This paper presents a steadystate operation analysis of fullbridge seriesresonant inverters focusing on the distorted load current due to lowqualityfactor resonant circuits in induction heating and other applications. The regions of operation based on the zerovoltage switching (ZVS) and nonzerovoltage switching (NONZVS) operations of the asymmetrical voltagecancellation control technique are identified. The effects of a distorted load current under a wide range of output powers are also analyzed for achieving a precise ZVS operating region. An experimental study is performed with a 1kW prototype. Simulation and experimental studies have confirmed the validity of the proposed method. An efficiency comparison between the variable frequency method and the conventional fixedfrequency method is provided.
I. INTRODUCTION
Highfrequency resonant inverters for induction heating (IH) technologies have been widely used in industrial, automotive, pipeline and consumer applications where high efficiency, system reliability, safety, cleanliness, compactness in volumetric physical size, light weight, and performance are required
[1]
. The use of a higher switching frequency results in higher switching losses, resulting in a lowered efficiency. However, this switching loss can greatly be reduced by the softswitching technique
[2]

[6]
. The zerovoltage switching (ZVS) technique is one of the softswitching techniques. It is the representative feature of resonant inverters and is suitable for highswitching frequency operation. The ZVS operation avoids switching losses, reduces electromagnetic interference (EMI) and device stresses, and allows for the possibility of snubberless operation
[4]
,
[7]

[10]
. Voltagesource resonant inverter topologies have received a great deal of attention because of their output power control capability under ZVS operation. Several switching techniques have been reported in highfrequency IH applications such as the pulsefrequency modulation (PFM)
[11]

[13]
, pulsedensity modulation (PDM)
[14]
,
[15]
, asymmetrical dutycycle (ADC)
[16]
,
[17]
, phaseshift (PS)
[18]

[20]
, and asymmetrical voltagecancellation (AVC)
[21]

[24]
. In
[24]
, the variablefrequency AVC control is used in a fullbridge resonant inverter with a lowqualityfactor resonant circuit (
Q_{r}
) to identify the condition of ZVS operation by the fundamental harmonic approximation technique. However, this technique may not guarantee ZVS operation in the entire range of output power. By using the AVC technique in the case of a low
Q_{r}
resonant circuit (less than 2.5
[25]
), the output current (load current) is nonsinusoidal due to a high damping factor (
α
) value. The transient response is oscillatory and exponentially damped in nature. The output current is unavoidably distorted and may result in hardswitching conditions during switching transitions at the end of the positive cycle, causing the socalled nonzerovoltage switching (NONZVS). Consequently, an increase in the switching losses and device stresses results in a lower efficiency.
In practice, the switching loss due to the effect of the parasitic capacitances associated with the charging and discharging of switching devices has been observed during a switching transition period. To mitigate this switching loss, the positive output current diverted from the resonant circuit should be large enough to completely discharge the parasitic capacitors and the switching frequency must be suitably increased above the resonant frequency.
The regions of ZVS and NONZVS operations of the fullbridge inverters for IH applications with a low
Q_{r}
resonant circuit based on the asymmetrical control technique have been identified in this paper. The influence of parasitic capacitors are taken into consideration through computer simulations and verified by experimental results. The remainder of this paper consists of six sections. The circuit configurations and operations are described in Section II. Section III presents a steady state circuit analysis. In Section IV, an analysis of the softswitching operation is provided. The experimental setup and results are provided in Section V. Section VI concludes the work.
II. CIRCUIT CONFIGURATION AND OPERATIONS
 A. Circuit Configuration
Fig. 1
shows a fullbridge seriesresonant inverter circuit for induction heating applications. A voltagesource inverter consisting of four IGBTs (
S
_{1}

S
_{4}
) with antiparallel diodes (
D
_{1}

D
_{4}
) and parasitic capacitors (
C
_{1}

C
_{4}
or
C_{o}
), is connected with a seriesresonant load. To eliminate the turnon switching loss, all of the switches (
S
_{1}

