design methodology for ipt.pdf

Copyright (c) 2011 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing [email protected].

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.

grid

/ ba

ttery

50/60 Hz

Rectifier HF-Inverter

HF-rectifier Filter Load

Energy source

D.C. link

20..400 kHz

Primary coil

Secondary coil

Fig. 1. Minimum configuration of a voltage fed inductive power transfer (IPT) system

Design methodology for high efficient inductive power transfer systems

with high coil positioning flexibility

Daniel Kürschner, Member, IEEE, Christian Rathge and Ulrich Jumar

Abstract−With contactless inductive power transfer (IPT) it is possible to transfer electrical energy to stationary or movable consumers without contacts, cables or slip rings. To reduce the very high development effort of new contactless inductive energy supplies, a new systematic and modular design methodology is presented in the paper. This methodology includes new methods to increase the transfer efficiency and the positioning flexibility of the consumer device and is particularly implemented into a simulation software tool. The positioning tolerance is improved by the optimisation of the coil and ferrite geometry. Thereby, the influence of physical and geometrical parameters on the magnetic coupling and on the electrical transfer characteristics is investigated. As a result of the design methodology, a new inductive power transfer system for household appliances in the output power range of 1 kW at an overall efficiency of more than 90 % and with a high positioning tolerance is presented.

I. INTRODUCTION

The basics of contactless inductive power (energy) transfer (IPT, CET) were already discovered by M. Faraday, H. C. Oersted and N. Tesla in the 19th century. The law of induction by M. Faraday describes the possibility for electrical energy transfer not by wire but by a time varying magnetic field. Today, because of new magnetic materials and fast switching power electronics and because of new app-

Manuscript received January 31, 2011. Accepted for publication November 15, 2011.

Copyright © 2009 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]

D. Kürschner was with the Institut f. Automation und Kommunikation, Magdeburg. He is now with the company Paul Vahle, Westicker Str. 52, 59174 Kamen (phone: +49 2307 704334; fax: +49 2307 704482; e-mail: [email protected]).

C. Rathge and U. Jumar are with the Institut f. Automation und Kommunikation, Werner-Heisenberg-Str. 1, 39106 Magdeburg (e-mail: [email protected], [email protected]).

lications that need a wireless energy supply, the inductive power transfer technology is commonly utilised [1-3]. Over the last few years IPT technology has greatly improved for example in automatic guided vehicle (AGV) systems or in automation to supply electrical drives, sensors or actuators. Apart from industrial applications, today IPT can also be used for household appliances and for battery charging of mobile entertainment (cell phone, music player) or even for the contactless charging of electric vehicles.

Fig. 2 shows a minimum configuration of an IPT system. The electrical energy is transferred via the magnetic field between the coils. The transfer performance can be increased by using high transmission frequencies, resonance operation of the coils and special materials like Litz wire and ferrite cores [1-3, 6-7]. Compared to a conventional transformer and because of the high frequencies, special power electronics are needed to feed the primary coil and to convert the electrical energy on the secondary side [2]. At AGV or linear powered electric vehicles, several consumers are mostly supplied by one or more primary conductor loops at a constant current [6]. At a point-to-point energy transfer (only one receiver) often a primary voltage-fed inverter with D.C. link is used.

As shown, compared to a cable based power supply, IPT technology results in more complex systems. Because of the increasing range of applications, a lot of new solutions for inductive powered devices with very different technical requirements (e. g. voltage and power level, transfer distance, installation size) are needed. As already mentioned in [4], to allow a high efficient (η > 90 %) and safe power transfer, the entire IPT system has to be designed carefully and syste-matically for each of these applications. Thereby, mostly new concepts or adapted designs of both, magnetic coil system and power electronics are needed. Generally, the develop-ment is done by extensive experimental analyses and iterative practical redesigns. To reduce the developmental period and



the costs, a new systematic design methodology for the computer-aided design was developed and is proposed in the paper. Thereby, the power loss of the IPT system (efficiency) as well as tolerances caused by incorrect alignments of the coils (positioning flexibility) or by straying values of electronic devices are considered by using new numerical models and analytic functions. To apply the developed design methodology, the models are implemented in a new simulation software tool and validated by an IPT test system.

II. DESIGN METHODOLOGY

A. Design Concept and Calculation Modules

As the most important component for an efficient inductive power transfer, this work focuses on the magnetic coil sys-tem. For the analysis, using the T equivalent circuit is favour-able, because the main and leakage inductances (LH, L1σ, L2σ) can directly be determined as a result of the FEM simulation [2]. Compared to a conventional transformer LH and Lxσ are in the same dimension. At a defined frequency, the power loss of the transformer can be considered by the resistances R1, R2 and RFe. The transfer ratio is respected by x*=N1/N2⋅x.

LH

L2σ*L1σR1 R2*

RL*RFe

i1 i2*

iHu1

u2*

Fig. 2. T equivalent circuit of an air gapped transformer with main and leakage inductances and with winding and core loss resistors

TABLE I: INPUT AND OUTPUT PARAMETERS AT A SYSTEMATIC DESIGN

Performance characteristics (System requirements)

System parameters (Degrees of freedom)

Output power Geometry of the coil system

Input and output voltage level Leakage inductance compensation strategy

Maximum power loss (Efficiency) Absolute windings (N1, N2)

EMC, EMF Winding ratio (N1/N2)

Maximum installation size, weight, costs

Transmission frequency (f)

Transmission distance (air gap a)

Tolerances (capacitor straying ΔC, coil misalignment Δv, air gap Δa)

The system parameters (e. g. coil geometry, windings,

frequency) have to be determined in compliance with user-defined requirements (performance characteristics), such as voltage and power level, installation size or costs. Important requirements and parameters are shown in Table 1. The air gap, straying capacitor values or coil misalignments can be both, required values or degrees of freedom.

