Theoretical and experimental study of a wireless power

Eur. Phys. J. Appl. Phys. 80, 10903 (2017)© EDP Sciences, 2017DOI: 10.1051/epjap/2017160422

THE EUROPEANPHYSICAL JOURNAL

Regular Article
APPLIED PHYSICS
Theoretical and experimental study of a wireless power supplysystem for moving low power devices in ferromagnetic andconductive mediumSalaheddine Safour and Yves Bernard*

GeePs Laboratory, CENTRALESUPELEC-CNRS-UPSud-UPMC, Gif-sur-Yvette, France

* e-mail: y

Received: 10 November 2016 / Received in final form: 2 May 2017 / Accepted: 22 September 2017

Abstract. This paper focuses on the design of a wireless power supply system for low power devices (e.g.sensors) located in harsh electromagnetic environment with ferromagnetic and conductive materials. Suchparticular environment could be found in linear and rotating actuators. The studied power transfer system isbased on the resonant magnetic coupling between a fixed transmitter coil and a moving receiver coil. Thetechnique was utilized successfully for rotary machines. The aim of this paper is to extend the technique to linearactuators. A modeling approach based on 2D Axisymmetric Finite Element model and an electrical lumpedmodel based on the two-port network theory is introduced. The study shows the limitation of the technique totransfer the required power in the presence of ferromagnetic and conductive materials. Parametric and circuitanalysis were conducted in order to design a resonant magnetic coupler that ensures good power transfercapability and efficiency. A designmethodology is proposed based on this study.Measurements on the prototypeshow efficiency up to 75% at a linear distance of 20mm.

1 Introduction

Nowadays, mechatronic systems become highly automateddue to the increasing use of the artificial intelligence. Suchsystems require additional information regarding theenvironment in which they operate; therefore, significantnumber of sensors is utilized to measure different physicalquantities that will be used to supervise, control ordiagnostic the state of the full system. The increasingdemand at the system level to increase the reliability and todecrease the maintenance time involves each component ormodule of the mechatronic system.

This paper focuses on the power supply module formoving sensors in linear and rotating actuators (Fig. 1a)which could be part of a mechatronic system. The powersupply of the sensors could be achieved by simple directcable, battery or wireless solution. Recently energyharvesting based solutions for low power consumptionsystems arises [1–5]. The selection of the technique dependsin many factors: required power, life time, mobilityconstraint, accessibility and maintainability. The batterybased solution is not preferred in many applications; theirreplacement is expensive over the sensor lifetime. In thisstudy, wireless solution based on magnetic couplingtechnique was selected in order to increase the system lifetime and reliability. The technique was utilized successful-ly for rotary machines [6–8]. The aim of this paper is to

[email protected]

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extend the technique to linear actuator by taking intoconsideration the variable distance between the coils (Fig.1b) in conductive and ferromagnetic environment.

Figure 1b shows a high-level bloc diagram of a completewireless power supply module assuming an external DC-Bus as the available energy source and a DC-voltagerequired by the low power device. In this study, we targeteda 500mW power transfer to the device, which covers mostof the current sensors in the market. The sensor is modeledby an equivalent resistance RS=300V that was calculatedbased on the power consumption and voltage. The design ofthe wireless power supply system has to take intoconsideration two main constraints: the geometry andthe limited available space.

The resonant magnetic coupling utilizes two coils:transmitter and receiver. The large air gap between thecoils leads to a poor magnetic coupling coefficient k definedby equation (1) where f11, f22 are the self-magnetic fluxand f12, f21 are the mutual magnetic flux.

k ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffif12

f11

f21

f22:

sð1Þ

Operating the system in resonance mode allows theincrease of the power transfer capability and the enhance-ment of the system efficiency while ensuring the equipmentsizes remain manageable [9,10]. The resonance is achievedby connecting capacitors to the transmitter and receivercoils (Fig. 1b) and operating at the resonance frequency.With two capacitors, four compensation topologies appearSS/SP/PS/PP, where S and P stand, respectively, for

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(a)

(b)

Fig. 1. (a) Wireless power supply in the linear and rotating actuator and (b) the components of the system.

