Efﬁcient Protection Scheme Based on Y-Source Circuit Breaker in Bi-Directional Zones for MVDC Micro-Grids

: A new bi-directional circuit breaker is presented for medium-voltage dc (MVDC) systems. The Y-source impedance network topology is used to implement the breaker. The current transfer function is derived to show the frequency response and the breaker operation with the high frequencies. Mathematical analysis is achieved with different conditions of coupling among the breaker inductors. The minimum level of the magnetic coupling is determined, which is represented by the null condition. The effect of the turns-ratio on this condition is investigated as well. The breaker is designed with two types of fault conductance slope rates. The Y-source breaker is simulated, and the results verify the breaker operation during the fault condition and the load change. The results also demonstrate the effect of the coupling level on the minimum values of the source current when the fault occurs. Based on the expected fault type in the MVDC systems, the proposed breaker is developed to interrupt the overcurrent due to any of these fault types. A protection scheme is proposed for a 12-bus, two-level micro-grid, where the Y-source breakers are used in the bi-directional zones. The results verify the ability of the breaker to conduct and interrupt the current in both directions of the power ﬂow.


Introduction
Due to the developments of the solid-state power transformer (SSPT), medium-voltage dc (MVDC) micro-grids are used to integrate many types of renewable energy sources (RESs), charging stations, electrical vehicles (EVs), and local distribution generators (DGs). The MVDC grids are utilized for that purpose because of their many features such as high efficiency, high controllability, no reactive power, no synchronization problems, no requirements for the output regulation of frequency and voltage, and low cost [1,2]. With these renewable energy sources, the MVDC micro-grids became more desirable. The popular RESs that are integrated into this level of the DC grids are photovoltaics (PVs) and wind farms [3]. Moreover, using MVDC in the distribution systems of modern shipboards is interested in reducing fuel consumption with a larger size of the ship capacity [3,4].
The fault current elimination in the MVDC power systems is considered the main challenge because of the absence of the fault zero-crossing point. In addition, the low impedance characteristics of the MVDC systems causes a high fault current during milliseconds [3,[5][6][7][8][9][10]. For these reasons, the circuit breakers used to interrupt the fault current must have a fast response and create a zero-crossing point naturally during the occurrence of the fault.
The first type of protection device is the molded-case circuit breakers (MCCBs). This breaker contains three main parts, which are a contactor, a quenching chamber, and a thermal-magnetic or electronic tripping device. The tripping device operation depends on the value of the instantaneous current [11]. The MCCBs trip when passing an adequate value of current to heat the thermal-magnetic device and expand the contacts to interrupt the fault current. The disadvantage of this device is tripping the high-magnitude current during non-faulty conditions, such as the discharging current in the DC grid converter applications [12].
The second type of protection device for the MVDC power systems used semiconductor devices such as insulated gate commutated thyristors, insulated gate bipolar transistors, and gate turn-off thyristors to implement these breakers with a higher capability of the inductive current interruption [13,14]. These types of circuit breakers are hybrid breakers, where a mechanical switch is connected in parallel with the semiconductor device [15][16][17][18][19]. When the fault occurs, the mechanical switch opens, and the fault current is forced to pass through the semiconductor element that interrupts it. Many components are required to add to this breaker, such as metal-oxide varistors (MOVs), capacitors, and switched resistors in order to dissipate the interrupting energy [20,21].
The third type of MVDC circuit breakers is fully solid-state circuit breakers (SSCBs). They have the ability to protect the MVDC grids against the high current during the fault conditions automatically and fast. Many techniques are used to implement the SSCBs, such as using a free-wheeling diode to eliminate the fault current, where the diode is connected across the breaker output. In addition, they can be achieved by using a resonant circuit, where the fault current is dropped to zero naturally [22]. Furthermore, impedance source networks are used to build SSCBs for MVDC systems. The novel sourced-impedance circuit breaker for the MVDC power systems is introduced in [23,24] by using a Z-source impedance network. This network, as mentioned, consists of two inductors and two capacitors that were arranged in the shape of a cross and a Silicon Control Rectifier (SCR). The SCR commutates OFF state due to zero current crossing that is provided by the Zsource network [25][26][27]. By making these two inductors coupled as in [9], the Z-source breaker can operate with fewer components, smaller size, and reduced weight compared with the non-coupled breaker. The inductor size is reduced by 50% compared with noncouple-inductor Z-source breakers. The coupling of these inductors also provides a path for the reflected current and gives the ability to remove one of the two capacitors that were used in the non-coupled windings breaker [9]. By rearranging these two coupling inductors as in [7], the circuit operates as a coupled-winding Z-source circuit breaker with a Γ shape. Authors in references [7,9] proposed, analyzed, and simulated this circuit with a perfect coupling between these two coils of the breaker. In reference [28], the performance of the Γ shape source impedance breaker was stated under a variable coupling coefficient. The Z-source DC circuit breakers that were produced and designed in the previous work allow the DC current to flow in one direction. The T-source impedance is also presented as a unidirectional solid-state DC circuit breaker in [8]. This topology consists of an SCR, and two coupled inductors with a capacitor were arranged as a T-shape to provide a reverse current forcing the SCR to turn OFF and reduce the source current to zero during the fault conditions.
In many DC power systems, the lines may conduct power in both directions. Therefore, unidirectional circuit breakers are unable to pass the current in the opposite direction. In addition, the capability of the circuit breaker to interrupt the fault current of these lines in both directions of the power flow is required. Based on that, the protection devices that are connected to protect these lines should be bi-directional breakers [29,30].
The purpose of this paper is to propose a new solid-state bi-directional circuit breaker topology for the MVDC systems. The magnetically coupled Y-source impedance network is utilized to implement this breaker. It is developed to operate with two-level MVDC systems. This new work shows the effect of the coupling coefficient and the turns-ratio on the breaker performance during the fault conditions. The breaker is also tested in case the load current changes, and the results show the ability to allow the source to provide the extra load with a higher current without interruption. In this article also, a protection scheme for a 12-bus MVDC micro-grid is implemented. The proposed Y-source impedance circuit breaker is placed in the lines that the bi-direction power flow is expected. The results proved the ability of the breaker to conduct the current in the opposite direction and to interrupt the source current in case of a fault occurring.
The remainder of the paper is structured as follows: In Section 2, we describe the proposed topology of the Y-source impedance bi-directional circuit breaker; in Section 3, we investigate the proposed topology under fault and load change conditions. We develop the breaker according to the three types of faults that are expected to occur in the MVDC systems. The proposed Y-source breaker also deploys into a 12-bus MVDC micro-grid. Finally, we report the conclusions of the study in Section 4.

