Satellite Solar Power

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Satellite Solar Power Problem

Given a satellite having solar cells wrapped around a cylindrical drum with a diameter of 2.38 meters and a height of 2.92 meters, that is rotating at approximately 60 revolutions per minuet (rpm) in order to provide spin stabilization to the spacecraft. This drum satellite is designed to deliver 708 watts of electrical power from its solar cells at the end of the satellites life. Use these parameters in the following calculations:

a) Calculate the efficiency of the solar cells at the end of life. Assume an incident solar power of 1.39kW/m²

b) If the solar cells degraded by 15 percent over the lifetime of the satellite, what was the initial output power produced by the satellite?

c) How much electrical energy was dumped into the load resistors when the satellite was initially turned-on, given a margin of 80 watts was provided at the end of the satellites life?

d) If this spinner design has been replaced by solar sails that rotated to face the sun at all times, what area of solar sails would have been needed? Assume that the cells on the solar sails generate 10 percent less power then those on a spinner due to their higher operating temperature.

Solution:

a) The solar cells efficiency at the end of life is:
P = (Incident Solar Power) (Projected Cell Area) (Efficiency)
P = (1.39kW/m²)(2.38m)(2.92m)( η )
Where η = 708 / (1390)(6.95) = 7.33%

b) Define:
Power End of Life = P_EOL
Power Beginning of Life = P_BOL
Therefore, P_EOL = P_BOL x 0.85
Solve for P_BOL, and P_BOL = 708 / 0.85 = 832.9 watts

c) At P_EOL the satellite will deliver 708watts, with an 80watt margin. Therefore, the satellite requires 628watts for the satellite systems. So if at the beginning of the satellite’s life the power provided was 832.9watts and 628watts needed to operate the satellite; a total of 204.9watts was dumped into the load resistors when the spacecraft was initially turned-on.

d) Solar Sails Power = P_SS = P_spinner / 0.9
So, P_SS = 786.7watts
The Area of the Sails = (P_SS) / (Incident Solar Power)(Efficiency)
P_SS = (786.7watts) / (1390 w/m²)(0.0733)
P_SS = 7.72m²

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