## 4 Case Verification
### Case Verification
The prediction results obtained with this method are basically consistent with the actual measured AWTT change trend. Among them, the AWTT corresponding to the daytime is higher, and the AWTT at night is reduced, which is consistent with the actual situation. The daytime is the peak period of electricity consumption every day. Especially  
Figure 8: Prediction for AWTT results. from 9:00 to 17:00, the demand for the power grid is large. The transformer will bear a large load, and the load current will increase accordingly. The current in the primary and secondary transformer windings increases, resulting in a large amount of copper consumption in the coil resistor made of copper wire. The main heat sources during the operation of the transformer are iron core loss and winding loss. The increase in copper loss leads to more energy inside the winding to be converted into heat energy. This heat will first be transmitted to the winding and transformer oil in the form of heat conduction, affecting the AWTT and oil temperature. Heat is emitted from the outer wall of the fuel tank to the air through convective heat dissipation and thermal radiation. The expression between the heat and the temperature rise of the natural convection of the air, and the expression between the heat radiated from the tank wall to the air and the ambient temperature, are provided in (10) and (11). \[\phi=Sh(T_{w}-T_{h}) \tag{10}\]  
\[\phi=\sigma ES(T_{w}^{4}-T_{h}^{4}) \tag{11}\]  
where \(S\) is the surface area, \(h\) is the convective heat transfer coefficient, \(T_{w}\) is the outer surface temperature of the transformer tank, \(T_{h}\) is the ambient temperature, \(\sigma\) is the Stephen-Boltzmann constant, and \(E\) is the surface radiation coefficient. The greater the difference between the temperature of the oil tank wall and the ambient temperature, the more conducive it is for heat dissipation of the oil-immersed transformer to reduce the internal temperature. In most cases, 9:00 to 17:00 is a period of high temperature in the day. The temperature difference between the transformer tank and the surrounding air medium is small. The heat emitted into the air can be reduced accordingly, affecting the heat dissipation effect of the transformer. During this period, the AWTT is higher. On the contrary, in the low-power period with smaller load, that is, late at night and early in the morning, the corresponding heat generation is reduced, and the heat dissipation is increased. The AWTT during this period is relatively reduced. Figures 9  
(3) Comparative analysis  
To further show the effectiveness and superiority of the proposed method, the results of the thermal circuit guidelines, the results obtained with factor analysis of the original data, and the results obtained by using the Levenberg-Marquardt (L-M) method to train the network are compared with the actual measured values. The results are shown in Figures 11 and 12 and Table 8. Obviously, the prediction results obtained with the proposed method are optimal in terms of RMSE, mean absolute error (MAE), mean absolute percentage error (MAPE), \(R^{2}\), and absolute error compared with the results of other methods mentioned above. As a result, the proposed method can achieve more accurate prediction of the AWTT considering that the fitting results are more accurate with the actual measured values. Among those methods, the error result of the thermal circuit guideline method is the largest, and the RMSE reaches 14.72164. The reason is that the method relies on empirical values. However, the oil index and rated oil time constant values used in the calculation process are difficult to accurately obtain. They can only be roughly estimated based on parameters such as transformer capacity level, and the accuracy in reflecting the existing performance of transformers and the degree of oil aging is limited. There are errors between the actual values, resulting in significant deviations between the final results and the measured values.