Tuesday, 9 June 2015

Why does a delta/wye transformer make 30 degrees phase shift ?


I'v heard that a delta/delta or Wye/Wye transformers do not make any phase shift. In delta/wye or wye/delta transformers, There is a 30 degrees phase shift between the primary and secondary coils. So, Why is there a phase shift ? and Why is it 30 degrees ?.. Why not 60 or 120 ?



I googled and I found calculations with phasor diagrams that proves the 30 degrees phase but I'm confused because of too many calculations and diagrams, I didn't get it.


Would you give me a simple answer, please ? and I prefer the physical meanings and concepts rather than equations and mathematics.


Thank you very much,



Answer



Let's call the 3 phases A, B and C and let's say we notionally have a neutral wire. Neutral is basically 0V in the system.


The "A" phase voltage (to neutral) is my chosen reference that all other voltage phase angles are measured from hence, V$_B$ is 120 lagging V$_A$ and V$_C$ is 120 degrees leading V$_A$.


OK so far?


What about the voltage between line A and line B (aka V$_{AB}$) - this is called line voltage (not to be mistaken with voltages between phase and neutral). Line voltages are $\sqrt3$ times bigger than phase voltages.


OK so far?


If you are not just examine what happens here: -



enter image description here


If you use trigonometry and resolve all the triangles you can find the length of V$_{AB}$ - it is $\sqrt3$ times bigger than either A or B to neutral.


It's also 30 degrees leading A and this is where the 30 degrees comes from.


So, a delta primary will receive primary line voltages of V$_{AB}$. V$_{BC}$ and V$_{CA}$.


Given that a transformer doesn't inherently phase shift anything (other than the trivial cases of 0 degrees and 180 degrees), any secondary winding voltage must be in phase with their respective primary voltage no-matter whether the secondary is connected delta or wye.


OK so far?


Then you have it because, a delta primary works with line voltages and these are 30 degrees shifted to their nearest phase voltage. The secondary outputs are also 30 degrees shifted and hence a wye secondary will produce a phase voltage that is 30 degrees shifted from the equivalent (but not directly connected to) phase voltage on the primary.


It's trivial to do the wye-delta transformer so I'll leave it to someone else.


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