Applying a Deep-Learning Method to Diagnose the Capacitor Voltage Transformers with Excessive Measurement Errors
基于深度学习方法诊断具有过度测量误差的电容电压互感器

Power systems rely on high-voltage substations where Capacitor Voltage Transformers (CVTs) play a crucial role in metering, monitoring, and protection. In practice, all devices’ measurement data are engaged with errors, and CVTs are not protected similarly. However, errors in measurement devices can threaten safe power system operation and fair electricity trading. Accurate metering is essential to ensure efficient energy markets. To address these issues, a new method has been proposed that employs a deep-learning model to analyze data attributes and provide online error measurement of CVTs. By applying the proposed method, the online measurement error of CVTs will be fully applicable to the power system operators, only acquired by analyzing data attributes and employing the proposed deep-learning model. With the support of fast-growing technologies and the recent novel data science advancements, the proposed prominent model satisfies the measurement accuracy requirements with evaluated adequate accuracy indexes and fit results. This method can also detect and diagnose anomaly CVTs with excessive measurement errors and facilitate preventive maintenance and supervision. The model’s efficiency has been demonstrated through experimental results, making it a promising solution for online metering in power systems.
電力系統依賴於高压变电站，其中电容式电压互感器 (CVT) 在计量、监测和保护中发挥着至关重要的作用。实际上，所有设备的测量数据都存在误差，CVT 的保护也并非如此。然而，测量设备的误差可能威胁电力系统的安全运行和公平的电力交易。精确的计量是确保高效能源市场的重要保障。为了解决这些问题，提出了一种新的方法，该方法采用深度学习模型来分析数据属性并提供 CVT 的在线误差测量。通过应用所提出的方法，CVT 的在线测量误差将完全适用于电力系统运营商，只需分析数据属性并采用所提出的深度学习模型即可。在快速发展的技术和最近新数据科学进步的支持下，所提出的突出模型满足测量精度要求，并通过评估足够的精度指标和拟合结果。该方法还可以检测和诊断测量误差过大的异常 CVT，并有助于预防性维护和监管。 该模型的效率已通过实验结果得到验证，使其成为电力系统在线计量的一个很有前景的解决方案。

Measurement Error Modelling, Fair Electricity, Online Measurement Error, Deep Learning, Preventive Maintenance, Capacitor Voltage Transformers.
测量误差建模，公平用电，在线测量误差，深度学习，预防性维护，电容电压互感器。

