Wireless power transfer (WPT) technology is now recognized as an efficient means of transferring power without physical contact. However, frequency detuning will greatly reduce the transmission power and efficiency of a WPT system. To overcome the difficulties associated with the traditional frequencytracking methods, this paper proposes a Direct Phase Control (DPC) approach, based on the SecondOrder Generalized Integrator PhaseLocked Loop (SOGIPLL), to provide accurate frequencytracking for WPT systems. The DPC determines the phase difference between the output voltage and current of the inverter in WPT systems, and the SOGIPLL provides the phase of the resonant current for dynamically adjusting the output voltage frequency of the inverter. Further, the stability of this control method is analyzed using the linear system theory. The performance of the proposed frequencytracking method is investigated under various operating conditions. Simulation and experimental results convincingly demonstrate that the proposed technique will track the quasiresonant frequency automatically, and that the ZVS operation can be achieved.
I. INTRODUCTION
Wireless Power Transfer (WPT) technology is a promising technique for use in our daily lives. It gets rid of various problems, such as friction and aging. The sparks produced in power transfer are eliminated. This is advantageous since they negatively impact the lifespan of electrical equipment and pose a hazard to human safety. Furthermore, WPT can meet the requirements of some special cases, like mining and underwater operations. It also proves to be convenient in such fields as portable electronics, implanted medical instruments, sensor networks and electric vehicles
[1]

[3]
. However, for a typical WPT system, the inherent parameters of the resonant tank may dynamically drift away from the designed parameters due to load variations and mutual coefficient changes
[4]
,
[5]
. This often results in frequency detuning. This is a problem since frequency detuning greatly reduces the transmission power and efficiency of WPT systems.
Obviously, the topics of the transmission power and efficiency are crucial for WPT systems, since they are necessary for safety and energy preservation
[6]
,
[7]
. Accordingly, for the sake of large transmission power and high powerdelivery efficiency, resonant frequencytracking for WPT systems is of great significance
[8]
. A typical method of adaptive impedance matching is proposed in
[9]
, which is regarded as a kind of passive tracking method. In this method, an adaptive impedance matching network based on a capacitormatrix is introduced. This can dynamically change the impedance values to maintain a reasonable level of maximum power transfer. However, this kind of method is difficult in terms of hardware implementation. In addition, this method cannot accurately realize impedance matching.
Meanwhile, various frequencytracking methods have been proposed in the past to assure operation in the resonant state for WPT systems. The most popular among these methods is the PLL method
[10]
. To track the resonant frequency, the method of a PLL with zerocrossing detection is widely used. Unfortunately, it is sensitive to distortions and disturbances of the input signal
[11]
,
[12]
. The SecondOrder Generalized Integrator PhaseLocked Loop (SOGIPLL) based on an adaptive filter is widely used in grid connected converters synchronization techniques. Compared with the traditional PhaseLocked Loop (PLL), the SOGIPLL is lesssensitive to distortions and disturbances of the input signal
[13]
,
[14]
. However, it is impossible to accurately regulate the phase difference between the output voltage and current of an inverter in WPT systems, which is not conducive to the operation of SoftSwitching. Therefore, to overcome the difficulties associated with the traditional frequencytracking methods, this paper proposes a Direct Phase Control (DPC) approach, based on the SOGIPLL, to provide accurate frequencytracking for WPT systems. The DPC determines the phase difference between the output voltage and current of an inverter in WPT systems, and the SOGIPLL provides the phase of the resonant current for dynamically adjusting the output voltage frequency of the inverter. Thus, the phase of the resonant current can be accurately detected regardless of distortions and disturbances, and the dead time imposed by the drivers can be regulated precisely. Moreover, the necessary dead time imposed by the drivers can be compatible with the resonant current phase lag control
[15]
,
[16]
. With the proposed method a WPT system can track the quasiresonant frequency automatically and the ZVS operation can be achieved.
