Efficiency Improvement at Light Load in
Bidirectional DC-DC Converterby Utilizing Discontinuous Current Mode
Hoai Nam Le, Daisuke Sato, Koji Orikawa, Jun-ichi Itoh
Nagaoka University of Technology
1603-1 Kamitomioka-cho
Nagaoka city Niigata, Japan
Tel.: +81 / (258) – 47.9533.
Fax: +81 / (258) – 47.9533.
E-Mail: lehoainam@stn.nagaokaut.ac.jp
URL: http://itohserver01.nagaokaut.ac.jp/itohlab/index.html

Keywords«Discontinuous Current Mode», «Bidirectional DC-DC Converter», «Nonlinearity Compensation»

Abstract
This paper proposes a feedback current control for bidirectional DC-DC converter which is operated in
Discontinuous Current Mode (DCM) at light load and Continuous Current Mode (CCM) at heavy load inorder to improve light load efficiency. In the proposed method, the nonlinearity compensation for DCM
operation is constructed by using the duty ratio at previous calculation period. Moreover, the introductionof DCM current feedback control into bidirectional power conversion is accomplished by detecting theoperation mode at the output of the control system. This make the control becomes parameterindependent. The validity of the proposed control is confirmed by a 1-kW prototype. In the ramp
response, the slope of the DCM current almost agrees to the design value with the error of 0.8%.
Moreover, the smooth transition among 4 current modes: CCM-powering, DCM-powering, DCMgeneration, CCM-generation, is also confirmed. On the other hand, in order to further improve theefficiency at light load, the synchronous switching for DCM is proposed. As a result, at load of 0.1 p.u.
the efficiency of the DCM synchronous switching is improved by 1.5% from 97.2% to 98.7% comparedwith the CCM synchronous switching. Besides, it is confirmed that, the efficiency of the CCM/DCM
synchronous switching is higher by 0.2% than that of the CCM/DCM asynchronous switching at all rangeof load. Furthermore, the efficiency at rated load is 98.8%, whereas the maximum efficiency is 99.0% atload of 0.45-0.65 p.u..

I.

Introduction

Recently, high power bidirectional DC-DC converters are widely applied to electric vehicles, andhybrid electric vehicles. This DC-DC converter is required to have small size and high efficiency.
Generally, the Continuous Current Mode (CCM) control is applied in such converter due to its simple
control. Nevertheless, because the current ripple in CCM is constant at all load range, it is difficult toachieve high efficiency at light load when the average current is low. Therefore, reducing the current
ripple is the direct method to avoid the decrease of efficiency at light load. In order to reduce the current
ripple, the conventional methods are increasing the inductance or the switching frequency [1]-[5].
However, when the circuit parameters have already been optimized at full load operation, any increase in
inductance or switching frequency only leads to the increase in size of inductor or heat sink.

On the other hand, in the Discontinuous Current Mode (DCM) control, because the current ripple
becomes smaller at light load, high efficiency can be maintained. Therefore, many papers in which CCM
is applied at heavy load and DCM is applied at light load have been proposed [5]-[9]. In particular, it iswell known that different operation modes can result in very different dynamics in the frequency domain[10]. The reason is that, in DCM the zero-current intervals which is dependent on the average current,
introduces the nonlinearity to the duty-ratio-to-current transfer function. As the result, the conventional
method to control CCM and DCM is using two controllers; one of which is designed based on the linear
transfer function of CCM, whereas the other controller is designed based on the nonlinear transfer
function of DCM [5]-[6]. However, when the current alternates between CCM and DCM, the current
control performance worsens due to the initialization of the controller [11]. Therefore, the control of
CCM and DCM without alternating controller is desired.
In this paper, the control method which uses only one PI controller for both CCM and DCM in order toachieve the high current control performance without alternating controller, is proposed. In order tocontrol both CCM and DCM, a compensation part is introduced at the output of PI controller tocompensate the nonlinearity in DCM. The compensation part is designed as a function of the duty ratio at
previous sampling period, which makes the calculation for the compensation part become parameterindependent compared to [5]-[9]. This paper is organized as follows; first, the circuit model in CCM and
DCM is derived. Second, the nonlinear part in DCM is linearized at stable points in order to design thecompensation factors. Third, the technique to apply the proposed CCM/DCM controller in bidirectional
current control is explained. Next, in order to further improve efficiency, the synchronous switching isapplied to DCM by estimating the zero crossing point of the current. After that, the current response of
the proposed control is verified by a 1-kW prototype. Finally, the comparison of efficiency among the
DCM synchronous switching, the DCM asynchronous switching and the CCM synchronous switching is
conducted to verify the efficiency improvement by applying the DCM synchronous switching.

