I really can't wrap my head around this. Three single phase transformers are connected to create a 3 phase transformer. They all have the same nominal values :

voltage conversion : 1.2kV/120 V (primary/secondary)

impedence: Z=0,05 pu

power: 7.2 kVA. They are connected in 4 different ways , star-star, star-delta, delta-star, delta-delta.

My problem is finding the actual value of the impedence when the primary side is connected in delta. I would normally find the base in the primary side like this : $$Z_b=\frac{V_b^2}{S}$$ where Vb is the primary side voltage and S the nominal apparent power value given.

Having a look at the solution manual though the base is supposed to be this $$Z_{b,old}=\frac{(V_b/\sqrt 3)^2}{S}$$

I've wasted too much time on this. Can somebody help? How can the connections matter since that 0.05 per unit value was assigned for the single phase transformers. Does a transformer's impedence change based on how it is connected?

  • \$\begingroup\$ I was confused when I first started these problems as well. Pu means per unit, that should be obvious as well if someone has studied the per unit system. You find a base for all your parameters and you divide everything by that base. It's like when you take an exam and you are marked from 0 to 10 and you score 8 .Here the base is 10. If you take another exam in which you are marked from 0 to 100 and let's say you score 78 then you divide by the base of 10 and you get 7,8. Now you can compare your performance. Something similar is going on here. \$\endgroup\$ Aug 5, 2017 at 22:25
  • \$\begingroup\$ This is the first time I ever hear about Per Unit, and I'm doing my thesis right now. \$\endgroup\$ Aug 5, 2017 at 22:30
  • \$\begingroup\$ My only experience with this is looking at a set of 1 MVA, 10 kV / 400 V, delta-star transformers at work. Questions: (1) What would the 'unit' be in a per unit specification? 1 V or 1 kV? (2) You've given one solution but there are four problems. Which case is it for and what are the other solutions? (3) What does the 'old' subscript mean? \$\endgroup\$
    – Transistor
    Aug 5, 2017 at 22:46
  • \$\begingroup\$ Per unit values don't have units if that's what you mean. My problem is for the last two cases. The first formula I wrote applies for the first two cases and it's also the one used by the solution manual. The trouble begins with case 3 and it's the same with case 4. The base is different according to the book for those cases but it makes no sense. The impedence has one 'actual' value.The per unit is just relevant.Choosing any base if I wanted to convert back to the real value I should always get the same impedence.That is what I'm looking for here. The manual says it's different in the last 2. \$\endgroup\$ Aug 5, 2017 at 22:51
  • \$\begingroup\$ The 'old' is just used in the manual to distinct the old base from the new base which it chooses for the rest of the problem. I added it here so that people don't think that it's just another base chosen. \$\endgroup\$ Aug 5, 2017 at 22:52

1 Answer 1


In fact, the connection does not change the inductance of the transformers, but it does change the voltage that is applied to the coil terminals.

If you take three coils and connect in D (delta), you will have the line voltage applied directly over each coil. This means that the phase voltage will be equal to the line voltage.

If you take those same three coils and connect Y (star), the phase voltage will become √3 times lower than the line voltage.

Probably from this, the formula you presented was derived.


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