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Transactions on Power Electronics
1
Constant Current/Voltage Charging Operation
for Series-Series and Series-Parallel
Compensated Wireless Power Transfer Systems
Employing Primary-Side Controller
Kai Song, Member, IEEE, Zhenjie Li, Jinhai Jiang, and Chunbo Zhu, Member, IEEE
Abstract--This paper proposes a new control technique,
which only employs the primary-side controller and load
identification approach to adjust charging voltage/current
for series-series (SS) and series-parallel (SP) compensated
wireless power transfer (WPT) systems. The advantages
are that dual-side wireless communication for real-time
charging current/voltage adjustment is avoided as well as
it is suitable for different charging modes, e.g. constant
voltage (CV) and constant current (CC) charging defined
by the battery charging profile. The load identification
approach, which utilizes reflected impedance theory and
quadrature transformation algorithm for calculating the
active power, is proposed to estimate the equivalent load
resistance of battery. Then, the CV/CC charging for both
SS and SP compensation are achieved by the PI controlled
phase shift H-bridge inverter. The simulation and
experimental results validate the feasibility of proposed
control method. During the CC charging, the 3.01A and
3.03 A for SS and SP compensation with the error of 1.2%
and 1.4% are achieved. During the CV charging, the 25.8
V and 25.7 V for SS and SP compensation with the error of
1.1% and 1.3% are realized. The proposed method
improves the performance of both SS and SP compensated
WPT systems to be more suitable for the applications that
require compact and light weight receiver.
I. INTRODUCTION
ireless power transfer (WPT) systems employing the
alternating magnetic field to transfer power have been
used for charging electric vehicle (EV), portable electronics
and implantable biomedical devices [1]-[3]. Contrasts to the
traditional plug-in charging systems, the WPT systems achieve
the advantages of electrical and mechanical isolation, safe
operation in harsh environment, and fully automatic charging.
The researches in this field mainly focus on compensation
topologies, power electronics converters and control schemes
[4]-[6]. For practical applications, the electronic devices are
powered by high-performance lithium-ion battery that requires
CC/CV charging to meet its charging profile. As shown in Fig.
1, the CC charging is used to charge the battery at the
beginning, then battery voltage increases. When the battery
voltage rises to voltage Ub, the CC charging switches to CV
charging immediately, then charging current decreases. When
charging current is lower than one-tenth of the preset charging
current, the charging process is over [7]. During the CC/CV
charging process, the equivalent load resistance Ro, which is
defined as the ratio of charging voltage to charging current,
varies with the charging time [8]. Further, the variation of Ro
influences charging current/voltage and system efficiency, then
the research on closed-loop control scheme is vital to achieve
accurate and robust control of the WPT systems [9].
W
Index Terms—Constant current/voltage charging,
series-series and series-parallel compensation, load
identification, phase shift control, wireless power transfer.
Manuscript received June 6, 2017; revised September 15, 2017; accepted
October 23, 2017. Date of publication X, X; date of current version X, X.
This work was supported by the National Natural Science Foundation of
China under Project 51677032 and 51577034. Natural Science Foundation
of Heilongjiang Province No. E2017045. Harbin Science and Technology
Innovation Talents Special Fund Project under Grant No.2016RAQXJ002
and No. 2016FX2GJ013. Recommended for publication by Associate Editor
XXX. (Corresponding author: Zhenjie Li)
The authors are with the school of electrical engineering & automation,
Harbin Institute of Technology, Harbin, 150001, China (email:
[email protected];
[email protected];
[email protected];
[email protected]).
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TPEL.2017.XXXXXX
Fig. 1. Typical CC/CV charging profile of the Li-ion battery
Based on the literature review [10]-[15], it points out that
through properly designing the compensation topology, the
approximate CC/CV charging can be achieved without
closed-loop control schemes. However, it also shows that the
control accuracy and stability are limited, which will be
analyzed in-depth in section II. D. In practice, the basic
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Transactions on Power Electronics
2
compensation topologies are categorized into four types,
which are labeled as SS, SP, PS and PP, where the first S or P
stands for primary-side series or parallel compensation and
second S or P stands for secondary-side series or parallel
compensation. In [10], it shows that when primary-side
resonant current is maintained constant, the secondary-side
series compensation performs as a voltage source, while the
parallel compensation acts as a current source. Hence, the SS
and SP compensation provide a possibility to realize CC and
CV charging for the variable load through adjusting the
primary-side resonant current. In [11]-[13], it points that both
SS and SP compensation achieve CC/CV charging by
choosing suitable system operating frequency. However, with
considering both system efficiency and Zero Voltage
Switching (ZVS) of H-bridge inverter, the conditions for
CC/CV charging are always invalidated as analyzed in Section
II. D. In [14]-[15], through designing the hybrid compensation
on either primary or secondary side, the battery CC/CV
charging is achieved. However, this method requires additional
switches, inductors and capacitors, which leads to the problem
of component and control complexity. In addition, the system
parameters need to be properly optimized to meet CC/CV
charging. Therefore, the closed-loop control method is still
essential and deserved to be analyzed.
Generally, the closed-loop control methods in the WPT
system are classified as primary-side and secondary-side
control [16]-[17]. Due to the secondary-side control methods
require additional circuits (such as Buck and Boost converter)
on the receiver, it may violate the compact and light weight
requirements for smart phone, unmanned aerial vehicle (UAV)
and implantable devices. Therefore, the primary-side control
methods are fully considered in this paper. The traditional
primary-side control methods mainly consists of three groups,
named as dc-dc converter, variable frequency/phase shift Hbridge inverter and impedance matching network [18]-[20].
The dc-dc conversion requires Buck/Boost converter, which
may influence the system efficiency and increase additional
weight/cost [18]. Frequency adjusting results in the decrease of
