Abstract—Working as a DC-DC transformer (DCX), which operates at the resonant frequency, is a suitable solution to achieve maximum conversion efficiency of LLC converter. However, because the fixed frequency modulation is applied, the voltage regulation performance is limited. To achieve tight voltage regulation and fully utilize the advantages of LLC DCX operation under bidirectional isolated power application, a single-stage DAB-LLC hybrid bidirectional converter based on the sigma converter structure is proposed in this paper. In the proposed converter, the main power flows through LLC converter, and dual active bridge (DAB) is used for the power flow direction control and output voltage regulation. In addition, a mathematical model of the proposed converter is derived for controller design, which is verified by circuit simulation. Based on the model, the design of the controller and circuit parameters are discussed with the goal of fast dynamics. Finally, the experimental results of a 1200 W prototype verify the effectiveness and advantages of the proposed topology and controller design.

Index Terms—Single-stage DAB-LLC Hybrid Bidirectional Converter, Dual active bridge, Tight voltage regulation, Bidirectional power flow

I. INTRODUCTION

N recent years, because of wide zero voltage switching (ZVS) range, low turn-off current and other features, LLC

converters are widely used in applications requiring isolation and high efficiency, such as photovoltaic energy storage [1], new energy vehicles [2], solid state transformer [3]–[4] and point of load applications [5].

When operating at the resonant frequency, LLC converter has the maximum conversion efficiency, which can obtain soft

Manuscript received Month xx, 2xxx; revised Month xx, xxxx;

accepted Month x, xxxx. This work was supported in part by the National Natural Science Foundation of China under Grant 51907206, in part by the Key Technology R&D Program of Hunan Province of China under Grant 2018SK2140, in part by the Major Project of Changzhutan Self-Dependent Innovation Demonstration Area under Grant 2018XK2002, in part by the Project of Innovation-Driven Plan in Central South University under Grant 2019CX003, in part by the Hunan Provincial Key Laboratory of Power Electronics Equipment and Grid under Grant 2018TP1001, and in part by the Fundamental Research Funds for the Central Universities of Central South University under Grant 2019zzts869. (Corresponding author: Guo Xu.)

The authors are with the School of Automation, Central South University, Changsha 410083, China (e-mail: liaoyuefeng_uav@126.com; xuguocsu@csu.edu.cn; yaosuncsu@gmail.com; pandtao@csu.edu.cn; binguo_mail@csu.edu.cn; sumeicsu@csu.edu.cn; csu.xiong@163.com).

switching and low conduction loss. While, when the voltage gain is deviated from the gain at the resonant point, LLC converter would suffer from increased circulating current, thus reducing the conversion efficiency. Consequently, for applications requiring wide voltage gain, two-stage conversion structure is studied [6]-[7]. The two-stage solution uses LLC converter as a LLC DCX to achieve the voltage isolation, and a non-isolated DC-DC converter as another conversion stage to adjust the voltage gain. The line impedance and the internal resistance of switches in DCX converter will reduce the load regulation capability, especially at the case when output current is high. Even though, the output voltage can be used as the reference to achieve close-loop regulation as in [8], the indirect control could cause time delay in the control loop, and the dynamic performance is still limited because relative large electrolytic capacitor is used to support the DC link voltage.

To overcome the shortcomings and limitations of the two-stage converter, many scholars studied the single-stage DCX converter to realize high efficiency and voltage regulation. In [9], a LLC type converter with two interleaved pulse-width-modulated rectifiers is proposed, which can achieve a wide voltage regulation range independent of load. However its transmission power is unidirectional. In addition, frequency regulation of DCX can be applied. While under bidirectional power applications, PWM modulation logic has to shift according to the power direction, which loses the natural bidirectional power capability of DCX operation [10].

Fig. 1. The structure of sigma converter.