This paper is organized in six sections. After the introduction, the resonance principle is analyzed, which mainly investigates the importance of resonance to improve transmission power and efficiency. In Section III, the frequencytracking method is presented. The linearization and stability analysis are discussed in Section IV. In Section V, the performance of the proposed method is presented, and some conclusions and suggestions for future work are given in Section VI.
II. WPT SYSTEM AND ANALYSIS
Apart from the power source and load, as shown in
Fig. 1
, the WPT system is mainly composed of the following three parts: the inverter, the coupler and the rectifier. Unlike traditional transformers, the primary and secondary sides of the coupler are separate from each other. The WPT system is divided into the following two parts by the coupler: the transmitting terminal and the receiving terminal. The introduction of the transmitting terminal, which consists of a DC source and a highfrequency inverter, makes it possible to provide a highfrequency AC current for the primary side of the coupler. At the receiving terminal, the rectifier and circuits of the filter are applied. With this the AC voltage that comes out of the coupler is converted into a DC voltage.
Main circuit of the WPT system.
Fig. 2
shows an equivalent circuit model of the WPT system as shown in
Fig. 1
. According to this model, the WPT system can be expressed by the following equations.
Equivalent circuit model of the WPT system.
Substituting (2) into (1), the input impedance of the WPT system is:
According to (3), the value of the input impedance can be expressed as:
According to (3) and the principle of the inverter circuit, the RMS value of the fundamental current on the primary side can be expressed as:
where
U_{in}
is the input DC voltage. Overlooking the loss of the rectifier bridge, according to (2) and (5), the output power can be expressed as:
With the help of (3), the input power factor of the equivalent circuit presented in
Fig.2
is:
By analyzing equations (4)(7), the relationships between the output power and other factors which include the frequency and load, and the relationships between the input power factor and these factors can be depicted as
Fig. 3
(a)(b) respectively. The specifications of the system are displayed in
Table I
.
(a) Output power according to R_{L} and ω; (b) Input power factor according to R_{L} and ω.
SPECIFICATIONS OF THE SYSTEM
SPECIFICATIONS OF THE SYSTEM
Fig. 3
shows that the output power and the input power factor vary with respect to the factors of frequency and load. In addition, the output power obtains its maximum value at those points where the input power factor is close to one, and the WPT system works in the resonant state. Thus, for the sake of the maximum output power and high transmission efficiency, an effectively control approach should be taken to assure that the WPT system is automatically working in resonant state.
According to equation (3), the phase difference
φ
between the output voltage
and current
of the inverter can be expressed as:
By analyzing (8), the relationship between the phase difference and the factors, which include the frequency and load, can be depicted as in
Fig. 4
. When the WPT system works in the resonant state, the phase difference is zero. Accordingly, the resonant points are located in the junctions of the phasedifference plane and the zeroplane.
Phase difference according to R_{L} and ω; the zero plane.
It is evident from (8) that the WPT system works in the resonant state when the output voltage and current of the inverter have the same phase angle. This can be realized by controlling the switching frequency of the inverter according to the resonant frequency.
III. FREQUENCYTRACKING METHOD
In order to keep the WPT system working in the resonant state, a DPC approach, as shown in the shaded area of
Fig. 5
, based on the SOGIPLL, is proposed to provide frequencytracking. By sensing the primary side current, the output phase angle
θ′
of the SOGIPLL acts as a control signal for the PWM driver. According to the cosine value of
θ′
the PWM driver signals
V_{GS}
are obtained as presented in
Fig. 6
. In addition, the dead angle
θ_{d}
between the two sets of gate signals
V
_{GS,14}
and
V
_{GS,23}
can be regulated precisely. Where d is a constant whose value is close to zero and the dead angle
θ_{d}
is expressed as:
With the help of the proposed frequencytracking method, the output voltage frequency of the inverter in the WPT system can track the resonant frequency automatically if the parameter Δ
θ
^{∗}
is set to zero, so that the phase difference between the output voltage and current of the inverter will be zero correspondingly. Furthermore, the phase difference can be accurately regulated by the parameter Δ
θ
^{∗}
.
