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Dynamic Enhancement for Dual Active Bridge Converter with a Deadbeat Current Controller

This paper investigates the deadbeat current controllers for isolated bidirectional dual-active-bridge dc-dc converter (IBDC), including the peak current mode (PCM) and middle current mode (MCM). The controller uses an enhanced single phase shift (ESPS) modulation method by exploiting pulse width as an extra control variable in addition to phase shift ratio. The control variables for PCM controllers are derived in detail and the two different current controllers are compared. A double-closed-loop control method is then employed, which could directly control the high-frequency inductor current and eliminate the transient DC current bias of the transformer. Furthermore, load feedforward was introduced to further enhance the dynamic of the converter. With the proposed control method, the settling time could be reduced within several PWM cycles during load disturbance without transient DC current bias. A 5 kW IBDC converter prototype was built and the settling time of 6 PWM cycles during load change with voltage regulation mode was achieved, which verifies the superior dynamic performance of the control method.


Introduction
The isolated bi-directional dual-active-bridge dc-dc converter (IBDC) has been a hot topic in recent years due to its simple structure, high efficiency and ultrafast response [1]. The transient DC current offset of the transformer and the inductor, which might saturate the transformer and increase the system's current stress during the abrupt load change, has attracted people's attention. Different dynamic modulation methods have been proposed to solve the problem [2][3][4][5]. Additionally, to increase the dynamics of IBDCs, the current mode controller could be a competitive alternative. It also has other inherent benefits including over-current protection, elimination of transient DC current offset and easy implementation of current sharing between multiple IBDCs [6].
Digital predictive current controllers based on conventional single phase shift (CSPS) modulation was proposed in [7,8], where the phase shift ratio was used to control the transformer current. In [7], the average current calculated by an analog integrator of the DC bus current was used as the feedback signal, which can achieve fast dynamic performance. However, transient DC current offset occurs during the sudden change in phase shift ratio for CSPS modulation.
The predictive duty cycle mode (PDCM) controller, shown in Figure 1b, was proposed in [6] to eliminate the transient DC current offset, which was applied in [8]. The drive signals of the primary side are fixed. The transformer current needs to be oversampled, and duty cycles d1 for S2,3 and d2 for S1,4 are calculated in turn in every half cycle. Another limitation of this method is that the controller only works in the ZVS range (IP1 > 0) shown in Figure 1b and may lose effectiveness when IP1 < 0. A deadbeat current controller based on the middle current and enhanced PWM modulation was proposed in [9]. However, regulation of the output voltage and current was not introduced, which is more important in real application. To overcome the drawbacks, this paper investigated the deadbeat current controllers, including the peak current mode (PCM) and middle current mode (MCM). Based on the controllers, a double-closed-loop control method with load feedforward was introduced. Furthermore, a 5 kW IBDC converter prototype was built, and the settling time of 6 PWM cycles during load change could be achieved, which validates its superior dynamic performance.

Basic Model of IBDC for SPS Modulation
The basic model of SPS modulation-based IBDC is presented prior to introducing the proposed current controller. Figure 2 illustrates the theoretical waveforms of the IBDC using the SPS modulation method when converter voltage gain 1 k ≥ , where k = V1/(nV2) and n is the turn ratio of the transformer. The waveforms are symmetrical for the same transmission power of two opposite directions. The symbols in Figure 2 are defined as follows: TS is the switching cycle, f is the switching frequency, D is the phase shift ratio and tph is the shifted time. D ≥ 0 (tph ≥ 0) stands for P ≥ 0 and D < 0 (tph < 0) for P < 0. IP1 and IP2 are the two "switching currents" and IP2 is the peak current when k > 1. The middle current IM, defined as the instantaneous A deadbeat current controller based on the middle current and enhanced PWM modulation was proposed in [9]. However, regulation of the output voltage and current was not introduced, which is more important in real application. To overcome the drawbacks, this paper investigated the deadbeat current controllers, including the peak current mode (PCM) and middle current mode (MCM). Based on the controllers, a double-closed-loop control method with load feedforward was introduced. Furthermore, a 5 kW IBDC converter prototype was built, and the settling time of 6 PWM cycles during load change could be achieved, which validates its superior dynamic performance.

