Design and Analysis of a DC Solid-State Circuit Breaker for Residential Energy Router Application

Abstract

Energy routers act as an interface between the distribution network and electrical facilities, which meet the requirements of clean energy substitution and achieve the energy sharing and information transmission in the energy network. However, the protection of the dc load side of residential energy routers including interruption and isolation of short-circuit fault currents is vital for discussion. Since the traditional mechanical and hybrid circuit breakers for dc fault protection have the drawback of slow operation, a solid-state circuit breaker (SSCB) is an optimal solution for fast dc fault interruption. In this paper, a dc SSCB is proposed that uses an RCD + MOV snubber circuit, which is considered the best and most complete circuit used in common SSCBs. There are two main contributions in this paper: First, a dc SSCB is designed, which isolates both positive and negative terminals of a circuit and its working principle and operating modes along with the formulas for calculation of crucial time intervals, voltages, and currents along with the design procedure are provided. Second, a soft turn-on auxiliary is designed to prevent a high current surge caused by the capacitance difference between the source and the load. The experimental results demonstrate the proper performance of the topology and the validity of the findings.

1. Introduction

In the last decade, the investigation of different aspects of energy routers has become popular. An energy router is a kind of intelligent power electronics equipment, which can dispatch distributed energy quantitatively, regularly, and accurately [1]. The structure of a typical energy router is shown in Figure 1. As it interfaces various sources and converts the power to ac and dc, an energy router can flexibly manage the dynamic power within the regional power grid on the premise of ensuring power quality [2]. The architectures, functionalities, and demonstration of energy routers have been introduced in [3]. Energy routers play an important role in smart grids since in these grids energy is generated mostly from distributed energy sources [4]. The local loads are powered by these energy resources; however, when the supply of the energy resources surpluses the local demand, the energy flows into the grid through energy routers. The energy router also tracks the variations in the user’s demands to distribute the energy dynamically [5,6,7].

As a critical technique to guarantee the safe operation of the dc side in residential energy routers, a dc circuit breaker is considered as a reliable method of isolating faults in dc systems quickly and selectively [8]. However, since there is no zero-crossing point in the dc current along with a high fault current rising rate, the operation of interrupting the fault current in the dc system is much more difficult compared with the ac system. Therefore, the design of dc circuit breakers becomes crucial, making it a key technology for dc systems [9]. Different kinds of dc SSCBs have been collected and reviewed in [10,11,12,13,14].

Direct current circuit breakers are mainly divided into three categories: electromechanical, hybrid, and solid-state circuit breakers. Electromechanical breakers typically cause arcs during the interruption and cannot meet the speed requirements for the protection of semiconductor-based converters. The arcs also erode the breaker contacts, which increases the maintenance costs [15]. To provide fast fault isolation without causing arcs, power electronic switches have been applied. A hybrid dc SSCB scheme, which is a combination of mechanical and solid-state technology, is now considered as an acceptable solution [16]. However, the mechanical ultrafast disconnector in these dc circuit breakers slows the current breaking process and increases their weight, volume, and investment price. With the development of electronic components, dc SSCBs have been greatly developed. They are extremely faster than mechanical and hybrid circuit breakers [17].

Solid-state circuit breakers are divided into two categories in terms of using either semi-controlled switching devices such as SCRs or fully controlled switching devices such as IGBTs and MOSFETS. Impedance-source SSCBs, which are the most popular solutions for using half-controlled switching devices, are reviewed in [18]. The SCR-based SSCBs benefit from smaller conduction losses, larger capacity, and lower price compared with the ones with fully controlled switches. However, since the turn-off process of SCR requires reverse voltage, the most important issue when designing an SCR-based SSCB is a reliable generation of a reverse voltage on the SCR during the turn-off process [19,20]. On the other hand, in SSCBs with fully controlled switching devices, there is full control of the breaking process.

When a short-circuit fault occurs in the system, a high $di/dt$ is usually generated during the turn-off process of the SSCB, which generates serious $dv/dt$ and overvoltage through the huge inductive energy applied across the main switches due to the transmission line inductance and current-limiting line inductors. It might exceed the device rating and cause failure [21]. Also, a high $dv/dt$ can induce gate oscillation, gate-oxide degradation, and false turn-on, causing reliability and lifetime issues. To reduce this voltage, rise rate, and voltage spike, snubber circuits must be added. Various snubber configurations have been reported for SSCBs, which are reviewed in

Table 1. Different types of snubbers including the pros and cons of each.