Schematic diagram of frequencytracking.
Regulation of the PWM driver signals.
To realize the above control strategy, the key is to obtain an accurate phase angle
θ′
. The proposed frequencytracking method, as shown in
Fig. 7
, is composed of five parts as follows, the SecondOrder Generalized Integrator Quadrature Signal Generator (SOGIQSG), the Park transformation, the DPC, the Lowpass Filter (LF), and the Frequency/PhaseAngle Generator (FPG). The proposed method has two feedback loops, where the FPG provides the phase and central frequency for the Park transformation and the SOGIQSG, respectively
[17]
,
[18]
. The introduction of the SOGIQSG improves the phase detection performance.
Proposed frequencytracking method.
 A. SOGIQSG
The SOGIQSG is a kind of Adaptive Filter (AF). A traditional filter can only deal with signals that lie in the fixed frequency range. What is worse, the parameters of this kind of filter are static and their values are assigned during the design progress of the filter. However, an AF can adapt its parameters automatically according to the optimization algorithm. In addition, during the design process of an AF, information on the signal to be filtered is not needed
[19]
,
[20]
. The SOGIQSG can deal with signals that lie in any frequency range. Moreover, it can be used in occasions with distortions and disturbances.
According to
Fig. 7
, the transfer functions of the SOGIQSG can be expressed as:
where
ω′
represents the central frequency of the SOGI and
k
is the gain of the SOGIQSG.
Suppose that the input signal with distortion is:
where
V_{n}
,
nω
, and ∅
_{n}
represents the amplitude, angular frequency and initial phase angle of the nth harmonic
v_{n}
of the input signal
v
, respectively. As a result, the nth harmonic can be indicated as a phasor
, and the amplitude, angular frequency and initial phase angle are
V_{n}
,
nω
, and ∅
_{n}
, respectively. With the help of (10) and (11), the outputs of the SOGIQSG can be expressed as:
Once the value of the angular frequency
ω
is equal to the central frequency
ω′
, equation (13) can be calculated as:
For a criticallydamped response
is chosen as shown in the bode diagram presented in
Fig. 8
. This value presents a valuable selection in terms of the setting time and overshoot limitation
[17]
,
[18]
. It can be observed that the SOGIQSG possesses the bandpass filtering property. The bandwidth of the SOGIQSG relies on the gain
k
rather than the central frequency
ω′
. As a result, it is suitable for occasions with frequency variations.
Bode plot of SOGIQSG (, ω′ = 400000π).
From (14), it can be observed that the input signal has the same angular frequency as the central frequency at
n
= 1, and that the amplitudes of the outputs share the same values with the input signal. Otherwise, the amplitudes will decay obviously at
n
≠ 1. In addition, there is a phase difference of
π
/2 between the signals
and
. Furthermore, the two orthogonal signals have the same amplitudes as
v_{n}
, while the input frequency is equal to the central frequency
ω′
. Thus, the outputs of the SOGIQSG can be expressed as:
where
V
and
θ
are the amplitude and phase of the input signal, respectively. They are equal to the values of the fundamental component of the input signal, whose amplitude, angular frequency and initial phase angle are
V
_{1}
,
ω
and ∅
_{1}
, respectively.
The dynamic response of the SOGIQSG is presented in
Fig. 9
, where
v
= 5
cos
(
ωt

π
/2) + 0.8
cos
(3
ωt

π
/2) + 0.3
cos
(5
ωt

π
/2) , and a disturbance of
π
/4 leading phase hits is applied at 19.4 μs. It is evident that the SOGIQSG can work well regardless of distortions and disturbances.
Waveforms of the input signal v and the two outputs v′ and qv′ of SOGIQSG, where v = 5 cos(ωt  π/2) + 0.8 cos(3ωt  π/2) + 0.3 cos(5ωt  π/2) , ω = ω′ = 400000π rad/s and .
