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Inductances in electrical transformers



Hi all.
I am trying to calculate mutual and leakage inductances in single phase
trasformer as in attached file.
I have modeled this transformer with core EI having a cross section of 50x80
mm, 220 turns at the primary and 117 turns at secondary.
The core extends 0.08m in the into-the-page direction.
I also added a small gap between E and I to be sure that there is no
relevant saturation.
First i evaluated the self inductance Ls1 = 290.6mH and Ls2 = 82.2 mH using
A,J integral as explained in tutorial.
I set primary windings to circuit primary+ and primary- having + or - 10A,
so the current I1 is 10/220 = 45.45 mA
Then i turned off primary winding and set secondary to a circiut carring 10
A.
Theese results are in according with the classical formulas.

Then i evaluated mutual inductance as described in Femm manual at
page 34. N2= 117 , I1=10/220 , a2 = 1.139E-3 m², integ A1dV2 = 4.339E-7 but
the result was M = 77.1 mH
( i multiplied the integ x 0.08 , the 3 dimension of core )
So the cooupling factor k = M / sqr(L1*L2) = 0.498

that is wrong. ( I think k is near 1 )

What is wrong in this model ?
Can someone help me ?
Best regards
Fabio



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