Design of a snubber circuit for low voltage DC solid-state circuit breakers

Solid-state circuit breakers (SSCBs) are designed to interrupt fault currents typically several orders faster than its electromechanical counterparts. However, such an ultrafast switching operation would produce a dangerous overvoltage which might cause damages to SSCBs and other circuit elements in the system. This paper proposes a novel snubber circuit for suppressing the overvoltage. It takes the advantages of both resistor-capacitor-diode (RCD) snubbers and metal oxide varistors (MOVs). Its operating process is analysed before the proposed snubber circuit for 400V DC SSCBs is designed. Pspice simulator is employed for simulating the operating process and a prototype SSCB with the proposed snubber is built and tested in a lab-scale DC system. The results of simulation and experiment validate the effectiveness of the proposed snubber.


INTRODUCTION
DC distribution networks are gaining popularity in data centres, commercial buildings and transport power systems [1][2][3][4] because in comparison to traditional AC systems, they demonstrate higher efficiency and more readiness for integrating with various local renewable power sources and ever-increasing DC electronic loads. However, one of the major issues hindering this trend is the lack of effective DC short-circuit fault protection devices. Though working well in AC power networks, conventional electromechanical circuit breakers are not suitable for DC systems because their response time is typically in the range from tens of milliseconds to hundreds of milliseconds which is far longer than the survival time of most power electronic devices (a few tens of microseconds) in DC systems.
In recent years, solid-state circuit breakers (SSCBs) have been intensely researched as promising candidates to replace mechanical circuit breakers for DC protection due to its ultrafast switching speeds [5][6][7][8]. However, such a fast switching operation would produce an unacceptably high voltage across SSCBs because of the rapid fall of fault current and small system inductance [9]. Furthermore, the large magnetic energy stored in the system inductance must be dissipated by energy absorption elements since such a huge amount of burst energy during shortcircuit faults is usually far higher than what SSCBs can contain. Therefore, some effective methods must be in place to suppress the overvoltage and meanwhile absorb the energy stored in the system inductance during turn-off of SSCBs. Several approaches were reported and discussed for SSCB applications [10][11][12][13]. Generally, two topologies are commonly adopted alone or combined to serve this purpose: resistor-capacitor-diode (RCD) snubbers [14,15]and metal oxide varistors (MOVs) [16,17].
In this paper, to start with, the operating process of both conventional RCD snubber circuits and MOVs are reviewed and their pros and cons are discussed. In the following, a novel snubber circuit combining a RCD with a MOV is proposed and analysed before the proposed snubber for 400V DC SSCBs is designed and its components are selected. Both simulation and experimental results validate the effectiveness of the proposed snubber design. Finally, the impact factors on the response time of SSCBs are investigated and conventional RCDs, MOVs are compared with the proposed snubbers.
The main contribution of this paper is: • Proposal of a novel hybrid snubber configuration which takes into account the advantages offered by both conventional RCD snubbers and MOVs. • Analytical expressions describing each stage of the operating process provide guidance for the snubber design for SSCB application.
IET Power Electron. 2021;1-10. wileyonlinelibrary.com/iet-pel 1 FIGURE 1 RCD snubber circuit • The impact factors involved in the snubber on the response time of SSCBs have been identified to optimise the snubber design to meet different application requirements.