Basic Model of IBDC for SPS Modulation
The basic model of SPS modulation-based IBDC is presented prior to introducing the proposed current controller. Figure 2 illustrates the theoretical waveforms of the IBDC using the SPS modulation method when converter voltage gain k ≥ 1, where k = V 1 /(nV 2 ) and n is the turn ratio of the transformer. The waveforms are symmetrical for the same transmission power of two opposite directions. A deadbeat current controller based on the middle current and enhanced PWM modulation was proposed in [9]. However, regulation of the output voltage and current was not introduced, which is more important in real application. To overcome the drawbacks, this paper investigated the deadbeat current controllers, including the peak current mode (PCM) and middle current mode (MCM). Based on the controllers, a double-closed-loop control method with load feedforward was introduced. Furthermore, a 5 kW IBDC converter prototype was built, and the settling time of 6 PWM cycles during load change could be achieved, which validates its superior dynamic performance.

Basic Model of IBDC for SPS Modulation
The basic model of SPS modulation-based IBDC is presented prior to introducing the proposed current controller. Figure 2 illustrates the theoretical waveforms of the IBDC using the SPS modulation method when converter voltage gain 1 k ≥ , where k = V1/(nV2) and n is the turn ratio of the transformer. The waveforms are symmetrical for the same transmission power of two opposite directions. The symbols in Figure 2 are defined as follows: TS is the switching cycle, f is the switching frequency, D is the phase shift ratio and tph is the shifted time. D ≥ 0 (tph ≥ 0) stands for P ≥ 0 and D < 0 (tph < 0) for P < 0. IP1 and IP2 are the two "switching currents" and IP2 is the peak current when k > 1. The middle current IM, defined as the instantaneous The symbols in Figure 2 are defined as follows: TS is the switching cycle, f is the switching frequency, D is the phase shift ratio and tph is the shifted time. D ≥ 0 (t ph ≥ 0) stands for P ≥ 0 and D < 0 (t ph < 0) for P < 0. I P1 and I P2 are the two "switching currents" and I P2 is the peak current when k > 1. The middle current IM, defined as the instantaneous current at T S /2, is taken into consideration instead of the average current, which equals zero in one cycle. The basic equations for the IBDC are derived as follows:

Sampling, interupt and calculation
The relationships among the variables P, I P1 , I P2 , I M , D and t ph at steady state can then be derived. Therefore, for a given value of one variable, other variables can be calculated.

Peak Current Mode Controller
Peak current mode (PCM) controllers are introduced in this section. Figure 3a,b show the transient waveforms of a PCM current controller in one cycle for forward and reverse power transmission, respectively. P 1 , P 2 , P 3 and P 4 are the drive signals for the primary side and S 1 , S 2 , S 3 and S 4 are the drive signals for the secondary side. The variable t ph,ref is shifted-time at the steady state for the given I P2,ref which can be derived from (1). A sawtooth carrier with the same frequency of the converter was utilized to generate the reference signals. The "switching on" moment t 1 and "switching off" moment t 2 should meet the constrains as: 0 < t 1 < T S /2 and 3T S /4 < t 2 < T S . The variables t D and t W are defined as "delay time" and "width time", respectively. P ref is the power reference, and I P2,ref and I P1,ref are the references for the corresponding "switching currents", respectively.
Micromachines 2022, 13, x FOR PEER REVIEW 3 of 13 current at TS/2, is taken into consideration instead of the average current, which equals zero in one cycle. The basic equations for the IBDC are derived as follows: The relationships among the variables P, IP1, IP2, IM, D and tph at steady state can then be derived. Therefore, for a given value of one variable, other variables can be calculated.

Peak Current Mode Controller
Peak current mode (PCM) controllers are introduced in this section. Figure 3a,b show the transient waveforms of a PCM current controller in one cycle for forward and reverse power transmission, respectively. P1, P2, P3 and P4 are the drive signals for the primary side and S1, S2, S3 and S4 are the drive signals for the secondary side. The variable tph,ref is shifted-time at the steady state for the given IP2,ref which can be derived from (1). A sawtooth carrier with the same frequency of the converter was utilized to generate the reference signals. The "switching on" moment t1 and "switching off" moment t2 should meet the constrains as: 0 < t1 < TS/2 and 3TS/4 < t2 < TS. The variables tD and tW are defined as "delay time" and "width time", respectively. Pref is the power reference, and IP2,ref and IP1,ref are the references for the corresponding "switching currents", respectively. , ,