In power systems, Capacitor voltage transformers are typically operated in high-voltage substations, heading to be the base part of metering, monitoring, and protection. In practice, all devices’ measurement data are engaged with errors, and CVTs are not protected similarly. Unexpected measurement errors threaten the safe operation of the power system regardless of conflicting impacts on fair electricity trading, whereas accurate metering is essential in energy markets.
在电力系统中，电容电压互感器通常运行于高压变电站，作为计量、监测和保护的基本部分。实际上，所有设备的测量数据都会存在误差，而 CVT 却没有得到类似的保护。意外的测量误差威胁着电力系统的安全运行，无论其对公平电力交易造成的影响如何，而准确的计量在能源市场中至关重要。
To diminish the adverse effects of measurement errors due to increasing the measurement error of CVT during its operation, which is mainly caused by its embodied sensitive capacitors, we have two main strategies: first, assigning a maximum allowable measurement error value that each CVT’s gathered measurement data shall not surpass it else, the anomaly CVT will be considered for repairing or substituting. The second is building a measurement error prediction model. Adjusting the measurement data regarding the actual values would be preferred instead of unnecessarily replacing the CVTs or conducting on-site calibrating, which are costly, timeconsuming, and may even require power outages.
为了减轻测量误差对 CVT 运行期间的测量误差增大产生的负面影响，主要原因是其内部敏感电容器，我们制定了两个主要策略：首先，分配一个最大允许测量误差值，每个 CVT 收集的测量数据不得超过该值，否则，将考虑修复或更换异常 CVT。其次，建立测量误差预测模型。调整关于实际值的测量数据将比不必要地更换 CVT 或进行现场校准更可取，后者成本高、耗时，甚至可能需要停电。
On the other hand, the power system will be shielded from pushing to the critical states due to incorrect measurements, such as relay protection mis-operation, which could result in power interruption. In traditional approaches to finding online error measurements, models are made mainly by building a mathematical model whose tuning parameters are difficult to obtain, causing undesired accuracy and model weakness.
另一方面，电力系统将免受误操作（例如继电保护误操作）引起的不正确测量导致的推向临界状态的保护，而这可能导致停电。在传统的在线误差测量方法中，模型主要是通过建立一个参数难以获得的数学模型来构建的，这会导致不理想的精度和模型缺陷。
To address the limitations of traditional mathematical models, machine learning prediction models, such as those outlined in the references below, offer valuable insights into the potential of these techniques for state-of-the-art measurement error modeling for CVTs. In [1], AlMohammedawi proposed a new approach for reducing the effects of noise in CVT voltage measurements using wavelet transform and neural networks. Singh et al. presented a measurement error correction of CVT using a neural network [2]. In [3], Kumar and Ali proposed fault detection in CVT using wavelet transform and artificial neural networks. Wang et al. proposed a deep learning approach for fault diagnosis of CVTs based on EMD and CNN [4]. Similarly, in [5], Zhang et al. proposed a novel fault diagnosis method for CVT based on EMD and LSTM. In [6], K. Zhang et al. proposed a method that combines Empirical Mode Decomposition (EMD) with Long Short-Term Memory (LSTM) networks to diagnose faults in CVTs. In [7], M. Zhu et al. proposed a method that uses a Convolutional Neural Network (CNN) and LSTM network to diagnose faults in CVTs. S. Liu et al. presented a method that uses Ensemble Empirical Mode Decomposition (EEMD) and a deep learning model for fault diagnosis of CVTs [8].
为了解决传统数学模型的局限性，机器学习预测模型，例如以下参考文献中概述的模型，为了 CVT 的先进测量误差建模，为这些技术的潜力提供了宝贵的见解。在[1]中，AlMohammedawi 提出了一种使用小波变换和神经网络来降低 CVT 电压测量噪声影响的新方法。Singh 等人使用神经网络提出了 CVT 的测量误差校正[2]。在[3]中，Kumar 和 Ali 提出使用小波变换和人工神经网络进行 CVT 故障检测。王等人提出了一种基于 EMD 和 CNN 的 CVT 故障诊断深度学习方法[4]。同样，在[5]中，张等人提出了一种基于 EMD 和 LSTM 的 CVT 新型故障诊断方法。在[6]中，K. Zhang 等人提出了一种结合经验模态分解（EMD）和长短期记忆（LSTM）网络来诊断 CVT 故障的方法。在[7]中，M. Zhu 等人提出了一种使用卷积神经网络（CNN）和 LSTM 网络诊断 CVT 故障的方法。S. Liu 等人 利用集合经验模态分解 (EEMD) 和深度学习模型的 CVT 故障诊断方法。
In [9], S. Zhang et al. proposed a method that uses LSTM networks to predict real-time measurement errors in CVTs. In addition, Zhang et al. [10] and Cao et al. [11] proposed fault diagnosis of CVT based on EMD and CNN, and measurement error correction of CVT based on wavelet transform and RBF neural network, respectively. Li et al. proposed a measurement error correction of CVT based on wavelet transform and extreme learning machine [12]. In [13], Liu et al. proposed a novel approach for CVT fault diagnosis using the EEMD method based on deep learning. Y. Zheng et al. [14] discuss the application of wavelet transform and Long Short-Term Memory (LSTM) neural network to correct the measurement errors in the Capacitive Voltage Transformer (CVT). Moreover, Cao et al. proposed a deep learning approach for CVT measurement error correction based on EEMD [15]. Wang et al. proposed a measurement error correction of CVT using EMD and LSTM neural network [16]. Moreover, Zhang et al. proposed a fault diagnosis of CVT based on EMD and LSTM neural networks [17]. In [18], Hu et al. proposed a measurement error correction of CVT using EMD and a convolutional neural network.
在文献[9]中，张三等提出了一种利用 LSTM 网络预测 CVT 实时测量误差的方法。此外，张三等[10]和曹三等[11]分别提出了基于 EMD 和 CNN 的 CVT 故障诊断，以及基于小波变换和 RBF 神经网络的 CVT 测量误差校正。李四等提出了基于小波变换和极限学习机的 CVT 测量误差校正方法[12]。在[13]中，刘五等提出了一种基于深度学习的 EEMD 方法的 CVT 故障诊断新方法。郑六等[14]讨论了小波变换和长短期记忆(LSTM)神经网络在电容式电压互感器(CVT)测量误差校正中的应用。此外，曹七等提出了基于 EEMD 的 CVT 测量误差校正的深度学习方法[15]。王八等提出了基于 EMD 和 LSTM 神经网络的 CVT 测量误差校正方法[16]。此外，张九等提出了基于 EMD 和 LSTM 神经网络的 CVT 故障诊断方法[17]。在[18]中，胡十等提出了基于 EMD 和卷积神经网络的 CVT 测量误差校正方法。

