1
Contactless Energy Transfer to a Moving Actuator
Jeroen de Boeij, Student Member, IEEE, Elena Lomonova, Jorge Duarte Member, IEEE and
André Vandenput, Senior Member, IEEE
Abstract— In this paper a new topology for contactless energy
transfer is proposed and tested that can transfer energy to a
moving actuator using inductive coupling. The proposed topology
provides long-stroke contactless energy transfer capability in
a plane and a short-stroke movement of a few millimeters
perpendicular to the plane. In addition, it is tolerant to small
rotations. The experimental setup consists of a platform with
one secondary coil, which is attached to a linear actuator and
a 3-phase brushless electromotor. Underneath the platform is
an array of primary coils, that are each connected to a halfbridge square wave power supply. The energy transfer to the
electromotor is measured while the platform is moved over the
array of primary coils by the linear actuator. The secondary coil
moves with a stroke of 18 cm at speeds over 1 m/s, while up to
33 W power is transferred with 90% efficiency.
Index Terms— Contactless energy transfer, inductive coupling,
moving load.
I. I NTRODUCTION
Most high-precision machines are positioning stages with
multiple degrees of freedom (DOF), which often consist
of cascaded long- and short-stroke linear actuators that
are supported by mechanical or air bearings. Usually, the
long stroke actuator has a micrometer accuracy, while the
submicron accuracy is achieved by the short-stroke actuator.
To build a high-precision machine, as much disturbances
as possible should be eliminated. Common sources of
disturbances are vibrations, Coulomb and viscous friction in
bearings, crosstalk of multiple cascaded actuators and cable
slabs.
A possibility to increase throughput, while maintaining
accuracy is to use parallel processing, i.e. movement and
positioning in parallel with inspection, calibration, assembling,
scanning, etc. To meet the design requirements of high accuracy while improving performance, a new design approach
is necessary, especially if vacuum operation is considered,
which will be required for the next generation of lithography
machines. A lot of disturbance sources can be eliminated by
integrating the cascaded long- and short-stroke actuator into
one actuator system. Since most long-stroke movements are
in a plane, this can be done by a contactless planar actuator.
A contactless planar actuator or planar motor is supported by
magnetic bearings that levitate the actuator platform, while
controlling all six DOF of the platform. Long-stroke linear
movement in 2D is also provided by the magnetic bearing
This research is sponsored by SenterNovem. SenterNovem is an agency of
the Dutch Ministry of Economical Affairs.
J. de Boeij is with the Department of Electrical Engineering of the
Eindhoven University of Technology, Eindhoven, The Netherlands; (email:j.d.boeij@tue.nl)
while small translations in height and small rotations remain
possible. Magnetic bearings can also operate in vacuum.
Parallel processing requires power on the platform to
drive the actuators on the platform. In order to remove as
much disturbances as possible, the power transfer needs to
be contactless, i.e. without wires from the ground to the
platform. A coil topology and geometry for a contactless
energy transfer system is proposed for energy transfer to
a planar moving platform. The platform is equipped with
permanent magnets and is levitated and propelled by a matrix
of coils, which are fixed to the ground. Such a planar actuator
is currently under investigation at Eindhoven University
of Technology [13]. The aim of this research project is to
transfer energy to the moving platform continuously and
at every position in order to enhance the functionality of
the platform, while maintaining the advantages of operating
without contact and cables slabs.
When energy is transferred to a moving load (i.e. an
electromotor) by means of inductive coupling, one has to deal
with a changing coupling between a primary and secondary
coil. The change in coupling results in a different characteristic
of the energy transfer capability of the system as is shown
in [1], [2], [3], [4] and [5]. Most of these systems can only
transfer energy at certain positions ([1], [2]) or they suffer
from large changes in power transfer capability throughout
the range due to the changing coupling ([4], [5]).
Another solution for transferring energy to a moving load is
using elongated primary coils in combination with elongated
cores [7]. This results in a stable energy transfer but the
stroke is limited by the size of the primary coil. If long
strokes are required, the system becomes heavy and bulky.
The topology proposed and tested in this paper provides longstroke contactless energy transfer (CET) in a plane with only
small changes in power transfer capability.