Sampling and interupt
Parameters update

Sampling and interupt
Parameters update As shown in Figure 3a, there are two cases according to the initial current I 0 and reference current I p2,ref : u 2 leads u 1 (t ph < 0) for the solid line waveforms and u 2 lags u 1 (t ph > 0) for dotted line waveforms. For the sake of brevity, the superposition principle was used to derivate the inductor current when calculating t D and t W.
For forward power transmission, the requirement was imposed that I P2 = I P2,ref and t ph,ref > 0. According to the superposition principle, the inductor current ripple ∆I L during 0 and 3T S /4 can be calculated by adding up the two ripple currents as follows: where ∆I L,u 1 and ∆I L,u 2 are current ripples generated by the two dependent voltage source u 1 and u 2 , respectively. t D is then derived as: Furthermore, t W is derived as: With regard to reverse power transmission, the switching current at t 2 is set to be-I P1,ref and t ph,ref < 0 as shown in Figure 4. Similar to forward power transmission, t D and t W can be obtained. Thus, the equations for the PCM controller are written as: Micromachines 2022, 13, x FOR PEER REVIEW 5 of 13

Double-Closed-Loop Control with Load Feedforward
In practice, instead of the high-frequency inductor current, the DC voltage, current or power should always be regulated. In this section, the voltage mode control strategy based on the MCM-ESPS controller is introduced. Figure 4 shows the output voltage control scheme based on the deadbeat current controller, where two control loops are involved. The load feedforward control could substantially increase the system dynamic [11,12]. In order to improve the stability of output voltage under load disturbance, load feedforward under double-closed-loop control is presented. As shown in Figure 4, the feedforward current iM,F corresponding to the load was superimposed on the current reference iM,VR, which is the output of the outer voltage loop, to form the final current reference value iM,ref.
The relationships of the middle current were derived as: Without considering the power loss of the converter, we could obtain: Thus, the relationship between the middle current IM and the load current io could be expressed as (9) and (10): As in the aforementioned Equations (6) and (7), initial current I 0 is sampled to calculate the t D and t W . However, a one-cycle delay exists between the sampling instant and control update due to the algorithm implementation of the digital processor. I P2 for the PCM controller is sampled at 3T S /4, and DSP interrupt occurs to calculate the new parameters shown in Figure 3. t D and t W update at the beginning of the next cycle. Assuming DC bus voltage V 1 and V 2 are constant in two adjacent periods, the relationships between the I P2 (n − 1), I M (n − 1) in the (n − 1)th cycle and the initial current in the nth switching cycle I 0 (n) could be derived as: According to the power transmission directions in two adjacent cycles, four situations are considered for the PCM controller: case 1 when P ref (n − 1) ≥ 0 and P ref (n) ≥ 0; case 2 when P ref (n − 1) < 0 and P ref (n) ≥ 0; case 3 when P ref (n − 1) ≥ 0 and P ref (n) < 0; and case 4 when P ref (n − 1) < 0 and P ref (n) < 0. Combining (6)-(9), the control variables t D and t W with delay compensation can be derived as shown in Table 1. With the control variables in Table 1, the inductor peak current could be tracked to the reference in two cycles, which is consistent with the idea of the deadbeat control in ref [10].