Proposed Topology (Coupled-Inductor Y-Source Impedance Bi-Directional Circuit Breaker)
A Y-source impedance network is proposed as a bi-directional circuit breaker for MVDC power systems. Three coupled inductors (L 1 , L 2 , and L 3 ) and a capacitor are arranged in a Y shape to create the breaker. This topology is able to conduct and interrupt the current in both directions of power flow, as shown in Figure 1. The breaker also contains silicon control rectifiers (SCRs), where these thyristors commutate ON when a triggering gate signal is applied to each thyristor. These signals are removed after the SCRs switch to the ON state; the states of these SCRs are explained in Table 1. 18 3 of 20 extra load with a higher current without interruption. In this article also, a protection scheme for a 12-bus MVDC micro-grid is implemented. The proposed Y-source impedance circuit breaker is placed in the lines that the bi-direction power flow is expected. The results proved the ability of the breaker to conduct the current in the opposite direction and to interrupt the source current in case of a fault occurring. The remainder of the paper is structured as follows: In Section 2, we describe the proposed topology of the Y-source impedance bi-directional circuit breaker; in Section 3, we investigate the proposed topology under fault and load change conditions. We develop the breaker according to the three types of faults that are expected to occur in the MVDC systems. The proposed Y-source breaker also deploys into a 12-bus MVDC microgrid. Finally, we report the conclusions of the study in Section 4.

Proposed Topology (Coupled-Inductor Y-Source Impedance Bi-Directional Circuit Breaker)
A Y-source impedance network is proposed as a bi-directional circuit breaker for MVDC power systems. Three coupled inductors (L1, L2, and L3) and a capacitor are arranged in a Y shape to create the breaker. This topology is able to conduct and interrupt the current in both directions of power flow, as shown in Figure 1. The breaker also contains silicon control rectifiers (SCRs), where these thyristors commutate ON when a triggering gate signal is applied to each thyristor. These signals are removed after the SCRs switch to the ON state; the states of these SCRs are explained in Table 1.

SCR Gates i1 and i2 Direction Positive
Negative The states of the gate signals are 1s when a positive DC voltage from the gate signal circuit is applied from the triggering circuit, as shown in Figure 1. The push-button, S1, is used to send the gate signals to G1 and G3 of the SCRs T1 and T3, respectively, to turn them ON at the same time. The power direction, in this case, is from V1 to V2. The gate states of the SCRs, T2 and T4, are 0s. On the other hand, the push-button, S2 is used to send the gate signals to G2 and G4 of the SCRs T2 and T4, respectively, to turn them ON at the same time. The power, in this case, flows from V2 to V1, and the gate states of the SCRs, T1 and T3, are 0s.

SCR Gates i 1 and i 2 Direction
Positive Negative The states of the gate signals are 1s when a positive DC voltage from the gate signal circuit is applied from the triggering circuit, as shown in Figure 1. The push-button, S1, is used to send the gate signals to G 1 and G 3 of the SCRs T 1 and T 3 , respectively, to turn them ON at the same time. The power direction, in this case, is from V 1 to V 2 . The gate states of the SCRs, T 2 and T 4 , are 0s. On the other hand, the push-button, S2 is used to send the gate signals to G 2 and G 4 of the SCRs T 2 and T 4 , respectively, to turn them ON at the same time. The power, in this case, flows from V 2 to V 1 , and the gate states of the SCRs, T 1 and T 3 , are 0s.

Breaker Operation
Based on the proposed breaker shown in Figure 1, the power flow direction in the normal operation is from V 1 to V 2 . The forward steady-state load current passes through T 1 , L 1 , L 3 , T 3 to the load. However, the load current passes through T 4 , L 3 , L 1 , T 2 to the load in case of the other power direction. During transient current conditions, like fault or load change, the capacitor feeds that current through two inductors, L 2 -L 3 or L 2 -L 1 , depending on the power flow direction. The coupling between the inductors provides a path for the reflected current. In case the opposite current reaches the value of the normal forward current, SCRs will be OFF, which interrupts the source current. Figure 2 explains the equivalent circuit that is used for analyzing the Y-source impedance breaker. The equivalent inductance of the breaker in a matrix form is shown in Equation (1).

