Isolated Dc-dc Converter for Bidirectional Power Flow Controlling with Soft-switching Feature and High Step-up/down Voltage Conversion

In this paper, a novel isolated bidirectional DC-DC converter is proposed, which is able to accomplish high step-up/down voltage conversion. Therefore, it is suitable for hybrid electric vehicle, fuel cell vehicle, energy backup system, and grid-system applications. The proposed converter incorporates a coupled inductor to behave forward-and-flyback energy conversion for high voltage ratio and provide galvanic isolation. The energy stored in the leakage inductor of the coupled inductor can be recycled without the use of additional snubber mechanism or clamped circuit. No matter in step-up or step-down mode, all power switches can operate with soft switching. Moreover, there is a inherit feature that metal–oxide–semiconductor field-effect transistors (MOSFETs) with smaller on-state resistance can be adopted because of lower voltage endurance at primary side. Operation principle, voltage ratio derivation, and inductor design are thoroughly described in this paper. In addition, a 1-kW prototype is implemented to validate the feasibility and correctness of the converter. Experimental results indicate that the peak efficiencies in step-up and step-down modes can be up to 95.4% and 93.6%, respectively.


Introduction
In order to reduce carbon emission and mitigate global warming, green energies, such as photovoltaic (PV) panel, fuel cells, and wind turbine, attract a great deal of interest and have a high rate of growth in installed capacity.A complete configuration of distributed generation system (DGS), as shown in Figure 1, not only includes green-energy sources but also combines an energy storage system for power conditioning to use electricity optimally.For grid connection, a DC-bus voltage up to around 400 V is required, which is much higher than a battery voltage.Therefore, a bidirectional DC-DC converter (BDC) with high voltage ratio to charge/discharge battery is mandatory in the DGS.
Conventional high step-up converters used in PV panel and fuel cells can boost a low voltage to a higher level to serve as an interface between the distributed generator and the DC bus [1][2][3].Nevertheless, they only control power flow in unique direction.Bidirectional power flow control is necessary for battery system.A solution is to adopt two high-voltage-ratio converters.One is high-step-up converter for battery discharging and the other is high-step-down converter for charging, but this approach increases cost significantly.Therefore, BDC is the current design trend, which is Increasing switching frequency of a power converter can reduce the size of magnetic and capacitive elements and thus has the benefit of achieving high power density.However, the higher switch frequency is, the lower conversion efficiency will be.In order to eliminate switching loss, employing resonant unit with auxiliary switches for soft-switching achievement is a common approach [9][10][11].In literature [12], the authors develop a dual-bridge converter to fulfill bidirectional power flow controlling along with zero voltage switching (ZVS) at main switch, in which even resonant tank is utilized but the use of additional auxiliary switch can be avoided.Nevertheless, a great many switches are needed and its voltage ratio is incapable of high step-up/down applications.
The open H-bridge converter can function as a non-isolated BDC [13].Even though this converter can achieve ZVS feature and possesses simple structure, its voltage gain is less than 2 at the duty ratio of 0.5.For higher voltage ratio, heavy switch duty cycle is the only solution to this problem, but this approach will degrade converter efficiency.To avoid excessive duty cycle operation, switched capacitor technology will be an alternative for high voltage-gain conversion [14].However, current spike that occurs at the switching transients confines its applications and accompanies electromagnetic interference (EMI) problem, especially in high power rating.Incorporating switched capacitor along with coupled inductor into a power converter is a key to suppressing inrush current and obtaining enough voltage conversion ratio [15][16][17][18].Since the coupled inductor can also feature electrical isolation, a BDC including coupled inductor is the major development.However, the energy dissipation caused from leakage inductor will degrade converter efficiency [19,20].That is, clamped circuit or snubber mechanism for leakage energy harvesting is imperative.Isolated BDCs based on H-bridge topology have been proposed in the literature [21,22], which can achieve ZVS feature inherently, avoiding additional device usage.Nevertheless, low voltage ratio and more power switches required become their disadvantages.In [23], another isolated BDC which accomplishes leakage-energy recycling and can obtain high voltage-ratio conversion is presented.Nevertheless, some limitations still exist, such as ZVS only occurs at high-voltage side and duty ratio has to be greater than 0.5.
In this paper, a novel BDC is proposed, which has the advantages of galvanic isolation, high voltage conversion ratio, soft-switching feature at all power switches, high efficiency, being suitable for high power applications, and low component count.Figure 2 shows its configuration of the power stage.The symbols in the circuit are summarized in the followings.VL and VH denote the terminal voltages at low-voltage side and high-voltage side, respectively; L1 is a choke inductor; S1, S2, S3, S4, S5, and S6 are active switches, while DS1-DS6 and CS1-CS6 express their related anti-parallel body diodes and parasitic capacitors; the magnetically-coupled device has winding N1, magnetizing inductor Lm1, and leakage inductor Lk1 at low-voltage side, meanwhile N2, Lm2, and Lk2, respectively, at Increasing switching frequency of a power converter can reduce the size of magnetic and capacitive elements and thus has the benefit of achieving high power density.However, the higher switch frequency is, the lower conversion efficiency will be.In order to eliminate switching loss, employing resonant unit with auxiliary switches for soft-switching achievement is a common approach [9][10][11].In literature [12], the authors develop a dual-bridge converter to fulfill bidirectional power flow controlling along with zero voltage switching (ZVS) at main switch, in which even resonant tank is utilized but the use of additional auxiliary switch can be avoided.Nevertheless, a great many switches are needed and its voltage ratio is incapable of high step-up/down applications.
The open H-bridge converter can function as a non-isolated BDC [13].Even though this converter can achieve ZVS feature and possesses simple structure, its voltage gain is less than 2 at the duty ratio of 0.5.For higher voltage ratio, heavy switch duty cycle is the only solution to this problem, but this approach will degrade converter efficiency.To avoid excessive duty cycle operation, switched capacitor technology will be an alternative for high voltage-gain conversion [14].However, current spike that occurs at the switching transients confines its applications and accompanies electromagnetic interference (EMI) problem, especially in high power rating.Incorporating switched capacitor along with coupled inductor into a power converter is a key to suppressing inrush current and obtaining enough voltage conversion ratio [15][16][17][18].Since the coupled inductor can also feature electrical isolation, a BDC including coupled inductor is the major development.However, the energy dissipation caused from leakage inductor will degrade converter efficiency [19,20].That is, clamped circuit or snubber mechanism for leakage energy harvesting is imperative.Isolated BDCs based on H-bridge topology have been proposed in the literature [21,22], which can achieve ZVS feature inherently, avoiding additional device usage.Nevertheless, low voltage ratio and more power switches required become their disadvantages.In [23], another isolated BDC which accomplishes leakage-energy recycling and can obtain high voltage-ratio conversion is presented.Nevertheless, some limitations still exist, such as ZVS only occurs at high-voltage side and duty ratio has to be greater than 0.5.
In this paper, a novel BDC is proposed, which has the advantages of galvanic isolation, high voltage conversion ratio, soft-switching feature at all power switches, high efficiency, being suitable for high power applications, and low component count.Figure 2 shows its configuration of the power stage.The symbols in the circuit are summarized in the followings.V L and V H denote the terminal voltages at low-voltage side and high-voltage side, respectively; L 1 is a choke inductor; S 1 , S 2 , S 3 , S 4 , S 5 , and S 6 are active switches, while D S1 -D S6 and C S1 -C S6 express their related anti-parallel body diodes and parasitic capacitors; the magnetically-coupled device has winding N 1 , magnetizing inductor L m1 , Energies 2017, 10, 296 3 of 23 and leakage inductor L k1 at low-voltage side, meanwhile N 2 , L m2 , and L k2 , respectively, at high-voltage side; C b1 and C b2 are low-voltage capacitors; and C o1 and C o2 are high-voltage capacitors.The conversion efficiency of proposed BDC can be improved because of the following reasons: (1) No matter in buck or boost mode, the energy stored in leakage inductors, L k1 and L k2 , can be recycled without any snubber mechanism or clamped circuit.(2) All active semiconductor components can be switched with ZVS or zero current switching (ZCS) to eliminate switching losses.(3) Switches S 1 -S 4 endure a low voltage stress so that semiconductor device with a smaller R ds (on) can be chosen to reduce conduction losses.Following the introduction described in Section 1, this paper is organized as follows.The operation principle of the proposed converter is explained in Section 2. Section 3 presents the steady-state analysis.Experimental results measured from a 1-kW prototype are illustrated and discussed in Section 4, while conclusion is summarized in Section 5.

