4758 ieee transactions on industrial ...pe.csu.edu.cn/lunwen/field orientation based on...

4758 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 65, NO. 6, JUNE 2018

Field Orientation Based on Current Amplitudeand Phase Angle Control for Wireless

Power TransferQi Zhu , Graduate Student Member, IEEE, Mei Su , Yao Sun , Member, IEEE, Weiyi Tang,

and Aiguo Patrick Hu, Senior Member, IEEE

Abstract—The low coupling coefficient between thetransmitter and receiver is the major constraint of a wirelesspower transfer (WPT) system. Although some approaches,such as increasing the quality factor and achieving preciseimpedance matching, can reduce the adverse impacts ofthe low coupling coefficient and improve the system per-formance, high leakage magnetic flux between the trans-mitter and receiver remains a problem. With the increase intransfer distance and the misalignment between the trans-mitter and receiver, the increasing leakage magnetic fluxof nondirectional fields degrades the WPT system perfor-mance. This paper proposes an active field orientationmethod to shape the magnetic flux so as to minimize theleakage flux. The amplitude and phase angle of the mag-netizing current are controlled, and a coil structure forminimizing the coupling among the transmitters and gener-ating a three-dimensional magnetic field is proposed. Thismethod realizes three-dimension full-range field orientationwith adjustable magnitude and direction of B-field at an ar-bitrary point, and as a result the B-field is concentrated withreduced leakage magnetic flux. The proposed field orienta-tion shaping technique is verified by theoretical analysis,simulation, and experimental results.

Index Terms—Current amplitude and phase angle control,field orientation shaping, leakage magnetic field, wirelesspower transfer (WPT).

I. INTRODUCTION

W IRELESS power transfer (WPT) has attracted muchattention due to the convenience, simplicity, and safety.

But when it is used for home appliances, implementable biomed-ical devices, and electric vehicles, the demand for a large transfer

Manuscript received March 2, 2017; revised June 2, 2017 and July 18,2017; accepted October 13, 2017. Date of publication October 30, 2017;date of current version February 13, 2018. This work was supported inpart by the National Natural Science Foundation of China under Grant51677195 and Grant 61622311 and in part by the scholarship from theChina Scholarship Council under Grant CSC 201706370068. (Corre-sponding author: Yao Sun.)

Q. Zhu, M. Su, Y. Sun, and W. Tang are with the School of Infor-mation Science and Engineering, Central South University, Changsha410083, China (e-mail: [email protected]; [email protected];[email protected]; [email protected]).

A. P. Hu is with the Department of Electrical and Computer Engi-neering, University of Auckland, Auckland 1142, New Zealand (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIE.2017.2767556

distance and efficiency still needs to be satisfied. Hence, the mainissues the recent studies are focusing on include the tradeoff be-tween transfer efficiency and distance, and the spatial freedombetween the transmitter and receiver. In order to increase thetransfer distance, several studies introduced magnetic resonantcoupling to realize the transmission distance beyond the rangeof near field [1]–[5]. Based on the previous studies, the transferdistance has been increased by adding repeaters between thetransmission and receiver coils [6], [7]. To improve the energytransfer efficiency, devices along with new antenna materialsand structure have been exploited, such as power amplifiers anddc–dc converters [8]. Meanwhile, if the spatial freedom of WPThas been improved, the electric equipment powered by WPTwill have higher mobility. Adjustable impedance matching andmultiple transmitter resonant coil topologies have been intro-duced to expand the spatial freedom of the WPT system [9–12].However, even with state-of-the-art technologies, improvementsin transfer efficiency and distance, and spatial freedom have be-come saturated. Optimizing the control of the shape of magneticfield, as a new technique further advancing WPT, has attractedmore attention [13]. Magnetic field shaping technology has beenregarded as a new approach in WPT systems with the feature ofthe shaped magnetic field pointing to a specific direction, hence,increasing the transfer efficiency and reducing unnecessary fluxleakage. Magnetic field shaping technology includes passiveand active methods. In the passive methods, a magnetic core isused to provide a path with low magnetic resistance for mag-netic flux, which further strengthens the magnetic flux linkagebetween the transmitter side and the receiver side [14]. In theactive method, the magnetic field is shaped by changing thedistribution of current flowing in the antenna [13], [15]. In orderto satisfy both the demands of distance and spatial freedom, Limand Park [15] have proposed a novel WPT system based on anactive magnetic field shaping technique with two crossed-loopcoils. The shaped magnetic field forms an energy beam directingto the receiver coil so that less leakage magnetic flux will existin the space, the transfer distance can be further extended ascompared with the conventional method. The current phasecontrol method shapes the magnetic field in the range of twocoils and the orientation of magnetic field can be controlled

0278-0046 © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

https://orcid.org/0000-0002-4307-3694

https://orcid.org/0000-0001-7293-7669

https://orcid.org/0000-0002-7268-9201

ZHU et al.: FIELD ORIENTATION BASED ON CURRENT AMPLITUDE AND PHASE ANGLE CONTROL FOR WPT 4759

Fig. 1. Block diagram of the proposed WPT system.

to any direction. However, the direction of shaped magneticfield is limited in a two-dimensional (2-D) transection, and themagnetic flux density at a given point in the whole 3-D spaceis unadjustable.

This paper proposes an active field orientation method toshape the magnetic flux so as to minimize the leakage flux;meanwhile, by controlling the amplitude and phase angle of themagnetizing current, a 3-D magnetic field for WPT with ad-justable magnitude and direction is generated. The major studyin this paper can be summarized as follows.

1) The detailed synthesis of magnetic field generated bythree transmitter coils at an arbitrary point is presented.

2) The 3-D magnetic field orientation is realized by currentamplitude and phase angle control.

3) A prototype WPT system for 3-D magnetic field orienta-tion is implementation.

The rest of the paper is organized as follows. In Sec-tion II, the coils structure choice and design are explained. InSection III, the distribution and synthesis of B-filed generatedby crossed-loop coils are explained. In Section IV, the field ori-entation based on current amplitude and phase angle control isexplained. In Section V, the hardware implementation is intro-duced, and the experimental results are shown. In Section VI,a conclusion is drawn, and future application of the proposedmethod is suggested.

II. COILS STRUCTURE DESIGN

In order to maximize the magnetic field formed in the near-field range of coils, the WPT coils are often in the shape of acoil or loop. The maximization of coupling between the trans-mitter and receiver coils and the minimization of leakage fluxin the space will improve the efficiency and increase the dis-tance; meanwhile, the minimization of the coupling among thetransmitter coils that are used to shape the magnetic field isnecessary. This paper introduces a 3-D full-range field orienta-tion technique based on amplitude and phase control of threeindependent currents. The block diagram of the proposed WPTsystem is shown in Fig. 1.

This study considers the three crossed-loop transmitter coilsstructure to keep the coupling among transmitting coils aslow as possible and avoid magnetic resonance failure when

magnetic coupling occurs among transmitter coils. Fig. 2 showsthe detailed structure of the proposed coils.

