Where the inverse tangent the power factor the real power loss the line

Solved Step by Step With Explanation- Transmission Line Analysis: ABCD Parameters

Questions

(b) The line delivers 1800 MVA at 0.85 p.f. lagging at 730kV. Determine the sending end quantities, voltage regulation, and line efficiency.

Answer

Geometric mean distance (GMD)

Inductance (L) per unit length

The GMR for a bundled conductor line is given by:

GMR = (D1 * D2 * D3 * D4)^(1/4)

Now, calculate the GMR:

GMR = (1,511.35 * 1,511.35 * 1,511.35 * 1,511.35)^(1/4) = 1,511.35 cm

The inductance per unit length can be calculated using the GMR and GMD:

L = 2 * 10^(-7) * log10(D/GMD) H/m

L = 2 * 10^(-7) * log10(1511.35 cm / 20 cm) H/m

L = 0.05894 H/km

C is capacitance per unit length.

ε is the permittivity of the material between the conductors (approximately 8.854 x 10^(-12) F/m).

C = 6.897 x 10^(-12) F/m

Now, we have the necessary parameters to calculate the ABCD parameters:

D = 0.05 km (line length)

Now, we have the ABCD parameters.

Load power (P) = 1800 MVA

Power factor (p.f.) = 0.85 lagging

Load current (I_l):

I_l = (P + jQ) / (V_l * p.f.)

Line efficiency (Efficiency):

Efficiency = (P / (P + R_loss)) * 100

Q = 1800 MVA * tan(acos(0.85)) ≈ 417.73 MVAR

Now, calculate load current (I_l):

V_r = j(2π * 50 Hz * 6.897 x 10^(-12) F/m * 1000 m/km) * 730 kV + 0.05 km * (2.1234 - j0.4916) kA ≈ j0.0042 kV + 36.5 kV

Now, calculate voltage regulation (VR):

Efficiency = (1800 MVA / (1800 MVA + 5.99 MW)) * 100 ≈ 99.67%

So, the sending end quantities are approximately: