Chapter-4 - Shodhgangashodhganga.inflibnet.ac.in/bitstream/10603/7909/9/09...The capacitor C is of...
Transcript of Chapter-4 - Shodhgangashodhganga.inflibnet.ac.in/bitstream/10603/7909/9/09...The capacitor C is of...
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CIRCUIT ANALYSIS OF MIRROR INVERTER-
FED INDUCTION HEATER / COOKER
This chapter is based on the published articles,
1. Dola Sinha, Pradip Kumar Sadhu, Nitai Pal, Mathematical Analysis of the
Mirror Inverter based High Frequency Domestic Induction Cooker,
International Journal of Engineering, Science and Metallurgy, vol. 1, no. 2,
pp. 271-277, 2011.
2. Pradip Kumar Sadhu, Dola Sinha, Nitai Pal and Atanu Bandyopadhyay, A
New Generation IGBT Based High-Frequency Mirror Inverter for Induction
Heating, International Journal of Electrical Engineering and Electrical
Systems, Vol. 03, Issue No. 01, Fall Edition 2010, July 2010 – September
2010, pp. 38-44.
Circuit Analysis of Mirror Inverter-Fed Induction Heater / Cooker 43
In this chapter, a mirror inverter-fed induction cooker (Sadhu et al., 2008, patent
no.216361 and 2010, patent no. 244527, Govt. of India) has been analyzed. Firstly,
an analytical solution has been made. Thereafter, a P-SPICE-based simulation has
been carried out and its results are compared with a real-time experimental model.
Finally, the summary of the chapter is presented.
4.1 Introduction
Mirror inverters are basically half bridge series resonant inverter and commonly
used for medium power induction heating applications. The series-resonant radio-
frequency mirror inverter system has been introduced as a new conception for
induction-heated pipeline or vessel fluid heating in medicinal plant, sterilization
plant and drier for surgical instruments (Sadhu et al., 2001b). Fig. 4.1 illustrates
the mirror inverter circuit. The AC main (220V, 50Hz) is routed through AC filter
before being fed to the bridge rectifier.
Rsn1
Rsn2
Cooking vessel
Vessel support
Harmonic filter
Signal for detection of cooking vessel
220 V, 50 Hz1-Ph
Choke
Brid
ge
rect
ifier
IGBT1
IGBT2C
C1
C2
A
Q R
MN
POB
CXRX
Fig. 4.1: Mirror inverter circuit.
The output of the rectifier is passed through an inductor and a capacitor C as
shown in Fig. 4.2. The capacitor C is of small capacity (5uF) so that the DC
voltage (Vdc) across C does not get leveled. This in-turn help to improve the
overall power factor of the system. The return path of the high frequency current is
through this capacitor C, as at high frequency ‘C’ offers negligible capacitive
reactance ( 1 2cX fC ), where f is in kHz range. Hence, the capacitor C acts as a
Circuit Analysis of Mirror Inverter-Fed Induction Heater / Cooker 44
short circuited path and allows high frequency current to flow. It also acts as higher
order harmonic filter at the same cost.
Rsn2
Signal for detection of cooking vessel
Link inductor Cooking pan
From RFI Bridge Rectifier
C
C1
C2
A Q R
MN
Rsn1I G B T 1
IGBT2
POB
Heating coil
Fig. 4.2: Power circuit of radio frequency mirror inverter.
The main power circuit consists of switching devices IGBT1 and IGBT2 and
parallel high resistances Rsn1 and Rsn2 connected one across each device as
shown in Figs. 4.2 and 4.3. The resonant circuit is composed of resonant inductor
(Leq) and capacitors C1 and C2. Resistance Req represents the series equivalent
resistance of the heating coil and the referred value of the load resistance, while Leq
represents the inductance of the same as shown in Fig. 4.4.
Cooking pan
C
A Q R
M
Rsn1
Rsn2
IGBT1
IGBT2
POB
NVdc
Heating coil
Fig. 4.3: Main power circuit of radio frequency mirror inverter.
Circuit Analysis of Mirror Inverter-Fed Induction Heater / Cooker 45
Rsn2
Vdc
Rsn1
POB
C
C1
C2
A Q R
M
IGBT 1
IGBT 2N
Req Leq
Fig. 4.4: The equivalent circuit of mirror inverter.
Resonance occurs while the inductor Leq and the either of capacitor C1 or
C2 exchange energy between them. As some energy is lost in Req in the form of
induction heating during the process of resonance, the total amount of stored
energy gets reduced in each resonant exchange. However, the energy is again
restored by the switching devices IGBT1 and IGBT2 at the starting of each
resonant cycle.