REVIEW OF SNUBBER CIRCUITS FOR SSCBS
Snubber circuits in the form of capacitor(C), resistorcapacitor(RC) or resistor-capacitor-diode(RCD) have been discussed in [10,18]. C type is the simplest. However, a high discharge current will flow through the main semiconductor switch of SSCBs during the turn-on operation, which tends to cause the nuisance trip of SSCBs. To address this issue, a current-limiting resistor is added in series to the capacitor forming RC snubbers. However, a high voltage drop across the resistor during high fault current interruption would damage semiconductor components of SSCBs. To solve this issue, a diode is added in parallel with the resistor to form an RCD snubber as shown in Figure 1.
The use of RCD snubbers has been very common for suppressing overvoltage. The operating process is simply divided into four stages as below: Stage 1 starts when a short-circuit event occurs, the fault current ramps up until reaching the trip current level of SSCB. Stage 2 starts when SSCB turns off and the diode D S turns on until the fault current completely commutates from SSCB to the branch of snubber capacitor C S and the diode D S . Stage 3 starts when C S is charged until the energy stored in system inductance L DC is completely transferred to C S . Stage 4 starts when C S discharges through the resistor R S until its stored energy is fully exhausted and fault current is dampened to zero.
The main advantages of the RCD snubber is very effective on slowing down the rising speed of the overvoltage and reducing the oscillations during the turn-off. However, this solution requires a very high power resistor to exhaust the stored energy in a very short period. For example, a system with L DC = 100 µH, trip current 100 A and response time 100 µs, would require a resistor with peak power as high as 5 kW, leading to the whole snubber circuit bulky and expensive.  MOVs are another common type of voltage clamping components which are widely used for protecting devices against overvoltage caused by either lightning surges or switching operations thanks to its highly nonlinear voltage-current characteristics like back-to-back Zener diodes. Figure 2 shows a MOV for SSCBs application. Its operating process is divided into two stages: Stage 1 starts when a short-circuit event occurs, the fault current rapidly ramps up to the trip current level before SSCB turns off. Once the voltage across SSCB exceeds the reference voltage of MOV, fault current starts to commutate from SSCB to MOV. Stage 2 starts when SSCB turns off and the fault current fully commutates to MOV where the voltage across SSCB is clamped to the protection level of MOV and the energy stored in system inductance L DC is dissipated until fault current is dampened to zero.
The main advantages of MOVs are its simplicity and high energy absorption capability with the typical value in the range of hundreds of joules per cubic centimetre [19]. However, it suffers from deterioration over time when frequently exposed to surges and overvoltage transients [20]. Furthermore, compared to the RCD snubber, it has no dv/dt control and displays larger transient oscillations during turn-off of SSCBs [21,22].
To take benefits of both RCD snubbers and MOVs, a novel snubber circuit is proposed herein by combining a MOV with a RCD snubber as shown in Figure 3. This approach exploits both effective overvoltage suppression of RCD snubbers and high energy absorption capability of MOVs. Meanwhile, it eliminates the high-power resistor of RCDs and mitigates the transient oscillations of MOVs.

ANALYSIS OF OPERATING PROCESS OF THE PROPOSED SNUBBER CIRCUIT
Under normal operating conditions, SSCB stays on and the snubber capacitor is pre-charged to the supply voltage. When a short-circuit fault occurs, the operating process is divided into four stages shown in Figure 4(a)-(d) respectively. The equivalent circuit includes a SSCB, a DC supply voltage source V DC , an equivalent system inductor L DC , an equivalent short-circuit resistor R SC and the proposed snubber circuit constructed by C S , D S and MOV.
To serve the main purpose of analysing the operating principle and meanwhile reducing the complexity, several assumptions are made below: 1. Ideal SSCB: turn off instantly and has zero on-resistance. 2. Ideal Diode: reverse recover characteristic is neglected. 3. MOV: Leaking current is neglected.
Stage 1: Fault current ramps up ( Figure 4a) When a short-circuit fault occurs, the fault current ramps up until it reaches the trip current I trip of SSCB. At this stage, the snubber is inactive and no currents flow through C S , D S and MOV.
By applying Kirchhoff voltage law (KVL) to the main power circuit loop, the expression (1) is obtained: Integrating the Equation (1) and rewriting it, fault current i f at this stage can be derived as Hence, time period T 1 when fault current rise from rated load current I r to trip current I trip at this stage can be calculated as: Due to the assumption of an ideal SSCB, the on-state voltage across SSCB is zero, thus:  When SSCB starts turning off and then the snubber diode D S turns on, the fault current is commutating from SSCB to the branch of snubber capacitor C S and diode D S .A ga i n ,d u e to the assumption of an ideal SSCB, fault current and voltage across SSCB V SSCB at this stage are considered constant. Thus, Stage 3: C S is charged until MOV is activated (Figure 4c) The snubber capacitor C S is charged until the voltage across MOV reaches its activated level (reference voltage V ref ). Fault current i f and V SSCB at this stage can be derived as Time period T 3 at this stage can be obtained as Stage 4: Fault current commutates from the branch of C S and D S to MOV (Figure 4d) MOV is activated and fault current is redirected from C S and D S to MOV where stored energy in L DC and C S is dissipated.
For simplicity, the V-I characteristic of MOV in its active region is assumed to be linear. Thus, V-I relationship of MOV can be simply expressed as: Where V A and R B are constant. The initial activated current of MOV I o can be estimated as Hence, fault current i f and V SSCB can be obtained respectively as: System inductance L DC 1-100 µH Time period T 4 is estimated as Table 1 lists the main technical specification of the targeted low voltage DC SSCB for a 400 V DC system.

