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Question

For the 4-bus system, containing transmission lines and transformers. The admittance matrix is Ybus=⎢ ⎢ ⎢ ⎢j20j2000j20j60j4000j40j60j2000j20j25⎥ ⎥ ⎥ ⎥

If a transmission line having π-equivalent circuit as shown below is connected between 2nd and 4th buses. Then the modified Ybus matrix will be


Where, Zse = series impedance of transmission line.

Ysh= shunt admittance of transmission line.

A
Ybus=⎢ ⎢ ⎢ ⎢j20j2000j20j50j4000j40j60j2000j20j15⎥ ⎥ ⎥ ⎥
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B
Ybus=⎢ ⎢ ⎢ ⎢j20j2000j20j50j4000j40j60j200j20j20j15⎥ ⎥ ⎥ ⎥
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C
Ybus=⎢ ⎢ ⎢ ⎢j20j2000j20j50j40j200j40j60j200j20j20j15⎥ ⎥ ⎥ ⎥
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D
Ybus=⎢ ⎢ ⎢ ⎢j20j2000j20j40j40j200j40j60j200j20j20j5⎥ ⎥ ⎥ ⎥
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Solution

The correct option is C Ybus=⎢ ⎢ ⎢ ⎢j20j2000j20j50j40j200j40j60j200j20j20j15⎥ ⎥ ⎥ ⎥
Only Y22,Y24,Y42,Y44 will change because transmission line is connected between 2nd and 4th buses.

Y22=j60+1Zse+Ysh2
=j60+1j0.1+j20=j60j10+j20=j50


Y24=Y42=0Ysh2=j20

Y44=j25+1Zse+Ysh2=j25+1j0.1+j20=j25j10+j20

Y44=j15

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