alpha \le 0.8$$, T\le t_2-t_1\le 10T$
Interruption	C04	$s\left(t\right)=A\left[1-\alpha \left(u\left(t-t_1\right)-u\left(t-t_2\right)\right)\right]sin\left(\omega t\right)$	$0.9\le \alpha \le 1$$, T\le t_2-t_1\le 10T$
Harmonics	C05	$$\begin{gathered} s\left(t\right)=A\left[{\alpha }_{1}sin\left(\omega t\right)+{\alpha }_{3}sin\left(3\omega t\right)+{\alpha }_{5}sin\left(5\omega t\right) \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}+{\alpha }_{7}sin\left(7\omega t\right)\right] \end{gathered}$$	$0.05\le {\alpha }_3,{\alpha }_5,{\alpha }_7\le 0.15$$, {\sum }^{ }{\alpha }_i^2=1$
Flicker	C06	$s\left(t\right)=A\left[1+\lambda sin\left({\omega }_{f}t\right)\right]sin\left(\omega t\right)$	$5\le f_f\le 25$$, w_f=2\pi f_f$$0.1\le \lambda \le 2$
Transient oscillation	C07	$s\left(t\right)=A\left[sin\left(\omega t\right)+\beta e^{-\left(t-t_1\right)/\tau } sin\left({\omega }_n\left(t-t_1\right)\right)\left(u\left(t-t_2\right)-u\left(t-t_1\right)\right)\right]$	$$\begin{gathered} 300\le f_n\le 900, {\omega }_n=2\pi f_n,0.5T\le t_2-t_1\le \frac{Nc}{4}T, \\ 8 \mathrm{ms}\le \tau \le 40 \mathrm{ms}, 0.1\le \beta \le 0.8 \end{gathered}$$
Periodic notch	C08	$$\begin{gathered} s\left(t\right)=sin\left(\omega t\right)-sign\left(sin\left(\omega t\right)\right)\times \\ \{\sum _{n=0}^{9}k\left[u\left(t-(t_1-sn\right)-u\left(t-(t_2-sn\right))\right]\} \end{gathered}$$	$$\begin{gathered} 0.01T\le t_2-t_1\le 0.05T \\ {t}_2\le s, t_1\ge 0, 0.1\le k\le 0.4, \mathrm{c}=\left\{1,2,4,6\right\}, s=\frac{T}{c} \end{gathered}$$
Sag with harmonics	C09	$$\begin{gathered} s\left(t\right)=A\left[1-\alpha \left(u\left(t-t_1\right) \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}-u\left(t-t_2\right)\right)\right]\left[{\alpha }_{1}sin\left(\omega t\right) \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}+{\alpha }_{3}sin\left(3\omega t\right)+{\alpha }_{5}sin\left(5\omega t\right)\right] \end{gathered}$$	$$\begin{gathered} 0.1\le \alpha \le 0.9, T\le t_2-t_1\le 10T, \\ 0.05\le {\alpha }_3,{\alpha }_5,{\alpha }_7\le 0.15, {\sum }^{ }{\alpha }_i^2=1 \end{gathered}$$
Swell with harmonics	C10	$$\begin{gathered} s\left(t\right)=A\left[1+\alpha \left(u\left(t-t_1\right) \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}-u\left(t-t_2\right)\right)\right]\left[{\alpha }_{1}sin\left(\omega t\right) \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}+{\alpha }_{3}sin\left(3\omega t\right)+{\alpha }_{5}sin\left(5\omega t\right)\right] \end{gathered}$$	$$\begin{gathered} 0.1\le \alpha \le 0.8, T\le t_2-t_1\le 10T \\ 0.05\le {\alpha }_3,{\alpha }_5,{\alpha }_7\le 0.15, {\sum }^{ }{\alpha }_i^2=1 \end{gathered}$$
Interruption with harmonics	C11	$$\begin{gathered} s\left(t\right)=A\left[1-\alpha \left(u\left(t-t_1\right) \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}-u\left(t-t_2\right)\right)\right]\left[{\alpha }_{1}sin\left(\omega t\right) \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}+{\alpha }_{3}sin\left(3\omega t\right)+{\alpha }_{5}sin\left(5\omega t\right)\right] \end{gathered}$$	$$\begin{gathered} 0.9\le \alpha \le 1, T\le t_2-t_1\le 10T \\ 0.05\le {\alpha }_3,{\alpha }_5,{\alpha }_7\le 0.15, {\sum }^{ }{\alpha }_i^2=1 \end{gathered}$$
Flicker with harmonics	C12	$$\begin{gathered} s\left(t\right)=A\left[1+\lambda sin\left({\omega }_{f}t\right)\right]\left[{\alpha }_{1}sin\left(\omega t\right)+{\alpha }_{3}sin\left(3\omega t\right) \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}+{\alpha }_{5}sin\left(5\omega t\right) \right] \end{gathered}$$	$$\begin{gathered} 0.1\le \lambda \le 2, 5\le f_f\le 25 \\ 0.05\le {\alpha }_3,{\alpha }_5,{\alpha }_7\le 0.15, {\sum }^{ }{\alpha }_i^2=1 \end{gathered}$$
Flicker with sag	C13	$$\begin{gathered} s\left(t\right)=A\left[1+\lambda sin\left({\omega }_{f}t\right) \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}(1-\alpha \left(u\left(t-t_1\right) \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}-u\left(t-t_2\right)\right)\right]sin\left(\omega t\right) \end{gathered}$$	$$\begin{gathered} 0.1\le \alpha \le 0.9, T\le t_2-t_1\le 10T \\ 0.1\le \lambda \le 2, 5 \le f_f\le 25 \end{gathered}$$
Flicker with swell	C14	$$\begin{gathered} s\left(t\right)=A\left[1+\lambda sin\left({\omega }_{f}t\right) \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}(1+\alpha \left(u\left(t-t_1\right) \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}-u\left(t-t_2\right)\right)\right]sin\left(\omega t\right) \end{gathered}$$	$$\begin{gathered} 0.1\le \alpha \le 0.8, T\le t_2-t_1\le 10T \\ 0.1\le \lambda \le 2, 5 \le f_f\le 25 \end{gathered}$$

