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Theoretical analysis of the efficiency of a V2G

wireless charger for Electric Vehicles
Alicia Triviño, Jose M. Gonzalez-Gonzalez, and Jose A. Aguado

Abstract—V2G (Vehicle-to-grid) technology will report im-
portant benefits for the operation and safety of the grid. In
order to facilitate the expansion of the V2G technology in a
future, it is recommended to offer the drivers with easy to
use methods to charge and discharge their EV batteries. In
this sense, wireless chargers are expected to play a relevant
role in the future electrical networks as it reduces the users’
intervention. The development of this kind of system is still open
to improve them in terms of their operation, their compliance
and their control. An important issue for the evaluation of
these systems is the efficiency, which measures the power losses
occurring in the system. This paper addresses a deep study about
the losses in a bidirectional wireless charger. Then, it provides
with a mathematical model to characterize them. This model is
validated by means of experimental results conducted in a 3.7-
kW prototype.

Index Terms—V2G, wireless charge, wireless discharge, losses,
efficiency, electric vehicle, inductively-coupled power system,
ICPT, bidirectional.

I. INTRODUCTION

E
LECTRIC vehicles (EV) represent a clear eco-friendly

mobility solution. Firstly, it is able reduce CO2 emissions

[1–3]. On the other hand, it also helps for the integration

of renewable energy sources [3, 4]. Despite these potential

benefits, the proliferation of electric vehicles must be carefully

controlled as a big number of them stands out for a consider-

able aggregated load to the grid. Market-driven solutions [5]

aims at prompting the charge of the vehicles in those times

when it is more convenient for the grid, avoiding the periods

with a high demand too [6].

In a V2G context, the vehicles operate in an active discharge

mode that needs to be also controlled [6]. Specifically, when

recommended, the vehicles could decide to deliver energy

to the grid from their batteries. If correctly coordinated, this

operation leads to important advantages for the grid.

In order to promote the controlled charge and discharge

modes and to obtain important advantages, it is highly recom-

mended to reduce the user’s intervention. This can be achieved

with wireless chargers for Electric Vehicles (EV) [7].

Wireless power transfer technology can be realized by

different techniques. By now, the most popular one is the

one based on a pair of loosely coupled coils operating under

resonant conditions. This is known as Inductively Coupled

Power Transfer or ICPT [7]. In this technique, one coil is

placed in the pavement (named the primary side) and the

other in the chassis (known as the pickup or secondary side).

A. Triviño, J. M. Gonzalez-Gonzalez and J. A. Aguado are with the
Electrical Engineering Department, Universidad de Málaga, Málaga, Spain
(e-mail: atc@uma.es).

The current through the primary coil induces a voltage in

the secondary coil, which is used to charge the battery. The

magnetic field involved in this charger is ranged in the 20

kHz - 100 kHz interval [8]. To generate this high-frequency

sinusoidal current, power converters need to be included in the

charger.

The non-idealities of the switches of the power converters

and the parasitic resistances of the reactive components are

responsible for the losses in the whole system, which degrades

the charger efficiency. This paper addresses the proposal and

verification of a model to characterize the efficiency of a

bidirectional wireless charger. The main contribution of our

work are the following ones:

• In contrast to [9, 10], our work is focused on a bidi-

rectional wireless charger operating at 85 kHz and 3.7

kW. The change in the frequency and on the power

requires the use of specific semiconductors. In particular,

SiC MOSFETs are used [11, 12]. The particularities of

these devices need to be considered for the model as

they clearly affect in the losses of the system and in the

efficiency.

• It extends the work in [13] by focusing on the efficiency

and adding a comprehensive analysis of the experimental

results, which is the basis for the computation of this

parameter in a prototype.

The rest of the paper is structured as follows. Section

II reviews some related works about the study of losses in

wireless chargers basing on ICPT technology. Section III

presents the ICPT wireless charger topology used in this

work. The theoretical model to compute the efficiency and

the losses is presented in Section IV. Section V evaluates

the methods basing on the real measurements performed in

a 3.7-kW prototype. Finally, Section VI describes the main

conclusions of this work.

II. RELATED WORK

The losses of an EV wireless charger are mainly due to

the semiconductors employed in the power converters and the

parasitic resistance of the real reactive elements.

