Deep Learning Aided Power Quality Disturbance Detection with Improved Time-frequency Resolution Employing Adaptive Superlet Transform

doi:10.21203/rs.3.rs-4718947/v1

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Deep Learning Aided Power Quality Disturbance Detection with Improved Time-frequency Resolution Employing Adaptive Superlet Transform

https://doi.org/10.21203/rs.3.rs-4718947/v1

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In the present work, a novel technique for detection and classification of power quality disturbance events (PQDE) in noisy environment is proposed employing adaptive superlet transform (ALST)-based time-frequency analysis and deep learning technique. ALST is a powerful signal processing tool for analysis of non-stationary signals in time-frequency frame. To this end, synthetic PQDEs were initially generated following IEEE std. 1159–2009. The generated 1D PQDEs were transformed to 2-D time-frequency RGB images using ASLT. The transformed time-frequency images of 1D PQDEs employing ALST showed enhanced resolution in time-frequency frame. In addition, ALST analysis of PQDEs showed distinct representations in time-frequency plane even in presence of very high noise level. The obtained PQDEs obtained using ASLT were finally fed as inputs to a designed lightweight customized convolutional neural network (CNN) architecture for automated feature extraction and classification. In addition, the performance of the proposed model was further evaluated using benchmark CNN models. It has been found that the proposed approach is highly accurate and has returned better performance compared to other time-frequency representation and existing approaches. The results showed that the proposed framework is capable of diagnosis of power quality disturbance events in both noise-free and strong noisy environment. In addition, the proposed CNN model is light weight and fully customized and required less computational time and memory compared to existing CNN models.

Classification

deep learning

machine learning

power quality

signals and time-frequency analysis

N recent times, with the development of smart grids, more numbers of renewable energy (RE) sources like photovoltaic (PV) and wind energy are integrated into the distribution network [1–2]. Most of the RE based distributed generation (DG) systems require power electronic based converters and inverters, which may allow high level of energy penetration. High penetration of distributed generation (DG) systems can lead to sudden voltage fluctuation, transient, sag, swell, notch, harmonics and power factor collapse [1–2]. The aforesaid power quality disturbance events can also be generated in grid-connected DG system due to the connection of heavy nonlinear loads, sudden load changes, fault and

switching of lines. These power quality disturbance events (PQDEs) can result in unwanted tripping of circuit breakers and protective relays, damaging of sensitive equipment and malfunctioning of digital equipment [3]. Therefore, reliability of smart grid can be affected which is not desirable from economical point of view [4]. Considering the fact, accurate classification and diagnosis of different PQDEs are the essential tasks in power distribution system so that suitable preventive techniques can be implemented.

In existing literature, various signal processing and machine learning techniques have been proposed over the years for accurate detection and classification of PQDEs. Non-stationary signal processing tools like discrete wavelet transform (WT) [5], wavelet packet transform [6], tunable Q factor Wavelet transform [4], empirical wavelet transform [7] Wigner-Ville distribution [8], different versions of Stockwell transform (ST) [9–11] are used to analyze different PQDEs in joint time-frequency (T-F) plane. In [12], degree of nonlinearity in PQDEs has been analyzed through detrended fluctuation analysis (DFA). Based on DFA analysis, several features have been extracted which were found to be useful to diagnose single and mixed PQDEs. In addition to signal processing, many machine learning algorithms like recurrent neural network (RNN) [13], modular neural network (PNN) [14], support vector machines (SVM) [15], decision tree [3] etc. have been implemented for classification of PQDEs based on features extracted form analysis of PQDEs using aforesaid signal processing techniques. Though the existing methods are proven to be useful for classification and identification of both single and mixed PQDEs, most of the frameworks are based on handcrafted feature extraction techniques. The handcrafted feature extraction technique not only requires prior expertise but also depends on human intervention which often imposes the risk of misclassification due to selection of redundant features [16]. The problem related to the manual feature extraction process can be overcome by deep learning (DL). The benefit of deep learning algorithms is that it can learn meaningful and significant features from input signal or image data automatically. Hence, eliminates the requirement of handcrafted feature extraction and hence can be used in real-time applications.