II. CET T OPOLOGY
The design of the primary and secondary coil is optimized
to get a coupling that is as constant as possible for a
sufficiently large area. This area should be large enough to
allow the secondary coil to move from one primary coil to
the next one without a large reduction in coupling. If this can
be achieved, the power can be transferred by one primary coil
that is closest to the secondary coil. When the secondary coil
moves out of range the first primary coil is turned off and
the next one will be energized. To ensure a smooth energy
transfer to the moving load, the position dependence of the
coupling should be minimized, while keeping the coupling
high enough to get a high-efficiency energy transfer.
2
r2
r1
c h
c t
Fig. 1.
c w
c w
Coil dimensions
TABLE I
D IMENSIONS OF PRIMARY AND SECONDARY COIL
Parameter
cw
ct
ch
r1
r2
Primary coil
Value
Dimension
60.0
mm
10.0
mm
10.0
mm
1.0
mm
11.0
mm
Secondary coil
Value
Dimension
130.0
mm
30.0
mm
2.0
mm
1.0
mm
31.0
mm
Fig. 3.
Secondary coil above a matrix of nine primary coils
Surface fitted through measurements
0.3
0.28
0.26
0.24
0.02
0
−0.02
y [m]
Fig. 4.
Surface fitted through FEM simulation
0.32
Coupling [−]
0.32
Coupling [−]
A lot of systems use 2D spiral coils for the primary
and secondary coil, since the spiral coil geometry allows
relatively high coupling (up to 60 %) and some tolerance
for misalignment of the coils [8], [9]. However, to allow the
secondary coil to move from one primary coil to the next,
the tolerance for misalignments should be increased. In the
proposed system this is done by using a 3D geometry for
the primary coil. This results in a fairly constant B-field
around the primary coil, which accommodates good coupling
in a large area. Furthermore, since the system is supposed to
transfer power to a load moving in a plane, it is convenient to
use a shape that is symmetrical in 2D for both the primary coil
and the secondary coil: a square for instance. The geometry of
the primary and the secondary coils are optimized with FEM
using Maxwell 3D 10 Optimetrics. The resulting geometry of
the coils is shown in Fig. 1 and 2 and the dimensions are
listed in Table I. More information on the considerations for
the topology can be found in [10].
The drawing in Fig. 3 shows one secondary coil above nine
primary coils. The black square shows the area in which the
center of the secondary coil can move while maintaining good
coupling with the middle primary coil. The secondary coil is
situated in the bottom-left corner of the area of interaction with
0
−0.02
x [m]
0.02
0.3
0.28
0.26
0.24
0.02
0
−0.02
y [m]
0
−0.02
x [m]
0.02
Coupling between primary and secondary coil
the middle primary coil. The coupling between the primary
coil and the secondary coil within that area is calculated with
Maxwell 3D 10 Optimetrics and measured. The results are
shown in Fig. 4, which show that the FEM predictions are
very close to the measured values.
The coupling k is fairly constant within most of the area,
only on the outer edges it drops fast. However, the ripple
defined by Eq. 1 is 25%, which is quite small considering
the large displacement of the secondary coil:
ripple =
max(k) − min(k)
· 100%
max(k)
(1)
Although this system is designed with square shaped coils, it
is also possible to design a system with similar characteristics
using rectangular coils.
III. S TEADY-S TATE E LECTRIC C IRCUIT A NALYSIS
Fig. 2.
Primary and secondary coil
Since the system will be used in a maglev application
based on repulsive forces between coils and permanent
magnets, the use of iron or ferrites is prohibited. In addition,
the use of cores will limit the stroke of the system. Therefore,
a coreless or aircore inductive coupling is used to transfer
the energy. To keep the efficiency of an aircore inductive
coupling high a resonant capacitor is used for both the
3
chosen:
C
V
+
Fig. 5.
