Deep learning-based fault location framework in power distribution grids employing convolutional neural network based on capsule network
基于胶囊网络的卷积神经网络的配电网中基于深度学习的故障定位框架

Hamid Mirshekali $^{a}$ , Ahmad Keshavarz $^{b}$ , Rahman Dashti $^{a}$ , Sahar Hafezi $^{b}$ , Hamid Reza Shaker $^{c,^{*}}$
哈米德·米尔谢卡利 $^{a}$ ，艾哈迈德·凯沙瓦尔兹 $^{b}$ ，拉赫曼·达什蒂 $^{a}$ ，萨哈尔·哈菲兹 $^{b}$ ，哈米德·礼萨·沙克 $^{c,^{*}}$ 尔 $^{a}$ Clinical-Laboratory Center of Power System & Protection, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr, 7516913817, Iran
$^{a}$ 波斯湾大学智能系统工程与数据科学学院电力系统与保护临床实验室中心，布什尔，7516913817，伊朗 $^{b}$ IoT and Signal Processing Research Group, ICT Research Institute Engineering Department, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr, 7516913817, Iran
$^{b}$ 波斯湾大学智能系统工程与数据科学学院 ICT 研究所工程系物联网与信号处理研究组，7516913817 $^{c SDU Center for Energy Informatics, University of Southern Denmark, Odense DK-5230, Denmark}$

ARTICLE INFO 文章信息

Keywords: 关键字：

Convolutional neural network
卷积神经网络
Capsule network 胶囊网络
Deep machine learning 深度机器学习
Power distribution grid 配电网
Fault Location 故障定位

Abstract 抽象

Power distribution grids (PDGs) are one of the main parts of electrical logistic chains with the task of transferring electricity to the consumers continually. Adverse weather conditions, equipment failure, and human disruption can bring about the PDGs to faulty situations leading to the inevitable interrupting power consumption which results in financial losses. Therefore, it is vital to locate the faulty spot accurately and quickly. In this paper, an automatic deep learning framework is implemented to locate faults in the PDGs with limited measurement requirements i. e. only the voltage at the substations. The Spectrogram time-frequency analysis is performed on the voltage signal to obtain more informative training data. A convolutional neural network (CNN) model is utilized and trained to identify the location of the fault in the distribution grid. To provide a more precise outcome, the capsule network is used. This approach determines the location of the faulty section using an offline databank and then estimates the exact faulty point using an online databank of multiple fault scenarios in that section. To evaluate the powerfulness of the proposed method, several simulations are performed on the IEEE 34-node feeder in MATLAB (2020b). For further verification of the proposed method’s effectiveness, several laboratory tests are done as well. The results demonstrate that the proposed technique performs exceptionally well in terms of accuracy compared to other state-of-art counterparts, even when merely using the recorded voltage at the substations.
配电网（PDG）是电气物流链的主要部分之一，其任务是将电力持续传输给消费者。恶劣的天气条件、设备故障和人为干扰会导致 PDG 出现故障情况，从而导致不可避免的电力消耗中断，从而导致经济损失。因此，准确快速地定位故障点至关重要。在本文中，实现了一个自动深度学习框架，以定位测量要求有限的 PDG 中的故障，即仅定位变电站的电压。对电压信号执行 Spectrogram 时频分析，以获得信息更丰富的训练数据。使用和训练卷积神经网络（CNN）模型来识别配电网中故障的位置。为了提供更精确的结果，使用了胶囊网络。这种方法使用离线数据库确定故障路段的位置，然后使用该路段中多个故障场景的在线数据库估计确切的故障点。为了评估所提出的方法的强大性，在 MATLAB （2020b）中的 IEEE 34 节点馈线上进行了多次仿真。为了进一步验证所提出的方法的有效性，还进行了几次实验室测试。结果表明，与其他最先进的技术相比，所提出的技术在精度方面表现得非常出色，即使仅使用变电站的记录电压也是如此。

