Considering these problems ... under non-ideal cases, a unique snubber circuit is used in each bi-directional switch. .... Block Diagram of the power circuit and its controller .... Idealized waveforms of currents and voltage of a Mapham ..... When on, the device looks like a resistor of value Ron which consists of two parts. The.
NASA-CR-193105
NASA
Report
STUDY OF SWITCHING TRANSIENTS IN HIGH FREQUENCY CONVERTERS NASA
Grant Final
NAG
3-1236
Report
Department
of Electrical Engineering University of Akron Akron, OH 44325-3904
Donald Co-Principal
S.
Zinger Investigator
Malik Co-Principal
Tony Research
NASA
Linda NASA
Elbuluk Investigator
Lee Assistant
Prepared For Lewis Research
Cleveland,
E.
OH
Center
44135
Burrows
Project
Manager
N93-28327
(NASA-CR-193105) STUDY OF SWITCHING TRANSIENTS IN HIGH FREQUENCY CONVERTERS Fina| Report (Akron Univ.) 160 P
Unclas
G3/33
0167271
ABSTRACT
As the semiconductor switching
frequencies
technology,
an ac/ac which
of many
high frequency
advantageous
technologies power
power
in many aspects.
devices
zero voltage
A high frequency
is still in it infancy
stage.
such
a high
drop,
Considering
on-voltage
these
MOS-Controlled
problems,
Thyristor
There
makes
the
existing
Use of such a system is
However,
are problems
switching
With
This converter
techniques.
the switching (MCT)
improved.
and
ac source is used as the direct input to
converter.
switching
converter as
are
systems become possible.
pulse-density-modulation(PDM)
employs
progress rapidly, the power densities
transients
the device
the development
associated and
speed and power
is a new concept
with this converter
zero-crossing handling
the most
of this
detecting.
capabilities
promising
of the
candidate
for
this application. This report an ac/ac first
PDM
presented
conduct switches switches
converter
Two.
current
for the converter
using
experimental
and zero-voltage
The ac/ac
studies
switching
has to be completed
of component power
system.
bi-directional power
A power
Chapter
voltage.
for building
device switches
review
is
that can
These
bi-directional
Different
bi-directional
Two.
of the characteristics
converter
instantaneously
requires
devices.
are also presented
of an ac/ac
considerations
PDM converter
existing
are investigated
One disadvantage switches
insight
and block
be constructed
Detailed switching
a complete
for a high frequency
in Chapter
bi-directional can
gives
when
of the MCT
in Chapter
is that
under
hard
Three.
turn-on
the ac source
and
turn-off
is at zero
of the voltage.
Otherwise
shoot-through
the devices.
In order for the devices
under non-ideal Detailed
current or voltage
theory
cases, and
spikes can occur which can be hazardous
to switch softly in the safe operating
area even
a unique snubber circuit is used in each bi-directional experimental
results
for
circuits
using
these
to
switch.
snubbers
are
presented in Chapter Four. In Chapter
Five, a current regulated
ac/ac
PDM converter
built using MCTs
and IGBTs is evaluated.
ii
.._.,=,m
ACKNOWLEDGEMENTS
We are grateful to the Power Technology Center
for
cooperation
their
support
throughout
Special Semiconductor
TM
for
this work.
Special
Division at NASA thanks
to Linda
Lewis Research Burrows
for
her
the project.
thanks
to
the
Research
and
Development
group
Inc. for providing samples of MCTs used in the experiment
research.
iii
of
Harris
work of the
TABLE
OF CONTENTS Page
UST OF TABLES
.........................
UST OF RGURES
.........................
vi vii
CHAPTER I.
INTRODUCTION
.....................
Statement of The Goals II.
Switching 2.1
Devices
..................
II1.
TESTING 3.1
3.2
7 (BJTs) .......
9 10
Transistors
(IGTs)
Mos-Controlled-Thyrsitor
Bidrectional OF
.................
...................
Insulated-Gate
2.3
7
Bipolar-Junction-Transistors
Thyristors
The
7
..................
Power MOSFETs
2.2
3
...................
Devices Overview
Power
1
(MCT)
Switch Configurations
MOS-CONTROLLED
..........
12
.........
...........
THYRISTORS
1 7 (MCTS)
Testing of MCT under hard switching ........... 3.1.1
Procedure
3.1.2
Results and Comments
14
................
....
24 24 24
............
Testing of MCT under soft switching
...........
32
3.2.1
The Block Diagram
3.2.2
The Zero Crossing Detector With Compensation
32
3.2.3
The Control Logic Circuit
33
iv
.............
27
...........
32
CHAPTER
Page 3.2.4
IV.
Results And Discussions
SNUBBER CIRCUITS FOR MCTS CONVERTER .....................
VI.
IN AN AC/AC
Introduction
...........
4.2
Snubber
Circuits
4.3
Snubber
Circuit for Ac Link Bidirectional
4.4
Experimental
TESTING THE REGULATED
.
........
45
Switches
Switches
.... .....
................
45 4 8 67
...............
MCT IN A THREE PHASE AC/AC PDM CONVERTER
73 CURRENT...........
5.1
Introduction
5.2
Three Phase Ac Link PDM Converter
5.3
Current Regulated Ac/ac PDM Converter
76
....................
76 ...........
7 6
.........
8 0
5.3.1
Single phase current regulation
........
8 1
5.3.2
Three phase current regulation
........
87
5.4
The drive circuit
5.5
Experimental
SUMMARY
PDM
For Dc link Bi-Directional
Results
34
45
4.1
Anode Kelvin Current V.
...........
..................
Results
AND SUGGESTED
89
................ FUTURE
89 WORK
.........
100
6.1
Summary
.....................
100
6.2
Suggested Future Work ................
102
.........................
103
BIBUOGRAPHY APPENDICES
..........................
104
APPENDIX
I
MCT DATA SHEET
..................
APPENDIX
II
THE SCHEMATICS OF THE PDM CONTROL CIRCUIT
......
109
APPENDIX
III
ANALYSIS AND SIMULATION OF THE 20KHZ AC SOURCETHE MAPHAM INVERTER ..............
114
'v
105
LIST
OF TABLES Page
TABLE .... 2.1
Summary
of the Bidrectional
20
switch configurations. • 81
5.1.
A General Comparison
Of PDM and PWM Technique
vi
LIST
OF FIGURES
RGURE 1.1
PDM
1.2
(a}Simplified single phase PDM circuit (b)Example of timing and control of switches and low frequency output voltage, Vout and current, lout ..................
3
Snubber capacitors used to prevent voltage spikes across the devices..
5
Snubber inductors in series with switches current ........................
6
ac motor drive
2
with portability for different control schemes
to limit shoot through
2.1
Circuit symbol
2.2
Circuit symbol for (a)NPN
2.3
Using a Baker's
2.4
Thyristor
25
(a)The
circuit
symbol,
26
(a)The circuit
symbol,
27
Circuit
28
Bidirectional
29
Examples
210
Three phase ac/ac PDM inverter using twelve MCTs. It requires the MCTs to be able to block voltage in both forward and reverse direction ..................
2 1
Three phase ac/ac PDM inverter using twelve MCTs and twenty four diodes. They do not require the MCTs to have bidirectional voltage blocking capability. (a) Six isolated power supplies are needed but only six only drive circuits. (b) Needs five isolated power supplies but twelve gate drive circuits .....................
23
A dc/dc down converter
2 5
2.11
3.1
-
Page
for (a)N-type
(b)PNP
MOSFET
BJT
.........
and model
of power
9 .......
1 1
.................
(b) simplified
1 1
Model
and (c) structure
of IGTs.
(b) the model and (c) the layout of an MCT
of a triac switch
8
............
Clamp Circuit to avoid hard saturation
symbol
symbol
(b)P-type
..................
configurations devices
with built-in
vii
16 1 8
..............
...................
.
14
anti-parallel
19 diodes
....
19
FIGURE
Pare
3.2
A single phase PDM converter
3.3
A simple push-pull gate drive circuit
3.4
Turn-off snubber connected in parallel with the diode to limit the dVAK/dt when the MCT is turned off . , . .........
2 7
3.5
Hard switching waveforms
29
3.6
Hardswitching
3.7
An improved gate drive circuit that can provide 200ns
3.8
An RLC filter acts like a 4kHz current source load
3.9
Example timing and control
3.10
Block Diagram of the power circuit and its controller
3.11
Zero crossing detector that can detect before zero crossing
3.12
Illustration of the adjustable zero-crossing where Vn and Vp are the adjustable "zero-levels"; tcr and tcf are the positiveand negative-going zero-crossing compensations respectively
3.13
waveforms
................
25
.............
without snubber with snubber
26
........... ............
of the switches
30 rise time
3 1
.........
3 5
...........
3 6 .......
3 6
......
3 7
,
3 8
Timing diagram for the outputs of the ring counter and the control signals of $1 and S2 ................
3 8
3.14
Kanaugh Map for the control signal of $1
3 9
3.15
Circuit that generates
3.16
Voltage across the switches $1 and $2
.............
4 0
3.17
Detail of voltage
.............
4 0
3.18
Detail of voltage across a conducting switch
3.19
Detail of current as $1 turns off and $2 turns on
3.20
Equivalent voltage across a bi-directional
3.21
Waveforms of ac link voltage and voltage across each device in a bi-directional switch when off ...............
43
A sketch of anode current IA and anode-to-cathode voltage VAK during turn-off with and without snubber circuits. And comparison of power losses ................
4 7
4.1
............
the control signal for $1 and $2
rise during turn-off
viii
.......
3 9
...........
4 1
.........
switch that is off
4 1 .....
43
Page
FIGURE 4.2
4.3
4.4
4.5
A non-dissipative turn-off snubber circuit. This is supposed to connect in parallel with the free wheeling diode ....... An ac/ac PDM converter with simplified switches, $1 and $2 shown. Each switches consist of two MCTs and Two diodes
4 8
.....
50
A turn-on delay of AT in $2 causes an instant of open circuit for the current source load. Two snubber capacitors are used to keep the current continue and reduce voltage spike across the devices .................... Graphical representation
51
of ac link voltage, Vac, and the voltage
across each switch during AT
...............
53
4.6
Ordinary
4.7
An PDM converter
4.8
An example waveforms of voltages across the ac link and the switches during an instant of short-circuit across the ac source.
55
A turn-off delay of AT in S1 causes an instant of short circuit for the voltage source. Two snubber inductors are used to limit the shoot through current ...............
57
For small AT the area under the sinewave by a triangle ......................
57
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
turn-off
snubbers
used
in a Bidirectional
with a Mapham
switch
inverter as a voltage
......
source
54 ....
55
can be approximated
The best location of the snubber inductor and free wheeling diode in each bidirectional switch ..............
