15th International Power Electronics and Motion Control Conference, EPE-PEMC 2012 ECCE Europe, Novi Sad, Serbia

One-Sensor Current Sharing in MultiphaseInterleaved DC/DC Converters with Coupled

InductorsJens C. Schroeder, Marinus Petersen∗, Friedrich W. Fuchs∗∗

Institute for Power Electronics and Electrical Drives, University of Kiel, Kiel, Germany,email: jsc@tf.uni-kiel.de, ∗mp@tf.uni-kiel.de, ∗∗fwf@tf.uni-kiel.de

Abstract—To improve the efficiency and to reduce thevolume of dc-dc converters and their filters, interleavedconverters are used. For further reduction of the induc-tor volume, coupled inductors can be applied. In thesemultiphase converters, appropriate active current sharingis necessary due to the inherent current unbalance causedby the parameter deviations of the components and theduty cycles of the phases. The common method to realizecurrent sharing is to use a single current sensor for eachphase whereas the current in each phase is controlledindependently. Due to the costs of the current sensors, areduction of the quantity is desirable. In this contribution,a method is presented which allows the current sharing bymeans of only one current sensor without extra circuitryand computation effort. This method is analyzed exemplarilyfor the application in a threephase interleaved converterwith coupled inductors in theory and practice. Successfuloperation can be stated.

Keywords—interleaved converter, current sharing, coupledinductors.

I. INTRODUCTION

The main issues in electric vehicles are the maximiza-tion of range and the lifetime of the cost-intensive battery.In a common electric propulsion system, the battery isconnected to the voltage source inverter (VSI) which feedsthe machine. So the battery has to deliver or absorb all thepower which is demanded or recuperated by the propul-sion system in all operating points. Due to the internalbattery resistance, the battery voltage varies significantlydepending on the battery current. Operating under highcurrents, the lifetime decreases in an accelerated way andin general the recuperation efficiency is poor. To optimizebattery lifetime, efficiency and voltage stabilization, abattery buffer system (BBS) can be implemented [1],[2]. The block diagram of an exemplary system can beseen in Fig. 1. The regenerative braking energy is fedinto the BBS during recuperation. During accelerationof the vehicle, the energy is fed back into the systemto support the battery. Thus, the battery stress can bereduced. To improve the efficiency and to reduce thevolume, a threephase interleaved converter with coupledinductors (CI) is used here, which is shown in Fig. 2.The research work for the special converter with the one-sensor current sharing principle has been done for thislift truck propulsion system. The results are of generalimportance. Interleaved converters show several benefitscompared with conventional converters. Especially in au-tomotive applications, the resulting volume reduction andthe efficiency improvement by interleaved operation are

Fig. 1. Lift truck propulsion system

Fig. 2. Threephase interleaved converter with coupled inductors

fundamental [3], [4], [5]. Interleaved converters consistof N parallel arranged identical topologies whose pulsewidth modulation (PWM) is phase shifted 360◦/N againstone another. Interleaved operation results in the benefitof current ripple reduction and inductor volume reduction[4]. For further reduction of the inductor volume, coupledinductors can be applied in such converters [6], [7], [8],[9]. For this parallel converter section, current balancingis necessary.

The investigated current sharing method should beable to be applied to systems with coupled inductors aswell. The components in an N-phase interleaved convertershould be rated for 1/N part of the current. Due to possiblecomponent and duty cycle deviations between the differentphases, the current might not be divided equally withoutan active current sharing. For a safe operation, an activecurrent sharing is mandatory to load all phases with thesame current.