According to Neumann’s formula, we have

M12 =μ0

4π

∮ ∮dl1 · dl2

d12

=μ0

4π

(2∫ b

−b

∫ a

−a

cosθdxdy√x2 + y2 − 2xycosθ

− 2∫ b

−b

∫ a

−a

cosθdxdy√x2 + y2 − 2xycosθ + (2c)2

−∫ c

−c

∫ c

−c

dz dz√(z1−z2)

2 +d21

−∫ c

−c

∫ c

−c

dz dz√(z3−z4)

2 +d21

+∫ c

−c

∫ c

−c

dz dz√(z2−z3)

2 +d22

+∫ c

−c

∫ c

−c

dz dz√(z4−z1)

2 +d22

⎞⎠.

(1)

So, all the conditions that the coupling of two wires occursare classified into the following four groups.

1) Two equal-length wires placed in parallel at a distance d:between coils 1 and 2—contours A and E, contours A andG, contours C and E, and contours C and G; between coils1 and 3—contours B and I, contours B and K, contoursD and I, and contours D and K; between coils 2 and 3—contours H and L, contours H and J, contours F and L,and contours F and J. The mutual inductance M1 can becalculated by the following equation:

M1 (l, d) = 0.002 · l ·⎛⎝ln

⎛⎝ l

d+

√1 +

(l

d

)2⎞⎠

−√

1 +(

d

l

)2

+(

d

l

)2⎞⎠ (2)

where l is the length of the contour, and d is the distancebetween the two contours.

2) Two wires of unequal lengths are placed with an angle θon the same plane: between coils 1 and 2—contours Band F, and contours D and H; between coils 1 and 3—contours A and L, and contours C and J; between coils2 and 3—contours E and I, and contours G and K. Themutual inductance M2 can be calculated by the followingequation:

M2 (l1 , l2 , d, θ) = 0.002 · cosθ ·[

l12· tanh−1

(l22

d + l12

)

+l22· tanh−1

(l12

d + l22

)](3)

where l1 and l2 are the lengths of the two contours, respec-tively, d is the distance between the ends of the two contours,and θ is the angle between the two crossed contours.


Fig. 2. Detailed structure of the proposed coils.

3) Noncoplanar wires of unequal length were apart fromeach plane by 2a or 2b or 2c: between coils 1 and 2(2c)—contours B and H, and contours D and F; between coils1 and 3(2a)—contours A and J, and contours C and L;between coils 2 and 3(2b)—contours E and K, and con-tours G and I. The mutual inductance M3 can be calcu-lated by the following equation:

M3 (l1 , l2 , d, l, θ) = 0.002 · cosθ

·⎡⎣ l1

2· tanh−1

⎛⎝ l2

2√d2 + l2 +

√(l12

)2+ l2

⎞⎠+

l22

·tanh−1

⎛⎝ l1

2√d2 + l2 +

√(l22

)2+ l2

⎞⎠− Ω(l)

sinθ

⎤⎦ (4)

Ω(l) = tan−1

(l2cosθ + l1 l2

4 sin2θ

l√

d2 + l2sinθ

)

− tan−1

⎛⎝ lcosθ√(

l12

)2+ l2sinθ

⎞⎠

− tan−1

⎛⎝ lcosθ√(

l22

)2+ l2sinθ

⎞⎠+ tan−1

(cosθsinθ

)(5)

where l1 and l2 are the lengths of the two contours, respec-tively, d is the distance between the ends of the two contoursprojected on the same plane, l is the distance between the twoplanes, and θ is the angle between the two crossed contours.

4) Two wires are perpendicular to each other, the mutualinductance of two perpendicular wires is zero: betweencoils 1 and 2—contours A and F, contours A and H,contours C and F, contours C and H, contours B and E,contours B and G, contours D and E, and contours D andG; between coils 1 and 3—contours A and I, contours Aand K, contours C and I, contours C and K, contours B

and L, contours B and J, contours D and L, and contours Dand J; between coils 2 and 3—contours E and L, contoursE and J, contours G and L, contours G and J, contours Fand I, contours F and I, contours F and K, contours H andI, and contours H and K.

For example, the total mutual inductance M12 between coils 1and 2 can be the summation of M1 , M2 , and M3 (“+” means thesame current direction, “–” means the opposite current direction)

MAE = MC G = M1 (2c, d2) , MAG

= MC E = −M1 (2c, d1) (6)

MBF =∑

M2 (l1 , l2 , d, θ)

= MB+F + + MB+F − + MB−F − + MB−F +

= M2 (2a, 2b, d2 , π − θ) − M2 (2a, 2b, d1 , θ)

− M2 (2a, 2b, d1 , θ) + M2 (2a, 2b, d2 , π − θ)

= 2M2 (2a, 2b, d2 , π − θ) − 2M2 (2a, 2b, d1 , θ) (7)

MDH =∑

M2 (l1 , l2 , d, θ)

= MD+H + + MD+H− + MD−H− + MD−H +

= M2 (2a, 2b, d2 , π − θ) − M2 (2a, 2b, d1 , θ)

− M2 (2a, 2b, d1 , θ) + M2 (2a, 2b, d2 , π − θ)

= 2M2 (2a, 2b, d2 , π − θ) − 2M2 (2a, 2b, d1 , θ) (8)

MBH =∑

M3 (l1 , l2 , d, l, θ)

= MB+H + + MB+H− + MB−H− + MB−H +

= −M3 (2a, 2b, d2 , 2c, π − θ) + M3 (2a, 2b, d1 , 2c, θ)

+ M3 (2a, 2b, d1 , 2c, θ) − M3 (2a, 2b, d2 , 2c, π − θ)

= 2M3 (2a, 2b, d1 , 2c, θ) − 2M3 (2a, 2b, d2 , 2c, π − θ)(9)


MDF =∑

M3 (l1 , l2 , d, l, θ)

= MD+F + + MD+F − + MD−F − + MD−F +

= −M3 (2a, 2b, d2 , 2c, π − θ) + M3 (2a, 2b, d1 , 2c, θ)

+ M3 (2a, 2b, d1 , 2c, θ) − M3 (2a, 2b, d2 , 2c, π − θ)

= 2M3 (2a, 2b, d1 , 2c, θ) − 2M3 (2a, 2b, d2 , 2c, π − θ) .

(10)

Hence, according to (6)–(10), M12 is expressed as follow:

M12 = MAE + MAG + MC E + MC G + MBF

+ MDH + MBH + MDF

= 2 [M1 (2c, d2) − M1 (2c, d1)]

+ 4 [M2 (2a, 2b, d2 , π − θ) − M2 (2a, 2b, d1 , θ)]

+ 4 [M3 (2a, 2b, d1 , 2c, θ) − M3 (2a, 2b, d2 , 2c, π − θ)] .(11)

From (2)–(11), when d1 = d2 and θ = π − θ, M12 = 0, thetwo coils should be perpendicular and have the same length (a =b). Based on the same principle, the total mutual inductanceM13 between coils 1 and 3 and the total mutual inductance M23

between coils 2 and 3 can be zero when these three coils areperpendicular and have the same length (a = b = c).