58
Proposed snubber for the by directional switch which combines the features of both capacitive and inductive snubbers ......
60
Simplified ac/ac PDM converter with proposed snubber circuit. Each snubber inductor has a free wheeling diode (not shown) in parallel with so that no voltage spike across the devices at turn-off .............
'60
Voltage and current responds as a current step inputs to a parallel LC and diode circuit ...............
62
Voltage and current responds as a current step inputs to a parallel LC and diode circuit with the switch has a turn-on delay of AT .......................
64
B-H curve for a saturable
66
inductor
ix
..............
Paoe
FIGURE 4.17
An ac/ac converter With Proposed snubber Circuit
4.18
Voltage across anode to cathode and cathode current of M11 without snubber ....................
69
Voltage across anode to cathode and cathode current of M11 with capacitive snubber .................
70
Voltage across anode to cathode and cathode current of M11 with inductive snubber ..................
71
Voltage across anode to cathode and cathode current of M11 with both capacitive and inductive snubber ..........
72
4.22
Output voltage and load current with proposed snubber
73
4.23
The MCT pinout and symbol
4.24
(a) Anode Kelvin Current IKEL1 of M1, (b) Cathode current of Mll
75
5.1
Demonstration
77
5.2
(a) Example of maximum possible fundamenta, line-to-common, Vao, and line-to-line voltages, Vba.(b) maximum possible equivalent line-to-line voltage ...............
79
Implementation of a Bidirectional switch for (a) ac link converters (b) dc link inverters ..............
79
Current regulation of a single phase PDM converter using a two state comparator ..................
82
Current regulation of a single phase PDM converter using a three state comparator .................
83
4.19
4.20
4.21
5.3
5.4
5.5
Single-phase
........
.......
.................
74
of (a) single (b) three phase ac/ac converters
current regulated
67
PDM converter to be simulated
....
....
84
Simulations of Output Voltage and Current using two-state switching ....................... 5.8
Simulation of Output Current and Voltage using three state switching, zero-state is chosen when error current eta is within 3% of the peak command
5.9
5.10
85
(a) Implementation PDM converter.
current
..........
86
of a three phase current regulated ac/ac (b) the three phase PDM bridge ........
The MCT and IGBT drive circuit used in the ac/ac PDM experiment
X
88 .
89
FIGURE 5.11
5.12
5.13
5.14
5.15
5.16 5.17
Paoe (a) line-to-common voltage, (b) details (c) line current, Ic ...................
of,
Vco, 91
(a)Details of voltage across a switch made of IGBTs, (b)current through the switch ...............
92
(a) Voltage across the MCT of a bi-directional switch, (b) collector current through the MCT, (c) product of (a)&(b); instantaneous power ...............
93
(a) Details of voltage across an individual MCT, through the MCT ....................
94
(b) current
(a)Details of voltage across a switch made of MCTs, (b) current through the switch ...................
95
The line-to-line
95
voltage, Vbc
................
The ac/ac PDM converter with a modified
starting
sequence
A1.1
Manufacturer's
A2.1
Zero-crossing
A2.2
The triangle
A2.3
Current
A2.4
Cable pinout
A3.1
Using a synchronous
A3.2
Using a Mapham
A3.3
Idealized waveforms of currents and voltage of a Mapham inverter in steady state under no load ............
Test circuit switching
for MCTA75P60
control
wave generator
limit
signal,
LMT,
circuit
that provides generator
....
...........
107
............ "TRI"
110 .
........
111
.............
112
.......................
113
generator
(resonant)
to generate
ac voltage
inverter to generate
........
ac voltage
115 .....
The simulation
of a Mapham
inverter with a 4 _ load connected
A3.5
The simulation
of a Mapham
inverter with a 10 .Q load connected.
A3.6
The output voltage
regulations
A3.7
A Mapham
loaded by a ac/ac PDM converter .........
A3.8
Simulation of A Mapham inverter loaded by an ac/ac PDM converter .....................
at different
xi
loads ..........
116
118
A3.4
inverter
99
.....
120 . 121 121 122
124
Page FIGURE A3.9
A simulation result with Lr and Cr equal to 6_H, 6p.F ....
A3.10
A Mapham
A3.11
The current of the resonant inductor, Lr, and output voltage of
Inverter loaded by a full-wave
the Mapham
rectifier
inverter shown in Fig. A3.10
....
125
....
126
.... • 126
........ • 127
A3.12
The output current, Io, of the Mapham
xii
inverter
in Fig. A3.10
....
CHAPTER
I
INTRODUCTION
Since solid state devices conversions,
by means
of power
Recent work has suggested [1,2].
With
electronic
today's circuits
Although
power
efficiency,
has been introduced to industry,
made
electronics
the
space application
20kHz
technology
Thus,
is questioned.
size and mass
voltage
source
is characterized
such as switching
the reliability
simpler
of power
The objectives
of power
and more
ac link for space station
the reduced
there are still problems
the semiconductors.
has become
the use of 20kHz
technology, has
electronics,
the controls
power
efficient.
distribution
of high frequency
in space by high
transients, converters
station power
losses
power possible.
density
and
and stresses
and voltage
on
sources
of this study are to minimize
at
the effects
of these problems. Ac/ac conversion using high frequency A converter
it involves
report.
An
switching
ac/ac
The technique
PDM
the devices
of this report because of pulse density
converter
[3] which, is a power
low frequency
voltage
at zero voltage
crossing
switching
Unfortunately,
at zero voltage,
however, converter and current. which
most switching devices
(PDM)
source.
If adc
will not be discussed using
this
new
It takes the
minimizes
fast switching
of the advantages
modulation
work off either an ac or dc voltage
quasi-resonance
to synthesis
order to guarantee converters.
ac link.
using the technique
is used,
technique
is the main stream
devices
trade off between
switching
is used. source in this
modulation
advantage
of
losses.
In
are required speed
of
in PDM
and electrical
2 ratings (e.g.
maximum blocking voltage and maximum
conducting
current).
Therefore
selection of switching devices is a main concern. In most
applications,
electric motors are needed. control
or
if an
maintenance
technology, many control
source
is not
available,
has made
availability
is the
ultimate
output
therefore
however,
are especially
expense
important
ac motors an alternative
of reliable
the
of their
high
Ac motors, on the other hand, are rugged and have
cost, and such features
research
power
Dc motors have been used because of the simplicity of their
cost is generally high.
low maintenance Advanced
ac
mechanical
ac source for space
in space application.
to dc motors.
With today's
station is possible.
Moreover,
schemes for induction motors such as field oriented control and direct self
control [4] have shown fast torque response. Although control of ac motors will not be discussed
in detail in this report, a
"portable" PDM ac motor drive shown in Fig. 1.1, will be presented. ias*, ibs* and ics* are obtainable
from most control methods
Command
like field
currents
oriented
Thus the PDM ac motor drive can become part of any control loop.
20kHz
ias* ibs* its*
ias
PDM CONVERTER Induction motor
Fig. 1.1 PDM
ac motor drive with portability
for different
control
schemes.
control.
3 The simplifiedsingle phase PDM circuit is shown in Fig. 1.2(a), which is just one third of the PDM convertershown in Fig. 1.1. A low frequency
output of 4kHz is
used as an example.
are
In practical
applications,
output frequencies
compared to the ac link making the high frequency
component
a lot smaller
easily filtered.
vacoj t+ s2
Vout
(a)
Vac _
_
20khz
I_AAAAAAAAAAAAAA
.-
_1!r-!iii-i Mi-ii-ii-i!-ii-ii-ii-i ii .Ivvvvvvvvvvvvvvv s_h Filli-!11 rill FINI-I1-1 I-I 41daz_ Vout
AAA
v
Iout
vvv
AAA
/-
v
i./1 iJ.. ._1
II O
N -r"
{3)
O r,,I >
Fig. 3.11
O O
:3
Zero crossing detector
that can detect before
zero crossing
38
Input Sinwave m
Output of the Zero
r
/tcf
Crossing Detector
CLK
Fig. 3.12 Illustration of the adjustable zero-crossing where Vn and Vp are the adjustable "zero-levels"; tcr and tcf are the positiveand negative-going zerocrossing compensations respectively.
CIk
Qo Q1
DOOOOO-LFLFL _--_J F-L
Q3
I
$I $2
Fig. 3.13 Timing
diagram
for the outputs of the ring counter $1 and $2
and the control
signals
of
39 :LK
Qo
Q1
O0
O0
d
01
fl
11
d
01
11
_.1
10
I.,2
i
10
m
Sl
= CLK Q2 + QoQI = CLK¢0.2
+ CLKQ;
+ QoQI
Fig. 3.14 Kanaugh Map for the control signal of $1
5V
: Sl
7 S2
CLK
Fig. 3.15
Circuit that generates
the control
signal for S 1 and S2
ii.ii
Vsl
:
A
4O
.-.; ........i .........! .........: ........:........."...................i .........!
Vs?_
501..ts/div
Fig. 3.16
....
Voltage across the swilches S1 and S2
i,
V$1
O.OV
............
i ......................................................................
{ .........
i.,
...............................................
t
i
..............................................
:
i
i
:
.................. ' ...... _......... _...... ;8:_;_iv ....... _......... _......... ':......... i VGA1
•
I
2gs/div Fig. 3.17 detail
of voltage
rise during
turn-off
41
iilfl.j. ¸,;.......... .........
I I I
V
.........
I Sl I
:
.J......
i .......
II ]: ] o.ov'_,_ .'Hi _
-
,
............ __ lili50J_sldiv
Fig. 3.18
151
Detail of voltage across a conducting
I
:
i
•/ •
i
i
I
;
;
]li
3.58AJdlv
'
]
i
!
switch.
i
.
i
;
.................. !..... !If!..... i....... '........ i....... i................. i i .....................
i
: !......... !...................
"
: i ! ! :.....................................
:
i
Is 2 :
:
•
i
3.58Afdiv
:
O.OA
'
• : .........
•
't
: .............
.-_
_t I
..-
:
....
!
: .........
: .........
: .........
:
......................................................................................
2.5_.s/div Fig 3.19 Detail of current
as $1 turns off and $2 turns on
42 As mentioned above, the MCT is a latching device and has a problem at zero voltage.
However,
in the zero-voltage
switching experiment,
switches were able to turn on at the zero crossings. from
the structure
The bidirectional
of the bi-directional
the bi-directional
To explain this, one should start
switch configuration
switch used has a back-to-back
turning on
used in this experiment.
diode pair in each switch which helps
turn the devices on at zero crossing. Since only one bi-directional switch can be on at a time, the voltage across the one that is off is then at the high frequency similar to that in Fig. 3.20.
shown
Vac, and the scenario
is
The voltage drop across the switch that is on is assumed to
be negligible and therefore capacitors
ac link voltage,
not shown in Fig. 3.20.
in the figure
Note that there are two parasitic
and they play an important
role.