In Fig. 3, a proposal for a systematic design methodology of circular coil systems is shown. Several modular determina-tion steps are executed sequentially and associated by itera-tion paths. To be able to start the parameter determination, an initial coil geometry is needed (Chapter II.C). Based on the initial coil geometry and after choosing a proper type of leakage inductance compensation strategy (Chapter II.B), the magnetic coupling parameters (LH, L1σ, L2σ) (Fig. 2) can be determined. In this matter, geometrical tolerances for example the position of the transmitter and receiver coil to each other (lateral misalignments Δv, variable air gaps Δa) can be considered.

With all T parameters (LH, L1σ, L2σ, R1, R2), the steady-state and the transient electrical transfer behaviour can be ana-lysed. At the required output power, the needed windings and currents (N1⋅i1, N2⋅i2) can be determined. If no valid parame-ters are found, an iteration is necessary and the coil geometry or other parameters have to be changed (Fig. 3).

Important aspects of contactless inductive power transfer systems are reaching higher transferable power and smaller installation size and weight at the same time. This requires the analysis of the power loss of the entire system. At high transmission frequencies, power loss increases because of the SKIN- and Proximity effect (increasing winding resistances), hysteresis effects in the ferrite core and switching of the power electronic devices. Furthermore, to meet the require-ments of a mechanical interface and ingress protection, often an enclosed metallic housing is needed. This results in additional eddy current power loss. With the knowledge of N1⋅i1 and N2⋅i2, in the next design step (Fig. 3) the absolute power loss of the coil system can be determined [5].

For the calculations it has to be noticed, that the power loss also affects all T parameters. As the ohmic parameters (R1, R2) directly depend on the frequency, the core loss resistor RFe can not be dimensioned until the absolute hysteresis loss is determined. Furthermore, induced eddy currents in metallic housings or in any electrical conductive region affect the magnetic field distribution around the coil system. This results in a change of the magnetic coupling parameters. By another iteration path, all parameters of the T equivalent circuit can be fitted. In this way, the electrical transfer behaviour and finally all system parameters can be determined more exactly.

By the knowledge of the electrical transfer characteristics, in the same calculation step the magnetic flux density can be determined and evaluated by EMF regulations [11][16-17].

Apart from EMF, the temperature rise of the system com-ponents is another important limiting factor for the transfer-able power of IPT systems. Thereby, the biological impact, melting temperatures, the thermal stress of power semicon-ductors as well as the curie temperature of ferrite cores must be considered. Based on the calculated power loss and the coil geometry, in the next step, the heat-flow analysis gives information about the temperature rise of the IPT system [5].

As a result of the design process, valid system parameters are proposed. If the electrical values, the magnetic flux density or the temperature rise exceed the valid ranges or if no valid parameters are found, the iteration paths can be used to apply different kinds of optimisation strategies.



Exce

ed th

e E

MC

-lim

its

Exce

ed th

e m

axim

um c

ore

or h

ousi

ng te

mpe

ratu

re

No

valid

par

amet

ers

foun

d

Exc

eed

valid

el

ectri

cal v

alue

s

Power lossanalyses (coil system)

Thermalanalysis

EMF analyses (e. g. magnetic flux density)

Power lossanalyses (power electronics)

Variation of system performance characteris-tics

Variation of• Coil

geometry• Coil type• Material

properties

Selection of leakage inductance compensa-tion and preselection of coil geometry

Input system parameters

• Output power• Efficiency• Voltage level• Size, weight

Selection of valid output parameters

• P2,max• ηmax• N1, N2• N1/N2

Calculation of the winding ratio and the electrical transferbehaviour at tolerances

Adaption of the T equivalent circuit parameters

Determination of the magnetic couplingparameter

IterationSignal flow Abort criterion

Fig. 3. Proposal for solution of a systematic and modular design of contactless inductive power transfer systems

B. Leakage Inductance Compensation Strategy

Mostly, IPT systems should work at high transfer distances and with a high system efficiency. However, high transfer distances result in a small magnetic coupling. Therefore, and to improve the efficiency, the large leakage inductances have to be compensated by capacitors (Fig. 3, step 2). The resul-ting resonance operation allows the supply of reactive power, a high gain voltage or current transfer ratio and sinusoidal transformer values. Furthermore, the last ones allow a loss-less switching characteristic of the primary inverter, a favour-able electromagnetic compatibility (EMC) and the use of well known mathematical modelling methods, such as first harmo-nic approximation (FHA) or time harmonic FEM simulation.

The electrical transfer behaviour of a resonant transformer is strongly influenced by the type of leakage inductance compensation strategy. Thereby, the resonance capacitors can be placed in series or parallel to the coils (Fig. 4) [14-15] and the resultant LC-circuits can be tuned by the capacitor values in different ways. In previous investigations, good results are achieved by the series-parallel-compensation (Fig. 4, C2S not implemented) and by tuning the capacitors equal to equa-tion (1) (secondary shorten circuit) and (2) (primary open circuit) and at the same resonance frequency ωR [1-3].

