# A Deep Learning through DBN Enabled Transmission Line Fault Transient Classification Framework for Multimachine Microgrid Systems

Authors: Erphan Ahmmad Bhuiyan; Maeenul Azad Akhand; Shahriar Rahman Fahim; Subrata K. Sarker; Sajal K. Das
Journal: International Transactions on Electrical Energy Systems
 (2022)

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## Abstract

The reliable operation of power systems becomes a formidable job these days due to the high amount of complexities in the expanded power system networks. The power system networks often comprise microgrids that encounter over 80% of faults due to their exposure to unpredictable weather conditions, which reduce the insulation strength of the conductors which damaged the distribution system. Therefore, detection, classification, and location of such faults in the distributing systems are a must to ensure the flawless operation of the power systems. Machine learning methodologies are getting more attention to detect these types of faults due to their capability to handle complex fault information. Nevertheless, the obstacles are even now on the board as the traditional machine learning techniques rely on oversimplified frameworks that are incapable of analyzing a wide range of latent and explicit parameters and are also time-consuming. In this work, a unique defect diagnosis technique based on a multiblock deep belief network (DBN) and the fundamental discrete wavelet transform (DWT) is proposed, allowing the architecture to identify the deterministic reconstructing throughout its inputs. This method enables a strong multilevel generative network to utilize fault-related properties, decodes high variability functionalities, and requires minimal previous knowledge. The suggested approach is validated using a wide set of input data at various sampling frequencies. To evaluate the efficiency of DBN, a benchmark methodology based on the International Electrotechnical Commission (IEC) standard was used. White Gaussian Noise (WGN) was also implemented to test the envisioned network’s resilience. The findings show that the approach is capable of executing exact diagnosis procedures.


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## Body

## 1. Introduction

The world is discovering options and solutions to decrease the catastrophic impact of industrialization which is causing unnatural weather changes and the ascent of contamination. Since the future is electric, the process of generation and distribution of electricity is also finding its innovative and efficient approaches. Conventional generation, transmission, and distribution procedures are being replaced with advanced methods and technologies [1]. The microgrid is one of them, several interconnected loads and distributed energy resources (DERs) with distinctly characterized electrical boundaries which perform as a single controllable system concerning the grid [2]. Owing to the conspicuous developments in distributed generations (DG), microgrids are appearing as a vital part of the power distribution. Microgrids might incorporate different kinds of DGs, consisting of microturbines, diesel generators, battery storage, fuel cells, power devices, and sustainable power resources [3]. The duration and frequency of power interruptions are responsible for reducing the efficiency and stability of the distribution systems and microgrids can reduce these interruptions which improve the power efficiency along with durability and stability of distribution systems [4]. Microgrids can be operated in two modes, power consumption supported by the external grid, which is known as grid-connected mode, and islanded mode which can contribute independently in the case of external grid disturbances such as voltage fluctuations, frequency deviations, etc. [5].Despite all the benefits, the combination of DGs is affected by numerous protection problems, which may influence the performance of the existing protection scheme. These difficulties arise for operating, controlling, and protecting the microgrid in the case of applying numerous types of DG for power generations. Hence, an effectual protection strategy is required for secure microgrid operation and to eradicate fault occurrences and failure possibilities in microgrids [6]. The stratagem demands three essential intents: the identification of fault type, fault phase, and determination of fault location. All are to promote fault diagnosis, fault-isolation, and service-restoration operations and to improve microgrid device resilience.Over the last few years, many efforts have been endeavored by researchers to provide fault diagnosis strategies. Reference [7] proposes a mathematical model that minimizes blindness and annoyance tripping aids a model-based diagnosis procedure. However, this strategy is not proven in the condition of ambiguity. Two fault classifiers break down based on current-angle and current-magnitude, according to the method described in [8]. Consequently, the threshold selection is not reactive throughout this case. In [9], an adaptive approach is described, although it is only applicable when the presence of fault current is significant. It is also unable to identify fault categories. In [10], a method based on mathematical morphology was implemented using electromagnetic transients. To generate data sets of critical-system parameters, several framework approaches apply a threshold. An event is triggered when the measurements exceed the threshold. In [11, 12], threshold-based analysis employing Hilbert-Huang transform (HHT) and S-transform has been used. Because different thresholds are specified for different modes, these methods add a lot of complexity. The consequences of fault resistance are also not considered in these approaches. A wavelet transform (WT) based approach is proposed in [13]; the WT is used to determine whether or not there is a high-frequency transient disturbance. A digital protection procedure based on WT employing a threshold value to generate a braking signal is proposed in [14]. These approaches, from the other end, do not incorporate the islanded mode of operation. A design technique in a static switch employing WT is provided for both operational modes in [15]. However, unbalanced faults between the islanded and the main grid are not taken into account by the method. A fault determination scheme for distribution systems in DERs based on impedance is presented in [16, 17]. However, the efficacy of this method is not enough when lines are shorted and fault resistance is undefined. A protection strategy presented in [18] uses a sequence-component based technique. These studies only include IIDGs. In [19–21], wave-based fault location techniques are presented with DERs. Nonetheless, a high sampling rate and communication are needed for these techniques.In recent years, machine learning and other intelligent methods have gained considerable attention for the fault diagnosis of microgrids. For example, a Decision Tree (DT) is employed for the detection of faults in microgrids in [3]. In [22], a data-mining model using DT and Discrete Fourier Transform (DFT) is proposed. DT is also combined with fuzzy rule in [23] and with K-Nearest Neighbor (KNN) in [24] for microgrid protection schemes. In [25], DT and Naive Bayes (NB) classifiers are implemented and compared as statistical classifiers for isolated inverter-based microgrids. The method in [26] applies four separate machine learning techniques DT, KNN, NB, and Support Vector Machine (SVM). Here, these are used to automatize the approach of fault classification in microgrids. Particle Swarm Optimization (PSO) is also used here as an optimization tool for decision variable vector components. In the study [27], a combined approach is taken based on HHT, SVM, NB, and Extreme Learning Machine (ELM) for fault diagnosis and classification. However, all these aforementioned methods are not examined for uncertainties of measurement, reinforcements safeguard, and synchronization inaccuracies. Another combination of discrete wavelet transform (DWT) and ELM is presented in [28] for section determination, model identification, and fault diagnosis of microgrids. DWT is also combined with deep neural networks (NN) for fault phase, type, and location in [5]. DWT and a Taguchi-based artificial NN are combined for the same type of operation in [29]. NN is also applied in [30] for DC microgrid protection. In [31], authors proposed a diagnosis scheme for residential microgrid appliances using Kernel Canonical Variate Analysis. However, most of the methods do not detect fault location and consider the effect of noises.Therefore as a matter of fact, this study introduces a deep belief network (DBN) approach in association with discrete wavelet transform (DWT) for the microgrid condition monitoring process, considering the necessity for a comprehensive fault diagnostic procedure. This research investigates a deep belief network (DBN) based method. It is a multiple-layer probabilistic generating network with hidden variables. DBN can be effectively trained to acquire key characteristics with limited resources, make observations, and utilize fault-related traits, a robust hierarchical generative model based on prior information. It may also be taught to extract significant features from a variety of sources. It uses an initial weight measurement policy provided by a robust layered generative model; it outperforms typical machine learning techniques. DBN uses efficient weighted distributions as a representation learning technique, resulting in better classification results. DWT is used to prepare the fault dataset by decomposing the signal information in the corresponding frequency band. The contributions of the study are fourfold:(i)
Using the training model, DBN can be efficiently trained to extract significant qualities from experiences, allowing the methodology to identify the probability reconstructing throughout its inputs.(ii)
A resilient multilevel generative model is also used in this approach to leverage fault-related characteristics with minimal previous information.(iii)
The unprocessed inputs were sent straight into the DBN in this investigation, which recognized the distinguishing features and classified the different defects.(iv)
Additionally, the approach detects failure patterns, broadening its applicability to a variety of diagnostic issues in the microgrid industry. The proposed infrastructure is evaluated using a vast set of input data at different sample frequencies.The prime objective of this study is to provide a fault detection and classification scheme for the microgrid domain. This research inclusively established the method as an efficient process of detecting and classifying short circuit faults in microgrid power transmission.The rest of the paper is structured as follows: Section II introduces the tested system. The data processing in Section III is illustrated with wavelet transform analysis and energy computation. Section IV represents the suggested strategy, which covers the network’s training stages. In Section V, the performance of fault detection and classification is evaluated. Finally, in Section VI, there are some concluding remarks.


