Smart Protection Relay for Power Transformers Using Time-Domain Feature Recognition

Abstract

Conventional transformer protection schemes are limited by the difficulty in distinguishing inrush currents from internal and external faults, which restricts operational accuracy to below 70%. Existing solutions are constrained by a trade-off: sensitivity is compromised when setting values are increased, while speed is sacrificed when time delays are introduced. To address these limitations, a novel deep learning-based method for transformer fault identification is proposed. First, a feature model is constructed utilizing the time-domain sum of voltage and current fault components alongside current polarity characteristics. Subsequently, a channel attention-based Capsule Network (SE-CapsuleNet) is employed to automatically extract deep features across normal operation, inrush currents, and fault types. Simulation results demonstrate that inrush conditions are accurately differentiated from fault states. Robustness is maintained under high fault resistance (400 Ω) and 20 dB noise interference, while immunity to current transformer (CT) saturation and core residual magnetism is exhibited. The proposed protection relay simultaneously meets the requirements of rapid response, high sensitivity, and safety stability.

1. Introduction

1.1. Background

The safe operation of transformers is directly linked to grid reliability and power quality [1]. However, traditional differential protection is hindered by technical challenges.

First, a trade-off between sensitivity and selectivity is encountered in inrush identification. While inrush currents are avoided by increased setting values, sensitivity to internal faults, particularly high-resistance grounding faults, is sacrificed [2], whereas maloperation risks are increased by lowered thresholds. Second, response time is constrained by the conflict between speed and security. Selectivity is ensured via delay strategies at the expense of system stability [3], while maloperation probabilities are elevated by shortened operation times [4]. Finally, operational accuracy is compromised by external factors. Waveform distortion is caused by current transformer (CT) saturation [5], and high-resistance fault detection is complicated by small differential amplitudes, resulting in insufficient sensitivity near the neutral point [6]. These limitations are exacerbated by renewable energy integration, necessitating intelligent protection solutions.

1.2. Recent Work

Various protection strategies are proposed to address these challenges. Regarding inrush current, solutions are categorized into identification and suppression [7]. Identification is achieved through techniques such as harmonic ratio [8], wavelet analysis [9], Extended Kalman Filter (EKF) [10], and mathematical morphology [11,12]. Conversely, suppression is implemented via series resistance [13], core premagnetization [14], and closing timing control [15]. Furthermore, CT saturation is addressed through detection, compensation algorithms [16], and improved ratio differential characteristics [17]. However, these approaches are limited by high computational complexity. Similarly, high-resistance grounding faults are detected using sequence current criteria [18]; nevertheless, adaptation is hindered by reliance on manual thresholds [19], resulting in limited flexibility for engineering applications.

Significant potential is demonstrated by deep learning methods in transformer protection. These approaches are primarily categorized into two streams. First, differential current is utilized directly as input. Techniques such as artificial neural network [20] and accelerated convolutional neural networks (CNNs) [21] are employed to integrate feature extraction and detection, including structures like CLGNN [22]. However, these methods are characterized by reliance on large-scale data and weak interpretability. Second, features are preprocessed prior to model input. For instance, time-domain features are extracted via Variational Mode Decomposition (VMD) for hybrid models [23], or deep networks are constructed using Continuous Sparse Autoencoders based on DGA data [24]. While signal processing is combined with deep learning, expertise in feature engineering is necessitated.

Despite these advancements, several critical shortcomings persist. First, feature integration is insufficient; single current characteristics are predominantly used [25], leaving combined effects of multiple time-domain features underexplored. Second, advanced architectures are underutilized. Capsule Networks are employed significantly less in electrical diagnosis compared to mechanical diagnosis [26], and the integration of attention mechanisms is rare. Finally, unified solutions are lacking. A comprehensive scheme addressing inrush identification, CT saturation, and high-impedance faults simultaneously is absent from current methodologies.

Current research progress is systematically summarized and categorized into traditional methods and deep learning methods, as detailed in

Table 1. Summary of existing approaches to inrush current, CT Saturation, and high-impedance faults in transformer protection.

	Domain	Contribution
Traditional Methods	Inrush Current Identification	Harmonic ratio [8] Wavelet analysis [9] Extended Kalman filter (EKF) [10] Mathematical morphology [11,12]
	Inrush Current Suppression	Series resistance in the main circuit [13] Combined core pre-magnetization and controlled switching [14] Controlled switching strategy [15]
	CT Saturation Handling	Saturation detection and current compensation algorithm [16] Modified ratio differential characteristic [17]
	High-Impedance Fault Handling	Negative-sequence/zero-sequence current criteria [18]
Deep Learning Methods	Directly Using Differential Current as Input	Artificial neural network [20] Accelerated convolutional neural network [21] CNN-GRU hybrid [22]
	Using Preprocessed Differential Current as Input	VMD combined with CNN-BiLSTM [23] Continuous sparse autoencoder based on DGA [24]

.