II.

Proposed CCM/DCM control method

A. Conventional CCM inner current loop design
Fig. 1 shows typical bidirectional DC-DC converter configuration. The average modeling technique isused to model the bidirectional DC-DC converter for the inner current control loop design [6]-[9]. The
output voltage is assumed to be constant, because the response of the inductor current is much higher thanthat of the output voltage in outer voltage loop design step.
Fig. 2 shows the conventional inner current loop in CCM. In this paper, the closed loop of the innerFig. 1. Typical bidirectional DC-DC converter. Due to simple configuration, theabove converter is widely applied in bidirectional power conversion.

Fig. 2. Conventional inner current loop in CCM. Due to simple design and good
performance, PI controller is widely used by power electronics engineers.

current loop is designed based on the second-order standard form. Hence, the coefficients of PI controller
is designed as follows,K p  2 n L .................................................. (1)2Ti ......................................................... (2)nwhere L is the inductance, Kp is the proportional gain, Ti is the integral period of PI controller, ωn is thenatural angular frequency, ζ is the damping factor, and ωn, ζ are designed in order to achieve the desired
inductor current response.

B. Proposed CCM/DCM inner current loop design
Fig. 3 shows inductor current waveform in DCM, where D1, D2 and D3 denote the duty ratio of the first,
the second and the zero-current interval respectively. A circuit model for both CCM and DCM isobtained as follows. First, the average current iavg and the current peak ipeak can be expressed as,i peaki peaki avg ( D1  D2 ) (1  D3 ) ............ (3)22V  Voi peak  i
D1Tsw ........................................ (4)L
where Vo, Vi are the output and input voltages, and Tsw is the switching period. Besides, the voltage VA
across the SW2 and the voltage VL across the inductor can be expressed as,
VA  D1Vi  D3Vo ............................................ (5)VL  VA  Vo ................................................... (6)Substituting (3),(4), and (5) into (6),iavg
2LVL  D1Vi  [1 ]Vo  Vo ........ (7)(Vi  Vo )Tsw D1Then, the circuit model is established based on (7).
Fig. 4 shows circuit model of bidirectional DC-DC converter. In CCM, the dash line part does notexist, because the average current iavg equals to the half current peak ipeak/2. On the other hand, in DCM,
the voltage which occurs during the zero-current interval introduces the nonlinearity into DCM transfer
function. This worsens the current response in DCM when same PI controller is applied for both CCM
and DCM. Therefore, the output of PI controller is necessary to be compensated when the circuit isoperated in DCM. The design of the compensation part for the nonlinearity of DCM is explained asfollows. First, the circuit model in Fig. 4 is linearized at stable points.
Fig. 5 shows the linearized circuit model. In order to simplify the coefficients in the linearized circuit
model, the relationship between such coefficients at stable points are derived as follows [7],2
Tsw D1 _ s Vi (Vi  Vo )I avg _ s ........................ (8)L 2
VoFig. 3. Inductor current waveform in DCM. The zero-current interval makes it
difficult to sample average current and introduces the nonlinearity into the duty-tocurrent transfer function.

Fig. 4. Circuit model of boost converter in the DCM operation. The zero-current
interval makes the duty-to-current transfer function become nonlinear.

Fig. 5. Linearized circuit model. Controlling DCM by PI controller of CCM isachieved by compensating the nonlinear part at the output of PI controller.

Fig. 6. Simplified and linearized circuit model. The duty ratio at steady-state
operating points in the circuit model is approximated as the duty ratio at previous
sampling period in order to eliminate the nonlinearity in DCM.

