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Design and analysis of a wireless power transfersystem with alignment errors for electrical vehicleapplications

Sakir Kuzey a, Selami Balci b, Necmi Altin c,*

a Giresun University, Sebinkarahisar Vocational Schools of Technical Sciences, Electricity and Energy Department,

28400, Giresun, Turkeyb Ministry of National Education, Ankara, Turkeyc Gazi University, Faculty of Technology, Electrical and Electronics Engineering Dept., 06500, Ankara, Turkey

a r t i c l e i n f o

Article history:

Received 8 November 2016

Received in revised form

18 March 2017

Accepted 22 March 2017

Available online xxx

Keywords:

Inductively coupled power transfer

(ICPT)

Wireless power transfer

Electric vehicles

Alignment error

* Corresponding author.E-mail address: [email protected] (N. Alt

http://dx.doi.org/10.1016/j.ijhydene.2017.03.10360-3199/© 2017 Hydrogen Energy Publicati

Please cite this article in press as: Kuzey S,electrical vehicle applications, Internationa

a b s t r a c t

In this study, a 15 kWwireless power transfer system with high frequency and large air gap

for electrical vehicle battery charge systems is designed and co-simulations with ANSYS-

Maxwell and Simplorer software are performed. The air gap between the primary and

the secondary windings are determined as 20 cm for the 15 kW wireless power transfer

system. Operation of the designed system for different operation conditions such as

completely aligned windings (ideal condition) and windings with alignment errors, which

can occur because of user error or another reason, are analyzed and obtained results are

reported. The resonant frequency of the designed system which has a 60 � 60 cm sec-

ondary winding and a 60 � 100 cm primary winding is 17.702 kHz, and the maximum ef-

ficiency of the system is obtained as 75.38% for completely aligned windings. The

distribution and density of the electromagnetic flux, and variation of efficiency versus load

level of the system and responses of the system in case of different alignment errors are

also investigated and reported for both ideal operation conditions and in case of alignment

errors.

© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

Introduction

Nowadays, reasons such as increase in the price of oil and its

derivatives, extinction of fossil fuels and global warming in-

crease the attention on electrical vehicles (EVs). Environ-

mental friendly EVs have become the main driving force for

automotive industry with their zero emission feature [1e3].

While the battery bank of the conventional EV is charged

through the grid with a power cable and a plug, more safe

in).60ons LLC. Published by Els

et al., Design and analysl Journal of Hydrogen Ene

wireless charge systems have become to use for the same

purpose with the improvements in technology.

Similar to electrical machines and transformers, power

transmission from one winding to the other one, which are

magnetically coupled, is essentially known method. The

overall objective of the inductively coupled power transfer

(ICPT) systems is to provide wireless power transfer effi-

ciently. The inductive coupling coefficient is one of the most

important parameter of these systems. Since the power is

transferred form primary winding to the secondary winding

evier Ltd. All rights reserved.

is of a wireless power transfer system with alignment errors forrgy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.03.160

mailto:[email protected]

www.sciencedirect.com/science/journal/03603199

www.elsevier.com/locate/he

http://dx.doi.org/10.1016/j.ijhydene.2017.03.160



i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y x x x ( 2 0 1 7 ) 1e1 22

through the air gap according to the magnetic induction

principle, the electromagnetic coupling coefficient is decisive

variable that affects the system performance. Therefore,

many studies have been proposed on determining optimal

coupling coefficient and power factor compensation to obtain

efficient power transfer [4].

Effects of ICPT systems on human body is an important

issue and should be examined. These systems should comply

with standards defined by International Commission on Non-

Ionizing Radiation Protection (ICNIRP). Many studies have

been performed to analyze effects of electromagnetic systems

on human body. Although the operation frequency of

communication systems is in range from MHz to GHz, the

operating frequency values of the ICPT systems are usually

lower than a few kHz because of efficiency and power level

limitations. It is reported that, a proper designed ICPT system

comply with the standards and they do not have hazardous

effects on the human health [5].