Ideal semiconductors in the power converters are operated

in such a way that no losses result. However, the real behavior

leads to conductive and switching losses for these elements.

Conductive losses are produced because of the difference of

the element from an ideal switch. To understand the losses

by this event, we can rely on semiconductors models, which

represent the device as an equivalent circuit with parasitic

components such as resistances or capacitors. Conductive

TRANSACTIONS ON ENVIRONMENT AND ELECTRICAL ENGINEERING ISSN 2450-5730 Vol 3, No 1 (2018) 
© Alicia Trivino, Jose M. Gonzalez-Gonzalez, and Jose A. Aguado


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losses occur because of the resistances. When the current

flows through the resistances, losses occur. On the other

hand, the capacitors prevents the semiconductors from having

instantaneous commutations, which implies switching losses.

As for the reactive components, the conductive losses are

due to the resistance offered by the cables on which they are

built. An equivalent model for these elements adds a series

resistance to the reactive component. It is known as the ESR

(Equivalent Series Resistance) and its value greatly depends

on the material of the reactive components. For instance, Litz

wire minimizes the skin effect and, in turn, the ESR [14].

The work in [9] makes a deep theoretical study about the

switching losses of a wireless charger. The impact of them

depends on the fact whether they are hard or soft. A similar

study but in a low-power application is proposed in [10].

The prototype under evaluation uses a different power transfer

technique working at 6.78 MHz and transferring 2 W.

The work in [15] presents the model for the computation of

the switching losses for MOSFET in a unidirectional wireless

charger. However, they do not rely on the equivalent model

and they employ the parameters observed in the experimental

results to derive this type of loss. The use of the parasitic

capacitors, as we do in the present work, eases the estimation

of the losses before the prototype is built.

Our present work uses the model presented in [9] to derive

the efficiency of an EV bidirectional wireless charger. It

represents an extension to the study presented in [13] as it

makes a deep analysis of the experimental results.

III. ICPT WIRELESS CHARGER FOR EV

In this work, we will focus on ICPT technology for charging

and discharging the battery of an EV. The generic scheme of

a unidirectional wireless charger is represented in Figure 1.

Fig. 1. Structure of a unidirectional wireless charger.

The charger is connected to the grid, whose alternating

current has a frequency of 50 Hz or 60 Hz depending on the

region. Nevertheless, these frequency values are not enough

to transfer power inductively. Consequently, it is necessary

to convert this current to high frequency current, using power

electronics for that. Firstly, the alternating current is converted

to direct current using a rectifier. Both single-phase and three-

phase rectifiers can be used. Despite its higher cost, the three

phase rectifier has some advantages as for example lower

losses, lower ripple factor and higher transformer utilization

factor. The direct current is necessary to obtain high frequency

current using an inverter. The generated high frequency current

flows through the primary coil, creating a magnetic field which

mainly depends on the coil structures. The magnetic field

created by the primary coil induces an alternating voltage in

the secondary coil, which is rectified again to provide Direct

Current, which is appropriate for the battery. Additionally, a

compensation system composed of capacitors is introduced on

both sides to enable the operation under resonant conditions.

When implementing a bidirectional wireless charger, the

power flow must be also allowed from the battery to the grid.

As a consequence, the power converters should have a dual

behavior to cope with the two senses of the power flows. This

modification can be observed in Figure 2.

Fig. 2. Structure of a bidirectional wireless charger.

In order to allow the power flow in both senses, the primary

inverter has to be capable to work also as a rectifier, while

the rectifiers have to perform the functions of an inverter.

This issue is solved using bidirectional AC/DC converters. As

in the unidirectional wireless charger, the connection to the

grid can be done through both a single-phase and three-phase

converter. The three-phase converter has benefits to the single-

phase converter because using three phases allows to convert

the same power with less current per phase, thereby reducing

the losses on the components of the converter.

IV. THEORETICAL MODEL FOR THE EFFICIENCY

The efficiency (η) of a wireless charger measures the rela-

tionship between the real power delivered to the load (Pload)

and the real power generated by the source (Psource). So that:

η =
Pload

Psource
(1)

At resonant operation and with ideal components, all the

power generated by the source is delivered to the battery,

that is η equals 1. However, due to conduction and switching

losses (Lcond and Lsw respectively), this parameter decreases

as follows:

η =
Psource − Lcond − Lsw

Psource
(2)

where the calculation of Lcond and Lsw is presented in the

following subsection.

