Analysis of Wireless Power Supplies for
`Industrial Automation Systems
`
`K. O'Brien, G. Scheible*, H. Gueldner
`
`Dresden University of Technology
`Department of Electrical Engineering
`01062 Dresden, Germany
`*ABB Corporate Research
`Wallstadter Str. 59
`68526 Ladenburg, Germany
`used
`sensors
`Abstract-Abundant
`non-stationary,
`in
`maintenance-free industrial environments with high sensor
`densities are preferably powered. by a wireless power system.
`For most industrial applications this is possible with a magnetic
`supply principle, based on unconventional transformers with
`large air-gaps. This paper presents an analytical description of
`the magnetic components of a wireless power supply system
`based on the magnetic coupling of multiple spatially separated
`coils. The power transfer through the large air-gap transformer
`is accurately predicted using a coupling model.
`
`-. . Y
`
`I. INTRODUCTION
`
`Novel power supplies for use in applications such as
`robotics, automated production machines, and applications
`with high
`insulation requirements where wired energy
`transfer is not suitable have recently been proposed [I], [2],
`[3],[4]. These power supplies together with suitable wireless
`communication devices eliminate wires and connectors which
`were identified as one of the major causes of equipment
`down-time. Alternatives, such as batteries, are not well suited
`for long-term, reliable operation in high volume applications
`(e.g. > 10.000 units for >10 years).
`Unconventional transformers with large air-gaps are used to
`supply energy to the load via magnetic fields over distances
`up to several meters and provide for the wireless supply of
`power to devices such as sensors, coinmunication devices, or
`actuators.' As an example, Figure 1 depicts the main
`transformer components being used. Multiple primary coils
`consisting of one or several coils per plane form an
`orthogonal system. The secondary coils, each consisting of
`three coils each wound around one of the three axes of a
`cube-shaped ferrite core are placed inside the box formed by
`the primary coil(s).
`Both the primary and secondary
`components operate
`in resonance, which allows power
`transfer to the load to be optimized.
`In order to properly analyze the system, the coupling
`between each individual primary and secondary must be
`understood and described. Formulas describing the coupling
`between all possible coil combinations are presented in this
`paper, and a transformer equivalent circuit model is used to
`further explain the operation of the system.
`~ ' Patents pending
`0-7803-7906-3/03/$17.00 02003 IEEE.
`
`figure I - Example automation application with a robot and a
`power supply using a large air-gap transformer:
`A Secondary coils (in wireless sensor modules)
`B: Communication antenna(s)
`C Wireless VO module with field bus plug
`. D Primary power.supplies
`E: Primary coil@)
`
`11. SYSTEM CHARACTERIZATION
`
`The coils can be represented as a system of loosely coupled
`inductors with the self-inductances Lyy and L, of each. coil
`coupled with each other coil by kpr,y, kyxyy, and/or ksxAy (where
`p represents a primary coil, s represents a secondary coil, and
`and y'
`x and y represent the x'
`coil). However, each time
`that a coil is moved the entire set of coupling factors relating
`to that coil must be recalculated. The system becomes
`extremely complicated as the number of elements
`is
`increased. The number of coupling factors Nk that must be
`calculated is given by
`
`where Cs is the number of secondary coils and Cp is the
`number of primary coils in the system.
`Figure 2 shows a system with two primary coils and three
`secondary coils. Note that although each secondary shown in
`Figure 2 is actually comprised of three coils wrapped around
`a ferrite core, these coils are 90 degrees apart spatially and
`therefore are not coupled to each other in the ideal case.
`
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`
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`Exhibit 1022
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`
`

