ELECTRIC DRIVES
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Transcript ELECTRIC DRIVES
ELECTRIC DRIVES
CONVERTERS IN ELECTRIC DRIVE SYSTEMS
MODULE 2
Dr. Nik Rumzi Nik Idris
Dept. of Energy Conversion, UTM
2013
CONVERTERS - Module 2
AC-DC controlled rectifier
approximate model
SIMULINK examples
open-loop
closed-loop
Switch Mode DC-DC
converter
2-Q and 4-Q converters
Small signal modeling
unipolar
bipolar
SIMULINK example
Current-controlled for SM
converters
Bridge converter
hysteresis
fixed frequency
3-phase VSI
hysteresis
fixed frequency
SVM-based
Switch mode DC-DC converter
Two-quadrant converter
Va
+
T1
D1
ia
Vdc
Q2
Ia
+
T2
Q1
D2
Va
-
T1 conducts va = Vdc
Switch mode DC-DC converter
Two-quadrant converter
Va
+
T1
D1
ia
Vdc
Q2
Q1
Ia
+
T2
D2
Va
-
D2 conducts va = 0
Va
T1 conducts va = Vdc
Eb
Quadrant 1 The average voltage is made larger than the back emf
Switch mode DC-DC converter
Two-quadrant converter
Va
+
T1
D1
ia
Vdc
Q2
Ia
+
T2
Q1
D2
Va
-
D1 conducts va = Vdc
Switch mode DC-DC converter
Two-quadrant converter
Va
+
T1
D1
ia
Vdc
Q2
Q1
Ia
+
T2
D2
Va
-
T2 conducts va = 0
Va
D1 conducts va = Vdc
Eb
Quadrant 2 The average voltage is made smallerr than the back emf, thus
forcing the current to flow in the reverse direction
Switch mode DC-DC converter
Two-quadrant converter
Vdc
Switching signals obtained by comparing
control signal with triangular wave
+
Va
−
vtri
q
vc
We want to establish a relation between vc and Va
AVERAGE voltage
vc(s)
?
Va(s)
DC motor
Ttri
Switch mode DC-DC converter
Two-quadrant converter
1
q
0
vc
1
1
d
Ttri
0
Vc > Vtri
Vc < Vtri
t
t Ttri
q dt
t on
Ttri
ton
Vdc
1 dTtri
Va Vdc dt dVdc
Ttri 0
0
Switch mode DC-DC converter
Two-quadrant converter
d
0.5
vc
-Vtri
Vtri
vc
-Vtri
For vc = -Vtri d = 0
Switch mode DC-DC converter
Two-quadrant converter
d
0.5
vc
Vtri
-Vtri
Vtri
vc
Vtri
For vc = -Vtri d = 0
For vc = 0
d = 0.5
For vc = Vtri
d=1
Switch mode DC-DC converter
Two-quadrant converter
d
0.5
Vtri
-Vtri
vc
Vtri
Vtri
vc
1
d 0.5
vc
2Vtri
For vc = -Vtri d = 0
For vc = 0
d = 0.5
For vc = Vtri
d=1
Switch mode DC-DC converter
Two-quadrant converter
Thus relation between vc and Va is obtained as:
Va 0.5Vdc
Vdc
vc
2Vtri
Introducing perturbation in vc and Va and separating DC and AC components:
DC:
Vdc
Va 0.5Vdc
vc
2Vtri
AC:
Vdc ~
~
va
vc
2Vtri
Switch mode DC-DC converter
Two-quadrant converter
Taking Laplace Transform on the AC, the transfer function is obtained as:
v a ( s)
Vdc
v c ( s) 2Vtri
vc(s)
Vdc
2Vtri
va(s)
DC motor
Switch mode DC-DC converter
Four-quadrant converter
leg A
+
Q1
leg B
D3
D1
+
Va
Q3
Vdc
Positive current
va = Vdc
when Q1 and Q2 are ON
Q4
D4
D2
Q2
Switch mode DC-DC converter
Four-quadrant converter
leg A
+
Q1
leg B
D3
D1
+
Va
Q3
Vdc
Q4
D4
Positive current
va = Vdc
when Q1 and Q2 are ON
va = -Vdc
when D3 and D4 are ON
va = 0
when current freewheels through Q and D
D2
Q2
Switch mode DC-DC converter
Four-quadrant converter
leg A
+
Q1
leg B
D3
D1
+
Va
Q3
Vdc
Q4
D4
Positive current
va = Vdc
when Q1 and Q2 are ON
va = -Vdc
when D3 and D4 are ON
va = 0
when current freewheels through Q and D
D2
Q2
Negative current
va = Vdc
when D1 and D2 are ON
Switch mode DC-DC converter
Four-quadrant converter
leg A
+
Q1
leg B
D3
D1
+
Va
Q3
Vdc
Q4
D4
Positive current
D2
Q2
Negative current
va = Vdc
when Q1 and Q2 are ON
va = Vdc
when D1 and D2 are ON
va = -Vdc
when D3 and D4 are ON
va = -Vdc
when Q3 and Q4 are ON
va = 0
when current freewheels through Q and D
va = 0
when current freewheels through Q and D
Switch mode DC-DC converter
Four-quadrant converter
Bipolar switching scheme
Vdc
-Vdc
q
vtri
vc
2vtri
+
Vdc
vA
Vdc
+ VAB
0
−
vc
Vdc
vB
0
q
Vdc
v
d A 0.5 c
2Vtri
VA 0.5Vdc
Vdc
vc
2Vtri
v
dB 1 d A 0.5 c
2Vtri
VB 0.5Vdc
Vdc
vc
2Vtri
vAB
-Vdc
VA VB VAB
Vdc
vc
Vtri
Switch mode DC-DC converter
Four-quadrant converter
Bipolar switching scheme
v a ( s) Vdc
v c ( s) Vtri
vc(s)
Vdc
Vtri
va(s)
DC motor
Switch mode DC-DC converter
Four-quadrant converter
Unipolar switching scheme
Vdc
vc
Leg b
Vtri
-vc
+
vtri
Vdc
qa
vc
−
vA
Leg a
vtri
d A 0.5
vB
qb
-vc
vc
2Vtri
VA 0.5Vdc
Vdc
vc
2Vtri
dB 0.5
VB 0.5Vdc
vc
2Vtri
Vdc
vc
2Vtri
vAB
VA VB VAB
The same average value we’ve seen for bipolar !