power transfer capability when system operating frequency
deviates too much from the optimal frequency [19]. In addition,
the available frequency ranges are regulated by the Industrial
Scientific Medical (ISM) of ITU Radio Communication Sector,
J2954 of society of automotive engineers (SAE) and Qi
standard of wireless power consortium (WPC). The impedance
matching that needs bulky capacitors or inductors array add
additional weight, size and control complexity of the system
[20]. Finally, although phase shift H-bridge inverter avoids the
above disadvantages, the dual-side wireless communication is
required to adjust the charging current/voltage that has the
disadvantages of system instability and failure, when wireless
communication is disturbed [21]-[22].
For primary-side control method without dual-side wireless
communication, the primary-side power frequency droop
control concept is proposed to regulate the output power [23].
In [24], it shows that the power flows to secondary side can be
regulated by the transmitter-side electrical information. In [25],
a systematic approach that analyzes the output power control
of a wireless charging system without direct measuring load
information is presented and verified with the designed eight
coil resonators. Those methods mainly focus on the power
flow regulation and no further analysis about CC/CV charging
for battery charging. In [26], a single primary-side controller
based on LCL-P compensation and phase shift H-bridge
inverter are proposed to achieve CV charging for the variable
load. The inadequacy of this method is that only CV charging
is realized for resistive load and conditions for CC charging
required by battery is not considered. Then, the primary-side
control method that realizes CC/CV charging for battery is
analyzed, which is the main contribution of this paper.
It is straightforward to deduce that if charging current Io or
charging voltage Uo is regulated by primary-side control
method, the corresponding charging voltage (Uo= IoRo) or
charging current (Io=Uo/Ro) may also be adjusted by estimating
the equivalent load resistance Ro. In WPT systems, the
commonly used load identification approaches are based on
the impedance analysis and power conservation principle [27],
the usage of energy injection mode and free resonant mode
[28], the current characteristics under ZVS condition of a
current-fed WPT system [29], the additional capacitor to make
the system to work in two operating mode [30], and the input
power measurement on the primary side [31]. Among the
above methods, the method proposed in [31] is suitable for
general load identification, and load resistance is estimated by
detecting the primary-side input power, which is a simple and
intuitive method. In this paper, the load identification approach,
which is achieved by measuring the resonant current and
voltage of primary-side coil, is proposed to estimate the Ro.
The main motivation of this paper is to propose a novel
primary-side controller that realize CC/CV charging for both
SS and SP compensation through the PI controlled phase shift
H-bridge inverter and load identification approach. The
advantage is that dual-side wireless communication link for
adjusting Io and Uo is avoided, then the stability and
simplification of the system is ensured. In practice, depending
on system requirements, the essential dual-side wireless
communication signals, which can be realized by Zigbee, WiFi
and Bluetooth, may still be reserved for system startup, shutoff
and monitoring the SOC of battery. The rest of the sections are
organized as follows: Section II gives the system structure and
basic theoretical analysis. Section III proposes the load
identification approach and verifies CC/CV charging for both
SS and SP compensation. Section IV analyzes the closed-loop
PI control scheme with simulations. Section V validates the
proposed method with experiments. Finally, last section
summarizes the conclusions drawn from the investigation.
II. SYSTEM STRUCTURE AND THEORETICAL ANALYSIS
In this section, the system structure and methodology for
analyzing the WPT system are discussed. Then, basic output
characteristics for both SS and SP compensation are analyzed
to propose the primary-side control method.
A. System structure
The WPT system consists of two insulated parts named as
primary side and secondary side, as depicted in Fig. 2.
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Transactions on Power Electronics
3
Fig. 2. Structure diagram of the designed WPT system.
On the primary side, the designed controller is employed to
estimate the equivalent load resistance of battery and achieve
CC/CV charging. The PI controlled phase shift H-bride
inverter, which is a voltage source type inverter (VSI) and
widely used in WPT systems due to their simplicity and
effectiveness, is adopted to convert the dc voltage to ac
voltage for the magnetic coupler. The primary-side series
compensation is used to reduce volt-ampere rating, improve
system efficiency and help achieve soft switching for the Metal
Oxide Semiconductor Field Effect Transistor (MOSFET) [32].
Through the magnetic coupler, the alternating magnetic field
energy is transferred from primary side to secondary side. On
the secondary side, combined with suitable compensation, full
bridge rectifier and filter, the obtained ac voltage is converted
to dc voltage. Then, the CC/CV charging is realized by the
proposed primary-side controller. In Fig. 2, the abbreviation of
SSC and SPC indicates secondary-side series compensation
and secondary-side parallel compensation, respectively. As
usual, the selection of system operating frequency is a balance
and overall consideration between system performance (such
as system efficiency, power losses and thermal loss) and the
selection of Litz wire, power electronic elements, magnetic
coupler size and so on [33]. Therefore, with considering the
system performance and commonly used experimental setup in
the lab, the system operating frequency of 85.5 kHz is used to
perform the theoretical analysis and verify the feasibility of
proposed control method that is intend to be applied to the EV
wireless charging. Further, it should be noted that the proposed
method is suitable for other system operating frequency
according to different applications and requirements.
B. Secondary-side Rectifier and Filter Model
Note that, based on different secondary-side compensation
topology, the output filter is also different. As shown in Fig. 2,
the full-bridge rectifier connected with a capacitive output
filter (Co) is used for SS compensation. The input voltage and
current of the rectifier are square and sine wave, respectively.
In practice, only the fundamental component of voltage and
current is considered for simplicity during the analysis of WPT
system. Then, the charging current Io is expressed as
2I
1 
(1)
I o   I 2 sin t dt  2
 0