1. Introduction 1. 引言

Electricity systems are continually developing to meet the rising demand for energy. PDGs are expanding rapidly across the streets and alleys with many branches and sub-branches. A PDG has the task of transferring the power from transmission lines to small industries, commercial buildings, and domestic consumers continuously. Distribution grids are vulnerable to lightning, equipment failure and malfunction, and accidental disruption, all of which can result in a grid fault, jeopardizing system reliability [1]. Distribution grid faults result in power outages, financial losses, and customer frustration, all of which reduce the overall system’s reliability. Faults in distribution grids are unavoidable and they can arise at any time [2]. As a consequence, methods for automatic, quick, and precise fault location (FL) are needed. The FL problem in PDGs has become more complex and challenging than
电力系统不断发展，以满足不断增长的能源需求。PDG 在大街小巷中迅速扩张，拥有许多分支和子分支。PDG 的任务是将电力从输电线路持续传输到小型工业、商业建筑和家庭消费者。配电网容易受到雷击、设备故障和故障以及意外中断的影响，所有这些都可能导致电网故障，危及系统可靠性 [1]。配电网故障会导致停电、经济损失和客户挫败感，所有这些都会降低整个系统的可靠性。配电网故障是不可避免的，它们随时可能出现 [2]。因此，需要自动、快速和精确的故障定位（FL）方法。PDG 中的 FL 问题已经变得比
ever before due to the number of branches and sub-branches of PDGs and the non-homogeny in loads [3]. The recorded current signal is required for most FL methods to locate faults in the grid. Regardless of CT measurement inaccuracy, CT saturation might compromise the FL procedure [4]. Therefore, an FL method’s main benefit in terms of getting more precise results is its independence from the current signal and using only recorded voltage for determining fault spot [5]. FL methods can be categorized into four classes: impedance-based [6], traveling wave-based [7], state estimation-based [8], and artificial intelligent-based approaches [9]. Some of the recent FL techniques are a combination of the aforementioned classes [10]. A comprehensive review of different FL methods is presented in [11]. However, a brief survey of the most recent studies is reviewed in the following.
由于 PDG 的分支和子分支的数量以及载荷的非均匀性 [3]。大多数 FL 方法都需要记录的电流信号来定位电网中的故障。无论 CT 测量不准确，CT 饱和度都可能影响 FL 程序 [4]。因此，FL 方法在获得更精确结果方面的主要好处是它独立于电流信号，并且仅使用记录的电压来确定故障点 [5]。联邦学习方法可以分为四类：基于阻抗的 [6]、基于行波的 [7]、基于状态估计的 [8] 和基于人工智能的方法 [9]。最近的一些 FL 技术是上述类的组合 [10]。[11] 对不同的 FL 方法进行了全面回顾。但是，下面回顾了对最新研究的简要调查。

Impedance-based methods are mostly applying the recorded voltage and current at the substation of the PDGs in the phase domain to locate
基于阻抗的方法主要是在相域中应用 PDG 变电站记录的电压和电流来定位

the fault point. One of these approaches’ drawbacks is the requirement for each node’s accurate load value [12]. To address this challenge, the auxiliary load estimation technique and a particular form of measurement for load value recording must be used, which increases the calculation error [13]. In [14], a novel FL algorithm is presented to locate faults in PDGs both fully and not fully observable. A novel heuristic load estimation approach is proposed to calculate the precise load value of each node with the use of specific devices, overcoming one of the primary shortcomings of impedance-based methods, which is the necessity for comprehensive information of each node’s load. Using current signal could be this method’s primary drawback. In order to measure the network’s quantities, smart meter devices are widely used in PDGs. The method of [14] for FL is provided in [15] to determine the potential locations of fault. The primary distinction is the application of a new section estimation approach based on data from smart meter devices. One of the method’s major downsides is that it can not handle PDGs with a lot of branches and sub-branches.
断层点。这些方法的缺点之一是需要每个节点的准确载荷值 [12]。为了应对这一挑战，必须使用辅助负载估计技术和一种特殊的负载值记录测量形式，这会增加计算误差 [13]。在 [14] 中，提出了一种新的 FL 算法来定位 PDG 中的故障，既可以完全观察，也可以不完全可观察。提出了一种新的启发式负载估计方法，使用特定设备计算每个节点的精确负载值，克服了基于阻抗的方法的主要缺点之一，即需要每个节点负载的全面信息。使用电流信号可能是这种方法的主要缺点。为了测量网络的数量，智能电表设备广泛用于 PDG。[15] 中提供了 [14] 对 FL 的方法，以确定潜在的故障位置。主要区别在于应用了基于智能电表设备数据的新截面估计方法。该方法的主要缺点之一是它无法处理具有大量分支和子分支的 PDG。

