**1. Introduction**

Low voltage dc grids have gained attention due to the potential advantages over low voltage ac grids when power electronic devices are proliferated in the system. Firstly, in such systems, the required number of conversion steps is generally reduced leading to improved system efficiency. Secondly, because the switching frequencies of power electronic converters are typically much higher than the native 50/60 Hz frequency of ac grids, the size of passive components can be reduced. Lastly, the absence of frequency and phase can make the control of dc grids significantly simpler [1–5].

The protection of low voltage dc grids is more challenging than the protection of conventional low voltage ac systems. Fundamentally, it is more difficult to interrupt inductive currents and extinguish arcs, since the voltages and currents in dc grids do not have a natural zero crossing [6,7]. Furthermore, these grids are often meshed and subjected to bi-directional power flows, complicating the detection and selectivity compared to conventional radial networks [8]. Moreover, in order to prevent high fault currents and blackouts, low voltage dc grids usually require fast fault interruption [9,10].

Because of the limited overload capability of power electronic devices, being able to withstand short-circuit conditions for milliseconds leads to oversized components in terms of current-carrying capability [10–12]. Furthermore, for dc systems with low inertia, a blackout is inevitable when a fault is sustained for a longer period of time. Fuses, electromechanical devices and hybrid circuit breakers

provide solutions for clearing faults in the order of milliseconds to seconds, but faster fault detection and interruption is required for low voltage dc systems [10,13–15]. To achieve this, the low voltage dc systems can be protected with solid-state circuit breakers (SSCBs), which can detect and interrupt faults within microseconds [16,17].

Several non-unit and unit protection schemes for low voltage dc grids have been reported in literature [18–20]. Non-unit protection schemes utilize local measurements in order to detect faults. Many of these protection schemes measure the current and current rate-of-change, and circuit breakers are opened when preset thresholds are exceeded, but the utilization of higher order derivatives of the current and the grid's voltage are also reported [21–23]. The main advantages of non-unit protection schemes are their simplicity, and their resilience to the failure of protection devices when a hierarchical structure of circuit breakers is used. However, these schemes have difficulty isolating only the faulted areas of the grid and thus achieving selectivity. Therefore, protection schemes were proposed that utilize knowledge about the system's topology in order to achieve selectivity. For example, faults can be located by measuring the grid's impedance and comparing it to known line parameters, or a wavelet transform can be used to identify faults by comparing them to simulations of the system [24–28]. Furthermore, a handshaking protection scheme was introduced, which locates and isolates a fault by temporarily powering down the dc system [29]. Nevertheless, these methods struggle to ensure selectivity when system parameters are uncertain or the system topology is changing. On the other hand, unit protection schemes achieve selectivity by utilizing a communication infrastructure. For instance, differential protection schemes locate faults by comparing the currents at different locations in the system, and event-based protection schemes ensure selectivity by combining local detection with central decision-making [30–36] However, since fast fault detection and interruption is required in low voltage dc grids, utilizing a communication infrastructure is not desirable.

The main contribution of this paper is a decentralized plug-and-play protection scheme, which contrary to other protection schemes, ensures selectivity without utilizing communication and only requires minimal knowledge about the system. Selectivity is achieved by augmenting the standard solid-state circuit breaker topology with RC dampers and by utilizing the proposed time-current characteristic. The protection scheme is plug-and-play in the sense that selective protection is provided on both sides of the circuit breakers in the system, regardless of the system's configuration or where the circuit breakers are located in the system and without requiring (re)configuration of the circuit breakers. Furthermore, the protection scheme is experimentally validated, showing the effectiveness of the protection scheme for different low voltage dc systems under various conditions.

This paper is structured as follows. In Section 2, it is discussed that current limiting inductances and fast fault interruption are crucial for the protection of low voltage dc grids. In Section 3, the experimental setup is presented and the operation of the designed solid-state circuit breaker (SSCB) is validated. In Section 4, it is experimentally shown that fast fault propagation and the commutation of inductive currents pose two challenges for the selectivity of non-unit protection schemes. In Section 5, it is proposed to add an RC damper to the output terminals of the SSCBs in order to delay fault propagation and smoothe current commutation. Furthermore, a time-current characteristic is proposed that coordinates upstream and downstream circuit breakers and also prevents tripping due to current commutation. In Section 6, the proposed plug-and-play protection scheme is experimentally validated. Finally, in Section 7, conclusions are drawn.