In this paper, to overcome the deficiencies of conventional mathematical models, we conduct a deep learning method, a data-driven approach, that excavates the near-to-real data from raw measurement data and enables us to operate the power system more efficiently and securely. We have accomplished the redistribution, elimination, and normalization processes to the measurement data derived from an online measurement strategy to train the model; this is our contribution to this article, employing an artificial intelligence approach for making a machinelearning prediction model.
在本文中，为了克服传统数学模型的缺陷，我们进行了一种深度学习方法，这是一种数据驱动的方法，它从原始测量数据中挖掘接近真实的数据，使我们能够更有效率、更安全地运行电力系统。我们已经完成了对由在线测量策略得出的测量数据的重新分配、消除和规范化处理，以训练模型；这是我们利用人工智能方法建立机器学习预测模型的贡献。
Anomaly detection is one of the tasks of this research. There are several approaches to anomaly detection in time series data. In this paper, anomaly detection is available by applying the proposed model to under-examining CVT. Anomaly detection in time series data is challenging because of the need to balance the trade-off between false positives and false negatives. False positives occur when standard data points are incorrectly classified as anomalies, while false negatives occur when actual anomalies are not detected. To overcome this challenge, we have developed a thresholding method that improves the accuracy and reliability of anomaly detection in time series data.
异常检测是这项研究任务之一。时序数据中的异常检测有很多种方法。在本文中，通过将提出的模型应用于未检测 CVT，可以实现异常检测。时序数据中的异常检测是一项挑战，因为它需要在误报和漏报之间进行权衡。误报是指将标准数据点错误地分类为异常，而漏报是指未检测到实际异常。为了克服这一挑战，我们开发了一种阈值方法，可以提高时序数据中异常检测的准确性和可靠性。
When the error measurements exceed the standard values by a certain limit, for instance, 10 percent beyond the limit, it indicates that there is an anomaly in the CVT. In such cases, we must replace the anomaly to prevent further damage or system errors. However, if the measurements are below the limits, we can use this model to calibrate the CVT. Once the calibration is complete, the error is reduced. Insights from the model can also be utilized to predict any potential anomalies in the future, which can be addressed before they cause any significant damage.
当误差测量值超出标准值一定限度时，例如超出限度 10%，则表明 CVT 存在异常。在这种情况下，我们必须更换异常，以防止进一步损坏或系统错误。但是，如果测量值低于限值，我们可以使用此模型来校准 CVT。完成校准后，误差将减小。模型的见解还可以用于预测未来可能出现的任何异常情况，这些异常情况可以在造成任何重大损坏之前得到解决。
The proposed method needs historical data of CVTs’ measurement errors derived from evaluating with an installed precise voltage transformer. Therefore, we already have some preknown measurement error data to train the model, which does not rely on specified and accurate tuning parameters.
该方法需要先前由已安装的精密电压互感器评估得出的 CVTs 测量误差的历史数据。 因此，我们已经具备了一些预先的测量误差数据来训练模型，这无需依赖明确和精确的调优参数。
The practical part of the research, acquiring sufficient historical measurement error data, has been conducted in a power system laboratory. In this paper, the characteristics of CVT error data are studied. The CVT error data is a time-series data with long-term dependencies, and therefore, the prediction task is challenging. To address this issue, we have proposed a novel CVT error prediction model based on deep learning. Redistributing the implicit layer data of the deep network can help solve the gradient disappearance issue, which in turn leads to a more stable convergence of the model. This technique also improves the model’s generalization ability. Additionally, dynamically weighting the loss value of each task ensures training balance across all tasks. We designed several experiments to showcase the superior performance of our model after implementing these techniques.
本研究的实践部分，获取足够的历史测量误差数据，已在电力系统实验室完成。本文研究了 CVT 误差数据的特点。CVT 误差数据是具有长期依赖关系的时间序列数据，因此预测任务具有挑战性。为了解决这个问题，我们提出了一种基于深度学习的 CVT 误差预测新模型。重新分配深度网络的隐层数据可以帮助解决梯度消失问题，进而使模型更稳定地收敛。该技术还提高了模型的泛化能力。此外，动态加权每个任务的损失值确保了所有任务的训练平衡。在实施这些技术后，我们设计了几个实验来展示我们模型的优越性能。
The main contributions of this paper are:
本论文的主要贡献有： ##