1.3. Motivations and Contributions

A novel protection method integrating time-domain feature fusion and deep learning is proposed to address the security-reliability conflict in differential protection [27]. Deep learning is leveraged to optimize the sensitivity-selectivity trade-off via automatic feature extraction. While applied in transmission lines [28], this approach remains underexplored for transformers.

The main contributions are as follows: (1) A time-domain fusion method is developed, combining voltage/current components with polarity ratios to enhance fault characterization. (2) A channel attention-based SE-CapsuleNet is constructed; features are weighted adaptively and spatial correlations preserved for improved discrimination. (3) Robustness is validated via PSCAD simulations, maintaining stability under 400 Ω resistance and 20 dB noise. (4) A protection scheme utilizing a multipoint continuous confirmation mechanism is introduced.

The remainder part is organized as follows: Feature analysis is presented in Section 2, followed by the SE-CapsuleNet architecture in Section 3. Dataset generation and training are described in Section 4. Performance under interference is examined in Section 5. The protection scheme is detailed in Section 6, and the work is summarized in Section 7.

2. Transformer Time-Domain Feature Signal Fusion Method

2.1. Analysis of the Transformer Time-Domain Electrical Quantity Characteristics

Taking a three-phase two-winding transformer as the research object, as shown in Figure 1, I and II represent the high-voltage side and low-voltage side, respectively. The time-domain three-phase voltage and current fault components on both sides of the transformer are clearly the most fundamental electrical characteristics. However, relying solely on these methods is insufficient for fault discrimination and inrush current identification. Further exploration of characteristic quantities is conducted below.

The reference direction is conventionally assumed to be positive when current flows into the transformer. Ideally, under normal operation or external fault conditions, there is a 180° phase difference between the time-domain current signals of the same phase on the high-voltage side and the low-voltage side. However, when an internal fault occurs in the transformer, the phase difference between the same-phase currents on both sides becomes 0°. Therefore, the current polarity characteristic $p$ is defined to denote the polarity relationship of the currents on both sides. For instance, $p_{I-II}$ represents the current polarity relationship between the high-voltage side and the low-voltage side of a transformer.

$$p_{I-II}=\mathrm{sgn}(i_I(t)\cdot i_{II}(t))$$

(1)

where sgn is the sign function, which takes the value of +1 when the current is positive, −1 when it is negative, and 0 when it is zero. Clearly, when the transformer operates normally or experiences an external fault, $p_{I-II}$ = −1; when an internal fault occurs in the transformer, the corresponding phase is $p_{I-II}$ = 1. When the current is zero, the corresponding phase is $p_{I-II}$ = 0. This ratio is a dimensionless integer used to characterize the consistency or discrepancy between the current polarities on both sides.

CT saturation can cause distortion in the secondary side output current waveform, making it unable to accurately reflect the magnitude and phase of the actual current on the primary side. Taking CT saturation caused by internal and external faults of a transformer as examples, the $p_{I-II}$ values under CT saturation and nonsaturation conditions are compared, as shown in Figure 2. Under internal fault conditions, $p_{I-II}$ is dominated by 1; under external fault conditions, $p_{I-II}$ is dominated by −1. The current polarity ratio effectively retains the positive and negative polarity characteristics, compensating for the loss of fault features caused by current distortion.

To make the time-domain current signal characteristics more significant under normal and fault conditions, the current polarity ratio and $p_s$ are defined. The historical sampling moments and the current sampling moment $p_{I-II}$ are accumulated to obtain $p_{sI-II}$:

$$p_{sI-II}={\displaystyle \sum _{i=1}^n{p}_{I-II}}$$

(2)

Taking an internal fault as an example, Figure 3 shows the $p_{iaI-II}$ of the phase A current. Both the nonsaturated and saturated conditions tend to increase in terms of the sum of the current polarity ratios.

