PEDS 2007
Analysis of a Full-Bridge Inverter for Induction
Heating Using Asymmetrical Phase-Shift Control
under ZVS and NON-ZVS Operation
N. Yongyuth*, P. Viriya* and K. Matsuse**
Dept. of Electrical Engineering, Faculty of Engineering, King Mongkut's Institute of Technology Ladkrabang,
Bangkok, 10520, Thailand, Tel. 662-7373000 EXT. 3515, 3516 Fax. 662-3264550, E-Mail: kpviriya gkmitl.ac.th
** School of Science and Technology, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasaki-shi 214, Japan,
Tel. +81-44-934-7293, Fax. 03(3296)4339, E-Mail: matsuse dics.meiji.acjp
*
Abstract-This paper presents a detailed analysis of
circuit operation under ZVS and NON-ZVS switching
conditions in a high-frequency full-bridge inverter for
induction heating, using the principle of asymmetrical
phase-shift control over a wide control range both in
positive and negative directions. A variety of modes of
circuit operation with the voltage and current equations
during phase-shift power control under the operating
conditions of ZVS and NON-ZVS are analyzed as a first
step and the output voltage and current waveforms are
obtained by MATLAB program. These waveforms will be
analyzed by Fourier analysis which can lead further to the
calculation of ac output power PO, dc input power Pd, and
hence the conversion efficiency 17 of the full-bridge
inverter. The analysis results shows that the control ranges
of ac output power PO and dc input power Pd are limited
by the occurrence of NON-ZVS operating condition, which
changes according to the switching frequency fs .
control both in positive and negative directions will be
analyzed in details for various quantities of circuit
parameters, since the phase-shift control range in both
directions will be limited when ZVS circuit operation
becomes NON-ZVS operation. These quantities are, for
examples, ac output voltage vo, ac output power PO, dc
input power Pd and inverter efficiency 7, etc.
VO
Vd
Vd
~~~ ~ ~ ~
Sv vevS
v<Fe<Fv<F v E<FM< #
Index Terms - full-bridge, induction heating,
asymmetrical phase-shift, inverter, ZVS, NON-ZVS
I_
0
I. INTRODUCTION
The concept of this paper is achieved by considering
further as a continuous idea from the research work [1-6]
starting from a single phase full-bridge phase-shift power
control under the switching conditions of ZVS and NONZVS for induction heating. The circuit operation and its
corresponding output voltage and current waveforms for
= 40 are
phase-shift power control at phase-shift
l
illustrated in the upper-part of Fig. 1 with two repeated
periods of powering (P), free-wheeling (F), and
regenerating (R). Then, reducing the phase-shift 0 from
0 = 400 to zero phase-shift zs = 0 , the output waveform
with only two repeated periods of powering (P), and
regenerating (R) is obtained with the operating circuit of
two free-wheeling modes (F) eliminated [3]. The output
waveform with zero phase-shift ( 1 = 00 ) will be used as
a mid-point between the positive and negative directions
of phase-shift control as shown by the output waveforms
of asymmetrical phase-shiftl 0 = 400 and phase-shift
0 = -400 in the lower part of Fig. 1. So, in this paper, the
full-bridge inverter with the load of induction heating of
Fig. 2 which operates under the switching conditions of
ZVS and NON-ZVS during asymmetrical phase-shift
1-4244-0645-5/07/$20.00©2007 IEEE
o
Fig. 1 Circuit operation of asymmetrical phase-shift related to
that of symmetrical phase-shift full-bridge inverter
10
I
IN'
Cd, C=O.6p 4700pF
C
Cd-=
=
-
Ct-Ct-CC 2
1 0
Work-piece High frequency
transformer
Fig. 2 Full-Bridge Inverter fed induction heating
476
II. ANALYSIS OF CIRCUIT OPERATION
First, we show a variety of modes of circuit operation
for the main power circuit which are illustrated in Fig. 3
for the case of phase-shift control ( 0 =0180°
). The circuit operation in one cycle of
and =-180
0
output voltage and current waveforms V0, io is shown in
6 modes under the case of ZVS operation ( Modes
000000 ). Fig. 4 shows the linear variation of the
phase difference between the fundamental output voltage
V0,1 and the front edge of square wave output voltage
vo during phase-shift control both in positive and
negative directions. It can be seen that with positive
phase-shift from o0 to +180°, the phase angle of the
fundamental output voltage V0,1 will move away from
60 -
b O
©D
...