The common way to realize current sharing is to useN single current sensors, i.e. one for each phase, whereas

Fig. 3. Coupled inductors on E-E ferrite core

the current in each phase is controlled independently. Tominimize costs and the complexity of the converter, thegoal is the reduction to only one single current sensor. Inthis work, a one-sensor current sharing for a threephase in-terleaved converter with coupled inductors is investigated.The converter is used in an electric lift truck to connect a24 V lead acid battery and electric double layer capacitors(EDLC) in a battery buffer system. The system power is5 kW, the EDLC voltage level is in the range of 26 V-38 V. In this system, coupled inductors are applied. Theyare wounded on an E-E core like it is shown in Fig. 3[4], [5], [10]. Several authors have designed methods ofcurrent sharing in the past. In [11], a method is presentedin which a current sensor is switched between the differentphases. Due to the additional switches, the componentnumber increases considerably. In [12], a master slavemethod is developed. All slave phases have to be operatedin discontinuous current mode there, thus it cannot beimplemented in continuous current mode. The author in[13] measures the voltage at the output capacitor andcan detect a phase unbalance via a fourier analysis, [14]adapts the method. This method demands high calculationcapability and very fast sampling. In [15] a current sharingmethod for a twophase interleaved converter is presented.The current through the highside MOSFETs is measuredby one sensor. By symmetrical sampling during a pre-calculated timestep, the phase currents can be detectedand controlled independently for a limited range of dutycycles.

This method has been extended in [16] by furtherinvestigations to realize a current sharing in a threephaseinterleaved converter with uncoupled inductors and thegiven margins of the battery buffer system. Here, aninvestigaton is done to apply this method in interleavedconverters with coupled inductors.

In section II, the demand for current sharing is shown.In section III the new current sharing method is introducedand analyzed, simulation results are presented. In sectionIV, measurement results verify the applicability of the newmethod for coupled inductor operation and in section V aconclusion is given.

II. VERIFICATION OF THE DEMAND FOR CURRENTSHARING

At first, the demand for a current sharing control isshown. Therefore, the current characteristics are presentedfor a system without current sharing. In this system, thetarget duty cycle in all three phases is the same. An openloop control or a closed loop control with a feedback of the

Fig. 4. Equivalent magnetic circuit of threephase coupled inductor

resulting current can be used. To validate the consequencesof such a control, some deviations in the different phasesare set. The phase resistances, for instance in the inductor,can deviate as well as the inductance and the duty cyclewhich is applied at the MOSFETs.

Unequal current distribution causes higher losses inthe converter, and components which are not rated forcurrents equal to the maximum occuring one could bedestroyed in the worst case. For interleaved converterswith coupled inductors, an unequal current distribution cancause another important problem, which is explained in thefollowing.In Fig. 4 the equivalent magnetic circuit of the the coupledinductor with a ferrite E-E-core is shown. The reluctanceof the airgap is strictly higher than from ferrite material.Thus, each leg is represented by the magnetic reluctanceRm,C . The flux’s leakage path reluctance through the airis given as Rm,L.

The coupling factor k between two phases can be cal-culated via (1) for a symmetrical inductor. Ideal couplingin a threephase system results in k = 0.5 .

k =

Rm,C ·Rm,L

Rm,C+Rm,L

Rm,C +Rm,C ·Rm,L

Rm,C+Rm,L

(1)

The magnetic flux, here exemplarily Φ1, can than becalculated like in (3). It is assumed that the turns foreach phase are equal, thus NL,1=NL,2=NL,3=NL. Forsimplicification, Rm,eq is introduced in (2).

Rm,eq = Rm,C +Rm,C ·Rm,L

Rm,C + 2 ·Rm,L(2)

Φ1 =NL,1 · I1Rm,eq

− k · NL,2 · I2Rm,eq

− k · NL,3 · I3Rm,eq

=NL

Rm,eq· (I1 − k · I2 − k · I3) (3)

It can be seen that the DC part of the magnetic flux iscompletely cancelled for the case that k=0.5 and I1=I2=I3.The coupling factor of the inductor which is selected inthe lift truck’s interleaved converter is k=0.42. So the corecross section was rated to a maximum DC flux, which canbe calculated in (4). Ii,max is one third of the nominalconverter current.

