A Bidirectional DHC-LT Resonant DC-DC Converter with Research on Improved Fundamental Harmonic Analysis Considering Phase Angle of Load Impedance

: This paper presents a novel 400 V–50 V bidirectional DHC-LT resonant DC-DC converter. By adding a resonant capacitor and an auxiliary transformer based on LLC, zero-voltage switching (ZVS) and zero-current switching (ZCS) are achieved, while the output voltage gain range is broadened in two directions. Operation principles and robustness are discussed with equations. Then, the error factor of fundamental harmonic analysis (FHA) in resonant converters is analyzed. Considering the phase difference between the output voltage and resonant tank current, an improved method is proposed to describe the behavior of the DHC-LT converter more precisely. A comparison is conducted to prove the effectiveness of the proposed FHA. Furthermore, in order to reduce the output voltage and provide a ripple-free charging current, a ﬁxed-frequency phase-shift strategy is introduced in the DHC-LT converter. ZVS can be realized through the reasonable design of dead time and phase-shift angle. Finally, a 2.5 kW prototype of the DHC-LT resonant DC-DC converter with a digital signal processor (DSP) platform and a battery/PV DC test system is established in the lab to validate the theoretical analysis. process when illumination intensity decreases.


Introduction
At present, many power electronics applications, such as renewable energy storage systems (RESSs), automobiles and microgrids, need bidirectional DC-DC converters (BDCs) to transmit power between two different DC buses [1][2][3][4][5][6][7][8]. Since galvanic isolation is an important security guarantee for many applications, isolated bidirectional DC-DC converters are widely used, which can be classified into two kinds: PWM converters and resonant converters [9]. Many PWM converters benefit from zero-voltage switching (ZVS) and a wide output voltage range [10][11][12][13][14][15]. Meanwhile, power can be transmitted naturally between the two sides [16][17][18]. However, as zero-current switching (ZCS) cannot be realized easily in many PWM converters, the switching loss cannot be further reduced. By means of resonance between inductors and capacitors, the AC currents in resonant BDCs present as sinusoidal waveforms. Therefore, ZCS can be realized by reasonable design, and efficiency can be further increased. A large number of resonant BDCs with a wide voltage range have been studied recently [19][20][21][22][23][24].
Thanks to its excellent features of ZVS and ZCS, LLC has attracted attention [25][26][27]. However, without magnetic inductance, LLC is a traditional series-resonant DC-DC converter when power is transmitted backward, whose voltage gain cannot be increased further. According to [23], with a new control strategy to increase the output voltage, it is possible to achieve a voltage gain greater than 1. Unfortunately, the efficiency is not high enough. To overcome the disadvantage in backward mode, in [24], an auxiliary inductor This paper is organized as follows: Section 2 introduces the topology structure and operation principles of the proposed DHC-LT BDC. Section 3 analyzes the error factor of the traditional FHA method and proposes an improved FHA method with modification of the AC load impedance. Section 4 compares the proposed improved FHA with the experimental results, simulation, traditional FHA and FHA with an improved model of the AC port equivalent resistance to prove the effectiveness of the improved FHA in this paper. Section 5 shows the waveforms of the 2.5 kW DHC-LT prototype and PV/battery system, which proves the ZVS + ZCS characteristics and wide voltage gain range. Section 6 concludes this paper.

Topology Structure and Characteristics
The topology of the proposed DHC-LT BDC is illustrated and analyzed in this section. Then, the operation principles in step-down mode and step-up mode are given. The following sections are demonstrated based on this section.

