# Transformer equivalent circuit values

I was given the following data about a transformer

• 1 $\phi$
• 25 kVA
• 220/440
• 60Hz gave the following test results

Open circuit test (440V side open)

• 220 V, 9.5 A, 650 W

Short circuit test(220V side shorted)

• 37.5, 55A, 950 W

While the values of the $R_{CL}$ and $X_{ML}$ are right (74.46 and 24.36 Ohms, respectively), the values $R_{eqH}$ and $X_{eqH}$ are not. It was solved in class way different from what I did, (sorry I understand that the nomenclature is changed sometimes) so I don't know which way is the valid one.

simulate this circuit – Schematic created using CircuitLab

• What I was told - To calculate the values of $R_eqH$ from to apply
$P=I^2R$
and then from the Short circuit test $\frac{950}{55^2}=0.31404\Omega$

then from the $V=RI$,
$R=\frac{37.5}{55}=0.681\Omega$ and then, apply the Pythagorean theorem

$X_eqH=\sqrt{.681^2+.31404^2}=0.605\Omega$

(fairly easy)

• What I did First I referred the values of the short circuit test to the primary side using the ratio $\frac{220}{440}$ giving the values
18.75 V, 110 A and 950 W

then since the 110A are different to the nominal current $I_{1N}=25kVA/220=113.63A$
I again adjusted the values to calculate if the nominal current was applied.
$\frac{113.63}{110}=1.033$
and the square is 1.067089,then the final values of
19.35 V, 113.63 A and 1013.73 W

To calculate the final equivalent values required then,

$\frac{1013.73}{19.35*113.63}=.4608$,
the angle is 62.55 degress and the sine is .8874

calculate $Z_{sc}=\frac{19.35}{113.63}=.17035$

and then the values of $R/X_eqH$ are
$R_eqH=.4608*.17035=.0785\Omega$
$X_eqH=..8874*.17035=0.1511\Omega$

that clearly does not match the other values, what did I miss?

• 240 or 440? Make your mind up. – Andy aka May 19 '18 at 14:31
• Short circuit test(220V side shorted)? Make your mind up again! – Andy aka May 19 '18 at 15:50
• Hey bro, its true the first one was a mistake, but this time the information is correct, in the short circuit test it was the 220 V side what was shorted. – riccs_0x May 19 '18 at 15:55
• So the short circuit test was with 37.5 volts applied to the secondary 440 volt winding? If so then you need to make that clear in the numbers you quote. – Andy aka May 19 '18 at 15:57
• Your answer makes no sense. Which winding was voltage applied to during the short circuit test? – Andy aka May 19 '18 at 19:34