"Power Electronics & Drives : AC to DC Converters

**Phase Control Rectifier**

Phase Control Rectifiers can be classified as Single Phase Rectifier and **3 Phase Rectifier**. Further Single phase rectifier is classified as 1-Փ half-wave and 1-Փ full-wave rectifier, In a similar manner, 3 phase rectifier is classified as 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**, then the following terms, characterizing the properties of “f”, can be defined.

**RMS (effective)**value of f**(f**: For f , periodic over the time period T_{RMS})**,**

**Form factor of f (f**Form factor of ‘f' is defined as_{FF}) :

**Ripple factor of f (f**Ripple factor of f is defined as_{RF}):

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

**Peak to peak ripple of (f _{pp}): By definition **

**Fundamental component of f (F**It is the RMS value of the sinusoidal component in the Fourier series expression of f with frequency 1/T_{1}):**.**

**Kth harmonic component**of**f (F**It is the RMS value of the sinusoidal component in the Fourier series expression of f with frequency K/T._{K}):

**Crest factor**of**f**(**C**): By definition_{f}

**Distortion factor**of f**(D.F**: By definition ⇒ DF_{f})_{f}= F_{1}/F_{RMS}**Total Harmonic Distortion**of f (**THD**): The amount of distortion in the waveform of f is quantified by means of the index Total Harmonic Distortion (THD)._{f}

**Displacement Factor**of a Rectifier (**DPF**): If**v**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._{i}

**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**respectively then

_{i} If the rectifier is supplied from an ideal sinusoidal voltage source then ⇒ Vi_{1 }= 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 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 the load. In this section, operation of this rectifier with resistive, inductive and capacitive loads will be discussed.

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**

**i _{1}= i_{o} =0**

**v _{0} = i_{0}R = 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**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 inductor and put 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 semiconverter

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

**Three-Phase Rectifier**

As the application Point of view **Three-phase controlled rectifiers** have a wide range of applications, from small rectifiers to large High Voltage Direct Current (HVDC) transmission systems. They are used for electro-chemical process, many kinds of motor drives, traction equipment, controlled power supplies, and many other applications.

From the point of view of the commutation process, they can be classified in two important categories: Line Commutated Controlled Rectifiers (Thyristor Rectifiers), and Force Commutated PWM Rectifiers.

The 3-Phase Controlled rectifier provide a maximum dc output of "

**V**the output ripple frequency is equal to the twice the ac supply frequency._{dc(max)}=2V_{m/∏}"

**Three-Phase Diode Rectifier**

The circuit shown in the given figure by using 6 diodes Named as three phase Rectifier. It shows the AC side currents and DC side voltage for the case of high load inductance.

we see that on the AC side, the RMS current, **I _{s} **will be

while the fundamental current, i.e. the current at power frequency is:

Again, inductance on the AC side will delay commutation, causing a voltage loss, i.e. the DC voltage will be less than that predicted by equation Vd_{o}.

** Waveforms of a three-phase full-wave rectifier with diodes and inductive load**

**Three Phase Half Controlled Rectifier**

In the given figure below shows the circuit diagram of three phase half controlled converter supplying an **R-L-E load**. In the continuous conduction mode only one thyristor from top group and only one diode from the bottom group conduct at a time. However, unlike fully controlled converter here both devices from the same phase leg can conduct at the same time. Hence, there are nine conducting modes as shown in Figure.

**3- Phase Full Controlled Rectifier**

In **3-phase full controlled rectifier** **6 thyristors** are needed to accommodate three phases. In the given figure below shows the schematic of the system, and Figureshows the output voltage waveforms.

Output Waveform for 3-Phase Full Controlled Rectifier

- The delay angle α is again measured from the point that a thyristor becomes forward biased, but in this case the point is at the intersection of the voltage waveforms of two different phases. The voltage on the DC side is then (the subscript o here again meaning Ls = 0).

which leads to

Is_{1} = 0.78 I_{d}

and the relationship between V_{do} and V_{dα}

**V _{dα} = V_{do} Cos(α)**

- Again, if the delay angle α is extended beyond 90º,the converter transfers power from the DC side to the AC side, becoming an inverter. We should keep in mind, though that even in this case the converter is drawing reactive power from the AC side.
- For both 1-phase and 3-phase controlled rectifiers, a delay in α creates a phase displacement of the phase current with respect to the phase voltage, equal to α. The cosine of this angle is the power factor of the fundamental harmonic.

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