\\~~~~~~~~~~~~....
40
i
..
.60
........
-100
200
160
s0
120
40
0
-40
-s0 -120 -160 -200
Phase-Shift, 0 (degrees)
Fig. 4 Linear variation of phase angle /3 of VO,1 vs.
phase-shift angle 0b
20.
1
0ll
SI:g)
(~J1~
o
(
..
V0,1
CtS *
S*S
-I )4 1Ddg¢QiIT
Cs2
C2
V0
V
b=54°
//
/'
#
V04l W#50
'0=o
0 =54°
flo°
Vo
Vo,t
(R
0
0 = 0°
ttl
1
/
))=b-54~
~~NON-ZVS
Fig. 5 Circuit operation for the case of NON-ZVS at phaseshift sb 54° o° and -54°
0=- 540
Fig. 3 Circuit operation for the case of ZVS at phase-shift
S = 54°, 0° and -54'
................. ........
m-20\
the font edge of output voltage vo with an increasing
leading angle. This makes the zero-crossing of output
current io move toward the font edge of output voltage
vO, where NON-ZVS operation may occur, but in case of
negative phase-shift control, the NON-ZVS operation
may occur at the tailing edge of positive half-cycle of
square wave voltage vo, and in case of zero phase-shift
control, NON-ZVS operation may occur both at the front
and tailing edges, especially when the operating
frequency is not high enough. In Fig. 5, we also show the
circuit operation in one cycle of output voltage and
current waveforms vo io in another 6 modes under the
cases of the following NON-ZVS operation: (1) Modes
0D
..
601
©®®©®O(E@) for phase-shift , =54O can cause a
breakdown to the switch pair S1 -Si, by considering
Mode 0. (2) Modes 000000)@) for phase-shift
477
0 = 0° can cause a breakdown to the switch pair S1 -S2,
by considering Mode 0 and the switch pair S2-S2, by
considering Mode 0. (3) Modes 000000 for phaseshift
-54- can cause a breakdown to the switch pair
S2-S', by considering Mode 0. So, there are three
possibilities for the full-bridge inverter switches to
become breakdown (the switch pair S1 -S', the switch
pair S2 -SI, or both).
=
III. VOLTAGE AND CURRENT EQuATIoNs IN EACH
MODE OF CIRCUIT OPERATION
From these modes of circuit operation, various
equations of output voltage Vo and output current io can
be also calculated and obtained in the following equations:
Case (1) Equations 0 0 0 © © 0 for ZVS operation
Case (2) Equations 0 0 © © 0 0 for 0 > 0
00(© 00 for 0 = 0°
Case (3) Equations (0 ( (
( 0
0 (© ) for 0 < 0°
Case (4) Equations (0 ((0
Vo = Vd
Vd -V-aLi snt+Icos0co,0
(D
io =eat
e
Cl=
V
I
£02
=
1 -2 _a'Isinw2t+w2Icosw2tl
2V2
2L)j
B1 = {(-Cdj/C)(Vt -V2 +VI v-2)-2(V+Vl -V2)
+CdsL(V1 -V2 +V1
+W2) }(1/4L)
V2)((a2
z{ (Cd/C)(V- V2+VI'+V2')+2(V-V -V2) } (1/4L)
VV2 V1)(a2 +W2 )-2LI(ac2 +22 )
-2a(V+V2-V )-a(Cd/Cd))(V2' -V1'+V2 -V1)
-aCdsL(V2 V 2 V )(a2 +W2 )} (1/4CO2L)
A2 z{ RC,(V
B2 ={ (-Cd, /C)(V2 -V,+V2 -V )-2(V+V2 -V )
+CdQL(V v- +V2 -Vt)(a2 +02a ) } (1/4L)
D2= { (CdI/C)(V2'-v,'+V2+v1)+2(V-V2-v') } (1/4L)
The above equations in cases (2), (3) and (4) are those of
NON-ZVS. Fig. 6 shows the calculated and experimental
