$2.$ A utility expecting significant load growth in a city wants to build new transmission lines to bring additional power from a wind farm $400$ km away. The transmission lines have to be designed to carry $2200$ MW of power with one line out with VS $=1\mathrm{.}0$ per unit, VR $=0\mathrm{.}95$ per unit, $=30$o$,$ and $=5000$ km$.$ There are three voltage options, which are $345$ kV$,500$ kV$,$ and $765$ kV$.$ The data for lines at these voltage levels are as follows: VOLTAGE Zc COST$/$km Right of Way Needed Per Line Substation Cost $345$ kV $300$ $$1\mathrm{.}0$ Million $150$ ft $500$ kV $$200$ Million $285$ $$1\mathrm{.}5$ Million $175$ ft $765$ kV $$300$ Million $270$ $$2\mathrm{.}0$ Million $200$ ft $$400$ Million All the lines have to be placed in the available right of way with the total width of $900$ ft$.$ How many lines will be needed at each voltage level? Which option is cheaper? Investigate the option of building a substation at the midpoint in all the cases to reduce by one the number of lines. Which is the overall best option for the given cost of substations at different voltage levels?