1
R
1
I
-
R
1
L
1
L
k
1
I
2
2
R
2
L
V
1
+
R
1
I
-
Z
1
1
L
1
V
1
+
I
-
1
Z
1
R
a
C2
=
C1
=
1
ω02 L2
1
2
ω0 L1
(5)
(6)
This choice of the resonant capacitors ensures that the
impedance of the secondary circuit Z2 , the reflected
impedance of the secondary circuit to the primary circuit ZR
and the impedance seen by the power supply Z1 are purely
resistive at ω = ω0 :
1
Z2 = R2 + RL + j(ω0 L2 −
)
ω0 C2
= R2 + RL
(7)
ω02 M 2
ω02 k 2 L1 L2
=
(8)
ZR =
Z2
R2 + RL
1
) + ZR
Z1 = R1 + j(ω0 L1 −
ω0 C1
ω 2 k 2 L1 L2
= R1 + 0
(9)
R2 + RL
By substituting Eq. 5 into Eq. 4 for ω = ω0 the relation
between I1 and I2 becomes:
Electric circuit of contactless energy transfer system
C
Fig. 6.
C
2
b
Simplified electric circuit of contactless energy transfer system
I2
K
= KI1
ω0 M
= j
R2 + RL
(10)
(11)
primary and the secondary coil. Moreover, due to the
position dependent coupling, a series resonant capacitor is
used for both coils to ensure that the resonant frequency of
the circuit does not depend on the coupling as discussed in [6].
where |K| is a gain relating the current I2 to I1 . Eq. 11 shows
that I2 leads I1 by 90 degrees. Now the power transferred to
the load Pout , the power supplied by the power supply Pin
and the efficiency of the total system η are calculated:
The electric circuit of the CET system is shown in Fig.
5, where V1 is the RMS voltage of the power supply, I1
the RMS current supplied by the power supply, I2 the RMS
current induced in the secondary circuit. C1 and C2 are the
series resonant capacitors in the primary and secondary circuit,
respectively, R1 the resistance of the primary coil, R2 is
the resistance of the secondary coil, L1 and L2 are the self
inductance of the primary and secondary coil, respectively,
k is the inductive coupling factor between the primary and
secondary coil and RL is the resistance of the load. The load
RL represents the rectifier and additional power electronics.
Simplified versions of the circuit are shown in Fig. 6 a and b,
where ZR is the reflected load of the secondary circuit on the
primary circuit and Z1 is the load seen by the power supply.
= I12 Z1
(12)
2 2
= |K| I1 RL
(13)
Pout
|K|2 RL
η =
=
(14)
Pin
Z1
From Eq. 5 and 6 it is clear that the resonant frequency of
the circuit does not depend on the coupling, since the choice
of the resonant capacitors only depends on the inductance of
the coils. In reality the two series resonant capacitors will
not cancel the inductances of the primary and secondary coil
completely. Therefore, the load seen by the power supply will
not be purely resistive. The load seen by the power supply
Z1 does depend on the coupling. This implies that the power
transfer capability of the system depends on the coupling as
well.
The equations for this system with an AC voltage source
with angular frequency ω [rad/s] are:
M
= k L1 L2
(2)
V1
= R1 I1 + j(ωL1 −
(3)
=
(4)
jωM I1
1
)I1 − jωM I2
ωC1
1
(R2 + RL )I2 + j(ωL2 −
)I2
ωC2
where M is the mutual inductance of the primary and sec0
ondary coil. To obtain the desired resonant frequency f0 = w
2π
[Hz], the resonant capacitors C2 and C1 must be suitably
Pin
Pout
IV. E XPERIMENTAL S ETUP
An experimental setup was built to test the CET design,
which consists of an array of three stationary primary coils
that are fixed in a row on top of a ceramic structure. The
ceramic structure is used to allow heat from the coils to be
conducted to the iron base frame and at the same time to
prevent eddy current losses in the iron base frame.
The primary coils are made of litz wire. Each bundle of
litz wire consists of 60 strands of 71 µm and the strands are
wrapped together with a layer of cotton. The strand size has
4
V DC bus
VB
HO
VS
IN
__
SD
VCC
LO
COM
VCC
L
O
A
D
IR 2104
Ground
Fig. 7.
Schematic of the primary coil power supply
TABLE II
E LECTRIC CIRCUIT PARAMETERS OF THE THREE PRIMARY CIRCUITS IN
THE EXPERIMENTAL CET SETUP
Inductance
Resistance
Capacitance
Resonance
Primary Circuit 1
970 µH
4.6 Ω
0.72 nF
191 kHz
Primary Circuit 2
937 µH
4.5 Ω
0.74 nF
190.5 kHz
Primary Circuit 3
864 µH
4.1 Ω
0.81 nF
190 kHz
been chosen after examining the AC losses using the method
described in [12]. The turns of the coil are fixed by glue that
has been applied during the winding process. Approximately
120 turns fitted in the cross-section, resulting in a 0.3 filling
factor.