Topology Structure
The topology of the DHC-LT BDC is shown in Figure 1. DHC means double highvoltage side (HVS) capacitors. U H represents the high-voltage port, referring to the highvoltage lithium battery system or DC bus, while U L represents the low-voltage DC link voltage. Two full-bridge networks are formed with eight power switches, where M 1 , M 2 , M 3 and M 4 constitute the high-voltage full bridge, and M 5 , M 6 , M 7 and M 8 constitute the low-voltage full bridge of the proposed converter. The biggest difference between DHC-LT, CLTC, CDT-LC is the position of C r2 . In CLTC or CDT-LC, the resonant capacitor C r2 is located in the low-voltage side (LVS) of the resonant tank. In order to reduce conduction loss and improve power density, C r2 is placed in the HVS of the resonant tank. The resonant inductor L r and the resonant capacitor C r1 are at the same position as the CLTC or CDT-LC converter. T 1 is the main transformer, similar to the transformer in the LLC resonant converter. The magnetic inductor of T 1 , L m1 , is used to obtain a voltage gain greater than 1. T 2 , the auxiliary transformer, is used to make the resonant tank symmetrical. The symbols of "." mean dotted terminals of T 1 , and the symbols of "*" mean dotted terminals of T 2 . In this way, the topology can obtain a voltage gain greater than 1 in step-up mode. The DHC-LT converter is modulated with pulse-frequency modulation (PFM). In step-down mode, M 5 , M 6 , M 7 and M 8 are driven by synchronous rectification (SR). In step-up mode, SR is not used, and antiparallel diodes of M 1 -M 4 , D 1 -D 4 , work to realize rectification. This paper is organized as follows: Section 2 introduces the topology structure and op ation principles of the proposed DHC-LT BDC. Section 3 analyzes the error factor of the t ditional FHA method and proposes an improved FHA method with modification of the A load impedance. Section 4 compares the proposed improved FHA with the experimental sults, simulation, traditional FHA and FHA with an improved model of the AC port equi lent resistance to prove the effectiveness of the improved FHA in this paper. Section 5 sho the waveforms of the 2.5 kW DHC-LT prototype and PV/battery system, which proves ZVS + ZCS characteristics and wide voltage gain range. Section 6 concludes this paper.

Topology Structure and Characteristics
The topology of the proposed DHC-LT BDC is illustrated and analyzed in this s tion. Then, the operation principles in step-down mode and step-up mode are given. T following sections are demonstrated based on this section.

Topology Structure
The topology of the DHC-LT BDC is shown in Figure 1. DHC means double hig voltage side (HVS) capacitors. UH represents the high-voltage port, referring to the hig voltage lithium battery system or DC bus, while UL represents the low-voltage DC li voltage. Two full-bridge networks are formed with eight power switches, where M1, M M3 and M4 constitute the high-voltage full bridge, and M5, M6, M7 and M8 constitute the lo voltage full bridge of the proposed converter. The biggest difference between DHC-L CLTC, CDT-LC is the position of Cr2. In CLTC or CDT-LC, the resonant capacitor Cr2 is cated in the low-voltage side (LVS) of the resonant tank. In order to reduce conduction l and improve power density, Cr2 is placed in the HVS of the resonant tank. The resona inductor Lr and the resonant capacitor Cr1 are at the same position as the CLTC or CDTconverter. T1 is the main transformer, similar to the transformer in the LLC resonant co verter. The magnetic inductor of T1, Lm1, is used to obtain a voltage gain greater than 1. the auxiliary transformer, is used to make the resonant tank symmetrical. The symbols "." mean dotted terminals of T1, and the symbols of "*" mean dotted terminals of T2. In t way, the topology can obtain a voltage gain greater than 1 in step-up mode. The DHCconverter is modulated with pulse-frequency modulation (PFM). In step-down mode, M M6, M7 and M8 are driven by synchronous rectification (SR). In step-up mode, SR is not us and antiparallel diodes of M1-M4, D1-D4, work to realize rectification.

Operation Principles
In order to simplify the analysis, the operation waveforms of currents, voltages a gate signals are depicted in Figure 2. In Figure 2, i14 is the drain-source current flowi through M1 and M4, i23 is the drain-source current flowing through M2 and M3, i58 is the dra source current flowing through M5 and M8, and i67 is the drain-source current flowi through M6 and M7. iLm1 is the excitation current of transformer T1 on the HVS, iLm2 is excitation current of transformer T2 on the HVS, iLr is the current flowing through reson inductor Lr, i'Lm1 is the excitation current of transformer T1 on the LVS, i'Lm2 is the excitati current of transformer T2 on the LVS, iCr1 is the current flowing through resonant capaci

Operation Principles
In order to simplify the analysis, the operation waveforms of currents, voltages and gate signals are depicted in Figure 2. In Figure 2, i 14 is the drain-source current flowing through M 1 and M 4 , i 23 is the drain-source current flowing through M 2 and M 3 , i 58 is the drain-source current flowing through M 5 and M 8 , and i 67 is the drain-source current flowing through M 6 and M 7 . i Lm1 is the excitation current of transformer T 1 on the HVS, i Lm2 is the excitation current of transformer T 2 on the HVS, i Lr is the current flowing through resonant inductor L r , i' Lm1 is the excitation current of transformer T 1 on the LVS, i' Lm2 is the of this interval, t0, M2 and M3 are turned off. The HVS resonant current, iLr, charges the output capacitors of M2 and M3 and discharges the output capacitor of M1 and M4. Then, the voltage of M1 and M4 decreases to 0, and the HVS current passes through the antiparallel diode of M1 and M4, which makes the switches turn on under the ZVS condition. The directions of the state variables are shown in Figure 3a. The relevant expressions in this interval are listed below:

Step-Down Mode
The equivalent circuits when power flows from the HVS to the LVS are listed in Figure 3. The DHC-LT BDC can work in DCM and continuous current mode (CCM). When the switching frequency is lower than the main resonant frequency and higher than the secondary resonant frequency, DCM appears. On the contrary, the switching frequency is equal to or bigger than the main resonant frequency, and DHC-LT works in CCM. Working in DCM, DHC-LT has three intervals in a half cycle: Intervals A, B and C, as Figure 3 shows. Meanwhile, in CCM, DHC-LT has two intervals: Intervals A and B. Detailed descriptions and explanations of the operational modes in the half period are shown as follows:  Interval B [t1-t2]: At t1, M1, M4, M5 and M8 turn on, and power is transmitted from the HVS to the LVS. The resonant current changes in a sine wave with main resonant frequency fr. At t2, iLr is equal to the sum of iLm1, and iLm2, iCr2 and i58 become zero. The directions of the state variables are shown in Figure 3b. The relevant expressions in Interval B are listed below: n u t n n U di t L dt n n n u t n n U di t L dt n n n u t n n U di t L U u t dt n n Interval C [t2-t3]: M1 and M4 are still on in this interval, but M5 and M8 turn off. As iCr2 and i58 are zero in t2, M5 and M8 turn off under the ZCS condition. The HVS goes into

Step-Up Mode
The equivalent circuits in step-up mode are listed in Figure 4. Similar to step-down mode, DHC-LT can work in CCM mode and DCM mode. Interval C disappears when the working frequency is higher than the main resonant frequency. The corresponding waveforms are described as follows: Step-Up Mode The equivalent circuits in step-up mode are listed in Figure 4. Similar to step-down mode, DHC-LT can work in CCM mode and DCM mode. Interval C disappears when the working frequency is higher than the main resonant frequency. The corresponding waveforms are described as follows:   Interval B [t 1 -t 2 ]: M 5 and M 8 turn on under ZVS at t 1 ; D 1 and D 4 also turn on, and power is transmitted from the LVS to the HVS. The resonant current on the LVS changes in a sine wave until t 2 . The relevant expressions in this interval are listed below: Interval C [t 2 -t 3 ]: M 5 and M 8 are still on in this interval, but no power is transmitted from the LVS to the HVS. The LVS goes into secondary resonance with the frequency of f r2u . The resonant tank is rebuilt by C r2 , T 1 and T 2 . The output current is supplemented by capacitor C H . Since no current flows through the diodes of the HVS, the switch voltages at the HVS are clamped to U H /2. The relevant expressions in this interval are listed below:

Simulation Verification
A simulation in PSIM software is used to verify the analysis. In PSIM, idealized components are used to build circuits, and the trapezoidal method is adopted to solve system equations. In this way, the simulation velocity is increased, and the robustness of the simulation is improved. Figure 5 shows the simulation model of the DHC-LT BDC. R mos_H , R mos_L , R Cr1 , R Cr2 , R Lr , R T1_H , R T2_H , R T1_L , R T2_L , ESR CH and ESR CL are the resistances of the components. In Figure 6a,b and Figure 7a,b, the waveforms in two directions are shown, proving that secondary resonance exists in DCM mode. The output voltages V CD and V AB are not clamped to U L and U H when secondary resonance appears. On the contrary, in Figures 6c and 7c, when the switching frequency increases beyond the main resonant frequency, the resonant currents in the tank, i AB and i CD , are continuous. V CD and V AB are clamped to U L and U H in the half period.