The following sections are based on the three orthograph-ically assembled coils structure, which effectively reduces themutual inductance between the transmitter coils to avoid systemperformance degradation and is beneficial for the simplificationof synthesis of magnetic field. If the structure has slight defor-mation, the mutual inductance between the transmitter coils in-creases and the precise impedance matching between the trans-mitter and receiver becomes a little more difficult, and the threevectors of magnetic field generated by three coils are not or-thogonal. However, the synthesis of magnetic field can be stillrealized by three nonorthogonal B-field vectors, which will bemore complex, and the magnetic field orientation can still workif the performance degradation caused by structure deformationis acceptable.

III. MAGNETIC FLUX DENSITY ANALYSIS AND SYNTHESIS

OF CROSSED-LOOP COILS

According to Fig. 2, coil A lies on the XOZ plane, coil Blies on the YOZ plane, and coil C lies on the XOY plane.The direction of the contours of each coil can be expressed invector form

dlA = ez dz, dlB = exdx, dlC = ez dz, dlD = exdx,

dlE = ez dz, dlF = ey dy, dlG = ez dz, dlH = ey dy,

dlI = exdx, dlJ = ey dy, dlK = exdx, dlL = ey dy. (12)

Assume that a point A on the coil A p1(x1 , y1 , z1), apoint B on the coil B p2(x2 , y2 , z2), a point C on the coil Cp3(x3 , y3 , z3), and an arbitrary point P p(x, y, z) in the space.

The unit vector r1 from A to P, r2 from B to P, and r3 from Cto P are ⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

r1 =−−→AP∣∣∣−−→AP

∣∣∣ = (x−x1 )ex +(y−y1 )ey +(z−z1 )ez√(x−x1 )2 +(y−y1 )2 +(z−z1 )2

r2 =−−→BP∣∣∣−−→BP

∣∣∣ = (x−x2 )ex +(y−y2 )ey +(z−z2 )ez√(x−x2 )2 +(y−y2 )2 +(z−z2 )2

r3 =−−→CP∣∣∣−−→CP

∣∣∣ = (x−x3 )ex +(y−y3 )ey +(z−z3 )ez√(x−x3 )2 +(y−y3 )2 +(z−z3 )2 .

(13)

Assume that three currents through coils A, B, and C areIAcos(ωt + θA ), IB cos(ωt + θB ), and IC cos(ωt + θC ), re-spectively. Based on the Biot–Savart law, the magnetic fluxdensity components generated by coils A, B, and C at pointP are calculated as follows (the number of turns of each coilis N ):

BCoil.A =∮

μ0

4π

NIAcos (ωt + θA ) dl × r1

r21

=μ0NIAcos (ωt + θA )

4π

×∮

dl × [(x − x1) ex + (y − y1) ey + (z − z1) ez ]((x − x1)

2 + (y − y1)2 + (z − z1)

2)3/2

=μ0NIAcos (ωt + θA )

4π

×⎧⎨⎩∫

A

1r31

[ey (x − x1) dz − ex (y − y1) dz]

+∫

B

1r31

[ez (y − y1) dx − ey (z − z1) dx]

+∫

C

1r1

3 [ey (x − x1) dz − ex (y − y1) dz]

+∫

D

1r1

3 [ez (y − y1) dx − ey (z − z1) dx]}

(14)

BCoil.B =∮

μ0

4π

NIB cos (ωt + θB ) dl × r2

r22

=μ0NIB cos (ωt + θB )

4π

×∮


2 + (y − y1)2 + (z − z1)

2)3/2

=μ0NIB cos (ωt + θB )

4π

×{∫

E

1r32

[ey (x − x2) dz − ex (y − y2) dz]

+∫

F

1r32

[−ez (x − x2) dy − ex (z − z2) dy]


+∫

G

1r2

3 [ey (x − x2) dz − ex (y − y2) dz]

+∫

H

1r32

[−ez (x − x2) dy + ex (z − z2) dy]}

(15)

BCoil.C =∮

μ0

4π

NIC cos (ωt + θC ) dl × r3

r23

=μ0NIC cos (ωt + θC )

4π

×∮


2 + (y − y1)2 + (z − z1)

2)3/2

=μ0NIC cos (ωt + θC )

4π

×{∫

I

1r33

[ez (y − y3) dx − ey (z − z3) dx]

+∫

J

1r33

[−ez (x − x3) dy − ex (z − z3) dy]

+∫

K

1r33

[ez (y − y3) dx − ey (z − z3) dx]

+∫

L

1r33

[−ez (x − x3) dy + ex (z − z3) dy]}

(16)

where ω is the angular frequency of three independent currents.IA , IB , and IC are the amplitudes of three independent cur-rents, respectively. θA , θB , and θC are the phases of threeindependent currents, respectively. μ0 is the permeability ofvacuum, valued 4π × 10−7N · A−2 .

According to (14)–(16), the B-field at p(x, y, z) is the sum ofthe B-fields induced by coils A, B, and C as follows:⎡⎣Bx

By

Bz

⎤⎦ =

⎡⎣Bx

By

Bz

⎤⎦

Coil.A

+

⎡⎣Bx

By

Bz

⎤⎦

Coil.B

+

⎡⎣Bx

By

Bz

⎤⎦

Coil.C

=

⎡⎢⎢⎢⎢⎢⎢⎢⎣

Bx|A + Bx|C + Bx|E + Bx|F + Bx|G + Bx|H+Bx|J + Bx|L

By |A + By |B + By |C + By |D + By |E + By |G+Bx|I + By |K

Bz |B + BZ |D + BZ |F + Bz |H + BZ |I + Bz |J+Bx|K + Bz |L

⎤⎥⎥⎥⎥⎥⎥⎥⎦

(17)

where Bm |n is the B-field of m-axis component induced bycontour n. The x-axis, y-axis, and z-axis components of B-fieldat p(x, y, z) are listed in the Appendix.

IV. FIELD ORIENTATION BASED ON CURRENT AMPLITUDE

AND PHASE CONTROL

In order to simplify the analysis of the B-field synthesis in thespace, including the magnitude and direction, we have taken thegeometric center of coils A, B, and C po(0, 0, 0) as the exampleto discuss the B-field. From the Appendix, each axis componentof the B-field at po(0, 0, 0) is given as follows⎧⎪⎪⎪⎨⎪⎪⎪⎩

Bxp o= −μ0 N IB cos(ωt+θB )

4π

(4bc

b2√

b2 +c2 + 4bcc2

√b2 +c2

)

Byp o= −μ0 N IA cos(ωt+θA )

4π

(4ac

a2√

a2 +c2 + 4acc2

√a2 +c2

)

Bzp o= −μ0 N IC cos(ωt+θC )

4π

(4ab

a2√

a2 +b2 + 4abb2

√a2 +b2

).