Vdc
vc
Vtri
Switch mode DC-DC converter
Four-quadrant converter
Unipolar switching scheme
v a ( s) Vdc
v c ( s) Vtri
vc(s)
Vdc
Vtri
va(s)
DC motor
Switch mode DC-DC converter
MATLAB v6.5, SIMULINK v5
2-quadrant converter
SIMULINK EXAMPLES
Open-loop control
Closed-loop control (current control)
Switch mode DC-DC converter
SIMULATION EXAMPLES
Id
2-quadrant converter
+
vtri
Vdc
q
vc
vc
To Workspace2
Sine Wave
qA
-K Relay
vau
Gain 1
To Workspace 3
Out 1
1
iau
0.01 s+10
Subsystem
Transfer Fcn
vave
To Workspace 1
1
-K-
iave
0.01 s+10
Gain 3
To Workspace5
Transfer Fcn 1
100
Constant
iD
rl_2q_average.mdl
Dot Product
To Workspace8
To Workspace4
Switch mode DC-DC converter
SIMULATION EXAMPLES
2-quadrant converter
vc
To Workspace2
Sine Wave
qA
-K Relay
vau
Gain 1
To Workspace 3
Out 1
1
iau
0.01 s+10
Subsystem
Transfer Fcn
vave
To Workspace 1
1
-K-
iave
0.01 s+10
Gain 3
To Workspace5
Transfer Fcn 1
100
Constant
iD
Dot Product
Average model
To Workspace8
To Workspace4
Switch mode DC-DC converter
SIMULATION EXAMPLES
4-quadrant converter
Vdc
Leg b
+
vtri
Vdc
qa
vc
−
Leg a
vtri
-vc
qb
Switch mode DC-DC converter
SIMULATION EXAMPLES
4-quadrant converter
Sine Wave
Relay
iau
Continuous
To Workspace1
powergui
Out1
Subsystem
Relay 1
+
-1
Sine Wave 1
DC Voltage Source
Relay 2
Gain 1
Relay 3
Scope 1
g
+ -i
A
Current Measurement
Series RLC Branch
B
Universal Bridge
-K-
1
iave
0.01 s+10
Gain 3
Average model
unipolar_4q_with_id.mdl
Transfer Fcn 1
To Workspace5
Switch mode DC-DC converter
SIMULATION EXAMPLES
Closed-loop current control
iref
+
PI
+
H-bridge
converter
Small signal model
Iref(s)
s
v (s)
c
1
ki k
p
ki
s
Vdc
Vtri
Va(s)
1
sL R
Ia(s)
Switch mode DC-DC converter
SIMULATION EXAMPLES
Closed-loop current control
Continuous
powergui
PID
Signal
Generator 1
PID Controller 1
8
Gain 3
-1
+v
-
Relay
Voltage Measurement
Constant
ia
Scope 1
To Workspace1
Out1
Subsystem
Relay 1
+
DC Voltage Source
Relay 2
-
Relay 3
closed_loop_unipolar_4q_with_id.mdl
Scope 2
g
A
+ -i
Current Measurement
Series RLC Branch
B
Universal Bridge
iref
To Workspace2
Switch mode DC-DC converter
SIMULATION EXAMPLES
Closed-loop current control
7
Controlled rectifier
DC-DC Switch mode
For both DC-DC and Contr.
Rectifier:
7
6.5
6.5
Current controlled, Iref = 5 A
6
6
Load: 250m , 20
5.5
5
5.5
5
Disturbance in DC source:
±70V, at 5Hz
4.5
4.5
4
4
3.5
3.5
3
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
ftri = 10 000 Hz
4-quadrant
Unipolar
0.9
0.95
1
3
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
3-phase, 50Hz
2-quadrant
0.9
0.95
1
Switch mode DC-DC converter
SIMULATION EXAMPLES
Closed-loop current control
Controlled rectifier
DC-DC Switch mode
For both DC-DC and Contr. Rectifier:
8
8
Current controlled,6Iref = 5 ± 3 A, freq 5Hz
6
4
4
2
Load: 250m , 202
0
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0
0.3
600
600
400
400
200
200
0
0
-200
-200
-400
-400
-600
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
ftri = 10 000 Hz
4-quadrant
Unipolar
0.7
0.75
0.8
-600
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
3-phase, 50Hz
2-quadrant