For the design of new IPT systems, important transformer values often are the voltage transfer ratio (u2/u1), the currents in the coils (i1, i2) and the phase angle between the primary

voltage and current ϕu1i1 to reduce the switching loss of the feeding inverter. The mentioned series-parallel-compensation allows a load independent voltage transfer ratio u2/u1 = const. and a load independent and zero phase angle ϕu1i1 = 0. The investigations on 24 different arrangements [18][19] have shown that this favourable characteristics can only be reached by using the mentioned compensation strategy.

L2σ*L1σ

C2P*

R1 R2*

RL*

C1S C2S*

u1

u2*

LH RFe

i1

Fig. 4. T equivalent circuit with leakage inductance compensation capacitors

11

222

21

222

21

12

1

−−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+= σσσω L

NNLLL

NNLC HHRS

(1)

1

21

22

22

2

−

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+= HRP L

NNLC σω (2)



C. Preselection of the Circular Coil System Geometry

In the third calculation step (Fig. 3), the magnetic coupling parameters can be determined based on a given coil geome-try. Before it, this (initial) coil geometry must be determined and dimensioned for the required transferable power. The transferable power can be increased by increasing the input power (higher flux), by using higher frequencies (law of induction), by resonance operation or by a higher magnetic coupling. Apart from EMC and the electrical stress of any electrical circuit element, the transferable power is limited by the absolute power loss (dissipated energy) and the resultant thermal stress. To minimise the heat to be dissipated, in the first order (neglecting power loss of the semiconductors) the coil geometry should be optimised for maximum system efficiency. Therefore and in this work, a coil system with circular coils, which is characterised by the coil diameter d and the transmission distance a, is considered (Fig. 5).

i1

i2a

d

Fig. 5. Circular coil system (no core) and field lines at a large air gap

The efficiency analyses is done by using the T equivalent

circuit and the transfer function G(s) = u2*/i1 of the secondary

parallel-compensated transformer, given in equation (3) [18] (RFe not implemented).

( ) 1**2

**2

*2

*22

**2

**2

*2

*

**2

*

1

*2

+⋅⎟⎟⎠

⎞⎜⎜⎝

⎛+

⋅⋅+++⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛+

+⋅⋅

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅

=s

RRRCRLLs

RRLLCR

sRRLR

iu

L

LH

L

HL

L

HL

σσ

(3)

As a function of RL, there is a maximum of the system

efficiency, which can be fixed as an extreme value. The resul-tant conditional equation for the maximum efficiency value η can be written as a function of all T parameters and of the frequency [1][18]. A generalised form can be achieved by using the quality factors of the coils (Q1, Q2) (eq. 9-10) and the magnetic coupling factor of the coil system k (eq. 11) instead of the T parameters. The Q-values already include the consideration of the frequency depending winding resistances and other loss effects. The Q-values and the magnetic coup-ling k can also be written independent from the absolute windings. Therefore, the T parameters are normalised to one turn (N = 1) as in equation (4 - 8).

( ) MNNLNL HH1

212

10−− == (4)

σσ 12

101 LNL −= (5) σσ 2

2202 LNL −= (6)

12

110 RNR −= (7) 2

2220 RNR −= (8)

( ) ( )

10

001

1

11 R

LLR

LLQ HRHR +

=+

= σσ ωω (9)

( )20

002

2

21

22

2

2 RLL

R

LNNL

Q HRHR +

=⎟⎟⎠

⎞⎜⎜⎝

⎛+

= σσ ω

ω (10)

( )( )

( )( )002001

0

21

22211

2

HH

H

HH

H

LLLLL

LNNLLL

LNNk

++=

++=

−

σσ

σσ (11)

In this way, the coil system is characterised by geometrical

and material properties only. At identical primary and secon-dary coil (equal leakage inductances: L1σ0 = L2σ0 = Lxσ0), the magnetic coupling factor k simplifies to equation (12).

( ) 1001

1−+

=Hx LL

kσ

(12)

All inductances, accordingly k, relate of the air gap and coil

diameter ratio a/d and can be determined by the FEM simu-lation [2]. The best magnetic coupling is achieved at the same size of the transmitter and receiver coils and by using ferrite cores. The larger the coil diameter or the smaller the air gap, the higher the magnetic coupling k. At IPT systems, typical values are between k = 0 ... 0.5. At high frequencies, own studies have shown that the quality factor of the transmitter and receiver structures (incl. ferrite cores, Litz wired coils and Aluminium plates) have values up to Q = 250 that can be realised. The maximum efficiency η (at the resonance fre-quency ωR) is a function of Q1, Q2 and k only and can be written as in equation (13) (assumption: RL>>R1 and RL>>R2). The full mathematical description is given in [18].

