Why there is not a sqrt(3) factor between rated currents on the delta-wye transformer?

Question

When calculating the rated current on either side of a delta-wye transformer, we will use the following equation:

$$
I_{LL}= dfrac{S_{3Phi}}{sqrt3*V_{LL}}
$$

Since this same equation is used for either the delta and the wye side, there is no square root of 3 factor between these two currents. For example, if the high side is 66 kV and the low side is 12 kV, then for a 28 MVA transformer, the rated currents on each side will be:

$$
I_{LL}= dfrac{28 MVA}{sqrt3*66 kV} = 245 A
$$

$$
I_{LL}= dfrac{28 MVA}{sqrt3*12 kV} = 1347A
$$

So according to this equation, the only factor between the line to line currents of the low and the high side is the transformer ratio, which happens to be 5.5 in this example. My question is, why isn't the square root of 3 also a factor?

For example, if we were to find the rated current of the high side to be 245 A, then shouldn't the rated current on the low side be given by:

$$
I_{LL}= sqrt3*Tranformer_ratio*245 = 2334 A
$$

Why do we ignore the square root of 3 factor between the high and the low side of a delta-wye transformer when calculating rated currents?

AlexVB · Answer

The root of 3 factor applies when you switch the same windings from delta to wye and back.
But your transformer is already designed to have primary delta and secondary wye windings. So its rated voltages and currents already account for any wye/delta conversion. For example, every phase of its delta winding has square root of 3 times higher rated current than it would be, if the same winding would  be connect in wye configuration.
If you don't build, but just use the tranformer, then you don't even have to know how windings are connected inside to calculated "outer" rated currents.

sdarella · Answer

Alright, I found out why, and it's very simple. We do this calculation for relay settings. But it so happens that microprocessor relays are the ones to do the calculation for the phase shift (magnitude and angle), so there is no need for us to calculate the phase shift manually.

Answered by sdarella on November 8, 2021

user105652 · Answer

The square root of 3 factor has to do with the voltage relation between the 3 phases and neutral, which normally is consistent. That they are 120 degrees out of phase is a moot point. Current depends on the load and is not always a balanced load.

Since the load is unknown, dynamic and maybe unbalanced it cannot be used as a reference for static equations such as the square root of 3.

This assumes all 3 phases are sampled at the same time, so there is no artificial add-on delay in current readings.

Why there is not a sqrt(3) factor between rated currents on the delta-wye transformer?

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