Power Electronics Circuits
In a power supply whose input current is not sinusoidal but contains many harmonics, which of the following correctly explains why the power factor is not 1 even if the fundamental of the current is in phase with the voltage?
- AThe harmonic currents are also multiplied by the voltage and greatly increase the active power, so the active power becomes larger than the apparent power
- BHarmonic currents at frequencies different from the sinusoidal voltage carry no average power, but they increase the RMS current
- CWhen harmonic currents flow, the fundamental of the voltage lags the current by 90°
Show answer and explanation
Answer: B. Harmonic currents at frequencies different from the sinusoidal voltage carry no average power, but they increase the RMS current
The power factor is the active power divided by the apparent power (RMS voltage × RMS current). The product of a sinusoidal voltage and a harmonic current at a different frequency averages to zero over a cycle, so the active power is determined by the fundamental current alone. The harmonics, however, also increase the RMS current and hence the apparent power, so the power factor becomes the product of the power factor from the phase difference of the fundamental (cos φ) and the ratio of the RMS fundamental current to the total RMS current. For example, with cos φ = 0.9 and a fundamental that is 0.8 times the total current, the power factor is 0.9 × 0.8 = 0.72. The input current of a rectifier with capacitor smoothing is such a case, and power factor correction circuits bring the current closer to a sine wave.
- A. Active power never exceeds apparent power. The power factor lies between 0 and 1.
- B. Correct. Only the RMS current increases, not the active power, so the power factor falls.
- C. Harmonic currents do not shift the phase of the voltage. The power factor falls because the RMS current increases.