The initial voltage
across the parasitic capacitor has to be zero because this switch has been on. Vac will charge one of the parasitic capacitors
(through the other diode) during the first quarter
cycle, then the other capacitor will be charged during the second quarter cycle. first
half cycle,
the voltage
never cross zero voltage. are shown in Fig. 3.21. frequency
across
each of the capacitors
After the
will still be sinusoidal
but
The diode voltage therefore has a dc offset and the waveforms
As can be seen in Fig. 3.21, at each the zero crossing of the high
link, the voltages across the devices are always half of the peak of Vac.
In
another words, the devices will be turned on at half of the peak of Vac instead of at zero voltage.
Therefore
as soon as an MCT is turned on a parasitic capacitor is discharged.
The discharge energy
1 Cd( 2
is, however,
very small because
Vac'peakl2 2 /
the parasitic
capacitance,
(3.1)
C d, is negligible.
43
7 Vd2
d2
Vac
+
Vdl_
Fig. 3.20
Equivalent
i
voltage
_
across
dl
a bi-directional
M?I_
switch
that is off.
Vac
/'kl
Fig. 3.21 Waveforms
of ac link voltage and voltage across each device switch when off.
in a bi-directional
44 Turn-on voltage
switching
compared
and turn-off tests.
failures
In many
of the device
cases,
to the rating of the device.
it failed
have at low
The causes of failures
been
reported
voltage
under zero
and current
are still uncertain.
level In an
effort to investigate the failure modes, the damaged MCTs were examined. Under noticeable
normal
operation
in our experiment,
thermal dissipation, therefore,
a cause of failure.
Except for some unexplained failures,
of the resistance
logic causing high frequency
Most of the damaged
Example
transients are a step mixed into the control
that does not necessarily occur at zero voltage.
devices measured
finite resistance of about 20.(2 to 30.(2
between gate to anode which seems to imply damage to the "MOS" part of the MCT. of the damaged
MCTs
any
it has been noticed that a device
in the RLC load and misinformation switching
do not have
it can be concluded that thermal heating is not
would fail when some transient occurred in the circuit. increase
the devices
were still able to switch and block voltages
below
Some
=30V This,
however, differs from case to case. Since the damaged devices
were still able to switch, often the failure
be detected until a high current drawn by the gate drive circuit was observed.
could not When an
MCT failed, the negative gate drive current went lower when the devices were switching. Under these conditions it is believed that part of the anode current flowed while the device was conducting.
into the gate
CHAPTER SNUBBER
CIRCUITS
FOR
MCTS
IV
IN AN AC/AC
PDM
CONVERTER
4.1 INTRODUCTION Conventional example,
physical
movements sizes
losses
maintenance the other power there
For
ac and dc motors with one driving
the other.
The
cause One
significant
attractive
on a dc motor),
devices
the reliability being
used.
are a few things
(2)
increases
the
total
maintains
the device
dissipation faults
ratings,
electronics
of power
electronics
known
circuit
to:
snubber
circuits
losses)
it reduces
low
With sufficient reliable. mainly
On
on the
of a power
device,
maximum
current,
area (SOA) of the
current,
voltage
spikes,
are used.
(and most of the times it even
the device
Two kinds of snubbers
power
dissipation
and
used in ac and dc power
in the later sections
For Dc Bi-Directional
of turn-on
text books.
depends
there
is very
is fairly
as the safe operating
power
within its SOA.
methods.
(1) the device's
reduce the total power losses but
to mention
electronics
the dependability
like shoot-through
the device,
not
system
system
cannot
Circuits basics
losses,
the conventional
pay attention
of the
will be discussed
Snubber
feature
In order to guarantee
To reduce faults and protect A snubber
power
power conversions
of a power
one should
possible
The
systems.
(especially hand,
conversions
coupling
to the conventional
device,
power
often
involve mechanically
compared
and thermal
4.2
requires
and weights.
voltage
etc.
conversions
an ac/dc conversion
mechanical
power
power
and turn-off In this chapter 45
Switches snubber
circuits
we concentrate
can
be found
on snubber
in most
circuits
for
46 MCTs.
As found in the hard switching
instantaneous
and does not dissipate
the device
to operate
at turn-off
will in turn increase
corrected,
this problem
Therefore,
the suggested There
experiment in Chapter Three, significant
power by observation.
out of the SOA is the current tail during thermal
will eventually protecting
are two kinds
turn-on
dissipation
This current
a longer
tail.
make the MCT "run away" and become device for an MCT is a turn-off
of turn-off
snubber
circuits,
is
What could cause
turn-off.
and thus create
of MCTs
tail
If not
damaged.
snubber.
one is dissipative
and the
other is non-dissipative. They both limit the rate of change of anode-to-cathode voltage, dVAK at turn-off. Consider the circuit shown earlier in Fig. 3.4. As the MCT is dt switched
off, it becomes
assumed
to pass through
a high impedance
capacitor
voltage
is equal
snubber
capacitor
voltage
the snubber to Vdc.
capacitor
to zero.
the capacitor
CsdVc
by integrating
and diode.
The freewheeling
is discharged
diode turns on, the current through
path and, therefore,
all the inductor
Before
diode
Therefore,
will
turn-off,
before
the freewheeling as:
(4.1)
• t (4.2)
and since
VAK
combining
until the
both sizes gives
Vc(t) = Vdc -lioad Cs
(4.2)
& (4.3)
= Vdc
-
Vc(t)
(4.3)
gives VAK = Iload * Cs
is
the snubber
not turn-on
is Iload and can be described
= -Iload
current
t (4.4)
47 Figure 4.1 shows graphically how the snubber circuits reduce the power dissipationby decreasingdVAK/dtat turn-off.
VAK w/o turn-off
snubber
IA
_A I w/turn-off I load
snubber
Cs
turn-off
VAK * IA
energy loss w/o snubber
energy loss w/snubber turn-off
Fig. 4.1
A sketch of anode current IA and anode-to-cathode voltage VAK during turn-off with and without snubber circuits. And comparison of power losses
The snubber capacitor will be charged MCT is turned on. in the capacitor,
The energy dissipated
in the resistor,Er,
loss.
through
the resistor
when the
is equal to the energy
stored
Ec, and are given by 1 Er = Ec =_-Cs
The energy
to Vdc
dissipated
in the resistor
The losses due to the snubber
* Vdc2
is unrecoverable
(4.5)
and therefore
circuit (Ploss) at the switching
PIoss
=
Er*
fsw
all contribute
frequency,
fsw, is
(4.6)
to
48
The power
loss in the snubber
as disadvantages non-dissipative snubber.
of this snubber dissipative
is no dissipative
snubber
but
and the increase circuit.
the
dissipating
in a energy
element,
load
any power.
recovery
is not significant,
time are considered
of the power
in Fig. 4.2, can be used to replace like a resistor,
a cross the free wheeling
now
in turn-off
If recovery
current
snubber
discharges
However circuit.
in this circuit.
diode of Fig.
At turn-on the dc voltage source, charges
in series without
circuit
as shown
when placed
instead of one.
required
of this kind of snubber snubber,
There
circuit
two
of power
it is better just to use the dissipative
The operation
capacitors
more components
a
the dissipative
3.4 is similar
two capacitors
If losses
is important,
to the
at turn-off
and one inductor
and larger sizes are due to the snubber
snubber.
CS 2
Fig. 4.2
4.3.
A non-dissipative
Snubber
Circuit
turn-off snubber circuit. This is the free wheeling diode.
for Ac Link Bidirectional
As mentioned an MCT at zero voltage
in parallel
with
Switches
in Chapter One, the PDM converter and thus minimizing
connected
turn-on
takes advantage
and -off losses.
of switching
It is not necessary
49 to further
reduce
the switching
losses by using snubber
circuits.
The
reasons
for
needing a snubber in this case are different than those in the dc chopper. In an ac/ac PDM converter that may cause damage
with inductive load, there are two possible faults
to the devices: 1) an instant of open circuit ,2)
short circuit.
Due to the fast switching capability of MCTs, the fault could occur due to delays of turnon, turn-off achieved.
or control of the gate-drive.
In such situations
Consider the simplified ac/ac PDM converter
soft switching
will not be
shown in Fig. 4.3 in which each
switch, $1 or $2, consists of two diodes and two MCTs.
For example,
a turn-on delay of
an oncoming switch causes a high impedance path for an inductive load.
Therefore
high
voltage spikes will appear across both switches $1 and $2 during that time. The possible converters
or inverters
freewheeling devices
diodes
electronic
as a pulse
can always
shoot-through
circuits.
width
not happen
modulation
pick up the load current
therefore
voltage
source.
smaller
than
instead
of shorting
converter,
there
is a small
In an ac/ac
in a PWM
trigonometry cause
caused instant
PDM
inverter
fault,
is more
in most of other
(PWM)
inverter
where
even when
all the switching
a concern
in
this shoot
for the switches
it is found
high shoot through
turn-off
both switches
converter
delay
other
a voltage
However
in the off-going
current
is definitely
around
in a 20kHz
of the ac link, Vac, is 400V,
that the switches current.
Since
power
are on and will short the
through
short
inverter.
is 1.51J.s and the peak
calculation
of
by a small
when
the dc link in a PWM
if the delay
possibly
current
It is basically
switch,
very
such
above will normally
are off. The
simple
fault mentioned
are shorting
the source
zero
volts
ac/ac
PDM
with some
-75V
voltage
and still
is ac, this
current
spike can either be positive or negative, this converter requires a snubber that di can protect _ in both polarities. Conventional solutions to this problem include delaying the turn-on
time of the oncoming
switch and connecting
an inductor-diode
pair in series
50 with the switches. conduction
Due to the nature of ac/ac PDM converters such as the bidirectional
requirement,
these solutions cannot apply to this problem.
Iload
Mac
20kHz
t=O
Fig. 4.3
An ac/ac PDM converter with simplified switches, $1 and $2 shown. switches consist of two MCTs and Two diodes.
Theoretically, occurs
when the turn-on
at t=0, as shown known
delays
the control change
for turn-on
and drive
There
non-ideal
of one switch and turn-off
in Fig. 4.3.
as current
unfeasible. under
only an ideal case can guarantee
A possible
and turn-off
circuits.
and/or
method
times
Unfortunately,
voltage
levels
conditions.
In the following
of the other to achieve
accurately
circuit
thus
The ideal case
happens
simultaneously
this is to compensate
at the expense
the turn-on
varies,
is a need for a snubber
soft switching.
and turn-off
making
that can
paragraphs,
Each
of complicating delay
accurate
still maintain different
the
times
can
compensations soft switching
snubber
circuits
for
different cases will be considered. Case switching
!
