Identifying single-phase to ground fault based on line multi-dimensional data in cyber-physical distribution system

Single-phase to ground fault is the most common line fault in power distribution systems, which may result in an electrical ﬁre and personal safety problems. Particularly, it is more difﬁcult to identify the fault occurring in the system in which the neutral point is grounded via Petersen coil. This paper proposes a new scheme based on line multi-dimensional data in cyber-physical distribution system, where line multi-dimensional data is used to extract the fault characteristics and thus to identify the faulty line. First, the circuit is analyzed and the difference-like algorithm is used to extract the current signal difference value from the line multi-dimensional data as the feature quantity. In order to reduce the impact of the measurement error on the result, the authors employ the deep neural networks to process the line multi-dimensional data, and demonstrate that this method can effectively resist the error interference. A simulation based on a previously studied model has been carried out and the results show the superiority compared to the ﬁfth harmonic identiﬁcation method. In addition, the test results obtained in the Dynamic Simulation Laboratory of Huazhong University of Science and Technology also demonstrate the practicality of the scheme.


INTRODUCTION
The power distribution system is highly user-oriented. Compared with the transmission system, the structure of the distribution system is more complicated and the operation situation is more variable. As a result, the distribution system is more prone to failure, and the single-phase to ground (SPG) fault occurs more often [1]. An SPG fault may result in rise of the voltage of the other two normal phase and even cause insulation breakdown, which presents a serious threat to personal and property safety.
In medium-and low-voltage distribution systems, the neutral point is generally not grounded. For such systems, an SPG fault may result in excessive current at the fault point. In order to reduce the fault current, Petersen coil is widely employed [2].
For a system where the neutral point is not grounded, the fault is relatively easier to identify since the zero-sequence This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2020 The Authors. IET Generation, Transmission & Distribution published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology current amplitude of the faulty line is larger than the others. However, when an SPG fault occurs in the system with Petersen coil, the zero-sequence current amplitude of the faulty line is much reduced due to the compensation of the coil [3], thereby making the fault detection difficult. In order to solve this problem, some schemes are proposed, based on the steady-state model, transient model and intelligent algorithm comprehensive analysis. The former two are called model-driven methods, and the latter is called data-driven methods.
The schemes based on steady-state model are generally not applicable to the system with Petersen coil, since there is almost no difference in the fundamental steady-state signal between the lines due to the compensation. Instead, higher than third harmonic signals, such as the fifth harmonic signal, can be used to identify the faulty line, because the inductance value of the coil is set according to the fundamental capacitive current. Such method is indeed applied in some areas in China, but the measurement accuracy is not sufficient due to excessively small harmonic components. In [4], short-time Fourier transform is used to extract the main harmonic components of phase current, such as the second, third and fifth harmonics, which are used to identify line fault.
The schemes based on transient model can be adopted in system with Petersen coil. In [5], Dong and Shi identified the faulty line by wavelet transforming and highlighted the characteristics of the fault line by comparing the wavelet analysis results of the transient electrical signal. In some cases, it has excellent performance but a quite high sampling rate is needed and it affected by the moment when the fault occurs; Nezamzadeh-ejieh and Sadeghkhani studied a method for comparing transient current waveforms based on Kullback-Leibler divergence to identify high-impedance fault (HIF) [6]. Apparently, the waveforms are also required to be recorded for analysis so that a high sampling frequency is needed. Tao et al. proposed to use the Hilbert transform to extract the instantaneous power information for fault detection [7] but it is hard to implement in practice. In [8] [10], which can distinguish HIF, capacitor switching and load switching successfully. However, these methods require rigorous data collection. Usually, some of them require measured signals to be strictly synchronized. Once the correct and complete waveform is not obtained in the transient process, the methods will fail.
There are also proposals where the algorithms in the field of artificial intelligence and machine learning are applied to identify the faulty lines in the distribution networks. Zeng et al. proposed a C-means clustering algorithm to classify fault data and non-fault data to detect the faulty line [11]. However, it pays little attention to the physical systems. As an important class of algorithms in the field of machine learning, artificial neural networks (ANNs) have also been proposed for faulty line inspection of distribution networks [12]. Nonetheless, the data they care about are rarely from the entire system but near the transformer substation. In [13], wavelet multi-resolution signal decomposition and adaptive neural fuzzy inference system are adopted to identify and classify line fault. In [14], a data mining algorithm, the decision tree method, has also been proposed as a line fault protection scheme.
Although a lot of research has been done on the line fault identification problem, in practice, the accuracy of fault identification is not satisfactory. The model-driven methods are limited by the physical model. If the operation of the distribution network is different from what the methods assume, the methods will fail. On the contrary, the data-driven methods concentrate more on the data obtained rather than the physical model. However, little attention paid to the physical model is not beneficial. What is expected is the data-driven methods combined with the characteristics of the physical model to solve the problem.

