I would appreciate some clarification.
If you had a supply of 2 volts and another supply of 4 volts and each powered a 1 ohm resistor, the wattages would be 4 watts and 16 watts respectively. The total power is 20 watts.
What I am thinking is that the 3-phase current and voltage will just
So let’s try this. The average voltage is 3 volts and into two lots of 1 ohm resistors, that’s a total power of 9 watts plus 9 watts. That’s a total of 18 watts and not 20 watts.
How inaccurate an assumption are you prepared to accept?
P = sqrt(3) * pf * I * V
That’s assuming that the load is linear i.e. produces a sinusoidal current from a sinusoidal voltage. If it isn’t linear then power factor is somewhat meaningless.
Given that you are specifying phase voltage in your question then the root 3 isn’t relevant for either total power or single phase power. This is the formula for total 3 phase power with a linear load: -
Picture from here.
Notice that the above formula uses line voltage and not phase voltage. If phase voltage were used (as per the detail in your question) then total power is 3 x and not root 3 x.