Exact Equivalent Circuit of transformer

Exact Equivalent Circuit transformer

Resistances and reactances of transformer, which are described above, can be imagined separately from the windings (as shown in the figure below). Hence, the function of windings, thereafter, will only be the transforming the voltage.

The no load current I0 is divided into, pure inductance X0 (taking magnetizing components Iμ) and non induction resistance R0 (taking working component Iw) which are connected into parallel across the primary. The value of E1 can be obtained by subtracting I1Z1 from V1. The value of R0 and X0 can be calculated as, R0 = E1 / Iw and X0 = E1 / Iμ.

But, using this equivalent circuit does not simplifies the calculations. To make calculations simpler, it is preferable to transfer current, voltage and impedance either to primary side or to the secondary side. In that case, we would have to work with only one winding which is more convenient.

From the voltage transformation ratio, it is clear that,
E1 / E2 = N1 / N2 = K

Now, lets refer the parameters of secondary side to primary.
Z2 can be referred to primary as Z2'
where, Z2' = (N1/N2)2Z2 = K2Z2.   ............where K= N1/N2.
that is, R2'+jX2' = K2(R2+jX2)
equating real and imaginary parts,
R2' =  K2R2 and X2' = K2X2 .
And V2' = KV2

Now, as the values of winding resistance and leakage reactance are so small that, V1 and E1 can be assumed to be equal. Therefore, the exciting current drawn by the parallel combination of  R0 and X0 would not affect significantly, if we move it to the input terminals as shown in the figure below.


Now, let R1 + R2' = R'eq  and X1 + X2' = X'eq

Approximate Equivalent Circuit Of Transformer

If only voltage regulation is to be calculated, then even the whole excitation branch (parallel combination of R0 and X0) can be neglected.

Book

• Power System Analysis by Grainger and W.D. Stevenson

• Power System Analysis and Design by J. Duncan Glover,Mulukutla S. Sarma and Thomas J. Overbye.

• Power System Analysis by Hadi Sadat.

• Principles of Power Systems by Mehta.

     
Author        Bilal masood
lecture       06
Type         ppt
Availability Available online
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