transfer system for a notebook battery charger. Pascal Meyer, Paolo Germano and Yves Perriard. AbstractâSome applications require an energy transfer.
XIX International Conference on Electrical Machines - ICEM 2010, Rome
Modelling and design of a contactless energy transfer system for a notebook battery charger Pascal Meyer, Paolo Germano and Yves Perriard Abstract—Some applications require an energy transfer without contacts and wires. The mutual inductive effects between two coils allow to transfer energy to an electronic consumer through an air gap. This paper presents an analytical model of a coreless transformer used to design a contactless energy transfer from a platform to a notebook battery charger. By defining the geometric parameters of the transformer, the model is able to compute its magnetic parameters. It is then possible to get the electric quantities with a circuit simplification process. In the scope of an industrial project, this study has been successfully applied to a notebook battery charging platform. Index Terms—Coreless transformer, induction, contactless, energy transfer.
I. I NTRODUCTION The principle of coreless transformers consists in applying a high frequency current in a primary coil. In the surrounding air, it generates a magnetic field that induces a voltage in a secondary coil if placed in proximity. It is necessary to operate at high frequencies because coreless transformers suffer from weak mutual coupling. Most applications work at a frequency range between 100 kHz and 1 MHz. To enhance the coupling between primary and secondary, both coils must be well aligned and the air gap must be as small as possible. Furthermore, contactless energy systems are usually characterised by high leakage inductances compared to the main inductance, which generates large reactive loss. To solve this problem, a resonant circuit is implemented on both primary and secondary sides, by adding coupling capacitors in parallel or in series (Fig. 1).
phone battery with two PCB windings [1], [2], to provide power and information from a stationary part to a rotating one [3], or to charge a vehicle battery through large air gaps [4]. A possibility to transfer energy to a few loads simultaneously has been proposed in [5]. It is also possible to apply contactless energy transfer to linear actuators, vehicles or platform systems that need to be continuously supplied. It allows to suppress the contacts, thus friction and wear. The primary and secondary coils may have different shapes, like a meander type configuration [6], [7], or a track of rectangular coils [8]. In order to supply contactlessly one or a few moving loads, a frequent solution consists in an array of multiple primary coils. Such systems are generally more complicated because they integrate a system to detect the presence of a load and to activate only the primary coils situated under it. An example of an array of four PCB primary coils is given in [9], with smaller coils at their periphery for the detection. Another study on many primary square coils realised with Litz wires led to a prototype of a contactless planar actuator [10]. Different shapes (square, rectangular, hexagonal, . . . ) of the primary PCB coils, concentrated in one layer or distributed in many ones, are tested in [11], [12], [13]. The aim of this paper is to present a method to design a coreless transformer. An analytical model is presented in Section II. A general methodology to design coreless transformers is described in Section III and applied to an industrial application in Section IV. II. A NALYTICAL M ODEL
AC-hf
DC
DC to AC-hf converter
Primary resonant circuit
Fig. 1.
Air t ransf ormer
Secondary resonant circuit
High-f req. Load rect if ier
General coreless transformer system.
Inductive coupling is a widely applied method to contactlessly transfer energy. It is typically used to charge a mobile P. Meyer, P. Germano and Y. Perriard are with Integrated Actuators Laboratory (LAI), Ecole Polytechnique Federale de Lausanne (EPFL), Switzerland.
978-1-4244-4175-4/10/$25.00 ©2010 IEEE
The analytical model can be split into two parts: 1) With the geometry of the coreless transformer completely defined, the magnetic part of the model computes the self and mutual inductances; 2) The electric part computes the resistances, the capacitances, the currents, the voltages, the power, and the efficiency of the coreless transformer. It only requires the value of the load, as well as the magnitude of the voltage supply. A. Magnetic Model The geometric parameters of a coreless transformer are shown in Fig. 2 and defined in Table I. Indices 1 and 2 correspond respectively to the primary and secondary coils. The crucial point of the model is to accurately calculate the inductances. First of all, the self inductance is determined as
the formula for theorem and the magnetic vector potential A, the external inductance becomes: Le = (4) ∇ × A1 · dS = B1 · dS
d1,2
r1
a1,2
g
r2
S2
b 1 ,2
(a)
(b)
Fig. 2. (a) Parameters of a coil. (b) Cross section of a secondary coil above a primary coil.
