1308 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO.

5, OCTOBER 2005

Design Considerations for a Contactless Electric

Vehicle Battery Charger
Chwei-Sen Wang, Oskar H. Stielau, and Grant A. Covic, Senior Member, IEEE

Abstract—This paper overviews theoretical and practical design

issues related to inductive power transfer systems and verifies the
developed theory using a practical electric vehicle battery charger.
The design focuses on the necessary approaches to ensure power
transfer over the complete operating range of the system. As such,
a new approach to the design of the primary resonant circuit is pro-
posed, whereby deviations from design expectations due to phase
or frequency shift are minimized. Of particular interest are sys-
tems that are neither loosely nor tightly coupled. The developed
solution depends on the selected primary and secondary resonant
topologies, the magnetic coupling coefficient, and the secondary
quality factor.
Index Terms—Battery charging, electric vehicle, electromag- Fig. 1. Structure of inductive power transfer system.
netic coupling, inductive power transfer, resonance.
handling systems [6], [7] and public transport systems [8] where
I. INTRODUCTION the secondary systems are electrically isolated and move along a
long track. Electric isolation is also essential for power supplies

I NDUCTIVELY coupled power transfer (ICPT) systems are

designed to deliver power efficiently from a stationary pri-
mary source to one or more movable secondary loads over rel-
in harsh environments such as mining and outdoor lighting. The
advantages of such systems are safety, reliability, low mainte-
nance, and long product life.
atively large air gaps via magnetic coupling. The fundamental
Both the primary and secondary resonant circuits of the ICPT
principles of such systems are identical to well known closely
systems are normally designed to operate at the nominal reso-
coupled electromechanical devices such as transformers and in-
nant frequency, but care must be taken in such designs since
duction motors, where the leakage inductance is much lower
system performance could deviate from design expectations if
than the mutual inductance.
the loading becomes significant. Generally, such deviations are
The mutual coupling within ICPT systems is generally weak.
small if the mutual inductance is much lower than the leakage
To deliver the required power and ensure equipment sizes re-
inductance, but become more significant if the mutual induc-
main manageable, it is necessary to operate at high frequency
tance is comparable to the leakage inductance as is the case in
(normally above the audible range). At present, the operational
many practical applications. In this paper, a general design ap-
frequency for high power applications is limited to below 100
proach is proposed that includes the magnetic coupling effect
kHz as a result of switching losses. Moreover, resonant circuits
in the primary resonance design for the commonly used reso-
are normally employed in the primary and/or secondary net-
nant topologies. A design example for contactless electric ve-
works to further boost the power transfer capability, while min-
hicle battery charging using a variable-frequency controller is
imizing the required voltage and current ratings of the power
proposed and verified.
supply.
Modern power electronics have enabled many new applica-
tions such as contactless power supply for professional tools II. FUNDAMENTAL ANALYSIS
[1], contact-less battery charging across large air gaps for elec-
tric vehicles [2], compact electronic devices [3], mobile phones A. Fundamental Structure
[4], and medical implants [5]. Other examples include material
An ICPT system essentially is comprised of two magneti-
cally coupled electrical systems, as shown in Fig. 1, driven by a
Manuscript received December 11, 2002; revised April 2, 2004. Abstract pub- high-frequency switching power supply. The primary winding
lished on the Internet July 15, 2005. This work was supported in part by the (stationary track or coil) is normally compensated in order to
Foundation of Research, Science and Technology (FRST), New Zealand. minimize the VA rating of the supply. Compensation is often re-
C.-S. Wang and G. A. Covic are with the Department of Electrical and Com-
puter Engineering, The University of Auckland, Auckland 1001, New Zealand quired for the secondary winding (movable pickup) to enhance
(e-mail: ga.covic@auckland.ac.nz). the power transfer capability. A switched-mode controller may
O. H. Stielau was with the Department of Electrical and Electronic Engi- be used to control the power flow from the pickup to the load. In
neering, The University of Auckland, Auckland, New Zealand. He is now at
152B Forrest Hill Road, Forrest Hill, Auckland 1309, New Zealand. more complex systems many individual pickups can exist, sup-
Digital Object Identifier 10.1109/TIE.2005.855672 plied by a single track.
0278-0046/$20.00 © 2005 IEEE
WANG et al.: DESIGN CONSIDERATIONS FOR A CONTACTLESS ELECTRIC VEHICLE BATTERY CHARGER 1309

