Transcript dc drives - elfizon24
ELECTRICAL DRIVES:
An Application of Power Electronics
Power Electronic Converters in ED Systems DC DRIVES
AC-DC-DC DC-DC: Two-quadrant Converter
V a
+ V dc T1 D1 T2 D2 +
V a
i a Q2 T1 conducts
v a = V dc
Jika vdc=110 Volt dan duti cycle=0.75.
Tentukan: (a). Va (avg, dan V(rms) (b). Cara Kerja rangkaian untuk operasi 2 kuadran Q1
I a
Power Electronic Converters in ED Systems DC DRIVES
AC-DC-DC DC-DC: Four-quadrant Converter leg A leg B + V dc Q1 D1 + V a D3 Q3 Q4 D4 D2 Q2 Jika vdc=110 Volt dan duti cycle=0.75.
Tentukan: (a). Va (avg, dan V(rms) (b). Cara Kerja rangkaian untuk operasi 4 kuadran
v a = V dc when Q1 and Q2 are ON Positive current
Power Electronic Converters in ED Systems DC DRIVES
AC-DC-DC DC-DC: Two-quadrant Converter
V a
+ V dc T1 D1 T2 D2 +
V a
i a Q2 T1 conducts
v a = V dc
Jika vdc=110 Volt dan duti cycle=0.75.
Tentukan: (a). Va (avg, dan V(rms) (b). Cara Kerja rangkaian untuk operasi 2 kuadran Q1
I a
Power Electronic Converters in ED Systems DC DRIVES
AC-DC-DC DC-DC: Two-quadrant Converter
V a
T1 D1 + V dc T2 D2 + V a i a Q2 Q1
I a
D2 conducts
v a = 0
T1 conducts
v a = V dc V a E b Quadrant 1
The average voltage is made larger than the back emf
Power Electronic Converters in ED Systems DC DRIVES
AC-DC-DC DC-DC: Two-quadrant Converter
V a
T1 D1 + V dc T2 D2 + V a i a Q2 Q1
I a
D1 conducts
v a = V dc
Power Electronic Converters in ED Systems DC DRIVES
AC-DC-DC DC-DC: Two-quadrant Converter
V a
T1 D1 + V dc T2 D2 + V a i a Q2 Q1
I a
T2 conducts
v a = 0
D1 conducts
v a = V dc V a E b Quadrant 2
The average voltage is made smallerr than the back emf, thus forcing the current to flow in the reverse direction
Power Electronic Converters in ED Systems DC DRIVES
AC-DC-DC DC-DC: Two-quadrant Converter 2v tri + v A v c + v c V dc 0
Power Electronic Converters in ED Systems DC DRIVES
AC-DC-DC DC-DC: Four-quadrant Converter leg A leg B + V dc Q1 D1 + V a D3 Q3 Q4 D4 D2 Q2
Positive current v a = V dc when Q1 and Q2 are ON
Power Electronic Converters in ED Systems DC DRIVES
AC-DC-DC DC-DC: Four-quadrant Converter leg A leg B + V dc Q1 D1 + V a D3 Q3 Q4 D4 D2 Q2
Positive current v a v a v a = V dc when Q1 and Q2 are ON = -V dc when D3 and D4 are ON = 0 when current freewheels through Q and D
Power Electronic Converters in ED Systems DC DRIVES
AC-DC-DC DC-DC: Four-quadrant Converter leg A leg B + V dc Q1 D1 + V a D3 Q3 Q4 D4 D2 Q2
Positive current v a v a v a = V dc when Q1 and Q2 are ON = -V dc when D3 and D4 are ON = 0 when current freewheels through Q and D Negative current v a = V dc when D1 and D2 are ON
Power Electronic Converters in ED Systems DC DRIVES
AC-DC-DC DC-DC: Four-quadrant Converter leg A leg B + V dc Q1 D1 + V a D3 Q3 Q4 D4 D2 Q2
Positive current v a v a v a = V dc when Q1 and Q2 are ON = -V dc when D3 and D4 are ON = 0 when current freewheels through Q and D Negative current v a v a v a = V dc when D1 and D2 are ON = -V dc when Q3 and Q4 are ON = 0 when current freewheels through Q and D
v c + _
Power Electronic Converters in ED Systems DC DRIVES
AC-DC-DC Bipolar switching scheme – output swings between V DC and -V DC 2v tri V dc + v A + v B v A v B v AB v c V dc 0 V dc 0 V dc -V dc
v c + _
Power Electronic Converters in ED Systems DC DRIVES
AC-DC-DC Unipolar switching scheme – output swings between V dc and -V dc
V tri
V dc + v A + v B v A v B v AB -v c
v c -v c
0 V dc 0 V dc 0 V dc
Power Electronic Converters in ED Systems DC DRIVES
AC-DC-DC DC-DC: Four-quadrant Converter V dc V dc 200 150 100 50 0 -50 -100 -150 -200 0.04
0.0405
0.041
0.0415
0.042
0.0425 0.043
0.0435
0.044
0.0445
0.045
Armature current V dc 200 150 100 50 0 -50 -100 -150 -200 0.04
0.0405
0.041
0.0415
0.042
0.0425 0.043
0.0435
0.044
0.0445
0.045
Armature current Bipolar switching scheme Unipolar switching scheme • • Current ripple in unipolar is smaller Output frequency in unipolar is effectively doubled
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters Switching signals obtained by comparing control signal with triangular wave
v c
v tri q We want to establish a relation between
v c
and
V a
+ V a − V dc AVERAGE voltage v c (s)
?