, 14 categories of PQD signals s(t) were applied.

The values of parameters such as intensity (α), distortion of the transient (β), distortion of the flicker ($\lambda$), and time (t₁ and t₂) were randomly generated to obtain the variety of each PQD category. The nominal value of fundamental frequency (f) was set to be 60 Hz, varying in the range of 59.5 and 60.5 Hz, whereas the sampling frequency (f_s) was 7680 Hz, the number of sampling cycles (N_c) was 12, the total sampling points (N_s) was 1536, and the amplitude (A) was normalized to 1. T is the fundamental period. The synthetic signals generated for each PQD category were 10,000 samples and then the total number of samples was 140,000.

2.2. Signal Synchronization (SS)

Due to the variation of fundamental frequency, the traditional signal transformation for the training of the neural network in the literature would be deteriorated, where the splitting process of the PQD signal to form the image matrix is incorrect. To solve this problem, the signal synchronization of fundamental frequency followed by IEC 61000-4-7 is introduced in this paper to regulate the image matrix [19]. The synchronization process of fundamental frequency is represented in Figure 2, where the detection method for the fundamental frequency is not specified, which provides design flexibility for the instrument manufacturer, f₀ is the nominal fundamental frequency, and f(k) and f(k − 1) are the present and previous estimated values of fundamental frequency, respectively. As a result, a simple detection method of fundamental frequency is introduced in this section.

