*5.3. Plug-and-Play Design Guidelines*

In the previous subsections a solid-state circuit breaker topology and time-current characteristic were proposed in order to ensure selectivity. In this subsection it is described how these concepts can be incorporated in an SSCB, with a nominal current of *I*nom and a nominal voltage of *U*nom, in order to achieve system-wide plug-and-play protection selectivity.

The SSCB's di/dt detection is tripped if the voltage over the current limiting inductance is more than *UL*,max. However, in the worst case the voltage is still *U*nom for *tmax*. Therefore, assuming a sawtooth shaped pulse, the required current limiting inductance is determined by

$$L\_{CB} = \frac{\sqrt{3} l I\_{\text{nom}} t\_{\text{max}}}{I\_{\text{pulse}} (t\_{\text{max}})} \, ^\prime \tag{11}$$

where *<sup>I</sup>*pulse(*<sup>t</sup>*max) is the current carrying capability of the semiconductor switches for a *t*max pulse, which usually is several times higher than then nominal current of the switches.

When the current is above two times the nominal current, the clearing time is given by *tmax*, while for currents between one and two times the nominal current (10) is used to determine the clearing time. Consequently, the maximum current when the overcurrent protection is tripped is given by

$$I\_{\text{max}} = 2I\_{\text{nom}} + \frac{\mathcal{U}I\_{L,\text{max}}t\_{\text{max}}}{L\_{CB}}.\tag{12}$$

Although lowering the di/dt threshold *UL*,max decreases the maximum fault current, the detection will also become more sensitive to, for example, electromagnetic interference. The authors found a reasonable threshold voltage to be around

$$\mathcal{U}I\_{L,\text{max}} = \frac{2I\_{\text{norm}}L\_{CB}}{t\_{\text{max}}}.\tag{13}$$

In general, changes in load current will not trigger the di/dt detection with this threshold, since the time constants of distribution lines and power electronic converters are several orders of magnitude higher than the time constant of the SSCB.

The topology that is used for the SSCB is shown in Figure 14, where the MOVs clamp the voltage to below the maximum rating of the switches. Alternatively, other circuits can be used to limit the voltage on the switches. Regardless, the rating of the clamping circuits determines the maximum inductive energy that the SSCBs can dissipate.

To size the damper components (7) and (8) are used. To ensure a smooth commutation of inductive current and prevent instant fault propagation, the resonant frequency of the SSCB is chosen to be an order of magnitude lower than the inverse of the maximum clearing time *t*max (in this paper a factor of 10 is chosen). The damper capacitor is then given by

$$\text{C}\_{\text{d}} \gg \frac{t\_{\text{max}}^2}{4\pi^2 L\_{\text{C}B}}.\tag{14}$$

For a damped response, the damper resistance is sized such that the attenuation frequency is higher than the resonant frequency. Therefore,

$$R\_d > 2\sqrt{\frac{L\_{CB}}{C\_d}}.\tag{15}$$

If possible, in order to clamp the voltage over the inductor to below the threshold voltage during commutation, the damper resistance should also be

$$R\_d < \frac{\mathcal{U}\_{L,\text{max}}}{I\_{\text{norm}}}.\tag{16}$$

Utilizing these guidelines, the parameters of the SSCB in this paper are given in Table 2. As a consequence of the damper capacitance and damper resistance, the resonant frequency *fr* of the SSCB is 113 kHz and the attenuation frequency *α* is 170 kHz. Furthermore, the maximum steady-state losses in the SSCB are 26 W, which is only around 0.7% of the conducted power. Moreover, the losses in the SSCB can be reduced even further by, for example, parallelling multiple semiconductors.


**Table 2.** Design parameters of the solid-state circuit breaker.

#### **6. Experimental Validation of the Plug-and-Play Protection Scheme**

To show that the plug-and-play SSCBs delay the propagation of the fault, the experiment shown in Figure 10 is repeated. The experimental results for the currents in the SSCBs for this experiment are shown in Figure 18. Observe that, contrary to the experiment in Figure 11, only CB3 is tripped, while the currents in the other SSCBs are largely unaffected by the whole process. The current rises fast until the switches of CB3 are opened, after which CB1 and CB2 remain closed. Furthermore, it is seen that the oscillations in the system are attenuated significantly because of the RC dampers.

**Figure 18.** Experimental results for the system shown in Figure 10, showing that fault propagation is delayed with the plug-and-play SSCBs.

To show that the plug-and-play SSCBs ensure smooth commutation and selectivity, the experiment shown in Figure 12 is repeated. The experimental results for the SSCBs' currents for this experiment are shown in Figure 19. Note that the commutation of the inductive current is smoothed out over roughly a 10 μs interval, which is an order of magnitude longer than in Figure 13. Furthermore, although the inductive current is commutated to CB1, its thresholds are not exceeded and therefore its fault detection is not tripped.

**Figure 19.** Experimental results for the system shown in Figure 12, which show smooth commutation and selectivity with the plug-and-play SSCBs (the right figure is a zoom in).

From the previous experiment, it is clear that the plug-and-play protection scheme accounts for commutated currents, but does not prevent them. The addition of a significant capacitance at the interface of the SSCBs can reduce the commutated current by (temporarily) storing the inductive energy. The experimental results for the same experiment, but with an added 240 μF capacitance at the interface of the SSCBs, is shown in Figure 20. The commutated current is reduced, but applying this solution in a plug-and-play fashion is impractical, since information about the system's capacitances and inductances is required. Therefore, this paper adopted the proposed time-current characteristic.

**Figure 20.** Experimental results for the system shown in Figure 12 when a capacitance of 240 μF is added at the interface of the plug-and-play SSCBs, showing that the commutated current is reduced (the right figure is a zoom in).

To show that the decentralized plug-and-play protection scheme also works for meshed systems, the experiment shown in Figure 21 is used. The setup consists of a constant voltage source of 350 V connected to two 5 A constant current loads in a ring configuration. The lines in this system are emulated by equivalent *π*-circuits described in Section 3. This situation can occur, for example, when dc households are interconnected.

**Figure 21.** (**a**) Schematic and (**b**) picture of the experimental setup connecting a constant voltage source to two constant current loads via lines in a meshed configuration.

The experimental results for the currents inside the SSCBs, when a short-circuit with a fault resistance of 2.5 Ω is induced at the load-side terminals of CB3, are given in Figure 22. Observe that the fault current is first mostly supplied by the damper capacitances of CB3 because this path contains the lowest inductance, and consequently CB3's di/dt detection is triggered. Subsequently, the fault current is supplied mainly by the capacitance of the load in the non-faulted part of the system through CB2 and its overcurrent detection is triggered after around 20 μs. Most importantly, CB1 is not triggered and the non-faulted section of the grid remains operational.

**Figure 22.** Experimental results for the system shown in Figure 21, showing that selectivity is also achieved in meshed systems.
