Load Sharin Scd Dc Converter41

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Load-Current-Sharing Control for Parallel Operation of DC-to-DC Converters

Ren-Hua Wu*. eruhiko Kohama, Yuichi Kodera, Tamotsu Ninomiya and Fumiaki Ihara**

InputPower\-

Department of ElectronicsKyushu UniversityFukuoka. 812Japan

fo r CB Control

.OutpurPowerConverter

#k

bConnection Terminal

for CB Control

Converter -#n

Abstract

The conuol strategy for parallel operation of multiple converters isinvestigated. Analysis and design consideration of load-current sharingfor the parallel system are presented and the superiority of current-balance control is discussed. The prominent features of the load-currentsharing and analytical results are confirmed experimentally for a three-paralleled forward-converter system.

1. Introduction

The use of paralleled power supply modules is a key technology for

any large-capacity power supply system. The basic requirements forparallel systems are the full-automatic load-current balance, the simpleconfiguration of feedback controllers, the high reliability and easymaintenance, etc. Most of the studies reported recently concentrate on thedevelopment of control schemes for parallel systems in which the powersupply modules share the same source and load. The basic parallelcontrol scheme is the "drooping" method. with which the power supplymodules in the parallel system sha re the total load current according to thepredetermined load characteristics of all paralleled modules. However,this scheme cannot provide the automatic load-current balance. The"master/ slave" method [ l , 21 is a kind of active control scheme. With thetypical master/slave method, it is necessary to intercommunicate betweenthe master and slave modules, and therefore the interconnection lines arecomplicated. Another kind of active control scheme is the "output-currentfeedback" method. A control scheme was presented in [3], in which thecurrent sharing is accomplished by sensing the switching device currentsof individual modules and balancing them. The sam e principle of current-

sharing control has been used and the alternative connectionimplementations of current -balance controllers have been proposed in14). These control schemes provide an r-out-of-n redundant configurationfor a high-reliability power supply system.

Analysis 6f the parallel system has been the topic of numerouspapers[5-8]. For parallel operation, the most important concern is thestatic load-current sharing between paralleled converters. Based on theload characteristics, a more general analysis of load sharing of paralleledmodules with the control scheme of the "drooping" method was given in[ 5 ] , and the load-sharing ability of some converters was investigated in

[61.In this paper, the novel control strategy proposed in [3 , 41 are briefly

introduced in Section 2. Then the analysis of load-current sharing ofparalleled converters with the proposed strategy and the superiority ofcurrent-balance control are presented in Section 3. The prominentfeatures of the load-current sharing and analytical results are verifiedexperimentally for a three-paralleled forward-converter system in Section

4. The design consideration of the parallel system on the parameterdesign of current-balance controllers is discussed in Section 5 . Finallythe dynamic characteristics of the parallel system are discussed in Section6.

2 . Control Strategy for Parallel Operation

A paralleled-converter system to be discussed here comprises n unitsof converters as shown in Fig. 1. Every converter comprises a switchingpower converter, a PWM controller and a current-balance controller (C B

* Visiting scholar on leave from Department of Electrical EngineeringTsinghua UniversityBeijing, 10084China

**Applied Engineering Department

Fujitsu Denso Ltd.Kawasaki, 213Japan

Controller) as shown in Fig. 2. Compared with usual converters, thedifference is that the proposed converter has a CB Controller which iscomposed of two parts: a feedback control circuit and a parallelconnection circuit.

Connection Terminalfor CB Control

Fig. 1 Paralleled converter system

DC-to-DC 1 ;c4 onvener

ControlleI

I C

I Converter ' ITV*

Voltage Reference ,

Fig. 2 Converter Configuration

2-1. Controller for Parallel Operation

Consider the output cument to be shared by the paralleled converter asthe output-current reference. On the assumption that every converter hasthe same power-capacity, this reference means the average of all or

partial converter output currents which is denoted by Ulk. and obtainedby the parallel connection circuits of CB Controllers. The transducer

shown in Fig. 2 produces the signal Ulk proportional to the output current

of Converter #k. The difference between ulk and the output-current

reference Ulk. which represents the unbalance of output current, is

used as the negative feedback signal so that the converter output current

101



Iok can follow the output-current reference and the paralleled convertersautomatically share the total load. From the viewpoint of simpleconfiguration, the proportional control (P ontrol) is chosen as follows:

where KcBk and UcBk are the fe edbac k gain and the o utput sign al of CBController #k, respectively.