 B. Park Transformation
Fig. 10
shows the Park transformation schematic diagram. There are two coordinates, including the stationary coordinates and the rotating coordinates, where
θ
represents the phase angle of the input signal and
θ′
is the output phase angle of the SOGIPLL.
The schematic diagram of Park transformation.
According to the Park transformation principle, the
dq
components are obtained by:
Substitute (15), (16) into (17) and the
dq
components are:
By analyzing (18), the value of
v_{q}
reveals the difference between the output phase
θ′
and the input phase
θ
of the PLL. According to
Fig. 10
it can be seen that:
(1)At the moment when
v_{q}
< 0, the axis d is ahead of
v
, and the frequency of the PLL should be reduced.
(2)At the moment when
v_{q}
> 0, the axis d lags behind
v
, and the frequency of the PLL should be increased.
(3)At the moment when
v_{q}
= 0, the axis d is collinear with
v
.
 C. DPC
For the highfrequency applications in WPT systems, in order to decrease the switching losses, it is essential to assure operation in the SoftSwitching mode. In addition, a dead time in the voltage source bridge inverter is required to prevent shootthrough current
[15]
,
[16]
. The inverter of WPT system is presented in
Fig. 11
(a), and the ZVS operation is introduced as shown in
Fig. 11
(b).
(a) Inverter of WPT system, (b) ZVS operation.
Fig. 11
(b) shows that a resonant current phase lag
θ_{l}
is introduced where
V_{DS}
and
i_{DS}
represent the voltage across the MOSFET and the current through the MOSFET, respectively, and
i_{LP}
repesents the output resonant current of the inverter. The phase lag
θ_{l}
refers to the difference between the zerocrossing point of the current
i_{DS}
and the falling edge of the voltage
V_{DS}
. The voltage across the MOSFET is zero if the MOSFET turn on during the phase lag
θ_{l}
, and then the ZVS operation is achieved.
In a real circuit, the phase lag
θ_{l}
is redefined as the difference between the zerocrossing point of the output resonant current
i_{LP}
and the falling edge of the driver signal of the MOSFET as shown in
Fig. 12
. In order to assure the ZVS operation, it is very important that the phase lag
θ_{l}
should be greater than the dead angle
θ_{d}
.
ZVS operation sequence.
In this paper, the Adaptive Gain (AG) is used and it can be expressed as:
where Δ
θ
^{∗}
is the reference value of the phase difference between the output and input signal of the SOGIPLL, and
v_{d}
is one of the
dq
components of the Park transformation.
In addition, the component of
v_{qunit}
, as shown in
Fig.7
, can be expressed as:
According to (18)(20), the actual phase difference Δ
θ
is:
At the moment when the SOGIPLL operates steadily, as shown in
Fig. 7
, the condition of
v_{qunit}
= 
sin
(Δ
θ
^{∗}
) is satisfied. With equation (21), Δ
θ
= Δ
θ
^{∗}
. Thus, it is possible to regulate the actual phase difference Δ
θ
by setting the parameter Δ
θ
^{∗}
, as presented in
Fig. 13
.
Block diagram of the proposed method.
The DPC makes it possible for the resonant current phase lag angle
θ_{l}
to have the same value as the parameter Δ
θ
^{∗}
. Once the dead angle has been assigned, the parameter of Δ
θ
^{∗}
should be set so that it is greater than
θ_{d}
. On the other hand, for the sake of resonant frequencytracking, the minimum input power factor
ρ_{min}
, which is close to one, is introduced. Therefore, the parameter of Δ
θ
^{∗}
should be given by:
Thus, the dead time imposed by the drivers is compatible with that of the resonant current phase lag control. In this case, the WPT system operates in a quasiresonant state and the ZVS operation is achieved.
IV. LINEARIZATION AND STABILITY ANALYSIS
According to
Fig. 13
, some relationships can be depicted as the following equations.