where, I2 is the amplitude of secondary-side resonant current.
Since the battery charging process is slow and charging
voltage is dc voltage, the battery can be modeled as a resistor
Ro in WPT system [9]. However, it is noted that Ro has no
relation with the battery internal resistance that decreases with
the increase of battery’s state of charge (SOC). Assuming that
the rectifier power losses are ignored in the following
derivation, the power balance equation is given by
2
 I2 
2
(2)
I
R

 o  o   Re
 2
where, Ro is the equivalent load resistance of battery and Re is
the equivalent input resistance of the rectifier. From (1) and
(2), the Re and input current Ie of the rectifier are deduced as
Re =
8
2

Ro
(3)
(4)
Io
2 2
When the rectifier that is connected with an inductive and
capacitive output filter (LoCo) is applied for SP compensation,
input voltage and current of the rectifier are sine and square
wave, respectively. The Re and Ie of the rectifier are given by
Ie =
Re =
Ie =
2
8
Ro
2 2

Io
(5)
(6)
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Transactions on Power Electronics
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C. Mutual Inductance Model
As shown in Fig. 3, the Us is the equivalent output voltage
of H-bridge inverter. The Ri, Li, Ci and Ii (i=1, 2) are resistance,
inductance, compensation capacitor and resonant current of
primary and secondary side, respectively. The M is mutual
inductance. The U1 is induced voltage of L1. The Zp is
impendence seen after the primary-side capacitor C1.
Fig. 4. The PWM signals and output waveform of the phase shift H-bridge
inverter.
(a)
(b)
Fig. 3. Mutual inductance model. (a) SS compensation and (b) SP
compensation.
According to the Kirchhoff’s voltage law (KVL), the
following equations are deduced as
 
j M   I1  U 
 Zp
(7)
 j M
    s
Z


s 

0
I2   
where, the primary and secondary side impedance of both SS
and SP compensation are expressed as
SS : Z p  R1  j L1  1 jC1 Z s  R2  Re  j L2  1 jC2
SP : Z p  R1  j L1  1 jC1 Z s  R2  j L2  Re 1+jC2 Re 
(8)
From (7) and (8), the resonant currents of primary and
secondary side are given by
Zs

Us
2
 I1 
 M   Z p Z s

(9)

 M 
I  1
U
 2 j  M 2  Z Z s
p
s

It shows that the variation of Ro influences I1, and then the
active power P1 transferred to the battery changes, which
indicates Ro has relationship with P1. Through calculating P1,
it is possible to estimate Ro indirectly. The relationship
between I1 and Io or Uo are deduced by (3), (5) and (9), which
indicates Io or Uo can be regulated by adjusting I1 even without
knowing Ro. Further, when Ro is estimated, the Uo=RoIo or
Io=Uo/Ro can also be regulated accordingly. It is noted that I1
and P1 are measureable/computable variable on the primary
side, which just satisfies the proposed idea that primary-side
controller can regulate Io or Uo without dual-side wireless
communication link.
Generally, the phase shift H-bridge inverter is used to adjust
the primary-side resonant current. As shown in Fig. 4, duty
width of Pulse Width Modulation (PWM) signal for MOSFET
Q1, Q2, Q3, and Q4 are 50% without considering the dead time.
The PWM signals for Q3 and Q4 lag that of Q1 and Q2 a certain
phase shifted angle α whose value range is 0~180°.
Based on the Fundamental Harmonic Analysis (FHA) that
gives acceptable accurate results for operating points near/at
resonance frequency of resonant tank, the Root Mean Square
(RMS) value of Us is expressed as
2 2

(10)
U s _ RMS =
U bus cos

2
Through adjusting α, the Us_RMS is regulated along with the
adjustment of Io and Uo. Therefore, phase shift H-bridge
inverter is used to realize the proposed control method.
D. Basic Output Characteristics of Both SS Compensation
and SP Compensation
As analyzed in [11], [34], when no control method is
applied, both SS and SP compensation can achieve the
approximate CC/CV charging by meeting specific conditions.
However, the control accuracy is always limited and system
parameters should be properly designed and optimized. Take
SS compensation for example, the detailed analysis is
performed to illustrate the limitations, the current/voltage gain
between the primary and secondary side are given by

 M   2C1C2 
 Gi v  I 2  1

U s j Z11 Re +Z12

(11)

2

U
1  M   C1C2 
Gv v  e 

U s j Z11 + Z12 Re
 Z11  R1  2C1C2  +j C2   2 L1C1  1

2

2
2
2
 Z12   M   C1C2  +R1 R2  C1C2  +j C1 R1   L2C2  1

  2 L1C1  1 2 L2C2  1 +j C2 R2   2 L1C1  1

(12)
where, ω is the system operating angular frequency, the first
subscript of the gain indicate I2 or Ue of the secondary side and
the secondary one stands for Us. For instance, the Gi-v denotes
the gain for secondary side I2 and primary side Us. Assuming
that WPT system operates at resonant state (ω=ω1=ω2), R1 and
R2 are neglected, the Io is maintained constant by meeting (13).
8U
2 2
2 2
(13)
Io 
I2 
Gi v U s
 2 bus



 M 
 =1 =2
where, ω1 and ω2 are the resonant angular frequency of
primary and secondary side, respectively. When Ubus and M
are constant, the SS compensation achieves the approximate
CC charging without using closed-loop control method [11].
However, for practical WPT systems, the assumptions for (13)
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may not be always met, such as R1 and R2 cannot be ignored
and system operates at near resonant state. Then, the Gi-v is not
a constant value as shown in the zoomed part of Fig. 5 (a). It
also shows that the accuracy of Io is limited by the variation
range of Ro and Ubus. When the range of Ro and Ubus is small,
the charging current changes a little, which dues to the small
variation of Gi-v. Then, the SS compensation realizes the
approximate CC charging. However, when the variation range
of Ro and Ubus are large, the Io decreases drastically with the
increase of Ro, which is caused by the large variation of Gi-v, as
shown in Fig. 5 (b). Although SS compensation can achieve
the approximate CC charging under specific assumptions, it
may be unacceptable for practical variable load applications
that require accuracy control of Io and large variation of Ro.
h 
12  22 +
2 1  k 2 
= 12  22  -4 1  k 2  1222
2
(16)
(17)
where, k is the coupling coefficient of magnetic coupler. Based
on Pspice simulations, the frequency response characteristic of
the voltage gain and system efficiency are plotted in Fig. 6. Fig.
6 (a) shows that the approximate CV charging is achieved at
either 77.5 kHz or 95.5 kHz. Generally, the primary-side
impedance should be inductive to realize zero voltage
switching (ZVS) for the H-bridge inverter, which means ω
should be larger than ω1, and then 95.5 kHz is chosen [12].
However, Fig. 6 (b) shows that when ω deviates too much
from ω1, system efficiency decreases rapidly. Hence, although
SS compensation realizes the approximate CV charging by
choosing suitable ωh, system efficiency may be unacceptable
for practical applications.
(a)
(a)
(b)
Fig. 5. Analysis of charging current for SS compensation. (a) Frequency
response characteristic and (b) different dc input voltage.
Through properly designing ω, the SS compensation can
also realize the approximate CV charging against the variation
of Ro. Based on (11), in order to achieve the load independent
characteristic of Uo, the Z12 in gain Gv-v should be zero. Then,
the constant Uo is given by
 2 MC U


(14)
Uo 
Ue 
Gv v U s
 s 2 1 bus
s L1C1  1
2 2
2 2
 =s
where, ωs is the angular frequency that realizes the CV
charging for SS compensation. Assuming that R1 and R2 are
neglected, the ωs (s=l, h) is deduced as
l 
12  22  
2 1  k 2 
(15)
(b)
Fig. 6. Analysis of charging voltage for SS compensation. (a) Frequency
response characteristic and (b) system efficiency.
The similar conclusions are also suitable for SP
compensation. The current/voltage gain between primary and
secondary side are given by
 2 MC U


