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###### Abstract

High-impedance faults (HIF) are difficult to detect because of their low
current amplitude and highly diverse characteristics. In recent years, machine
learning (ML) has been gaining popularity in HIF detection because ML
techniques learn patterns from data and successfully detect HIFs. However, as
these methods are based on supervised learning, they fail to reliably detect
any scenario, fault or non-fault, not present in the training data.
Consequently, this paper takes advantage of unsupervised learning and proposes
a convolutional autoencoder framework for HIF detection (CAE-HIFD). Contrary
to the conventional autoencoders that learn from normal behavior, the
convolutional autoencoder (CAE) in CAE-HIFD learns only from the HIF signals
eliminating the need for presence of diverse non-HIF scenarios in the CAE
training. CAE distinguishes HIFs from non-HIF operating conditions by
employing cross-correlation. To discriminate HIFs from transient disturbances
such as capacitor or load switching, CAE-HIFD uses kurtosis, a statistical
measure of the probability distribution shape. The performance evaluation
studies conducted using the IEEE 13-node test feeder indicate that the CAE-
HIFD reliably detects HIFs, outperforms the state-of-the-art HIF detection
techniques, and is robust against noise.

###### keywords:

high-impedance fault; power system protection; unsupervised learning; deep
learning; convolutional autoencoder; convolutional neural network

14 12 3623 Academic Editors: Djaffar Ould-Abdeslam, Igor Simone Stievano and
Riccardo Trinchero 11 May 2021 16 June 2021 18 June 2021
https://doi.org/10.3390/en14123623 Deep Learning for High-Impedance Fault
Detection: Convolutional Autoencoders Deep Learning for High-Impedance Fault
Detection: Convolutional Autoencoders Khushwant Rai , Farnam Hojatpanah ,
Firouz Badrkhani Ajaei  and Katarina Grolinger * Khushwant Rai, Farnam
Hojatpanah, Firouz Badrkhani Ajaei and Katarina Grolinger Rai, K.; Hojatpanah,
F.; Badrkhani Ajaei, F.; Grolinger, K. Correspondence<EMAIL_ADDRESS>Tel.:
+1-519-661-2111 (ext. 81407)

##  1 Introduction

High-impedance faults (HIF) typically occur when a live conductor contacts a
highly resistive surface Wang et al. (2018); Gautam and Brahma (2013); Cui et
al. (2019); Ghaderi et al. (2017). They commonly have characteristics such as
asymmetry of the current waveform, randomness, and non-linearity of the
voltage-current relationship. These characteristics are diverse and are
affected by multiple factors including surface types and humidity conditions
Ghaderi et al. (2017). As a result, the HIF current magnitude typically ranges
from 0 to 75 A Wang et al. (2018). Such low current magnitudes compared to
normal load current levels together with a high diversity of characteristics
and patterns make HIFs difficult to detect. Specifically, the conventional
overcurrent relays fail to discriminate most HIFs from load unbalance Wang et
al. (2018); Gautam and Brahma (2013); Wang et al. (2019). Nevertheless, the
arcing ignition caused by an HIF is a safety hazard Ghaderi et al. (2017);
Chaitanya et al. (2020). Moreover, undetected HIFs have been reported to cause
instability of renewable energy systems Wang et al. (2017). As a result,
reliably detecting and clearing HIFs in a timely manner are crucial to ensure
the safety of personnel and maintain the power system integrity Ghaderi et al.
(2017); Chaitanya et al. (2020); Wang et al. (2019).

Various HIF detection techniques have been proposed. The harmonic-based
detection is one of the most common techniques Wang et al. (2018); Lee (1982);
Emanuel et al. (1990); Jeerings and Linders (1990, 1991); Yu and Khan (1994).
It operates well when the measured signals contain a large amount of
harmonics, but it loses sensitivity when the HIF is far from the relay Wang et
al. (2018). An HIF detection scheme based on a power line communication system
is proposed by Milioudis et al. Milioudis et al. (2015). This method is
successful in detecting and locating HIFs, but requires costly communication
systems and is not suitable for large and complex networks Mortazavi et al.
(2019).

The discrete wavelet transformation-based HIF detection technique Sedighi et
al. (2005) operates by examining the measured signals in both the time and
frequency domains. Although this method reduces the HIF detection delay, its
performance is highly dependent on the choice of the mother wavelet and is
adversely affected by the presence of unbalanced loads and noise Soheili and
Sadeh (2017).

HIF detection by Kalman Filtering Girgis et al. (1990) is based on tracking
randomness in the current waveform. Because the small HIF current does not
cause significant variations in the current waveforms seen by the relay at the
substation Chakraborty and Das (2019), this approach exhibits low sensitivity.

The approach based on mathematical morphology Gautam and Brahma (2013) detects
close-in HIFs but is not sufficiently reliable in presence of non-linear loads
and under remote HIFs Soheili and Sadeh (2017). Empirical mode decomposition
(EMD) Xue et al. (2017) and variational mode decomposition (VMD) Chaitanya et
al. (2020); Wang et al. (2019) have been recently proposed for HIF detection.
These techniques operate by extracting HIF-related features from the signals.
However, the EMD-based method suffers from modal mixing and is sensitive to
noise Yao et al. (2019). On the other hand, the VMD-based technique is more
robust against noise, nevertheless, it requires a large number of
decomposition modes, as well as a high sampling frequency to perform well,
which results in a large computational burden. Moreover, the VMD technique
utilized in Wang et al. (2019) for HIFs detection cannot reliably detect HIFs
when a large non-linear load is in operation.

In recent years, machine learning (ML) approaches have been gaining
popularity. A support vector machine (SVM)-based model is used with features
extracted by VMD for HIF detection in distribution lines incorporating
distributed generators Chaitanya et al. (2020). This method prevents false
detection of switching events as HIFs; however, it is sensitive to noise for
signal to noise ratios (SNR) below 30 dB. Moreover, the transformations
associated with the VMD require high computational capability Ghaderi et al.
(2017). An artificial neural network (ANN) is combined with discrete wavelet
transforms (DWT) for HIF detection in medium-voltage networks. The DWTs are
responsible for extracting the relevant features from the current waveforms,
whereas the ANN acts as a classifier using those extracted features Baqui et
al. (2011). Probabilistic neural networks and various fuzzy inference systems
have also been combined with wavelet transform (WT) for HIF detection Tonelli-
Neto et al. (2017); Moravej et al. (2015). In another study Wang and
Dehghanian (2020), a modified Gabor WT is applied on the input signal to
extract features in the form of two dimensional (2-D) scalograms. The
classifiers such as adaptive neuro-fuzzy inference system and SVM are utilized
along with DWT-based feature extraction to detect HIFs and to discriminate
them from other transients in medium-voltage distribution systems Veerasamy et
al. (2019). The neural networks are sensitive to frequency changes, whereas
the WT faces challenges in terms of selecting the mother wavelet. The decision
tree algorithm with the fast Fourier transform is also an alternative
approach, but it is sensitive to noise Sheng and Rovnyak (2004).