Φi,max =2NL

3Req·(

1

3IN − 0.42 · 1

3IN − 0.42 · 1

3IN

)=

2NL

3Req· (0.053 · IN ) (4)

Thus, the core rating has been done for a maximum mag-netization, which is generated by 0.053 ·IN , approximately10A. This resulting DC current, from which the DC-magnetization can be calculated, is introduced as Im,DC

here. In case of unequal current distribution, alreadysmall current differences in the phases are able to causesaturation in the core due to the occurance of additionalDC flux.Thus, a current sharing is needed which guarantees equalcurrent distribution between the phases.In Fig. 5 the current characteristics are shown in case ofphase inequalities. In (a) a 20 % increase of the phaseresistance is set, in (b) a 0.01 duty cycle increase in phasetwo. It is obvious that especially an inequality in the dutycycles, which is rather a problem in analogue controlcircuits, results in high deviations between the phasecurrents. Phase resistance inequalities cause problems aswell. Inductance deviations do not influence the averagecurrent, they only result in different current ripples.

To get a reference on how the current can be sharedunder perfect circumstances, Fig. 6 is shown. The cur-

Fig. 5. Simulated current characteristics without current sharing andinductors without saturation effects, (a) 20 % resistance increase in phase2 (b) 0.01 duty cycle increase in phase 2 (d=0.2, IDCDC = 150A,VEDLC = 30V )

Fig. 6. Simulated current characteristics with current sharing atphase current measurement, 0.01 duty cycle increase in phase 2 (d=0.2,IDCDC = 150A, VEDLC = 30V )

rents of the inductors are measured by three sensors andcontrolled independently in each phase, thus the differentphases carry the same current despite deviations in theduty cycle or the phase resistance. The goal is to achievethis behavior by means of only one current sensor.

III. REDUCING THE NUMBER OF CURRENT SENSORS

The challenge is to realize current sharing with only onecurrent sensor. The derivation of the method is presentedfor an interleaved converter with uncoupled inductors in[16]. It is derived from [15], where a method to realizecurrent sharing in a twophase interleaved converter is pre-sented in which the resulting current through the highsideMOSFETs is measured. The limitations concerning theallowed operating duty cycles are presented as well: Theminimum duty cycle in boost operation is dependent onthe number of phases and the ratio between the minimumtime Tmin,AD which is needed by the AD-converter tomeasure the current and the period time TP . dmin can becalculated in (5) [15]. The maximum duty cycle in boostoperation can be calculated with (6) [15].

dmin,boost =N − 2

N+Tmin,AD

TPWM(5)

dmax,boost = 1 − Tmin,AD

TPWM(6)

In a threephase interleaved converter which is used inthe lift truck’s battery buffer system, operated at a switch-ing frequency of 16 kHz and an estimated Tmin,AD of5 µs, it results in dmin,boost=0.413 and dmax,boost=0.92.The EDLC voltage level, which is within the range of25V-38V, is always higher than the battery voltage, whichis around 24V. The resulting duty cycle is strictly lowerthan d=0.413. Thus, this method cannot be used to realizecurrent sharing in this system. So the location of thecurrent sensor was changed to the common branch belowthe lowside MOSFETs like it is shown in Fig. 7.

In Fig. 8, the current characteristics of the converter areshown for one period in boost mode. ILS exceeds zeroonly during conducting of the lowside switches, which

Fig. 7. Topology of converter with single current measurement belowlowside MOSFETs

is during the switch-on time in boost mode and duringswitch-off time in buck mode. If the sampling of thecurrent is done in the middle of the respective currentslope (topt,1,topt,2,topt,3) the average currents of the threesingle phases can be detected by only one current sensor.