ICPT systems are usually designed as spiral circles and

rectangle geometries. The mutual inductance value of a ICPT

systemwith spiral circles is also 45e50% higher than the ICPT

system with rectangle geometries. Although, magnetic

coupling value of the ICPT system with the spiral circles is

higher, the ICPT systemwith rectangle geometries have better

performance under alignment errors. Therefore, rectangle

geometries are more common in EV applications [6]. In addi-

tion, ferrite core can be used in primary and secondary

windings to increase the coupling coefficient [7]. In this con-

dition, windings can be designed in different forms to ob-

tained maximum efficiency. However, in this case, increasing

core temperature triggers some disadvantages such as

decreasing on coupling coefficient and linearity reduction on

system control [8e10].

Enlarging size of the primary winding will not increase the

system efficiency. In addition, this increases the system cost

because of increasing conductor length and size of mechani-

cal design. At this point, concordance between primary and

secondary windings has come to the forefront. Themaximum

system efficiency is obtained with optimum inductive

coupling coefficient, proper compensation topology, and

providing operation at resonant frequency [11,12].

Since these ICPT systems are supplied with high frequency

voltage, resonant converters, which are commonly used in

different applications such as induction heating, electronic

ballasts, power supplies, etc., are used at the converter stage

to obtain higher efficiency values [13,14]. Therefore, there are

Fig. 1 e Electrical equivalent

Please cite this article in press as: Kuzey S, et al., Design and analyselectrical vehicle applications, International Journal of Hydrogen Ene

number of studies on electromagnetic design of the ICPT

system [15,16], converter and resonator circuit design issues

[17,18]. In addition, the placement of the ICPT system receiver

and transmitter windings directly affects the system perfor-

mance. Alignment errors are very common in a practical

wireless power transfer system for EV applications Therefore,

some studies on auto-alignment of the EVs are also proposed

[19]. However, effects of different alignment errors on system

performance are rarely analyzed.

In this study, a 15 kW ICPT system with 20 cm air gap is

designed. Then the designed system is simulated with finite

element analysis software. The model of the ICPT system is

also co-simulated with inverter and compensation circuits to

obtain more realistic results. Besides the ideal operation

conditions without any alignment error, presence of different

alignment errors between thewindings are also analyzed. The

flux distribution, and efficiency of the ICPT system are inter-

preted. In addition, efficiency variation versus load is also

analyzed. It is seen from the simulation results that the pro-

posed system is low magnetic coupled systems with 0.1556

electromagnetic coupling coefficient. In addition, the

maximum efficiency value of the ICPT system is obtained as

75.38% for ideal condition, and 33.35% and 46% for alignment

error and 2-degree gradient alignment error conditions,

respectively.

Inductive magnetic coupled power transfersystems

Uncompensated circuit model of inductive magnetic coupled

power transfer system, which makes understanding the sys-

tem easy is seen in Fig. 1. This is the most fundamental figure

[20]. Here, Vp is rms value of sinusoidal signal applied to pri-

mary winding. Assuming that voltage and current are sinu-

soidal, the induced voltage in secondary winding due to the

primary current Ip is juMIp, reflected voltage in the primary

winding due to the secondary current Is is�juMIs where “M” is

on themutual inductanceandu is theoperation frequency [21].

Mathematical equation of system's equivalent circuit must

be derived in order to follow power flow of ICPT system. Ac-

cording to equivalent circuit, Eq. (1) can be written for input

voltage Vp [7,8,11].

Vp ¼�Rp þ j

�uLp

��Ip � juMIs ¼

�Rp þ jXp

�Ip � juMIs

¼ ZpIp � juMIs (1)

circuit of ICPT system.




Fig. 2 e Windings with rectangular geometry.

i n t e r n a t i o n a l j o u r n a l o f h yd r o g e n e n e r g y x x x ( 2 0 1 7 ) 1e1 2 3

ICPT systems provides high efficiency at low power, low

frequency such as 50e60 Hz and at high mutual inductance

[7]. However, when high power is concern, power trans-

mission becomes more difficult. System must have an

appropriate magnetic coupling coefficient at high resonance

frequency. Furthermore, it is realized that losses which may

occur in the system affect the efficiency of the system. For this

reason, these systems are operated at resonance frequency in

order to minimize the losses. Despite this, the operating fre-

quency is usually under 100 kHz for high power applications

due to switching losses [21]. Besides, Litz wire is used to

reduce skin effect and proximity effect losses which occur in

windings [8,11].