Recurrent neural network (RNN)-based long short term memory (LSTM) approach is
used with features obtained by DWT analysis to detect the HIFs in the solar
photovoltaic integrated power system Veerasamy et al. (2021). However, this
method detects HIFs with a success rate of only 92.42% and, moreover, this
study uses DWT-based features which are sensitive to noise Soheili and Sadeh
(2017). In another study, the HIFs were detected and classified with 2-D
convolutional neural network (CNN) which employs supervised learning to learn
from the extracted features Wang and Dehghanian (2020). This method was
accurate in the presented experiments; however, as it is a supervised
learning-based method, it may fail to reliably detect HIF and non-HIF
scenarios that are not present in the training data.

All reviewed ML studies apply a supervised approaches to learn the mapping
from the input to the output based on a limited set of HIF and non-HIF
scenarios present in the training set. Here, the non-HIF scenario refers to
normal steady-state operation and any transient response to non-HIF
disturbance, such as capacitor switching and load variations. A supervised
learning system may fail to reliably identify any fault scenario or any non-
fault disturbance which is not present in the training set. However, there is
a wide range of non-fault operating conditions and it is difficult to include
them all in the training set. Therefore, a different way of training ML models
is required. Moreover, the existing technical literature on ML-based HIF
detection relies on features extracted by resource intensive signal processing
and data transformation techniques L’Heureux et al. (2017).

Consequently, this paper proposes the convolutional autoencoder (CAE)
framework for HIF detection (CAE-HIFD), which utilizes an unsupervised
approach that learns solely from the fault data, thus avoiding the need to
take into account all possible non-fault scenarios in the learning stage. The
ability of the CAE to model the relationship between the data points
constituting a signal enables the CAE-HIFD to learn complex HIF patterns. The
CAE discriminates steady-state conditions from HIFs by identifying deviations
from the learned HIF patterns using cross-correlation (CC). The security
against false detection of non-HIF disturbances (e.g., capacitor and load
switching) as HIFs is achieved through kurtosis analysis.

The performance of the proposed protection strategy is evaluated through
comprehensive studies conducted on the IEEE 13-node test feeder taking into
account various HIF conditions involving seven different fault surfaces, as
well as diverse non-HIF scenarios. The results indicate that the proposed CAE-
HIFD (i) reliably detects HIFs regardless of the type of the surface involved
and the fault distance, (ii) accurately discriminates between HIFs, steady-
state operating conditions, and non-HIF disturbances, (iii) achieves higher
accuracy than the state-of-the-art HIF detection techniques, and (iv) is
robust against noise.

The paper is organized as follows: Section 2 provides an overview of
autoencoders, Section 3 presents the proposed CAE-HIFD, Section 4.5 evaluates
the performance of the CAE-HIFD, and finally Section 5 concludes the paper.

##  2 Unsupervised Learning with Autoencoders

A supervised machine learning model learns the mapping function from the input
to output (label) based on example input–output pairs provided in the training
dataset. In contrast, an unsupervised learning model discovers patterns and
learns from the input data on its own, without the need for labeled responses,
which makes this approach a go-to solution when labels are not available.
Autoencoders are trained through unsupervised learning where the model learns
data encoding by reconstructing the input Goodfellow et al. (2016). They are
commonly used for dimensionality reduction Goodfellow et al. (2016); Ghosh and
Grolinger (2020), but the non-linear feature learning capability has made them
also successful in denoising and anomaly detection Fan et al. (2018); Araya et
al. (2017); Li et al. (2019).

As shown in Figure 1, a conventional autoencoder is a feed-forward neural
network consisting of an input, an output, and one or more hidden layers. The
encoder part of the autoencoder reduces dimensionality. The input $x$ of
dimension $f$ is multiplied by the weights $W$ and, together with the bias
$b$, is passed through the activation function $\sigma$ to produce
representation $z$ of dimension $m$, $m<f$ Goodfellow et al. (2016), as
follows.

$z=\sigma(Wx+b)$ (1)

Next, the decoder attempts to reconstruct the input $x$ from the encoded value
$z$. The product of weights $W^{\prime}$ and $z$ is added to biases $c$, and
the resultant is utilized as an input to the activation function $\sigma$ to
generate the reconstructed signal $y$ as follows:

$y=\sigma(W^{\prime}z+c)$ (2)

Over a number of iterations (epochs), the autoencoder optimizes the weights
and biases by minimizing an objective function, such as mean squared error
(MSE) Goodfellow et al. (2016):

$MSE=\frac{1}{f}\sum_{i=1}^{f}(x_{i}-y_{i})^{2}$ (3)

The described feed-forward autoencoder ignores the spatial structure present
in data and, to address this issue, the CAE was introduced Masci et al.
(2011). A CAE replaces the fully connected layers of the feed-forward
autoencoder with convolutional and deconvolutional layers. The convolutional
layer performs the convolution operation on local spatial regions of the
input. The two-dimensional (2D) and one dimensional (1D) convolutions have led
to significant advancements in image processing Hossain et al. (2019) and
sensor data processing Ince et al. (2016); Wang et al. (2019);
Gholamiangonabadi et al. (2020), respectively. In this study, the CAE-HIFD
employs a 1D-CAE for HIF detection. In addition to the convolutional layer,
the encoder typically has a max-pooling layer(s) which perform(s) down-
sampling to reduce dimensionality. The decoder in the CAE reconstructs the
input with the help of transposed convolution or up-sampling layer(s).

Figure 1: Conventional Autoencoder structure.

##  3 Convolutional Autoencoder for HIF Detection

Traditionally, for fault detection, autoencoders are trained with normal data
and then used to detect abnormal operating conditions by identifying
deviations from the learned normal data Araya et al. (2017). On the contrary,
in the proposed CAE-HIFD, the CAE is trained using fault data only and
recognizes non-fault operating conditions by detecting deviations from the
learned fault scenarios. The spatial feature learning and generalization
capability of the CAE assist the CAE-HIFD to detect new HIF scenarios that are
not present in the training set. Furthermore, since the CAE is only trained on
the fault data, any non-fault cases will not be identified as HIF, which
increases the security of the proposed protection strategy.

