06544303

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 4, APRIL 2014 2037

A Two-Mode Control Scheme With Input VoltageFeed-Forward for the Two-Switch Buck-Boost

DCDC ConverterChuan Yao, Xinbo Ruan, Senior Member, IEEE, Weijie Cao, and Peilin Chen

AbstractThe two-switch buck-boost (TSBB) converter is suit-able for wide input voltage applications. In order to achieve highefficiency over the entire input voltage range, the TSBB converteris operated in buck mode at high input voltage and boost mode atlow input voltage. Such operation is called the two-mode controlscheme. The objective of this paper is to propose an input voltagefeed-forward (IVFF) method to reduce the influence of the inputvoltage disturbance on the output voltage. The small-signal modelsof the TSBB converter are built, and based on which, the IVFFfunctions under different operating modes of the TSBB converterare derived. The IVFF function in boost mode is simplified for easyimplementation. The two-mode control scheme with IVFF com-pensation is then proposed for the TSBB converter, which realizesautomatic selections of operating modes and the correspondingIVFF functions. Besides, nearly smooth switching between buckand boost modes is also guaranteed. For exhibiting the advantagesof the proposed control scheme clearly, comparisons between thetwo-mode control with and without IVFF compensation have beenpresented in this paper, including the output signal of the voltageregulator and input-to-output voltage transfer function. Finally, a250500-V input, 360-V output, and 6-kW-rated power prototypeis fabricated to validate the effectiveness of the proposed controlscheme in the laboratory, and the experimental results show thatthe TSBB converter has an improved input transient response andhigh efficiency over the entire input voltage range with this pro-posed control scheme.

Index TermsInput voltage feed-forward, small-signal model,two-mode control, two-switch buck-boost converter.

Manuscript received November 10, 2012; revised March 24, 2013 and May24, 2013; accepted June 13, 2013. Date of current version October 15, 2013.This work was supported in part by the National Natural Science Foundation ofChina under Award 50837003 and Award 51007027, and in part by the NationalBasic Research Program of China under Award 2009CB219706. Recommendedfor publication by Associate Editor F. L. Luo.

C. Yao and P. Chen are with the Department of State Key Labora-tory of Advanced Electromagnetic Engineering and Technology, HuazhongUniversity of Science and Technology, Wuhan 430074, China (e-mail:[email protected]; [email protected]).

X. Ruan is with the Department of State Key Laboratory of Advanced Elec-tromagnetic Engineering and Technology, Huazhong University of Science andTechnology, Wuhan 430074, China, and also with the Aero-Power Sci-TechCenter, College of Automation Engineering, Nanjing University of Aeronauticsand Astronautics, Nanjing 210016, China (e-mail: [email protected]).

W. Cao is with the Department of Aero-Power Sci-Tech Center, College ofAutomation Engineering, Nanjing University of Aeronautics and Astronautics,Nanjing 210016, China (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2013.2270014

I. INTRODUCTION

THE two-switch buck-boost (TSBB) converter, as shownin Fig. 1, is a simplified cascade connection of buck andboost converters [1]. Compared with the basic converters, whichhave the ability of both voltage step-up and step-down, suchas inverting buck-boost, Cuk, Zeta, and SEPIC converters, theTSBB converter presents lower voltage stress of the powerdevices, fewer passive components, and positive output volt-age [2][4], and it has been widely used in telecommuncationsystems [4], battery-powered power supplies [5], [6], fuel-cellpower systems [7], [8], power factor correction (PFC) applica-tions [9], [10], and raido-frequency (RF) amplifier power sup-plies [11], all of which have wide input voltage range. It is thusimperative for the TSBB converter to achieve high effieciencyover the entire voltage range. Moreover, consindering that theinput voltages from battery and fuel cell fluctuate with the out-put power, and the input voltage in the PFC applications varieswith the sinusoidal line voltage, a satisfactory input transientresponse preventing large output votlage variation in case ofinput voltage variation is also desired for the TSBB converter.

There are two active switches in the TSBB converter, whichprovides the possibility of obtaining various control methods forthis converter. If Q1 and Q2 are switched ON and OFF simul-taneously, the TSBB converter behaves the same as the single-switch buck-boost converter. This control method is called one-mode control scheme [12], [13]. Q1 and Q2 can also be con-trolled in other manners. For example, when the input voltageis higher than the output voltage, Q2 is always kept OFF, andQ1 is controlled to regulate the output voltage, and as a result,the TSBB converter is equivalent to a buck converter, and issaid to operate in buck mode. On the other hand, when the inputvoltage is lower than the output voltage, Q1 is always kept ON,and Q2 is controlled to regulate the output voltage, and in thiscase, the TSBB converter is equivalent to a boost converter, andis said to operate in boost mode. Such control method is calledtwo-mode control scheme [3], [4]. Compared with one-modecontrol scheme, two-mode control scheme can reduce the con-duction loss and switching loss effectively, leading to a highefficiency over a wide input voltage range, as explained in [4].Besides, in order to achieve automatic switching between buckand boost modes, the two-mode control scheme based on twomodulation signals with one carrier or one modulation signalwith two carriers was proposed in [14].