Once the component
v_{qunit}
, as shown in (23), is small enough the equation can be depicted as:
As for the FPG component, which works as the voltage controlled oscillator (VCO) of a PLL, the output frequency is:
where
ω_{c}
is the central frequency of the VCO and its value relies on the frequency range of the signal to be detected. Δ
ω
represents the frequency compensation, which achievs robust operation for frequency variations.
k_{vco}
is the gain of the VCO and it works as an input sensitivity parameter. The parameter scales the input voltage. Thus, it controls the shift from the central frequency. The unit of the parameter is in radians per volt.
Therefore, a small fluctuation of the output frequency is:
Thus, a small fluctuation of the phase angle is:
With the introduction of the Laplace Transform, equations (24) and (27) can be respectively converted as:
In addition, another relationship in terms of the component of the LF can be expressed as:
Accordingly, the linearization for the SOGIPLL, as shown in
Fig.13
, can be presented in
Fig. 14
. In
Fig. 14
the combination of the SOGIQSG, the Park transformation and the AG works as a special Phase Detector (PD). A PI controller works as a Lowpass Filter. The Frequency/PhaseAngle Generator (FPG) works as the voltage controlled oscillator (VCO).
Linear PLL loop.
The closedloop transfer function of the linearized PLL can be expressed as:
where
k_{p}
is the proportional gain and
T_{i}
is the integral time constant of the PI controller.
The natural frequency and the damping ratio are:
For a good transient response, a damping ratio
ξ
= 0.7 is advisable. Allow for the lock range of the PLL as depicted in (35). The natural frequency
ω_{n}
should not be too low.
In addition, the lock time, as presented in (36), is another issue that needs to be taken into account.
According to the criteria in the previous analysis, a natural frequency of
ω_{n}
= 113140
rad/s
is chosen. According to (35), (36) Δ
ω_{L}
≈ 160000
rad/s
,
T_{L}
≈ 54
us
, the bode plot and the step response are displayed in
Fig. 15
and
Fig. 16
, respectively.
Bode plot of the PLL system.
Step response of the PLL system.
With the help of
Fig. 15
it is possible to obtain some information about the PLL system. Firstly, the lowfrequency gain of the closedloop PLL is nearly 0. As a result, when it works under steady working conditions, the PLL system is extremely accurate. Secondly, it has a peak value of 2.3dB at the resonant point. This indicates that the PLL system shows a low overshoot. Thirdly, because of its wide bandwidth a good transient response is obtained. In addition, the system has a large lock range indicating that the PLL can get locked in a single beat with a high initial frequency deviation. As shown in
Fig. 16
, the system shows a good transient response and a low overshoot.
V. PERFORMANCES AND RESULTS ANALYSIS
 A. Simulation Results Analysis
In order to verify the proposed method discussed above, simulations have been done according to
Fig. 5
. The main parameters for the simulated system are presented in
Table I
. In this experiment the load is
R_{L}
= 16Ω and the central frequency of PLL is
f_{c}
= 200kHz.
The WPT system, which operates with the DPC approach, works in a quasiresonant state after setting the parameters as discussed above. As a result, the current out of the inverter is approximately in phase with the voltage as shown in
Fig. 17
. The waveforms of the voltage and current of the MOSFET are displayed at the bottom of
Fig. 17
. It is obvious that the ZVS operation for the inverter of the WPT system is achieved.
Waveforms of u_{ac} and i_{Lp}; Waveforms of the voltage and current of MOSFET operates in ZVS mode.
The load
R_{L}
changes from 16Ω to 8Ω at 6ms.
Fig. 18
(a) provides the waveforms of the WPT system without the DPC. As shown in
Fig. 18
(a), the transmitterside voltage
u_{ac}
is not synchronized with the transmitterside current
i_{Lp}
when the load
R_{L}
changes.
Fig. 18
(b), (c), and (d) display some simulation performances of the WPT system operating with the DPC.
Fig. 18
(b) and (c) show that the phase difference between the voltage
u_{ac}
and the current
i_{Lp}
of the transmitterside returns approximately to zero at the end of the transition during which the load
R_{L}
changes from 16Ω to 8Ω.
Fig. 18
(d) shows that at the end of the transition, the frequency can be tracked automatically.