V a (s) DC motor
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters T tri v c q 1 0 V c > V tri V c < V tri t on 1 0 d 1 T tri t t T tri q dt t on T tri
0 V dc
V a 1 T tri 0 dT tri V dc dt dV dc
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters d 0.5
v c V tri -V tri -V tri v c For v c = -V tri d = 0
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters d 0.5
V tri -V tri -V tri v c v c V tri For v c = -V tri For v c = 0 d = 0 d = 0.5
For v c = V tri d = 1
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters d V tri 0.5
-V tri d 0 .
5 1 2 V tri v c -V tri v c v c V tri For v c = -V tri For v c = 0 d = 0 d = 0.5
For v c = V tri d = 1
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters Thus relation between v c and V a is obtained as: V a 0 .
5 V dc V dc 2 V tri v c Introducing perturbation in v c and V a and separating DC and AC components:
DC: AC:
V a 0 .
5 V dc V dc 2 V tri v c v~ a V dc 2 V tri v~ c
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters Taking Laplace Transform on the AC, the transfer function is obtained as: v a v c ( s ) ( s ) V dc 2 V tri v c (s) V dc 2 V tri v a (s) DC motor
v c
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Bipolar switching scheme
V dc -V dc 2v tri v tri q + V dc −
+ V AB
v A v B q v AB d A 0 .
5 v c 2 V tri V A 0 .
5 V dc V dc 2 V tri v c d B 1 d A 0 .
5 v c 2 V tri V B 0 .
5 V dc V dc 2 V tri v c V A V B V AB V dc V tri v c v c V dc 0 V dc 0 V dc -V dc
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Bipolar switching scheme
v a v c ( s ( s ) ) V dc V tri v c (s) V dc V tri v a (s) DC motor
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters V dc
Unipolar switching scheme
Leg b
V tri
+ v tri V dc q a v c − v A Leg a v tri -v c q b v B d A 0 .
5 v c 2 V tri d B 0 .
5 v c 2 V tri v AB V A 0 .
5 V dc V dc 2 V tri v c V B 0 .
5 V dc V dc 2 V tri v c V A V B V AB
The same average value we’ve seen for bipolar !
V dc V tri v c
v c -v c
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Unipolar switching scheme
v a v c ( s ( s ) ) V dc V tri v c (s) V dc V tri v a (s) DC motor
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters DC motor – separately excited or permanent magnet v t i a R a L a di dt a e a T e T l J d m dt T e = k t i a e e = k t Extract the dc and ac components by introducing small perturbations in V t , i a , e a, T e , T L and m e v~ t ac components T ~ a R a e L a k E ( ~ a d i a dt ) e~ a ~ e k E ( ~ ) T L B J d ( ) dt dc components V t I a R a E a T e k E I a E e k E T e T L B ( )
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters DC motor – separately excited or permanent magnet Perform Laplace Transformation on ac components v~ t ~ a R a L a d i a dt e~ a V t (s) = I a (s)R a + L a sIa + E a (s) T e k E ( ~ a ) T e (s) = k E I a (s) ~ e k E ( ~ ) E a (s) = k E (s) e T L B J d ( ) dt T e (s) = T L (s) + B (s) + sJ (s)
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters DC motor – separately excited or permanent magnet V a ( s ) + R a 1 sL a I a ( s ) k T T e ( s ) + T l ( s ) B 1 sJ ( s ) k E
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters q v tri Torque controller + T c
+ –
V dc − T e ( s ) + Torque controller Converter V dc V tri , peak V a ( s ) + q k t
DC motor
R a 1 sL a I a ( s ) k T T e ( s ) + T l ( s ) B 1 sJ ( s ) k E
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters Closed-loop speed control – an example Design procedure in cascade control structure • Inner loop (current or torque loop) the fastest – largest bandwidth • The outer most loop (position loop) the slowest – smallest bandwidth • Design starts from torque loop proceed towards outer loops
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters Closed-loop speed control – an example OBJECTIVES: • Fast response – large bandwidth • Minimum overshoot good phase margin (>65 o ) • Zero steady state error – very large DC gain BODE PLOTS METHOD • Obtain linear small signal model • Design controllers based on linear small signal model • Perform large signal simulation for controllers verification
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters Closed-loop speed control – an example Ra = 2 B = 1 x10 –4 kg.m
2 /sec k e = 0.1 V/(rad/s) La = 5.2 mH J = 152 x 10 –6 kg.m
2 k t = 0.1 Nm/A V tri = 5 V V d = 60 V f s = 33 kHz • PI controllers • Switching signals from comparison of v c and triangular waveform
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters Torque controller design
Open-loop gain
Bode Diagram From: Input Point To: Output Point 150 100 50 0 -50 90 45 0 -45 -90 10 -2 10 -1 10 0 10 1 10 2 Frequency (rad/sec) 10 3 compensated compensated 10 4 10 5 k pT = 90 k iT = 18000
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters Speed controller design * + – Speed controller T* 1 T B 1 sJ Torque loop
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters Speed controller design
Open-loop gain
Bode Diagram From: Input Point To: Output Point 150 100 50 0 compensated k ps = 0.2
k is = 0.14
-50 0 -45 -90 -135 -180 compensated 10 -2 10 -1 10 0 10 1 Frequency (Hz) 10 2 10 3 10 4
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters Large Signal Simulation results Speed 40 20 0 -20 -40 0 Torque 2 1 0 -1 -2 0 0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
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