When the TSBB converter operates in continuous currentboost mode, it presents a right-half-plane (RHP) zero. This RHP

0885-8993 2013 IEEE

2038 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 4, APRIL 2014

Fig. 1. Two-switch buck-boost (TSBB) converter.

zero limits the bandwidth of the control loop, penalizing the tran-sient response [15]. Moreover, in the two-mode control schemewith automatic mode-switching, only one voltage regulator isused for both buck and boost modes, and it is often designedto have enough phase margin in boost mode by reducing thebandwidth of the control loop, thus the transient responses ofthis converter are deteriorated in the whole input voltage range,including both buck and boost modes. To improve the tran-sient response of the TSBB converter, average current modecontrol [16], current-programmed mode control [17], [18], andvoltage mode control with a two-mode proportional-integral-derivative (PID) [19], Type-III (2zeros and 3poles) [20] com-pensator, or passive RC-type damping network [21] are em-ployed. With these control schemes mentioned earlier, the in-fluence of the input voltage and load disturbances on the outputvoltage can be well reduced, but cannot be fully eliminated.

For the converter in the applications with wide input voltagevariation, input voltage feed-forward (IVFF) compensation isan attractive approach for improving the transient response ofthe converter, for it can eliminate the effect of the input voltagedisturbance on the output voltage in theory. The IVFF of thebuck or boost converter can be implemented in several meth-ods: 1) vary either the amplitude of the carrier signal [22], [23]or the value of the modulation signal [24][26] according to theinput voltage. However, the variations of the carrier signal forthe IVFF of the boost converter and the modulation signal forIVFF of the buck converter are both inversely proportional tothe input voltage, which imply that the implementation of thisIVFF method is complicated relatively for the TSBB converter.2) Calculate the duty ratio [27][30]. Since the duty ratio cal-culation for the buck converter is inversely proportional to theinput voltage, a little complicated realization is also required.3) Derive the IVFF function producing zero audio susceptibilitythrough the small-signal model [31][34]. As derived in [31],the IVFF functions of buck and boost converters are both inproportion to the input voltage, and they are easy to be imple-mented. So, the IVFF method with derived IVFF function fromthe small-signal model will be adopted in this paper.

IVFF compensation for the TSBB converter with two-modecontrol scheme has been achieved by varying the peak and valleyvalues of the carrier signal in proportion to the input voltage inbuck and boost modes, respectively [35], or the peak value of thecarrier signal and modulation signal in proportion to input volt-age simultaneously [36]. In these control schemes, the selectionand switching of operating modes and IVFF compensations arenot automatic, but require a rather complicated mode detector,which is realized by comparing the input voltage and outputvoltage and adding auxiliary circuits. In addition, consideringthe carrier signal generators of most IC-controllers operate froman internally derived power supply, the IVFF methods by vary-

ing the carrier signal with input voltage are not very general.Thus, this paper will combine the two-mode control schemewith automatic mode-switching ability and the IVFF functionsderived from the small-signal models under different operat-ing modes together, and propose a general, easy implementa-tion, and effective two-mode scheme with IVFF compensation,achieving automatic selections of the operating modes and thecorresponding IVFF functions simultaneously. In other words,when the input voltage is higher than the output voltage, theTSBB converter with this proposed control scheme can operatein buck mode and select the IVFF function of this mode au-tomatically. On the other side, when the input voltage is lowerthan the output voltage, the TSBB converter can operate in boostmode and select the IVFF function of boost mode automatically.

This paper is organized as follows. Section II introduces thetwo-mode control scheme with automatic mode-switching abil-ity for the TSBB converter, and Section III derives its small-signal models under different operating modes. Based on thederived small-signal models, the IVFF functions under differentoperating modes are derived, and a two-mode control schemewith IVFF compensation is proposed to achieve automatic se-lections of operating modes and the corresponding IVFF func-tions simultaneously, and nearly smooth mode-switching. Be-sides, the comparisons between the two-mode control schemewith and without IVFF compensation are given in Section IV.Section V presents the experimental results from a prototypewith this proposed control scheme, and finally, Section VI con-cludes this paper.

II. TWO-MODE CONTROL SCHEME WITH AUTOMATICMODE-SWITCHING ABILITY

As shown in Fig. 1, the voltage conversion of the TSBBconvetrter operated in continuous current mode (CCM) is [4]

Vo =d1

1 d2 Vin (1)

where d1 and d2 are the duty cycles of switches Q1 and Q2 ,respectively.

