GATE Electrical Engineering (EE) 2018 Solved Paper

Question : 65 of 65

Marks: +1, -0

A three-phase,

900 {kVA}, 3 {kV} {/} √{3} {kV}(∆ {/}{Y},) 50 {Hz}

, transformer has primary (high voltage side) resistance per phase of

0.3 Ω

and secondary (low voltage side) resistance per phase of

0.02 Ω

. Iron loss of the transformer is

10 {kW}

. The full load \% efficiency of the transformer operated at unity power factor is (upto 2 decimal places).

Solution:

900 kVA, Δ/Y, 3-phase transformer,

Given,

R_{1}=0.3 Ω{/} {ph}

R_{2}=0.02 Ω {/} {ph}

Phase voltage on delta (HV) side

=3 {kV}

Phase voltage on star (LV) side

=\;{√{3}}/{√{3}}=1 {kV}

Primary resistance referred to secondary

=(\;{1}/{3})^{2} × 0.3=0.033

Total resistance on secondary side

=0.033+0.02=0.0533

Full load phase current on secondary side

{I}=\;{900 × 10^{3}}/{√{3} × √{3} × 10^{3}}=300 {A}

Total copper loss or ohmic loss

=3 {I}^{2} {R}=3 × 300^{2} × 0.0533=14400 {W}=14.4 {kW}

Efficiency

η=\;{\;\text " output "\;}/{\;\text " output+losses "\;}

η=\;{900 × 1}/{900 × 1+14.4+10}=0.9736=97.36 \%

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