As depicted in Figure 2, the CAE-HIFD is comprised of offline training and
online HIF detection. The analog three-phase voltage and current signals are
sampled and converted to digital signals using A/D converters. Training
happens in the offline mode using a dataset prepared from multivariate time
series consisting of three-phase voltage and current signals. The online HIF
detection uses the weights and thresholds obtained from the offline training.
As the data preprocessing step is the same for both training and detection,
the preprocessing is described first, followed by the explanation of training
and detection.

Figure 2: CAE Framework for HIF Detection (CAE-HIFD).

2

###  3.1 Data Preprocessing

The first step of data preprocessing entails the sliding window approach
applied to time-series data to transform it into a representation suitable for
the CAE. As illustrated in Figure 3, the first $n$ samples (readings) make the
first data window; thus, the data window dimension is $n$ time steps $\times$
$f$ number of features. In each iteration of the algorithm, the data window
slides for $s$ time steps, where $s$ is referred to as a stride, to create the
second data window and so on. Note that Figure 3 illustrates a case where $s$
= $n$.

Figure 3: Sliding window approach.

Each voltage and current phase signal (each feature) in the sliding window is
processed individually by differencing. The first-order $d^{1}$ and second-
order $d^{2}$ differencing of signal $y(t)$, e.g., phase A voltage, are as
follows:

$d^{1}(t)=y(t)-y(t-1)$ (4) $d^{2}(t)=d^{1}(t)-d^{1}(t-1)$ (5)

The HIF causes small distortions in the voltage and current waveforms. The
second-order differencing helps the CAE to learn and detect the HIF pattern by
amplifying these distortions and suppressing the fundamental frequency
component of each input signal. Differencing also amplifies noise;
nevertheless, the generalization and spatial feature extraction capabilities
of the CAE make the CAE-HIFD robust against noise as demonstrated in Section
4.5.

###  3.2 Offline Training

The CAE is trained solely with the fault data, and the non-fault data are only
utilized for the system validation. As illustrated in Figure 2, the
preprocessed data are passed to the CAE as one data window, $n\times f$
matrix, at a time. As shown in Figure 4, the CAE is composed of two main
components: encoder and decoder Goodfellow et al. (2016).

Figure 4: Convolutional autoencoder (CAE) structure.

The first layer in the encoder performs the 1D convolution operation on the
$n\times f$ input matrix with the kernel of size k $\times$ f. This kernel
moves across the time steps of the input and interacts with $k$ time steps
(here $k<n$) of the input window at a time; thus, during the CAE training, the
kernel learns the local spatial correlations in the input samples. There are
$m$ kernels in the first layer and each kernel convolves with input to
generate an activation map. Consequently, the output of the first layer has a
dimension of $(n-k+1)\times m$, and every column of this output matrix
corresponds to the weights of one kernel. These kernel weights are learned
during the CAE training process. Rectified linear unit (ReLU) activation
function is often used to introduce non-linearity after the convolution.
However, here LeakyReLU, a leaky version of ReLU, is used instead because ReLU
discards the negative values in the sinusoidal wave Goodfellow et al. (2016).
Next, the batch normalization layer re-scales and re-centers data before
passing them to the next layer in order to improve the training convergence.
The batch normalized data are passed to the max-pooling layer to reduce data
dimensionality and the associated computational complexity. The size of the
max-pooling operation is $p$; therefore, the output of the pooling layer is
$\frac{1}{p}$ of the convolved input. As illustrated in Figure 4, the
convolution, batch normalization, and max-pooling layers are repeated two
times to extract features on different levels of abstraction. These encoder
layers create an encoded representation of the input signal which is passed to
the decoder.

Although the encoder decreases the dimensionality of the input, the decoder
reconstructs the original signal from these encoded values. In the decoder, as
illustrated in Figure 4, the convolutional layer first generates the
activation map, and then the up-sampling operations increase the
dimensionality of the down-sampled feature map to the input vector size.
During up-sampling, the dimensionality of the input is scaled by repeating
every value along the time steps in the signal with the scaling factor set
according to the max-pooling layer size in the encoder. Similar to the
encoder, in the decoder, the convolutional and up-sampling layers are repeated
twice (Figure 4).

The CAE optimizes the weights and the biases using the back-propagation
process in which the gradient descent is applied based on the loss function,
typically MSE. In the proposed CAE-HIFD, the MSE is utilized as the loss
function for training the CAE using fault data. In an autoencoder, the MSE is
also referred to as a reconstruction error as it evaluates the similarity
between the input signal and the reconstructed signal given by the autoencoder
output. As the objective of the gradient descent algorithm is to minimize the
MSE for training data, the MSE is expected to be low for the training data and
high for any deviations from the training patterns.

In the CAE-HIFD, the CAE sees only the fault data during training, and
consequently, the trained CAE is expected to fail in reconstructing the non-
fault data input. Therefore, the MSE for the non-fault data is expected to be
higher than the MSE for the learned fault data. Traditionally, in
autoencoders, the separation between fault and non-fault data is done based on
a threshold which is determined using the MSEs of the training dataset.
However, in HIF detection, when CAE is trained with fault data, MSE is not a
reliable metric for calculating the threshold. As illustrated in Figure 5, the
differentiated fault data forms a complex pattern with a high number of
fluctuations causing the dissimilarities between the CAE output and input. The
magnitude of these fluctuations varies from $-$2.0 to 1.0 and, as a result,
even a small mismatch between input and CAE output leads to high MSE: for
example, in Figure 5a, MSE for fault data window is 0.0244. On the other hand,
in Figure 5b, MSE for steady state data window is 0.0002 because of a
relatively simpler pattern compared to HIFs and small amplitudes of
differentiated signal oscillations varying from $-$0.04 to 0.04. Consequently,
the MSE is not a reliable indicator to discriminate between HIF and non-fault
cases.

In signal processing, a metric commonly used to evaluate the similarity
between signals is the cross-correlation (CC) Chi et al. (2006) which is
defined as:

$CC=(f*g)(\tau)=\int_{-\infty}^{\infty}\overline{f(t)}g(t+\tau)dt$ (6)

where $f$ and $g$ are two signals and $\tau$ is a time shift in the signal.

Figure 5: Input and output of the CAE for (a) HIF and (b) Non-HIF scenario.

In CAE-HIFD, CC is used to measure the similarity between the CAE input and
output signals. As illustrated in Figure 2, after the CAE training is
completed, the trained CAE reconstructs all data windows from the training set
and obtains reconstructed signals. Next, for each window in the training set,
the CC value is calculated for the input signal and the corresponding CAE
output. As seen in Figure 5a, the HIF data window has a CC value of 27.677
because the input and output signals of the CAE are similar. On the contrary,
a normal steady-state operating condition data window, Figure 5b, has a low CC
value of 0.143 as the output deviates from the input. As the minimum CC value
from the training set represents the least similar input–output pair from the
training set, this minimum CC value serves as the CC threshold for separating
HIF and non-HIF cases.