Each primary coil is connected in series with a resonant
capacitor. Each resonant circuit is driven by a separate halfbridge power supply, that applies a square wave voltage of
191 kHz over the resonant circuit. The schematic of the halfbridge power supply is shown in Fig. 7. An overview of the
primary coils and the corresponding series capacitors is shown
in Table II.
The secondary coil is fixed onto a ceramic plate that is
bolted to the mover of a linear actuator. Again ceramic material
is used for heat conduction and the minimization of eddy
current losses. The linear actuator can move the secondary coil
over the three primary coils. The position of the secondary coil
with respect to the array of primary coils is measured by the
encoder of the linear actuator. A picture of the experimental
setup is shown in Fig. 8.
Fig. 9.
CD electrical drive and rectifier connected to secondary coil
The secondary coil is connected in series with a resonant
capacitor. The circuit is then connected to a full-bridge diode
rectifier to generate a DC output. The DC output of the rectifier
is connected to the load, which is an electromotor of a CD
drive running at 12 VDC as shown in Fig. 9
All subsystems are connected to a ds1103 dSpace system
running the control program at 8 kHz. This way the DC bus
voltage of the primary coil power supplies is controlled as
well as which of the primary coil power supplies is enabled.
The position of the linear actuator is controlled using a PID
controller running on the dSpace system. Depending on the
position of the linear actuator the dSpace system enables the
primary coil that is completely overlapped by the secondary
coil.
The primary coil activation is controlled by a multi-port
switch. The multi-port switch has four active coil states, state
1 enables the power supply of the first primary coil, state 2
and 3 enable the power supply of the second and third primary
coil, respectively. State 4 disables all power supplies and this
state is used for switching from one power supply to the next.
When the secondary coil moves out of range of primary
coil 1 (active coil state 1), the active supply is switched off
(active coil state 4) and one sample time later the second
supply is switched on (active coil state 2). For one sample
time none of the power supplies is active (active coil state
4), which is necessary to allow the triac in the power supply
that is switched off (see Fig. 7) to block the circuit after the
current in the resonant circuit is damped. There is no other
control mechanism in the power electronics, and the system
operates without any measurement on the secondary site,
except for the position of the secondary coil.
V. R ESULTS
Fig. 8.
Picture of experimental CET setup
An electromotor of a CD drive that runs on 12 VDC
is connected to the rectifier. The voltage and current from
the DC bus supply as well as the voltage and current to
the CD drive are measured and shown in Fig. 10 and 11.
The secondary coil is moving over all three primary coils
following a sinusoidal position reference, which represents a
total displacement of 18 cm (i.e. the amplitude of the sine
wave is 9 cm). The frequency of the sinusoidal position
reference is 2 Hz, so in one second the secondary coil makes
5
TABLE III
VALUES OF VOLTAGES , CURRENTS , POWER AND EFFICIENCY OF THE CET
Power supply voltage
Voltage [V]
52
TO A
51
50
49
0
0.2
0.4
0.6
Time [s]
Power supply current
0.8
1
0.2
0.4
0.6
Time [s]
Active Coil State
0.8
1
0.15
0.1
RMS Value
51.1
76.6
3.84
12.5
276
3.44
89.4
0
0
0.4
4
0.2
3.5
3
Current [A]
Active Coil
4.5
Primary coil 1
Primary coil 2
0.3
4
2
1
0
0.2
0.4
0.6
Time [s]
0.8
1
0.1
0
2
−0.2
1.5
−0.4
0
Measured voltage, current and active primary coil for the DC bus
3
2.5
−0.1
−0.3
Fig. 10.
supply
Dimension
[V]
[mA]
[W]
[V]
[mA]
[W]
[%]
0.05
Active coil
Current [A]
CD DRIVE ELECTROMOTOR
Variable
VDCbus
IDCbus
Pin
Vload
Iload
Pout
η
1
1
2
Time [s]
3
4
−4
x 10
0.5
0
1
2
Time [s]
3
4
−4
x 10
Fig. 12. Plot of current in primary coil 1 and 2 during switching and the
active coil command.