Operation Principle of the Proposed Converter
As shown in Figure 2, the direction of energy flow can be handled by controlling the active switches so that the converter can operate in either step-up mode or step-down mode.In step-up mode, main switches S1, S2, S3, and S4 are in switching pattern while S5 and S6 are in charge of rectifying.At this mode, S1 and S2 operate complementarily and so do both switches S3 and S4.The voltage gain of VL to VH is determined by the duty ratio of S1.With respect to step-down mode, main switches S2, S4, S5, and S6 will be in switching pattern and the rest of main switches serve as rectifier.In addition, S2, S4, and S5 are turned on and off simultaneously and complementary to S6.The duty ratio of S6 dominates the voltage gain of VH to VL in step-down mode.To describe the operation of the converter, some assumptions are made as follows: (1) In Figure 2, capacitances of Cb1, Cb2, Co1, and Co2 are large enough so that all the voltages across them can be regarded as constant in a switching cycle.(2) Parasitic capacitor and body diode of each switch are considered, but the internal resistance is neglected.
(3) The leakage inductance of the coupled inductor is much less than magnetizing inductance.(4) All the magnetic components are designed in continuous conduction mode (CCM).(5) The turns ratio of secondary to primary of the coupled inductor, N2/N1, is defined as n.Following the introduction described in Section 1, this paper is organized as follows.The operation principle of the proposed converter is explained in Section 2. Section 3 presents the steady-state analysis.Experimental results measured from a 1-kW prototype are illustrated and discussed in Section 4, while conclusion is summarized in Section 5.

Operation Principle of the Proposed Converter
As shown in Figure 2, the direction of energy flow can be handled by controlling the active switches so that the converter can operate in either step-up mode or step-down mode.In step-up mode, main switches S 1 , S 2 , S 3 , and S 4 are in switching pattern while S 5 and S 6 are in charge of rectifying.At this mode, S 1 and S 2 operate complementarily and so do both switches S 3 and S 4 .The voltage gain of V L to V H is determined by the duty ratio of S 1 .With respect to step-down mode, main switches S 2 , S 4 , S 5 , and S 6 will be in switching pattern and the rest of main switches serve as rectifier.In addition, S 2 , S 4 , and S 5 are turned on and off simultaneously and complementary to S 6 .The duty ratio of S 6 dominates the voltage gain of V H to V L in step-down mode.To describe the operation of the converter, some assumptions are made as follows: (1) In Figure 2, capacitances of C b1 , C b2 , C o1 , and C o2 are large enough so that all the voltages across them can be regarded as constant in a switching cycle.(2) Parasitic capacitor and body diode of each switch are considered, but the internal resistance is neglected.(3) The leakage inductance of the coupled inductor is much less than magnetizing inductance.(4) All the magnetic components are designed in continuous conduction mode (CCM).(5) The turns ratio of secondary to primary of the coupled inductor, N 2 /N 1 , is defined as n.