Double-Closed-Loop Control with Load Feedforward
In practice, instead of the high-frequency inductor current, the DC voltage, current or power should always be regulated. In this section, the voltage mode control strategy based on the MCM-ESPS controller is introduced. Figure 4 shows the output voltage control scheme based on the deadbeat current controller, where two control loops are involved. The load feedforward control could substantially increase the system dynamic [11,12]. In order to improve the stability of output voltage under load disturbance, load feedforward under double-closed-loop control is presented. As shown in Figure 4, the feedforward current i M,F corresponding to the load was superimposed on the current reference i M,VR , which is the output of the outer voltage loop, to form the final current reference value i M,ref .
The relationships of the middle current were derived as: Without considering the power loss of the converter, we could obtain: Thus, the relationship between the middle current I M and the load current i o could be expressed as (9) and (10): The small signal model of the system, as shown in Figure 5, can be obtained from the control block diagram in Figure 4, where i S is the average output current of an H bridge in a single period and G o (s) is the transfer function of capacitance voltage and capacitance current, denoted as: The average output current of H bridge in the secondary side is derived as: Combing (1) with (16), the GMS(s) could be derived as: According to the small signal model in Figure 5, the output impedance Ro1(s) without and with feedforward could be calculated as (17) and (18), respectively. G VR (s) is the volatge regulation transfer function, where the conventional PI controller is always used. K P and K I are the proportional and integral coefficients of the PI regulator, respectively. Thus, we could obtain: G F (s) represents the transfer function of the load feedforward and G MS (s) is the relationship between i M and i s . G C (s) is the transfer function of the deadbeat current controller. Considering a one-cylce delay, it could be written as: The feedforward transfer function G F (s) can be calculated using small-signal analysis based on Equation ( The average output current of H bridge in the secondary side is derived as: Combing (1) with (16), the G MS (s) could be derived as: According to the small signal model in Figure 5, the output impedance R o1 (s) without and with feedforward could be calculated as (17) and (18), respectively.
By substituting the circuit parameters and control parameters into Equations (17) and (18), baud diagrams of output impedance with different loads under the double-closed-loop control strategy can be drawn as shown in Figure 6. In this case, the inductance L = µH, the voltage V 1 = 300V and V 2 = 280V.The coefficients of the PI regulator are K P = 2 and K I = 4000.
By substituting the circuit parameters and control parameters into Equations (17) and (18), baud diagrams of output impedance with different loads under the double-closedloop control strategy can be drawn as shown in Figure 6. In this case, the inductance L = μH, the voltage V1 = 300V and V2 = 280V.The coefficients of the PI regulator are KP = 2 and KI = 4000. As shown in Figure 6, the closed-loop output impedance at low frequency decreases significantly after the feedforward is added. When IM = 4 A, the output impedance at a frequency of 100 Hz decreases from −15 dB to −35 dB, whereas when IM = 15 A, the output impedance decreases from −8 dB to −30 dB at 100 Hz. If the frequency is further reduced, the amplitude attenuation of the closed-loop output impedance brought by the feedforward control become more obvious, which indicates a more robust output voltage under the load disturbance.

Experimental platform
The laboratory IBDC experimental platform shown in Figure 7 was used to verify the proposed control method. The main circuit parameters are listed in Table 2. The current sensor LA55-P had a 200 kHz bandwidth from LEM. PE-Expert4 from Myway was utilized as the digital controller including DSP and FPGA cores. FPGA XC6SLX45 was used to generate PWM signals. The control variables were calculated in each cycle in DSP, and the corresponding PWM compare values CMP1 and CMP2 were updated at the beginning of the next cycle. As shown in Figure 6, the closed-loop output impedance at low frequency decreases significantly after the feedforward is added. When I M = 4 A, the output impedance at a frequency of 100 Hz decreases from −15 dB to −35 dB, whereas when I M = 15 A, the output impedance decreases from −8 dB to −30 dB at 100 Hz. If the frequency is further reduced, the amplitude attenuation of the closed-loop output impedance brought by the feedforward control become more obvious, which indicates a more robust output voltage under the load disturbance.

Experimental Platform
The laboratory IBDC experimental platform shown in Figure 7 was used to verify the proposed control method. The main circuit parameters are listed in Table 2. The current sensor LA55-P had a 200 kHz bandwidth from LEM. PE-Expert4 from Myway was utilized as the digital controller including DSP and FPGA cores. FPGA XC6SLX45 was used to generate PWM signals. The control variables were calculated in each cycle in DSP, and the corresponding PWM compare values CMP1 and CMP2 were updated at the beginning of the next cycle.

Comparisons of Different Current Controllers for Forward Power Transmission
The performance of the CSPS modulation-based current controller in [5] and the proposed ESPS-PCM were compared for the forward power transmission mode. Figure 8 shows the experimental waveforms of current i L when the references have step changes. The references could be tracked for all the controllers when the current reference steps up from 3 A to 8 A and steps down from 8 A to 3 A. The settling time t set in Figure 8a is obvious, while the settling time in Figure 8b