For this study, rectangular shaped coils are used, which makes the computations simpler. It allows to calculate the magnetic flux density and then to integrate it on the surface S2 determined by the coil. To obtain the magnetic flux density produced by an electrical current, the model uses the BiotSavart’s law (5):
TABLE I G EOMETRIC PARAMETERS . Parameter a1,2 b1,2 d1,2 r1,2 N1,2 g
= μ0 I B 4π
Definition First side length of coils Second side length of coils Distance between two turns Wire radius Number of turns Air gap
(1)
where Le is the external inductance and Li the internal inductance. According to [14], the internal inductance is related to the energy in the coil, and using the Ampere’s law for a circular conductor, is given by: μ0 l (2) 8π with l the total length of the conductor. The external inductance is calculated with the Neumann’s formula: dl2 · dl1 μ0 (3) Le = 4π R Li =
C2 C1
where C1 is the integration path on the wire axis, C2 is the integration path on the wire surface, and R is the distance between the two elementary integration lengths dl1 and dl2 (Fig. 3). C1 C2 y
dl1
x
l2 l1
Fig. 3.
C1
dl1 × R 3 R
(5)
Bz (x, y, z) = Bz,1 + Bz,2 + Bz,3 + Bz,4
L = Li + Le
R
As a first step, a rectangular closed coil of one turn is considered, like in Fig. 3. This coil is separated in four straight segments, and their contribution to the magnetic flux density can be computed at a position (x, y, z). This provides the following equations for the flux density in the z-direction:
follows. Its value is split into two parts:
dl2
S2
Computation of the self inductance.
The Neumann’s formula is complicated to integrate in a model, so that it must be simplified. By using the Stokes’
with Bz,1 (x, y, z)
l2 −y 2 (l1 +x)2 +z 2 +(l 2 −y) l +y l1 +x 2 +√ (l1 +x)2 +z 2 (l1 +x)2 +z 2 +(l2 +y)2
=
μ0 I 4π
(6)
√
(7)
where Bz is the magnetic flux density of the one-turn coil, Bz,1 , Bz,2 , Bz,3 , Bz,4 are the contributions of the segments. The formulations for Bz,2 , Bz,3 and Bz,4 are similar to (7) and therefore not repeated. Finally, the external inductance is determined by numerically integrating (6) on the internal surface of the coil: 1 Le = I
l 1 −r
l 2 −r
Bz (x, y, 0)dy dx
(8)
−(l1 −r) −(l2 −r)
The above calculations concern the self inductance in the case where the coil is a closed loop of one turn. The calculation of mutual inductance M12 between a pair of two turns follows the same way, but in (3), C1 is the contour on the wire axis of the primary coil, and C2 is the contour on the wire surface of the secondary coil (Fig. 4). For coils with more than one turn, the self inductance is obtained by summing the self inductances of each turn to the mutual inductances between all possible pairs: L11 =
N1 i=1
Li +
N1 N1
Mij
(9)
i=1 j=1,j=i
where L11 is the self inductance of the primary coil, N1 is the number of turns, Li the self inductances of each turn, Mij the mutual inductances between two turns.
dl2
IL1
l4 R
C2 C1
I1
l3
L2
L1
C1
C2
RL
x
dl1
l2 l1
Fig. 4.
R2
R1
IC1
U1
y
I2
Fig. 5.
Equivalent circuit of a coreless transformer.
IL1
Computation of the mutual inductance.