Perfect
timing (Fig.
4.3)
Switching
Timing
and zero-crossing
(Fig. 4.3): switching,
As said earlier, an ac/ac
PDM
under perfect converter
has
51 dv
negligible
losses and a limited _"
turn-off,
under
compared
perfect
to that
switching
of other
Even when there is current
in the devices. timing,
power
losses
the
in the
Therefore,
converters.
device
are
a snubber
still
circuit
tail at small is not
necessary.
_.]$1
+
o,I vsw
-2 Vac
20kHz
_
Fig. 4.4
_
Cs
+
SZ
A turn-on delay of AT in $2 causes an instant of open circuit for the current source load. Two snubber capacitors are used to keep the current continuous and reduce voltage spike across the devices.
Case I! A turn-on the switches
are both off for a time period of AT.
is very
high
voltage
spike
depends
delay of AT in the oncoming
and the inductive will
appear
load current
across
mainly on the parasitic
each
capacitance
4.4):
The off state impedance
has
switch.
switch(Fig.
to continue The
during
magnitude
of the devices.
of the switches
this
of this
In this case,
time, voltage
Since this capacitance
thus
a
spike is very
small, the voltage spike will be so high and can damage the MCTs. With two snubber magnitude
can be limited.
capacitors
connected
The maximum
as shown in Fig. 4.4, the voltage
possible
value
of the voltage
across
spike each
52 switch, Vsw can be obtained by superposition of two voltages; one due to the ac source and the other due to the load current:
I, , c_, = therefore
(4.7)
lllo,;,,TI IVsw(AT)_"
since AT is very small compared
( 4.8 )
to a cycle of Vac, thus
Vac(AT)
=
[dVac t
*AT (4.9)
and
at 20kHz
Mac(AT
Let Vac,pea possible
transient
k be 500V.
turn-on
(4.7)-(4.10),
are 400V,
the required
voltage
across
When
lp.s
capacitance
each switch, spikes
k
allowable
20A and
snubber
the voltage
problem.
10 3) * Mac,pea
If the maximum
delay
Although another
) = 2_ (20*
* AT
(4.10)
voltage
spike,
respectively,
will
load current
then,
be 0.03_F.
using
Figure
and
equations
4.5 shows the
Vsw. are limited
the oncoming
switch
to a permitted starts
value,
to turn-on
it can still cause
at &T, it will short
a
capacitor
that has just been charged to 400V in the worst case. This discharging current . di is unbounded and its rate of increase, _', is limited only by the lead inductance. This can damage the device in many cases. The dc chopper, connected
in series
discharging)
current
bidirectional
switches
with
in the previous a resistor-diode
is limited.
In fact,
like that in Fig. 4.6.
section, pair
has
so that
a similar
a snubber the
snubber
This snubber
capacitor
charging can
circuit
still
needs
(or be
which
is
sometimes used
in the
two resistors,
53 20kHz Mac
!
Vsw
,
! I
AT Fig. 4.5 Graphical representation of ac link voltage, Vac, and the voltage across each switch during &T the turn-on delay.
two diodes snubber, charged
and one more capacitor. it is found
that for every cycle
to the peak of Vac.
the one with a single this discharging
structure
which
damage
on each bi-directional
is questionable
suggested
handle high current density di that "the high _ and good hard turn-on
consisting
of a capacitor
The
maximum
specified there from
stored
in [9].
Cs*VCs,
snubber
disadvantage current
will be
are much higher than
A better
way of limiting
damaging.
of this snubber
due to an instant
However,
because an MCT has a thyristor di and _. A recent study on MCTs capability cost
allows
use of a snubber
and simplifying
that the MCT can discharge
Even if it is safe to use a capacitor
is still another shoot-through
charge,
reducing
switch.
current is considered
can
alone,
circuit
capacitor
later in this Chapter.
a large discharge an MCT
on the single
of Vac, at least one of the capacitors
losses in this snubber
will be presented
For most devices, this will
Energy
capacitor
current
whether
By using the same analysis
snubber
the circuit"[9]. is, however,
not
alone when used with MCTs,
is that it cannot
of short circuit.
protect
the devices
54
Fig. 4.6
Case III (4.10),
Ordinary
A turn-off
at 20kHz,
devices
one microsecond
will be shorting
might
inverter
either
is.
after zero crossing
the voltage
Whether
and rate of change one of the resonant
the current
The ac source
the voltage
inductors,
Lrl
the source
through
is still
maintained.
up to 1/8 of
delay in the off-going
will
the current
shoot-through
is shorted
or Lr2, as shown
switch,
through
the
depends
on
of a Mapham
at zero voltage,
$1 and $2 can actually in Fig° 4.7.
fault will only delay a resonant cycle by AT as shown in Fig. 4.8. switching
rises
being used is just the output
When
of currents
switch
Note that from Equation
source from 63V to 0V.
which is not an ideal source.
currents
used in a Bidirectional
If there is a one microsecond
rise unboundedly.
how ideal the ac source
snubbers
delay of AT in lhe off-going switch:
Vac,pea k, --63V for example. the devices
turn-off
be limited Therefore
the by this
It can be seen that soft
55 Mapham Inverter ac/ac
PDM Converter
! D1
V_
I I I I
--T 2
Lrl
t = AT
I
Cr
I
I
I load SW_
I +
+
t=O Lr2
Q2 I
Fig. 4.7
L2
D2
An PDM converter with a Mapham inverter
,
_
y \ =
._.
Vac
as a voltage source.
\
vs_
J
Ii
/,,""-_sw2
W
Fig. 4.8 An example waveforms of voltages across the ac link and the switches during an instant of short-circuit across the ac source.
56 Although an instant short-circuit
fault at zero voltage will not cause problem
if the ac link voltage source is a resonant inverter, in the original interest of this research, a stiff voltage source is assumed and needs to be considered.
The following
discussions is about the possible shoot-through current caused by shorting an ideal ac link source. Figure 4.9 shows a PDM converter with a snubber inductor in series with each switch.
The purpose of these snubber inductors is to limit the shoot through
current due to a short circuit. The sizes of these inductors can be determined
by
expressing the switch current in $1 and $2 as:
isw(A T) = ,1__
Vac(t ) dt
%
Note that equation load current Equation
(4.11)
expresses
only the shoot through
can be
(4.11) can be modified
area(0,
Mac(AT),
geometrically
approximated,
AT) is defined
using
without taking the
Equation
to
Vac(AT),
AT) (4.12)
in Fig. 4.10.
The area under
Vac from 0 to AT
for small AT, by
area(0, Hence
current
into account.
isw(AT ) = "1 area(0, Ls
where
(4.11)
Vac(AT ), AT) = _ Vac(t_T)*
(4.9) - (4.13),
the shoot through
current
3
isw(_.T ) =
10"10
t_T
(4.13) at 20kHz
is
2
lt*Vac,pea
k*_,T
Ls (4.]4)
57
_,I
Vs?l
-_
Iload
Vac
A turn-off source.
+
t=,,T .20kHz
Fig. 4.9
$1
:
delay of AT in $1 causes an instant of short circuit for the voltage Two snubber inductors are used to limit the shoot through current.
Vac
20kHz
\ AT
_-1 Mac(AT) 2
*
Fig. 4.10 For small AT the area under the sinewave
An inductance from
interesting to limit
the previous
AT
can be approximated
by a triangle.
result
from Equation (4.14) is that it does not need much di_w(AT) isw(AT ) and dt As an example, using the same parameter
case, i.e. AT = 1US and now the maximum
permitted
shoot-through
/
current,
isw(AT),
due to this fault
= 10A, it is found
that _
needs to be as small as
58 only 0.78uH. rating
Also,
of the MCT
disw(/,T) dt
of current directional
which
is far below
in the snubber
inductor
has to continue,
at turn-off.
The
snubber
switch should be placed however
inductor
and
the direction
and therefore
analysis,
the
of the current
freewheeling
the size of this inductor
of the switch
diode is
by the sudden diode
as shown in Fig. 4.11 so that the current
dfw, can always pick up the inductor current
from the above
the maximum
a free wheeling
in parallel with the inductor to avoid voltage spike caused
in one direction diode,
to 80.6A/us
(5000A/us).
Since current connected
is limited
is.
when the devices
change in a bi-
always
flow
The free wheeling are off.
It is known
is much less than a few microhenrys
it will not be too bulky for the circuit.
,_dl
dfw
M2_
1 Fig. 4.11
The best location of the snubber bidirectional switch.
Note that there
is an advantage
case.
First of all, the purpose
current
caused
conducting
by an instant
current,
the snubber
inductor
of using
of this inductor
of short-circuit
and free wheeling
saturable
is to limit
at switching.
is, in fact, not needed.
inductor the possible
When
A saturable
diode
snubbers shoot
the switch inductor
in each
in this through
is already can provide
59 the required inductance
when the switch is just turned on.
After the current passes
the
saturation level, the inductance of the snubber becomes negligible and invisible to other parts of the circuit. only a small voltage saturation
level.
turns to provide occupy diode,
The energy stored by the saturable inductor is limited drop. Thus it has a small influence
on the other parts above the
Usually a saturable core has high permeability the required
much space.
inductance
for the snubber
and needs only a few
circuit so that it does not
Since the inductor stores only small energy,
dfw, can discharge
the snubber inductor
during the off cycle of the switch.
the free
current to zero through
Thus, the snubber
and causes
can always
wheeling
its on-voltage
start with zero initial
current. The inductive
snubber
is, in fact,
this snubber
is the dual of the capacitive
snubber.
The disadvantages
snubber.
It cannot protect the device from voltage spikes
open circuit.
of the snubber are also the dual of that of the capacitive
It can even cause voltage
spikes
due to a step change
inductor current when the device is just turned on. capacitive
that caused by an instant
A combination
of
in the snubber
of both inductive and
snubbers may solve the possible problems associated with both snubbers used
alone and the faults discussed in cases ! and II. 4.12,
which
The
analysis
individual
combines
for the proposed
snubbers.
the devices
the features
at switching.
of both capacitive
snubber
The purpose
The proposed
circuit
is more
of the capacitor
The inductor
limits
and
snubber
inductive
complicated
is shown in Fig. snubber than
is to limit the voltage
the inrush
current
of each spikes
through
circuits. the
across
the devices
at
switching.
4.4
Analysis
of The Proposed
A simplified 4.13.
Snubber Circuit
circuit diagram
of the proposed
As can be seen in Fig. 4.13, the snubber
again, takes advantages
circuit
of soft changes of resonating
snubber
circuit
is shown in Fig.
itself is a resonant
voltage and current.
circuit which,
The snubber
6O
1
kl
_3
I-H
Fig. 4.12
Proposed snubber for the by directional switch which combines of both capacitive and inductive snubbers.