## 2. System Modeling and Fault Description

In this study, three-phase signals are decomposed with the discrete wavelet transform (DWT); then energy computation was done before going through DBN for fault identification. The inputs are voltages of phase A, phase B, phase C, and current of phase A, phase B, phase C, and fault resistance fault distance; these 8 features are considered as input, to apply the method we have done with the system modeling to generate the dataset of faults. Then we have imposed them through wavelet transform in order to compute the energy, which is then converted through DBN for fault detection by training the prepared DBN model. Eventually, the model is able to detect the faults more adequately and precisely.


### 2.1. Test IEC Microgrid System Model

A microgrid system, structured according to the International Electrotechnical Commission (IEC) standard [32], is evaluated in this paper to test the performance of the proposed connection as illustrated in Figure 1. To provide broad information to prepare and simulate the required data, the entire connection system is created in the MATLAB/Simulink environment, as shown in Figure 1. The system is structured with four DG units where G-1 is a turbine connected with an asynchronous machine, G-2 and G-3 are inverter-based generators, and G-4 is a wind farm, based on DFIG. Bus-1 is connected to the main grid through the main circuit breaker which allows the microgrid system to turn into an islanded mode when there arises any disturbance in the main grid or when necessary to turn into islanded mode. Moreover, the system also operated through the loop or the radial topology by switching the CB loop-1 and CB loop-2. The system frequency is 50 Hz and 48 MVA is evaluated as the base power. The necessary system parameters are shown in Table 1.Figure 1
IEC microgrid system diagram with DG interface.Table 1
System parameters of the test system.
System ParametersTypes or ValuesFaultsTypes of faultsa–g, b–g, c–g, ab–g, bc–g, ac–g, ab, bc, ac, abc–g, nonfaultyLines (DL)DL-1, DL-2, DL-3, DL-430 km each, Vbase = 25 kVDistribution generators (DG)Utility grid1000 MVA, 120 kV, 50 HzDG-1 and DG-3 (synchronous)Rated 9 MVA, rated kV: 2.4 kVDG-2 (inverter-based)MVA: 2 MVA, rated kV: 575 VDG-4 (DFIG)MVA: 1.5 MVA, rated kV: 575 VTransformers (TR)TR-1120/25 kV, 50 MVA, 50 HzTR-2, TR-42.4/25 kV, 12 MVA, 50 HzTR-3, TR-5575 V/25 kV, 10 MVA, 50 Hz


### 2.2. Faults Encountered

Faults found in the power distribution system are the defect in the system which distracted the current from the intended path. These faults create an abnormal situation that reduces the insulation strength of the conductors which prompts excessive damage to the distribution system [33]. As a microgrid is the integration of numerous DGs, the same types of faults arise which reduce the efficiency of the system. Our proposed method will be able to detect these faults, classify them, and isolate the system to run the distributed generation.The faults of the power system are mainly classified into two categories as illustrated in Figure2 [34]. The open-circuit fault occurs due to the failure of conductors. As the fault arises in a series line, it is also considered a series fault. These types of faults reduce the reliability of the system. When the conductors from different phases come into contact with each other through a power line, power transformer, or any other circuit, short circuit faults arise in the system, also known as shunt faults. These types of faults are classified into two types, symmetrical faults and unsymmetrical faults.Figure 2
Types of faults encountered in power distribution system.