Despite having similar structures in both sides, wireless

chargers can use different components in the primary and

the secondary sides. One important component of the charger


3

I1

C1

RL1

L1

C2

I2

L2

RL2

M

CoilsPrimary Side Secondary Side

DC-Link Battery

Fig. 3. Topology of the analyzed bidirectional wireless charger.

which can differ are the coils because having a bigger coil

on the primary side can help with misalignments. Different

coils also require different compensation systems. Due to this

asymmetrical structure of the bidirectional wireless charger, it

is necessary to define two efficiencies, one for each sense of

the power flow. Thus, we have ηch to characterize the power

flow from the grid to the battery and ηdis to define the charger

performance in the opposite sense. We can reformulate Eq. 2

as:

ηch =
Pgrid − L

ch
cond − L

ch
sw

Pgrid
(3)

and

ηdis =
Pgrid − L

dis
cond − L

dis
switch

Pgrid
(4)

where Pgrid represents the real power generated by the grid

and Pbat is the real power delivered by the EV battery.

In the next subsections, we formulate the equations to

estimate both efficiencies for the bidirectional wireless charger

topology presented in Fig. 3.

A. Charge mode

In this operation mode, the DC/AC power converter in

the primary side acts an inverter whereas the AC/DC power

converter in the pickup is a rectifier. The conduction losses

are:

Lchcond = L
ch
con,inv + L

ch
con,rec + L

ch
coils + L

ch
match (5)

where Lchcon,inv are the conductions losses of the inverter,

Lchcon,rec are the conductions losses of the rectifier, L
ch
coils

are the losses in the coils and Lchmatch are the losses in the

compensation system. The superscript ch indicates that these

values correspond to the charging mode.

In order to simplify the control, a full-bridge topology with a

phase-shift control of a duty cycle equal to 50% is employed.

In this scheme, there is only one transistor in each leg in

conduction. Thus, the conduction losses of the inverter are:

Lchcon,inv = 2 · Rds · Î
2

1
(6)

being Î1 the rms (root-mean squared) current in the primary

side and Rds the internal resistance drain-source of the MOS-

FET in the inverter.

For the conduction losses of the rectifier, we also rely on the

equivalent model of the diodes. In a full-bridge rectifier, two

diodes are simultaneously conducting, both of them provoking

some losses as:

Lchcon,rec = 2 · Rd · Î
2

rec + 2 · Vth · Îrec (7)

where Rd represents the internal resistance of the diodes, Vth

their forward voltage and Îrec the rms value of the current

traversing these elements. In a series-series compensation

topology as we are using in this work, Irec equals I2, that

is, the secondary current.

The coils and the matching networks also incur in conduc-

tion losses to the system due to their parasitic resistances.

Specifically, the losses of the coils are estimated as:

Lcoils = RL1 · Î
2

1
+ RL2 · Î

2

2
(8)

where RL1 and RL2 are the resistances associated to the

primary and secondary coil respectively.

The currents injected to the coils are the same as those in

the capacitors as a series-series compensation network is used.

Thus, the conduction losses in the matching networks are:

Lmatch = RC1 · Î
2

1
+ RC2 · Î

2

2
(9)

where RC1 and RC2 are the resistances associated to the

primary and secondary capacitors respectively


4

Concerning the switching losses, they are due to the inverter.

Theoretically, these losses can be estimated by the addition of

multiple terms, being the one due to the output capacitance

(Coss) the most relevant (LCoss). Thus, we simplify as:

Lchsw
∼= LCoss =

1

2
fsCossV

2

ds (10)

being fs the switching frequency and Vds the voltage between

the drain and the source.

B. Discharge mode

In the discharge mode, the power flow from the battery to

the grid. Making use of the dual behavior of the power con-

verters, in this operation mode, the power converter attached

to the battery acts as an inverter while the power converter in

the primary side works as a rectifier.

In this way, the conduction losses can be expressed as:

Ldiscond = L
dis
con,inv + L

dis
con,rec + L

dis
coils + L

dis
match (11)

where the superscript ch indicates these values correspond to

the discharging mode.