Convolutional neural network (CNN) is one of the efficient DL algorithms effectively used in PQDE classification [17–19]. As the PQDEs are recorded as 1-D time domain signal, 1-D CNN can be employed for its automatic feature extraction and classification. It is noteworthy to mention that CNN delivers promising results in feature extraction and classification from input image compared to 1-D signal [9]. Considering this issue, in several literatures, time-domain PQDEs have been transformed into 2-D image format such as T-F spectrograms and then the images are classified using a CNN model [8,9,19]. For conversion of 1D PQDEs to T-F spectrogram images, Stockwell transform (ST) [9], continuous wavelet transform (CWT) [19] etc. have been implemented in existing literature. However, conversion of 1D PQDEs to 2D images using existing T-F spectrogram methods has some limitations from the practical point of view which are discussed below.

The problem of using ST based time-frequency (T-F) analysis is that a Gaussian window is used to probe the signal, which is not signal adaptive and offers poor resolution in T-F frame. Another important issue is the signal noise. The time-frequency image obtained using ST is noisy when the signal to noise ratio (SNR) of the input signal is low. Recently, it has been reported in [11, 20], that detection of PQDEs in noisy environment is more challenging and several attempt have been made by the researchers to precisely detect PQDEs in noisy environment. To provide better resolution of T-F images under noisy environment, it is necessary to modify the Gaussian window by optimizing its parameters [11]. Even then the T-F spectrogram is not completely devoid of noise which makes it difficult to identify different PQDEs. In the case of CWT, the resolution in T-F plane depends on the number of cycles (bandwidth). Increasing the number of cycles will lead to precise frequency resolution while decreasing number of cycles provide better temporal resolution [21]. Thus, there is always a trade-off between time and frequency resolution in joint time-frequency analysis following uncertainty principle. Considering the above said facts, in this study, a novel signal processing technique has been proposed for analysis of PQDEs using superlet transform. The superlet transform (SLT) is an improvement over CWT, where the number of cycles of mother wavelet are varied by combining shorter wavelets for (better temporal resolution) and longer wavelets (for better frequency resolution) to obtain better time-frequency resolution [21]. To make the SLT adaptive in nature, adaptive superlet transform (ASLT) has been proposed by varying the order as a function of the central frequency to achieve better time and frequency representation of any signal [22]. In this study, ASLT has employed to analyze PQDEs in joint T-F frame. Thus, ASLT is not only signal adaptive but gives better T-F resolution compared to ST, which uses a Gaussian window only. In other words, superlet transform overcomes the problem of time-frequency resolution suffered by both CWT and ST. Thus, the proposed method offers distinct advantages over existing methods and hence used for analysis of PQDEs.

Table I. Description of PQDEs

Signal Label	Description	Class label
PQDE₁	Sine	1
PQDE₂	Harmonics	1
PQDE₃	Sag	1
PQDE₄	Swell	1
PQDE₅	Flicker	1
PQDE₆	Transient	1
PQDE₇	Interruption	1
PQDE₈	Notch	1
PQDE₉	Harmonics with Sag	2
PQDE₁₀	Harmonics with Swell	2
PQDE₁₁	Harmonics with Flicker	2
PQDE₁₂	Harmonics with Interruption	2
PQDE₁₃	Harmonics with Transient	2
PQDE₁₄	Sag with Flicker	2
PQDE₁₅	Swell with Flicker	2
PQDE₁₆	Sag with Transient	2
PQDE₁₇	Swell with Transient	2
PQDE₁₈	Transient with Interruption	2
PQDE₁₉	Harmonics with Interruption	2
PQDE₂₀	Notch with Harmonics	2
PQDE₂₁	Notch with Interruption	2
PQDE₂₂	Transients with Harmonics	2

To this end, the synthetic 1D PQDEs were initially simulated using mathematical relations as prescribed in IEEE std. 1159–2009. Following this, joint T-F analysis of 1D PQDEs were conducted by converting the signals from time domain to T-F domain. The T_F representation of PQDEs yields distinct 2-D RGB images for different PQDEs. A lightweight 2D CNN architecture has been configured to classify the 1D PQDE signal transformed into 2-D images. In addition, several benchmark CNN models have been used to compare classification performance.

The original contributions of the present work are briefly explained as follows:

A novel framework employing adaptive superlet transform is proposed for the first time to analyze single and multiple class PQDEs in time-frequency frame.

The performance of ASLT was compared with Stockwell transform to indicate the superiority in analyzing PQDEs in both noisy and noise free environment.

A lightweight CNN model has been designed to classify the time-frequency PQDE images.

