AC voltage controller with resistive load at α = 90° A single-phase full-wave AC regulator (antiparallel thyristors) supplies a purely resistive load with firing angle α = 90°. What is the input power factor (considering distortion and displacement effects)?

Introduction / Context:
For AC voltage controllers feeding resistive loads, firing angle control chops the input voltage within each half-cycle. The current remains in phase with the instantaneous voltage during conduction but is discontinuous, producing harmonic distortion. The practical input power factor therefore reflects both displacement (≈ unity for R load during conduction) and distortion due to waveform chopping.

Given Data / Assumptions:

• Single-phase, full-wave controller with antiparallel thyristors.
• Purely resistive load, so within conduction intervals current and voltage are in phase.
• Firing angle α = 90°; conduction from ωt = π/2 to π in each half-cycle.
• Power factor defined as real power over apparent power, including distortion effects.

Concept / Approach:

The input power factor PF can be expressed as PF = (Fundamental active power)/(Apparent power). For a resistive load the displacement factor is ≈ 1, and the PF reduction is dominated by distortion. At α = 90°, the fundamental component of the chopped sine is reduced such that the effective PF is about 0.707. This commonly cited result arises from Fourier analysis of the conduction window and is a standard benchmark for AC regulators at quarter-cycle conduction per half-cycle.

Step-by-Step Solution:

Verification / Alternative check:

Design examples in AC voltage controller texts often quote PF ≈ 0.707 for α = 90° with R load, consistent with the intuitive “half-power-like” reduction linked to conduction over a quarter cycle per half-cycle.

Why Other Options Are Wrong:

• Unity PF: ignores distortion due to chopping.
• 0.5 or 0.2 lagging: too low for R load at α = 90°; these would imply significantly poorer utilization than observed.

Common Pitfalls:

Confusing displacement factor with total power factor; for R loads the displacement is near 1 but distortion can be significant at large firing angles.

Final Answer:

0.707 lagging