Suppose the discrete-time PQD signal, s_i, through the low-pass filter s_{LP_i} can be expressed as:

$$s_{LP\_i}=A\cos (\frac{2\pi fi}{f_s}+\theta ), i=1, 2, 3, \dots , I$$

(1)

where f is the fundamental frequency, A is the amplitude, f_s is the sampling frequency, θ is the phase angle, and I is the number of samples. Equation (1) can also be represented in the complex form as:

$$s_{LP\_i}=A_c{\Omega }^i+A_{{}^c}^{\ast }{\Omega }^{\ast i}, i=1, 2, 3, \dots , I$$

(2)

where $A_c=\frac{A}{2}{e}^{j\phi }$, $\Omega =e^{\frac{j2\pi f}{f_s}}$, and * represents the complex conjugate. Followed by the autoregressive prediction model, the total squared error, E, for the signal approximation can be expressed with the linear combination of three successive samples in Equation (3), where η is the parameter for the signal approximation [20]:

$$E={\displaystyle \sum _{i=3}^I{(\eta s_{LP\_i}+s_{LP\_i-1}+\eta s_{LP\_i-2})}^2}$$

(3)

Besides, the transfer function of the second-order autoregressive prediction model can be given by:

$$\eta {\Omega }^2+\Omega +\eta =0$$

(4)

To minimize the approximation error, the relationship of Equation (5) shall be met:

$$\frac{dE}{d\eta }=2{\displaystyle \sum _{i=3}^I(\eta s_{LP\_i}+s_{LP\_i-1}+\eta s_{LP\_i-2})(s_{LP\_i}+s_{LP\_i-2})}=0$$

(5)

Then, η can be solved in Equation (6):

$$\eta =\frac{-{\displaystyle \sum _{i=3}^I{s}_{LP\_i-1}(s_{LP\_i}+s_{LP\_i-2})}}{{\displaystyle \sum _{i=3}^I{(s_{LP\_i}+s_{LP\_i-2})}^2}}$$

(6)

By substituting Equation (6) into Equation (4) and solving Ω, the fundamental frequency, f, can be calculated adaptively based on the sliding window of I samples, as listed in Equation (7):

$$f=f_s\times {\cos }^{-1}\left(\frac{{\displaystyle \sum _{i=3}^I{(s_{LP\_i}+s_{LP\_i-2})}^2}}{2{\displaystyle \sum _{i=3}^I{s}_{LP\_i-1}(s_{LP\_i}+s_{LP\_i-2})}}\right)$$

(7)

In this way, the deviated fundamental frequency can be easily obtained with the above-mentioned IEC-based synchronizer to regulate the image matrix.

2.3. Image Regulation (IR)

In this section, the PQD signal is divided into multiple cycles, where the obtained fundamental frequency from the IEC-based synchronizer in Equation (7) was utilized to determine the regulated cycle duration according to the variation of fundamental frequency. The signals of divided cycles were transformed into the submatrices, and these submatrices were then merged to form a regulated matrix. Finally, the regulated matrix was converted to the 2D grayscale image. The advantages of this approach are that the image resolution can be reduced, and the image matrix can be correctly regulated when the frequency variation is present. The main steps of the proposed approach are as follows:

Step 1. 

Determine the submatrix dimension.

The square submatrix (number of the rows (N_row) is equal to the number of the columns (N_col)) is chosen. N_col is determined by Equation (8),

$$N_{col}=\lceil \frac{f_s}{f}\rceil$$

(8)

where f is the regulated fundamental frequency obtained in Equation (7).

Step 2. 

Divide the PQD signal into multiple cycles.

The PQD signal is divided into N_c cycles according to the value of f.

Step 3. 

Transform the divided cycles into submatrices.

(1)

Initialize all the elements of the lth submatrix M_{l_x,y} with Equation (9), where x and y are the row and column indices, respectively.

$$M_{l\_x,y}=0,l=1, 2, 3, \dots , N_c$$

(9)

(2)

Determine the column index y of the lth submatrix M_{l_x,y}.

The discrete-time index of the divided cycle is assigned as the column index to the submatrix, as listed in Equation (10), where y is the remainder of division between i and N_col:

$$y=i-\lfloor \frac{i}{N_{col}}\rfloor \times N_{col}$$

(10)

(3)

Determine the row index x of the lth submatrix M_{l_x,y}.

