A Single-Stage Three-Phase AC-AC Converter forInductive Power Transfer Systems

Masood MoghaddamiElectrical and Computer Engineering

Florida International UniversityMiami, Florida 33174

Email: mmogh003@fiu.edu

Amir MoghadasiElectrical and Computer Engineering

Florida International UniversityMiami, Florida 33174

Email: amogh004@fiu.edu

Arif I. SarwatElectrical and Computer Engineering

Florida International UniversityMiami, Florida 33174

Email: asarwat@fiu.edu

Abstract—A three-phase ac-ac matrix converter for inductivepower transfer (IPT) systems with soft-switching operation andbidirectional power flow is introduced. The proposed convertercan generate high-frequency current directly from a three-phaseac power source without a dc link. Unlike conventional ac-dc-ac converters, the proposed converter can provide a highfrequency current without any current sag around ac source zero-crossings for IPT systems. The proposed topology is expectedto have high reliability and extended lifetime due to the soft-switching operation and elimination of short life electrolyticcapacitors. Soft-switching operation will also reduce switchingstress, switching losses, and electromagnetic interference (EMI) ofthe converter. A simple control strategy based on energy injectionand free oscillation technique is used as the control method.The proposed converter is comprised only seven switches, whichin turn increase the reliability, efficiency and reduce cost. Theconverter operates in eight modes, which are described in detail.Theoretical analysis and simulation results on a 2kW IPT system,show that the current control method can fully regulate theoutput current with low ripple which is suitable waveforms forIPT applications.

Index Terms—AC-AC converter, inductive power transfer,matrix converter, soft switching.

I. INTRODUCTION

Inductive power transfer (IPT) systems are emerging tech-nology for transferring electric power to a variety of appli-cations without any physical contacts [1]. This technologytransfers power from one system to another across a large airgap and through a loosely coupled inductive link. It offershigh efficiency typically between 85-90%, robustness, andhigh reliability, even when used in hazardous environments, asit is unaffected by dust or chemicals and eliminates sparkingand the risk of electrical shocks [2],[3]. Therefore, it is a safe,robust and clean way of transferring power and has rapidlygained increased interest in the commercial and industrialapplications. The IPT technology has been successfully em-ployed in many applications, including systems for materialshandling [1], biomedical implants and transportation systems[4],[5]. Especially this innovative technology can be used forstatic and dynamic wireless power transfer for electric vehicles(EVs) [2],[6].

This work was funded by the National Science Foundation under grantnumber RIPS-1441223.

3~

input

Load

Power

ConverterPrimary

Compensation

Secondary

Compensation

Primary Track

Power

Converter

Receiver

Coil

Fig. 1. A typical loosely coupled IPT system.

In a loosely coupled IPT system due to weak couplingof the coils the inductive link requires a strong magneticfield to be created to deliver high power levels at large airgaps. To achieve this, it requires the use of power convertersthat can generate large currents at high frequencies often inthe kilohertz ranges. In order to generate a high-frequencycurrent on the primary side, specific power converters areemployed in IPT systems. Power converters play a key role inthe performance of the IPT systems. Recent developments inIPT systems have heightened the need for high power reliableand efficient converters. Normally, these converters take 50/60Hz mains and convert to high-frequency using an ac-dc-actwo-stage power conversion. A typical configuration of anIPT system is shown in Fig. 1. The power source of an IPTsystem is usually the electric utility (single-phase or three-phase) supplying power at 50/60 Hz.

Voltage-source inverters (VSI) based on pulsewidth mod-ulation (PWM) with a front-end rectifier have become thepreferred choice for most practical applications [7]. This ismainly due to its simple topology and low cost. On the otherhand, this two-stage topology has low-frequency harmonicson the dc link and the ac input line, which requires the useof very bulky short-life electrolytic capacitors for the dc linkand a large low-pass filter at the output [7]. Several topologieshave been proposed to solve the problems of the traditionalac-dc-ac power converters,[8]-[10]. The main alternatives for

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Direct three-phase AC-AC Matrix

Converter

Resonant Tank

Cp

Lp

Req

SA1 SB1 SC1

SA2 SB2 SC2

SF

Fig. 2. Proposed three-phase ac-ac matrix converter.