Although the conduction losses of the coils (Lcoils) and the

compensation system (Lmatch) can be calculated following

the same equations of the charging mode (Eq. 8 and 9), the

conduction losses of the inverter and the rectifier differ in the

current values because in this mode they are working on the

secondary and the primary side respectively. Theses losses can

be computed as:

Ldiscon,inv = 2 · Rds · Î
2

2
(12)

Ldiscon,rec = 2 · Rd · Î
2

1
+ 2 · Vth · Î1 (13)

Finally, the switching losses are estimated following the

same equation of the charging mode (Eq. 10).

V. VALIDATION OF THE MODEL: EXPERIMENTAL RESULTS

The developed theoretical model is verified with a 3.7-kW

bidirectional prototype based on ICPT technology. The coils

are both square but with different sizes. The compensation net-

works are uniresonant and in series with the coils. As for the

magnetic field, it is generated at 85 kHz as recommended by

SAE TIR J2954 [16]. CREE C2M0080120D SiC MOSFETs

are the components of the power converters as they support

the power demanded and the switching frequency. The main

properties of the charger, including the values related to the

non-idealities of the components, are summarized in Table I.

Firstly, we derive the theoretical results for the losses

and the efficiencies considering the model presented in the

previous Section. These results are exposed in Table II.

The resistance of the coils has the highest impact in the

efficiency of the system. The rest of the components of

the system have similar losses with the exception of the

switching losses of the inverter which, thanks to the use of SiC

MOSFETs, are negligible. Due to security reasons with the

operation of the battery, the power transferred in the discharge

mode has been reduced.

TABLE I
PARAMETERS OF THE ICPT SYSTEM.

Charger specifications
TX-RX parameters

(prototype values)

Output 3.7 kW
300V

L1[mH] 240.5

fs [kHz] 85 L2[mH] 230.6

Coils geometry C1[nF ] 14.3

Primary coil

[m2]
0.75 x 0.75 C2[nF ] 15.6

Secondary

coil [m2]
0.5 x 0.5 RL1 [mΩ] 196

C2M0080120D MOSFET RL2 [mΩ] 143

Rd[mΩ] 40 RC1 [mΩ] 67

Vth[V ] 0.98 RC2 [mΩ] 52

Coss[pF ] 80 M[mH] 54.5

Rds[mΩ] 80
k =

M(L1L2)
1/2 0.231

TABLE II
COMPUTED LOSSES.

Charge mode Discharge mode

Lcon,inv[W ] 25 Lcon,inv[W ] 3.3

Lsw,inv[W ] 1 Lsw,inv[W ] 1

Lcon,rec[W ] 34 Lcon,rec[W ] 15

Lcoils[W ] 64 Lcoils[W ] 11

Lmatch[W ] 23 Lmatch[W ] 4

To validate the computed results, the losses are also carried

out by obtaining the real power which flows for each compo-

nent of the system. To get these values is necessary to analyze

the oscilloscope captures both at the input and at the output of

the components, with which the current and voltage are taken

into account. Figure 4 shows an oscilloscope capture of the

current and the voltage measure at the output of the primary

DC/AC converter in charge mode. As can be observed, voltage

measurement consists on a square signal which can be used

to computed the real power assuming a fundamental harmonic

approximation. The difference between input and output real

power of each component corresponds to the losses.

The measurements of the electrical signals in the prototype

leads to the values exposed in Table III.

The following subsections presents the calculation methods

to obtain the results from the experimental measurements.

Using these equations and the measures of Table III, the

prototype losses has been computed to validate the model.

These losses are shown in Table IV.

As can be observed, the use of the model based on the

nonidealities leads to higher losses estimation in comparison

with those derived from the analysis of the waveforms. In

particular, for the charge mode, the inverter is assumed to loss

26 W whereas the waveform analysis states that these losses


5

Fig. 4. Voltage (channel 1) and current (channel 2) measurements at the
output of the primary DC/AC converter.

TABLE III
ELECTRICAL SIGNALS MEASURED IN THE PROTOTYPE.

Electrical signals Charge mode Discharge mode

Vinvinput [V ] 288 298

Vinvoutput [V ] 290 293

Iinvinput [A] 12.56 4.56

Vinvinput [A] 13.78 5.14

Vrecinput [V ] 285 247

Vrecoutput [V ] 288 250

Irecinput [A] 13.74 6.02

Irecoutput [A] 12.16 5.30

are 20 W. Concerning the rectifier operation, this difference is

11 W. For the discharge mode, there are also some deviations.

Specifically, the difference in the inverter is 1.3 W whereas

the rectifier is associated to a deviation equals to 1 W. Taking

into account the total values, the differences are significant.