Fig. 7. Discretized circuit model. Utilizing the duty ratio at previous sampling
period in order to eliminate the nonlinearity in DCM makes the controller
parameter-independent.

Vi  Vo
D1_ sTsw .................................. (9)Lwhere Iavg_s, Ipeak_s and D1_s are the average current, the peak current and the duty ratio of SW1 at stable
points, respectively. Then, (8) and (9) are substituted into Fig. 5 to express all coefficients as functions of
D1_s.
Fig. 6 shows the simplified circuit model. In order to eliminate the dash line part in Fig. 6, in thecontrol system, the value of D1_s is approximated as the duty ratio of SW1 at previous sampling period
D1[n-1]. As the result, the circuit model is necessary to be analyzed in discrete model.
Fig. 7 shows the discretized circuit model. In order to use same PI controller of CCM for DCM, thedash line part in Fig. 7 is necessary to be set as unity when the circuit is operated in DCM. Therefore, inthe control system, the inverse part of the dash line part in Fig. 7 is multiplied at the output of PI
controller in order to compensate for the nonlinearity of DCM.
I peak _ s Fig. 8 shows the proposed CCM/DCM control. The compensated part to eliminate the nonlinearity in
DCM, is arranged into two compensation factors KDCM and aDCM in order to simplify the control system.
By introducing two compensation factors KDCM and aDCM, the integral part of the PI controller is not
required to be initialized when current mode alternates between CCM and DCM. This ensures a smoothtransition between DCM and CCM.
Table I shows the values of two compensation factors in case of CCM and DCM. When the circuit
operates in CCM, all the compensation factors are set as unity. On the other hand, when the circuit
operates in DCM, two compensation factors are calculated as in Table I.

C. Control of DCM current in bidirectional power conversion
Fig. 9 shows the circuit operating in either regeneration mode or powering mode when DCM
asynchronous switching is applied. It can be understood that with same value of D1, the operation modeis determined by driving one of switches and turning off the other switch. Therefore, it is necessary to
determine which switching pattern should be used. This is accomplished as follows; different from CCM,
in DCM the duty ratio D1 is a function of average current iavg as shown in (8). Hence, when the current
becomes negative, the duty ratio D1 also becomes negative. This problem can be overcome by output theabsolute value of duty ratio to the switches. Furthermore, which switch is turned off in DCM
asynchronous switching is determined by the state of duty ratio D1.

Fig. 8. Proposed CCM/DCM control system and circuit model. Smooth transition
between CCM and DCM is achieved by compensating only the output of PI
controller.
Table I. Values of two compensation factors.

(a) DCM in powering mode(b) DCM in regeneration mode
Fig. 9. Operation of bidirectional DC-DC converter when DCM asynchronous
switching is applied. Which mode the circuit is operated is determined by the outputof the control system D1 in Fig. 8.

Table II shows the duty ratios which are used to drive the switches in DCM regeneration mode and
DCM powering mode. When the duty ratio D1 from the control system in Fig.8 is negative, the circuit isoperated in powering mode, which means SW1 is turned off while SW2 is driven by the duty ratio D2
calculated as in Table II. On the other hand, when the duty ratio D1 becomes positive, the circuit isoperated in regeneration mode, which means SW2 is turned off while SW1 is driven by the duty ratio |D1|.
By using this method, the integral part of the PI controller is not required to be initialized when thecurrent mode alternates between regeneration mode and powering mode.

