Can it be enough to know the rms voltage and the current at the same time without taking the power factor into account to be able to distinguish between active (kW) and reactive (kVAR) power? 
Doesn’t the rms voltage and current only allow you to get the apparent (kVa) power? 
That would be a indication that you only measure the apparent power and not the active power that you are pay for 
The change is rather high that when you use a higher power device that it has a “better” power factor. Maybe even resistive load like a heating element that has a power factor of 
(apparent power = active power in that case 
)