results of output voltage and current waveforms under
ZVS operation, using the equations in case (1) with the
use of M\ATLAB program. The calculated waveforms are
obtained with phase-shift , = 54 ,O ,-54o at switching
frequency 68 kHz. It can be observed that the peak value
of output current waveforms becomes the highest at
phase-shift 5 = 0° and then become decreasing with the
increase or decrease of phase-shift from O0 to 54 or
o to-54', respectively. Moreover, at only the mid-point
of phase-shift 5 = 0°, the output current io can be
obtained with almost a sinusoidal waveform. These
calculated waveforms with the principle of circuit
operation are also verified by comparison with the
-jVd
-Vd
io = e oat
V0
le-at(Aisinw2t+Bicosw2t)+D I]
( 2CC2
)J['2
V1)
+(V2 -VI)
-2V
io =
vo
srw+
I
A1 ={RCd (VI-l2 +VI -V2)(c2 +w2) 2LI(X22+w2)
-2x(V+Vl-V2)-a(Cd,/C) (VI -V2 +VI -V2)
-~~~ 'rd
~~
1--V22+V
2) ((a 2 + c~}(/w
a22 ) } ( 1/4 W2 L )
-aCd,L(Vl
+VIj JV)
C
j{a2 +
+ (VI -'V2
io=e 02
00(
aLI )sinml t+Icoswltj
-eat (A2 sin w2t + B2 cos w2t) + D21
e
+VV ,,
2V
(.
_aIsin
) w2t+ w2Ic0sw2tj
i
j
Where
V1 the initial value of voltage vc,
vi the initial value of voltage vc,
v2 the initial value of voltage Vc2
v2, the initial value of voltage vc2,
I the initial value of load current io in each mode of
circuit operation
V: the initial value of load capacitor voltage in each
mode of circuit operation
a
i
2../div
(2 div
t
~~~NORM:AOOMS/s
-
Experiment
phase shift; 0'
CH1-50V iCH2=500.V:
DO 100:1
DC 10:1
V
0
jio
...X
R
Experiment
= 2L
st2 = (LC
CH2=500.V
DC 10:1
CH1-50V
DC 100:1
phase shift 07 54
I,
....
Fig. 6 Calculated and experimental output voltage and current
waveforms under ZVS operating condition at fs = 68 kIHz
50 V/div, 5 A/div, 2 ,us/div
LCd,) (2L
478
DC 100:1
DC 10:1
i.
2sdv
b cos co t
-V +-[{2 sin ( O)}
V
..NORM :lGOMSIs
V0
+ {2 - 2 cos (if - z)}sin cot]
o0
[{2sin2(z-Z)}cos2a)wt
+{2 -2cos2(rb)}sin2cq,t]
+ Vd
Experiment
phase shift 0 = 54
+
V
[{21sin 3(ir- s)}cos3wot
+2- 2cos3(f-
Experiment
d
io
phase shift #-0
(5)
zb)}sin3wot]+
[12 sin (ir- S)lcos(co, t
1)
+{2 - 2cos (iz- Z)}sin(cot - 1)]
+-Vd [2sin 2 (i -S )} cos(2 cot-02)
(6)
2ifZ2
oL
+{2 - 2 cos 2 (iz -
)}sin(2c,t - 02)]
+-Vd [{ 2sin 3(ifz- i)}Icos(3w t -93)
Fig. 7 Calculated and experimental output voltage and current
waveforms under NON-ZVS operating condition
50 V/div, 5 A/div, 2 ,us/div
+{2-2cos3(if-b)}sin(3co,t-033 )]+
cos9n = cos(tan (
experimental ones. Fig. 7 shows the calculated and
experimental results of output voltage and current
waveforms under NON-ZVS operation, using the
equations in cases (2), (3) and (4) with the use of
M\ATLAB program. The calculated waveforms are
obtained with phase-shift is= 54', o -54- at switching
frequency 64 kHz, 58 kHz and 64 kHz, respectively.