( )

212

2122

2

12

21

2

2212

2122

221

2

212

1

11

2

QQkQQkQ

QkQQk

QQQkQQkQ

QQk

QQk

+

+

++⎟⎟

⎠

⎞⎜⎜⎝

⎛+

+

+++

=η

(13)

Evidently, an important mathematical term is k⋅Q1⋅Q2. This

means that low quality factors can be compensated by a high magnetic coupling and vice versa. In Fig. 6 the magnetic coupling factor and the maximum efficiency is shown as a function of the quality factors (Q1, Q2) and the ratio between the air gap and the coil diameter a/d. The coupling decreases



with lower coil diameter and larger air gap. The efficiency decreases significantly at lower coupling and at lower Q-values. Assuming Q = 100, efficiencies greater than η > 80 % can only be obtained if the air gap is smaller than a half of the coil diameter (a/d < 0.5). Otherwise, the requirement of η > 90 % correlates with the geometrical precondition a/d < 0.25. At very large air gaps (a/d > 1) the efficiency decreases significantly even at very high Q-values, which allows only a low power or a lower duty cycle operation. Today, this lower efficiency operation often is used at IPT systems with multi stage coils (also called "High-Q" or "Magnetic resonant coupling"), for example at [21][22].

It was shown that the efficiency of the inductive trans-former depends on geometrical and material properties of the coil system. As a result, the equation (13) can also be used for the design methodology to determine an initial coil geometry and to keep a required efficiency (Tab.1).

0.0

0.5

1.0

0 0.5 1 1.5 2 2.5 3 3.5

Q=10 Q=100 Q=1000 Q=10000 k

Fig. 6. Maximum efficiency η as a function of the ratio of air gap and coil diameter a/d as given by equation (13)

D. Implementation

The presented design methodology (Fig. 3) was particularly implemented into a simulation software tool. This tool was used to design an IPT system in the power range of 1 kW. The system requirements and parameter ranges (coil design, power and voltage level, tolerances and coil misalignment ranges) are defined by the user. In Fig. 7a, for example the input mask for the core geometry is shown. Here, commer-cially availably pot cores with a diameter of d = 70 mm are chosen. Based on the results of Chapter II.C, to allow an efficiency greater than 90 %, the investigated air gaps should be smaller than a quarter of the coil diameter (d < 17.5 mm).

With the given coil properties, the tool at first determines the T parameters for the predefined air gap range (Fig. 7b). At large air gaps and when using ferrite materials (here: µr = 6600), the determination of the coupling parameters by using the FEM simulation is favourable [2-3]. Therefore COMSOL Multiphysics, ANSYS and FEMM [20] are used.

In the next step, the FEM-modules are linked with modules to calculate the electrical transfer characteristics. Assuming sinusoidal transformer values, therefore the FHA is used. Example: Based on the required electrical characteristics and limits (P2 = 1 kW, u2 = 270 V, Nxix < 250 A) and by using simple parameter variation algorithms, Fig. 7c shows calcula-

b)

Fig. 7: Simulation software tool: a) Input mask for the system requirements and parameter ranges, b) Evaluation results (FEM) of the T parameters (LH0, L1σ0, L2σ0, R10, R20), c) Evaluation results (FHA) of possible windings (N1, N2) and electrical quantities

tion results (f = 100 kHz, series-parallel-compensation) for N1, N2 and for electrical circuit parameters (i1, i2, η).

To minimise the current in the coils and consequently to minimise the copper loss and the EMF in the vicinity of the coils, at a = 10 mm the best winding ratio is approximately N1 = 32 and N2 = 16 (Fig. 7c). At the considered system and based on further power loss analyses (core loss, eddy current loss), the best air gap was also determined to 10 mm. For the core loss analyses [5], the Steinmetz parameter of the material SiFerrit N27 are loaded from the library (Fig. 7a). At smaller air gaps the core loss increases rapidly and high coil current harmonics appear. At higher air gaps the lower magnetic coupling result in higher Nxix and in increasing copper loss.

Aside from the mentioned modules, also additional calcu-lation modules for tolerances [3], EMF [3] and thermal stress analyses [5] are already developed and implemented as

Air gap / coil diameter (a/d)

Effi

cien

cy η

and

m

agne

tic c

oupl

ing

fact

or k

c)

a)



standalone solutions. So far, some of the modules as well as the iteration paths (optimisation) have to be activated by the user manually. Coupling the standalone calculation modules with the existing software tool is a very important task for future work. With this, the design methodology as shown in Fig. 3 can be applied at its full functionality.

III. IPT SYSTEM WITH HIGH POSITIONING FLEXIBILITY

Based on the presented design methodology, a transmission system for home appliances with the following requirements (performance characteristics) was developed: The output power of PL = 1 kW should be transferred to the load device at an overall efficiency of η > 90 % and over a distance of 10 ... 30 mm (tabletop). The coil diameter is limited to 130 mm and the positioning flexibility should be at least 30 mm in any lateral direction. In the previous Chapter, for the initial coil geometry with EPCOS P70 P core halves (d = 70, in the following denoted as Pcore70) the optimum air gap (a = 10 mm) and the windings (N1 = 32, N2 = 16) were determined by the software tool. In the next step, the coil geometry has to be optimised to allow the required positioning flexibility of the coils (not yet implemented in the software tool).

Different approaches for this problem are described in previous investigations. In [8], the ferrite cores were split into angular segments. However, with this option the change of the magnetic coupling depends on the lateral direction of misalignment. In [6-7], the tolerance of lateral misalignments of the receiver coil (roadway e-vehicle pickups) is improved by using a multiphase primary conductor [6] or by using an optimised design for the pickups and the windings [7]. In [9], the positioning dependence of the magnetic coupling is mini-mised by using a matrix of primary coils. The last mentioned options let the complexity and the costs of the system increase. At circular coil arrangements, in [3] the optimisation of the coils (size and position of the windings, ferrite cores) has been shown as a proper solution and is applied here.