Snubber	Circuit	Pros and Cons
C		✓ The snubber capacitor absorbs some of the energy stored in the inductance of the system by getting charged. This slows down the voltage rise rate and the peak voltage of the switching devices. ⊠ When the switch is turning off, the capacitor oscillates with the inductance of the circuit. In addition, during the turn-on process, it causes a high discharge current through the switching device.
C + MOV		✓ The varistor provides overvoltage protection using voltage clamping. ⊠ When the switch is turning off, the capacitor oscillates with the inductance of the circuit. In addition, during the turn-on process, it causes a high discharge current through the switching device.
RC		✓ The resistor damps the oscillations caused by the snubber capacitor and the system inductance being in series. It also decreases the turn-on current, which is discharged through power semiconductor. ⊠ When the switch is turning off, the voltage drop across the snubber resistor is reflected on the switching device, which increases its peak turn-off voltage requirement of the switch.
RCD		✓ This combination eliminates the additional drop of voltage across the resistor as well as significantly reduces the voltage oscillations during the turn-off. ⊠ It includes more components.
RCD + MOV		✓ In addition to the benefits of the RCD snubber, the varistor provides overvoltage protection using voltage clamping. ⊠ It includes more components.

.

Reference [22] utilizes a metal-oxide varistor (MOV) with a capacitor to suppress the overvoltage during the turn-off process and analyzes the effects of capacitor variation on the voltage suppression capability. However, there are two major problems associated with a pure C snubber (even with a MOV), including the oscillation of the current because of the system inductance and the high discharge current during the turn-on process. By using a snubber resistor in series with the capacitor, the discharge current can be reduced and the current will be damped [23]. In addition, using a MOV in parallel with the RC snubber significantly reduces the required capacitance [24,25].

However, in an RC snubber (or RC + MOV), the voltage across the resistor is reflected on the power semiconductors during turn-off, which causes extra voltage stress and power shock [26]. Alternatively, a resistor-capacitor-diode (RCD) snubber can separate charging and discharging paths. The MOV-RCD snubber is analyzed in [27] using analytical investigations, where the short-circuit current capability, clearance time, and transient power shock are considered.

In this paper, a bidirectional SSCB is designed and prototyped, which isolates both the positive and negative terminals of the system quickly and efficiently. A complete set of formulas to calculate all time intervals, voltages, and currents is presented. In addition, a soft turn-on auxiliary is designed to prevent a high current surge caused by the capacitance difference between the source and the load. The experimental results demonstrate the proper performance of the topology and the validity of the findings.

2. Investigation of the Topology

The topology is composed of two back-to-back MOSFETS, with an RCD snubber for each MOSFET as shown in Figure 2. On the negative side, there is a mechanical switch that gets turned off when the current of the circuit reaches almost zero. In traditional bidirectional SSCBs with two switches, just the positive terminal gets disconnected. Therefore, there will still be voltage on the components in the system. By using the mechanical switch, safety is increased and the disturbance in the system when using more than one SSCB gets suppressed [28]. This mechanical switch acts when the current of the circuit reaches very close to zero.

Figure 2 also represents an auxiliary circuit for the driver of the MOSFETs facilitating the turn-on process of the switches, which is crucial in the energy router applications that often face the voltage difference between the source and the load. This part is further discussed in Section 3.

The operating modes of the designed SSCB are shown in Figure 3. In the normal operation and even when the fault occurs before the reaction of the SSCB, the current flows through both MOSFETs (Figure 3a). When the short-circuit fault occurs, both MOSFETs get turned off but the current finds its way through the snubber capacitor and the snubber diode (Figure 3b). However, as the energy and current of the inductor reach zero, the current is reversed and flows through an RCL circuit, which prevents it from oscillating (Figure 3c). Finally, when the current of the circuit reaches zero, the mechanical switch M gets turned on and disconnects the dc source (Figure 3d).

2.1. Stage 1

The first stage is the normal mode when both switches are turned on, and the circuit breaker passes the current as shown in Figure 3a through the switches $S_1$, and $S_2$. As shown in Figure 4, it is evident that before $t_1$, the voltages of the capacitors and switches are zero and the current of the inductor is at its nominal value. For a simpler calculation, we assume $t_1=0$.

$$i_L=I_N$$

(1)

2.2. Stage 2

In the ($t_1-t_2$) interval, at $t_1$ a short-circuit fault occurs at the output terminals and the current of the circuit increases to reach $i_{limit}$ at $t_2$. $i_{limit}$ is the current that is determined in the controller at which the SSCB should operate. By assuming $R_{SW}=R_{Line}=0$, and initial value: $i_L\left(t=0\right)=I_N$,

$$L\frac{d{i}_L}{dt}-V_{dc}=0$$

(2)