$1
Cs
+
2
20kHz
the features
Vswl
,s T,
Ioa
Vac
$2
-I-
Vsw2
Fig. 4.13
Simplified ac/ac PDM converter with proposed snubber circuit. Each snubber inductor has a free wheeling diode (not shown) in parallel so no voltage spike occurs across the devices at turn-off.
61
inductors are also saturable because that the rate of change non-linear linearity
inductor,
circuit drop.
accurate
are tedious, Consider consists
second
analysis
the two quasi-resonant
of an ideal capacitor,
order circuit
Since
is presented circuits
Io, flows
of
consists with
of a
the
non-
in the following.
shown
in Figs. 4.14 and 4.15.
Each
and a diode with finite on-voltage
the on-voltage
the capacitor
circuit
resonance
into the LC circuit
voltage reaches
analysis,
this snubber
calculations
an ideal inductor
a step current,
biased until the capacitor
a simple
is limited.
quantitative
a qualitative
In Fig. 4.14,
reverse
of current
inductance is needed only when a switch is closed so
voltage
at t=O.
The diode
drop of the diode.
and inductor
current
is
From of Fig.
4.14 can be found as
Vc(t)
IL(t)
= Io* ,_
*sin(cot)
= Io * (1-
(4.15a)
COS(Cot))
(4.15b)
where
Co
1
_
(4.15c) However,
Equation
4.15
voltage
forward
voltage
and discharges
describes
biases the diode,
the voltage because
the inductor through
of the inductor current can be expressed diL dt
The waveforms
of voltage
and current
only
before
when the diode turns on it clips
the capacitor the capacitor
its on voltage drop, Vdo n. The rate of change
as =.
Vdon L
and current are described
(4.]6)
in Fig. 4.14.
62
lsw
-ST
.
ill
III
i|" I
:
! |
! I lilt
I
li
!
!
I
lltllll|llll
L
_
diL
-
Vdon
2.1o ! /
"
I
I I
;
_
"I I
" " •
I I
! I I
I I
" : I' I "I
li i i
I:
I
Ii
"
i
I
I
I
i
I
.
Isw 2"10
I0-
Fig. 4.14
y
to be modified
capacitor
represent
_
l _,
!
response
the behavior
is turned
ii
•:
I IIIiii
as seen in Fig. 4.15.
The switch
_
lilll
Voltage and current diode circuit.
To better
Fig. 4.14.
"_T_l;iliilll
'
for a step current
illl
input
i I i I
I_
i
to a parallel
of the snubber the circuit
LC and
of Fig. 4.14 needs
In Fig. 4.15, a switch is added to the circuit shown in on at t -- ,_T.
is charged to some initial voltage,
Vc(AT)
Before
the
switch
and can be found as
is turned
on the
63
Vsw,peak
During
this
superposition results
time
the
applies.
diode
Me(AT) = I_ * AT C
--
is
reverse
The resulting
voltage
due to Io and the initial voltage
order analysis,
the capacitor
Vc(t)
biased
voltage
(4.16)
it
is
and current
of the capacitor
a
linear
circuit,
can be found Vc(AT ).
therefore
easily
by adding
Using a simple
second
is
= Io _
= Io •_
sin(cot)
+ Vc(AT ) cos(cot)
sin(cot)
+
I°*AT C
(4.17a)
cos(cot)
(4.17b)
where (4.17d)
and the inductor
current
is
I
+
iOOs(_t))
(I
Vc(AT) IL(t ) = Io
sin(cot) (4.18a)
Io*AT Io (1-COS(cot)) + L_C
Using phasors
and simple trigonometry,
IL(t ) =! o
where
Equation
(4.18b)
(Jew 1+
¢2 = -tan
!+
_.
1(L_C )
sin(cot) (4.18b)
can be simplified
sin(cot+C2)
to •
)
(4.18c)
(4.18d)
64 + Vsw
-
, _
,,."
i\
/i
,o ..... ..... i..... l
I,
lsw
ii
----i---
.
i]
,
i
!
i
i
.
i
---_ _
i
i
i l
Fig. 4.15 Voltage and current responds as a current step inputs to a parallel LC and diode circuit with the switch has a turn-on delay of tLT.
i k---
i
65 From Equation (4.16), across the device can be found. from
Equation (4.18c),
in case of an instant of open circuit
the peak voltage
The maximum discharging current through the device,
is limited to about twice as Io for small AT.
The above equations are only valid before the diode turns on. resonant circuits, the diode turns on when the capacitor voltage Once
Similar to other
tries to forward
bias it.
the diode turns on, the capacitor voltage is clipped at Vdon and Equation
describes the inductor current.
(4.16)
Fig. 4.15 shows the idealized waveforms.
The circuits in Fig. 4.15 describes the proposed resonant type snubber in case of a turn-on delay. switching device.
Vsw and Isw are the voltage Io is the load current.
across and the current through
the
With this snubber circuit, the switching device
is always turned on at zero current. An LC circuit has been theoretically current to finite values. from Equation (4.16). before 20A
turn-on,
The value of the snubber capacitance,
then,
possible turn-on
and
Cs, can be determined
For example, if a 200V voltage spike across the MCTs
the maximum
respectively,
shown to limit the transient voltage
delay and load current
is allowed
are l.Sus
and
from
Equation (4.16), Cs is found to be 0.15uF. The Cs capacitance of each snubber capacitor, _-, equals to 0.075uF. In other words, when the MCT is turned on, it discharges the snubber capacitor with a worst case voltage of 200V. The discharging protects example, device, wheeling
current is limited by the snubber
the device
from
the energy
dissipating
high energy
inductor. during
stored in the snubber capacitor
In general,
a short fault
is not dissipate
the snubber time
AT.
For
in the switching
MCT in our case, but, instead, goes through the snubber inductor into the free diode.
As the snubber
inductor first
absorbs energy
from
both the snubber
capacitor and the load current, the inductor current rises from zero then passes the peak where the diode starts to turn on and the capacitor diode's on-voltage,
Vdon, see Fig. 4.15.
Io up to
voltage is clipped at the
The free wheeling diode discharges the inductor
66 until it reachesIo, can be verify
the initial energy stored in the capacitor has gone to the diode and it
by simple
arithmetic.
As for the shoot inductor
should
the capacitor
definitely
a short
fault
dissipates capacitor
the power.
a resistor
dissipate
as a short
The snubber inductor
is found
through
circuit
small
But if the energy
energy
that the snubber as shown
device
very high energy
when
is designed
time.
dissipate
circuit,
the
The energy
and the free wheeling
to limit current.
high energy
free
wheeling
stored
during diode
in the snubber
diode should
be able to
is large that it may be over the rating of the diode,
inductor
in Fig.4.16.
the snubber
higher than the shoot through
or open
a longer
is assumed
by the turn-off delay,
in series with the diode will help dissipating Note
limited
caused
instead of letting the switching
energy
and inductor
dissipate
current which
time such
smaller
current
be able to limit it.
discharging
In general,
through
the energy.
is saturable,
and,
Thus the free wheeling
the devices
are off.
therefore, diode
will
store only
is not required
If a non-saturable
inductor
to
were
used, the stored energy would be much higher and the diode would not be able to discharge all the current.
Energy Stored in a saturable
:_:_._.._:;:"
..::::_
_...:_,'._:_'.._."
inductor
.....
i_;i%i!i ....
H Fig. 4.16
B-H curve for a saturable
inductor.
67 4.4
EXPERIMENTAL RESULTS A single phase
4.17.
The low frequency
PDM
converter with the proposed
current
source load is implemented
circuit which has very high quality,
Q, and resonates
In the ideal case, when no snubber completely
off and vice versa.
snubber
This is difficult
is shown
by connecting
a series RLC
$1 is completely
on and $2 is
at 4kHz.
is needed,
to achieve
due to delays
in the device
M11
.= 0.05pF
s = 10pH
D S
Fig. 4.17
An ac/ac
converter
With
in Fig.
Proposed
snubber
Circuit.
68 itself and the drive circuit.
Since it is impossible to test the device at all power levels
and observe
in turn-on and turn-off delay,
the difference
lp.s is created causes
intentionally
in this experiment
by shifting the control signal of switch $1 by l_s.
both an open circuit and a short circuit at different
experiment
is basically
a stress test.
MCT, a l_s delay can create almost short-circuit proposed
at the other.
a delay of
The
With
This
edges of switching.
the fast switching
This
characteristics
of the
a complete open circuit at one switching edge and
goal is to show that
under this situation,
with
the
snubber circuit, soft switching is still maintained. In this experiment,
it is more important to observe
the individual devices of a
switch than the switch as a whole. Without a snubber, the stress on current spikes occur at different edges. found,
however,
that
if the voltage
Mll
is shown in Fig. 4.18.
The MCTs did survive these
level was further
increased
mixed into the control logic and cause random switching. devices were then damaged. any snubbing.
Therefore,
Voltage
spikes.
It was
misinformation
Under such conditions
the power level could not be increased
and
was the
without
The misinformation was believed to be due to either the voltage spikes or
the poor voltage regulation of the ac bus. In Fig. 4.19 the voltage level was increased to a higher level than that in Fig. 4.18
without inducing misinformation
spikes are reduced
significantly
current spikes, however,
into the control logic circuit because
using only a capacitor
are still high.
Cs (O.05_F)
the voltage
as snubber.
On the other hand, if the a snubber
inductor Ls (lOp.H), the current spikes are reduced (see Fig. 4.20).
The
is just an
Again, the voltage
level could not be increased due to the voltage spikes causing random switching. When current reveals,
a combined
capacitor
spikes are both reduced
and inductor snubber
as shown in Fig. 4.21.
is used the voltage
As the theoretical
the snubber inductor slows down the rise of current through
and
analysis
the switch and it
69 takes voltage
some
finite
of the
those
shown
peaks,
thus
here,
from
time
for the
parallel in Figs.
the
stress
diode).
to rise
therefore
output
voltage
and
The
on the
MCT
it was
soft
spikes
Therefore
4.18-4.20.
the oscilloscope
starts
current
the
MCT
seen
is full-on
that
/
before
Although
in Fig•
4.21
on the is wider
the
current
spikes
the
details
cannot
voltage
maintained
depends
finishes
in spite
than
reach
the
be shown
before
of the
on-
current
delays•
The
in Fig. 4.22.
Vak Of Mll
I
spikes
the transient
is still
are shown
down(which
current
is still small.
switching
load current
to come
Without Snubber
_1 V tn
!
I
0.00010
I
0.00020
I
0.00030
|
0.00040
0.00050 time(sec)
Cathode 4.003.50-
Current of Mll
Without Snubber
Amps
3.002.502.001.501.000.50-
0oo-0.50 -1.00 !
0.00000
0.00010
!
0.00020
!