Comparisons of Different Current Controllers for Forward Power Transmission
The performance of the CSPS modulation-based current controller in [5] and the proposed ESPS-PCM were compared for the forward power transmission mode. Figure 8 shows the experimental waveforms of current iL when the references have step changes. The references could be tracked for all the controllers when the current reference steps up from 3 A to 8 A and steps down from 8 A to 3 A. The settling time tset in Figure 8a is obvious, while the settling time in Figure 8b  To verify the performance of the current controllers during bidirectional power transmission, a sequence of current references was set to investigate the response.  To verify the performance of the current controllers during bidirectional power transmission, a sequence of current references was set to investigate the response. Figure 9 shows the waveforms of the ESPS-PCM controller. The transmission power P stepped up from 600 W to 1450 W at t 1 , changed direction to −1450 W at t 3 , reversed direction to 1450 W at t 5 and then stepped down to 600 W at t 7 . The current references were smoothly reached with a one-cycle delay during the whole transient process, including the transition between two opposite power transmissions.
Micromachines 2022, 13, x FOR PEER REVIEW 9 of 13 9 shows the waveforms of the ESPS-PCM controller. The transmission power P stepped up from 600 W to 1450 W at t1, changed direction to −1450 W at t3, reversed direction to 1450 W at t5 and then stepped down to 600 W at t7. The current references were smoothly reached with a one-cycle delay during the whole transient process, including the transition between two opposite power transmissions.

Dynamic Performance Comparison between Different Control Methods
The experimetal results with traditional single-voltage loop control, double-closedloop control and double-closed-loop control with feedforward under load disturbance are shown in Figures 10-12. The output voltage V2 was 280 V, and the load increased abruptly

Dynamic Performance Comparison between Different Control Methods
The experimetal results with traditional single-voltage loop control, double-closedloop control and double-closed-loop control with feedforward under load disturbance are shown in Figures 10-12. The output voltage V 2 was 280 V, and the load increased abruptly at t 1 with load resistance decreases from 75 Ω to 25 Ω and decreased sharply at t 2 with load resistance increases from 25 Ω to 75 Ω. When the load increases, the DC voltage will fall, and the control loop will increase the phase shift angle to transfer more power to maintain the DC load. Simillarly, when the DC load decreases, the DC voltage will rise and the control loop will decrease the phase shift angle to reduce the transmitted power.