Step-Up Mode
The converter operation in step-up mode is divided into nine main stages over one switching cycle, which are discussed stage by stage below.The equivalents of the nine stages are depicted in Figure 3, while Figure 4 illustrates the corresponding conceptual waveforms.
Stage 1 [t 0 , t 1 ]: In this stage, referring to Figure 3a, all the switches are in off state.The energy stored in the parasitic capacitor C S3 is drawn out but capacitor C b1 is charged, as referred to the red dashed line in Figure 3a.Meanwhile, energy of L m1 is forwarded to capacitor C o2 and the output V H , where L m1 stands for the total amount of magnetizing inductance seen looking into the primary (at low-voltage side) of the coupled inductor.After the voltage across C S3 drops to zero, the body diode D S3 conducts to continue the currents flowing through L 1 and L k1 thus to create ZVS turn-on condition for S 3 .
Stage 2 [t 1 , t 2 ]: This stage begins at the moment the switches S 1 and S 3 are turned on.The S 3 is turned on with ZVS.During this time interval, S 2 , S 4 , S 5 , and S 6 are still in off-state.The voltage of the parasitic capacitor C S1 drops.After the voltage v ds1 is less than input voltage V L , inductor L 1 will absorb energy from V L and the current i L1 increases, as referred to the blue dashed line in Figure 3b.In stage 2, the energy of L k1 is continuously releasing to C b1 .The equivalent circuit of this stage is illustrated in Figure 3b.When the current i Lk1 falls to zero, this mode ends.
Stage 3 [t 2 , t 3 ]: Figure 3c depicts the equivalent circuit of this stage, in which all the switch have the same statuses as in Stage 2. Inductor L 1 continuously absorbs the energy from V L .Capacitor C b1 transmits energy to L k1 , L m1 and the secondary (at high-voltage side) of the coupled inductor, of which current path is indicated by the red dashed line in Figure 3c.The currents i Lk1 and i Lm1 increase.In the high-voltage side, C o1 is charged via the loop of This mode ends when S 3 is turned off.
Stage 4 [t 3 , t 4 ]: This stage begins at time t = t 3 , and the equivalent circuit is illustrated in Figure 3d.During this time interval, all the switches are in off state except S 1 .Input V L and capacitor C b1 charge inductor L 1 and capacitor C b2 , respectively.In addition, C b1 forwards energy to high-voltage side via the coupled inductor to charge C o1 .The C S4 releases energy.That is, v ds4 decreases.The body diode of S 4 will be forward biased after v ds4 drops to zero, which provides ZVS condition for S 4 .The associated current path is referred to the red dashed line in Figure 3d.The leakage energy in L k2 is recycling to C o1 over the interval of Stage 4.
Stage 5 [t 4 , t 5 ]: When S 4 is turned on, the operation of the converter enters into Stage 5.As shown in Figure 3e, in this stage switches S 1 and S 4 are closed, whereas S 2 , S 3 , S 5 , and S 6 are open.The voltage polarity of L k1 is reversed and the current i Lk1 begins decreasing.Capacitor C b2 is charged by L k1 and C b1 and the current flowing through S 4 is decreased, as referred to the red dashed line in Figure 3e.The energy in L k2 is kept on recycling to C o1 , which is the same as in Stage 4. At the moment that i Lk2 equals zero, this stage ends and D S6 is reversely biased.
Stage 6 [t 5 , t 6 ]: During the time interval of Stage 6, the switches S 1 and S 4 are still in on state and S 2 , S 3 , S 5 , and S 6 in off state.Figure 3f is the corresponding equivalent, in which C b1 charges L k1 , L m1 , and C b2 , as referred to the red dashed line.The currents flowing through L k1 and L m1 are identical and increase simultaneously.With respect to current i L1 , since the voltage across L 1 is V L , the current i L1 continues linearly increasing.This stage continues until S 1 is turned off.
Stage 7 [t 6 , t 7 ]: Figure 3g depicts the equivalent circuit of Stage 7, in which all switches are open except S 4 .There are two loops, V L -L 1 -C b1 -C S2 and L k1 -L m1 -S 4 -C b2 -C S2 , to draw the energy stored in the parasitic capacitor of S 2 .When the voltage across C S2 falls to zero, the body diode of S 2 conducts and S 2 can achieve ZVS, as referred to the both dashed lines in red and blue in Figure 3g.In the high-voltage side of the converter, the both in-series capacitors C o1 and C o2 supply power to output.3h.As referred to the both red and purple dashed line in Figure 3h, capacitor C b1 is charged by V L and L 1 , while the C b2 absorbs energy from L m1 and L k1 .All the currents i L1 , i Lk1 and i Lm1 decrease.In addition, the energy stored in magnetizing inductor is forwarded to the secondary of the coupled inductor to charge C o2 .This stage ends as the current i Lk1 falls to zero.
Stage 9 [t 8 , t 9 ]: During the time interval of Stage 9, the switches S 2 and S 4 are still in on state and S 1 , S 3 , S 5 , and S 6 in off state.The equivalent circuit is illustrated in Figure 3i.Capacitor C b1 is still charged by V L and L 1 .Additionally, capacitor C b2 pumps energy to inductor L k1 via switches S 4 , as referred to the red dashed line in Figure 3i.The energy stored in the magnetizing inductor is transferred to the secondary to charge C o2 and power the output.In this stage, inductor currents i L1 and i Lm1 decrease but i Lk1 and i Lk2 increase.When switches S 2 and S 4 are turned off at t = t 9 , this stage ends.The operation in step-up mode over one switching cycle is completed.

Step-Down Mode
In step-down mode, S2, S4, and S5 are controlled at high switching pattern and complementary to SW6, while SW1 and SW3 serve as rectifiers.The converter operation over one switching cycle in step-down mode can be divided into 12 stages, which are described stage by stage in the following.The related equivalents and corresponding waveforms are depicted in Figures 5 and 6, respectively.
Stage 1 [t0, t1]: Referring to Figure 5a, all the switches are in off state.Since S5 has been turned off, the voltage of CS5 increases.Accordingly, the voltage across L'm2 (the inductance seen looking into the high-voltage side of the coupled inductor) and Lk2, which is equal to vCo2 − vds5, decreases; meanwhile the energy stored in the parasitic capacitor of S6 releases via the loop of CS6-Co1-Lk2-L′m2.In low voltage side, the body diodes of S2 and S4 are forward biased because of the continuity of iLk1.The voltage across L1 equals vCb1 − VL.Since vCb1 is larger than VL, the current iL1 increases negatively, as referred to the red dashed line in Figure 5a.During this stage, Co2 will energize Cb2 via the coupled inductor and the loop Lk1-N1-DS4-Cb2-DS2.This mode ends at the moment vds5 reaches the magnitude of VH.That is, S5 is completely turned off and its blocking voltage is clamped to VH.
Stage 2 [t1, t2]: During this time interval, all the switches still stay in off state.The equivalent circuit of this stage is illustrated in Figure 5b.The voltage polarity across L′m2 and Lk2 reverses and the value of vLm2 + vLk2 is equal to vCo1.That is, magnetizing inductor L′m2 and leakage inductor Lk2 release energy to Co1 and VH via body diode DS6, as indicated by the purple dashed line in Figure 5b.Since voltage polarity of the coupled inductor has been changed, the body diode DS2 will be reversely