A CVT includes a Capacitive Voltage Divider (CVD), an Intermediate Voltage Transformer (IVT), a Compensating Reactor (CR), a Ferro-Resonance Damping Unit, and Adjustment Windings as shown in Fig. 1 [19].
CVT 包括电容式分压器（CVD）、中间电压变压器（IVT）、补偿电抗器（CR）、铁谐振抑制单元以及调节绕组，如图 1 [19]所示。
In this study, the experimental data used in the evaluation of the CVT error measurement model were obtained from a single-phase 66 kV CVT in a testing laboratory. The evaluation period lasted for six days with a 1-minute time interval. The data collected included the phase voltage ratio and phase data measured by the target CVT and a 66 kV Standard Inductive Voltage Transformer (IVT), which is installed in the same bus. The errors in CVT metering are characterized by ratio error and phase error. The ratio error is the difference between the magnitudes of the second winding’s voltage and the transformed voltage of the primary winding of the CVT. The phase error, on the other hand, is the difference between the phase voltages of the secondary and the primary winding of the CVT.
在这项研究中，用于评估 CVT 误差测量模型的实验数据来自测试实验室中的单相 66 kV CVT。评估持续了六天，时间间隔为 1 分钟。收集的数据包括目标 CVT 和与其安装在同一母线中的 66 kV 标准电感电压互感器 (IVT) 测量的相电压比和相位数据。CVT 计量的误差以比值误差和相位误差来表征。比值误差是指 CVT 次级绕组电压的幅值与一次绕组的变压电压之差。另一方面，相位误差是 CVT 二次绕组和一次绕组的相位电压之差。
Assuming k , the turns ratio of the CVT, the following formulas are employed to calculate the ratio error (1) and the phase displacement (2) of a CVT:
假设 CVT 的转速比 k，则使用以下公式计算 CVT 的比值误差 (1) 和相位差 (2)：

$\mathrm{\Delta }\phi =\mathrm{\angle }\overrightarrow{U_{Sr}}-\mathrm{\angle }\overrightarrow{U_{Pr}}$$\mathrm{\Delta }\phi =\mathrm{\angle }\overrightarrow{U_{Sr}}-\mathrm{\angle }\overrightarrow{U_{Pr}}$Delta varphi=/_ vec(U_(Sr))-/_ vec(U_(Pr))\Delta \varphi=\angle \overrightarrow{U_{S r}}-\angle \overrightarrow{U_{P r}}
where ${\epsilon }_U,\mathrm{\Delta }\phi$${\epsilon }_U,\mathrm{\Delta }\phi$epsi_(U),Delta varphi\varepsilon_{U}, \Delta \varphi is the Voltage Error % and phase displacement, respectively. $\left|\overrightarrow{U_{Pr}}\right|$$\left|\overrightarrow{U_{Pr}}\right|$| vec(U_(Pr))|\left|\overrightarrow{U_{P r}}\right| is the magnitude of the primary winding voltage and $\left|\overrightarrow{U_{Sr}}\right|$$\left|\overrightarrow{U_{Sr}}\right|$| vec(U_(Sr))|\left|\overrightarrow{U_{S r}}\right| is magnitude of the secondary winding voltage. Correspondingly, $\mathrm{\angle }\overrightarrow{U_{Pr}}$$\mathrm{\angle }\overrightarrow{U_{Pr}}$/_ vec(U_(Pr))\angle \overrightarrow{U_{P r}} is the phase of the primary voltage and $\mathrm{\angle }\overrightarrow{U_{Sr}}$$\mathrm{\angle }\overrightarrow{U_{Sr}}$/_ vec(U_(Sr))\angle \overrightarrow{U_{S r}} is the phase of the secondary voltage.
在本文中， ${\epsilon }_U,\mathrm{\Delta }\phi$${\epsilon }_U,\mathrm{\Delta }\phi$epsi_(U),Delta varphi\varepsilon_{U}, \Delta \varphi 分别表示电压误差百分比和相位差。 $\left|\overrightarrow{U_{Pr}}\right|$$\left|\overrightarrow{U_{Pr}}\right|$| vec(U_(Pr))|\left|\overrightarrow{U_{P r}}\right| 表示初级绕组电压的幅值， $\left|\overrightarrow{U_{Sr}}\right|$$\left|\overrightarrow{U_{Sr}}\right|$| vec(U_(Sr))|\left|\overrightarrow{U_{S r}}\right| 表示次级绕组电压的幅值。相应地， $\mathrm{\angle }\overrightarrow{U_{Pr}}$$\mathrm{\angle }\overrightarrow{U_{Pr}}$/_ vec(U_(Pr))\angle \overrightarrow{U_{P r}} 表示初级电压的相位， $\mathrm{\angle }\overrightarrow{U_{Sr}}$$\mathrm{\angle }\overrightarrow{U_{Sr}}$/_ vec(U_(Sr))\angle \overrightarrow{U_{S r}} 表示次级电压的相位。