The minimum and maximum duty cycles can be calcu-lated by (7) and (8).

dmin,boost =Tmin,AD

TPWM(7)

dmax,boost = 1 −(N − 2

N+Tmin,AD

TPWM

)(8)

For the margins of the threephase converter in the lifttruck propulsion system, it results in 0.08 < d < 0.587,

Fig. 8. Current characteristics in a threephase interleaved converter andoptimum sample time in boost mode (d > 1

3)

so it can be applied here.It has to be proven that the phase current is in its

average in the middle of the switches on-time in the caseof coupled inductors as well. It has to be done a distinctionof cases here due to different overlappings according tothe operated duty cycle. In case A it is d < 1

3 and incase B it is 1

3 < d < 23 . In case A, no change in

the effective inductance occurs during the switch-on timeof one phase. The valves of the remaining phases arecontinuously off due to d < 1

3 . So the slope gradientis constant. The average current can be sampled in themiddle of the switch-on time. In Case B, which is shownin Fig. 8, there are two slope changes during the switch-ontime of one phase. They are caused by the turning-off ofphases 2 and 3, which operate under d > 1

3 . Due to thesystem’s and inductor’s symmetry, the effective inductanceand thus the current slope gradients are not dependent onwhich of the two remaining phases are switched on at thelowside MOSFET. Furthermore, the lengths of the twotime intervals, in which the effective inductance changesdue to the other phases’ switching, are the same due to theduty cycle’s symmetry. Thus, in the middle of the switch-on time, the current is in its average. Of course, in case ofunbalanced inductors or duty cycles, the accuracy of thecurrent sampling decreases. But to prevent the inductorsfrom magnetic saturation, an adequate symmetry in thesystem is given anyway. The same behaviour can be shownfor buck mode for d > 2

3 and 13 < d < 2

3 .The optimal sampling times topt,boost and topt,buck for

continuous current operation can be calculated by (9) and(10), whereas i is the phase number:

topt,boost = T ·(d

2+i− 1

N

)(9)

topt,buck = T ·(d

2+

1

2+i− 1

N

)(10)

In Fig. 9, the simulation results are presented again foran inequality in the duty cycle and the phase resistance.

It has been shown that the current sharing control workswell and that the characteristics are the same as in thethree-sensor current sharing. This nearly perfect behavioris caused by the fact that each current can be controlledseperately. The only drawback of this kind of currentsharing method is the location of the current sensor. Ithas to be implemented between the lowside MOSFETsand the ground plane, which is within the commutationpath of the semiconductors. Thus, on-circuit sensors haveto be used to keep the stray inductance as low as possible.

A constraint of this single-sensor method has to be madefor the discontinous current mode. The operation can beseen in Fig. 10. If the sampling is done in the middleof the rising slope, the average current is obviously notmatched. Thus, the controller adjusts a current which islower than the desired one, as can be deduced from thecurrent characteristics in Fig. 10.

This can be tolerated because discontinuous currentoperation only occurs if less then 10% of the nominalsystem power is demanded. Slight differences in the targetcurrent is not of importance. Anyway, for systems whichare operating in the discontinuous current mode in a wider

Fig. 9. Simulated current characteristics with current sharing by meansof one sensor below the lowside MOSFETs: (a) 0.01 duty cycle increasein phase 2 (b) 20 % resistance increase in phase 2 (d=0.2, IDCDC =150A, VEDLC = 30V )

Fig. 10. Simulated current characteristics with current sharing indiscontinuous current mode (d=0.08, IDCDC = 7A, VEDLC = 30V )

power range, a correction factor could be implemented inthe controller for low duty cycles or currents.

IV. LABORATORY SETUP AND MEASUREMENTRESULTS

The developed current sharing method is implementedin the laboratory test bench in an FPGA. The FPGAgenerates the threephase interleaved PWM and realizesthe symmetric sampling of the three currents. IRFS3006-

Fig. 11. PCB of the three phase interleaved converter (26-34V, 200A);red circle marks the current sensor between lowside MOSFETs andpower ground

7PPbF MOSFETs (60V /240A ) are chosen for the three-phase interleaved converter. The AD-conversion is doneby a fast 10 bit AD-converter ADC101S051. The printedcircuit board (PCB) of the converter with the ACS758xCBcurrent sensor is shown in Fig. 11.

