High-Power Three-Port Three-Phase BidirectionalDC-DC Converter

Haimin Tao, Jorge L. Duarte, Marcel A.M. HendrixGroup of Electromechanics and Power Electronics

Eindhoven University of Technology5600 MB Eindhoven, The Netherlands

Email: h.tao@tue.nl

AbstractThis paper proposes a three-port three-phase bidi-rectional dc-dc converter suitable for high-power applications.The converter combines a slow primary source and a fast storageto power a common load (e.g., an inverter). Since this type ofsystem is gaining popularity in sustainable energy generation sys-tems and electrical vehicles, the proposed topology is of practicalinterest. The proposed converter consists of three high-frequencyinverter stages operating in a six-step mode, and a high-frequencythree-port three-phase symmetrical transformer. The converterprovides galvanic isolation and supports bidirectional power owfor all the three ports. An arbitrary power ow prole in thesystem can be achieved by phase shifting the three inverterstages. Thanks to the three-phase structure, the current handlingcapability of the circuit is larger and the ripple currents at the dcsides are much lower owing to the interleaving effect of the three-phase, and thus the VA rating of the lter capacitors is muchlower. The operating principle and, in particular, the transformerdesign which is based on conventionally and coaxially woundstructures are presented. Circuit simulation results are includedto verify the proposed converter topology and the dual-PI-loopcontrol strategy.

I. INTRODUCTION

In the past decades, traditional power converter topologieshave been evolving in various directions, for example, fromsingle-phase to multiphase interleaving, and from two-level tomultilevel. Nowadays, most dc-dc power converters deal withsingle-input and single-output. Recently, attention has beenpaid to multiport converters [1]. Power conversion systemswhich combine a slow primary source with a fast storage topower a common load, which could be downstream converters(e.g., an inverter), are gaining popularity in sustainable energygeneration [2], [3] and electrical vehicles [4].

Alternative energy generators like fuel cells have slowdynamics and quite specic dc voltage and current charac-teristics. Furthermore, energy supplied by renewable sourcessuch as solar and wind energy has an intermittent nature,which necessitates a battery-type storage capable of long-termenergy buffering. For electrical vehicle applications, transientenergy storage is required to cope with the acceleration andbraking of vehicles. A three-port energy management systemaccommodates a primary source and a storage and combinestheir advantages automatically, while utilizing a single powerconversion stage to interface the three power ports. Having thetwo energy inputs, the instantaneous power can be redistrib-uted in the system in a controlled manner. The storage acts as

Primary Source

Storage

LoadThree-Port

Bidirectional Converter

t

t

P3

t

P1 P2

P1 P2

P30

0

0

Power Flow

Fig. 1. A three-port energy ow management system.

a power lter to smooth the power ow of the primary source,as shown in Fig. 1.

A second advantage of using such a system is that theprimary source only needs to be sized according to theaverage power consumed by the load for a specic application,not necessarily to the peak power. Such operation wouldavoid oversizing of the primary source and is economicallybenecial. Moreover, with the auxiliary storage, not only canthe system dynamics be improved, but also the storage canserve as a backup energy source in the event of a main sourcefailure.

In this regard, a few attempts have been made to exploredc-dc topologies suitable for multiple sources and/or storageelements [1], [2], [3], [4], [5], [6], [7], [8]. However, most ofthem are intended for medium- and low-power applications.

In this paper, a three-port three-phase converter topologysuitable for power management is proposed, and its potentialfor high-power applications is investigated. The converter isa direct extension of the single-phase version of the three-port converter in [6] and [8]. It is shown that the three-phaseconguration enhances the current rating of the system andthus the power rating. The converter is promising for electricalvehicles (e.g., fuel cell/battery cars) and electricity generationsystems. The three-phase concept has also been recognized in[5] for a multiple-input converter which can be regarded asan extension of the single-phase topology in [3] that uses acombination of a dc-link and magnetic-coupling to interfacemultiple power ports. The system modeling, operation princi-ple, control strategy, transformer design, and simulation resultsare presented in the following sections.