In the two-mode control scheme, d1 and d2 are controlledindependently. When the input voltage is higher than the out-put voltage, the TSBB converter operates in buck mode, whered2 = 0, i.e., Q2 is always OFF, and d1 is controlled to regulatethe output voltage; when the input voltage is lower than the out-put voltage, the TSBB converter operates in boost mode, whered1 = 1, i.e., Q1 is always ON, and d2 is controlled to regulatethe output voltage. Thus, the voltage conversion of the TSBBconverter with two-mode control scheme can be written as

Vo =

d1Vin , d2 = 0 (Vin Vo)Vin

1 d2 , d1 = 1 (Vin < Vo) .(2)

Fig. 2 shows the TSBB converter under the two-mode controlscheme based on two modulation signals and one carrier, andFig. 3 gives the key waveforms of this control scheme, whereve buck and ve boost are the modulation signals of Q1 and Q2 ,respectively, and vsaw is the carrier. The maximum and min-imum values of the carrier are VH and VL , respectively, and

YAO et al.: TWO-MODE CONTROL SCHEME WITH INPUT VOLTAGE FEED-FORWARD FOR THE TWO-SWITCH BUCK-BOOST 2039

Fig. 2. TSBB converter under the two-mode control scheme.

Fig. 3. Two-mode control scheme based on two modulation signals and onecarrier. (a) Vbias = Vsaw . (b) Vbias > Vsaw .

the peak-to-peak value of the carrier is Vsaw = VH VL . Withthe same carrier, in order to achieve the two-mode operation asdescribed in (2), only one of ve buck and ve boost can intersectvsaw at any time. So, it is required that

ve buck ve boost Vsaw . (3)

Hence, the output signal of the voltage regulator vea , as shownin Fig. 2, can be taken as ve boost , and ve buck is composed byadding a dc bias voltage, Vbias , to vea , i.e.,

{ve buck = vea + Vbiasve boost = vea .

(4)

Substituting (4) into (3) yieldsVbias Vsaw . (5)

So, the modulation signal in (4) with Vbias Vsaw canachieve the two-mode operation of the TSBB converter. WhenVin > Vo, ve buck will be within [VL , VH ], and it intersectsvsaw and thus determines d1 ; and meanwhile, ve boost =veave buck Vsaw < VL , and thus d2 = 0. Such case cor-responds to the buck mode of the TSBB converter. WhenVin < Vo, ve boost = vea will be within [VL , VH ], and it inter-sects vsaw and thus determines d2 ; and meanwhile, ve buck =vea + Vbias vea + Vsaw > VH , and thus d1 = 1. Such casecorresponds to the boost mode of the TSBB converter. WhenVin = Vo , which is the switching point of the buck and boostmodes, ve boost = VL , and thus d2 = 0; and meanwhile,ve buck VH , and thus d1 = 1. It can be found that ve buck =VH if Vbias = Vsaw , and ve buck > VH if Vbias > Vsaw at themode-switching point, as depicted in Fig. 3(a) and (b), respec-tively. So, by letting Vbias = Vsaw , i.e., ve buck ve boost =Vsaw at the mode-switching point, the buck and boost modescan be smoothly switched from each other.

III. IVFF FOR TWO-MODE CONTROL SCHEME

A. Derivations of DC and Small-Signal Models of the TSBBConverter

As described in [37] and [38], in the averaged switch model ofa dcdc converter, the switch is modeled by a controlled currentsource with the value equaling to the average current flowingthrough the switch, and the diode is modeled by a controlledvoltage source with the value equaling to the average voltageacross the diode. With this method, the averaged switch modelof the TSBB converter can be obtained, as shown in Fig. 4(a),where iQ1 = d1iL and iQ2 = d2iL , which are the average cur-rents flowing through switches Q1 and Q2 , respectively, andvD1 = d1vin and vD2 = d2vo , which are the average voltagesacross diodes D1 and D2 , respectively.

The average values of voltage, current, and duty cycle in theaveraged switch model can be decomposed into their dc and accomponents, so iQ1 , iQ2 , vD1 , and vD2 can be expressed as

iQ1 = IQ1 + iQ1 =(D1 + d1

)(IL + iL

)

= D1IL + D1 iL + d1IL + d1 iL (6)iQ2 = IQ2 + iQ2 =

(D2 + d2

)(IL + iL

)

= D2IL + D2 iL + d2IL + d2 iL (7)vD1 = VD1 + vD1 =

(D1 + d1

)(Vin + vin)

= D1Vin + D1 vin + d1Vin + d1 vin (8)vD2 = VD2 + vD2 =

(D2 + d2

)(Vo + vo)

= D2Vo + D2 vo + d2Vo + d1 vo (9)where the upper-case letter denotes the dc value, and the lower-case letter with hat () denotes the small-signal perturbation.


Fig. 4. Models of the TSBB converter. (a) Averaged switch model. (b) DCmodel. (c) Small-signal model.