Ablation studies with benchmark CNN models have been done to indicate the superiority of the proposed CNN model.

The proposed method has been validated on real-life PQDE signals to verify the practicability of the proposed method.

A. Numerical Models for generation of PQDEs

In power system, PQDE event data can be acquired through continuous monitoring over a long duration. However, uncertainty in occurrence of PQD events can lead to scarcity in real time data. Considering this issue, in this paper, single and combined PQD events were generated employing the numerical model prescribed in IEEE std. 1159–2009 [23]. The signals were generated using MATLAB programming at a sampling frequency of 10kHz. It is to be mentioned here that PQDE data generated using the prescribed numerical models closely resemble real life data [9]. Using the numerical model described in [23], twenty-two PQDEs were generated in this paper. The details of the eighteen PQD events are presented in Table.1. In Table 1, class label ‘1’ and ‘2’ indicate single and multiple PQDEs, respectively. Thus, in this study, single and multiple PQDEs were generated to test the practicability of the proposed PQ detection model. This is done because, in several literatures, it is reported that more than one PQDEs can occur at same time [9]. Considering this issue, in this paper, along with single multiple PQD events were generated concatenating numerical models of the corresponding single PQD events. In addition, a white gaussian noise component (SNR value 30 dB) was added to the synthetic PQD data, which closely resembles real-life PQDE data.

A. Superlet transform

The superlet transform (SLT) was proposed by Moca eta al. in [24] as an improvement of continuous wavelet transform to improve resolution of any non-stationary signal in time-frequency frame. WT provides a trade-off between time and frequency resolution in joint T-F domain analysis. For e.g., CWT using a ‘Morlet’ wavelet with less number of cycles provides precision temporal information but poor frequency resolution. On the contrary, increasing the number of cycles of “Morlet” wavelet will lead to poor temporal resolution and accurate frequency resolution. To overcome the aforesaid issue, basic idea of the “superlet” was proposed which improves the TFR by combining both shorter wavelets (with high time resolution, less cycles) with longer wavelets (more cycles with poor time resolution), simultaneously. In other words, the superlet transform makes use of “Morlet” wavelets having fixed central frequency (ω), and different number of cycles progressively (for better frequency resolution or constrained bandwidth). Mathematically, superlet transform can be expressed as [24]:

$$\:{SLT}_{\omega\:,k}{=\{Ѱ}_{\omega\:,c}|c={c}_{1},\:{c}_{2},........{c}_{k}\}$$

In the above equation, Ѱ is the mother wavelet with centre frequency ω, and k is the order of the SLT and c is the number of cycles. In the case of SLT, the number of cycles can be selected either additively or multiplicatively, which are given by c_i = c₁ + i − 1, for i = 2,…,k and c_i = i.c₁, respectively. In the other words, SLT is a multi-ordered wavelet transform, which covers multiple frequency bandwidth with fixed centre frequency. Also, a superlet with fixed centre frequency and order k = 1, is analogous to CWT. The computation of SLT is done in the same way as that of CWT with the exception that here SLs are used instead of wavelets. The response of SLT to any arbitrary signal g(t) is defined as the geometric mean GM of the responses of individual wavelets in the set which is expressed as:

$$\:R\left[{SLT}_{\omega\:,k}\right]=\sqrt[k]{\prod\:_{n=1}^{k}R\left[{\text{Ѱ}}_{\omega\:,{c}_{n}}\right]}$$

In the above equation, $\:R\left[{\text{Ѱ}}_{\omega\:,{c}_{n}}\right]$ is the response of the i^th wavelet to any signal. In the case of complex wavelets like Morlet or Gabor, complex convolution is used and Eq. (2) can be modified as:

$$\:R\left[{SLT}_{\omega\:,k}\right]=\surd\:2\times\:g\left(t\right)*{\text{Ѱ}}_{\omega\:,{c}_{n}}$$

In Eq. (3), * indicates complex convolution operation and $\:\surd\:2$ is a term used strictly for the analytic wavelets and g(t) is any arbitrary signal. The SLT can estimate the oscillation packets present in any non-stationary signal at the central frequency, ω. The magnitude of ALST is computed by taking the GM of the magnitude of each individual wavelets. Finally, the magnitude of SLT is squared to obtain the time-frequency scalogram.

