The bus admittance matrix of a three-bus three-line system

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The bus admittance matrix of a three-bus three-line system is

If each transmission line between the two buses is represented by an equivalent π-network, the magnitude of the shunt susceptance of the line connecting bus 1 and 2 is

1. 4
2. 2
3. 1
4. 0

Correct Option: B

For three bus system

Y₁₁ = Y₁₁ + Y₁₂ + Y₁₃
Y₁₂ = – Y₁₂ = 10j, Y₁₃ = – Y₁₃ = 5j
⇒ Y₁₁ = – 13j = Y₁₁ + Y₁₂ + Y₁₃
⇒ – 13j = Y₁₁ – 10j – 5j
⇒ Y₁₁ = 2j
Equivalent π network between Bus 1 and Bus 2

Shunt-susceptance, y₁₁ = 2