The process of row determination for each sampling point is displayed in Figure 3. The sampling values of the PQD signal are arranged into different levels. The number of levels should be the same as the number of rows, and the width of the level interval should be the same as well. The width of the level interval (L_Int) is calculated with Equation (11):

$$L_{Int}=\frac{H_s-L_s}{N_{row}}$$

(11)

where H_s represents the highest sampling value and L_s represents the lowest sampling value from all the sampling values. In addition, the lower (B_L) and upper (B_U) boundaries are used to define the limits of levels, which can be obtained through the process in Figure 3. The order of levels is started from the highest sampling value as the first level, while the lowest sampling value is in the final level. According to the level arrangement in Figure 3, the row index, x, of each sampling point, s_i, can be obtained in Equation (12) by comparing the sampling value to all the levels:

$$x=m$$

(12)

(4)

Insert the sampling values of a divided cycle as the matrix elements with the obtained row and column indices.

(5)

Repeat the process to transform the rest of the cycles into the submatrices.

Step 4. 

Merge the submatrices to form a regulated matrix.

All the corresponding elements in each submatrix are summed, as shown in Equation (13), where M is the element of the combined matrix, M_l is the element of the submatrix, and x and y are the matrix indices. The combined matrix has the same dimensions as the submatrices.

$$M_{x,y}={\displaystyle \sum _{l=1}^{N_c}{M}_{l\_x,y}}\begin{array}{cc}& \end{array},\begin{array}{ccc}& x\le N_{row},& y\le N_{col}\end{array}$$

(13)

Step 5. 

Convert the regulated matrix to the 2D grayscale image.

The elements of the matrix are converted to the grayscale color (0–255) to create the grayscale image. The resulted image resolution is N_row × N_col pixels.

2.4. Disturbance Classification (DC)

The 2D deep CNN methods were employed to perform the classification of PQD. As depicted in Figure 4, the applied deep CNN structure is composed of six convolution layers, three max pooling layers, a dropout layer, and two dense or fully connected layers. The details of these compositions are presented in

Table 2. Details of model architecture.

Layer	Parameters
Convolution 1	Number of kernal filters = 32, Kernal size = 5 × 5, Activation function: ReLU
Convolution 2	Number of kernal filters = 32, Kernal size = 5 × 5, Activation function: ReLU
Pooling 1	Max pooling, Size = 2 × 2, Step: 2
Convolution 3	Number of kernal filters = 32, Kernal size = 5 × 5, Activation function: ReLU
Convolution 4	Number of kernal filters = 32, Kernal size = 5 × 5, Activation function: ReLU
Pooling 2	Max pooling, Size = 2 × 2, Step: 2
Convolution 5	Number of kernal filters = 32, Kernal size = 5 × 5, Activation function: ReLU
Convolution 6	Number of kernal filters = 32, Kernal size = 5 × 5, Activation function: ReLU
Pooling 3	Max pooling, Size = 2 × 2, Step: 2
Dense 1	Number of neurons: 128, Activation function: ReLU
Dense 2	Number of neurons: 14, Activation function: softmax

.

2.5. Indices of Performance Evaluation

To evaluate the performance of the proposed PQD classifier, the confusion matrix was applied to measure the indices such as accuracy, recall, precision, and f1-score, as listed in Equations (14)–(17) [21,22,23]. The four kinds of outputs from the confusion matrix, such as true positive (TP), false positive (FP), true negative (TN), and false negative (FP), were calculated to obtain the values of the indices.

$$accuracy=\frac{TP+TN}{TP+TN+FP+FN}$$

(14)

$$recall=\frac{TP}{TP+FN}$$

(15)

$$precision=\frac{TP}{TP+FP}$$

(16)

$$f1-score=\frac{\left(2\times precision\times recall\right)}{\left(precision+recall\right)}$$

(17)

3. Results

To provide sufficient and diverse PQD data for the training of the power quality classifier, the generation of 14 types of datasets is performed in this section. Then, the PQD datasets used in this work are transformed to the regulated 2D grayscale images according to the procedure proposed in this paper. Furthermore, the results of the training and testing are analyzed to evaluate the performance of the proposed model and the models in the literature. Finally, the field verification is implemented based on a microgrid in the campus of National Central University, Taiwan, to examine the PQD classification.