0197-2618/07/$25.00 2007 IEEE 2022

V1

V3

V2

High-frequency three-port three-phase symmetrical transformer

or

MOSFET IGBT

v1A

P S

T

G1 G2

G3

L1APrimary Secondary

Tertiary

AB

C

Coupled windings, phase ACoupled windings, phase BCoupled windings, phase C

L1BL1C

v1Bv1C

i1Ai1Bi1C

v3Av3Bv3C

i3Ai3Bi3C

L3AL3BL3C

v2Av2Bv2C

i2Ai2Bi2C

L2AL2BL2C

Port 1:Primary Sorce

Inv 3

iP1 iP2

iP3

P1

P3

P2

Port 3:Storage

Port 2:Load

Inv 1 Inv 2

C1

C3

C2

Fig. 2. Topology of the proposed high-power three-port three-phase triple-active-bridge (TAB) bidirectional dc-dc converter.

II. THREE-PORT THREE-PHASE TOPOLOGY

The three-port triple-active-bridge (TAB) topology has beenproposed for a fuel cell system for home applications ratedat a maximum power of 1 kW [7], [9] and 3.5 kW [10].To extend the topology towards high-power applications, thestandard way is to replace the single-phase bridge with a three-phase bridge, which enables higher current handling ability.The resulting converter topology is shown in Fig. 2. The three-phase concept used in the dual-active-bridge (DAB) converter[11] is applied to the TAB converter in this paper. As shown,the circuit consists of three inverter stages operating in a six-step mode with controlled phase shifts. The three bridgesare interconnected by a three-port three-phase symmetricaltransformer, and the inductors in the circuit represent theleakage inductance of the transformer (and external inductorsif necessary). The transformer can be either in Y-Y or in -connection. Note that coupling of the windings is between theports and there is no interphase coupling. As indicated in thegure, windings marked with the same symbol are coupled.

The major advantage of the three-phase version is the muchlower VA rating of the lter capacitors. Thanks to the natureof the symmetry, the current stress of the switching deviceis signicantly reduced compared to the single-phase version.As the current through the transformer windings is much moresinusoidal than in the single-phase situation (this is shown inthe simulation section), there are less high frequency losses inthe transformer. The proposed converter has the potential forhigh-power applications (say, tens of kilowatts). The operatingprinciple is very similar to the single-phase version. In additionto galvanic isolation, a major advantage of this converter isthe ease of matching the different voltage levels in the overallsystem. The leakage inductances of the transformer are anintegral part of the circuit. With reference to the primary side,

each bridge generates a high-frequency six-step mode voltagewith a controlled phase angle. The control scheme aims toregulate the output voltage and power of the primary sourcesimultaneously, using two phase shifts as control variables.The storage supplies/absorbs the transient power differencebetween the load and the primary source. This is an automaticsystem, matching the variations of the power drawn by the loadwhile the power of the primary source is kept at a constantlevel.

III. THREE-PORT SYSTEM MODELINGA. -Model Representation

The power ow in the three-port system has been exten-sively investigated in [2] and [8]. Since no interphase couplingexists in the system, one can analyze the circuit based on theper-phase model. For phase A, the circuit model shown inFig. 3(a) can be viewed as a network of inductors driven bycontrolled voltage sources that are phase-shifted with respectto each other. The controlled phase displacements imposethe power ow between the ports. Fig. 3(b) illustrates themodeling approach based on a -model equivalent trans-former representation [2]. The -model facilitates the systemsanalysis, and simple formulas allow converting the parametersfrom a T-model to the -model description [2].

Let us set the primary side as the reference for the phaseshift, and denote the phase angles of the load side and storageside as 12 and 13, respectively (see Fig. 4). According tothe denitions in Fig. 3(b), for a lossless system the powerow in the system can be described as

P1A = P12A P31AP2A = P23A P12AP3A = P31A P23AP1A + P2A + P3A = 0

(1)

2023

L12AL31A L23Av1A v2ALmA

1:m2

v3A

1:m3

L1A v2A

1:n2

v3A1:n3

L2A

L3ALMA

v1A

(a)

(b)

P1A , i1A P2A , i2A

P3A , i3A

P31A , i31A

P12A , i12A

P 23A, i 23

A

Fig. 3. T-model (a) and -model (b) representation of the three-porttransformer and inductors netwerk (per-phase model: phase A).

where P1A, P2A, P3A are the powers delivered by the primarysource, load and storage through phase A, respectively. Apositive value means supplying the power and a negative valuesuggests consuming the power. Note that for a lossless system,we have P3A = P1AP2A; therefore P3A is redundant. Thesame model can be applied to phase B and C. Obviously, thetotal power of the port is the sum of the power through eachphase:

P1 = P1A + P1B + P1CP2 = P2A + P2B + P2CP3 = P3A + P3B + P3C .