The CAE perceives the responses to disturbances, such as capacitor and load
switching, to be HIFs because these disturbances cause waveform distortions.
However, these disturbances usually occur for a shorter duration of time than
HIFs making their statistical distribution different from those of HIFs and
steady-state operation. Figure 6 shows that the disturbances and HIFs both
exhibit Gaussian behavior, but the disturbances have a thinner peak and
flatter tails on the probability density function (PDF) plot. In contrast,
steady-state operation data (sinusoidal waveforms) have an arcsine
distribution.

To distinguish disturbances from HIFs, the statistical metrics kurtosis is
used. The kurtosis provides information about the tailedness of the
distribution relative to the Gaussian distribution Chi et al. (2006). For
univariate data $y_{1},y_{2},y_{3},…,y_{n}$ with standard deviation $s$ and
mean $\bar{y}$, the kurtosis is:

$K=\frac{\sum_{i=1}^{n}(y_{i}-\bar{y})^{4}/n}{s^{4}}$ (7)

As Figure 6 shows, flatter tails and thinner peaks results in higher kurtosis
values. For example, the distribution of the differentiated capacitor
switching disturbance in Figure 6b has a kurtosis value of $K=76.6$ which is
higher than the $K=1.9$ for the HIF distribution in Figure 6f.

The kurtosis is calculated from the training set individually for each data
window after applying differencing. To prevent misinterpretation of the $K$
values and avoid treating HIFs as non-fault disturbances, the kurtosis
threshold must be higher than every $K$ value present in the training set.
Accordingly, the kurtosis threshold is the value below which all the $K$
values of the training data lie.

Figure 6: Kurtosis analysis: (a) differentiated voltage signal corresponding
to a capacitor switching disturbance, (b) PDF of the voltage signal
corresponding to a capacitor switching disturbance (c) differentiated normal
steady-state voltage, (d) PDF of the normal steady-state voltage, (e)
differentiated HIF voltage, and (f) PDF of the HIF voltage.

The artifacts of the offline training are the CC threshold, the learned CAE
weights, and the kurtosis threshold. These artifacts are used for online HIF
detection.

###  3.3 HIF Detection

The online HIF detection algorithm uses the artifacts generated by offline
training as illustrated in Figure 2. First, the analog input signal is
converted to digital by the A/D converter and the data preprocessing module
generates data windows which proceed through the remaining HIF detection
components, one window at the time.

The value of kurtosis is calculated for each data window and compared with the
corresponding threshold obtained from the offline training. Any data window
with the kurtosis value above the threshold is identified as a non-fault
disturbance case for which the CAE is disabled because there is no need for
additional processing as the signal is already deemed to be a disturbance.
Next, the timer is reset for processing the next input signal segment.

If the kurtosis value is less than the threshold, the data window is sent to
the trained CAE which encodes and reconstructs the signal. As the CAE is
trained with fault data, for HIFs, the reconstructed signal is similar to the
original signal. This similarity is evaluated by calculating the CC between
the reconstructed signal and the original signal. If the CC value of the data
window is greater than the CC threshold determined in the training process,
the signal is identified to be corresponding to a HIF.

Under transient disturbances, such as capacitor switching, the value of CC may
exceed the corresponding threshold for a short time period immediately after
the inception of disturbance. False identification of disturbances as HIFs is
prevented using a pick-up timer. The timer is incremented when the CC exceeds
its threshold and is reset to zero whenever the CC or K indicates a non-HIF
condition, as shown in Figure 2. A tripping (HIF detection) signal is issued
when the timer indicates that the time duration of the HIF exceeds a
predetermined threshold.

##  4 Evaluation

This section first describes the study system and the process of obtaining
data for the performance verification studies. Next, the details of CAE-HIFD
model training and the effects of different CAE-HIFD components are presented.
Furthermore, the response of the CAE-HIFD to different case studies is
demonstrated. Finally, the CAE-HIFD performance is compared with other HIF
detection approaches, and its sensitivity to noise is examined.

###  4.1 Study System

The dataset utilized for model training and evaluation is obtained through
time-domain simulation studies performed in the PSCAD software. The study
system is the IEEE 13 node test feeder of Figure 7, a realistic 4.16 kV
distribution system with a significant load unbalance. This test feeder was
selected in order to examine the system behavior under challenging load
unbalance conditions and because of its common use in HIF studies Kersting
(1991). Detailed information regarding the line and the load data are provided
in the Appendix A, and further information about this benchmark system can be
found in Kersting (1991). For an accurate representation of the HIF behavior,
the antiparallel diode model of Figure 8, Gautam and Brahma (2013); Cui et al.
(2019); Chaitanya et al. (2020); Wang et al. (2019); Soheili et al. (2018) is
utilized. The HIF model parameters representing seven different faulted
surface types are given in Table 4.1 Gautam and Brahma (2013); Kavi et al.
(2018). These parameters lead to effective fault impedances as high as 208
ohms in 4.16 kV distribution system.

Figure 7: IEEE 13 node test feeder. Figure 8: Nonlinear HIF model utilized for
time-domain simulation studies.

In total, 210 faulty cases were simulated: 7 different surfaces, 10 fault
locations, and 3 phases. After the windowing technique, this resulted in 1372
HIF data windows. Additionally, the dataset obtained from simulations
contained 272 non-fault data windows. Using data obtained from simulation
studies enables considering diverse fault types, locations, and surfaces while
obtaining such diverse data from real-world experiments would be difficult or
even impossible. Of the fault data, 80% are assigned for the model training
and the rest for testing. As CAE-HIFD requires only fault data for training,
all non-fault data are assigned for testing. Of the training set, 10% are used
as a validation set for the hyperparameter optimization.

[H] HIF Model parameters For different surfaces. Surfaces R1 ($\Omega$) R2
($\Omega$) V1 ($V$) V2 ($V$) Wet Sand 138 $\pm$ 10% 138 $\pm$ 10% 900 $\pm$
150 750 $\pm$ 150 Tree Branch 125 $\pm$ 20% 125 $\pm$ 20% 1000 $\pm$ 100 500
$\pm$ 50 Dry Sod 98 $\pm$ 10% 98 $\pm$ 10% 1175 $\pm$ 175 1000 $\pm$ 175 Dry
Grass 70 $\pm$ 10% 70 $\pm$ 10% 1400 $\pm$ 200 1200 $\pm$ 200 Wet Sod 43 $\pm$
10% 43 $\pm$ 10% 1550 $\pm$ 250 1300 $\pm$ 250 Wet Grass 33 $\pm$ 10% 33 $\pm$
10% 1750 $\pm$ 350 1400 $\pm$ 350 Rein. Concrete 23 $\pm$ 10% 23 $\pm$ 10%
2000 $\pm$ 500 1500 $\pm$ 500

###  4.2 CAE-HIFD Model Training

The performance of the CAE is evaluated using accuracy (Acc), security (Sec),
dependability (Dep), safety (Saf), and sensibility (Sen) Ghaderi et al.
(2015).