2.2. Input Model of Time-Domain Characteristic Quantities for Transformers

The time-domain characteristic information from both sides of the transformer, including the three-phase voltage and current fault components, as well as the three-phase current polarity ratio defined in this paper $p$ and the sum of the three-phase current polarity ratios $p_s$, is combined to form the input model of the transformer’s time-domain characteristic quantities. The fault components are calculated by taking the difference between the sampled values of three-phase electrical quantities within a specific data window and the corresponding sampled values from one cycle before fault occurrence. To demonstrate the effectiveness of the characteristic quantities constructed in this paper, the following three models are proposed:

Model 1: Composed of the three-phase voltage and current fault components from the high- and low-voltage sides of the transformer, including $d{u}_{aI}, d{i}_{aI}, d{u}_{bI}, d{i}_{bI},$$d{u}_{cI}, d{i}_{cI}, d{u}_{aII}, d{i}_{aII}, d{u}_{bII}, d{i}_{bII}, d{u}_{cII}, d{i}_{cII}$, totaling 12 sets of time-domain electrical characteristic quantities (corresponding to 12 channels), denoted as DM1.

Model 2: Combine the time-domain signals of Model 1 with the three-phase current polarity ratio $p$, resulting in $d{u}_{aI}, d{i}_{aI}, d{u}_{bI}, d{i}_{bI}, d{u}_{cI}, d{i}_{cI}, d{u}_{aII}, d{i}_{aII}, d{u}_{bII}, d{i}_{bII},$$d{u}_{cII}, d{i}_{cII}, p_{aI-II}, p_{bI-II}, p_{cI-II}$, totaling 15 sets of time-domain electrical characteristic quantities (corresponding to 15 channels), denoted as DM2.

Model 3: Combine the time-domain signals of Model 1 with the sum of the three-phase current polarity ratios $p_s$, resulting in $d{u}_{aI}, d{i}_{aI}, d{u}_{bI}, d{i}_{bI}, d{u}_{cI}, d{i}_{cI}, d{u}_{aII},$$d{i}_{aII}, d{u}_{bII}, d{i}_{bII}, d{u}_{cII}, d{i}_{cII}, p_{saI-II}, p_{sbI-II}, p_{scI-II}$, totaling 15 sets of time-domain electrical characteristic quantities (corresponding to 15 channels), denoted as DM3.

2.3. Data Fusion Method

The time-domain signals need to undergo effective fusion to form the training and testing datasets. The data fusion processing flow is shown in Figure 4.

When the time-domain feature quantity model is fused, the quantities of each channel are aligned in time stamps with data points as identifiers, thereby generating a sample set. Each channel covers data information from one cycle before and after fault occurrence. The power system frequency studied in this paper is 50 Hz. At the commonly used transformer sampling frequency of 4 kHz, one cycle contains 80 sampling points, while one sample comprises 160 sampling points, denoted as {0, 159}.

Subsequently, a sliding time window is employed to extract sample data with an equal step size starting from 0, thereby forming data segments for the training dataset. The length of the time window is set to 1/4 cycle, which corresponds to 20 sampling points at the 4 kHz sampling frequency. During the extraction of data segments for the training dataset, a sliding time window with a step size of 5 is adopted to enhance the speed of fault category discrimination by the model while preventing training overfitting. For instance, if the first extracted data segment is {0, 19}, the second extracted data segment is {5, 24}.

Similarly, a 1/4-cycle time window is applied. Starting from 0, the time window slides every step to extract sample data, forming the test dataset’s data segments. On the basis of the operational state information at the end time of each data segment, corresponding labeling is subsequently performed. The labeling method is illustrated in Figure 4. In this paper, 22 types of transformer operating states are set. Specifically, these correspond to 20 fault conditions, including single-phase-to-ground short circuits, phase-to-phase short circuits, two-phase-to-ground short circuits, and three-phase short circuits occurring both internally and externally to the transformer, as well as 2 nonfault conditions: normal operation and magnetizing inrush current.

3. Capsule Network Model Based on Channel Attention

3.1. Capsule Network

In traditional convolutional neural networks, positional information is lost when input vectors enter the pooling layer. The input model constructed in this paper consists of a combination of multichannel temporal electrical characteristic quantities, which inherently contain significant spatial structures. To effectively utilize and preserve the relative positional information between features, a capsule network is introduced to precisely capture the spatial correlations of various features in the equivalent image formed by the input vectors. Taking the phase change of the input signals as an example, the internal vectors of the capsule network adjust their values to accurately represent this new phase while keeping the vector length unchanged. The capsule network consists of a convolutional layer, a primary capsule layer, and a digit capsule layer.

