***Need help with these questions*** 1.) You are helping the city of Chicago in

Question

***Need help with these questions***

1.) You are helping the city of Chicago in its environmentally sustainable plan of delivering to its population 9760 MW of electrical power from wind generator farms in western Kansas and Nebraska, which are 800 miles away. You are concerned about power losses from heating the power lines delivering this electrical power, which you have to deliver via 115 kV high-voltage transmission lines each carrying about 7 MW with a resistance of 0.30 Ohms/mile. You are considering using instead a single superconducting wire that has to be cooled to liquid nitrogen temperatures, but that can carry very large currents with no ohmic-heating losses. Of course, you have to spend energy in maintaining this wire at this temperature over 800 miles.

a.) How many miles of high-voltage transmission line would be replaced by your plan?

b.) What is the maximum amount of power that you can spend cooling the superconducting wire in this project in order to be worthwhile?

c.) How much power do you have to produce at the wind farms in the west to meet your project’s needs?

Explanation / Answer

Q1. each transmission wire will carry 7 MW

so no of transmission wires required= total power to be delivered/power to be carried by wire

= 9760 / 7 = 1394.28 or say 1395

length of each transmission wire = 800 miles

so total length of transmission wires = 1395 x 800 miles= 1116000 miles

b. Total resistance of all wires = resistance/mile x total length in miles = 0.3 x 1116000= 334800 ohm

power lost while transmitting power at 115 kV= V2/R = 1150002/334800= 0.0395 MW

so that is the maximum power can be used for heating to make the project worthwhile.

c. project should produce total power= power demand + power loss

= 9760 +0.0395 =9760.0395 MW

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