3.1. Generation of Datasets and Regulated 2D Grayscale Image

The 14 synthetic PQD types were generated with the mathematical models from Table 1. Then, the PQD signal was converted to the regulated 2D grayscale image based on the proposed procedure, as shown in

Table 3. Representation of the PQD signal and the regulated 2D grayscale image.

PQD Type	PQD Signal	2D Grayscale Image	PQD Type	PQD Signal	2D Grayscale Image
Normal			Sag wit harmonics
Flicker			Swell with harmonics
Harmonics			Interruption with harmonics
Interruption			Flicker with harmonics
Notch			Flicker with sag
Sag			Flicker with swell
Swell			Transient

. It was found that the information of the original PQD signal can be preserved in the image, even though the values of sampling points were converted into the grayscale color. To realize the performance of the proposed regulated 2D transformation, the existing conversion methods in [15,16,17] were also implemented to obtain two 2D image datasets for comparison. For the training and validation purposes, 9000 and 1000 samples of each PQD category were utilized in the training and evaluation phases, respectively.

3.2. Results of Training and Evaluation Phases

The model structure in Table 2 was utilized for the training phase, where the 2D grayscale images obtained with the proposed approach and the methods in [15,16,17] were fed as the inputs. In the deep CNN model, an Adam optimizer with a learning rate of 0.001 was adopted and a categorical cross-entropy was applied for the loss function. The hardware for model training is based on a Nvidia Tesla T4 Graphics Processing Unit (GPU) accelerator with 16 GB of memory and an Intel Xeon (R) Central Processing Unit (CPU) at 2.20 GHz. All the algorithms of power quality classifiers were implemented with Go language, which is an open-source software developed by Google.

The fitting graphs between the training and validation of models are displayed in Figure 5. It was found that the models were trained at 50 epochs since the accuracy and loss values of training and validation after the 50 epochs were unstable for the compared models. In addition, the values in the dropout layer were adjusted to achieve the fitting accuracy and loss values between training and validation for each method. In this way, the dropout values were selected as 0.36 for the proposed method, 0.46 for Karasu’s method in [15,16], and 0.55 for Zheng’s method in [17], respectively. The performance evaluation for the compared models is listed in

Table 4. Performance comparison of models.

Models	Training Accuracy (%)	Validation Accuracy (%)
Proposed Method	99.25	99.46
Karasu’s Method in [15,16]	98.69	98.94
Zheng’s Method in [17]	97.98	98.43

. It was realized that the performance of the proposed approach in the conversion task was better than the previous approaches.

For the model evaluation phase, the testing results are represented in the confusion matrices of

Table 5. Confusion matrix of the proposed method.

Category	C01	C02	C03	C04	C05	C06	C07	C08	C09	C10	C11	C12	C13	C14
C01	998	0	0	2	0	0	0	0	0	0	0	0	0	0
C02	0	988	0	12	0	0	0	0	0	0	0	0	0	0
C03	0	0	998	0	0	0	2	0	0	0	0	0	0	0
C04	0	2	0	998	0	0	0	0	0	0	0	0	0	0
C05	0	0	0	0	1000	0	0	0	0	0	0	0	0	0
C06	0	0	0	0	0	1000	0	0	0	0	0	0	0	0
C07	0	0	0	0	0	0	1000	0	0	0	0	0	0	0
C08	0	0	0	0	0	0	0	1000	0	0	0	0	0	0
C09	0	0	0	0	0	0	0	0	992	0	8	0	0	0
C10	0	0	0	0	0	0	0	0	0	1000	0	0	0	0
C11	0	0	0	0	0	0	0	0	0	0	1000	0	0	0
C12	0	0	0	0	0	0	0	0	0	0	0	1000	0	0
C13	0	0	0	0	0	0	0	0	0	0	0	0	1000	0
C14	0	0	0	0	0	0	0	0	0	0	0	0	0	1000

,

Table 6. Confusion matrix of Karasu’s method in [15,16].