B. Adaptive superlet transform

In [24], the concept was adaptive superlet transform was proposed where the order of the central frequency of the superlets were adjusted to tackle the problem decreasing bandwidth as the frequency increases. An adaptive superlet transform (ASLT), starts with low order, k = 1, that can estimate low frequencies. The order k is then increased monotonically as a function of central frequency (ω) as follows [24]:

$$\:{{ASLT}_{\omega\:,k}=SLT}_{\omega\:,k}|k=p(\omega\:)$$

so that the improved resolution for both time and frequency is attained for the entire frequency domain. In Eq. (4), p is an integer. The general choice to order linearly using the following equation [24]:

$$\:p\left(\omega\:\right)={k}_{min}+\left[{{(k}_{max}-k}_{min})\frac{\omega\:-{\omega\:}_{min}}{{\omega\:}_{max}-{\omega\:}_{min}}\right]$$

In Eq. (5), k_min and k_max denotes the orders corresponding to the smallest and largest central frequencies $\:{\omega\:}_{max}$ and $\:{\omega\:}_{min}$, respectively and [] is the nearest integer operator. When the desired frequency range of interest is wider, then it is recommended to use ASLT while SLT may be used for narrower frequency bands. Since the frequency of PQDEs can fluctuate over a wide range from standard power frequency (50Hz) to several kHz for high frequency transients, therefore, we have used ALST for analysis of PQDEs to achieve better resolution in T-F frame.

C. Convolutional neural network

Convolutional neural network or CNN is mathematical model, which can process input image data to a new feature representation field. A basic structure of CNN consists of following layers [9,,25]

• Input layer:

This is the first layer of CNN architecture. In input layer, image is given as input. The input image needs to be resized accordingly before feeding into the convolution layer.

• Convolution layer:

Convolution layer (CL) is the core block of CNN architecture, comprises of a set of learnable filters known as “kernel”. In this layer, input image or output of previous layer is transversely convolved with kernels to extract feature map [15–19]. The convolution operation can be mathematically expressed as [25]:

$$\:P*Q(i,j)=\int\:P(a,b)Q(i+a,j+b)$$

It is noteworthy to mention that performance of a CL depends on some factors such as size of kernel and the number of kernels. During convolution operation, kernels are moved by a fixed length known as “stride”. In addition, zero padding has been applied to the output in order to maintain the image size. For an input image with dimension, W_m × H_m × K_m where W_m is the width, H_m is the height, and K_m are the number of channels. With K₀ number of kernel filters with size r × r, the output feature map W₀ × H₀ × K₀ can be written as [25]

$$\:{W}_{0}=\frac{{W}_{m}-r+2z}{q}+1$$

$$\:{H}_{0}=\frac{{H}_{m}-r+2z}{q}+1$$

In the above Eq. (7), “q” is stride whereas “z” is size of zero padding [17]. It is pertinent to mention that convolution operation is combined with activation layer. This activation layer introduces the non-linearity in the network.

• Pooling layer:

After convolution operation, the dimension of convolved features is very large, which may cause excessive computational cost if the convolved features are directly adopted. Considering the fact, the pooling layer (PL) reduces the dimension of convolved feature conserving the features with a high degree of spatial structure [11]. Pooling layer also helps to regulate overfitting. There are two types of pooling methods namely, average and max pooling. Average pooling takes average value of convolved feature map within a pooling window, whereas max pooling selects the feature with maximum value within a pooling window.

• Fully connected layer:

In fully connected layer (FC), the output of CL/PL has been converted into a one-dimension feature vector and the score for each category is calculated. It is noteworthy to mention that fully connected layer is similar to ordinary neural network and each hidden unit in this layer is connected to all activations in the previous layer [25].

• Softmax layer:

Softmax function maps the score obtained from FC into probabilistic value [9]. Based on the probabilistic value, probable class can be predicted.

Combining the above layers, one can build a customizable CNN architecture. The number layer in a customizable CNN architecture is completely empirical and it completely depends on the type of classification task. It is noteworthy to mention that performance of a CNN architecture is governed by various factors such as number and size of kernel, number of CL, type of activation function, type of pooling, number of FC, number of hidden units in FC. In existing literature there are several benchmark CNN models like AlexNet, VGGNet, ResNet etc. have been proposed by various researchers for image classification. A brief overview of different CNN models are shown below.