S
_{4}
) are operated at a frequency slightly higher than the resonant frequency under the ZVS condition.
Circuit configuration of fullbridge seriesresonant inverter.
 B. SteadyState ZVS Operation
The gate signals for the switching devices (
S
_{1}

S
_{4}
) and typical steadystate waveforms of the output voltage and current of the inverter for ZVS and NONZVS operations are shown in
Fig. 2
. As shown in
Fig. 2
(a), the inverter operates with the desired ZVS operation.
Figs. 2
(b) and (c) show steadystate waveforms for the NONZVS operations. The output power
P_{o}
is adjusted by varying the shifted angle
β
through switch
S
_{4}
. The output voltage
v_{o}
of the inverter assumes the form of a square wave while the output current
i_{o}
is lagging the output voltage by the angle
θ_{io}
at the end of the positive cycle of
i_{o}
.
θ_{Co}
is an angle defined at the completion of charging and discharging processes of
C
_{1}
and
C
_{2}
, respectively. The fundamental components of the output voltage and current are illustrated by the sinusoidal signals
V
_{o}
_{1}
and
I
_{o}
_{1}
, respectively. The
I
_{o}
_{1}
signal lags the
V
_{o}
_{1}
signal by the phase angle
θ
_{z}
_{1}
. The modes of operation with ZVS are described in eight stages (
t
_{0}

t
_{4}
), as illustrated in
Fig. 3
by the solid arrows.
The gate signals for all switches and typical steadystate waveforms of the output voltage and current. (a) Desired ZVS. (b) NONZVS I. (c) NONZVS II.
Mode 1
(t_{0}−t'_{0}):
The switches
S
_{2}
and
S
_{3}
are already turned off, and the switches
S
_{1}
and
S
_{4}
are still off. Negative output current flows through the parasitic capacitors
C
_{1}
,
C
_{2}
,
C
_{3}
and
C
_{4}
. The parasitic capacitors
C
_{2}
and
C
_{3}
are completely charged by the
L
_{eq}

C
_{r}
resonant circuit while the parasitic capacitors
C
_{1}
and
C
_{4}
are completely discharged. At the same time, the output voltage increases from 
V
_{DC}
to +
V
_{DC}
. From the Laplace transform, the output current
i_{o}
and voltage
v_{o}
during this mode are given as follows:
where:
is the initial value of the output current
i_{o}
, and
A
1=2
V
_{0}

