1. Space Vector Pulse Width Modulation Space Vector Pulse Width Modulation Space Vector Pulse Width Modulation Space Vector Pulse Width Modulation Dr. Pedro Ponce & M. en C. Alfonso Monroy

2. Inverter Depending on the conducting switches, an inverter has 2 3 =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.

3. Example For the load configuration shown, the phase voltages are (2/3) V DC, - (1/3) V DC, and, -(1/3) V DC.

4. 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.

5. 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

6. 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 V1V1 V2V2 V3V3 V4V4  V5V5 V 8 V 7  d V ref V6V6

7. 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

8. Space Vector Pulse Width Modulation From the figure where T=T 1 +T 2 +T 3 is a switching period U k,U k+1 are non-zero voltage space vectors U o is a zero voltage space vector

9. Space Vector Pulse Width Modulation Developing the last equation But U 3 =0

10. Space Vector Pulse Width Modulation Another form to express the last equation is The solution of the previous system is

11. 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.

12. 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 1010 1010 1010 time

13. Space Vector Pulse Width Modulation In order to diminish the harmonic content in the current waveforms a symmetrical switching pattern is chosen. T 3 /4T 1 /2T 2 /2T 3 /4 T PWM branch A B C 1010 1010 1010 T 3 /4T 2 /2T 1 /2T 3 /4

14. 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.

15. 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.

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

17. Results Comparison of current and voltage waveforms for six-steps PWM and SVPWM at 5 Hz. Six-stepsSVPWM

18. Results Comparison of current and voltage waveforms for six steps PWM and SVPWM at 60 Hz. Six-stepsSVPWM

19. Results Comparison of current and harmonic contents for six steps PWM and SVPWM at 5 Hz. Six-stepsSVPWM

20. Results Comparison of current and harmonic contents for six steps PWM and SVPWM at 60 Hz. Six-stepsSVPWM

21. Results SVPWM symmetric pulses (branches A and B)

22. Results Deadtime insertion