The formula for mutual inductance between two coils of more than one turn is obtained by summing all the mutual inductances between pairs: L12 =
N1 N2
Mij
I1 U1
IC1
R1 L1
C1 ZR
(10)
i=1 j=1
where L12 is the mutual inductance between primary and secondary coil, and N2 the number of secondary turns. B. Electric Model
Fig. 6.
The main parameters of coreless transformers are listed in Table II-B. Fig. 5 shows an equivalent electric circuit of a coreless transformer. The connection of the resonance capacitors for the primary and secondary coils must be chosen according to the application [4], [15]. For the one developped in this paper, the connection is chosen in series for the secondary coil and in parallel for the primary coil, because it allows to compensate the inductive component of the secondary coil and to generate high currents in the primary coil.
Definition Primary inductance Secondary inductance Mutual inductance Primary resistance Secondary resistance Load resistance Primary capacitor Secondary capacitor RMS source current RMS current in the primary capacitor RMS current in the primary coil RMS secondary current
1 ) = R2 + RL (13) ω0 C2 By substituting I 2 from (12) under resonnance frequency condition, the term jω0 L12 I 2 of (11) becomes: ω02 L212 I = −Z R I L1 = −RR I L1 (14) R2 + RL L1 where Z R is the secondary impedance reflected on the primary, that is also purely resistive at the resonnance frequency. Finally, the total impedance Z eq seen by the voltage source is given by: jω0 L12 I 2 = −
Z eq =
The approach to design the coreless tranformer parameters is similar to the one presented in [10]. It is based on electric circuit analysis. The voltage equation in the primary (11) and in the secondary (12) are given by: U 1 = R1 I L1 + jωL11 I L1 − jωL12 I 2
1 I (12) jωC2 2 √ At the resonance frequency ω0 = 1/ L2 C2 , the total secondary impedance Z 2 is purely resistive: jωL12 I L1 = (R2 + RL )I 2 + jωL2 I 2 +
Z 2 = R2 + RL + j(ω0 L2 −
TABLE II E LECTRIC PARAMETERS . Parameter L11 L22 L12 R1 R2 RL C1 C2 I1 IC1 IL1 I2
Simplified electric circuit.
(11)
jω0 L1 + RR + R1 −ω02 L1 C1 + jω0 C1 (RR + R1 ) + 1
(15)
The primary capacitor is dimensionned so that the imaginary part of Z eq is equal to zero, which occurs when: C1 =
L1 ω02 L21 + (RR + R1 )2
(16)
The primary current generated by the voltage supply is given by the following equation:
I1 =
TABLE III VOLTAGE SUPPLY AND NOTEBOOK CHARGER SPECIFICATIONS .
U1 Z eq
(17)
It is then easy to compute all the voltages and currents that are needed to design a coreless transformer. The power of different components and the system efficiency can as well be deduced.
U1 355 Vrms
RL 7Ω
PL 80 W
TABLE IV F INAL DESIGN OF THE CORELESS TRANSFORMER FOR THE BATTERY CHARGER . Parameter N1 N2 r1,2 a1,2 b1,2 g
III. D ESIGN M ETHODOLOGY Fig. 7 shows the general methodology to design a coreless transformer. It is an iterative process that reaches an end only if the specifications are fulfilled. First, the specifications must be defined: the size of the coils and the air gap, as well as the voltage supply, the load resistance and the voltage needed by the load (1). For the notebook charger, the coils have to be integrated respectievely for the primary and the secondary coil on the platform and under the notebook. Therefore, the maximal size of both coils is about 240 × 160 mm2 . The electrical specifications of the voltage supply and of the battery charger are given in Table III. The working frequency is fixed at around 250 kHz, and the air gap of 15 mm is constrained by the thickness of the platform. The variable parameters for this application are the ones given in Table I. Based on the specifications, a geometry of the coreless transformer is generated with a set of parameters (2). The analytical model is applied and provides the inductances and electric quantities (3-4). At this point, a success criterion is checked. For the notebook charger, the load voltage has to be at least UL = 24 V . If the condition is not fulfilled, the process comes back to point (2) and generates a new geometry with a different set of parameters. If it is fulfilled, the final design is obtained (5). For the battery charger, the final design is presented in Table III.