Fig. 2. Transmitter and receiver coils within the actuator.

Transmittercoil

Receiver coil(moving)

Moving bar

Stationary housing

(a) (b)

Fig. 3. Geometry meshing for (a) low frequency and (b) highfrequency.

2 S. Safour and Y. Bernard: Eur. Phys. J. Appl. Phys. 80, 10903 (2017)

series and parallel at the transmitter coil (first letter) andthe receiver coil (second letter) [11]. The compensationtopology is to be chosen according to the source (type:current or voltage, maximum amplitudes) and the loadrequirements (voltage or current amplitude). For instance,for current source, parallel compensation in the transmitterside will lead to high voltage across the source, which couldbe an issue for the switching components (exceed themaximum operating voltage).

More passive components could be connected to eitherthe transmitter coil or the receiver coil to achieve loadindependent voltage or current gain [12], to increase thepower transfer capability [13] or to reduce losses in thepowerelectronics [14], however, this could add more designcomplexity for application with variable magnetic couplingcoefficient. The coils number is another degree of freedom toenhance the power transfer distance. The use of a thirdintermediate resonantcoil is reported in [15].Four coilsmakea popular wireless power transfer architecture consisting ofdriver coil, transmitter coil, receiver coil and load coil [16],this architecture is space demanding and also suffers fromhigh sensitivity to the design parameters which lead tomoredesign complexity, such as tuning the distance between bothtransmitter coils (driver and transmitter coils) or tuning the

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resonance frequency of the system [17].The available space,the transfer distance rate, the level of power tobe transferredand the system efficiency are the main requirements for thedesign of such systems. This paper aims to provide a designconsideration andmethodology to achieve optimal design ofresonant magnetic coupler for linear and rotating actuatorbased on the results of parametric analysis and experimentalmeasurements.

2 Wireless power supply system analysis

2.1 Studied system

The analyzed structure (Fig. 2) is composed of moving androtating carbon-steel bar (ferromagnetic material) andstationary aluminum housing (conductive material). Theshape of these parts is assumed to be cylindrical. For thestudy presented in this paper we have chosen the two coilsarchitecture for its simplicity of integration and tuning.The transmitter coil is clamped to the housing; the receivercoil that feeds the sensor is clamped to the bar. The turns

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Fig. 4. Electrical lumped model of the resonant magnetic coupler.

(a) (b)

Fig. 5. (a) m-identification setup and (b) simulated and measured impedance of the coil.

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number (NT=20,NR=40) of the coils was guided by theavailable space constraints and cost (minimum turnsnumber). Litz wire is used to reduce skin depth andproximity effects. The transmitter and the receiver coilhave, respectively, 14.5 and 18.6mm outer radius. Thepower transfer range d defined by the distance between themiddle section plane of coils varies between 0 and 20mm.

To achieve the resonance the series-series topology wasadopted since we have a voltage source (DC-Bus) at thetransmitter side and a capacitive filter at the receiver sidewith a constant load (the sensor).

2.2 Modeling approach

A system modeling approach that combines a FiniteElement (FE) model and an electrical lumped model isintroduced in order to analyze the effect of the surroundingmaterials, the resonance topology and the load on theperformance of the wireless power supply system. Theanalysis of the results obtained with this approach will giveguidance to ensure an effective design.

The structure is analyzed using FE method basedsoftware (COMSOL Multiphysics). The problem wasreduced to 2D axisymmetric and the magneto-quasistatic

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equations were solved in the frequency domain. Theconstitutive relations were assumed to be linear. Thehysteresis losses in the materials were modeled by acomplex magnetic permeability (Eq. (2)). The residuallosses of the materials, the skin and proximity effects in thecoils were not taken into account. The winding is modeledby a rectangular shape with uniform current density.

m� ¼ m0 þ jm00: ð2ÞThe surrounding materials are ferromagnetic or

conductive; therefore, the skin depth varies with respectto the frequency. In order to well take into account thiseffect while respecting a compromise between the error onthe simulation results and time of calculation, dynamicmeshing is achieved by updating the setting of the meshingin the FE model at each frequency using a MATLAB codebased on the skin depth calculation (Fig. 3).