TABLE I
SECONDARY IMPEDANCE, LOAD VOLTAGE/CURRENT, AND PROPERTIES AT THE
SECONDARY RESONANT FREQUENCY. (a) SECONDARY IMPEDANCE
AND LOAD VOLTAGE/CURRENT. (b) PROPERTIES AT THE SECONDARY
RESONANT FREQUENCY !

Fig. 2. (a) Basic topologies. (b) Mutual inductance coupling model.

B. Basic Topologies
Four basic topologies labeled as SS, SP, PP, and PS are The current flowing through the secondary winding is
shown in Fig. 2(a), where the first S or P stands for series or
parallel compensation of the primary winding and the second S (4)
or P stands for series or parallel compensation of the secondary
winding. Here, the subscripts “ ”, “ ”, “ ”, and “ ” stand for The voltages across the primary and secondary windings are,
“inverter”, “primary”, “secondary”, and “load”, respectively. therefore, given by
The resistance represents the load on the secondary. Using
a mutual inductance coupling model, each of these topologies (5)
can be modeled by the circuit shown in Fig. 2(b) for sinusoidal and
steady state analysis. The induced and reflected voltages in this
model are specified in terms of the mutual inductance “ ”, (6)
the operational frequency “ ”, and the primary and secondary
currents. The mutual inductance is related to the magnetic The secondary impedance is given in Table I(a) for series-
coupling coefficient by and parallel-compensated networks. The load voltage and cur-
rent are also given in the same table. Normally, the primary and
(1) secondary resonant frequencies are identical as given by

(7)
C. Single Pickup
The reflected resistance and reactance calculated from (2) at
The reflected impedance from the secondary to the primary the secondary resonant frequency are also given in Table I(b)
can be found by dividing the reflected voltage by the primary and depend on the compensations used. The secondary quality
current resulting in factor defined at the secondary resonant frequency is also given
in the same table. Here, the quality factor is the ratio between
(2) reactive and real power.
The series-compensated secondary resembles a voltage
where is the impedance of the secondary network and de- source, while the parallel-compensated secondary looks like
pends on the selected compensation topology. a current source. Both properties can be verified by (3) using
The power transferred from the primary to the secondary is the reflected resistance in Table I(b) and assuming that the
the reflected resistance multiplied by the square of primary cur- primary current is maintained constant, which is normally
rent as given by the case in ICPT designs [7], [8]. One of the advantages of
a series-compensated secondary is that there is no reflected
(3) reactance at the secondary resonant frequency. In contrast, the
parallel-compensated secondary reflects a capacitive reactance
where the operator “ ” represents the real component of cor- at the secondary resonant frequency, but this can be tuned out
responding variable. because it is independent of the load.
1310 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 5, OCTOBER 2005