(18)

The magnetic flux density induced by coils A, B, and C atany arbitrary point p(x, y, z) can be expressed by using sphericalcoordinates

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

Rp =√

B2x + B2

y + B2z

θp = tan−1(√

B2x + B2

y /Bz

)

ϕp = tan−1 (By/Bx)

(19)

where Rp is the magnitude of the B-field at point p, θp

is the angle between the zenith direction and the directionof the B-field, and ϕp is the signed angle measured fromthe azimuth reference direction to the orthogonal projec-tion of the direction of the B-field on the reference plane(Rp > 0, 0 ≤ θp ≤ π, 0 ≤ ϕp ≤ 2π).

Hence, according to (18) and (19), in order to simplify theanalysis, the coils are assumed to be a square (a = b = c = l),and the magnetic flux density induced by coils A, B, and C atpo(0, 0, 0) is given by (20), shown at the bottom of this page.

The implementation using absolute values θA , θB , and θC

is not convenient, so, for introducing the relative value to fur-ther reduce the equations, let θA = 0, θB − θA = Δθ1 , θC −θA = Δθ2 , as shown in (21) at the bottom of this page.

⎧⎪⎪⎨⎪⎪⎩

Rpo=

√2μ0 Nπl

√I2Acos2 (ωt + θA ) + I2

B cos2 (ωt + θB ) + I2C cos2 (ωt + θC )

θpo= tan−1

(−√I2

Acos2 (ωt + θA ) + I2B cos2 (ωt + θB )/IC cos (ωt + θC )

)

ϕpo= tan−1 (IAcos (ωt + θA ) /IB cos (ωt + θB ))

(20)

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

Rpo=

√2μ0 Nπl

√I2Acos2 (ωt) + I2

B cos2 (ωt + Δθ1) + I2C cos2 (ωt + Δθ2)

θpo= tan−1

(−√I2

Acos2 (ωt) + I2B cos2 (ωt + Δθ1)/IC cos (ωt + Δθ2)

)

ϕpo= tan−1 (IAcos (ωt) /IB cos (ωt + Δθ1))

(21)


Fig. 3. Simulation results of shaped B-field at different times.

From the aforementioned equations, all the current ampli-tudes and phase angles IA , IB , IC and θA , θB , θC , respec-tively, are the controllable variables. When the requirement ofthe B-field at point po is fulfilled, including the magnitude anddirection of the B-field, a set of currents meeting the requirementcan be solved.

For example, assume that the length of the side of eachcoil is 1 m, the number of turns of each coil is 10, and ω =40 000π rad/s, the requirements of the magnitude and directionof the B-field at po(0, 0, 0) are B(amplitude) = 10μT, θpo

=45◦, ϕpo

= 45◦. The results can be solved: IA = 0.884 A,IB = 0.884 A, IC = 1.25 A, Δθ1 = 0, and Δθ2 = 0. The coilsare excited by three independent sources, and the sources aresimulated by software “Maxwell Circuit Editor.” The theoreticalB-field can be simulated by using calculated values in software“Ansoft Maxwell,” shown in Fig. 3, where T = 50 μs.

From Fig. 3, the B-field in the region of the proposed coilsstructure is shaped at θ = 45◦ and ϕ = 45◦, when t = 0.25 Tand t = 0.75 T, respectively, and the magnitude of the B-fieldachieves the maximum. Fig. 4 shows the trend of the B-fieldmagnitude at point po from 0 to 100 μs. Within the error rangeallowed, the amplitude of the B-field is about 12 μT, which isclose to the reference value 10 μT. All the simulation resultsagree with the theoretical results.

At the different requirements of B, θ, and ϕ, the followingfour specific conditions, including all the directions in the space,verify the proposed algorithm that realizes the 3-D full-rangefield orientation. The calculated values of amplitude and phaseangle of currents are listed in Table I, where Bm means the

Fig. 4. Trend of B-field magnitude at point po .

TABLE IREQUIREMENTS AND CALCULATED VALUES FOR DIFFERENT CONDITIONS

Requirements Calculated Values

NO Bm θ ϕ IA IB IC Δθ1 Δθ2

1 10 μT 45◦ 45◦ 0.884 A 0.884 A 1.25 A 0◦ 0◦2 20 μT 45◦ 135◦ 1.768 A 1.768 A 2.5 A 180◦ 0◦3 10 μT 135◦ 45◦ 0.884 A 0.884 A 1.25 A 0◦ 180◦4 20 μT 135◦ 135◦ 1.768 A 1.768 A 2.5 A 180◦ 180◦

amplitude of the B-field. The shaped B-fields under four condi-tions are shown in Fig. 5, when t = 0.5 T.

From above-mentioned analysis, a universal conclusion canbe achieved, which will provide a criterion for further appli-cation. The whole space, taking the geometric center of theproposed coils structure as origin, can be divided into eight


Fig. 5. Shaped B-fields under four conditions.

Fig. 6. 3-D field orientation WPT system. (a) Prototype of the 3-D field orientation WPT system. (b) Detailed structure of three transmitter coils.

sections. Considering the B-field is alternating, the eight sec-tions can be further grouped into the following four regions:

1) x > 0, y > 0, z > 0 and x < 0, y < 0, z < 0;2) x > 0, y〈0, z〉0 and x〈0, y〉0, z < 0;3) x〈0, y〉0, z > 0 and x > 0, y < 0, z < 0;4) x < 0, y〈0, z〉0 and x > 0, y > 0, z < 0.

When the receiver coil is located in region 1), θ and ϕ aregiven as constant, 0 ≤ θ < π/2, 0 ≤ ϕ < π/2 (or π/2 ≤ θ ≤π, π ≤ ϕ < 3π/2 π/2 ≤ θ ≤ π, π ≤ ϕ < 3π/2); only whenΔθ1 = 0 and Δθ2 = 0 can the second and third equations of(21) have the effective and physically realizable solutions ofIA , IB , and IC . Similarly, when the receiver coil is located

in regions 2), 3), and 4), 0 ≤ θ < π/2, 3π/2 ≤ ϕ ≤ 2π (orπ/2 ≤ θ ≤ π, π/2 ≤ ϕ < π), 0 ≤ θ < π/2, π/2 ≤ ϕ < π

(or π/2 ≤ θ ≤ π, 3π/2 ≤ ϕ ≤ 2π) and 0 ≤ θ < π/2, π ≤ϕ < 3π/2 (or π/2 ≤ θ ≤ π, 0 ≤ ϕ < π/2), respectively; onlywhen Δθ1 and Δθ2 are 180◦ and 180◦, 180◦ and 0◦, 0◦ and 180◦,respectively, can the second and third equations of (21) have theeffective and physically realizable solutions of IA , IB , and IC .So, when the receiver coil(s) are located in regions 1), 2), 3), and4), respectively, Δθ1 and Δθ2 are accordingly set as 0◦ and 0◦,180◦ and 180◦, 180◦ and 0◦, 0◦ and 180◦, respectively. Accord-ing to the location of receiver coil(s), the current phase anglescan be first decided and a rough field orientation is completed.