On another hand, a MATLAB routine that includes:electrical lumped model of the magnetic part, resonanceelements, voltage source and resistive load (Fig. 4) isachieved in order to assess the influence of each element onthe whole system performance (active/reactive power,efficiency, resonance frequency) within a frequency rangeunder the assumption of sinusoidal voltage source.

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(a) (b)

Fig. 6. Numerical results of (a) magnetic coupling coefficient and (b) system efficiency (RL=100V, system operating at resonance atall frequencies) as a function of frequency.

Stationary housing (Aluminum)


The values of the following electrical lumped modelparameters are derived from the FE model simulationresults:

Receiver coil
– Rt_dc, Rr_dc the coil resistance; (moving) –
Transmitter coil

Rt_ac(f), Rr_ac(f) the equivalent series resistance withfrequency dependence to take into account losses in thesurrounding materials;

(stationary)
– Lt(f), Lr(f) the coils self-inductance; –
Moving bar (Carbon steel)

(a) (b)

Fig. 7. Simulation results of the magnetic field lines distributionat 50Hz (a) and 20 kHz (b).

M(f) the mutual inductance.

In order to achieve circuit analysis, the two-portnetwork method was adopted due to its flexibility (e.g.adding components, changing their connection (series orparallel)). Each component of the circuit in Figure 4 isconsidered as a two-port network and modeled with anABCD-parameters matrix given by:

V 1

I1

� �¼ a11 a12

a21 a22

� �V 2

�I2

� �¼ A B

C D

� �V 2

�I2

� �; ð3Þ

where a11 ¼ V 1

V 2jI2¼0; a12 ¼ �V 1

I2jV 2¼0; a21 ¼ I1

V 2jI2¼0;

a22 ¼ �I1I2jV 2¼0.

For instance, the two port network of the magneticcoupler is described first by the following z-parametersmatrix:

V 1

V 2

� �¼ z11 z12

z21 z22

� �zfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflffl{Zcoupler

¼ Rtdc þRtac þ jvLt jvMjvM ðRrdc þRrac þ jvLrÞ

� �I1I2

� �:

ð4ÞThen theABCD-parametersmatrix isderivedfromthez-

parametersmatrix (Eq. (4))usingthe interrelations formula:

V 1

I1

� �¼ 1

z21

z11 z11z22 � z12z211 z22

� �V 2

�I2

� �: ð5Þ

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The method allows accessing multiple quantities: voltagegain, current gain, circuit input impedance, input power,output power and efficiency. The calculations of thosequantities are derived using symbolic mathematics soft-ware (Maxima) based on the two-port network matrices.

2.3 Carbon steel mr identification

The FE model requires the electromagnetic properties ofeach part in the simulation setup. The value of theelectrical conductivity of the carbon steel and thealuminum is, respectively, sb=6� 106 S/m and sh=4� 107 S/m, however, the relative magnetic permeability ofthe carbon steel was estimated in small-signal domain usinga coil and a carbon-steel bar on its center. The valuemb=100 was obtained byminimizing the error between theimpedance spectrum obtained by measurement using animpedance analyzer and the one obtained by FE simulation(Fig. 5).

2.4 Resonant magnetic coupling limitation

In a series-series resonant magnetic coupling, whenoperating at the resonance frequency f0 at which the coilsreactances are compensated by the capacitors reactances,

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Fig. 9. Cross section view of the magnetic coupler with the twoSFM based tubes.

Fig. 10. Parameter diagram of the resonant magnetic coupler.

Fig. 8. 3-D view of themagnetic coupler with the two SFMbasedtubes.


the obtained system efficiency (for Rs=0V) is given by:

h ¼ l

lþ 1

k2QtQr

1þ lþ k2QtQr

; ð6Þ

where l ¼ RL�Rr; Qt ¼ Ltv0

�Rt; Qr ¼ Lrv0

�Rr.

Equation (6) is obtained by calculation using theelectrical lumped model; it shows that the magneticcircuit of the wireless power supply system could becharacterized by two quantities: the magnetic couplingfactor (k) and the quality factor of the coils (transmitterQt and receiver Qr) [18].

