Apparent power calculation of different loads for transformer sizing

Question

Let's say we have two electrical loads and we would want to calculate the total apparent power in order to size the transformer to supply the demand. I'm currently confused between which two calculation method to use.

Load A: P: 3kW, Q: 4kVAr
Load B: P: 4kW, Q: 3kVAr

Method 1:
If we sum up P and Q, we will get P: 7kW and Q: 7kVAr.
Then we can just use

$$ S = \sqrt{P^2 + Q^2} $$

to calculate the required apparent power, 9.899kVA.

Method 2:
Calculate individual load's apparent power using same equation above.
S of load A = 5kVA
S of load B = 5kVA

Sum of these will arrive to 10kVA.

So clearly, there is a difference in result when power factor of the loads are different. And this difference will be even more apparent when there is a long list of loads involved.

I'm more inclined towards method 2 since these are the actual kVA demand of the loads. Whereas in method 1, we only calculate the overall demand with a generalized power factor.

Hence, i'm wondering if I am making a mistake of undersizing if I size my transformer based on method 1 instead of method 2?

Answer 1

Method one gives the correct KVA if you sum the lagging VARs as positive and the leading VARs as negative. Method two will always overstate the KVA except in the unlikely event that all of the loads have the same power factor. It may be useful to overstate the KVA if you want to be sure you have some safety factor in the transformer loading. Also, If the loads are under the supervision of separate people it will be easier to enforce a KVA limit for each one rather than state both VAR and watt limits for each.