Error state prediction method for electronic voltage transformer based on empirical mode decomposition and auto-regressive moving average

Electronic voltage transformers have been used in the power system in conjunction with the development of power grid intelligence due to their good insulation structure, economy, volume, and other advantages. However, in its long-term operation, the phenomena of error overshooting and unstable operation will inevitably occur, and the existing periodic off-line testing methods require a high calibration cycle, which is difficult to achieve. To solve these problems, an error state prediction method based on empirical mode decomposition and autoregressive moving average model is proposed. Firstly, according to the physical correlation between the secondary output signal and the error, the output signal is quantified as a statistic Q by the method of principal component analysis, and then the statistic is used as the prediction object to establish a prediction model for predicting the operating state of the electronic voltage transformer. The simulation results show that the model can accurately predict the trend of the transformer error, which meets the prediction requirements.


Introduction
For the power system measurement, protection, and other secondary equipment, Electronic Voltage Transformers (EVT) can convert the primary side of the high voltage into a certain proportion of lowvoltage and easily measurable instrumentation of small signals, to provide accurate voltage signals [1][2] .However, under the complex operating environment of smart substations, the long-term stability of the metering error of EVTs is poor and the phenomenon of error overshooting will occur, which will have an impact on power metering [3][4] .Therefore, to ensure the safe and stable operation of intelligent substations, it is necessary to research the metering error state detection and prediction technology of EVT.
The detection of measurement errors in electronic transformers is now generally performed by comparison with the standard [5][6] .Compared with the traditional electromagnetic transformer, EVT has a shorter calibration period, and it is difficult to achieve frequent non-faulty outages, resulting in the EVT exceeding the calibration period, which is a potential safety hazard [7] .
Existing online detection methods are mainly classified into three categories: error detection methods based on signal processing, model analysis, and knowledge diagnosis, respectively.A method based on a wavelet singular entropy algorithm is used for online monitoring of the operating state of the transformer [8] .An online assessment of the error state is proposed based on factor analysis, realizing the abnormal positioning of the three-phase electronic voltage transformer through the contribution rate of the statistics [9] .However, this method can only be used for short-term error state detection, and cannot adapt to the changing environment in the long-term operation of the power grid.A method to establish a π-type equivalent circuit is proposed, but due to the complex operating environment of the power system, the generality of the mathematical model is not strong [10] .Corresponding assessment methods for different operating states are proposed based on knowledge diagnosis, but this method is more subjective and the assessment reliability is not enough [11] .Therefore, it is necessary to study a more accurate online self-testing method of EVT to ensure the normal operation of the power system.
In the actual operation of EVT, it is not only necessary to make a fast diagnosis when its metering error is abnormal, but furthermore, it is necessary to make a timely prediction of the deterioration trend of EVT metering error to reflect the long-term operation status of the transformer.Aiming at the shortcomings of existing methods, this paper proposes a method for predicting the error state of electronic voltage transformers based on principal component analysis and EMD-ARMA.By using the principal component analysis method, the characteristic statistic Q is extracted from the secondary output signals, and the prediction model is established with the statistic Q as the prediction object.The EMD method is used to decompose and reconstruct the nonlinear and non-stationary statistic Q time series, and then the ARMA prediction model is established to realize the prediction of the error state of EVT.

Selection of prediction object
Due to the dynamic equilibrium of the grid operation state, the three-phase voltage vector sum is zero, and there is a time-invariant physical relationship in the power system.The secondary output signal of the three-phase transformer will be bound by the physical relationship of the primary voltage and can be analyzed by the method of statistical analysis.

Construction of the statistic Q
Principal Component Analysis (PCA) is a commonly used multivariate statistical analysis method.When the metrological error state of the EVT is abnormal, the projection of the three-phase measurement data in the residual subspace will be shifted.The degree of deviation of the error state of the error in the EVT secondary measurement data can be determined by comparing the Q statistic with the statistical control limit Q in the residual space.

Empirical mode decomposition
Empirical Mode Decomposition (EMD) is widely used in the field of signal decomposition and processing.EMD does not require any pre-set basis function and can decompose the original signal into multiple Intrinsic Mode Function (IMF) components and residual terms according to its time scale.IMF has the characteristics of localization and adaptivity, which can effectively decompose non-linear and Unstable signals.
The decomposition process of EMD is as follows: (1) For the input signal, we find the extreme value point and the minimal value point; (2) We construct the upper and lower envelopes by interpolating the cubic spline function to the extreme value point and the minimal value point, and calculate the mean value function of the upper and lower envelopes; (3) We examine whether the condition of the IMF is satisfied.If so, we will go to the next step, and otherwise, we will carry out the first two steps until the condition of IMF is satisfied.Then, first IMF is obtained; (4) We repeat the above until the signal is monotonic or only one pole exists, and the decomposition is complete.
The statistical Q data is decomposed by EMD to obtain a set of IMF components ci (t) (i=1, 2,......., s) and a residual residue r(t), and each IMF component represents the vibration mode of the signal on different time scales.The high-frequency IMF components in the front will appear in the noise sequence, through the correlation coefficient between the IMF components and the original data to determine whether the decomposition of the IMF components is valid or not.The correlation coefficient for the first time to obtain the smallest value of the corresponding component is the bounding IMF function, and then we reconstruct the low-frequency IMF components and residuals of the bounding to get the smoother statistical quantities of the sequence.

