Grid pollution & power factor

01

Live experiment

Educational example · phase RMS quantities · balanced three-phase system

VoltageCurrent

Normalized waveforms · voltage / peak, current / fundamental peak

Harmonic amplitudes · % of fundamental

Active power80 kWDisplacement power factor0.74

Diode bridge

Reactive load power: 72.71 kvar
Current THD: 0 %
Voltage drop: 16.34 V
True power factor: 0.74

02

Model & equations

The red current lags the voltage by φ. With the diode bridge enabled, the same fundamental carries 5th, 7th, 11th and 13th harmonics. This truncated Fourier model is illustrative, not a detailed diode commutation simulation.

Q=P\tan(\arccos(\cos\varphi)),\qquad I_1=\frac{P}{3V_g\cos\varphi}

\mathrm{THD}_i=\sqrt{\sum_{h\in\{5,7,11,13\}}(I_h/I_1)^2},\quad I_h/I_1=1/h

\Delta V\approx\frac{R_{cc}P+X_{cc}Q}{3V_g},\qquad \mathrm{PF}=\frac{\cos\varphi}{\sqrt{1+\mathrm{THD}_i^2}}

03

Example parameters

Vg: 230 V RMS
f: 50 Hz
E: 750 V
Rcc: 0.05 Ω
Xcc: 0.1 Ω
R: 0.05 Ω
Rf: 0.6 Ω
P: 80 kW
cos φ: 0.74
fc: 10 kHz
L: 0.87 mH
Δt: 1 ms