When the input voltage is high, the inputs of multiple

DC-DC modules can be connected in series to reduce the voltage stress of power devices for each module. In [11], it is deduced that the series low voltage device can reduce the conduction loss of the original side. But its ability of voltage regulation was not specified. In order to achieve tight voltage regulation and also fully utilize the high efficiency of non-regulated DCX operation for LLC converter, Wu et al. [12] proposed an isolated LLC DCX with load regulating capacity, which utilizing series connection of two transformers. Most of the power is provided by the main transformer and the auxiliary transformer followed by a DC-DC converter is used to obtain

Single-stage DAB-LLC Hybrid Bidirectional Converter with Tight Voltage Regulation under

DCX Operation Yuefeng Liao, Student Member, Guo Xu, Member, Yao Sun, Member, Tao Peng, Member, Bin

Guo, Student Member, Mei Su, and Wenjing Xiong, Member

I

load regulation. Compared with two-stage structure, the total conversion efficiency is no longer the multiply of each conversion stage, because most of the power is transferred to the load from LLC DCX directly, and the small portion of power is transferred through the auxiliary circuit with lower conversion efficiency. An isolated DC-DC converter was proposed in [13] which adds an auxiliary winding to the transformer. The output voltage is regulated by regulating the input voltage of the auxiliary non-isolated PWM DC-DC stage which is series in the input source. Fred C. Lee et al. [14] introduced a sigma converter for 12V voltage regulation modules powering the CPU. It is a kind of quasi-parallel converter consisting of an LLC DCX converter and a D2D (DC to DC) converter, like a buck converter, which are series connected at the input and parallel at the output, as shown in Fig.1. This architecture can achieve high conversion efficiency and also has output regulation ability [15]. However, it is a non-isolated converter and the soft switching for buck converter is not easy to realize, which could cause EMI noise and reduce the efficiency. In [16], a natural bidirectional input-series-output-parallel LLC-DCX converter was proposed. It has a fixed gain and can achieve natural bidirectional power transfer. However, the output regulation is affected by the load because of the open-loop operation.

The various types of converters in [11]-[16] proposed above can effectively realize the voltage regulation capability of DCX with high efficiency, but their power directions are unidirectional, and it is hard to achieve soft switching for the auxiliary circuit, or the auxiliary circuit is non-isolated. To achieve bidirectional power and wider ZVS range with isolation, the topology of non-isolated D2D for sigma converter should be replaced by isolated converter. Among bidirectional isolated converters, DAB converter can achieve natural bidirectional power transfer, and can realize the regulation of output power through controlling of the phase shift angle between primary bridge and secondary bridge [16]-[17]. However, when the load is light, it is difficult to realize soft switching, and high turn-off loss exists at rated load, resulting in lower efficiency than LLC converter [18]. If DAB converter is used as D2D and LLC converter is used as DCX in Fig.1, with proper design, most of the power can flow through LLC converter, and DAB converter can undertake only small portion of power with the purpose of adjusting the output voltage. In this way, the advantages of the two converters can be fully utilized, and the disadvantages of them can be avoided. Based on this concept, a single stage DAB-LLC hybrid bidirectional converter is proposed in this paper.

In addition, in all these works from [11]-[16], the foci are mainly on the working principle and parameter design, and the modeling and controller design are not presented in details. However, in order to achieve tight voltage regulation, it is necessary to establish a model for this new type of the hybrid converter, which is another contribution in this paper. The traditional modeling methods for DAB converter mainly include first harmonic approximation (FHA) method [19], extended describing function (EDF) method [20], reduced order modeling [21] and generalized average modeling (GAM) [22]. Among them, the reduced order modeling has low complexity and can achieve relative high accuracy under a certain frequency range [23]. Therefore, the model of the

hybrid converter is analyzed and derived based on the reduced order modeling of DAB converter in this paper.