#### 2.2.1. Symmetrical Faults

These types of faults are balanced faults that arise infrequently in the power systems. The system remains balanced but significantly damaged by the faulty situation [35]. Symmetrical faults are classified into L-L-L-G fault and L-L-L fault as illustrated in Figure 2. The faults between the three phases and ground are considered as L-L-L-G fault; the occurrence rate of the fault is about 2–3%. The L-L-L faults arise very rarely which implies substantial current which determines the rating of the circuit breaker of the system.


#### 2.2.2. Unsymmetrical Faults

Fluctuation in magnitude and phases that raise unsymmetrical current is considered as unsymmetrical faults. These types of faults unbalanced the system and can be classified into three types, L-G fault, L-L-G fault, and L-L fault, illustrated in Figure3. Among these faults, the L-G fault is the most common which is about 65–70% of unsymmetrical faults [36]. L-G faults arise when conductors create contact with the ground. L-L-G faults happen when two conductors create contact with the ground and when contact with each other L-L fault occurred. The percentage of these types of faults is 15–20% and 5–10%, respectively.Figure 3
Fault signature and decomposition of the current signal.


### 2.3. Fault Dataset

The data set contains 11 classes including 10 faulty states and 1 normal state. Each class contains 396 data, having 8 features which are voltage and current of phase A, phase B, phase C, and fault resistance fault distances.


## 2.1. Test IEC Microgrid System Model

A microgrid system, structured according to the International Electrotechnical Commission (IEC) standard [32], is evaluated in this paper to test the performance of the proposed connection as illustrated in Figure 1. To provide broad information to prepare and simulate the required data, the entire connection system is created in the MATLAB/Simulink environment, as shown in Figure 1. The system is structured with four DG units where G-1 is a turbine connected with an asynchronous machine, G-2 and G-3 are inverter-based generators, and G-4 is a wind farm, based on DFIG. Bus-1 is connected to the main grid through the main circuit breaker which allows the microgrid system to turn into an islanded mode when there arises any disturbance in the main grid or when necessary to turn into islanded mode. Moreover, the system also operated through the loop or the radial topology by switching the CB loop-1 and CB loop-2. The system frequency is 50 Hz and 48 MVA is evaluated as the base power. The necessary system parameters are shown in Table 1.Figure 1
IEC microgrid system diagram with DG interface.Table 1
System parameters of the test system.
System ParametersTypes or ValuesFaultsTypes of faultsa–g, b–g, c–g, ab–g, bc–g, ac–g, ab, bc, ac, abc–g, nonfaultyLines (DL)DL-1, DL-2, DL-3, DL-430 km each, Vbase = 25 kVDistribution generators (DG)Utility grid1000 MVA, 120 kV, 50 HzDG-1 and DG-3 (synchronous)Rated 9 MVA, rated kV: 2.4 kVDG-2 (inverter-based)MVA: 2 MVA, rated kV: 575 VDG-4 (DFIG)MVA: 1.5 MVA, rated kV: 575 VTransformers (TR)TR-1120/25 kV, 50 MVA, 50 HzTR-2, TR-42.4/25 kV, 12 MVA, 50 HzTR-3, TR-5575 V/25 kV, 10 MVA, 50 Hz


## 2.2. Faults Encountered

Faults found in the power distribution system are the defect in the system which distracted the current from the intended path. These faults create an abnormal situation that reduces the insulation strength of the conductors which prompts excessive damage to the distribution system [33]. As a microgrid is the integration of numerous DGs, the same types of faults arise which reduce the efficiency of the system. Our proposed method will be able to detect these faults, classify them, and isolate the system to run the distributed generation.The faults of the power system are mainly classified into two categories as illustrated in Figure2 [34]. The open-circuit fault occurs due to the failure of conductors. As the fault arises in a series line, it is also considered a series fault. These types of faults reduce the reliability of the system. When the conductors from different phases come into contact with each other through a power line, power transformer, or any other circuit, short circuit faults arise in the system, also known as shunt faults. These types of faults are classified into two types, symmetrical faults and unsymmetrical faults.Figure 2
Types of faults encountered in power distribution system.


### 2.2.1. Symmetrical Faults

These types of faults are balanced faults that arise infrequently in the power systems. The system remains balanced but significantly damaged by the faulty situation [35]. Symmetrical faults are classified into L-L-L-G fault and L-L-L fault as illustrated in Figure 2. The faults between the three phases and ground are considered as L-L-L-G fault; the occurrence rate of the fault is about 2–3%. The L-L-L faults arise very rarely which implies substantial current which determines the rating of the circuit breaker of the system.


### 2.2.2. Unsymmetrical Faults

Fluctuation in magnitude and phases that raise unsymmetrical current is considered as unsymmetrical faults. These types of faults unbalanced the system and can be classified into three types, L-G fault, L-L-G fault, and L-L fault, illustrated in Figure3. Among these faults, the L-G fault is the most common which is about 65–70% of unsymmetrical faults [36]. L-G faults arise when conductors create contact with the ground. L-L-G faults happen when two conductors create contact with the ground and when contact with each other L-L fault occurred. The percentage of these types of faults is 15–20% and 5–10%, respectively.Figure 3
Fault signature and decomposition of the current signal.


## 2.2.1. Symmetrical Faults

These types of faults are balanced faults that arise infrequently in the power systems. The system remains balanced but significantly damaged by the faulty situation [35]. Symmetrical faults are classified into L-L-L-G fault and L-L-L fault as illustrated in Figure 2. The faults between the three phases and ground are considered as L-L-L-G fault; the occurrence rate of the fault is about 2–3%. The L-L-L faults arise very rarely which implies substantial current which determines the rating of the circuit breaker of the system.


## 2.2.2. Unsymmetrical Faults

Fluctuation in magnitude and phases that raise unsymmetrical current is considered as unsymmetrical faults. These types of faults unbalanced the system and can be classified into three types, L-G fault, L-L-G fault, and L-L fault, illustrated in Figure3. Among these faults, the L-G fault is the most common which is about 65–70% of unsymmetrical faults [36]. L-G faults arise when conductors create contact with the ground. L-L-G faults happen when two conductors create contact with the ground and when contact with each other L-L fault occurred. The percentage of these types of faults is 15–20% and 5–10%, respectively.Figure 3
Fault signature and decomposition of the current signal.


