# Question on Harmonics and Power factor

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.

• Maybe show your working so others can follow instead of expecting others to repeat the process. Jul 2, 2014 at 19:27
• Added the working Jul 2, 2014 at 19:58
• Displacement power factor is a new term to me. I understand power factor and I also understand that there can be several power factors (each harmonic). I was in agreement up till cos(13.68) then I wrote this. Maybe someone else can help from hereonin Jul 2, 2014 at 20:18