Three Phase Full Converter

Three Phase Full Converter

The figure above shows a full-wave converter circuit with the highly inductive load. This circuit is known as a three-phase bridge. A thyristor is fired at an interval of π/3.

At wt = π/6 + α, a thyristor T6 is already conducting and thyristor T1 is turned on. During interval (π/6 + α) ≤ (π/2 + α), thyristor T1 and T6 conduct and the line-to line voltage Vab(= Van - Vbn) appear across the load. At wt =(π/2 + α), a thyristor T2 is fired and thyristor T6 is reversed biased immediately. T6 is turned off due to natural commutation. During interval (π/2 + α) ≤ wt ≤ (5π/6 + α), thyristor T1 and T2 conduct and the line to line voltage Vac appears across the load. If thyristor is numbered as shown in the figure above, the firing sequence is 12,23,34,45,56, and 61.
The line to neutral voltages are defined as below:
Van = Vm sin(wt)
Vbn = Vm sin(wt - 2 π/3)
Vcn = Vm sin(wt + 2 π/3)

The line to line voltages are calculated as:
Vab = Van - Vbn = √3 Vm sin(wt+π/6 )
Vbc = Vbn – Vcn = √3 Vm sin(wt-π/2 )
Vca = Vcn – Van = √3 Vm sin(wt+π/2 )

Important points
One rectifier has the conducting agnle of 120^o.
If α = 60 degrees, the wave is delayed by one pulse.
If 60^o< α<120^o, the wave is discontinuous.
If α = 120^o, there is no result.

The average output is calculated as:

$$\eqalign{
& Vdc\,\,\, = {3 \over \pi }\int\limits_{\pi /3 + \alpha }^{\pi /2 + \alpha } {{\rm{Vab}}} \;\;d(\omega t) \cr
& \,\,\,\,\,\,\,\,\,\, = {3 \over \pi }\int\limits_{\pi /3 + \alpha }^{\pi /2 + \alpha } {\sqrt 3 \,{\rm{Vm}}} \;Sin(\omega t\, + {\pi \over 6})\;d(\omega t) \cr
& \;\;\;\;\;\; = \;{{3\sqrt 3 {\rm{V}}m} \over {2\pi }}\cos \alpha \cr} $$

The rms value is calculated as:$$\eqalign{
& Vrms\,\,\, = {\left[ {{3 \over \pi }\int\limits_{\pi /3 + \alpha }^{\pi /2 + \alpha } {{\rm{Va}}{{\rm{b}}^2}} \;\;d(\omega t)} \right]^{1/2}} \cr
& \,\,\,\,\,\,\,\,\,\, = {\left[ {{3 \over \pi }\int\limits_{\pi /3 + \alpha }^{\pi /2 + \alpha } {3\,V_m^2} \;Si{n^2}(\omega t\, + {\pi \over 6})d(\omega t)} \right]^{1/2}} \cr
& \;\;\;\;\;\; = \;\sqrt 3 {\rm{V}}m{({1 \over 2} + {{3\sqrt 3 } \over {4\pi }}cos2\alpha )^{1/2}} \cr} $$

And finally, a brief insight into the gating sequence

• A gate signal is generated at the positive zero crossing of the phase voltage V_an and delay the pulse by the desired angle α + π/6 and apply it to the gate and cathode terminals of T1 through isolation circuit(May be opto-coupler or transformer based )
• Again generate five more pulses each delayed by π/3 for gating of the other five thyristors, through gate isolating circuit.

REFERENCES

1) H.Rashid, M. (2013). THREE PHASE FULL CONVERTER. India: PEARSON PUBLICATION.

Information from class notes and handouts provided by my subject teacher have also been used.