# Space vector analysis of 3 phase -- stuck on a concept

1. Aug 29, 2016

### fahraynk

I am trying to understand space vectors in 3 phase machines. If you have a balanced 3 phase system, the 3 phasors of voltage, current or whatever... should sum to 0. i<0 + i<-120 + i<-240 = 0. But in this image of a rotating space vector : (http://people.ece.umn.edu/users/riaz/animations/spacevecmovie.html) you can see that the 3 voltage phasors do not sum to 0, but they sum to the space vector.

I think the space vector (SV) equation is this : $SV = Acos(wt) + Acos(wt-120)<120 + Acos(wt-240)<240$

Why do you have those extra <120, <240 ? If the fact that the 3 vectors are out of phase is already represented by their changing magnitude, why are they put at different angles a second time?

2. Aug 30, 2016

### Baluncore

It is normal to resolve a sinusoidal wave as two phases, the Cosine(wt) and Sine(wt) components. They do not sum to zero in time because the neutral is at the origin, but the plot of x=a.Cos(wt) and y=a.Sin(wt) obviously describes a circle when the space vectors are plotted on a polar diagram.

The same circle can be made for a polar plot of a 3PH signal. The advantage of 3PH is that the individual phases can sum to zero in the time plot.

When 4PH, such as Sin, –Sin, Cos and –Cos are considered, then they will sum to zero in the time plot and the polar plot. In the polar plot there are really two circles being described that are 180° out of phase.

Any circle(s) in the polar plot represent a steady availability of energy.

3. Aug 31, 2016

### fahraynk

How can you make a circle in the polar plot of a balanced 3 phase system? The 3 vectors always add to 0. I get how 1 phase becomes a polar circle, but I dont see how 3 phasors added becomes that.
This is a good idea of my understanding :http://www.electrician2.com/electa1/electa3htm.htm
In this image of a space vector http://people.ece.umn.edu/users/riaz/animations/spacevecmovie.html <--- it says the space vector equation is the already polar forms of the 3 phases, sort of polarized a second time. I stiill for the life of me cant figure out why they do this

Edit :: Actually after hours of googling I figured out that it has something to do with the direction of wingdings in the physical system. Still not sure why, gonna spend more time researching tomorrow. Any tips would be appreciated though. (this is about space vector control of a 3 phase permanent magnet synchronous motor)

Last edited: Aug 31, 2016
4. Sep 1, 2016

### jim hardy

I think that in your diagram those colored arrows are not phasors. I was taught phasors have fixed length and they rotate. Those don't rotate, their direction is constant. Their length varies. I don't know what they are.. .

I'm not versed in 'space vectors'. What are they ?

5. Sep 4, 2016

### fahraynk

Okay, well... Space Vectors are some method of controlling ac synchronous motors. I've traced back some references until I found that it is something similar to the method of synchronous components. So I've been studying synchronous components to try to get a framework to understand space vectors. Synchronous components is a method of breaking up a 3 phase unbalanced system into 2 balanced phase and a 0 phase system. As far as the space vectors... I think they are just putting the 3 out of phase signals on a 120* angle because the coils of the motor are on a 120* angle.

6. Sep 4, 2016

### jim hardy

Ahhhh , okay, it's a new field for me too.

Here's an appnote written for people who are more skilled in the craft than i .
At first glance it appears to me
the "space vector" is generated by adding together unequal portions of the three individual phase-to-neutral voltages

which could be what your gyrating circle linked in first post represents. Is that why the red green and blue arrows have varying lengths ?
They then go on to describe PWM'ing each phase , which is i suppose how they vary the voltage applied to each winding.

What powerful building blocks you young guys have nowadays.

If you keep this up i'll someday understand how Fair Anne's newfangled washing machine works .

old jim

7. Sep 4, 2016

### dlgoff

I was waiting for @fahraynk to reply. Since I know how you like images of things like this, from http://people.ece.umn.edu/users/riaz/animations/listanimations.html,[/PLAIN] [Broken] here's a couple .gifs that you my like. (these images were too large to upload, hence I had to post via the image link)

[PLAIN]http://people.ece.umn.edu/users/riaz/animations/spavecab.gif[/COLOR][/URL] [Broken]

edit: I can't get the second image to stick. Here's it's link: http://people.ece.umn.edu/users/riaz/animations/spavecdq.gif
edit, edit: Ah. the file was too large but could resize and upload the static pic. go to link for animation.

Last edited by a moderator: May 8, 2017
8. Sep 4, 2016

### fahraynk

Thanks guys. I am going to build a brushless DC(BLDC) and a permanent magnet synchronous motor(PMSM). The BLDC is easy to control, but I have been having a really tough time finding information on easily controlling a PMSM.

I found a textbook on space vector control, but they expected you to know how the space vector works as a prerequisite. I traced back about 10 articles references until I found the method of synchronous components. I think its a good intro to understanding space vectors. Cant find any good practice problems for line to line faults (which is what the method is really for) but I found a decent course on MIT OCW http://ocw.mit.edu/courses/electric...-electric-power-systems-spring-2011/index.htm

If anyone knows an easier way to control a PMSM that would help to. I can move forward and take my time with this Space Vector control. Otherwise ill be studying this for a while because I am stubborn :-/
I read a whole book about the construction and physics of the PMSM and BLDC motors, but it barely covered controlling them :-/

9. Sep 4, 2016

### jim hardy

Thanks Don

i'm beginning to think this is one of those cases where the math is a lot harder than the physics.
It's intuitive that three pulsating mmf's add to one rotating mmf, that's what three phase does as Tesla figured out.
When we learn to teach it better it'll become easy as 1 + 1 = √3 .
Was it necessary to call them "Space Vectors" ? Looks to me like a simple sum. Write in rectangular coordinates and add.

Just looking at that Microchip i can sorta see what they're up to in figure 2, PWM'ing Q0 thru Q5 to make three variable voltages that are applied to coils spaced 120 degrees apart. Express in rectangular coordinates of your choice, X-Y , D-Q, rotor or stator, and add.
Am i on right track ?

But i'm a long way off from Clark transforms and field oriented control....

10. Sep 4, 2016

### dlgoff

11. Sep 4, 2016

### jim hardy

Thanks Don

hmmmmm i may get to try it out.....
just put in a bid for a lathe with 7hp 230V 3 phase motor......

12. Sep 4, 2016

### dlgoff

You have 3 phase service at your house?

13. Sep 4, 2016

### jim hardy

No, but i have some huge rectifiers, capacitors, SCR's and a 3 phase autotransformer that weighs 400 lbs.

14. Sep 4, 2016

### dlgoff

You're my hero.

15. Sep 5, 2016

### fahraynk

Finally figured it out. The original phases are put on an axis of the motor because the coils physically are $120^\circ$ apart. Then you take the 3 phase current waveform of the coils and using Parke and Clarke transforms you put the waveform on the rotating axis of the rotor to give you a space vector. The current space vector for max torque has to be $90^\circ$ ahead of the rotor flux. The Parke transform gives you a D and Q axis, the D axis will be the rotor axis. So since you want your signal $90^\circ$ ahead, you ignore the D axis and put max current on the Q axis.

Then you take your waveforms, use inverse Clarke and Parke transforms, use a pi controller to give a Va, Vb, Vc for each phase. The better term to google is not space vector control, its field oriented control.

Anyway, thanks a lot. Ill probably be posting more questions from this project in the future... Anyway for now problem solved.

16. Sep 5, 2016

### jim hardy

Very Good !
I guess that by knowing where the rotor is , one can run the motor at reduced voltage and match max torque to just what the load needs ?

Nice explanation there. Thanks !

old jim