The load impedance seen by the power supply is determined shifting the operational frequency of the power supply. This
by combining the primary and secondary networks. For a series- approach is not suitable for many multiple pickup applications
compensated primary system, this load impedance is where the load condition on each pickup can be different. Here,
detuning the power supply affects all the secondary pickups
(8) so that some pickups may be unable to deliver the necessary
power. An alternative approach is to use a switched-mode
For a parallel-compensated primary system, this load controller within the secondary pickup for power flow control
impedance is [4], [7], [8]. Using this approach, each pickup can be controlled
separately or even decoupled completely from the primary.
(9) However, the disadvantages are increased switching losses and
a higher cost of the secondary pickups.
2) Fixed-Frequency Control: With fixed-frequency-con-
D. Multiple Pickups trolled applications, variations in load and coupling between
the primary and secondary will cause a phase shift in the load
With multiple pickup ICPT systems, all pickups are normally impedance. If this phase shift is significant, then the power
designed identically so that secondary impedances are iden- supply must have a higher VA rating for the same power
tical for each loading condition. As a result, the total reflected transfer.
impedance from all pickups is 3) Variable-Frequency Control: As noted in Section III-A,
most variable-frequency controllers operate at the primary
(10) ringing frequency. However, the operational frequency (ZPA
frequency of the load impedance) will shift away from the
where is the number of pickups. nominal resonant frequency because of the variations in the
This is equivalent to the reflected impedance of a single iden- load and the degree of coupling between the primary and
tical pickup with an equivalent mutual inductance of secondary. This results in a loss of power transfer capability if
the frequency shift is too large, and may also result in a loss of
(11) frequency stability and controllability because of the onset of
bifurcation with increasing load, where more than one primary
The equivalent coupling coefficient is then ZPA frequency exists [7], [9], [10].
(12) C. Design Procedure
The design of ICPT systems relies strongly on experience and
III. GENERAL DESIGN CONSIDERATIONS experimental verification because of the complexity regarding
the interactions of the primary and secondary resonant circuits.
A. Operational Frequency
A generalized design methodology is proposed in [9] assuming
In some applications where frequency is adjusted to regulate the system is operated at the nominal resonant frequency. With
power flow, operation above or below the secondary resonant this iterative design procedure, the electromagnetic structure as
frequency may be preferred in order to improve the controlla- well as the primary current can be determined for the required
bility [5] because in such applications the relationship between power transfer. The physical limit to the power transfer capa-
frequency and power has been found to be approximately linear bility of a proposed electromagnetic coupling structure is its VA
over the operating frequency range. For most applications, how- rating. In this design process, power transfer capability is as-
ever, operation at or near the secondary resonant frequency is sured under the primary and secondary VA ratings.
a logical choice because maximum power transfer capability The selection of the primary and secondary compensation
can be achieved. Furthermore, it is also desired that the output topologies are generally application oriented as described in [9].
voltage and current of the power supply be in phase in order A series-compensated secondary can supply a stable voltage,
to minimize the VA rating of the power supply. This can be while a parallel-compensated secondary is able to supply a
achieved by operating at the zero-phase-angle (ZPA) frequency stable current. A series-compensated primary is normally
of the load impedance. Consequently, the nominal frequency of required to reduce the primary voltage to manageable levels
the ICPT system is normally designed to achieve primary ZPA for long track applications, whereas a parallel-compensated
operation at the secondary resonant frequency. primary is usually used to give a large primary current.
In the above design procedure, there are two fundamental as-
B. Control sumptions. The first is that the operating frequency remains con-
The power supply and primary controller normally control stant at the nominal resonant frequency as determined by (7).
both the frequency and the primary current to achieve maximum The second is that the primary current is constant. However,
power transfer capability. Both fixed- and variable-frequency as described in the above subsection, there could be significant
controllers can be used. Power flow regulation is also required frequency or phase shift with changing load. With a large fre-
because of variations in load and other system parameters. quency shift, the assumption of operation about the nominal res-
1) Power Flow Regulation: One common approach to onant frequency is not valid. With a large phase shift, the desired
achieve power flow regulation is to detune the system by constant primary current is not available when the required VA
WANG et al.: DESIGN CONSIDERATIONS FOR A CONTACTLESS ELECTRIC VEHICLE BATTERY CHARGER 1311

