INTRODUCTION
Inductively coupled power transfer (ICPT) technology allows electrical energy
to be transferred from a stationary primary source to one or more movable secondary
loads over relatively large air gaps (Si et al.,
2008; Li et al., 2008). Due to the elimination
of physical electric contacts, it is widely used in special fields, such as
inflammable and explosive areas and wet or undersea environment (Sample
et al., 2011; Li et al., 2012a,
2013; Dai and Sun, 2011; Tang
et al., 2009). Moreover, in most industrial ICPT applications, only
ac mains are available, so several research have been done to achieve AC output
(Boys et al., 2008; Keeling
et al., 2010; Sun et al., 2012).
Normally, in order to generate a highfrequency current on the primary side,
an ACDCAC twostage power conversion is employed in ICPT systems (Wang
et al., 2010, 2011). However, extra semiconductor
switches and large DC electrolytic capacitors can be costly and bulky (Safaee
et al., 2012; Wu et al., 2011a) which
also compromises system reliability. Meanwhile, for high power application,
power factor correction circuitry is usually employed along with the rectification
stage.
Recently, one of the options to design a direct ACAC ICPT system is to generate
a highfrequency current on the primary side based on free oscillation and energy
injection control (Li et al., 2012b). The converter
is simplicity but neglect the envelop characteristic of the track current and
the design of the pickup. Moreover, it has been pointed out that a low energy
storage power supply can be used to achieve ACAC conversion (Wu
et al., 2011b). Such technique can directly generate high frequency
track currents whereas the ACDC stage is still used because that such technique
needs a small filter capacitor after the rectifier to reduce the energy storage
of the power supply.
In this study, a novel direct sinusoidal input/output ACAC ICPT system is
presented without energy storage links. Compared with the traditional ACDCAC
ICPT system, its structure and control are simple and the cost is lower. This
technique combines the primary direct ACAC converter with a secondary ACAC
converter based on energy injection control that converts the high frequency
AC directly to a low frequency AC output. The expression for the steady load
current based on impulse theorem has been discussed in detail. Simulations and
experiments have been carried out to verify the theoretical results.
BASIC CIRCUIT OPERATION
The ICPT system can be classified by voltagefed system and currentfed system.
The voltagefed system normally matches series tuned types of resonant tanks,
while currentfed system matches parallel tuned types of resonant tanks. This
study uses a typical voltagefed resonant tank as an example. The main ACAC
topology of voltagefed ICPT system can be shown in Fig. 1.
As shown in Fig. 1, the system has the symmetric circuit
topology from primary part to secondary part. The series resonant network of
the primary part consisting of a capacitor C_{p} in series with an inductor
L_{p}, such series resonant tank is assumed to be driven to produce
a highfrequency sinusoidal current with low distortion directly from input
AC supply. This sinusoidal current provide the Zero Current Switching (ZCS)
conditions for IGBT switches (P_{1}~P_{4}).

Fig. 1: 
Symmetric ACAC voltagefed ICPT system 
The secondary part consists the pick up coil L_{s} which is completely
tuned by the series capacitor C_{s} and the M is the mutual inductance
between L_{p} and L_{s}, such series resonant tank receives
the highfrequency energy by the magnetic fields coupling. The symmetric ACAC
converter that includes four switches (S_{1}~S_{4}) converts
the induced high frequency AC directly to a low frequency AC output to the load
R_{L}.
Primary ACAC converter operation (the energy injection and free oscillation
control method): The four IGBTs (P_{1}~P_{4}) and four antiparallel
diodes (PD_{1}~PD_{4}) constitute two pairs bidirectional switch
to convert the input AC supply into a series of the high frequency rectangular
voltage waveform whose amplitude changed according to sinusoidal law (Fig.
2). The primary ACAC converter operate based on energy injection mode and
free oscillation mode: When the polarity of the input AC supply and the resonant
current is positive, P_{1} switched “on”, while other switches
(P_{2}~P_{4}) be “off” and the energy is injected
into the primary resonant tank, as the polarity of resonant current is negative
then P_{2} switched “on”, while other switches (P_{1},
P_{3}, P_{4}) be “off” and the energy free oscillate
in the resonant tank. The signals and waves corresponding to the principle are
seen as Fig. 2.
Impulse theorem: There is a very important conclusion called impulse
theorem in sample control theory which is the narrow pulses of equal impulse
and different shape have the same effect when added to the inertia link. Impulse
is the area of narrow pulses and the same effect means to get the same output
response wave (Zheng et al., 2010).
Based on the impulse theorem (also called equivalent area principle), in order
to make the output voltage waveform equivalent with the desired voltage waveform,
the area sum of surrounded by sinusoid half wave with power grid frequency within
the half output voltage period must be equal to the one of desired output voltage
wave. It especially needs to be pointed that the wave of sinusoid half wave
of the input supply is chopped by high frequency pulse signals based on energy
injection and free oscillation principal (Fig. 3).