Small-Signal Modeling
By applying the EDF concept and derivation procedures in [27] to the DHC-LT resonant converter, the small-signal mode is illustrated in this section. The open-loop transfer function from the control to the output voltage is shown in List 1 of the Appendix A. As

Small-Signal Modeling
By applying the EDF concept and derivation procedures in [27] to the DHC-LT resonant converter, the small-signal mode is illustrated in this section. The open-loop transfer function from the control to the output voltage is shown in List 1 of the Appendix A. As shown in Figure 8, the low-frequency gain is about −55 dB, so the robustness of the proposed converter is strong, but the dynamic response is slow, which is similar to the LLC resonant converter. As the two sides of the DHC-LT converter are controlled by other converters or clamped by batteries, the fast dynamic response of the DHC-LT converter is not needed to make the DC power system stable, so it can be inferred that the DHC-LT converter is suitable in the DC power use of buildings and community microgrids.

Small-Signal Modeling
By applying the EDF concept and derivation procedures in [27] to nant converter, the small-signal mode is illustrated in this section. The function from the control to the output voltage is shown in List 1 of th shown in Figure 8, the low-frequency gain is about −55 dB, so the rob posed converter is strong, but the dynamic response is slow, which is resonant converter. As the two sides of the DHC-LT converter are c converters or clamped by batteries, the fast dynamic response of the D not needed to make the DC power system stable, so it can be inferred converter is suitable in the DC power use of buildings and community

Improved FHA with Modification of AC Load Impedance
In this section, an improved FHA method is proposed to impro calculation. The main work is modifying the AC load impedance in the the phase angle of the AC load.
Traditional FHA is a simple and direct method to calculate volt essential for the design of resonant DC-DC converters, such as LLC a converters. Compared to traditional FHA, the improved FHA method damental waveforms of the AC output voltage and current in DCM mo angle of the AC load impedance is obtained by Fourier decomposition culation. The procedure of the improved FHA is: (1) calculate the ou resonant tank in Interval C, USD or USU; (2) extract the fundamental

Improved FHA with Modification of AC Load Impedance
In this section, an improved FHA method is proposed to improve the accuracy of calculation. The main work is modifying the AC load impedance in the FHA, considering the phase angle of the AC load.
Traditional FHA is a simple and direct method to calculate voltage gain, which is essential for the design of resonant DC-DC converters, such as LLC and series-resonant converters. Compared to traditional FHA, the improved FHA method establishes the fundamental waveforms of the AC output voltage and current in DCM mode. Thus, the phase angle of the AC load impedance is obtained by Fourier decomposition and taken for calculation. The procedure of the improved FHA is: (1) calculate the output voltage of the resonant tank in Interval C, U SD or U SU ; (2) extract the fundamental components of the output voltage and current; (3) compute the output impedance of the resonant tank considering its phase angle; (4) calculate the new DC voltage gain using the output impedance in (3) as the AC output load.

Improved FHA in Step-Down Mode
The equivalent FHA circuit in step-down mode is shown in Figure 9, and relevant waveforms are shown in Figure 10.

Improved FHA in Step-Down Mode
The equivalent FHA circuit in step-down mode is shown in Figure 9, and r waveforms are shown in Figure 10. Figure 9. Equivalent FHA circuit in step-down mode (The symbols of "*" are dotted terminal  output voltage and current; (3) compute the output impedance of the resonant tank considering its phase angle; (4) calculate the new DC voltage gain using the output impedance in (3) as the AC output load.

Improved FHA in Step-Down Mode
The equivalent FHA circuit in step-down mode is shown in Figure 9, and relevant waveforms are shown in Figure 10. Figure 9. Equivalent FHA circuit in step-down mode (The symbols of "*" are dotted terminals of T2).   With the method of Fourier decomposition, the angle between the fundamental wave of the output AC current i CD and the fundamental wave of the input AC voltage u CD , ϕ 1 , is estimated as The angle between the fundamental wave of the output AC voltage u CD and the fundamental wave of the input AC voltage u AB , θ 1 , is estimated as In the above equation Therefore, the output AC impedance is R o,e,MSD is obtained by Reference [36]. R o,SD is the DC load in step-down mode.
The RMS value of the output AC peak voltage, U CD,FHA , is expressed as The RMS value of the input AC peak voltage u AB , FHA, is expressed as The modified voltage conversion ratio is In the above equation

Improved FHA in Step-Up Mode
The equivalent FHA circuit in step-up mode is shown in Figure 11, and relevant waveforms are shown in Figure 12.

