Question

3. Electrical power is transmitted southwards from a hydroelectric plant over a distance of 1000 km via a DC (direct current) transmission line to a consumer. The output is 800 KV at the plant. The transmission line consists of one isolated aluminum strand with 2.0 cm diameter; an identical cable returns back north to the generator. The resistivity of aluminum is 2.20 x 10-8 Ωm. The power fed into the original transmission line at the plant is 1000 MW.

   1. a) Draw a circuit diagram of the problem with power plant, transmission lines and a single resistor as consumer (load). What is the total current that flows out of the plant into the cable?

   2. b) How much power arrives at the consumer, i.e. is dissipated in the load resistor, and what is the voltage one measures between the incoming and outgoing cable at the consumer?

   3. c) The utility company wants to decrease the power losses. They add an identical cable in both directions in parallel to the first one. If you assume the load resistor (consumer) and the output voltage of the power plant stay the same, what would be the new power output of the plant and the fraction of power arriving at the consumer?

   4. d) With now 2 strands in both directions, how would the load resistor have to be set to get the original output power of 1000MW and what fraction of the power would arrive now at the consumer?

   5. e) Briefly discuss if and how the power loss would change if the voltage was increased or decreased, while the output power and resistances of load and transmission lines remain constant.

Answer 1

supply voltage=V

power dissipitaed at load= PR_L