These calculated waveforms with the principle of circuit
operation are also verified by comparison with the
experimental ones. Also, it is observed that at different
phase-shift control, NON-ZVS operation occurs at
different position of the output voltage (front edge at
0 = 540, tailing edge at 0 -54 and both at = 0 ).
cos ttan
cs
-1
R
)
cos(tan (
)'(7)
R
3c L-(L13oAC)A
)
R
c +sV9+J2d2I02 cOs
PO= VloOS1
92
+ V03103 cos93 +.
(8)
,
,
=
,
IV. ANALYSIS OF OUTPUT POWER PO, Dc INPUT POWER
Pd AND EFFICIENCY
160
The calculated output voltage V0 of Fig. 6 can be
analyzed into various component waveforms as shown in
(5), by Fourier analysis. Then, applying these component
waveforms as the input voltage to the RLC load
equivalent circuit, the current equation io can be
obtained as shown in (6). Again, the voltage vo in (5)
can be used to find out the rms values of output voltage in
terms of ac-dc components (Vo,rms(ac,dc)), dc
component (Vo,rms(dc) ), ac component (Vo,rms(ac) ), and
fundamental component (Vo,rms(1)) as shown in Fig. 8.
-
140
1 120
100
-+.
0
80
-
60
002
40
20200
160
120
80
40
0
-40
-80
Phase-Shift, 0 (degrees)
-120
-160
Fig. 8 Variation of various output voltages Vo,rm,(ac,dc), Vo,rms(dc)
Vo,rms(ac) and Vo,rms(l) vs phase-shift
479
0
These equations can also lead to the calculation of ac
output power PO, using the definition of PO in (8). Fig. 9
shows the output voltage and current waveforms vo io
with the phase difference angle of each harmonic. With
phase-shift 0 = +540 and = -54' there will be harmonic
orders 1, 2, 3, 4, 5,
and with phase-shift = o there
will be harmonic orders 1, 3, 5, ... . From this
harmonic content, it can be seen that from the second
harmonic order upward, each pair of output voltage and
current waveforms will have the phase difference angle
almost equal to 900, since the RLC equivalent circuit of
the load now becomes equivalent to almost a pure
inductive reactance and consequently cannot generate
.
.
.
vo
vo
\\i
any output power. So, it is quite reasonable to calculate
approximately the output power from the fundamental
pair of output voltage and current waveforms without
considering other harmonic orders. The calculated result
and the experimental one are shown for comparison in the
same graph of Fig. 10 with each switching frequency held
constant at 66 kHz, 67 kHz, 68 kHz, 69 kHz and 70 kHzz,
while changing the phase-shift 0 starting from 0° to
both the positive and negative directions. From the
starting point of phase-shift (q oo ) to both the positive
and negative directions, it is observed that there is a
certain limitation for the control range of phase-shift for
each characteristic curve of output power P0 under a
constant operating frequency. This can be understood by
io at zero phase-shift
considering first the waveforms
( = 00) and switching frequency fs = 66 kHlz and also
the waveforms
io at the same zero phase-shift but at
switching frequency fs = 70 kHlz It can be seen that the
phase difference between the output voltage and current
waveforms
io for these two cases are quite different.
Higher switching frequency of 70 kHz can results in a
larger phase difference due to lower level of output
power. So, higher switching frequency can result in a
wider control range of phase-shift under ZVS operation
and when NON-ZVS operation is encountered the control
range begin to be terminated.
=
V0
10,,,,,
/
V0
,
,
.
V0
Vo, 2
L'-'
.
2
..
...
--mO2 lu- Nw3
Vo,
O,_
o
__4
,
""
VO,3
io 3_
,
'3
Vo,5
4 y
05
lw
Vo, 5 io,
lo5
xv
w
v v v v
1v
I'
w
05
10 =54°
0 o°
500,,
v.
40
to
Vo
°301
07
P 20
0
-
o 10!