Waveforms when R_{L} changes from 16Ω to 8Ω(a) Waveforms of u_{ac} and i_{Lp} (without DPC); (b) Waveforms of u_{ac} and i_{Lp} (with DPC); (c) Magnification of one segment of waveforms of u_{ac} and i_{Lp} (with DPC); (d) Frequency variations behavior.
Changes in the load
R_{L}
and its effect on the input power factor
ρ
expressed in (6) are displayed in
Fig. 19
.
The input power factor ρ according to R_{L}.
Fig. 19
shows that the factor
ρ
is approximately equal to one and stabilized enough. This indicates that the WPT system works in a quasiresonant state steadily with a stable phase difference between the output voltage and current of the inverter. This is essential for the implementation of the ZVS operation.
 B. Experimental Results Analysis
In order to further verify the validity of the proposed technique, a hardware implementation has been done and the obtained experimental results are presented in this paper.
The load
R_{L}
changes from 16Ω to 8Ω.
Fig. 20
(a) shows waveforms of the frequencytracking system without the DPC. As shown in
Fig. 20
(a), the transmitterside voltage
u_{ac}
is not synchronized with the transmitterside current
i_{Lp}
at the moment when the load
R_{L}
changes. What is worse, when the voltage swings back and forth, the ZVS operation is doomed to fail.
Fig. 20
(b) displays the waveforms of the system operating with the DPC.
Fig. 20
(b) shows that the phase difference between the voltage
u_{ac}
and the current
i_{Lp}
remains approximately zero when the load
R_{L}
changes. In addition, a stable and slight phase lagangle
θ_{l}
is introduced, which results in successful ZVS operation. It is obvious that the system can track the frequency automatically at the moment when the load changes.
Waveforms of u_{ac} and i_{Lp} when R_{L} changes from 16Ω to 8Ω (a) without DPC; (b) with DPC.
Fig. 21
(a) shows waveforms of the proposed frequencytracking system without any parameter changes. By analyzing these waveforms it can be seen that the system can track the frequency automatically, and that the ZVS operation can be achieved simultaneously.
Waveforms of u_{ac} and i_{Lp} with DPC (a) waveforms without any parameter variations; (b) waveforms with distance variation between primaryside and secondaryside; (c) waveforms with misalignment between primaryside and secondaryside.
In addition, the performance of the proposed algorithm under both distance variations and sourcetarget misalignment has been presented.
The distance between the two coils changes from 10cm to 5cm and the waveforms are presented in
Fig. 21
(b).
Fig. 21
(b) shows that the phase difference between the voltage
u_{ac}
and the current
i_{Lp}
remains approximately zero when the distance between the two coils changes. In addition, a stable and slight phase lagangle
θ_{l}
is introduced, which results in successful ZVS operation.
Secondly, the receiving coil deviated from the central axis of the two coils by about 5cm and the waveforms are presented in
Fig. 21
(c). Similarly,
Fig. 21
(c) shows that the phase difference between the voltage
u_{ac}
and the current
i_{Lp}
remains approximately zero when the receiving coil deviated from its best position. In addition, a stable and slight phase lagangle
θ_{l}
is introduced, resulting in successful ZVS operation.
It is obvious that with the proposed method, the system can track the frequency automatically when the distance between the two coils changes and when the receiving coil deviates from its best position. The ZVS operation can be achieved simultaneously.
VI. CONCLUSIONS AND FUTURE WORKS
In this paper, the importance of resonant frequencytracking to a WPT system has been discussed and a DPC approach, based on the SOGIPLL, to provide accurate frequencytracking for WPT systems is proposed. The DPC determines the phase difference between the output voltage and current of the inverter in a WPT system, and the SOGIPLL provides the phase of the resonant current for dynamically adjusting the output voltage frequency of the inverter. The phase of the resonant current can be detected accurately regardless of distortions or disturbances. The phase difference of a WPT system and the dead angle imposed by the drivers can be regulated precisely. Moreover, the necessary dead time imposed by the drivers is compatible with the resonant current phase lag control. With the proposed method a WPT system can track the quasiresonant frequency automatically and the ZVS operation can be achieved. This method can be used on occasions when the load has changed and when the resonant parameters have changed. With the proposed frequencytracking method the maximum transmission power and powerdelivery efficiency of a WPT system can be obtained. This is of significance for the research and application of WPT systems.