(2)

Again, P3 is redundant because P3 = P1 P2.The average power consumed by the load over a typical

operating cycle shall be equal to the power delivered bythe primary source. The storage port thereby functions as anexternal leveling device, smoothing out the uctuation in theinstantaneous power drawn by the load port.

Owing to symmetry, an analytical expression of the currentcan be derived [11]. By integrating the product of voltageand current with respect to time over one cycle, the averagepower transferred between the two ports in the six-step wavemode, taking bidirectional power ow into consideration, iscalculated to befor 0 || /3:

P =VaVbmL

(23 ||

2

)(3)

and for /3 || 2/3:

P =VaVbmL

(1 ||

18 ||)

(4)

v1A

v2A

i12A

v3A

i23A

i31A

V1/32V1/3

12

13

t

vPG12V1/3 V1/3

vSG2

vTG3

Fig. 4. Idealized operating waveforms (phase A) of the proposed three-portthree-phase TAB converter at 12 = /3 and 13 = /6.

where = 2fs (fs is the switching frequency); Va andVb are the dc voltages of the ports; denotes the phaseshift (in radians) between the two ports; L represents theequivalent inductance between the two ports; and m is theequivalent transformer turns ratio between the two ports [2](if the magnetizing inductance is neglected, m is equal to thephysical turns ratio n in the T-model.) The maximum powerow occurs at = /2. To illustrate the operation of theconverter, some ideal operating waveforms are shown in Fig. 4,according to the model in Fig. 3(b).B. First Harmonic Approach

Since the system can be regarded as voltage sources inter-connected through inductors, similar to the parallel operationof grid-frequency inverters where the active power control isachieved by controlling the phase displacement between theinverters, the three-port system can be treated like such ananoscale grid. The difference, however, is that this systemoperates at a much higher frequency (e.g., 100 kHz) than theconventional grid frequency.

Let us dene the switching function Sx = 1 when the upperswitch is ON and Sx = 0 when the lower switch is ON. Then,as an example, the primary port can be modeled as (referringto the denitions in Fig. 2)

S1AV1 = (v1A + vPG1)S1BV1 = (v1B + vPG1)S1CV1 = (v1C + vPG1)

(5)

where V1 is the dc voltage of the port, v1A, v1B and v1C arethe phase-to-neutral voltages, and vPG1 is the neutral (P) to

2024

v1A

L1A L2A

LMA

L3Av2A

v3A

v0A

Fig. 5. Primary referred per-phase model of the system (phase A).

ground (G1, the negative terminal of the source) voltage. Sinceeach inverter is a perfectly balanced three-phase system, wehave

v1A + v1B + v1C = 0. (6)The voltage vPG1 pulsates between V1/3 and 2V1/3 as de-picted in Fig. 4.

Fig. 5 shows the per-phase model of the converter whenreferred to the primary. The place where the magnetizing in-ductance is connected can be regarded as the connecting point.Assume that the magnetizing inductance is much larger thanthe leakage inductance. Fig. 6 shows a simplied three-phasemodel which is analogous to the parallel operation model ofgrid-frequency inverters. The voltage at the connecting pointcan be calculated by superposition, which gives, for instance,for phase A:

v0A =v1AL

2AL

3A + v

2AL1AL

3A + v

3AL1AL

2A

L1AL2A + L1AL

3A + L

2AL

3A

(7)

where L2A, L3A, v

2A and v

3A represent the primary-referred

values of L2A, L3A, v2A and v3A, respectively. Since v0A isneither accessible nor measurable, it can only be determinedby the status of v1A, v

2A and v

3A. For a symmetrical system

(i.e., L1A = L2A = L3A), we have

v0A = (v1A + v2A + v

3A)/3. (8)

With v0A, the power injected into the transformer cansimply be given by the familiar equation for the active powercontrol, e.g., for phase A of the primary port

P1A =U0AU1AL1A

sin(01) (9)

where 01 is the phase displacement between v0A and v1A,and U0A and U1A are the amplitudes of the fundamentalcomponents of v0A and v1A, respectively.

The power ow in the three-port system is mainly deter-mined by the fundamental components. This is an acceptableapproximation and the error is within 10% [11]. Therefore,the rst harmonic model may be used to estimate the powerow.