The magnetic coupling coefficient (k) is a value which

shows how much of the magnetic flux created by the primary

is transferred to the secondary circuit. Therefore, the effi-

ciency of the power transferred from the primary to the sec-

ondary depends on the magnetic coupling coefficient. The

magnetic coupling coefficient is given in Eq. (2).

k ¼ MffiffiffiffiffiffiffiffiLpIs

p (2)

It can be seen that themutual inductance and themagnetic

coupling coefficient have a strong impact on each other. But, it

does not mean that an increase at mutual inductance in-

creases the magnetic coupling coefficient. Other determining

parameters are the primary and the secondary inductance

values. According to this, it is understood that the windings

must have optimal parameter values.

Themagnetic coupling coefficient must be within a certain

range depending on the compensation topology. There must

be a strong magnetic connection between the primary and

secondary windings in order to provide high efficient power

transfer. Increase in air gap between the windings decreases

the magnetic coupling coefficient and systems which have

magnetic coupling coefficient under 0.2 are accepted as low

magnetic coupled systems. In addition, the air gap distances

between the windings must be homogenous and the winding

conductors must be aligned. In the absence of this alignment

themagnetic connectionwill not be strong and this reduce the

system efficiency.

In air-gapped transformers, the coupling coefficient and

the quality factors (Q) of the windings are two important pa-

rameters. The quality factor reflects a largemagnetic field and

minimal loss creation capacity of the windings. The relation-

ship between the secondary reactive and active power has

been given in Eq. (3) which is considered to be equal to the

secondary winding quality factor [11].

Qs ¼ VArsPs

(3)

ICPT system with rectangle geometry

In the scaling of the windings the width and the lengths of the

primary and the secondary windings, are denoted as a1, a2, b1and b2, respectively. Following equations given by Sall�an et al.,

the single side lengths created by the windings (r1 and r2 given

in Fig. 2) are given by Eq. (4) and Eq. (5) [8].


r1 ¼ffiffiffiffiffiffiffiffiffiffiffiNpSp

p

r(4)

r2 ¼ffiffiffiffiffiffiffiffiffiffiNsSs

p

r(5)

The ‘c’ and ‘e’ given in Fig. 2 are alignment errors and they

must be zero to obtain high efficient ICPT system. The primary

and secondary windings resistances (Rp and Rs, respectively)

are given in Eq. (6) and Eq. (7), respectively [8].

Rp ¼ rcuNp2ða1 þ b1Þ

Sp(6)

Rs ¼ rcuNs2ða2 þ b2Þ

Ss(7)

Since the Litz wire is used in windings, the skin effect and

the proximity effect is neglected. The primary and secondary

winding impedances are given in Eq. (8) and Eq. (9) [8].

Lp¼m0

pN2

p

26664a1ln

2a1b1

r1

�a1þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�a21þb2

1

r þb1ln2a1b1

r1

�b1þ


1

r

�2

�a1þb1�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia21þb2

1

q þ0:25ða1þb1Þ

37775:

(8)





Ls¼m0

pN2

s

26664a2ln

2a2b2

r2

�a2þ


2

r þb2ln2a2b2

r2

�b2þ


2

r

�2

�a2þb2�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia22þb2

2

q þ0:25ða2þb2Þ

37775:

(9)

Assuming that the primary and secondary windings are at

the same dimensions and the alignment error is zero (ideal

case), the mutual inductance value is calculated as shown in

Eq. (10).