(1) Primary Capsule Layer

The primary capsule layer normalizes the values of the output vector lengths between 0 and 1 using the squashing function, thereby representing the confidence of the capsules through their magnitudes. The formula for the squashing function is as follows:

$$v_j={\displaystyle \frac{{\parallel s_j\parallel }^2}{1+{\parallel s_j\parallel }^2}}{\displaystyle \frac{s_j}{\parallel s_j\parallel }}$$

(3)

where $v_j$ is the output vector of capsule j, $s_j$ is the input vector of capsule j, and $\parallel s_j\parallel$ represents the magnitude of vector $s_j$.

(2) Digit Capsule Layer

The digit capsule layer incorporates a dynamic routing algorithm, which iteratively optimizes the connection weights between primary capsules and digit capsules. Its core lies in updating weights on the basis of the directional alignment between the prediction vectors of lower-level capsules and the output vectors of higher-level capsules. The iterative formula is as follows:

$${\widehat{u}}_{j|i}=W_{ij}{u}_i$$

(4)

$$b_{ij}=b_{ij}+{\widehat{u}}_{j|i}\cdot v_j$$

(5)

$$c_{ij}={\displaystyle \frac{\exp (b_{ij})}{{\displaystyle \sum _k}\exp (b_{ij})}}$$

(6)

Here, ${\widehat{u}}_{j|i}$ is the prediction capsule, $W_{ij}$ is the weight matrix, $u_i$ is the output vector of the i-th primary capsule, $b_{ij}$ reflects the connection between the prediction vector and the output vector, with an initial value of 0, $v_j$ is the output vector of the j-th digit capsule, and $c_{ij}$ is the coupling coefficient used to evaluate the importance of lower-level capsules to higher-level capsules.

(3) Loss Function

The capsule network adopts the margin loss function as the optimization objective, calculates the loss values for each category and accumulates them to obtain the overall loss value. The formula is as follows:

$$L_k=T_k\max {(0,m^{+}-\parallel v_k\parallel )}^2+\lambda (1-T_k)\max {(0,\parallel v_k\parallel -m^{-})}^2$$

(7)

Here, $\parallel v_k\parallel$ represents the magnitude of the output vector from the k-th class capsule. $T_k$ serves as a label indicator variable, which is 1 when the sample belongs to the k-th class and 0 otherwise. $m^{+}$ defines the minimum value for the magnitude of the output vector of correctly classified capsules, typically set to 0.9. $m^{-}$ defines the maximum value for the magnitude of the output vector of incorrectly classified capsules, typically set to 0.1. $\lambda$ represents the weight coefficient for the lower-bound loss, balancing the proportion of classification loss between positive and negative samples, typically set to 0.5.

3.2. Capsule Network Based on a Channel Attention Mechanism

To enable the network to balance the weights of different channels, this paper introduces the squeeze-and-excitation block (SE block), whose processing flow is shown in Figure 5. Here, $H\times W\times C$ represents the shape and size of the input feature map F, $H$ and $W$ denote the height and width of the feature map, respectively, and $C$ indicates the number of channels.

In the squeeze stage, the feature map F is compressed into a one-dimensional vector via global average pooling, followed by nonlinear transformation through a fully connected layer to learn the dependencies between channels and generate corresponding weight coefficients for each channel. Finally, in the recalibration stage, the channel weights are multiplied channelwise with the feature map F, ensuring that the output dimensions remain $H\times W\times C$. Through this approach, the network enhances the feature responses of important channels while suppressing information from less critical channels, thereby improving the model’s expressive power and discriminative performance.

On this basis, in this paper, a channel attention-based capsule network, SE-CapsuleNet, is constructed on top of a convolutional neural network, whose structure is illustrated in Figure 6.

Convolutional layer C1 contains 28 $3\times 3$ convolutional kernels for preliminary feature extraction. The features subsequently pass through the SE module to balance the weights of each channel. The processed features are then fed into the convolutional layer C2, which employs 28 $4\times 4$ convolutional kernels for deep feature extraction.

The capsule network consists of 20 $3\times 3$ convolutional kernels. Afterward, the two-dimensional feature maps output by the convolutional layer are flattened into one-dimensional vectors through the primary capsule layer. These vectors are grouped into sets of 18 and concatenated into high-dimensional vectors, forming the digit capsules. The digit capsule layer uses a dynamic routing algorithm for three iterative operations, ultimately outputting several vectors. The number of these vectors corresponds to the total number of categories in the classification task, i.e., the number of operating conditions of the transformer. The magnitude of each vector represents the predicted probability of the corresponding category. The dimensional transformations during the forward propagation of SE-CapsuleNet are shown in

Table 2. Dimension transformation during SE-CapsuleNet forward propagation.