2-2. Connection Implementations

described as follows:

(a) Bus type connection

buffer amplifier in every CB Controller can be expressed as

UCBk = - KCBk (UIk-UIk, av ) (1)

Three types of connection implementations of CB Controllers are

Bus type connection is shown in Fig. 3. The output signal of the

CB Controller

--f # 1 +UI I

U124 CB Controller 4# 2

e

e

CB Controller# k

I a1

I

I

Ie I

e I

I Uln I

2 U k

U1av =%-

CB Controllerucd

le

a gU1.

Fig. 3 Connection of CB Controllers

(Bus type)

U1 represents the average output current of al l paralleled converters.A switch is inserted in each CB controller. If one of n conv erters fails,this switch is turned off and the corresponding CB Controller is removedfrom the bus. As aresu lt, the average output current becomes

5 kUlav =L=l

n - 1 (3 )and then the current balance is also maintained. This m eans an r-out-of-nredundant configuration for a highly reliable power supply system.

(b)Single-loop type connectionSingle-loop type connection is shown in Fig. 4. In CB Controller #k,

the averaging procedure is the partial one among two neighboring

converters and the average output cu rrent is obtained asUI k -l + U1k when k+l

U k , av =uI n + 1 when k=l

(4)

(c) Double-loop type connectionDouble-loop type connection is shown in Fig. 5 . There are two loops

in this type of connection implementation. In CB Controller #k, theaveraging procedure is the partial one among three neighboringconverters and the average output current is obtained as

0-7803-1243-0/93$03.00Q 1993IEEE

CB Controller

CB Controller

CB Controller

CB Controller# n

Fig. 4 Connection of CB Controllers(Single-Loop type)

Fig. 5 Connection of CB Controllers(Double-Loop type)

2-3. Unification Concept of CB Controllers

parallel operation of different-capacity converters.(a) Balance condition of the parallel system

system, the balance condition means that every

converter share the total load proportional to its power capacity, i.e. thenormalized output currents of all paralleled converters and the parallelsvstem are equal as follows:

The unification concept of CB controllers is presented to perform the

In the parallel

(b) Unification of CB ControllersThe measuring characteristic of Transducer #k is shown in Fig. 6.

Designate the output signal of Transducer #k corresponding to lokmax by

Uil;max. Then Ulk is proportional to the converter output current asfollows:

102

(7)



The proposed control scheme results in that the output signals of allthe transducers are almost equal, i.e.

uI1" u12- ..." UIk" ..." UIn

When we choose Uillmsl to be the same for all the transducers, i.e.

U11max=.. .=Ulkmax=. ..= UInmax,CB controllers derive the balance condition (6 ) for multiple paralleledconverters with different power capacities. This depicts that the same

configuration of the CB controllers can be utilized for any paralleledconverters with different

. (8 )

( 9 )

-lek Iokmax

Output Current (A )

Fig. 6 Measuring Characteristic of Trasducer #k

3. Analysis of Load-Cun-entSharing

Analysis of load-current sharing of paralleled converters is animportant item when designing a parallel system. In this section,modeling and analysis of load-current sharing by the proposed controlstrategy are given.

3-1 Modeling of Load-Current SharingDenote the output voltage and the total load current of a parallel

system by V L and IL, respectively. The output equations of the parallelsystem are as follows:

(10)o l = v 0 2 = .. = vo, =V L

(11)Le t %k be the output resistance of Converter #k with'the PWM

output-voltage controller. A load-characteristic model of every converteris shown in Fig. 7. In practice, the load characteristic of a paralleledconverter is nonlinear , .e. &k is not constant. From Fig. 7, the staticload characteristic of a paralleled converter with PWM controller can bemodeled generally as follows:

Vo k = vrk - &k Iok

A

r

0 b k maxOutput Current (A )