(18)
Uo 
Ue 
Gv v U s
 s 2 1 bus
s L1C1  1
2 2
2 2
 =s
 Z11  1   2 L1C1  jC1 R1 1   2 L2C2  jC2 R2 

2

(19)
  M   2C1C2 


2
2
 Z12  jC1  M   1   L1C1  jC1 R1   R2  j L2 
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Transactions on Power Electronics
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Assuming that the WPT system operates at resonant state,
R1 and R2 are neglected, the constant Uo for SP compensation
is achieved by meeting (20).
2 2
2 2
8 LU
(20)
Uo 
Ue 
Gv v U s
 2 2 bus
M



 =1 =2
Based on Pspice simulations, it show that only when Ro is
relative large, the approximate CV charging can be realized
(20). The approximate CV charging is invalidated when Ro is
relative small. Further, the condition for the approximate CC
charging is obtained by solving (18), and corresponding roots
ωl and ωh are same with (15) and (16). To realize ZVS for Hbridge inverter, the ωh is used and constant Io is given by


Io 
Ue 
Gi v U s
2 2
2 2
 =h
(21)
h M hC1 U bus

2
hC1 h M   1  h2 L1C1  h L2 
Although the approximate CC charging for SP
compensation is achieved by setting ω as ωh, the drawback of
low system efficiency that is similar with Fig. 6 (b) still exists.
In summary, for practical applications, the range of Ro and ω
may violate the conditions that are required by both SS and SP
compensation for realizing the approximate CC/CV charging.
Therefore, closed-loop control method is essential to achieve
the accurate and robust control of Io and Uo. As a remark, it is
noted that if no accurate control of Io and Uo is allowed, the
basic output characteristic of both SS and SP compensation
can be applied by properly optimizing system parameters.
III. THE PROPOSED PRIMARY-SIDE CONTROL AND LOAD
IDENTIFICATION APPROACH
Through adjusting the primary-side resonant current, the
principle of CV charging for SS compensation and CC
charging for SP compensation are verified. Combined with the
proposed load identification approach, the feasibility of CC
charging for SS compensation and CV charging for SP
compensation can also be validated with the estimated Ro.
A. Primary-Side Controllable Charging Capability for Both
SS and SP Compensation
The analysis in this section focuses on the deduction of the
relationship between Io or Uo and α, so as to verify the
proposed primary-side control approach. When the WPT
system operates at resonant state, R1 and R2 are ignored, the
RMS value of I1 for both SS and SP compensation are deduced
by (3)~(6) and (9)~(10).
16 2 Ro

SS : I1_ RMS  3
U bus cos
 ( M )2
2
(22)
L2
16 2

U bus cos
 3 ( M )2 Ro C2
2
From (22), it shows that the variation of Ro influences I1_RMS
that is adjusted by α. Then, the adjustment of Io or Uo by
controlling I1_RMS is analyzed as below.
SP : I1_ RMS =
2
Io  A  
8


   R2  2 Ro 

2 2  M  C2  


SS : I1_ RMS 
2
2
2
 

2 2 Io 
2
2
R
R
A
L
RoC2 R2 




 2
 2
o 
 M 
8
8
 

(23)
where, A=1-ω2L2C2. Assuming that R1 and R2 are ignored and
system operates at resonant state, the Uo for SS compensation
and Io for SP compensation are obtained from (23).
SP : I1_ RMS 
2 2 1
U o =U o
 M
(24)
2 2 L2
SP : I1_ RMS 
I o = I o
 M
It shows that once the WPT system is designed, the Uo for
SS compensation and Io for SP compensation have a linear
relationship with I1_RMS. The ratio are β and γ, respectively.
During the battery charging process, the change of Uo and Io
will manifest in the form of an increase or decrease in I1_RMS.
With (22) and (24), it shows that phase shift H-bridge inverter
can be used to adjust I1_RMS, and then the desired Uo or Io is
achieved. Based on the system parameters listed in Table I,
open-loop MATLAB Simulink simulations (α is 150°, Ro
varies from 8.5 Ω to 90 Ω for SS compensation; α is 90°, Ro
varies from 7 Ω to 8.5 Ω for SP compensation) verify the
above theoretical analysis and waveforms are shown in Fig. 7.
SS : I1_ RMS 
TABLE I SUMMARY OF THE SYSTEM PARAMETERS
Symbol
Parameter
Value
Ubus
System input dc voltage
36 V
f
System operating frequency
85.5 kHz
L1
Primary side coil inductance
104.5 μH
R1
Primary side coil resistance
0.15
L2
R2
Secondary side coil
inductance
Secondary side coil
resistance
51.2 μH
0.1
k
Coupling coefficient
0.21
Ubattery
Battery voltage range
20 V-26 V
Io
Constant charging current
3A
Uo
Constant charging voltage
25.8 V
Ro
Equivalent load resistance of
the battery
6.75 Ω-8.5 Ω (CC charging)
8.5 Ω-85 Ω (CV charging)
Fig. 7 shows that the envelope of I1 is same with Uo and Io.
The corresponding ratio β and ratio γ are constant value
(β=0.12 and γ=3.1). Therefore, the assumption that Io and Uo
can be adjusted by I1_RMS without measuring the secondaryside information is verified. It also proves that Uo for SS
compensation and Io for SP compensation changes as Ro varies.
The main reason is that system operating frequency deviates
from the required one, as analyzed in Section II. D.
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 2   M  I1_ RMS
2

(27)



R
2
8  P1  R1 I1_2 RMS



The similar analysis is also suitable for SP compensation
and Zp is given by
2
 M   R2e   2C22 R2 Re2 
Z p  R1 
2
 R2e   2 L2C2 Re    L2  C2 R2 Re 2 (28)
2