The FE simulation results obtained for the structure inFigure 2 shows that the weak magnetic coupling (Fig. 6a)combined with the high losses in different components leadto poor system efficiency (Fig. 6b).

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The reason behind the drop of themagnetic coupling fora given distance is the fact that eddy current on the carbonsteel and the aluminum part repels the magnetic field at itssurface (skin effect), therefore the magnetic flux on thereceiver coil decreases (Fig. 7) leading to inefficient systemat the maximum distance regardless of the operatingfrequency.

3 Resonant magnetic coupler design andvalidation

The materials (carbon steel and aluminium) from whichthe parts of the structure are made cannot be changed tomaterials with better electromagnetic properties due tosomemechanical design constraints. In order to address theissue, a new structure based on two tubes made of soft

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(a) (b)

(c) (d)

Fig. 11. Simulation results of (a) magnetic coupling coefficient, (b) transmitter side quality factor as a function of the relativemagnetic permeability of the SFM tubes at different frequencies, (c) efficiency and (d) received power (fres=50 kHz,RL=100V,Vin=5V) for different relative magnetic permeability.


ferromagnetic material (SFM) with very low electricalconductivity is proposed. The added tubes with the lengthLs will canalize the magnetic field from the transmitter tothe receiver coil (Fig. 8). The first one is clamped to the barand the second to the housing.

Figure 9 shows a cross section of the proposed structureshowing two design dimensions:

–
dct is the distance between the SFM tube and the bar orhousing;
–
es is the thickness of the SFM tubes.
To analyse the new structure, the worst configurationwas considered (20mm as maximal transfer distance). Theresonance operating mode is achieved by tuning thecapacitors Ct and Cr using a simple resonant LC circuitformula:

Ct ¼ 1

Ltv2res

and Cr ¼ 1

Lrv2res

:

The parameter diagram in Figure 10 summarizes thedifferent factors that might have an impact on theperformance of the resonant magnetic coupling. The noisefactors are out of the scope of this paper, only some of thecontrol factors are analyzed in the next section in order togive guidance for optimal design.

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3.1 Parametric analysis

In this section, we analyse the effect of the properties of theSFM tubes and their dimensions on the resonant magneticcoupling performance. To reduce the number of the degreesof freedom, the coils dimensions have been chosen based onthe maximum available space and positioned in a mannerthat their revolution axes match the ones of the other parts(Fig. 9). It would be also possible to position the coils in amanner that their revolution axes are perpendicular to thelateral surface of the SFM tubes.

First, the effect of the relative magnetic permeability(mr) was analyzed. Figure 11a shows that at low frequency(50Hz) increasing slightly mr through a value of 50decreases the magnetic coupling coefficient, exceeding thisvalue, the magnetic coupling coefficient increases. Thisbehaviour is due to the effect of the eddy current in theferromagnetic and conductive parts. At high frequencies,the magnetic coupling coefficient increases rapidly with therelative magnetic permeability then slowly after the valueof 500. The system efficiency is enhanced and the receivedpower is maximal at the resonance frequency (50 kHz)when increasing the relative magnetic permeability, this isdue to the fact that the added tubes concentrate themagnetic flux without suffering from high losses or skineffect (very low electrical conductivity) at the studiedfrequencies.

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(a) (b)

(c) (d)

Fig. 12. Simulation results of (a) magnetic coupling coefficient, (b) transmitter side quality factor as a function of the SFM tubeslength at different frequencies, (c) efficiency and (d) received power (fres=50kHz, RL=100V) for different SFM tubes length(mr=2000, es=1mm, dct=0mm).


Increasing the length of the SFM tubes, increases themagnetic coupling coefficient and the quality factor for agiven operating frequency (Fig. 12a and b). Good systemefficiency is obtained when the length is higher than 60mm(Ls>3d). High magnetic coupling coefficient (obtained forLs=90mm) leads toabifurcationphenomenon that appearsin the received power (Fig. 12d) with two locals maximum.

The magnetic coupling increases when increasing thethickness of the SFM tubes (on the bar and the housing)and the magnetic flux density decreases, which helps toavoid saturation in the material. Good performance andlow magnetic flux density are obtained for thicknesseshigher than 0.5mm (Fig. 13).

