**Table 4.** Switching time.


The overall average response and clearings times for PU, TCT, and SWT were 43.74, 47.53, and 3.79 μs, respectively. As the amperage increases, the TCT and PU have an increasing average, while the SWT shows a decreasing trend of nearly 100 ns/A due to the snubbing circuit's overdamped response across Vce at low current levels. The SSCB's response time, when compared to the generalized curve of its mechanical circuit breaker (MCB) counterpart depicted in Figure 11, shows that the average TCT during an instantaneous fault is greatly reduced by a factor of 1000. Furthermore, slower MCBs often have an instantaneous trip time between 40 and 55 ms, faster units will trip within 16 ms or one 60 Hz cycle [25,26]. The resulting SSCB's average TCT was 294.7 times faster than that of the single-cycle MCB using purely ADC techniques.

**Figure 11.** Generalized trip curve for mechanical circuit breakers [27].

The PU time is the main contributing factor in the speed of the SSCB under test, resulting in 92% of the overall average TCT delay. The PU speed is governed by the speed of the ADC capabilities of the microcontroller used in the experiment. Further reduction of the SSCB response time is accomplished via improved external sensing or faster ADC equipment, but may come at an increased cost to the design. The TCT of the SSCB is important for the success of the overall design due to the lack of large inductances from transformers in DC systems. In many cases, the wire inductance will be the largest limiting factor in the DC system. The change in current over time from a DC source, di/dt, is governed by Equation (12).

$$\text{di/dt} = \text{V}\_{\text{dc}}/\text{L},\tag{12}$$

where Vdc is the system voltage and L is the system inductance. Therefore, a 10-m 8 AWG wire with roughly 13 μH of inductance and a bus voltage of 50 volts would result in a di/dt of 3.85 A/μs, producing a 180.8 A increase in just 47 μs if limited by wire inductance alone. The same fault sustained for 16 ms would reach an excess of 61 kA, causing extreme thermal and physical stress on the system. This problem is further compounded as voltages and wire diameters increase in higher-rated systems [11,18]. Fast, easily programmable SSCBs can be used in tandem with fault-limiting converters and advanced protection algorithms to minimize the effects of extreme faults in the DC system.
