Svpwm

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 – extended to 3-phase Sinusoidal PWM


Va*


Vb*


Vc*


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)


)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

+ 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

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)


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


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:

2oo


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



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.


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.

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Svpwm