Circuit Breaker Analysis
where the diagonal elements, the Liis, for i = 1, 2, 3 are the self-inductances. The offdiagonal elements Mijs, are the mutual-inductances between the coils i and j. The mutual inductances, Mij can be expressed as shown in Equation (2) M ij = k ij L ii L jj (2) where i = j, i = 1, 2, 3, j = 1, 2, 3, and k ij is the magnetic coupling coefficient between ith and jth inductors. Based on the equivalent circuit of the proposed Y-source breaker shown in Figure

Breaker Operation
Based on the proposed breaker shown in Figure 1, the power flow direction in the normal operation is from V1 to V2. The forward steady-state load current passes through T1, L1, L3, T3 to the load. However, the load current passes through T4, L3, L1, T2 to the load in case of the other power direction. During transient current conditions, like fault or load change, the capacitor feeds that current through two inductors, L2-L3 or L2-L1, depending on the power flow direction. The coupling between the inductors provides a path for the reflected current. In case the opposite current reaches the value of the normal forward current, SCRs will be OFF, which interrupts the source current.

=
(1) where the diagonal elements, the Liis, for i = 1, 2, 3 are the self-inductances. The offdiagonal elements Mijs, are the mutual-inductances between the coils i and j. The mutual inductances, Mij can be expressed as shown in Equation (2) = where i ≠ j, i = 1, 2, 3, j = 1, 2, 3, and kij is the magnetic coupling coefficient between ith and jth inductors. Based on the equivalent circuit of the proposed Y-source breaker shown in Inventions 2021, 6, 18

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The equivalent series resistance (ESR) of the capacitor C is represented by a small resistor r c as shown in the equivalent circuit of the breaker.
To verify the effect of the coupling coefficient (k) variation on the breaker current gain, the output to the input current transfer function is derived. The equivalent circuit shown in Figure 3 is used to find the current transfer function, where two currents are assumed, as shown in the breaker equivalent circuit.
The equivalent series resistance (ESR) of the capacitor C is represented by a small resistor rc as shown in the equivalent circuit of the breaker.
To verify the effect of the coupling coefficient (k) variation on the breaker current gain, the output to the input current transfer function is derived. The equivalent circuit shown in Figure 3 is used to find the current transfer function, where two currents are assumed, as shown in the breaker equivalent circuit.  Two current loops are assumed as shown in Figure 3 to analyze the circuit breaker. Based on these loops, the circuit voltage equations can be written as in Equation (7) Loop1: Loop2: where: ZRC is the equivalent impedance of the breaker capacitor, RL is the load resistance. By solving Equations (7) and (8), I1(s) and I2(s) are shown below.
From Equations (9) and (10), the current transfer function is given in Equation (11) By substituting Equations (3)-(5) into Equation (11), and the impedance of the breaker capacitor (ZRC) equals rc + (1/sC), the current transfer function can be written as shown below. Two current loops are assumed as shown in Figure 3 to analyze the circuit breaker. Based on these loops, the circuit voltage equations can be written as in Equation (7) Loop1: Loop2: where: Z RC is the equivalent impedance of the breaker capacitor, R L is the load resistance.
From Equations (9) and (10), the current transfer function is given in Equation (11) By substituting Equations (3)-(5) into Equation (11), and the impedance of the breaker capacitor (Z RC ) equals r c + (1/sC), the current transfer function can be written as shown below.
where β is defined in Equation (13) In case of perfect coupling between the inductors, the current transfer function becomes as shown below.
The magnitude and phase of the current transfer functions are plotted, as shown in Figure 4. The parameter values of Table 2 are used to plot the breaker current frequency response. In Figure 4a, the values of the coupling coefficient are larger than the null value. In this case, the current response at high frequencies is −5 dB and −2 dB with a coupling coefficient of 90% and 80%, respectively, and the phase is 180 • . According to the inputoutput current frequency response, the breaker produces an opposite output current higher than the SCRs forward current (source current) in case k is more than the null value. This current reduces the forward current less than the holding current and commutates the SCRs to OFF-state. where β is defined in Equation (13) In case of perfect coupling between the inductors, the current transfer function becomes as shown below.
The magnitude and phase of the current transfer functions are plotted, as shown in Figure 4. The parameter values of Table 2 are used to plot the breaker current frequency response. In Figure 4a, the values of the coupling coefficient are larger than the null value. In this case, the current response at high frequencies is −5 dB and −2 dB with a coupling coefficient of 90% and 80%, respectively, and the phase is 180°. According to the inputoutput current frequency response, the breaker produces an opposite output current higher than the SCRs forward current (source current) in case k is more than the null value. This current reduces the forward current less than the holding current and commutates the SCRs to OFF-state.   If case k is equal to the null value, the current high frequencies gain goes to infinity with a constant slope, as shown in Figure 4b. The input current is higher than the output current (positive dB gain). Based on that gain, the current source increases to feed the abnormal current during the fault conditions, and the breaker is unable to interrupt the fault current with k is equal to the null value. The magnitude at high frequencies still has a positive dB gain, and the phase is zero for k less than the null value of the coupling coefficient (knull) as shown in Figure 4b. Two values of the coupling coefficient are chosen  If case k is equal to the null value, the current high frequencies gain goes to infinity with a constant slope, as shown in Figure 4b. The input current is higher than the output current (positive dB gain). Based on that gain, the current source increases to feed the abnormal current during the fault conditions, and the breaker is unable to interrupt the fault current with k is equal to the null value. The magnitude at high frequencies still has a positive dB gain, and the phase is zero for k less than the null value of the coupling coefficient (k null ) as shown in Figure 4b. Two values of the coupling coefficient are chosen to verify the breaker current response with k less than k null . Based on the frequency response (phase and magnitude), the input current is higher than the output current at the same phase, which keeps the SCRs in the ON-state during the transient conditions.

