GATE Electrical Engineering (EE) 2021 Solved Papers

Question : 50 of 65

Marks: +1, -0

Suppose

{I}_{ {A}}, {I}_{ {B}}

and

{I}_{ {C}}

are a set of unbalanced current phasors in a three-phase system. The phase

{B}

zero-sequence current

{I}_{ {B} 0}=0.1 ∠ 0^{∘}

p.u. If phase

{A}

current

{I}_{ {A}}=1.1 ∠ 0^{∘}

p.u. and phase

{C}

current

{I}_{ {C}}=(1<120^{∘}+0.1)

p.u., then

{I}_{ {B}}

in p.u. is

Solution:

Facilitate per phase analysis of a complex 3-phase unbalanced system.
Given

{I}_{ {B} 0}=0.1 ∠ 0^{∘}

p.u.

=0.1

{I}_{ {A}}=1.1 ∠ 0^{∘}

p.u.

=1.1

{I}_{ {C}}=1 ∠ 120^{∘}+0.1

p.u.

{I}_{ {B}}=?

[\table I_{A 0} ; I_{A 1} ; I_{A 2}]=\;{1}/{3}[\table 1 , 1 , 1 ; 1 , α , α^{2} ; 1 , α^{2} , α][\table I_{A} ; I_{B} ; I_{C}]

I_{B 0}=I_{A 0}=\;{1}/{3}(I_{A}+I_{B}+I_{C})

α=1 ∠ 120^{∘}, α^{2}=1 ∠ 240^{∘}

I_{A 0}=I_{C 0}

( Cophesal )

{I}_{ {B}}=0.1+1 ∠ 240^{∘}

p.u.

I_{B 0}=\;{1}/{3}(I_{A}+I_{B}+I_{C})

{I}_{ {B}}=3 {I}_{ {B} 0}- {I}_{ {A}}- {I}_{ {C}}=3 × 0.1-1.1-1 ∠ 120^{∘}-0.1=0.3-1.1-0.1-1 ∠ 120^{∘}

=-0.9-1 ∠ 120^{∘}=-0.9-(-\;{1}/{2}+j \;{√{3}}/{2})

{I}_{ {B}}=-0.9+0.5- {j} \;{√{3}}/{2}=-0.4- {j} \;{√{3}}/{2}=0.4+0.5+[-\;{1}/{2}- {j} \;{√{3}}/{2}]=0.1+1 ∠ 240^{∘}

0.1+1 ∠-120^{∘}

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