With small-signal assumption, the average values in (6)(9)can be linearized by neglecting the second-order ac terms [1].Then, the dc model of the TSBB converter can be gotten byreplacing the average values in Fig. 4(a) with the dc componentsin (6)(9), as depicted in Fig. 4(b). Besides, the inductor Lf isshort circuit, and the capacitor Cf is open circuit in the dcmodel. Likely, by replacing the average values in Fig. 4(a) withthe first-order ac components in (6)(9), the small-signal modelof the TSBB converter can be obtained, as illustrated in Fig. 4(c).According to (2), setting d2 = 0, i.e., D2 = 0, d2 = 0, and d1 =1, i.e., D1 = 1, d1 = 0 in Fig. 4(c), respectively, the small-signalmodels in buck and boost modes can be derived.

B. Derivation of IVFF FunctionsFig. 5(a) shows a general control block diagram of a dcdc

converter [1], where Gvd(s), Gvo v in(s) and Zo(s) are the trans-fer functions of the duty ratio d, input voltage vin , and outputcurrent io to the output voltage vo , respectively, Gvr (s) is thetransfer function of the voltage regulator, GPWM(s) is the trans-fer function of the pulse-width modulation (PWM) modulator,vo ref is the output voltage reference, and Hvo(s) is the sensegain of the output voltage. As seen, the disturbance of input volt-age vin affects the output voltage through the path with transferfunction Gvo v in (s). This effect can be eliminated by intro-ducing an additional path with transfer function Gvo v in(s)from the input voltage to the output voltage, as illustratedwith the dashed line shown in Fig. 5(a). Moving the outputof Gvo v in (s) to the output of voltage regulator and corre-sponding transfer function being changed to G (s), the controlblock is equivalently transformed to that shown in Fig. 5(b).The path from vin to v is called the IVFF path, and the IVFF

Fig. 5. Control block diagram with IVFF of a dcdc converter. (a) Introductionof IVFF. (b) Equivalent transformation of IVFF.

function G (s) is

G (s) =vvin

= Gvo v in (s)GPWM (s)Gvd (s)

. (10)

As shown in Fig. 5(b), the output of G (s), i.e., v , is addedto the output signal of the voltage regulator, i.e., vea , formingthe modulation signal ve .

As discussed earlier, by setting D2 = 0 and d2 = 0 in thesmall-signal model of the TSBB converter shown in Fig. 4(c),the small-signal model in buck mode can be obtained, and thetransfer functions of duty ratio and input voltage to the outputvoltage in this mode, Gvd buck(s) and Gvo v in buck(s) can bederived as

Gvd buck (s) =vo (s)

d (s)

v in =0

=Vin dc

s2Lf Cf + sLfRL d

+ 1

(11)

Gvo v in buck (s) =vo (s)vin (s)

d=0

=1

s2Lf Cf + sLfRL d

+ 1

VoVin dc

(12)where Lf ,Cf , and RLd are the filter inductor, filter capacitor,and load resistor of the TSBB converter, respectively, and Vin dcand Vo are the input voltage and output voltage at the quiescentoperation point, respectively.

Likewise, by setting D1 = 1 and d1 = 0 in Fig. 4(c), thesmall-signal model in boost mode can be gotten, and the trans-fer functions of duty ratio and input voltage to the output volt-age in this mode, Gvd boost(s) and Gvo v in boost(s), can be,


TABLE IPARAMETERS OF THE PROTOTYPE

respectively, derived as

Gvd boost (s)=vo (s)

d (s)

v i n =0

=1 s LeRL d

s2LeCf + s LeRL d + 1V 2o

Vin dc

(13)

Gvo v in boost (s)=vo (s)vin (s)

d=0

=1

s2LeCf + s LeRL d + 1Vo

Vin dc

(14)where Le = Lf V 2o /V 2in dc .

The transfer function of the PWM modulator GPWM(s) canbe expressed as [1]

GPWM (s) =d (s)ve (s)

=1

Vsaw. (15)

Substituting (11), (12), and (15) into (10), the IVFF transferfunction in buck mode can be derived as

G buck (s) = VoV 2in dc

Vsaw . (16)

Similarly, substituting (13)(15) into (10), the IVFF transferfunction in boost mode can be derived as

G boost (s) = 1Vo

(1 s LeRL d

)Vsaw . (17)

In (17), the term sLe/RLd = sLf V 2o /(RLdV

2in dc

)is

a function of frequency, and the factor Le/RLd =Lf V

2o /

(RLdV

2in dc

)reaches its maximum value at full load

and minimum input voltage. According to the parameters ofthe prototype listed in Table to appear in Section V, the mag-nitude of sLe /RLd with the full load resistor RLd = 21.6 and the minimum input voltage Vin min = 250 V is depictedin Fig. 6. Fortunately, the input voltage of the battery-poweredpower supply [5], PFC application [9], RF amplifier supply [11],and fuel-cell power system [39] fluctuates at low frequency, andthus |sLe /RLd | 1, as shown in Fig. 6. Therefore, (17) can besimplified as

G boost (s) = 1Vo

Vsaw . (18)

Fig. 6. Magnitude of sLe /RLd as the function of frequency.