TABLE IIACTUAL COIL PARAMETERS OF THE 3-D FIELD ORIENTATION WPT SYSTEM

Coil Frequency (kHz) L (μH) C (μF) R (mΩ) Length of Side (mm) Turns Wire Radius (mm)

Coil A (red) 19.517 10.06 6.61 50.23 328 3 2.2Coil B (yellow) 19.518 10.09 6.59 50.30 328 3 2.2Coil C (green) 19.513 10.11 6.58 50.43 328 3 2.2Coil Frequency (kHz) L (μH) C (μF) R (mΩ) Diameter (mm) Turns Wire Radius (mm)Receiver coil 19.609 15.61 4.22 43.10 276 5 2.2

TABLE IIIPARAMETERS OF THREE CASES FOR SHAPED MAGNETIC

FIELD MEASUREMENTS

Case IA rm s IB rm s IC rm s Δθ1 Δθ2

I. θ = 45◦, ϕ = 45◦ 7.07 A 7.07 A 10 A 0 0II. θ = 55◦, ϕ = 45◦ 8.16 A 8.16 A 8.16 A 0 0III. θ = 45◦, ϕ = 135◦ 7.07 A 7.07 A 10 A 180◦ 0

Fig. 7. Implementation of shaped magnetic field measurements.

Then, the magnitude of the B-field and further precise fieldorientation are realized by the current amplitude control. Forexample, when θ = 30◦, ϕ = 60◦, the field orientation locatesin region 1), and Δθ1 and Δθ2 are set as 0◦ and 0◦, respectively,hence the following equations will be derived:

⎧⎨⎩

(I2A + I2

B )/I2C = tan2 (30◦)

IA/IB = tan (60◦) .(22)

From (22), IA = IC /2 and IB =√

3IC /6. Then, accordingto the reference magnitude of the B-field, the following equationis obtained:

Bref =√

2μ0N

πl

√I2Acos2 (ωt) + I2

B cos2 (ωt) + I2C cos2 (ωt).

(23)

Fig. 8. Waveforms in case I. (a) Waveforms of θ = 45◦, ϕ = 45◦.(b) Waveforms of θ = 45◦, ϕ = 135◦. (c) Waveforms of θ = 45◦, ϕ =225◦.

From (23), the actual value of IA , IB , and IC can besolved. The whole steps of the proposed field orientationtechnique are done. In practical application, the solutionsIA , IB , IC , Δθ1 , and Δθ2 can be applied, and the shaped B-field will be formed.


Fig. 9. Waveforms in case II. (a) Waveforms of θ = 55◦, ϕ = 45◦.(b) Waveforms of θ=0, ϕ=45◦. (c) Waveforms of θ=90◦, ϕ = 45◦.

V. HARDWARE IMPLEMENTATION AND

EXPERIMENTAL RESULTS

Based on the previous theoretical analysis, a 3-D field orien-tation WPT system is implemented, which is shown in Fig. 6.Fig. 6(a) shows the prototype of a 3-D field orientation WPTsystem, which is composed of a controller equipped with afloating-point digital signal processor (DSP, TMS320F28335)and a field programmable gate array (FPGA, EP2C8J144C8N),an ac/dc converter with three independent channel 12 V output,three independent controllable dc/ac converters, three indepen-dent resonance tanks, including series resonant capacitors andtransmitter coils, one receiver coil connected with series res-onant capacitor and resistance load. The inductance of each

Fig. 10. Waveforms in case III. (a) Waveforms of θ = 45◦, ϕ = 135◦.(b) Waveforms of θ=45◦, ϕ=225◦. (c) Waveforms of θ=45◦, ϕ = 315◦.

transmitter coil is designed as 10 μH, the inductance of the re-ceiver coil is designed as 15.6 μH, the capacitance of each seriesresonant capacitor for the transmitter is designed as 6.6 μF, thecapacitance of the series resonant capacitor for the receiver isdesigned as 4.23 μF, the frequency of ac voltage generated bydc/ac converters is designed as 19.59 kHz, DSP is in charge ofmathematical calculation, and FPGA is in charge of generatingpulse width modulation signals for switches. Fig. 6(b) showsthe detailed structure of three transmitter coils, including coil Alabeled red, coil B labeled yellow, and coil C labeled green, eachcoil is a square with the length of side 328 mm, each coil hasthree turns of Litz wire with radius 2.2 mm. The actual coil pa-rameters of the 3-D field orientation WPT system are presentedin Table II.


Fig. 11. Experimental setups used for measuring the energy transferefficiency. (a) The setup for case I. (b) The setup for case II.

The experimental results of the implemented 3-D field ori-entation WPT system are presented below. In order to furtherverify the previous theoretical analysis, two sets of experimentsare carried out, shaped magnetic field measurements and energytransfer efficiency measurements.

For shaped magnetic field measurements, it is not easy todirectly measure the magnetic flux density; hence, we used theinduced electromotive force induced in the receiver coil to in-directly measure the shaped magnetic field in the region of thereceiver coil. The following cases are set to compare the mag-netic field pointing to the receiver coil and the magnetic field notpointing to the receiver coil, which are presented in Table III.The distance between the center of receiver coil and the center ofthree transmitter coils remains constant, i.e., 30 cm. The planeof receiver coil is perpendicular to the line from the center ofreceiver coil and the center of three transmitter coils. The exper-imental results of each case include the induced electromotive

Fig. 12. Waveforms in case I.

Fig. 13. Waveforms in case II.

force when the receiver coil is located in the given direction andthe induced electromotive force when the receiver coil is notlocated in the given direction. The implementation in shapedmagnetic field measurements is shown in Fig. 7.

In case I, IA rms = 7.07 A, IB rms = 7.07 A, IC rms =10 A, Δθ1 = 0, and Δθ2 = 0. First, let the receiver coil beat θ = 45◦, ϕ = 45◦, then let the receiver coil be at θ = 45◦,ϕ = 135◦ and θ = 45◦, ϕ = 225◦, respectively. As shown inFig. 8, from top to bottom in each figure, the waveforms are theinduced voltage in the receiver coil, the current in coil A, thecurrent in coil B and, the current in coil C.

In case II, IA rms = 8.16 A, IB rms = 8.16 A, IC rms =8.16 A, Δθ1 = 0, and Δθ2 = 0. First, let the receiver coil be atθ = 55◦, ϕ = 45◦, then let the receiver coil be at θ = 0, ϕ = 45◦

and θ = 90◦, ϕ = 45◦, respectively. As shown in Fig. 9, fromtop to bottom in each figure, the waveforms are the inducedvoltage in the receiver coil, the current in coil A, the current incoil B, and the current in coil C.