Category	C01	C02	C03	C04	C05	C06	C07	C08	C09	C10	C11	C12	C13	C14
C01	994	0	0	0	0	0	6	0	0	0	0	0	0	0
C02	28	960	0	12	0	0	0	0	0	0	0	0	0	0
C03	0	0	998	0	0	0	2	0	0	0	0	0	0	0
C04	0	20	0	980	0	0	0	0	0	0	0	0	0	0
C05	0	0	0	0	1000	0	0	0	0	0	0	0	0	0
C06	0	0	0	0	0	1000	0	0	0	0	0	0	0	0
C07	4	4	4	0	0	0	986	2	0	0	0	0	0	0
C08	2	0	0	0	0	0	0	998	0	0	0	0	0	0
C09	0	0	0	0	0	0	0	0	980	0	20	0	0	0
C10	0	0	0	0	0	0	0	0	0	1000	0	0	0	0
C11	0	0	0	0	0	0	0	0	8	0	992	0	0	0
C12	0	0	0	0	0	0	0	0	0	0	0	1000	0	0
C13	0	0	0	0	0	0	0	0	0	0	0	0	1000	0
C14	0	0	0	0	0	0	0	0	0	0	0	0	2	998

and

Table 7. Confusion matrix of Zheng’s method in [17].

Category	C01	C02	C03	C04	C05	C06	C07	C08	C09	C10	C11	C12	C13	C14
C01	998	0	0	0	0	0	0	2	0	0	0	0	0	0
C02	32	926	0	42	0	0	0	0	0	0	0	0	0	0
C03	0	0	1000	0	0	0	0	0	0	0	0	0	0	0
C04	0	10	0	990	0	0	0	0	0	0	0	0	0	0
C05	0	0	0	0	1000	0	0	0	0	0	0	0	0	0
C06	0	0	0	0	0	1000	0	0	0	0	0	0	0	0
C07	16	4	0	2	0	0	974	4	0	0	0	0	0	0
C08	4	0	0	0	0	0	0	996	0	0	0	0	0	0
C09	0	0	0	0	0	0	0	0	958	0	42	0	0	0
C10	0	0	0	0	0	0	0	0	0	1000	0	0	0	0
C11	0	0	0	0	0	0	0	0	6	0	994	0	0	0
C12	0	0	0	0	0	0	0	0	2	0	0	998	0	0
C13	0	0	0	0	0	0	0	0	0	0	0	0	1000	0
C14	0	0	0	0	0	0	0	0	0	0	0	0	2	998

. Then, the values of indices such as the recall, the precision, and the f1-score were obtained, as presented in

Table 8. Summary of the models’ performance between the proposed and existing methods.

Index	Karasu’s Method [15,16]	Zheng’s Method [17]	Proposed Approach
Accuracy (%)	99.88	99.74	99.97
Precision (%)	99.19	98.80	99.81
Recall (%)	99.18	97.81	99.80
F1-score (%)	99.18	98.30	99.80
Training time per epoch (seconds)	15	16	28

and Figure 6.

The experimental results revealed that Karasu’s method in [15,16] obtained 99.88% for accuracy, 99.19% for precision, 99.18% for recall, and 99.18% for f1-score. Zheng’s method in [17] reached 99.74% for accuracy, 98.80% for precision, 97.81% for recall, and 98.30% for f1-score. It can be seen that the proposed approach outperformed the other methods, with 99.97% for accuracy, 99.81% for precision, 99.80% for recall, and 99.80% for f1-score. From the results in the confusion matrix, the capability of the proposed regulated model to detect only the PQD of interest in the dataset was also higher than the previous methods. It was indicated that the synchronization process of fundamental frequency is important to the 2D image transformation, which can effectively and correctly split the PQD signal to regulate the 2D image matrix. However, the computational time of the proposed approach was higher compared with the other methods since the larger 2D image size was utilized in the training phase.

