Phase Control Rectifier-1 notes for GATE EE 2024 Exam

Phase Control Rectifier

Phase Control Rectifiers can be classified as Single Phase Rectifier and 3 Phase Rectifier. Further Single phase rectifier is classified as a 1-Փ half-wave and 1-Փ full-wave rectifier, In a similar manner, 3 phase rectifier is classified as a 3-Փ half-wave rectifier & 3-Փ full-wave rectifier.

• 1-Փ Full wave rectifier is classified as 1-Փ mid point type and 1-Փ bridge-type rectifier.
• 1-Փ bridge type rectifier is classified as 1-Փ half controlled and 1-Փ full controlled rectifier.
• 3-Փ full wave rectifier is again classified as 3-Փ mid point type and 3-Փ bridge-type rectifier.
• 3-Փ bridge type rectifier is again divided as 3-Փ half controlled rectifier and 3-Փ full controlled rectifier.

Important Terminologies Related to Phase-Controlled Rectifiers 

There are certain terms that are frequently used in the study of Phase Controlled rectifiers, here we have listed the terminologies related to Phase COntrolled Rectifiers. Let “f” be the instantaneous value of any voltage or current associated with a rectifier circuit, and then the following terms, characterizing the properties of “f”, can be defined.

• RMS (effective) value of f (f_RMS): For f, periodic over the time period T,

• The form factor of f (f_FF): The form factor of ‘f' is defined as 

• Ripple factor of f (f_RF): Ripple factor of f is defined as

Note: Ripple factor can be used as a measure of the deviation of the output voltage and current of a rectifier from the ideal dc. 

Peak to peak ripple of (f_pp): By definition 

• A fundamental component of f (F₁): It is the RMS value of the sinusoidal component in the Fourier series expression of f with frequency 1/T.

• Kth harmonic component of f (F_K): It is the RMS value of the sinusoidal component in the Fourier series expression of f with frequency K/T.

• Crest factor of f (C_f): By definition

• Distortion factor of f (D.F_f): By definition ⇒ DF_f = F₁/F_RMS
• Total Harmonic Distortion of f (THD_f): The amount of distortion in the waveform of f is quantified by means of the index Total Harmonic Distortion (THD). 

• Displacement Factor of a Rectifier (DPF): If v_i and i_i are the per phase input voltage and input current of a rectifier respectively, then the Displacement Factor of a rectifier is defined as.

DPF = Cos φ_i

       Where φ_i is the phase angle between the fundamental components of v_i and i_i.

• Power factor of a rectifier (PF): As for any other equipment, the definition of the power factor of a rectifier is

       if the per-phase input voltage and current of a rectifier are v_i and i_i respectively then

     If the rectifier is supplied from an ideal sinusoidal voltage source then ⇒ Vi₁ = V_iRMS

In terms of THD_ii  

• Firing angle of a rectifier (α): Used in connection with a controlled rectifier using thyristors. It refers to the time interval from the instant a thyristor is forward-biased to the instant when a gate pulse is actually applied to it. 
• Extinction angle of a rectifier (γ): Also used in connection with a controlled rectifier. It refers to the time interval from the instant when the current through an outgoing thyristor becomes zero (and a negative voltage is applied across it) to the instant when a positive voltage is reapplied. It is expressed in radians by multiplying the time interval with the input supply frequency (ω) in rad/sec. The extinction time (γ/ω) should be larger than the turn-off time of the thyristor to avoid commutation failure.
• Overlap angle of a rectifier (μ): The commutation process in a practical rectifier is not instantaneous. During the period of commutation, both the incoming and the outgoing devices conduct current simultaneously. This period, expressed in radians, is called the overlap angle “μ” of a rectifier. It is easily verified that α + μ + γ = π radian.

Single-phase uncontrolled half-wave rectifier

This is the simplest and probably the most widely used rectifier circuit albeit at relatively small power levels. The output voltage and current of this rectifier are strongly influenced by the type of load. In this section, the operation of this rectifier with resistive, inductive and capacitive loads will be discussed.

The circuit diagram and the waveforms of a single-phase uncontrolled half-wave rectifier are shown above in the figure. If the switch S is closed at t = 0, the diode D becomes forward biased in the interval 0 < ωt ≤ π. If the diode is assumed to be ideal then

For 0 < ωt ≤ π

v_o = v_i = √2 V_i sin ωt  & v_D = v_i – v_o = 0 

Since the load is resistive

For ωt>π, _vi becomes negative and D becomes reverse biased. So in the interval π < ωt ≤ 2π

i₁= i_o =0

v₀ = i₀R = 0

v_D= v_i-v_o = v_i = √2 V_i sin wt

From these relationships

Single Phase Uncontrolled Half Wave Rectifier with R-L load

From the preceding discussion

For 0 ≤ ωt ≤ β

v_D=0

v_o= v_i.i_o = i_i

For β ≤ ωt ≤ 2π

v_o =0

i_o = i_i = 0

v_D = v_i–v_o=v_i

Single phase half wave Controlled Rectifier with R-L load

 Single Phase-Controlled Rectifier (firing angle α)

•  So with a phase-controlled converter, we can regulate the output voltage by varying the firing angle α. We can even cause power flow from dc-side to ac-side as long as I_d>0 (e.g., pull power out of the inductor and put it into line).
• In a semi-controlled rectifier, control is affected only for positive output voltage, and no control is possible when its output voltage tends to become negative since it is clamped at zero volts.
• For a Resistive load the output of the semi converter

• The Output of Full Wave Rectifier with R-L-E load 

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