Three Phase Bridge Rectification with Diodes and the Fourier Analysis of waveforms

Three Phase Bridge Rectifier With Diodes

Let V₁,V₂ and V₃be the three phase voltage waveforms which is fed to the three phase Bridge Rectifier.V₁ = V_max * Cos(wt); V₂ = V_max * Cos(wt – 120^o); V₃ = V_max * Cos(wt – 240^o)

The waveform of these voltages on per unit system(where V_max is considered base of voltage) is traced below :

In each time point, two diodes of the diode bridge conducts ,the first conducting diode is from the group of odd-indexed diodes { D5,D3,D1, }, and it is connected by its anode to the highest of the phase voltages at the time point considered. The second conducting diode is from the group of even-indexed diodes {D6,D4,D2} and it is connected by its cathode to the lowest of the phase voltages. Since, one voltage cannot be highest and lowest at the same time. Thus, two of the phases are connected to the load at a time while one remaining phase voltage remains unconnected.

Now, the function of the greatest voltage and smallest voltage among three phase voltages are created.

V_A = max(V₁,V₂,V₃)

And

For the minimum voltage,

V_B = min(V₁,V₂,V₃)

Depending upon whether V₁ ,V₂ or V₃ is greatest among the three phase voltage supply, one of the odd-indexed diode conducts and in the same way, depending upon whether V₁,V₂ or V₃ is lowest among the three phase voltage supply, one of the even-indexed diode conducts. So, at a time two diodes conduct, one odd-indexed diode from upper half and another even-indexed diode from the lower half of the circuit diagram.So, at a time only two supply voltage remains in conduction completing the current flow through the load in the circuit.

Tracing V_A and V_B in the graph, we get[Note V_A and V_B represent the maximum and minimum voltage among all the three input voltage supply]

For the maximum voltage among three input voltage supply, three phase voltages are compared at 0^o and we get, V₁ is maximum among all the three input voltages. And it will be maximum up to 60^owhich can be verified by the figure of the three phase voltage above. Again,in the same way, V₂ will be maximum from 60^o to 180^o and V₃ will be maximum from 180^o to 300^o.So, based on this concept V_A/V_max is traced. By following same steps mentioned above, one can trace the waveform for V_B in p.u.

Now, the voltage across the load is the difference between V_A and V_B .So, the output voltage will be V_o = V_A - V_B. And when the output waveform for V_o is traced, the following output waveform is obtained.

And the conduction scheme of the diode for the output waveform is provided below.

From the output waveform, we found that it is maximum at 30 degrees and the waveform is symmetrical. For the calculation of the maximum output value which occurs at 30^o:

Vo = V_A- V_B{Refer above what V_A and V_B means]
= V₁ – V₃
= Vm Cos(wt) – Vm Cos(wt – 240^o)

Subsituting the value of wt = 30^o, we get
=√3 Vm

The value of output waveform will be maximum at 90 degrees, 150 degrees, and so-on..[U can verify it urself at 90o by following conduction table and above procedure of calculation).

Now for the Average D.C voltage,

$$\eqalign{
& Vdc = {3 \over \pi }\int\limits_0^{\pi /3} ( \;Vm{\rm{ }}Cos\left( {wt} \right) - Vm{\rm{ }}Cos\left( {wt - 240} \right)){\rm{ }}d(\omega t) \cr
& \;\;\;\;\; = \;{{3\sqrt 3 } \over \pi }Vm \cr} $$
So, this is the d.c value of the output waveform of the three phase bridge rectifier for diode.

References

1)Springer. "Three Phase Diode Rectifier." n.d. Springer. 016 05 2016. <http://www.springer.com/cda/content/document/cda_downloaddocument/9780387293103-c1.pdf?SGWID=0-0-45-396734-p107950590>.

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