TABLE ISWITCH STATES IN DIFFERENT MODES OF OPERATION.

Mode Resonant Current Input Voltages On Switches1 |ip| < Ir , ir > 0 Vc < Vb < Va SA1, SC2

2 |ip| < Ir , ir > 0 Vb < Vc < Va SA1, SB2

3 |ip| < Ir , ir > 0 Vc < Va < Vb SB1, SC2

4 |ip| < Ir , ir > 0 Va < Vc < Vb SB1, SA2

5 |ip| < Ir , ir > 0 Vb < Va < Vc SC1, SB2

6 |ip| < Ir , ir > 0 Va < Vb < Vc SC1, SA2

7 |ip| > Ir , ir > 0 − DF8 il < 0 − SF

two-stage converters that can convert energy directly from anac source to a load with different frequency and amplitudewithout any energy storage elements [11]. These convertershave the advantages of the simple and compact topology,bidirectional power flow capability, high-quality input-currentwaveforms, and adjustable input power factor independent ofthe load [11],[12]. Particularly different converter typologieshave been proposed for IPT applications [13]-[18]. A simple,compact and highly efficient single-phase matrix converter forIPT applications is presented in [13]. The energy injectionand free oscillation control strategy is applied to the topology.However this matrix converter suffers from current sags aroundinput ac voltage zero-crossings.

In this paper, a new three-phase ac-ac matrix converter forIPT systems is proposed. The proposed matrix topology iscomposed of seven switches which six of them are reverseblocking switches and one is regular switch. A variablefrequency control strategy of the converter is based on energyinjection and free oscillation technique. The key benefits of theproposed converter are soft-switching operation, bi-directionalpower flow, high efficiency, reduced number of switches andlow electromagnetic interference (EMI).

II. PROPOSED THREE-PHASE AC-AC CONVERTER

The proposed direct three-phase ac-ac converter is shownin Fig. 2. It consists of six reverse blocking switches and

Vm

-Vm

-Ir

Ir

SA1

SA2

SB1

SB2

SC1

SC2

SF

DF

VA VB VC

Mode 8 5 8 7 8 1 8 2 8 7 8 2 8 3 8 7 8 4 8 6 8 7 8 68 7 8 7 8 7 8 7 8

Fig. 3. Proposed three-phase ac-ac matrix converter.

one regular switch (IGBT/MOSFET) which is in parallel withthe resonant tank. In this figure, Cp represents the primarycompensation capacitor, Lp is the primary self inductance andReq is the reflected resistance of the load at the secondary tothe primary circuit. In [2], a control strategy for a single phaseac-ac converter based on energy injection and free oscillationof the resonant circuit is presented. This control method isfurther developed in this paper and is applied to the proposedthree-phase converter.

The operation of the converter can be described in eightmodes which are presented in Table I. Each mode takes placeonly in one half cycle of the output current. Modes 1 to 6 areenergy injection modes and modes 7 and 8 are free oscillationmodes. In mode 1 to 6, the resonant current (ir) is positivethe absolute value of the previous peak current (ip) is lowerthan the reference current (Ir) and therefore energy should beinjected to the LC tank for a half cycle to increase the currentand the output is switched between the most positive and themost negative input lines and the energy is injected into theLC tank for a half cycle of the output resonant current. Theswitching is performed based on the measured input voltagesaccording to Table I and using six switches, SA1,SA2, SB1,SB2, SC1 and SC2 which are used to switch the three-phaseinput lines to the output during modes 1 to 6.

