• Circuit Diagrams

• Waveforms

• Equivalent circuit diagram during commutation

1) Fig. 3(a) shows a three phase fully controlled converter with source inductance. For simplicity it has been assumed that the converter operates in the continuous conduction mode. Further, it has been assumed that the load current ripple is negligible and the load can be replaced by a dc current source the magnitude of which equals the average load current. Fig. 3(b) shows the corresponding waveforms

2) Current in the outgoing thyristor gradually decreases to zero while the incoming thyristor current increases and equals the total load current at the end of the overlap period.

3) Due to the conduction of two devices during commutation either from the top group or the bottom group the instantaneous output voltage during the overlap period drops (shown by the hatched portion of Fig. 3(b) resulting in reduced average voltage.

4) The exact amount of this reduction can be calculated as follows.

In the time interval α < ωt ≤ α + μ, T6 and T2 from the bottom group and T1 from the top group conducts. The equivalent circuit of the converter during this period is given by the circuit diagram of Fig. 3 ( c )

Therefore, in the interval α < ωt ≤ α + μ

$$ v_b=L\frac{di_b}{dt}-L\frac{di_c}{dt}+v_c \\ \; \\ or \ \ \ v_{bc}=L\frac{d}{dt}(i_b-i_c) \\ \; \\ But \ \ i+i_c+i_0=0 \ \ \ \therefore \frac{di_b}{dt}=-\frac{di_c}{dt} \\ \; \\ \therefore 2L\frac{d}{dt}i_b=v_{bc}=\sqrt2V_Lsinωt \\ \; \\ \therefore i_b=C-\frac{\sqrt2V_L}{2ωL}cosωt \\ \; \\ \therefore i_b=\frac{\sqrt2V_L}{2ωL}(cosα-cosωt)-I_0 \\ \; \\ at \ \ ωt=α+\mu,i_b=0 \\ \; \\ \frac{\sqrt2V_L}{2ωL}(cosα-cos(α+\mu))=I_0 \\ \; \\ or \ \ cosα-cos(α+\mu)=\frac{\sqrt2ωL}{V_L}I_0---eq(2) $$

Equation 2 holds for $\mu ≤ 60^0$ It can be shown that for this condition to be satisfied

Equation 3 suggests the same dc equivalent circuit for the three phase converter with source inductance as shown in Fig. 3 ( c) with OC L 3 2 V = V cosα π and commutation resistance C 3 R = ωL π . It should be noted that RC is a “loss less” resistance, since the overlap process does not involve any active power loss.

NOTE: Different 3-phase PWM techniques are as under follows

• Sinusoidal PWM

• Square wave operation

• State vector based