Processing Stage	Operation Description	Tensor Shape Transformation
Initial Input	Raw Feature Matrix	$15\times 20$
Convolution Extraction 1	3 × 3@28 kernels, stride 1, ReLU	$13\times 18\times 28$
Attention Enhancement	SE Channel Weighting	$13\times 18\times 20$
Convolution Extraction 2	3 × 3@28 kernels, stride 1, ReLU	$10\times 15\times 28$
Primary Capsule Layer	3 × 3@20 kernels, stride 2, ReLU	$4\times 7\times 7\times 20$
Dynamic Routing	Squash Function Aggregation	$22\times 18$
Output Layer	Vector Modulus Calculation	$22\times 1$

.

4. SE-CapsuleNet-Based Transformer Operational State Discrimination

4.1. Transformer Simulation Dataset

A transformer model, as shown in Figure 1, is built on the PSCAD platform, with a system frequency of 50 Hz and a sampling frequency of 4 kHz. The rated capacity of transformer T1 is 200 MVA, with a voltage ratio of 220/110 kV, and it adopts a Y/Y connection. Line Line1 has a total length of 60 km, with a resistance of 0.025 Ω/km and an inductance of 0.379 Ω/km.

For the transformer shown in Figure 1, after the protection elements S1 and S2 are disconnected, when S1 is closed, the transformer generates an inrush current when no load is close to the system. Three-phase voltage and current time-domain data from protection elements S1 and S2 of the transformer are collected to form sample data. The sample data under fault conditions include data from one cycle before and after the fault, i.e., 160 sampling points; the sample data under inrush current conditions include data from ten cycles after closing, i.e., 800 sampling points.

The simulation parameters for the training and testing datasets are shown in

Table 3. Simulation parameter settings of the dual-winding transformer.

Dataset Type	Operating Condition	Fault Setting Location	Initial Power Angle (°)	Fault Insertion Angle/ Closing Angle (°)	Fault Resistance (Ω)	Fault Distance (km)
Training Set	External Fault	Line1, Bus3	12/18/22/28/32	0~315 (sampled at 45° intervals)	0.1, 12, 85, 105, 210, 320	Line1: 22
	Internal Fault	Transformer High-Voltage Winding, Low-Voltage Winding	12/18/22/28/32	0~315 (sampled at 45° intervals)	0.1, 12, 85, 105, 210, 320	None
	Inrush Current	None	12/18/22/28/32	0~330 (sampled at 30° intervals)	None	None
Test Set	External Fault	Line1, Bus3	7/19/29	0~330 (sampled at 30° intervals)	0.5, 6, 155	Line1: 18, 38
	Internal Fault	Transformer High-Voltage Winding, Low-Voltage Winding	7/19/29	0~330 (sampled at 30° intervals)	0.5, 6, 155	None
	Inrush Current	None	3/7/19/25/29/35	0~330 (sampled at 15° intervals)	None	None

. Here, the initial power angle is defined as the phase difference between Source1 and Source2, which can be adjusted by modifying the phase angle value of Source1. The fault distance is defined as the distance from the fault point to protection unit S1 of Line1. In this paper, the fault occurrence time is set at 0.2 s.

The training set is partitioned into training, testing, and validation subsets in a ratio of 7:2:1. These subsets are utilized for model construction and fine-tuning during the training phase. The test set is obtained using parameter combinations and sliding windows that are completely different from those of the training set, which facilitates independent testing of the model under a broader range of operating conditions.

4.2. Training and Testing Results

After the time-domain features are input into models DM1–DM3 to complete the fusion processing operation, they are fed into the SE-CapsuleNet network for training. The performance changes in models DM1–DM3 during the training period are shown in Figure 7. Expected convergence is exhibited by the network during iterative optimization, evidenced by increasing recognition accuracy and decreasing loss values, consistent with typical deep learning training patterns.

When the test set in Table 3 is used for online performance verification, when the time window is set to 1/4 cycle, the 60th data segment first captures fault information. The changes in the identification accuracy of models DM1–DM3 for internal and external faults of the transformer are shown in Figure 8. During normal system operation, all the models demonstrate good state recognition capabilities. Starting from the 60th data segment, the identification accuracy of each model significantly decreases. However, identification accuracy is recovered as the proportion of fault characteristics within data segments increases.

The probabilities of models DM1–DM3 still misjudging abnormal states as normal states after a fault occurs are shown in Figure 9. The results indicate that, at the latest within 3 sampling points after the fault, the faulty state is no longer misclassified as a nonfault type.