`

`inductance between opposite sides of a
`The mutual
`rectangular coil (parallel conductors of the same length) is
`given by [51 as
`
`L
`mutual
`
`where l is the length of the conductor and d is the distance
`between the parallel conductors. In this case the radius of the
`wires can be neglected, as it is very small relative to d [51.
`The mutual inductance of two conductors meeting at a right
`angle is zero. For the purposes of this calculation, the wires
`forming the primary coils are assumed to form an ideal
`rectangular system.
`Summing the self-inductance (given by (2)) of each of the
`four wires and the mutual inductances (given by (3)) between
`each of the possible wire pairs, the self-inductance of a
`rectangular coil can be described by
`
`~
`
`~
`
`P
`
`1-
`
`Lsev
`
`2(1+ w) .tq 1 (I + w)
`
`(4)
`
`J
`
`where 1 and w are the lengths of the sides of the rectangle,
`and N is the number of turns in the coil.
`Effects of flux concenrration due to the presence of a
`ferromagnetic material: Equation (4) provides a good
`approximation of the inductance of the primary coils (within
`approximately 1.5%). ‘While the secondary coils are also
`rectangular in shape, they are wrapped around a ferrite core.
`The inherent high initial permeability of the core provides a
`low reluctance path for the flux created by the primary coils,
`thereby concentrating tbe flux lines within the core and
`increasing the density of the magnetic field. A concentration
`will
`of flux in the core (when the core material has ~
`1
`)
`increase the inductance of the coil wrapped around that core.
`Equation (4) is multiplied by a flux concentration or
`demagnetisation factor L), which accounts for this effect.
`This factor is based on the permeability of the core material
`and on the geomevy of the core. Although the exact value of
`D is extremely difficult to calculate, [61 shows that D for
`prisms with two sides of equal length can be approximated
`using the value of D for a cylinder. The demagnetisation
`factors of cylinders are well known. Reference 171 shows that
`for cylinders having long: and short axes of equal length (a
`good approximation of the ferrite cube used in this system)
`and a relative permeability in the range of a few thousands, D
`is approximately equal to 3.
`
`
`
`Secondary Side
`Rgure 2 -Coupling between primary and secondary coils
`Although prototypes show coupling between these three coils
`of up to 0.6%. this does not cause significant problems in
`normal operation of. the system. These three coils allow the
`load to receive constant power regardless of the orientation of
`the secondary with respect to the primary coil or coils. For
`the purpose of this analysis, coupling between coils on one
`secondary will be neglected. The term “secondary coil” will
`refer to one ferrite cube with one coil wrapped around each of
`its axes.
`Figure 2 can be simplified by ignoring the coupling
`between secondary coils that are not located within a few
`centimeters of each other as the coupling between cube
`shaped secondary coils separated spatially by a distance
`greater than the value of one side-length of the ferrite core
`has been seen in preliminary tests and simulations to have a
`negligible effect on the overall performance of the system.
`
`A. Calculation of Coil Selflnductances
`All primary and all secondary coils are of rectangular
`shape. Other coil shapes were discussed in 141. The self-
`inductance of a coil that is comprised of straight elements can
`be described by the sum of the self-inductance of each
`straight wire and the mutual inductances of all of the possible
`wire pairs.
`Starting with the differential form of the Biot-Savart Law,
`[5] approximates the self-inductance of a straight round
`conductor as
`
`S
`
`where p is the radius and 1 is the length of the conductor.
`
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`

