GATE Electrical Engineering (EE) 2020 Solved Paper

Question : 44 of 65

Marks: +1, -0

A single-phase, full-bridge, fully controlled thyristor rectifier feeds a load comprising a 10

Ω

resistance in series with a very large inductance. The rectifier is fed from an ideal

230 {V}

50 {Hz}

sinusoidal source through cables which have negligible internal resistance and a total inductance of

2.28 {mH}

. If the thyristors are triggered at an angle

{a}=45^{∘}

, the commutation overlap angle in degree (rounded off to 2 decimal places) is

Solution:

v_{0}=\;{1}/{π} ∫↙{α+µ}↖{(π+α)} V_{m} \sin ω t d ω t

=\;{V_{m}}/{π}[\cos α+\cos (α+µ)]

I_{0}=\;{V_{0}}/{R}=\;{V_{m}}/{π R}[\cos α+\cos (α+µ)]

........(1)

\;\text " from a to "\;(a+µ)

L_{s} \;{d i}/{d t}=V_{m} \sin ω t

∫↙{-I_{0}}^{I_{0}} d i=\;{V_{m}}/{ω L_{s}}[-\cos ω t]_{α}^{(α+µ)}

2 I_{0}=\;{V_{m}}/{ω L_{s}}[\cos α-\cos (α+µ)]

{I}_{0}=\;{ {V}_{ {m}}}/{2 ω {L}_{5}}[\cos α-\cos (α+µ)]

..... (ii)
from eqn. (i) & eqn. (ii)

\;{ {V}_{ {m}}}/{π R}[\cos α+\cos (α+µ)]=\;{ {V}_{ {m}}}/{2 ω {L}_{ {s}}}[\cos α-\cos (α-µ)]

\;{V_{m}}/{π R}[\cos α+\cos (α+µ)]=\;{V_{m}}/{2 ω L_{s}}[\cos α-\cos (α+µ)]

\;{2 ω L_{s}}/{π R}[\cos α+\cos (α+µ)]=[\cos α-\cos (α+µ)]

\cos α[1-\;{2 ω {L}_{s}}/{π R}]=\cos (α+µ)[1+\;{2 ω L_{s}}/{π R}]

\cos (α+µ)=\;{\cos α[1-{2 ω L_{s}}/{π R}]}/{(1+\;{2 ω L_{s}}/{π R})}

\cos (45^{∘}+µ)=\;{1}/{√{2}}(\;{1-0.0456}/{1+0.0456})

=\;{1}/{√{2}}(\;{0.9544}/{1.0456})

\cos (45^{∘}+µ)=0.6454

45^{∘}+µ=49.804

µ=4.804^{∘}

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