In the laboratory setup, two different system mea-surements are performed to show the demand for thecurrent sharing and the functionality with the one-sensormethod. Each measurement is done once with the currentsharing and once without current sharing. Without currentsharing means, the current in phase 1 is controlled and theresulting duty cycle which is defined by the controller, isapplied in phase 2 and phase 3 as well. In the measurementresults in Fig. 12 the current characteristics are shown for aduty cycle inequality, that means the duty cycle in phase 1is set 0.01 higher, which is 140 ns, than in the other phases.The duty cycle error is implemented between controllerand MOSFETs, so it symbolizes a hardware inequality inlogical or driver ICs.

It can be seen that the currents are not equally dividedfor the case without current sharing in (a). Due to themarginal higher duty cycle in phase one, the current inphase one is strictly higher than in the other phases. Dueto the coupled inductors, this unequal distribution influ-ences the system behaviour significantly. The magneticDC flux cannot be eliminated anymore due to (3). Thecurrent Im,DC , which produces the DC flux results inapproximately 20-25A, which is significantly higher thanthe rated magnitude. Thus, the magnetic material showssaturation effects in phase one. This saturation effectincreases the inequality of the currents due to the reductionof inductance in this case. Especially at high currentoperation, the maximum allowed phase-current would beexceeded in case of saturation. Thus, unequalities in caseof coupled inductors must be prevented necessarily.If the current sharing is implemented, the currents aredistributed equally, which can be seen in Fig. 12b.In Fig. 13, the current characteristics are shown for a phaseresistance inequality. It can be seen that the currents arenot equally divided for the unbalanced case (a) withoutcurrent sharing.

Due to the increased phase resistance in phase one,the current is lower than in the other phases if operatedwith the same duty cycle. In phase one, one third of thecontrollers target current is adjusted. Due to the same dutycycle in phase two and three, the equivalent currents are

Fig. 12. Measured current characteristics with 0.01 increased duty cyclein phase one; IDCDC*=50A (a) without current sharing, IDCDC =30A, (b) with current sharing, IDCDC = 50A, (d=0.2, VEDLC =30V )

appreciably higher, so the resulting current exceeds thedemanded current more then 20%.By means of the single-sensor current sharing operationin (b), the currents can be controlled independently andso they can be divided equally. Thus, the appropriateoperation of the single-sensor current sharing method isshown.

To analyze the influence of the current sensor in thecommutation path to the MOSFETs overvoltage duringswitch-off, further measurements are performed. First,a maximum voltage of 66.8V occurs during maximumEDLC voltage operation of 36V. The voltage can bereduced by an additional 10 nF capacitor, which is appliedbetween the drain source connectors of the MOSFETs.The maximum voltage can be reduced to 54.4V, which istolerable.

V. CONCLUSION

In this contribution, the demand for current sharing ininterleaved converters with coupled inductors has beenshown and a method has been investigated to realizecurrent sharing in such a converter by means of onlyone current sensor and without further effort. Simulationresults show the ability of this method to replace thethree-sensor current sharing without further complexityor drawbacks. A threephase interleaved converter with anon-circuit current sensor between the lowside MOSFETsand power ground has been built up in the laboratory.The importance of the demand for current sharing inconverters operated with coupled inductors due to inductor

Fig. 13. Measured current characteristics with approx. 20 % increasedphase resistance in phase one; IDCDC*=40A (a) without current shar-ing, IDCDC = 50A, (b) with current sharing, IDCDC = 40A, (d=0.2,VEDLC = 30V )

saturation at unequal current distribution could be shown.The functionality of the single-sensor method has beensuccessfully approved. The occuring overvoltage duringswitching due to the current sensor in the commuta-tion path has been analyzed and the operation could besatisfactorily improved by an additional capacitor. Thus,the single-sensor current sharing has been succesfullydesigned, analyzed and tested in the laboratory and isready to be implemented in the lift truck’s battery buffersystem.

REFERENCES[1] M. Ortuzar, J. Moreno, and J. Dixon, “Ultracapacitor-based aux-

iliary energy system for an electric vehicle: Implementation andevaluation,” Industrial Electronics, IEEE Transactions on, vol. 54,pp. 2147 –2156, aug. 2007.

