The voltage regulation and transmission efficiency of a three-phase transmission line can be computed using the nominal π method. The line impedance, admittance, series impedance, shunt admittance, and equivalent impedance and admittance are calculated to determine the sending-end voltage, current, receiving-end voltage, current, voltage regulation, and transmission efficiency.
To compute the voltage regulation and transmission efficiency of a three-phase transmission line, we can use the nominal π method.
Calculate the line impedance: Z = R + jX = (0.3 + j0.9) Ω/km
Calculate the line admittance: Y = jB = j(0.3x10^-6) S/km
Calculate the series impedance per phase: Zs = Z × l = (0.3 + j0.9) × 150 km
Calculate the shunt admittance per phase: Ys = Y × l = j(0.3x10^-6) × 150 km
Calculate the equivalent transmission line impedance: Zeq = Zs + jXs = Zs + j(1/ωC) = Zs + j(1/2πfC) = Zs + j(1/2π(50)(0.3x10^-6))
Calculate the equivalent transmission line admittance: Yeq = Ys + jBs = Ys + j(ωC) = Ys + j(2πfC) = Ys + j(2π(50)(0.3x10^-6))
Calculate the sending-end voltage: V_s = V_r + I_l × Zeq
Calculate the sending-end current: I_s = (P + jQ)/(3 × V_s) = (25 MW + j0.85x25 MW)/(3 × V_s)
Calculate the receiving-end voltage: V_r = V_s - I_s × Zeq
Calculate the receiving-end current: I_r = I_s - I_l
Calculate the voltage regulation: VR = (V_s - V_r)/V_r × 100%
Calculate the transmission efficiency: η = (P_r/P_s) × 100%
The probable question may be:
A three phase 50 Hz transmission line is 150 km long and delivers 25 MW at 0.85 power factor lagging and at 110 KV. The resistance and reactance of the line per conductor per km are 0.3 ohms and 0.9 ohms respectively. The line charging admittance is 0.3×10−6 mho per km per phase. Compute by applying the nominal π method the voltage regulation and transmission efficiency.