 M  C2 Re2   L2   2C22 L2 Re2  

 j  L1 
2

 R2e   2 L2C2 Re    L2  C2 R2 Re 2 

2
Ro =
(a)
where, R2e=R2+Re. For SP compensation, the P1 is obtained by
the real part of Zp in (28). When the WPT system operates at
resonant state, the estimated Ro is derived as
8  2 AC  B  +  B  2 AC   4CD  B  AC  E
2
2CD 2  B  AC 
2
Ro =
A   P1  R1 I1_2 RMS  I1_2 RMS B   M 
2
2
C  R2
(29)
D  C2 E  BC  AC 2  A D
In practice, once the WPT system is designed, the
parameters of magnetic coupler (R1, R2, L1, L2) and ω are
assumed to be constant. The P1 and I1_RMS can be calculated
and measured by the controller and sensors, and then the
estimated Ro in (27) and (29) are obtained.
2
C. Calculation of the Active Power P1
The commonly used methods for measuring the active
power P1 in the power system are classified into two types,
which are defined as the integration of instantaneous current
(b)
and voltage during one period (method I) and definition of the
Fig. 7. Open-loop simulations. (a) SS compensation and (b) SP compensation.
active power (method II) [36]-[37]. For method I, it requires
the same sampling interval and simultaneous sampling, which
B. Load Identification Approach
proposes a challenge on the hardware especially when the
Based on (23), when Ro is known, the Io for SS
signal frequency is high. For method II, the phase angle φ
compensation and Uo for SP compensation can be adjusted by
between the current and voltage should be measured. The
I1_RMS. In [7], it points out that battery appears to the WPT
corresponding difficulty is the accurate measurement of φ.
system as a variable resistive load, which is calculated by Uo/Io.
Therefore, a new active power calculation method based on
It is also the commonly used theoretical method for analyzing
quadrature transformation algorithm and reflected impedance
the battery charging. Then, during the analysis of load
theory is proposed [38]-[39]. Further, the principle diagram is
identification approach, the battery is assumed to be a resistor.
shown in Fig. 8 (a) and operating waveforms are shown in Fig.
From Fig. 3 (a), the primary-side impedance Zp seen into the
8 (b). Compared with the original frequency of the input
magnetic coupler for SS compensation is given by
current/voltage, it shows that the frequency of HI1, HQ1, HQ2,
2
2


H

M

C
R

R
I2 transferred to the A/D converter is largely reduced, which






2
2
e

Z p   R1 
2
is
meaningful and helpful for selecting the A/D converter and
2
2
2

C2   R2  Re   1   L2C2  

microprocessor.
(25)
2

 M  C2  1   2 L2C2  
 j  L1 
2
2
2

C2   R2  Re   1   2 L2C2  

Assuming that the secondary-side losses are ignored, the
power transferred to the battery equals to the power consumed
by the real part of Zp. Then, the active power P1 is deduced as
2
2


 M  C2   R2  Re 
2

 (26)
P1  I1_ RMS R1 
2
2
2
2



C
R

R

1


L
C





2
2
e
2 2 

When the system operates at resonant state, the estimated Ro
is derived from (26) and expressed as
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
U1 cos  2  f  f1  t 
 H I1 
2


U1 sin  2  f  f1  t 
 H Q1 

2
(33)

I1 cos  2  f  f1  t   

 HI2 
2

 I1 sin  2  f  f1  t   

HQ2 

2
Based on (32), the P1 is calculated by the controller. During
the calculation of P1, it is obvious that the phase angle φ
between i1(t) and u1(t) is not measured. Further, the I1_RMS is
obtained by the average of the definite integral i1(t) within the
controller. Finally, combined with the analysis in Section III. B
and C, the load identification approach is achieved.
(a)
(b)
Fig. 8. Quadrature transformation algorithm. (a) Principle diagram and (b)
simulation waveforms.
The i1(t) and u1(t) are synchronous acquired by the
current/voltage sensor and expressed as

 u1  t   2U1_ RMS sin  2 ft 


i1  t   2 I1_ RMS sin  2 ft   
(30)
where, φ is the phase angle between i1(t) and u1(t), f and T are
the signal frequency and period. The i1(t) and u1(t) are
processed by the conditioning circuit firstly. Then, the
conditioned i11(t) and u11(t) are multiplied by the mutually
orthogonal signals SI(t) and SQ(t).
 S I  t   cos  2 f1t 

(31)

S
t

sin
2

f
t





Q
1

where, f1 is the frequency of orthogonal signal. The signals
after the multiplying unit are processed by the low pass filter
(LFP). When the bandwidth B of the LPF meets 2|f1-f|, high
frequency (f+f1) is filtered and low frequency (f-f1) is reserved.
Finally, the equation of P1 is
(32)
P1  2 H I 1H I 2  H Q1H Q 2

D. Parameter Sensitivity Analysis
It is necessary to analyze the sensitivity of proposed control
method for variations in system parameters to verify it as a
robust technique [40]. As discussed in Section III, the CC/CV
charging and load identification approach for both SS and SP
compensation are derived with specific assumptions. In
practice, the system operates at/near resonant state, so as to
enhance the power transfer and improve the system efficiency.
Then, the main factors that influence (24), (27) and (29) are M
and L2. The M is influenced by the vertical and horizontal
misalignment, then simulation results obtained by the Ansoft
Maxwell software are plotted in Fig.9 (a). It shows that the
vertical misalignment has much more influence on M than L2.
Further, the influences of M on Io, Uo and estimated Ro are
analyzed in detail, and corresponding results are plotted in
Fig.9 (b) and (c).
Fig. 9 (b) shows that a small variation of M (vertical
misalignment dx is less than 10 mm) has little influence on Io
and Uo versus the load variation. Compared with M=15 μH
(dx=0 mm) and M=14.7 μH (dx=10 mm), the change rate of Io
and Uo are 1.5% and 1.8%, respectively. When dx becomes
much larger, the change rate of Io and Uo increases. Fig. 9 (c)
shows that the influence of M on estimated Ro is much more
obvious than Io and Uo. Therefore, the available range of dx in
this paper is relatively small, which is a flaw of the designed
system at present. Fortunately, the auxiliary positioning device
can be used to decrease the misalignment as small as possible,
and the magnetic coupler can also be optimized to be
misalignment insensitivity. Further, the methods that estimate
the mutual inductance and execute adaptive control could be
used to make the primary-side controlled WPT system be
much more suitable and flexible for practical applications.