Circuit Breaker Design
The fault conductance plays a role in detecting the minimum value of the fault current. This current will be reflected in a different value to break the source current [25]. Some assumptions that are considered in the previous works of [7][8][9] are used in this work. The load capacitance is also assumed to be zero (C l = 0) [7].

Infinite Fault Conductance Slope Rate
In this analysis, the rising time of the fault conductance is assumed to be zero. The currents of the inductors are also assumed constant. The capacitor of the breaker discharges through the L 2 -L 3 to the fault branch when the fault occurs. The discharging current is given in Equation (15) i where G f is the fault conductance. The reflected current (i ref ) can be expressed as below Assume k 12 = k 13 = k, the reflected current can be written as below.
To satisfy the condition for breaker operation, the G f should make the breaker produce a current in the reverse direction to the source with an amplitude that is equal to or greater than the normal steady-state current to force the SCRs to commutate to the OFFstate in order to interrupt the source current. The minimum value of the G f is shown in Equation (18).
Obviously, the G f is inversely proportional to the square of the coupling coefficient. If case k is decreased to 90%, 82.3% of the load current higher than its normal value makes the breaker reflects enough current to interrupt the source. If case k is unity, increasing 66% in the load current above the normal value is adequate to make the SCRs turn off.

Linear Fault Conductance Slope Rate
In this case, the slope rate of the conductance rises linearly with the time until it reaches its final value, as assumed in [26]. The capacitor current can be written as shown below.
where C is the breaker capacitor and v f is the output voltage when the fault occurs. From Equations (15) and (19), the fault current can be written as in Equation (20) i where the fault conductance (G f ) equals mt. By solving (20) for v f , the instantaneous output voltage across the load during the fault (v f (t)) is descripted by the equation below.
Inventions 2021, 6, 18 where v 1 is the source voltage. The fault current can be written now as in the Equation below.
At t = √ (C/m), the value of the capacitor current is maximum and can be written as below.
The value of the capacitor current on the N 1 side (i c (N 1 )) is shown in Equation (24) i c( To satisfy the condition of the reflected current value to commutate the SCR OFF state, Equation (25) describes the minimum value of that slope, which is represented by m min .
where τ is the time constant that depends on the R L and C.
The ability of the breaker to cut off the source current during fault conditions is operative as long as the fault conductance rises with a rate equal to or faster than the rate in Equation (25). From Equation (25), the coupling coefficient k affects the m min with a rate of (1/k 4 ), where increasing k makes the required value of the slope decrease. By using the values of the parameters as in Table 2, the minimum value of m min is equal to 604 s −1 Ω −1 with tightly coupled inductors, while with 90% of coupling level, the minimum value of m min is equal to 920.68 s −1 Ω −1 .

The Effect of Turns-Ratio on k null
The Y-source circuit breaker shown in Figure 1 has three coupled inductors. The first, second, and third inductors have N 1 , N 2 , and N 3 number of turns, respectively. The numbers of turns for the coupled inductors have a direct effect on the minimum value (null value) of the coupling coefficient. At this value, the term of Cβs 2 in the Equation (12) disappears. At this condition, the k null is shown below.
The inductance of a coil L = (1/C core ).N 2 , where N is the number of turns and C core is the constant of magnetic core physical characteristics [31]. The magnetic coupling between the inductors can be expressed as shown in Equation (27) with the same magnetic core characteristics.
When the value of k is equal to or less than the value in Equation (27), the breaker cannot interrupt the abnormal current. Figure 5 illustrates the effect of the turns ratio on the null value of k. This value of k becomes higher when the turns-ratio increases. For Figure 5, in case the coils have an equal number of turns, the breaker cannot work even though the coils are tightly coupled. In that aspect, increasing the value of the turns ratio gives the Y-source circuit breaker a wide range of coupling levels to work with.

Coupled-Inductor Y-Source Impedance Bi-Directional Circuit Breaker
In this section, the proposed topology, illustrated in Section 2, is investigated under fault condition and load change. The investigation has been accomplished using a 6 kV DC source to supply the load through the proposed breaker.

Fault Interruption
In order to verify the operation of the Y-source impedance DC circuit breaker with different values of the coupling coefficient k, three coils magnetically coupled have been simulated with a 6Ω load resistance. A 10 mΩ is applied across the load resistance after 200 ms, where this resistance represents a fault resistance. The rest of the parameters are in Table 2. The source-current response in the time domain with different values of the coupling coefficient is shown in Figure 6. These three values of the coefficient are above the null value. In Figure 6a, where the turns-ratio equals 2, the first value is chosen to reduce the source-current to zero. The two other values of the coefficient are randomly chosen to show different minimum values of the source-current (isource(min)) during the occurrence of the fault. This simulation was also repeated with another value of L2, as in Figure 6b. Table 3

Coupled-Inductor Y-Source Impedance Bi-Directional Circuit Breaker
In this section, the proposed topology, illustrated in Section 2, is investigated under fault condition and load change. The investigation has been accomplished using a 6 kV DC source to supply the load through the proposed breaker.

