svpwm
DESCRIPTION
TRANSCRIPT
Submitted by,Soumya Ranjan Pradhan
Introduction:Introduction:
Principle of Space Vector PWM
This PWM technique approximates the reference voltage Vref by a combination
of the eight switching patterns (V0 to V7).
The vectors (V1 to V6) divide the plane into six sectors (each sector: 60 degrees).
Vref is generated by two adjacent non-zero vectors and two zero vectors.
Coordinate Transformation ( abc reference frame to the stationary d-q frame)
: A three-phase voltage vector is transformed into a vector in the stationary d-q coordinate
frame which represents the spatial vector sum of the three-phase voltage.
Treats the sinusoidal voltage as a constant amplitude vector rotating
at constant frequency.
Open loop voltage control
VSI ACmotor
PWMvref
Closed loop current-control
VSIAC
motorPWMiref
if/back
PWM – Voltage Source InverterPWM – Voltage Source Inverter
vtri
Vdc
qvc
q
Vdc
Pulse widthmodulator
vc
PWM – single phase
PWM – Voltage Source InverterPWM – Voltage Source Inverter
PWM – extended to 3-phase Sinusoidal PWM
Pulse widthmodulator
Va*
Pulse widthmodulator
Vb*
Pulse widthmodulator
Vc*
PWM – Voltage Source InverterPWM – Voltage Source Inverter
Output voltages of three-phase inverter
PWM METHODS
where, upper transistors: S1, S3, S5
lower transistors: S4, S6, S2
switching variable vector: a, b, c
The eight inverter voltage vectors (V0 to V7)
The eight combinations, phase voltages and output line to line voltages
Basic switching vectors and Sectors
Fig. Basic switching vectors and sectors.
6 active vectors (V1,V2, V3, V4, V5, V6)
Axes of a hexagonal
DC link voltage is supplied to the load
Each sector (1 to 6): 60 degrees
2 zero vectors (V0, V7)
At origin
No voltage is supplied to the load
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
)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
)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
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
Three phase quantities vary sinusoidally with time (frequency f)
space vector rotates at 2f, magnitude Vm
+ 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
+ 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
)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
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
Conversion from 3 phases to 2 phases :
For Sector 1,
Three-phase line modulating signals (VC)abc = [VCaVCbVCc]T
can be represented by the represented by the complex vector VC = [VC]αβ = [VCaVCb]T
by means of the following transformation:VC α = 2/3 . [vCa - 0.5(vCb + vCc )] VC β = √3/3 . (vCb - vCc)
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
110V2
If T is sampling period,
V1 is applied for T1,
TT
1V 1
V2 is applied for T2
TT
2V 2
Zero voltage is applied for the rest of the sampling period,
T0 = T T1 T2
Where,T1 = Ts.|Vc|. Sin (π/3 - θ)T2 = Ts.|Vc|. Sin (θ)
Sector 1
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
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?
Space Vector Modulation Space Vector Modulation
2oo
d1dref T)60sinj60(cosV32
TV32
Tv
7,021 TTTT
100V1
110V2
Sector 1
sinjcosvv refref
q
d
Space Vector Modulation Space Vector Modulation
Solving for T1, T2 and T0,7 gives:
2oo
d1dref T)60sinj60(cosV32
TV32
Tv
2d1dref TV31
TV32
cosvT 2dref TV3
1sinvT
T1= 3/2 m[ (T/√3) cos α - (1/3)T sin α ]
T2= mT sin α where,M= Vref/ (Vd/ √3)
Comparison of Sine PWM and Space Vector PWM
Fig. Locus comparison of maximum linear control voltagein Sine PWM and SV PWM.
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
Comparison of Sine PWM and Space Vector PWM
Comparison of Sine PWM and Space Vector PWM
Space Vector PWM generates less harmonic distortion
in the output voltage or currents in comparison with sine PWM
Space Vector PWM provides more efficient use of supply voltage
in comparison with sine PWM
Sine PWM
: Locus of the reference vector is the inside of a circle with radius of 1/2 Vdc
Space Vector PWM
: Locus of the reference vector is the inside of a circle with radius of 1/3 Vdc
Voltage Utilization: Space Vector PWM = 2/3 or (1.1547) times of Sine PWM, i.e. 15.47% more utilization of voltage.
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 15.47%
1. Power Electronics: Circuits, Devices and Applications by M. H. Rashid, 3rd edition, Pearson2. Power Electronics: Converters, Applications and Devices by Mohan, Undeland and Robbins, Wiley student edition 3. Power Electronics Handbook: M.H. Rashid, Web edition4. Modern Power Electronics And Ac Drives: B.K. Bose5. Extended Report on AC drive control, IEEE : Issa Batarseh6. Space vector modulation: Google, Wikipedia ; for figures.