$\displaystyle Acc$ $\displaystyle=\frac{TP+TN}{TP+TN+FP+FN}\times 100\%$ (8)
$\displaystyle Sec$ $\displaystyle=\frac{TN}{TN+FP}\times 100\%$ (9)
$\displaystyle Dep$ $\displaystyle=\frac{TP}{TP+FN}\times 100\%$ (10)
$\displaystyle Saf$ $\displaystyle=\frac{TN}{TN+FN}\times 100\%$ (11)
$\displaystyle Sen$ $\displaystyle=\frac{TP}{TP+FP}\times 100\%$ (12)

Here, true positives (TP) and true negatives (TN) are the numbers of correctly
identified fault and non-fault cases, and false negatives (FN) and false
positives (FP) are the numbers of miss-classified fault and non-fault cases.
The accuracy is the percentage of overall correctly identified states, the
security is the healthy state detection precision, the dependability is the
fault state detection precision, the safety is resistance to faulty tripping,
and the sensibility is resistance to unidentified faults Ghaderi et al.
(2015). Note that dependability is also referred to as true positive rate
(TPR) or sensitivity, while security is referred to true negative rate (TNR)
or specificity Araya et al. (2017).

To achieve high accuracy, the CAE hyperparameters must be tuned; this includes
the number and size of kernels, learning rate, optimizer, and batch size.
Hyperparameter tuning is performed with grid search cross-validation (GSCV),
wherein an exhaustive search is conducted over pre-specified parameter ranges.
The GSCV determines the best performing parameters based on the scoring
criteria provided by the model, in our case accuracy. The tuned CAE has
256-128-128-256 filters of size $3\times 3$ in the four convolution layers,
the optimizer is Adam, the learning rate is 0.001, and the batch size is 16.

The window size after differencing is 166 voltage/current samples, which
corresponds to one cycle of the 60 Hz power frequency signal sampled at a rate
of 10 kHz. The proposed method does not operate based on the fundamental
frequency components of the input signal and, thus, is not sensitive to
frequency deviations as shown in Section 4.4.7. The sliding window stride
during training impacts the CAE-HIFD performance: its value is determined on
the training dataset. Once the system is trained, it is used with the stride
of one. The upper bound for the stride value is 166 as a higher value would
lead to skipped samples. The performance metrics for varying stride values are
shown in Figure 9. It can be observed that the safety and dependability are
not affected by the change in the stride value as none of the non-HIF cases
are misclassified as a HIF case. The accuracy, security, and sensibility are
100% for the stride size of 166, and for shorter strides, these metrics are
slightly lower. As the stride decreases, a few data windows are mistakenly
identified as faults resulting in decrease in security, sensibility, and
accuracy. Hence, the stride value of 166 is selected for the sliding window in
the preprocessing of the training dataset.

Figure 9: Impact of the sliding window stride on the performance metrics of
the CAE-HIFD.

The CAE-HIFD prevents false detection of disturbances as HIFs using kurtosis
value. As the distributions of the HIFs and disturbances both exhibit Gaussian
behavior, an HIF window can have a $K$ value close to the $K$ value of a
disturbance. The kurtosis threshold is determined starting from the kurtosis
values for which all HIFs scenarios in the training data lie below this
threshold: in this case 10. Next, accuracy on the training data is examined
with thresholds close to this initial threshold. As illustrated in Figure 10,
the accuracy is 100% when kurtosis thresholds are between 9.5 and 10.5. The
accuracy decreases when threshold is below 9.5 because some of the HIF
scenarios are mistakenly detected as non-HIF scenarios ($FN>0$). Furthermore,
the threshold above 10.5 leads to low accuracy as some non-HIF scenarios are
falsely declared as HIFs ($FP>0$). Consequently, the kurtosis threshold of 10
is selected to discriminate the non-fault disturbances from the HIFs.

Figure 10: Impact of the kurtosis threshold on the accuracy of the CAE-HIFD.

###  4.3 Effects of CAE-HIFD’s Components

The proposed CAE-HIFD uses differencing and cross-correlation in addition to
the main component, the CAE, to increase various performance metrics.
Furthermore, kurtosis is utilized to improve the security of the proposed
method. Consequently, as depicted in Table 4.3, the CAE-HIFD achieves 100%
performance in all five considered metrics regardless of the surface type,
inception angle, and fault locations.

Additionally, Table 4.3 includes variants of the CAE-HIFD with only some of
the three components included. With only CC and kurtosis, the accuracy and
sensibility drop to nearly 51%, and the security decreases by 99.6%. In the
absence of differencing, the CAE cannot learn patterns to distinguish between
the HIF and the non-HIF data windows and, as a result, a large number of the
non-HIF data windows are falsely classified as the HIF which means high FP,
thus low security.

To examine the impact of CC, the traditional MSE is used in place of CC to
measure the similarity of the input and reconstructed signal. As shown in
Table 4.3, in the absence of CC, the values of accuracy and sensibility drop
to nearly 50%. This happens because the MSEs calculated for the HIF and non-
HIF data windows are similar and, thus, non-HIFs are falsely detected as HIFs.
Furthermore, the security value is low (0.40%), whereas the dependability
value is high (92.67%) as there are only a few TN and FN compared to TP and
FP.

[H] Impact of differencing, cross-correlation, and kurtosis on CAE-HIFD
performance. Model Acc Saf Sen Sec Dep Proposed CAE-HIFD 100 100 100 100 100
CAE with CC, K 51.19 100 51.10 0.37 100 CAE with K, Diff 48.29 4.76 50.10 0.40
92.67 CAE with CC, Diff 96.38 100 93.31 92.70 100 CAE with CC 51.10 100 50.64
1.84 100 CAE with Diff 48.9 37.93 49.51 4.04 93.43 CAE with K 89.64 96.67
84.16 82.77 96.35

Omitting the kurtosis evaluation results in only a small increase in the
number of FP cases which are the non-fault disturbances falsely declared as
HIFs. Therefore, as shown in Table 4.3, all the performance metrics values
decrease by less than 8%.