Fig. 7 Load characteristic of Converter #k

Figure 2 shows that the CB control is performed by adjusting theoutput voltage reference. In other words, the CB control equivalentlymoves the drooping load characteristic up or down, but does not changethe drooping load characteristic. Therefore, the static load characteristicof a paralleled converter with PWM controller and CB controller isexpressed as

Vok = vrk + UCBk - %k Iok (12)

(13)CBk = -KPk(Iok - la", k

where

Kpk =UIkmaxKCBk

lokmax

l0k = okmax UIk

Ulkmax

l av , = l okmaxUlav, k

Ulkmax

Equation ( I O ) to (13) are the basic equations for the analysis of load-current sharing.

3-2. Load-Current Sharing of Paralleled ConvertersThe basis of analysis of load-current sharing is to calculate the static

output currents of all paralleled converters with the proposed strategy.The derivation of the load-current sharing of paralleled converters isdescribed here.

Equation ( I O ) can also be expressed asn

V L = q v J

n

Substituting (12) and (13 ) into (14) yields

(15)Subtracting (15) from (12) yields

-1Z.k Iok - 1i zo j Ioj ) = 0n J= I

From (16) . a general expression for the load-current sharing of all

(16)

Daralleled converters is finally derived as follow s:

The current feedback gain KR is a parameter to be designed.

Assuming K p k > > Z o k . the sensitivity of load-current sharing to Zok an d

v r k is considerably suppressed and then the output currents of allparalleled converters are approximately rewritten into (18). In general,analysis of load-current sharing can be performed by means of ( IO ) , (1 1).(12) . (13) and (18).

whereI

Iav, k = Okmax UIav, kUlkmax

Ulkmax Io kUlk =

lokmax

under the condition of Bus type connection:

under the condition of Single-loop type connection:

UUC, v =

1uI x l ; " I k when k + l

\yhenk=l

under the condition of Double-loop type connection:

U1 k-l + U1 k + U1 k+ l when k+l or

uk, i 3I n + "1 1 + U1 2 when k=]

3

I 3f l - I + ' fl + ' 1 when k=n

103



For example of Bus type connection with the same capacity, outputresistance, feedback gain and transducer output voltage, the load-currentsharing of paralleled converters is as follows:

capacity system. The power stage of the dc-to-dc converter is a forwardtype shown in Fig. 7,where the experimental circuit parameters areVi= ~ O V , ,= IOv, andf,= 100kHz.

4-1. The Equal-Capacity Converter SystemThe first parallel system is composed of three equal-capacity

converters of lokmax =S A (k=l, 2, 3). The static load characteristics ofall paralleled converters is shown in Fig. 9 (a). Fig. 9 (a) shows that the

output resistance& of the converter is about 0.03R nd the nonlinearityoccurs when the output current is small. The output voltage reference

v o k is nearly equal to IOv, U h a X s chosen to be Sv, and the current

feedback gain Km is chosen to be 1.25R so as to be much larger than&. The analytical load-current sharing under condition of Bus type and

Single-loop type of connection implementations are the same as follows:

lav, k=kIL. J=loj = IL and j=l lav, j = 1L

[v,,-': Iok=$L+ vq]

KPk +,&k

[ rk - 'x vq ]

KPk

1 l L + "j=t

n

l0 1 = 1 L

I 3,3 = IL

l 3ok = vr k - %k [kIL].

12 = 1 L and vok = vrk - 0.01 1LD1 3

The analytical and experimental load-current sharing of paralleledconverters are shown in Fig. 9 (b) and (c), where the experimentalunbalances are less than 0.5% and there is almost no difference amongdifferent types of connection implementations. As seen from these

results, the analytical method of load-current sharing proposed in Section

3 is verified for the normal parallel operation of equal-capacityconverters. (Note: the Double-loop type connection is the same as Bustype connection in case of n=3.)

To investigate the sensitivity of load-current sharing to the va riation ofimportant parameters of CB controllers, the analytical and experimentalresearches are done under the four kinds of exaggerated variations of theimportant parameters in the parallel system.