## 2.3. Fault Dataset

The data set contains 11 classes including 10 faulty states and 1 normal state. Each class contains 396 data, having 8 features which are voltage and current of phase A, phase B, phase C, and fault resistance fault distances.


## 3. Signal Processing and Input Feature Generation

The signatures of the fault occurrence are that the three-phase waveforms are assessed from a substation throughout the faulty situation [37]. It signifies that the signature information can be used to identify the appropriate phase that caused the fault situation. Substantially, this information is the component of forms regarding fault situations, line constraints, and network architecture. Taking the unprocessed three-phase waveforms into an account is quite complicated as the signals involve a massive range of sampled data points. Therefore, to put up with the highly useful attribute inputs, this research transforms the unprocessed time-domain signals into wavelet packets for the feature extracting procedure. The half power-frequency cycle waveforms after the fault occurrence are perceived inherently for solving the diagnosis problem. After that, energy is computed from the wavelet information for the feature extraction operation. However, extended waveforms are not analyzed because they increase the system’s training time. At a system frequency of 50 Hz and a sampling frequency of 20 kHz, signal samples were recorded for 200 data points. Figure 3 illustrated no-fault estimation of current signal.Voltage and current transients are dissected in a period span using a computational filtration approach in the digital wavelet transform (DWT). The high-frequency time-domain inputs are passed via a sequence of high pass (HP) filters, which decompose the waveforms into approximation components by using a parent wavelet that depicts the high-scale and low-frequency components. Low pass (LP) filters split nonstationary waveforms into detail coefficients by utilizing a mother wavelet to characterize the signal’s high and low components. The following is a definition of the breakdown of faulty information into approximation components:(1)Fmkt=2−m/2F2−it−N,Mmkt=2−m/2M2−it−N.Here,N∈z where N denotes the time shifting parameter for conversion of functions adjusted by a factor 2m and m, k are integers variable. The Daubechies MW of order 4 was chosen for dissecting the fault signals into detailed components in our investigation because it allows for discontinuous deployment. For the preceding two computations, the filtration operation that creates the route is expressed as(2)Ft=∑hn2F2t−n,Mt=∑ngn2M2t−n,where h is high pass filter coefficient and g is low pass filter coefficient. At a decomposition level of j, the expression is sampled at a rate by 2 to achieve approximation and detail component. The technique is repeated until the detail coefficient and level five approximation are reached. As an outcome, the fault information is fragmented into a wavelet decomposition tree, which is a low-frequency segment. The fault signals are denoted by W as(3)Wt=∑k=02M−m−1amkFmkt+∑m∑k=02M−m−1dmkMmkt,where M represents to the level of decomposition. Using the coefficient gained, the energy of a signal can be obtained as(4)Ei=∑j=1Ndmk2,where dmk denotes the detailed signal coefficient. For every three-phase voltage output, the signal energy is estimated in order to obtain the essential input features for the suggested fault detector.


## 4. Fault Detection and Classification Strategy

This research presents a deep belief network (DBN) based microgrid fault diagnosis system to enhance the generalization capability and reliable relaying security. Due to its capacity to extract features, DBN has good performance. DBN’s hidden layers detect feature information from the previous layer’s outputs. To learn different level features by pushing the different hidden layers from the data layer to the feature layer, the neuron counts of each layer decrease, and so the dimension of data can be lowered without major information loss. Unlike the existing methods, this strategy discovers the deep and shallow attributes of fault information through a block-by-block learning mechanism via an assembled structure of a Restricted Boltzmann Machine (RBM). The acquired properties are subsequently employed to address the microgrid failure system analysis and setup issue.The utilization of deep learning in this research is quite reasonable. Deep learning can provide better and more effective processing models; having the ability to learn without supervision allows it to increase accuracy and results over time. It can also account for the accuracy of the following outputs and can adjust needed steps. As faulty data is not in an organized formation, however, deep learning is capable of working with unstructured data with its own capability. Without any further human intervention, deep learning algorithms may produce new features from a small set of features in the training dataset.


### 4.1. RBM

Restricted Boltzmann Machine (RBM) provides a learning model for unknown data distributions as a special instance of energy-based generative models. Each RBM has two layers: one visible and one hidden. Units in the same layer are not linked together. Directed symmetrical connections exist among units in two adjacent levels, as shown in Figure4.Figure 4
Basic RBM structure illustrated with visible (v) and hidden (h) layer.For a visible vectorv=0,1 and hidden vector h = 0,1, weight matrix w, visible biases s, and hidden biases t, then the energy equation for joint configuration can be shown as E(v,h):(5)Ev,h=−∑n=1nsnvn−∑m=1mtmhm−∑n=1n∑m=1mvnwnmhm,where the number of visible units is denoted by n and the hidden units are denoted by m. The visible layer and hidden layer’s joint probability distribution is defined as(6)pv,h=e−Ev,hZ,where Z is denoted for summing the pair of visible and hidden vectors:(7)Z=∑v∑he−Ev,h.


