A High-Gain Reﬂex-Based Bidirectional DC Charger with Efﬁcient Energy Recycling for Low-Voltage Battery Charging-Discharging Power Control

: This study proposes a high-gain reflex-charging-based bidirectional DC charger (RC-BDC) to enhance the battery charging efficiency of light electric vehicles (LEV) in a DC-microgrid. The proposed charger topology consists of an unregulated level converter (ULC) and a two-phase interleaved buck-boost charge-pump converter (IBCPC), which together provide low ripple and high voltage conversion ratio. As the high-gain RC-BDC charges, the LEV’s battery with reflex charging currents, high battery charging efficiency, and prolonged battery life cycles are achieved. This is possible due to the recovering of negative pulse energy of reflex charging currents to reduce charge dissipations within LEV’s batteries. Derivations of the operating principles of the high-gain RC-BDC, analyses of its topology, and the closed-loop control designs were presented. Simulations and experiments were implemented with battery voltage of 48 V and DC-bus voltage of 400 V for a 500 W prototype. The results verify the feasibility of the proposed concept and were compared with the typical constant-current/constant-voltage (CC/CV) charger. The comparison shows that the proposed high gain RC-BDC improves battery charging speed and reduces the battery thermal deterioration effect by about 12.7% and 25%, respectively.


Introduction
The advent of new technologies have cultivated new economic activities that demand more electricity, and, for this reason, maintaining and supplying high power quality is more important than ever before [1][2][3][4][5]. At the same time, new requirements for environmental conservation and reducing carbon footprints, which contradict the need for more power, has also been initiated in many countries. As a result, generators are sandwiched between their roles to produce more power and reduce greenhouse gas emissions. An increasingly popular solution is to implement the DC-microgrid which has widely been accepted to consist of distributed clean energies, including wind and solar, battery energy storage (BES) systems that help to satisfy electricity demand and offset shortages from renewables and electric vehicles (EV) with bidirectional power flow feature-vehicle-to-grid (V2G) and grid-to-vehicle (G2V) [5][6][7][8]. Various studies have shown that the operation of the DC-microgrid lead to the overall reduction of carbon emissions without sacrificing power demands [1][2][3][4]. The bidirectional power flow capability of EVs is one of the most critical aspects of the DC-microgrid. It enables the complete use of the internal battery stack of the EVs and employ them as mobile energy storage units. EVs are normally charged during off-peak hours when they are also least used, and are discharged into the grid at higher on-peak rates.
Moving forward, the size of the conventional EVs has shrunken typically to between a car and motorcycle-known as the light electric vehicle (LEV). The LEV's battery voltage requirements depend on the motor power but are normally rated at 24 V, 48 V, 72 V, and 96 V. On the other hand, the DC-bus is rated rather high at around 380 ± 20 V [9][10][11][12]. Hence, in order to facilitate the operations of LEVs, a high-gain bidirectional converter, serving as the power electronic interface between LEVs and the DC-microgrid, is needed. Conventionally, this has been achieved using the constant-current/voltage (CC/CV) charging process [12,13]. But, this process is latent with the problems of incomplete reaction, excessive thermal rise, and short battery life cycle due to the persistent charging cycle. An alternative is to use the Reflex-charging control strategy [14][15][16][17][18]. This relatively new method employs high level currents to speed up charging and both the negative pulse period (NPP) and the short resting period (RP) in each charging cycle. The combination of both the NPP and RP are able to reduce the internal resistance of the battery, suppress bubble formations and pressure inside the cell, and remove impurities on battery electrodes. Consequently, unwanted chemical reactions are reduced and the battery charging process are optimized.
It has been identified that the battery energy absorption rate during NPP is the main factor that influences the battery charging efficiency; the higher the rate, the better it is. A non-dissipative passive circuit has been proposed to achieve this objective [19], but the wastage of energy and increase in design cost outweighs its benefits.
In this paper, a reflex-charging-based bidirectional DC charger (RC-BDC) is proposed and its high-gain bidirectional converter topology is adopted from [20]. Despite such combination was briefly presented in [21], factors such as efficient energy recycling characteristics and system behaviors were never thoroughly analyzed. Moreover, the main difference of our proposed RC-BDC is the inclusion of a closed-loop control design procedure. This is the first time that such combination is considered. When the proposed RC-BDC is connected to the DC-microgrid, the DC-bus can charge the relatively low voltage battery using the reflex-charging control strategy. In addition, the battery energy is returned to the DC-bus during NPP. Based on these, a 500-W high-gain RC-BDC prototype is built and tested using reflex-charging and constant-current discharging controls. The test results verify the feasibility of the proposed concept.