(a). Different output resistances:The first exaggerated condition is that the output resistances are

z01 =O.lR,Z,z =O.mndZ,,3 = 0 . 3 8 . From(17),theanalytical load-current sharing under the B~~ type connection and Single-loop typeconnection are derived respectively as ollows:

PWM and CBController

Fig. 8 Forward converter diagram6

4. Experimental Verifica tion

TWO kinds Of parallel Systems compos ed of three dc-to-d c converte rswere implemented fo r the experimental verification of load-current-shafing analysis: the equal-capacity converter system and the different-

........... ............ . .

...........

............ . . .

5 9.1U

0 1 2 3 4 5Converter output current (A )

(a).Load characteristic (Theconverter)

Total load current (A )

(c). Load-current sharingotal load current (A )

(b). Load characteris tic (The parallel system)

Fig.9 Static characteristics of the parallel system composed of three equal-capacityconverters


(a). Bus ype

12

3

1

0 3 6 9 1 2 1 5


(b). Single-loop ype


(Bus and single-loop ype)(c). Load characteristic

' case of different output resistancesig.10 Load-current sharing of paralleled equal capacity conv erters for@ I= 0.lQ Zo2=0.2R, zo3= 0.3R)

104



Bu s type:l01 = 0.3569 IL

102 = 0.3322 IL and vok = v r k - 0.075 1L

103= 0.3109 1~

1 = 0.3035 IL

The analytical and experimental load-current sharing are shown in Fig.10 (a), (b) and (c). Although the values and differences of outputresistances are very large, the analytical and experimental results showthat the load-current sharing of the parallel system can also be performedand the load-current unbalances are considerably suppressed (themaximum unbalance is about 7.1% for Bus type and 9% for Single-loop

type).

(b) Different feedback gains:The second exaggerated condition is that the current feedback gains

ar e Kpl J 0.625Q. Kn = 1.25Q and KB = 1.87551. From (18) . theanalytical load-current sharing under the Bus type connection and Single-loop type connection are derived as follows:

Io l =0.3513 IL

102 = 0.3451 IL and v& = v r k - 0.075 IL

{Single-loop type:

1 ol =1L

3\Io2 =1'' and v o k = vrk - 0.011L

1,3 = 11 ,

The analytical and experimental load-current sharing are shown in Fig. 11 (a), (b). Although the differences amon g current feedback gains arelarge, the analytical and experimental results show that the load-currentunbalances are zero.

0 3 6 9 1 2 1 5

Total load current (A)

(a). Bus type


(b). Single-loop type

Fig. 11 Load-current sharing of paralleled equal-capacityconverters for case of different feedback g ains(KP1=0.625Q, Kpz= 1.25Q 0 3 , 3.875Q)

(c ) Different voltage references:The third exaggerated condition is that the variation of converter

voltage references is *lo%, i.e. V,I = 11V ,Vr2= 1OV ,Vr3 = 9V. From(18). the analytical load-current sharing under the Bu s type connectionand Single-loop type connection are derived respectively follows:

Bu s type:

l01 = L IL + 0.8

Wh e n 1 ~ t 2 . 4 A31 103 = I L - 0.8

I l o l = IL + 0.4

12 = 1 L - 0.4 When 0.8A SILS2.4A

l 2,3 = 0

When OA <ILS0.8A

bo 3 = 0

Single-loop types:

l01 =1 L + 0.533

l 302 = 1 1 ~0.533 When l ~ t.2A\ 1 ~ 3 = , 1 ~ - 1 . 0 6 7

\ l o l = IL + 0.533

1,2 = 2, I L - 0.533

l 33 = 0

101= 1L

When 0.8A <-1~5.2A

102 = 0 When OA 51~5.8Ai03 = 0

5 I O 15

(a). Bu s type


................... ...

,0 3 6 9 1 2 1 5

Total load current (A )(b). Single-loop type

Fig. 12 Load-current sharing of paralleled equal-capacityconverters for case of different voltage references

(Vrl = 1 I v , Vr 2 = 10v, Vr3 = 9v)

The analytical and experimental load-current sharing are shown in Fig. 12 (a), (b). Although the differences among output voltage references arelarge, the analytical and experimental results show that the load-currentsharing of the parallel system can also be performed and the load-currentunbalances are considerably suppressed (the maximum unbalance is about16% for Bu s type and 21.34% for Single-loop type).