#### **2. Short-Circuit Fault Currents in Low Voltage DC Grids**

In low voltage dc grids overvoltages can occur when, for instance, lightning strikes one of the conductors. Therefore, surge arresters such as Metal Oxide Varistors (MOVs) or spark gaps should be used to clamp the voltage. Furthermore, short-circuits can occur when, for example, a tree falls on one of the overhead lines or the insulation deteriorates in one of the underground lines. In those cases, one or more conductors are short-circuited to each other or to the ground [37].

To calculate the short-circuit fault current in a monopolar dc grid, the equivalent circuit in Figure 1 is used [18,21,25]. The fault current is highest when the voltage on the non-faulted part of the system remains constant, and therefore this part of the system is modelled by a voltage source *U*dc. Furthermore, the SSCB is modelled by an ideal switch, its on-state resistance *R*CB and its (intrinsic) inductance *L*CB. Since the lines in low voltage dc grids are short, the propagation delay can be neglected and lumped element models are sufficiently accurate [38]. Therefore, the overhead or underground line(s) between the SSCB and the short-circuit are modelled by a lumped element *π*-model.

**Figure 1.** Equivalent circuit to calculate the worst-case short-circuit fault current in dc grids.

Simulation results for the current during a low resistance fault (0.1 Ω) and a high resistance fault (10 Ω) are shown in Figure 2. The fault current is shown for different lengths of the distribution line between the SSCB and the fault, which have a typical resistance of 1 Ω/km, an inductance of 0.25 mH/km and a capacitance of 0.5 μF/km. Furthermore, during these simulations the grid voltage *Udc* is 350 V, the on-resistance *RCB* is 0.1 Ω, and the SSCB's inductance *LCB* is 1 μH.

**Figure 2.** Simulation results for the fault current in the equivalent circuit of Figure 1 for different fault resistances and distribution line lengths.

Since the capacitance of the line *CL* is small, the fault current can be approximated by

$$I\_F(t) = \frac{\mathcal{U}\_{dc}}{R\_{CB} + R\_L + R\_F} \left(1 - e^{-\frac{R\_{CB} + R\_L + R\_F}{L\_{CB} + L}t} \right),\tag{1}$$

where *RF* is the resistance of the fault.

Note that the steady-state fault current is only determined by the total resistance, which is the reason short-circuit currents are so high in dc grids. Moreover, the line length only has a significant influence on the steady-state current when the fault resistance is low. Furthermore, by differentiating (1) it becomes clear that the current rate of change is only determined by the sum of the inductances in the system.

The thermal and electrical design of the SSCBs and other components in the grid are dependent on the duration and magnitude of the worst-case fault current that they need to be able to sustain. In the worst case, the short-circuit occurs close to the terminals of the SSCB, making the total inductance close to *LCB*. Furthermore, SSCB's are designed to have as low on-state resistance as possible in order to improve the system's efficiency. Therefore, if the current before the fault was the nominal current *I*nom, the worst-case fault current can be approximated by

$$I\_{\rm F,max} = \frac{\mathcal{U}\_{\rm dc} t\_{\rm max}}{L\_{\rm CB}} + I\_{\rm nom} \tag{2}$$

where *t*max is the maximum time that the SSCB needs to detect the fault and open its switches.

From (2) it is clear that, in order to reduce the worst-case fault current, fast fault detection and interruption are essential. Furthermore, even though SSCBs can detect and clear faults within 1 μs, a current limiting inductance is often added to SSCBs in order to further limit the maximum fault current. For example, assuming a grid voltage of 350 V, an SSCB clearing time of 1 μs, a nominal current of 20 A, and a current limiting inductance of 1 μH, the maximum fault current is 370 A.

Since the worst-case fault current develops when the short-circuit occurs at the SSCB's terminals, this worst-case fault current is not dependent on the system's parameters or uncertainty in the system. Furthermore, pole-to-pole faults in (grounded) unipolar and bipolar grids exhibit similar behavior to the behavior described in this section, although the resistance and inductance of the return path has to be taken into account. However, because ground faults in these grids have an identical equivalent circuit and behavior, the maximum fault currents in these grids are the same.
