In a single-phase full-wave AC voltage regulator using antiparallel thyristors, what is the usual relationship between the firing angles in the positive and negative half-cycles to avoid DC components?

Introduction / Context:
AC voltage regulators that use two antiparallel thyristors (or a triac) control the RMS output by delaying firing in each half-cycle. A key practical requirement is to avoid any DC component in the load current, which can saturate transformers and cause torque pulsations in motors.

Given Data / Assumptions:

• Single-phase full-wave regulator with antiparallel thyristors.
• Firing angle in the positive half-cycle is α₊; in the negative half-cycle is α_-.
• Objective is normal operation without intentional DC offset.

Concept / Approach:

A DC component arises when the conduction in the positive half-cycle is not symmetrically matched by the conduction in the negative half-cycle. Equal firing angles (symmetrical control) ensure that the average of the output over a full period is zero, preventing DC magnetization and minimizing even-harmonic content.

Step-by-Step Solution:

Verification / Alternative check:

Using Fourier analysis, asymmetrical gating introduces even harmonics and a nonzero average value. Symmetrical gating (equal α) removes these issues in standard applications.

Why Other Options Are Wrong:

• different / different but sometimes equal: Asymmetry introduces DC and even harmonics unless special reasons exist.
• equal or different / randomly varied: Not a recommended default practice; design targets symmetry.

Common Pitfalls:

• Assuming motor loads tolerate DC components—this risks heating and torque ripple.
• Believing asymmetry always improves control—usually it degrades power quality.

Final Answer:

equal