To achieve tight voltage regulation and fully utilize the advantages of DCX operation for bidirectional isolated power application, a single-stage DAB-LLC hybrid bidirectional converter is proposed. Compared with sigma converter, each module of the proposed converter can realize ZVS, and the isolation can be realized to ensure the security. At the same time, the proposed converter can achieve naturally bidirectional power switching.

The main contributions could be summarized as, 1) A single-stage DAB-LLC hybrid bidirectional converter is

proposed. Referring to the sigma structure, it consists of an LLC converter and a DAB converter which is a bidirectional isolated topology. The main power flows through LLC converter to ensure high efficiency, and DAB converter is used to control the power flow direction and regulate the output voltage.

2) A mathematical model is established for the DAB-LLC hybrid converter based on reduced order modeling of DAB converter, which is verified by the circuit simulation and experimental results.

3) According to the demand of crossover frequency and phase margin, step-by-step design method of the controller and converter parameters based on the system model is presented to improve the dynamic response. Experimental results from a 1200 W prototype are given to show the effectiveness of the proposed topology and controller design.

This paper is organized as follows. Section II mainly introduces the topology, modeling of single-stage DAB-LLC hybrid bidirectional converter and the modeling verification. Section III introduces controller design based on the derived system model. Section IV focuses on the design considerations of circuit parameters. Section V shows the experimental results from a 1200 W prototype, which verify the effectiveness of the proposed topology and controller. Section VI draws the conclusion.

II. SYSTEM STRUCTURE AND CONVERTER MODELING

A. System Structure

The structure diagram of the single-stage DAB-LLC hybrid bidirectional converter proposed in this paper is shown in Fig.2. The system is composed of an LLC converter and a DAB converter, whose inputs are in series and the outputs are in parallel.

Fig. 2. The proposed circuit topology of the single-stage DAB-LLC hybrid bidirectional converter.

In Fig.2, Vin represents the input voltage, Vo represents the output voltage, VC1 and VC2 are the input voltages of LLC converter and DAB converter, respectively. vab and vcd are the voltage between the midpoint of the leading and lag bridge arms in primary and secondary side, respectively. C1, C2 and Co are LLC converter input capacitor, DAB converter input capacitor and output filter capacitor, respectively. R is the load resistor. Transformers T1 and T2 are independent. Lr, Lm and Cr are the resonant inductor, magnetizing inductor and resonant capacitor in LLC converter, respectively. Lk and Lm1 are the leakage inductor and magnetizing inductor of DAB converter. In LLC, Q1-Q4 are the primary side switches and S1-S4 are the secondary side switches. In DAB converter, Q5-Q8 are the primary side switches, and S5-S8 are the secondary side switches.

B. Converter Modeling

Fig. 3 shows the key waveforms of the proposed converter. The operating frequency of LLC converter is fixed at the resonant frequency, and the duty cycle is 50% for all the power switches. The switch driving signal of Qi at the primary side is the same with driving signal of Si at the secondary side (i = 1, 2, 3 and 4), which can easily realize synchronous rectification of LLC converter. Under this modulation strategy, LLC converter is equivalent to a non-regulated DC transformer. DAB converter regulates the output power through adjusting the phase shift angle between the driving signal of the primary side switches and the secondary side switches to control the phase angle between vab and vcd, thereby changing the voltage on the leakage inductor to realize the adjustment of output power. It is worth noting that the power transfer from left to right is considered to be the positive direction.

Fig. 3. The key waveforms of proposed converter.

DAB converter uses phase shift modulation to achieve

energy transfer and the power transmitted from the primary to the secondary side can be expressed by [22]

2 22

1

2C o

k s

K V V D DP

L f

(1)

where P2 is the transfer power of DAB, D is the phase shift angle (value range from -1 to 1), fs is the switching frequency and K2 is the transformer ratio of DAB converter from primary side to secondary side.

Neglecting the transmission loss, the power relationship between input and output is shown in (2)

2 2o s C LV I V I (2)

where IL is the average inductor current and Is2 is the average secondary current of DAB converter.

