Power factor correction of a linear inductive load is exactly the same as tuning a parallel circuit of a capacitor and inductor. You pick a capacitor that works with the value of the transformer's magnetizing inductance to satisfy this: -
60Hz = \$\dfrac{1}{2\Pi\sqrt{L_M.C}}\$
Where \$L_M\$ is the transformer's magnetizing inductance and C is the capacitor chosen to "neutralize" the current taken by the coil.
For a pure lossless inductance and capacitance, the resultant current taken from the supply is zero.
If your transformer primary indicates an inductive reactance at 60Hz of 300 ohms, the magnetizing inductance value is this divided by \$2\Pi\times 60\$ = 0.8 henries.
The capacitive reactance required is 300 ohms and this is 8.8 uF. As a sanity check: -
F = \$\dfrac{1}{2\Pi\sqrt{0.8\times 8.8\times 10^{-6}}}\$ = 59.98Hz
I found a study that showed various brands of LED bulbs rated 3 to 8 watts with power factors ranging from .48 to .79. If you can find 8 watt LED bulbs with .5 power factor that give equivalent light as your 40 watt incandescents, you would need 16 VA per bulb vs 40 for the incandescents. If you distribute the bulbs equally among the phases, you should not have any difficulty with the neutral currents. You should still have some concern about extra heating in the generator due to harmonics. It is difficult to determine how much the generator should be oversized for harmonics. The generator manufacturer may have a recommendation.
A harmonic filter would both reduce the harmonics and increase the power factor. I don't believe that you should purchase a 3-phase choke and harmonic filter separately. You should be able to get the most effective filter if it is purchased as a package.
Estimating Harmonic Distortion
For estimation purposes, it can be assumed that the power factor of the fundamental current of an LED bulb is 1.0. It can also be assumed that the source voltage is not significantly distorted. Total power factor = Watts / (Voltage X Total RMS current). Total or “true” RMS current is the RMS value of the distorted current waveform. It calculated as the square root of the sum of the squares of the fundamental current plus each of the harmonic currents. You can break that down as Irms = (If^2 + Ih^2)^.5 where If is the fundamental current and Ih is the square root of the sum of the squares of the individual harmonics.
If the voltage, total RMS current and power is known for an LED bulb, the harmonic current and total harmonic current distortion can be calculated as follows:
Only the fundamental current (If) produces power (W). W = V X If X pf. Assuming pf for the fundamental = 1, If = W / V
From Irms = (If^2 + Ih^2)^.5, Ih = (Irms^2 – If^2)^.5
Total harmonic current distortion, THDi = (Ih^2 / If^2)^.5 = Ih / If
The total RMS current and power may be marked on the bulb. If it is not marked it can be measured with an inexpensive power meter like a Kill-A-Watt.
Here is a link to the study mentioned above.
Best Answer
Power factor is equal to
$$ \frac{P}{S} $$
and it's not determined by if the 3 phase are balanced or not, any reactive power on any phase may result a non-unity power factor, whether 3-phase or single phase system, whether the system balanced or not.