Fault Interruption
In order to verify the operation of the Y-source impedance DC circuit breaker with different values of the coupling coefficient k, three coils magnetically coupled have been simulated with a 6Ω load resistance. A 10 mΩ is applied across the load resistance after 200 ms, where this resistance represents a fault resistance. The rest of the parameters are in Table 2. The source-current response in the time domain with different values of the coupling coefficient is shown in Figure 6. These three values of the coefficient are above the null value. In Figure 6a, where the turns-ratio equals 2, the first value is chosen to reduce the source-current to zero. The two other values of the coefficient are randomly chosen to show different minimum values of the source-current (i source(min) ) during the occurrence of the fault. This simulation was also repeated with another value of L 2 , as in Figure 6b. Table 3 shows the minimum values of the source current at the moment of the fault occurring for different values of the coupling coefficient.

Coupled-Inductor Y-Source Impedance Bi-Directional Circuit Breaker
In this section, the proposed topology, illustrated in Section 2, is investigated under fault condition and load change. The investigation has been accomplished using a 6 kV DC source to supply the load through the proposed breaker.

Fault Interruption
In order to verify the operation of the Y-source impedance DC circuit breaker with different values of the coupling coefficient k, three coils magnetically coupled have been simulated with a 6Ω load resistance. A 10 mΩ is applied across the load resistance after 200 ms, where this resistance represents a fault resistance. The rest of the parameters are in Table 2. The source-current response in the time domain with different values of the coupling coefficient is shown in Figure 6. These three values of the coefficient are above the null value. In Figure 6a, where the turns-ratio equals 2, the first value is chosen to reduce the source-current to zero. The two other values of the coefficient are randomly chosen to show different minimum values of the source-current (isource(min)) during the occurrence of the fault. This simulation was also repeated with another value of L2, as in Figure 6b. Table 3 shows the minimum values of the source current at the moment of the fault occurring for different values of the coupling coefficient.

Load Change
In the second case of simulation, the load current is increased by 50% of its normal value. The source current in this condition decreases and then increases to feed the new load without interrupting the power. The capacitor current increases due to the transient situation and then drops to zero again. Figure 7 shows the source and capacitor current waveforms during the load current change.

Load Change
In the second case of simulation, the load current is increased by 50% of its normal value. The source current in this condition decreases and then increases to feed the new load without interrupting the power. The capacitor current increases due to the transient situation and then drops to zero again. Figure 7 shows the source and capacitor current waveforms during the load current change.

Developed Y-Source Bi-Directional Circuit Breaker
In the DC power system configuration, there are three different basic types of fault that are expected to occur. The fault type expectation depends on the system voltage level. These types of faults include a pole-to-pole short circuit (P-P), positive pole-to-Ground Fault (P-G), and negative pole-to-ground fault (N-G) [32]. The circuit breaker of the Ysource topology that is illustrated in Figure 1 is connected through the positive pole of the system. This topology works as a bidirectional breaker in case a fault occurs between the positive pole and the second pole, where it could be a ground or negative pole.
According to the aforementioned faults that are expected to occur in the MVDC systems, the breaker topology has been developed as shown in Figure 8. The parameter values are the same as in Table 2, and vs is equal to ±6 kV. This topology is able to operate with a two-level DC system where the negative pole is also connected to the load through a Y-source impedance network. The capacitor across the output port is used to force the other pole SCRs to be OFF and interrupts the current that is fed by that pole.

Developed Y-Source Bi-Directional Circuit Breaker
In the DC power system configuration, there are three different basic types of fault that are expected to occur. The fault type expectation depends on the system voltage level. These types of faults include a pole-to-pole short circuit (P-P), positive pole-to-Ground Fault (P-G), and negative pole-to-ground fault (N-G) [32]. The circuit breaker of the Ysource topology that is illustrated in Figure 1 is connected through the positive pole of the system. This topology works as a bidirectional breaker in case a fault occurs between the positive pole and the second pole, where it could be a ground or negative pole.
According to the aforementioned faults that are expected to occur in the MVDC systems, the breaker topology has been developed as shown in Figure 8. The parameter values are the same as in Table 2, and v s is equal to ±6 kV. This topology is able to operate with a two-level DC system where the negative pole is also connected to the load through a Y-source impedance network. The capacitor across the output port is used to force the other pole SCRs to be OFF and interrupts the current that is fed by that pole.

Positive Pole-to-Ground Fault
In case a fault occurs at point F 1 , shown in Figure 8, to the ground, the Y-source impedance that is connected to protect the positive pole will interrupt the current supplied by that pole. The fault current will only be supplied by the negative pole (i fn ) in case there is no terminal capacitor (C t ). Equation (28) describes the value of i fn .

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The terminal capacitor (C t ) that is connected to the breaker terminal is to discharge through the fault path during the moment the short circuit occurs. The transient current of this capacitor activates the operation of the negative pole Y-source network. The reflected current in the primary negative pole inductor (L n1 ) causes the SCRs to commutate to the OFF state and interrupt the negative source current. Figure 9 shows the simulation results of the current waveforms of the positive pole, negative pole, and terminal capacitor.  Figure 8. Two levels bi-directional Y-source circuit breaker.