Fig 1. Schematic Diagram of a Capacitor Voltage Transformer [19]
图 1. 电容电压互感器示意图 [19]

Data series prediction is an essential problem in various fields, including finance, weather forecasting, and healthcare. The ability to accurately predict future data series values can enable decision-making and planning and improve the efficiency and effectiveness of various processes.
数据序列预测在各个领域都是一个至关重要的命题，包括金融、天气预报和医疗保健。准确预测未来数据序列值的能力可以使决策和计划成为可能，并提高各种流程的效率和效果。
In recent years, deep learning techniques, such as recurrent neural networks (RNNs) and long short-term memory (LSTM) networks, have shown great promise in data series prediction due to their ability to capture complex temporal dependencies and patterns in data. Deep learning can be applied to many domains of a power system; for instance, it can be used to model and predict measurement errors.
近年来，由于深度学习技术，如循环神经网络 (RNN) 和长短期记忆 (LSTM) 网络，能够捕捉数据中复杂的时序依赖关系和模式，在数据序列预测方面显示出巨大的潜力。深度学习可以应用于电力系统的许多领域；例如，它可以用来建模和预测测量误差。
One of the critical advantages of deep learning techniques for data series prediction is their ability to handle high-dimensional and noisy data. Deep learning models can learn features directly from raw data without the need for manual feature engineering. This can be particularly useful for time series data, which often exhibit complex patterns and trends that may not be immediately apparent.
深度学习技术在数据序列预测中的一大优势是它们能够处理高维和噪声数据。深度学习模型可以直接从原始数据中学习特征，而不需要手动进行特征工程。这对于时间序列数据尤其有用，因为时间序列数据通常表现出复杂的模式和趋势，这些模式和趋势可能不是立即可见的。
In data series prediction with deep learning, the first step is to preprocess the data and split it into training and testing sets. The training set is used to train the deep learning model, while the testing set is used to evaluate the model’s performance on unseen data. The next step is to design the deep learning model architecture, which typically involves selecting an appropriate type of neural network, such as RNNs or LSTMs, and tuning its hyperparameters, such as the number of hidden layers and the learning rate.
在深度学习数据序列预测中，第一步是预处理数据并将其划分为训练集和测试集。训练集用于训练深度学习模型，而测试集用于评估模型在未见数据上的性能。下一步是设计深度学习模型的架构，这通常包括选择一种合适的模型类型，例如 RNNs 或 LSTMs ，并调整其超参数，例如隐藏层的数量和学习率。
The measurement error data are time-series data, and due to the nonlinear characteristics, a suitable algorithm with adequate fitting ability should be chosen. The first step in measurement error modeling is data collection.
测量误差数据是时间序列数据，由于其非线性特征，应选择具有足够拟合能力的合适算法。 测量误差建模的第一步是数据收集。
The collected data is preprocessed to remove noise and outliers. The preprocessing step includes data cleaning, normalization, and feature extraction. Data cleaning involves removing any data that is corrupted or missing.
收集到的数据经过预处理以去除噪声和异常值。预处理步骤包括数据清理、规范化和特征提取。数据清理包括删除任何已损坏或丢失的数据。
The preprocessed data is then used to train a deep neural network model. The model is designed to predict measurement errors based on the real-time data. The model architecture includes multiple hidden layers, each consisting of a large number of neurons. The model is trained using a large dataset of real-time data. The presented model is constructed by Long Short-Term Memory (LSTM) Networks.