M ¼ m0

pNsNp

2664a1ln

�a1 þ

� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ a2

1

p � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ b2

1

q �a1 þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ a2

1 þ b21

q h

þ b1ln

�b1 þ

� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ a2

1

p � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ b2

1

q �b1 þ


1 þ b21

q h

� 2

�h�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ a2

1

q

þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ b2

1

qþ


1 þ b21

q 3775

(10)

It can be seen that when Eq. (8), Eq. (9) and Eq. (10) are

analyzed, the primary and secondary impedance and mutual

impedance value calculations change depending on distances

between the windings and the properties of the magnetic

material, numbers of turn of the primary and secondary

windings, windings' cross-sectional area and dimensions of

the windings. Besides, these calculations are independent to

the electrical circuit equations. When the primary and the

secondary windings are considered to be non-aligned and

have different dimensions, mutual inductance value calcula-

tion becomes different as given in Appendices [8].

Fig. 3 e Compensation topologies


Compensation topologies

Disadvantages of the inductive magnetic coupling can be

removed by adding compensation capacitors to both primary

and secondary sides and thus total system efficiency can be

improved [22]. Compensation capacitors are used to increase

the power transfer efficiency and system capacity in ICPT

systems. Compensation capacitors have different effect at

both sides. They help to decrease the input current when they

added to the primary side, while they are used to increase the

power transfer capacity of the ICPT system at secondary side.

There are four basic compensation topologies such as Serial-

eSerial (SS), SerialeParallel (SP), ParalleleParallel (PP) and

ParalleleSerial (PS). These topologies are depicted in Fig. 3 [11].

Each topology has some advantages and disadvantages in

terms of transfer capacity, cost etc. and has different appli-

cation areas according to their specifications.

The secondary side of the Serial compensation has voltage

source specifications, while the secondary side of the Parallel

compensation has current source specifications [18,23]. SS

and SP compensation topologies provide an advantageous

power transfer. Besides, PS and PP topologies can operatewith

larger air gaps for same operation frequency at low power

levels where winding specifications are not an important

parameter [24]. When capacitor requirement of the deter-

mined topology is not considered, parallel compensation to-

pologies bring out the result of operation at lower frequency,

higher current and lower voltage values. This constitutes

higher current requirements at low operating frequency

values [24]. In addition, in case of horizontal axis alignment

errors, the leakage inductance of the primarywindingmust be

higher to minimize the supply side VA ratings [25]. This cri-

terion should not be ignored while the primary side

compensation topology is selected. In the secondary side, the

compensation topology is used to improve the power transfer

capability. The VA rating is completely a function of the ge-

ometry and material properties of the secondary winding.

Thus, VA rating of a certain geometry is obtained as a function

of operating frequency [23]. Optimum topology can be selected

used in ICPT system design.





by analyzing these topologies for specifications of the

application.

ICPT system with SerialeSerial (SS) compensation

The structure of the SS compensation topology is simple.

The primary side capacitor is independent from magnetic

coupling and load [8,26]. Values of the compensation ca-

pacitors and quality factor can be obtained from equations

presented by Wang et al. [8,11]. Secondary side capacitor is

used to operate the system at resonant, thus to obtain

maximum power transfer capacity, while the primary side

capacitor is used to keep the reactive power demand at zero.

The size and volume of the windings in SS topology are

lower than other topologies, and the winding size is not

linear with the transferred power. A general circuit model of

the ICPT system with SS compensation topology is given in

Fig. 4. This circuit can be analyzed in two parts as primary

circuit and secondary circuit. Power is transferred from the

primary side to the secondary side at the desired quality and

the load which is depicted as RL is supplied. In addition, all

parameters and their effects can be obtained by transferring

secondary side components to primary side. Here, Vp is

output voltage of the power converter and input voltage of

the ICPT system [27].