Decreasing the distance between the SFM tube and thebar impact slightly the performance of the system. Nulldistance achieves the best performance (Fig. 14).

3.2 Proposed design

The parametric analysis provides guidance to design theSFM tubes: the length should be three times higher thanthe maximal required power transfer distance, thethickness higher than 0.5mm and null distance betweenthe coils and the tubes is preferred. Table 1 shows thematerial properties and dimensions of the SFM tubeschosen based on cost, available space, operating frequency,flux density level and temperature.

Simulation results show that the proposed design of theresonant magnetic coupler increases the magnetic couplingand achieves high system efficiency (Fig. 15a and b). The

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case where the system is tuned to operate at a resonancefrequency of 50 kHz is shown in Figure 15c and d, thefrequency corresponding to the maximum received powerpoint changes with the distance between the coils.

The proposed design is capable of achieving ∼500mWat all distances with efficiency of ∼80%. According toFigure 16, the efficiency of the system is also loaddependent; therefore, the power electronics between thereceiver side of the resonant magnetic coupler and thesensor should include an impedance transformationfunction. The level of the transferred power to the sensorcould be controlled by adjusting the amplitude of thevoltage source or by controlling the operating frequency.However, by adopting the first strategy the system mightnot be operating in resonance mode, which leads to highVA rating and switching losses. Operating at constantfrequency requires stable values of the components(capacitor, inductance, SFM properties) to achieve stableresonance frequency, leading to additional cost to have lowtolerances of the system components. The system showsbifurcation phenomena (multiple zero phase angle points)in the condition d=10mm and RL=10 kV, we observethree zero phase angle points (Fig. 17b) within thefrequency range 20–100 kHz, this could lead to systeminstability [19] in case of frequency closed loop control.Decreasing the load resistance (RL=100V) leads to thebifurcation phenomena to disappear (Fig. 17a). Thefrequency corresponding to zero phase angle is then uniqueand increases with the distance between the transmitterand the receiver coils. This frequency could be utilized as

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(a) (b)

(c) (d)

(e) (f)

Fig. 13. Simulation results of (a) magnetic coupling coefficient, (b) transmitter side quality factor as a function of the SFM tubesthickness at different frequencies, maximal flux density in the SFM tube (c) for the bar, (d) for the housing, (e) efficiency and (f)received power (fres=50kHz, RL=100V) for different SFM tubes thickness (mr=2000,Ls=60mm, dct=0mm).


measured quantity to achieve a 1D position sensor of thebar on which the receiver coil is clamped. Several degrees offreedom are available to avoid the bifurcation phenomenaearlier in the design: load adjustment (impedance trans-formation), dimensions of the SFM tubes and the materialproperties, coils dimensions and number of turns.

3.3 Prototype and models validation

Figure 18 shows two pictures of the wireless power transferprototype. The transmitter and the receiver coils are madeof Litz wire in order to reduce the skin and the proximityeffects. The experiment is conducted at frequencies widely

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below the self-resonance frequency of the coils. Multipleceramic capacitors are connected in parallel to make thecapacitors Ct and Cr.

Experimental measurements were conducted to assessthe performance of the prototype. The experimental setup(Figure 19) used a sinusoidal wave generator, linear poweramplifier (HSA 4101 from NF), and an oscilloscopeequipped with voltage probes and current probes capableof measuring a current as low as 1mA (Hioki CT6700).The input power, output power and efficiency areprocessed by the oscilloscope (Keysight InfiniiVisionDSO-X 3024T).

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(a) (b)

Fig. 14. Simulation results of (a) efficiency and (b) received power (fres=50 kHz) for different distance dct (mr=2000,Ls=60mm,es=0.5mm).

(a) (b)

(c) (d)

Fig. 15. Simulation results of (a) magnetic coupling coefficient and (b) system efficiency (RL=100V, system operating at resonanceat all frequencies) as a function of frequency (c) efficiency and (d) received power (fres=50 kHz;RL=100V) for different bar positions.

Table 1. Material properties and dimensions of the SFMtubes.