`

`The effective permeability of the core is then described by
`P I as
`
`where p is the true permeability of the core material and p’ is
`the effective permeability of the core material.
`
`E. Calculation of Mutual Inductances
`The mutual inductance between coils in the system can be
`found using the Neumann formula for mutual inductance
`
`inductance, LP3. between one
`the mutual
`Alternatively,
`primary and one secondary coil can be calculated by
`-
`integrating the flux density B, created when current passes
`through the primary coil over the surface S2 bounded by the
`(Figure 3). This method is made simpler
`secondary coil
`because the flux density at the secondary can be assumed
`constant over the small area bounded by the secondary coil.
`The field density generated by a rectangular coil lying in
`the y-z plane (where wires 1 and 2 are parallel to the z-axis
`and wires 3 and 4 are parallel to the y-axis) at any point in the
`system is shown in [4] to be
`I
`
`Figure 3 - Flux density Bp passing through the surface S2
`hounded by the secondary coil
`
`Integrating (7) over the surface of the secondary coil to find
`the flux linking the secondary and assuming that the field is
`uniform over the surface bounded by the secondary coil
`
`Yps = D j B p .
`SS
`
`(8)
`
`where the subscripts p and s refer to the primary and to the
`secondary coils, respectively, gives
`vps = 4 P 0 I BP I
`
`(9)
`
`where As is the area encompassed by a secondary coil.
`
`Flux linkage APT is defined as
`
`A ps = N s Y p s
`
`(10)
`
`where Ns is the number of turns on the secondary
`
`Finally, the .mutual inductance between the primary and
`secondary coils is
`
`A P S
`Lps =-
`‘P
`
`where L,...4 are one half the lengths of each of the four sides
`of the rectangle, N is the number of turns in the coil, I is the
`current in the wire, r is the perpendicular distance between
`the point at which the field is being calculated and the current
`carrying wire, and 4 is the angle between the imaginary line
`of length r connecting the field point with the wire and the x-
`axis.
`
`where Iy is the current in the primary.
`
`The mutual inductance between primary and secondary
`coils is obviously highly dependcnt on the position of the
`secondary coil in question. The mutual inductance between
`one primary and one secondary coil is found by combining
`(E), (9). (IO) and (11) and simplifying
`
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`Exhibit 1022
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`

`

`L2
`Lf
`+s1nm2
`i2A7,m Z m 2 m
`
`Lpr = DN N A p
`P ’ r O
`
`(12)
`
`C. Calculation of coupling factors
`
`The coupling factor kP.” between the primary and secondary
`coils is defined as
`
`d
`
`LPs
`Lpp Lss
`k p s =
`where Lpp and L,, are the self-inductances of the primary and
`secondary coils and Lp, is the mutual inductance between the
`primary and secondary coils.
`
`(13)
`
`Substituting (4) and (12) into (13) gives an expression for
`the coupling factor between the primary and secondary coil
`which is obviously quite cumbersome. Some simplifications
`can be made to make the equation easier to use.
`
`D. Simplifications and approximations of inductance and
`coupling factor calculorioris
`For primary coils of square shape equation (4) describing
`the self-inductance of rectangular coils can be simplified. The
`inductance of a square coil where s is the length of one side
`of the coil is approximated by [5] as
`
`t) 1
`
`In - -0.5240
`
`L = 0.8sN
`2[
`
`If the secondary is assumed to be near to the axis of a
`square primary coil, (12) can be approximated by
`
`Lps DN,NpAs/104.
`
`I
`
`f x \
`
`L
`
`\
`
`(15)
`
`111. SYSTEM MODELLING
`
`secondary coil and the field intensity at the position on the
`axis of the primary coil that is closest to the actual position of
`the secondary coil. The bolume in which this approximation
`is accurate can be found using methods for finding the
`volume of a certain field strength [41.
`Substituting (14) and (15) into (i3) gives an approximation
`of the coupling factor.
`Although the coupling factor kPs between the primary and
`importance; an accurate
`secondary coils ’ is of central
`representation of the system will also include coupling factors
`between the primary coils, kpp, and between the secondary
`coils, kAr
`The mutual inductance between two primary coils can be
`found using the Neumann Formula. Assuming that the
`primary coils are square loops both of side length a, separated
`by a distance don the same axis
`
`IT
`
`+ J z x 7 - 4 x F
`
`L
`
`J
`
`(16)
`
`The coupling factor between two primary coils can then be
`approximated by substituting (4) and (16) into (13).
`Primary coil systems generally consist of sets of coils
`placed at 90 degrees of spatial separation. If the ideal case
`(exactly 90 degrees of separation) is assumed, coupling
`between coils must be calculated only between coils lying on
`the same axis, as coils xparated by 90 degrees have zero
`coupling between them.
`Although flux density can normally be considered constant
`over the relatively small area bounded by the secondary coil,
`this is not the case when two secondary coils are placed in
`close proximity to each other. As the case of two secondary
`coils coming into close proximity is the main reason for
`studying the coupling between them, this problem cannot be
`integration of
`the
`A method of numerical
`neglected.
`Neumann formula can also be used to find the coupling factor
`between two secondary coils, taking into account the angle at
`which the axes of each secondary coil intersects with the axis
`of the other.
`
`Now that Lpp, L, kpA, I:,,,
`and kuy have been found, the
`coils can be represented as a system of coupled inductors
`with the self-inductances Lpp and LsA of each coil coupled with
`each other coil by kps, kpxoy. and/or krw as shown in Figure 2.
`In order to integrate the coupled inductors in a full system
`for a system optimisation, an
`description and to allow
`equivalent circuit was developed.
`
`where L is the length of one side of the coil.
`The error in (I5) increases as the
`is moved
`further off axis. The error is proportional to the difference
`between the field intensity at the actual position of the
`
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`Exhibit 1022
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`
`