TABLE II
PRIMARY COMPENSATION

rating exceeds the capability of the selected power supply. In Fig. 3. Normalized primary capacitance.
either case, the system will be unable to deliver the required
power.
Theoretically, SS is the best topology, as the primary capac-
D. Choice of Primary Compensation Capacitance itance is then independent of either the magnetic coupling or
the load. The other three topologies are all dependent on the
To minimize the above problems associated with frequency
magnetic coupling, while parallel-compensated primaries are a
or phase shift, primary ZPA operation at or near the secondary
function of the load as well. Although SS topology seems to
resonant frequency is desired. One simple approach is to select
be the best choice regarding primary resonance design, parallel
the primary capacitance deliberately by letting the imaginary
compensation may be preferred in the primary and/or secondary
component of the load impedance equal zero at the secondary
resonant circuits for many applications [1]–[3], [6]–[8], [10] be-
resonant frequency. This design approach compensates not only
cause of practical considerations as noted in Section III-B.
the primary inductance but also the existing reflected impedance
in series with the primary winding. The solutions are given in
Table II for the four basic topologies in Fig. 2. F. Effects of Coupling and Secondary Quality Factor
For a general analysis, a normalized primary capacitance can
be defined as the primary capacitance in Table II divided by the As shown above, the magnetic coupling and/or the secondary
primary capacitance determined by (7). The result is quality factor (corresponding to the rated load) must be included
in the choice of the primary compensation capacitance. In order
(13) to investigate the effects of the magnetic coupling and the sec-
ondary quality factor on the proposed primary resonance de-
sign, the normalized primary capacitance determined by Table II
This normalized primary capacitance is unity when the pri- is shown in Fig. 3 as a function of the magnetic coupling co-
mary capacitance is determined by (7). According to Table II, efficient for selected secondary quality factors that range typ-
the primary capacitance for achieving primary ZPA operation at ically from 2 to 10. As shown here, no change from that de-
the secondary resonant frequency depends on three factors: the termined by (7) is required for SS topology. The SP topology
selected primary and secondary topologies, the magnetic cou- requires a larger primary capacitance with better coupling. The
pling coefficient, and the secondary quality factor. PP topology requires a slightly larger primary capacitance for
loose coupling with low secondary quality factor, but needs a
E. Topology Dependency smaller primary capacitance if the coupling is improved or the
As can be seen from the results above, the selected topology secondary quality factor is increased. A smaller primary capac-
plays a large role in the correct choice of the primary capac- itance is always required for PS topology and the change be-
itance. Since the series-compensated secondary reflects no re- comes larger with better coupling or higher secondary quality
actance at the nominal resonant frequency, the primary induc- factor.
tance can be tuned out independent of either the magnetic cou- To increase the power transfer capability of ICPT systems,
pling or the load by a series-connected capacitance in the pri- much effort has gone into improving the magnetic coupling be-
mary network. As the parallel-compensated secondary reflects tween the primary and secondary, and coupling coefficients for
a load-independent capacitive reactance at the nominal resonant single pickup applications of between 0.3–0.6 are often achiev-
frequency, series tuning in the primary is dependent on the mag- able [1]–[3], [5], [10]. For multiple pickup applications, system
netic coupling but not the load. Because the reflected impedance constraints usually result in coupling coefficients of less than 0.1
contains a real component representing the load, parallel tuning per pickup [6]–[8], but the effect of all pickups together is often
in the primary becomes dependent on both the magnetic cou- again equivalent to a single pickup with a coupling coefficient
pling and the load. of about 0.5.
1312 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 5, OCTOBER 2005

