Three-phase AC voltage controller (full-wave) feeding a star-connected resistive load What is the permissible firing angle range α for a 3-phase full-wave regulator with a resistance load (star connection)?

Introduction / Context:
Three-phase AC voltage controllers (also called regulators) use phase control on each phase to vary the RMS output voltage supplied to a load. For a resistive, star-connected load, the achievable control range of the firing angle α is limited by natural commutation intervals and overlap between phases.

Given Data / Assumptions:

• Three-phase, full-wave regulator topology (two antiparallel thyristors per phase).
• Star-connected purely resistive load (no significant inductance).
• Idealized commutation without overlap for the range reasoning.

Concept / Approach:
In a 3-phase full-wave controller, each phase can be delayed by α with respect to its phase voltage zero crossing. Because line-to-line voltages are displaced by 60°, the control range is restricted so that proper conduction sequences still occur without creating undefined intervals. For R-loads, the classical limit for full control is α up to 150° so that at least one device can conduct as phase voltages cycle.

Step-by-Step Solution:
Phase-angle control is measured from each phase voltage zero crossing.With three phases 60° apart, conduction windows must overlap sufficiently to maintain defined output.Analysis of the conduction pattern shows that beyond α = 150°, proper conduction ceases; therefore α is limited to 0–150°.

Verification / Alternative check:
Standard drive and power-electronics texts tabulate these limits: for 3-phase full-wave controllers on R-loads, α ∈ [0°, 150°] ensures continuous, predictable gating sequences.

Why Other Options Are Wrong:

• 0–180°: exceeds the permissible commutation window.
• 0–120° or 0–90°: needlessly restrictive; full control up to 150° is achievable.
• 15–165°: does not reflect the standard definition of α or the true upper bound.

Common Pitfalls:

• Confusing rectifier α limits with AC controller limits.
• Ignoring the 60° phase displacement effect on conduction windows.

Final Answer:
0 ≤ α ≤ 150°