In addition, the topology is input series and output parallel. The relationships are deduced as follows

1 1 2Lr C L Ci i i i i (3)

1 2s s si i i (4)

1 2in C CV V V (5)

where i1 is the total input current and is is the total current in secondary. iC1 and iC2 are the currents flowing through C1 and C2, respectively.

Because LLC converter operates only at the resonant frequency, the impedance is very low. LLC converter in the sigma structure can be regarded as an ideal DC transformer (DCX) [15]. The relation between input voltage and output voltage can be expressed by (6)

1 1C oV V K (6)

where K1 is the transformer ratio of LLC converter from primary side to secondary side.

Then, the primary current and secondary current can also be expressed as

1 1s Lri K i (7)

where iLr is the resonant current and is1 is the corresponding secondary current of LLC converter.

Thus, from (2)-(7), is can be expressed as

11

1 1 2 1 1 1+

in os Lr L

o

inL C C L L

o

V V Ki K i i

V

VK i K i K i i K i

V

(8)

Three current expressions in (8) are as follows 22

2

1

2o

Lc k s

K V D DPi

V L f

(9)

11 1 1 1

C oC

dV dVi C K C

dt dt (10)

22 2 2 1 2

C in oC

dV dV dVi C C K C

dt dt dt (11)

Substituting (9)-(11) into (8) can obtain 22 2

1 2 1 2 1 1

1

2inin o o

sk s

K V D DdV dV dVi K C K C K C

dt dt dt L f

(12)

Then, the output voltage state equation is expressed as

o oo s

dV VC i

dt R (13)

Substituting is into (13) yields (14)

22 21 2 1 1 1 2

1

2ino in o

ok s

K V D DdV dV VC K C K C K C

dt L f dt R

(14)

It can be seen from (14) that the system output voltage state equation is related to the phase shift angle, input voltage and output voltage.

Setting the differential part to be zero, then the phase shift angle in steady-state is derived as

2

21 1 4

2

o k s

in

V L f

K V RD

(15)

In the phase shift modulation, the linear range of D is from -0.5 to 0.5, so D can be determined as

2

21 1 4

2

o k s

in

V L f

K V RD

(16)

C. Transfer Function

Injecting disturbance near the steady-state solution, the small-signal model can be obtained.

o o o

in in in

V V V

V V V

D D d

(17)

where oV , inV and D represent the steady state value, while

oV , inV and d represent the injected disturbance.

Substituting (17) into (14) yields a small signal state equation which is expressed as

2 21 2 1 1

2 2

1 2

1 2 1

2 2

oo

ino inin

k s k s

dVC K C K C

dt

K V D K D DV dVd V K C

R L f L f dt

(18)

where the high order items are ignored. The Laplace transform is performed on the small signal

model, as shown in (19)

1o o in inAsV BV Cd DV EsV (19)

where the corresponding variables are shown as follows

2 21 2 1 1

2 2

1 1 2

1

1 2 1

2 2

o

in

k s k s

A C K C K C BR

K V D K D DC D E K C

L f L f

，

， ，

(20)

Finally, the transfer function of single-stage DAB-LLC hybrid bidirectional converter is derived as

1o in d in in

D EsCV d V G s d G s V

As B As B

(21)

where Gd(s) is transfer function from control to output voltage and Gin(s) is transfer function from input voltage to output voltage.

D. Model Verification

In order to verify the correctness of the calculated model, two cases of parameters are selected, as shown in Table I. The proposed topology is simulated in PSIM software to get the amplitude frequency and phase frequency curves by using frequency sweep function. Meanwhile, bode graph of system transfer function Gd(s) is drawn by MATLAB. The comparison results are shown in Fig. 4.