Distribution power network based on CPDS
The traditional distribution network is gradually evolving into the cyber-physical distribution system (CPDS) to suit the new characteristics of the distribution network [15] (shown in Figure 1). The term cyber-physical system (CPS), coined in 2006 by the US National Science Foundation, essentially describes a broad range of complex, multidisciplinary, physically aware next-generation engineered systems that integrate embedded computing technologies (cyber part) into the physical world [16]. CPS combines physical system with cyber system to realize the state monitoring, identification and control of the physical system through information communication and data calculation, to improve the efficiency of the system operation [17]. The power grid is one of the largest and most complex interconnected systems, and is a typical research object of CPS. The reorganization of power grids into smart CPS has become a trend, where the devices are not only used for power transmission but also utilized to transmit data for state evaluation and system control [18].
Some techniques employed for the fault identification in the distribution system such as the feeder terminal units and widearea measurement system have already facilitated the collection of the electrical information along the lines [19,20]. In fact, fault indicators (FIs) are commonly used for fault detection in power distribution system [21,22], which can also be used as the measuring devices. FI is the most practical and affordable ways making significant contributions to improve the system reliability. When a fault occurs on the network, FI will provide system operators with an indication regarding the passage of the  [23]. The devices, which are usually installed along the lines in the networks, as shown in Figure 2, can simultaneously measure the electrical data such as root mean square value and phase angle of the voltage and current at each measuring point.
The power distribution system being studied can be regarded as a CPS. The power system and the physical devices are physical equipment, to which the node model is built accordingly. The physical system is sensed by the measuring devices. The data collected and the algorithm designed in cyber system reflect the characteristic of the physical model.
The structure of the physical model, the locations of the measuring devices and the physical parameters of the system and the devices are considered as the implicit information since this information is usually hard to manifest in explicit way but are not negligible. This information is significant for fault identification and is expected to reflect its role through explicit data.

Line multi-dimensional data
In a CPDS, the devices are set at suitable position on the lines. If there occurs an SPG fault in the CPDS, the devices measure the electrical data at every measuring point and generate a database. In order to fully reflect the condition of the system, it is necessary to measure the voltage and current amplitude, as well as the power factor angle. Based on the physical quantities measured above, active and reactive power and harmonic values can be calculated. Besides, inspired by difference calculation, in the case of faulty line detection, a difference-like calculation is proposed. A certain value f (x k ) is recorded by the measuring devices (x k is the length of the line from the measuring device to the bus), with which the difference-like calculation can be performed, i.e.
The measured quantities of all adjacent measuring points are calculated according to Equation (1) and can be combined with the measurement database to form LMDD. We also proposed the algorithms which take the LMDD for the identification of the faulty lines.

Principles of fault detection
Due to installing the measurement devices, each line is divided into multiple segments. Each segment contains two measurement points and a fraction of a line. Apparently, each measurement point is reckoned twice except the first and last one. If an SPG fault occurs, these segments are classified as one faulty segment and several normal segments according to whether there is a fault on the segment. The segments with two measurement points can be regarded as two-port networks, as shown in Fig In order to highlight the contrast characteristics, all the segment line parameters are considered to be the same. r ′ and l ′ are the line resistance and inductance of the faulty segment from input point to the fault point, respectively; R f is the fault resistance and its value is 0 when the fault point is directly grounded.
The phasor diagrams of the voltage and current of the two segments are shown in Figure 4. in , on , i f and o f are the phase difference between the voltages and the corresponding currents in Figure 4, respectively. We consider a simplified case where the fault is supposed to occur at the end of the faulty segment, which means r = r ′ and l = l ′ .
When an SPG fault occurs on one line, the value of the current flowing through the line is recorded by the measuring devices. If the fault is not eliminated in time, as the load fluctuates, the current value for a period of time after the fault occurs will be stored for data analysis. It is assumed that the current measured by each measuring device is I m i, j (t ) (m = a, b or c, i is the line serial number, and j is the measuring device serial number on each line). The measurement current I m i, j (t ) includes the load current I m i, j (L) (t ), the ground current I m i, j (G ) (t ), and the Difference calculation is performed for all segments For any given line, the measuring current flowing to the load should be the same, i.e.
1. If there is not a fault on the line and the measurement error is not considered, the difference between the current measured by the j th and the j + 1th measuring device is mainly derived by the capacitance to ground between the two points. Apparently, this value is small. 2. If there is an SPG fault on the line, the differencelike value of the normal segment is consistent with the normal line. Assuming that the phase a ground fault occurs between the qth and the q + 1th measuring device, then ΔI a i,q (t ) is related to the difference between I a i,q(G ) (t ) and I a i,q+1(G ) (t ), which is affected by the fault impedance whose value will be larger than the other segments. This can be used as the criterion to detect the fault line.

