A 220 {V} (line), three-phase, Y-connected, synchronous motor has a synchronous impedance of (0.25+ {j} 2.5) Ω phase. The motor draws the rated current of 10 {A} at 0.8 {pf} leading. The rms value of line-to-line internal voltage in volts (round off to two decimal places) is__________________.

GATE Electrical Engineering (EE) 2019 Solved Paper

Question : 56 of 65

Marks: +1, -0

220 {V}

(line), three-phase, Y-connected, synchronous motor has a synchronous impedance of

(0.25+ {j} 2.5) Ω

phase. The motor draws the rated current of

10 {A}

0.8 {pf}

leading. The rms value of line-to-line internal voltage in volts (round off to two decimal places) is__________________.

Solution:

{V}_{ {L}}=220 {V} ⇒ {V}_{ {p}}=\;{220}/{√{3}}=127.01 . {V}

{Z}_{ {s}}=0.25+ {j} 2.5 {W}=2.512 ∠ 84.28^{∘} ; {I}_{a}=10 {A}, 0.8 {lead} {pf}

E_{\;\text "ph "\;}=√{(V \cos φ-I_{a} R_{a})^{2}+(V \sin φ+I_{a} X_{a})^{2}}

=√{(127.01 × 0.8-10 × 0.25)^{2}+(127.01 × 0.6+10 × 2.5)^{2}}

=141.64 {V}

{E}_{ {L}}=√{3} × E_{ {pt}}=√{3} × 141.64=245.32 {V}

Method 2:

{E}_{ {ph}}= {V} ∠ 0- {I}_{ {a}} ∠ ϕ {Z}_{ {s}} ∠ θ

=127.0 .1 ∠ 0-10 ∠ 36.86 × 2.512 ∠ 84.28^{∘}

=141.64 ∠-8.71^{∘}

{E}_{ {L}}=√{3} × 141.64=245.32 {V}

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