UL 24 Vdc
Value 10 1 1 mm 220 mm 140 mm 15 mm
IV. P ROTOTYPE AND E XPERIMENTAL M EASUREMENTS According to the obtained final design, a prototype is built. Fig. 8 shows a photograph of the prototype while it is working, and Fig. 9 shows a photograph of electronics and the coreless transformer. The primary coil is integrated on the platform and the secondary coil is integrated under the notebook.
Fig. 8.
Photograph of the prototype.
(1)Specifications
(2)Geometry design
Analytical model
(3)Inductancescomputations (4)Electriccomputations
UL ?
No
Yes (5)Finaldesign
Fig. 9. Fig. 7.
Design methodology.
More detailed photograph of the prototype with electronics.
Table IV contains the measured values compared to the ones obtained with the analytical model.
TABLE V I NDUCTANCES COMPARISON . Parameter L11 L22 L12
Model 49.2 μH 791 nH 2.60 μH
Measurement 52.2 μH 821 nH 2.58 μH
TABLE VI E LECTRIC COMPARISONS IN RMS VALUES . Parameter U1 IL1 UL
Model 177.0 V 2.15 A 10.52 V
Measurement 177.3 V 2.18 A 10.27 V
A set of measurements of the mutual inductance has been realised by varying the air gap. The comparison between the measurements and the analytical model is presented in Fig. 10 and the absolute error is shown in Fig. 11. Finally, the electric quantities have been measured with a 5 Ω resistive load and are given in Table IV in RMS value. The working frequency for these measurements is about 250 kHz, and the alternative voltage U1 is generated by a full bridge converter developped for this project.
Fig. 10.
Comparison between analytical model and measurements.
Fig. 11.
Difference in % between model and measurements.
The results show that the analytical model is accurate and reliable. Tests have been carried out to verify the prototype efficiency and stability. Regardless of the presence or absence of the notebook on the platform, the coreless transformer and the full bridge converter show a good behavior and work well. V. C ONCLUSION An analytical model that allows to compute accurately magnetic and electric parameters has been implemented. By integrating this model in a general design methodology, the process is able to generate simple solutions to design coreless transformers. It has been successfully applied to the industrial application developped in this paper, that is a contactless energy transfer to a notebook battery charger. As a result, we have measured an efficiency of 90 %, which is a good performance even in laboratory conditions. R EFERENCES [1] S. Tang, S. Hui, and H.-H. Chung, “Characterization of coreless printed circuit board (pcb) transformers,” Power Electronics, IEEE Transactions on, vol. 15, pp. 1275–1282, Nov 2000. [2] B. Choi, J. Nho, H. Cha, T. Ahn, and S. Choi, “Design and implementation of low-profile contactless battery charger using planar printed circuit board windings as energy transfer device,” Industrial Electronics, IEEE Transactions on, vol. 51, no. 1, pp. 140–147, Feb. 2004. [3] T. Bieler, M. Perrottet, V. Nguyen, and Y. Perriard, “Contactless power and information transmission,” Industry Applications, IEEE Transactions on, vol. 38, no. 5, pp. 1266–1272, Sep/Oct 2002. [4] C.