By solving the above first-order differential equation, the current is calculated as follows:

$$i_L=\frac{V_{dc}t}{L}+I_N$$

(3)

By $i_L=I_{limit}$,

$$t_2=\frac{L\left(I_{Limit}-I_N\right)}{V_{dc}}$$

(4)

However, $t_2$ is not the actual time that the SSCB acts since there is a delay in both the microcontroller and measurement system, which is named $t_{Delay}$. Therefore, the actual time of breaking is $t_3$.

$$t_3=t_2+t_{Delay}$$

(5)

By calculating $t_{Delay}$ and consequently $t_3$ by (2), the maximum current of the switches is obtained as follows:

$$I_P=\frac{V_{dc}{t}_3}{L}+I_N$$

(6)

2.3. Stage 3

During the ($t_3-t_4$) interval, the current flows through the snubber C and the inductor of the line. Therefore, the following equations are derived:

$$L\frac{d{i}_L}{dt}+V_C-V_{dc}=0$$

(7)

$$i_C=C\frac{d{V}_C}{dt}$$

(8)

$$i_C=i_L$$

(9)

The current of the inductor and the voltage of the capacitor can be obtained from the above equations by considering the initial values: $i_L\left(0\right)=I_P$ and $v_C\left(0\right)=0$:

$$i_L=I_P\cos \frac{t}{\sqrt{LC}}+V_{dc}\sqrt{\frac{C}{\mathrm{L}}}\sin \frac{t}{\sqrt{LC}}$$

(10)

$$v_C=V_{dc}-V_{dc}\cos \frac{t}{\sqrt{LC}}+I_P\sqrt{\frac{L}{\mathrm{C}}}\sin \frac{t}{\sqrt{LC}}$$

(11)

$t_B$ can be calculated by putting $i_L=0$.

$$t_B=-\sqrt{LC}Arctang\left(\frac{I_P}{V_{dc}}\sqrt{\frac{L}{\mathrm{C}}}\right)$$

(12)

The maximum voltage on the switches combined can be obtained by putting $t_B$ in the equation of the capacitor voltage:

$$V_P=V_{dc}-V_{dc}\cos \frac{t_B}{\sqrt{LC}}+I_P\sqrt{\frac{L}{\mathrm{C}}}\sin \frac{t_B}{\sqrt{LC}}$$

(13)

Therefore, the time that the voltage of the switch reaches its maximum is calculated as follows:

$$t_4=t_B+t_3$$

(14)

2.4. Stage 4

During the ($t_4-t_5$) interval, as the inductor’s energy has reached zero, energy now flows from the charged capacitor to the inductor. However, because of the resistor in the path, the current of the circuit does not oscillate and reaches zero after $t_C$. Thus, the equation of the circuit in this stage is as follows:

$$L\frac{d{i}_L}{dt}+V_C-V_{dc}+R_S{i}_L=0$$

(15)

$$i_C=C\frac{d{V}_C}{dt}$$

(16)

$$i_C=i_L$$

(17)

By solving the above second-order differential equation, the current is calculated as follows with the initial value: $i_L\left(0\right)=0$, $v_C\left(0\right)=V_P$.

$$i_L=A_1{e}^{S_{1}t}+A_2{e}^{S_{2}t}$$

(18)

where:

$$S_1=-\alpha +\sqrt{{\alpha }^2-{\mathsf{\omega }}^2},S_2=-\alpha -\sqrt{{\alpha }^2-{\mathsf{\omega }}^2}$$

$$\alpha =\frac{R}{2L}, \mathsf{\omega }=\frac{1}{\sqrt{\mathrm{LC}}}$$

$$A_1=S_1\left(L{C}^2{S}_2+L\right)\left(V_P-V_{dc}\right) , A_2=S_2\left(L{C}^2{S}_1+L\right)\left(V_P-V_{dc}\right)$$

Since the plot of $i_L$ is exponential, the current of the inductor does not reach zero but it tends to zero, so by considering $i_L\le ϵ$, $t_C$ will be obtained.

The time when the system is completely out of current is calculated as:

$$t_5=t_C+t_4$$

(19)

2.5. Stage 5

The system is out of current but there is still a dc input voltage connected. The mechanical switch starts to operate at the time $t_6\ge t_5$ and the negative terminal of the circuit will be isolated. Finally, after $t_M$, the negative terminal is isolated, and the circuit is completely out of current and voltage at the time $t_7$.