I
0.00030
!
0.00040
0.00050 time(sec)
Fig. 4.18
Voltage
across
anode
to cathode
and cathode
current
of Mll
without
snubber.
70
Details of Voltage across Anode to Cathode of M11 With Capacitive Snubber 300 250200A
:>_
150-
50-
0> 1°°-i, jr ,
J
-50 -100-150'
I 0.00010
0.0000o
'1 0.00020
I 0.00030
I 0.00040
I 0.00050 Tlme(sec)
Details
of Cathode
Current of Mll
With Capacitive
Snubber
14.012.010.08.0-
,¢. 6,04.02.0-
0.0-
I
'-'-
-2.0 _ 0.00000
t,
I-_
..... I 0.00010
L
r .... II........ I 0.00020
I 0.00030
I 0.00040
I 0.00050 Time(see)
Fig. 4.19 Voltage
across anode to cathode and cathode current of M11 with capacitive snubber.
71
Vak of M11 With Inductive Snubber
400300200-
> v
100-
v ,
-I00-200-300 0.00000
I 0.00010
I 0.00020
I 0.00030
i 0.00040
i 0.00050
time(sec)
Cathode Current of Mll
7.0--
With Inductive Snubber
6.05.0A
,
50-
_
0-
of voltage across a switch made of MCTs, switch.
(b)current
through
100-
--0 >
-50 -
o
-100 -
-1so
I
0.0000
I
II
I
I
iilI
I
0.0050
I
Ill
Jill
lineal
le
0.01 O0
I
lill
0.01 50
Time (see) Fig. 5.16 The line-to-line
voltage,
Vbc.
I
II
I
l
I
0.0200
the
96
losses are still expected to be small due to the small voltage and short rise and fall time of the current during switching. Figure 5.16 shows the line-to-line voltage, Vbc.
It has the same peak value as
the phase voltage, Vco shown in Fig. 5.10(a), but has a higher density.
Estimated calculated standard about
:
from the dc voltage operation
200W
However,
efficiency
using
point.
The power
and current
method.
It is believed
resonant
current.
As
efficiency
(see Appendix
It was found
three-phase Therefore
that most
the 3).
nature
output the
of the three ac/ac PDM converter
the input power from the high frequency wattmeter.
applied.
The low frequency
two-wattmeter
the efficiency
input to the Mapham
inverter can easily be to be about power
lost in the
of a Mapham
The power
losses
Mapham
inverter,
is about
to measure
ac source cannot be measured power
was found to be
efficiency
is difficult
700W at a
29%.
because
with an ordinary
inverter
due
to high
load
yields
higher
higher
in the PDM converter
are estimated
in
the following. First,
consider
the average
current
through
each
leg of the converter.
This
current equals to the peak of the phase current multiplied by 2/_:
.2 lavg =lpeak
=13"
_
(5.3)
2 --
= 8.28 A
One switching Ioss,Pcond,
in each leg has to be on for any given in each
leg equals
to the on-voltage
diode and the MCT or IGT) multiplied
by the average
time.
Therefore
the conduction
drop of the bi-directional current:
switch
(the
97 Pcond = lavg * Von
(5.4)
The on-voltage of those made of each MCT is _1.9V (Fig. 5.11(a)), --3.5V (Fig. 5.12(a)).
Therefore
the total conduction
and that of an IGT is
loss of the PDM bridge
is
Pcond =8"28A*(1"9V+3"5v+3"5v) = Under
accurate
losses.
zero-crossing
From
every
5.14(c)
time it switches
be much smaller calculated
74W
switching,
the worst
the conduction
switching
the loss would
only
and can be ignored.
loss is dominant
loss was 0.17m J, even be 15kHz
* 0.17mJ
is, however,
devices
a little higher
the MCTs
satisfactorily
in an ac/ac
when
used
The
feedback
scheme
control
in applications
output
source
current
presented
methods
For this voltage
than
In conclusion,
capability.
other
but it should can be
the actual
connected
that require
of the PDM
is needed.
converter
timing
switch
configuration
better
than
and high voltage
is well
Incorporation
are always
at zero voltage.
It is especially
critical
there
regulated
other
blocking
by the current
of this converter
with some
as future work.
to be tested
As an attempt
because
in a bi-directional
PDM converter.
in this Chapter.
PDM
efficiency
due to not switching
will be considered
ac/ac
)* 100%
73%
losses in the PDM converter
performed
= 2.55W,
to happen
as:
=
switching
it were
So, the efficiency of the PDM converter
Pcond eff % = (1 - Pcond + Po
This
to the switching
with full power,
to run this ac/ac
a well
regulated
PDM converter
20kHz
at high power,
98 the 10kW Mapham
Inverter
converter
at the University
increased
gradually
to the ac link. few MCTs
from NASA
Lewis
Research
Center
was used.
Unlike
the
of Akron the voltage of this Mapham inverter could not be dv causing a high _- across the device when the converter was connected
The controller
to be damaged
was not able to respond
opened
To ensure
until the ac link voltage
unchanged
until
'EN' is opened.
start-up.
causing
a
a drive therefore,
was then modified
the clock signal 'clk' is stable,
was stable. The starting
More MCTs were damaged suspected
The circuit
to the transition
to the circuit dv shown in Fig. 5.17. The switch 'PW' was place before the LC tank so that the _" across the bridge was limited.
during
safely
In other words, sequence
Unfortunately,
it was not possible
the gating
'EN' was not
signals
remained
is turn on 'PW' first then 'EN'.
as the voltage on the ac link was increased.
that this damage was caused by a loose connection circuit.
the switch
these
failures
to run the converter
depleted
between the
at full power.
It was
a control signal and
supply
of MCTs,
and,
99 m
I_ _ I_ _ i_'
.___ _ L..._
121 u -_._ m
-_"----_--tl, 15
_,,b-O-_. 31.6pH
i(
1,F I
C
I.-
.,- il_
N
i
J ib,
N
"1-
o
o i (M
E
L_
t_
G)
=E_= Fig. 5.17 The ac/ac PDM converter
with a modified
starting
sequence.
CHAPTER SUMMARY
6.1
AND SUGGESTED
FUTURE
WORK
Summary As semiconductor
of many
devices
frequencies
have
component also
technology
enabled
and power.
space application
can
VI
has been studied.
used
progresses,
many power
The advantages
sizes and weights be
rapidly
electronics
the speed systems
of using high frequency
to operate ac power
Other than making high voltage
and easily
providing
as a voltage
source
PDM converter
directly
for
isolation,
ac/ac
and power
density
at higher
distribution
in
more safe, reducing
the high frequency
ac link
pulse-density-modulation
(PDM)
converters. An ac/ac several
orders
of magnitude
lower
modulates
frequency
usually filtered by the load like an induction converter
is the zero-crossing
switching
The ac/ac PDM converter current
conduction
directional
switch
PDM converter Among
and
is discused
needs
the existing
the best candidates
voltage
switching
power
such as 60Hz.
motor.
topology
requires blocking
in Chapter
the high frequency
which minimizes switches
capabilities. Two.
The
a MOS-Controlled-Thyristor
for this application.
has the best features of a MOSFET
100
is
of using a PDM
the switching
losses.
that has bi-directional configuration
of
a bi-
of the ac/ac
drop and fast switching. (MCT)
The MCT is a newly emerged
and a thyristor.
to a
component
For the best performance
device that has low on-voltage
devices,
The 20kHz
The major advantage
high speed
ac source
was found
to be
power device which
101 An initial test was made at 600V/60A the MCTs
having
such a high power
voltage
and current
safely,
the the gate
discrete
gate-drive
handling
were experienced. drive
MCTs
under hard switching.
capability
the MCTs
It was noticed
has to have
a fast
have, failures
in order for the device
rise-time
circuit for MCTs was developed
In spite of
of about
200us
at low
to operate
at turn-off.
A
and used for most of the experiments
in this research. In the dc chopper
experiment
100V and 20A at 20kHz, the devices circuit.
Turn-off
switching
to rise
away occurred. After crossing
performed
satisfactorily
without
time is about 1us at 20A and which constitute
experiment.
temperature
in Chapter Three, the MCT was switched
At 30kHz which
further
With a turn-off the
switching
hard
the
MCT's
increased
snubber
switching
turn-off the
the problem
experiment,
in a single phase
a major
loss
current
needing
a snubber
loss in the hard
increased
fall-time,
at about
and
thus
caused
thermal
run-
was avoided.
the
device
ac/ac PDM converter.
was
tested
In Chapters
under
zero-
Two and Three
and the MCTs were shown to be able to switch at zero volts easily while connected bi-directional minimizes delay
switch switching
may
completing
configuration losses,
harm
it was
the devices
of one switch
difficult
to achieve.
A bi-directional
against
voltage
snubber
circuit
limits
Chapter
spikes
voltage
of the other
caused
by the turn-on
to protect turn-off
spikes
turn-off
In practice,
at the same
and
and current
and
spikes.
was designed
topology
moment
is
the device
delays.
The
and dissipates
the
by the MCTs.
the experimental
results
made of IGBTs and MCTs.
MCTs and the other two used IGBTs.
in turn-on
and current
circuit
of voltage
switching
a difference
snubber
be dissipated
Five presents
phase ac/ac PDM converter
to the
zero-crossing
that
and turn-off
the magnitude
energy that would otherwise
noticed
due
turn-on
and current
Although
in a
of a current-regulated
One leg of the PDM converter
MCTs and IGBTs have similar characteristics
threeused but the
102 overall features found
of an MCT such as low on-voltage
that the conduction
loss of a hi-directional
lower than one made of IGBTs. regulated by the current feedback
are better.
switch made of MCTs
The output currents of the PDM
is designed
and is expected
to drive
However, due to a latching problem in the Mapham was not operated inverter
have
at 20kHz.
at the motor full power level.
a turn-off time of 15_s
Although,
is significantly
converter
are well
a 5hp induction
motor
IGBTs.
The
at full
load.
inverter at high load, the converter
The thyristors used in the the Mapham when the inverter
is switched
of the inverter has been reduced to 15kHz so
that it allows more time for the thyristors increases.
MCTs and 600V/25A
which is marginal
the resonant frequency
latch as the temperature
it was
scheme.
The ac converter was built using 600V/75A converter
In the experiment,
to regain the blocking
Under this circumstance,
capability,
the ac/ac
they still
PDM converter
has not been tested under full load.
6.2
Suggested Being
Future Work rated
at such a high power
level, this converter
should
be tested
with
higher power such as 5hp. To command speed work.
made
currents
information.
the
converter
of the induction Applying
control
more motor
practical
as an
induction
can be calculated
methods
to this converter
from
motor the flux,
is considered
drive, torque
the or
as future
BIBUOGRAPHY [1]
Irving G. Hansen, Gale R. Sundberg, "Space Station 20-kHz Power Management and distribution System" power Electronics Specialists Conference (1986).
