Question

Question:In deriving expressions for capacitance for a balanced three-phase three wire line with equal phase spacing, the following relationships may have been used.

(i) Sum of positive-sequence charges,${\mathbf{q}}_{\mathbf{A}}+{\mathbf{q}}_{\mathbf{b}}+{\mathbf{q}}_{\mathbf{c}}=\mathbf{0}$

(ii) The sum of the two line-to-line voltages ${\mathbf{V}}_{\mathbf{ab}}+{\mathbf{V}}_{\mathbf{bc}}$is equal to three times the line-to-neutral voltage V_bn.

Which of the following is true?

(a) Both

(b) Only (i)

(c) Only (ii)

(d) None

Short answer

Answer

Therefore the correct option is (a) Both

Step-by-step solution

Explain the capacitance matrix 

Deriving the capacitance matrix for a parallel three phase circuit, all the vector phase currents and positive sequence charges are added to account the coupling between all the three lines.

This is why the vector phase currents of all the line current increases as the capacitance is increased by adding the charges.

Explain the voltage matrix

The neutral voltage drop is lumped into the voltage drops across the three phase conductors, which eliminates the neutral and earth return currents.

Thus, sum of all the line voltage is equal to the three times of the neutral voltage.

Since both the statements are correct, the correct option is (a).

Explanation for option (b)

All the vector phase currents and positive sequence charges are added to account the coupling between all the three lines and the neutral voltage drop is lumped into the voltage drops across the three phase conductors, which eliminates the neutral and earth return currents.

Thusboth the statements are true. Since, Thus the option (c) is incorrect as it says only statement (ii) is correct.

Explanation for option (c)

All the vector phase currents and positive sequence charges are added to account the coupling between all the three lines and the neutral voltage drop is lumped into the voltage drops across the three phase conductors, which eliminates the neutral and earth return currents.

Thusboth the statements are true. Since, thus the option (c) is incorrect as it says both statements are incorrect.