## 2 Set-Up and Experimental Method  
The Karamay 45 transformer oil for national test standard GB/T 507 was chosen as the base liquid, whose breakdown voltage can reach 70 kV after a series of filtration and purification [39]. It has been demonstrated that the semiconductor nano-particles have the potential to improve the insulation performance [40]. In our experiments, we purchased the TiO\({}_{2}\) nano-particles and Al\({}_{2}\)O\({}_{3}\) nano-particles with diameters of 30 nm from DKNANO (Beijing, China).  
The typical preparation processes of nano-liquids are as follows: First, the nano-particles should be dried in vacuum at 100 \({}^{\circ}\)C for 24 h. Then, these nano-particles were dispersed in the transformer oil for about an hour by the use of planetary and vertical mixers. Subsequently, the mixtures were poured into an ultrasonic pulverizer for about 0.5 h. In the end, the mixtures were ground in an agate pot for 24 h. By repeating these processes, we prepared the evenly dispersed TiO\({}_{2}\) nano-liquids and Al\({}_{2}\)O\({}_{3}\) nano-liquids with different volume fractions [41].  
The experimental equipment is shown in Figure 1 and is composed of a microsecond pulse generator, breakdown test cell, and high-speed frequency camera(HSFC). Specifically, the microsecond pulse generator shown in Figure 1a can output 380 kV peak voltage with 10 \(\upmu\)s pulse width for a single microsecond pulse. As shown in Figure 1b, the breakdown test cell is a 20 cm hollow hexahedron based on a standard oil cup. In particular, it comes with a built-in brass needle-plate electrode with an electrode gap of 2 mm when shooting the streamer. There is another case where, when measuring the breakdown voltage, the brass spherical electrodes with an electrode gap of 0.5 mm were inlaid. The high-speed camera, model HSFC-pro, is shown in Figure 1c, which is used for the shooting of streamer. The exposure time of the high-speed camera can be adjusted between 3 and 1000 ns and the grayscale value in the range of 0 to 4096, which can capture photographs with 1280- by 1024-pixel.  
The simulation circuit diagram is shown in Figure 2. Under the room temperature (approximately 25 \({}^{\circ}\)C) and standard atmospheric pressure (0.1 MPa), the system is powered by the main supply (220 V/50 Hz), and the primary capacitor is adjusted to 200 V by the voltage regulator. The trigger outputs two synchronizing signals: one controls the conduction of the main thyristor, and the other controls the HSFC-pro high-speed camera.  
Figure 1: Experimental equipments of the microsecond-pulse breakdown strength test platforms: (**a**) microsecond pulse generator, (**b**) breakdown test cell, and (**c**) HSFC-pro high-speed camera.  
When the circuit is triggered, the primary capacitor is boosted and the pulse-forming line is charged under Tesla transformer. With the increase in pulse voltage, the liquid breaks down when voltage goes beyond the threshold level (breakdown voltage). Once the breakdown occurs, the high-speed camera shoots the streamer at the same time. Since the development time of streamer refers to nanoseconds, we chose the exposure time of 3 ns. Figure 3 shows the breakdown waveforms obtained by the oscilloscope; the typical voltage-rising duration from trough to peak is approximately 10 us.