SVPWM

Space Vector Modulation (SVM) Space Vector Modulation (SVM)

Open loop voltage control

VSI ACmotor

PWMvref

Closed loop current-control

VSIAC

motorPWMiref

if/back

PWM – Voltage Source InverterPWM – Voltage Source Inverter

+ vc -

+ vb -

+ va -

n

N

Vdc a

b

c

S1

S2

S3

S4

S5

S6

S1, S2, ….S6

va*

vb*

vc*

Pulse Width Modulation


vtri

Vdc

qvc

q

Vdc

Pulse widthmodulator

vc

PWM – single phase


PWM – extended to 3-phase Sinusoidal PWM


Va*


Vb*


Vc*


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


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

)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)


)t(va)t(av)t(v32

v c2

ba

)t(va)t(av)t(v32

v c2

ba


t=t1

At t=t1, t = (3/5) (= 108o)

va = 0.9511(Vm)

vb = -0.208(Vm)

vc = -0.743(Vm)



At t=t1, t = (3/5) (= 108o)

va = 0.9511(Vm)

vb = -0.208(Vm)

vc = -0.743(Vm)

b

c

a


)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

How could we synthesize sinusoidal voltage using VSI ?


+ 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


+ 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


van = vaN + vNn

vbn = vbN + vNn

vcn = vcN + vNn

)t(va)t(av)t(v32

v c2

ba

)aa1(vvaavv32

v 2NncN

2bNaN


= 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


c2

badc SaaSSV32

v


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


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


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?


2oo


TV32

Tv

7,021 TTTT

100V1

110V2

Sector 1

sinjcosvv refref

q

d


Solving for T1, T2 and T0,7 gives:

sinT31

cos3

Tm

23

T1 sinmTT2

2oo


TV32

Tv

2d1dref TV31

TV32

cosvT 2dref TV3

1sinvT

where3

Vv

md

ref


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


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%

SVPWM

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