经过预处理的数据被用来训练一个深度神经网络模型。该模型旨在根据实时数据预测测量误差。模型架构包括多个隐藏层，每一层都包含大量的隐藏层。模型使用大量实时数据的训练数据集进行训练。所提出的模型由长短期记忆（LSTM）网络构建
Once the model is trained, it can be used to predict the measurement error data series. The approach is to use a sliding window technique, where the model is fed a sequence of input values and asked to predict the next value in the sequence. The predicted value is then added to the input sequence, and the process is repeated to generate a sequence of predicted values.
模型训练完成后，可以用于预测测量误差数据序列。方法是使用滑动窗口技术，其中模型被喂入一系列输入值并被要求预测序列中的下一个值。然后将预测值添加到输入序列中，并重复该过程以生成一系列预测值。
Mining a large amount of measurement error data with the aid of multiple hidden layers will be done in this algorithm.
利用多个隐藏层来挖掘大量测量误差数据，这是本算法将要完成的任务。
The high-level structures of the proposed model’s layers are illustrated in Fig. 2. Two prediction outputs are fetched by implementing the model: the amplitude and phase error time series of one of the three-phase voltages.
所提出模型各层的结构图示于图 2 中。通过模型执行，可以得到两个预测输出：三相电压之一的幅值和相位误差时间序列。
In this model, we have the conditioning range [1,t0-1] and the prediction range $[\mathrm{t}0,\mathrm{T}].\mathrm{t}0$$[\mathrm{t}0,\mathrm{T}].\mathrm{t}0$[t0,T].t0[\mathrm{t} 0, \mathrm{~T}] . \mathrm{t} 0 denotes the time instant from which Zi, (historical data time series) is assumed to be unknown at the prediction range. xi,t is the known covariate values. hi,t and ci,t denote respectively the hidden state and cell state of LSTM i at time instant $t$$t$tt.
$[\mathrm{t}0,\mathrm{T}].\mathrm{t}0$$[\mathrm{t}0,\mathrm{T}].\mathrm{t}0$[t0,T].t0[\mathrm{t} 0, \mathrm{~T}] . \mathrm{t} 0 以及预测范围 $t$$t$tt 。  $[\mathrm{t}0,\mathrm{T}].\mathrm{t}0$$[\mathrm{t}0,\mathrm{T}].\mathrm{t}0$[t0,T].t0[\mathrm{t} 0, \mathrm{~T}] . \mathrm{t} 0 表示时间实例，从该实例开始 Zi（历史数据时间序列）在预测范围内被假定为未知。 xi,t 是已知的协变量值。 hi,t 和 ci,t 分别表示 LSTM i 在时间实例 $t$$t$tt 处的隐藏状态和单元状态。
During the model’s training process, the voltage data from the under-examination CVT and the standard IVT are time series; consequently, the calculated error data, including training data, are also time series. They are calculated by differentiating the voltage data from the selected CVT and the standard IVT, the fundamental dataset used as the model’s unprocessed input data. The data is directed into the pre-processing part of the proposed deep-learning model, which
在模型的训练过程中，在研 CVT 和标准 IVT 的电压数据是时间序列；因此，计算误差数据（包括训练数据）也是时间序列。它们是通过对选定的 CVT 和标准 IVT 的电压数据进行微分计算得到的，这是作为模型未经处理输入数据的基础数据集。数据被导入到提出的深度学习模型的预处理部分，该部分
outputs two historical time series error data for one of the three-phase measured voltages. Subsequently, the calculated loss function and its gradients balance the model’s weights. Finally, after finishing all learning epochs, the model will be ready for prediction. The testing time series data is inputted into the model to validate it, and the model then outputs online predicted time series error data.
模型将三个相测量电压之一的历史时间序列误差数据作为输出。 然后，计算出的损失函数及其梯度平衡模型的权重。 最后，在完成所有学习纪元后，模型将准备好进行预测。 将测试时间序列数据输入模型以进行验证，然后模型输出在线预测的时间序列误差数据。