By using Eq. (7) and Eq. (10), Vp can be obtained as given

below:

Vp ¼�Rp þ j

�uLp � 1

uCp

�Ip � juMIs ¼

�Rp þ jXp

�Ip � juMIs

¼ ZpIp � juMIs (11)

where ZS is the impedance of the secondary side circuit and it

can be written as:

Zs ¼ Rs þ RL þ j

�uLs � 1

uCs

(12)

The primary side impedance ZP is obtained as follows:

Zp ¼ Rp þ j

�uLp � 1

uCp

þ Zr (13)

The secondary side impedance Zr transferred to the pri-

mary side can be written as given below:

Zr ¼ u2M2

ZS(14)

By substitution Eq. (14) into Eq. (13), Eq. (15) is obtained:

Fig. 4 e ICPT sys


Zp ¼ Rp þ j

�uLp � 1

uCp

þ u3CsM2

uCsðRs þ RLÞ þ jðu2LsCs � 1Þ (15)

Similarly, by substituting Eq. (12) into Eq. (14), real and

imaginal components of the Zr is obtained as given Eq. (16)

and Eq. (17), respectively:

ReZr ¼ u4C2sM

2RL

ðu2CsLs � 1Þ2 þ ðuCsRLÞ2(16)

ImZr ¼ �u3CsM2ðu2CsLs � 1Þðu2CsLs � 1Þ2 þ ðuCsRLÞ2

(17)

The resistance transferred to the primary side at resonant

frequency can be obtained by using Eq. (18) and Eq. (19):

ReZr0 ¼ ReZrðu¼u0Þ (18)

ReZr0 ¼ uo2M2

RL(19)

The imaginal component of the impedance that trans-

ferred to the primary side should be zero to obtain resonant

mode operation. The input voltageVp can be obtained as given

with Eq. (20) by using above equations:

Vp ¼ ZpIp (20)

Thus, root mean square (rms) value of the input voltage

that should be generated by the power converter is deter-

mined. In addition, the secondary side current IS can be ob-

tained as given in Eq. (21):

Is ¼ juMIpZs

(21)

The load voltage, VL, can be obtained by subtracting resis-

tive and inductive voltages from secondarywinding voltage as

given in Eq. (22):

VL ¼ juMIp ��Rs þ j

�uLs � 1

uCs

�Is (22)

The power value (P) that transferred from primary side to

secondary side is given as below:

P ¼ Re½Zr�I2p (23)

If the system is operating at secondary side resonant fre-

quency, there is not any limit about its power transfer ca-

pacity. Then, the angular resonant frequency, uo, is given in

Eq. (24) [11]:

tem model.




Table 3 e Calculated ICPT system parameters.

Symbol 15 kW system

N1 6

N2 6

S1 (mm2) 38

S2 (mm2) 28

R1 0.0085

R2 0.0073

Rp (ohm) 0.0089

Rs (ohm) 0.0090

L1 (mH) 91.217

L2 (mH) 67.103

M 12.175

k 0.1556

f (kHz) 17.702

C1 (mF) 0.88619

C2 (mF) 1.2046

VLh 133.7968

PLh 14.734

Qp 6.7225

Qs 6.1428

h (efficiency) 0.986


uo ¼ 1ffiffiffiffiffiffiffiffiffiffiLsCs

p ¼ 1ffiffiffiffiffiffiffiffiffiffiLpCp

p (24)

Therefore, the condition that given in Eq. (25) should be

realized to obtained maximum system efficiency [8].

uo[

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiRpðRs þ RLÞ

pM

(25)

When RL ¼ 0, in other words at no load condition, since the

primary current is assumed as constant, the secondary

resistance transferred to the primary side and the power

transfer capacity is to infinity [11]. When the quality factor

equation given in Eq. (3) is rearranged according to the SS

compensation topology, Eq. (26) is obtained [11]:

Qs ¼ uoLsRL

(26)

Design of ICPT system

In this study, 15 kW ICPT system is designed. The method

proposed by Kalwar et al [28]. is used but the windings di-

mensions are kept constant. TheMATLAB code is designed for

this aim, and system parameters are calculated for predefined

design considerations. The initial values in MATLAB code are

used as zero. The geometric specifications of the ICPT system

given in Table 1 are used as input data, and then the

maximum number of turns value which is an important

parameter in terms of desired maximum power and total

system cost is determined. In the MATLAB code, some con-

ditions which are given in Table 2 are used to ensure the al-

gorithm to work properly [8]. All conditions are given in Table

2 are analyzed, and the parameters of the ICPT system which

are valid for all these conditions are calculated and given in

Table 3. While these values are calculated, the transformer is

Table 1 e Dimensions of the ICPT system.