In case III, IA rms = 7.07 A, IB rms = 7.07 A, IC rms =10 A, Δθ1 = 180◦, and Δθ2 = 0. First, let the receiver coil beat θ = 45◦, ϕ = 135◦, then, let the receiver coil be at θ = 45◦,ϕ = 225◦ and θ = 45◦, ϕ = 315◦, respectively. As shown inFig. 10, from top to bottom in each figure, the waveforms are


the induced voltage in the receiver coil, the current in coil A,the current in coil B, and the current in coil C.

From the aforementioned experimental results, the magneticfield is shaped according to expected direction, and the magneticfield is concentrated at a certain direction. Comparing case Iwith case II, when Δθ1 and Δθ2 remain unchanged, changingthe relative values of IA rms , IB rms , and IC rms , and keepingthe sum of squares of IA rms , IB rms , andIC rms constant, thedirection of shaped magnetic field changes from θ = 45◦ toθ = 55◦. Comparing case I with case III, when IA , IB , and IC

remain unchanged, changing Δθ1 and Δθ2 , the region of shapedmagnetic field changes from region 1) to region 3).

For energy transfer efficiency measurements, the load of re-ceiver coil is a resistance 0.5 Ω. In order to explain the improve-ments of energy transfer efficiency, two experiments are carriedout with the following: case I—three transmitter coils and onereceiver coil; case II—one transmitter coil and one receiver coil.In both cases, the initial magnitude of magnetic field at the cen-ter is equally set same for comparison, which means the currentsof three transmitter coils in case I is

√3/3 of the current of the

single transmitter coil in case II. The receiver coil is placedvertically with the direction of shaped magnetic field. The dis-tance from the center of three transmitter coils to the center ofreceiver coil in case I is along with the direction of magneticfield in the center of three transmitter coils, the distance fromthe center of one transmitter coil to the center of receiver coil incase II is along with the direction of magnetic field in the centerof one transmitter coil, and both the distances are set as 25 cm.The experimental setups used for measuring the energy transferefficiency are shown in Fig. 11, where Fig. 11(a) is for case Iand Fig. 11(b) is for case II.

In case I, IA rms = 10A, IB rms = 10A, IC rms = 10A,Δθ1 = 0, and Δθ2 = 0. As shown in Fig. 12, from top to bot-tom, the waveforms are the input dc voltage of three powersupplies, the total input dc current of three power supplies, theoutput voltage of receiver coil, and the output current of receivercoil.

In case II, IA rms = 0A, IB rms = 0A, IC rms = 17.32A,Δθ1 = 0, and Δθ2 = 0. As shown in Fig. 13, from top to bot-tom, the waveforms are the input dc voltage of single powersupply, the input dc current of single power supply, the out-put voltage of receiver coil, and the output current of receivercoil.

From the aforementioned results, the proposed magnetic fieldorientation method improves the energy transfer efficiency andoffers larger effective transmission distance when the powerneeded in the receiver coil is given. Comparing case I and case II,when the distances and the sum of squares of IA , IB , andIC re-main the same in the two cases, the output voltage of receivercoil in case I is larger than the output voltage of receiver coil incase II, which means when the expected output voltage of re-ceiver coil is given, the proposed three transmitter coils structure

has longer transmission distance, the energy transfer capacityof the proposed magnetic field orientation method is better thanthat of the conventional method. Similarly, in this group of ex-periments, the efficiency is equal to the ratio of the load powerand the input dc power. According to Figs. 12 and 13, the loadpower and efficiency of the proposed magnetic field orienta-tion method are about 13.7 W and 28.2%, respectively, and theload power and efficiency of the conventional method are about3.2 W and 10.8%, respectively. For the result of efficiency ofthe conventional method, because the calculated efficiency in-cludes the loss of a dc/ac converter, when the required currentbecomes larger, the loss of a dc/ac converter will become larger.Meanwhile, because the given transfer distance 25 cm is rel-atively large compared with the size of transmitter coil, whenjust single transmitter coil works, the excited magnetic fieldwill sharply diverge and some energy will be wasted. Hence,the single transmitter coil structure will lead to lower efficiencywhen the distance highly increases. However, the proposed threetransmitter coils structure can reduce the requirement of currentflowing in one transmitter coil and shape the magnetic field toreduce unnecessary energy waste, which will obviously improvethe energy transfer efficiency compared with the conventionalsingle transmitter coil structure. Generally, the proposed 3-Dmagnetic field orientation method can effectively improve theperformance of a WPT system.

VI. CONCLUSION

This paper introduced a universal algorithm to realize 3-Dfull-range field orientation to adjust the magnitude and directionof the B-field at an arbitrary point. The B-field is concentrated ina beam with reduced leakage magnetic flux, consequently, thepower transfer efficiency and distance are effectively improved.The proposed algorithm is very useful to guide practical 3-DWPT system design with more flexible coupling tolerance. Theanalytical, simulation, and experimental results obtained fromthis research demonstrate that if the mathematic relationshipsbetween the B-filed generated by the transmitter and the powerreceived by the receiver are established, together with orienta-tion and power closed-loop accurate steady-state controls, thewhole 3-D WPT system will be able to eliminate the steady-state error, have certain ability of anti-interference, and achievemore precise power transfer and direction orientation to targetedloads.

APPENDIX

The x-axis, y-axis, and z-axis components of the B-field atp(x, y, z) are listed in Table IV, where Bm is the B-field of them-axis in the space, and Bm |Coil N is the B-field of the m-axiscomponent induced by coil N.


TABLE IVx-AXIS, y-AXIS, AND z-AXIS COMPONENTS OF B-FIELD AT p(x, y, z)

Bm Bm |Coil N Value

Bx Bx |Coil A

μ 0 N IA cos(ω t+ θA )4π

{(y (z−c )

[(x−a )2 + y 2 ][(x−a )2 + y 2 + (z−c )2 ]12

− y (z + c )

[(x−a )2 + y 2 ][(x−a )2 + y 2 + (z + c )2 ]12

)

+

(y (z + c )

[(x+a )2 + y 2 ][(x+a )2 + y 2 + (z + c )2 ]12

− y (z−c )

[(x+a )2 + y 2 ][(x+a )2 + y 2 + (z−c )2 ]12

)}

Bx |Coil B

μ 0 N IB cos(ω t+ θB )4π

{((y + b )(z−c )

[x 2 + (y + b )2 ][x 2 + (y + b )2 + (z−c )2 ]12

− (y + b )(z + c )

[x 2 + (y + b )2 ][x 2 + (y + b )2 + (z + c )2 ]12

)

+

((y + b )(z−c )

[x 2 + (z−c )2 ][x 2 + (y + b )2 + (z−c )2 ]12

− (y−b )(z−c )

[x 2 + (z−c )2 ][x 2 + (y−b )2 + (z−c )2 ]12

)

+

((y−b )(z + c )

