svpwm
TRANSCRIPT
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Space Vector Modulation (SVM) Space Vector Modulation (SVM)
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Open loop voltage control
VSI ACmotor
PWMvref
Closed loop current-control
VSIAC
motorPWMiref
if/back
PWM – Voltage Source InverterPWM – Voltage Source Inverter
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+ vc -
+ vb -
+ va -
n
N
Vdc a
b
c
S1
S2
S3
S4
S5
S6
S1, S2, ….S6
va*
vb*
vc*
Pulse Width Modulation
PWM – Voltage Source InverterPWM – Voltage Source Inverter
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vtri
Vdc
qvc
q
Vdc
Pulse widthmodulator
vc
PWM – single phase
PWM – Voltage Source InverterPWM – Voltage Source Inverter
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PWM – extended to 3-phase Sinusoidal PWM
Pulse widthmodulator
Va*
Pulse widthmodulator
Vb*
Pulse widthmodulator
Vc*
PWM – Voltage Source InverterPWM – Voltage Source Inverter
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SPWM – covered in undergraduate course or PE system (MEP 1532)
In MEP 1422 we’ll look at Space Vector Modulation (SVM) – mostly applied in AC drives
PWM – Voltage Source InverterPWM – Voltage Source Inverter
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Definition:
Space vector representation of a three-phase quantities xa(t), xb(t) and xc(t) with space distribution of 120o apart is given by:
x – can be a voltage, current or flux and does not necessarily has to be sinusoidal
a = ej2/3 = cos(2/3) + jsin(2/3) a2 = ej4/3 = cos(4/3) + jsin(4/3)
)t(xa)t(ax)t(x32
x c2
ba
Space Vector Modulation Space Vector Modulation
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Space Vector Modulation Space Vector Modulation
)t(xa)t(ax)t(x32
x c2
ba
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)t(xa)t(ax)t(x32
x c2
ba
Let’s consider 3-phase sinusoidal voltage:
va(t) = Vmsin(t)
vb(t) = Vmsin(t - 120o)
vc(t) = Vmsin(t + 120o)
Space Vector Modulation Space Vector Modulation
)t(va)t(av)t(v32
v c2
ba
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)t(va)t(av)t(v32
v c2
ba
Let’s consider 3-phase sinusoidal voltage:
t=t1
At t=t1, t = (3/5) (= 108o)
va = 0.9511(Vm)
vb = -0.208(Vm)
vc = -0.743(Vm)
Space Vector Modulation Space Vector Modulation
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Let’s consider 3-phase sinusoidal voltage:
At t=t1, t = (3/5) (= 108o)
va = 0.9511(Vm)
vb = -0.208(Vm)
vc = -0.743(Vm)
b
c
a
Space Vector Modulation Space Vector Modulation
)t(va)t(av)t(v32
v c2
ba
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Three phase quantities vary sinusoidally with time (frequency f)
space vector rotates at 2f, magnitude Vm
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How could we synthesize sinusoidal voltage using VSI ?
Space Vector Modulation Space Vector Modulation
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+ vc -
+ vb -
+ va -
n
N
Vdc a
b
c
S1
S2
S3
S4
S5
S6
S1, S2, ….S6
va*
vb*
vc*
We want va, vb and vc to follow v*a, v*b and v*c
Space Vector Modulation Space Vector Modulation
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+ vc -
+ vb -
+ va -
n
N
Vdc a
b
c
From the definition of space vector:
)t(va)t(av)t(v32
v c2
ba
S1
S2
S3
S4
S5
S6
Space Vector Modulation Space Vector Modulation
van = vaN + vNn
vbn = vbN + vNn
vcn = vcN + vNn
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)t(va)t(av)t(v32
v c2
ba
)aa1(vvaavv32
v 2NncN
2bNaN
Space Vector Modulation Space Vector Modulation
= 0
Sa, Sb, Sc = 1 or 0vaN = VdcSa, vaN = VdcSb, vaN = VdcSa,
c2
badc SaaSSV32
v
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Sector 1Sector 3
Sector 4
Sector 5
Sector 2
Sector 6
[100] V1
[110] V2[010] V3
[011] V4
[001] V5 [101] V6
(2/3)Vdc
(1/3)Vdc
Space Vector Modulation Space Vector Modulation
c2
badc SaaSSV32
v
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Space Vector Modulation Space Vector Modulation
Reference voltage is sampled at regular interval, T
Within sampling period, vref is synthesized using adjacent vectors and zero vectors
100V1
110V2If T is sampling period,
V1 is applied for T1,
TT
1V 1
V2 is applied for T2
TT
2V 2Zero voltage is applied for the rest of the sampling period,
T0 = T T1 T2
Sector 1
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Space Vector Modulation Space Vector Modulation
Reference voltage is sampled at regular interval, T
If T is sampling period,
V1 is applied for T1,
V2 is applied for T2
Zero voltage is applied for the rest of the sampling period,
T0 = T T1 T2
T T
Vref is sampled Vref is sampled
V1
T1
V2
T2T0/2
V0
T0/2
V7
va
vb
vc
Within sampling period, vref is synthesized using adjacent vectors and zero vectors
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Space Vector Modulation Space Vector Modulation
They are calculated based on volt-second integral of vref
dtvdtvdtvdtvT1
dtvT1 721o T
07
T
02
T
01
T
00
T
0ref
772211ooref TvTvTvTvTv
0TT)60sinj60(cosV32
TV32
0TTv 72oo
d1doref
2oo
d1dref T)60sinj60(cosV32
TV32
Tv
How do we calculate T1, T2, T0 and T7?
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Space Vector Modulation Space Vector Modulation
2oo
d1dref T)60sinj60(cosV32
TV32
Tv
7,021 TTTT
100V1
110V2
Sector 1
sinjcosvv refref
q
d
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Space Vector Modulation Space Vector Modulation
Solving for T1, T2 and T0,7 gives:
sinT31
cos3
Tm
23
T1 sinmTT2
2oo
d1dref T)60sinj60(cosV32
TV32
Tv
2d1dref TV31
TV32
cosvT 2dref TV3
1sinvT
where3
Vv
md
ref
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Space Vector Modulation Space Vector Modulation
Comparison between SVM and SPWM
SPWM
oa
b
c
Vdc/2
-Vdc/2
vao
For m = 1, amplitude of fundamental for vao is Vdc/2
amplitude of line-line = dcV
23
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Space Vector Modulation Space Vector Modulation
Comparison between SVM and SPWM
SVM
We know max possible phase voltage without overmodulation is
amplitude of line-line = Vdc
dcV3
1
Line-line voltage increased by: 100xV
23
V23
V
dc
dcdc 15%