TABLE I SYSTEM PARAMETERS

Symbol Quantity Value case 1

Value case 2

Vin Input Voltage 400 V 48 V Vo Output Voltage 48 V 5 V R Load 1.92 Ω 0.12 Ω

fs Switching Frequency 100 kHz 100 kHzLk DAB Leakage Inductor 25 H 1.6 H D Steady Phase Shift Angle 0.09 0.409 C1 LLC Converter Input Capacitor 220 F 100 F C2 DAB Converter Input Capacitor 220 F 100 F Co Output capacitor 2100 F 2100 FK1 LLC Converter Transformer Ratio 40/6 40/5 K2 DAB Converter Transformer Ratio 8/6 8/5

(a)

(b)

Fig. 4. The comparison between calculated model and PSIM simulation results. (a) Case 1. (b) Case 2.

It can be seen from Fig. 4(a) and (b) that within the frequency

range from 10 Hz to 10 kHz, which is 1/10 of the switching frequency, the amplitude frequency curves obtained by the mathematical model and the hardware topology simulation are almost overlapped.

III. CONTROLLER DESIGN

The system transfer function has been obtained in the previous section and the corresponding controller will be designed in this section. The input voltage disturbance is considered to be negligible, and the system model is considered as follows

o dV G s d G s d (22)

Ignoring the delay of sensor, the feedback transfer function is a constant value Hv, as follow

vH s H (23)

The PWM modulation transfer function is shown as

1PWM

PWM

G sK

(24)

where KPWM is the modulation factor. Therefore, the system open loop transfer function is shown

as follows

vos PWM

PWM

HG s G s G s H s G s

K (25)

Fig. 5. The system control block diagram.

A. Controller Design

The PI controller Gc(s) is shown in (26)

ic p

KG s K

s (26)

The control block diagram is shown in Fig. 5. Based on the

bode diagram, Kp and Ki can be determined according to the design targets which are crossover frequency wc and phase margin.

The open-loop transfer function is written by

2

p v i vo c os

PWM PWM

K CH s K CHG s G s G s

AK s BK s

(27)

Substituting s=jwc into (27) and calculate Go(s) as follow

2

p v c i vo c

PWM c PWM c

K CH w j K CHG jw a bj

AK w BK w j

(28)

where wc=2 fc. The relationship among the transfer function, phase angle θ

and wc can be expressed as follows

cos sino cG jw r jr (29)

2 2= 1o cr a b G jw (30)

180 (31)

where is phase margin.

Then the expression of a and b are obtained as

2 23cos

PWM v c i PWM v c p

PWM c PWM c

AK CH w K BK CH w Ka

AK w BK w (32)

2

2 23

+sin

PWM v c p PWM v i

PWM c PWM c

AK CH w K BK CH Kb

AK w BK w (33)

Based on (32) and (33), Kp and Ki are solved as sin cos

PWM cp

v

K Aw BK

CH (34)

cos sin PWM c c

iv

K w Aw BK

CH (35)

B. Controller Verification

According to (34) and (35), the parameters of PI controller can be obtained. In order to verify the accuracy of the controller design, parameters of case 2 in the Table I are substituted into (34) and (35) to get the values of Kp and Ki. The expected crossover frequency and phase angle margin are set to be 5 kHz and 45 degrees, respectively. The bode graph of open-loop transfer function with and without introducing PI controller are drawn respectively, as shown in Fig. 6. It can be seen that the crossover frequency increases to the expected value and the phase margin meets the requirement after controller is designed.

Fig. 6. The bode graph of open loop transfer function with and without introducing controller

IV. PARAMETER DESIGN CONSIDERATION

A. Capacitor

The crossover angle frequency of system is calculated as

1

1 2 2 21 1

cc

c c

BC ACw jCG jw

A jw B A w B

(36)

where wc1 = 2 fc1. According to (28)-(30), wc1 is expressed as 2 2 2 2

1 2 2 21 2 1 1

=co

C B C Bw

A C K C K C

(37)

Combined with (20), it can be seen that the larger the sum of capacitors, the smaller the crossover frequency will be, which means the weaker the dynamic performance of the system will be. But when the capacitors are small, the ability of voltage disturbance suppressing will be weaken. Therefore, the maximum capacitor value can be selected in combination with the crossover frequency according to the dynamic requirements, substituting (20) into (37) can obtain

2 2

221 1 2

_ min

1 2 2

2

in k s

ok s c

K V D R L fC K C C

L f Rw

(38)

where wc_min is the minimum crossover angle frequency.