The arrival time difference between the transmitting and receiving waves to the faulty spot is used in traveling wave-based algorithms to identify the location of the fault. This concept is applied to PDGs in an intuitive way by coordinating measurements at various locations within the network [16]. Applying the traveling wave approach in PDGs requires high sampling rate measurement devices which is not cost-effective [17]. [18] presents a traveling wave-based FL automated framework for PDGs that uses variational mode degradation and the teager electricity integrator. In this paper every single node linked to the network through a single line requires a measuring device. Under this procedure, all measuring instruments must capture the three-phase current and voltage signals.
在基于行波的算法中，发射波和接收波到达故障点的时间差用于识别故障的位置。通过协调网络内不同位置的测量，这一概念以直观的方式应用于 PDG [16]。在 PDG 中应用行波方法需要高采样率测量设备，这并不具有成本效益 [17]。[18] 提出了一个用于 PDG 的基于行波的 FL 自动化框架，该框架使用变分模式衰减和 teager 电力积分器。在本文中，通过单线连接到网络的每个节点都需要一个测量设备。在此程序下，所有测量仪器都必须捕获三相电流和电压信号。

One of the most promising artificial intelligent-based methodologies for FL in PDGs is the deep machine learning approach. Without requiring information about the system’s dynamics, these approaches use a set of training data to map the inputs of the most complicated structures to the proper outputs [19]. The most prevalent machine learning approaches that may be utilized for FL procedures are support vector machines, k -nearest neighbor, decision trees, artificial neural networks, and CNNs [20]. A new machine learning-based FL approach for smart PDGs equipped with micro-PMU sensors is provided in [21]. The features of the collected voltage signals are extracted using frequency spectrum analysis in this approach. The first 100 harmonics of the voltage signals are then subjected to neighborhood component analysis to obtain additional informative features. The fundamental advantage of this strategy is that it does not need current data, which reduces measurement error in calculations and CT saturation in short circuit faults. The specific location of the fault cannot be determined using this procedure. A novel gated recurrent unit (GRU) structure for defective section detection in the PDG is suggested in [22]. This approach makes use of the measurement data that has been captured in all nodes. Because of the cost implications, one of the major downsides of this method is the inability to supply massive data of all nodes in the real-world network. The long short-term memory (LSTM) model, which is a more advanced version of GRU, is utilized in [23] for fault detection, classification, and localization. The model is trained using the data collected from a limited number of PMUs in the network. For the training procedure, only data on frequency is utilized. One of the method’s key disadvantages is that it requires more than one PMU data to perform properly.
PDG 中最有前途的基于人工智能的 FL 方法之一是深度机器学习方法。这些方法不需要有关系统动力学的信息，而是使用一组训练数据将最复杂结构的输入映射到适当的输出 [19]。可用于 FL 程序的最普遍的机器学习方法是支持向量机、k 最近邻、决策树、人工神经网络和 CNN [20]。[21] 中提供了一种基于机器学习的智能 FL 方法，适用于配备微型 PMU 传感器的智能 PDG。在这种方法中，使用频谱分析来提取收集的电压信号的特征。然后对电压信号的前 100 个谐波进行邻域分量分析，以获得额外的信息特征。这种策略的基本优点是它不需要电流数据，从而减少了计算中的测量误差和短路故障中的 CT 饱和。使用此过程无法确定故障的具体位置。[22] 中提出了一种用于 PDG 缺陷切片检测的新型门控循环单元（GRU）结构。此方法利用了在所有节点中捕获的测量数据。由于成本影响，这种方法的主要缺点之一是无法提供实际网络中所有节点的海量数据。长短期记忆（LSTM）模型是 GRU 的更高级版本，在 [23] 中用于故障检测、分类和定位。该模型使用从网络中有限数量的 PMU 收集的数据进行训练。对于训练过程，仅使用有关频率的数据。该方法的主要缺点之一是它需要多个 PMU 数据才能正常运行。