Positive Pole-to-Ground Fault
In case a fault occurs at point F1, shown in Figure 8, to the ground, the Y-sour impedance that is connected to protect the positive pole will interrupt the current supplie by that pole. The fault current will only be supplied by the negative pole (ifn) in case the is no terminal capacitor (Ct). Equation (28) describes the value of ifn.
The terminal capacitor (Ct) that is connected to the breaker terminal is to discharg through the fault path during the moment the short circuit occurs. The transient curre of this capacitor activates the operation of the negative pole Y-source network. Th reflected current in the primary negative pole inductor (Ln1) causes the SCRs to commuta to the OFF state and interrupt the negative source current. Figure 9 shows the simulatio results of the current waveforms of the positive pole, negative pole, and termin capacitor.

Negative Pole-to-Ground Fault
In this case, the negative pole is shorted to the ground at point F 2 , as illustrated in Figure 8. The negative Y-source impedance will control the fault current and reduce it to zero. The fault current that is supplied by the positive pole (i fp ) will be limited to the value as in the Equation below: The terminal capacitor (C t ) acts the same as in the previous case, where it discharges through the fault path when the short circuit occurs. The transient current activates the operation of the positive Y-source network to force the current of that pole to go to zero due to the reflected current in the primary positive pole inductor L p1 . Figure 10 shows the current waveforms of the positive pole, negative pole, and terminal capacitor.

Negative Pole-to-Ground Fault
In this case, the negative pole is shorted to the ground at point F2, as illustrated in Figure 8. The negative Y-source impedance will control the fault current and reduce it to zero. The fault current that is supplied by the positive pole (ifp) will be limited to the value as in the Equation below: The terminal capacitor (Ct) acts the same as in the previous case, where it discharges through the fault path when the short circuit occurs. The transient current activates the operation of the positive Y-source network to force the current of that pole to go to zero due to the reflected current in the primary positive pole inductor Lp1. Figure 10 shows the current waveforms of the positive pole, negative pole, and terminal capacitor.

Pole-to-Pole Fault
If case s fault occurs between the points F1 and F2, shown in Figure 8, the rising in the current due to the fault occurring causes a reflected current in the primary inductor of the Y-source impedance in both poles (positive and negative), where the voltage of each pole is 6 kV. The reflected current decreases the SCRs current to zero in both poles, as shown in Figure 11a,b. The terminal capacitor discharges through the fault path, as shown in Figure 11c. Compared to the two previous types of faults, the value of the capacitor discharging current is higher when a pole-to-pole fault occurs.

Pole-to-Pole Fault
If case s fault occurs between the points F1 and F2, shown in Figure 8, the rising in the current due to the fault occurring causes a reflected current in the primary inductor of the Y-source impedance in both poles (positive and negative), where the voltage of each pole is 6 kV. The reflected current decreases the SCRs current to zero in both poles, as shown in Figure 11a,b. The terminal capacitor discharges through the fault path, as shown in Figure 11c. Compared to the two previous types of faults, the value of the capacitor discharging current is higher when a pole-to-pole fault occurs.

Y-Source Breaker Deployment into MVDC Micro-Grid (Case Study)
A 12-bus MVDC micro-grid is presented for the proposed protection scheme, as shown in Figure 12. The microgrid is structurally similar to the test MVDC micro-grid in [32,33]. The voltage level of this grid is ±2.5 kV, which is the typical voltage for medium voltage DC systems [34]. The utility grid is connected through a two-level voltage source converter (VSC) at bus1, where this VSC controls the DC voltage of the MG. A local AC generator (DG) is connected to the micro-grid at bus9 through AC/DC converters. Additionally, the grid has two photovoltaic (PV) generation units. Each PV unit has a 1 kV array voltage regulated by a maximum power point tracking algorithm. The PV units are interfaced through DC/DC converters to the grids with a voltage of 5 kV. Three DC loads are connected to the grid, as well. The rated powers of these loads, as mentioned, are 1 MW, 3 MW, and 4 MW with rated voltage of 1.5 kV at buss 3, 7, and 11, respectively. DC/DC converters are used to reduce the voltage and interface those loads.
According to the structure of the proposed grid, three types of DC faults can occur.

Y-Source Breaker Deployment into MVDC Micro-Grid (Case Study)
A 12-bus MVDC micro-grid is presented for the proposed protection scheme, as shown in Figure 12. The microgrid is structurally similar to the test MVDC micro-grid in [32,33]. The voltage level of this grid is ±2.5 kV, which is the typical voltage for medium voltage DC systems [34]. The utility grid is connected through a two-level voltage source converter (VSC) at bus1, where this VSC controls the DC voltage of the MG. A local AC generator (DG) is connected to the micro-grid at bus9 through AC/DC converters. Additionally, the grid has two photovoltaic (PV) generation units. Each PV unit has a 1 kV array voltage regulated by a maximum power point tracking algorithm. The PV units are interfaced through DC/DC converters to the grids with a voltage of 5 kV. Three DC loads are connected to the grid, as well. The rated powers of these loads, as mentioned, are 1 MW, 3 MW, and 4 MW with rated voltage of 1.5 kV at buss 3, 7, and 11, respectively. DC/DC converters are used to reduce the voltage and interface those loads.  The protection scheme for the loads, lines, and sources is shown in Figure 12, where bidirectional and unidirectional circuit breakers are placed to protect the grid. Whether unidirectional or bidirectional breaker, the need to place circuit breakers on the power line depends on the power flow in that line. In that aspect, the bidirectional coupled inductors breakers are placed on the lines that have expected power flow in both directions. Meanwhile, the unidirectional breakers are placed to detect the faults in the zones of sources and loads, so there is one expected power flow. The description of the breakers is shown in Table 4. Table 4. Description of the protection scheme circuit breakers.