As can be seen in Fig. 3, systems with such high coupling

coefficients behave very differently to traditional loosely cou-
pled systems. For coupling coefficients of less than 0.2, the
system can be considered loosely coupled and traditional de-
sign approaches as discussed in [9] that use (7) to determine
the primary capacitance give good results. However, as the cou-
pling improves the system characteristics change substantially.
This change is a strong function of both the system topology as
well as the secondary quality factor . The SS topology does
not present a problem, but the other three topologies do. With
equal to 10, PP and PS topologies start deviating from the
loosely coupled theory at coupling coefficients exceeding about
0.2, while for lower values of 2 the deviation only occurs at
coupling coefficients exceeding about 0.5.
Examples of the normalized primary capacitance are given in
Table II. Here, the design changes of three different coupling
coefficients are compared assuming a secondary quality factor
of 10. The required primary capacitance is close to that designed
by (7) if the coupling coefficient is small. With a coupling coef-
ficient of 0.1, the reflected impedance is negligible and as such
affects the primary compensation design by less than 1%. When
the coupling coefficient is around 0.2, the design can change by Fig. 4. Selected structure of the contactless electric vehicle battery charger. (a)
as much as 4% for SP topology, 11% for PP topology, and 14% Geometry. (b) Schematic.
for PS topology. A coupling coefficient of 0.3 changes the de-
sign significantly by 10% for SP topology, 44% for PP topology, TABLE III
and 45% for PS topology. PARAMETERS OF THE CONTACTLESS ELECTRIC VEHICLE BATTERY CHARGER
From the above it can be seen that care needs to be taken
when applying the loosely coupled ICPT theory. The traditional
design rules work well for the SS topology, and for other topolo-
gies with low (less than 2) or coupling coefficients less than
0.2. Special care needs to be taken when designing system with
PP or PS topologies that have good coupling and high .

IV. PROPOSED DESIGN EXAMPLE

A contactless electric vehicle battery charging system was
designed to deliver 30 kW across a 45-mm air gap at a nominal the inverter current is controlled to follow the resonant tank
frequency of 20 kHz with a primary current of 150 A. The voltage using a variable-frequency controller. The system
selected magnetic coupling structure is shown in Fig. 4(a). Here, is, therefore, operated at the ringing frequency of the primary
the primary and secondary windings are identical, each having resonant tank.
concentrated coils with a magnetic linking path. It is assumed The measured coupling parameters are given in Table III
that the secondary coil is attached to the underside of an electric along with other system parameters. The magnetic coupling
vehicle, while the primary coil is buried in the ground. Once an coefficient is 0.45 and the secondary quality factor is 1.77.
electric vehicle has stopped over the charging system, electric According to Table II, the normalized primary capacitance is
power is transferred across an air gap via magnetic coupling 1.04 and as such the primary capacitance is selected 4% larger
between the primary coil in the ground and the secondary coil than that determined by (7).
on the vehicle.
The electric circuit schematic is shown in Fig. 4(b). Both
V. DESIGN VERIFICATION
the primary and secondary windings are compensated using a
parallel-connected capacitor (PP topology in Fig. 2(a)). The As noted above, the inverter current is controlled to be in
current source characteristic of the parallel secondary is suitable phase with the resonant tank voltage and as such the opera-
for battery charging. The parallel primary is used to generate tional frequency is identical to the ZPA frequency of the load
a large primary current. The parallel-compensated primary impedance. This frequency can be calculated from (9) by let-
winding acts as the resonant tank of the full-bridge inverter fed ting the imaginary component equal zero. The power transferred
by a dc voltage . A series inductor is used to regulate from the primary to the secondary at each ZPA frequency is
the inverter current flowing into the parallel-resonant tank. then given by (3). The ZPA frequencies and the corresponding
In order to make the current rating of the inverter as low as power transferred at each operating point are shown in Fig. 5 as
possible to achieve minimum cost and maximum efficiency, functions of the load. As shown, three different ZPA frequencies
WANG et al.: DESIGN CONSIDERATIONS FOR A CONTACTLESS ELECTRIC VEHICLE BATTERY CHARGER 1313