Dynamic Performance Comparison between Different Control Methods
The experimetal results with traditional single-voltage loop control, double-closedloop control and double-closed-loop control with feedforward under load disturbance are shown in Figures 10-12. The output voltage V2 was 280 V, and the load increased abruptly at t1 with load resistance decreases from 75 Ω to 25 Ω and decreased sharply at t2 with load resistance increases from 25 Ω to 75 Ω. When the load increases, the DC voltage will fall, and the control loop will increase the phase shift angle to transfer more power to maintain the DC load. Simillarly, when the DC load decreases, the DC voltage will rise and the control loop will decrease the phase shift angle to reduce the transmitted power.  Figure 10 shows the waveform using the conventional single-loop control. The inductor current shows obvious transient DC bias during abrupt load change. When the load increased, the peak current reached 25.1 A, and the current overshoot was 9.1 A. In the experiment, both the static and dynamic performances under load increase and decrease were considered when tuning the PI parameters. The waveform showed that the voltage sag was 9.2 V, and the settling time was 3 ms when the load increased. The voltage overshoot was 10 V, and the settling time was 1.6 ms when the load decreased. Figure 11 shows the waveform using the double-closed-loop control. The inductor current was symmetrical, and the transient DC bias was eliminated. When the load increased, the voltage sag was 8.2 V, and the settling time was 1.9 ms. The voltage overshoot was 9 V, and the settling time was 1.3 ms when the load decreased.  Figure 10 shows the waveform using the conventional single-loop control. The inductor current shows obvious transient DC bias during abrupt load change. When the load increased, the peak current reached 25.1 A, and the current overshoot was 9.1 A. In the experiment, both the static and dynamic performances under load increase and decrease were considered when tuning the PI parameters. The waveform showed that the voltage sag was 9.2 V, and the settling time was 3 ms when the load increased. The voltage overshoot was 10 V, and the settling time was 1.6 ms when the load decreased. Figure 11 shows the waveform using the double-closed-loop control. The inductor current was symmetrical, and the transient DC bias was eliminated. When the load increased, the voltage sag was 8.2 V, and the settling time was 1.9 ms. The voltage overshoot was 9 V, and the settling time was 1.3 ms when the load decreased. Figure 10 shows the waveform using the conventional single-loop control. The inductor current shows obvious transient DC bias during abrupt load change. When the load increased, the peak current reached 25.1 A, and the current overshoot was 9.1 A. In the experiment, both the static and dynamic performances under load increase and decrease were considered when tuning the PI parameters. The waveform showed that the voltage sag was 9.2 V, and the settling time was 3 ms when the load increased. The voltage overshoot was 10 V, and the settling time was 1.6 ms when the load decreased. Figure 11 shows the waveform using the double-closed-loop control. The inductor current was symmetrical, and the transient DC bias was eliminated. When the load increased, the voltage sag was 8.2 V, and the settling time was 1.9 ms. The voltage overshoot was 9 V, and the settling time was 1.3 ms when the load decreased.  Figure 12 shows the waveforms using the double-closed-loop control with load feedforward. The transient DC bias was eliminated. During the transient process, the DC voltage variation was significantly reduced, and the settling time was obviously shortened compared with the double-closed-loop control without load feedforward. The voltage sag was 3 V when the load increased, and the voltage overshoot was 4.4 V when the load decreased. In the process of load surge, the recovery time for DC voltage was 0.5 ms, which is five switching cycles. The recovery time was 0.6 ms, which is six switching cycles, in the process of load decreases.
Compared with the traditional single-voltage loop control, the double-closed-loop control utilizes the deadbeat current controller as the inner loop, which directly regulates the high-frequency AC current of the transformer. Thus, the transient DC current bias could be eliminated. Meanwhile, the dynamic performance the of the IBDC with voltage mode mainly depends on the bandwidth of the feedback signal [12]. With the feedforward control samples, the load changes directly, which could significantly increase the robutness of the DC voltage under the load disturblances. The dynamic performance enhancement of the proposed control can be seen by comparison of Figures 11 and 12.  Figure 12 shows the waveforms using the double-closed-loop control with load feedforward. The transient DC bias was eliminated. During the transient process, the DC voltage variation was significantly reduced, and the settling time was obviously shortened compared with the double-closed-loop control without load feedforward. The voltage sag was 3 V when the load increased, and the voltage overshoot was 4.4 V when the load decreased. In the process of load surge, the recovery time for DC voltage was 0.5 ms, which is five switching cycles. The recovery time was 0.6 ms, which is six switching cycles, in the process of load decreases.
control utilizes the deadbeat current controller as the inner loop, which directly regulates the high-frequency AC current of the transformer. Thus, the transient DC current bias could be eliminated. Meanwhile, the dynamic performance the of the IBDC with voltage mode mainly depends on the bandwidth of the feedback signal [12]. With the feedforward control samples, the load changes directly, which could significantly increase the robutness of the DC voltage under the load disturblances. The dynamic performance enhancement of the proposed control can be seen by comparison of Figures 11 and 12. (a)

Conclusions
A double-closed-loop control strategy based on the deadbeat current controller was proposed in this paper, which directly regulates the high-frequency inductor current to the reference and eliminates the transient DC current bias during the transient process. Furthermore, load feedforward was introduced to enhance the dynamic of the converter. The proposed control method shows potential in the application of IBDC under voltage mode. With the proposed method, the settling time could be reduced to within several PWM cycles during load disturbance. A 5 kW IBDC converter prototype was built, and the superior dynamic performance of the proposed control strategy was verified by the experimental results. Compared with the traditional single-voltage loop control, the double-closed-loop control utilizes the deadbeat current controller as the inner loop, which directly regulates the high-frequency AC current of the transformer. Thus, the transient DC current bias could be eliminated. Meanwhile, the dynamic performance the of the IBDC with voltage mode mainly depends on the bandwidth of the feedback signal [12]. With the feedforward control samples, the load changes directly, which could significantly increase the robutness of the DC voltage under the load disturblances. The dynamic performance enhancement of the proposed control can be seen by comparison of Figures 11 and 12.

Conclusions
A double-closed-loop control strategy based on the deadbeat current controller was proposed in this paper, which directly regulates the high-frequency inductor current to the reference and eliminates the transient DC current bias during the transient process.
Furthermore, load feedforward was introduced to enhance the dynamic of the converter. The proposed control method shows potential in the application of IBDC under voltage mode. With the proposed method, the settling time could be reduced to within several PWM cycles during load disturbance. A 5 kW IBDC converter prototype was built, and the superior dynamic performance of the proposed control strategy was verified by the experimental results.