Three-phase semi-converter (average DC voltage) For a certain firing angle in a 3-phase semi-converter, the average DC output voltage equals 50% of the maximum possible value. What is the firing angle α?

Introduction / Context:
Average DC output voltage in phase-controlled converters depends on firing angle. The three-phase semi-converter (half-controlled bridge) has a characteristic equation involving (1 + cos α). Knowing this helps set α for a desired fraction of maximum DC output.

Given Data / Assumptions:

• Topology: 3-phase semi-converter.
• Vdc,max occurs at α = 0°.
• Required Vdc is 50% of Vdc,max.

Concept / Approach:

For a 3-phase semi-converter, Vdc = (3Vm / 2π) * (1 + cos α). At α = 0°, Vdc,max = (3Vm / π). Setting Vdc to half of Vdc,max gives a simple trigonometric relationship for α.

Step-by-Step Solution:

Verification / Alternative check:

At α = 90°, the converter’s DC output is exactly half of its maximum, consistent with the formula and standard curves.

Why Other Options Are Wrong:

• 30° or 60° yield cos α > 0, giving more than 50% of maximum.
• 120° yields cos α < 0, giving less than 50% of maximum.

Common Pitfalls:

Using the full-converter equation Vdc ∝ cos α (omitting the 1 + term) leads to incorrect α. Always match formula to topology.

Final Answer:

90°