`

`A classic single-phase equivalent transformer model can be
`used to represent the energy transfer between one primary
`and one secondary coil in a wireless power system.
`A wireless power system with its inherent large air-gap is
`characterized by a small magnetizing inductance and large
`leakage inductances. The core loss resistance, r,, can be
`neglected as the core losses are small enough to be
`considered negligible for the core selected in this case.
`The conventional transformer model can be simplified and
`applied to the wireless power system by referring all values to
`the secondary side of the transformer and replacing the
`primary voltage, leakage inductance, and resistance with an
`ideal current source representing the.current flowing in the
`primary coils. The equivalent circuit model extended by the
`resonant capacitor, rectifier, dc-filter, and load, is shown in
`Figure 4.
`Winding resistances can be calculated with conventional
`equations using wire diameter, copper characteristics, number
`of turns, and the dimensions of the system, taking into
`account the skin and proximity effects.
`Figure 5 shows simulation results using the model shown in
`Figure 4 for several values of load resistance. Figure 6 shows
`the current in the primary coil, the magnetic field at the
`position of the secondary coil, and'the dc side voltage for a
`load of 2kC. The simulation model and the practical results
`confirm the fact that the power available to the load is highly
`dependant on
`the coupling between
`the primary and
`secondary coils. Figures 7 show the test set-up used in
`obtaining Figure 6.
`Only one set of primary coils was energized during this test
`and the secondary was aligned along the same axis so that
`voltage was induced on only one of the coils comprising the
`secondary.
`For the multi-dimensional systems used
`in
`practical set-ups, Figure 4 must be expanded into a multi-,
`winding transformer model.
`
`Vd,
`
`30
`
`25
`
`20
`
`15
`
`10
`
`5
`0
`0
`
`R,=IOkR
`
`RL=6kR
`
`RL=4kCl
`
`RL=2kR
`
`R,=lkR
`
`0.5m
`
`1 . h
`Time (s)
`
`1.5m
`
`2 . h
`
`Figure 5 - Simulation results showing rectified secondary
`voltage for a range of load values
`
`Figure 6 - Primary terminal voltage (V,),,primary current(l,,).
`magnetic field intensity at secondary coil position (HJ, dc
`voltage ( V d at Rr=2kn.
`
`Figure 4 -Simplified equivalent transformer model where
`
`h =mutual inductance
`R, = secondary side winding resistance
`h' =secondary side leakage inductance
`C , = Secondary side resonant capacitance
`C ~ E = dc-side capacitance
`I, = Primary side current
`a = Tums ratio (Nd").
`RI& = h a d resistance
`
`37 1
`
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`Momentum Dynamics Corporation
`Exhibit 1022
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`
`

