SOLUTION

The three-phase semi-converter is shown in the figure. The thyristor T₁ receives the gate pulse and conducts from (30° + α) to 150°, thyristor T₂ will conduct from (150° + α) to 270°, and thyristor T₃ conducts from (270° + α) to 390°.

The semi-converter bridge operation for different angles is shown in the form of voltage and current waveforms, and its conduction angles for the SCRs, diodes and freewheeling diode are also shown in Fig(a). For the firing angle α = 0, T₁, T₂ and T₃ would behave as diodes, and the voltage of semi-converters would be asymmetrical six-pulse for each cycle as shown in Fig. (a). The output voltage consists of pulses V_ab, V_ac, V_bc, etc. as shown in Fig. The triggering of the thyristors T₁, T₂ and T₃ are delayed but return diodes D₁, D₂ and D₃ remain unaffected so that alternate pulses are altered. The load current is continuous and has a little ripple. The forward diode does not come into play for α = 15°, and each SCR and diode conducts for 120°.

In Fig. V_Cb is the load voltage from  = 0° to 60°, as the first subscript indicates conduction in the positive group, voltage V_Cb, that T₃ is already conducting through diode D₂ of the negative group. Voltages V_ab and V_ac, according to the first subscript, conduct for 120° and begin to conduct at ωt = 60° for α = 0 as shown in Fig. Similarly, V_bc and V_ca indicate that T₂ conducts for 120° and it begins to conduct at ωt = 180° for α = 0. The thyristor with α = 0 behaves like a simple diode; therefore the thyristor T₁ conducts for ωt = 60°, ωt = 180° for T₂, ωt = 300° for thyristor T₃, and so on. 

For ωt = 60° as shown in waveform the thyristors are triggered so that the current returns through one diode for each conduction period of 120° for voltage V_ac. T₁ and D₃ conduct simultaneously for 120° as shown in Fig.c. The situation is similar for the other elements. The freewheeling diode doesn’t exist for its conduction even for α = 60°; therefore, the voltage pulses V_ab, V_bc, and V_ca do not appear in the output waveforms. For α = 60°, therefore, the load current is assumed to continue for α = 60°.

For firing angle ωt = 90°, output voltage V_O is discontinuous. As V_O tends to become negative at ωt = 120°, 240°, 360°, the freewheeling diode (FD) gets forward-biased there for each periodic cycle of 120°. The output voltage is equal to the supply voltage. When FD conducts, V_O = 0 for α = 90°, the conduction angle of SCR and diodes is seen to be less than 120° for every output pulse. Voltage pulses V_ab, V_bc, and V_ca provide output voltage V_O for this firing angle as well. Without a freewheeling diode, after load voltage V_O reaches zero, a diode from the negative group would become conducting, reducing V_O to zero till the next thyristor from the negative group starts conducting.

Conclusion:-  A freewheeling diode is added across the load to conduct the load current during the negative half cycle and prevent it from being reduced to zero. Since in 3-phase semi converter conduct for 120° therefore till firing angle “α” 60° the freewheeling diode will not work.