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(a)
(b)
(c)
Fig. 9. Parameter sensitivity analysis. (a) Misalignment versus M and L2, (b)
Influence of M on Io, Uo and (c) Influence of M on estimated Ro (note that (b)
has the same legend in (c)).
IV. ANALYSIS OF THE PROPOSED PRIMARY-SIDE CONTROLLER
The proposed control method is verified by MATLAB
Simulink simulations. Firstly, the PI controlled phase shift Hbridge inverter realizes CV charging for SS compensation and
CC charging for SP compensation. Secondly, the load
identification approach is verified for both resistor and battery
load. Finally, based on the estimated Ro, the CC/CV charging
for both SS and SP compensation are achieved.
A. Principle of the Proposed Closed-Loop Control Strategy
As described in Fig. 10, the closed-loop control block
diagram consists of load identification unit, CC/CV charging
unit and PI controlled phase shift H-bridge inverter. The load
identification unit includes active power measurement shown
in Fig. 8 (a) and equivalent load resistance estimation
algorithm. Through measuring the active power P1 and
calculating (27) or (29), the Ro can be estimated. Combined
with (24), the PI controller and MOSFET driver generate four
PWM signals that drive the phase shift H-bridge inverter, and
then the primary-side resonant current is regulated.
Fig. 10. Closed-loop control block diagram.
Take SS compensation for example, the battery charging
process is shown as follow. During the CC charging, the Ro is
estimated by the load identification approach, which is realized
by acquiring primary-side resonant current i1(t) and inductor
voltage u1(t) and calculating corresponding equations. The
estimated Io_est is compared with a preset reference Io_ref, which
represents the desired Io. The error ΔIo=Io_ref-Io_est is fed into
the PI controller that generates the phase shifted angle α. Then,
the I1_RMS is regulated to maintain the constant Io, and then Uo
increases with the charging time. When Uo reaches the preset
reference Uo_ref, the CC charging switches to CV charging.
During the CV charging, the PI controller adjusts I1_RMS to
maintain the constant Uo. When Io decreases to the pre-set stop
Io_stop, the battery CC/CV charging process is over. It should be
noted that the load identification approach does not work until
α decreases from a large value αo to a small one α1, which aims
to realize the system soft-starting. Therefore, the initial small
primary-side active power P1 and resonant current I1 have no
influence on the load identification approach. When α
decreases to α1, which corresponds to a large P1 and I1, the
load identification approach and PI controller for CC/CV
charging starts to work. The above operation principle is also
suitable for SP compensation.
B. Simulations of CC/CV Charging for Both SS and SP
Compensation
The closed-loop simulation results are shown in Fig. 11. The
preset Io and Uo are 3 A and 25.8 V, which are required by the
battery parameters listed in Table I. From Fig. 11 (a), when Ro
changes from 20 Ω to 60 Ω, the Uo is maintained constant and
Io decreases from 1.28 A to 0.43 A for SS compensation. Fig.
11 (b) shows that when Ro changes from 7 Ω to 8.5 Ω, the Io is
maintained constant and Uo increases from 21.2 V to 25.8 V
for SP compensation. Compared with open-loop simulations
shown in Fig. 7, it is obvious that CV charging for SS
compensation and CC charging for SP compensation are
realized by the PI controlled phase shift H-bridge inverter.
Further, the feasibility of CC charging for SS compensation
and CV charging for SP compensation will be verified by
estimating Ro in the following sections.
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(a)
For SS compensation, Table II shows that Δ for both resistor
and battery are less than 5.5% and Δ decreases with the
increase of load resistance or battery voltage, while Δ for SP
compensation is relative large. It further points out that the
errors are mainly originated from the measurement noise and
the assumption that system losses are ignored during the
equation derivation. In practice, the average value of Ro_est can
be used to reduce the errors and least-square method also
enables Ro_est to converge to Ro with more data sets [28], [31].
As analyzed in Section III. A, the CC charging for SS
compensation and CV charging for SP compensation can be
achieved by estimating Ro. Then, the closed-loop simulations
are performed to verify it and Ro is averaged to reduce the
error during the simulations. Fig. 13 shows that CC charging
for SS compensation and CV charging for SP compensation
are realized. Combined with closed-loop simulations shown in
Fig. 11 and Fig. 13, it shows that CC/CV charging for both SS
and SP compensation are achieved by the proposed primaryside control method.
(b)
Fig. 11. Closed-loop simulations. (a) CV charging for SS compensation and
(b) CC charging for SP compensation.
As shown in (27) and (29), the Ro is estimated by calculating
the primary-side active power P1 and RMS value of resonant
current I1_RMS. Both resistor and battery load are simulated to
verify the proposed load identification approach, the
MATLAB Simulink model is shown in Fig. 12.
(a)
Fig. 12. Simulink model for the proposed load identification approach.
In Fig. 12, the phase shift control unit generates four PWM
signals for the H-bridge inverter. The active power
measurement unit that is based on Fig. 8 (a) and load
identification unit that is based on (27) and (29) estimates Ro.
The Li-ion battery model in the Simulink is used as the system
load. During the simulations, the Ro within the range of 6.75
Ω-85 Ω, which corresponds to the battery voltage varies from
20 V to 26 V, is tested and results are listed in Table II (the
symbols are described as: actual load resistance Ro (Ω),
estimated load resistance Ro_est (Ω), charging voltage Uo (V),
charging current Io (A) and load identification error Δ).
(b)
Fig. 13. Closed-loop simulations with estimating Ro. (a) CC charging for SS
compensation and (b) CV charging for SP compensation.
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TABLE II SIMULATION RESULTS OF THE LOAD IDENTIFICATION APPROACH
SS compensation
SP compensation
Ro
Ro_est
Δ
Uo
Io
Ro_est
Δ
Ro
Ro_est
Δ
Uo
Io
Ro_est
Δ
6.75
7.12
5.5%
20.3
2.97
7.2
5.3%
6.75
7.28
7.9%
20.4
2.96
7.26
6.8%
7
7.37
5.3%
21.26
2.98
7.5
5.1%
7
7.54
7.7%
21.1
2.95
7.62
6.5%
7.5
7.87
4.9%
22.6
2.98
7.92
4.8%
7.5
8.05
7.3%
22.3
2.96
7.97
6.1%
8
8.37
4.6%
24.7
2.96
8.69
4.3%
8
8.54
6.8%
24.5
2.98
8.69
5.7%
8.5
8.87
4.4%
25.8
2.96
8.98
4%
8.5
9.04
6.4%
25.6
2.98
9.04
5.3%
10
10.41
4.1%
25.7
2.57
10.48
3.8%
10
10.51
5.1%
25.6
2.58
10.35
4.4%
20
20.44
2.2%
25.5
1.25
20.78
1.9%
20
20.76
3.8%
25.4
1.28
20.44
3.6%
40
40.43
1.1%
25.4
0.63
40.57
0.9%
40
40.68
1.7%
25.5
0.64
40.45
1.5%
60
60.35
0.58%
25.4
0.42
61.1
0.3%
60
59.7
0.5%
25.6
0.44
59.65
0.3%
80
80.36
0.45%
25.6
0.32
80.5
0.2%
80
77.3
3.4%
25.4
0.33
79.2
2.9%
85
85.34
0.4%
25.8
0.3
85.2
0.1%
85
81.8
3.8%
25.8
0.3
83.3
3.2%
V. EXPERIMENTAL EVALUATION
As shown in Fig. 14, an experimental setup in the laboratory