Fig. 2(ag): 
Control sequence of the ACAC resonant softswitched converter
of primary part, (a) Input voltage waveform, (b) Control pulse waveform
of P_{1}, (c) Control pulse waveform of P_{2}, (d) Control
pulse waveform of P_{3}, (e) Control pulse waveform of P_{4},
(f) Output voltage waveform of the primary inverter and (g) Resonant current
waveform of the L_{P} 

Fig. 3: 
Output voltage waveform of primary ACAC inverter 
From Fig. 3, let the amplitude of the input AC supply be
V_{am}, frequency be f_{a}, period be T_{a}, then the
voltage waveform of the input AC supply can be expressed as follow:
In order to facilitate analysis of the circuit and highlight the main issues,
supposed the resonant frequency f_{c} is large enough, then the area
of each trapezoidal curve (S_{ABCE}) can be replaced by the rectangle
area (S_{ABCD}), then each area of the voltage S_{j} can be
expressed as:
where, V_{i}(j) is the length of the rectangle (S_{ABCD}) that
is replaced by the instantaneous voltage (t = j) and the width of the rectangle
is the half resonant period (0.5T_{c}). The zero phase frequency must
be equal to the secondary resonant frequency so that the maximum output power
could be achieved (Wang et al., 2004). Therefore,
the resonant period T_{c }should be:
where, the ω_{0} is the zero phase angular frequency of the system,
as shown in Fig. 3, the area of surrounded by every sinusoid
half wave with the input power after inverted by the high frequency control
pulse (S) is expressed as follow:
where, the N is:
Then the voltage injected into the primary resonant tank should be:
The resonant current of primary part i_{Lp }can be derived as:
where the reflected impedance R_{r }that is dependent on the transformer
coupling and operating frequency is given by:
where, Z_{s} is the impedance of the secondary part and M is the mutual
inductance between primary coil and secondary coil.
Secondary ACAC converter operation: Similarly, the working principle
of the secondary part is also based on the energy injection and free oscillation
mode, it is the inverse process of the primary part. The high frequency resonant
current induced from the primary part is converted into low frequency current
waveform whose amplitude changed according to sinusoidal law, the signals and
waves corresponding to above principle are seen as Fig. 4.
The equivalent circuit of the secondary part based on the mutual induction
model is shown in Fig. 5.
According to the AC impedance model of system resonant tank, the induced voltage
V_{oc }of the secondary resonant inductance L_{s} can be:
Then, the current of the secondary inductance i_{Ls} should be :
where, R_{eq }is the equivalent resistance of the output port of the
secondary resonant link and R_{s }is the inherent resistance of inductor
L_{s}. Substituting Eq.79 into
Eq.10, the secondary inductance current i_{Ls} is
derived as:
It can be seen from Eq.11 that the i_{Ls }is independent
of the load R_{L}, in addition, the onandoff period of the switch
S_{L }is equal, suppose the working time of the circuit is σ, the
expression of the equation as follow can be given according to energy conservation
principle:
Then substituting Eq.12 into Eq.11, the
load current i_{L} can be obtained as follow:

Fig. 4(ag): 
Control sequence of the ACAC resonant softswitched converter
of secondary part, (a) Resonant current waveform of the L_{S}, (b)
Control pulse waveform of S_{1}, (c) Control pulse waveform of S_{2},
(d) Control pulse waveform of S_{3}, (e) Control pulse waveform
of S_{4}, (f) Output voltage waveform of the primary inverter and
(g) Load current waveform of the secondary 
From Eq.13, it can been obviously seen that the load current
i_{L} is completely independent of the load R_{L}, in other
words, the system exactly has the constant current characteristic.
Frequency stability: Form Eq. 13, it can be seen
that the constant current characteristic of the system depend on the resonant
frequency f_{c}. In order to ensure there is only one zero phase angle
frequency, parameters of the system should be satisfied as follow (Zhang
et al., 2013):

Fig. 5: 
Equivalent circuit diagram of the ACAC resonant softswitched
converter of secondary part 
where the expression of the coupling coefficient k is given by:
The M is the mutual inductance between primary coil and secondary coil. In
addition the Γ is defined as shown below:
SIMULATION AND EXPERIMENTAL RESULTS
Simulation analysis: On the basis of the analysis discussed above, the
simulation model in MATLAB/SIMULINK software of the proposed ACAC ICPT system
can be easily built with the parameters shown in Table 1.
The simulation waveforms of the system are as shown in Fig. 6
and 7. It can be seen from Fig. 6b that
the primary resonant current i_{Lp} can be directly generated by the
input AC supply that is shown in Fig. 6a. The steadystate
waveform is achieved after 5 msec and the envelope of the resonant current is
in good quality by using the energy injection and free oscillation control method,
the current amplitude of i_{Lp} is 20 A. The enlarged drawing of the
resonant current (39.5~40.5 msec) shown as Fig. 6c shows that
the frequency of current i_{Lp} is 20 kHz and made to be a low distortion
sinusoidal shape, the system operates at ZCS condition because the control pulse
waveform of P_{1} is in phase with i_{Lp}.