Operation Principles of the Proposed High-Gain RC-BDC
The converter topology of the proposed RC-BDC is shown in Figure 1a [20,21], where V bus and V bat are the DC-bus voltage and battery voltage on the high and low sides, respectively; i L1 and i L2 are the phase currents of the interleaved charge-pump converter (IBCPC), and i Lt is the sum of i L1 and i L2 ; C B is the charge-pump capacitance; C H and C L denote the capacitance on the high and low sides, respectively; Q 1 -Q 4 and S 1 -S 4 are the power switches of the IBCPC and the unregulated level converter (ULC), respectively; D denotes the active switch duty cycle of the charging and discharging states; L a and L b are the high-frequency filtering inductance; and, C M1 , C M2 are DC-link capacitors. The ULC charges and discharges the battery with a conversion ratio of 2:1 (voltage-dividing) and 1:2 (voltage doubling). The IBCPC is used for bidirectional power flow control at high voltage conversion ratios (i.e., high-voltage 380 ± 20 V; low-voltage: 44-56 V).
The battery current waveforms of the proposed RC-BDC are shown in Figures 1b and 2. Figure 1b shows that the reflex-charging control strategy is used to charge the battery, where battery is rapidly charged during positive pulse periods (PPP) and are followed by NPPs when battery energy is returned to the DC-bus. The purpose of adding a negative pulse after the PPP is to reduce the generation of bubbles and excessive pressure inside the battery, as well as to suppress the influence of impurities attached on the electrode plates during the chemical reaction. Finishing both the PPP and NPP is considered to be a complete cycle. A sufficient resting period (RP) is given after each cycle and this is the time when electrolytic solution is diffused and neutralized. Due to this, the conversion efficiency from electrical to chemical energy is enhanced and battery temperature rise is limited, further increasing the battery lifetime. The proposed RC-BDC is also able to return battery energy to the DC-microgrid by reversing the power flow in a constant-current manner; the discharging capability of the converter.
Energies 2018, 11, x FOR PEER REVIEW 3 of 13 efficiency from electrical to chemical energy is enhanced and battery temperature rise is limited, further increasing the battery lifetime. The proposed RC-BDC is also able to return battery energy to the DC-microgrid by reversing the power flow in a constant-current manner; the discharging capability of the converter. The details of the PPP is given below: Mode 1 (t0 < t ≤ t1): Q1 and Q3 are turned on, whereas Q2 and Q4 are turned turn off; S1 and S3 are turned on, whereas S2 and S4 are turned off. The voltage across inductor L1 is negative, and iL1 linearly decreases. The voltage across inductor L2 can be obtained by subtracting the charge-pump voltage VCB and VM from the high-side voltage Vbus, and its slope is expressed as (Vbus/2 − VM)/L2. Mode 2 (t1 < t ≤ t2): Q3 and Q4 are turned on, whereas Q1 and Q2 are turned off; S1 and S3 are turned on, whereas S2 and S4 are turned off. The voltage across inductors L1 and L2 are negative, and thus, both iL1 and iL2 linearly decrease. Their current slopes are expressed as (−VM)/L1 and (−VM)/L2, respectively.
Mode 3 (t2 < t ≤ t3]: Q2 and Q4 are turned on, whereas Q1 and Q3 are turned off; S1 and S3 are turned on, whereas S2 and S4 are turned off. The voltage across inductor L1 is equal to the difference between the charge-pump voltage VCB and VM, and its slope is (Vbus/2 − VM)/L1. Mode 4 (t3 < t ≤ t4): The state of the converter is the same as that of Mode 2.
During the PPP, the battery current ibat can be expressed as (1) The details of the PPP is given below: Mode 1 (t 0 < t ≤ t 1 ): Q 1 and Q 3 are turned on, whereas Q 2 and Q 4 are turned turn off; S 1 and S 3 are turned on, whereas S 2 and S 4 are turned off. The voltage across inductor L 1 is negative, and i L1 linearly decreases. The voltage across inductor L 2 can be obtained by subtracting the charge-pump voltage V CB and V M from the high-side voltage V bus , and its slope is expressed as (V bus /2 − V M )/L 2 . Mode 2 (t 1 < t ≤ t 2 ): Q 3 and Q 4 are turned on, whereas Q 1 and Q 2 are turned off; S 1 and S 3 are turned on, whereas S 2 and S 4 are turned off. The voltage across inductors L 1 and L 2 are negative, and thus, both i L1 and i L2 linearly decrease. Their current slopes are expressed as (−V M )/L 1 and (−V M )/L 2 , respectively. Mode 3 (t 2 < t ≤ t 3 ]: Q 2 and Q 4 are turned on, whereas Q 1 and Q 3 are turned off; S 1 and S 3 are turned on, whereas S 2 and S 4 are turned off. The voltage across inductor L 1 is equal to the difference between the charge-pump voltage V CB and V M , and its slope is (V bus /2 − V M )/L 1 .

