## 4 Actual Detected Temperature and Numerical Simulation Results
### Fully Distributed Internal Temperature Revelation
Figure 10: Spatiotemporally continuous temperature distribution along the (**a**–**c**) iron core limbs, phase A, B, and C, respectively and (**d**) inside wall of the oil tank. The actual status and life expectancy of a transformer is mainly determined by its insulation condition which is directly influenced by the hotspot temperature (HST). According to the traditional IEC calculation [13], the hotspot always appears at the top of windings with a relatively higher temperature, which may be attributed to the ignoration of the top area heat dissipation conditions in its idealized model. In fact, the cooling conditions in top area exhibit a great impact and cannot be easily ignored, as shown in Table 2, which will cause different shifts of hotspot location for different windings. Meanwhile, the IEC standard model also cannot obtain the distributed temperature data for different windings and lacks information about the iron core, oil tank, etc. Obviously, the actual internal temperature distribution exhibits a strong position dependence, which can be possibly attributed to the different surrounding circumstances, such as irregular oil flows, various structural components, etc. Thus, the point-type detecting method would inevitably exist huge monitoring blind zones, leaving hidden dangers for the transformer's safe operation. Thus, the direct contact detection of DOFS is of great significance for the field applications compared to the traditional model-based calculation and point-to-point measuring methods. The hotspot spatial distribution (phase A) and the transient temperature changes are also exhibited in Figures 12 and 13. The transient hotspot temperature showed a rapid increase before 1 h and then a slow upward trend. This phenomenon was caused by the insulating oil flow. At the very start, the cold oil was static, resulting in a fast local temperature rise (no flow means no heat convection). However, with the heat generated from windings continuing to accumulate, once the oil lifting force was larger than its gravity (1 h for this transformer), the static oil which carried lots of heat, began to circulate. This process explains the slow ascent of the temperature in the later part. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Monitoring Method**} & \multicolumn{2}{c}{**Phase A**} & \multicolumn{2}{c}{**Phase B**} & \multicolumn{2}{c}{**Phase C**} \\ \cline{2-7}  & **Pos. 1 (\%)** & **Temp. (\({}^{\circ}\)C)** & **Pos. 1 (\%)** & **Temp. (\({}^{\circ}\)C)** & **Pos. 1 (\%)** & **Temp. (\({}^{\circ}\)C)** \\ \hline \multirow{4}{*}{DOFS} & HV winding & 89.5 & 54.8 & 90.2 & 53.7 & 91.1 & 51.9 \\  & LV winding & 88.4 & 72.9 & 91.3 & 77.8 & 88.7 & 74.8 \\  & Core limb & 94.3 & 52.9 & 94.4 & 53.7 & 96.2 & 50.9 \\  & Oil tank & & & \multicolumn{2}{c}{T\({}_{\text{max}}\): 66.2 Pos.: upper or lower part} \\ \hline \multirow{4}{*}{IEC method 2} & HV winding & & & Pos.: cannot be obtained Temp.: 57 \({}^{\circ}\)C & \\  & LV winding & & & Pos.: cannot be obtained Temp.: 79 \({}^{\circ}\)C & \\  & Core limb & & & cannot be obtained & \\  & Oil tank & & & cannot be obtained & \\ \hline \hline \end{tabular}  
* On average and within 2% fluctuation (possibly caused by the oil flows). 2 Based on thermocouples and assumes that the hotspot always appears at the top of the windings and there is no difference between three phases [13].  
\end{table} 
Table 2: Hotspot detecting results compared with the IEC calculation. Figure 12: Hotspots distribution in phase A of (**a**) HV windings, and (**b**) LV windings.