D. Application of DCM synchronous switching
Because the mechanism of the DCM synchronous switching is same in both powering mode andregeneration mode, only the powering mode is explained.
Fig. 10 shows two switching patterns which occur in DCM when the switch (MOSFET) is operated
instead of being turned off to use as the diode. This operation can improve the efficiency because theconduction loss of MOSFET is smaller than that of diode. In conclusion, this converter can realize threeoperation modes in light load depending on the turn on and off of SW 1; i) Simple CCM synchronous
switching in which SW1 is switched alternately to SW2, ii) DCM asynchronous switching in which SW1 isturned off in light load and iii) DCM synchronous switching in which SW1 is turned on only during thesecond interval as shown in Fig. 3.
The boost inductor current of the simple CCM synchronous switching becomes continuous. Therefore,
the boost inductor current ripple is constant. However, this results in high current ripple at light load,
which makes the efficiency decrease. In order to improve the efficiency in light load, the DCM
asynchronous switching is applied. Although the DCM asynchronous switching can reduce the boost
inductor current in light load, the conduction loss of the body diode in the MOSFET is still high. In the
DCM synchronous switching, if SW1 is turned on exactly only during the second interval as shown in Fig.
3, the current flows through MOSFET. As a result, the conduction loss will be reduced. In order to apply
the DCM synchronous switching, the duty ratio D1 is calculated in the proposed DCM feedback control
and (10) in the conventional DCM feedforward control [5], respectively.

D1 _ conv . _ ff *
2 Li avg(Vout  Vin )2............(10)

Tsw inTable II. Duties to control switches for DCM regeneration mode and DCM
powering mode in DCM asynchronous switching.

(a) DCM asynchronous switching(b) DCM synchronous switching
Fig. 10. DCM asynchronous switching and DCM synchronous switching in
powering mode. Generally power loss emits when the current flows through
MOSFET than diode. Therefore, the improvement in efficiency is expected when
the synchronous switching is applied in DCM.

Table III shows the DCM synchronous switching in powering mode and regeneration mode. Becauseof the mismatch between the nominal values and the actual values, the duty ratio calculated from the feed
forward control method in (10) makes SW1 turn off too early or too late when the inductor current reaches
zero. This leads to the increase of switching losses and conduction losses. On the other hand, the duty
ratio D1 calculated from the feedback control method represents precisely for the value of the inductor
current. This enables SW1 to be turned off exactly at the moment the inductor current reaches zero, which
results in Zero Current Switching (ZCS). Because generally lower loss emits when the current flows
through MOSFET than diode, the improvement of the efficiency is expected when the DCM synchronous
switching is applied. Besides, it is noted in Table III that, in powering mode and regeneration mode, theturn on order of the switches for the DCM synchronous switching is different.

III.

Experimental Results

Table IV shows the parameters in experiments. In this chapter, first, the experiment of the current
ramp response is conducted in order to confirm the operation of the proposed CCM/DCM current
feedback control in bidirectional power conversion. Next, the waveform of the current and the switching
signal when the circuit is operated at the DCM synchronous switching is shown. Finally, the comparisonof the efficiencies at light load among the CCM synchronous switching, the DCM synchronous switching,
and the DCM asynchronous switching is conducted.

A. Current ramp response
The current ramp response of the current control block in Fig. 8 is confirmed. The incline of the ramp
command is the maximum controllable values (diavg*/dt)max of the designed PI controller and is calculated
as,Table III. Duties to control switches for DCM regeneration mode and DCM
powering mode in DCM synchronous switching.

Table IV. Parameters in experiments.

diavg *n iavg *................................... (11)dt max2 2where Δiavg* is the amplitude of current command.
Fig. 11 shows the ramp response of inductor current by the conventional CCM control and the
proposed CCM/DCM control. At light load, the variation width of current command is 3.2 A. Hence, themaximum controllable ramp command is 3.55 A/ms. It is concluded from Fig. 11(a), (b) that the DCM
response is almost as same as the designed value with error of 0.8%, whereas the error of the CCM
response is 7.6%. It is understood that the ripple of the current in DCM is reduced compared to CCM,
which leads to the reduction of loss at light load. This also results in the better control performance in
DCM operation. On the other hand, the detection of CCM and DCM in this paper is to compare thefeedback current with the value of the current at the boundary between CCM and DCM. It is confirmed
from Fig. 11(c) that the current smoothly alternates among 4 current modes; CCM regeneration, DCM
regeneration, DCM powering and CCM generation. By those results, the validity of the proposed
CCM/DCM control for bidirectional power conversion is confirmed.