C. Two-Mode Control Scheme With IVFF CompensationSince the TSBB converter can operate in buck and boost

modes, and the IVFF transfer functions for the two operatingmodes are different, it is important to ensure that the TSBBconverter operates in correct mode with correct IVFF transferfunction and switches between the two modes automatically.

According to (16) and (18), the output signals of the IVFFpath under different operating modes can be expressed as

v buck = G buckVin = VoV 2in dc

VsawVin

v boost = G boostVin = 1Vo

VsawVin .

(19)

As seen from (19), the ouput signal of the IVFF path inboost mode is independent of Vin dc , so the value of Vin dcis considered only in the buck mode. If the value of Vin dc inv buck is changed with the quiescent operation of the converter,a division operation on input voltage [33], [34], which requiresrather complicated implementation, will be involved. For easyimplementation, a tradeoff point, i.e., the middle value of theinput voltage region in buck mode is set as Vin dc , i.e., Vin dc =(360 + 500) / 2 = 430 V, in this paper.

As seen in Fig. 5(b), the modulation signal ve is the sum of theoutput signals of the IVFF path and the voltage regulator, i.e.,ve = v + vea . Hence, according to (4) and (19), the modula-tion signals of the TSBB converter under the two-mode controlscheme with IVFF compensation can be expressed as

ve buck = v buck + vea + Vbias

= VoVsawV 2in dc

Vin + vea + Vbias

ve boost = v boost + vea= VsawVo

Vin + vea .

(20)

As discussed in Section II, the condition shown in (3), i.e.,ve buck ve boost Vsaw , should be satisfied for the propertwo-mode operation. Substituting (20) into (3) leads to

Vbias Vsaw VoVsawVin(

1V 2o

1V 2in dc

)

. (21)

As mentioned earlier, Vin dc is set to the middle value of theinput voltage region in buck mode, and it is greater than Vo .So, the right-hand side of (21) decreases with the input voltage


Fig. 7. Schematic diagram of the two-mode control scheme with IVFF.

Vin , and it gets its maximum value at the minimum input voltageVin min . So, here Vbias is set to this maximum value for ensuringsmooth mode-switching between buck and boost modes withcorresponding IVFF compensation as much as possible, i.e.,

Vbias = Vsaw VoVsawVin min(

1V 2o

1V 2in dc

)

. (22)

By substituting (22) into (20), the final modulation signals ofthe TSBB converter can be written as

ve buck = v buck + vea + Vbias = VoV 2in dc

Vsawvin

+vea + Vsaw VoVsawVin min(

1V 2o

1V 2in dc

)

ve boost = v boost + vea = 1Vo

Vsawvin + vea .

(23)According to (23) and Table , the value of ve buck ve boost

at the mode-switching point is 1.09Vsaw , which can be treatedas nearly smooth switching between buck and boost modes.

Fig. 7 gives the schematic diagram of the two-mode controlscheme with IVFF compensation, where G buck and G boostare the IVFF functions for buck and boost modes, expressedas (16) and (18), respectively, and Vbias is the dc bias voltageexpressed as (22).

IV. COMPARISONS BETWEEN THE TWO-MODE CONTROLSCHEME WITH AND WITHOUT IVFF COMPENSATION

A. Output Signal of the Voltage RegulatorAccording to Fig. 3, the relationship between the modulation

signal and the duty ratio under different operating modes can beexpressed as

ve buck VLd1Ts

=VsawTs

, ve boost < VL (Vin Vo)ve boost VL

d2Ts=

VsawTs

, ve buck > VH (Vin < Vo) .(24)

Fig. 8. Comparison of vea between the two-mode control scheme with andwithout IVFF compensation.

Substituting the duty ratio expressions shown in (2) into (24)yields

ve buck =VoVin

Vsaw + VL , ve boost < VL (Vin Vo)

ve boost =(

1 VinVo

)

Vsaw + VL , ve buck > VH (Vin < Vo).

(25)It can be found from (25) that the modulation signals under

the two-mode control scheme are the functions of only inputvoltage. After the input voltage being known, the correspond-ing modulation signal will be determined, no matter the IVFFcompensation being incorporated or not.

Combining (23) and (25), the output signal of the voltageregulator under the two-mode control scheme with IVFF com-pensation can be derived as

vea =

Vsaw

(VoVin

+Vo

V 2in dcVin +

Vin minVo

VoVin minV 2in dc

1)

+VL (Vin Vo)VH (Vin < Vo) .