Fig. 6(ac): 
Input AC voltage, resonant current and control pulse waveform
of primary part, (a) Primary input ac supply, (b) Resonant current and (c)
Enlarged drawing of the resonant current 

Fig. 7(ab): 
Resonant current waveform of primary part and load 
Table 1: 
Parameters of proposed ACAC ICPT system 

The resonant current waveform of primary part and load current waveform of
secondary part with dynamic load switching is shown as Fig. 7.
Current waveform of secondary part with dynamic load switching (a) Primary
resonant current waveform with the load R_{L1} = 400 Ω varying
from R_{L2} = 200 Ω and (b) Load current waveform with the load
R_{L1} = 400 Ω varying from R_{L2} = 200 Ω.
From Fig. 7a, as the load R_{L }varies from R_{L1}
= 400 Ω to R_{L2} = 200 Ω the primary resonant current i_{Lp
} varies from 20 to 10 A, simultaneously, the load current i_{L}
shown as Fig. 7b keeps at 2 A, this proves that the symmetric
ACAC ICPT system exactly has the constant current characteristic.
It also can be seen from Fig. 7b that the load current i_{L}
is 50 Hz and made in good quality by the lowpass filtering tank followed of
the inverter.
DISCUSSION
The symmetric ACAC ICPT system shown in Fig. 1 has been
implemented in a laboratory scale. The inverter consists of four IGBTs (International
Rectifier IRGBC40K). The zerocrossing points of inductance current are detected
by the current sense transformers (Talema AS103).

Fig. 8: 
Experimental waveforms of proposed symmetric ACAC ICPT system
with the load R_{L1} = 400 Ω varying from R_{L2} =
200 Ω. (CH1: Control pulse of P_{1}5 V/div; CH2: Current of
the primary inductor i_{Lp}10 A/div; CH3: Current of the load i_{L}2
A/div) 
Phaselocked loop (CD4046) is selected to achieve the ZCS operation for the
converter with variable frequency. According to the parameters in Table
1. The experimental results of the proposed ICPT system are shown below.
Figure 8 shows the experimental waveforms the symmetric ACAC
ICPT system, the primary resonant current i_{Lp }is controlled based
on the energy injection and free oscillation mode, it can be seen from Fig.
8 that the peak resonant current i_{Lp} decrease from 8 to 14.9
A as the load R_{L} is switched from 400 to 200 Ω, while the amplitude
of the output load current i_{L} still remains at 1.86 A and the frequency
keeps at 49.8 Hz. Considering the coil resistance and conduction loss in actual
system, the experimental results are lower than the simulation value which is
obtained under ideal situation. In addition, the load current i_{L}
shown in Fig. 8 (CH3) has slight ripple which is caused by
the output filter capacitor C_{fs} whose discharge time is affected
by the sudden change of the load resistance. However, compared with the fact
that the power of the system decreased by 50% under dynamic load switching condition,
such slight current ripple will not affect our conclusion that the system does
have the constant current characteristic.
From Fig. 9, it can be seen that the system has achieved
ZCS as the resonant current i_{Lp }is in phase with control pulse of
P_{1}. It also can be seen that the experimental curve of the current
i_{Lp} deviates of by about 0.8 kHz from the theoretical value. This
is caused by deviations in actual component values from the nominal values.
The theoretical results are based on the simplifications in the model that ignores
losses in the capacitors and electromagnetic structure.

Fig. 9: 
Steadystate experimental waveforms of the resonant current
and control pulse of primary part (CH1: Control pulse of P_{1}5
V/div; CH2: Current of the primary inductor i_{Lp}10 A/div; CH3:
Current of the load i_{L}2 A/div) 
Therefore, this error in practice doesn’t affect the analyzed results
above this section.
CONCLUSION
This study put forward a symmetric ACAC ICPT system without requiring energy
storage links. The expression for the steady load current based on impulse theorem
has been discussed in detail under dynamic load switching condition. Simulations
and experiments have been carried out to validate the constant current characteristic
of the system and it realizes 50 Hz sinusoidal mains input and generates 50
Hz sinusoidal mains output without any large filter capacitor and rectifier,
this could save cost and volume of the ICPT system and the system complexity
is also been reduced.
ACKNOWLEDGMENTS
This study is financially supported by National Natural Science Foundation
of China (No. 51207173, 51277192). I also would like to give my special thanks
to the anonymous reviewers for their contributions to this study.