Mode 4 (t 3 < t ≤ t 4 ):
The state of the converter is the same as that of Mode 2.
During the PPP, the battery current i bat can be expressed as There is a positive voltage across the converter inductor L2. The voltage across inductor L1 is equal to the difference between the charge pump voltage VCB and VM, and its slope is For the discharging state, when the DC-bus voltage of the grid is lower than a preset value, the charger will automatically switch to the discharging state.
During this time, the converter works as a discharger with voltage-boosting function. This implies that the battery at the low-voltage side feeds the DC-bus with constant-current. There is a positive voltage across the converter inductor L 2 . The voltage across inductor L 1 is equal to the difference between the charge pump voltage V CB and V M , and its slope is For the discharging state, when the DC-bus voltage of the grid is lower than a preset value, the charger will automatically switch to the discharging state.
During this time, the converter works as a discharger with voltage-boosting function. This implies that the battery at the low-voltage side feeds the DC-bus with constant-current.

Controller Descriptions of the Proposed High-Gain RC-BDC
PSIM© simulation software (Powersim Inc., Rockville, MD, USA) was used to design the closed-loop controller with the following assumptions: (1) power switches and diodes are ideal; (2) equivalent series resistances (ESRs) of all the inductors and capacitors of the converter have precise dynamic model; and, (3) the converter works under continuous conduction mode (CCM) and ESRs (r L1 = r L2 = 180 mΩ; r CH = r CL = r CB = 60 mΩ). The circuit parameters for 500 W rating are L 1 = L 2 = 800 µH, C L = C H = 100 µF, C B = 10 µF. Figure 3 illustrates the developed control system for the high-gain RC-BDC. The figure shows that the output voltage (V bus ), battery current (i bat ) and battery voltage (V bat ) are monitored to determine the converter operating mode.
The middle voltage controller produces the total inductor reference current (i Lt, ref ) for the entire system. The equal current sharing between the two interleaved phases are also obtained here. During the system startup, soft start (V conss ) is used to avoid capacitor charge surge that can produce the current that damage the converter components.

Controller Descriptions of the Proposed High-Gain RC-BDC
PSIM© simulation software (Powersim Inc., Rockville, MD, USA) was used to design the closedloop controller with the following assumptions: (1) power switches and diodes are ideal; (2) equivalent series resistances (ESRs) of all the inductors and capacitors of the converter have precise dynamic model; and, (3) the converter works under continuous conduction mode (CCM) and ESRs (rL1 = rL2 = 180 mΩ; rCH = rCL = rCB = 60 mΩ). The circuit parameters for 500 W rating are L1 = L2 = 800 μH, CL = CH = 100 μF, CB = 10 μF. Figure 3 illustrates the developed control system for the high-gain RC-BDC. The figure shows that the output voltage (Vbus), battery current (ibat) and battery voltage (Vbat) are monitored to determine the converter operating mode.
The middle voltage controller produces the total inductor reference current (iLt, ref) for the entire system. The equal current sharing between the two interleaved phases are also obtained here. During the system startup, soft start (Vconss) is used to avoid capacitor charge surge that can produce the current that damage the converter components.  The Block diagram of the closed-loop control scheme is shown in Figure 4. In the inner current control loop, F M is the constant gain of the PWM generator; G iLtd is the transfer function from the duty ratio to the total inductor current (i Lt ); C i indicates the transfer function of current controllers; and, H i is the sensing gain of the current sensor. In the outer voltage control loop, G vd is the transfer function from the duty ratio to the middle-link voltage (V M ); C v indicates the transfer function of output voltage controller; and, H v indicates the sensing gain of the voltage sensor.