Fault detection process
When an SPG fault occurs in the kth line as shown in Figure 2, the grounding phase voltage decreases. In other words, the system can be deemed to operate with faults when the zero sequence voltage has been significantly elevated, and the LMDD recorded by each measuring device will be stored and transmitted to the data analysis platform for difference-like calculation. The data acquisition time can depend on the field conditions, but it is necessary to ensure that the virtual values of current and voltage data can be calculated.
The virtual value of the current data recorded by each measuring device is selected as the characteristic quantity. The current measurement data I m i, j (t ) are recorded for a period of time after the fault occurs, during which the difference-like calculation is used. Then, the calculation result ΔI m i, j (t ) of several channels is obtained. A calculation window is chosen to calculate the virtual value. Since only the virtual values are required, it is enough to take a few cycles of signal to calculate. So, ΔI m i, j (t ) is a set of virtual values that changes with time.
For a certain time slice, ΔI m i, j (t 0 ) is compared for each segment. In general, it can be assumed that there is only one faulty line in the system. By comparing the results produced in the above calculation, the line with the largest value is then identified as the faulty line and its subscript i is noted as the serial number.
At the same time, if the measurement error is small enough, the line subscript j can be identified as the subscript of the measuring devices at the fault front end. Therefore, the location of the fault can be found with the spatial resolution of the installation distance between the two measuring devices. After the results of all time are given, the number of times that each line is considered as a faulty one can be counted, and recorded as n i . If there is N time slices, we consider decision probability (DP) of each line is and then we get If DP max = DP k , we believe that the line whose subscript is k is the faulty line and DP = DP max . The calculation results need to be normalized in the algorithm, as shown in the following equations: For each line, two sets of values can be calculated according to the different reference values. For instance, assuming that the fault occurs on the first segment of the first line, the first difference reference value ΔI m 1,1 of the first line is the largest. If ΔI m 1,1 is selected to reference value, we may obtain a series of normalized values that are no larger than 1. In this way, it is confused whether a fault is on the line. On the other hand, provided that the second difference value Despite ΔI ′m 1,1 = 1, there is evidence that the first line is faulty.

Simulation conditions
We build the simulation model according to [3] in PSCAD, which is shown in Figure 5. The step-down transformer is of the 35/10 kV class, through which the upper system is stepped down to distribute electric power from the bus to the four lines. Among the four lines, three are overhead lines and one is a cable. The detailed parameters are shown in Table 1. This scheme requires collecting the steady-state data for a period of time after the fault occurs, during which the loads will fluctuate. Therefore, the Gaussian random numbers within certain given range are selected as the loads parameters, as shown in Table 1. The simulation time is set to be 50 s, and the loads change every 0.5 s. Meanwhile, a set of measured values is obtained every 0.5 s for the algorithm analysis. It should be noted that the time interval of 0.5 s chosen here for the simulation is not always required and can be longer in practical applications. In this simulation, 100 sets of data can be obtained after occurrence of an SPG fault, corresponding to 100 time intervals of 0.5 s. The measuring sampling frequency of the simulation is 2 kHz. Factually, the sampling frequency can be set lower as long as the phasor data can be obtained. In order to facilitate the calculation, the distance between the measuring devices is set to be 2 km, so that the denominators in Equation (3) are the same in the difference-like calculation. In practice, we can adjust such distance according to the actual installation setup. And yet in order to ensure Equations (3), (8) and (9) can be applied, at least three measuring devices per line are required.

Simulation results and assessment
As shown in Table 2, without considering the measurement error, the difference-like algorithm can accurately distinguish the faulty line from the normal lines regardless of the fault resistance and the fault location. It demonstrates the efficacy of the scheme based on the LMDD for the identification of the faulty lines in the distribution network.

