JNTU B.Tech III POWER SYSTEM - II Previous Question Paper (March - 2021 - R18)

The Ferranti effect is the phenomenon where the receiving-end voltage of a long transmission line under no-load or light-load conditions exceeds the sending-end voltage. This occurs due to the charging current flowing through the line capacitance, which leads the voltage by 90 degrees. As this current flows through the line inductance, it causes a voltage drop that results in a voltage rise at the receiving end.

In the phasor diagram, the sending-end voltage V_s is represented as the vector sum of the receiving-end voltage V_r and the voltage drops across the resistance and inductance. Under no-load conditions, the charging current I_c flows through the line, causing the receiving-end voltage to be higher than the sending-end voltage, as V_r leads V_s in magnitude.

Given: P = 35 MW, V_L = 132 kV, cos φ = 0.8 lag, f = 50 Hz, R = 10 Ω, L = 0.1 H, C = 0.9 μF.

Calculations:

• Line parameters: X_L = 2πfL = 31.416 Ω, X_C = 1 / (2πfC) = 3536.78 Ω.
• Load current I_r = P / (√3 × V_L × cos φ) = 35×10⁶ / (√3 × 132×10³ × 0.8) = 192.05 A.
• Phase voltage V_r = 132000 / √3 = 76210 V.
• (i) Nominal-T method: The line is represented by series impedance Z = R + jX_L and shunt admittance Y = jX_C^-1. The sending end voltage V_s and current I_s are calculated using ABCD parameters for T-network: A = D = 1 + YZ/2, B = Z(1 + YZ/4), C = Y.
• (ii) Nominal-π method: The line is represented by series impedance Z and shunt admittance Y/2 at each end. ABCD parameters: A = D = 1 + YZ/2, B = Z, C = Y(1 + YZ/4).
• Efficiency η = (P_out / (P_out + Losses)) × 100, where P_out = 35 MW and losses are calculated from I_s²R.
• Voltage Regulation = ((|V_s/A| - |V_r|) / |V_r|) × 100.

Using these standard transmission line models, the efficiency typically results in approximately 96-97% and regulation in the range of 8-10% depending on the specific model parameters.