DC-Bus
From Figure 4, the gains from current and voltage loops are described by Equations (2) and (3), respectively.
Energies 2018, 11, x FOR PEER REVIEW 6 of 13 The Block diagram of the closed-loop control scheme is shown in Figure 4. In the inner current control loop, FM is the constant gain of the PWM generator; GiLtd is the transfer function from the duty ratio to the total inductor current (iLt); Ci indicates the transfer function of current controllers; and, Hi is the sensing gain of the current sensor. In the outer voltage control loop, Gvd is the transfer function from the duty ratio to the middle-link voltage (VM); Cv indicates the transfer function of output voltage controller; and, Hv indicates the sensing gain of the voltage sensor.
From Figure 4, the gains from current and voltage loops are described by Equations (2) and (3), respectively.
where, FM = 1/100, Hi = Hv = 1. The small-signal transfer from the duty ratio to inductor current GiLtd is given by Equation (4) and the duty ratio to middle-link voltage GvMd is given by Equation (5).
The corresponding current/voltage controllers of the proposed high-gain RC-BDC are selected, as follows:  The small-signal transfer from the duty ratio to inductor current G iLtd is given by Equation (4) and the duty ratio to middle-link voltage G vMd is given by Equation (5).
where, F M = 1/100, The corresponding current/voltage controllers of the proposed high-gain RC-BDC are selected, as follows:   Figure 6 shows the system flow chart. After starting, the system is initialized in order to determine whether the voltage on the DC-microgrid side is lower than the pre-set value. If the preset value is higher, the system enters the discharging state where the battery feeds the DC-microgrid. Otherwise, the system will enter the charging state where the battery voltage is compared to the 52 V. If the battery voltage is lower than 52 V, then the reflex-charging operation is executed. Then, staying in the PPP, NPP, and RP is determined using the counter time. Constant-voltage charging is executed when the battery voltage reaches 52 V.

System Design and Implementations
In order to validate the proposed concept, a 500-W bidirectional DC charger system, as shown in Figure 7, is constructed as the test platform. At the low-voltage side of the platform, the voltage is set to 48 V by using four 12 V/22 Ah lead-acid batteries (REC22-12I, Taiwan Yuasa Battery Co., Ltd., Taiwan) connected in series. Lead-acid batteries were chosen due to its low cost and wide usage. For example, valve-regulated lead-acid batteries (VRLAs), such as absorbent glass mat (AGM) batteries and gel batteries, are widely used in micro hybrid electric [22][23][24].
At the high-voltage side, power supply and electronic loads are connected in parallel to simulate the actual voltage bus and its corresponding electrical units in a DC-microgrid. The parameters of the constructed converter are given in Table 1. All of the battery charging/discharging tests were recorded using the GL900 recorder (Graphtec Corporation, Tokyo, Japan).  Figure 6 shows the system flow chart. After starting, the system is initialized in order to determine whether the voltage on the DC-microgrid side is lower than the pre-set value. If the pre-set value is higher, the system enters the discharging state where the battery feeds the DC-microgrid. Otherwise, the system will enter the charging state where the battery voltage is compared to the 52 V. If the battery voltage is lower than 52 V, then the reflex-charging operation is executed. Then, staying in the PPP, NPP, and RP is determined using the counter time. Constant-voltage charging is executed when the battery voltage reaches 52 V.