A. Optimisation of the Coil Geometry

As shown in Chapter II.C, an energy transfer of 1 kW with P core halves (d = 70 mm) should be realised at an air gap of 10 mm. However, for the desired household application it is necessary to be able to realise higher air gaps. As shown in Fig. 6, at a defined efficiency the air gap is related to the coil diameter. For this reason, different coil arrangements with higher diameter have been investigated. Thereby, the winding space (copper cross section area) and the coil weight of the investigated arrangements are fixed at constant values.

To be able to compare different coil arrangements and their characteristics at misalignments, the influence of the ferrite geometry on the magnetic coupling must be normalised. Therefore, the following approach is used: For every circular coil geometry it is possible to determine a nominal air gap aN. At this air gaps aN, the percentage change of the magnetic coupling at air gap changes is identical for all systems.

The best results are obtained with flat coils, in the follow-ing denoted as Flat130 (dinner = 40 mm, douter = 130 mm). At the considered arrangements Pcore70 and Flat130, the ratio

of the nominal air gaps is approx aN,Flat130/aN,Pcore70 ≈ 3. Thus, to keep the required efficiency (Fig. 6), the absolute air gaps were determined to aPcore70 = 10 mm and aFlat130 = 30 mm. The simulation results (ANSYS) in Fig. 8 show the flux lines (vector potential A) of the arrangements Pcore70 and Flat130 at a lateral misalignment of the coils v.

Fig. 8. Simulation result (section plane) of the circular coils Pcore70 at a = v = 10 mm (top) and Flat130 at a = v = 30 mm (bottom)

0.00

0.05

0.10

0.15

0 20 40 60 Fig. 9. Simulated (lines) and measured (symbols) magnetic coupling parameters (inductances at one turn N = 1) of the coil arrangements Pcore70 and Flat130 at a lateral coil misalignment v

Coil misalignment v / mm

Lxσ0 (Flat130)

LH0 (Flat130)

LH0 (Pcore70)

Lxσ0 (Pcore70)

Coil misalignment v

Coil misalignment v

70 mm

130 mm

30 mm

10 mm

Ferrite core

Copper windings

L / µ

H



For the ferrite cores the relative permeability can be assumed with µr = 6600 (Pcore70: EPCOS SiFerrit N27; Flat130: TRIDELTA Manifer 198). The primary and the secondary copper winding is modelled by a circular ring (N = 1). As a result of the field distribution, the main and the leakage inductances of the air gapped transformer are determined. Therefore, the primary (lower) coil is fed by a current of 1 A. As shown in Fig. 9, at the nominal coil posi-tion, LH0 and Lxσ0 are in a similar dimension. However, at a lateral coil misalignment, the arrangement Flat130 shows a less sensitive change of LH0 and Lxσ0. Thereby, at misalign-ments the sum of LH0 and Lxσ0 (that means the self induc-tances of the coils) are nearly constant at both arrangements.

B. Electrical Transfer Characteristics at Misalignments

Based on Chapter III.A, the electrical transfer characteristic is analysed. To let the results be independent of the windings, the load is written with the quality factor QL (ωR = 2πfR).

( ) ( )( ) 1001

22

1

22

21

1−

−

+=⎟⎟⎠

⎞⎜⎜⎝

⎛+= LHRLHRL RLLNR

NNLLQ σσ ωω (14)

Fig. 10 shows the calculation and measurement results of

the voltage transfer ratio u2/u1 of the coil arrangement Pcore70 at a lateral misalignment up to v = 20 mm (C1 = 52.0 nF, C2 = 41.9 nF, N1 = N2 = 20, fR = 100 kHz, R1 = R2 = 180 mΩ, RL = {200; 50; 15} Ω corresponds to QL = {0.18; 0.72; 2.43}). At nominal coil position (v = 0), u2/u1 is independent of the load QL. At higher misalignment, the voltage transfer ratio u2/u1 is very sensitive because of the detuned resonance and depends on both, coil misalignment and load. This is a typical behaviour of the series-parallel resonance operation and occurs in a similar way at variable air gaps or at a variable inverter frequency. A nearly constant ratio of u2/u1 at misalignments can be obtained at QL ≈ 1. If also the load is variable, additional control techniques must be applied. Thus, the proper dimension of the windings (N1/N2 = const.) or the load resistor are useful degrees of freedom for the optimisation.

