# Transmission Line, Max Real Power Transfer

1. Feb 25, 2014

### jegues

1. The problem statement, all variables and given/known data

A 230kV, 160km long transmission line has the following parameters expressed on a 230kV, 100MVA base.

R = 0.0151
X = 0.1476
Y = 0.288

The sending end voltage of the line is held constant at 1.0 pu. The load at the receiving end has a lagging power factor of 0.8.

Show that the Thevenin equivalent yields,

$$V_{Th} = 1.022 \angle -0.13^{\circ}$$

$$Z_{Th} = 0.0158 + j0.15077$$

2. Relevant equations

3. The attempt at a solution

See figure attached for my attempt.

I'm confused regarding the maximum real power transfer limit.

Is this supposed to be calculated assuming,

$$Z_{load} = Z_{Th}^{*}$$

or are we supposed to use the PF of the load stated in the question somehow?

Thanks again!

#### Attached Files:

• ###### TlineAt.JPG
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2. Feb 26, 2014

### Staff: Mentor

While it may seem to be hinting at conjugate matching, as far as power transmission goes that sounds unrealistic to me. Who would be happy to have a load voltage just half of what the power station was supplying? With half of the station's power output going to heat in the powerline? It's overdoing the de-icing just a tad.

Maybe they are asking what power you could get to that load if you used powerfactor correction?