Symbol 15 kW system

h (cm) 20

a1 (cm) 60

a2 (cm) 60

b1 (cm) 100

b2 (cm) 60

c (cm) 0

e (cm) 0

V1 (volt) 150

RL (ohm) 1.215

Table 2 e Defined conditions for the ICPT system.

Parameter Condition

Power PLðN1;N2Þ ¼ PloadVoltage VLðN1;N2Þ ¼ Vload

Frequency fopðN1;N2Þ � fmax

Quality factor QpðN1;N2Þ>QsðN1;N2ÞPrimary winding current d1ðN1;N2Þ � d1maxðN1;N2ÞSecondary winding current d2ðN1;N2Þ � d2maxðN1;N2Þ


considered to operate in ideal conditions and inverter losses

are neglected.

Simulation results

After parameters of the system have been determined, the

ICPT system is modelled with ANSYS-Maxwell according to

the calculated parameters, and co-simulation studies are

performed with electrical circuits such as compensation cir-

cuits and inverter, which are designed with Simplorer. The

ANSYS-Maxwell model of the proposed ICPT system designed

with parameters given in Tables 1 and 3 is depicted in Fig. 5.

Here, the alignment error between windings is assumed as

zero and simulation studies of the system is performed for

20 cm air gap between the primary and the secondary wind-

ing. As it is seen from the figure, while dimensions of the

secondary winding are 60 � 60 cm, dimensions of the primary

winding are 60 � 100 cm for 15 kW ICPT system. The system is

loaded with a 1.215 U resistor and supplied with a AC supply

voltage of 150 V (rms). The ANSYS-Simplorer circuit used in

co-simulation studies is shown in Fig. 6. The ICPT system

designed with ANSYS-Maxwell is linked to the Simplorer cir-

cuit, and thus two models are simulated together, and the

designed ICPT system is tested under conditions closer to real

operation conditions.

The designed ICPT system is supplied with single phase H-

bridge inverter which is operated in resonant via the

compensation circuits connected to the primary and second-

ary windings. The electromagnetic flux distribution and effi-

ciency values obtained from simulation studies are

investigated. The electromagnetic flux distribution for full

load condition is given in Fig. 7. While the flux density is 1 mT

on thewindings, it ismeasured as 0.54mT at the air gap. Since

the air gap between the windings of the proposed wireless

power transfer system is large as 20 cm, the electromagnetic

flux density value is low. In addition, the electromagnetic




Fig. 5 e ANSYS-Maxwell model of the proposed ICPT

system.


coupling coefficient is 0.1556, and therefore this system is

grouped into low magnetic coupled systems. In order to

transfer high power levels, the ICPT system must be operated

at high frequencies. This increases the primary side imped-

ance value and decrease the power factor. This also causes

high VA ratio at inverter side and reduces the power transfer

efficiency. The system efficiency can also be increased by

decreasing the air gap length. However, since the system

designed for battery charger of electrical vehicles, decreasing

air gap length is not a desired situation.

In simulation studies, the resistance, which is representing

the battery, is increased parametrically and the efficiency

variation with the load level is analyzed. Low load, rated load

Fig. 6 e The ANSYS-Simplorer mo


and overload operation conditions are analyzed, and variation

of the efficiency with load level is depicted in Fig. 8. As it is

seen from the figure, maximum efficiency value is obtained as

75.38%. In addition, it is seen that, in overload conditions,

system efficiency decreases quickly. In the past studies higher

and lower efficiency values have been reported (40%e92%)

with different coupling coefficient, air gap and operation fre-

quency values. However, one should consider the distance

between primary and secondary windings which greatly af-

fects the coupling coefficient. Since the coupling coefficient of

the designed ICPT system is 0.2, by considering this value, it

can be said that a high efficiency design is obtained [4,27 and

28].

