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A 50 Hz,3-phase 100 km long transmission line has a total resistance of 35Ω, series reactance of 140Ω and shunt admittance (line to neutral) of 9.3×10⁻⁴ S. The line delivers 40MW at 220kV at 0.9 p.f. lagging. Using the nominal- π method, determine the following:

(i) A, B, C, D constants
(ii) Sending end voltage
(iii) Sending end current
(iv) Sending end power factor
(v) Voltage regulation
(vi) Transmission efficiency

User Ekuusela
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Final answer:

In the nominal-π method, the constants A, B, C, and D can be determined using the series impedance, shunt admittance, and cross admittance. The sending end voltage, current, power factor, voltage regulation, and transmission efficiency can be calculated using various formulas.

Step-by-step explanation:

To determine the constants A, B, C, and D in the nominal-π method, we need to calculate the series impedance, shunt admittance, and cross admittance. The series impedance can be found using the formula Zs = R + jXs, where R is the resistance and Xs is the series reactance. The shunt admittance can be found using the formula Ysh = Yn + Y0, where Yn is the positive sequence shunt admittance and Y0 is the zero sequence shunt admittance. The cross admittance can be found using the formula Yc = Yn - Y0.

The sending end voltage can be calculated using the formula Vs = Vr + (Is × Zs), where Vr is the receiving end voltage and Is is the sending end current. The sending end current can be calculated using the formula Is = (Sr × (√3))/(Vs × P.F.), where Sr is the apparent power, Vs is the sending end voltage, and P.F. is the power factor.

The sending end power factor can be calculated using the formula P.F. = (P × (√3))/(Is × Vs), where P is the true power, Is is the sending end current, and Vs is the sending end voltage. The voltage regulation can be calculated using the formula V.R. = ((Vs - Vr)/Vr) × 100%, where Vs is the sending end voltage and Vr is the receiving end voltage.

The transmission efficiency can be calculated using the formula η = (Pr/Ps) × 100%, where Pr is the receiving end power and Ps is the sending end power.

User Stephen Henderson
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