A 3-bus power system network consists of 3 transmission

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A 3-bus power system network consists of 3 transmission lines. The bus admittance matrix of the uncompensated system is
-j6     j3     j4 pu.
j3     -j7     j5
-j4     j     -j8

If the shunt capacitance of all transmission line is 50% compensated, the imaginary part of the 3^rd row 3^rd column element (in pu) of the bus admittance matrix after compensation is

1. – j 7.0
2. – j 8.5
3. – j 7.5
4. – j 9.0

Correct Option: B

y_Bus =	y₁₀ + y₁₂ + y₁₃	-y₁₂	-y₁₃
	-y₁₂	y₂₀ + y₂₁ + y₂₃	-y₂₃
	-y₁₃	- y₂₃	y₃₀ + y₃₁ + y₃₂

Now comparing with the given matrix, we get and
y₃₁ = y₁₃ = – j₄
y₃₂ = y₂₃ = – j₅
thus, y₃₀ + y₃₁ + y₃₂
∴ y₃₀ + (-j4) + (-j5) = -j8
∴ y₃₀ = j1
Now, after compensating, y₃₀ = j1/2
∴ y₃₀ + y₃₁ + y₃₂ = j0.5 – j4 – j5 = – j8.5
∴ Option (b) is correct.

-j6	j3	j4	pu.
j3	-j7	j5
-j4	j	-j8