Circuit Breaker Numbers
Type CB3, CB4, CB6, CB7, CB8, CB9, CB11, CB12, CB14, CB16, CB24, and CB25 Unidirectional CB1, CB2, CB5, CB10, CB13, CB15, CB17, CB18, CB19, CB20, CB21, CB22, CB23, and CB26 Bi-directional The bi-directional proposed circuit breaker (Y-source network) does not need to detect the fault location to interrupt the overcurrent. Therefore, the CB response is completely automatic, and the gate signals do not control the operation of the breaker According to the structure of the proposed grid, three types of DC faults can occur. These faults are pole-pole (P-P), positive pole-ground (P-G), and negative pole-ground (N-G) [32,35,36]. Additionally, in some of the grid lines, the power flow has a probability of being in the opposite direction after the fault clears and disconnects the faulty zone. These lines should be equipped with bi-directional circuit breakers to allow the power to flow in the other direction.
The protection scheme for the loads, lines, and sources is shown in Figure 12, where bidirectional and unidirectional circuit breakers are placed to protect the grid. Whether unidirectional or bidirectional breaker, the need to place circuit breakers on the power line depends on the power flow in that line. In that aspect, the bidirectional coupled inductors breakers are placed on the lines that have expected power flow in both directions. Meanwhile, the unidirectional breakers are placed to detect the faults in the zones of sources and loads, so there is one expected power flow. The description of the breakers is shown in Table 4. The bi-directional proposed circuit breaker (Y-source network) does not need to detect the fault location to interrupt the overcurrent. Therefore, the CB response is completely automatic, and the gate signals do not control the operation of the breaker during the fault conditions. In particular cases, an external control to SCRs gate signals is required, such as maintenance, power flow direction changes before reaching the steady-state (during transient) where the current is high, and after the fault is clear. There are three options to control the operation of the grid breakers, which are central, local, and paired breaker controls [22].
In the central control, all breakers are controlled by a main unit. This unit receives information from each circuit breaker. This information contains the input and the output current compared with a threshold value. Depending on this information, if the output current is larger than a large threshold value, it means the breaker experienced a fault, and a minimum number of breakers should be off to isolate the fault. Additionally, the input current of the breaker is compared to a small value of threshold to know if the breaker switched ON or OFF. In addition, the central control unit is able to send gate signals through a communication system to the SCRs of the breakers to make them operate as DC switches [22].
The second option of the breaker control is local breaker control. In this option, the output current to the input current for each circuit breaker is monitored. If these currents are similar means, the breaker works under normal conditions. In another case, if these currents are different, the breaker should be an open state [22]. In the case of bi-directional breakers, clearing a faulty zone causes a reverse current in the different breaker. During that, the current goes to zero. The circuit breaker has no gate signal to allow the breaker to pass the current in the opposite direction. The local control of the breakers responds to indicate the change in the power flow and gates the SCRs with signals that give the required direction of the power flow. An example for this case, in the MVDC system that is shown in Figure 12, if a fault occurs at bus11 and the breaker at that bus will isolate the faulty bus, the current between bus 5 and bus 10 will be in the opposite direction. In this case, the circuit breakers CB10 and CB15 should be gated to switch them back ON and allow the current to pass through the line in the other direction.
The third option, utilized in this work, of the breaker control, is paired or matching breaker control. This option of control can be applied for breakers that operate in the same path of current. These breakers can receive gate signals at the same time and operate together as a pair. The paired breakers pass the same current or cut that current off. In that aspect, both paired breakers turn off regardless of which breaker takes action to clear the fault [22]. For example, in the system of Figure 12, breakers CB17 and CB18 are shared to conduct the current of the line between buses 8 and 10. Their SCRs gate signals should be applied at the same time to conduct them and allow the current to flow through the line. Table 5 shows the breaker pairs and their locations.  The test grid of Figure 12 is simulated by using MATLAB software. The grid has two levels of voltage ±2.5 kV with different lengths of lines, as shown in the grid diagram. The DC/DC boost converter is designed to build step-up converters that are located in buses 4 and 12. These converters are used to connect the photovoltaics (PVs) to the grid. The distribution generator and the AC grid are connected to the grid through VSCs. DC loads are connected to the grid through DC/DC buck converters to reduce the voltage and drive the loads that are connected to buses 3, 7, and 11. According to the expected power flow, the circuit breakers are required to be bidirectional in some zones as explained in the protection scheme of Figure 12.
In the first event, a pole-to-pole fault will apply at bus 11, where the fault position is represented by point F A as shown in Figure 12. Bus 11 feeds a load of 4MW load through a DC/DC converter. The breaker CB11 will cut off the bus current and disconnect the converter and the load. Figure 13a shows that the current of bus 11 reaches zero when the fault occurs by the action of the unidirectional breaker, which is CB11. The load of the 4 MW is disconnected, and the current in the line between bus 10 and bus 11 is zero. The current of the line that is connected between bus 5 and bus 10 is changed and reduced from 700.85A to 63A, as shown in Figure 13c. the circuit breakers are required to be bidirectional in some zones as explained in the protection scheme of Figure 12.
In the first event, a pole-to-pole fault will apply at bus 11, where the fault position is represented by point FA as shown in Figure 12. Bus 11 feeds a load of 4MW load through a DC/DC converter. The breaker CB11 will cut off the bus current and disconnect the converter and the load. Figure 13a shows that the current of bus 11 reaches zero when the fault occurs by the action of the unidirectional breaker, which is CB11. The load of the 4 MW is disconnected, and the current in the line between bus 10 and bus 11 is zero. The current of the line that is connected between bus 5 and bus 10 is changed and reduced from 700.85A to 63A, as shown in Figure 13c. The same current of the line between bus 5 and bus 10 will pass through the line of bus 10-8. The direction of that current will be opposite its direction before the occurrence of the fault and disconnect 4MW load; Figure 13c shows that current. At that point, the circuit breakers CB17 and CB18 placed on the line between bus 8 and bus 10 should be bidirectional breakers to allow the power to flow from bus 10 to bus 8. Figure 13b shows the line current between bus 8 and bus 10 is changed from its original positive value to the The same current of the line between bus 5 and bus 10 will pass through the line of bus 10-8. The direction of that current will be opposite its direction before the occurrence of the fault and disconnect 4MW load; Figure 13c shows that current. At that point, the circuit breakers CB17 and CB18 placed on the line between bus 8 and bus 10 should be bi-directional breakers to allow the power to flow from bus 10 to bus 8. Figure 13b shows the line current between bus 8 and bus 10 is changed from its original positive value to the negative. Based on that, the Y-source breakers placed on this line allow the current flow in the opposite direction.
In order to test the bi-directional Y-source breaker, a fault will apply at the middle of the line between bus 8 and 10 as represented by point F B as shown in Figure 12. The fault will apply after the current of the line flows in the opposite direction. CBs 17 and 18 will respond and take action to reduce the line current to zero immediately when the fault occurs. Figure 14a,b illustrate the current waveforms of the lines between bus 8-10 and bus 5-10, respectively. The current of CBs 10 and 15 goes to zero also after clearing the faults because the CB11 is still open and load 3 is disconnected, so the power through the line between bus 5 and 10 flows only through the line between bus 10-8.
Inventions 2021, 6, 18 18 of 20 respond and take action to reduce the line current to zero immediately when the fault occurs. Figure 14a and Figure 14b illustrate the current waveforms of the lines between bus 8-10 and bus 5-10, respectively. The current of CBs 10 and 15 goes to zero also after clearing the faults because the CB11 is still open and load 3 is disconnected, so the power through the line between bus 5 and 10 flows only through the line between bus 10-8.