Improved FHA in Step-Up Mode
The equivalent FHA circuit in step-up mode is shown in Figure 11, and relevant waveforms are shown in Figure 12. With the method of Fourier decomposition, the angle between the fundamental wave of the output AC current iAB and the fundamental wave of the input AC voltage uAB, ϕ 2 , is estimated as The angle between the fundamental wave of the input AC voltage uCD and the fundamental wave of the output AC voltage uAB, θ 2 , is estimated as  [36]. Ro,SU is the DC load in step-up mode.

Comparison of Different Modeling Approaches
In order to prove the effectiveness of the improved FHA method propo per, the methods of the experiment, the improved FHA in this paper, traditio with an improved model of the AC port equivalent resistance in [36] and With the method of Fourier decomposition, the angle between the fundamental wave of the output AC current i AB and the fundamental wave of the input AC voltage u AB , ϕ 2 , is estimated as The angle between the fundamental wave of the input AC voltage u CD and the fundamental wave of the output AC voltage u AB , θ 2 , is estimated as Therefore, the output AC impedance in the HVS is R o,e,MSU is obtained by Reference [36]. R o,SU is the DC load in step-up mode.
The modified voltage conversion ratio is In the above equation

Comparison of Different Modeling Approaches
In order to prove the effectiveness of the improved FHA method proposed in this paper, the methods of the experiment, the improved FHA in this paper, traditional FHA, FHA with an improved model of the AC port equivalent resistance in [36] and simulation are used simultaneously. The simulation results almost coincide with the experimental results, which means that the simulation model is effective. The parameters of the experimental prototype are listed in Section 5. In Figures 13 and 14, the errors between the experimental results and other methods are minimum around the main resonant frequency. The reason is that, when the DHC-LT converter is working around the main resonant frequency, resonant voltages and resonant currents in the tank are sinusoidal waveforms, and nearly no distortion exists. As the working frequency is reduced, the methods of traditional FHA and FHA with the improved model of the AC port equivalent resistance have a major error. However, when the phase angle of the AC load is considered, in Figure 13, from 80 kHz to 120 kHz, the biggest error between the improved FHA in this paper and the experimental results is around 9%, less than the other methods. Similarly, in Figure 14, from 80 kHz to 120 kHz, the biggest error between the improved FHA in this paper and the experimental results is around 10%. The working frequencies under the peak voltage gain in the improved FHA and experiments are almost the same. The theoretical work is verified by experiments and found to be in good agreement. Therefore, the improved FHA method in Section 3 of this paper is effective in describing the gain characteristics of the DHC-LT converter.
results is around 9%, less than the other methods. Similarly, in Figure 14, from 80 kHz 120 kHz, the biggest error between the improved FHA in this paper and the experiment results is around 10%. The working frequencies under the peak voltage gain in the improve FHA and experiments are almost the same. The theoretical work is verified by experimen and found to be in good agreement. Therefore, the improved FHA method in Section 3 this paper is effective in describing the gain characteristics of the DHC-LT converter.

Experimental Results
A 2.5 kW experimental prototype was established in the lab. Table 1 shows its p rameters. A DSP of TMS320F280048 is used to control the proposed DHC-LT converte To realize ZVS, Lm1 and Lm2 are set comparatively small. The power is transmitted main from T1, so the ratio of T1 is mainly designed by the voltage gain of the converter. As result, n1 is significantly smaller than n2. Compared to CDT-LC, the capacitance of Cr2 much smaller than that of the LVS resonant capacitor, which is 4.5 μF in [29]. The MOSFE results is around 9%, less than the other methods. Similarly, in Figure 14, from 80 kHz to 120 kHz, the biggest error between the improved FHA in this paper and the experimental results is around 10%. The working frequencies under the peak voltage gain in the improved FHA and experiments are almost the same. The theoretical work is verified by experiments and found to be in good agreement. Therefore, the improved FHA method in Section 3 of this paper is effective in describing the gain characteristics of the DHC-LT converter.