Fig. 10. Measurement and simulation of the voltage transfer ratio u2/u1 of the coil arrangement Pcore70 as a function of the coil misalignment Δv and the load QL

C. Electrical Transfer Characteristics at Changes of the Compensation Capacitor Values

Using the design methodology, the developed numerical models and the FHA analyses, the combined tolerance of geometric parameters (Δa, Δv) and the capacitor values can be investigated. The example in Fig. 11 shows the influence of the capacitor values on the voltage transfer ratio u2/u1 at a lateral coil misalignment up to v = 60 mm (assembly Flat130). In Fig. 11 (top) the primary series capacitor value C1S (QL = 1) is varied and the secondary capacitor C2P is at nominal value. The ratio u2/u1 depends on both, the capacitor value (even at nominal position v = 0) and the lateral coil alignment. The higher the tolerance value of C1S the higher the variance of u2/u1. In Fig. 11 (bottom), the secondary capacitor C2P is varied (C1S at nominal value). The influence of C2P at lateral misalignment is quite small. Considering the voltage transfer ratio only and at a nominal allowed range of u2/u1 of ± 25 %, the allowed alignment is limited by C1S to vmax ≈ 24 mm at ΔC1S,max = ± 10 % or limited to vmax ≈ 33 mm at ΔC1S,max = ± 5 %. Thus, the allowed positioning flexibility can be determined during the design process by the definition of permissible tolerance ranges of electrical and capacitor values. However, apart from the voltage transfer ratio, many further electrical parameters like coil currents, capacitor voltages or the phase shift ϕu1i1 must be considered to enable a safe operation. In summary, a higher coil positioning flexibility is obtained by using flat coils with a high coil dia-meter and a large air gap, by using well tuned capacitors with a small tolerance and by ensuring constant load conditions.

0

1

2

3

4

5-10%

-5%0%5%

10%

nominal range

vmax,±10%

vmax, ±5%

0

1

2

3

0 10 20 30 40 50 60

-10%0%

10%

nominal range

Fig. 11. Voltage transfer ratio (u2/u1) at lateral misalignment v and at a variable primary capacitor C1S (top) and at a variable secondary capacitor C2P (bottom) (coil arrangement Flat130, QL = 1)

0

2

4

0 5 10 15 20 Coil misalignment v / mm

u 2/u

1

ΔC

Coil misalignment v / mm

ΔC QL = 0.18

QL = 0.72

QL = 2.43

u 2/u

1

u 2/u

1

d = 70 mmd = 130mm



D. Test System for Household Appliances

Fig. 12 shows a developed IPT system for the wire and plug-less supply of consumer devices on a tabletop. As a result of the proposed design methodology (Chapter II.D and III.C), the coil system was assembled with flat ferrite cores (d = 130 mm, a = 30 mm, N1 = 32, N2 = 16, Litz wire: 735x71 µm). The primary power electronics are realised by a voltage-fed (D.C. linked) half-bridge inverter with discrete IGBTs at 100 kHz switching frequency (off-time: 600 ns). On the secondary side, a full bridge HF-rectifier, a D.C. link and an additional inverter are used to allow supplying any D.C. or A.C. load (50/60 Hz). The secondary coil, the D.C. link and the power electronics as well as additional control and communication modules are integrated into the consumer device. The last mentioned modules should ensure a stabilised output voltage and a safe operation (consumer detection and identification). These are very important for nearly all IPT systems used in non-industrial applications, for example also at e-vehicle charging systems.

The IPT system in Fig. 12 is optimised for constant real power (e.g. toaster, kettle, coffee maker, lamps, electronic devices). Fig. 13 (top) shows the measured primary voltage u1 and current i1 at v = 0 and at nominal load (QL ≈ 1).

Consumer module (secondary coil, compensation, power electronics)

Output:115 V, 1 kW

Output:115 V, 1 kW

Air gap (tabletop, 30mm)

HF-

outp

ut1

HF-

outp

ut2

Prim

ary

coils

with

com

pens

atio

n-ca

paci

tor

Feed

ing

inve

rter

Input: 230VAC

Fig. 12. IPT system to supply consumer electronics with high positioning flexibility (incl. feeding inverter, resonance capacitors, magnetic assembly with flat coils, heat sink module, up to two consumer devices with double A.C. output 1 x 1 kW or 2 x 500 W)

-600

0

600

0 5 10 15-30

-20

-10

0

10

20

30

u_1 i_1

0

200

400

0 5 10 15 20

u_L (1kW) / V u_L (idle) / V

Fig. 13. Measured output voltage u1 and current i1 of the primary inverter (top), load voltage uL at 1 kW and at idling (bottom)

The current i1 is sinusoidal (low harmonics) to enable zero current switching operation (reduce switching loss and EMI). By using small D.C. link capacitors on the primary and the secondary side, the load voltage uL is not constant, but variable (sinusoidal half waves). As an alternative to [12-13], in this case, supplying the A.C. (50/60 Hz) consumer with a half wave switching matrix converter is possible and favour-able [10]. According to the results of the proposed design methodology and Chapter III, the allowed positioning tolerance of the system is v ≈ 30 mm in all lateral directions. The overall efficiency of the system (incl. feeding inverter, magnetic system and secondary power electronics) is η = 87 .. 92 % and the output voltage is uL = 115 VRMS (± 10 %), depending on the alignment of the consumer device (misalignment of the coils).

Investigations on the EMF have shown that the magnetic flux density always dominates in the vicinity of the windings (copper wire) and the ferrite layer and falls below the limits [16-17] at a probe distance from the coils of approximately 10 cm. For human safety, the housing can be used to cover the high flux region.