B. DAB converter inductor

The DAB converter leakage inductor is a power link between primary and secondary side, and it is related to the maximum power of the converter. The design considerations are shown as follows:

The capability of the transferred power for DAB converter should be greater than or equal to the rated output power Po_rated, as shown in (39)

22 2 2 2

_

1

2c o c c o

DAB o ratk s

edin in

K V V D D V V VP P

L f V V R

(39)

The maximum transfer power occurs at the point when D =0.5. Substituting it into (16) leads to the maximum limit for DAB converter leakage inductor, which is expressed as

2

8in

ks o

K RVL

f V (40)

In addition, (41) can be derived from (37) 2 2 2 2

1 cA w B C (41)

Substituting C in (20) into (41) can obtain the relationship between the system open loop crossover frequency and DAB converter leakage inductor.

2

2 2 2

1 2=

2

ink

s c

K V DL

f A w B

(42)

From (39), it can be seen that the smaller leakage inductor is, the larger the crossover frequency will be. Unlike analog control, the digital controller introduces a 1.5-step delay in the loop due to the presence of a zero-order holder and one-step delay [24]. So, in order to keep the system with sufficient phase margin under digital control, the crossover frequency will be at least lower than half of the switching frequency. In that situation, substituting (20) into (41), the minimum value of the leakage inductor can be expressed as

2

22 2 21 1 2 _ max

1 2

2 1

ink

s o c

K V D RL

f C K C C R w

(43)

where, wc_max is the maximum crossover frequency.

C. Transformer Turns Ratio

The power distribution of the two converters ignoring the conversion loss is shown as

2 1 2

1 1 2 1 1 2

= =CDAB DAB

o LLC DAB C C

V iP P K

P P P V i V i K K

(44)

where λ is power distribution coefficient. It can be seen that λ is related to the transformer turns ratio.

In ideal case, the proportion of the power that flows through DAB converter should be as low as possible to ensure that as much power as possible flows through LLC converter. However, it can be seen from (37) that the crossing frequency decreases when the transformer ratio K1 increases. Therefore, the maximum K1 can be determined according to the minimum dynamic response requirements.

2 2

11_ min 1 2 1 2

o

c

CC BK

w C C C C (45)

In addition, ZVS of DAB converter at 10% of the total power can also be considered. The energy relationship between the inductor and the capacitor is shown in (46), where IL_off is the turn-off current and Cp is the junction capacitor of primary side.

2 2_ 2k L off p CL I C V (46)

Then, the boundary of K2 can be deduced in (46)

2 2

8

5 2 16

o k s

in p s k

V L fK

V R C f L (47)

So, the boundary of K1 can be obtained by introducing the total turn ratio of the proposed converter.

2 2 2

1 2 2

5 2 16 8

5 2 16

in p s k o k sin

o in o p s k

V R C f L V L fVK K

V V V R C f L (48)

Therefore, the maximum value of K1 should be selected considering both the dynamic response and ZVS of DAB converter.

V. EXPERIMENTS RESULTS

A 1200 W single-stage bidirectional DAB-LLC hybrid converter prototype is built up with 400 V (±30 V) input and 48 V output voltage, as shown in the Fig. 7. The upper module is DAB converter and the lower module is LLC converter. MOSFET is used for primary and secondary side switching devices. The system circuit parameters and control parameters are shown in Table II. The PI controller is implemented in a TI digital signal processor TMS320F28069. is designed to be 0.2, which determines transformer turns ratios of LLC converter and DAB converter. During the experiment, the load step change from 1.9 Ω to 5.5 Ω, which means the output power step change from 1200 W to 420 W.