Step-Down Mode
In step-down mode, S 2 , S 4 , and S 5 are controlled at high switching pattern and complementary to SW 6 , while SW 1 and SW 3 serve as rectifiers.The converter operation over one switching cycle in step-down mode can be divided into 12 stages, which are described stage by stage in the following.The related equivalents and corresponding waveforms are depicted in Figures 5 and 6, respectively.
Stage 1 [t 0 , t 1 ]: Referring to Figure 5a, all the switches are in off state.Since S 5 has been turned off, the voltage of C S5 increases.Accordingly, the voltage across L m2 (the inductance seen looking into the high-voltage side of the coupled inductor) and L k2 , which is equal to v Co2 − v ds5 , decreases; meanwhile the energy stored in the parasitic capacitor of S 6 releases via the loop of C S6 -C o1 -L k2 -L m2 .In low voltage side, the body diodes of S 2 and S 4 are forward biased because of the continuity of i Lk1 .The voltage across L 1 equals v Cb1 − V L .Since v Cb1 is larger than V L , the current i L1 increases negatively, as referred to the red dashed line in Figure 5a.During this stage, C o2 will energize C b2 via the coupled inductor and the loop L k1 -N 1 -D S4 -C b2 -D S2 .This mode ends at the moment v ds5 reaches the magnitude of V H .That is, S 5 is completely turned off and its blocking voltage is clamped to V H .
Stage 2 [t 1 , t 2 ]: During this time interval, all the switches still stay in off state.The equivalent circuit of this stage is illustrated in Figure 5b.The voltage polarity across L m2 and L k2 reverses and the value of v Lm2 + v Lk2 is equal to v Co1 .That is, magnetizing inductor L m2 and leakage inductor L k2 release energy to C o1 and V H via body diode D S6 , as indicated by the purple dashed line in Figure 5b.Since voltage polarity of the coupled inductor has been changed, the body diode D S2 will be reversely biased and the parasitic capacitor C S1 releases energy to V L .In stage 2, the current flowing L k1 almost equals that in L 1 .Therefore, switch S 2 is turned off at ZCS.When S 6 is turned on with ZVS, the operation of the converter enters into next stage.
Stage 3 [t 2 , t 3 ]: In this stage, switch S 6 is closed.L m2 and L k2 proceed with energy releasing toward C o1 and V H , and leakage energy in L k1 is dumped to C b2 at the same time.Accordingly, all the currents in them decrease.As referred to the blue dashed line in Figure 5c, the current of L 1 draws out the stored energy in C S1 and then force the parasitic diode D S1 in forward bias.The L 1 delivers energy to V L and its current decreases linearly.In stage 3, the current flowing through L k2 is greater than that in L m2 but its magnitude drops much steeper.This stage continues until i Lk1 drops to zero. Figure 5c shows the equivalent circuit of this stage.
Stage 4 [t 3 , t 4 ]: This stage begins at time t = t 3 , and the equivalent circuit is illustrated in Figure 5d.During this time interval, all switches are still in turn-off condition except S 6 .Magnetizing inductor L m2 forwards energy to C o1 and C b1 via switch S 6 and the ideal transformer, respectively.The current direction of L k1 changes, which results in energy releasing of C S3 and the charging of C S4 .Associated current path is shown as the red dashed line in Figure 5d.The leakage inductor L k1 will confine the charge current of C S4 , resulting in ZCS turn-off at S 4 .When the voltage v ds4 rises to v Cb2 , Stage 5 begins.
Stage 5 [t 4 , t 5 ]: The equivalent circuit of this stage is illustrated in Figure 5e, in which all the switches are turned off except S 6 .Capacitor C o1 still absorbs energy from L m2 and L k2 .In addition, L m2 forwards energy to C b1 by the ideal transformer and via the loop of N 1 -L k1 -D S1 -C b1 -D S3 .This current path is referred to the red dashed line in Figure 5e.The current flowing through L k2 keeps on decreasing.This stage ends at the time that i Lk2 is zero.That is, energy in L k2 is completely recycled.
Stage 6 [t 5 , t 6 ]: Figure 5f depicts the equivalent circuit of this mode, in which all switches have the same statuses as in Stage 5.The current direction of i Lk2 changes at t = t 5 , and L k2 absorbs energy from C o1 , as referred to the green dashed line in Figure 5f.The circuit operation in low voltage side is identical to that in Stage 5. Therefore, the inductor L 1 keeps on energy supplying toward V L and its current decreases linearly.Stage 6 continues until switch S 6 is turned off at t = t 6 .
Stage 7 [t 6 , t 7 ]: During the interval that S 6 is open, the voltage v ds6 increases.Therefore, the voltage, v Lm2 + v Lk2 , drops and the parasitic capacitor C S5 dumps its stored energy, as referred to the green dashed line in Figure 5g.The circuit operation in low-voltage side behaves identically to Stage 6.When the energy in C S5 is drawn out completely and v ds6 rises to V H , this stage stops.Figure 5g expresses the operation of the converter in Stage 7.
Stage 8 [t 7 , t 8 ]: In Stage 8, the body diode D S5 is in forward bias, which provides a ZVS condition for S 5 .The green dashed line in Figure 5h shows this current path.Leakage energy in inductors L k2 and L k1 is recycled to C o2 and C b1 .In addition, L 1 proceeds with energy releasing to V L while L m2 still forwards energy to low voltage side via the ideal transformer.When switches S 2 , S 4 , and S 5 are turned on simultaneously, this stage ends.The corresponding equivalent circuit is depicted in Figure 5h.
Stage 9 [t 8 , t 9 ]: At t = t 8 , the operation of the converter enters into Stage 9. Figure 5i is the equivalent.The voltage polarity of the ideal transformer reverses because S 2 and S 4 are closed.Over the time interval of Stage 9, L k2 and L k1 continuously dump their stored energy and thus the currents i Lk1 and i Lk2 reduce.Additionally, the voltage level of v Cb1 is higher than V L , which results that the inductor L 1 absorbs energy from C b1 and its current increases negatively and linearly, as referred to the blue dashed line in Figure 5i.This stage lasts until i Lk2 drops to zero.
Stage 10 [t 9 , t 10 ]: After the time t = t 9 , the current direction of L k2 changes and i Lk2 increases.Switch statues in Stage 9 are identical to that in Stage 10.That is, S 2 , S 4 , and S 5 are in on state, whereas S 1 , S 3 , and S 6 stay in off state.The equivalent circuit is shown in Figure 5j, in which the L m2 draws energy from C o2 and the voltage across L 1 is still kept at V Cb1 − V L .As the red dashed line in Figure 5j indicates, leakage inductor L k1 continues releasing energy and i Lk1 decreases.When i Lk1 is zero at t = t 10 , this stage ends.5k shows the equivalent circuit of this stage, in which the statuses of all switches are kept as in Stage 10.During this time interval, C b1 continuously supplies energy to V L and L 1 by the loop of C b1 -L 1 -V L -S 2 , of which current path is referred to the blue dashed line in Figure 5k.The current directions of N 1 and N 2 reverse and the current i Lk1 rises positively.Meanwhile, capacitor C b2 charges and C o2 discharges.
Stage 12 [t 11 , t 12 ]: From the equivalent circuit depicted in Figure 5l, switches S 2 , S 4 , and S 5 remain closed, while S 1 , S 3 , and S 6 are open.In Stage 12, inductors L k2 and L m2 are magnetized by C o2 with the same circuit behavior in Stage 11.Since the magnitude of i Lk1 is greater than i L1 , the current flowing through S 2 becomes reverse, and then S 2 achieves ZCS at turn-off transition, as referred to the red dashed line in Figure 5l.The operation of the converter over one switching cycle is completed when the switches S 2 , S 4 , and S 5 are turned off simultaneously.According to the aforementioned operation principle, the switching characteristics of all power switches are summarized in Table 1.

Steady-State Analysis
In this section, the steady-state analysis of the BDC includes voltage conversion ratio, voltage stress derivation, and magnetic element design.To simplify the analysis, the assumptions made in Section 2 are considered except the neglect of leakage inductors.In addition, the phenomenon that occurs at switching transient is also ignored.According to the aforementioned operation principle, the switching characteristics of all power switches are summarized in Table 1.

Steady-State Analysis
In this section, the steady-state analysis of the BDC includes voltage conversion ratio, voltage stress derivation, and magnetic element design.To simplify the analysis, the assumptions made in Section 2 are considered except the neglect of leakage inductors.In addition, the phenomenon that occurs at switching transient is also ignored.

