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Unformatted text preview: 41 Chapter 4
Basic Understanding of Power
Processing in Electric Drives Exit 2001 by N. Mohan Print TOC " ! 42 Power Processing Unit (PPU)
❏ Efficient conversion of power from line frequency AC to
appropriate form required by the motor Subblocks of PPUs
utility +
Vd
− M switch  mode
converter Rectifier
controller ❏ Rectifier: Line frequency AC to DC
❏ SwitchMode Converter: DC to form required by motor
Exit 2001 by N. Mohan TOC " ! 43 SwitchMode Converters for
dc and acmotor drives + A ia
M For DC Drives Exit 2001 by N. Mohan A + Vd
− ia B B Vd
− M
C For AC Drives TOC " ! 44 Analysis of SwitchMode Converters
❏ Pole as a Building Block
poleA + Vd
− voltage port i A (t )
A
+ current
v AN (t ) port −
q A (t ) N vc, A (t )
vtri (t )
PWMIC ❏ Vd uncontrolled
❏ vc, A : control voltage depicting desired output voltage
❏ Switch modulated to produce desired average voltage v AN
Exit 2001 by N. Mohan TOC " ! 45 Pulse Width Modulation ( PWM )
if vc, A (t ) > vtri( t) ⇒ q A ) = 1 ⇒ switch "up" ⇒ v AN t = Vd
( t
()
if vc, A (t ) < vtri( t) ⇒ q A ) = 0 ⇒ switch "down" ⇒ ( AN t = 0
v)
( t
!
Vtri vtri (t ) vc, A (t ) t 0 v AN (t ) = q A (t )Vd
1
q A (t )
0 Vd t d ATs v AN (t )
0 v AN t Ts = 1 / f s Exit 2001 by N. Mohan TOC " ! 46 Average Representation of a Pole
Output Voltage
Average output voltage over one switching cycle
1
v AN =
∫ v AN (t ) dt = d AVd
Ts Ts Duty ratio
⇒ v AN dA = 1 1 vc, A
+
ˆ
2 2 Vtri Vd
Vd / 2
=
+
vc, A
ˆ
2
Vtri
"
"
dc offset k
pole Pole gain V /2
k pole = d
ˆ
Vtri !
Vtri vtri (t ) vc, A (t ) t 0 1
q A (t )
0
Vd t
d ATs v AN (t )
0 v AN t Ts = 1 / f s Pulsating v AN (t ), relatively smooth i A (t )
Exit 2001 by N. Mohan TOC " ! 47 Average Representation of a Pole
Input and Output Currents
❏ Assuming ripple in i A (t ) to be negligible, i.e. i A (t ) = iA (t )
average values of input and currents can be related as,
idA (t ) = d A (t ) iA (t )
idA (t )
+ Vd
− vc, A (t ) Exit 2001 by N. Mohan poleA control function
t 0
i A (t ) voltage port vtri (t )
PWMIC q(t ) q A (t ) i A (t )
ideal output current
iA t
A
0
+ idA (t ) current
idA t
v AN (t ) port
dTs 0
− ideal and average input current
=1 / fs
Ts
N
i A (t )
i
A 0 t
actual output current
(ripple often ignored)
TOC " ! 48 Average Representation of a Pole as An
Ideal Transformer
idA (t ) + v AN (t ) = d A (t )Vd
Vd idA (t ) = d A (t ) iA (t ) iA (t ) +
1 − d A (t )
v AN (t ) − vc, A (t ) 1 +
!