Despite the limitations of the proposed design methodology and the implemented simulation tool, both have provided and speeded up the development of the presented inductive powered household application. In particular, the optimum coil geometry and the copper windings have been determined to keep the system requirements (P2 = 1 kW, η > 90 %, d ≤ 130 mm, a ≤ 30 mm), to improve the coil positioning flexibility and to keep the EMF limits. The presented series-parallel leakage inductance compensation strategy allows a load independent voltage transfer ratio and a zero phase angle between the primary current and voltage, which enables a loss-less resonant switching operation.

volta

ge /

V

curr

ent /

A

volta

ge /

V

time / ms

time / us



IV. CONCLUSION AND OUTLOOK

The transfer characteristics of IPT systems can be im-proved by using high frequencies, ferrite cores and resonant operation of the coils. This allows the complexity of the system to increase. Therefore, the design of any new IPT system needs at least the consideration of special power loss (efficiency), tolerances (coil positioning flexibility, straying capacitor values) and EMF. To reduce the developmental period and the costs, a new systematic design methodology for IPT systems is proposed. Thereby, the most significant aspects of the coil system were modelled by the T equivalent circuit and by the FEM simulation. As an important part of the design methodology, an analytical expression to find an initial coil geometry for the design and optimisation process has been derived. For the computer-aided design, some parts of the methodology were already implemented into a simulation software tool, which is also presented in the paper. The proposed design methodology and the developed models are used to develop an IPT system supplying household appliances with an output power of 1 kW and at an overall efficiency of 90 %. As another important system requirement, the transmitter and receiver coil positioning flexibility was improved to 30 mm in any lateral direction by the optimisa-tion of the coil and ferrite core geometry.

In the next step, models for heat flow analyses (thermal stress), tolerances and EMF as well as the proposed iteration (optimisation) paths have to be implemented in the software tool. Thereby, other approaches than the FHA-analysis or the time-harmonic FEM simulation should be necessary to be able to consider non-sinusoidal electrical transformer values. Tasks for the extension of the design methodology are the consideration of linear coil geometries, power electronic topologies and devices and voltage control systems. In future and not least for the wire and plug-less inductive charging of e-vehicles, the design of an IPT system should also include concepts for a combined inductive energy and data transfer, a bidirectional energy transfer and for loss-less, cost-saving and lightweight magnetic materials.

REFERENCES [1] Mecke, R. ; Rathge, C. ; Fischer, W. ; Andonovski, B.: Analysis of

inductive energy transmission systems with large air gap at high frequencies. European Conference on Power Electronics and Applications, Toulouse, 2003, Proceedings on CD-ROM

[2] Mecke, R.: Contactless inductive energy transmission systems with large air gap. European Conference on Power Electronics and Applica-tions, Graz, 2001, Proceedings on CD-ROM

[3] Kürschner, D. ; Rathge, C.: Contactless energy transmission systems with improved coil positioning flexibility for high power applications. IEEE Power Electronics Specialists Conference - PESC, Rhodes (Greece), 15. - 19.06.2008, Proceedings p. 4326-4332

[4] Pedder, D. A. G. ; Brown, A. D. ; Skinner, J. A.: A contactless electri-cal energy transmission system. IEEE Transactions on Industrial Electronics, Vol. 46, Issue 1, February 1999, p. 23-30

[5] Kürschner, D. ; Rathge, C. ; Hoppe, A.: Design of inductive power transmission systems considering tolerances and power loss. 35th Annual Conference of the IEEE Industrial Electronics Society - IECON, Porto (Portugal), 03. - 05.11.2009, Proceedings p. 383-388

[6] Kissin, M. L. G. ; Boys, J. T. ; Covic, G. A.: Interphase Mutual Induc-tance in Polyphase Inductive Power Transfer Systems. IEEE Transactions on Industrial Electronics, Vol. 56, No. 7, July 2009, pp. 2393

[7] Elliott, G. ; Raabe, S. ; Covic, G. A. ; Boys, J. T.: Multiphase Pickups for Large Lateral Tolerance Contactless Power-Transfer Systems. IEEE Transactions on Industrial Electronics, Vol. 57 , Issue 5, May 2010, pp. 1590

[8] Nakao, F. ; Matsuo, Y. ; Kitaoka, M. ; Sakamoto, H.: Ferrite core couplers for inductive chargers. Power Conversion Conference, Osaka, 2002, Vol. II, p. 850-854

[9] De Boeij, J ; Lomonova, E. ; Duarte, J. L. ; Vandenput, A. J. A.: Contactless Planar Actuator with Manipulator., European Conference on Power Electronics and Applications, 2007, Aalborg, ISBN: 978-9-0758-1510-8

[10] Dockhorn, M. ; Kürschner, D. ; Mecke, R.: Contactless power transmis-sion with new secondary converter topology. Power Electronics and Motion Control Conference - EPE-PEMC, Poznan (Poland), 01. - 03.09.2008, Proceedings p. 126-131

[11] Waffenschmidt, E.; Staring, T.: Limitation of inductive power transfer for consumer applications. 13th European Conference on Power Electronics and Applications - EPE, Barcelona, 2009, p. 1-10

[12] Wu, H. H. ; Boys, J. T. ; Covic, G. A.: An AC Processing Pickup for IPT Systems. IEEE Transactions on Power Electronics, Vol. 25, No. 5, May 2010, pp. 1275

[13] Wu, H. H. ; Covic, G. A. ; Boys, J. T. ; Robertson, D.: A Series-Tuned Inductive-Power-Transfer Pickup With a Controllable AC-Voltage Output. IEEE Transactions on Power Electronics, Vol. 26, No. 1, January 2011, pp. 98

