Phase-Controlled Rectifiers
Single-phase half-wave and full-wave controlled rectifiers with R and RL loads, freewheeling diode, semi and full converters, three-phase converters, inversion mode, and overlap.
Phase-controlled rectifiers (converters) use thyristors fired at an angle α to give an adjustable DC voltage from AC. They drive DC motors and HVDC links.
Single-phase half-wave
With a resistive load and supply V_m sin ωt:
V_dc = (V_m/2π)(1 + cos α)
With an RL load the current continues past π (negative voltage appears) until it falls to zero; a freewheeling diode stops the negative part and improves the output.
Single-phase full-wave
| Converter | V_dc (continuous current) | Operation |
|---|---|---|
| Full converter (4 SCRs or centre-tap) | (2V_m/π) cos α | Two-quadrant: rectifier for α < 90°, inverter for α > 90° |
| Semi-converter (2 SCRs + 2 diodes) | (V_m/π)(1 + cos α) | One quadrant, built-in freewheeling |
| Full converter, resistive load | (V_m/π)(1 + cos α) | Current is discontinuous |
Input power factor of a full converter with ripple-free current = 0.9 cos α (distortion factor 0.9 × displacement factor cos α).
Three-phase converters
With line voltage V_L (RMS), V_mL = √2 V_L:
- Three-phase full converter (6 SCRs): V_dc = (3V_mL/π) cos α = 1.35 V_L cos α. Output ripple is at 6f.
- Three-phase half-wave: V_dc = (3√3 V_mp/(2π)) cos α (V_mp = peak phase voltage).
- Semi-converter: (3V_mL/(2π))(1 + cos α).
Inversion and dual converters
With α > 90° and a DC source on the load side (for example a motor during regenerative braking), a full converter feeds power back to the AC side: line-commutated inverter. Limit α to about 165° to leave margin for commutation. A dual converter (two full converters back to back) gives four-quadrant operation.
Overlap
Source inductance L_s delays current transfer between thyristors by the overlap angle μ, reducing the output voltage: drop = (3ωL_s/π) I_d for a three-phase full converter (2ωL_s I_d/π for single phase).
Worked example
A single-phase full converter on 230 V, 50 Hz feeds a highly inductive load at α = 60°.
- V_m = 325.3 V; V_dc = (2 × 325.3/π) × 0.5 = 103.5 V.
Practice
A three-phase full converter is fed from a 415 V line supply. What is its output voltage (V) at α = 30°? (Give 1 decimal place.)
Show answer and explanation
Answer: 485.4V_dc = (3√2 × 415/π) cos 30° = 560.5 × 0.866 = 485.4 V.
A single-phase half-wave controlled rectifier with resistive load has V_m = 200 V and α = 90°. What is V_dc in V? (Give 2 decimal places.)
Show answer and explanation
Answer: 31.83V_dc = (V_m/2π)(1 + cos 90°) = 200/(2π) = 31.83 V.
A single-phase full converter with continuous current operates as an inverter when:
Show answer and explanation
Answer: B(2V_m/π) cos α becomes negative for α > 90°; with a suitable DC source, power flows to the AC side.
What is the input power factor of a single-phase full converter with ripple-free load current at α = 0°? (Give 1 decimal place.)
Show answer and explanation
Answer: 0.9pf = 0.9 cos α = 0.9 (the 0.9 comes from the square-wave input current's distortion factor).