Σ
2Vtri
+ 1/ 2 ❏ Transformer turnsratio is adjustable via Pulse Width Modulation
❏ This Transformer can pass AC and DC currents but only unipolar
voltages
Exit 2001 by N. Mohan TOC " ! 49 Pole as a Two Quadrant Converter
idA (t ) ❏ v AN always positive
❏ iA can reverse
x iA > 0 if v AN > Ea
power Vd → Ea
⇒ + Vd − voltage port i A (t )
+ v AN
− N Buck Mode power Ea → Vd 2001 by N. Mohan current port +
− Ea Ra IA
+ Vd − + 1 dA VAN = d AVd +
Ea
− − Boost Mode
vc, A (t ) Exit Ra q A (t ) x iA < 0 if v AN < Ea
⇒ A La 1 +
Σ
ˆ
2Vtri +
1/ 2
TOC " ! 410 Calculation of Ripple Current
Ra i A (t ) La + v AN (t ) − IA
+ Ea = − +
VAN +
Ea −
vripple (t ) i A (t ) = I A + iripple (t )
v AN (t ) = V AN + vripple (t )
VAN − Ea
Ra
iripple (t ) = sawtooth with zero DC
average
IA = ∆i A =
Exit 2001 by N. Mohan iripple Ra + − La +
vripple (t )
− Vd −V AN 0
dTs t VAN Ts iripple (t )
0
i A (t ) t IA 0 t (V − VAN )dTs
V (1 − d )Ts
volt − seconds
= d
, or AN
La
La
La
TOC " ! 411 Implementation of BiPositional Switches
Buck Boost
iC + iA ON Vd
− q vc, A +
A 0 Von
q−
A approx switching
trajectory OFF
switching power loss
for a very short time VCE q A (t ) vtri ❏ Switching frequency 6kHz to 50kHz
❏ Switching power loss: kept low by fast switching devices
❏ Conduction loss: kept low by having switches fully ON or
fully OFF
Exit 2001 by N. Mohan TOC " ! 412 id SwitchMode Converters for
DCMotor Drives
idA
iA Vd idB
+
vo + − − idA
io
+
iB ea
− + +
d A (t ) 1 Vd v AN (t ) − +
d B (t )
vBN (t ) 1 q A (t )
− vc (t ) qB (t )
vc (t ) vtri (t ) DC motor io
idB +
vo (t )
− − 1
Σ
ˆ
2Vtri + + 1/ 2 −1 1 +
Σ
ˆ
vc, B (t ) 2Vtri + 1/ 2 1 v (t )
d A (t ) = + c
ˆ
2 2Vtri
1 v (t )
d B (t ) = − c
ˆ
2 2Vtri V
V
v AN (t ) = d + d vc (t )
ˆ
2 2Vtri
V
V
vBN (t ) = d − d vc (t )
ˆ
2 2Vtri ❏ Output voltage can be positive or negative
Exit 2001 by N. Mohan TOC " ! 413 Analysis of DCMotor Drives Based on
Average Quantities
v (t )
d (t ) = d A (t ) − d B (t ) = c
ˆ
Vtri
( −1 ≤ d ≤ + 1) vo (t ) = v AN (t ) − vBN (t ) =
( −Vd ≤ vo ≤ + Vd )
V
k PWM = d
ˆ
Vtri Vd
v (t )
ˆtri c
V vo (t ) = k PWM ⋅ vc (t ) id DC motor
io (t )
+ +
1 Vd
− d (t )
vo (t )
− vc (t ) 1
ˆ
V tri ❏ Combined transformer
❏ Four quadrant capability
❏ Transformer can pass AC or DC currents and voltages
Exit 2001 by N. Mohan TOC " ! 414 Three Phase Inverter ACMotor Drives
iA
A
+ Vd iB
B n − iC C q A (t )
vc, A (t )
ˆ
Vc PWM v (t )
c, B
f1 IC qB (t ) vc,C (t )
vtri qC (t ) #
vc, A (t ) = Vc sin(ω 1t )
#
vc,B (t ) = Vc sin(ω 1t − 1200 )
#
vc,C (t ) = Vc sin(ω 1t − 2400 )
Exit 2001 by N. Mohan ˆ
Vc sin(ω t )
d A (t ) = 0.5 +
1
ˆ
2Vtri
ˆ
d B (t ) = 0.5 + Vc sin(ω1t − 1200 )
ˆ
2Vtri
ˆ
dC (t ) = 0.5 + Vc sin(ω1t − 2400 )
ˆ
2Vtri
TOC " ! 415 Transformer Equivalent of a
Three Phase Converter iA (t ) Voltages with respect to
to N
V
V
v AN (t ) = d + d
2
2
$ + Vd ˆ
V sin(ω1t )
ˆtri c
2V
"
k pole ˆ
= k pole Vc sin(ω1t )
$ + ˆ
Vd
Vc
sin(ω1t )
ˆ
Vtri
− +
d B (t ) 1 v A (t ) 1 d A (t ) 1 vB (t )
− − idC (t ) A
B
C iB (t )
iC (t ) +
dC (t ) eB (t ) n eC (t ) vC (t )
− N Voltages with respect to
loadneutral n
v An (t ) = idB (t ) idA (t ) e A (t ) vc, A (t ) 1 +
Σ
ˆ
2Vtri
+ vc, B (t ) 1 +
Σ
ˆ
2Vtri
+ vc,C (t ) 1 +
ˆ
2Vtri + Σ 1/ 2 DC offset voltages disappear when voltages are with respect to load neutral
