This figure of 0.60$/kWh does not take into account the cost of environmental damage caused by oil spills or the greater damage caused globally by CO2 and the depletion of fossil fuels. Thus a maximum cost of electricity must be determined by the customer realizing that the motivation for providing this alternative energy source is calculated from indirect costs. As an arbitrary figure lets choose $10.0/kWh which because of costs of building actually means charging $4.0/kWh. The calculations described below indicate that $1 billion is the most that could be returned on a project costing around $3 billion. This in and of itself may challenge the feasibility of the program. Assume a large base in a dry valley would receive 1.5 MW of power. To optimize the kW hours we would need a Molniya orbit (with the average distance taken to be 25,(XX) km) transmitting 35 GHz from an antenna with a 100 m diameter.To receive 98% of the power would take a rectenna of a 5.2 km diameter. For cost reasons we choose a rectenna of 520 m to receive about 20% of the power although in actuality we would only receive about 10% of the beamed power due to the elliptical path of the satellite. Assume coverage of 16 hours per day which results in 58,400 hours over the ten year life span of the satellite (365 x 10 x 16 = 58,400). Therefore the satellite must beam 15 MW in order to produce 1.5 MW on the ground at 5.66 W/m^ excluding weather interference and other losses. Assuming a highly inflated cost of fuel at $10/kWh, the total market would be 58,400 hours times $10 times 1500 kW or $876 million (1500 x 58,400 x 10 = 876,000,000). But it will cost at least $3 billion to put a 15 GW satellite in orbit. Thus we have demonstrated the ability to lose over $2 billion. Clearly some advances need to be made before space solar power for Antarctica is a viable energy alternative. In the subsequent chapters, several technologies will be identified that need to be advanced in order to beam power from space to Earth more efficiently and cheaply. 10.3.2 Mission Analysis Altitude Selection The altitude selected for this design example is mainly driven by the system cost constraint. Indeed, this constraint limits the size of the spacecraft, which in turn limits the power available from the satellite. Therefore, the altitude will be imposed by the amount of power the system can get back on ground. The results of a trade-off analysis are presented in Table 10.3.2 showing that, assuming a given system (power output, rectenna), the lower the altitude is, the more energy there is that can be stored on the ground. A typical 1000 km altitude orbit can be selected for the purpose of this exercise. Actually the precise value shall be the result of a compromise between the performance and the air drag problems which appear at lower altitudes (attitude and orbit control). Table 10.3.2 Altitude Selction Trade-Off Analysis Orbit Selection According to the previous point, two typical orbits are discussed here: the sun-synchronous orbit (SSO, inclination = 100°) and the “ near” equatorial orbit (inclination < 30°), both in low Earth orbits (typically in the range of 1000 to 1500 km). Table 10.3.3 makes a tentative comparison of the orbits. The SSO orbit can be used as a baseline for this design example because it allows more power, and has the potential to supply any location in the world.
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