ARMA modelling
ARMA is an important method for studying the time series, and it is a prediction model based on the autoregressive moving average (AMAR) model.
ARMA prediction needs to go through the steps of model type identification, model ordering, parameter estimation, and residual series autocorrelation tests.The model type can be determined based on the nature of its autocorrelation and partial correlation coefficients, where p is the order of the auto-regressive model, and q is the order of the moving average model.The model order is often determined by the Akaike information criterion (AIC).The smaller the value of the information criterion is, the better the ARMA model is for the corresponding (p, q)-order.The model parameters are estimated based on the historical state data of the time series, which can be directly estimated by using the least-squares method.Finally, the obtained model is subjected to the DW (Durbin-Watson) statistic to detect the autocorrelation of the residual series and to verify the reasonableness of the model.

EMD-ARMA prediction model
The ARMA model is based on a smooth data series, so the Q-statistics need to be processed before prediction.After EMD decomposition, the complexity of the series can be reduced and the prediction accuracy can be improved.The EMD-ARMA prediction model proposed in this paper includes the following five steps: (1) We collect data on the normal operation of the EVT, establish a PCA model, and quantify it as the statistic Q; (2) We build an EMD model to decompose the statistics and test the smoothness of each disintegrated IMF component and residual term.If the sample series is a non-smooth time series, the series shall be processed until the data series becomes smooth; (3) We select the effective IMF components and reconstruct them to obtain a smooth new signal; (4) We determine the model order of the time series and each model parameter; (5) We establish the ARMA model for the reconstructed statistic signals and make predictions to obtain the predicted value of statistic Q.

Predictive evaluation indicators
Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) were chosen as the basis for discriminating the prediction accuracy, and the RMSE and MAE were calculated as follows: where n is the number of predicted statistics, ypre is the predicted value of the statistic, and yreal is the true value of the statistic.

PCA-based EVT error state assessment
To truly reflect the fluctuation information of the primary voltage, the 110 kV three-phase EVT secondary output data is collected to obtain a data set of 3, 000×3.The PCA model is built by using MATLAB to analyze the secondary output information of the EVT and obtain the Q statistics under normal operating conditions, as shown in Figure 1

EMD-ARMA model prediction results
under normal operating conditions.The establishment of a time series prediction model needs to accurately grasp its internal relationship and set appropriate parameters.Due to the non-stationarity and non-linearity of the Q-statistic series, it is not suitable to build the model directly for prediction.Therefore, the EMD model is used to decompose the Qstatistics data, remove the invalid components to reconstruct them, and then build an ARMA prediction model for the reconstructed signals to make predictions.
The first 1, 000 data sets of the data were selected as the training group for model training, and the last 1, 000 data sets were predicted.The autoregressive and sliding average model orders were selected based on the AIC values at different orders, as shown in Table 1.According to the autocorrelation and partial autocorrelation coefficients and the AIC values at each order, the autoregressive model order p of the ARMA model was selected as 4, the moving average model order q was selected as 3, and the model DW value was 2.05.The final obtained statistic prediction map is shown in Figure 2. As can be seen from Figure 2 (a), the EMD-ARMA model can predict the Q-statistics data series of EVT under normal operation conditions with more accuracy.The prediction evaluation index RMSE is 0.13% and MAE is 0.08%.
The predicted values of the Q-statistics data series are compared with the statistic thresholds to determine the operational status of the EVT.The monitoring graph of the predicted value of the statistic in the normal operation state is shown in Figure 2 (b).The total number of abnormal points exceeding the statistic threshold is 0, and the EVT is in the normal operation state, which is consistent with the actual operation state.After the EMD decomposition was completed, each IMF component and residual residue term obtained from the decomposition was reconstructed to build an ARMA prediction model for prediction.According to the AIC values at different orders, the autoregressive model order p of the ARMA model is selected as 5, the moving average model order q is 5, and the model DW value is 2.0084.The first 1, 000 data sets of the data are selected as the training group for training, and the prediction is carried out on the last 1, 000 data sets to obtain the predicted value of the Q-statistic under the error state of 0.2%.The Q statistic data series prediction graph obtained through simulation experiments is shown in Figure 3.As can be seen from Figure 3 (a), the EMD-ARMA model can predict the trend of the statistic more accurately.The prediction evaluation index RMSE is 0.48% and MAE is 0.26%.
Comparing the predicted value of statistics in the error state with the threshold value, the monitoring graph is shown in Figure 3 (b).The total number of abnormal points exceeding the statistics threshold is 1, 000, and the percentage of abnormal points is as high as 100%, so it can be judged that the EVT is in an abnormal operation state, which is consistent with the actual operation state.

Conclusion
In this paper, a study is conducted on the online detection of metering error and prediction of the operating state of electronic voltage transformers (EVTs).By analyzing the secondary output data of three-phase EVTs, the signals characterizing the metering error are separated and quantified as Q statistics by the method of principal component analysis.To predict the trend of EVT metering error, an EMD-ARMA-based EVT error state prediction model was established with the Q statistic as the prediction object, and the ARMA model predicted the data after determining the smoothness of the data series.Because the Q statistic data is a nonlinear and non-smooth complex time series, it is difficult to guarantee prediction accuracy by direct prediction, so the EMD-ARMA model is proposed.Firstly, we decompose the data and then select the appropriate components to reconstruct, and finally, the reconstructed signals are used as the new statistical data to make the prediction.The simulation and comparison results show that the EMD-ARMA model can more accurately predict the trend of the electronic voltage transformer error state, and have a positive impact on the smooth operation of intelligent transformer stations.

Figure 1 .
Figure 1.Statistic monitoring graph in normal state and error state.

Figure 2 .
Figure 2. Prediction and monitoring graph of statistics in normal state.

Figure 3 .
Figure 3. Prediction and monitoring graph of statistics in the error state of 0.2%.