space vector pulse width modulation space vector pulse width modulation space vector pulse width...

Space Vector Pulse Width Space Vector Pulse Width ModulationModulation

Space Vector Pulse Width Space Vector Pulse Width ModulationModulation

Dr. Pedro Ponce & M. en C. Alfonso Monroy

Inverter

• Depending on the conducting switches, an inverter has 23=8 possible configurations.

• Only six configurations supply voltage at the output.

• The other two vectors have no effect on the motor, because the three upper (lower) switches are simultaneously connected to the positive (negative) terminal.

Example

• For the load configuration shown, the phase voltages are (2/3) VDC, -(1/3) VDC, and, -(1/3) VDC.

Park’s transformation

• By mean of the Park’s transformation, a quantity may be changed from a abc three-phase system to a dq two-phase system.

1 1/ 2 1/ 22

3 0 3 / 2 3 / 2

ad

bq

c

VV

VV

V

Vector description of a voltage source inverter

• According to eight possible switching states, a voltage source inverter can be represented by an hexagon of voltage vectors.

d

q

001

110010

011 100

101

111

000

1/3

2/3

Space Vector Pulse Width Modulation

• The objective of SVPWM is to approach any voltage space vector by a vectorial sum of two of six vectors in the hexagon.

q

V1

V2V3

V4

V5

V8

V7

d

Vref

V6


• Define a mean voltage vector U and suppose it is constant during a switching period.

• Under this assumption, the mean value is calculated by

m

TUdttU

T0 )(

1


• From the figure

where

T=T1+T2+T3 is a switching period

Uk,Uk+1 are non-zero voltage space vectors

Uo is a zero voltage space vector

321

21

1 21

103

1

21

111 TTT

TTo

T TT

Tkkm dtU

TdtU

TdtU

TU


• Developing the last equation

• But U3=0

33211 TUTUTUU kkm

211 TUTUU kkm


• Another form to express the last equation is

• The solution of the previous system is

sin

cos

)3/sin(

)3/cos(

32

0

1

32

21 refcdcd VTVTVT

3

sin||3

1cd

ref

VVT

T sin||3

2cd

ref

VVT

T

3 2 1T T T T


• In linear SV-PWM, the reference voltage is restricted to the inner zone of the circle shown in the figure.


• To reduce the switching frequency it is needed to choose such a sequence where the change from one state to another is made by switching just one branch.

branch

A

B

C

1

0

1

0

1

0

time


• In order to diminish the harmonic content in the current waveforms a symmetrical switching pattern is chosen.

T3 /4 T1 /2 T2 /2 T3 /4

TPWM

branch

A

B

C

1

0

1

0

1

0

T3 /4 T2 /2 T1 /2 T3 /4

SVPWM and DSP56F80x Family

• Some of the advantages of implementing space vectors PWM in a DSP5680x are

– DSP56F80x is optimised for motor control applications. It includes six PWM outputs.

– Software Development Kit (SDK) allows an easy configuration of PWM characteristics such as PWM period, PWM waveform alignment, and interrupts handling.

SVPWM and DSP56F80x Family

– The six PWM outputs may be used as three complementary channel outputs.

– An easy to use deadtime insertion avoids short circuiting the DC bus.

– Independent output polarity control.

– 15-bit resolution PWM registers.

Results

• A comparison on the achieved current waveforms by six-step PWM and SVPWM in Direct Torque Control (simulation results).

Results

• Comparison of current and voltage waveforms for six-steps PWM and SVPWM at 5 Hz.

Six-steps SVPWM

Results

• Comparison of current and voltage waveforms for six steps PWM and SVPWM at 60 Hz.

Six-steps SVPWM

Results

• Comparison of current and harmonic contents for six steps PWM and SVPWM at 5 Hz.

Six-steps SVPWM

Results

• Comparison of current and harmonic contents for six steps PWM and SVPWM at 60 Hz.

Six-steps SVPWM

Results

• SVPWM symmetric pulses (branches A and B)

Results

• Deadtime insertion

space vector pulse width modulation space vector pulse width modulation space vector pulse width...

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