V
_{C1}
+
V
_{C2}
+
V
_{C3}

V
_{C4}
is the total initial voltage of the capacitor in each mode when
V
_{0}
is the initial voltage of the resonant capacitor
C
_{r}
.
V
_{C1}
,
V
_{C2}
,
V
_{C3}
, and
V
_{C4}
are the initial voltages of the parasitic capacitors
C
_{1}
,
C
_{2}
,
C
_{3}
, and
C
_{4}
, respectively.
Mode 2
(t'_{0}−t_{1}):
At
t'
_{0}
, the switches
S
_{2}
and
S
_{3}
are still off. The negative output current is diverted from the parasitic capacitors
C
_{1}
and
C
_{4}
to the antiparallel diodes
D
_{1}
and
D
_{4}
. Then it reaches zero at
t
_{1}
. After the switch dead time
t_{d}
, the switches
S
_{1}
and
S
_{4}
receive positive gating signals and the output voltage is equal to +
V
_{DC}
. The current
i_{o}
and voltage
v_{o}
in this mode are expressed as:
where:
Mode 3
(t_{1}−t'_{1}):
At
t
_{1}
, the switches
S
_{1}
and
S
_{4}
start conducting after the antiparallel diodes
D
_{1}
and
D
_{4}
are turned off, and the ZVS operation is obtained. The positive output current flows from zero until
t'
_{1}
, and the output voltage is still equal to +
V
_{DC}
. At this stage, the current
i_{o}
and voltage
v_{o}
in this mode are expressed as:
where:
Mode 4
(t'_{1}−t_{2}):
At
t'
_{1}
, while the switch
S
_{1}
still conducts, the switch
S
_{4}
is turned off due to the shifted angle
β
that is adjusted to control the output power. During this mode, the output current flows in the same direction. The parasitic capacitor
C
_{4}
is charged while the parasitic capacitor
C
_{3}
is discharged. At this stage, the output voltage decreases to zero. The current
i_{o}
and voltage
v_{o}
are expressed as:
where:
Mode 5
(t_{2}−t'_{2}):
At
t
_{2}
, with a given value of the shifted angle
β
, the switch
S
_{4}
is already turned off while the switch
S
_{1}
still conducts and the output current flows through the antiparallel diode
D
_{3}
. During this stage, the output voltage is already zero and the positive output current is decreasing. The current
i_{o}
and voltage
v_{o}
become:
where:
Mode 6
(t'_{2}−t_{3}):
At
t'
_{2}
, all of the switches are off. A part of the positive output current flows through the antiparallel diode
D
_{3}
and the parasitic capacitors
C
_{1}
and
C
_{2}
. At the same time, the capacitor voltage
V
_{C1}
increases from zero to +
V
_{DC}
, whereas the capacitor voltage
V
_{C2}
decreases from +
V
_{DC}
to zero. In this mode, the output voltage reduces from zero to 
V
_{DC}
at
t
_{3}
. The current
i_{o}
and voltage
v_{o}
are:
where:
Mode 7
(t_{3}−t'_{3}):
At
t
_{3}
, the switch
S
_{1}
is still off during the dead time. The antiparallel diodes
D
_{2}
and
D
_{3}
naturally conduct while the positive output current decreases to zero at
t'
_{3}
. At this stage, the output voltage is equal to 
V
_{DC}
. The switches
S
_{2}
and
S
_{3}
receive the same positive gating signal. Therefore, the current
i_{o}
and voltage
v_{o}
in this mode are:
where:
Mode 8
(t'_{3}−t_{4}):
At
t'
_{3}
, as soon as the antiparallel diodes
D
_{2}
and
D
_{3}
are turned off, the switches
S
_{2}
and
S
_{3}
conduct under ZVS operation. During this stage, the output current and voltage are both negative and a full cycle of waveform is achieved. This can be expressed by:
where:
 C. NONZVS Operation
Two NONZVS operations have been observed as illustrated in
Fig. 3
. The first one emanated from an increase in the shifted angle
β
with the aim of reducing the output power without varying the switching frequency
f_{s}
. The first category of NONZVS operations (NONZVS
I
) is indicated by the dashed arrows where the previously described operation of mode 7 is replaced by mode 7'. Mode 6 begins after the gate signal of
S
_{1}
is removed at
t'
_{2}
, as depicted in
Fig. 2
(b). The positive output current flows through the circuit formed by
C
_{1}
,
C
_{2}
,
D
_{3}
, and the DC input voltage source. During this interval, the capacitor voltage
V
_{C1}
increases whereas the capacitor voltage
V
_{C2}
decreases. The output voltage becomes negative in this mode. At the beginning of mode 7', after the antiparallel diode
D
_{3}
is turned off at
t
_{3}
with no gate signals of
S
_{2}
and
S
_{3}
, the output current becomes negative and flows through the parasitic capacitors
C
_{1}
,
C
_{2}
,
C
_{3}
and
C
_{4}
. Therefore, the voltages across the switches
S
_{2}
and
S
_{3}
increase. At
t'
_{3}
, the switches
S
_{2}
and
S
_{3}
start conducting under the NONZVS. The parasitic capacitors
C
_{1}
and
C
_{2}
experience an instantaneous voltage change. This results in high current spikes in the switches
S
_{1}
and
S
_{2}
. In this case, the modes of operation are sequenced as
Operation modes of a fullbridge resonant inverter: (a) desired ZVS, (b) NONZVS I, and (c) •••► NONZVS II.
The second category of NONZVS operations (NONZVS
II
) is indicated by the dotted arrows in
Fig. 3
. It can also be divided into eight stages as
The original operations of modes 6 and 7 in the ZVS operation are changed to modes 6' and 7", respectively. The operation in mode 6' begins when the positive output current becomes zero at
t'
_{2}
before the end of the gate signal of
S
_{1}
, depicted in
Fig. 2
(c). The negative output current flows through the antiparallel diode
D
_{1}
and the parasitic capacitors
C
_{3}
and
C
_{4}
. During this mode, the capacitor voltage
V
_{C3}
increases whereas the capacitor voltage
V
_{C4}
decreases, adding up to a high value for the output voltage depending on the operating frequency. At the same time, the capacitor voltages
V
_{C1}
and
V
_{C2}
remain unchanged at zero and +
V
_{DC}
, respectively. Mode 7" begins at
t
_{3}
. The switches
S
_{2}
and
S
_{3}
start conducting instantaneously under the NONZVS operation. Since the capacitor voltage
V
_{C1}
is initially zero, this creates a shortcircuit path of the input voltage source through the switch
S
_{2}
. All of the parasitic capacitors suffer from a sudden voltage change that results in current spikes in the capacitors (
C
_{1}