Step-Up Mode
Voltage gain of the converter in step-up mode is first investigated.Because the output voltage V H is the sum of V Co1 and V Co2 , the relationships of V Co1 to V L and V Co2 to V L have to be found in advance.The voltage V Co1 is n times the magnitude of V Cb1 and V Co2 is n times the V Cb2 under the condition that leakage inductor is neglected.Accordingly, V Cb1 and V Cb2 in terms of V L should be determined before the finding for V Co1 and V Co2 .Since S 1 and S 2 are switched complementarily, the input voltage V L can be boosted via inductor L 1 .As a result, the voltage across C b1 is given by where D 1 is the duty ratio of S 1 .Refer to Figure 4 at any time there are two switches in closed state simultaneously over one switching cycle.While S 1 and S 3 are on, the voltage across L m1 is V Cb1 and thus the amount of current increase can be estimated by In Equation ( 2), the D 3 denotes the duty ratio of S 3 .After S 3 is turned off, switch S 4 will be turned on.That is, the both switches S 1 and S 4 are in on state.The voltage across L m1 becomes V Cb1 − V Cb2 .If V Cb1 is greater than V Cb2 , the L m1 will proceed with current increasing.The increment can be expressed as The switch S 2 will be turned on when switch S 1 is turned off.That is, S 2 and S 4 are in on state simultaneously and the voltage across L m1 is −V Cb2 .The current flowing through L m1 decreases, which is given by In steady state, the net current change on L m1 is equal to zero.From Equations ( 2)-( 4), the following relationship can be derived Substituting Equation (1) into Equation ( 5) becomes The output voltage V H = V Co1 + V Co2 , which can be also obtained from Therefore, the conversion ratio of output voltage to input voltage in step-up mode, M step-up , can be found by As referring to the switching sequence in step-up mode, during the interval that S 2 and S 4 are open but S 1 and S 3 are closed, the S 2 and S 4 endure the voltages of V Cb1 and V Cb2 , respectively.After the above switch status, S 2 and S 3 will be open but S 1 and S 4 are closed.The blocking voltages at S 2 and S 3 are V Cb1 and V Cb2 , respectively.The switch status that S 1 and S 3 are off but S 2 and S 4 are on Energies 2017, 10, 296 11 of 23 proceeds the converter operation.The voltages across S 1 and S 3 in this time interval are also V Cb1 and V Cb2 in turn.In brief, the voltage stresses with respect to S 1 , S 2 , S 3 and S 4 can be determined as follows: At high-voltage side, the switch S 5 will withstand a voltage of at least V H when the intrinsic diode of S 6 is forward biased.Similarly, S 6 also endures a reverse voltage up to V H during the interval that the diode D S6 is on.That is, With respect to inductance design, the average current carried by magnetic component has to be calculated in advance.For L m1 , the application of amp-second balance criterion (ASBC) at C b2 can give an assistance to the finding for the average of i Lm1 .The C b2 charges during the time interval [t 5 , t 6 ], in which S 1 and S 4 are in on state.On the contrary, C b2 discharges during [t 8 , t 9 ], while S 2 and S 4 are closed.The charging current of C b2 is equal to i Lm1 and discharging current will be i Lm1 + ni ds5 .Thus, the following relationship holds: From Equation ( 12), the average current carried by L m1 can be given as If the voltage across C b1 is close to V Cb2 , the current i Lm1 can be regard as constant in Stage 6.This phenomenon can be found in Figure 4. Assume that L m1 is in BCM.The following relationship can be found: Solving for L m1 results: where L m1,min is the minimum inductance of L m1 for CCM operation, R H stands for load resistance at high-voltage side, and f s is switch frequency.
To determine the minimum inductance of L 1 , L 1,min , for CCM operation, average current of i L1 has to be contacted.This average current can be found by applying ASBC to C b1 .Capacitor C b1 charges during the time interval [t 7 , t 9 ], in which both switches S 2 and S 4 are closed.There are two intervals to discharge the energy in C b1 .One is [t 2 , t 4 ], in which S 1 and S 3 are closed, and the other is and [t 4 , t 7 ], in which S 4 and S 1 are in on state.Based on ASBC, the following relationship holds: Using Equation ( 13) and substituting for i Lm1 , the average current flowing through L 1 can be represented as Energies 2017, 10, 296 12 of 23 The current increment on L 1 , ∆i L1 , is estimated by Hence, the minimum of i L1 , I L1,min , is given by At BCM, I L1,min = 0. Solving for L 1 yields Using Equation ( 13) and substituting for iLm1, the average current flowing through L1 can be represented as The current increment on L1, ΔiL1, is estimated by Hence, the minimum of iL1, IL1,min, is given by At BCM, IL1,min = 0. Solving for L1 yields (1 ) (1 ) 2 ( 1)

Step-Down Mode
All the assumptions in the above subsection are also adopted for the steady-state analysis in step-down mode.The switches S2, S4, and S5 are controlled simultaneously and complementary to S6.During the interval that S6 is in turned-on state and S2, S4, and S5 are in turned-off state, the voltage VCo1 will directly impose on the high-voltage side of the transformer.Then, the body diodes Ds1 and Ds3 forward conduct and the voltage VCb1 will be equal to VCo1/n.The inductor L1 supplies energy to VL.This state will last for D6Ts.During the interval (1 − D6)Ts, S6 becomes off but S2, S4, and S5 are on.The voltage polarity of the coupled inductor at high-voltage side reverses and its magnitude equals VCo2.In addition, the voltage across inductor L1 is VCb1 − VL while VCb2 equals VCo2/n.Applying volt-second balance criterion (VSBC) to L1 yields (1 )