Voltage [V]
Load voltage
14
12
Current [A]
10
0
0.2
0.4
0.6
Time [s]
Load current
0.8
1
0.2
0.4
0.6
Time [s]
Active Coil State
0.8
1
0.5
0
0
Active Coil
4
In Fig. 12, the transient behavior is shown when the
secondary coil is moving from primary coil 1 to primary coil
2. It is clearly visible that all power supplies are switched
off when the active coil state has value 4. There is also
some delay between the active coil state switch and the
response from the power electronics, which is caused by a
slow rising edge of the enable signal and by delay in the
power electronics. In Fig. 10 and 11 the switching is also
visible in the current waveforms, since no current is drawn
from the DC bus supply and no current is available for the
electromotor of the CD drive.
3
2
1
0
0.2
0.4
0.6
Time [s]
0.8
1
Fig. 11. Measured voltage, current and active primary coil for the CD drive
electromotor load
two cycles (one cycle implies moving from primary coil 1
over primary coil 2 to primary coil 3 and back). The cycle is
clearly visible from the Active Coil plot in Fig. 10 and 11,
which represents the state of the active coil multi-port switch.
The secondary coil reaches a maximum speed of 1.1 m/s over
the second primary coil. Due to this speed the secondary coil
is in range of the second primary coil for only 60 ms.
By calculating the RMS values of the voltages and currents
the power from the DC bus supply Pin as well as the power
to the CD drive load Pout and the efficiency η according to
Eq. 14 can be calculated. This calculation includes losses in
the power electronics. The values are listed in Table III.
The ripples visible in the voltage and current waveforms
from the DC bus power supply and to the CD drive are
related to the changing coupling. However, since the CD
drive does not represent a purely resistive load, the ripple is
somewhat smoothed by the inductance of the load. This effect
is more visible when a purely resistive load will be connected
to the system. In addition, the CD drive does not need much
power to operate and a resistive load can be operated at
higher power levels. Therefore, a 50 Ω resistive load is used
at a higher power level. The same trajectory is used for the
secondary coil. The measured voltage and current waveforms
of the DC bus supply and the load are shown in Fig. 13
and 14 respectively. The RMS values of voltage, current and
power as well as the efficiency are shown in Table IV.
The variation in coupling is now clearly visible in the
current and voltage waveforms of the load. This suggests
that the power transfer can be further smoothed by measuring
the coupling and changing the voltage of the DC bus supply
accordingly, as is discussed in [11]. The results are very similar
to the results of the CD drive. Higher power levels have not
been tested using the linear actuator, since the capacitors in
6
the resonant circuit cannot operate above 800 V. Operating
at higher power requires new capacitors which have not been
realized yet. It is expected that power transfer up to 300 W is
feasible.
Power supply voltage
Voltage [V]
160
150
140
0
0.2
0.4
0.6
Time [s]
Power supply current
0.8
1
0.2
0.4
0.6
Time [s]
Active Coil State
0.8
1
0.2
0.4
0.6
Time [s]
0.8
1
Current [A]
0.5
0
0
Active Coil
4
3
2
1
0
Fig. 13. Measured voltage, current and active primary coil for the DC bus
supply (resistive load)
Voltage [V]
Load voltage
50
Current [A]
0
0
0.2
0.4
0.6
Time [s]
Load current
0.8
1
0.2
0.4
0.6
Time [s]
Active Coil State
0.8
1
0.2
0.4
0.6
Time [s]
0.8
1
1
0.5
0
0
Active Coil
4
3
2
1
0
Fig. 14. Measured voltage, current and active primary coil for the 50 Ω load
TABLE IV
VALUES OF VOLTAGES , CURRENTS , POWER AND EFFICIENCY OF THE CET
TO A
Variable
Vdcbus
Idcbus
Pin
Vload
Iload
Pout
η
50 Ω RESISTOR
RMS Value
150
239
35.9
40.8
807
32.9
91.8
Dimension
[V]
[mA]
[W]
[V]
[mA]
[W]
[%]
VI. C ONCLUSION
A new topology for contactless energy transfer (CET) to a
moving load has been proposed, built and tested. The CET
topology allows for a long-stroke movement in a plane and
a short-stroke movement of a few millimeters perpendicular
to the plane. In addition, it is tolerant to small rotations. The
power electronics consist of a half-bridge square wave power
supply for each primary coil and series resonant capacitor and
a full-bridge diode rectifier at the load.