105



(d) Different transducer output voltages:The fourth exaggerated condition is that the variation of the transducer

output signal U I L ~ ~ ~s & lo % , i.e. U I I ~ ~5.5V , U I W = 5V ,

Ui3- =4 .5 V. From (18). the analytical load-current sharing under theBus type connection and Single-loop type connection are derived as

follows:Io1 =0.3 IL

I,,2 = 0.333 IL

i03 = 0.366 IL

The analytical and experimental load-current sharing are shown in Fig.13. where there is almost no differen ce among differen t types ofconnection implementations. Although the differences among transduceroutput signal Uii- are large, the analytica l and experim ental resultsshow that the load-current sharing of the parallel system can also beperformed and the load-current unbalances are considerably suppressed(the maximum unbalance is about 10%).


Fig. 13 Loadcurrent sharing of paralleled equal-capacityconve ners for case of differen t transducer output voltages

( l J I lm~=5 .5~ ,Ihu=5v, Ul3ma~4.5~)

The above analytical and experimental results show that the novelcontrol strategy for parallel operation proposed in 14) have goodadaptability to the parameter variations ant that the analytical method ofload-current sharing proposed in Section 3 is verified by means ofcomparing them. The good adaptability also means that it is easy todesign and set the parameters of CB controllers in paralleled modules.

4-2. The Different-Capacity Converter System:

The second parallel system is composed of three different-capacityconverters, and the maximum-rated output currents are l0lmu = 10A,Iozmu =7.5A, and103, = 5A . %k is about O.O3R, v o k is nearly equal to

lOv, UilunU is chosen to be 5v and KPL s chosen to be 1.25R. Theanalytical load-current sharing under condition of Bus type and Single-loop type of connection implementations are the same as follows:

Io1 = 0.444 IL

102 = 0.333 IL{ 03 = 0.222 IL

The analytical and experimental load-current sharing of paralleledconverters are shown in Fig. 14, where the experimental unbalances areless than 0.5% and there is almost no difference among different types ofconnection implementations. As seen from these results, the analyticalmethod of load-current sharing proposed in S ection 3 is verified for thenormal parallel operation of different-capacity converters.

2 10

0 4.5 9 13.5 18 22.5


Fig. 14 Load-current sharing of paralleleddifferent-capacity converters

(bImaa=lOA. IoZmu=7.5A. b3mx=SA)

5. Design Consideration of the Parallel System

The above mentioned results clarified that the proposed strategy hasmany good propertie s. In this section, some aspects on the design of theproposed strategy are discussed.

In general, the controller design procedure for a parallel system is:

First. a small-signal model of the parallel system is derived. Secondly,the small-signal model for the parallel system is simplified to anequiva lent single-module model. Finally , the controll er design isimplemented using the single-module model. Because the some kinds ofsimplification are introduced in the controller design procedure, thedesign results must be confirmed by other different manners. There aretwo kinds of manners: the experiment or the large signal simulation[7,8].Different from the usual control design procedure, the control design forthe novel control strategy proposed in 14) is implemented using the staticanalysis of load-current sharing. But the design results also need to beconfirmed by the experiments on the parallel system or the large signalsimulation.

In the parallel system, the most important specification is theunbalance of converter output currents. The unbalance criterion Uck ofConverter #k is defined as

(19)

There are two kinds of parameters in a paralleled converter: thecontrol parameters U l h a and Kpk. and the converter parameters v r k and

&k. v r k is nearly equal to the converter output voltage. Because thesensitivity of load-current sharing by the proposed strategy to Zok isconsiderably suppressed, the converter parameters to be designed are only

U~L- and KPk. Accord ing to the unification concept of CB controller s,Un, of every paralleled converter must be designed to be the same. The

minimum of Kpt is designed as below.On condition that the allowable maximum uck and the maximum

variation of parameter Vr k are given, we can determine the minimum Kpk

of all CB controllers with assumption of the same Kpk by means of (18)and (19). Taking the equal-capacity system with bus type connectionshown in Section 4-1 (c) as a example, if the maximum variation ofconverter voltage references is 10% and the maximum unbalance is

required less than 20%. the minimum of Kpk is calculated to be larger than

I Q . In the experiment, 1.25R is chosen.

controller #k is determined easily. This means that the proposed strategyis very practical.