4.1.1
Selection of capacitor C S First condition: The energy stored in C S must be greater than the energy stored in system inductance L DC .Thus: Second condition: Rated voltage of C S must be higher than the maximum blocking voltage across SSCB (1000 V).

4.1.2
Selection of diode D S First of all, a soft and fast recovery power diode is expected. Secondly, pulse current of D S must be higher than the maximum trip current (100 A).

FIGURE 5 MOV V-I characteristic and its linear fitted curve
Hence, 120 A pulse current, 650 V diode IDP40E65D2 from Infineon [24] is selected.

Selection of MOV
First condition: the energy absorption capability of MOV must be higher than the energy stored in the system inductance (L DC = 100µH). Thus, Second condition: the protection level of MOV must be lower than a certain level to assure the voltage across SSCB below allowed maximum value (1000 V). Thus, Hence, MOV B72220S0171K101 from TDK [25] is selected. Figure 5 illustrates the selected MOV voltage-current characteristic against its linear fitted curve in the active current region (10-100 A). Hence:

Theoretic calculations in each stage for the proposed snubber
Substituting those parameters of selected components into corresponding equations derived in Section 3 and assuming worst scenario L DC = 100µH and short-circuit resistance R SC = 0.4Ω, fault current i f , voltage across SSCB V B(SSCB) and time period T in each stage can be calculated in Table 2.

SIMULATION VALIDATION
Pspice is employed for simulating the snubber operating process. All parameters used for simulation are identical to the aforementioned theoretic calculations and an ideal semiconductor switch model is selected as SSCB. Figure 6 shows the simulation waveforms including fault current (red line), capacitor current (green line), MOV current (blue line) and voltage across SSCB (black line). As can be seen, SSCB turns off right after fault current reaches 100 A. In the following, fault current is redirected to the snubber capacitor C S then to MOV where it eventually damps to zero. Meanwhile, the voltage across SSCB starts rising after turn-off of SSCB until it reaches the peak value around 870 V the moment MOV is activated. In the end, the voltage converges to the steady supply voltage V DC (440 V) when fault current is cleared off at around 53 µs. The simulation results confirm the proposed snubber can Furthermore, the analytical results for fault currents in each stage obtained from Table 2 are compared with simulation. As demonstrated in Figure 7, the analytical results match simulation very well. Furthermore, analytical results of the voltage across SSCB are also compared with simulation results in Figure 8. As can be seen, the simulation results show reasonable matching with calculated results except for some discrepancies during transient period between each stage due to the assumption involved in ideal SSCB and linear I-V relationship of MOV in the calculations. The simulation results verify the correctness of the theoretic analysis.  FIGURE 9 Schematic of the snubber test bench

EXPERIMENT VALIDATION
The experiment of the proposed snubber circuit is conducted in a lab-scale DC system. Table 3 lists the parameters of experimental set-up. A test bench is built as sketched in Figure 9 where a power switch IGBT IRG4PSH71UD from Infineon [26]i s selected as the main switch controlled by a gate driver setting the pulse duration of short-circuit current. Figure 10 shows the experimental results of SSCB without the snubber and with the proposed snubber under the same test condition: L DC = 100 µHandV DC = 100 V. As observed, the peak voltage across SSCB is as high as 974 V without the snubber in Figure 10(a) compared to only 212 V with the proposed snubber in Figure 10(b). Figure 11 presents the waveforms under the test conditions: L DC = 180 µH subjected to various supply voltages of 150, 200 and 250 V respectively. The results demonstrate the overvoltage across SSCB can be effectively suppressed less than twice of the supply voltage with the proposed snubber. Meanwhile, it is worth noticing that in Figure 11(a), (b) voltage ringing appears at the end of the process, leading to longer recovery time of SSCB. The reason is that MOV under lower supply voltage system has not been fully activated, resulting in less dampening effect on  Figure 11(c) shows no ringing due to effectively activated MOV under higher supply voltage. Figure 12 compares the waveforms of fault currents and voltages across SSCB of experiment results against simulation results under the same condition: L DC = 100 µH and V DC = 135 V. It demonstrates a reasonable match between them though there are noticeable discrepancies mainly attributed to the parasitic impedance of the wires and PCB traces, which are not accounted for the simulation.
In summary, the experimental results validate the effectiveness of the proposed snubber circuit.