This is due to the errors in the measurements, which impact

on both the waveform analysis and on the model based on the

nonidealities.

A. Charge mode

Concerning the output of the primary inverter, the voltage is

a square-wave of Vinvoutput amplitude while the current is in-

phase and sinusoidal (with a peak value equals to Iinvoutput ).

The shape and phase of the output current is the consequence

of forcing the system to operate under resonant conditions.

For the active power, we must extract the peak value of the

fundamental harmonic of the voltage signal (V 1invoutput ) and

operate as follows:

P chinvoutput =
V 1invoutput · Iinvoutput

2
=

4 · Vinvoutput · Iinvoutput

π ·
√
2

(14)

Thus, the losses in the primary inverter (Lchinv) are:

Lchinv = P
ch
invinput

− P chinvoutput (15)

TABLE IV
LOSSES COMPUTED FROM THE ELECTRICAL SIGNALS MEASURED IN THE

PROTOTYPE.

Charge mode Discharge mode

Lchinv[W ] 20 L
dis
inv[W ] 3

Lcoils + Lmatch[W ] 73 Lcoils + Lmatch[W ] 17

Lchrec[W ] 23 L
dis
rec[W ] 14

The rectifier input consists of a square-wave voltage (with

a peak value of Vrecinput ) and a sinusoidal current wave with

a peak value equal to Irecinput . Applying the decomposition

of harmonics, we can state that:

P chrecinput =
4 · Vrecinput · Irecinput

π ·
√
2

(16)

The output of the rectifier in conjunction of the low-pass

filter results in two constant signals for voltage and current.

The voltage equals to Vrecoutput while the current is Irecoutput .

This lead to an output power computed as follows:

P chrecoutput = Vrecoutput · Irecoutput (17)

Consequently, the losses in the controlled rectifier (Lchrec)

are:

Lchrec = P
ch
recinput

− P chrecoutput (18)

B. Discharge mode

In the discharge mode, the battery of the EV provides

energy to the grid so that the power flow is reverse to the

previous mode. This means that the power converter attached

to the battery acts as an inverter while the power converter in

the primary side works as a rectifier. The waveforms of the

converters change according to their new functionality but it

follows a form equivalent to the previous case. Thus, these are

the losses that are defined in a different way in comparison

with the afore mentioned definitions. Alternatively, Lcon,inv,

Lsw,inv, Lcon,rec, Lcoils and Lmatch can be computed as

previously. In the discharge mode, for the inverter attached

to the battery:

P disinvoutput =
V 1invoutput · Iinvoutput

2
=

4 · Vinvoutput · Iinvoutput

π ·
√
2

(19)

P disinvinput = Vinvinput · Iinvinput (20)

On the other hand, the losses in the primary inverter (Ldisinv)

are:

Ldisinv = P
dis
invinput

− P disinvoutput (21)

The rectifier input, which is now in the primary side,

corresponds with a square-wave voltage (with a peak value

of Vrecinput ) and a sinusoidal current wave with a peak value

equal to Irecinput . Applying the decomposition of harmonics,

we can assure that:


6

P disrecinput =
4 · Vrecinput · Irecinput

π ·
√
2

(22)

The output of the rectifier is now connected to the grid.

The voltage equals to Vrecoutput while the current is Irecoutput .

Both signals are constant as a low-pass filter is used. This

implies that the output power is computed as follows:

P disrecoutput = Vrecoutput · Irecoutput (23)

As a consequence, the losses in the controlled rectifier for

the discharge mode (Ldisrec) are:

Ldisrec = P
dis
recinput

− P disrecoutput (24)

VI. CONCLUSION

This paper presents a model for the estimation of the charge

and discharge efficiency in a bidirectional ICPT wireless

charger for EV. Specifically, the model relies on the equivalent

circuit of the semiconductors and of the reactive components to

derive the conduction and the switching losses of the system.

The model is contrasted with the experimental results obtained

in a 3.7 kW wireless charger at 85 kHz. There exist some

differences among them, which are assumed to be due to

measurement errors.

As future work, we intend to model the switching losses

when the resonant conditions do not hold because of mis-

alignments between the two coils.

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