C
_{4}
) and the switches
S
_{2}
and
S
_{3}
for a short interval. Such an operation reduces the inverter efficiency due to the high turnon switching loss and it causes device stress, which may destroy all of the switches.
Therefore, for the case of a low
Q_{r}
resonant circuit, the damping frequency
ω_{d}
of the seriesresonant circuit is less than the resonant angular frequency
ω_{r}
due to a high damping factor
α
. Two NONZVS operations on the switches
S
_{2}
and
S
_{3}
are likely to be encountered if the inverter is operated at an unsuitable switching frequency.
III. STEADY STATE CIRCUIT ANALYSIS
The induction heating load can be modeled as an equivalent resistor (
R_{eq}
) and inductor (
L_{eq}
). The resonant circuit is formed by adding a resonant capacitor (
C_{r}
), as shown in
Fig. 1
. The load quality factor of the resonant circuit is defined as:
where
f_{r}
is the resonant frequency, and
A steadystate analysis of the seriesresonant circuit is based on the equivalent parameters and typical waveforms under the ZVS operation as shown in
Fig. 1
and
Fig. 2
(a), respectively. To simplify the analysis, the conventional assumptions are made for the analysis in this section as follows.

1) The converter elements are ideal.

2) The effect of the ripples from the DC input voltage is neglected.

3) The parasitic inductance and capacitance in the switches are neglected.
With the stated assumption, the magnitude of the impedance
Ẑ_{eq}
of the seriesresonant circuit can be obtained as:
where
h
is the order of harmonic components, and
f_{n}
is the normalized frequency (
f_{s}
/
f_{r}
).
The impedance phase angle of the harmonic components is given by:
The output voltage is given by:
The amplitude of the harmonic components of the output voltage can be written by means of the Fourier series as:
where
β
is the shifted angle of the switch
S
_{4}
with a value from 0º to 180º, and
V
_{DC}
is the DC bus voltage. The angle
θ_{vh}
between the output voltage
v_{o}
and its harmonic voltage (
V_{oh}
) can be determined by:
The output current can also be written by:
where the angle
θ_{ih}
is the phase difference between the output voltage and the impedance phase angle (
θ_{ih}
=
θ_{vh}