### 4.2. DBN

The ideal technique to capture the features in the data is not to use a single hidden layer RBM. The learned features can be used as input data for a second RBM after RBM training. DBN can be built using this type of layer-by-layer learning system [38]. The lower layers of a DBN can retrieve low-level features in a greedy manner, while the upper layers are utilized to reflect the original signal’s more abstract qualities. The complexity of feature selection and diagnostic uncertainty of classic feature extraction approaches could be reduced without human participation [39]. DBN can gradually extract deep features from input data in this fashion. DBN, in other words, learns a deep characteristic of input by multilevel supervised training. This procedure gradually fine-tunes the variables of all DBN blocks starting from the last. Supposing an r-block DBN architecture (r number of RBM) the vector input is denoted as s and the vector output can be defined as(8)urs=11+exp−cr−vrur−1s.Theith sample to be trained in rth RBM block belongs to the class Ci (where Ci∈1,2,…,k) and the probability function of Ci can be defined as(9)fCi=j|ursi;ϕ=eϕT/jursi∑n=1keϕT/nursi.Here, ϕ1,ϕ2,…,ϕk∈ℜn+1 are the softmax variables. By selecting the highest probability, the softmax classifier predicts the probability of a class’s formation. The error function at rth block can be determined as(10)Qϕ=−1f∑i=1f∑j=1j1Ci=jlogeϕT/jursi∑n=1keϕT/nursi.The goal of the training stage is to minimize the error with iteration process. Throughout the iteration process, the upgrading order of the parameterϕ is(11)ϕ←ϕ−τ∇ϕQϕ.During the supervised fine-tuning stage, all the model parameters starting from block 1 to blockr are fine-tuned within the utilization of learning-rate τ. A pseudocode is shown in Figure 5.Figure 5
Basic algorithmic structure of the proposed network.Algorithm: Deep belief network.
Input: RBM (v1…vm, h1…hm), Training Batch SOutput: Achieve fault classification(1)
Prepare the data for normalization.(2)
Establish the model framework for setting the first layer, x=h0.(3)
Start the DBN attributes with a number close to 0 arbitrarily.(4)
Construct a hidden perceptron by the RBM training that is filtered by mean activation p(h1 = 1| h0).(5)
With the hidden units from the previous layer, train the RBM of the next layer.(6)
Iterate steps 2, 3, and 4 for a significant period.(7)
Optimize the pretraining DBN structure by fine-tuning the model.(8)
Check the model and return 1 if it overfits.(9)
end.


## 4.1. RBM

Restricted Boltzmann Machine (RBM) provides a learning model for unknown data distributions as a special instance of energy-based generative models. Each RBM has two layers: one visible and one hidden. Units in the same layer are not linked together. Directed symmetrical connections exist among units in two adjacent levels, as shown in Figure4.Figure 4
Basic RBM structure illustrated with visible (v) and hidden (h) layer.For a visible vectorv=0,1 and hidden vector h = 0,1, weight matrix w, visible biases s, and hidden biases t, then the energy equation for joint configuration can be shown as E(v,h):(5)Ev,h=−∑n=1nsnvn−∑m=1mtmhm−∑n=1n∑m=1mvnwnmhm,where the number of visible units is denoted by n and the hidden units are denoted by m. The visible layer and hidden layer’s joint probability distribution is defined as(6)pv,h=e−Ev,hZ,where Z is denoted for summing the pair of visible and hidden vectors:(7)Z=∑v∑he−Ev,h.


## 4.2. DBN

The ideal technique to capture the features in the data is not to use a single hidden layer RBM. The learned features can be used as input data for a second RBM after RBM training. DBN can be built using this type of layer-by-layer learning system [38]. The lower layers of a DBN can retrieve low-level features in a greedy manner, while the upper layers are utilized to reflect the original signal’s more abstract qualities. The complexity of feature selection and diagnostic uncertainty of classic feature extraction approaches could be reduced without human participation [39]. DBN can gradually extract deep features from input data in this fashion. DBN, in other words, learns a deep characteristic of input by multilevel supervised training. This procedure gradually fine-tunes the variables of all DBN blocks starting from the last. Supposing an r-block DBN architecture (r number of RBM) the vector input is denoted as s and the vector output can be defined as(8)urs=11+exp−cr−vrur−1s.Theith sample to be trained in rth RBM block belongs to the class Ci (where Ci∈1,2,…,k) and the probability function of Ci can be defined as(9)fCi=j|ursi;ϕ=eϕT/jursi∑n=1keϕT/nursi.Here, ϕ1,ϕ2,…,ϕk∈ℜn+1 are the softmax variables. By selecting the highest probability, the softmax classifier predicts the probability of a class’s formation. The error function at rth block can be determined as(10)Qϕ=−1f∑i=1f∑j=1j1Ci=jlogeϕT/jursi∑n=1keϕT/nursi.The goal of the training stage is to minimize the error with iteration process. Throughout the iteration process, the upgrading order of the parameterϕ is(11)ϕ←ϕ−τ∇ϕQϕ.During the supervised fine-tuning stage, all the model parameters starting from block 1 to blockr are fine-tuned within the utilization of learning-rate τ. A pseudocode is shown in Figure 5.Figure 5
Basic algorithmic structure of the proposed network.Algorithm: Deep belief network.
Input: RBM (v1…vm, h1…hm), Training Batch SOutput: Achieve fault classification(1)
Prepare the data for normalization.(2)
Establish the model framework for setting the first layer, x=h0.(3)
Start the DBN attributes with a number close to 0 arbitrarily.(4)
Construct a hidden perceptron by the RBM training that is filtered by mean activation p(h1 = 1| h0).(5)
With the hidden units from the previous layer, train the RBM of the next layer.(6)
Iterate steps 2, 3, and 4 for a significant period.(7)
Optimize the pretraining DBN structure by fine-tuning the model.(8)
Check the model and return 1 if it overfits.(9)
end.


## 5. Decision Making

The feasibility of the suggested strategy in detecting and classifying is examined in this section. The confusion matrix measures the feasibility of the suggested approach in the first place from the standpoint of overall accuracy. In addition, to appropriately analyze the method’s efficacy, a precision and sensitivity analysis of the suggested model is carried out.


