Transformer is an important equipment in power system, which is related to the safety and stability of power system (Wu et al., 2021; Su et al., 2022). During the operation of the power transformer, several gases are generated in oil by the influence of life cycle, load, oil temperature and other factors. When the transformer overheats or discharges, there will be abnormal changes in gases (Gómez et al., 2014). Insulation will be broken down as the transformer fault develops, affecting the stability of the power system (Huang et al., 2021). Therefore, the state data of the power transformer can be obtained and its trend can be predicted by installing monitoring equipment on the transformer, which can provide a reliable judgment basis for the state maintenance of the transformer (Xie et al., 2020).

In recent years, a lot of research work has been done on the prediction of dissolved gas content in transformer oil. Chen et al. (2021) constructed an improved grey model for the time series prediction of gas in oil. K-nearest Neighbor was used to predict the furan level in transformers in (Shaban et al., 2016). In addition, many machine learning methods such as artificial neural networks (Ghunem et al., 2012) and support vector machines (Atherfold and van Zyl, 2020) are used for gas content prediction. The above methods process the data of each moment synchronously, so the feature significance of different moments cannot be considered, which means that their prediction accuracy is limited.

Recurrent neural network (RNN) extracts current and historical information by loop structure, which is suitable for processing time series. However, RNN is weak in learning information at too far time, which is called as “Long-term dependency problem.” The Long short-term Memory (LSTM) developed based on RNN introduces gating mechanism to alleviate the problem of RNN. Therefore, some prediction methods for gas content based on LSTM have been proposed (Lin et al., 2018b; Ma et al., 2021). But the complexity of LSTM leads to long training time. Gated Recurrent Unit (GRU) network was proposed as another variant of RNN, simplifies the gating mechanism, which can process long series efficiently and be trained fast (Minh et al., 2018).

There are complex dynamic relationships in gases in transformer oil (Fessler et al., 1989). When the hot spot temperature is low or the fault is slight, the insulating material produces hydrogen and alkanes through decomposition. When the fault is severe, the energy will be released by overheating or discharge, alkenes and alkynes will be produced by further decomposition. Therefore, the production of dissolved gases in oil has a certain correlation, and varies according to the fault type and development. Above methods are based on the prediction by single gas variable, which ignores the inherent correlations between gases, and the results are obtained with low accuracy and reliability. In the study of (Ma et al., 2021), temperature and seven gas content series were put into LSTM to predict gas content. Lin et al. (2018a) took the gas content and the ratios of various gas as the input features of neural network for the prediction. These methods consider the influence of various factors in the prediction, but the feature extraction methods of correlation factors are simple, and the promotion in prediction performance is limited.

For above problems, a content prediction method of gas in transformer oil based on gated recurrent unit and adaptive graph convolution network (GRU-AGCN) is proposed. GRU is used to extract time series information of gas content. To describe the correlation among gases, the original adjacency matrix of the model is constructed based on grey correlation analysis (GRA), and the adjacency matrix is real-time updated according to the input to ensure that the correlation obtained is accurate and reliable. The dynamic relation feature among gases is extracted by adaptive graph convolution network (AGCN). The accurate prediction of gas content can is achieved by integrating the historical information of gas itself and other relevant gas information.

GRU network is one of the variants of RNN. In GRU, gating mechanism is introduced to RNN to selectively transmit temporal features.

The structure of GRU network is shown in Figure 1A. Data [ x ₁, x ₂, …, x _T ] with length T are input into corresponding units chronologically. The structure of GRU is shown in Figure 1B. Take GRU of time t as an example (1 < t < T), the input of the unit includes current original data x _t and hidden feature h _t−1 output by the last unit. And the output of the unit is the hidden feature at time t denoted as h _t . The workflow of GRU is as follows, Firstly, input is passed to reset gate and update gate to obtain reset state r _t and update state u _t . Secondly, the candidate hidden state h ^ t at time t is calculated by reset state r _t . Finally, the hidden feature h _t at time t is updated by combining the updated state u _t with the hidden feature h _t−1 at time (t−1) and candidate hidden state h ^ t at time t. The working principle is written as follows: r t = f s i g x t W r 1 + h t − 1 W r 2 + B r (1) u t = f s i g x t W u 1 + h t − 1 W u 2 + B u (2) h ^ t = f tan ⁡ h x t W h 1 + r t ⊗ h t − 1 W h 2 + B h (3) h t = u t ⊗ h t − 1 + 1 − u t ⊗ h ^ t (4)

In above equations, f _sig(.) and f _tanh(.) are sigmoid function and hyperbolic tangent function, W _r1 and W _r2 are the weight of the reset gate, B _r is the bias of the reset gate, W _u1 and W _u2 are the weight of the update gate and B _u is the bias of the update gate. W _h1 and W _h2 are the weight and B _h is the bias in the candidate hidden state calculation. Hadamard Product operation is denoted as.

By above principle, historical information and current information can be filtered and processed flexibly in GRU network.

To verify the superiority of the proposed model, a GRU-AGCN model is built by Python language based on Spyder platform and PyTorch library.