Fig. 7. The hardware prototype of single-stage DAB-LLC hybrid bidirectional converter.

TABLE II SYSTEM PARAMETERS

Symbol Quantity Value

Vin Input Voltage 370 V-430 VVo Output Voltage 48 V Lr LLC Converter Resonant Inductor 25 H Cr LLC Converter Resonant Capacitor 0.1 F Lk DAB Converter Leakage Inductor 25 H R Rated Load 1.9 Ω fs Switching Frequency 100 kHz fc Crossover Frequency 5 kHz Kp Proportionality Coefficient 0.48 Ki Integration Coefficient 15125 K1 LLC Converter Transformer Ratio 40/6 K2 DAB Converter Transformer Ratio 10/6

The steady state waveforms of proposed converter under 420

W load condition and 1200 W load condition are shown in Fig. 8, which include output voltage, output current, resonant current of LLC converter and leakage inductor current of DAB converter, respectively. It can be seen from the experimental results that the output voltage remains unchanged at 48 V under different loads. It also can be seen from Fig. 8(b) and Fig. 8(c) that LLC converter always operates at the resonant frequency point. In addition, the phase shift angle of DAB converter is changed corresponding to the load, which indicates that the output is regulated through DAB converter.

(a)

(b)

VO: 50 V/divIO: 10 A/diviLr: 5 A/div

iL: 5 A/div

time:10 us/div

D

(c)

Fig. 8. The key waveforms under different load. (a) Load is step changing between 420 W and 1200 W. (b) 420 W load. (c) 1200 W load.

Fig. 9 shows the key waveforms of primary side and secondary side under full load condition. It can be seen from Fig. 9(a) that the ratio of input voltage of LLC converter and DAB converter is nearly 4/1. And the amplitude of leakage inductor current is almost the same as the amplitude of the resonant current. From Fig. 9(b), it can be seen that the secondary current of DAB converter is much smaller than the secondary current of LLC converter, which can verify that most power flows through LLC converter.

(a)

（b) Fig. 9. The key waveforms in different side. (a) Primary side. (b) Secondary side.

In order to verify the voltage regulation capability, the

experimental results are compared with a conventional full-bridge LLC DCX structure. The conventional LLC DCX is built up with 400V input and 48V output. Its transformer turns ratio is 50/8, and the output power is also designed to 1200 W. It operates at the resonant frequency (100 kHz) and is open loop

control. During the experiment, the output power is also switched from 420 W to 1200 W. The output voltage waveforms of the conventional LLC-DCX and the proposed converter are shown in Fig. 10(a) and Fig. 10(b), respectively. As seen from Fig. 10(a), 1V difference occurs under the two load conditions, which shows that the load regulation of the conventional converter is poor. While for the proposed converter, the output voltage is remained almost constant, as shown in Fig.10(b).

(a)

(b)

Fig. 10. The output voltage waveforms between the conventional LLC DCX converter and the proposed converter. (a) Conventional LLC DCX. (b) Proposed converter.

Fig. 11. Dynamic response waveforms with load step changing.

Fig. 11 shows the dynamic response waveforms for proposed

converter when the output voltage channel is under AC coupling condition. While the output power jumps between 420 W and full load, the output voltage overshoot is less than 1 V (2%), and the settling time is less than 2 ms.

Fig.12 shows the measured open-loop Bode plots of the proposed converter using PSM1700 loop analyzer. It can be

seen that after introducing the designed PI controller, the crossing frequency is increased to 3.38 kHz and the phase margin is 46.7°, which is close to the theoretical analysis. In the high frequency region, the difference of phase is mainly caused by the damping, line impedance, sampling delay and other factors.

