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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.

schematic

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?

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  • 1
    \$\begingroup\$ 240 or 440? Make your mind up. \$\endgroup\$ – Andy aka May 19 '18 at 14:31
  • 1
    \$\begingroup\$ Short circuit test(220V side shorted)? Make your mind up again! \$\endgroup\$ – Andy aka May 19 '18 at 15:50
  • \$\begingroup\$ 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. \$\endgroup\$ – riccs_0x May 19 '18 at 15:55
  • 1
    \$\begingroup\$ 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. \$\endgroup\$ – Andy aka May 19 '18 at 15:57
  • 1
    \$\begingroup\$ Your answer makes no sense. Which winding was voltage applied to during the short circuit test? \$\endgroup\$ – Andy aka May 19 '18 at 19:34

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