Conclusions
The Y-source impedance network is used to build a bi-directional solid-state circuit breaker for MVDC systems. The breaker frequency response demonstrates that the reflected current to the source through the SCRs is higher than their forward current. This current forces the SCRs to commutate OFF during the fault conditions. The coupling levels among the inductors of the breaker affect the value of the reflected current. The proposed breaker has the ability to interrupt the fault current if the magnetic coupling level is higher than a specific level, which is called a null condition. The turns−ratio affects this value, where an increase in the turns-ratio causes decreasing in the required level of the coupling. The fault conductance must have a minimum value and slope rate in order to make the Y-source breaker products an adequate reflected current to drop the forward SCRs current to zero. The simulation results verify the operation of the breaker with a fault condition, where the minimum value of the source current is affected by the level of the coupling. The condition of a load change is simulated, and the results verify that the breaker allows the load current to change without interrupting the source current. The Ysource breaker is developed to clear the fault current during the different expected types of fault in the MVDC systems. The simulation results approved the ability of the developed breaker to reduce the positive and negative pole currents to zero during three types of occurring faults. The proposed protection scheme for a 12-bus, ±2.5 kV microgrid is tested by applying a fault at two different locations in the grid. The Y-source proposed breaker is connected to the lines that may conduct the power in both directions.

Conclusions
The Y-source impedance network is used to build a bi-directional solid-state circuit breaker for MVDC systems. The breaker frequency response demonstrates that the reflected current to the source through the SCRs is higher than their forward current. This current forces the SCRs to commutate OFF during the fault conditions. The coupling levels among the inductors of the breaker affect the value of the reflected current. The proposed breaker has the ability to interrupt the fault current if the magnetic coupling level is higher than a specific level, which is called a null condition. The turns−ratio affects this value, where an increase in the turns-ratio causes decreasing in the required level of the coupling. The fault conductance must have a minimum value and slope rate in order to make the Y-source breaker products an adequate reflected current to drop the forward SCRs current to zero. The simulation results verify the operation of the breaker with a fault condition, where the minimum value of the source current is affected by the level of the coupling. The condition of a load change is simulated, and the results verify that the breaker allows the load current to change without interrupting the source current. The Y-source breaker is developed to clear the fault current during the different expected types of fault in the MVDC systems. The simulation results approved the ability of the developed breaker to reduce the positive and negative pole currents to zero during three types of occurring faults. The proposed protection scheme for a 12-bus, ±2.5 kV micro-grid is tested by applying a fault at two different locations in the grid. The Y-source proposed breaker is connected to the lines that may conduct the power in both directions. During the first fault event, the breaker located nearby the fault point interrupts the current and isolates the faulty zone. That causes passing an opposite current in an adjacent line. Based on the obtained results, the Y-source breaker allowed this current to pass in the opposite direction. The second fault event is applied at the line where the Y-source breakers are placed. In this case, the results show that the Y-source breaker clears the fault by reducing the current naturally to zero. The results verify the ability of the breaker to allow the normal current to pass and to interrupt the abnormal current in both directions.