Mode 7, occurs when the previous peak current (ip) ispositive and is higher than the reference current (Ir) andtherefore energy injection to the LC tank should be avoided

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Cp

Lp

Req

SA1 SB1 SC1

SA2 SB2 SC2

SF

Cp

Lp

Req

SA1 SB1 SC1

SA2 SB2 SC2

SF

Cp

Lp

Req

SA1 SB1 SC1

SA2 SB2 SC2

SF

Cp

Lp

Req

SA1 SB1 SC1

SA2 SB2 SC2

SF

Cp

Lp

Req

SA1 SB1 SC1

SA2 SB2 SC2

SF

Cp

Lp

Req

SA1 SB1 SC1

SC2SB2SA2

SF

Cp

Lp

Req

SA1 SC1

SA2 SB2 SC2

SF

Cp

Lp

Req

SA1 SC1

SB2SA2 SC2

SF

SB1SB1

Mode 1 Mode 2

Mode 3 Mode 4

Mode 5 Mode 6

Mode 7 Mode 8

Fig. 4. The current path in the proposed converter in eight modes of operation.

for a half cycle to decrease the current. In this mode, the LCtank goes in a free oscillation state and the resonant current ispositive which is conducted through the intrinsic body diode(DF ) of the parallel switch (SF ) as shown in Fig. 4 for mode7. In mode 8, the resonant current is negative and the switchSF is on. Since the resonant current becomes negative afterany mode from 1 to 7, mode 8 always occurs after any othermode of operation.

The output current of the proposed converter is regulatedaround the reference current by alternating the state of theconverter between energy injection and free oscillation modes.In Fig. 3, a conceptual plot of three-phase input voltages,resonant current and corresponding switching signals of theconverter in different modes of operations are presented. Also,Fig. 4 demonstrates the resonant current path in the proposedconverter, in 8 modes of operation. Based on these figures itcan be seen that the SF is repeatedly switching the circuit tothe free oscillation mode (mode 8) with a negative current andDF turns on whenever the resonant current is positive and thecircuit should go into free oscillation mode.

III. THEORETICAL STUDY

The differential equation of a LC tank with primary selfinductance of L and compensation capacitor C with an equiv-alent resistance of R can be expressed as:

Ldi

dt+R i+

1

C

∫ t

0

i dt+ Vc(0) = Vt (1)

where i is the resonant current, Vc is the voltage of thecompensation capacitor and Vt is the input voltage. Equation(1) can be rewritten as the following second order differentialequation:

d2i

dt2+R

Li+

1

LCi = 0 (2)

where the initial conditions of the circuit is:

i(0) = 0

Ldi

dt(0) = Vt − Vc(0)

(3)

The solution of (2) based on initial conditions in (3) is derivedas:

i = Ke−t/τsin(ωt) (4)

where the natural damped frequency ω =√ω20 − α2, resonant

frequency ω0 = 1/√LC, damping coefficient α = R/2L,

damping time constant τ = 2L/R and the coefficient K isexpressed as:

K =Vt − Vc(0)

ωL(5)

Equation (5) shows that the value of K changes in eachhalf cycle depending on the input voltage and initial voltageof the compensation capacitor. It should be noted that in thefree oscillation modes the input voltage is zero (Vt = 0). Alsothe compensation capacitor voltage can be expressed as:

Vc(t) = Vc(0)+

Kτ

C(1 + τ2 ω2)

(τω − e−t/τ [sin(ωt) + τωcos(ωt)]

)(6)

The resonant current and voltage equations, (4) and (6) areuseful in finding the peak values of current and voltage ineach half cycle. In order to find the peak value of the resonantcurrent in which occurs at the time tn corresponding to thenth current peak, the following equation can be solved to findthe exteremum points of the resonant current:

di

dt= K e−t/τ

[ω cos(ωt)− 1

τsin(ωt)

]= 0 (7)

Therefore we have:

tan (ω tn) = τω (8)

tn =atan (τω) + nπ

ω(9)

therefore the nth peak value of the resonant current can becalculated using (4) and (9) as the following equation:

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Direct 3-phase AC/AC Converter

SA1 SC1SB1

Cp

3~

voltage

Grid

7 pulses

SF

Cs

Magnetic Coupler

and Compensations

Cf

Lf

LC Filter

Current

Measurement

Voltage

Measurements Gate Drivers

SA2 SB2 SC2

DF

Controller

Peak

Measurement

Trigger Zero-cross

Detection

Secondary Converter

and EV Battery

Va

Vb

Vc

ir

ip

Battery

iref

Fig. 5. The IPT model and its components simulated in MATLAB/SIMULINK.