In the field of machine learning-based, a key factor in achieving great performance is the pre-processing step. Using raw signals as input to deep learning models can make the training process more complex and time-consuming. As a solution, time or frequency domain transformations can be employed. In this study, a new algorithm called timefrequency spectrogram analysis is utilized, which extracts more informative features from faulty signals by transforming them into a twodimensional space of time and frequency. However, previous studies have often utilized different transformations, such as Fourier transformation-based algorithms [24], which may fail to capture
在基于机器学习的领域，实现出色性能的一个关键因素是预处理步骤。使用原始信号作为深度学习模型的输入会使训练过程更加复杂和耗时。作为解决方案，可以采用时域或频域变换。在这项研究中，使用了一种称为时频频谱图分析的新算法，该算法通过将故障信号转换为时间和频率的二维空间，从错误信号中提取更多信息特征。然而，以前的研究经常使用不同的变换，例如基于傅里叶变换的算法 [24]，这些算法可能无法捕获
important time-related information in the signal. Other studies have used raw signals as input data to the model [25], which can negatively impact the training process. One alternative approach used in another study is a graph convolutional network [26] that applies network topology-based voltage and current records to construct input data for the model. In [24]-[26], CNN models are used. However, a significant drawback of CNN models is that they employ pooling layers to extract features from the input image, which eliminates some features. This process of eliminating input data features can result in the deletion of crucial characteristics of faults stored in the faulty signal, potentially decreasing the accuracy of the classification and/or regression procedure.
Signal 中重要的时间相关信息。其他研究使用原始信号作为模型的输入数据 [25]，这可能会对训练过程产生负面影响。另一项研究中使用的另一种方法是图卷积网络 [26]，它应用基于网络拓扑的电压和电流记录来构建模型的输入数据。在 [24]-[26] 中，使用了 CNN 模型。然而，CNN 模型的一个显着缺点是它们使用池化层从输入图像中提取特征，从而消除了一些特征。这种消除输入数据特征的过程可能会导致存储在故障信号中的故障的关键特征被删除，从而可能降低分类和/或回归过程的准确性。

An automated deep learning-based FL approach for PDGs is proposed in this study. The voltage measured at the substation is regarded as the only data available. For the training process, the recorded three-phase voltage signal is transformed to its aerial mode or alpha component, which is much more straightforward. A Spectrogram time-frequency analysis is used in an intuitive approach to facilitate the training and feature extraction stages in order to extract more informative data. The input signal is converted to a picture of its constituent frequency and time scale via spectrogram analysis. A novel CNN based on the capsule network framework is suggested. The faulty image of a voltage signal obtained by Spectrogram analysis is the model’s input data. To address the limitation of traditional CNNs in detecting the location of the object in the picture, a capsule network is chosen. The identification of the faulty portion, as well as the precise location of the fault, are both taken into account. The identification of faulty sections is the initial stage of the algorithm. It is trained using an offline fault data bank that contains the great majority of faulty situation scenarios in all sections, allowing it to cover the widest range of defects in the PDG. Following the detection of the faulty section, an online databank of various faults in that defected area is created in order to pinpoint the specific location of the fault. To demonstrate the efficacy of the suggested technique, many simulations and laboratory tests are conducted in MATLAB on the IEEE 34-node test feeder and power simulator, respectively. Various fault scenarios are simulated to cover all locations on the network. The datasets contain different faulty conditions of

