kW Loss for a Transformer

Where did these numbers come from? Work the 100% figure backwards:

1516.7 kW / 133 = 11.404 kW per transformer

which is less than the 11.497 kW "load loss" (full load loss per transformer). So they don't look quite right.

The 50% point is 1.844 kW (No Load Loss) + 0.25 * 11.497 kW = 4.718 kW per transformer, or 627.49 kW total. The 0.25 factor is because the load loss is proportional to the load current squared (in this case 0.5 full load).

The problem appears to be in the data in the list. If one splits the losses at full load as 1.844 +11.497 =13.341 KW per transformer, then, at 100% load the total loss for 133 transformers should be 1774 KW, not

1517. Then at 50% load the loss should be about 133 *[1.844 +0.25*11.497]=627KW The exciting current as a % also appears to be low. Consider total loss =core loss + I^2R loss. On the basis of constant output voltage core (no-load) losses should rise slightly while copper losses will rise as the square of the output KVA

Thanks for your help! The data was from another project that I am reviewing. I thought the results were incorrect but I wanted to make sure with you guys first.

I appreciate your help!

Would these values change with a power factor. If so, how do I include the power factor in the calculation. Lets assume the power factor is .94 at a 100% load.

Thanks,

Troy

No. The core losses are voltage dependent and the only effect power factor would have on these is secondary, through an effect on the internal voltage drop. This is normally negligable. Copper losses depend on the square of the current - and at any given KVA will be the same at any pf. All the power factor will do is change the real and reactive output at any given KVA

i.e. at 1750KVA 1.0pf, the output would be 1750KW, 0KVAR at 0.94 pf lag the output would be 1750*0.94 =1645 KW ( and 597KVAR) In both cases the losses would be the same except for a negligable change in the core loss. The differences are not negligable and the table doesn't make sense. However, if you assume that the "load loss" given is the "total loss" at full load, there is a better correlation At full load the copper loss would be (133*11.495)-245=1284 KW so at any load the loss would be 245+(1284*(per unit load^2) this would give losses of 245 ,274, 325, 566, 967, 1529 which are in the ballpark of the given data-but no cigar.