IV. SYMMETRICAL TRANSFORMER DESIGNThe main challenge of the proposed high-power three-

phase three-port converter is the design of the three-phasesymmetrical transformer. It is important to keep the symmetryof the leakage inductances. Otherwise, the current (transferred

L1A

L1BL1C

v1A L2AL2BL2C

L3AL3BL3C

v0A

Inv 1 Inv 2

Inv 3

v1Bv1C

v0Bv0C

v2A

v3Av3Bv3C

v2Bv2C

Fig. 6. Simplied three-phase model of the converter.

1B2B

3B1A2A3A

1C

2C3C

CoreWindings

Topview

Fig. 7. Conventionally wound three-port three-phase spatially symmetricaltransformer.

power) will not be equal for the three phases. The transformerconstruction may be necessary to be physically symmetricalin order to have an identical leakage inductance in each phase.Otherwise, the external inductances should be adjusted toachieve an equal per-phase leakage inductance.

Basically, there are two ways to wind a transformer: conven-tionally and coaxially. A conventional winding technique fordesigning the three-phase symmetrical transformer for a two-port converter has been proposed in [11]. The designed spatialthree-phase symmetrical transformer can easily be extended tothe three-port version as illustrated in Fig. 7. However, suitablehigh-frequency core shapes are commercially unavailable.Note that for a simple solution it would be possible to designthe transformer as three separated subtransformers since thereis no interphase coupling; however this results in a highertransformer core loss, because the ux canceling effect doesnot apply (the sum of the three phase uxes equals zero).

Coaxial winding techniques are commonly used in radio-frequency transformers. Fig. 8 shows the structure of a coax-ially wound transformer. This technique offers a feasiblesolution to contain the leakage ux within the inter-windingspace and thus prevents the core from being saturated locally[12]. As a result, the core and copper losses are lower, andlocalized heating is avoided [12]. Furthermore, from a mechan-ics point of view, this technique offers reduced forces withinthe transformer and a robust construction. In [12], it has beendemonstrated that coaxial windings can lead to low loss, lowleakage inductance power transformers in high-frequency soft-switched dc-dc and resonant converters. Some of the importantloss aspects such as the inuence of skin effect on winding

2025

Primary - Tube

Secondary - Litz

Toroid Core

Toroid Core Primary - Tube

Secondary - Litz

Fig. 8. Coaxially wound transformer.

A

B C

CorePrimary (tube)

Secondary(litz)

Tertiary(litz)

Fig. 9. Coaxially wound three-port three-phase symmetrical transformer.

resistance, the variation of core loss caused by non-uniformcore ux density, and the choice of the principle dimensionsand aspect ratios for maximum efciency were examined in[13]. Moreover, it is also possible for the primary to havemultiple turns [14]. Coaxial winding techniques thereforeprovide a viable method for the construction of the convertertransformer.

Fig. 9 shows the schematic of the proposed coaxially woundthree-port three-phase transformer. The primary of each phaseconsists of a straight tube of circular cross section. The starpoint is realized by shorting the tubes at one end. Toroidalcores are slipped over each tube to form the magnetic medium.The secondary and tertiary wires can now be wound inside theprimary tube. For the proposed converter, the windings canbe arranged as: the primary using a tube and the secondaryand tertiary using twisted litz wires. With the coaxial windingtechniques, the leakage inductance can be minimized. Henceexternal inductors should then be designed according to thedesired amount of power ow.

V. CONTROL STRATEGY

The control scheme aims to regulate the output voltageand the power of the primary source simultaneously by usingthe two phase shifts as control variables. An arbitrary powerow prole in the system can be achieved by phase shiftingthe three inverter stages as in the single-phase version [2].The storage supplies/absorbs the transient power differencebetween the load and the primary source. Since the three-portconverter can be viewed as a two-input two-output rst-ordersystem [9], the control system can be implemented with PIregulators based on the dual-PI-loop control strategy [7], one

PI

PI

P1

+ -V2

P1

V2

LimiterPhase- ShiftedPWMSOC

Manager

12

13

Inv 1

Inv 2

Inv 3+

-

High bandwidth

Low bandwidth

*

*

Fig. 10. Control scheme employing two PI compensators.

being employed to regulate the output voltage and the othercontrolling the power of the primary source, as illustrated inFig. 10. Also incorporated in the control scheme is a state-of-charge (SOC) manager for the storage [10].