25 %

and

75 %

of each section location for faulty section identification, and every 50 m of the faulty section for exact FL, both in the training process, and every 100 m of the network for the testing process. In terms of accuracy and error percentage, the results indicate an outstanding performance for the proposed FL algorithm. In the following the main advantages and disadvantages of this work are summarized as follows:
本研究提出了一种基于 PDG 的基于深度学习的自动化 FL 方法。在变电站测得的电压被视为唯一可用的数据。在训练过程中，记录的三相电压信号被转换为其航空模式或 alpha 分量，这要简单得多。Spectrogram 时频分析以直观的方式使用，以促进训练和特征提取阶段，以便提取更多信息数据。通过频谱图分析，输入信号被转换为其组成频率和时间尺度的图片。提出了一种基于胶囊网络框架的新型 CNN。通过三维频谱图分析获得的电压信号的故障图像是模型的输入数据。为了解决传统 CNN 在检测图片中物体位置的局限性，选择了胶囊网络。故障部分的识别以及故障的精确位置都被考虑在内。识别有缺陷的部分是算法的初始阶段。它使用离线故障数据库进行训练，该数据库包含所有部分的绝大多数故障情况场景，使其能够涵盖 PDG 中最广泛的缺陷。在检测到故障部分后，将创建该缺陷区域中各种故障的在线数据库，以便确定故障的具体位置。为了证明所建议技术的有效性，在 MATLAB 中分别在 IEEE 34 节点测试馈线和电源仿真器上进行了许多仿真和实验室测试。模拟各种故障场景以覆盖网络上的所有位置。数据集包含用于错误部分识别的每个部分位置的不同

25 %

75 %

故障条件，以及用于精确 FL 的每 50 m 故障部分，无论是在训练过程中，还是在测试过程中每 100 m 的网络。在准确率和错误百分比方面，结果表明所提出的 FL 算法具有出色的性能。下面将这项工作的主要优缺点总结如下：

A new approach based on capsule network and spectrogram analysis is proposed to locate faults in electrical distribution networks.
提出了一种基于胶囊网络和频谱图分析的新方法来定位配电网络中的故障。
The capsule network model is preferred over the traditional convolutional neural network due to its ability to retain more information in the input data.
胶囊网络模型优于传统的卷积神经网络，因为它能够在输入数据中保留更多信息。
Spectrogram analysis is used to convert the faulty signal into a twodimensional representation, allowing for better visualization and feature extraction.
频谱图分析用于将故障信号转换为二维表示，从而实现更好的可视化和特征提取。
The method only requires recorded voltage data from the beginning of the network, avoiding the use of current waveform that can be affected by CT saturation and measurement errors.
该方法只需要从网络开始时记录电压数据，避免使用可能受 CT 饱和和测量误差影响的电流波形。
The proposed method can accurately identify both the faulty section and the exact location of the fault in two steps using offline and online data banks.
所提出的方法可以使用离线和在线数据库分两步准确识别故障段和故障的确切位置。
However, the method has limitations such as the need for highsampling rate devices and the inability to handle networks with distributed generations.
但是，该方法存在局限性，例如需要高采样率设备以及无法处理具有分布式发电的网络。

The remainder of the paper is laid out as follows. The suggested approach is provided in Section 2, which consists of three steps: preprocessing, capsule network structure, and fault identification utilizing capsule network. In Section 3, the simulation results of several failure
本文的其余部分布局如下。建议的方法在第 2 节中提供，包括三个步骤：预处理、胶囊网络结构和利用胶囊网络进行故障识别。在第 3 节中，几个失败的模拟结果

Fig. 1. Converted data of several faults as an input of CNNs, abc sequence of voltage signal, alpha component of faulty voltage, and spectrogram time-frequency image of faulty voltage.
图 1.将多个故障的数据转换为 CNN 的输入、电压信号的 abc 序列、故障电压的 alpha 分量和故障电压的三维频谱图时频图像。
situations are shown. The laboratory verification is presented in Section 4. Finally, in the final section, the conclusion is achieved.
情况被展示出来。实验室验证在第 4 节中介绍。最后，在最后一部分，得出结论。

