**Three-phase full-wave Controlled Rectifier with highly inductive load (Continuous load current)**

__Average Load/Output Voltage__

*V*

_{m}peak phase voltage*V rms phase voltage*

**Three-phase full-wave Controlled Rectifier with highly inductive load**

Voltage and current waveforms of a three-phase full converter with a highly inductive load is shown in figure. This converter provides two quadrant operation and thyristors are fired at an interval of π/3 degrees. Since thyristors are fired every 60°, the frequency of the output ripple voltage is six times the frequency of the supply voltage. At ωt = π /6 + α, thyristor S

_{6}is already conducting and thyristor S_{1}is turned on. For the interval ωt of π/6 to π/2 thyristors S_{1}and S_{6}conduct, and line to line voltage v_{ab}appears across the load. At ωt = π /2 + α, thyristor S_{2}is turned on and thyristor S_{6}is turned off due to natural commutation. This occurs because when thyristor S_{2}is turned on, the line to line voltage across thyristor S_{6}is the positive voltage v_{bc}from cathode to anode which reverse biases thyristor S_{6}. During the interval ωt of (π /2 + α) (5 π /6 + α), thyristors S_{1}and S_{2}conduct and line to line voltage appears across the load. The firing sequence of the thyristors is: 12, 23, 34, 45, 56 and 61.
The average output voltage is given by

The maximum output dc voltage is given by

The rms output voltage is given by

**Three-phase Converter Output Characteristics for continuous load current (Full Converter)**

For fully controlled rectifier, The DC Motor operates in two modes.

Rectification [As Motoring]

VInversion [As Regenerative Braking]_{0}= positive

E_{a}= Positive

I_{o}= positive

Power Flow (+ve) from input AC to DC machine

V_{0}= negative

E_{a}= negative

I_{o}= positive

Power Flow (-ve) from DC machine to AC supply

**Thyristor based Rectifiers (3-phase)**

E

_{d}becomes smaller as α increases, but still each thyristor conducts 120 deg. Power flow is from AC side to DC side. I_{d}=(E_{d}-E_{0})/R**Thyristor based Line Commutated Inverter (3-phase)**

I

_{d}=(E

_{o}-E

_{d})/R, real power flow is from DC to AC side, Polarity of E

_{d}is reversed.

**Triggering range:**

Rectifier 15°-90°, inverter: 90°-165°. Thyristor may misfire for α less than 15° (def. 8°) for sudden change in line voltage and hence discontinuity in output current. If we go beyond 165°, the inverter may lose its ability to switch from one thyristor to the next. As a result currents build up very quickly until the CB trips. For safety margin max α is 150°.

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**Three-phase half-wave Controlled Rectifier**
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**THREE-PHASE DUAL CONVERTER**
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