The three-port converter can be modeled, using an averagingmethod, as three controlled dc current sources whose ampli-tudes are determined by the two phase shifts [9]. The currentat each port (iP1, iP2 and iP3, see Fig. 2) can be averagedover one switching cycle, being a function of the two phaseshifts. We can assume that the voltages at the ports are keptconstant. Then the average current is the power divided bythe port voltage. Thereby, the current source functions can beobtained. They are nonlinear functions of the two phase shiftsand should be linearized at the operating point for a control-oriented model [9].

The control variables are 12 and 13. Fig. 11 shows thesmall signal control loop block diagram of the TAB converter[9], where Gc1(s) and Gc2(s) are the transfer functions of thePI controllers. G11, G12, G21 and G22 are the small signallinearized gain of the converter, which can be derived fromthe power ow equations [9]. The block with gain -1 is dueto the denition of the direction of iP2 in Fig. 2. The blockwith gain V1 is needed because the power is equal to theaverage current times the port voltage. KM is the gain of thephase shift modulator. H1(s) is transfer function of the loadport formed by the lter capacitor C2 and the equivalent loadresistance RL:

H1(s) =RL

1 + RLC2s(10)

and H2(s) is the transfer function of the RC lter which ltersout ac components in iP1:

H2(s) =1

1 + Is(11)

where I is the time constant of the lter.Not surprisingly, the two PI control loops are coupled and

inuence each other [15]. The bandwidth of the voltage controlloop (12) is tuned higher (5 to 10 times higher) than that ofthe power control loop (13) so that the interaction is reducedwhile a fast response to the load variations is guaranteed. Onecan regard the former controller as the master while the latteris the slave.

A further improvement will employ a decoupling network,which eliminates the mutual effect, as also briey discussed

2026

KM+

G11

KF1

KM

G21

G12

G22+

KF2

++

+

+-112

%

13%

2PI%

1PI%

Gc1(s)

Gc2(s)

H1(s)

V1H2(s)1P%

2V%

**1P%

*2V%

Fig. 11. Small signal control loop block diagram of the three-port TABconverter.

in [8]. In theory, the decoupling matrix D is the inverse of thesmall signal gain matrix Go of the converter:

D = G1o =1

G11G22 G12G21

[G22 G12G21 G11

]. (12)

Therefore, the total system gain matrix becomes diagonal andthe interaction is eliminated, and the system can be controlledas two single-input single-output (SISO) systems:[

Ip2Ip1

]= DG1o

[1213

]=[

1213

]. (13)

Notwithstanding its elegance, the decoupling network re-quires more computation power and needs real-time updatingof the gain matrix Go. It should also be noticed that the delaybetween the control/gating signals and the actual voltagesapplied to the transformer has to be taken into account becausethese affect the operating point (the actual phase shifts) whichdirectly inuences the gain matrix of the converter. Withoutthis measure, the system cannot be satisfactorily decoupled.

VI. SIMULATION RESULTS AND DISCUSSIONTo investigate the performance of the proposed topology, the

converter and control scheme were simulated with PSIM7.0under a variety of operating conditions. Table I gives a listof parameters used for simulation including the controllerparameters. A standard voltage set, 48 V primary source, 48 Vstorage and 800 V dc output, is assumed. Because of the highswitching frequency (100 kHz), high power (10 kW) and thelow voltage (48 V), the required inductances are very smallfor the source and storage sides in this simulated case.

Suppose that the system is symmetrical; that is, all theinductances are equal when referred to the primary. Then thepower rating of each port is identical. For the situation that theaverage power of the storage port over one switching cycle iszero, the phase shifts should obey 13 = 0.512. Simulationresults in Fig. 12 illustrate the operating waveforms of theconverter, i.e., the voltages applied to the transformer andinductors network and the corresponding currents through thewindings at 12 = /6 and 13 = /3. In this operating pointthe average power of the storage port equals zero. The currentdrawn from the primary source port iP1 (before ltering,