3. Design Procedure

The design procedure of the SSCB is performed for both the circuit itself and its auxiliary circuit for the soft turn-on operation.

3.1. Short-Circuit Fault Operation

In order to find the optimized value of snubber capacitor $C$, the following assumptions can be considered to simplify the equations:

$$V_{dc}-V_{dc}\cos \frac{t_C}{\sqrt{LC}}\ll I_P\sqrt{\frac{L}{\mathrm{C}}}\sin \frac{t_C}{\sqrt{LC}}$$

(20)

$$\sin \frac{t_C}{\sqrt{LC}}\approx \frac{t_C}{\sqrt{LC}}$$

(21)

Therefore, the peak voltage of the capacitor can be rewritten as follows:

$$V_P\approx I_P\frac{t_C}{\mathrm{C}}$$

(22)

Therefore, the value of the capacitor is obtained using Equations (6) and (22):

$$\mathrm{C}\approx \left(\frac{V_{dc}{t}_B}{L}+I_N\right)\left(\frac{t_C}{V_P}\right)$$

(23)

The minimum value of the snubber capacitor can now be obtained by considering $V_{clamp}$ of the MOV as $V_P$. Therefore, based on the desired $\Delta t_C$, the optimized value of $\mathrm{C}$ can be found.

In order to obtain the optimal size of the snubber resistor, since the circuit forms an RLC circuit during stage 4, the formula of the inductor’s current (Equation (18)) should be overdamped. In order to overdamp the current of the inductor, the following equation must be valid:

$$\alpha >\mathsf{\omega }$$

(24)

where:

$$\alpha =\frac{R}{2L} , \mathsf{\omega }=\frac{1}{\sqrt{\mathrm{LC}}}$$

Therefore, the minimum value of the snubber resistance is obtained as follows:

$$R>2\sqrt{\frac{L}{\mathrm{C}}}$$

(25)

3.2. Soft Turn-On Operation

When the fault is cleared and the system is going to run again, there is usually a voltage difference between the input and output voltage terminals, especially in the energy router applications in which the dc link is connected to some different energy sources. This voltage difference can create a huge current passing through the switches and running the SSCB. Therefore, the turn-on process should be as soft as possible.

The aforementioned problem is addressed using an auxiliary circuit for the switches. As shown in Figure 5a, it is assumed that there is a voltage difference between $V_{dc}$ and $V_O$. If we consider the gate-source voltage of the MOSFET as shown in Figure 5b, for soft turn-on an RC circuit as demonstrated in Figure 5c is needed. Hence, the gate-source voltage ($V_{GS}$) can be calculated by solving the first-order equation of the RC circuit as follows:

$$V_{GS}=V_K\left(1-e^{\frac{-t}{RC}}\right)$$

(26)

where $V_K$ is the voltage of the gate driver. Time $t$ can be considered as the minimum time needed for equalizing the voltages in the circuit. This depends on the capacitance of the input and output terminals and the resistance of the line.

$$t=5RC$$

(27)

The minimum gate-source voltage ($V_{GS}$) that can turn on the MOSFET can be obtained by testing a MOSFET or using the datasheet.

By placing $V_{GS}$ and $t$ in Equation (23), the value of RC can be calculated.

It now seems that the simplest solution for the soft turn-on is by placing a capacitor in parallel to the gate-source of the MOSFET and a resistor in series with the gate terminal. However, placing the capacitor will also affect the turn-off time. Thus, the solution is to increase the resistance R by placing a huge resistor in series with the gate terminal and turn-off resistor $R_{G1}$, and in parallel with a diode in the other structure so as not to affect the turn-off time (Figure 6a). In the other structure, the resistor and diode are placed in series together and in parallel with the turn-off resistor $R_{G1}$ (Figure 6b).

However, the aforementioned solution severely affects the gate driver’s performance. Therefore, the most complete approach is one using the structure in Figure 6c. In the turn-off mode, the mechanical relay $K_1$ is ON and relay $K_2$ is OFF. This means that only the resistor $R_{G1}$ is in the gate auxiliary circuit. On the other hand, in the turn-on mode, the state of the relays $K_1$ and $K_2$ is reversed and they are turned OFF and ON, respectively, which puts the calculated RC in the gate auxiliary circuit. In this circuit, the resistor $R_{G3}$ is in parallel with the capacitor to discharge the capacitor for the next turn-on.