Fig 2. The high-level structures of the proposed model’s layers
图 2. 所提议模型的层的高级结构。
By applying the proposed method, the online measurement error of CVTs will be fully applicable to the power system operators, which is only acquired by analyzing data attributes and employing the proposed deep-learning model.
通过应用所提出的方法，CVT 的在线测量误差将完全适用于电力系统运营商，这只需要通过分析数据属性和采用所提出的深度学习模型来实现。

To evaluate the performance of both the target CVT and the standard IVT, voltage readings were analyzed over a period of six days, with measurements taken every five minutes for optimal accuracy. The evaluation utilized the main parameter settings detailed in Table 1 and was carried out using the widely popular Python programming environment, known for its effective data analysis and modeling capabilities. These tools and techniques produced dependable and precise results.
为了评估目标 CVT 和标准 IVT 的性能，对六天内的电压读数进行了分析，每五分钟进行一次测量以获得最佳精度。评估使用了表 1 中详细列出的主要参数设置，并使用 Python 编程环境进行，Python 编程环境以其有效的数据分析和建模能力而闻名。这些工具和技术产生了可靠且精确的结果。

Table 1. Model’s main parameters
## 表 1. 模型的主要参数 | 参数 | 值 | |---|---| | 输入大小 | 256 | | 隐藏大小 | 1024 | | 层数 | 4 | | 头数 | 8 | | 学习率 | 0.001 | | 优化器 | Adam | | 训练步数 | 100000 |

The error index for the ratio error is Mean square error (MSE), formulated as (3) for a sample size of n :
$$ \text{比率误差的误差指标为均方误差 (MSE)，对于样本量为 n 的情况，其公式为 (3)：} $$ $$ MSE = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y_i})^2 $$ $$ 其中，$y_i$ 是真实值，$\hat{y_i}$ 是预测值。 $$
$r{e}_{\text{MSE}}=\frac{1}{n}\sum _{i=1}^n{({\hat{r}}_t-r_i)}^2(3)$$r{e}_{\text{MSE }}=\frac{1}{n}\sum _{i=1}^n {\left({\widehat{r}}_t-r_i\right)}^2(3)$re_("MSE ")=(1)/(n)sum_(i=1)^(n)( widehat(r)_(t)-r_(i))^(2)(3)r e_{\text {MSE }}=\frac{1}{n} \sum_{i=1}^{n}\left(\widehat{r}_{t}-r_{i}\right)^{2}(3)
where $r{e}_{\text{MSE}}$$r{e}_{\text{MSE }}$re_("MSE ")r e_{\text {MSE }} is the MSE index for the ratio error and ${\hat{r}}_l$${\widehat{r}}_l$widehat(r)_(l)\widehat{r}_{l} and $r_i$$r_i$r_(i)r_{i} are the actual and measured error values of the target CVT at the time instant $i$$i$ii.
其中 $r{e}_{\text{MSE}}$$r{e}_{\text{MSE }}$re_("MSE ")r e_{\text {MSE }} 是目标 CVT 在时间点 $i$$i$ii 实际误差值与测量误差值之比的 MSE 指数， ${\hat{r}}_l$${\widehat{r}}_l$widehat(r)_(l)\widehat{r}_{l} 和 $r_i$$r_i$r_(i)r_{i} 分别是实际误差值和测量误差值。
$p{d}_{MSE}=\frac{1}{n}\sum _{i=1}^n{({\widehat{pd}}_l-p{d}_i)}^2$$p{d}_{MSE}=\frac{1}{n}\sum _{i=1}^n {\left({\widehat{pd}}_l-p{d}_i\right)}^2$pd_(MSE)=(1)/(n)sum_(i=1)^(n)( widehat(pd)_(l)-pd_(i))^(2)p d_{M S E}=\frac{1}{n} \sum_{i=1}^{n}\left(\widehat{p d}_{l}-p d_{i}\right)^{2}
The equation (4), $p{d}_{MSE}$$p{d}_{MSE}$pd_(MSE)p d_{M S E}, represents the MSE index for a sample size of $n$$n$nn used to measure phase displacement of the target CVT; where at time instant $i$$i$ii, the actual and measured error values of the phase displacement correspond to variables ${\widehat{pd}}_l$${\widehat{pd}}_l$widehat(pd)_(l)\widehat{p d}_{l} and $p{d}_i$$p{d}_i$pd_(i)p d_{i}, respectively.
The equation (4), $p{d}_{MSE}$$p{d}_{MSE}$pd_(MSE)p d_{M S E} , 表示用于测量目标 CVT 相位位移的样本大小为 $n$$n$nn 的 MSE 指标; 在时刻 $i$$i$ii , 实际相位位移的误差值分别对应于变量 ${\widehat{pd}}_l$${\widehat{pd}}_l$widehat(pd)_(l)\widehat{p d}_{l} 和 $p{d}_i$$p{d}_i$pd_(i)p d_{i} 。