### 5.1. Overall Accuracy

After a huge proportion of part of the training process has been generated, the diagnostics method can be performed. Rather than completing each diagnostic separately, they are all done at the same time to ensure reliability. As a result, a fault type is represented as a circumstance that is not faulty in this manner (nf). Whenever the output moves to any class other than ‘nf,’ the fault diagnosis procedure is activated.A confusion matrix is used to describe the functionality of the implemented DBN aided fault identification strategy in relation to the test-dataset in Figure6. The confusion matrix depicts a categorization scheme that has become perplexed among fault classes. The nondiagonal parts of this matrix refer to the proportion of classes that were bypassed, whereas the sloped elements illustrate the proportion of classes that were properly classified. Because the test data are perceived by reorganizing the underlying database rather than being used to train the classifier, the confusion matrix reflects the categorizing outcomes for different kinds of underlying data. The confusion matrix in Figure 7 indicates that the most of the fault information for the dataset in concern is correctly identified. The smallest interclass misclassification is determined for the nonfaulty form. Other fault circumstances resulted in a large rise in misclassification. The overall accuracies (OA) for the four systems tested are calculated as follows:(12)OA=NcNt×100%.Here, Nc and Nt display the total number of classes and the number of classes that have been classed.Figure 6
Accuracies under different SNR levels.Figure 7
Classification performance of the proposed network.The OAs utilized in this study were computed by combining the outcomes of five repetitions of the training and testing stages. More than 99 percent of all fault situations within the test-dataset are properly characterized, indicating that the reported OAs for all of the components underneath the investigation are appropriate. In an attempt to comprehend the provided classification method mixtures throughout fault categories, the OAs for separate categories are also obtained using the confusion matrix. The maximum observed total accuracy is 99.70 percent. The nonfault classification accuracy is also known as the no-fault situation predictive accuracy, and it is calculated to be 99.58 percent. Despite this, the OAs show that the suggested diagnosing approach is capable of reliably identifying and classifying abnormal signals.


### 5.2. Precision and Sensitivity Analysis

In fact, many faults in overhead power lines are fairly prevalent, while certain faults occur infrequently. As a result, the information obtained during the training phase for different fault scenarios is not equivalent. As a result, the detection process is an uneven categorizing problem as this volume of information for each fault situation is not equal. The classifier’s overall accuracy in the situation is steered by the large variety of diverse fault situations. Precision (Pr) and sensitivity (Se) analysis are also conducted out in order to ensure a desirable evaluation. The relevancy requirement is the basis of both precision and sensitivity. Precision denotes the proportion of the suitable data point that exists among the data points obtained. The ratio between the quantity of the model’s accurate estimation and the total number of true samples is called sensitivity.(13)Pr=TPTP+FP,Se=TPTP+FN.False positives (FPs) are real negative cases that the model defines as positive. True positives (TPs) are the actual positive cases labeled as positive by the model, while false positives (FPs) are the actual negative cases labeled as positive by the model.Individualized accuracy maximization causes the expense of sensitivity or vice versa (Figure8). As a result, the f1-score is calculated to determine the best combination of these two metrics. The harmonic mean for both values is implied by the f1-score, which ranges from 0 to 1. The model’s improved classification performance is shown by a higher f1-score.(14)f1−score=2×Pr×SePr+Se.Table 2 shows the precision, recall, and f1-score (F1) evaluations for various types of faults generated on the examined power system model during the first hearing. The graphic depicts the highest f1-score for the model’s separate fault information.Figure 8
Individual accuracies of fault classes.Table 2
Precision, recall, and F1-scores for DBN-based fault detection scheme.
ClassA–GB–GC–GAB–GBC–GCA–GA-BB-CC-AABC–GNFPrecision1110.990.99110.9910.991Recall110.9910.9910.991111F1-score110.9910.99110.9910.991


### 5.3. Analysis under Different Sampling Frequencies

The signals regarding line voltage and current are obtained with a 20 kHz sampling frequency in this suggested approach. Due to extreme limitations of the information gathering mechanism, the sampling frequency can be far lower over 20 kHz throughout practical scenarios. Since all voltage and current signals are not available at the identical period in certain real-world situations, the scheme needs to use different types of signals to execute categorization tasks precisely. As a result, the envisaged classifier’s fault diagnosis behavior was tested using different waveform kinds and sampling frequencies. These different kinds of input waveforms can be mainly within current signal, voltage signal, or both signals in a compound configuration. Hence, the sampling frequencies investigated in this study are 2, 5, 10, 15, 20, and 25 kHz. The average score of the accuracies was then calculated to obtain the end findings depicted in Figure9.Figure 9
Accuracies under different sampling frequencies.


### 5.4. Robustness Analysis against Noise

The defective voltage and current waveforms collected from the grid lead to instability due to the presence of perturbation. Distortion, on the other hand, is a critical component that might affect fault detectability, leading to a higher probability of false positives or false negatives. The elevated component that spontaneously integrates with the recorded signals owing to the sensor’s exposure to undesirable environmental conditions is known as noise or perturbation. The dataset for the suggested active learning, on the other hand, is obtained from a modeled network instead of the actual world. As a result, White Gaussian Noise (WGN) is introduced to the sample dataset to simulate a typical setting. The learning does not include noise infusions, which verifies the offered approach’s noise resilience. The noise insertion procedure for the testing data is as follows:(15)Scorrupt=Soriginal+Srandom×Pnoise,where the noisy signal Scorrupt can be gained by inducing a random array Srandom of specified noise power Pnoise to the real signal Soriginal, where the noise power can be defined as(16)Pnoise=Poriginal10SNRdb/10.Here,Poriginal denotes the power or original signal. Six distinct noise levels ranging from 10 to 20 dB are evaluated in this investigation. The main takeaway from the graph is that a higher noise level (or lower SNR) reduces the effectiveness of the current strategy substantially. Conversely, the DBN-based approach is noise-resistant, yielding more than 99% accuracy within the noise range studied. Additionally, even with a low SNR of 10 dB, the suggested method’s performance deviates just 1% from the no-noise scenario. As demonstrated in Figure 6, the above investigation validates the applicability of the suggested approach with variable levels of noise.