Power transfer up to 33 W with resistive load of 50 Ω
has been demonstrated The CET system was used to power
a 3-phase brushless electromotor of a CD drive and showed
stable power transfer of 3.44 W. The power was transferred at
approximately 90 % efficiency, while the secondary coil was
moving with speeds up to 1.1 m/s over the primary coils.
R EFERENCES
[1] G.A. Covic, G. Elliott, O.H. Stielau, R.M. Green, J.T. Boys, The
Design of a Contact-less Energy Transfer System for a People Mover
System, Proceedings IEEE International Conference on Power System
Technology, PowerCon 2000, Vol 1, December 2000, pp. 79-84.
[2] H. Ayano, K. Yamamoto, N. Hino, I. Yamato, Highly-Efficient Contactless Electrical Energy Transmission System, 28th Annual Conference of
the IEEE Industrial Electronics Society, IECON 2002, Vol 2, November
2002, pp. 1364-1369.
[3] S. Adachi, F. Sato, S. Kikuchi: Considerations of Contactless Power
Station with Selective Exitation to Moving Robot, IEEE Transactions
on Magnetics, Vol. 35, No. 5, September 1999, pp. 3583-3585.
[4] F. Sato, J. Murakami, H. Matsuki, S. Kikuchi, K. Harakawa, T. Satoh:
Stable Energy Transmission to Moving Loads Utilizing New CLPS,
IEEE Transactions on Magnetics, Vol. 32, No. 5, September 1996, pp.
5034-5036.
[5] F. Sato, H. Matsuki, S. Kikuchi, T. Seto, T. Satoh, H. Osada, K. Seki:
A New Meander Type Contactless Power Transmission System - Active
Excitation with a Characteristics of Coil Shape, IEEE Transaction on
Magnetics, Vol. 34, No. 4, July 1998, pp. 2069-2071.
[6] C. Wang, G.A. Covic, O.H. Stielau: Power Transfer Capability and
Bifurcation Phenomena of Loosely Coupled Inductive Power Transfer
Systems, IEEE Trans. on Industrial Electronics, Vol. 51, No. 1, February
2004, pp. 148-157.
[7] G.L.M. Jansen: 2-Dimensional Displacement Device, International
Patent Application, WO 2005/013464 A1.
[8] C. Fernandez, O. Garcia, R. Prieto, J.A. Cobos, S. Gabriels, G. Van
der Borght: Design Issues of a Core-less Transformer of a Contact-less
Application, 17th Annual IEEE Applied Power Electronics Conference
and Exposition, APEC 2002, Vol.1 pp. 339-345
[9] R. Mecke, C. Rathge: High Frequency Resonant Inverter for Contactless
Energy Transmission over Large Airgap, 25th Annual IEEE Power
Electronics Specialist Conference, 2004, pp 1737-1743.
[10] J. de Boeij, E. Lomonova, A.J.A. Vandenput: Contactless Energy
Transfer to a Moving Load Part I: Topology and FEM Simulation,
International Symposium on Industrial Electronics, Montreal, Canada,
July 2006.
[11] J. de Boeij, E. Lomonova, J.L. Duarte, A.J.A. Vandenput: Contactless
Energy Transfer to a Moving Load Part II: Simulation of Electrical and
Mechanical Transient, International Symposium on Industrial Electronics, Montreal, Canada, July 2006.
[12] C.R. Sullivan: Computationally Efficient Winding Loss Calculation
with Multiple Windings, Arbitrary Waveforms and Two-Dimensional or
Three-Dimensional Field Geometry, IEEE Trans. on Power Electronics,
Vol. 16, No. 1, January 2001, pp. 142-150.
[13] J.W. Jansen, E.A. Lomonova, A.J.A. Vandenput, C.M.M. Van Lierop:
Analytical Model of a Magnetically Levitated Linear Actuator, IAS 2005
Annual Meeting, Hong Kong, China, October 2005.
[14] Ansoft: Maxwell 10 User’s Guide, Pittsburgh PA, USA.