(26)Similarly, combining (4) with Vbias = Vsaw and (25), the out-

put signal of the voltage regulator under the two-mode controlscheme without IVFF compensation can be derived as

vea =

(VoVin

1)

Vsaw + VL (Vin Vo)(

1 VinVo

)

Vsaw + VL (Vin < Vo) .(27)

According to (26), (27), and Table I, vea under the two-modecontrol scheme with and without IVFF compensation can be de-picted, as the solid and dashed lines shown in Fig. 8, respectively.It can be seen that the variation of vea under the two-mode con-trol scheme with IVFF compensation is much smaller than thatwithout IVFF compensation over the entire input voltage range,which implies that the IVFF mainly regulated the output volt-age, extremely alleviating the task of the voltage regulator andimproving the transient response on the disturbance of the inputvoltage. Additionally, it also can be seen that vea has a small leapat the mode-switching point when the IVFF compensation is in-corporated. This phenomenon is resulted from the introduction


Fig. 9. Modulation signals under the two-mode control scheme with IVFFcompensation.

of IVFF compensation, leading to ve buck ve boost =1.09Vsaw at the mode-switching point, i.e., a nearly smoothswitching between buck and boost modes, which has been dis-cussed in Section III. Substitution of (26) into (23) can obtainthe modulation signals over the whole input voltage range forthe TSBB converter under the two-mode control scheme withIVFF compensation, as shown in Fig. 9, which illustrates thatautomatic and nearly smooth mode-switching is achieved.

B. Input-to-Output Voltage Transfer FunctionAccording to Fig. 5, the loop gain of a dcdc converter is

T (s) = Gvr (s)GPWM(s)Gvd(s)Hvo(s) (28)

Setting Gvr (s) = 1, and substituting Gvd buck(s) andGvd boost(s) as described in (11) and (13) into (28) respec-tively, can obtain the uncompensated loop gains in buck andboost modes, which are defined as Tu buck(s) and Tu boost(s).According to Table , the bode diagrams of Tu buck(s) at themaximum input voltage Vin max = 500 V and Tu boost(s) atthe minimum input voltage Vin min = 250 V can be obtained,as the dashed lines shown in Fig. 10(a) and Fig. 10(b), respec-tively. Compared to Tu buck(s), Tu boost(s) presents a lowercrossover frequency and smaller phase margin, due to the RHPzero. Therefore, the design of Gvr (s) is considered in boostmode.

Proportional-integral (PI) regulator is widely adopted as thevoltage regulator. According to Fig. 10(b), Tu boost(s) has itsmaximum phase margin (PM) equaling 50 at 1 kHz. Given thenegative phase-shift of PI regulator, the crossover frequency ofthe loop gain is set to be 1 kHz to ensure enough PM in boostmode. It means that the turning frequency of PI regulator needsto be far below 1 kHz, so the proportional component Kp thatis mainly in effect at the crossover frequency and Kp = 30 isobtained. Then, by setting PM to 45, the integral component Kican be calculated as Ki = 100. On the other hand, consideringthe attenuation ability in high-frequency region of Tu boost is0 dB, a pole with the slope of20 dB is adopted, whose turningfrequency is 10 kHz. So the voltage regulator can be expressed

Fig. 10. Bode diagrams of the loop gains under different operating modes.(a) Vin max = 500 V, buck mode. (b) Vin m in = 250 V, boost mode.

as

Gvr (s) =30s + 100

s(

s10000 + 1

) . (29)

In Fig. 10(a) and (b), the bode diagrams of the compensatedloop gains in buck and boost modes, i.e., Tbuck(s) and Tboost(s),are given with the solid lines, respectively. As seen, enoughphase margins are ensured in both buck and boost modes. How-ever, the bandwidths of the two modes are very low, leading topoor dynamic performance over the entire input voltage range.Therefore, it is very necessary to use the IVFF compensationto improve the input voltage transient response of the TSBBconverter with the voltage regulator expressed in (29).

According to Fig. 5, the closed-loop input-to-output voltagetransfer function with IVFF compensation, vo v in , can be ex-pressed as

vo v in (s) =vo (s)vin (s)

=Gvo v in (s) + G (s)GPWM (s)Gvd (s)

1 + T (s). (30)


Fig. 11. Bode diagrams of the input to output voltage transfer function.(a) Vin max = 500 V, buck mode. (b) Vin m in = 250 V, boost mode.

Substituting G (s), Gvo v in(s) and Gvd(s) in buck and boostmodes derived in Section III into (30), the magnitude of vo v inwith IVFF compensation in buck and boost modes can be ob-tained, shown with the solid lines in Fig. 11(a) and (b), respec-tively. Likewise, the dashed lines in Fig. 11(a) and (b) are themagnitudes of vo v in without IVFF compensation in buck andboost modes with G (s) = 0, respectively. As seen, the abilityon suppressing the effect of the input voltage disturbance on theoutput voltage for the TSBB converter with IVFF compensa-tion is improved obviously, no matter in buck or boost mode.In addition, it also can be seen from Fig. 11 that the effect ofthe IVFF compensation in boost mode is more remarkable thanthat in buck mode in the low-frequency range. The reason isthat the IVFF function in buck mode is not so accurate due toVin dc equaling the middle value of the input voltage region ofthis mode, and the magnitude of the simplified IVFF function inboost mode is quite close to that without simplification in thisfrequency range, as described in (16)(18).

