Operating quadrants of a single-phase fully controlled converter A single-phase full converter supplying a load can operate in how many quadrants of the V–I plane (considering rectification and inversion modes with current direction maintained by the load)?

Introduction / Context:
A single-phase fully controlled bridge (using four SCRs) can both rectify power from AC to DC and, with appropriate firing angle and suitable load (e.g., back-EMF), return power to the AC source (inversion). This raises the classic question of how many quadrants of operation are achievable.

Given Data / Assumptions:

• Fully controlled bridge with SCRs and proper gating.
• Unidirectional current in the DC side (typical with RL or EMF-type loads).
• Firing angle α can be set from near 0 to beyond 90 degrees.

Concept / Approach:
With SCRs, current through the bridge is unidirectional, but the average DC voltage can be positive (rectification, α < 90°) or negative (inversion, α > 90°) while current keeps the same direction. That corresponds to two quadrants: voltage sign can change, current sign is fixed.

Step-by-Step Solution:
For α < 90°, Vdc > 0 and Idc > 0 → Quadrant I.For α > 90°, Vdc < 0 but Idc > 0 → Quadrant II or IV depending on chosen axes conventions; in any case, a second quadrant with opposite voltage sign.Current reversal is not allowed by the SCR bridge without additional circuitry → limited to two quadrants.

Verification / Alternative check:
Standard converter operation charts show two-quadrant capability for fully controlled single-phase bridges with passive DC loads.

Why Other Options Are Wrong:
1 quadrant: Ignores inversion capability.
3 or 4 quadrants: Would require current reversal and/or bidirectional DC-side current, which this bridge alone does not provide.

Common Pitfalls:
Confusing the fully controlled converter (2-quadrant) with dual converters or four-quadrant chopper-inverter systems that can reverse DC current.

Final Answer:
2 quadrants