Step-Down Mode
All the assumptions in the above subsection are also adopted for the steady-state analysis in step-down mode.The switches S 2 , S 4 , and 5 are controlled simultaneously and complementary to S 6 .During the interval that S 6 is in turned-on state and S 2 , S 4 , and S 5 are in turned-off state, the voltage V Co1 will directly impose on the high-voltage side of the transformer.Then, the body diodes D s1 and D s3 forward conduct and the voltage V Cb1 will be equal to V Co1 /n.The inductor L 1 supplies energy to V L .This state will last for D 6 T s .During the interval (1 − D 6 )T s , S 6 becomes off but S 2 , S 4 , and S 5 are on.The voltage polarity of the coupled inductor at high-voltage side reverses and its magnitude equals V Co2 .In addition, the voltage across inductor L 1 is V Cb1 − V L while V Cb2 equals V Co2 /n.Applying volt-second balance criterion (VSBC) to L 1 yields Equation ( 21) can also be expressed as Similarly, applying VSBC to magnetizing inductor L m2 , the following relationships can be found: Energies 2017, 10, 296 13 of 23 and Substituting Equation (23) into Equation ( 22) has the result: in which M step-down stands for the ratio of output to input voltage as in step-down mode.Figure 8a shows the curves of M step-up versus duty ratio D 1 , while M step-down versus duty ratio D 6 is illustrated in Figure 8b.
n Similarly, applying VSBC to magnetizing inductor L′m2, the following relationships can be found: (1 ) Substituting Equation (23) into Equation ( 22) has the result: (1 ) V n (25) in which Mstep-down stands for the ratio of output to input voltage as in step-down mode.Figure 8a shows the curves of Mstep-up versus duty ratio D1, while Mstep-down versus duty ratio D6 is illustrated in Figure 8b.The discussion relating to the voltage stresses of the semiconductor devices is followed up.Because the diode DS1 and switch S2 conduct complementarily, from the mesh of Cb1-S1-S2, it can be found that voltage stress of S1 is identical to that of S2 and equals VCb1.Similarly, DS3 and S4 are in complementary conduction, and the voltage stresses of S3 and S4 will be equal to VCb2.At high-voltage side, from the outermost loop, S5-S6-VH, the input voltage VH will impose on S5 and S6 alternately.That is, S5 and S6 have to stand a voltage of VH.
The current gain of the is a reciprocal of the voltage ratio shown in Equation (25).Therefore, the input current IH is given by (1 ) ( 1) where RL denotes the load resistance at low-voltage side.From Figure 5f, the average current of magnetizing inductance L′m2 is equals to − ids6, which can be further estimated by The discussion relating to the voltage stresses of the semiconductor devices is followed up.Because the diode D S1 and switch S 2 complementarily, from the mesh of C b1 -S 1 -S 2 , it can be found that voltage stress of S 1 is identical to that of S 2 and equals V Cb1 .Similarly, D S3 and S 4 are in complementary conduction, and the voltage stresses of S 3 and S 4 will be equal to V Cb2 .At high-voltage side, from the outermost loop, S 5 -S 6 -V H , the input voltage V H will impose on S 5 and S 6 alternately.That is, S 5 and S 6 have to stand a voltage of V H .
The current gain of the converter is a reciprocal of the voltage ratio shown in Equation (25).Therefore, the input current I H is given by where R L denotes the load resistance at low-voltage side.From Figure 5f, the average current of magnetizing inductance L m2 is equals to −i ds3 n − i ds6 , which can be further estimated by In addition, the current decrement on L m2 over one switching cycle, ∆i Lm2 , can be expressed as Using Equation (23) and Equation ( 25) to substitute for V Co1 yields Energies 2017, 10, 296 14 of 23 The minimum value of i Lm2 can be calculated by I Lm2 − ∆i Lm2 2 and is computed as At boundary, I Lm2,min = 0.Then, solving for L m2 can obtain the following relation for determining the minimum inductance for CCM: In order to find the minimum value of L 1 for continuous current operation, L 1,min , the average current of L 1 , I L1 , has to be found.The I L1 is equal to the output current I L , which is given by The change on inductor current i L1 can be computed from Accordingly, minimum of I L1 is Let I L1,min = 0 and solving for L 1 can obtains: Assume that R L is 9.216 Ω, f s is 40 kHz, and n = 3. Figure 9a depicts the relationship between D 6 and L m2 , while L 1 versus D 6 is illustrated in Figure 9b. Figure 10 is the equivalent circuit of proposed converter considering non-ideal parameters, in which rL1 represents the inductor resistance at the low voltage side and rds1, rds2, rds3, rds4, rds5, and rds6 are the on-state resistance of switches S1, S2, S3, S4, S5, and S6, respectively; and rlk1 and rlk2 are the primary winding resistances and the secondary one respectively.By using VSBC and ASBC, the non-ideal voltage conversion ratio M′step-up and conversion efficiency ηstep-up in step-up mode can be obtained as   Figure 10 is the equivalent circuit of converter considering non-ideal parameters, in which r L1 represents the inductor resistance at the low voltage side and r ds1 , r ds2 , r ds3 , r ds4 , r ds5 , and r ds6 are the on-state resistance of switches S 1 , S 2 , S 3 , S 4 , S 5 , and S 6 , respectively; and r lk1 and r lk2 are the primary winding resistances and the secondary one respectively.By using VSBC and ASBC, the non-ideal voltage conversion ratio M step-up and conversion efficiency η step-up in step-up mode can be obtained as In addition, step-down voltage ratio M step-down and efficiency η step-down are estimated by Based on Equations (36) to (39), relationships of voltage gain versus duty ratios D 1 and D 3 in step-up mode are depicted in Figure 11a,b, respectively; meanwhile, so do Figure 11c,d for step-down operation.Figure 12 shows the non-ideal voltage gain in step-up mode under different choke resistances.
Figure 10 is the equivalent circuit of proposed converter considering non-ideal parameters, in which rL1 represents the inductor resistance at the low voltage side and rds1, rds2, rds3, rds4, rds5, and rds6 are the on-state resistance of switches S1, S2, S3, S4, S5, and S6, respectively; and rlk1 and rlk2 are the primary winding resistances and the secondary one respectively.By using VSBC and ASBC, the non-ideal voltage conversion ratio M′step-up and conversion efficiency ηstep-up in step-up mode can be obtained as (1 )(1 ) ( 1) Step-up Step-up In addition, step-down voltage ratio M′step-down and efficiency ηstep-down are estimated by ) (1 ) Step-down Based on Equations (36) to (39), relationships of voltage gain versus duty ratios D1 and D3 in step-up mode are depicted in Figure 11a,b, respectively; meanwhile, so do Figure 11c,d for step-down operation.Figure 12 shows the non-ideal voltage gain in step-up mode under different choke resistances.

Low-Voltage Side
High-Voltage Side  Among all power switches, the main switch S1 will endure the maximum current stress no matter in step-up or step-down mode.Thereby, the current stress determination is focused on S1.This current stress can be estimated by the sum of the valley current of inductor L1 and the peak current of leakage inductance Lk1.That is, As for the current stresses of the other active switches in step-down mode, the ASBC should be applied to capacitors Co1, Co2, Cb2, and Cb1, which yields Among all power switches, the main switch S 1 will endure the maximum current stress no matter in step-up or step-down mode.Thereby, the current stress determination is focused on S 1 .This current stress can be estimated by the sum of the valley current of inductor L 1 and the peak current of leakage inductance L k1 .That is, As for the current stresses of the other active switches in step-down mode, the ASBC should be applied to capacitors C o1 , C o2 , C b2 , and C b1 , which yields Similarly, in step-up mode, current stresses of switches can be expressed as