0)
0
108
Vo, 2
02V03
°W
30
03
,3 4
Vo,
V0,5 io 5
&&a6a.
a a a 0
V V V V V V
14-V
05
0
=
O'
04
.0,5 "io, .%IV^v^ ^1
xv
05
°r
7 ~ ~ ~ ~ ~ kl
oCalculation
Vd=15 V
= * Experiment
72
36
0
Phase-Shift,
-36
(degrees)
-72
-108
j,3
A- alu v v
v-
1
7 kHz
w
IV
0 -:54'
=
Fig. 9 Output voltage and current waveform Von c
the phase difference angle of each harmonic
with
w
Fig. 10 AC output power P0 vs phase-shift
0 at switching frequency
f, = 66 kHz, 67 kHz, 68 kHz, 69 kHz and 70 kHz
"
For the calculation of dc input current Id, the output
current io can be used again to calculate the dc input
current Id, since the current flow on the dc input side for
a certain time duration is the same as that on the ac output
side. The calculated result of this dc input current Id is
480
obtained as shown by an equation in (9) and is also
obtained as shown in a graph of Fig. 11.
The dc input current Id can be also used to calculate
the dc input power Pd . The calculated result with the
experimental one are also shown in the graph of Fig. 12
with each switching frequency held constant at 66 kHz,
67 kHz, 68 kHz, 69 kHz and 70 kHz, during change of
phase-shift S from 0° to both the positive and negative
directions. From the starting point of phase-shift (o = oo )
to both the positive and negative directions, it is observed
that there is a certain limitation for the control range of
phase-shift for each characteristic curve of dc input
power Pd under each constant operating frequency.
[2
Z {2 sin ( - b)}
Id
x{2sin(zr--
sin(-
-
)
sin(2r - 0)}]
2 - 2 cos (f - )}
+Vd2
x{-21 +s( z-0- 1)±cos( 91)±cos(2ir
)}]
2 V22d Z {2 sin 2 (ff O)}
-
x{2sin(2f- 20 -02) sin(- 2) sin(2x2,r -2 )}]
Vd
.
[2-2co2 )-
j
{2 2cos2(ff-0)}
2x22r,
x{ -2cos(2ir -20-2 )+cos(-02 )+cos(2x2ff-02 )}]
2-
V
x{2sin(3f- 30 -93
+
500
[1{2 sin 3 (ff )}
Vd
sin (- 93
sin(3x2r-03 )}]
[12-2cos3(}zr )}
4
v 200
(10)
Vd Id
Zn =
Q300
,.
x{-2 cos (3ir - 3 0 - 03 ) + cos (- 3 )+ cos(3 x 2r - 3)}]
Where
-
-
2x3 2f2Z3[
Pd
^400
(9)
R2+ (lnsL-
- 100
C
Fig. 12 DC input power Pd vs phase-shift S at switching frequency
f, =66 kHz, 67 kHz, 68 kHz, 69 kHz, 70 kHz
160
120
80
40
0
-40
-80 -120 -160 -200
Phase-Shift, 0 (degrees)
Fig. 11 Variation of dc input current Id vs phase-shift
at switching frequency fs = 68 kHz
07
Then, the ratio of ac output power PO and dc input
power Pd makes possible the calculation of the fullbridge inverter efficiency 77 vs. phase-shift 5 which is
plotted in various curves, each of which is held at
constant switching frequency of 66 kHz, 67 kHz, 68 kHz,
69 kHz and 70 kHz. The calculated results are shown as
some examples in Figs. 13 and 14 for 66 kHz and 70 kHz
respectively and they are verified by comparing with the
experimental ones in the same figure. The result shows
that the efficiency is almost constant at 96 % over the
whole control range of phase-shift 1 which is not
constant but the control range will change according to
the switching frequency; that is, a wider control range of
phase-shift 5 will be obtained with a higher operating
frequency.
481
100
-80
...fs
Z- 60
66-kH
....
....
....Vd. 1:50 V
.1 40
o. Calculation:
Eperiment
20 F-
o
i
L
1
72
1018
0
36
-36
Phase - Shift , q5 (degrees)
Fig. 13 Inverter efficiency vs phase-shift
frequency fs 66 kH-z
100I
-72
-108
07 at switching
ppo-- O
o-
80 F1-11
"0
071
..fs.., :~70.kHz..
160
P'l-
1
.--4
L.