(1) AlexNet CNN

The AlexNet CNN was proposed by Alex Krizhevsky et al. in 2012 [26] as a winner of ImageNet Large Scale Visual Recognition Challenge (ILSVRC). In the ILSVRC dataset, 1.2 million images are present with 1000 different class labels. Detailed description of AlexNet model has been provided in earlier works in [26]. The basic structure of AlexNet consists of 8 layers. The initial two convolution layers have 96 and 256 filters with size 11×11×3 and 48×5×5, respectively followed by local response normalization and two maxpooling layers with filter size 3×3. The next three convolution layers consists of 384, 384, and 256 numbers of filters, with sizes 256×3×3, 192×3×3 and 192×3×3, respectively. These three convolution layers are followed by another maxpooling layer with filter size 3×3. Finally, two fully connected layers with 4096 number of neurons and two dropout layers and finally one FC is present at the output. AlexNet is a series connected CNN model with 60 million learnable parameters.

(2) VGGNet CNN

VGGNet is a popularly used CNN architecture originally proposed by the Oxford Visual Geometry Group (VGG) [27]. Like the AlexNet model, training of the VGGNet was also ILSVRC database. The number of layers in VGGNet CNN model varies from 11 to 19 among which in this work we have used 16-layer network known as VGGNet16. The VGGNet16 has 13 convolution layers with 3×3 convolution filters. There are 5 maxpooling layers of size 2×2 with step length of 2 is placed at the output of each convolution layers to reduce the spatial volume of the extracted feature output of the convolution layer. At the output of the final max pooling layer, three FC layers with 4096 number of neurons are connected. A softmax classification layer is connected at the output for the classification. Like AlexNet, VGGNet16 is also a series connected network with 138 million learnable parameters.

(3) ResNet CNN

Residul networks also known as ResNets are a set of popular CNN networks. ResNets proposed in [28], work on the principle of residual learning which was introduced to take care of the vanishing gradient problem often encountered in deeper networks. In a ResNet CNN model, a new technique known as the ‘identity mapping’ strategy has been incorporated in its hidden layers. This ‘identity mapping’ can solve the problem of vanishing gradient by providing skip connections i.e. by allowing shortcut paths for gradients to bypass through. Also, the skip connections aid in reducing overfitting issue during extraction of features. Different layers of ResNet like 18, 50, 101 etc. are proposed in existing literature. In this study, ResNet with 50 layers i.e. ResNet 50 has been used to classify PQDEs. The ResNet50 model consists of 5 stages with each stage contains a convolution block and an identity mapping block. The convolution block and identity mapping block contain 3 convolution layers. The total number of learnable parameters in ResNet50 is about 23 million.

D. Proposed CNN model

Although all these pre-trained deep learning models have delivered satisfactory performance in the context of image classification, yet one major limitation of the existing CNN

models is that neither of these aforesaid benchmark models are customized. In other words, the total number of layers used in the above benchmark CNNs are fixed and neither of them can be tuned as per the requirement of the user. Moreover, these CNN models are computationally expensive and require a greater number of learnable parameters. For classification of PQDEs T-F images, it may so happen that a lightweight CNN model with lesser number of learnable parameters may deliver better performance than the existing models and that too at reduced computational burden. This motivates us to design a lightweight CNN model for classification of PQDE images. The detailed architecture of the developed CNN model is given in Fig. 2.

The proposed CNN structure consists of 12 layers with 3 convolution layers, having filters size 3×3. The number of filters used in each convolution layer was kept fixed at 12, 32 and 64, respectively. Each convolution layer is followed by batch normalization (BN), ReLU activation and rank based average pooling layer (RAP) which were successively placed one after the other. The function of the BN layer is to reduce the feature dimensions at the convolution layer output, without causing any loss of information and at the same time reducing the training time. It is to be mentioned here that in the proposed CNN model, instead of using other activation functions sigmoid, tanh etc., ReLU activation function has been deployed since it does not suffer from vanishing gradient problem. Moreover, ReLU activation function can reduce learning time and at the same time computation complexity by producing sparse representation during training a CNN model. The RAP layer has been used here because it operates by computing the mean of the weighted feature values, thereby overcoming the loss of information. The output of the final RAP layer, there is a dropout layer with value of 0.5 (chosen empirically) followed by two FC layers in succession. The output of the last FC is added with 22 neurons to classify 22 PQDEs. Finally, a SoftMax layer is connected at the output of the last FC layer for classification. The total number of learnable parameters of the proposed CNN model is roughly 1 million.