θ_{zh}
). The amplitude of the harmonic components of the output current is given by:
Note that if the load quality factor is sufficiently high (more than 2.5), the output current
i_{o}
flowing through the seriesresonant circuit assumes the form of a sinusoidal wave. In addition, the angle
θ_{io}
in
Fig. 2
(a) can be reasonably approximated by the phase difference
θ
_{i}
_{1}
.
From (16), the average output power
P_{o}
is given as:
The maximum value of the output power in (17) occurs at
f_{n}
= 1 and
β
= 0. Clearly, if the normalized frequency
f_{n}
and
β
are increased, the output power is reduced, as shown in
Fig. 4
(i.e., an increase of
β
will result in a reduction of the output power). However, the minimum output power is limited to 25% of the maximum output power at
β
=180º since the output voltage control is through an adjustment of the positive cycle and the minimum achievable output voltage is at 50% of its rated value
[21]
.
The relationship of percent output power, β, and f_{n}.
IV. ANALYSIS OF THE SOFTSWITCHING OPERATION
A necessary requirement for the ZVS operation of a fullbridge resonant inverter with the asymmetrical voltagecancellation control technique is that the applied voltage across the switches must be zero during the turnon operation. Although, the switching frequency of the seriesresonant inverter is higher than the resonant frequency, the NONZVS operations may occur due to an increase in the shifted angle
β
, resulting in a variation of the angle
θ
_{v}
_{1}
, as shown in
Fig. 5
. From
Fig. 2
(a), neglecting the parasitic capacitances, the ZVS condition requires that the angle
θ
_{io}
must be greater than zero. This means that the positive output current waveforms become zero after the end of the gate signal
S
_{1}
(i.e., the antiparallel diodes
D
_{2}
and
D
_{3}
provide a path for the energy stored in the resonant circuit that must be conducted at
t'
_{2}
).
The angle θ_{v}_{1} as a function of shifted angle β.
In practice, the inverter is operated at high frequencies and the effects of the parasitic capacitors can be significant. They can alter the predetermined ZVS operation during a switching transition at the end of the positive cycle of
i_{o}
. The discharging processes of the parasitic capacitor
C
_{2}
must be complete before the output current reaches zero (i.e., the output current should be large enough to ensure the ZVS condition). Therefore, the output current continues to flow through the antiparallel diodes
D
_{2}
and
D
_{3}
. The critical angle of the parasitic capacitors is calculated by:
where
C_{o}
is the parasitic capacitor of the switch, and
i_{o}
(
t
)
_{t=π}
is the output current at 180º.
The angle
θ_{Co,cri}
may be used to define a proper dead time interval. The critical ZVS boundary of operation is obtained by setting
θ
_{io}
=
θ_{Co,cri}
=
θ_{td}
in (15) where
θ_{td}
is an angle of the dead time
t_{d}
. The critical ZVS boundary under the effect of
C_{o}
is obtained as indicated by the solid line while neglecting
C_{o}
as indicated by the dotted line in
Fig. 6
. If the load quality factor is high, for example
Q_{r}
= 5, the boundary line is rather flat with
f_{n}
around 1.06 at 110º of the shifted angle
β
. On the other hand, at
Q_{r}
= 1, the highest boundary value of
f_{n}
will shift to around 80º of the shifted angle
β
. Therefore, the regions of ZVS and the two NONZVS operations can be identified in terms of
f_{n}
as described in Section II. Again, the dotted line is the boundary between the NONZVS
I
and the NONZVS
II
operations (where
θ_{io}
= 0) whereas the solid line is the boundary between the desired ZVS and the NONZVS
I
operations. This implies that a switching frequency higher than the solid line will ensure the ZVS operation. If the shifted angle
β
is adjusted to 60º,
f_{n}
must be more than 1.24 to guarantee the ZVS operation. In addition, the conventional AVC control with fixed frequency control requires the inverter to operate above the resonant frequency (i.e.
f_{s}
>
f_{r}