`

`Hrns:21.43 - 19.29
`Hrns:>21.43 Aln
`Hrns:13.29 - 17.14
`Hrns:17.14 - 15.88
`Hrns:15.88 - 12.86
`Hrns:12.86 - 18.71
`Hrns:18.71 - 8.57
`Hrns: 8.57 - 6.43
`Hrns: 6.43 - 4.29
`Hrns: q.29 - 2.14
`Hrns: 2.14 - 1.94
`Hrms:< 1.94 film
`
`A/m
`Aln
`Alm
`A h
`Aim
`Alm
`Rlm
`A/.
`R/m
`R/m
`
`Hrmr:21.43 - 19.29 R/n
`Hrms:>21.43 Aln
`Hrms:19.29 - 17.14 Rln
`Hrms:17.14 - 15.88 A h
`Hrl~s:15.88 - 12.86 Rln
`Hrms:lZ.86 - 18.71 R/n
`Hrns:18.71 - 8.57 Aln
`Hrms: 8.57 - 6.43 Bin
`Hrms: 6.43 - 4.29 Rln
`Hrns: t.29 - 2.14 R/n
`Hrms: 2.14 - 1.94 R/n
`
`Figure 8 - Field distribution around one set of primary coils 3m
`x 3m in area, separated by 2.8 m, and carrying 24A. The field
`strength at the center of the system is 6.4 Alm..
`
`Figure 9 -Field dislributi,on around one set of primary coils 3m
`x 3m in area, separated by 2.8 m, carrying 24A, and positioned
`to the left of a conducting surface. The field strength at the
`center of the system is 3.4 Nm.
`
`REFERENCES
`
`IV. PRACTICAL CONSIDERATIONS
`
`A practical industrial installation of such a system will
`involve the interaction of the primary coils with metallic
`objects inherently present in a factory setting. The eddy
`currents induced in these objects by the field created when
`current flows in the primary coils will act to dampen the field
`values within the operating volume of the system. This can
`drastically lower the field strength available to secondary
`coils in the affected area, thereby lowering the coupling value
`between the primary and secondary coils and reducing the
`power available to the load. Figures 8 and 9 show the effect
`of placing a conducting surface (which might represent steel-
`reinforced floors, walls, or large pieces of machinery) to the
`right of such a coil system. The field available to a secondary
`coil located at the center of the system is reduced by nearly
`50% in this case. The losses created by placing the system in
`a metal-rich environment can be modelled by adding
`components representing those losses to the model shown in
`Figure 4. This method will be further detailed in future
`publications.
`
`V. CONCLUSIONS
`
`A single-phase transformer model was used to describe
`power transfer from primary to secondary through a large air-
`gap transformer. The low value of mutual
`inductance
`inherent to such a system was shown to be the dominant
`factor
`in determining
`the amount of power
`transfer.
`Equations describing the coupling between primary and
`secondary component in such a system are highly complex,
`and a method of approximation was found to reduce the
`number of required calculations to a practically usable level.
`
`(21
`
`I31
`
`[I1 G. Scheible, I. Schutz. C. Apneseth, "Load Adaptive Medium
`Frequency Resonant Power Supply." 28th Annual Conference of the
`IEEE Imiustrial Electronics Sociely, IECON 2002, vol. I. pp. 282-
`287.
`1. Schutz, G. Scheible, C. Willmes, "Novel Wireless Power Supply
`System
`for Wireless Communication Devices
`in
`Industrial
`Automation Systems," 281h Annual Conference of the IEEE Industrial
`Electronics Sociery, LECON 2W2. vol. 2. pp. 1358-1363.
`C. Femindea. 0. Garcia, R. Prieto, 1.A. C o b s , J. Uceda, "Overview
`of Different Altemativss for the Contact-less Transmission of
`Energy," 28th Annul Conference of the IEEE Industrial Electronics
`Society, IECON 2002, vol. 2, pp. 1318-1323.
`I41 K.0Brien. G. Scheible, H. Gueldner. "Deriga of Large Air-Gap
`Transformers for Wireless, Power Supplies," IEEE-PEW03
`F. Grover, "Inductance Calculations: Working Formulas and Tables."
`[SI
`Dover Publications, Inc.. iNew York, 1946
`I61 D. Chen, E. Pardo,
`.A. Sanchez, "Demagnetizing Factors of
`Rectangular Prism and Ellipsoids," IEEE Trans. on Magnetics, Vol.
`38, No. 4, July, 2002, pp. 1742-1752.
`R.Bazorth, "Ferromagnetism," Van Nostrand. Pnmceton, NI, 1968.
`
`I71
`
`312
`
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`Momentum Dynamics Corporation
`Exhibit 1022
`Page 006
`
`