Experimental Results
A 2.5 kW experimental prototype was established in the lab. Table 1 shows its parameters. A DSP of TMS320F280048 is used to control the proposed DHC-LT converter. To realize ZVS, Lm1 and Lm2 are set comparatively small. The power is transmitted mainly from T1, so the ratio of T1 is mainly designed by the voltage gain of the converter. As a result, n1 is significantly smaller than n2. Compared to CDT-LC, the capacitance of Cr2 is much smaller than that of the LVS resonant capacitor, which is 4.5 μF in [29]. The MOSFET

Experimental Results
A 2.5 kW experimental prototype was established in the lab. Table 1 shows its parameters. A DSP of TMS320F280048 is used to control the proposed DHC-LT converter. To realize ZVS, L m1 and L m2 are set comparatively small. The power is transmitted mainly from T 1 , so the ratio of T 1 is mainly designed by the voltage gain of the converter. As a result, n 1 is significantly smaller than n 2 . Compared to CDT-LC, the capacitance of C r2 is much smaller than that of the LVS resonant capacitor, which is 4.5 µF in [29]. The MOSFET on the HVS, SRC60R022FB, has a fast-recovery body diode, which is an advantage when power is transmitted from the LVS to the HVS. The MOSFET on the LVS, FDP2D3N10C, is used as a synchronous rectifier to attain higher efficiency.  Figure 15 shows the experimental results of the prototype converter. In Figure 15, U gs1 is the drive signal of M 1 , U ds1 is the D-S voltage of M 1 , U gs5 is the drive signal of M 5 , U ds5 is the D-S voltage of M 5 and i Lr is the current of the resonant inductor.  Figure 15 shows the experimental results of the prototype converter. In Figure 15, Ugs1 is the drive signal of M1, Uds1 is the D-S voltage of M1, Ugs5 is the drive signal of M5, Uds5 is the D-S voltage of M5 and iLr is the current of the resonant inductor.  Figure 15a,b shows the experimental results in step-down mode. In Figure 15a, the working frequency is around 125 kHz, which is the main resonant frequency. Therefore, the currents in the resonant tank are almost sinusoidal, which is determined by the designed resonant network. In Figure 15b, the working frequency is around 90 kHz, and secondary resonance happens when the main resonance ends. Figure 15c,d shows the experimental results in step-up mode. In Figure 15c, ZVS is Figure 15. Experimental results of the prototype converter: (a) working frequency is 125 kHz, and load is 1 Ω, step-down mode; (b) working frequency is 90 kHz, and load is 2.5 Ω, step-down mode (c) ZVS in step-up mode; (d) working frequency is 160 kHz, and load is 1.4 Ω, step-down mode. Figure 15a,b shows the experimental results in step-down mode. In Figure 15a, the working frequency is around 125 kHz, which is the main resonant frequency. Therefore, the currents in the resonant tank are almost sinusoidal, which is determined by the designed resonant network. In Figure 15b, the working frequency is around 90 kHz, and secondary resonance happens when the main resonance ends. Figure 15c,d shows the experimental results in step-up mode. In Figure 15c, ZVS is realized. U ds5 decreases to 0, before U gs5 comes. The dead time of 300 ns in this prototype is wide enough for both the HVS and LVS power switches, while the efficiency is not affected. In Figure 15d, as the working frequency is higher than the main resonant frequency, secondary resonance does not exist, which is consistent with Section 2.2.2.

Experimental Results of Steady-State Operation
The efficiency curves of the DHC-LT converter are shown in Figure 16, which were obtained by experiments. In step-down mode, the peak efficiency is 97.3% when the LVS voltage is 50 V, while the efficiency with 100% load is 96.8%. In step-up mode, the peak efficiency is 97.4% when the LVS voltage is 50 V, while the efficiency with 100% load is 95.7%. The resonant capacitor C r2 is moved from the LVS to the HVS, and the heat it produces decreases. As a result, it can be seen that the efficiency of the 2.5 kW DHC-LT converter is higher than that of the 2.5 kW CDT-LC in step-down mode [29]. The advantage of DHC-LT is shown through comparison.

Discussion of Phase-Shift Control
In order to reduce the output voltage, broaden the output voltage range and pro ripple-free charging current for batteries, a fixed-frequency phase-shift strategy is duced according to the DHC-LT converter [38]. When the voltage gain is high, trad PFM control is adopted. The gate signals of M1 and M4 are the same. M1 and M2 co alternately, as do M3 and M4. When the voltage gain decreases, the switching frequen creases until it reaches its upper limit, 200 kHz. Then, as shown in Figure 17, when the frequency phase-shift strategy is adopted in step-down mode, the switching frequen mains constant, and the phase angle between gate signals of M1 and M4, M2 and M3 inc When the phase angle increases, the RMS of the input voltage of resonant tank uAB dec As a result, the voltage gain is further reduced compared to eht traditional PFM cont In Figure 17, as the turn-off current of the leading leg, M1 and M2, is higher tha of the lagging leg, M3 and M4, in order to guarantee ZVS of four MOSFETs, the dea of the HVS MOSFETs should meet the requirement