In practice, control perturbations and transients affect the oper-

ational frequency of the variable-frequency controller in the bi-
furcation region. In order to investigate and measure the system
operating at the three different ZPA frequencies and thereby
verify the theory, the converter was made to operate in this re-
gion by increasing the load beyond the rated value while ad-
justing the turn-on interval of the inverter manually to force a
shift between these operational frequencies. Under steady state
conditions, the system was found to operate stably at either the
lowest or highest ZPA frequency since perturbations that give a
large positive phase angle will shift operation to the lowest ZPA
frequency and perturbations that give a large negative phase
angle will shift operation to the highest ZPA frequency.
As shown in Fig. 5, there is very good agreement between
the measured and calculated operational frequency and power
transfer. Small differences arise mainly from the violation of
the theoretical assumption that the voltage and current are sinu-
soidal. In fact the inverter current is not strictly sinusoidal since
some distortion of the voltage across the load impedance is un-
avoidable due to nonlinear switching control of the supply.

VI. CONCLUSION
Many practical ICPT systems are neither tightly nor loosely
coupled. In such cases, coupling effects must be included in
the system design to ensure phase or frequency shifts are mini-
mized. In this paper, a new approach to the design of the primary
compensation was presented that accounts for these coupling
effects. The result is shown to be dependent on the secondary
quality factor and the topology of the primary and secondary
resonant circuits. This effect is more critical with parallel than
series compensation. The proposed theoretical analysis and de-
sign considerations were confirmed using a contactless electric
vehicle battery charger operating off a variable-frequency-con-
Fig. 5. (a) Operational frequency. (b) Power transfer capability (I = 15 A).
trolled power supply.

exist if the load is greater than the normal operating level. This
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[9] O. H. Stielau and G. A. Covic, “Design of loosely coupled inductive Oskar H. Stielau received the B.Eng., M.Eng., and
power transfer systems,” in Proc. Int. Conf. Power System Technology, D.Eng. degrees from Rand Afrikaans University, Jo-
vol. 1, Dec. 2000, pp. 85–90. hannesburg, South Africa, in 1986, 1988, and 1991
[10] C.-S. Wang, G. A. Covic, and O. H. Stielau, “General stability criterions respectively.
for zero phase angle controlled loosely coupled inductive power transfer He currently consults in the high-frequency power
systems,” in Proc. IEEE IECON’01, vol. 2, 2001, pp. 1049–1054. electronic field, specializing in inductive technolo-
gies. He is based in Auckland, New Zealand. Prior
to this, he spent two years with the Inductive Power
Transfer research group at The University of Auck-
Chwei-Sen Wang received the B.E. degree in land and seven years working in industry, mainly in
mechanical engineering from National Chiao Tung the induction heating field.
University, Hsinchu, Taiwan, R.O.C., the M.E.
degree in mechanical engineering from National
Taiwan University, Taipei, Taiwan, R.O.C., and
the M.E. Hons. degree in electrical and electronic
engineering from The University of Auckland,
Auckland, New Zealand. Grant A. Covic (M’88–SM’04) received the B.E.
He is currently a Doctoral Fellow with the Foun- Hons. and Ph.D. degrees from The University of
dation of Research, Science and Technology, New Auckland, Auckland, New Zealand, in 1986 and
Zealand, while hosted in the Department of Electrical 1993, respectively.
and Computer Engineering, The University of Auckland. He has been a Re- He is a full-time Senior Lecturer in the Department
search Fellow in the Mechanical Industry Research Laboratory of the Industrial of Electrical and Computer Engineering, The Univer-
Technology Research Institute, Hsinchu, Taiwan, R.O.C., a Lecturer in the De- sity of Auckland. His current research interests in-
partment of Mechanical Engineering, National Chiao Tung University, and a clude power electronics, ac motor control, electric ve-
Project Manager with Rechi Precision Company Ltd., Hsinchu, Taiwan, R.O.C. hicle battery charging, and inductive power transfer.
His research interests include automatic production systems, computer graphics, He has consulted widely to industry in these areas.
CAD/CAM, refrigerant compressors, room air conditioners, power electronics, He also has a strong interest in improved delivery
and inductively coupled power transfer systems. methods for electronics and control teaching.