The performance of models DM1–DM3 in identifying the transformer inrush current is shown in Figure 10. At the 0.02 s mark, a transformer no-load closing condition is set to generate an inrush current. The results show that DM1 has the risk of misidentifying the inrush current state as an internal transformer fault starting from the 6th cycle, whereas DM2 and DM3 maintain accurate identification throughout the ten cycles after the closing operation.

On the basis of the performance of each model at different stages, their operation processes can be divided into three parts: the fault-free zone, the fuzzy zone, and the stable zone. Taking DM3 as an example, a specific illustration is shown in Figure 11. The boundary between the fault-free zone and the fuzzy zone is the time node at which the model first misidentifies an abnormal state as a normal state. The dividing line between the fuzzy zone and the stable zone is defined as the time node when the recognition accuracy reaches 100% again or when the fluctuation amplitude stabilizes.

Additionally, this paper evaluates the actual effectiveness of the proposed SE-CapsuleNet model by constructing two deep learning models: the SECNN and the CAP. The SECNN model replaces the capsule network part of the SE-CapsuleNet model with two convolutional layers, two max-pooling layers, one fully connected layer, and one softmax layer. The CAP model is obtained by removing the SE block layer from the SE-CapsuleNet model. Performance validation was conducted using the test samples from Table 3. The results are presented in

Table 4. Comparative analysis of accuracy, ambiguous zone, and F1 score for various models.

Performance	Overall Accuracy (%)			Ambiguous Zone (ms)			F1 Score (%)
	SECNN	CAP	SE-CapsuleNet	SECNN	CAP	SE-CapsuleNet	SECNN	CAP	SE-CapsuleNet
DM1	94.26	94.57	94.48	5	5.25	4	94.06	94.37	94.28
DM2	95.33	95.65	95.72	5.5	4.75	4.25	95.13	95.45	95.52
DM3	95.62	95.67	95.80	5	4.5	4	95.42	95.47	95.60

. It can be observed from the data in Table 4 that the proposed SE-CapsuleNet achieves the highest overall average accuracy and F1 score, and the duration of the fuzzy zone is the shortest. The overall online performance is the best among the three, which strongly verifies the superiority of the SE-CapsuleNet proposed in this paper in highlighting fault features and learning capabilities. Subsequent studies will systematically explore the performance of the SE-CapsuleNet model under different operating conditions, such as CT saturation, inrush current, and high-resistance grounding faults.

5. Analysis of Factors Influencing Model Performance

(1) CT Saturation Caused by Faults

In this study, a dataset containing CT saturation characteristics is constructed by adjusting the current transformer ratio parameters in the original test dataset. The model validation results for this dataset are shown in Figure 12a,b. The test results indicate that compared with the model without CT saturation samples, the model trained with CT saturation samples has shorter durations in the fuzzy region and maintains 100% fault discrimination accuracy in the stable region.

Additionally, within a certain period after the fault occurs, the accuracy rates of various models exhibit a specific trend of change: first decreasing, then increasing, followed by another decline, and then increasing again. To understand this phenomenon, the relationship between current distortion under CT saturation and the variation in model accuracy rates was further investigated.

Figure 13 presents the confusion matrix obtained by testing exclusively with samples involving CT saturation from the test set. It can be observed that the identification accuracy for various types of internal and external faults generally exceeds 96%. A small number of misclassifications are primarily concentrated among fault types with similar features; however, severe misjudgments crossing the internal/external boundary do not occur. This indicates that the model remains capable of accurately delineating the protection zone and correctly classifying faults under conditions of CT saturation.

The dynamic changes in current waveforms under high-voltage-side CT saturation conditions are shown in Figure 14. During the initial 3 ms after the fault is triggered, the current transformer can still maintain linear transmission characteristics, and the normal current signals captured within the sampling window remain undistorted. As time progresses, distorted current data gradually begin to mix into the sampling window, with its proportion continuously increasing. The narrower the time window is, the greater the relative proportion of distorted data; when the time window fully covers the saturated CT data, the sampled signals are completely dominated by distorted waveforms, leading to a sharp decline in recognition accuracy. As the time window subsequently shifts, the proportion of distorted signals within the window starts to decrease, and the model’s accuracy rate recovers accordingly.