Discussions of impact factors on the response time of SSCBs
It is well known that adoption of the snubbers can prolong the response time of SSCBs. For this reason, it is essential to investigate the factors in what way influence the response time. system inductance and trip current respectively. As indicated, the increase of MOV clamping voltage can reduce the response time whereas the response time would increase in concert with the rising of snubber capacitance, system inductance and trip current level. Therefore, designers can manipulate these factors to meet their own design objective.

Discussions of impact of the assumptions on the snubber performance
Despite a limited impact on the snubber performance due to the assumptions for simplifying the theoretic analysis, it will be discussed here for completeness.
First and foremost, the assumption of instant turn-off of SSCB tends to reduce the total response time. However, the turn-off time of semiconductor devices is generally on the order of several hundreds of nanoseconds, almost two orders lower than the total response time of SSCBs (tens of microseconds). Therefore, the influence is insignificant.
Secondly, the negligence of on-state voltage of SSCBs would increase the rising speed of fault current and tends to reduce the time period T1 in Stage 1 as defined by Equations (1)and (3). However, compared to the power supply voltage V DC , the onstate voltage drop of SSCBs is negligible and hence its influence is very limited.
The assumption of no reverse current for diode D S would have an impact on the snubber performance in the final stage where the diode is changing from a forward mode to a reverse mode. Since the diode with a slow and hard recovery characteristic would cause transient oscillations or high voltage spikes during this stage, a soft and fast recovery diode with the recovery time below 100 ns is expected. Undoubtedly, the selected diode should be verified in the actual circuit to ensure the snubber to perform as expected.
Lastly, the assumption of no leaking current of MOV has nothing influence of the snubber performance rather than MOV itself as a larger leaking current of MOVs tends to lead to the faster deterioration of MOV in the long run. In this scheme, the leaking current of MOV as a function of applied voltage is negligible as no voltage is exposed to MOV under normal operating conditions. To conclude, if designed properly, these assumptions have little impact on the total performance of snubbers.

Comparison with conventional RCD snubbers and MOVs
For comparison, a conventional RCD circuit is constructed by simply replacing the MOV of the proposed snubber with a 20 Ω snubber resistor R S while maintaining all other parameters of the system and other components identical to the proposed snubber.
As shown in Figure 14, the simulated fault current waveforms of both solutions are almost identical. In the meantime, the peak voltage across SSCB with the proposed snubber has the same level with that of the conventional RCD snubber. Figure 15 compares currents and powers through the resistor R s of the RCD snubber and the MOV of the proposed snubber. As observed, both R s and MOV experience very high peak power, 10 and 20 kW respectively. Furthermore, it is noticed that as long as 300 µs is needed to dampen the RCD snubber current to zero through the resistor R s whereas the proposed snubber with MOV can do so by around 55 µs.
In addition, Table 4 roughly compares the performances of the conventional RCD, MOV and the proposed snubber used for 400 V DC SSCBs defined in Table 1.I ts h o w st h a tM O V stands out for shorter response time and a much lower cost while the conventional RCD and the proposed snubber share better overvoltage suppression and lower transient oscillations. However, RCD are much more expensive than the proposed snubber for same peak current and clamping voltage requirements.
To conclude, the comparison demonstrates that the proposed snubber cannot only suppress the overvoltage as effectively as the conventional RCD snubber but also has a relatively low cost after replacing the bulky and expensive resistor with a simple and low-cost MOV.

CONCLUSION
In this paper, a novel snubber circuit has been proposed for low voltage DC solid-state circuit breakers. It exploits the advantages of effective overvoltage suppression of RCD snubbers and high energy absorption capability of MOVs while it eliminates the requirement of high-power resistor of RCD snubbers and mitigates the transient fluctuation of MOVs. Its operation principle has been analysed then a snubber design for 400V DC SSCBs is presented. Simulation results against the analytic results validate the correctness of the snubber design. Meanwhile, the impact factors on the response time of SSCBs have been investigated by simulation. Finally, a prototype lab-scale SSCB with the proposed snubber circuit has been constructed and tested. The experimental results further confirm the effectiveness of the proposed snubber circuit design.