The validity of the proposed technique has been demonstrated with simulation and experimental results. However, there is still something to do to improve the performances during the experimental process. Firstly, the switching frequency can be promoted if a much more efficient processor, such as a FPGA, is applied. Secondly, with the proposed DPC method, phase compensation can be achieved exactly and it will need to be exploited in the future. It is significant to deal with the phase delay derived from the hardware implementation. In the future, the switching frequency of the inverter will be improved in the frequencytracking system and the phase compensation will be implemented.
The proposed method has many advantages for the WPT applications. However, there are still some possible limitations in the proposed method. Firstly, the SOGIPLL is a computationally expensive and timeconsuming algorithm. In order to apply it to WPT applications whose operating frequency is high, a much more efficient processor has to be applied which will increase the cost of the WPT system. Secondly, protective measures have to be taken to prevent damage to the processor and other control circuit during the hardware implementation. Thirdly, the proposed method can be applied on occasions when the output current is sinusoidal.
Acknowledgements
This work was supported by National Natural Science Foundation of China (NSFC) (51207134). The authors would like to thank the associate editor and the peer reviewers for their constructive suggestions which significantly improve the quality of this paper.
BIO
Pingan Tan received his B.S. and M.S. degrees in Electrical Engineering from Xiangtan University, Xiangtan, China, in 2001 and 2004, respectively; and his Ph.D. degree in Electrical Engineering from the South China University of Technology, Guangzhou, China, in 2010. Since 2011, he has been an Associate Professor in the School of Information Engineering, Xiangtan University. His current research interests include wireless power transfer, power electronics, and nonlinear control.
Haibing He was born in China, in 1989. He received his B.S. degree in Automation from Xiangtan University, Xiangtan, China, in 2013; where he is expected to receive his M.S. degree in Electrical Engineering, in 2016. His current research interests include wireless power transfer, DCDC converters and switchedmode power supplies.
Xieping Gao was born in 1965. He received his B.S. and M.S. degrees from Xiangtan University, Xiangtan, China, in 1985 and 1988, respectively; and his Ph.D. degree from Hunan University, Changsha, China, in 2003. He is presently working as a Professor in the College of Information Engineering, Xiangtan University. He was a Visiting Scholar at the National Key Laboratory of Intelligent Technology and Systems, Tsinghua University, Beijing, China, from 1995 to 1996; and in the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, from 2002 to 2003. He is a regular reviewer for several journals and he has been a member of the technical committees of several scientific conferences. He has authored or coauthored over 80 journal papers, conference papers, and book chapters. His current research interests include wavelet analysis, neural networks, evolution computation, and image processing.
Kurs A.
,
Karalis A.
,
Moffatt R.
,
Joannopoulos J. D.
,
Fisher P.
,
Soljacic M.
2007
“Wireless power transfer via strongly coupled magnetic resonances,”
Science
317
(5834)
83 
86
DOI : 10.1126/science.1143254
Shin J.
,
Shin S.
,
Kim Y.
,
Ahn S.
,
Lee S.
,
Jung G.
,
Jeon S.J.
,
Cho D.H.
2014
“Design and implementation of shaped magneticresonancebased wireless power transfer system for roadwaypowered moving electric vehicles,”
IEEE Trans. Ind. Electron.
61
(3)
1179 
1192
DOI : 10.1109/TIE.2013.2258294
Zhang Y.
,
Zhao Z.
2014
“Frequency splitting analysis of twocoil resonant wireless power transfer,”
IEEE Antennas Wireless Propag. Lett.
13
400 
402
DOI : 10.1109/LAWP.2014.2307924
Hsu J. U. W.