) and the highest boundary value of
f_{n}
, specifically
f_{n}
> 1.26 for this case, at all times.
Regions of ZVS and NONZVS operations in terms of f_{n}.
V. EXPERIMENTAL SETUP AND RESULTS
 A. Experimental Setup
A hardware prototype is created where an induction cooker is used to illustrate the proposed analysis on the low
Q_{r}
resonant circuit. The system controller is an STM32F4 discovery board. To avoid acoustic noise from the induction coil and the cooking vessel, the resonant frequency must be over 20 kHz. The material used in the cooking vessel is essential in terms of efficiency. The cooking vessel is an offtheshelf lowcost vessel made of stainless steel that measures 235 mm in diameter and 75 mm in height. The bottom and wall thicknesses are 1.4 mm and 0.8 mm, respectively.
The induction coil is a 29turn flat spiral made of a litz wire consisting of 35 strands of 26 SWG wire to reduce the skin effect losses and the consequent increase of heat in the coil. The maximum coil current is approximately 12 A rms. A resonant capacitor
C_{r}
of 300 nF, 1000 V has been selected to provide the resonant frequency at 33 kHz, and the quality factor
Q_{r}
at resonance is approximately one. Note that the resonant capacitor needs to withstand the peak voltage, which may be greater than the DC input voltage because of voltage magnification due to the circuit quality factor.
The inverter specifications and circuit parameters are given in
Table I
. The dead time interval
t_{d}
is chosen as 320 ns based on the manufacturer’s data sheet. For the complete ZVS condition, the angle
θ_{io}
must be higher than the angle
θ_{td}
, as shown in
Fig. 2
(a). As mentioned before, an increase of the shifted angle
β
will cause a reduction of the angle
θ_{io}
. In this experiment, the angle
θ_{io}
is set at 7º by controlling the switching frequency. In the worst case scenario, where the shifted angle
β
is around 80º, the switching frequency must increase to 45.5 kHz (
f_{n}
= 1.37) so that the angle
θ_{io}
becomes 7º (425 ns). Thus, the switching frequency of the inverter is varied between 33.75 kHz and 45.5 kHz to assure operation in the desired ZVS region as shown in
Fig. 6
.
INVERTER SPECIFICATIONS AND CIRCUIT PARAMETERS
INVERTER SPECIFICATIONS AND CIRCUIT PARAMETERS
 B. Simulation and Experimental Results
A computer simulation is performed to illustrate the proposed boundaries of the ZVS and NONZVS operations using the inverter specifications and circuit parameters from
Table I
. To demonstrate the inverter operation in the ZVS, critical ZVS, NONZVS
I
, and NONZVS
II
regions, the corresponding switching frequencies are set to 45.5, 40.5, 39.5 and 36 kHz, respectively. In addition, the shifted angle
β
is initially set at 80º.
The steadystate phase plane trajectories of the current and voltage of the inverter (
i_{o}
and
v_{o}
) and the switches (
i
_{S2}
and
v
_{S2}
) for the desired ZVS, critical ZVS, and two NONZVS operations are shown in
Fig. 7
. In
Fig. 7
(a), the switch current
i
_{S2}
is negative while the switch voltage
v
_{S2}
decreases from +
V
_{DC}
to zero at
t
_{3}
. The negative current
i
_{S2}
flows through the diode
D
_{2}
then reaches zero at
t'
_{3}
, and ZVS operation is achieved. Under the critical ZVS operation, it can be seen that the switch voltage
v
_{S2}
, indicated in
Fig. 7
(b), decreases from +
V
_{DC}
to zero while the small negative value of the switch current
i
_{S2}
also flows through the capacitor
C
_{2}
. With an increase in the shifted angle
β
to reduce the output power, the angle
θ_{io}
decreases and becomes less than the angle
θ_{td}
. The inverter operates in the NONZVS
I
region as indicated in
Fig. 7
(c). The negative switch current
i
_{S2}
crosses zero and becomes positive while the switch voltage
v
_{S2}
is still positive. This causes a current spike in the switch
S
_{2}
during the turnon transition. Although this current spike is not likely to damage the switch, the inverter’s efficiency is sacrificed.
Fig. 7