A. Analysis of PQ events using ASLT

The time-frequency images of different PQDEs obtained using ALST is discussed in this section. Figure 3 (a-c) shows a class ‘1’ i.e. single PQDE₆ signal (oscillatory transient) and its T-F image obtained using ASLT and conventional ST. Similarly, Fig. 4 (a-c) shows a class ‘2’ i.e. multiple PQDE₂₂ (oscillatory transient with 5th harmonic) signal and its T-F

Representation obtained using ASLT and ST. The SNR of the sample PQDEs were kept fixed at 20 db. The order of the ALST and the number of cycles used to generate the T-F images are mentioned in the respective Figure captions. It can be seen from Fig. 3(a-c) that using ASLT, it is possible to distinguish single as well as multiple PQDEs from the T-F images using ASLT more distinctly than conventional ST. It is evident that for the above signals, ALST has provided better resolution in T-F images compared to ST. It is clearly visible from Fig. 3(c) and Fig. 4 (c) that the T-F images of conventional ST are noisy, and it is difficult to discern different PQDEs, whereas by using ASLT clear visibility of different events is obtained. Classification of PQDEs with T-F images obtained using ST will inevitably lead to misclassification as evident from the ST spectrogram. Hence, ASLT provides better resolution of PQDEs compared to ST.

B. Training of CNN models

The T-F images of different classes of PQDEs obtained using ASLT (described in the earlier section) were at first resized to 278×278×3 before being fed as inputs to the customized CNN model for automated feature extraction and classification of PQDEs. Besides, the T-F images of PQDEs were also inputted to the benchmark CNNs namely AlexNet, VGG16 Net and ResNet50 CNN models for comparison. For AlexNet, the size of the PQDE images were altered to 227×227×3, while for both the VGG16Net and the ResNet50 model, the same was changed to 224×224×3, respectively. Here, 500 PQDE events were simulated for each class and therefore for 22 class of PQDEs, a total of 11000 signals were generated. Now, the training of the proposed CNN model was done from scratch while in the case of pre-trained models, transfer learning technique (TL) has been adopted. TL is a strategy where a CNN intended to perform one classification task can be used to perform another classification task. In TL, the initial few layers of the benchmark CNNs were kept unchanged while the final few (FC) layers were replaced with the new finetuned layers. The training of the proposed CNN model was done using Adam optimizer. The initial learning rate was kept fixed at 0.001 and mini batch size was kept fixed at 30. For determination of the number of epochs during training phase of the CNN early stopping strategy has been implemented. The training and testing accuracy graph of the proposed CNN model is given in Fig. 5. Using the early stopping strategy, the maximum number of epochs and iterations obtained were 55 and 3400, respectively. Another observation from Fig. 5 is that as the number of epochs increase the training accuracy and the testing accuracy slowly converges with the latter being slightly less than the former for all epochs. This indicates that the model has performed satisfactorily without overfitting.

C. Performance analysis of CNN models

In this study, the performance of the proposed CNN model as well as for benchmark CNN models, was assessed using a 5-fold cross validation (CV) strategy. In a 5-fold CV method, the input PQDE images were divided randomly in the ratio of 4:1, for training and validation/testing purposes, respectively. The training and validation/testing data were then interchanged iteratively in a progressive manner (keeping the ratio fixed) and for each runtime the following performance parameters namely Accuracy (Acc), Sensitivity (Sen), Specificity (Spe) etc. were computed form the confusion matrix. Finally, the mean and standard deviation of the aforesaid statistical parameters was calculated, and the performance parameters are tabulated in Table II for the proposed CNN model as well as for the benchmark CNN models. The equations describing the performance parameters are as follows [9]:

Acc=$\:\frac{True\:Positive+True\:Negative}{True\:Positive+False\:Positive+True\:Negative\:+False\:Negative}\:\:$(8)

Sen=$\:\frac{True\:Positive}{True\:Positive+False\:Negative}$ (9)

Spe $\:=\frac{True\:Negative}{True\:Negative+False\:Positive}$ (10)