(2) Inrush Current Containing Residual Magnetism

The generation and development of the inrush current are constrained by two key parameters: the closing phase angle and the residual magnetic flux in the core. Among these, the closing phase angle determines the waveform characteristics of the inrush current, whereas the residual magnetic flux determines its peak magnitude and the angle of interruption. When residual magnetic flux exists in the core, the peak value of the inrush current generated at the instant of transformer energization significantly exceeds that under zero residual flux conditions. On the basis of the nonlinear magnetic flux-current characteristic curve of the transformer, this paper employs the superposition of a DC component in the PSCAD simulation environment to equivalently simulate the residual magnetic effect. In the simulation, the residual magnetic parameter is set to 0.7 p.u., thereby forming a test dataset for the closing inrush current that includes residual magnetic factors. The test results are shown in Figure 15.

As shown in Figure 15, model DM1 exhibits numerous identification errors within the first 10 cycles, which are primarily concentrated after the 6th cycle, with significant fluctuations in accuracy. In contrast, model DM3 achieves the best accuracy throughout all 10 cycles.

(3) Single-phase High-resistance Grounding Fault

To verify the identification capabilities of each model in high-impedance fault scenarios, in this paper, the fault resistance parameters are adjusted to three levels—260 Ω, 350 Ω, and 400 Ω—based on the original dataset, thereby constructing simulation conditions for minor faults inside and outside the transformer protection zone.

Testing revealed that in the nonfault zone and stable zone, the average accuracy of the three models under the three fault resistance levels essentially remained at 100%, whereas the average performance in the fuzzy zone is shown in

Table 5. Performance of models DM1–DM3 under single-phase high-impedance faults.

Input Model	Fault Resistance (Ω)	Average Fuzzy Zone Accuracy (%)	Fuzzy Zone Duration (ms)	Average Fuzzy Zone Duration (ms)
DM1	260	75.23	3.61	3.597
	350	76.15	3.45
	400	73.98	3.73
DM2	260	72.45	4.14	4.19
	350	73.82	3.86
	400	71.26	4.57
DM3	260	72.10	3.71	3.857
	350	75.23	3.61
	400	76.15	3.45

. The duration of the fuzzy region for all three models is less than 5 ms, indicating that the proposed deep learning method in this paper can identify single-phase grounding faults with fault resistances as high as 400 Ω, reliably achieving accurate discrimination of minor faults inside and outside the protection zone.

(4) Noise Interference

In this paper, three intensity levels of Gaussian white noise were superimposed on the original test samples, with the signal-to-noise ratio parameters set to 20 dB, 30 dB, and 40 dB. The experimental results show that the correct recognition rates of the DM1–DM3 algorithms for normal operating conditions are all 100%, with little difference in performance between the fuzzy and stable regions.

The number of sampling points occupied by fuzzy regions in each model is shown in Figure 16. Models DM1 to DM3 were not trained with noisy samples but still exhibited strong robustness. A comparison of the time spans of the recognition fuzzy regions among the three models reveals that the differences are small, and all the time spans are controlled within the selected time window length. In the stable region, the three models can still correctly identify all test samples, demonstrating good antinoise performance and effectively handling 20 dB noise interference environments.

(5) Different Short-Circuit Capacities and Voltage Levels

The input features selected in this paper primarily consider the following points:

(1)

The fault component is calculated by differentiating the post-fault electrical quantities from the pre-fault ones, thereby eliminating the steady-state component. The resulting transient feature waveforms possess similar morphological characteristics across transformers of different voltage levels;

(2)

As defined in Equation (1), the current polarity characteristic takes values only from {−1, 0, 1}, representing the polarity relationship between the currents on both sides of the transformer. This polarity-based feature is independent of voltage levels or topological structures and depends solely on the fault location;

(3)

The sum of the current polarity characteristics represents the trend of polarity variation over time, which is similarly independent of voltage levels or topological structures.

In this study, a new test set is constructed by altering the short-circuit capacity and voltage level based on the original test set to evaluate the model. The test results are shown in Figure 17:

It can be observed from the test results that the differences in accuracy and fuzzy zone duration under different conditions are insignificant. This indicates that variations in system short-circuit capacity have a negligible impact on model performance. Furthermore, by adjusting the normalization constant, the model can adapt to different voltage levels, confirming that features such as polarity and fault components are independent of voltage levels.

6. New Transformer Relay Protection Scheme

The SE-CapsuleNet proposed in this paper can effectively distinguish between normal transformer operation, internal/external faults, and inrush current phenomena without the need for additional activation criteria. Given that model DM3 demonstrates the best comprehensive performance, it is selected as the model for the protection scheme.

To effectively eliminate interference from ambiguous identification zones and reduce the likelihood of protection device maloperation, it is necessary to introduce an appropriate safety margin. Experimental verification reveals that when the safety margin is set to 1/8 cycle (with a 1/4 cycle time window for sample data capture), the total superimposed duration is 3/8 cycles. This parameter configuration successfully avoids misjudgment risks in ambiguous zones.