The designed 15 kW ICPT system is also analyzed with

alignment errors both on width (c) and length (e) of windings

by using ANSYS-Maxwell and Simplorer software. The align-

ment error on width and length of windings are 10 cm and

15 cm respectively. Side and top views of the ANSYS-Maxwell

model of the proposed system with alignment errors are

depicted in Fig. 9. The flux distribution of the ICPT system

obtained from ANSYS-Maxwell while there are alignment er-

rors are shown in Fig. 10. The flux density on windings is

measured as 0.84 mT, while the flux density at the air gap is

measured as 0.36 mT. It is seen that, the flux density of the

analyzed 15 kW ICPT systemdecreaseswhen alignment errors

occur. Thus, it can be easily said that, alignment errors will

affect the system efficiency.

The variation of the efficiency versus load is also investi-

gated for the system with alignment errors. The obtained ef-

ficiency variation curve is shown in Fig. 11. The efficiency

variation of both operation conditions (with and without

alignment errors) are depicted in Figure. It is seen that align-

ment errors cause a significant decrease on the maximum

efficiency value. The maximum efficiency of the system with

alignment errors is obtained as 33.35%. Although alignment

errors do not change the air gap value, which is 20 cm, they

cause a decrease in mutual inductance value and thus a

decrease in efficiency.

The modelled 15 kW ICPT system is also analyzed with

non-uniform air gap with ANSYS-Maxwell and Simplorer

software. The primary and the secondary windings are placed

with 2-degree gradient alignment error. The side and top

views of the windings' placement are depicted in Fig. 12. This

ICPT system is also co-simulated via Simplorer with power

del of the proposed system.




Fig. 7 e Flux distribution on windings.

Fig. 8 e The efficiency versus percentage of the load curve.

Fig. 9 e The 15 kW ICPT system with alignment errors, (a) Side view of windings, (b) Top view of windings.


Please cite this article in press as: Kuzey S, et al., Design and analysis of a wireless power transfer system with alignment errors forelectrical vehicle applications, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.03.160



Fig. 10 e Flux distribution of windings with alignment errors.

Fig. 11 e The efficiency versus load curve of the system with alignment errors.


electronics converter. The flux distribution of the ICPT system

with non-uniform air gap is shown in Fig. 13. The flux density

is measured as 0.1 mT in the air gap that the distance between

the windings is smaller, and it is measured as 0.046 mT in the

air gap that the distance between the windings is larger. The

efficiency variation versus load level of the ICPT system with

2-degree gradient alignment error is given in Fig. 14. The

maximum efficiency is obtained as 46% for this operation

Fig. 12 e 15 kW ICPT system with 2-


condition. Since the parameters are defined for a set of di-

mensions and ideal operation condition, the resonant opera-

tion cannot be achieved and therefore efficiency of the system

decreases. Although the efficiency of the system can be in-

crease by changing the system parameters, but this is not

possible in a practical system. The overload operation condi-

tion also decreases the system efficiency both ideal and non-

ideal operation conditions.

degree gradient alignment error.




Fig. 14 e The efficiency characteristics of the system with gradient alignment error.

Fig. 13 e Flux distribution of the 15 kW ICPT system with 2-degree gradient alignment error.


In Table 4, inductance values obtained for three different

operation conditions are given. As it is seen from Table 4,

values of the primary winding inductance (L1), the secondary

winding inductance (L2) and the mutual inductance (M)

decrease when alignment errors occur. Since compensation

circuit is designed for ideal condition, resonant frequency of

the system is also determined for ideal operation condition.

Therefore, in case of alignment errors, phase difference oc-

curs and VA ratings of the system increases and thus, effi-

ciency of the systemdecreases. If alignment errors are defined

in the MATLAB code and then parameters such as the number

of turns, the diameter of the windings, the operation fre-

quency and capacitor values are calculated, maximum

Table 4 e Inductance values of the 15 kW ICPT system fordifferent operation conditions.

Inductancevalues

Idealcondition

Misalignmentcondition(c ¼ 10 cm,e ¼ 15 cm)

Misalignmentcondition (2-degreegradient alignment

error)

L1 (mH) 91.217 70.01 78.15

L2 (mH) 67.103 49.65 54.60

M (mH) 12.175 9.15 10.72


efficiency for these conditions can be obtained. However, this

is not practical for EV battery charge system.