### 5.5. Comparison with Other Fault Diagnosis Strategies

This section compares the suggested neural network to three other artificially intelligent fault diagnostic approaches that are currently existent in the microgrid domain. Nevertheless, as distinct approaches applied distinct procedures and work on separate microgrid topologies, comparisons with them are not entirely compatible. Therefore, to bring it all into perspective, this research is contrasted with state-of-the-art alternative methodologies in respect of qualitative contrast. The initial approach involves using a gated recurrent unit (GRU) to constitute a neural network that can solve the three subsidiary tasks in the microgrid fault diagnostic challenge [5]. The approach accurately classifies a large range of qualities by identifying their basic pattern. However, it is not capable enough to handle exceedingly large patterns while utilizing tanh or ReLU as an activation function. The second method uses a discontinuous normalized Stockwell transform-based augmented Multikernel Extreme Learning Machine (MKELM) [40]. This method maintains the characteristics of extreme learning machines, such as quick learning efficiency, strong adaptation ability, and a lower risk of local optimal and computational complexity than gradient-based classification models. However, since this method only employs a one-cycle postfault waveform of current to define a fault category, reliable findings at a reduced frequency response cannot be confirmed. The third method is a Taguchi-based artificial neural network (T-ANN), along with DWT [29]. Wavelet energy of three-phase fault voltages, three-phase fault currents, and wavelet energy of neutralized fault current are used as input data to the ANN, which is developed utilizing multivariate information collected from Taguchi’s investigations. Nonetheless, this strategy does not handle power swing, sophisticated patterns, or high-impedance defects, which are all critical concerns.The proffered method, DBN, is more eligible and advantageous in terms of strong generalization capability, limiting the training data’s fitting problem, and uncovering the underlying pattern of a wide range of characteristics. However, evaluating the suggested methods to the aforementioned strategies is not completely coherent due to the usage of distinct topologies and aspects. Table3 represents a comparative evaluation of prediction accuracy with the strategies and Table 4 shows a qualitative comparison with traditional approaches, despite the fact that the findings were not exactly equivalent.Table 3
Quantitative comparison of the prediction accuracy between the proposed and other approaches [5, 29, 40].
Classification accuracy (%)GRUMKELMT-ANNDBN99.3198.2910099.58Table 4
Qualitative comparison of the proposed method with traditional approaches [41–43].
MethodAdvantagesDisadvantagesClassical methodsSimple operation; ease of utilization; less complexityLess accuracy; narrow amount of classification typesSignal processingLess information is lost; easy implementationArbitrary decision thresholds; lack of efficiencyStatistical methodSelf-adaptive; data drivenAdditional noise; mode mixing; access computationInformation basedDiscernible particular data structuresData validation not ensured; distorted data extractionArtificial intelligenceDetects nonlinear relation; fastRandom process; inconsistent outputProposed methodDirect analyzation of fault; highly elegant; precise computation; better performance during noise; need less heuristics—


## 5.1. Overall Accuracy

After a huge proportion of part of the training process has been generated, the diagnostics method can be performed. Rather than completing each diagnostic separately, they are all done at the same time to ensure reliability. As a result, a fault type is represented as a circumstance that is not faulty in this manner (nf). Whenever the output moves to any class other than ‘nf,’ the fault diagnosis procedure is activated.A confusion matrix is used to describe the functionality of the implemented DBN aided fault identification strategy in relation to the test-dataset in Figure6. The confusion matrix depicts a categorization scheme that has become perplexed among fault classes. The nondiagonal parts of this matrix refer to the proportion of classes that were bypassed, whereas the sloped elements illustrate the proportion of classes that were properly classified. Because the test data are perceived by reorganizing the underlying database rather than being used to train the classifier, the confusion matrix reflects the categorizing outcomes for different kinds of underlying data. The confusion matrix in Figure 7 indicates that the most of the fault information for the dataset in concern is correctly identified. The smallest interclass misclassification is determined for the nonfaulty form. Other fault circumstances resulted in a large rise in misclassification. The overall accuracies (OA) for the four systems tested are calculated as follows:(12)OA=NcNt×100%.Here, Nc and Nt display the total number of classes and the number of classes that have been classed.Figure 6
Accuracies under different SNR levels.Figure 7
Classification performance of the proposed network.The OAs utilized in this study were computed by combining the outcomes of five repetitions of the training and testing stages. More than 99 percent of all fault situations within the test-dataset are properly characterized, indicating that the reported OAs for all of the components underneath the investigation are appropriate. In an attempt to comprehend the provided classification method mixtures throughout fault categories, the OAs for separate categories are also obtained using the confusion matrix. The maximum observed total accuracy is 99.70 percent. The nonfault classification accuracy is also known as the no-fault situation predictive accuracy, and it is calculated to be 99.58 percent. Despite this, the OAs show that the suggested diagnosing approach is capable of reliably identifying and classifying abnormal signals.


## 5.2. Precision and Sensitivity Analysis

In fact, many faults in overhead power lines are fairly prevalent, while certain faults occur infrequently. As a result, the information obtained during the training phase for different fault scenarios is not equivalent. As a result, the detection process is an uneven categorizing problem as this volume of information for each fault situation is not equal. The classifier’s overall accuracy in the situation is steered by the large variety of diverse fault situations. Precision (Pr) and sensitivity (Se) analysis are also conducted out in order to ensure a desirable evaluation. The relevancy requirement is the basis of both precision and sensitivity. Precision denotes the proportion of the suitable data point that exists among the data points obtained. The ratio between the quantity of the model’s accurate estimation and the total number of true samples is called sensitivity.(13)Pr=TPTP+FP,Se=TPTP+FN.False positives (FPs) are real negative cases that the model defines as positive. True positives (TPs) are the actual positive cases labeled as positive by the model, while false positives (FPs) are the actual negative cases labeled as positive by the model.Individualized accuracy maximization causes the expense of sensitivity or vice versa (Figure8). As a result, the f1-score is calculated to determine the best combination of these two metrics. The harmonic mean for both values is implied by the f1-score, which ranges from 0 to 1. The model’s improved classification performance is shown by a higher f1-score.(14)f1−score=2×Pr×SePr+Se.Table 2 shows the precision, recall, and f1-score (F1) evaluations for various types of faults generated on the examined power system model during the first hearing. The graphic depicts the highest f1-score for the model’s separate fault information.Figure 8
Individual accuracies of fault classes.Table 2
Precision, recall, and F1-scores for DBN-based fault detection scheme.
ClassA–GB–GC–GAB–GBC–GCA–GA-BB-CC-AABC–GNFPrecision1110.990.99110.9910.991Recall110.9910.9910.991111F1-score110.9910.99110.9910.991


## 5.3. Analysis under Different Sampling Frequencies

The signals regarding line voltage and current are obtained with a 20 kHz sampling frequency in this suggested approach. Due to extreme limitations of the information gathering mechanism, the sampling frequency can be far lower over 20 kHz throughout practical scenarios. Since all voltage and current signals are not available at the identical period in certain real-world situations, the scheme needs to use different types of signals to execute categorization tasks precisely. As a result, the envisaged classifier’s fault diagnosis behavior was tested using different waveform kinds and sampling frequencies. These different kinds of input waveforms can be mainly within current signal, voltage signal, or both signals in a compound configuration. Hence, the sampling frequencies investigated in this study are 2, 5, 10, 15, 20, and 25 kHz. The average score of the accuracies was then calculated to obtain the end findings depicted in Figure9.Figure 9
Accuracies under different sampling frequencies.