-S. Wang, O. Stielau, and G. Covic, “Design considerations for a contactless electric vehicle battery charger,” Industrial Electronics, IEEE Transactions on, vol. 52, no. 5, pp. 1308–1314, Oct. 2005. [5] X. Liu and S. Hui, “Optimal design of a hybrid winding structure for planar contactless battery charging platform,” Power Electronics, IEEE Transactions on, vol. 23, no. 1, pp. 455–463, Jan. 2008. [6] N. Macabrey, Alimentation et guidage linaire sans contact. PhD thesis, EPFL, 1998. [7] F. Sato, H. Matsuki, S. Kikuchi, T. Seto, T. Satoh, H. Osada, and K. Seki, “A new meander type contactless power transmission systemactive excitation with a characteristics of coil shape,” Magnetics, IEEE Transactions on, vol. 34, no. 4, pp. 2069–2071, Jul 1998. [8] P. Germano and M. Jufer, “Contactless power transmission: Frequency tuning by a maximum power tracking method,” EPE ’97, 7th European Conference on power electronics and applications, Trondheim, vol. IV, pp. 693–697, Sept 1997. [9] F. Sato, J. Murakami, H. Matsuki, S. Kikuchi, K. Harakawa, and T. Satoh, “Stable energy transmission to moving loads utilizing new clps,” Magnetics, IEEE Transactions on, vol. 32, no. 5, pp. 5034–5036, Sep 1996. [10] J. de Boeij, E. Lomonova, and A. Vandenput, “Contactless energy transfer to a moving load part i: Topology synthesis and fem simulation,” Industrial Electronics, 2006 IEEE International Symposium on, vol. 2, pp. 739–744, July 2006. [11] J. Achterberg, E. A. Lomonova, and J. de Boeij, “Coil array structures compared for contactless battery charging platform,” Magnetics, IEEE Transactions on, vol. 44, no. 5, pp. 617–622, May 2008. [12] X. Liu and S. Y. R. Hui, “Equivalent circuit modeling of a multilayer planar winding array structure for use in a universal contactless battery charging platform,” Power Electronics, IEEE Transactions on, vol. 22, no. 1, pp. 21–29, Jan. 2007. [13] C. Sonntag, E. Lomonova, J. Duarte, and A. Vandenput, “Specialized receivers for three-phase contactless energy transfer desktop applications,” Power Electronics and Applications, 2007 European Conference on, pp. 1–11, 2-5 Sept. 2007. [14] I. Stefanini, Mthodologie de conception et optimisation d’actionneurs intgrs sans fer. PhD thesis, EPFL, 2006. [15] O. Stielau and G. Covic, “Design of loosely coupled inductive power transfer systems,” Power System Technology, 2000. Proceedings. PowerCon 2000. International Conference on, vol. 1, pp. 85–90 vol.1, 2000.
B IOGRAPHIES Pascal Meyer was born in Switzerland in 1984. He received the M.S. degree in Microtechnology engineering from the Federal Institute of Technology of Switzerland (EPFL) in 2008. He is currently doing a PhD thesis at EPFL on contacless energy transfer systems for different types of consumers. Paolo Germano was born in Lausanne in 1966 and is native of Italy. He received the M.Sc. in micro-engineering from the Swiss Federal Institute of Technology Lausanne (EPFL) in 1990. He joined the Laboratory of Electromechanics and Electrical Machines (LEME) in the same year. He is currently senior researcher at the Laboratory of Integrated Actuators (LAI). His activities as project leader are mainly focused on test benches and analysis of stepping motors, BLDC motors and linear actuators. In the field of inductive energy transmission, he took part in the development of the Swiss artificial heart project and led the Serpentine project (public transportation) as well as various industrial projects related to the machine tools. Yves Perriard was born in Lausanne in 1965. He received the M. Sc. in Microengineering from the Swiss Federal Institute of Technology - Lausanne (EPFL) in 1989 and the Ph D. degree in 1992. Co-founder of Micro-Beam SA, he was CEO of this company involved in high precision electric drive. Senior lecturer from 1998 and professor since 2003, he is currently director of Laboratory of Integrated Actuators. His research interests are in the field of new actuator design and associated electronic devices. Since 2009, he is appointed Vice-Director of the Microengineering Institute in Neuchtel.