B. DCM synchronous switching operation and efficiency comparison
Fig. 13 shows the synchronous switching waveforms in DCM powering. It is concluded that SW1 isturned off exactly when the current reaches zero, which achieves ZCS. Furthermore, before SW1 isturned on, during the dead time, the current flows through the diode. Therefore, SW1 turns on at theforward voltage of the diode. Therefore, ZVS is achieved when SW1 is turn on. In summary, thesynchronous switching in DCM causes almost no switching loss in SW1.
Fig. 14 shows the efficiency comparison among the CCM synchronous switching, the DCM
synchronous switching, and the DCM asynchronous switching. The efficiency of the CCM/DCM
synchronous switching and the CCM synchronous switching at full load are same as 98.8% because the(a) CCM operation at light load(b) DCM operation at light load(c) CCM/DCM operation at full load
Fig. 11. Current ramp response of conventional CCM control and proposed
CCM/DCM control at light load and full load. The current response of DCM
control is almost as same as the design value with error of 0.8%. Because thecurrent ripple of DCM is reduced at light load, the high efficiency can be
maintained at all load range. Besides, the smooth transition among 4 current modes:
CCM regeneration, DCM regeneration, DCM powering and CCM powering is
confirmed.

(a) At load of 0.2 p.u.
(b) At load of 0.4 p.u.
Fig. 13. DCM synchronous switching in powering mode. SW1 is turned off exactly
when the current reaches zero. This achieves ZCS. Furthermore, before SW1 isturned on, during the deadtime, the current flows through diode. Therefore, SW1
turns on at the forward voltage of diode. This achieves ZVS. To sum up, the DCM
synchronous switching causes almost no switching loss in SW1.

Fig. 14. Efficiencies among CCM synchronous switching, CCM/DCM synchronous
switching and CCM/DCM asynchronous switching. Due to the reduced current
ripple at light load, the efficiency in the CCM/DCM synchronous switching is
improved by 1.3% compared to the CCM synchronous switching. Besides, byapplying the synchronous switching into DCM, the efficiency is improved by 0.2%
compared to the asynchronous switching.

circuit is designed in order to operate in CCM at full load. When the load becomes lighter, whereas theefficiency of the CCM synchronous switching decreases as explained in Fig. 11, the efficiency of the
DCM synchronous switching is still maintained at high values over than 98.7%. Specifically, at load of
0.1 p.u., the efficiency is improved by 1.3% when the DCM synchronous switching is applied. Thisefficiency improvement especially benefits the application with a frequent variation between light load
operation and full load operation. On the other hand, compared to the CCM/DCM asynchronous
switching, the efficiency of the CCM/DCM synchronous switching is higher by 0.2% at all load range.

This efficiency improvement is because the conduction loss of MOSFET is lower than that of a diode inthis case. However, the conduction loss in the DCM synchronous switching increases with the square of
the current, whereas the conduction loss in the DCM asynchronous switching increases with the current.
Therefore, there might be case that the efficiency of the DCM synchronous switching is lower than one of
the DCM asynchronous switching. It can be concluded that the DCM synchronous switching benefits
mostly the switching device with a small on-resistance in the MOSFET part and a high forward voltage inthe parasitic diode such as SiC-MOSFET. Furthermore, the maximum efficiency reaches 99.0% at loadof 0.45-0.65 p.u.. From these results, the effectiveness of the DCM application into bidirectional power
conversion is confirmed.

IV.

Conclusion

This paper proposed the CCM/DCM control method for bidirectional DC-DC converter. The
nonlinearity of DCM was compensated by the utilization of the duty ratio at the previous calculation
period. On the other hand, the detection of powering mode and regeneration mode in order to apply DCM
was accomplished by observing the state of the duty ratio. In the experimental current ramp response, theerror of the DCM current response was 0.8%, and the smooth transition of the current among 4 current
modes: CCM regeneration, DCM regeneration, DCM powering and CCM powering was also confirmed.
Moreover, in order to further improve the efficiency at light load, the synchronous switching was applied
into DCM. As the results, the efficiency of above 98.7% was maintained at all load range from 0.1 p.u. to
1.0 p.u..
In future work, the technique to control both CCM and DCM independently from the value of
inductance will be explained. Furthermore, the design of the current ripple and the switching frequency
will be conducted. The power density of the bidirectional DC-DC converter will be optimized based onpareto-front curve.

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