TABLE ISIMULATION PARAMETERS FOR THE THREE-PORT SYSTEM

Description Symbol & ValuePrimary source voltage V1 = 48 V dcLoad side voltage V2 = 800 V dcStorage voltage V3 = 48 V dcSwitching frequency fs = 100 kHzTransformer turns ratio n2 = 16.7, n3 = 1Inductance L1A = L1B = L1C = 0.05 HInductance L2A = L2B = L2C = 0.05 HInductance L3A = L3B = L3C = 14 HPI controller Gc1(s) K1 = 1000, 1 = 10 msPI controller Gc2(s) K2 = 0.2, 2 = 10 msLPF time constant H2(s) I = 1 msPhase shift modulator gain KM = /500Feedback gain KF1 = 1Feedback gain KF1 = 1Nominal load resistance RL = 64 (for 10 kW)Output lter capacitor CL = 5000 F

v1A

v2A

v3A

i1A

i2A

i3A

iP1

(A)

(A)

(A)

(A)

(V)

(V)

(V)

Fig. 12. Simulation results showing the voltages generated by the three-phasebridges and the currents through the transformer windings at 12 = /3 and13 = /6 (phase A).

as indicated in Fig. 2) is also shown in the gure, beingunidirectional, and the ripple is much reduced compared tothe single-phase TAB converter.

Suppose that the power ow of the primary source isunidirectional, i.e., P1 > 0 under all situations. The maximumpower ow to the load port occurs when 12 = /2 and13 = 0. For this particular operating point, results fromsimulation are shown in Fig. 13. As can be seen, the currentsare close to sinusoidal waves.

2027

v1A

v2A

v3A

i1A

i2A

i3A

iP1

(A)

(A)

(A)

(A)

(V)

(V)

(V)

Fig. 13. Simulation results showing the voltages generated by the three-phasebridges and the currents through the transformer windings at 12 = /3 and13 = 0 (phase A).

Simulation results of the power ow control based on thedual-PI-loop control strategy are demonstrated in Fig. 14,where the load pulsates between 5 kW and 15 kW in a timeinterval of 10 ms. The step changes in the load were simulatedby suddenly adding/removing a resistor in parallel with the dccapacitor. As shown, the power supplied by the primary sourceP1 remains at 10 kW the average power consumed by theload, and the unmatched power between the source and loadis supplied/absorbed by the storage.

Furthermore, Fig. 15 displays the response of the controlsystem to an inverter-type load which draws sinusoidal currentfrom the capacitor at the load port. The average power isagain 10 kW. It is evident that the control system is capableof regulating the output voltage and power of the primarysource simultaneously. The amount of the ripple in P1 isdetermined by the bandwidth of the control loop. The higherthe bandwidth, the lower the ripple. In both of the simulatedcases, the PI regulators are implemented as

Gc1(s) = K11 + 1s

1s, Gc2(s) = K2

1 + 2s2s

. (14)

The controller parameters for simulation are listed in Table I.Thus far, the single-phase version has been investigated

using laboratory experimental setups at a rated power of 1 kW[7] and 3.5 kW [10]. It is intended to build a three-phaseversion prototype at 10 kW to further explore the idea.

P1

P2

P3

12

13

(rad

)(r

ad)

(W)

(W)

(W)

Fig. 14. Simulation results of power ow control with a pulsating load.

Due to the fact that the converter is symmetrical in three-phase, the only possible control variable is the phase shiftbetween the bridges. Therefore, other control methods suchas duty ratio control to extend soft-switching region [7] cannot be implemented in this topology straightforwardly. Thisconverter will be soft-switched under the condition that all thedc voltages at the ports remain near constant. The convertersuffers from a limited soft-switched operating region if one ormore ports have a wide operating voltage.

VII. CONCLUSIONSIn this paper, a high-power three-port three-phase bidi-

rectional dc-dc converter has been proposed. The convertercomprises a high-frequency three-port transformer and threeinverter stages operating in a high-frequency six-step mode.The circuit interfaces a primary source and storage to aload and manages the power ow in the system. With theexternal leveling system the operation of the primary sourcecan be optimized, for instance, operating it at a constantpower. The converter provides galvanic isolation and supportsbidirectional power ow for all the power ports. The advantageof the three-phase version compared to the single-phase oneis the higher current handling capability and much lowercurrent ripple at the dc side, thereby lower VA rating oflter capacitors owing to the interleaving effect of the three-phase. The analysis of the topology and design issues of thetransformer as both a conventionally and a coaxially wound

2028

P1

P2

P3

12

13

(rad

)(r

ad)

(W)

(W)

(W)

Fig. 15. Simulation results of power ow control with an inverter-type load.

structure were presented. Circuit simulation results under avariety of operating conditions have been provided, provingthat the operating principle of the circuit and its dual-PI-loopcontrol strategy are sound.

