3 phase power systems: per unit with transformers

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Joined Mar 23, 2016

I'm currently working a problem that looks like this:


There's more to this problem, but I'm sure I can solve the rest of it, there are just things I'm uncertain about. Actually, it's only one thing I'm uncertain about.

I'm looking through my notes, and when converting the voltage base at one bus to another, sometimes there's a conversion from line-to-line to line-to-neutral, and sometimes there's no conversion at all, just purely the transformer's coil ratios. I've looked through all these sample problems, and I cannot find a pattern of when to divide by sqrt 3 and when not to.

I'm not sure if I've explained myself fully. For example, let's try to find the bases at bus 1:

First, since there's no transformer between bus 2 and bus 3, we know their bases are the same:

bus 2: 115kv, 132.25 ohms

Now, find bus 1:

The coil ratio is 115/14.4, and the low voltage side is at bus 1, with the high voltage side at bus 2. Thus, the voltage base at bus 1 is (14.4/115) * 115 = 14.4 kv. But, do I have to divide by sqrt 3 for some line-to-line to line-to-neutral conversion? That's what I'm really unsure about and need to understand for this material. Is the voltage base at bus 1 14.4kv or is it 8.31kv?

I'd really appreciate some help on this subject and look forward to it.