Question

1. A 50-Hz, 3-phase line 100 km long delivers a load of 40,000 kVA at a lagging power factor of 0.7. The line constants (line-to-neutral) are: resistance 11 Ω: inductive reactance 38 Ω; capacitive susceptance 3 x 10-4 S (half at each end ), leakage negligible. Find the sending-end voltage, current, power factor and power input.

1. A 50-Hz, 3-phase transmission line has the following constants (line-to-neutral). Resistance 11 Ω, reactance 38 Ω; susceptance 3 x 10-4 S, leakage negligible. The capacitance can be assumed located half at each of the line. Calculate the sending-end voltage, the line current and the efficiency of transmission when the load at the end of the line is 40,000 kVA at kV power factor 0.7 lagging.

Answer 1

To find the sending-end voltage and other parameters for a 3-phase power system, load calculations are done using the power factor, followed by corrections for the line resistance and reactance.

Step-by-step explanation:

Calculation of Sending-End Voltage and Other Parameters

To find the sending-end voltage, current, power factor, and power input for a 3-phase transmission line, we will follow a systematic approach.

1. Calculate the load's apparent power (S) as S = VI* (where V is voltage and I* is the complex conjugate of the current).
2. Determine the load's resistive (P) and reactive (Q) power, using the power factor (pf).
   
3. Find the load's current using I = S / (V√3), and note that this is the receiving-end current.
4. Calculate the sending-end voltage by accounting for the voltage drop across the line's resistance (R) and reactance (X).
5. Use the calculated sending-end voltage (Vs) and current to find the sending-end power factor.
6. Finally, determine the power input at the sending-end by Pinput = 3 × Vs I × cos(φs), where φs is the sending-end power factor angle.

For the given parameters, let V = line-to-neutral voltage at the receiving end, I = receiving-end line current, φ = angle of the receiving-end power factor, R = resistance per phase, X = inductive reactance per phase, and B = capacitance susceptance (considering half at each end).

The line current and efficiency of transmission can also be calculated using similar methods, considering the power losses due to the resistance of the transmission lines.

Note that for detailed calculations, complex numbers should be used because of the presence of reactive components (inductive reactance and capacitive susceptance).

Answer 2

To calculate the sending-end voltage, current, power factor, and power input of a 3-phase transmission line, we can use formulas that involve the line-to-neutral voltage, power delivered to the load, and power factor.

Step-by-step explanation:

To calculate the sending-end voltage, current, power factor, and power input of a transmission line, we can use the given values and formulas.

1. Sending-end voltage:
2. The sending-end voltage can be calculated using the formula:
3. Vs = √3 * Vl * cos(θ + φ)
4. Where Vs is the sending-end voltage, Vl is the line-to-neutral voltage, θ is the phase angle, and φ is the angle of the lagging power factor.
5. Line current:
6. The line current can be calculated using the formula:
7. Il = S / (3 * √3 * Vl * cos(θ))
8. Where Il is the line current, S is the power delivered to the load, Vl is the line-to-neutral voltage, and θ is the phase angle.
9. Power factor:
10. The power factor can be calculated using the formula:
11. PF = cos(θ)
12. Where PF is the power factor and θ is the phase angle.
13. Power input:
14. The power input can be calculated using the formula:
15. P = S / PF
16. Where P is the power input, S is the power delivered to the load, and PF is the power factor.

By substituting the given values into these formulas, we can find the sending-end voltage, current, power factor, and power input of the transmission line.