4.2. Circuit Configuration and Analysis of Mirror Inverter
The single point MN of the radio-frequency mirror inverter circuit as depicted in
Fig. 4.2 is stretched as shown in Fig. 4.5. The non-smooth DC voltage is available
across the points A and B in the above-mentioned circuit.
Circuit Analysis of Mirror Inverter-Fed Induction Heater / Cooker 46
Signal for detection of cooking vessel
Rsn2
Rsn1
B
From RFI
Link inductor
Bridge Rectifi
C
C1
C2
A Q R
M
IGBT1
IGBT2
PO
Req Leq
N
Fig. 4.5: Equivalent circuit of the mirror-inverter of with the points NM stretched.
The principle of operation of the circuit is described by dividing it into four
different modes. One resonant cycle is due to combination of Req, Leq, IGBT1 and
C2 and the next resonant cycle is due to Req, Leq, C1 and IGBT2. Both the cycles
get repeated alternatively to push resonant current through the heating coil. These
two cycles are in ON period of IGBTs. Between these two cycles there is an OFF
period of IGBTs. The operating modes of mirror inverter are separately analyzed
below.
4.2.1. Initial mode: When both the IGBTs are OFF and capacitors C1 and
C2 are not initially charged
After full bridge rectification the alternating voltage becomes pulsating DC voltage
of an operating frequency of 100Hz. The series current flowing path is shown in
Fig. 4.6. The switching device IGBT1 and IGBT2 are turned off at t = t0. In this
mode the circuit current flows through the snubber resistors Rsn1 and Rsn2 and
capacitors C1 and C2. As the values of snubber resistors are very high (470kohm),
therefore, maximum current flows through the capacitors. There has been no
conduction through IGBTs.
Circuit Analysis of Mirror Inverter-Fed Induction Heater / Cooker 47
POB
C
C1
C2
A Q R
M
Rsn1
Rsn2
NVdc
Req Leq
I (t)1
Fig. 4.6: Capacitor charging current path when both switches are OFF.
Here, solid line denotes main working current and dotted line denotes less
magnitude of current flow through the circuit. A small voltage drop appears across
the coil impedance and the rest voltage is equally shared by the capacitor C1 and C2
and this voltage is stored as initial charge voltages (VC1 and VC2 respectively) of
these capacitors C1 and C2. The value of this voltage is almost2dcV .
Depending on the switching conditions of two IGBTs, there exist four
different modes of operation. These are explained below in step-by-step manner.
4.2.2. Mode–1 : When IGBT -1 is ON and IGBT-2 is OFF
The switching device IGBT1 is turned on at t = t1. During this mode, the DC-link
voltage Vdc charges the resonant elements to accumulate energy by supplying
power through IGBT1. At t = t2, the energy transfer from source to inductor (Leq)
and capacitor (C2) gets completed i.e. iL(t1) = Ipeak and VC2(t2) = Vdc. VC2 charged
through the path AQRMNOBA shown in Fig. 4.7. The high frequency alternating
current is flowing through capacitor C because at high frequency the capacitive
reactance offered by C is negligible hence the capacitor acts as a short circuit and
allowing the high frequency current to flow through it. In this mode C1 discharges
from 2dcV
to zero through the path QRMNQ. It is shown that charging current of C2
Circuit Analysis of Mirror Inverter-Fed Induction Heater / Cooker 48
and discharging current of C1 both follow the same path M to N (as shown in
Fig.4.8).
PB O
IGBT2
C
C1
C2
A Q R
M
IGBT1
NVdc
Req Leq
I (t)1Rsn1
Rsn2
Fig. 4.7: High frequency charging current path of C2.
O PB
IGBT2
C
C1
C2
AQ R
M
IGBT1
NVdc
Req Leq
I (t)2
Rsn1
Rsn2
Fig. 4.8: High frequency discharging current path of C1.
Circuit Analysis of Mirror Inverter-Fed Induction Heater / Cooker 49
4.2.3. Mode–2: When both the IGBTs are OFF
In this mode, the charge on capacitor C2 will act as a source of energy to drive
current and thus charge C1 from zero to 2dcV and the circuit current will be routed as
indicated in Fig. 4.9. At the end of this mode at t = t3 the capacitor voltage VC2 (t3)
is2dcV . So, C1 and C2 store equal voltage after mode 3.
Vdc
O PB
IGBT2
C
C1
C2
AQ
R
M
IGBT1
N
Req Leq
I(t)Rsn1
Rsn2
Fig. 4.9: High frequency reverse current flowing path from C2.