REFERENCES[1] H. Tao, A. Kotsopoulos, J. L. Duarte, and M. A. M. Hendrix, Family

of multiport bidirectional DC-DC converters, IEE Proceeding ElectricPower Applications, vol. 153, no. 3, pp. 451458, May 2006.

[2] J. L. Duarte, M. Hendrix, and M. G. Simoes, Three-port bidirectionalconverter for hybrid fuel cell systems, IEEE Trans. Power Electron.,vol. 22, no. 2, pp. 480487, Mar. 2007.

[3] H. Tao, A. Kotsopoulos, J. L. Duarte, and M. A. M. Hendrix, Multi-input bidirectional DC-DC converter combining DC-link and magnetic-coupling for fuel cell systems, in Proc. IEEE Industry ApplicationSociety Conference and Annual Meeting (IAS05), Hong Kong,China,Oct. 2005, pp. 20212028.

[4] A. D. Napoli, F. Crescimbini, L. Solero, F. Caricchi, and F. G. Capponi,Multiple-input DC-DC power converter for power-ow management inhybrid vehicles, in Proc. IEEE Industry Application Society Conferenceand Annual Meeting (IAS02), Oct. 2002, pp. 15781585.

[5] D. Liu and H. Li, A three-port three-phase DC-DC converter for hybridlow voltage fuel cell and ultracapacitor, in Proc. IEEE The 32nd AnnualConference of the IEEE Industrial Electronics Society (IECON06),Paris, France, Nov. 2006, pp. 25582563.

[6] M. Michon, J. L. Duarte, M. Hendrix, and M. G. Simoes, A three-port bi-directional converter for hybrid fuel cell systems, in Proc. IEEEPower Electronics Specialists Conference (PESC04), Aachen, Germany,Jun. 2004, pp. 47364742.

[7] H. Tao, A. Kotsopoulos, J. L. Duarte, and M. A. M. Hendrix, Asoft-switched three-port bidirectional converter for fuel cell and su-percapacitor applications, in Proc. IEEE Power Electronics SpecialistsConference (PESC05), Recife, Brazil, Jun. 2005, pp. 24872493.

[8] C. Zhao and J. W. Kolar, A novel three-phase three-port UPS employinga single high-frequency isolation transformer, in Proc. IEEE PowerElectronics Specialists Conference (PESC04), Aachen, Germany, Jun.2004, pp. 41354141.

[9] H. Tao, A. Kotsopoulos, J. L. Duarte, and M. A. M. Hendrix,Transformer-coupled multiport ZVS bidirectional DC-DC converterwith wide input range, IEEE Trans. Power Electron., to be published.

[10] H. Tao, J. L. Duarte, and M. A. M. Hendrix, High-resolution phaseshift and digital implementation of a fuel cell powered UPS system, inProc. 12th European Conference on Power Electronics and Applications(EPE07), Aalborg, Denmark, Sep. 2007, pp. 110.

[11] R. W. DeDoncker, D. M. Divan, and M. H. Kheraluwala, A three-phase soft-switched high-power-density DC/DC converter for high-power applications, IEEE Trans. Ind. Appl., vol. 27, no. 1, pp. 6373,Jan./Feb. 1991.

[12] M. H. Kheraluwala, D. W. Novotny, and D. M. Divan, Coaxially woundtransformers for high-power high-frequency applications, IEEE Trans.Power Electron., vol. 7, no. 1, pp. 5462, Jan. 1992.

[13] M. S. Rauls, D. W. Novotny, and D. M. Divan, Design considerationsfor high-frequency coaxial winding power transformers, IEEE Trans.Ind. Appl., vol. 29, no. 2, pp. 375381, Mar./Apr. 1993.

[14] M. S. Rauls, D. W. Novotny, D. M. Divan, R. R. Bacon, and R. W. Gas-coigne, Multiturn high-frequency coaxial winding power transformers,IEEE Trans. Ind. Appl., vol. 31, no. 1, pp. 112118, Jan./Feb. 1995.

[15] H. Tao, A. Kotsopoulos, J. L. Duarte, and M. A. M. Hendrix, Designof a soft-switched three-port converter with DSP control for powerow management in hybrid fuel cell systems, in Proc. 11th EuropeanConference on Power Electronics and Applications (EPE05), Dresden,Germany, Sep. 2005, pp. 110.

2029