Question

A small manufacturing plant is located 2 km down a transmission line, which has a series reactance of 0.5 Ω/km. The line resistance is negligible. The line voltage at the plant is 480/08 V (rms), and the plant consumes 120 kW at 0.85 power factor lagging. Determine the voltage and power factor at the sending end of the transmission line by using.a. Complex power approachb. Circuit analysis approach.

Answer 1

Complex analysis = 682.2 V

Step-by-step explanation:

1. Using a complex power approach:

Data:

Power drawn by the load, Q load = 120 kW

Power factor lagging = 0.85

The reactive power is solved as follows:

tan [arccos (power factor)] =
`(Qload)/(Pload)`

tan (cos⁻¹ [0.85]) =
`(Qload)/(120)`

solving the equation above gives Qload = 74. 4 kVar

The complex power drawn in by the load is given as:

S load = P load + jQload

= 120 + j74.4 kVA

using the complex analysis above, we can solve for the current into the load like this: I =
`(Sload)/(Vload)`

=
`(120 + j74.4)/(480/8)`

= 294 (-31.8⁰) A

The power factor will be 682.2

2. Circuit power approach:

using the KVL:

Vsource = Zline + Vload

= j 1(294 (-31.8⁰) + 480

= 682.4

The power factor will be cos (21.5 - 31.79) = 0.598 lagging