Space Vector Pulse Width Modulation Space Vector Pulse Width Modulation Space Vector Pulse Width Modulation Space Vector Pulse Width Modulation Dr. Pedro.
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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
Space Vector Pulse Width Modulation
• 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
Space Vector Pulse Width Modulation
• 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
Space Vector Pulse Width Modulation
• Developing the last equation
• But U3=0
33211 TUTUTUU kkm
211 TUTUU kkm
Space Vector Pulse Width Modulation
• 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
Space Vector Pulse Width Modulation
• In linear SV-PWM, the reference voltage is restricted to the inner zone of the circle shown in the figure.
Space Vector Pulse Width Modulation
• 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
Space Vector Pulse Width Modulation
• 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
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