[x 2 + (y−b )2 ][x 2 + (y−b )2 + (z + c )2 ]12

− (y−b )(z−c )

[x 2 + (y−b )2 ][x 2 + (y−b )2 + (z−c )2 ]12

)

+

((y−b )(z + c )

[x 2 + (z + c )2 ][x 2 + (y−b )2 + (z + c )2 ]12

− (y + b )(z + c )

[x 2 + (z + c )2 ][x 2 + (y + b )2 + (z + c )2 ]12

)}

Bx |Coil C

μ 0 N IC cos(ω t+ θC )4π

{((y + b )z

[(x+a )2 + z 2 ][(x+a )2 + (y + b )2 + z 2 ]12

− (y−b )z

[(x+a )2 + z 2 ][(x+a )2 + (y−b )2 + z 2 ]12

)

+

((y−b )z

[(x−a )2 + z 2 ][(x−a )2 + (y−b )2 + z 2 ]12

− (y + b )z

[(x−a )2 + z 2 ][(x−a )2 + (y + b )2 + z 2 ]12

)}

By By |Coil A


{((x−a )(z + c )

[(x−a )2 + y 2 ][(x−a )2 + y 2 + (z + c )2 ]12

− (x−a )(z−c )

[(x−a )2 + y 2 ][(x−a )2 + y 2 + (z−c )2 ]12

)

+

((x+a )(z−c )

[y 2 + (z−c )2 ][(x+a )2 + y 2 + (z−c )2 ]12

− (x−a )(z−c )

[y 2 + (z−c )2 ][(x−a )2 + y 2 + (z−c )2 ]12

)

+

((x+a )(z−c )

[(x+a )2 + y 2 ][(x+a )2 + y 2 + (z−c )2 ]12

− (x+a )(z + c )

[(x+a )2 + y 2 ][(x+a )2 + y 2 + (z + c )2 ]12

)

+

((x−a )(z + c )

[y 2 + (z + c )2 ][(x−a )2 + y 2 + (z + c )2 ]12

− (x+a )(z + c )

[y 2 + (z + c )2 ][(x+a )2 + y 2 + (z + c )2 ]12

)}

By |Coil B


{(x (z + c )

[x 2 + (y + b )2 ][x 2 + (y + b )2 + (z + c )2 ]12

− x (z−c )

[x 2 + (y + b )2 ][x 2 + (y + b )2 + (z−c )2 ]12

)

+

(x (z−c )

[x 2 + (y−b )2 ][x 2 + (y−b )2 + (z−c )2 ]12

− x (z + c )

[x 2 + (y−b )2 ][x 2 + (y−b )2 + (z + c )2 ]12

)}

By |Coil C


{((x+a )z

[(y + b )2 + z 2 ][(x+a )2 + (y + b )2 + z 2 ]12

− (x−a )z

[(y + b )2 + z 2 ][(x−a )2 + (y + b )2 + z 2 ]12

)

+

((x−a )z

[(y−b )2 + z 2 ][(x−a )2 + (y−b )2 + z 2 ]12

− (x+a )z

[(y−b )2 + z 2 ][(x+a )2 + (y−b )2 + z 2 ]12

)}

Bz Bz |Coil A


{((x−a )y

[y 2 + (z−c )2 ][(x−a )2 + y 2 + (z−c )2 ]12

− (x+a )y

[y 2 + (z−c )2 ][(x+a )2 + y 2 + (z−c )2 ]12

)

+

((x+a )y

[y 2 + (z + c )2 ][(x+a )2 + y 2 + (z + c )2 ]12

− (x−a )y

[y 2 + (z + c )2 ][(x−a )2 + y 2 + (z + c )2 ]12

)}

Bz |Coil B


{(x (y−b )

[x 2 + (z−c )2 ][x 2 + (y−b )2 + (z−c )2 ]12

− x (y + b )

[x 2 + (z−c )2 ][x 2 + (y + b )2 + (z−c )2 ]12

)

+

(x (y + b )

[x 2 + (z + c )2 ][x 2 + (y + b )2 + (z + c )2 ]12

− x (y−b )

[x 2 + (z + c )2 ][x 2 + (y−b )2 + (z + c )2 ]12

)}

Bz |Coil C


{((x−a )(y + b )

[(y + b )2 + z 2 ][(x−a )2 + (y + b )2 + z 2 ]12

− (x+a )(y + b )

[(y + b )2 + z 2 ][(x+a )2 + (y + b )2 + z 2 ]12

)

+

((x+a )(y−b )

[(x+a )2 + z 2 ][(x+a )2 + (y−b )2 + z 2 ]12

− (x+a )(y + b )

[(x+a )2 + z 2 ][(x+a )2 + (y + b )2 + z 2 ]12

)

+

((x+a )(y−b )

[(y−b )2 + z 2 ][(x+a )2 + (y−b )2 + z 2 ]12

− (x−a )(y−b )

[(y−b )2 + z 2 ][(x−a )2 + (y−b )2 + z 2 ]12

)

+

((x−a )(y + b )

[(x−a )2 + z 2 ][(x−a )2 + (y + b )2 + z 2 ]12− (x−a )(y−b )

[(x−a )2 + z 2 ][(x−a )2 + (y−b )2 + z 2 ]12

)}


REFERENCES

[1] A. Kurs, A. Karalis, J. D. Joannopoulos, and M. Soljacic, “Wireless powertransfer via strongly coupled magnetic resonance,” Science, vol. 317,no. 5834, pp. 83–86, Jul. 2007, doi: 10.1126/science.1143254.

[2] A. Karalis, J. D. Joannopoulos, and M. Soljacic, “Efficiency wirelessnonradiative mid-range energy transfer,” Ann. Phys., vol. 323, pp. 34–48,Jan. 2008, doi: 10.1016/j.aop.2007.04.017.

[3] S. L. Ho, J. Wang, W. N. Fu, and M. Sun, “A comparative study betweennovel witricity and traditional inductive magnetic coupling in wirelesscharging,” IEEE Trans. Magn., vol. 47, no. 5, pp. 1522–1525, May 2011,doi: 10.1109/TMAG.2010.2091495.

[4] A. P. Sample, D. T. Meyer, and J. R. Smith, “Analysis experimental re-sults, and range adaptation of magnetically coupled resonators for wirelesspower transfer,” IEEE Trans. Ind. Electron., vol. 58, no. 2, pp. 544–554,Feb. 2011, doi: 10.1109/TIE.2010.2046002.

[5] S. Y. R. Hui, W. X. Zhong, and C. K. Lee, “A critical review ofrecent progress in mid-range wireless power transfer,” IEEE Trans.Power Electron., vol. 29, no. 9, pp. 4500–4511, Sep. 2014, doi:10.1109/TPEL.2013.2249670.

[6] T. Imura, “Equivalent circuit for repeater coil for wireless power trans-fer via magnetic resonant coupling considering signed coupling,” inProc. IEEE Ind. Electron. Appl. Conf., 2011, pp. 1501–1506, doi:10.1109/ICIEA.2011.5975828.