Parameter Value

mr 2300s 0.2 S/mLs 60mmes 1mmdct 0.5mm


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In order to assess the prototype performance, thecapacitors values were calculated for Fres=50kHz using theformulaC ¼ 1=ðLv2

resÞ and the self-inductances values of thecoils at d=0mm. Figure 20 compares the obtained experi-mental results using the test bench and the simulation results:

–

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the experimental result is labeled “Measurement”;
– the simulation result using the electrical lumped modelwhere its parameters were identified using the FEmethod based model is labeled “FEA+ELM”;
–
the simulation result using the electrical lumped modelwhere its parameters were measured with the impedanceanalyzer is labeled “IA+ELM”.
9

(a) (b)

Fig. 17. Simulation results of the input impedance (Zin) magnitude and phase angle for (a) RL=100V and (b) RL=10 kV.

Fig. 19. The scheme of the experimental setup for the assessment of the resonant magnetic coupler performance.

Fig. 16. Simulation result of the system efficiency as a functionof the equivalent load resistance (fres=50 kHz). Fig. 18. Magnetic coupler prototype.


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(a)

(b)

(c)

Fig. 20. System efficiency and received power as a function of the operating frequency for (a) d=0mm, (b) d=10mm, (c) d=20mmwith fres=50kHz, RL=100V and Vin=5Vpeak.


It is worth mentioning the concurrence of thesimulation results and the measurement results shownin Figure 20. These experimental measurements on theprototype confirm the capability of the proposed design ofthe resonant magnetic coupling to achieve ∼500mW at alldistances with minimum efficiency of ∼70%.

The characterization of the uncertainties of theexperimental setup were carried out by connecting aresistor to the output of the linear power amplifier. Thisallowed the analysis of the accuracy of the phase anglemeasurement which is achieved by the voltage/currentprobes and the algorithm of the oscilloscope. The phase

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angle obtained for the resistor varies between �0.1° and+0.1° which is an accurate value for the assessment of ourprototype. The accuracy of the voltage and currentamplitude measurement is within 1mV. Another source ofuncertainty in our experimental test bench is themeasurement of the distance between the coils, the erroris assessed to be around 1mm.

Note that the aluminum housing in this design acts asshielding at the operating frequency (atF=50 kHz the skindepth in the aluminum tube is 0.356mm) which lead to anenhancement of the structure immunity to the electromag-netic interference.

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Fig. 21. Design methodology flowchart.


3.4 Design methodology

The design methodology flowchart shown in Figure 21 wasadopted to design the resonant magnetic coupler presentedin the previous section. The methodology starts withcollecting the relevant requirements and ends with theassessment of the system performance relying on thecombination of two simplified models: a FE model and anelectrical lumped model at different stages of the design.

4 Conclusion

This paper proposes a methodology to design wirelesspower supply system for moving low power devices (e.g.sensors) operating in harsh electromagnetic environment.The presence of ferromagnetic and conductive materialsleads to decrease the magnetic coupling between the coilsand the system efficiency according to the simulation and

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experimental results. The performance of the system wasenhanced by introducing a new structure based on tubesmade of SFM to the initial structure of the application. Theproposed resonant magnetic coupler design allows up to75% efficiency at the maximum studied distance. Thecircuit analyses show that the resonance frequency forwhich the capacitors are tuned, the operating frequencyand the load are key elements to optimize the deviceperformance once the magnetic coupler is designed. Anexperimental setup with the whole DC-to-DC conversionchain shows an efficiency of 25% while receiving∼[email protected] VDC across a resistance load. The lowefficiency is due to the fact that the input impedance of thepower electronics at the receiver side does not match theoptimal load of the magnetic coupler.

The wireless power transfer system could be utilized as aposition sensor [20].When the system is carefully designed toavoid the bifurcation phenomena, the position of themoving

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bar could be measured by simply tracking the resonancefrequency that shifts with the variation of the magneticcoupling between the transmitter and the receiver coil.

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Cite this article as: Salaheddine Safour, Yves Bernard, Theoretical and experimental study of a wireless power supply system formoving low power devices in ferromagnetic and conductive medium, Eur. Phys. J. Appl. Phys. 80, 10903 (2017)

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Theoretical and experimental study of a wireless power