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

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

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

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

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)

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

How could we synthesize sinusoidal voltage using VSI ?

Space Vector Modulation Space Vector Modulation

+ 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

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

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:

sinT31

cos3

Tm

23

T1 sinmTT2

2oo

d1dref T)60sinj60(cosV32

TV32

Tv

2d1dref TV31

TV32

cosvT 2dref TV3

1sinvT

where3

Vv

md

ref

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

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%