,
Hu A. P.
,
Swain A.
2012
“Fuzzy logicbased directional fullrange tuning control of wireless power pickups,”
IET Power Electron.
5
(6)
773 
781
DOI : 10.1049/ietpel.2011.0364
Dai X.
,
Sun Y.
2014
“An accurate frequency tracking method based on short current detection for inductive power transfer system,”
IEEE Transa. Ind. Electron.
61
(2)
776 
783
DOI : 10.1109/TIE.2013.2257149
Solja M.
,
Rafif E. H.
,
Karalis A.
2007
“Coupledmode theory for general freespace resonant scattering of waves,”
Physical Review
75
(5)
1 
5
Karalis A.
,
Joannopoulos J. D.
,
Soljai M.
2008
“Efficient wireless nonradiative midrange energy transfer,”
Annals of Physics
323
(1)
34 
48
DOI : 10.1016/j.aop.2007.04.017
Klaus B.
,
Lang B.
,
Leibfried T.
“Technical analysis of frequency tracking possibilities for contactless electric vehicle charging,”
in IEEE Innovative Smart Grid Technologies – Asia(ISGT ASIA)
2014
577 
582
Lim Y.
,
Tang H.
,
Lim S.
,
Park J.
2014
“An adaptive impedancematching network based on a novel capacitor matrix for wireless power transfer,”
IEEE Trans. Power Electron.
29
(8)
4403 
4413
DOI : 10.1109/TPEL.2013.2292596
Bosshard R.
,
Kolar J. W.
,
Wunsch B.
“Control method for inductive power transfer with high partialload efficiency and resonance tracking,”
in International Power Electronics Conference (IPECHiroshima)
May 2014
2167 
2174
Yuan J.W.
,
Lu Z.Y.
2011
“Research on a novel single phase PLL strategy,”
Power Electronics
45
(7)
81 
83
Arruda L. N.
,
Silva S. M.
,
Filho B. J. C.
“PLL structures for utility connected systems,”
in IEEE Industry Applications Conference
Sep./Oct. 2001
Vol. 4
2655 
2660
Silva S. A. O. d.
,
Campanhol L. B. C.
,
Goedtel A.
,
Nascimento C. F.
,
Paiao D.
“A comparative analysis of pPLL algorithms for singlephase utility connected systems,”
in 13th European Conference on Power Electronics and Applications(EPE)
2009
1 
10
Gupta A.
,
Porippireddi A.
,
Srinivasa V. U.
,
Sharma A.
,
Kadam M.
2012
“Comparative study of single phase PLL algorithms for grid synchronization applications,”
International Journal of Electronics & Communication Technology (IJECT)
3
(4)
237 
245
Lopez V. M.
,
NavarroCrespin A.
,
Schnell R.
,
Branas C.
,
Azcondo F. J.
,
Zane R.
2012
“Current phase surveillance in resonant converters for electric discharge applications to assure operation in zerovoltageswitching mode,”
IEEE Trans. Power Electron.
27
(6)
2925 
2935
DOI : 10.1109/TPEL.2011.2174384
Rodriguez P.
,
Teodorescu R.
,
Candela I.
,
Timbus A. V.
,
Liserre M.
,
Blaabjerg F.
1
“New positivesequence voltage detector for grid synchronization of power converters under faulty grid conditions,”
in 37th IEEE Power Electronics Specialists Conference (PESC)
2006
Ciobotaru M.
,
Teodorescu R.
,
Blaabjerg F.
“A new singlephase PLL structure based on second order generalized integrator,”
in 37th IEEE Power Electronics Specialists Conference(PESC)
2006
1 
6
Salamah A. M.
,
Finney S. J.
,
Williams B. W.
2007
“Threephase phaselock loop for distorted utilties,”
IET Electric Power Appl.
1
(6)
937 
945
DOI : 10.1049/ietepa:20070036
Haykin S. S.
2002
Aaptive Filter Theory
Prentice Hall
Upper Saddle River, NJ