Furthermore, to enhance protection security, this paper adopts a multipoint continuous confirmation mechanism instead of directly outputting results based on single-sampling-point judgments. The core concept involves setting continuous detection windows with a length of s data points. A trip command is issued only when s consecutive data points confirm the same internal fault type. The value of s can be adjusted according to actual protection requirements. Practical applications demonstrate that setting s to 10 sampling points ensures sufficient safety in protection operations. In a 4 kHz sampling environment, one cycle corresponds to 80 sampling points. Furthermore, the test dataset in this paper is obtained by extracting sample data using a time window with a step size of one sampling point; therefore, 10 sampling points correspond to 1/8 cycle.

A flow chart of the novel protection scheme proposed in this paper is illustrated in Figure 18. When the parameter s is determined to be 10, the specific implementation steps of the proposed SE-CapsuleNet model for transformer relay protection are as follows: When the model first detects a fault signal, regardless of whether it belongs to an internal or external fault category, a 7.5 ms delay is triggered to avoid interference from ambiguous regions. During this delay period, the model does not output any discrimination information. After the delay ends, the model resumes its discrimination output. At this point, if the discrimination results of 10 consecutive sampling points are completely consistent and all point to a specific internal fault type, it is confirmed that the transformer has experienced that type of internal fault, and the tripping procedure is initiated to disconnect all sides of the transformer. Additionally, the protection does not operate in scenarios such as inconsistent discrimination results across 10 consecutive points or when 10 consecutive points are identified as external faults. The pseudo-code for the flowchart is provided in Appendix B to describe the protection scheme more clearly.

The timing sequence is illustrated in Figure 19. Upon an internal fault occurrence at time 0, the fault is detected by the SE-CapsuleNet at t1, initiating a 3/8-cycle delay. Data sampling resumes at t2 following a 1/8-cycle safety margin. Given the 1/4-cycle time window, the discrimination result is re-evaluated 1/4 cycle after t2. Transformer protection is actuated at t4 when 10 consecutive points are identified as the same internal fault type. Consequently, the total operating time, comprising t1, the 3/8-cycle delay (consisting of the safety margin and time window), and the 1/8 cycle for point verification, is maintained within 12 ms.

The proposed relay protection scheme in this paper eliminates the need for complex settings and offers a more flexible configuration. It effectively avoids inrush current and CT saturation without the need for additional discrimination conditions. When facing single-phase high-resistance grounding faults, it can withstand fault resistances up to 400 Ω. Even in a 20 dB noise environment, it maintains rapid and accurate fault discrimination capabilities, fully demonstrating excellent anti-interference characteristics and system stability. Furthermore, as the time-domain features adopted in this paper can all be calculated from three-phase electrical quantities, and the sampling frequency is consistent with that commonly used in transformer protection, the relay protection method proposed in this paper does not require additional sensors compared to traditional transformer protection, thereby demonstrating superior economic efficiency.

7. Summary

Transformer protection faces challenges in inrush, CT saturation, and high-resistance faults. A time-domain model utilizing voltage-current components and polarity ratios is constructed, and an SE-CapsuleNet is employed for classification. Validation is performed via PSCAD simulations. Key findings are as follows:

(1)

Polarity ratios are incorporated for input integration. While misjudgments occur in voltage-current-only models (DM1) after the 6th cycle, a fairly high accuracy is maintained by the proposed model (DM3) within 10 cycles. This is sufficient for fault type classification in the steady state.

(2)

The fuzzy zone is reduced to 4 ms by SE-CapsuleNet, outperforming SECNN (5 ms) and CAP (4.5 ms). Furthermore, in the stable zone, each type of working condition is given a very high confidence coefficient, such as nearly 100%. This validates the architecture’s efficiency.

(3)

Clear working condition classifications are sustained under adverse conditions (CT saturation, 0.7 p.u. remanence, 400 Ω fault resistance, 20 dB noise). Fuzzy zones for high-resistance faults are limited to 5 ms.

(4)

A scheme utilizing a 3/8 cycle delay and 10-point confirmation is proposed. Identification is completed within 12 ms at 4 kHz, eliminating manual threshold dependence.

The limitations of this study are hereby acknowledged. First, retraining is required for distinct topologies. Second, renewable energy characteristics (e.g., weak infeed) are not addressed; future work is directed towards relevant feature incorporation. Finally, as this study is simulation-based, hardware-in-the-loop (HIL) verification and complexity quantification remain to be performed.