## 3 Prediction of AWTT  
### Correlation Analysis of Original Variables  
The load borne by the transformer is real-time fluctuations during the operation. The heat transfer process includes the heat generated by load loss at the corresponding moment. This process is continuous and uninterrupted, so the AWTT is dynamic, influenced by ambient temperature, oil temperature, load [18], wind velocity [21], harmonics [22], insulation paper [23], and solar radiation [24]. In the on-site situation, the placement of sensors is relatively strict, and some parameters are inconvenient to measure. In addition, if the cooling method of the transformer is ONAN, it is impossible to assign initial values to the  
Figure 1: Internal heat transfer process of transformer.  
oil flow velocity and fit the oil flow direction through mathematical formulas. Therefore, ambient temperature, load current, and top oil temperature, affecting the temperature elevation characteristics of transformers, are selected as the fundamental parameters to predict AWTT.  
Figure 2 shows the trend of data points in the scatter plot clearly among ambient temperature, load current, and top oil temperature. The purple are data points. The orange shows the relationship between top oil temperature and load current. The blue shows the relationship between top oil temperature and ambient temperature. The green shows the relationship between ambient temperature and load current. Preliminary assessments are conducted on the correlation between these three key parameters. With the increase in one characteristic parameter, another characteristic parameter also tends to rise, indicating a rough positive linear correlation between any pair of the parameters within the three.  
In order to obtain more accurate and reliable results for quantitative analysis, the Pearson correlation coefficient is adopted to further analyze the numerical correlation among ambient temperature, load current, and top oil temperature. The Pearson correlation coefficient can assess the correlation between two variables, and the calculated value is within the range of \(-1\) to \(1\) and can be expressed as follows:  
\[\rho_{X,Y}=\frac{s(X,Y)}{\sigma_{X}\sigma_{Y}}=\frac{\sum\limits_{i=1}^{n}{(X_ {i}-\overline{X})(Y_{i}-\overline{Y})}}{\sqrt{\sum\limits_{i=1}^{n}{(X_{i}- \overline{X})^{2}\sum\limits_{i=1}^{n}{(Y_{i}-\overline{Y})^{2}}}}} \tag{4}\]  
where \(s\) is covariance; \(\sigma_{X}\) and \(\sigma_{Y}\) are the standard deviations of variables \(X\) and \(Y\); \(\overline{X}\) and \(\overline{Y}\) are the average values of \(X\) and \(Y\); \(n\) is the number of samples; and \(X_{i}\) and \(Y_{i}\) are the variables, respectively.  
In accordance with the correlation coefficient in Table 2, the correlation coefficients among the ambient temperature, load current, and top oil temperature are all above \(0.6\). Among them, the strongest correlation is found between the top oil temperature and the  
Figure 2: Scatter plot.  
ambient temperature. The transformer dissipates internally generated heat to the external environment through the heat dissipation system. Radiation and convection are driven by temperature differences. Both are impacted by ambient temperature, changing the top oil temperature. Furthermore, the transformer is an intercoupling thermal system. The thermal coupling effect also results in a strong positive correlation between the load current and the top oil temperature. When the load current passes through the winding, resistance and eddy current loss are generated. The heat converted by the loss is transmitted to the cooling medium transformer oil through the heat transfer mode, causing an increase in the oil temperature. In addition, the increase in load current will lead to the accumulation of heat inside the transformer. The heat is dissipated to the external environment, affecting ambient temperature distribution.