Finally, only one out of the three components is included in the CAE-HIFD
framework. Whereas the simultaneous use of differencing and cross-correlation
achieves relatively high performance metrics, with only one of the two
components, there is a major decrease in security (more than 95%). With
kurtosis only, all metrics are between 82% and 97% in comparison to 100%
obtained in the presence of all three components. This is caused by the
absence of differencing which assists in amplifying sign wave distortions and
omission of cross-correlation which facilitates signal comparisons. The
results shown in Table 4.3 highlight the necessity of each CAE-HIFD component
and the contribution of each component to the HIF detection performance.

###  4.4 CAE-HIFD Response to Different Case Studies

In this section, seven case studies have been conducted to depict the response
of the proposed CAE-HIFD.

####  4.4.1 Case Study I—Close-in HIF

Figure 11 illustrates the performance of the CAE-HIFD under both normal and
HIF conditions. In this case study, the HIF is applied at Node 632 starting at
0.05 s, as seen in Figure 11a. The input voltage and current signals observed
at the substation relay are shown in Figure 11b,c, and the kurtosis calculated
from those voltages and currents is displayed in Figure 11d. During normal
operation, the kurtosis is below the threshold; upon the HIF inception, it
raises over the threshold for approximately 8–10 ms returning quickly back to
below threshold values. The HIF causes the CC value to rise above the
threshold, Figure 11e, and, therefore, a trip signal is issued approximately
60 ms after the HIF inception as seen in Figure 11f.

Figure 11: CAE-HIFD performance under normal and close-in HIF conditions: (a)
HIF current,(b) three-phase input voltages, (c) three-phase input currents,
(d) kurtosis, (e) cross-correlation, and (f) trip signal.

####  4.4.2 Case Study II—Remote HIF

Figure 12 depicts the result of the CAE-HIFD in presence of a remote HIF: the
HIF is applied at Node 652 starting at 0.05 s, as seen is Figure 12a. The
input voltage and current signals are observed in Figure 12b,c, and the
calculated kurtosis is shown in Figure 12d. Due to the remote location of HIF,
the HIF influence on the voltages and current signals is highly attenuated. As
a result, the kurtosis surpasses the threshold for shorter duration of time
(approximately 1–2 ms) remove as compared to Case study I. As shown in Figure
12e, the CC value raises above the threshold after the inception of HIF.
Consequently, a trip signal is issued approximately 50 ms after the HIF
inception as seen in Figure 12f.

Figure 12: CAE-HIFD performance under normal and remote HIF conditions: (a)
HIF current,(b) three-phase input voltages, (c) three-phase input currents,
(d) kurtosis, (e) cross-correlation, and (f) trip signal.

####  4.4.3 Case Study III—Capacitor Switching

The proposed HIF detection method successfully discriminates HIFs from
switching events as demonstrated in Figure 13 with a three-phase capacitor
bank located at node 675. Figure 13a depicts phase A current caused by the
capacitor energization at t = 0.05 s. The current and voltage signals seen by
the relay at the substation exhibit significant oscillations, as shown in
Figure 13b,c. This switching event causes sudden increase in the kurtosis for
a short duration of time, approximately 15 ms (Figure 13d). Although the CC
for the switching event is higher than its threshold, Figure 13e, this
disturbance is not falsely identified as an HIF, due to the high kurtosis
value. Moreover, the CC for the remaining non-HIF signal is below the
threshold. Consequently, a trip signal is not issued throughout the switching
event, Figure 13f.

Figure 13: CAE-HIFD performance under a capacitor switching scenario: (a)
capacitor current,(b) three-phase input voltages, (c) three-phase input
currents, (d) kurtosis, (e) cross-correlation, and (f) trip signal.

####  4.4.4 Case Study IV—Non-linear Load

Figure 14 shows the performance of the proposed CAE-HIFD in presence of a non-
linear load which causes significant harmonics. The load at node 634 is
replaced by a DC motor fed by a six-pulse thyristor rectifier. The motor is
started at t = 0.05 s. Figure 14a illustrates the phase A current of the non-
linear load, while Figure 14b,c show voltages and currents measured by the
relay at the substation. Although the CC is higher than its threshold (Figure
14e), the trip signal (Figure 14f) is not issued because the kurtosis
surpasses its threshold (Figure 14d).

Figure 14: CAE-HIFD performance under non-linear load switching: (a) non-
linear load current,(b) three-phase input voltages, (c) three-phase input
currents, (d) kurtosis, (e) cross-correlation, and (f) trip signal.

####  4.4.5 Case Study V—Transformer Energization

This case study investigates the performance of the CAE-HIFD under a
transformer energization scenario: the transformer at node 633 is energized at
t = 0.05 s. The inrush current for phase-A is shown in Figure 15a while Figure
15b,c display voltages and currents measured at the substation. Both the
resulting kurtosis shown in Figure 15d, and the CC shown in Figure 15e are
below their corresponding thresholds. As a result, the proposed protection
strategy does not cause any unnecessary tripping (Figure 15f) under the
transformer energization scenario.

Figure 15: CAE-HIFD performance under inrush currents: (a) Inrush current, (b)
three-phase input voltages, (c) three-phase input currents, (d) kurtosis, (e)
cross-correlation, and (f) trip signal.

####  4.4.6 Case Study VI—Intermittent HIFs

This case study demonstrates the effectiveness of the proposed CAE-HIFD in
detecting intermittent HIFs. A tree branch momentarily connects the phase-A to
the ground for approximately 3.5 cycles (55 ms) as illustrated in Figure 16a.
The voltage and current signals shown in Figure 16b,c are measured by the
relay at the substation. As depicted in Figure 16d, the kurtosis does not
exceed the threshold. The CC in Figure 16e crosses the threshold during the
intermittent faults. As shown in Figure 16f, the trip signal is issued after
50 ms. The trip signal is reset after the intermittent fault is cleared.

Figure 16: CAE-HIFD performance under intermittent HIF condition: (a) fault
current, (b) three-phase input voltages, (c) three-phase input currents, (d)
kurtosis of the input, (e) cross-correlation, and (f) trip signal.

####  4.4.7 Case Study VII—Frequency Deviations

To demonstrate the effectiveness of the proposed method in presence of
frequency deviations, the system frequency is increased to 61 Hz in this case
study. The HIF is initiated at t = 0.05 s. Figure 17a,b represent currents and
voltages measured by the relay at the substation. As shown in Figure 17c,
before the HIF takes place, the kurtosis is below the threshold. As the the
HIF samples enters the sliding window, the kurtosis exceeds the threshold
because the distribution suddenly changes during the transition. Next, the
kurtosis returns to values below the threshold. The CC in Figure 17d is above
the CC threshold; therefore, the system trips within three cycles of the HIF
inception.