4.2.4. Mode–3: When IGBT -1 is OFF and IGBT-2 is ON
The switching device IGBT2 is turned on at t = t3. During this mode the DC-link
voltage Vdc lets the resonating elements to accumulate energy by supplying power
through IGBT2. At, t = t4 the energy transfer from source to inductor (Leq) and
capacitor (C1) gets completed i.e. VC1(t4) = Vdc. VC1 charged through the path
AQNMPOBA shown in Fig. 4.10. In this mode C2 discharges from 2dcV to zero
through the path NMPON. It is shown that charging current of C1 and discharging
current of C2 both flow in the same path N to M (refer to Fig. 4.11).
Circuit Analysis of Mirror Inverter-Fed Induction Heater / Cooker 50
IGBT2
Leq
O
C
C1
C2
AQ R
M
IGBT1
PB
NVdc
Req
I (t)1 Rsn1
Rsn2
Fig. 4.10: High frequency charging current path of C1.
Fig. 4.11: High frequency discharging current path of C2.
4.2.5. Mode–4: When both the IGBTs are OFF
This mode is the second mode (Mode 2) where both the switching devices Q1 and
Q2 are off. The charge on capacitor C1 will now act as a source of energy to drive
IGBT2
Leq
O
C
C1
C2
AQ R
M
IGBT1
PB
NVdc
Req
I (t)2
Rsn1
Rsn2
Circuit Analysis of Mirror Inverter-Fed Induction Heater / Cooker 51
current and thus charge C2 from zero to 2dcV and the circuit current will be routed as
indicated in Fig. 4.12. At the end of this mode at t = t5 the capacitor voltage VC1
(t5) is2dcV . After end of this mode both C1 and C2 store same voltage i.e.,
2dcV .
IGBT2
C
C1
C2
A Q R
M
IGBT1
POB
NVdc
Req Leq
I (t)1
Rsn2
Rsn1
Fig. 4.12: High frequency reverse current flowing path from C1.
Mode 1 to Mode 4 these four modes will repeat for continuous conduction.
Analyzing all the modes, series current flowing through the heating coil is
expressed as:
11
1 22 1eq
1 1 2 2 2
V dc (t)= cos tanR
cos sin
c eq
eqc eq
C LI t
RC L
Exp k t A k t A k t
(4.1)
1 21 2 1where, and k ( )
2 eq ceq
Rk L C kL
Where Cc = C1 or C2, used according to the operation of C1 or C2.
Moreover, A1 and A2 can be calculated from the initial conditions.
Circuit Analysis of Mirror Inverter-Fed Induction Heater / Cooker 52
Voltage across heating coil can be obtained using the expression
11
( )( )coil eq eqdI tV R I t L
dt
( 4.2)
The first part of the equation (4.1) shows the steady state condition and the second
part is due to transient condition. The voltage stored in capacitors C1 and C2 during
charging will be expressed as:
1 2 10
1 ( )t
C Cc
V V I t dtC
(4.3)
4.3. Sample Results and Discussions
In this study, currents and voltages have been compared across the heating coil.
Three different methods have been adopted during this study. In the first method,
those two parameters are obtained using the expressions (4.1) and (4.2). In the next
method, a P-SPICE-based simulation has been carried out. On the other hand,
experiments have been conducted with a real induction cooker in the next method.
During this study, the values of snubber resistors (Rsn1 and Rsn2) are considered
as 470kohm each. Coil inductance (Leq) and internal resistance (Req) are taken as
119µH and 0.69ohm, respectively. Capacitors C1 and C2 are each of 0.4µF and C is
5µF. Values of A1 and A2 are calculated from initial values of voltage stored in the
capacitors and obtained as 1.99 and 48.67, respectively. The main supply voltage
Vdc is 220V and applied operating frequency at the main is 50Hz. During the
analytical derivation, an IGBT is replaced by its equivalent circuit as shown in
Fig.4.13.
Fig. 4.13: Equivalent circuit of IGBT.
Circuit Analysis of Mirror Inverter-Fed Induction Heater / Cooker 53
4.3.1. METHOD 1: Analytical Solution
The four modes (Mode 1 to Mode 4) will repeat according to specified IGBT ON
time and OFF time. The depth of heat penetration on cooking pan is inversely
proportional to operating frequency and the operating frequency is inversed of
operating time period. So, by changing the IGBT ON-OFF time operating
frequency can be changed and thus the heat penetration on cooking pan can be
controlled. The circuit of mirror inverter is analytically analyzed by MS Excel
2007 and different graphs are shown in Figs. 4.14 to 4.17 at different frequency.