## 5.4. Robustness Analysis against Noise

The defective voltage and current waveforms collected from the grid lead to instability due to the presence of perturbation. Distortion, on the other hand, is a critical component that might affect fault detectability, leading to a higher probability of false positives or false negatives. The elevated component that spontaneously integrates with the recorded signals owing to the sensor’s exposure to undesirable environmental conditions is known as noise or perturbation. The dataset for the suggested active learning, on the other hand, is obtained from a modeled network instead of the actual world. As a result, White Gaussian Noise (WGN) is introduced to the sample dataset to simulate a typical setting. The learning does not include noise infusions, which verifies the offered approach’s noise resilience. The noise insertion procedure for the testing data is as follows:(15)Scorrupt=Soriginal+Srandom×Pnoise,where the noisy signal Scorrupt can be gained by inducing a random array Srandom of specified noise power Pnoise to the real signal Soriginal, where the noise power can be defined as(16)Pnoise=Poriginal10SNRdb/10.Here,Poriginal denotes the power or original signal. Six distinct noise levels ranging from 10 to 20 dB are evaluated in this investigation. The main takeaway from the graph is that a higher noise level (or lower SNR) reduces the effectiveness of the current strategy substantially. Conversely, the DBN-based approach is noise-resistant, yielding more than 99% accuracy within the noise range studied. Additionally, even with a low SNR of 10 dB, the suggested method’s performance deviates just 1% from the no-noise scenario. As demonstrated in Figure 6, the above investigation validates the applicability of the suggested approach with variable levels of noise.


## 5.5. Comparison with Other Fault Diagnosis Strategies

This section compares the suggested neural network to three other artificially intelligent fault diagnostic approaches that are currently existent in the microgrid domain. Nevertheless, as distinct approaches applied distinct procedures and work on separate microgrid topologies, comparisons with them are not entirely compatible. Therefore, to bring it all into perspective, this research is contrasted with state-of-the-art alternative methodologies in respect of qualitative contrast. The initial approach involves using a gated recurrent unit (GRU) to constitute a neural network that can solve the three subsidiary tasks in the microgrid fault diagnostic challenge [5]. The approach accurately classifies a large range of qualities by identifying their basic pattern. However, it is not capable enough to handle exceedingly large patterns while utilizing tanh or ReLU as an activation function. The second method uses a discontinuous normalized Stockwell transform-based augmented Multikernel Extreme Learning Machine (MKELM) [40]. This method maintains the characteristics of extreme learning machines, such as quick learning efficiency, strong adaptation ability, and a lower risk of local optimal and computational complexity than gradient-based classification models. However, since this method only employs a one-cycle postfault waveform of current to define a fault category, reliable findings at a reduced frequency response cannot be confirmed. The third method is a Taguchi-based artificial neural network (T-ANN), along with DWT [29]. Wavelet energy of three-phase fault voltages, three-phase fault currents, and wavelet energy of neutralized fault current are used as input data to the ANN, which is developed utilizing multivariate information collected from Taguchi’s investigations. Nonetheless, this strategy does not handle power swing, sophisticated patterns, or high-impedance defects, which are all critical concerns.The proffered method, DBN, is more eligible and advantageous in terms of strong generalization capability, limiting the training data’s fitting problem, and uncovering the underlying pattern of a wide range of characteristics. However, evaluating the suggested methods to the aforementioned strategies is not completely coherent due to the usage of distinct topologies and aspects. Table3 represents a comparative evaluation of prediction accuracy with the strategies and Table 4 shows a qualitative comparison with traditional approaches, despite the fact that the findings were not exactly equivalent.Table 3
Quantitative comparison of the prediction accuracy between the proposed and other approaches [5, 29, 40].
Classification accuracy (%)GRUMKELMT-ANNDBN99.3198.2910099.58Table 4
Qualitative comparison of the proposed method with traditional approaches [41–43].
MethodAdvantagesDisadvantagesClassical methodsSimple operation; ease of utilization; less complexityLess accuracy; narrow amount of classification typesSignal processingLess information is lost; easy implementationArbitrary decision thresholds; lack of efficiencyStatistical methodSelf-adaptive; data drivenAdditional noise; mode mixing; access computationInformation basedDiscernible particular data structuresData validation not ensured; distorted data extractionArtificial intelligenceDetects nonlinear relation; fastRandom process; inconsistent outputProposed methodDirect analyzation of fault; highly elegant; precise computation; better performance during noise; need less heuristics—


## 6. Conclusion

This study proposes a deep belief network-based paradigm for appropriately interpreting microgrid problems. Unlike traditional fully connected neural network topologies, the suggested method does not require manual data labeling. Furthermore, many experiments on an IEC standard test model were conducted to confirm that the proposed technique is feasible, including noise impact, sampling frequency impact, and precision and sensitivity analysis. According to the results, the proposed framework has a classification accuracy of 99.3 percent. The real-time data was used to assess the approach’s efficiency. Additionally, a comparative functional analysis of the suggested method and some other ways available in the literature reveals that the proposed scheme outperforms the others. Different testing instances, such as different features, electric power swinging, and high-impedance faults, are various areas of interest for future study paths.



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*Source: 6820319-2022-08-25.xml*