GATE Electrical Engineering (EE) 2019 Solved Paper

Question : 60 of 65

Marks: +1, -0

A delta-connected

3.7 {kW}, 400 {V}

(line), three-phase, 4 -pole, 50 -

{Hz}

squirrel -cage induction motor has the following equivalent circuit parameters per phase refereed to the stator:

{R}_{1}=5.39 Ω, {R}_{2}=5.72 Ω, {X}_{1}= {X}_{2}=8.22 Ω

Neglect shunt branch in the equivalent circuit. The starting line current in amperes (round off to two decimal places) when it is connected to a

100 {V}

(line),

10 {Hz}

, three-phase

{AC}

source is________.

Solution:

Given equivalent circuit parameters at

50 {Hz}, 400 {V}

(Line),

3 ϕ

, delta connected induction motor, reference to stator side

{R}_{1}=5.39 Ω, {R}_{2}=5.72 Ω

X_{1}=X_{2}=8.22 Ω

starting current at

100 {V}, 10 {Hz}

supply. Parameter which depends on frequency are

{X}_{1} \& {X}_{2}

. Therefore new value of

{X}, \& {X}

10 {Hz}

are.

{X}_{1 \;\text " new "\;}= {X}_{1 \;\text " old "\;} × \;{ {f}_{\;\text "new "\;}}/{ {f}_{\;\text "old "\;}}

=8.22 × \;{10}/{50}=1.644 Ω

{X}_{2 \;\text " new "\;}= {X}_{2 \;\text " new"\;} × \;{ {f}_{\;\text "new"\;}}/{ {f}_{\;\text "old "\;}}

=8.22 × \;{10}/{50}=1.644 Ω

{I}_{s t} {/} {ph}=\;{ {V}_{\;\text "ph(new) "\;}}/{√{( {R}_{1}+\;{ {R}_{2}}/{1})+( {X}_{1} new+ {X}_{2 new})}}

{I}_{ {s}} {/} {Ph} \;\; =\;{100}/{√{(5.39+5.72)^{2}+(1.644+1.644)^{2}}}

\;\; =\;{100}/{11.5863}

=8.63 {A}

I_{L}=√{3} I_{p u}=√{3} × 8.63

=14.94 {A}

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