Exit 2001 by N. Mohan TOC " ! 416 Power Devices
❏ Voltage rating up to 9kV ❏ Current rating ~ kA ❏ Switching items ~ 0.1 µ s ❏ OnState voltage drop 1V to 3V ❏ Cost Exit 2001 by N. Mohan TOC " ! 417 Controlled Switches
❏ MOSFET
+ iD G VDS G x Insulated gate for low
gate requirements D D iD VGS − S S VGS = 7V
6V
on state
5V
4V VDS x Builtin diode
x rds increases exponentially with voltage rating
x Good for low voltage, high frequency
Exit 2001 by N. Mohan TOC " ! 418 ❏ IGBT  Insulated Gate Bipolar Transistor
C iC
+
G VCE VGE +
VGE − − E VCE x Insulated Gate for low drive requirements
x Moderately high switching frequency
x Lower conduction losses than MOSFETs in high voltage
devices
x Higher voltage (up to 3.3 kV) and current rating
(up to 1200A)
Exit 2001 by N. Mohan TOC " ! 419 ❏ Smart Power Modules
• Gate Driver ICs
• Power Modules (some with Gate drivers) Exit 2001 by N. Mohan TOC " ! 420 Summary
❏ What is the function of PPUs?
❏ What are the subblocks of PPUs?
❏ What are the roles of the rectifier and the filtercapacitor
subblocks?
❏ Qualitatively, how does a switchmode amplifier differ
from a linear amplifier?
❏ Why does operating transistors as switches result in much
smaller losses compared to operating them in their linear
region?
❏ How is a bipositional switch realized in a converter pole?
❏ What is the gain of each converter pole?
❏ How does a switchmode converter pole approach the output
of a linear amplifier?
❏ What is the meaning of v AN (t ) ?
Exit 2001 by N. Mohan TOC " ! 421 Summary
❏ How is the pole output voltage made linearly proportional
to the input control signal?
❏ What is the physical significance of the dutyratio, for
example d A (t ) ?
❏ How is pulsewidthmodulation (PWM) achieved and what
is its function?
❏ Instantaneous quantities on the two sides of the converter
pole, for example poleA, are related by the switching signal
q A (t ) . What relates the average quantities on the two sides?
❏ What is the equivalent model of a switchmode pole in
terms of its average quantities?
❏ How is a switchmode dcdc converter which can achieve an
output voltage of either polarity and an output current flowing
in either direction realized?
Exit 2001 by N. Mohan TOC " ! 422 Summary
❏ What is the frequency content of the output voltage
waveform in dcdc converters?
❏ In a dcdrive converter, how is it possible to keep the ripple
in the output current small, despite the output voltage
pulsating between 0 and Vd , or 0 and −Vd , during each
switching cycle?
❏ What is the frequency content of the input dc current?
Where does the pulsating ripple component of the dcside
current flow through?
❏ How is bidirectional power flow achieved through a
converter pole?
❏ What makes the average of the dcside current in a
converter pole related to the average of the output current
by its dutyratio?
Exit 2001 by N. Mohan TOC " ! 423 Summary
❏ How are threephase, sinusoidal ac output voltages
synthesized from a dc voltage input?
❏ What are the voltage and current ratings and the switching
speeds of various power semiconductor devices? Exit 2001 by N. Mohan TOC " ! ...
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 Fall '06
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