Space Vector PWM

[Vihaan]

I had this doubt for very long time. I am referring to the NXP user guide and regarding the space vector modulation.



and when it is plotted


For 1,0,0 it is 2UDCBus/3 but in the space vector diagram it is 2/sqrt(3) UDCBus, there is factor sqrt(3). How is this additional factor derived?

 

[Vihaan]

The document is nxp user guide page 48.

 

[mxlemming]

The switching states in the Star diagram are 3 phase, the U alpha and beta are 2 phase. The Star isn't actually a star but a Cartesian coordinate system viewed from the diagonal, so there are transforms...

The thing about this diagram and svpwm method is that it seems to have been copied between all the manufacturers appnotes with various degrees of omission and leaps of faith.

I'm 3 years into this, have written my own FOC code and have not once found these switching tables anything other than useless obfuscation.

FOC is
Measure current
Clark matrix transform
Park matrix
PID control on dq currents to get dq voltage
Inverse Park
Inverse Clark
Center and write those values to the pwm timer.


Don't make it more complicated than this. It doesn't need to be. I cannot find a single advantage of the mess that is space vector modulation.

 

[Vihaan]

Ok thank you very much for the reply, i am really confused with 2 other questions, i don't get answers

1. When we apply FOC what is the maximum bus voltage applied on the phases (line voltage or phase voltage), if the applied voltage from the power supply is Vbus. I read it is 2/sqrt(3)*Vbus. Is there a simple derivation?

2. Similarly if the input DC current is Idc what is the phase current applied. I mean what is the relation if the torque applied is T?

Thank you in advance.

 

[mxlemming]

Ok thank you very much for the reply, i am really confused with 2 other questions, i don't get answers

1. When we apply FOC what is the maximum bus voltage applied on the phases (line voltage or phase voltage), if the applied voltage from the power supply is Vbus. I read it is 2/sqrt(3)*Vbus. Is there a simple derivation?

2. Similarly if the input DC current is Idc what is the phase current applied. I mean what is the relation if the torque applied is T?

Thank you in advance.

1) is very simple. Just draw two lines labeled 0 and Vbus. Now rotate the 3 phase star inside those two lines... What's the maximum length of the Star arms (phase voltages) that can rotate in that space? Simple triangle trigonometry. This should be self evident... The inverter cannot output voltages outside 0 to Vbus.

2) is trickier but still simple. The equation is
VbusIbus=3/2(Vqxiq+Vdxid)

This comes from 3 for 3 phases
1/2 is from the fact that it's sinusoidal so we have to convert to rms current and voltage since FOC uses peak currents and voltage by convention (it's just easier this way).

 

[Vihaan]

1) is very simple. Just draw two lines labeled 0 and Vbus. Now rotate the 3 phase star inside those two lines... What's the maximum length of the Star arms (phase voltages) that can rotate in that space? Simple triangle trigonometry. This should be self evident... The inverter cannot output voltages outside 0 to Vbus.

This is what i tried but got stuck up. Could you please help me with next steps?

 

[mxlemming]

This is what i tried but got stuck up. Could you please help me with next steps?
View attachment 341288

You don't need the circle. You have to imagine rotating it without the circle. The middle would go up and down if the vectors were bigger but that's not a problem.

I'm not doing the basic trig for you...

 

[Vihaan]

I think it is VBus/2 the maximum vector of U.

 

[stancecoke]

I like this explanation very much:

Vector control for dummies — Switchcraft

Who doesn't want to get a quick and dirty understanding of the concepts behind vector control?

www.switchcraft.org

Space Vector PWM Intro — Switchcraft

Get rich, smart and famous by understanding the dark arts of space vector pulse width modulation! A must for everyone aspiring to become a star in the drives community!

www.switchcraft.org

 

[mxlemming]

A

View attachment 341296
I think it is VBus/2 the maximum vector of U.

Think harder.

 

[Vihaan]

Do i need to take the resultant of the 3 sine vectors, then i get the following result

The other method i understood from net using the clarke and park transformation is as below

 

[Vihaan]

The maximum is Vdc/sqrt(3) bus voltage, the rms voltage is Vdc/sqrt(6). The line to line RMS voltage is sqrt(3) * Vdc/sqrt(6) = Vdc/sqrt(2).