Phase Margin = 46.7°

Crossing frequency = 3.38 KHz

Phase Margin = 46.7°

Crossing frequency = 3.38 KHz

Phase

Gain

Frequency (Hz)10 100 1k 10k

0

20

-20

40

60

80

-40

-60

-80

0

45

-45

90

135

180

-90

-135

-180

Fig. 12. Measured Bode plots of the proposed converter.

Since LLC converter is used as a DCX in the system, its output voltage is determined by the input voltage. When the input voltage changes, the proposed converter can stabilize the output voltage by adjusting the phase shift angle in DAB converter. Fig. 13 shows the key waveforms when the input voltage drops from 400 V to 370 V and increases from 400 V to 430 V. It can be seen that the output voltage remains constant under different input voltage.

(a)

(b)

Fig. 13. The key waveforms with input voltage variation. (a) Input voltage drops. (b) Input voltage increases.

By paralleling a bidirectional current source at the output

side of the proposed converter, it can be seen from the experiment that the naturally bidirectional power flows is realized when the power changes between +1200 W and -1200 W, as shown in Fig. 14. Fig. 14(a) shows the waveforms of forward 1200 W switching to backward 1200 W and Fig. 14(b) shows the waveforms of backward 1200 W switching to forward 1200 W. During the switching process, the output

voltage is rarely affected, and the resonant current and the inductor current of DAB converter are smoothly changed.

(a)

(b)

Fig. 14. Dynamic waveforms with power direction switching (a) forward 1200 W switching to backward 1200 W (b) backward 1200 W switching to forward 1200 W

The loss breakdown and cost analysis for the proposed converter and conventional LLC DCX are presented in Fig.15. Although more switches are added in the proposed converter, the losses increased are pretty low because the total device power rating is similar under full load, as shown in Fig.15(a). Fig,15(b) shows the unit pricing of switch from the same manufacturer. The switches of the proposed converter are composed of Q1-Q8 and S1-S8. And, the switches of conventional LLC DCX are composed of Q1-Q4 and S1-S4. The total price of all switching devices of the proposed converter is just increased by 23.7%. Although the cost of the proposed converter is more expensive, it can take advantage of the natural bidirectional power of DAB converter to achieve tight voltage regulation. The measured efficiencies under different load are shown in Fig.15(c). It can be seen that the difference of the peak efficiency between the proposed converter and the conventional LLC DCX is within 0.5%.

0

10

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Total loss Switchesconduction

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Transformeriron loss

Transformercopper loss

PLoss(

W)

Loss Breakdown (Vin=400V , Vo=48V)

Proposed Converter Conventional LLC-DCX

(a)

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Q1-Q4 S1-S4 Q5-Q8 S5-S8

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cing

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95.1 96.2 96.0 95.9

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icie

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Proposed Converter Conventional LLC-DCX

_ 0.5%Peak efficiency

(c) Fig. 15. Comparisons of loss breakdown, cost and efficiency. (a) Loss breakdown analysis under full load. (b) Cost analysis. (c) Measured efficiencies under different load.

VI. CONCLUSION

In this paper, a single-stage DAB-LLC hybrid bidirectional converter is proposed, whose inputs are in series and outputs are in parallel. The tight voltage regulation capability is achieved through a DAB converter, and the advantages of LLC DCX operation under bidirectional isolated power application are fully utilized, because the main power flows through LLC converter. In order to improve the dynamic performance, a mathematical model of this new converter is built based on the reduced order modeling method. The accuracy of the model is verified by comparing circuit simulation and calculated results. Then the PI controller and circuit parameters are designed based on the model aiming at the requirements of crossover frequency and phase margin. Finally, the experimental results show that the topology and controller designed in this paper can achieve tight voltage regulation with good load regulation, fast dynamic response and natural bidirectional power flows. In addition, the proposed converter can maintain the constant output voltage within a certain range of input voltage variation.

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