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The bus admittance (Ybus) matrix of a 3-bus power system is given below. 1 2 3 1 -j15 j10 j5 2 j10 -j13.5 j4 3 j5 j4 -j8 Considering that there is no shunt inductor connected to any of the buses, which of the following can NOT be true?

1. (A) Line charging capacitor of finite value is present in all three lines
2. (B) Line charging capacitor of finite value is present in line 2-3 only
3. (C) Line charging capacitor of finite value is present in line 2-3 only and shunt capacitor of finite value is present in bus 1 only
4. (D) Line charging capacitor of finite value is present in line 2-3 only and shunt capacitor of finite value is present in bus 3 only

Correct answer: (A) Line charging capacitor of finite value is present in all three lines

Solution

Option A cannot be true because the negative imaginary components in the Ybus matrix indicate the presence of capacitive elements, and having line charging capacitors in all three lines would lead to an overall positive imaginary part, which contradicts the given Ybus values.

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