Influence of measurement error
In practice, measurement error cannot be ignored, which usually includes systematic error (SE) and random error (RE). For each measuring device, no SE and no more than 0.5% SE are added to the current data, respectively. The error between the measuring devices is not the same, whereas the  error of each device does not change in the time after the fault occurs. RE is generally caused by environmental factors or other random factors and that the RE is different from each other at a given moment. In this case, no more than 0.5% RE is added. In addition, white Gaussian noise with a signal-to-noise ratio of 60 dB is added to simulate nois interference.
The LMDD-based difference-like algorithm can be regarded as a steady-state method in essence. The fifth harmonic identification method working in the steady state can be compared with this algorithm to observe the influence of error and interference on the simulation result. The results of faulty line identification are shown in Table 3.
From Table 3, it can be seen there is no SE added, and the LMDD-based difference-like algorithm can identify the fault occurring on all lines, while the fifth harmonic identification method has almost failed in most cases. When there is no more than 0.5% SE added, the LMDD-based difference-like algorithm also seems difficult to identify the fault completely.
In general, the identification is not reliable if there is some measuring instrument error. However, such impact caused by the measurement error can, in principle, be reduced or even eliminated, when considering the fact that a larger amount of data in spatial and temporal dimensions can be collected in the distribution network with multiple measurement points and long data acquisition time.

Deep neural networks
ANN was published by Kenneth Levenberg and Marquardt in 1940s [24]. ANN was called a perceptron, and has an input layer, an output layer and an implicit layer. In 1980s, Rumelhart, Williams, Hinton, LeCun et al. invented multi-layer perceptrons with multiple hidden layers, namely deep neural networks (DNNs) [25]. DNNs have recently been widely used in various fields. The algorithm uses a large dataset to train a classifier, so that it can fit well to the label corresponding to the training data. Such training is also called process. The successfully trained network will then be able to classify the testing data unknown to the program with the correct labels. The neural network is similar to the structure of the intertwined connections of neurons in the human brain. Here the input layer of the network is used for receiving the input data, and the output layer is used for producing predictions. The most basic structure in a neural network is called a neuron. For the most common neural networks, the individual neurons between two adjacent layers are connected to each other, and each The simplified work process of applying DNNs to faulty line identification is shown in Figure 6. First, a training system and a test system model need to be established according to the distribution network studied, in which there are multiple measuring devices installed along the lines. In practical applications, the test system is just the distribution network being studied. The training system integrates physical models and measurement data, and produces a large amount of training LMDD to train the neural network. When the SPG fault occurs in the test system, test LMDD will be produced. By feeding the test LMDD to the trained neural network, the probability of each line being faulty will be calculated which can be used for fault identification. In addition, the successfully identified fault will be added to the training database to further improve the recognition accuracy of the network.

Data pre-processing
Faulty line detection can be regarded as a multi-class classification problem. Category labels include failures occurred on all lines. A training sample contains its category label and data which consist of the results from all measurement points. Every faulty line data contains certain number of samples. The category label of one sample is an integer from 0 to n − 1 (n is the number of lines), representing the category of the fault. Among the labels, 0 means that a fault occurs in the first line and so on. For data pre-processing, zero-mean normalization is first adopted, which conforms with the data to the standard distribution with the mean value of 0 and the standard deviation of 1. Normalization for data accelerates the training of neural networks.

Networks architecture
If we use all measurement point data on all lines at the same time for input, the neural network can utilize the global information. On the contrary, if we only use data on one line, network can only utilize the local information, which is not interfered by other information. In order to make full use of global and local information simultaneously, we design a network architecture for faulty line classification. As shown in Figure 7, the data of the four lines are first separated. Neural network is adopted to learn feature of measurement point data. Different neural networks are trained through the data of the four lines and the total data, respectively. The learned features are obtained through neural network, and then are concatenated to a final feature, which combines the local and global information. The final feature is fed to the last fully connected layer for classifying and the output is then obtained.

Feasibility test
In the case shown in Section 3.1, the distribution system containing three overhead lines and one cable line can be utilized to test the feasibility of the DNN algorithm. First, for each line, the simulation software produces 1500 samples, which contain the voltage, current, phase angle value and their difference-like value of all measuring points. After a fault occurs, 100 test samples are obtained from the test system LMDD and are utilized to detect the faulty line.
In order to verify that the DNN algorithm is resistant to measurement error interference, the faults in Table 3 were tested again and the results demonstrate that all of the faults tested were identified correctly regardless SE=0 or SE≤0.5%. It is obvious that compared with the above methods, the DNN algorithm can effectively resist the influence of measurement errors on the identification results.