[7] J. Kim, H. Son, K. Kim, and Y. Park, “Efficiency analysis of mag-netic resonance wireless power transfer with intermediate resonance coil,”IEEE Coils Wireless Propag. Lett., vol. 10, pp. 389–392, May 2011, doi:10.1109/LAWP.2011.2150192.

[8] Y. Moriwaki, T. Imura, and Y. Hori, “Basic study on reduction of reflectedpower using DC/DC converters in wireless power transfer system viamagnetic resonant coupling,” in Proc. Telecommun. Energy Conf., 2011,pp. 1–5, doi: 10.1109/INTLEC.2011.6099737.

[9] Y. Lim, H. Tang, S. Lim, and J. Park, “An adaptive impedance-matchingnetwork based on a novel capacitor matrix for wireless power transfer,”IEEE Trans. Power Electron., vol. 29, no. 8, pp. 4403–4413, Aug. 2014,doi: 10.1109/TPEL.2013.2292596.

[10] C. K. Lee, W. X. Zhong, and S. Y. R. Hui, “Effect of magnetic couplingof nonadjacent resonators on wireless power domino-resonator systems,”IEEE Trans. Power Electron., vol. 27, no. 4, pp. 1905–1916, Apr. 2012,doi: 10.1109/TPEL.2011.2169460.

[11] B. H. Waters, A. P. Sample, and J. R. Smith, “Adaptive impedance match-ing for magnetically coupled resonators,” in Proc. Prog. Electromagn.Res. Symp., Moscow, Russia, Aug. 2012, pp. 694–701.

[12] R. Johari, J. V. Krogmeier, and D. J. Love, “Analysis and practical consid-erations in implementing multiple transmitters for wireless power transfervia coupled magnetic resonance,” IEEE Trans. Ind. Electron., vol. 61,no. 4, pp. 1774–1783, Apr. 2014, doi: 10.1109/TIE.2013.2263780.

[13] W. Ahn et al., “Design of coupled resonators for wireless powertransfer to mobile devices using magnetic field shaping,” in Proc.IEEE Int. Symp. Electromagn. Compat., 2012, pp. 772–776, doi:10.1109/ISEMC.2012.6351667.

[14] S. Santalunai, C. Thongsopa, and T. Thosdeekoraphat, “An increasing thepower transmission efficiency of flat spiral coils by using ferrite materi-als for wireless power transfer applications,” in Proc. Int. Conf. Electr.Eng./Electron. Comput. Telecommun. Inf. Technol., 2014, pp. 1–4, doi:10.1109/ECTICon.2014.6839838.

[15] Y. Lim and J. Park, “A novel phase-control-based energy beamform-ing techniques in nonradiative wireless power transfer,” IEEE Trans.Power Electron., vol. 30, no. 11, pp. 6274–6287, Nov. 2015, doi:10.1109/TPEL.2014.2379672.

Qi Zhu (GS’16 ) was born in Anhui, China, in1993. He received the B.S. degree in electri-cal engineering and automation from the Cen-tral South University, Changsha, China, in 2014,where he is currently working toward the Ph.D.degree in electrical engineering.

His research interests include wireless powertransfer and matrix converter.

Mei Su was born in Hunan, China, in 1967. Shereceived the B.S. degree in automation and theM.S. and Ph.D. degrees in electric engineeringfrom Central South University, Changsha, China,in 1989, 1992, and 2005, respectively.

Since 2006, she has been a Professor withthe School of Information Science and Engineer-ing, Central South University. Her research inter-ests include matrix converter, adjustable speeddrives, and wind energy conversion system.

Yao Sun (M’13) was born in Hunan, China,in 1981. He received the B.S. degree in au-tomation and M.S. and Ph.D. degrees in elec-tric engineering from Central South University,Changsha, China, in 2004, 2007, and 2010,respectively.

He has been a Professor with theSchool of Information Science and Engineering,Central South University. His research interestsinclude matrix converter, microgrid, and wind en-ergy conversion system.

Weiyi Tang was born in Jiangsu, China, in 1991.He received the B.S. degree in automation fromthe Central South University, Changsha, China,in 2013, where he is currently working toward thePh.D. degree in control science and engineering.

His research interests include motor control.

Aiguo Patrick Hu (SM’07) received the B.E.and M.E. degrees in electrical engineering fromXi’an JiaoTong University, Xi’an, China, in 1985and 1988, respectively, and the Ph.D. degreein electrical and electronic engineering from theUniversity of Auckland, Auckland, New Zealand,in 2001.

Before receiving the Ph.D. degree, he servedas a Lecturer, the Director of China Italy Coop-erative Technical Training Center, Xi’an, China,and the General Manager of a technical devel-

opment company. Funded by Asian2000 Foundation, he stayed in theNational University of Singapore for a semester as an Exchange Post-doctoral Research Fellow. He is a leading researcher in wireless powertechnologies. He is currently the Deputy Head (Research) of the Depart-ment of Electrical and Electronic Engineering, University of Auckland.He is also the Head of Research of PowerbyProxi Ltd, Auckland, NewZealand, as well as a Guest Professor of ChongQing Univ, Chongqing,China, and TaiYuan Univ of Technology, Taiyuan, China. He has been aforeign expert reviewer of 973 projects for the Chinese Ministry of Sci-ence and Technology, and an assessor of ChangJiang Scholars for theMinistry of Education. He is the former Chairman of IEEE NZ Power Sys-tems/Power Electronics Chapter, and the Immediate Past Chairman ofNew Zealand North Section. He served as a Secretary/Treasurer of theNew Zealand Chinese Scientists Association, and is currently the VicePresident. He holds more than 50 patents in wireless/contactless powertransfer and microcomputer control technologies across the world, au-thored or co-authored more than 200 peer-reviewed journal and confer-ence papers with more than 3500 citations, authored the first monographon wireless inductive power transfer technology, and contributed 4 bookchapters on inductive power transfer modeling/control as well as electri-cal machines. His research interests include wireless/contactless powertransfer systems, and application of power electronics in renewable en-ergy systems.

Dr. Hu was the recipient of the University of Auckland VC’s FundedResearch and Commercialization Medal in 2017.

http://dx.doi.org/10.1126/science.1143254

http://dx.doi.org/10.1016/j.aop.2007.04.017

http://dx.doi.org/10.1109/TMAG.2010.2091495

http://dx.doi.org/10.1109/TIE.2010.2046002

http://dx.doi.org/10.1109/TPEL.2013.2249670

http://dx.doi.org/10.1109/ICIEA.2011.5975828

http://dx.doi.org/10.1109/LAWP.2011.2150192

http://dx.doi.org/10.1109/INTLEC.2011.6099737



http://dx.doi.org/10.1109/TIE.2013.2263780

http://dx.doi.org/10.1109/ISEMC.2012.6351667

http://dx.doi.org/10.1109/ECTICon.2014.6839838


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