From KcBk = 1okmsaKPk/ UIkmsx. the feedback gain KcBk in CB

6. Discussion on Dynamics of the Parallel system

In general, comparing with the output signal of PW M Controller, the

output signal UCBk of CB Controller is always smaller in the dynamicstate or static state. In Section 5, to meet the maximum unbalancespecification UCk in the parallel system, the minimum current feedback

ga in Kpk can be determined by means of analysis of load-current sharing.

Th e large r KPk is, the sm aller uck becomes. However, the larger Kpk ischosen, the better the current-balance control becomes, and on the otherhand, the current-balance control may affect the dynamic characteristics

of the parallel system . Therefo re, the maximum Kpk is limited by the

dynamics of the parallel system which are the transient overshoots andstability. The optimal Kpk can be determined by means of experimentalresults or the large signal simulation.

Transient responses of single converter and the parallel systemcom pose d by three equal-ca pacity converters for the rapid change of totalload current between 10% to 100% are shown in Fig. 15. Transientresponses of single converters and the parallel system composed by threedifferent-capacity converters are shown in Fig. 16. The experimentalresults show that the parallel system composed of equal-capacityconverters has the similar dynamics as the single converters and that thedynamics of the parallel system composed of different-capacityconverters is dependent on the dynamics of every single converter andthe current-balance controller.

106



(c). T he converter ( lozmu =7.5A)

capacitv converters (Total load change from 10%to 100%)Fig. 16 Transient responses of the parallel system composed of different-

. -(a). The parallel system

7. Conclusion

The usage of paralleled power supply modules is a key technology forany large-capacity po ue r supply system. In order to construct aparalleled dc-to-dc converter system w i t h good performance of load-current sharing and highly reLable configuration. a novel control suateg)for pxdlel operation of DC-to-DC converters has been discussed and theanalysis and design consideration on load-current sharing of paralleledconverters have been presented. and the effectiveness of the current-balance control h as been demonstrated.

Analytical results of load-current sharing she% that the sensitivity ofload-current sharing to the output resistances of paralleled conv eners isconsiderably suppressed and that the proposed strategy has goodadaptability to the parameter variations. The feedback gain of CBcontroller is the important parameter to be designed. The minimumfeedhack pain i s determined bv means of load-current-sharing analysis, - ~ -- _ _. ~ . ~ ~.- ~

(b). The converter (Iolmu= 5A ) and then the maximum feedback gain is limited by the dynamics of theparallel system.

The prominent features of the load-current sharing and analyticalresults have been confirmed experimentally for a three-paralleled

Fig. 15 Transient responses of the parallel system composed equal-capacity converters (Total load change from 10% o 100%)

(a). The parallel system

forward-converter system.

I References

V L

111 L. Tho rsell and P. Lin dman: "Reliability analysis of a directparallel connected n i l redundant power system based on highlyreliable DC/DC modules," Proc. 10th IEEE International Tele-communications Energy Conference (INTELEC'II), pp. 551-556.

[2 ] F. Petruzzirello, P. D. Ziogas, G. Joos: " A novel approachto paralleling of power converter units with true redundancy." 21thlEEE Power Electronics Specialists Conference Record (PESC '90). pp.

"

Method for cenualized voltage control and current balancing for paralleloperation of power supply equipm ent," Proc. 10th IEEE IntemationalTelecommunications Energy Conference (INTELEC'88), pp. 434--440.

[4] Tamotsu Ninomiya, Ren-Hua Wu, Yuichi Kodera, TeruhikoKohama and Fumiaki Ihara: "Novel Control Strategy for Parallel

808-813.[3 ] H. Tanaka, K. Kobayashi, F. Ihara, K. Asahi, M. Motoyama:

i1strategy for multi-module parallel converter system," 21 h IEEE PowerElectronics Specialists Conference Record (PESC '90). pp. 225-234.b). The converter (lolmu = 10A)

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Load Sharin Scd Dc Converter41

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