Assume a delta-Y winding Hello, I\'m learning about OC/SC testing methods for tr

Question

Assume a delta-Y winding

Hello,

I'm learning about OC/SC testing methods for transformers. My problem however is related to 3 phase transformers. I'm unsure of how exactly to refer an impedance in the secondary to the primary.

I'm under the impression that we can refer them simply using the windings ratio. However I've also noticed that a few books use the transformation ratio VLprimary/VLsecondary to transform the equivalent circuit to the primary. I'm really confused which is the correct approach.

I've attached a picture.

Explanation / Answer

3-phase transformers can be analyzed in the same way as single phase transformer, difference being that we need to consider, in 3-phase transformers, on per-phase basis.
hence, as per your diagram , if we analyze this and assume that it exhibits one of the phases of the 3-phase transformers then,

if, N1= NO. OF TURNS IN PRIMARY & N2= NO. OF TURNS IN SECONDARY

V1/N1= V2/N2 , :V1, V2: voltages at the primary & secndry respectively.........(1)
& I1 N1= I2 N2 , I1 , I2 : currents in the the primary & secndry respectively....(2)

DIVIDING (1) BY (2):

V1/I1 N12 = V2/I2 N22

==> Z1/N12 = Z2/N22 , SINCE V1/I1= IMPEDANCE OF PRIMARY = Z1 AND SIMILARLY Z2 IS IMPEDANCE OF SECONDARY.

HENCE, Z1 ( PRIMARY IMPEDANCE REFLECTED, FROM SECONDARY) = Z2 * (N1/N2)2.

thus, impedance is reflected in the inverse ratio with the ratio squared.

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