Question

A 60-Hz, 230-mile, three-phase overhead transmission line has a series impedance z = 0.8431 ∠79.04° Ω/mi and a shunt admittance y = 5.105 × 10^-6 ∠90° S/mi. Determine the voltage, current, and both real and reactive power at the sending end, as well as the percent voltage regulation of the line. Also, find the wavelength and velocity of propagation of the line.

Answer 1

To determine the voltage, current, and power on the transmission line, and to calculate the percent voltage regulation, you can use formulas involving impedance, current, voltage, and power. The wavelength and velocity of propagation can be calculated using formulas involving frequency, inductance, and capacitance.

Step-by-step explanation:

Calculation of Voltage, Current, Power, and Voltage Regulation:

To determine the voltage, current, real power, and reactive power at the sending end, we can use the following formulas:

• Voltage: V = IV = IZ, where I is the current and Z is the impedance.
• Current: I = V/Z, where V is the voltage and Z is the impedance.
• Real Power: P = IVcosφ, where I is the current, V is the voltage, and φ is the phase angle of the impedance.
• Reactive Power: Q = IVsinφ, where I is the current, V is the voltage, and φ is the phase angle of the impedance.

The percent voltage regulation of the line can be calculated using the formula: Percent Voltage Regulation = (Vsending - Vreceiving)/Vreceiving x 100%, where Vsending is the sending end voltage and Vreceiving is the receiving end voltage.

Calculation of Wavelength and Velocity of Propagation:

The wavelength (λ) of the line can be calculated using the formula: λ = (2πv)/f, where v is the velocity of propagation and f is the frequency.

The velocity of propagation (v) can be calculated using the formula: v = 1/√(LC), where L is the inductance per unit length and C is the capacitance per unit length.