has been built to verify the proposed primary-side control
method. The system parameters are listed in Table I. It points
out that the experimental setup is only a demonstration device
and used to verify the feasibility of proposed control method.
Based on different applications, the size and power capacity of
the setup can be scale down/up accordingly.
Fig. 14. The system experimental setup.
A. System Experimental Setup
For the phase shift H-bridge inverter, MOSFETs (Infineon
IPW60R041C6) in combination with the freewheeling diodes
(FAIRCHILD RHRP3060) are chosen. For the compensation
capacitors, the polypropylene film capacitors are chosen for
their low losses and high current bearing capability at high
frequency. The magnetic coupler is built with N1=21 turns on
the primary side (one layer with the optimized shape of ferrite
cores, 200 mm×200 mm) and N2=18 turns on the secondary
side (double layer, 150 mm×150 mm). The Litz wire (diameter
of 0.1 mm and 700 strands) constructs the coils due to its
lower frequency dependent resistance and smaller proximity
effect.
The parameters of coils and compensate capacitors are all
measured by Agilent Precision Impedance Analyzer E4990A.
The thickness of ferrite core is 5 mm. Note that the thickness
can be further optimized to realize light weight and low cost
on the condition that system performance is not compromised.
The liquid crystal display (LCD) is used to display the wireless
charging information. Fast recovery diodes (FAIRCHILD
RHRP3060) construct the secondary-side full bridge rectifier.
The electrolytic capacitor and inductor are used as the LC
filter for SP compensation and electrolytic capacitor is used as
the C filter for SS compensation. The current/voltage sensor
and corresponding condition circuits acquire the current and
voltage of primary-side coil. The DSP (Digital Signal
Processor) is used to generate the phase shift PWM signals,
execute the load identification algorithms, and realize the
closed-loop PI control algorithm. Also, the DSP detects the
system operation state, when over-voltage or over-current
occurs, system will be shut down safely.
B. Verification of CC/CV Charging for Both SS and SP
Compensation
Firstly, the CC charging for SP compensation and CV
charging for SS compensation are verified. Then, combined
with the estimated Ro of battery, the CV charging for SP
compensation and CC charging for SS compensation are also
achieved. The experimental waveforms are measured by the
Tektronix Oscilloscope MDO3054B (Blue: H-bridge
inverter’s output voltage Us, purple: charging voltage Uo,
green: charging current Io and cyan: primary-side resonant
current I1).
1) Without estimating Ro. During the CC charging for SP
compensation, the Uo increases from 21.5 V to 24.3 V and
I1_RMS increases from 9.31 A to 9.37 A, which is realized by
changing α from 136.6°to 133.8°, as shown in Fig. 15.
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Fig. 15. Experimental waveforms during the CC charging for SP compensation. (a) Uo=21.5 V and (b) Uo=24.3 V.
Fig. 16. Experimental waveforms during the CV charging for SS compensation. (a) Io=1.28 A and (b) Io=0.44 A.
Fig. 17. Experimental waveforms with estimating Ro. (a) CC charging for SS compensation and (b) CV charging for SP compensation.
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Transactions on Power Electronics
13
The measured ratio γtest is 3.1, which coincides with the
theoretical value γcal=3 from (24). It shows that I1_RMS changes
little, which verifies that I1_RMS can be applied to control Io for
SP compensation. Due to small fluctuation range of Ro during
the CC charging, the variation of α and I1 are also small.
As shown in Fig. 16, during the CV charging process for SS
compensation, through increasing α from 117.8°to 148.5°, the
I1_RMS decreases from 2.99 A to 2.93 A and Io decreases from
1.28 A to 0.44 A. The ratio βtest is 0.12, which coincides with
the theoretical value βcal=0.11 from (24). It shows that the
I1_RMS changes little, which further verifies that I1_RMS can be
applied to control Uo for SS compensation. Compared with the
CC charging, it is obvious that the variation of α is much more
obvious, because the fluctuation range of Ro and I1 are large
during the CV charging, as shown in Fig. 19.
2) With the estimated Ro. As analyzed in Section IV. B,
when Ro is estimated, the CC charging for SS compensation
and CV charging for SP compensation is also achieved by the
proposed primary-side control method. During the CC
charging for SS compensation, the Uo increases from 22.1 V to
24.4 V, α changes from 58.5° to 55.6°, and I1_RMS increases
from 2.43 A to 2.67 A , as shown in Fig. 17 (a). The ratio β is
0.11. During the CV charging for SP compensation, the Io
decreases from 1.31 A to 0.44 A, α increases from 119.6°to
131.5°, and I1_RMS decreases from 3.95 A to 1.32 A, as shown
in Fig. 17 (b). The ratio γ is calculated as 3.
In term of the soft switching of H-bridge inverter, two
bridge lags have opposite behavior when system operates at
resonant state. One of the bridge lags work in a zero current
switching (ZCS) mode while the other one will work in zero
voltage switching (ZVS) mode. Take the CV charging for SP
compensation as an example, the leading leg MOSFET Q1/Q2
operates in ZVS mode and lagging leg MOSFET Q3/Q4
operates in ZCS mode, as depicted in Fig. 18.
Fig. 18. The soft switching analysis for phase shift H-bridge inverter. (Note
that I1 and Id are multiplied by 5)
It shows that the leading leg has turn off loss PToff and
lagging leg has turn on loss PTon [41]. In [42], it points out that
the ZVS mode is influenced by other factors, such as α and Ro.
Therefore, the further analysis about soft switching technique
for the proposed primary-side control method will be our
future works, which is helpful to improve the system efficiency.
Combined with the above analysis, it is obvious that both SS
and SP compensation realize CC/CV charging through PI
controlled phase shift H-bridge inverter and load identification
approach. It shows that small deviation between experimental
and simulation results exists, which is caused by the difference
between simulation and actual model, the errors of the sensors
and parameters measurement. However, the feasibility of
proposed method can still be verified by the same variation
trend of experimental and simulation results.
Take SS compensation for example, the CC/CV charging
process is realized by the proposed control method, as shown
in Fig. 19. During CC charging, the Uo increases from 20 V to
25.8 V, then CV charging works along with Io decreases from
3 A to 0.3 A. The estimated Ro of Li-ion battery are also
plotted in Fig. 19. It shows that Ro increases slowly during CC
charging and increases rapidly during CV charging. The value
range is estimated as 6.7 Ω to 84.5 Ω [14]. Further, the same
conclusions are also suitable for SP compensation.
Fig. 19. The whole charging process and estimated Ro of Li-ion battery with
SS compensation.
C. System Efficiency and Losses Analysis