The measurement results of the voltage magnitudes for both the target CVT and IVT is shown in Fig 3. As well as, the measurement result of the phase displacement is presented in Fig 4. Our evaluation results showed that our deep learning proposed model was able to accurately predict the measurement errors of the target CVT. We achieved a Mean Squared Error (MSE) of $2.628\dots \mathrm{E}-06$$2.628\dots \mathrm{E}-06$2.628 dotsE-062.628 \ldots \mathrm{E}-06 and $1.309\dots \mathrm{E}-09\mathrm{\%}$$1.309\dots \mathrm{E}-09\mathrm{\%}$1.309 dotsE-09%1.309 \ldots \mathrm{E}-09 \% for the ratio error and phase displacement of the CVT, respectively. These results demonstrate the efficiency and effectiveness of our measurement error modelling approach using deep learning. The experimental results show that the proposed model improves the measurement accuracy of the CVT.
目标 CVT 和 IVT 的电压大小测量结果如图 3 所示。此外，相位移的测量结果如图 4 所示。我们的评估结果表明，我们提出的深度学习模型能够准确预测目标 CVT 的测量误差。我们对 CVT 的比率误差和相位移分别实现了 $2.628\dots \mathrm{E}-06$$2.628\dots \mathrm{E}-06$2.628 dotsE-062.628 \ldots \mathrm{E}-06 和 $1.309\dots \mathrm{E}-09\mathrm{\%}$$1.309\dots \mathrm{E}-09\mathrm{\%}$1.309 dotsE-09%1.309 \ldots \mathrm{E}-09 \% 的均方误差（MSE）。这些结果证明了我们使用深度学习的测量误差建模方法的效率和有效性。实验结果表明，该模型提高了 CVT 的测量精度。

Fig 3. Measurement Result of the voltage magnitudes and the calculated Error%
图 3. 电压幅值的测量结果和计算出的误差%

Pd Measurement Pd 测量

Fig 4. Measurement Result of the Phase Displacement
图 4 移相器的相移结果

Fig 5. The Loss function curve of the model for the ratio error%
图 5. 模型的比率误差 % 的损失函数曲线
The performance of the proposed model is evaluated using simulation and the measured data. The paper has evaluated the performance of the presented model using Mean Squared Error (MSE). The success of the proposed approach embraces the Loss function curve of the model
建议的模型的性能使用仿真和测量数据进行评估。本文使用均方误差 (MSE) 对所呈现模型的性能进行了评估。所提出方法的成功之处在于模型的损失函数曲线
for the ratio, error%, after intercepting the fourth round (Epoch=4) as exposed in Fig 5. Similarly, At Epoch=3, the convergence of the model for the phase displacement is chiefly completed, and the convergence of the curve, as demonstrated in Fig 6, remains steady.
关于误差率，在图 5 中显示， 在截获第四轮（Epoch=4）后，模型的收敛基本完成。 类似地，在 Epoch=3 时，模型对相位位移的收敛也基本完成，如图 6 所示， 曲线的收敛保持稳定。
The results demonstrate the effectiveness of the measurement error modeling approach while improving the measurement accuracy of CVTs.
该结果表明测量误差建模方法的有效性，同时提高了 CVT 的测量精度。

Fig 6. The loss function curve of the model for the phase displacement
图 6. 模型在相位移位下的损失函数曲线

The CVT measurement error data is a time-series data with long-term dependencies, and therefore, the prediction task is challenging. To overcome the deficiencies of conventional mathematical measurement error models, a deep learning method is conducted. This data-driven approach excavates the near-to-real data from raw measurement data and enables the power system to operate more efficiently and securely. By applying the proposed method, the online measurement error of CVTs will be fully applicable to the power system operators, which is only acquired by analyzing data attributes and employing the proposed deep-learning model. This method can also detect and diagnose anomaly CVTs with excessive measurement errors and facilitate preventive maintenance and supervision. The model’s efficiency has been demonstrated through experimental results, making it a promising solution for online metering in power systems. In conclusion, the study provides a reliable and efficient way to detect and diagnose measurement errors in CVTs. As part of our ongoing development efforts, we are considering applying the proposed method on a substation to get online error monitoring of its CVTs. By leveraging this method, we aim to achieve greater efficiency and accuracy in monitoring and maintenance activities.
## 翻译结果： 由于 CVT 测量误差数据属于具有长期依赖性的时间序列数据，因此其预测任务极具挑战性。为了克服传统数学测量误差模型的不足，本文提出了一种深度学习方法。这种数据驱动的 方法能够从原始测量数据中挖掘出接近真实的数据，并使电力系统运行更加高效和安全。通过应用本文提出的方法，电力系统运维人员可以仅通过分析数据属性和 使用所提出的深度学习模型，便能够全面适用 CVT 的在线测量误差。该方法还可以检测和诊断测量误差过大的异常 CVT，并进行预防性维护和 监督。实验结果表明，该模型的效率很高，使其成为电力系统在线计量的一种很有前途的解决方案。总之，该研究提供了一种可靠且有效的方法来检测和 诊断 CVT 中的测量误差。作为我们正在进行的开发工作的一部分，我们正在考虑将所提出的方法应用于变电站，以便对其 CVT 进行在线误差监测。 通过这种方法，我们旨在提高监控和维护活动的效率和准确性。

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