[2] M. Camara, H. Gualous, F. Gustin, and A. Berthon, “Design andnew control of dc/dc converters to share energy between super-capacitors and batteries in hybrid vehicles,” Vehicular Technology,IEEE Transactions on, vol. 57, pp. 2721 –2735, sep. 2008.

[3] M. Hirakawa, M. Nagano, Y. Watanabe, K. Ando, S. Nakatomi,S. Hashino, and T. Shimizu, “High power density interleaved dc/dcconverter using a 3-phase integrated close-coupled inductor setaimed for electric vehicles,” in Energy Conversion Congress andExposition (ECCE), 2010 IEEE, pp. 2451 –2457, sept. 2010.

[4] F. F. J. Schroeder, B. Wittig, “High efficient battery backup systemfor lift trucks using interleaved-converter and increased edlc voltagerange,” Industrial Electronics Conference, 2010.

[5] J. Schroeder and F. Fuchs, “Design of a powermanagement fora battery buffer system in an electric lift truck by means offuzzy control and genetic algorithm,” in Power Electronics andApplications (EPE 2011), Proceedings of the 2011-14th EuropeanConference on, pp. 1 –10, 30 2011-sept. 1 2011.

[6] H. Nagaraja, D. Kastha, and A. Petra, “Design principles of a sym-metrically coupled inductor structure for multiphase synchronousbuck converters,” Industrial Electronics, IEEE Transactions on,vol. 58, pp. 988 –997, march 2011.

[7] F. Yang, X. Ruan, Y. Yang, and Z. Ye, “Interleaved criticalcurrent mode boost pfc converter with coupled inductor,” PowerElectronics, IEEE Transactions on, vol. 26, pp. 2404 –2413, sept.2011.

[8] P. Zumel, O. Garcia, J. Cobos, and J. Uceda, “Magnetic integrationfor interleaved converters,” Applied Power Electronics Conferenceand Exposition, 2003. APEC ’03. Eighteenth Annual IEEE, vol. 2,pp. 1143 – 1149 vol.2, feb. 2003.

[9] M. Hirakawa, Y. Watanabe, M. Nagano, K. Andoh, S. Nakatomi,S. Hashino, and T. Shimizu, “High power dc/dc converter usingextreme close-coupled inductors aimed for electric vehicles,” inPower Electronics Conference (IPEC), 2010 International, pp. 2941–2948, june 2010.

[10] J. Schroeder and F. Fuchs, “Detailed characterization of coupledinductors in interleaved converters regarding the demand for addi-tional filtering,” unpublished.

[11] R. Singh and A. Khambadkone, “Current sharing and sensingin n-paralleled converters using single current sensor,” IndustryApplications, IEEE Transactions on, vol. 46, pp. 1212 –1219, may-june 2010.

[12] L. Huber, B. Irving, C. Adragna, and M. Jovanovic, “Implemen-tation of open-loop control for interleaved dcm/ccm boundaryboost pfc converters,” in Applied Power Electronics Conferenceand Exposition, 2008. APEC 2008. Twenty-Third Annual IEEE,pp. 1010 –1016, feb. 2008.

[13] G. Eirea and S. Sanders, “Phase current unbalance estimation inmultiphase buck converters,” Power Electronics, IEEE Transactionson, vol. 23, pp. 137 –143, jan. 2008.

[14] S. Mariethoz, A. Beccuti, and M. Morari, “Model predictive controlof multiphase interleaved dc-dc converters with sensorless currentlimitation and power balance,” in Power Electronics SpecialistsConference, 2008. PESC 2008. IEEE, pp. 1069 –1074, june 2008.

[15] H. Kim, M. Falahi, T. Jahns, and M. Degner, “Inductor currentmeasurement and regulation using a single dc link current sensorfor interleaved dc/dc converters,” Power Electronics, IEEE Trans-actions on, vol. 26, pp. 1503 –1510, may 2011.

[16] J. C. Schroeder, M. Petersen, and F. Fuchs, “Current sharing in athree-phase interleaved converter for ccm with measurement of onecurrent,” PCIM Europe 2012, Nuremberg, 2012.