Experimental Results
To validate the proposed BDC, a 1-kW prototype is built with the specifications and components summarized in Table 2.If a converter operates in discontinuous conduction mode (DCM), it can easily avoid switching loss.However, during the interval of high power loading, serious conduction loss will result in unacceptable efficiency.The proposed converter intrinsically has the outstanding feature of soft switching at all power switches even in CCM.Therefore, we design the converter operation from DCM into CCM at 250-W power loading for overall efficiency consideration.Accordingly, a Toroids 55195-A2 MPP core and an EE-55 core are adopted to form main inductor and coupled inductor, respectively.To make sure the CCM and DCM operate, as mentioned, the main inductance L 1 should be 46 µH and magnetizing inductance L m1 is 130 µH with a turns ratio of n = 3.According to the discussion in Section 3, voltage and current stresses of all active switches can be specified, which offers us a benefit to choose appropriate semiconductor devices for prototype constructing.Since a lower R ds(on) can achieve a higher conversion efficiency, active switches which meet the power rating and have conduction resistance as low as possible are considered.At low-voltage side, power MOSFETs IXFH160N15T2 with on-state resistance R ds(on) of 9 mΩ is chosen as S 1 and S 2 , while IXTP160N075T with 6 mΩ R ds(on) as S 3 and S 4 .With regard to the active switches S 5 and S 6 at high-voltage side, power MOSFET IXFH52N50P2 is considered, of which R ds(on) is 0.12 Ω. Microcontroller ATMEGA328P-PU is in charge of the converter controlling.Additionally, PV simulator Chroma 62050H-600S, high voltage power supply IDRC CDSP-500-010C, electronic load Chroma 63202 are adopted for terminal source or load.All waveforms are measured by oscilloscope KEYSIGHT DSOX4024A.Figure 12 shows the voltage and current waveforms measured from switches S 1 -S 6 , while D 1 = 0.44 and D 3 = 0.3.In Figure 13a, the first trace and second trace are the switch voltage and current of S 1 , respectively, whereas the third and fourth traces depict the measurements of S 2 .
From Figure 13a, it can be found that S 1 endures a voltage of around 100 V.This value is consistent with the estimation in Equation ( 9).The measured i ds1 matches the conceptual waveform in Figure 4.In addition, the waveforms of v ds2 and i ds2 release that ZCS turn-off feature is achieved at S 2 .Figure 13b presents the practical measurements of v ds3 , i ds3 , v ds4 , and i ds4 , which illustrates that both switches S 3 and S 4 can be turned on with ZVS.While operated in step-up mode, S 5 and S 6 of the converter are in the role of rectifier.Figure 13c presents the zoomed-in waveforms of S 1 and S 2 , and Figure 13d is for S 3 and S 4 .The blocking voltages of v ds5 and v ds6 are both equal to 400 V, as shown in Figure 13e, which conforms to the calculation of Equation (11). Figure 13f confirms a stable output and CCM operation in L 1 ; moreover, the measurements of i Lk1 and i Lk2 are consistent with the waveforms in Figure 4.
illustrates that both switches S3 and S4 can be turned on with ZVS.While operated in step-up mode, S5 and S6 of the converter are in the role of rectifier.Figure 13c presents the zoomed-in waveforms of S1 and S2, and Figure 13d is for S3 and S4.The blocking voltages of vds5 and vds6 are both equal to 400 V, as shown in Figure 13e, which conforms to the calculation of Equation (11). Figure 13f confirms a stable output and CCM operation in L1; moreover, the measurements of iLk1 and iLk2 are consistent with the waveforms in Figure 4.While operating in step-down mode with D6 = 0.37, related practical waveforms are shown in Figure 14.From Figure 14a,b, it can be seen that both switches S1 and S3 are just in charge of rectifying whereas S2 and S4 can accomplish ZCS turn-off feature.Figure 14c reveals that S5 and S6 are turned on with ZVS and their voltage stresses are about 400 V.The output voltage at low-voltage side and the currents of L1, Lk1, and Lk2 are also given in Figure 14d, in which a constant 48 V output and CCM operation in L1 are illustrated.While operating in step-down mode with D 6 = 0.37, related practical waveforms are shown in Figure 14.From Figure 14a,b, it can be seen that both switches S 1 and S 3 are just in charge of rectifying whereas S 2 and S 4 can accomplish ZCS turn-off feature.Figure 14c reveals that S 5 and S 6 are turned on with ZVS and their voltage stresses are about 400 V.The output voltage at low-voltage side and the currents of L 1 , L k1 , and L k2 are also given in Figure 14d, in which a constant 48 V output and CCM operation in L 1 are illustrated.
While operating in step-down mode with D6 = 0.37, related practical waveforms are shown in Figure 14.From Figure 14a,b, it can be seen that both switches S1 and S3 are just in charge of rectifying whereas S2 and S4 can accomplish ZCS turn-off feature.Figure 14c reveals that S5 and S6 are turned on with ZVS and their voltage stresses are about 400 V.The output voltage at low-voltage side and the currents of L1, Lk1, and Lk2 are also given in Figure 14d, in which a constant 48 V output and CCM operation in L1 are illustrated.Figure 15 depicts measured efficiency of the prototype.The maximum values of the practical efficiency in step-up and step-down modes are up to 95.4% and 93.6%, respectively, while P o is equal to 1 kW.The efficiency values are measured after 1hr burn-in test and the maximum temperature of all active components is around 56 • C. Figure 16 shows the photo of the prototype, where its length, width, and height are 17.2, 14.6, and 4.2 cm in turn.Therefore, its power density is 948.13 kW/m 3 .In addition, the converter's weight is 0.985 kg.That is, specific power is 1.015 kW/kg.all active components is around 56 °C. Figure 16 shows the photo of the prototype, where its length, width, and height are 17.2, 14.6, and 4.2 cm in turn.Therefore, its power density is 948.13 kW/m 3 .In addition, the converter's weight is 0.985 kg.That is, specific power is 1.015 kW/kg.Step-Up Mode Step-Down Mode  Table 3 summarizes the comparison of the proposed converter with other bidirectional converters in [24][25][26][27].The proposed converter has the better features such as galvanic isolation, soft switching at all switches, no any diode required, and high voltage-ratio conversion.For example, in step-up mode and under the conditions that n = 3 and duty cycle is 0.5 (in addition, D1 = D3 in the proposed converter), the proposed one can achieve a much higher voltage gain up to 12 while those in [24][25][26][27] are 11, 3, 6, and 12, respectively.For clearer presentation, the plots to express the comparison result among the mentioned converters are shown in Figure 17.In high conversion ratio converters, current-sharing path structure along with interleaved control can suppress current ripples and then lowers current stress and conduction loss [27][28][29][30].However, bi-directional power flow controlling or more power components needed are still their demerits.
Table 3. Performance comparisons of proposed BDC with other bidirectional DC-DC converters proposed in [25][26][27].Step-Up Mode Step-Down Mode Table 3 summarizes the comparison of the proposed converter with other bidirectional converters in [24][25][26][27].The proposed converter has the better features such as galvanic isolation, soft switching at all switches, no any diode required, and high voltage-ratio conversion.For example, in step-up mode and under the conditions that n = 3 and duty cycle is 0.5 (in addition, D 1 = D 3 in the proposed converter), the proposed one can achieve a much higher voltage gain up to 12 while those in [24][25][26][27] are 11, 3, 6, and 12, respectively.For clearer presentation, the plots to express the comparison result among the mentioned converters are shown in Figure 17.In high conversion ratio converters, current-sharing path structure along with interleaved control can suppress current ripples and then lowers current stress and conduction loss [27][28][29][30].However, bi-directional power flow controlling or more power components needed are still their demerits.

