Power Factor Correction

Problem

A 230 V RMS mains supply feeds a bridge rectifier with a capacitor filter drawing 2 A RMS. The displacement angle is $\varphi = 0^\circ$ and $THD_i = 150\%$ . Calculate the power factor before and after active PFC reduces $THD_i$ to 4%.

Step 1 — Power Factor Before PFC

With $\cos(0^\circ) = 1$ , the entire PF penalty comes from distortion.

PF_{before} = \frac{\cos(0^\circ)}{\sqrt{1 + 1.5^2}} = \frac{1}{\sqrt{3.25}} = 0.555

Step 2 — Apparent and Real Power

S = V_{rms} \times I_{rms} = 230 \times 2 = 460\,\text{VA}

P = S \times PF = 460 \times 0.555 = 255\,\text{W}

Step 3 — Power Factor After Active PFC

PF_{after} = \frac{1}{\sqrt{1 + 0.04^2}} = \frac{1}{\sqrt{1.0016}} = 0.999

Step 4 — New RMS Current

Real power stays at 255 W. With the improved PF, the source current drops significantly.

I_{rms} = \frac{P}{V_{rms} \times PF} = \frac{255}{230 \times 0.999} = 1.11\,\text{A}

Step 5 — Current Reduction

The mains current drops from 2 A to 1.11 A — a 44% reduction for the same delivered power.

Figure 1. Before PFC (red, peaky) vs after active PFC (green, sinusoidal) — same real power, much less RMS current

Active PFC nearly halves the RMS current for the same real power.