(d) shows the phase plane trajectory under the operation of the NONZVS
II
. At
t'
_{2}
, the output current
i_{o}
is negative flowing through the diode
D
_{1}
, before the switch
S
_{1}
is turned off. The output voltage
v_{o}
is exposed to the increasing voltage across the capacitor
C
_{3}
, causing a current spike several times the normal current on the switches
S
_{2}
and
S
_{3}
. Clearly, the current spike in the NONZVS
II
operation can cause damage to the switches.
Phaseplane trajectories of the current and voltage of the inverter and the switch S_{2}. (a) Desired ZVS. (b) Critical ZVS. (c) NONZVS I. (d) NONZVS II.
The relationship between the angle
θ_{io}
and the shifted angle
β
at various switching frequencies
f_{s}
is shown in
Fig. 8
. The output power regulation through the shifted angle
β
has an obvious effect on the angle
θ_{io}
. An unsuitable switching frequency can lead to ZVS or NONZVS operations. For instance, if the output power is set to the desired value at
β
= 80º. The switching frequency
f_{s}
at 45.5 kHz yields an operation in the ZVS region because the angle
θ_{io}
is greater than the angle
θ_{Co,cri}
at 4.7º (where
f_{s}
= 40.5 kHz). On the other hand, a switching frequency
f_{s}
at 39.5 kHz causes the angle
θ_{io}
to become less than the angle
θ_{Co,cri}
. This is an operation in the NONZVS
I
region. Note that if the angle
θ_{io}
is further decreased, through a switching frequency reduction, the inverter is operated in the NONZVS
II
region. In other words, the angle
θ_{io}
becomes negative as indicated by the dashed line.
Relationship between the angle θ_{io} and the shifted angle β at various switching frequencies f_{s}.
The simulation and experimental results under the desired ZVS and two NONZVS operations are shown in
Figs. 9
and
10
. The results under the ZVS operation are shown in
Figs. 9
(a) and
10
(a). The switching frequency of the inverter is then adjusted (45.5 kHz), according to
Fig. 6
, where the angle
θ_{io}
becomes 7º over the angle
θ_{Co,cri}
to assure operation in the desired ZVS region. The results under the operation of the NONZVS
I
are shown in
Figs. 9
(b) and
10
(b) where the angle
θ_{io}
is at 3.2º to allow for operation in the NONZVS
I
region. In addition, the NONZVS
II
results are shown in
Figs. 9
(c) and
10
(c) where the angle
θ_{io}
is 11º. For the NONZVS operations, as observed in the results, the switches
S
_{1}
and
S
_{4}
are turned on at zero voltage, but the switches
S
_{2}
and
S
_{3}
are turned on at nonzero voltage due to the load parameters and unsuitable switching frequency. This results in high switching losses in switches
S
_{2}
and
S
_{3}
which in turn reduces the inverter efficiency. In the case of the NONZVS
II
, the current spikes at the turnon switching period may cause damages to the switches
S
_{2}
and
S
_{3}
.
Simulation waveforms of v_{o}, i_{o}, v_{S2}, i_{S2}, v_{S4} and i_{S4} at β = 80º for: (a) Desired ZVS region with f_{s} = 45.5 kHz. (b) NONZVS I region with f_{s} = 39.5 kHz. (c) NONZVS II region with f_{s} = 36 kHz. (v_{o}: 50V/div, i_{o}: 5A/div,v_{S2}: 50V/div, i_{S2}: 5A/div, v_{S4}: 50V/div, i_{S4}: 5A/div and Time: 5us/div.).
Experimental waveforms of v_{o}, i_{o}, v_{S2}, i_{S2}, v_{S4} and i_{S4} at β = 80º for: (a) Desired ZVS region with f_{s} = 45.5 kHz. (b) NONZVS I region with f_{s} = 39.5 kHz. (c) NONZVS II region with f_{s} = 36 kHz. (v_{o}: 50V/div, i_{o}: 5A/div,v_{S2}: 50V/div, i_{S2}: 5A/div, v_{S4}: 50V/div, i_{S4}: 5A/div and Time: 5us/div.).
 C. Efficiency
An efficiency comparison between the proposed variable frequency and conventional fixedfrequency methods for AVC schemes are provided as shown in
Fig. 11
. As mentioned earlier, the switching frequency of the fixedfrequency method is set to 45.5 kHz while the switching frequency of the variable frequency method is in the range of 33.7545.5 kHz. Clearly, the variable frequency control yields a higher efficiency, especially in the low output power range, since the switching frequency is allowed to decrease. The benefits of knowing the regions of operation are the insight into the optimal operation as a systematic approach while maintaining the ZVS operation throughout all of the output power levels.