Figs. 4.14 and 4.15 show voltage and current across the heating coil at low
frequency.
Fig.4.14. Applied and capacitor voltages with the time at low frequency, when
both switches are OFF.
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.001 0.021 0.041 0.061 0.081 0.101 0.121 0.141 0.161 0.181
Time (sec)
Cur
rent
(Am
p)
Fig.4.15: Series current at low frequency, when both the switches are OFF.
Circuit Analysis of Mirror Inverter-Fed Induction Heater / Cooker 54
Since the current is very low at low frequency, therefore heat penetration is low.
The complete waveform of current and voltage across the heating coil including
ON and OFF time of each switch at high frequency (38.512 kHz) is shown in Fig.
4.16 and Fig. 4.17.
-20
-15
-10
-5
0
5
10
15
20
0 0.005 0.01 0.015 0.02 0.025 0.03Time (sec)
Coi
l Cur
rent
(A)
Fig. 4.16. Current through heating coil.
-600
-400
-200
0
200
400
600
0 0.005 0.01 0.015 0.02 0.025 0.03
Time (sec.)
Vol
tage
acr
oss c
oil (
V)
Fig. 4.17: Voltage through heating coil.
Circuit Analysis of Mirror Inverter-Fed Induction Heater / Cooker 55
4.3.2. METHOD 2: PSPICE Simulation
The developed PSPICE schematic circuit diagram is shown in Fig. 4.18. The
circuit simulation has been done with alternating supply voltage of 220 V. A
bridge rectifier is modeled using four diodes of 1N6392 type. Total time period is
taken as 26µsec where IGBT on time is 12μsec and off time is 14µsec. For high
frequency inverter, two IGBTs of HGTP6N50E1D are used. The input parameters
of mirror inverter used for PSPICE simulation are shown in Table 4.1. The
waveform of current through heating coil and waveform of voltage across heating
coil are shown in Figs. 4.19 and 4.20 respectively from PSPICE simulation.
Table 4.1: Input parameters of mirror inverter.
Operating high frequency = 38512Hz Supply Voltage = 220V
Coil inductance, (Leq=L9) = 119µH Coil resistance, (Req=R9)= 0.69 ohm
Capacitors, C10 and C11 = 0.4µF, each Capacitor, C9 = 5µF
Snubber resistors, R10 and R11 =
470kohm, each
IGBT ON and OFF timing = 12 µs
and 14 µs.
L8
100uH
C95uF
L9
119uH
R9
0.69
D201N6392
12
D21
12
D221N63921
2
D231N63921
2
V14
FREQ = 50HzVAMPL = 220V
VOFF = 0
C100.4uF
C110.4uF
0
Z5
HGTP6N50E1D
R10470k
R11470k
0
V15
TD = 0.01us
TF = 2usPW = 12usPER = 26us
V1 = -5V
TR = 2us
V2 = 5V
0
V16
TD = 20.01us
TF = 2usPW = 12usPER = 26us
V1 = -5V
TR = 2us
V2 = 5V
Z6
HGTP6N50E1D
Fig. 4.18: The circuit diagram for PSPICE simulation.
Circuit Analysis of Mirror Inverter-Fed Induction Heater / Cooker 56
Fig.4.19: The waveform of current through heating coil.
Fig. 4.20: The waveform of voltage across heating coil.
Circuit Analysis of Mirror Inverter-Fed Induction Heater / Cooker 57
4.3.3. METHOD 3: Real-time Experiment
One prototype model is developed and the real time experimental results from
oscilloscope are plotted. The series current flowing through heating coil and the
voltage appeared across heating coil at continuous conduction of mirror inverter at
high frequency is shown at Fig. 4.21 and Fig.4.22.
Fig. 4.21: The waveform of series current flowing through heating coil.
Fig.4.22: The waveform of voltage across heating coil.
Circuit Analysis of Mirror Inverter-Fed Induction Heater / Cooker 58
4.4. Summary
In this chapter, H. F. mirror inverter-fed induction cooker has been analyzed in
three ways. Firstly, analytical expressions have been developed for different modes
of operation. In the next case, it is simulated through P-SPICE software and finally
experiments have been carried with a real model. Results obtained through all three
methods are found to be similar. The series current flowing through heating coil
and the voltage across load depends on the resistance and inductance of the heating
coil. So calculation of these parameters is necessary to design an energy efficient
induction cooker.
****************