Figure 17: CAE-HIFD performance under 61 Hz fundamental frequency: (a) three-
phase input voltages, (b) three-phase input currents, (c) kurtosis, (d) cross-
correlation, and (e) trip signal.

###  4.5 Comparison with Other Approaches

This section first compares the proposed CAE-HIFD with other supervised and
unsupervised learning algorithms. The two supervised models selected for the
comparison are: support vector machine (SVM) Chaitanya et al. (2020) and
artificial neural network (ANN) Baqui et al. (2011). As supervised models
require the presence of both, HIF and non-HIF data in the training set, these
models are trained with a dataset containing an equal number of the HIF and
non-HIF instances. Moreover, as those models have originally been used with
the DWT applied on the current waveform Chaitanya et al. (2020); Baqui et al.
(2011), DWT is used here too. DWT extracts features by decomposing each phase
current into seven detail level coefficients and one approximate level
coefficient using the db4 mother wavelet. The features are formed by computing
the standard deviation of coefficients at each level; therefore, eight
standard deviations from each phase form a new input sample with 24 elements
Baqui et al. (2011). As with CAE-HIFD, the SVM and ANN hyperparameters are
tuned using GDCV. The SVM kernel is RBF with $\gamma$ of 0.05. The ANN has
three layers with 24-18-1 neurons, the activation function for input and
hidden layers is ReLU, and binary cross-entropy is the loss function.

As other studies have only used supervised learning, to examine unsupervised
learning techniques, variations of the proposed approach are considered in
this evaluation. Figure 18 shows the flowchart for the unsupervised ML models.
Preprocessing, kurtosis, and CC calculation components are exactly the same as
in the proposed CAE-HIFD, while two options are considered for the autoencoder
algorithm and the training dataset. As the autoencoder, the proposed CAE-HIFD
uses CAE while here we consider a variant of recurrent neural network, gated
recurrent units autoencoder (GRU-AE). GRU-AE is selected because it is
successful in extracting patterns from time-series data such as those present
in the current and voltage signals. The GRU-AE tuned with GDCV has two hidden
layers, each one with 32 GRU cells and the ReLU activation function. For both,
CAE-HIFD and GRU-AE, two types of studies are conducted: training on HIFs data
only and training on non-HIFs data only.

Figure 18: Flowchart for the alternative unsupervised HIF detection models.

The results of the comparison between CAE-HIFD and the other approaches are
shown in Table 4.5. It can be observed that CAE-HIFD outperforms other
approaches and is the only one not susceptible to false tripping as indicated
by the security metrics. In addition, the CAE-HIFD trained only with HIF data
is highly efficient in discriminating non-HIF instances by detecting
deviations from the learned HIF patterns. This prevents the algorithm from
false tripping in the case of a new non-HIF pattern not present in the
training set. The results of the studies presented in Table 4.5 indicate that
the CAE-HIFD achieves equally good results regardless of whether it is trained
on the HIF data or non-HIF data; however, when trained with non-HIF data,
there is a risk of identifying new non-HIF patterns as HIFs. The supervised
learning-based approaches category can only recognize the pattern present in
the training set and, thus, may recognize new non-HIF events as HIFs. Overall,
the proposed CAE-HIFD achieves better performance than the other approaches.

[H] Comparison of CAE-HIFD with other HIF detection approaches. Model Acc Saf
Sen Sec Dep Other Approaches-Supervised DWT+SVM Chaitanya et al. (2020) 97.97
100 97.78 78.99 100 DWT+ANN Baqui et al. (2011) 97.72 100 97.55 76.47 100
Variants of our approach-Unsupervised Train on non-faults GRU-AE 99.92 100
96.92 99.92 100 Proposed CAE-HIFD 100 100 100 100 100 Train on faults GRU-AE
34.61 32.24 83.22 97.52 5.66 Proposed CAE-HIFD 100 100 100 100 100

###  4.6 Robustness of the Proposed CAE-HIF against Noise

To examine CAE-HIFD robustness against noise, studies are conducted by
introducing different levels of noise. The white Gaussian noise is considered
because it covers a large frequency spectrum. The noise is added to the
current signals because current waveforms are more susceptible to noise Wang
et al. (2018). As shown in Figure 19, the proposed CAE-HIFD approach is immune
to noise when signal to noise ratio (SNR) value is higher than 40 dB. In a
case of high nose, SNR below 40 dB, the accuracy reduces to 97%. Thus, more
than one consecutive window is needed to be processed before making a tripping
decision in order to avoid undesired tripping and to ensure accurate HIF
detection. Therefore, three consecutive windows are utilized in all
performance evaluation studies in order to accurately detect all HIFs.
Increasing the timer threshold improves the resiliency against unnecessary
tripping, but prolongs HIF detection time. Even with the extremely noisy
condition of 1 dB SNR, the accuracy, security, and sensibility do not fall
below 97.65%, 94.03%, 96.28%, respectively. The reason behind this robustness
is the CAE de-noising ability and strong pattern learning capability. The
inherent de-noising nature of the autoencoders assists the CAE to generalize
the corrupted input. Additionally, the CAE-HIFD learns the complex HIF
patterns because of spatial feature learning proficiency of the CAE. The model
accurately detects non-HIF scenarios under considered noise levels; hence, the
safety and dependability remains at 100% even with high levels of noise.
Moreover, the values of other performance metrics are also greater than 90%
throughout the SNR range of 5dB to 50dB demonstrating noise robustness of the
CAE-HIFD.

Figure 20 shows CAE-HIFD performance in presence of noise of 20 dB SNR. Before
the HIF inception at 0.05 s, despite the significant noise, the kurtosis
(Figure 20b) and the CC (Figure 20c) remain below their thresholds. The CC
surpasses the threshold upon HIF inception and, as a result, the designed
protection system issues trip signal (Figure 20d).

Figure 19: Effect of noise on the CAE-HIFD performance. Figure 20: CAE-HIFD
performance under 20 dB SNR: (a) three-phase input currents, (b) kurtosis,(c)
cross-correlation, and (d) trip signal.

###  4.7 Discussion

The evaluation results demonstrate that the proposed CAE-HIFD achieves 100%
HIF detection accuracy irrespective of the surface type, fault phase, and
fault location. All metrics, including accuracy, safety, sensibility,
security, and dependability are at 100% as shown in Table 4.3. Moreover, for
all considered scenarios, the system trips within three cycles after the HIF
inception.

