Transmission Line, Max Real Power Transfer

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,



[tex]V_{Th} = 1.022 \angle -0.13^{\circ}[/tex]



[tex]Z_{Th} = 0.0158 + j0.15077[/tex]



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,



[tex]Z_{load} = Z_{Th}^{*}[/tex]



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



Thanks again!

Attached Images

TlineAt.JPG (73.8 KB)