V. EXPERIMENTAL VERIFICATION

In order to verify the effectiveness of the proposed two-modecontrol scheme with IVFF compensation, a 250500 V input,360 V output, and 6-kW rated power prototype is fabricated.The parameters of the prototype are listed in Table . Please benoted that the filter capacitor Cf is designed when the TSBBconverter operated as the front-end dcdc converter in a two-

stage fuel-cell power system, and it needs to provide all of thepulsating power of the down-stream dcac inverter.

Fig. 12 shows the specific diagram of the TSBB converterunder the two-mode control scheme with IVFF compensation,where UC3525 #1 and UC3525 #2, having the same carriervsaw (both peak-to-peak value and frequency), are employed forcontrolling Q1 and Q2 , respectively, and error amplifier (E/A)#2 in UC3525 #1 with R3R7 and E/A #3 in UC3525#2 withR8R11 are used to compose the modulation signals of Q1 andQ2 , i.e., ve buck and ve boost expressed as (23), respectively. InFig. 12, the expressions of ve buck and ve boost can be derivedas

ve buck =(

R7R6

+ 1)

R5R4R5 + R3R4 + R3R5

(R4VREF1 + R3vea) R7R6

vin s

ve boost =(

R11R10

+ 1)

R9R8 + R9

vea R11R10

vin s

(31)

where vin s = VinRs4 /(Rs3 + Rs4) is the sensed input voltagesignal, obtained by resistor divider with Rs3 = 100 k, Rs4 =1 k and the voltage follower OA #2, vea is the output signal ofthe voltage regulator, obtained by the E/A #3 with R1 = 10 k,R2 = 300 k, C1 = 330 pF, and C2 = 1 F, and VREF1 =5 V is a dc voltage from the VREF1 pin of UC3525 #1. Besides,vo s = VoRs2 /(Rs1 + Rs2) is the sensed output voltage signal,obtained by the resistor divider with Rs1 = 430 k, Rs2 = 3k and the voltage follower OA #1, and vo ref = 2.5 V is thereference signal of output voltage, obtained by resistor dividerwith R12 = R13 = 1 k from the VREF2 pin of UC3525 #2.

Combining (23) and (31), the values of R3R11 in Fig. 12can be obtained, which are R3 = 10 k, R4 = 3.9 k, R5 =36 k, R6 = 20 k, R7 = 10 k, R8 = 6.8 k, R9 = 10 k,R10 = 10 k, and R11 = 6.8 k, respectively, in the practicalcircuit.

Fig. 13 shows the experimental waveforms of the TSBB con-verter under the two-mode control scheme with IVFF compen-sation at the steady state, including cathode-to-anode voltageof D1 , vD1 , the drain-to-source voltage of Q2 , vds_Q2 , and theinductor current iLf from the top to bottom in each figure.Fig. 13(a) shows the waveforms at Vin = 500 V, where theTSBB converter operates in buck mode. It can be seen that Q2is always OFF and vds_Q2 equals the output voltage, and Q1is controlled to regulate the output voltage. Fig. 13(b) showsthe waveforms at Vin = 250 V, where the converter operatesin boost mode. Here, Q1 is always ON, vD1 equals the inputvoltage, and the output voltage is regulated by controlling Q2 .

Figs. 1416 show the experimental waveforms at full loadwith and without IVFF compensation when the input voltagesteps between 400 and 500 V, 250 and 320, and 250 and 500 V,respectively, corresponding to the TSBB converter operatingin buck mode, boost mode, and the switching between buckand boost modes. It can be seen from these figures that thetwo-mode control scheme with IVFF compensation can achieveautomatic selections of correct operating modes and the cor-responding IVFF compensations simultaneously, and the input


Fig. 12. TSBB converter under two-mode control scheme with IVFF.

Fig. 13. Waveforms under the two-mode control scheme with IVFF at the steady state. (a) Buck mode. (b) Boost mode.

Fig. 14. Waveforms of step input voltage in the buck mode. (a) Without IVFF. (b) With IVFF.

voltage transient response is improved. It should be noted thatthe stepped input voltage is from the programmable dc source,Chroma 62150 H-600 S, with maximum output current 25 Aand output voltage 600 V. Once the required current of the con-verter is greater than 25 A, the slew rate of the step input voltagewill be limited. As shown in Fig. 16, the slew rate of the inputvoltage without IVFF compensation is smaller than that withIVFF compensation, when the stepped input voltage between250 and 500 V happens. This reason is that the input current of

the converter without IVFF compensation is greater than 25 Ain this condition.

Fig. 17 shows the experimental waveforms of TSBB convertwith load step between 10 and 100% full load, including theoutput voltage Vo , output current Io , vD1 , and vds_Q 2 fromthe top to bottom in each figure. Fig. 17(a) and (b) are thewaveforms in buck mode at Vin = 500 V and boost mode atVin = 250 V, respectively. As seen, the load transient responseover the whole input voltage range is satisfactory.


