A 150 kVA transformer 2400/240 V rating has the following parameters:
$R_{1} = 0.2\Omega$ , $R_{2} = 2\times 10^{-3}$
$X_{1} = 0.45\Omega$ , $X_{2} = 4.5 \times10^{-3}$
$R_{i} = 10 k\Omega$ , $X_{m} = 1.6 k\Omega$ (referred to HV)
Calculate the leakage inductances, magnetizing inductance, mutual inductance and self-inductances.

Question

A 150 kVA transformer 2400/240 V rating has the following parameters:
[latex]R_{1} = 0.2\Omega[/latex] , [latex]R_{2} = 2 imes 10^{-3}[/latex]
[latex]X_{1} = 0.45\Omega[/latex] , [latex]X_{2} = 4.5 imes10^{-3}[/latex]
[latex]R_{i} = 10 k\Omega[/latex] ,[latex]X_{m} = 1.6 k\Omega[/latex] (referred to HV) Calculate the leakage inductances, magnetizing inductance, mutual inductance and self-inductances.

Accepted Answer

[latex]a=\frac{N_{1} }{N_{2} } \approx \frac{2400}{240} =10[/latex]
[latex]X_{1} = 2 \pi fl_{1} ,l_{1}=\frac{0.45}{314} imes 10^{-3} = 0.01433[/latex] mH
[latex]X_{2}= 2 \pi fl_{2} ,l_{2}=\frac{4.5 imes 10^{-3} }{314} = 0.01433[/latex] mH
Magnetizing inductance
[latex]2 \pi fL_{m1}=X_{m} =1.6 imes 10^{3} [/latex]
[latex]L_{m1}=5.096[/latex] H
Self inductances
[latex]l_{1} =L_{1} -L_{m1}[/latex]
[latex]L_{1}=5.096 + 0.01433 imes 10^{–3} = 5.096[/latex] H
[latex]L_{m1}=aM,M=\frac{L_{m1}}{a} =\frac{5.096}{10}=0.5096[/latex] H
[latex]l_{2}=L_{2}-\frac{M}{a} [/latex]
[latex]L_{2}=l_{2}+ \frac{M}{a} = 0.01433 imes 10^{-3} + \frac{0 5096}{10} =0.05098[/latex] H
Coupling factor [latex]k=\frac{M}{\sqrt{L_{1} L_{2}} }= \frac{0.5096}{\sqrt{5.096 imes 0.05098} } =0.09998\simeq 1[/latex]

Question 3.30: A 150 kVA transformer 2400/240 V rating has the following pa...

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