4. PHASE CONTROLLED RECTIFIERS

For 4th Semester Polytechnic EE Students
Written by Garima Kanwar | Blog: Rajasthan Polytechnic

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Course Code EE 4001
Course Title Fundamentals of Power Electronics

4. Phase Controlled Rectifiers

Phase Controlled Rectifiers are widely used in power electronics for converting AC (alternating current) to DC (direct current) with controlled output. They offer flexibility in controlling the average DC voltage by adjusting the firing angle of the thyristors or SCRs (Silicon Controlled Rectifiers). These rectifiers are commonly used in applications such as DC motor control, power supplies, and HVDC (High Voltage Direct Current) transmission.

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4.1 Phase Control: Firing Angle, Conduction Angle

• Firing Angle (α):
  • The firing angle (α) is the angle at which the SCR or thyristor is triggered in the AC cycle.
  • It is measured from the point where the AC voltage waveform crosses zero, and the SCR is fired at this particular angle.
  • Range: The firing angle can vary from 0° to 180° in a half-controlled rectifier or 0° to 360° in a fully controlled rectifier.
• Conduction Angle (θ):
  • The conduction angle is the interval during which the SCR remains in the conducting state, i.e., the time period when current flows through the SCR.
  • It depends on the firing angle and the load characteristics.
  • It is related to the firing angle and typically ranges between 0° to 180°.

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4.2 Circuit Diagram, Working, Input-Output Waveforms, Equations for DC Output, and Effect of Freewheeling Diode

Now let’s look at different types of phase-controlled rectifiers: Single-phase half-controlled, full-controlled, and midpoint-controlled with R and RL loads.

4.2.1 Single-Phase Half-Controlled Rectifier

A half-controlled rectifier uses one SCR (for controlled conduction) and one diode (for free conduction). It is also called a half-wave controlled rectifier.

Circuit Diagram:

 AC Input (V) ---> [SCR] ---> Load (R or RL) ---> [Diode] ---> AC Source

Working Principle:

• When the firing angle (α) is 0°, the SCR is triggered at the start of the AC cycle and conducts for the entire half-cycle.
• If the firing angle is increased (greater than 0°), the SCR turns on at a later point in the cycle, thus reducing the conduction time.

Input-Output Waveforms:

• Input AC waveform: A sinusoidal waveform with frequency $f$.
• Output DC waveform: The output will have a pulsating DC waveform with gaps where the SCR is off.

Equations for DC Output:

1. Average DC Output Voltage (V_dc):

   $$V_{dc} = \frac{V_m}{\pi} \left( 1 + \cos(\alpha) \right)$$
   

   where $V_m$ is the peak value of the input AC voltage, and $\alpha$ is the firing angle.

2. RMS Output Voltage (V_rms):

   $$V_{rms} = \frac{V_m}{2} \sqrt{1 + \cos^2(\alpha)}$$

Effect of Freewheeling Diode:

• A freewheeling diode is used to provide a path for the current when the SCR is off (during the negative half-cycle). It helps smooth the output by preventing sudden current changes, reducing the ripple in the DC output.

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4.2.2 Full-Controlled Rectifier

A full-controlled rectifier uses two SCRs for both positive and negative half-cycles of the AC input. It allows full control over the entire AC cycle.

Circuit Diagram:

 AC Input (V) ---> [SCR1] ---> Load (R or RL) ---> [SCR2] ---> AC Source

Working Principle:

• During the positive half-cycle, SCR1 is triggered, allowing current to flow through the load.
• During the negative half-cycle, SCR2 is triggered, allowing current to flow in the opposite direction through the load.
• The firing angle (α) determines when each SCR turns on in the cycle, thus controlling the average DC voltage output.

Input-Output Waveforms:

• Input AC waveform: A sinusoidal waveform with frequency $f$.
• Output DC waveform: The output is a smooth DC waveform, but it can still have some ripple based on the load.

Equations for DC Output:

1. Average DC Output Voltage (V_dc):

   $$V_{dc}=\frac{2V_m}{\pi }(1+\cos (\alpha ))$$

   where $V_m$ is the peak input AC voltage, and $\alpha$ is the firing angle.

2. RMS Output Voltage (V_rms):

   $$V_{rms}=\frac{V_m}{2}\sqrt{2+{\cos }^2(\alpha )}$$

Effect of Freewheeling Diode:

• Freewheeling Diode: It is often used in a full-controlled rectifier to smooth out the pulsating DC output and provide a path for current during the off periods of both SCRs.

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4.2.3 Midpoint-Controlled Rectifier with R and RL Load

A midpoint-controlled rectifier is a type of full-controlled rectifier where two SCRs are connected in a center-tapped transformer configuration. It is often used for higher power applications.

Circuit Diagram:

          V_m
           |
       [SCR1] ---> Load (R or RL) ---> [SCR2]
           |                           |
           ------------------------ Ground

Working Principle:

• The two SCRs are connected to a center-tapped transformer.
• SCR1 is triggered during the positive half-cycle, while SCR2 is triggered during the negative half-cycle of the AC input.
• The firing angle (α) is used to control when each SCR is triggered during the AC cycle, thus controlling the output voltage.

Input-Output Waveforms:

• Input AC waveform: A sinusoidal waveform with frequency $f$.
• Output DC waveform: The output is a smooth DC waveform, and the ripple can be reduced with a freewheeling diode.

Equations for DC Output:

1. Average DC Output Voltage (V_dc):

   $$V_{dc} = \frac{2V_m}{\pi} \left( 1 + \cos(\alpha) \right)$$
   

2. RMS Output Voltage (V_rms):

   $$V_{rms} = \frac{V_m}{\sqrt{2}} \sqrt{1 + \cos^2(\alpha)}$$

Effect of Freewheeling Diode:

• A freewheeling diode reduces the ripple in the DC output by providing a path for current when both SCRs are off.

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Conclusion:

Phase-controlled rectifiers are essential for controlling the output DC voltage from an AC supply. By adjusting the firing angle (α) of the SCRs, we can control the average DC voltage and the conduction time. The use of freewheeling diodes helps smooth out the pulsating DC and reduces ripple. The different configurations, such as half-controlled, full-controlled, and midpoint-controlled rectifiers, offer flexibility in different applications based on the load type (R, RL).

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Important Questions to Practice:

1. Explain the working of a single-phase half-controlled rectifier with an R load.
2. Derive the equations for DC output voltage in a full-controlled rectifier.
3. How does a freewheeling diode affect the output in a rectifier?
4. Compare the working and output of a half-controlled rectifier and a full-controlled rectifier.
5. Explain the construction and working of a midpoint-controlled rectifier.
6. How do you calculate the average DC output voltage for phase-controlled rectifiers?
7. What is the effect of varying the firing angle on the DC output voltage in a phase-controlled rectifier?

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