3.3. Field Verification

To examine the practical performance of the proposed regulated 2D deep CNN-based method in the field PQD classification, the microgrid system at National Central University, Taiwan, was tested. The system information and photo are displayed in

Table 9. System information of the microgrid at National Central University, Taiwan.

Building Size	four 20-foot containers
Load Demand	10 kWh/day
Solar Generation	The total power generation per day is 7.4 kW × 3.9 h = 28.86 kWh 3.9 h is the average sunshine hours at National Central University, Taiwan
Storage System	Lithium-ion Battery	21.6 kWh
	Fuel Cell	5 kW
Power Inverter	Three-phase 15 kW, AC output voltage is 220 V

and Figure 7, respectively.

According to numerous experimental tests, the proposed method can deal with most PQD classification accurately, compared with the threshold method (TM) in [24], the traditional fuzzy analysis (FA) in [25], the traditional back-propagation neural network (BPNN) in [26], the wavelet energy fuzzy neural network-based technique (WEFNNBT) in [27], Karasu’s method in [16,17], and Zheng’s method in [18], as listed in

Table 10. Comparison of classification accuracy between the proposed and existing methods.

PQD	TM	FA	BPNN	WEFNNBT	Karasu’s Method	Zheng’s Method	Proposed Approach
Normal	97.51%	98.15%	67.81%	99.26%	99.92%	99.75%	99.98%
Sag	97.12%	16.18%	97.85%	98.83%	99.45%	98.97%	99.79%
Swell	96.84%	17.57%	97.61%	98.66%	99.69%	99.48%	99.93%
Harmonic	13.72%	96.42%	97.15%	99.17%	99.91%	99.81%	99.97%
Transient	86.34%	95.83%	96.92%	98.22%	99.88%	99.76%	99.97%
Flicker	83.62%	94.45%	96.83%	97.84%	99.74%	99.68%	99.96%
Interruption	12.86%	15.29%	97.72%	98.93%	99.51%	99.13%	99.86%

.

From Table 10, it can easily be found that the TM and FA could not recognize some PQD accurately (accuracy lower than 90%) due to the short-time duration and waveform distortion of PQD. The incorrect classification would be obtained in BPNN since the noisy interference is present in the solution process of discrete wavelet transform. The classification of the proposed approach was superior to WEFNNBT in [27], Karasu’s method in [15,16], and Zheng’s method in [17]. It was realized that the proposed method can effectively provide PQD classification and a protection strategy for the microgrid system.

4. Conclusions

A regulated 2D deep CNN-based power quality classifier for the microgrid was presented in this paper. For the traditional 2D CNN power quality classifier (Karasu’s method and Zheng’s method), the signal-to-image transformation is based on the nominal fundamental frequency. Once the deviation is present in the fundamental frequency due to the power imbalance between the generation and the load demand, the image transformation would be deteriorated. To enhance the classification performance, the IEC-based synchronizer was proposed to detect the deviation of fundamental frequency and regulate the image matrix. In this way, the information and waveform characteristics of the signal can be preserved in the regulated 2D grayscale image. Through the testing results and field measurement, it was demonstrated that the proposed approach can improve the efficacy of the PQD classification with accuracy higher than 99.79%, and was superior to the previous existing approaches. In addition, the total computational burden of SS and IR stages was very low due to the simple calculation of Equation (7) and rearrangement of images, which takes approximately 0.53 ms. Even though the training phase of the proposed method takes longer than the compared methods, the validation phase only takes approximately 20 ms. As a result, the total computational time for the power quality classification is 20.53 ms, which is shorter than the data duration of 200 ms (12 cycles under a 60 Hz system). Therefore, it was found that the proposed solution procedure meets the real-time requirement for the power quality classification.