2. The proposed methodology
2. 建议的方法

The suggested FL approach is provided in three parts in this section. To begin, the pre-processing stage is described, which involves using Spectrogram time-frequency analysis to transform the aerial mode of fault data into a more informative format in an intuitive manner. Afterward, the capsule network as well as its use for overcoming the CNN disadvantage is presented. Finally, an automated protection framework is proposed using a CNN based on the capsule network to locate faults in the distribution grids.
建议的 FL 方法在本节中分三个部分提供。首先，描述了预处理阶段，其中包括使用 Spectrogram 时频分析以直观的方式将故障数据的航空模式转换为信息量更大的格式。之后，介绍了胶囊网络及其用于克服 CNN 缺点的用途。最后，提出了一种基于胶囊网络的 CNN 自动保护框架来定位配电网中的故障。

2.1. Pre-processing stage
2.1. 前处理阶段

In this part, a time-frequency analysis technique called Spectrogram is used to transform the format of the fault signal into an image that can subsequently be used in CNNs [27]. This analysis has many applications. The authors of [28] used spectrogram analysis as a fundamental tool for
在这部分，使用一种称为频谱图的时频分析技术将故障信号的格式转换为随后可用于 CNN 的图像 [27]。此分析有许多应用。[28] 的作者使用频谱图分析作为
more complex time-frequency transformations, such as Wigner distribution. In [29], spectrogram analysis is evaluated alongside other time-frequency transformations as a feature extraction technique that can assist CNN models. It is a good analysis which be utilized to convert signals into images with informative features for image-based machine learning models. The only accessible data of fault for the diagnostic procedure is the recorded faulty voltage signal at the substation. Because of the reliance on each phase, the three-phase recorded voltage of the fault in the abc frame cannot be utilized. The modal transformation matrix is therefore used to convert the three-phase voltage signal’s mode to its modal form. The modal form eliminates the reliance on voltage signals. The following formula is used to acquire two ground and aerial modes:
更复杂的时频变换，例如 Wigner 分布。在 [29] 中，频谱图分析与其他时频变换一起作为一种可以帮助 CNN 模型的特征提取技术进行评估。这是一个很好的分析，可用于将信号转换为具有信息功能的图像，用于基于图像的机器学习模型。诊断程序唯一可访问的故障数据是变电站记录的故障电压信号。由于对每个相位的依赖，不能利用 abc 帧中故障的三相记录电压。因此，模态变换矩阵用于将三相电压信号的模式转换为其模态形式。模态形式消除了对电压信号的依赖。以下公式用于获取两种地面和航空模式：

[\begin{array}{l} V_{0} \\ V_{1} \\ V_{2} \end{array}] = \frac{1}{3} [\begin{array}{ccc} 1 & 1 & 1 \\ 2 & - 1 & - 1 \\ 0 & \sqrt{3} & \sqrt{3} \end{array}] [\begin{array}{l} V_{a} \\ V_{b} \\ V_{c} \end{array}]

where

V_{0}, V_{1}

and

V_{2}

are zero, positive, and negative sequence modes, respectively.

V_{0}

represents the ground mode and it only has value for the case of grounded faults.

V_{1}

and

V_{2}

stand for aerial mode and they have
其中

V_{0}, V_{1}

和

V_{2}

分别是 0、正和负序列模式。

V_{0}

表示接地模式，它仅对接地故障有值。

V_{1}

并

V_{2}

代表空中模式，他们有

- Corresponding author. 通讯作者。
E-mail address: hrsh@mmmi.sdu.dk (H.R. Shaker).
电子邮件地址：hrsh@mmmi.sdu.dk （H.R. Shaker）。

Deep learning-based fault location framework in power distribution grids employing convolutional neural network based on capsule network 基于胶囊网络的卷积神经网络的配电网中基于深度学习的故障定位框架