Table II. Classification Performance of different CNN models

CNN model	Accu (%)	Sen (%)	Spe (%)	Total Learnable parameters
AlexNet	99.14 ± 0.40	98.13 ± 1.27	99.64 ± 0.17	60 million
VGGNet16	99.01 ± 0.35	99.21 ± 0.45	97.46 ± 1.85	138 million
ResNet50	98.92 ± 0.60	98.35 ± 1.01	100 ± 0	23 million
Proposed CNN	99.52 ± 0.28	100 ± 0	99.10 ± 0.46	1 million

For computing the above statistical parameters, the value of true positives cases, false positives cases, true negatives cases and false negatives cases were obtained from the PQDE classification confusion matrix. From the variation of the accuracy, specificity, sensitivity and F1 score, shown in Table II, it is evident that the performance parameters obtained for all the CNN models is reasonably satisfactory. The proposed CNN model has delivered marginally better performance than the benchmark CNN models. Among the benchmark CNN models, the performance of AlexNet is close to the proposed CNN model followed by the VGGNet16 and ResNet50. In addition, it can be observed that for all CNN models, the standard deviation is minimum indicating the performance of the proposed model is robust.

D. Performance of the proposed CNN model by alteration of different parameters

In this section, the performance of the proposed CNN model has been verified by varying different design parameters namely (i) the number of layers and (ii) Kernel size. For each case, the classification accuracies and computational (training time) have been computed. This analysis is done to justify the design of the customized CNN model. The variation of the classification accuracies with number of CNN layers and corresponding training time is shown in Fig. 6. It can be observed that as the number of layers increases, the accuracy of the proposed CNN model increases, but after 12th layer, no appreciable increment in accuracy is noticed. On the contrary, the training time (plotted in secondary y axis) gradually increases with increasing the number of layers. Therefore, the proposed CNN model is designed with 12 layers where the maximum accuracy has been achieved and training time is also less than the other layers. Now, in Fig. 7, the effect of varying the kernel size has been investigated. It can be seen from Fig. 7 that the kernel size also has a direct influence on the accuracy of PD detection. In this study, the kernel sizes of the proposed CNN

model were increased progressively from 1×1 to 7×7 and it has been observed that for the kernel size 3×3, maximum recognition accuracy has been achieved. So, in this work, a 12-layer CNN model with kernel size 3×3 has been chosen that delivered the optimum performance.

E. Computational cost

The computational complexity of the proposed model is discussed in this section. The extraction of time-frequency (T-F) images of PQDEs using ALST required approximately 1206 seconds. Using the proposed CNN model, classification of 22 classes of PQDEs required approximately 125 minutes. The classification time required by the AlexNet, VGGNet16 and ResNet50 models are approximately 140 minutes 294 minutes and 192 minutes, respectively. Thus, in comparison with the AlexNet, VGGNet16 and ResNet50, the overall training time has been reduced by 10.71%, 57.48% and 34.89% respectively. This reduction in computational time is mainly due to the reduced number of learnable parameters present in the proposed CNN model compared to the benchmark models. Hence, it can be inferred that the proposed CNN model is lightweight and has less computational burden compared to the benchmark models.

F. Analysis of PQ events using ASLT in presence of noise

In real life, PQDEs are often contaminated with high background noise which can lead to error in detection. Therefore, a reliable PQD monitoring framework should be able to detect the PQDE correctly in a noisy background.

Considering the aforesaid issue, performance of proposed framework was investigated for different background noise. For this purpose, white gaussian noise of signal to noise (SNR) value “5 dB”, “10 dB”, “20 dB” and “25 dB” was added to generated PQDEs. The time-frequency representation of a sample PQDE₄ (swell signal) obtained using ASLT in the presence of high noise level SNR = 5 dB is shown in Fig. 8 (b). In Fig. 8(c), time-frequency representation obtained using conventional ST is also shown along with. It is imperative from Fig. 8(a-c), that when the SNR is very low, the different frequency components present in PQDEs can be distinctly identified in time-frequency plane using ASLT, while the time-frequency image obtained using ST is very noisy and difficult to identify the events correctly. Thus, ASLT is more robust against noise compared to ST. In Table. III, the performance of proposed CNN model under noisy background is reported. Based on the result, it can be stated that proposed CNN model can accurately classify PQDEs even in presence of high background noise.