40
=
.u
t.4.-IlI
.20
o0 Calculation'
*Exp:eriment
F-
L
1018
RiEFERENCES
O
72
0
36
Phase-Shift,
Fig. 14
-36
0b (degrees)
Inverter efficiency vs phase-shift
frequency
fs
70
-108
-72
07 at switching
kH-z
Controlled
analysis of circuit operation under ZVS
switching conditions in a high-frequency
inverter
for
induction
full-bridge
heating
using
asymmetrical phase-shift control has been already
presented both theoretically and experimentally. There
are four main important points to be concluded here as
The detailed
and NON-ZVS
follows
1. For the positive phase-shift control of output voltage
v0, the phase angle of fundamental output voltage
vo,j
always lead the front edge of square wave voltage vo,
which makes the zero-crossing of output current
io move
edge, where NON-ZVS operation may
the
negative phase-shift control, the
toward the front
For
fundamental
output voltage
leading direction,
output current
wave
For
which
v0,j
makes
always
the
moves
to the
zero-crossing
of
io move toward the tailing edge of square
voltage vo, where NON-ZVS operation may occur.
zero
[1] P. Viriya , N. Yongyuth , I. Miki and K. Matsuse
"Analysis of Circuit Operation under ZVS and NON-ZVS
Conditions in Phase-Shift Inverter for Induction Heating,"
IEEJ Trans. IA., vol. 126, no. 5, pp. 560-567, May 2006.
[2] L. Grajales, J. A. Sabate, K. R. Wang, W. A. Tabisz, and F.
C. Lee, "Design of a 10 kW, 500 kHz Phase-Shift
Series-Resonant
Inverter
for
Induction
Heating," Proc. IEEE Industry Applications Soc. Annu.
Meeting, Toronto, Canada, 1993, pp. 843-849.
[3] P. Viriya , N. Yongyuth and K. Matsuse "Analysis of
V. CONCLUSION
occur.
occur both at the front and tailing edges, especially when
the operating frequency is not high enough. All these
three cases of the occurrence of NON-ZVS operation can
be avoided by increasing the operating frequency in order
to move the zero-crossing of current i0, away from the
front and tailing edges.
2. In phase-shift control, the maximum ac output
voltage will be obtained at phase-shift 0b = 0 and when
phase-shift angle 0 is increased away from zero degree,
the ac output voltage, current and power V0o,rms(ac)
Io,rms Po and consequently the dc input current and
power Id, Pd will become decreasing symmetrically
both in positive and negative phase-shift control.
3. In power control by phase-shift, the control range of
phase-shift is limited by the occurrence of NON-ZVS
operating condition for each operating frequency. At this
point, if further increase of phase-shift is required, this is
also possible by increasing the switching frequency to a
higher value and when NON-ZVS is encountered the
same process can be repeated again.
4. Higher switching frequency can results in a larger
phase difference due to lower level of output power. So,
higher switching frequency can result in a wider control
range of phase-shift under ZVS operation and when
NON-ZVS operation is encountered the control range
begins to be terminated.
Transition Mode from Phase Shift to Zero-Phase Shift
Under ZVS and NON-ZVS Operation for Induction
Heating Inverter," Proc. Power Conversion Conf (PCC2,
Nagoya, Japan, April 2007, pp. 1512-1519.
[4] L. Grajales and F. C. Lee, "Control System Design and
Small Signal Analysis of a Phase-Shift-Controlled SeriesResonant Inverter for Induction Heating," Proc. IEEE
Power Electronics Specialist Conf (PESC), 1995, pp.
450-456.
[5] P. Viriya, and T. Thomas, "Power Transfer Characteristics
of a Phase-shift Controlled ZVS Inverter for the
Application of Induction Heating," Proc. Int. Power
Electron. Conf. (IPEC), 2000, pp.423-428.
[6] J. M. Burdio, L. A. Barragan, F. Monterde, D. Navarro, and
J. Acero, "Asymmetrical Voltage-Cancellation Control for
Full-Bridge Series Resonant Inverter," IEEE Trans. Power
Electron., vol. 19, no. 2, pp. 461-469, Mar. 2004.
[7] J. A. Sabate, R. W. Farrington, M. M. Jovanovic, and F. C.
Lee, "Effect of Switch Capacitance on Zero-Voltage
Switching of Resonant Converters," Proc. Applied Power
Electron. Conf, 1992, pp. 2 13-220.
phase-shift control, NON-ZVS operation may
482