Cram for Exam Vol 3 Q1 - 3-phase transformer bank with mixed polarities

[akyip]

Hi guys,

I'm working on the Cram for PE Power Exam problems. Volume 3 Question 1 has a transformer bank made of three 1-phase transformers, both sides connected in delta.

2 of the transformers have additive polarity, but the last transformer has subtractive polarity.

The question is asking what is the angular displacement from the high side to the low side. The answer is 180 degrees, but I'm trying to understand and visualize why. Can anyone help with this? The solution provides the phasor diagrams, but even then I'm a bit stumped with the subtractive-polarity transformer mixed with the additive-polarity ones...

I appreciate anyone who helps explain this!

(I tried posting a photo of this question, but it seems I always have trouble posting photos on this forum...)

 

[Dude99]

Here's my take

in summary the prim line/phase and sec phase to line offset/cancel.  The polarity offset is opposite or 180

 

[Orchid PE]

That only proves one of the phases is shifted by 180°, but all three phases are shifted.

The typical transformer we are used to working with has subtractive polarity, which has no phase shift when connected with H1 & H2 as the inputs, and X1 & X2 as the outputs.

Additive polarity transformers appear to have a 180° phase shift when the input is H1 & H2 and the output is X2 & X1. (I say "appear" because it's not so much as shifted as it is inverted)

Notice the two additive transformers cause 180° phase shifts on those phases, and since the output of the subtractive transformer is reversed (essentially wired as additive), it will cause a 180° phase shift on that phase as well.

Take a look at this image.



Notice that in the problem, X2 of the left transformer is connected to X1 of the right transformer. With that connection, it's acting as an additive polarity transformer.

 

[JayD]

Can anyone explain  with phasors? It will be a better illustration to the problem?

 

[Cram For The PE]

Can anyone explain  with phasors? It will be a better illustration to the problem?

Using vectors is below I just assumed each transformer had a 1:1 ratio to make it easier. I will add to the solution of later book to make it more clear.