in = K e−atan (τω)+nπ

τω (−1)n τω√1 + (τω)2

(10)

Using (4), the resonant current in a period composed of bothenergy injection and free oscillation modes can be expressedas follows:

i(t) =

Ki e

−t/τsin(ωt) 0 < t < πω

Kf e−t/τsin(ωt), π

ω < t < 2mπω

(11)

where, m denotes the number of cycles composed of oneenergy injection half cycle and 2m − 1 free oscillation halfcycles and Ki and Kf are coefficients of (4) in the first energyinjection and free oscillation half cycles respectively and canbe calculated using (5) and (6) as follows:

Ki =τ

L[Vc(0)− Vt] (12)

Kf =τ

L

[Vc(

π

ω)]=

τ

L

[Vc(0) +

Kiτ2ω

C(1 + τ2ω2)

(1 + e−π/τω

)](13)

By assuming iref as the reference current, using (10) and(11) the number of cycles that the next energy injection shouldoccur (m) can be calculated as follows:

m =1

π

[τω ln

(Kfτω

iref√1 + (τω)2

)+ arctan(τω)

](14)

Equation (14) predicts the number of cycles that the LC tankwill continue its free oscillation mode, as a function of initialcondition (Kf ), circuit parameters (τω) and the referencecurrent iref .

IV. SIMULATION RESULTS

The proposed three-phase converter which is presented inFig. 2 is simulated using MATLAB/SIMULINK. The IPTmodel is shown in Fig. 5. This model is comprised a three-phase main grid with LC filter, the proposed three-phase ac-acprimary converter, primary and secondary magnetic structureswith compensations capacitors and secondary load which isa battery charger for an electric vehicle. The controller ofthe primary converter and its components are also shown inFig. 5. The measurements include three-phase input voltageand output resonant current of the LC tank. The controller istriggered in each zero-cross of the resonant current and basedon the voltage and current measurements the switching stateof the of the converter is determined. The switching signals ofthe converter does not change until the next current zero-cross.

The primary self inductance is 168µH and the primarycompensation capacitor is 0.1µF . The phase voltage of thethree-phase supply is 10V and the reference current is set to14.1A. The simulation results are shown in Fig. 6. This figureshows the three-phase input voltages and corresponding modesof operation, resonant current of the LC tank and switchingsignals of the SA1, SB1, SC2 and SF . As it can be seen thecurrent is fully controlled around the reference current with aripple less than 1A.

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2 4 6 8 10 12-10

0

10

2 4 6 8 10 12-20

0

20

2 4 6 8 10 12

2 4 6 8 10 12

2 4 6 8 10 12

2 4 6 8 10 12

i l (

A)

Vac

(V)

Time (ms)

VA VB VC

SA1

SB1

SC2

SF

-Ir=-14.1 A

Ir=14.1 A

mode 2, 7, 8 mode 1, 7, 8 mode 3, 7, 8 mode 4, 7, 8

Fig. 6. Simulation results of the sample IPT system.

V. CONCLUSION

This paper has introduced a three-phase single-stage ac-acconverter for inductive power transfer (IPT) systems with zero-current switching and bidirectional power flow capability. Keybenefits of the proposed converter are minimized number ofswitches, soft-switching operation, low switching stress, lowswitching losses, low electromagnetic interference (EMI), andelimination of short life electrolytic capacitors. This featureswill lead to high efficiency converter with high reliabilityand extended lifetime. The simulations results show thatthe proposed converter can generate regulated high-frequencycurrent for IPT applications directly from a three-phase acpower source without a dc link with only seven switches. Theoutput resonant current does not have any sags around inputvoltage zero-crossings and has maximum 5% ripple.

Energy injection and free oscillation control method pro-vides a simple and effective control strategy for the converter.In practice, the control method can be implemented basedon an analog or digital design. The simplicity of the con-trol strategy will further reduce the practical implementationcomplexity and cost.

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