Discussion of Phase-Shift Control
In order to reduce the output voltage, broaden the output voltage range and provide a ripple-free charging current for batteries, a fixed-frequency phase-shift strategy is introduced according to the DHC-LT converter [38]. When the voltage gain is high, traditional PFM control is adopted. The gate signals of M 1 and M 4 are the same. M 1 and M 2 conduct alternately, as do M 3 and M 4 . When the voltage gain decreases, the switching frequency increases until it reaches its upper limit, 200 kHz. Then, as shown in Figure 17, when the fixed-frequency phase-shift strategy is adopted in step-down mode, the switching frequency remains constant, and the phase angle between gate signals of M 1 and M 4 , M 2 and M 3 increases. When the phase angle increases, the RMS of the input voltage of resonant tank u AB decreases. As a result, the voltage gain is further reduced compared to eht traditional PFM control. In Figure 17, as the turn-off current of the leading leg, M 1 and M 2 , is higher than that of the lagging leg, M 3 and M 4 , in order to guarantee ZVS of four MOSFETs, the dead time of the HVS MOSFETs should meet the requirement i AB,off can be obtained when the voltage of C r1 and C r2 is 0. Figure 18 shows the waveforms using the fixed-frequency phase-shift strategy in step-down mode. i Lr decreases when MOSFETs on the leading leg turn off and MOSFETs on the lagging leg turn on. The working frequency reaches its upper limit, 200 kHz. ZVS is realized as the phase-shift angle is small.  Figure 18 shows the waveforms using the fixed-frequency phase-sh step-down mode. iLr decreases when MOSFETs on the leading leg turn off a on the lagging leg turn on. The working frequency reaches its upper limit, is realized as the phase-shift angle is small. Figure 18. Waveforms using fixed-frequency phase-shift strategy in step-down mod

Verification in Battery/PV System
To verify the proposed DHC-LT converter in a battery/PV system, the b Figure 18. Waveforms using fixed-frequency phase-shift strategy in step-down mode.

Verification in Battery/PV System
To verify the proposed DHC-LT converter in a battery/PV system, the battery/PV test system diagram is shown in Figure 19. In Figure 19a, the maximum power point tracking (MPPT) DC-DC converter and the DHC-LT bidirectional DC-DC converter transfer the energy from the PV and batteries to the 400 V DC bus. The power PV generated is stored in batteries and expended in the DC load. When the DC load is heavier than the power PV generated, the batteries start to release power to the DC bus and the DC load. Figure 19b shows the prototype of the DC power system, which consists of the MPPT DC-DC converter, the DHC-LT DC-DC converter and their control system. In Figure 19c, one DC source is used to simulate PV, while the other electronic load is used as the DC load on the 400 V bus. They are both controlled by the host computer on the desk. Figure 18. Waveforms using fixed-frequency phase-shift strategy in step-down mode.

Verification in Battery/PV System
To verify the proposed DHC-LT converter in a battery/PV system, the battery/PV system diagram is shown in Figure 19. In Figure 19a, the maximum power point track (MPPT) DC-DC converter and the DHC-LT bidirectional DC-DC converter transfer energy from the PV and batteries to the 400 V DC bus. The power PV generated is sto in batteries and expended in the DC load. When the DC load is heavier than the po PV generated, the batteries start to release power to the DC bus and the DC load. Fig  19b shows the prototype of the DC power system, which consists of the MPPT DC converter, the DHC-LT DC-DC converter and their control system. In Figure 19c, one source is used to simulate PV, while the other electronic load is used as the DC load the 400 V bus. They are both controlled by the host computer on the desk. Waveforms in the battery/PV test system are shown in Figure 20. Figure 20a,b shows the variation of battery voltage Ubat and battery current Iba, when the DC load changes. Ubat changes little because the battery voltage is mainly determined by the ideal voltage source inside. Figure 20c shows the waveforms, and when the illumination intensity decreases, the PV current Ipv decreases as a result. Then, the MPPT arithmetic works, Ipv increases and PV voltage Upv decreases to reach the new maximum power point. Waveforms in the battery/PV test system are shown in Figure 20. Figure 20a,b shows the variation of battery voltage U bat and battery current I ba , when the DC load changes. U bat changes little because the battery voltage is mainly determined by the ideal voltage source inside. Figure 20c shows the waveforms, and when the illumination intensity decreases, the PV current I pv decreases as a result. Then, the MPPT arithmetic works, I pv increases and PV voltage U pv decreases to reach the new maximum power point.
Waveforms in the battery/PV test system are shown in Figure 20. Figure 20a,b shows the variation of battery voltage Ubat and battery current Iba, when the DC load changes. Ubat changes little because the battery voltage is mainly determined by the ideal voltage source inside. Figure 20c shows the waveforms, and when the illumination intensity decreases, the PV current Ipv decreases as a result. Then, the MPPT arithmetic works, Ipv increases and PV voltage Upv decreases to reach the new maximum power point.

