*5.2. Proposed Time-Current Characteristic*

In ac systems selective coordination between upstream and downstream circuit breakers is often achieved in radial systems by using time-current characteristics for the protection devices. Time-current characteristics depict how long a protection device allows a current to flow before it interrupts it, and they are mainly determined by the thermal and magnetic characteristics of the circuit breakers. The upstream and downstream time-current characteristics are chosen in such a way that the downstream circuit breaker clears the fault first, and the upstream circuit breaker only clears the fault when the downstream circuit breaker fails.

It was shown in the previous section that the commutation of inductive currents can cause the undesired tripping of SSCBs in non-faulted sections. Therefore, coordination among downstream circuit breakers is also required, not just between upstream and downstream SSCBs. Furthermore, since this paper aims for a plug-and-play protection scheme, the coordination must also achieve selectivity in meshed low voltage dc grids.

To prevent unnecessary tripping due to commutated currents, the time-current current characteristic must take this current and its decay into account. In the worst-case, the commutated

current is the nominal current and this current decays with the time constant of the line. If the SSCB is carrying the nominal current before commutation, the worst-case current after commutation is characterized by the LR time constant and is given by

$$I\_{\text{total}} = I\_{\text{nom}} \left( \mathbf{1} + e^{-\frac{R\_L}{L\_L}t} \right). \tag{9}$$

Therefore, in order to prevent the SSCB from tripping unnecessarily from commutated inductive currents, the proposed characteristic only interrupts immediately if the current exceeds twice the nominal current. Furthermore, between *I*nom and 2*I*nom, the time-current characteristic is chosen as

$$t\_{\text{clear}} = t\_{\text{max}} - \frac{L\_L}{R\_L} \ln(I+1),\tag{10}$$

where *t*max is the maximum time the SSCB takes to detect and clear an overcurrent, and *I* is the current in the SSCB in multiple of the nominal current.

Note that it is only necessary to know the slowest expected time constant of the lines in the system. Therefore, knowledge about the length of the lines in the system or their interconnection is not required. Moreover, a safety margin can be implemented in order to anticipate uncertainty in the system parameters. The proposed time-current characteristic for SSCBs is shown in Figure 17.

**Figure 17.** Proposed time-current characteristic for the plug-and-play protection scheme, where *t*max is the maximum time that the SSCB needs to detect and interrupt an overcurrent.

Because the time-current characteristic scales with nominal current, the proposed time-current characteristic inherently coordinates upstream and downstream SSCBs. To illustrate this, imagine the system of Figure 12 with an upstream SSCB that has a nominal current of 32 A and two downstream SSCBs that have a nominal current of 16 A. Now if all the SSCBs operate at their nominal current and a fault occurs downstream, the downstream SSCB will trip immediately when the current reaches 32 A. In this case the upstream current is 48 A, for which the upstream breaker will wait a significant time.