Fig. 15. Waveforms of step input voltage in the boost mode. (a) Without IVFF. (b) With IVFF.

Fig. 16. Waveforms of step input voltage between buck mode and boost mode. (a) Without IVFF. (b) With IVFF.

Fig. 17. Waveforms of step load between 10% and 100% full loads. (a) Buck mode. (b) Boost mode.

Fig. 18. Efficiency of the TSBB converter under two-mode control with IVFF.

Fig. 18 shows the measured efficiency of the TSBB converterunder the two-mode control scheme with IVFF compensation, it

can be seen that the TSBB converter under this control schemeachieves high efficiency over the entire input voltage range,especially at the mode-switching point, as explained in [4].

VI. CONCLUSIONFor the TSBB converter operated with the two-mode control

scheme, the small-signal models in buck and boost modes arebuilt, and based on which, detailed derivations of the IVFFfunctions under different operation modes are given in thispaper. With reasonable simplification of the IVFF function inboost mode, a general, easy implementation and effective two-mode control scheme with IVFF compensation is proposed toachieve automatic selection of operating modes and the corre-sponding IVFF compensations for the TSBB converter. More-over, the switching between buck and boost modes in this


proposed control scheme is nearly smooth. In order to presentthe merits of this proposed control scheme clearly, comparisonsbetween the two-mode control scheme with and without IVFFcompensation, including the output signals of the voltage reg-ulator and the input-to-output voltage transfer functions, arediscussed in this paper. Finally, a 250500 V input, 360 V out-put and 6-kW-rated power prototype is built and tested, and theexperimental results demonstrate the validity of this proposedcontrol scheme, with which high efficiency over the whole inputvoltage range and improved input voltage transient response areachieved for the TSBB converter.

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Chuan Yao was born in Jiangxi, China, in 1986. Hereceived the B.S. degree in the electrical engineer-ing and automatization from Chongqing University,Chongqing, China, in 2007. He is currently workingtoward the Ph.D. degree in the College of Electricaland Electronic Engineering, Huazhong University ofScience and Technology, Huazhong, China.

His main research interests include soft-switchingdcdc converters and the renewable energy genera-tion system.

Xinbo Ruan (M97SM02) was born in Hubei,China, in 1970. He received the B.S. and Ph.D. de-grees in electrical engineering from the Nanjing Uni-versity of Aeronautics and Astronautics (NUAA),Nanjing, China, in 1991 and 1996, respectively.

In 1996, he joined the Faculty of Electrical En-gineering Teaching and Research Division, NUAA,where he became a Professor in the College of Au-tomation Engineering in 2002, since then, and hasbeen engaged in teaching and research in the field ofpower electronics. From August to October 2007, he

was a Research Fellow in the Department of Electronic and Information Engi-neering, Hong Kong Polytechnic University, Hong Kong. Since March 2008,he has been also with the College of Electrical and Electronic Engineering,Huazhong University of Science and Technology, China. He is also a GuestProfessor with Beijing Jiaotong University, Beijing, China, Hefei Universityof Technology, Hefei, China, and Wuhan University, Wuhan, China. He is theauthor or co-author of four books and more than 100 technical papers publishedin journals and conferences. His main research interests include soft-switchingdcdc converters, soft-switching inverters, power factor correction converters,modeling the converters, power electronics system integration, and renewableenergy generation system.

Dr. Ruan was a recipient of the Delta Scholarship by the Delta Environmentand Education Fund in 2003 and was a recipient of the Special Appointed Pro-fessor of the Chang Jiang Scholars Program by the Ministry of Education, China,in 2007. Since 2005, he has been serving as the Vice President of the ChinaPower Supply Society, and since 2008, he has been a member of the TechnicalCommittee on Renewable Energy Systems within the IEEE Industrial Elec-tronics Society. He has been an Associate Editor for the IEEE TRANSACTIONSON INDUSTRIAL ELECTRONICS and the IEEE JOURNAL OF EMERGING AND SE-LECTED TOPICS ON POWER ELECTRONICS since 2011 and 2013, respectively.He is a Senior Member of the IEEE Power Electronics Society and the IEEEIndustrial Electronics Society.

Weijie Cao was born in Jiangsu, China, in 1985. Hereceived the B.S. and M.S. degrees in electrical engi-neering and automatization from Chongqing Univer-sity and the Nanjing University of Aeronautics andAstronautics, China, in 2008 and 2011, respectively.

His main research interests include dcdc conver-sion and converter control techniques.

Peilin Chen was born in Hubei, China, in 1988. Shereceived the B.S. degree in electrical and electronicengineering from the Huazhong University of Sci-ence and Technology, Wuhan, China, in 2011, whereshe is currently working toward the M.S. degree.

Her current research interests include modelingand control of dcdc converters.

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