Efficiency comparison between the variable frequency and the conventional fixedfrequency methods.
VI. CONCLUSION
This paper addresses the issue of the regions of ZVS and NONZVS operations of a fullbridge inverter focusing on the distorted load current due to a lowqualityfactor resonant circuit in induction heating and other applications. The steadystate circuit analysis is based on the asymmetrical control scheme and a Fourier series analysis. The operations of ZVS and NONZVS are analyzed in terms of the typical waveform phenomenon of the inverter and the analytical equations in the operation modes. Under the ZVS operating criteria, the parasitic capacitances must also be taken into account. The presented circuit configurations and operations provide insight into the selection of optimal operation with the softswitching technique to achieve a high efficiency. In addition, this method can be applied to other applications.
BIO
Samart Yachiangkam was born in Lampang, Thailand. He received his B.S. degree in Technical Education from the Rajamangala Institute of Technology (Northern Campus), Chiang Mai, Thailand, in 1997, his B.S. degree in Engineering from the Rajamangala Institute of Technology, Pathum Thani, Thailand, in 2001, and his M.S. degree in Engineering from the King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, Thailand, in 2004. He is presently working toward his Ph.D. in Electrical and Computer Engineering, KMUTT. His current research interests include power electronics and control, and highfrequency softswitching power converters.
Anawach Sangswang was born in Bangkok, Thailand. He received his B.S. degree in Engineering from the King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, Thailand, in 1995, and his M.S. and Ph.D. degrees from Drexel University, Philadelphia, PA, USA, in 1999 and 2003, respectively. From 1999 to 2003, he was a Research Assistant with the Center for Electric Power Engineering, Drexel University. He is currently an Assistant Professor in the Department of Electrical Engineering, KMUTT. His current research interests include stochastic modeling, the digital control of power electronic converters, and power system stability.
Sumate Naetiladdanon received his B.S. degree in Engineering from Chulalongkorn University, Bangkok, Thailand, in 1995, his M.S. degree from Rensselaer Polytechnic Institute, Troy, NY, USA, in 1999, and his Ph.D. degree from Osaka University, Osaka, Japan, in 2006. He is presently a Lecturer in the Department of Electrical Engineering, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, Thailand. His current research interests include power electronics for power quality improvement and renewable energy.
Chayant Koompai was born in Surat Thani, Thailand. He received his B.S. degree in Engineering from the King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, Thailand, in 1973. He has had more than 30 years of experience working in the field of induction heating. His current research interests include circuit analysis and inductionheating systems.
Saichol Chudjuarjeen was born in Prachinburi, Thailand. He received his B.S. degree in Engineering from the Mahanakorn University of Technology, Bangkok, Thailand, in 2000, and his M.S. and Ph.D. degrees in Engineering from the King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, Thailand, in 2004 and 2011, respectively. He is presently a Lecturer with the Department of Electrical and Telecommunication Engineering, Rajamangala University of Technology Krungthep, Bangkok, Thailand. His current research interests include highfrequency resonant inverters for induction heating, currentsource and voltagesource inverters, and the control of powerelectronic systems.
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Chap. 6