Conclusions
A novel 400 V-50 V bidirectional DHC-LT converter is proposed in this paper. The topology structure and operation principles are discussed in detail. By moving the resonant capacitor from the LVS to the HVS, the volume and the conduction loss of the DHC-LT converter are decreased, the ZVS + ZCS characteristics are reserved, and a wide voltage range is obtained as well, which is proved by simulation. The Bode plot of the DHC-LT converter shows the converter is robust and suitable for DC power use of buildings and microgrids. To increase the accuracy of the FHA in the DHC-LT converter, the error factor of the FHA in resonant converters is analyzed, which are the AC output resistance and the phase angle. Then, an

Conclusions
A novel 400 V-50 V bidirectional DHC-LT converter is proposed in this paper. The topology structure and operation principles are discussed in detail. By moving the resonant capacitor from the LVS to the HVS, the volume and the conduction loss of the DHC-LT converter are decreased, the ZVS + ZCS characteristics are reserved, and a wide voltage range is obtained as well, which is proved by simulation. The Bode plot of the DHC-LT converter shows the converter is robust and suitable for DC power use of buildings and microgrids. To increase the accuracy of the FHA in the DHC-LT converter, the error factor of the FHA in resonant converters is analyzed, which are the AC output resistance and the phase angle. Then, an equivalent AC impedance model of the rectifier valid for DCM is proposed. By exacting FHA components from the output voltage and rectifier current, the phase angle of the AC impedance is taken into consideration. Therefore, the behavior in the resonant tank is described more precisely; the biggest relative error of voltage gain in step-down mode is around 9%, and that in step-up mode is around 10%, which is clearly lower than that of traditional FHA. The improved FHA method is proved to be effective. Then, a 2.5 kW DHC-LT prototype is established in the lab. The waveforms in CCM and DCM are presented, and the operation principles are confirmed. The peak efficiency is 97.3% in step-down mode, while the peak efficiency is 97.4% in step-up mode. By moving the resonant capacitor, the efficiency increases compared to the CDT-LC. A fixed-frequency phase-shift strategy is adopted to reduce the voltage gain, while ZVS is reserved by setting the dead time and the phase-shift angle reasonably. Finally, a battery/PV test system is established to verify the effectiveness of the DHC-LT converter in DC buildings and community microgrids.

Conflicts of Interest:
The authors declare no conflict of interest.

1.
Open-loop transfer function of the DHC-LT converter. Derivation of U CD and I CD in step-down mode.
In Interval C of step-down mode, i AB is approximately constant. Its value remains near the value of i AB in T main and i AB (T main ). Because the calculation of i AB (T main ) is complicated, it is estimated by half of the peak input current in the HVS resonant tank.
To facilitate the calculation, M rSD is defined as the voltage ratio at the main resonant frequency in step-down mode. The M rSD is obtained by the traditional FHA method when the switching frequency is equal to the main resonant frequency.
In Interval C, u Cr2 remains almost unchanged.
u Cr2 (T main ) = u Cr2 (T s /2) = −u Cr2 (0) (A3) In Interval C, i Lm1 and i Lm2 change a little, and i Lr is small, so the voltage of magnetizing inductance L m1 and L m2 in the HVS, u Lm1 (T main ) and u Lm2 (T main ), can form the following equations.
u Lm1 (T main ) and u Lm2 (T main ) can be expressed by u Lm1 (T main ) = (−L m2 /L m1 − 1)u Cr2 (T main ) u Lm2 (T main ) = L m2 (L m2 /L m1 + 1)/L m1 ·u Cr2 (T main ) The output voltage of the resonant tank in T main is As a result, u CD can be described as