I need help with the above circuit.
I first need to calculate the voltage and current distortion. I calculate this as 8.75%(voltage) and 5.7% (current).
I then need to find the displacement power factor. I calculate the current through the circuit using Ohm's law for the fundamental voltage and treat the harmonic as a short circuit and I get 0.97A<-13.68°.
For the fundamental:
Z(inductor) = 186m * 2pi * 50 j = 58.43j
By Ohm's Law: 240 = I(240 + 58.43j); I = 0.97A<-13.68°
For the 5th harmonic:
Z(inductor) = 186m * 2pi * 50 j *5 = 292.168jΩ
21 = I(240 + 292.168j); I = 0.056A<-50.6°
Therefore I assume the displacement power factor is cos(-13.68) as the voltage has no phase. This gives me a power factor of 0.97.
I then need to calculate the true power factor. I use the real power/apparent power equation. I find the total voltage in the circuit (RMS) to be 170.34V and the total current (RMS) to be 0.678A.
Total voltage = sqrt(harmonic voltage^2 + fundamental voltage^2) (all rms)
Total voltage = sqrt(169.7^2+ 14.85^2) = 170.34V
Total current = sqrt(harmonic current^2 + fundamental current^2) (all rms)
Total current = sqrt(0.686^2+ 0.039^2) = 0.678A
I multiply these two together for an apparent power of 115.49 VA. I then use I^2*R to find the real power on the basis that the impedance of the resistor will not vary with frequency. I obtain a true power factor of 0.95.
Have I approached this question in the right way and is my answer correct? Would appreciate some feedback/criticism.