## 4 Actual Detected Temperature and Numerical Simulation Results  
### Fully Distributed Internal Temperature Revelation  
The temperature-rise test was strictly performed according to the corresponding IEC standard [13], simultaneously, the spatiotemporal temperature changes inside the operating transformer were also monitored in a distributed manner. The temperature-rise test was performed with the short-circuit method. It was composed of two steps, that is, applying total losses (first 8 h) and applying the rated current (the last hour). The as designed optical fiber sensor displays an effective sensing performance under the complex thermal conditions inside the power transformer and works stably all the time. The fiber laying length of each monitoring area is also exhibited in Figure 9.  
For all the windings, the sensing fibers were connected with each other through the optical fiber patch cord on the outer side of the fiber flange (data of these extra fibers are not included in the results). The temperature distribution of the iron core limbs and the oil tank inside wall are shown in Figure 10.  
As for Figure 9a,c,e, the HV winding temperature presents an increasing trend with the height (the fiber was uniformly and spirally winded along the winding surface, so the fiber length can be normalized to the percentage of winding height). The hotspot gradually appeared after 3 h (80% of the highest temperature), around 44 \({}^{\circ}\)C, 43 \({}^{\circ}\)C, and 42 \({}^{\circ}\)C for phase A, B, and C, respectively. At the end of first step (8 h), the hotspot appeared at around 89%, 90%, and 91% of the winding height for phase A, B and C, respectively. The LV winding displays a higher temperature compared to the HV winding due to its higher current, as shown in Figure 9b,d,f. The temperature increases with the winding height except for a downtrend in the top area, which may be caused by its relatively better heat dissipation conditions. The hotspot gradually arose after 2 h, almost 60 \({}^{\circ}\)C located at 85-92% of the winding height. The hotspot continued to spread to a larger region with the passage of time. And at 8 h, the hotspot for phase A, B, and C appeared at 88%, 91% and 88% of the winding height, respectively. For the core limbs, exhibited in Figure 10a-c, the temperature distribution shows a positive correlation with the height for each phase. The hotspot appeared between 94% and 96% of the limb height for phase A, B, and C, respectively. However, there is little magnetic flux in the iron core during the short-circuit temperature-rise test and thus, the detected temperature may have a lower value compared to the actual situations. The temperature along the inner wall of oil tank is shown in Figure 10d, which displays an increasing trend with time. However, the temperature distributed in an uneven way due to the continuously unstable oil flows along the tank wall and the hotspot appeared alternately on the upper or lower part of tank. Figure 8: Field application of the DOFS integrated power transformer. The hotspots of all the windings were closely monitored and continuously located, as exhibited in Figure 11. And the DOFS detecting results are compared with the IEC traditional calculating results in Table 2.  
As shown in Figure 11, the hotspots gradually came to a steady position after around 1 h for both the HV and LV windings. It can be possibly attributed to the fact that the oil gradually started to circulate at around 1 h. Before this time, the cold oil has a relatively large viscosity and there is almost no heat convection process inside the transformer, leading to a random position of the hotspot. Figure 9: Spatiotemporally continuous temperature distribution along the (**a,c,e**) HV winding, phase A, B, and C, respectively and (**b,d,f**) LV winding, phase A, B, and C, respectively. Figure 11: Hotspots trajectory of (**a**) HV windings and (**b**) LV windings.