Conclusions
This paper has proposed a high efficiency and high voltage-ratio isolated bidirectional DC-DC converter.A coupled inductor is employed for achieving galvanic isolation, in which the energy stored in leakage inductor can be recycled without additional components.The main contribution of this paper is that voltage stress across semiconductor devices can be lowered by adjusting duty ratio, all power switches can complete soft switching feature in step-up and step-down modes, and higher voltage conversion can inherently be achieved.Because semiconductor device endures low voltage stress, MOSFETs with low Rds,on can be employed.Unlike conventional converters whose voltage gain is merely determined by a fixed duty ratio, the proposed converter has the ability of compromising the duty ratios of switches at primary side to meet a certain voltage gain and to find an available power component.Operation principle of the circuit and detailed derivation of voltage gain, voltage stress, and current stress are carried out.Finally, experimental results measured from a 1-kW prototype have verified the theoretical analysis and feasibility.

Conclusions
This paper has proposed a high efficiency and high voltage-ratio isolated bidirectional DC-DC converter.A coupled inductor is employed for achieving galvanic isolation, in which the energy stored in leakage inductor can be recycled without additional components.The main contribution of this paper is that voltage stress across semiconductor devices can be lowered by adjusting duty ratio, all power switches can complete soft switching feature in step-up and step-down modes, and higher voltage conversion can inherently be achieved.Because semiconductor device endures low voltage stress, MOSFETs with low R ds,on can be employed.Unlike conventional converters whose voltage gain is merely determined by a fixed duty ratio, the proposed converter has the ability of compromising the duty ratios of switches at primary side to meet a certain voltage gain and to find an available power component.Operation principle of the circuit and detailed derivation of voltage gain, voltage stress, and current stress are carried out.Finally, experimental results measured from a 1-kW prototype have verified the theoretical analysis and feasibility.

Figure 1 .
Figure 1.Configuration of distributed generation system.

Figure 2 .
Figure 2. Schematic of the proposed bidirectional converter.

Figure 2 .
Figure 2. Schematic of the proposed bidirectional converter.

Figure 4 .
Figure 4. Key waveforms of the proposed converter in step-up mode.

Figure 6 .
Figure 6.Key waveforms of the proposed converter in step-down mode.
20) in which L 1,min is the minimum inductance of L 1 for CCM.If R H = 640 Ω, f s = 40 kHz, n = 3, and D 1 = D 3 .Figure 7a depicts the relationships between inductance L m1 and duty ratio D 1 while Figure 7b is for inductance L 1 versus D 1 .

Figure 7 .
Figure 7. Magnetic component design for (a) L m1 and (b) L 1 under the duty ratio D 1 = D 3 .

Figure 8 .
Figure 8. Voltage conversion ratio of the proposed bidirectional converter: (a) step-up mode; and (b) step-down mode.

Figure 8 .
Figure 8. Voltage conversion ratio of the proposed bidirectional converter: (a) step-up mode; and (b) step-down mode.

Figure 9 .
Figure 9.The relationship between the inductance and duty ratio D 6 : (a) L m2 ; and (b) L 1 .

Figure 10 .
Figure 10.The non-ideal equivalent circuit of the converter.

Figure 12 .
Figure 12.The step-up voltage gain under different choke resistances.

Figure 13 .
Figure 13.Experimental results in step-up mode operation at P o = 1 kW: (a) measurements from S 1 and S 2 ; (b) measurements from S 3 and S 4 ; (c) zoomed-in waveforms measured from S 1 and S 2 ; (d) zoomed-in waveforms of S 3 and S 4 ; (e) measurements from S 5 and S 6 ; and (f) waveforms of V H , i L1 , i Lk1 , and i Lk2 .

Figure 15
Figure 15 depicts measured efficiency of the prototype.The maximum values of the practical efficiency in step-up and step-down modes are up to 95.4% and 93.6%, respectively, while Po is equal to 1 kW.The efficiency values are measured after 1hr burn-in test and the maximum temperature of

Figure 14 .
Figure 14.Experimental results in step-down mode operation at P o = 1 kW: (a) measurements from S 1 and S 2 ; (b) S 3 and S 4 ; and (c) S 5 and S 6 ; and (d) the waveforms of V L , i L1 , i Lk1 , and i Lk2 .

Figure 15 .
Figure 15.Measured efficiency of the proposed bidirectional DC-DC converter.

Figure 15 .
Figure 15.Measured efficiency of the proposed bidirectional DC-DC converter.

Figure 15 .Figure 16 .
Figure 15.Measured efficiency of the proposed bidirectional DC-DC converter.

Figure 16 .
Figure 16.The photo of the experimental setup.

Figure 17 .
Figure 17.The comparison plots of conversion ratio: (a) step-up mode; and (b) step-down mode.

Figure 17 .
Figure 17.The comparison plots of conversion ratio: (a) step-up mode; and (b) step-down mode.
Cb1 and Cb2 are low-voltage capacitors; and Co1 and Co2 are high-voltage capacitors.The conversion efficiency of proposed BDC can be improved because of the following reasons:(1) No matter in buck or boost mode, the energy stored in leakage inductors, Lk1 and Lk2, can be recycled without any snubber mechanism or clamped circuit.(2) All active semiconductor components can be switched with ZVS or zero current switching (ZCS) to eliminate switching losses.(3) Switches S1-S4 endure a low voltage stress so that semiconductor device with a smaller Rds(on) can be chosen to reduce conduction losses.
Stage 8 [t 7 , t 8 ]: After the time t = t 7 , switches S 2 and S 4 are in on state but S 1 , S 3 , S 5 , and S 6 are in off state.The equivalent circuit is illustrated in Figure

v ds5 v ds4 v ds3 v ds2 v ds1 Ts D 1 T s D 2 T s D 3 T s D 4 T s t i Lk1 i Lk2 i L1 i Lk1 i Lk2 i L1 t S 6 v ds6 t t i Lm1 Figure
4. Key waveforms of the proposed converter in step-up mode.

6 Stage 6 Stage 7 Stage 8 Stage 9 t 0 t 1 t 8 t 9 t 2 t 3 t 4 t 5 t 6 t 7 t v gs2 , v gs4 ,v gs5 i ds6 Stage 10 Stage 11 t 10 t 11 i ds1 i ds3 t 12
Figure 6.Key waveforms of the proposed converter in step-down mode.

Table 1 .
The switching characteristics of the proposed converter.

Table 1 .
The switching characteristics of the proposed converter.

Table 2 .
Specifications and components used in experimentations.