System Design and Implementations
In order to validate the proposed concept, a 500-W bidirectional DC charger system, as shown in Figure 7, is constructed as the test platform. At the low-voltage side of the platform, the voltage is set to 48 V by using four 12 V/22 Ah lead-acid batteries (REC22-12I, Taiwan Yuasa Battery Co., Ltd., Taiwan) connected in series. Lead-acid batteries were chosen due to its low cost and wide usage. For example, valve-regulated lead-acid batteries (VRLAs), such as absorbent glass mat (AGM) batteries and gel batteries, are widely used in micro hybrid electric [22][23][24].
At the high-voltage side, power supply and electronic loads are connected in parallel to simulate the actual voltage bus and its corresponding electrical units in a DC-microgrid. The parameters of the constructed converter are given in Table 1. All of the battery charging/discharging tests were recorded using the GL900 recorder (Graphtec Corporation, Tokyo, Japan).       Figure 8 illustrates the transient current control waveform of the proposed bidirectional converter. The figure shows that the battery charging current i bat rises from 5 A to 10 A and the total inductor current i Lt rises from 2.5 A to 5 A (100% load). Figure 9 shows the converter waveform in the charging state. The positive charging current i bat = 10 A, whereas the negative discharging current i bat = −10 A. During PPP, the total inductor current i Lt is 5 A, and it becomes −5 A during NPP. The reflex charging frequency is 5-Hz and the corresponding duty cycles for PPP and NPP are about 70% and 15%, respectively. Notably, a lot of methods [25][26][27] can be referred to adjust the reflex charging pattern (such as duty or frequency, etc.) for improving the charging efficiencies in future work.  Figure 8 illustrates the transient current control waveform of the proposed bidirectional converter. The figure shows that the battery charging current ibat rises from 5 A to 10 A and the total inductor current iLt rises from 2.5 A to 5 A (100% load). Figure 9 shows the converter waveform in the charging state. The positive charging current ibat = 10 A, whereas the negative discharging current ibat = −10 A. During PPP, the total inductor current iLt is 5 A, and it becomes −5 A during NPP. The reflex charging frequency is 5-Hz and the corresponding duty cycles for PPP and NPP are about 70% and 15%, respectively. Notably, a lot of methods [25][26][27] can be referred to adjust the reflex charging pattern (such as duty or frequency, etc.) for improving the charging efficiencies in future work.    Figure 8 illustrates the transient current control waveform of the proposed bidirectional converter. The figure shows that the battery charging current ibat rises from 5 A to 10 A and the total inductor current iLt rises from 2.5 A to 5 A (100% load). Figure 9 shows the converter waveform in the charging state. The positive charging current ibat = 10 A, whereas the negative discharging current ibat = −10 A. During PPP, the total inductor current iLt is 5 A, and it becomes −5 A during NPP. The reflex charging frequency is 5-Hz and the corresponding duty cycles for PPP and NPP are about 70% and 15%, respectively. Notably, a lot of methods [25][26][27] can be referred to adjust the reflex charging pattern (such as duty or frequency, etc.) for improving the charging efficiencies in future work.    Figure 10 shows the discharging process of the converter, it can be seen that the battery discharging current i bat is −12 A and the total inductor current i Lt is −6 A. Figure 11 shows the charging curve of lead-acid batteries, which shows the reflex charging and constant-voltage charging stages. Reflex charging begins at 46 V and constant-voltage charging begins at 52 V. The charging process ends when the battery current drops to 2 A (about 0.1 C-rate). By recording the charging voltage and current of the battery every minute using the recorder, it is determined that the full charging time is 111 min. Figure 10 shows the discharging process of the converter, it can be seen that the battery discharging current ibat is −12 A and the total inductor current iLt is −6 A. Figure 11 shows the charging curve of lead-acid batteries, which shows the reflex charging and constant-voltage charging stages. Reflex charging begins at 46 V and constant-voltage charging begins at 52 V. The charging process ends when the battery current drops to 2 A (about 0.1 C-rate). By recording the charging voltage and current of the battery every minute using the recorder, it is determined that the full charging time is 111 min.  In order to demonstrate the advantages of the proposed RC-BDC, its performance was compared with the conventional BDC with the CC/CV charging profile. Figure 12a,b show the battery charging current ibat and the increased battery temperature curves with respect to the charging time. From Figure 12a, it is clear that the charging time of the proposed RC-BDC and the typical BDC with CC/CV charging profile are about 1.85 h and 2.12 h, respectively. The charging speed of the proposed RC-BDC has been increased by about 12.7% as compared to the typical BDC. According to Figure 12b, the maximum increased in the battery temperature of the proposed RC-BDC and the typical BDC are 5.6 °C and 7 °C, respectively. The results also demonstrated that the maximum battery temperature of the proposed RC-BDC can be reduced by about 25%. This means that the thermal deterioration effect is improved by about 25% with the proposed RC-BDC. Figure 13 shows the measured conversion efficiency of the proposed high-gain RC-BDC. The result indicates that the maximum efficiency points of charging and discharging states are 95.1% and 94.2%, respectively.  Figure 10 shows the discharging process of the converter, it can be seen that the battery discharging current ibat is −12 A and the total inductor current iLt is −6 A. Figure 11 shows the charging curve of lead-acid batteries, which shows the reflex charging and constant-voltage charging stages. Reflex charging begins at 46 V and constant-voltage charging begins at 52 V. The charging process ends when the battery current drops to 2 A (about 0.1 C-rate). By recording the charging voltage and current of the battery every minute using the recorder, it is determined that the full charging time is 111 min.   0  5  10  15  20  25  30  35  40  45  50  55  60  65  70  75  80  85  90  95  100  105  In order to demonstrate the advantages of the proposed RC-BDC, its performance was compared with the conventional BDC with the CC/CV charging profile. Figure 12a,b show the battery charging current ibat and the increased battery temperature curves with respect to the charging time. From Figure 12a, it is clear that the charging time of the proposed RC-BDC and the typical BDC with CC/CV charging profile are about 1.85 h and 2.12 h, respectively. The charging speed of the proposed RC-BDC has been increased by about 12.7% as compared to the typical BDC. According to Figure 12b, the maximum increased in the battery temperature of the proposed RC-BDC and the typical BDC are 5.6 °C and 7 °C, respectively. The results also demonstrated that the maximum battery temperature of the proposed RC-BDC can be reduced by about 25%. This means that the thermal deterioration effect is improved by about 25% with the proposed RC-BDC. Figure 13 shows the measured conversion efficiency of the proposed high-gain RC-BDC. The result indicates that the maximum efficiency points of charging and discharging states are 95.1% and 94.2%, respectively. In order to demonstrate the advantages of the proposed RC-BDC, its performance was compared with the conventional BDC with the CC/CV charging profile. Figure 12a,b show the battery charging current i bat and the increased battery temperature curves with respect to the charging time. From Figure 12a, it is clear that the charging time of the proposed RC-BDC and the typical BDC with CC/CV charging profile are about 1.85 h and 2.12 h, respectively. The charging speed of the proposed RC-BDC has been increased by about 12.7% as compared to the typical BDC. According to Figure 12b, the maximum increased in the battery temperature of the proposed RC-BDC and the typical BDC are 5.6 • C and 7 • C, respectively. The results also demonstrated that the maximum battery temperature of the proposed RC-BDC can be reduced by about 25%. This means that the thermal deterioration effect is improved by about 25% with the proposed RC-BDC. Figure 13 shows the measured conversion efficiency of the proposed high-gain RC-BDC. The result indicates that the maximum efficiency points of charging and discharging states are 95.1% and 94.2%, respectively.

