Apparent power calculation of different loads for transformer sizing

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?

• method one give the best result. but I'm assuming both Qs are inductive (trailing) if one is capacitive (leading) then the total apparent power is even less. Feb 21 '18 at 4:46