[2]
A. C. Hoffman, I. G. Hansen, system for transport aircraft",
[3]
K.H.Liu,
F.C.Lee.
"Zero Voltage
Switching
Technique
Power
Electronics
Specialists
Conference
(1986):
[4]
D.W.Novotny, Performance Meeting
[5]
[7]
IEEE
58-70.
R.D.Lorenz. "Introduction to Field Orientation and High AC Drives" tEEE Industrial Industry A0plications Society Annual
(1985).
1989)
1-6
John G. Kassakian, Martin. F. Schlecht, George. C. Verghese. Electronics." Addison-Wesley Publishing Company (1991).
"Principle
Of Power
T.A.Lipo, I.Alan. "System, Component Design and Test of a 10 Hp, 18,000 RPM ac Dynamometer Utilizing a High Frequency ac Voltage Link" NASA Contractor BP,P..0.Lt, Contract
[8]
in Dc/Dc Converters"
power
R.W. De Doncker, T.M. Jahns, A.V. Radun, V.A.K. Temple, D.L. Watrous. "Characteristics of MOS-Controlled-Thyristors Under Zero Voltage Softswitching Conditions" Proceedinas of the IEEE Industry. Applications Society. (Oct.
[6]
R. F. Beach, et. al., "Advanced secondary NASA Technical Paper 2463 (1985)
No. NAG3-940
(June
1991)
Tony Lee, Don S.Zinger, Malik E.EIbuluk. "Modeling, Simulation And Testing Of MCT Under Zero Voltage Resonant Switching" IEEE Industrial Electronics _;ocietv
Conference
(1991):
342-346.
[9]
V.Temple, D.Watous, S.Arthur and P.Kendle. "MOS-Controlled Thyristor(MCT) Power Switches - Part h MCT Basics" PCIM(November 1992): 9-16.
[1 0]
N.Mapham. "An SCR Inverter with Good Regulation and Sine-Wave Output", IEEE Transaction on Ind. Gen. Application, Vol. IGA-3, (Mar/Apr. 1967): 176-187.
103
APPENDICES
104
105
APPENDIX MCT
P-CHANNEL MOS CONTROLLED
Features:
DATA
THYRISTOR
I SHEET
(MCT), MCTA75P60.
• MOS Insulated Gate Input • Gate Turn-Off • 1000
Amp
Capability
Current
Capability GATE
• 120 Amp • Vtm=
MAXIMUM
turn-Off
Capability
1.3@1=75A
RATINGS,
ANODE KELVIN
Absolute-Maximum
Values
(Tc = 25°C)
Peak Off-State Voltage
VDF_
-6OO
V
Peak Reverse Voltage
VRRM
+10
V
Ic25
120
A
Ic90
75
A
1000
A
ITC
120
A
VGA
+ 20
V
Cathode Current Continuous
@Tc = 25°C @Tc = 90°C
Non-repetitive
Peak Cathode
Peak Controllable Gate-Anode
Current
Current
Voltage Continuous
ITSM
Rate of Change of Voltage (Vga = +15)
dV/dT
10000
V/us
Rate of Change
dl/dT
1000
A/us
PT
2O8
W
of Current
(Vga - -10V)
Power Dissipation Total @Tc = 25oc
106 Power Dissipation Operating
1.67
Derating Tc > 25°C Tj, TST G
and Storage Junction
Temperature Maximum
-55
to
W/oC +150
o(3
Range
Lead Temperature
TL
for
260
°(3
Soldering
ELECTRICAL CHARACTERISTICS, At Case Temperature
CHARACTERISTICS
Peak Off-State Blocking
SYMBOL
IDRM
Current
Peak Reverse Blocking
(Tc) = 25oc
IRRM
Current
On-State Voltage
Gate-Anode Leakage
VTM
unless otherwise
specified.
TEST CONDITIONS
LIMITS
The test circuit
in Ficj. A1.1.
MIN
VAK = -600V,
T C = 150oc
---
VGA = +15V
T C = 25°C
- - -
VAK = + 5V,
T C = 150°C
---
VGA = +15V
T O = 25°C
IC = IC90,
IGAS
VGA = + 20V
Input Capacitance
Cis
VAK -- -20 V
Output Capacitance
Coss
VGA = +15 V
Current
td(on)i
TYP
UNIT MAX I
3
mA
100
uA
4
mA
- - -
100
uA
TC = 150°C
---
1.3
V
T O = 25oc
---
1.4
- - -
200
nA
11
nF
TBD
nF
400
ns
500
ns
Current
Turn-on
Tj = 25oC
I¢ = Ic9 o
L = 50uH,
Delay Time Current
Rise Time
tri
Rg = 1_,
VGA = +15V,-10V
Minimum
Rise Time
t(ot)
TBD
Current
Turn-off
td(off)i
Tj = 125oc
tfi
YAK = -300V
- - -
us 700
ns
1.4
us
15
mJ
.6
oC/W
Delay Time Current
Fall time
Turn-off
Energy
Thermal
Resistance
.
.
.
.
.
.
.
Eoff ReJC
"
"
"
o5
107
-_OOV
50uH
f
RUR880
+ 15V
OV
ANODE KELVIN
h,NCX3E
- lOV trise
= 100ns Fig. A1.1
Manufacturer's
Test circuit for MCTA75P60.
Handling Precautions for MCTs
MOS Controlled Thyristors are susceptible to gate-insulation
damage by the
electrostatic discharge of energy through the devices. When handling these devices, care should be exercised to assure that the static charge built in the handlers body capacitance is not discharged through the device. MCTs can be handled safely, if the following basic precautions
are taken:
108
1.
Prior to assembly into a circuit, all leads should be kept shorted together either by the use of metal shorting springs or by the insertion into conductive material such as *"ECCOSORB
2.
When devices should
LD26" or equivalent.
are removed
be grounded
by hand from their carriers,
by and suitable
the hand being used
means - for example,
with a metallic
wristband. 3.
Tips of soldering irons should be grounded.
4.
Devices Should never be inserted into or removed from circuits with power on.
5.
Gate Voltage Rating- Never exceed the gate-voltage rating of VGA. Exceeding the rated VGA can result in permanent damage to the oxide layer in the gate region.
6.
Gate Termination - The gates of these devices are essentially capacitors.
Circuits
that leave the gate open-circuited or floating should be avoided. These conditions can result in turn-on of the device due to voltage buildup on the input capacitor due to leakage current or pickup. 7.
Gate Protection - These devices do not have an internal monolithic from gate to emitter.
If gate protection
recommended. *
Trademark Emerson andCumming,
Inc.
is required,
an external
zener diode zener
is
APPENDIX THE
SCHEMATICS
The appendix
if current opening
Figure
A2.1
limit
signal,
"Jump
command "TRI". "TRI"
is the controller LMT,
1" open
shown in Fig. 5.8(a). currents The
is high
this
becomes
CIRCUIT
of the three phase
that provides circuit
the switching
will
shut
ac/ac controller. state.
off the
PDM
In this circuit converter
by
$1, $2 and $3 and close the lower three switches.
this circuit
With
frequency
"Jump
1" closed,
command
of "TRI"
functions
as a current
the current
voltages
regulated
feedback
to be modulated
With
controller
is disabled
and the
by the triangle
is 1/16 of the ac link frequency.
The
that
circuit
wave for the
signal is shown in Fig. A2.2. Figure
magnitude
A2.3
shows
of the current
the circuit
flowing
The interface
connector
that generates
in to the converter
Figure A2.4 is the pinout circuit.
PDM CONTROL
is for the documentation
the top three switches
the jumper
OF THE
II
for interfacing
is high
when
is over the preset current
level.
between
is a 14 pin dip connector.
109
LMT which
the converter
the
and the control
110
111
E
[I,
or
e-
9 ,_
o< tZ
m
";_-Z
_'-+ .w¢-
-1 > L_
LI_
.-I U
112
E
.m I
e-
II _4 I
iT
-c_l -J
_
r_
(.) U
113
g ,;_
++_
i111111 .--
CONNECTOR
ol "_
l
i
l
l
o
l
I
"2 'T
E
APPENDIX ANALYSIS
AND
III
SIMULATION OF THE 20KHZ THE MAPHAM INVERTER
AC
SOURCE
Introduction Traditional Fig. A3.1. adjusting
The magnitude the
generator. almost
The advantage
The prime voltage
outputs even
of the output
field
If, and shaft
power
generators,
voltage, speed,
generator
conversions
like a turbine
or dc motor,
a machine
Such a system
they
co, respectively,
is impractical
hundreds
in many
voltage
However
is
it involves
of energy
are always
by
of the
is that the output
losses.
bulky
are also very heavy.
would require
as shown in
Vo are controlled
which causes significant
made of iron and copper,
are wanted,
bigger.
current,
of using a synchronous
are basically
movers,
from synchronous
of the load, i.e. it is close to an ideal source.
to electrical
the machines
are obtained
and frequency
magnetizing
independent
mechanical
itself
ac sources
As
and heavy.
If high frequency
of poles that
applications
makes the
where
space
is
limited. In the era of power electronics, in a more inductors
convenient
and capacitors.
order-of-magnitude power
density
principles output
way.
Compared
better
and efficiency.
of how they
voltage
A dc/ac
in terms There
are operated
of a resonant
inverter
a resonant inverter
inverter
is made
to a synchronous of cost
using
are the same.
kinds of resonant The fundamental
ac
devices,
a dc/ac
portability,
is the same as the switching
114
semiconductor
generator,
effectiveness,
are different
can be used to generate
inverter
is
controllability, inverters, frequency
frequency
but the of the
provided
by
115
Vf Fig. A3.1 Using a synchronous
the control
circuit.
