Three Phase Rectifiers

Three phase rectifiers are essential in high-power industrial applications where single phase converters are inadequate due to unbalanced loading, high ripple, and limited power handling. By utilizing all three phases of the supply simultaneously, three phase converters deliver a much smoother DC output with significantly higher ripple frequency, reducing the size of output filters and improving efficiency. They are the standard choice for large DC motor drives, electrochemical processes, and HVDC transmission systems.

Core Concept Explanation

Three phase rectifiers take advantage of the three voltages, each displaced by 120 degrees, available from a three phase supply. At any instant, the rectifier output voltage equals the highest (or difference of highest and lowest, for full wave) of the three phase voltages. Because the three phases overlap smoothly, the output waveform has less ripple and a higher average value compared to single phase rectifiers.

The three pulse converter (also called M-3 or 3-phase half wave converter) uses three SCRs, one per phase, connected in a common cathode group. Each SCR conducts for 120 degrees per cycle in natural commutation. The output is the envelope of the three phase voltages, producing three pulses per cycle. Firing angle α is measured from the natural commutation point (NCP), which is the intersection of adjacent phase voltage waveforms (30° after the positive peak of each phase for common cathode connection).

The six pulse converter (B-6 or 3-phase full wave bridge) is the most widely used three phase topology. It uses six SCRs arranged in two groups: an upper group (common cathode) and a lower group (common anode). At any instant, one SCR from each group conducts simultaneously, applying a line voltage (difference of two phase voltages) across the load. This produces six pulses per cycle, with a ripple frequency of 6f (300 Hz for 50 Hz supply). The six pulse converter is far superior to the three pulse in terms of ripple, power factor, and supply current harmonic content.

The natural commutation point is a key concept for three phase converters. For the three pulse common cathode converter, the NCP for each SCR occurs when its anode voltage becomes the highest among all three phases. Firing angle α is measured from this point. For the six pulse bridge, the NCP is at the intersection of adjacent line voltages. The firing sequence for the six pulse bridge follows the order T1-T2-T3-T4-T5-T6, each triggered 60° apart.

Mathematical Expression

For the 3-pulse controlled converter, the average output voltage is Vdc = (3√3 × Vm_ph) / (2π) × cos α, where Vm_ph is the peak phase voltage. The ripple factor for uncontrolled three pulse is about 18.3%, significantly less than single phase. The operating range of α is 0 to 150° for continuous conduction with inductive load.

For the 6-pulse converter, the average output voltage is Vdc = (3√3 × Vm_L) / π × cos α = 2.34 × VL_rms × cos α, where VL_rms is the rms line voltage and Vm_L is the peak line voltage. The factor 2.34 is a commonly memorized constant. The uncontrolled output (α = 0) of a 6-pulse converter fed from a 415 V, 3-phase supply is Vdc = 2.34 × 415 = 970.5 V, approximately 970 V of DC. The ripple factor of the six pulse converter is only about 4.2%, making it suitable for applications requiring smooth DC without large filters.

Practical Understanding

In electrochemical plants and aluminum smelting facilities, six pulse converters supply very large DC currents at relatively low voltages to electrolysis cells. Multiple six pulse converters may be phase shifted using transformers with different secondary winding arrangements (star and delta) to create 12-pulse or 24-pulse converters, which have even lower harmonic content. This is the standard approach in large HVDC terminals.

The firing sequence in a 6-pulse bridge is T1, T2, T3, T4, T5, T6 at 60° intervals. For successful commutation, the incoming SCR must have a higher anode voltage than the outgoing SCR. For α ≤ 60°, natural commutation is always successful. For α > 60° with inductive load, the commutation overlap becomes significant and must be accounted for in the output voltage calculation using the commutation voltage drop formula.

Given:
Three phase 6-pulse fully controlled bridge rectifier
Line voltage VL = 415 V (rms), 50 Hz
Firing angle α = 30°
Load: Highly inductive (continuous current)

Why this formula applies:
For 6-pulse bridge, Vdc = 2.34 × VL_rms × cosα
or equivalently Vdc = (3√3/π) × Vm_L × cosα

Formula:
Vdc = 2.34 × VL_rms × cosα

Substitution:
Vdc = 2.34 × 415 × cos 30°
Vdc = 2.34 × 415 × 0.866

Calculation:
Vdc = 970.5 × 0.866

Final Answer: Vdc = 840.5 V

Exam Tip: Memorize Vdc = 2.34 × VL_rms × cosα for the 6-pulse bridge — this is the most tested formula for three phase rectifiers in GATE. For 3-pulse: Vdc = 1.17 × VL_rms × cosα (which is exactly half of 6-pulse). A common trap is confusing phase voltage with line voltage in these formulas.

Pulse Number and Ripple Relationship

• 3-pulse converter: 3 SCRs, ripple frequency = 3f = 150 Hz, ripple factor ≈ 18.3%. Simpler but higher ripple.
• 6-pulse converter: 6 SCRs, ripple frequency = 6f = 300 Hz, ripple factor ≈ 4.2%. Standard industrial choice.
• Higher pulse number → lower ripple factor → smaller filter requirements → better current waveform at supply.
• 12-pulse converters use two 6-pulse bridges with 30° phase shift (one star, one delta transformer), ripple frequency = 12f.
• For 6-pulse bridge at α = 0: Vdo = 2.34 VL_rms. This is the maximum uncontrolled output (reference value).
• Firing sequence for 6-pulse: T1(0°) → T2(60°) → T3(120°) → T4(180°) → T5(240°) → T6(300°) → repeat.

Quick Revision

• 3-pulse (M-3): Vdc = 1.17 × VL_rms × cosα. 3 SCRs common cathode. Ripple freq = 3f.
• 6-pulse (B-6): Vdc = 2.34 × VL_rms × cosα. 6 SCRs in bridge. Ripple freq = 6f = 300 Hz.
• For 415 V supply at α=0: Vdc(6-pulse) ≈ 970 V. Memorize this reference value.
• α measured from natural commutation point (NCP): intersection of adjacent phase (3-pulse) or line voltages (6-pulse).
• Ripple factor: Single phase ≈ 48%, 3-pulse ≈ 18.3%, 6-pulse ≈ 4.2%. Increasing pulses reduces ripple.
• For α > 90°, 6-pulse bridge operates in inverter mode: Vdc negative, energy flows from DC to AC.
• Exam trap: Do not confuse Vm_L (peak line voltage = VL_rms × √2) with VL_rms in the formula.