Which current is this?

I was given in class a problem about power transform but I don't understand which current is used in a stage of the resolution. It is asked to find the efficiency of a transformer in a period of a day (24 hours) given that;

• $S_{N}=110kVA$
• $2200V/110V$
• $60~ Hz$
• $R_{1}=.22\Omega$
• $R_{2}=.5m\Omega$
• $X_{1}=2\Omega$
• $X_{2}=5m\Omega$
• $R_{c}=5.5k\Omega$
• $X_{m}=1.1k\Omega$ with this power cycle
• 4 hrs with no load
• 8 hrs at 1/4 full load and pf .8
• 8 hrs at 1/2 at pf 1
• 4 hrs at full load and pf 1
• Constant core loss of 1.346 kW Both in the resolution given and my idea is to make this fraction

$\eta=\frac{output@24hrs}{input@24hrs}$

first
$output=(4\times0+8\times.25\times.8+8\times.5\times1+4\times1\times1)=1056kWh$
then the core loss is
$1346\times24=32.3kWh$
and finally the ohmic losses in the windings

• 8 hrs at .25 full load
($250^2\times0.005+14.1^2\times.22)8=2.85$
• 4hrs at .5 full load
($500^2\times0.005+26.6^2\times.22)4=5.62$
• 8hrs at full load
($1000^2\times0.005+51.7^2\times.22)8=44.70$

but I don't understand why 14.1, 26.6 and 51.7, isn't supposed to be the nominal current on the high voltage side $I_{1N}=\frac{110000}{2200}=50A$?

and that would be

• 8 hrs at .25 full load
($250^2\times0.005+12.5^2\times.22)8=2.85$
• 4hrs at .5 full load
($500^2\times0.005+25^2\times.22)4=5.62$
• 8hrs at full load
($1000^2\times0.005+50^2\times.22)8=44.70$

If not then which current is this and how to calculate?

UPDATE
the total ohmic loss will be 53.17kWh and then

$\eta=\frac{1056}{1056+32.3+53.17}=92.5\%$
But I still don't get how the 14.1...and respective currents are calculated

• What exactly are you asking? Why you should include the magnetizing current in the I^2*R loss calculations? Or why it has that specific value? (The details you gave are fine, but pretty much meaningless without the equivalent model they refer to) – Brian Drummond Mar 13 '18 at 18:05
• Rated voltage is done at full load, you are assuming Vout at no load So kVA rating= Ploss + Pload for R loads and effic = Ploss/kVA – Tony Stewart Sunnyskyguy EE75 Mar 13 '18 at 18:05
• How many circuits could be made from 3 resistors and 3 inductors? – Andy aka Mar 13 '18 at 18:59
• @BrianDrummond, what are the 14.1, 26.6 and 51.7 values? what current does stand for? – riccs_0x Mar 13 '18 at 22:19
• Primary current. Your second set of figures only accounts for the current delivered in the secondary, omitting the magnetizing current and any due to power factor considerations. – Brian Drummond Mar 13 '18 at 22:21