Adding Apparent Load

Thread Starter

DYLH

Joined Aug 13, 2013
28
Appologies, this isn't actually a homework problem, but I thought that this may be the best place to get academic input.

Which is the correct way to solve this?

Find the total VA and PF for a circuit with the two loads:
Apparent Load 1 = 250 VA w/ 0.75 PF
Apparent Load 2 = 150 VA w/ 0.90 PF

Method 1
Real Power 1 = 0.75 * 250 = 187.5 W
Real Power 2 = 0.90 * 150 = 135 W

Total Apparent Load = 250 VA + 150 VA = 400 VA
Total Real Power = 187.5 + 135 = 322.5 W

Resulting Power Factor = 322.5 / 400 = 0.80625

Method 2
Real Power 1 = 0.75 * 250 = 187.5 W
Real Power 2 = 0.90 * 150 = 135 W
Total Real Power = 187.5 + 135 = 322.5 W

Reactive Power 1 = sqrt(250^2 – 187.5^2) = 165.36 VAR
Reactive Power 2 = sqrt(150^2 – 135^2) = 65.38 VAR
Total Reactive Power = 230.7 VAR

Total Apparent Power = sqrt(322.5^2 + 230.74^2) = 396.55 VA
Resulting Power Factor = 322.5 / 396.55 = 0.813
 

WBahn

Joined Mar 31, 2012
29,979
How about just doing the math from the definitions.

Do you know about complex power? If so, things are very easy. If not, then things are a bit harder, but not too much.
 

WBahn

Joined Mar 31, 2012
29,979
You are neglecting to take into account whether the power factor is leading or lagging. If both are leading or both are lagging, then you will get the results in Method 2. But if one is leading and the other is lagging, which is precisely the case when you are doing power factor correction, then you have to take that into account.
 
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