In most
BJTs, MOSFETs etc., series or parallel
resonant
are switched
resonant
of the LC circuit
the output
voltage of a resonant
load, which decreases distortion
A Mapham inverter
which
distortion. that
thyristors
easier to drive. the related
advantage
a square
voltage
on the load. tank,
devices, is applied
like to a
is close to the resonant
The distortion
is dependent
Q, of the resonant
switching
of current
frequency
the harmonics.
as shown
to
have
a better
(disadvantage
can be used as the switching
literatures.
ac voltage.
fully controlled
The switching
converter
inverter[10],
Detailed
to generate
and magnitude For example,
thus causing
of
a heavy
more harmonic
the magnitude.
is designed
Another
so that
which filters
the quality,
and antenuating
inverters,
LC circuit.
frequency
generator
features
in Fig. A3.2, voltage
regulation
in some cases) devices
and analysis
is an improved
resoflant
and less
harmonic
of using such a inverter
is
meaning
higher power
density
and
of this inverter
can be found
in [10]
and
116 I L1
Vdc
_
D1 C
2
+
I
Cr I (
Lrl_
Vc
Linear Vc
J
or
Non-Linear Load
Lr2
_T--
Q2
Fig. A3.2
Using a Mapham (resonant)
The analytical very complicated. be obtained
expressions
However,
by simple
loss case, the positive
for the capacitor
the waveforms
qualitative and negative
battery
is same as what goes in.
voltage
is integral
inverter
piece-wise
of currents
to generate
voltage
and inductor
and voltages
linear analysis.
ac voltage.
currents
are
of this inverter
can
At no load, assuming
areas under ILl are equal, thus energy The capacitor
of IC. The thyristors
current
are switched
IC equals
a no-
that leaves the
to ILl - IL2, and its
above the resonant
frequency,
_0r,
where 1 ('Or= "yL'r:-rC r so that one thyristor inductor
current
(A3.1)
will not be fired while the other is still conducting,
waveforms,
ILl and ILZ. in Fig. A3.3
The resonant
see the current
frequency
is usually
117 chosen to be around when
both
the
213 of the switching
inductors
parallel, therefore
frequency,
are conducting,
resonant
frequency
thus
0_s. Note that
the capacitor
there
sees two
is sometime inductors
in
during that time becomes
(or'
1
-- r--
(A3.2) Cr
= 1.414 However, loaded.
it
frequency
of a cycle
waveforms
Although
IC is a distorted
distortion
because
it
is the
especially
of this inverter sinewave,
integral
when
the
operated
is
at no load are
the capacitor
of IC which
inverter
voltage,V
smooths
out
C, has
the
high
components. Turn-off always
current,
the thyristor
of the thyristors
crosses
has a potential carrying
and voltage
portion
in Fig. A3.3.
small
current
only a small
The current
sketched only
occupies
* cor
zero before
latching
problem.
they
will latch on.
turns
is a natural the other
commutation
one is fired.
If one thyristor Under no-load
off at zero current
within
about
process
Unfortunately,
is triggered condition --
as one thyristor this inverter
and the
other
or an undamped
seconds.
As the
is still system,
inverter
is
(or
loaded
by a resistor,
time taken for the current
where
c0d is called the damped frequency
Zo. 2 1 - (_-_)
to about
(A3.3)
impedance,
z°= r But the characteristic
becomes
and defined as
C°d = (or _/ Zo is the characteristic
to reach zero
impedance
also change when both inductors
(A3.4) are conducting.
--
(od
,
118
I LI_
I L2
2_ VC
k/ V V b Fig. A3.3 Idealized waveforms
of currents and voltage state under no load.
of a Mapham inverter
in steady
119
Zo' : _It---2J
y
To avoid this latching switching
problem,
frequency,
the damped
: 0.707* Zo
(A3.S)
Cr
frequency,
cod, should
be less than
cos, therefore COs< cod
For example, (A3.6),
frequency
to 4 _, simulation this
simulation
inverter cannot
were taken
is 200
deliver that
capability. thyristors
V.
The
about
high of power
The turn-off
In fact,
S.SkW.
the
are naturally
turn-off
turn off, see Fig. A3.S.
and
impedance,
bigger.
With R equal Vdc,
used in
VC, is 21S V, therefore,
in the
actual
situation
this
to regain voltage smaller
this
converter
time, tq, of the thyristors
tq, in our case is slightly
the negative
I Slls.
With
a I0_
inductor
to the I0 _ load is approximately,
inverter
has a better
voltage
as shown in Fig. A3.6,
regulation
current
voltage
load there
The peak of the output
delivered
simulation
voltage,
because the turn-off
has to block the forward
time is about
(A3.3)
has to blocking
because
the
commutated.
From the simulation, means the thyristor
output However,
time,
from
The dc voltage,
time is the time for the thyristor
turn-off
then,
R should be slightly
is shown in Fig. A3.4. peak
rad/s,
But if the changes of characteristic
into account
of this inverter
is delivering
be considered.
(A3.6)
if L r = 121_H, Cr = 31_F and cos = 1 25,664
R should not be less than 3. I _.
and damped
the
in 4llS.
than
other
the change of voltage
For a fast
is enough
sinewave 2.4kW.
last for about 411s, which
time
is _ 220V, As mentioned resonant
thyristor
for the device
the to
therefore,
the power
before,
a Mapham
inverters,
from
the
from no load to a 10 (2 load is
only _ S V out of 220V. The efficiencyof thisconverter is quite dependent on how much
itis loaded.
The more the inverterisloaded the higherthe efficiency.As the inverteris loaded, the
120 negative positive
current,
which conducts
current
increases
through
the anti-parallel
only slightly.
The reduced
diodes,
current
decreases
can greatly
reduce
and copper losses.
100 50
_5 o "
!
' .........
I
100
_- 50 0
-q p
toff i
•
I
'
!
100
v
u
0
-100
°
ii
•
'
'
•
•
•
'
'
'
'
"
"
"
"
'
'
i
"
"
"
I
V V v L,,
I
•
•
•
•
•
•
•
•
•
•
•
•
•
0.0004
.
•
0.0005
Time(sec) Fig. A3.4
The simulation
while the
of a Mapham inverter with a 4 £_ load connected.
core
121
80
,o 0 -4
20o-4 100 > v u >
0 -100 -200 " •
•
i
i
•
........
The
=_
0.0005
).0003
Fig. A3.5
i
0.0004
simulation
of a Mapham
300 -
inverter
Time(see)
with
a 10 D load connected.
no-load
200'
100"
u
0'
-100
-200
J O.O00S
-300 0,0004
Fig. A3.6
The
Tlrne(sec)
output
voltage
regulations
at different
loads.
lZ2 The Mapham inverter good regulation
and negligible
PDM converter,
there
analysis,
linear load can reduce
Mapham inverter filtered
for a non-linear
even in low power
_ 2kW to a resistive
to
phase
L, so that
16 sin(754
shown
inductor
current
transient
time,
in Fig. A3.8,
current
regulated
The output
voltage
as seen in Fig. A3.8(a),
Mapham Inverter Lr
=12_H
From the above
load, but driving
IR, has less ripple
the output
power
between
0.0018s
the turn-off
time
loading
$1 J
The resistor
current
is only polarity,
320W. there
to 0.0026s.
I
,_
Ia
A Mapham inverter
R
$1
loaded by a ac/ac
PDM converter.
the
is transient the
can become
VC
Vo_
From
During
for the thyristor
L
Vo is In the
re-triggered.
+
the
current.
Cr = 31_F
Fig. A3.7
a non-
of the PDM converter
each time the Vo switches
so small and cause the thyristor
fairly
like an ac/ac
PDM converter
voltage
the load current
t) A, then
and capacitor
load,
level.
L and R are chosen to be 5mH, and 2.5£2, respectively.
IR is regulated simulation
a linear load with
power output.
as shown in Fig. A3.7.
by the inductor,
simulation,
can deliver
single
can easily drive
However
problem
the maximum a the
above
distortion.
is a latching
the Mapham inverter
Consider
discused
123 Moreover,
the output
A3.8(b)).
voltage
Therefore,
this
of the inverter
"2kW"
inverter
is not well regulated cannot
deliver
during that
320W
to
time(Fig.
a non-linear
load
like the PDM converter. To avoid resonant
tank
impedance current
decreases
A simulation
latching
by decreasing
and power
voltage
this
one can increase
L r and increasing
and the output
rating
result
problem,
voltage
of the thyristors
the
Cr. By doing
of the inverter
and diodes
energy
that
the
size
characteristic
will be more stiff.
in the inverter
It can be seen in Fig. A3.9(a),
Fig. A3.9(b),
the turn-off
is better
regulated
time is more consistent
However,
need to be higher.
with Lr and Cr equal to 6BH, 61_Fis shown in Fig. A3.9.
of the Mapham inverter,
of the
The output
than in Fig. A3.8(b). and longer compared
to that in Fig. A3.8(a). For the circuit twice
with Lr and Cr equal to 6pH and 61_F, the inductor
as much as the one with Lr and Cr equal to 1 2BH, 31_F, the increased
also cause
high thermal
dissipation
thyristors
in parallel
dissipation,
but the size and cost effectiveness Another
does
not
lower
can spread
in the thyristors the
kind the non-linear the
power
rating
inductor
and latch
current
of the inverter
of the
Mapham
inverter.
sees a square wave load current with the magnitude
resistor
and the filter
are shown
resonant mentioned
in Figs. A3.1 1 and A3.12.
frequency above.
of the inverter The inductor
IR (see Fig. A3.1 1).
Since this
is not affected
current
Putting
the
thermal
This non-linear steady
of average/R.
to the Mapham inverter
can
questionable.
In the
equal to 10,Q and 2mH respectively.
the same as if a 10_Q load connected results
becomes
is
current
devices.
therefore,
load is shown in Fig. A3.10.
inverter
inductor
and,
the
current
The power
directly.
load
state,
the
The load output
is
The simulation
load is high impedance,
the
by the load as in the linear load case
is equal to the no-load
current
plus the dc offset
124 lo0
50
I
j
"
o.o'o;
o.oo2
0.003
Time(see)
(a)
3OO
!, 30
0 001
03 Tlme(sec)
(b) _°°1
!:t,
I Ii!II Time(sac)
(c) Fig. A3.8
Simulation of the Mapham inverter
loaded by a ac/ac
PDM converter.
125 200
100
'-"
0
-100
0.003
Ca) 3OO
200
100 >
b" 0 > -lOO
-200
rlllllllIIIllllllllllIIIIlllllIIII
-3oo
i
!
0.001
0.002
|
0.003
Tlme(sec)
(b) 300
200
100
E 0
0
-100
-200.
0.(;01
0._03
0.002 Time(see)
(c) Fig. A3.9
A simulation
result with Lr and Cr equal to 61_H, 611F.
126
Mapham Inverter L r = 12 I_H Cr = 3 I_F
Fig. A3.10
A Mapham Inverter
loaded by a full-wave
rectifier
1oo]
_
20
__ o
_
-2o
__)
\
-4o -60
200
-100 -200
I J
Fig. A3.11
0.000700
0.000750
0.000800 Time(s)
The current of the resonant inductor, Lr, and output voltage of the Mapham inverter shown in Fig. A3.10
127 ZO
!
o.oo'o7so
0.000700
Fig. A3.12
Although delivering
2kW,
able to provide 40%.
The output
0.000800
current, Io, of the Mapham inverter
the Mapham inverter used in this research
because full power
With a resistive
the PDM converter
was a non-linear
to the PDM converter.
load of 10 D, the efficiency
in Fig. A3.10.
was supposed
capable of
load, the inverter
The efficiency
was estimated
had been measured
to _, 90%.
was not to only