Resistance change test
When the fault fault resistance is not constant, the case of variable fault resistance was also tested. Furthermore, 1% SE and a 0.5% RE are added to the current data, and a Gaussian white noise with a signal-to-noise ratio of 60 dB is also introduced. For each test sample, the DNNs output a result that a certain line is fault. When all 100 samples have been tested, the DP of each line can be given by referring to Equation (6). A total of 12 cases are tested and the results are shown in Table 4. For all the examples tested, the results are reliable, which means that the impact of the measurement error on the discriminate result is eliminated by the introduction of a larger dataset and the DNNs. The SPG whose fault resistance changes with time can also be recognized by the DNNs algorithm, further expanding the scope of application.

Unbalanced loads test
In the actual distribution network, the load is often fluctuating, and in some cases, the load will be unbalanced. Traditional methods may fail due to that. However, if this situation is taken into account when forming the LMDD, the DNN will also incorporate the data characteristics of load imbalance into the classification considerations during the learning process, so as to generate more reliable results. In order to verify this, the three-phase load in Table 1 is set to fluctuate independently, which means that the loads are unbalanced in most cases. Three sets of faults are tested and the DNN test results are shown in Table 5. Hence, the DNN algorithm based on LMDD is not restricted by the unbalanced loads and solves the problem well in principle.
Compared to the difference-like algorithm, the DNN algorithm consumes more computing resources and requires the knowledge of the system parameters in advance in order to simulate and obtain the training samples. For every system in which the method is applied, it is necessary to build it in a simulation environment to generate system parameters and produce a fault database for DNN training. In spite of that, the benefits gained by increased computation complexity are the relaxed restrictions on the measurement errors and lowered measurement costs.
Nonetheless, it should be noticed that the increase of error will inevitably lead to the uncertainty of the result, but if sufficient data and algorithm optimization are available, the possibility of misjudgment is also minimized in the case of the increase of error.

EXPERIMENT
The scheme was tested in the Power System Dynamic Simulation Laboratory of Huazhong University of Science and Technology. A typical distribution power system of 10 kV with three lines was built in the laboratory. The structure diagram of the system is shown in Figure 8. In Figure 8, XL stands for the lines, where 64, 66, 68 and 72 stand for the cables, and the others are overhead lines. QF stands for the switch. Each switch is equipped with instrumental transformers, which can measure the current and voltage, and FH means the load. The measurement data are transmitted from the transformers to the recorders by cables.  First, a simulation model should be built using the PSCAD software in order to generate the system parameters. A fault database is then produced under various conditions. Finally, the neural network is trained by the fault database with a preset number of iterations.
Four different fault experiments were conducted in total, where the fault parameters are shown in Table 6. The LMDD measured in each fault are sent to the neural network for testing. The output results shown in Table 6 experimentally verify the scheme.

ATTEMPT ON FAULT LOCATION
Fault indicator has the function of fault location, but the accuracy is affected by the preset threshold. In practice, the effect of fault location is not satisfactory. If the result of faulty line identification has been given by the DNN algorithm, rough fault location can be attempted. Assume that the faulty line has been identified, we design a new DNN for the specific faulty line to locate the faulty segment. For example, the SPG fault has been determined to occur on L1 in Section 3.1, and then the LMDD is fed to a new DNN to determine which segment is the faulty one of the three segments on L1. We tested the three fault conditions on L1 shown in Table 4, and the results are shown in Table 7.
Therefore, it is possible to locate the SPG fault based on LMDD and DNN. However, the minimum range is limited by the distance between the measuring points. Further research on fault location can be carried out from two aspects: on the one hand, increase the number of the measuring points, but it will cost more for constructing the physical system. On the other hand, design an algorithm for LMDD analysis to locate the fault point accurately within the identified faulty segment.

CONCLUSION
This paper proposes a scheme based on LMDD for solving the problem of identifying the SPG fault line in CPDS. Different from existing solutions, it utilizes the electrical signal information of the entire line, not just the starting end, for the mathematical analysis and extraction of the fault characteristics. The difference-like algorithm is simple to implement and is able to resist small error interference. However, its functionality is jeopardized with larger errors commonly encountered in real settings. Based on the LMDD, the DNN algorithm is used to analyze data with larger measurement errors, and the simulation demonstrates the improved robustness with larger errors. Therefore, the method here proposed based on the LMDD analysis is capable of identifying the faulty lines with a high accuracy and is also robust under the interference of significant measurement errors. The method suggests a new solution to the problem of the faulty line selection. Finally, it verifies the possibility that the method can be used for fault location, but further work is needed to achieve accurate locating.