Phase Controlled Rectifiers

Phase controlled rectifiers form the backbone of modern power conversion systems, enabling precise control of DC output voltage by varying the firing angle of thyristors. Unlike uncontrolled rectifiers that deliver a fixed output, phase controlled rectifiers allow engineers to regulate power delivered to loads such as DC motors, battery chargers, and industrial heating systems. Understanding these converters is fundamental to power electronics and is heavily tested in GATE examinations.

Core Concept Explanation

A phase controlled rectifier uses thyristors (SCRs) instead of diodes to convert AC to DC. The key advantage is that the output DC voltage can be continuously varied by controlling the instant at which the thyristor is triggered into conduction. This triggering instant is defined by the firing angle α, measured from the zero crossing of the supply voltage.

In a single phase half wave controlled rectifier, one SCR conducts during the positive half cycle, starting from angle α and ceasing at angle π for a purely resistive load. For an inductive load, conduction extends beyond π due to stored energy in the inductance. This single SCR configuration is simple but produces high ripple and poor power factor.

A single phase full wave controlled rectifier uses either a centre-tap transformer with two SCRs, or a bridge configuration with four SCRs. The full wave configuration doubles the ripple frequency and improves the average output voltage and power factor compared to half wave. The two most common full wave topologies are the mid-point converter (M-2 connection) and the bridge converter (B-2 connection).

The commutation of thyristors in phase controlled converters relies on natural line commutation, meaning the AC supply voltage itself reverses to turn off a conducting thyristor. This natural commutation makes line commutated converters robust and simple compared to forced commutation inverters. The firing angle α is the primary control variable: increasing α reduces average output voltage, decreasing α increases it.

Mathematical Expression

For a single phase half wave controlled rectifier with a resistive load, the average output voltage is derived by integrating the supply voltage from α to π divided by 2π (the full period). The formula is Vdc = (Vm / 2π) × (1 + cos α), where Vm is the peak supply voltage. At α = 0, this reduces to Vm/π, which matches an uncontrolled half wave rectifier. As α increases toward π, Vdc approaches zero.

For a single phase full wave controlled rectifier, the integration covers two half cycles per period: Vdc = (2Vm / π) × cos α for a resistive load. This formula is critical for GATE problems. Notice the factor of 2 compared to half wave. At α = 0, Vdc = 2Vm/π, which is the standard full wave uncontrolled rectifier output. The RMS output voltage for half wave is Vrms = (Vm/2) × sqrt((π - α + sin 2α / 2) / π).

The form factor FF = Vrms / Vdc and the ripple factor RF = sqrt(FF² - 1) are used to quantify waveform quality. Higher α leads to higher ripple factor, meaning worsened DC quality. The displacement power factor for a full wave converter is approximately cos α, which decreases as α increases, indicating that higher firing angles lead to poor power factor at the supply side.

Practical Understanding

In practice, phase controlled rectifiers are used to drive DC motors in variable speed drives, control furnace heating elements, and regulate battery charging currents. The torque of a DC motor is proportional to armature current, which depends on the average output voltage. By varying α, the motor speed can be continuously adjusted without mechanical losses, unlike resistor-based speed control.

A critical practical concern is power factor. Because the SCR can only delay current conduction beyond the voltage zero crossing, the input current is inherently lagging. This lagging current draws reactive power from the supply, increasing the apparent power demand. Utilities penalize low power factor installations, making power factor correction capacitors or active front-end converters necessary in large industrial drives.

Another concern is harmonic distortion in the supply current. Phase controlled rectifiers generate significant lower-order harmonics (3rd, 5th, 7th), which can interfere with sensitive electronic equipment on the same supply bus. Filters and transformer isolation are often used to mitigate harmonics in industrial installations.

Given:
Single phase full wave controlled rectifier
Supply voltage Vs = 230 V (rms), frequency = 50 Hz
Firing angle α = 60°
Load: Resistive

Why this formula applies:
For full wave resistive load, both half cycles are utilized.
Vdc = (2Vm / π) × cos α

Formula:
Vdc = (2 × Vm / π) × cos α
Vm = Vs × √2 = 230 × 1.414 = 325.2 V

Substitution:
Vdc = (2 × 325.2 / π) × cos 60°
Vdc = (650.4 / 3.1416) × 0.5

Calculation:
Vdc = 207.03 × 0.5

Final Answer: Vdc = 103.5 V

Exam Tip: For GATE, the formula Vdc = (2Vm/π)cosα applies ONLY to full wave resistive load. For half wave: Vdc = (Vm/2π)(1+cosα). A common trap is applying the full wave formula to half wave problems or forgetting that cosα is negative for α > 90°, giving a negative Vdc in inverter mode.

Quick Revision

• Half wave controlled rectifier: Vdc = (Vm/2π)(1 + cosα). One SCR, conducts α to π for resistive load.
• Full wave controlled rectifier: Vdc = (2Vm/π)cosα. Two or four SCRs, higher average output and lower ripple.
• Firing angle α = 0 gives maximum output (same as uncontrolled rectifier). Increasing α reduces Vdc.
• For α > 90° in full wave converter, Vdc becomes negative: converter operates in inverter mode (energy returned to supply).
• Power factor ≈ cosα for full wave converter. Higher α means worse power factor and more reactive power demand.
• Natural commutation: supply voltage reversal turns off the SCR. No additional commutation circuit needed.
• Exam trap: Inductive load extends conduction beyond π (freewheeling diode prevents this in semi-converters).