Conclusions

In this study, design and simulation of the 15 kVA ICPT system

with a large air gap for wireless EV charge system is proposed.

The compensation topology which is an important parameter

in ICPT system design is evaluated and optimal topology is

determined. A MATLAB code is generated to calculate the

system parameters depending on the winding dimensions

and compensation topology, and system parameters are

calculated. According to calculated parameters, the ICPT

system model is generated with ANSYS-Maxwell. The gener-

ated model is linked to ANSYS-Simplorer and co-simulation

studies of both ICPT system model and power converter are

performed. The electromagnetic flux distribution and the

system efficiency are investigated in simulation studies.

Despite the large air gap, the maximum efficiency of the

proposed system for ideal operation conditions is obtained as

75.38%. Some effects such as switching losses, magnetic los-

ses are not considered in MATLAB code, therefore a difference

occurs between two efficiency values obtained from simula-

tion studies and calculated by MATLAB code. In addition,





modeled 15 kVA ICPT system is simulated for different

alignment errors and effect of these errors are analyzed. The

system efficiency is obtained as 33.35% and 46% for alignment

error and 2-degree gradient alignment error conditions,

respectively. Besides, the maximum flux density values in the

air gap is obtained as 0.54 mT for all operation conditions, and

then it is seen that, the magnetic field that human body may

expose is in the limits of international standards.

Appendices

In case of misalignment, mutual inductance value can be

calculated as follows:

M ¼ m0

4pNpNs

2666666666666664

26666666664

d lndþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�tÞ2 þ d2

q

dþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ d2 þ q2

q þ h lngþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ q2 þ g2

q

gþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ g2 þ ð�tÞ2

q þ c ln�cþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ q2 þ c2

q

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q

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ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�tÞ2 þ d2

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ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�tÞ2 þ c2

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d lndþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�pÞ2 þ d2

q

dþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ d2 þ e2

p þ g lnhþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ e2 þ g2

q

gþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ h2 þ ð�pÞ2

q þ c ln�cþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ e2 þ c2

p�cþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ c2 þ ð�pÞ2

q þ

m ln�mþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�pÞ2 þm2

q

�mþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þm2 þ e2

p þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ e2 þ d2

p�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ e2 þ g2

q�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ e2 þm2

pþ


pþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�pÞ2 þ g2

q�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�pÞ2 þ d2

qþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�pÞ2 þm2

q�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�pÞ2 þ c2

q

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þ

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t lntþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�gÞ2 þ t2

q

tþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ t2 þ c2

p þ p lnpþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ p2 þ c2

q

pþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�gÞ2 þ p2

q þ e ln�eþ


p�eþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ e2 þ ð�gÞ2

q þ q ln�qþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�gÞ2 þ q2

q

�qþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ c2 þ q2

q þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ c2 þ t2

p�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ c2 þ p2

q�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ c2 þ q2

qþ


pþ

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q�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�gÞ2 þ t2

qþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�gÞ2 þ q2

q�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�gÞ2 þ e2

q

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2666666664

t lntþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�dÞ2 þ t2

q

tþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ t2 þm2

p þ p lnpþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þm2 þ p2

q

pþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�dÞ2 þ p2

q þ e ln�eþ


p�eþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ e2 þ ð�dÞ2

q þ q ln�qþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�dÞ2 þ q2

q

�qþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þm2 þ q2

q þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þm2 þ t2

p�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þm2 þ p2

q�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þm2 þ q2

qþ


pþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�dÞ2 þ p2

q�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�dÞ2 þ t2

qþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�dÞ2 þ q2

q�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ ð�dÞ2 þ e2

q

3777777775

3777777777777775

where

d ¼ a1 � a2 � c

m ¼ a2 þ c

q ¼ b2 þ e

g ¼ a1 � c


p ¼ b1 � e

t ¼ b1 � b2 � e:

r e f e r e n c e s

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