4. Experimental Results

Figure 7 shows the schematic of the circuits used for the experiment. In the first experiment (Figure 7a), the short-circuit is created using a mechanical relay $K$ across the load. Figure 8 shows the laboratory prototype and test operation of the designed SSCB. The design parameters of the designed SSCB are given in

Table 2. Design parameters of the designed SSCB.

Parameters	Acronym	Value	Unit
Input Voltage	$V_{dc}$	240	$\mathrm{V}$
Snubber Capacitor	$C_1\& C_2$	100	$\mathsf{\mu }\mathrm{F}$
Snubber Diode	$D_1 \& D_2$	2	$\mathrm{A}$
Snubber Resistance	$R_1 \& R_2$	22	$\mathsf{\Omega }$
Line Inductor	$L$	10	$\mathsf{\mu }\mathrm{H}$
Clamp voltage of MOV	$V_{Clamp}$	675	$\mathrm{V}$
MOSFETs		NTHL040N120SC1
Capacitor of auxiliary circuit	$C_G$	100	$\mathrm{nF}$
Resistance of auxiliary circuit	$R_{G2}$	10	k$\mathsf{\Omega }$

. In the first part of this test, the input voltage is 60 V and the limit current of the SSCB is 10 A. The result as shown in Figure 9a is a peak current of 44 A while the peak voltage of the switch $S_1$ is 270 V. In the second part of the test (Figure 9b), the voltage of the dc source is increased to 240 V with a 30 A limit for the circuit’s current. The SSCB breaks the circuit after 16 μs when the current reaches 100 A and the voltage of the switch $S_1$ reaches 420 V. As discussed before, in reality there is a time delay that depends on the current sensor and the speed of the microcontroller programming. The delay time of the current sensor used in this prototype is 14 μs and the delay of the programming equals the sampling period, which is 5 μs. These delays do not sum up since they occur simultaneously. This time delay can be reduced using a current sensor with a larger bandwidth.

However, after reducing the time delay to the sampling period, to further decrease the delay, the sampling frequency should be increased. However, as discussed in the previous section this raises the peak voltage of the switch during the fault-clearing operation so there should be a lower limit for the delay according to the components’ capability.

In the second test as shown in Figure 7b, the main path of the circuit is connected through a mechanical switch. The capacitors are then charged to different voltages by turning on the switches $G_1$ and $G_2$ temporarily. By disconnecting these switches and connecting switch $K$, there will now be a huge current spike because of the input and output capacitors’ voltage difference dropped on the small resistance of the circuit. Therefore, the auxiliary circuit in Figure 6b is used in the main prototype for the soft turn-on.

As shown in Figure 10a, there is a 30 V voltage difference between the input and output capacitors, which by the benefit of using a 10 KΩ resistor and a 100 nF capacitor as mentioned before, the peak of the surge current is limited to 15 A. In the second test shown in Figure 10b, the voltage difference is 50 V, which is the maximum voltage difference in an energy router application. In this case, the peak surge current is 25 A, which is very desirable.

5. Conclusions

An SSCB is designed for energy router applications with a soft turn-on capability. The findings of the working principles of the SSCB and its operating modes are used to propose an SSCB design procedure. An SSCB prototype is developed and its performance is evaluated in different operating scenarios for both short-circuit tests and soft turn-on tests. Although, using a relatively large resistor in series with the gate terminal and placing a diode in parallel with it to prevent its effect on the turn-off process reduces the turn-on surge current, it severely affects the gate driver’s performance. Although, using a relatively large resistor in series with the gate terminal and placing a diode in parallel with it to prevent its effect on the turn-off process reduces the turn-on surge current, it severely affects the gate driver’s performance. Therefore, by using two small low-voltage switches, an auxiliary circuit is obtained that solves the surge currents during the turn-on in the energy routers. The designed bidirectional SSCB uses an RCD+MOV snubber, which as discussed in the paper is the best snubber for circuit breakers switches. The SSCB breaks the circuit very fast at 16 μs. However, this time delay depends on the current sensor and the sampling frequency of the microcontroller programming. In this case, using a current sensor with a larger bandwidth can reduce the time delay to some extent, which should be taken into consideration in the design procedure to find a balanced value as it increases the maximum voltage of the switches. On the other hand, the optimized value of the capacitor snubber is also calculated depending on the clamp voltage of the MOV and the desired time for discharging the line inductor’s energy. This SSCB, unlike the traditional bidirectional SSCBs, benefits from isolating both terminals, which allows the circuit breaker to disconnect the voltage and the current, further increasing the safety and omitting the disturbance in the system when using more than one SSCB.