Table III. Performance of proposed framework under noisy background

SNR value (dB)	Accuracy (%)
5	98.47
10	99.01
20	99.35
30	99.52

G. Performance analysis with real-life PQD data

To establish the effectiveness of proposed framework, the performance of the framework was validated with real-life PQD signals. For this purpose, the real life PQDEs were procured from several online available datasets [29-30]. In Table IV, the description of real-life PQDEs along with their sources are mentioned. The collected PQD signals were transformed into RGB T-F images using ALST. Finally, the PQDE images were fed to the proposed CNN model for diagnosis of PQDEs. The classification performance of proposed framework on real life PQDE is reported in Table V. It is evident from Table V, that the performance of proposed

Table IV. Information of collected real-life PQDEs

PQDE Description	Source of collected PQDE data
Sag	IEEE Dataport [29]
Harmonics	Kaggle [30]
Interruption	Kaggle [30]
Transient	IEEE Dataport [31]
Notch	Kaggle [30]

Table V. Validation Performance using real-life PQD data

Accuracy

(%)

Precision

(%)

Specificity

(%)

98.18

98.13

99.64

Frame work with real life data has been found to be little lower than the simulation data. This may be due to the dearth of availability of large real-life PQDE signal dataset. Nevertheless, the performance of the proposed CNN model is reasonably satisfactory and hence can be used for accurate real-life power quality monitoring.

H. Comparative analysis with state of-the-art techniques

The comparative study of proposed framework with some state of-the-art PQDE detection techniques and the results are displayed in Table VI. It may be observed from Table V that the proposed framework based on ASLT and CNN provided almost comparable and even better than some of the existing methodologies. The distinct advantage of the proposed framework is that it can classify single, double as well as triple class PQD event automatically with no dependency on manual feature extraction. The entire framework is automated and is therefore suitable for power quality monitoring in in real-time environment.

Table. VI. Comparisons of the proposed technique with other state-of-art techniques

Reference no.	PQDE classes	Feature extraction mode	Accuracy (%)
[32]	11	Manual	97.10
[33]	22	Manual	99.09
[34]	14	Manual	99.46
[20]	10	Manual	99.67
[15]	14	Manual	97.29
[35]	13	Manual	99.37
[36]	13	Automated	99.46
This work	22	Automated	99.52

In this contribution, an automated, accurate and robust framework based on ASLT and CNN has been presented for diagnosis of single, double and triple class PQDEs. For this purpose, the different PQDEs were analyzed in TF frame utilizing ASLT based signal processing technique. It has been observed that ASLT can provide better resolution with improved visibility of different events in T-F plane even when the SNR is very low. Unlike ST, no optimization of Gaussian window is necessary to improve time-frequency resolution for analysis of noisy PQDEs. Thus, ASLT can distinguish different PQDEs in noisy environment which conventional ST cannot. To classify the PQ events, a customized lightweight CNN architecture was designed to classify the PQDE signal encoded T-F images. In addition, several benchmark CNN models were trained for the purpose of comparison. The proposed CNN architecture not only achieved the best mean recognition accuracy among other benchmark CNN configurations but also is fast and computationally efficient. Thus, it can be concluded that the proposed CNN architecture can effectively be utilized for diagnosis of the various PQDEs both in noiseless and noisy environment. The accuracy of the proposed framework has been found to be comparable and even better than the state of-the-art techniques. Besides, the proposed framework has shown satisfactory performance with real-life PQDE data. Thus, being noise immune, fast and accurate the proposed framework is potentially worthy for online monitoring of PQD events in power distribution network.

Ethical Approval:

(Applicable for both human and/ or animal studies. Ethical committees, Internal Review Boards and guidelines followed must be named. When applicable, additional headings with statements on consent to participate and consent to publish are also required)

Not applicable

Competing interests:

(always applicable and includes interests of a financial or personal nature)

Not applicable

Authors' contributions

(applicable for submissions with multiple authors)

Subhajit Mukherjee: Paper writing

Soumya Chatterjee: Conceptualization

Ratan Mandal: Editing

Funding

(details of any funding received)

There is no funding provided to carry out the research work.

Availability of data and materials

(a statement on how any datasets used can be accessed)

Data can be made available upon request.

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No competing interests reported.

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Deep Learning Aided Power Quality Disturbance Detection with Improved Time-frequency Resolution Employing Adaptive Superlet Transform

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Abstract

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Introduction

PQD EVENT GENERATION

THEORETICAL BACKGROUND

RESULT AND DISCUSSIONS

G. Performance analysis with real-life PQD data

CONCLUSIONS

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References

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