The system efficiency from system dc input to battery is
measured by Yokogawa WT1800 precise power analyzer
during the charging process. The channel 5 and channel 6 are
used to measure the system dc input power and dc output
power of battery, respectively. The measured curves and print
screen are shown in Fig. 20.
Fig. 20 (a) shows that system efficiency of SS compensation
ƞSS changes slightly during the CC charging, and decreases
during the CV charging [43]-[44]. It also shows that ƞSS with
small Ro that takes place during the CC charging and at the
beginning of CV charging is much higher than large Ro during
the latter stage of CV charging. The measured maximum ƞSS is
75.1%, which occurs near the transition point between the CC
and CV charging. Fig. 20 (b) shows that the system efficiency
of SP compensation ƞSP is low during the CC charging,
whereas ƞSP is higher during the latter stage of CV charging.
The measured maximum ƞSP is 61.1%, which occurs at the end
of CV charging [7]. Fig. 20 shows that the variation trend of
the experimental results is same with the simulation results and
small deviation is caused by the power losses such as parasitic
resistance and ICs, which is not fully modelled in the
simulations. It is noted that the analysis of CC/CV charging for
both SS and SP compensation in this paper is mainly aimed to
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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2017.2767099, IEEE
Transactions on Power Electronics
14
verify the feasibility of proposed primary-side control method.
For practical applications, the SS compensation is more widely
used and suitable for battery charging because of its load
independent resonant characteristic, simple structure and high
efficiency [7], [45]-[46].
design of H-bridge inverter and magnetic coupler are vital to
improve the system performance.
(a)
(b)
Fig. 21. Experimental results of the system losses. (a) SS compensation and (b)
SP compensation.
(a)
Last but not least, the proposed primary-side control method
not only avoids dual-side wireless communication link for
CC/CV charging required by traditional primary-side control
methods, but also realizes the compact, low cost and light
weight receiver compared with secondary-side control
methods. Those advantages make it be a preferred candidate
for practical applications that requires CC/CV charging, such
as portable devices, unmanned aerial vehicle (UAV) and so on.
In further works, the methods for optimizing the system
efficiency will be analyzed to make the proposed primary-side
control method be much more suitable for commercial
applications. It should be noted that the analysis methodology
for the proposed primary-side control is also suitable for
analyzing the CC/CV charging for both LCL-P and LCL-S
compensation, which is also our later works.
VI. CONCLUSION
(b)
Fig. 20. Experimental results of the system efficiency. (a) SS compensation
and (b) SP compensation.
To further improve and optimize the system efficiency, the
system losses are analyzed. Generally, system losses mainly
consist of H-bridge inverter losses Pinverter (turn on/off losses
and conduction losses), magnetic coupler losses Pcoupler (coil
losses and ferrite core losses) and rectifier losses Prectifier (turn
on/off losses and conduction losses), and other losses Pothers
[47]. The system losses are measured when the maximum
system efficiency is achieved and results are plotted in Fig. 21.
It shows that the H-bridge inverter and magnetic coupler losses
account for a large proportion of system losses. Hence, the
In this paper, a novel primary-side control method that
realizes CC/CV charging is proposed for both SS and SP
compensated WPT system. The advantages are that the
measurement of secondary-side current/voltage is avoided and
the compact and light weight receiver are also met. Firstly, the
feasibility of CV charging for SS compensation and CC
charging for SP compensation are verified by theoretical
analysis and simulations. Then, through the load identification
approach that is realized by the quadrature transformation
algorithm and reflected impedance theory, the equivalent load
resistance is estimated by the primary-side active power and
resonant current. Finally, combined with the estimated
equivalent load resistance, the CC/CV charging for both SS
and SP compensation are realized by PI controlled phase shift
H-bridge inverter. The simulation and experimental results
validate the feasibility of the proposed control method with
sufficient accuracy.
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Transactions on Power Electronics
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Chunbo Zhu (M’05) received the B.S. and
M.S. degrees in electrical engineering and
the Ph.D. degree in mechanical engineering
from the Harbin Institute of Technology
(HIT), Harbin, China, in 1987, 1992, and
2001, respectively.
He was a Post-Doctoral Research Fellow
with the PEI Research Center, National
University of Ireland, Galway, Ireland,
from 2003 to 2004. He has been a Lecturer
with the Department of Automation
Measurement and Control, HIT, since 1987. He is currently a Full
Professor with HIT, where he leads the Laboratory of Wireless Power
Transfer and Battery Management Technologies. His current research
interests include energy management systems, electric and hybrid
electric vehicles, and wireless power transfer technologies.
Kai Song (M’12) received the B.S., M.S.
and Ph.D. degree in instrument science and
technology from the Harbin Institute of
Technology (HIT), Harbin, China, in 2005,
2007 and 2011, respectively. In 2011, he
joined the School of Electrical Engineering
and Automation, HIT, as a lecturer, and was
a visiting scholar in electrical engineering,
The University of Tokyo, Japan, from 2014
to 2015. He is currently an associate
professor with the School of Electrical
Engineering and Automation, HIT, since 2016.
His current research interests concentrate in wireless power
transfer, particularly in the high-power wireless power transfer
system for electric vehicles and robots.
Zhenjie Li received the B.S. degrees in the
school of measurement and control
technology and communication engineering
from Harbin University of Science and
Technology, Harbin, China in 2012, and M.S.
degrees in the school of electrical engineering
& automation from Harbin Institute of
Technology, Harbin, China in 2014, where he
is currently working toward Ph.D. degree.
His research interests include wireless
power transfer for supercapacitor and battery powered electric
vehicles.
Jinhai Jiang received the B.S. degrees in
school of Electronic Science from Northeast
Petroleum University, Daqing, China in
2010, and M.S. degrees in school of
electrical engineering & information from
Northeast Petroleum University, Daqing,
China in 2013.
He is currently working toward Ph.D.
degree at Harbin Institute of Technology.
His research interests include wireless
power transfer for supercapacitor and
battery powered on-line electric vehicles.
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