Mean absolute error (MAE) and mean absolute percentage error (MAPE) are used to evaluate the prediction performance of the model. Suppose that gas content series in time 1∼t is used for prediction, denoted as X = [x ₁, x ₂, …, x _t ], the corresponding predicted value series is denoted as Y = [y ₁, y ₂, …, y _t ]. The MAE and MAPE are calculated as follows: f M A E X , Y = 1 t ∑ i = 1 t x i − y i (12) f M A P E X , Y = 1 t ∑ i = 1 t x i − y i y i (13)

A converter transformer in Henan Province is taken as the research object. It was put into operation in 2014 and has been operating normally ever since. Dissolved gases monitored include hydrogen (H₂), methane (CH₄), ethane (C₂H₆), ethylene (C₂H₄), acetylene (C₂H₂), carbon monoxide (CO) and carbon dioxide (CO₂), and their content is within the normal range stipulated by IEC. Eight hundred and twenty sets of data of the transformer from May to October 2019 were selected for the experiment. The time period is 4 h. The content of C₂H₂ is always 0 in the monitoring interval, which is not used as model input. The input of the model is set as the content series of six gases in 20 consecutive time points, and the output is set as the predicted value of gases at the next time point. The original gas content data are processed according to the above steps and 800 groups of samples were obtained. The size of training set and test set are divided by 3:1. The first 600 groups are set as the training set, and the last 200 groups are the test set.

The grey relational degree table of six gas content is obtained by GRA. As shown in Table 1, the correlations rang is distributed in [0.634, 1.000], which indicates that there are clearly exists correlations among six gases, but their intensity are different. Regardless of the self-correlation, CO and CO₂ are the most correlated, while the correlation between H₂ and CO₂ is the weakest.

Based on Table 1, the correlation degrees are introduced into AGCN of the model as original adjacency matrix. And parameter σ ² in the AGCN is set to 0.5, because it achieves the best result in model training.

Then, GRU-AGCN model is trained for 200 times, and the initial learning rate is set to 0.0005. The sample loss curve in Figure 3 is obtained. As shown in Figure 3, the model parameters converge to the global optimum quickly and smoothly during training.

To verify the accuracy and reliability of the proposed model in gas content prediction task, the GRU-AGCN model and other traditional models are used for single-step prediction experiment. The models used for comparison include RNN and its variants GRU Net and LSTM Net. In addition, original GCN is introduced into GRU Net and LSTM Net to form new models, denoted as GRU-GCN and LSTM-GCN respectively. Specific parameter settings of models are shown in Table 2.

Except for the model proposed in this paper and models introduced GCN, all other models are designed for univariate prediction. The input time scale, prediction range and training conditions of all models remained consistent. Hidden features of models are output through a linear layer and ReLU activation function. All models were trained 200 times.

Limited by space, this section mainly analyzes the result of CO₂ content prediction experiment. Table 3 records the training time and prediction effect of CO₂ content prediction by above models.

Firstly, RNN and its variants GRU Net and LSTM Net are compared. Obviously, RNN has the fastest training, but its prediction accuracy is far lower than other networks. Both GRU Net and LSTM Net introduce gating mechanism, which selectively extract features at different moments. Compared with RNN, MAE percentage of the two models decreased by 1.12 and 0.87 respectively. However, the training time of LSTM Net is much longer than that of GRU Net. It is proved that GRU Net can extract temporal features of gas content efficiently and is easier to train than LSTM Net.

Then, GRU Net and LSTM Net are compared with GRU-GCN and LSTM-GCN respectively. The prediction accuracy of model introduced GCN is significantly higher than the original model. The reason lies in that the information of the related gases has been used for the prediction by GRU in GRU-GCN model and LSTM-GCN model.

Finally, GRU-AGCN model is compared with GRU Net and GRU-GCN model. The prediction result by above models are shown in Figure 4. Based on the analysis of Figure 4 and Table 3, it can be found that GRU Net model only accurately predict the stable development of CO₂, as shown in 1st∼125th point of Figure 4, which shows a poor prediction effect on series with large fluctuation. The GRU- GCN utilized the correlations between the gases. But the model cannot obtain satisfactory prediction effect in long time span, because the real-time changes in gas relationships cannot be represented by static adjacency matrices. The proposed GRU-AGCN model has the smallest MAE and MAPE in prediction, which is only 20.6 s slower than GRU Net during the training. The proposed method obtains the best effect with an acceptable time cost. The reason is that GRU part of the proposed model can efficiently extract the temporal features of gas series, while the AGCN part adaptively adjust the graph adjacency matrix and dynamically acquire the gas relationship from learning samples, which makes the prediction result more accurate and reasonable than other models. The proposed model keeps high accuracy and reliability for series in stable situation or large fluctuations.

The change of gas content in transformer oil reflects the health status of transformer, which needs to consider both the temporal information from gas itself and the dynamic correlation information from related gases. Base on above two aspects, a prediction method based on GRU-AGCN model is proposed. From the experiment comparison and analysis, it can be concluded that:

1) GRU Net can extract key information of important moments from gas series, and its prediction is more accurate than RNN. Compared with LSTM Net, GRU Net is simpler, training faster, and extraction efficiency for the temporal features is higher.