Industrial Electronics – I (Single-phase & polyphase controlled rectifier)

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 Calculation of Vdc, Vrms, Ripple Factor, PIV, and Efficiency of Single-Phase & Three-Phase Controlled Rectifiers: -

Power electronics plays a vital role in modern electrical and electronic systems. One of the most important circuits is the controlled rectifier, which converts alternating current (AC) into direct current (DC) using semiconductor devices like thyristors. Controlled rectifiers are widely used in power supplies, motor drives, HVDC transmission, and many other industrial applications.

In this document, we will discuss the calculation of key performance parameters—average DC output voltage (Vdc), RMS output voltage (Vrms), ripple factor, peak inverse voltage (PIV), and efficiency—for both single-phase and three-phase controlled rectifiers.

1. Basics of Controlled Rectifiers

A controlled rectifier is different from a diode rectifier because it uses a thyristor (SCR) instead of a diode. The SCR conducts only when it is forward-biased and triggered by a gate pulse. This makes it possible to control the output DC voltage by varying the firing angle (α).

  • Single-phase controlled rectifiers: used for low- and medium-power applications.
  • Three-phase controlled rectifiers: used for high power and high efficiency requirements.

2. Average DC Output Voltage (Vdc)

The average output voltage depends on the AC input, load type, and firing angle.

A. Single-Phase Half-Wave Controlled Rectifier (for a resistive load):
Vdc = (Vm / 2π) (1 + cosα), where Vm = √2 * Vrms.

B. Single-Phase Full-Wave (Bridge) Controlled Rectifier:
Vdc = (Vm / π) cosα.

C. Three-Phase Full-Wave Controlled Rectifier:
Vdc = (3√3 / π) Vm cosα.

Clearly, the three-phase rectifier gives a higher DC output and better voltage regulation.



3. RMS Output Voltage (Vrms)

The RMS value of the output voltage is important for determining the heating effect in the load.

A. Single-Phase Half-Wave Controlled Rectifier:
Vrms = Vm/2 √(1 - α/π + sin(2α)/(2π)).

B. Single-Phase Full-Wave Controlled Rectifier:
Vrms = Vm/√(2π) √(π - α + sin(2α)/2).

C. Three-Phase Controlled Rectifier: Derivation is more complex, but in general, Vrms is smoother compared to single-phase due to overlapping conduction.

4. Ripple Factor

The ripple factor (r) is a measure of how much of an AC component is present in the DC output.
r = √(Vrms² - Vdc²) / Vdc.

  • Lower ripple factor → better quality DC.
  • Single-phase rectifiers have higher ripple.
  • Three-phase rectifiers have lower ripple because of more frequent conduction intervals.

5. Peak Inverse Voltage (PIV)

The peak inverse voltage is the maximum voltage that a device must withstand when it is reverse-biased.

A. Single-Phase Half-Wave Rectifier:
PIV = Vm.

B. Single-Phase Full-Wave (Bridge) Rectifier:
PIV = Vm (for each diode/SCR in conduction).

C. Three-Phase Bridge Rectifier:
PIV = √3 Vm.

In high-voltage rectifiers, the PIV rating of devices becomes critical in selection.

6. Efficiency of Controlled Rectifiers 

The efficiency (η) is defined as:
η = (Pdc / Pac) × 100

where:

  • Pdc = Vdc × Idc
  • Pac is the total input power from the AC source.
Key points:
  • Efficiency depends on the firing angle (α).
  • For α = 0°, efficiency is maximum.
  • As α increases, output voltage decreases, reducing efficiency.
  • Three-phase rectifiers are more efficient than single-phase rectifiers because of reduced ripple and continuous conduction.

7. Comparison Table

Parameter

Single-Phase Rectifier

Three-Phase Rectifier

Vdc

Lower, depends on α

Higher, better control

Vrms

Higher ripple

Smoother output

Ripple Factor

Large

Small

PIV

Vm (bridge)

√3 Vm

Efficiency

Lower

Higher

8. Practical Applications

  • Single-Phase Controlled Rectifiers → battery chargers, domestic appliances, low-power supplies.
  • Three-Phase Controlled Rectifiers → industrial DC drives, HVDC systems, electrolysis, traction systems.
In real-world design, engineers carefully select firing angle, SCR ratings, and filtering circuits to achieve the required DC output with minimal losses.

Conclusion

The calculation of Vdc, Vrms, ripple factor, PIV, and efficiency is fundamental to understanding and designing controlled rectifiers. While single-phase rectifiers are simple and used for low-power applications, three-phase controlled rectifiers provide superior performance with higher output voltage, better efficiency, and lower ripple.

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