The challenging part of machine learning for HIF detection is in the diversity
of non-fault and fault signals together with similarities between non-HIF
disturbances and HIFs. By training on faults only, the proposed approach does
not require simulation of non-fault scenarios for training. Distinguishing
HIFs from the non-HIF steady-state operation can take advantage of the
smoothness of non-HIF steady-state signal; however, non-HIF disturbances, such
as capacitor and load switching, share many characteristics (e.g., randomness
and non-linearity) with the HIF signals making it difficult for a neural
network (in our case CAE) to distinguish between them. To address this
challenge, the proposed approach takes advantage of differences in data
distributions between non-fault disturbances and HIFs and employs kurtosis to
differentiate between the two.

In experiments, 210 fault cases were considered corresponding to 1372 fault
data windows as described in Section 4.1. Signals corresponding to these
faults are different from each other as simulations included different
surfaces, fault locations, and fault phases. From these fault cases, 80% is
selected randomly for training, therefore, some cases are present only in
testing. Moreover, all the case studies presented in Section 4.4 are conducted
with data that are not seen by the proposed CAE-HIFD in training. The proposed
system successfully distinguished between fault and non-fault signals for all
scenarios, which demonstrates its abilities to detect previously unseen HIF
and non-HIF scenarios.

Frequency deviations, as well as noise, impose major challenges for the HIF
detection. Approaches that operate on the fundamental frequency components
risk failures in presence of frequency deviations. However, CAE-HIFD does not
operate based on the fundamental frequency components of the input signals
and, consequently, is not sensitive to frequency deviations as shown in
Section 4.4.7. As noise is common in distribution systems, it is important to
consider it in HIF detection evaluation. HIF detection in presence of noise is
difficult as noisy signals are accompanied by randomness and have
characteristics that resemble HIFs. Nonetheless, experiments from Section 4.6
show that CAE-HIFD remains highly accurate even in presence of significant
noise.

##  5 Conclusions

Recently, various machine learning-based methods have been proposed to detect
HIFs. However, these methods utilize supervised learning; thus, they are prone
to misclassification of HIF or non-HIF scenarios that are not present in the
training data.

This paper proposes the CAE-HIFD, a novel deep learning-based approach for HIF
detection capable of reliably discriminating HIFs from non-HIF behavior
including diverse disturbances. The convolutional autoencoder in CAE-HIFD
learns from the fault data only, which eliminates the need of considering all
possible non-HIF scenarios for the training process. The MAE commonly used to
compare autoencoder input and output is replaced by cross-correlation in order
to discriminate HIFs from disturbances such as capacitor and load switching.
To distinguish switching events from HIFs, the CAE-HIFD employs kurtosis
analysis.

The results show that CAE-HIFD achieves 100% performance in terms of all five
metrics of protection system performance, namely accuracy, security,
dependability, safety, and sensitivity. The proposed CAE-HIFD outperforms
supervised learning approaches, such as the SVM with DWT and the ANN with DWT,
as well as the unsupervised GRU-based autoencoder. The CAE-HIFD performance is
demonstrated on case studies including steady-state operation, close-in and
remote HIFs, capacitor switching, non-linear load, transformer energization,
intermittent faults, and frequency deviations. The studies on the effect of
different noise levels demonstrate that the proposed CAE-HIFD is robust
against noise for SNR levels as low as 40 dB and provides acceptable
performance for higher noise levels.

Future work will examine HIF detection from only voltage or on current signals
in order to reduce computational complexity. Furthermore, HIF classification
technique will be developed to determine the phase on which the fault
occurred.

Conceptualization, K.R.; methodology, K.R.; software, K.R. and F.H.;
validation, K.R. and F.H.; formal analysis, K.R., F.H., K.G. and F.B.A.;
investigation, K.R. and F.H.; resources, K.G. and F.B.A.; data curation, F.H.;
writing—original draft preparation, K.R. and F.H.; writing—review and editing,
K.G., F.B.A., K.R., F.H.; visualization, K.R.; supervision, K.G. and F.B.A.;
project administration, K.G. and F.B.A.; funding acquisition, K.G. and F.B.A.
All authors have read and agreed to the published version of the manuscript.

This research has been supported by NSERC under grants RGPIN-2018-06222 and
RGPIN-2017-04772.

The data are not publicly available due to privacy.

The authors declare no conflict of interest.

Abbreviations The following abbreviations are used in this manuscript:

CAE-HIFD | Convolutional Autoencoder framework for HIF Detection
---|---
CAE | Convolutional Autoencoder
HIF | High-Impedance Fault
EMD | Empirical Mode Decomposition
VMD | Variational Mode Decomposition
ML | Machine Learning
SVM | Support Vector Machine
SNR | Signal to Noise Ratio
DWT | Discrete Wavelet Transform
WT | Wavelet Transform
CNN | Convolutional Neural Network
CC | Cross-Correlation
MSE | Mean Squared Error
ReLU | Rectified Linear Unit
K | Kurtosis
Acc | Accuracy
Dep | Dependability
Saf | Safety
Sen | sensibility
TP | True Positives
TN | True Negatives
FN | False Negatives
FP | False Positives
GSCV | Grid Search Cross-Validation
ANN | Artificial Neural Network
GRU-AE | Gated Recurrent Units Autoencoder

no

## Appendix A

[H] IEEE 13 node test feeder Load Information.

Node |  Load Model |  Phase 1 (kW) |  Phase 1 (kVar) |  Phase 2 (kW) |  Phase 2 (kVar) |  Phase 3 (kW) |  Phase 3 (kVar)
---|---|---|---|---|---|---|---
634 |  Y-PQ |  160 |  110 |  120 |  90 |  120 |  90
645 |  Y-PQ |  0 |  0 |  170 |  125 |  0 |  0
646 |  D-Z |  0 |  0 |  230 |  132 |  0 |  0
652 |  Y-Z |  128 |  86 |  0 |  0 |  0 |  0
671 |  D-PQ |  385 |  220 |  385 |  220 |  385 |  220
675 |  Y-PQ |  485 |  190 |  68 |  60 |  290 |  212
692 |  D-I |  0 |  0 |  0 |  0 |  170 |  151
611 |  Y-I |  0 |  0 |  0 |  0 |  170 |  80
|  Total |  1158 |  606 |  973 |  627 |  1135 |  735

[H] IEEE 13 node test feeder Line Length and phasing.

Node A |  Node B |  Length (ft) |  Phasing
---|---|---|---
632 |  645 |  500 |  C, B, N
632 |  633 |  500 |  C, A, B, N
633 |  634 |  0 |  Transformer
645 |  646 |  300 |  C, B, N
650 |  632 |  2000 |  B, A, C, N
684 |  652 |  800 |  A, N
632 |  671 |  2000 |  B, A, C, N
671 |  684 |  300 |  A, C, N
671 |  680 |  1000 |  B, A, C, N
671 |  692 |  0 |  Switch
684 |  611 |  300 |  C, N
692 |  675 |  500 |  A, B, C, N

References

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