What is difference in DQ transformation for delta vs Wye stator PMSM? 1

[telmatrix]

Hi Folks... Appreciate your help with this one that I have been wondering about lately.

It appears that most published literature (white papers) and texts like Krause or Ong really do not clarify if there are DQ transformation differences for PM synchronous machines with different stator winding configurations (delta vs wye). All tend to work out DQ transformations from wye (star) stator configuration. I assume however that it does in fact work out similarly, however perhaps the electromagnetic torque expression is likely impacted?

Can anyone clarify or point me to a paper, book, or other resource that does?

Thanks in advance...

 

[sreid]

Basically, if you look at a motor as a Black Box, you can't tell if the stator is connected WYE or Delta. Tested as a black box, the phase to phase parameters are what they measure.

 

[telmatrix]

Well yes... From a controller standpoint, the two styles of windings are treated exactly the same, although some less expensive controllers need to read voltage from the common center of the wye winding.

From a motor design standpoint however there are some important differences related to cost, circulating currents, harmonics, efficiency, etc.

That said, At this time I'm interested in the mathematical modeling, so my original question was an appeal to folks familiar with reference frame transformation theory. Thanks for taking the the time to respond though.

 

[Skogsgurra]

If it is the Park transformation and its inverse you are thinking about, then it doesn't care about wye or delta.

The "cheap controllers" you mention are usually stator voltage controllers made by people that didn't understand how to handle the return paths by keeping the thyristors open at the right angles. That's why they needed the star point connected. There's one US make that I saw about ten years ago that had that problem. I think they are out of business now. For obvious reasons.

Gunnar Englund

http://www.gke.org

--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[telmatrix]

Hey Skogsgurra... Many thanks for your reply.

I thought as much, but if one resides in the ABC reference frame, one should see differences in behavior (assuming the two different stator configuration machines are the same including test conditions). The wye winding is normally more efficient. At any given time, two-thirds of the windings in a delta configuration are running at half the voltage of the other, which is an impact on efficiency. The wye winding always powers only two windings in series, so higher voltages (or lower-resistance windings) can be used.

Therefore... I assume that since Eff = Pin/Pout, this implies that "all things being the same", that the expression that defines the torque should be slightly different. Perhaps differs by a factor of two or three? Any thoughts or comments on this?

Thanks again...

 

[telmatrix]

Oops... I should clarify one sentence. I meant to say...

Therefore... I assume that since Eff = Pin/Pout, this implies that "all things being the same", in the dq0 frame that perhaps the expression that defines the torque should be slightly different (between a wye versus a delta). Perhaps differs by a factor of two or three? Any thoughts or comments on this?

Thanks.

 

[Skogsgurra]

No. I can not see that it should influence the transformation in any way. Also, there is always a 1/sqrt(3) change in voltage when you go from wye to delta. So your thoughts about winding voltages are somewhat irrelevant.

There may (perhaps) be some second or, rather, third order effects but nothing that I am aware of and that we care about in the field.

Gunnar Englund

http://www.gke.org

--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[telmatrix]

Okay thanks again... Last question, and just a sanity check.

To mathermatically convert from delta to wye machine, assuming terminal measurements we have:

Nomenclature:
L2L = Line-2-Line
L2N = Line-2-Neutral

wye:
Rstator(L2L) = 2*R(L2N)
Lstator(L2L) = 2*L(L2N)
Ke(L2L) = Ke(L2N)*sqrt(3) - Note Usually L2L value
posted on mfr. datasheets.
Hence the V(BEMF) quantities picks up the Ke factor, where (for example)
vbemfa=Ke*w*cos(ang_elec)
vbemfb=Ke*w*cos(ang_elec-ang)
vbemfc=Ke*w*cos(ang_elec+ang)
where:
ang_elec = electrical angle of machine
ang = 2*pi/3

delta:
Rstator(L2L) = R(L2N)
Lstator(L2L) = L(L2N)
Ke(L2L) = Ke(L2N)
Hence now the Iphase current quantities pick up the sqrt(3) factor, yes?