Conclusions
In this study, a high-gain RC-BDC for connecting LEVs to DC-microgrid is proposed. Based on the proposed controller, the high-gain bidirectional converter in [17] was able to achieve both reflex charging and energy recovery. A 500 W test platform consists of a 48-V battery connected to a 400-V DC-bus voltage was built. The experimental results verify the feasibility of the developed concept. In comparison with a typical CC/CV charging profile, the proposed high-gain RC-BDC battery charging speed and the battery thermal deterioration effect improve by about 12.7%, and 25%, respectively. In regards to the conversion efficiency, the experimental results show that the highest efficiencies that were achieved for charging and discharging states are 95.1% and 94.2%, respectively. Finally, it is worth mentioning that the proposed high-gain RC-BDC can be extended to the galvanic isolated configuration by using two high-frequency transformers as shown in Figure 14 for safety insulation requirement and higher voltage conversion ratio applications.

Conclusions
In this study, a high-gain RC-BDC for connecting LEVs to DC-microgrid is proposed. Based on the proposed controller, the high-gain bidirectional converter in [17] was able to achieve both reflex charging and energy recovery. A 500 W test platform consists of a 48-V battery connected to a 400-V DC-bus voltage was built. The experimental results verify the feasibility of the developed concept. In comparison with a typical CC/CV charging profile, the proposed high-gain RC-BDC battery charging speed and the battery thermal deterioration effect improve by about 12.7%, and 25%, respectively. In regards to the conversion efficiency, the experimental results show that the highest efficiencies that were achieved for charging and discharging states are 95.1% and 94.2%, respectively. Finally, it is worth mentioning that the proposed high-gain RC-BDC can be extended to the galvanic isolated configuration by using two high-frequency transformers as shown in Figure 14 for safety insulation requirement and higher voltage conversion ratio applications.