[14] Keeling, N. A. ; Covic, G. A. ; Boys, J. T.: A Unity-Power-Factor IPT Pickup for High-Power Applications. IEEE Transactions on Industrial Electronics, Vol. 57, No. 2, February 2010, pp. 744

[15] Moradewicz, A. J. ; Kazmierkowski, M. P.: Contactless Energy Trans-fer System with FPGA controlled Resonant Converter. IEEE Trans-actions on Industrial Electronics, Vol. 57, No. 9, 2010, p. 3181-3190

[16] International Commission on Non-Ionizing Radiation Protection, “Guidelines for limiting exposure to time-varying electric, magnetic, and electromagnetic fields (up to 300 GHz)”, Health Physics 74 (4): 1998, p. 494-522

[17] IEEE - International Committee on Electromagnetic Safety ICES: Standard for Safety Levels with Respect to Human Exposure to Radio Frequency Electromagnetic Fields, 3 kHz to 300 GHz. C95.1, 1991

[18] Kürschner, D.: Methodischer Entwurf kontaktlos induktiver Energie-übertragungssysteme. Shaker Verlag Aachen, 2010, ISBN: 978-3-8322-8897-6

[19] Kürschner, D. ; Rathge, C. ; Schulze, E.: Optimisation of contactless inductive transmission systems for high power applications. PCIM Conference, Nuremberg, 22.-24.05.2007, Proceedings on CD-ROM

[20] Meeker, D. C.: Finite Element Method Magnetics - FEMM. Simulation software, http://www.femm.info, 28.04.2011

[21] Sample, A. P. ; Meyer, D. A. ; Smith, J. R.: Analysis, Experimental Results, and Range Adaptation of Magnetically Coupled Resonators for Wireless Power Transfer. IEEE Transactions on Industrial Electronics, Vol. 58, No. 2, February 2011, p. 544-554

[22] Cheon, S. ; Kim, Y.-H. ; Kang, S.-Y. ; Lee, M. L. ; Lee, J.-M. ; Zyung, T.: Circuit-Model-Based Analysis of a Wireless Energy-Transfer System via Coupled Magnetic Resonances. IEEE Transactions on Industrial Electronics, Vol. 58, No. 7, July 2011, p. 2906-2913

NOMENCLATURE a Air gap (transfer distance) B Magnetic flux density d Coil diameter fR Resonance frequency k Magnetic coupling factor LH Main inductance (LH0: normalized to one turn) L1σ Primary leakage inductance (L1σ0: normalized to one turn) L2σ Secondary leakage inductance (L2σ0: normalized to one turn) M Mutual inductance N Count of windings (turns) PL Output power (PRL) Q1 Primary coil quality factor Q2 Secondary coil quality factor QL Normalised load R1 Resistance of primary coil (R10 : normalised at one turn) R2 Resistance of secondary coil (R20 : normalised at one turn)



RL Load resistance u2 HF-output voltage (RMS) of the transformer (secondary coil) uL Load voltage (RMS) after secondary side rectifier and filter v Lateral coil misalignment (displacement) ϕ Phase angle (phase shift) η Electrical efficiency µr Magnetic relative permeability ωR Resonance angular frequency (ωR = 2⋅π⋅fR) AGV Automatic guided vehicle CET Contactless energy transfer EMF Electro magnetic fields FEM Finite elements method FHA First harmonic approximation IPT Inductive power transfer

Daniel Kürschner received the diploma and the Doctor engineer degrees in electrical engineering from the Otto-von-Guericke-University of Magdeburg, Germany, in 2005 and 2009, respectively.

Between 2005 and 2011, he was a research assistant at the Institut f. Automation und Kommunikation (ifak) Magdeburg in the Department of Wireless Power Transmission. He has published more than 20 papers in the field of power electronics, modelling and EMC of inductive power transfer systems. Besides IEEE,

he is a member of several standardisation activities in the VDE and DKE committees in Germany. Since 2011, he has been working for the company "Paul Vahle", which has been active in inductive power transfer systems since the early 1990s. His research and consulting interests include power electronics, electromagnetic compatibility and simulation methods for contactless IPT, especially for inductive charging of electric vehicles.

Christian Rathge received the diploma in electrical engineering from the University of Applied Sciences Magdeburg in 2001.

Since 2002, he has been a research assistant at the Institut f. Automation und Kommunikation (ifak), Magdeburg. He has published more than 20 papers and has a number of patent applications in the field of inductive power and data transmission. Currently, he is working for his Ph.D. degree. His research interests include power electronics and inductive power and data transfer.

Ulrich Jumar studied Technical Cybernetics and Electrical Engineering and received the Doctor engineer degree from the Otto-von-Guericke-University of Magdeburg, Germany, in 1986.

After teaching and research activities at this university and a research stay at the King’s College, University of London, he was one of the founders of the ifak – Institut f. Automation und Kommunikation, Magdeburg. He has been chairman of the executive board and head of the institute since 2005. At the same time Ulrich Jumar is professor for process automation at the Otto-von-Guericke-University Magdeburg. His

specialist research areas are mathematical modelling and simulation, computerised automation systems and Intelligent Transport Systems. He is vice chair of the Technical Committees “Computers for Control” and “Telematics – Control via Communication Networks” of the IFAC International Federation of Automatic Control.

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