LEO Constellation of Small SPS________ This section is intended to study technical and economical aspects of a LEO constellation of small solar power satellites (10 to 100 MW) as an alternative to provide a continuous and reliable source of energy to the Earth. Obviously, this concept is mainly suitable for a long term commercially oriented project. It could not be easily applied to a small scale profitable venture because such a constellation requires a complete fleet of satellites to feed many receiving sites (rectennas). We should notice than this concept is in opposition to the “classic” SPS design, which usually consists of a big satellite (5 GW) in GEO and one rectenna on the ground. We will try to outline the advantages of the LEO constellation over the GEO approach, but we will also discuss the drawbacks of this option. Analysis of a simple constellation (coplanar case) We will do a quick analysis of the simplest case, a constellation of satellites on coplanar and circular orbits. This is the case, for instance, of the equatorial orbits. We will evaluate technical characteristics of the power transmission infrastructure required (antenna and rectenna) for many orbit altitudes. We will try to explain why a LEO constellation can be a good solution to ensure the economical viability of a long term SPS development. The first factor which comes to mind is the amount of illumination of the spacecraft by the Sun. It is well known that high altitude orbits allow larger duration in sunlight. As shown in figure C.l, this visibility increases very rapidly with the altitude. But we observe a significant gap between LEO (65- 75%) and GEO (96%). We must also consider the total visibility of the rectenna from the spacecraft. Obviously, it will vary significantly with the altitude. GEO are chosen for many space applications because they allow a permanent link with the ground. On the other hand, LEO suffer from their very short visibility time. To illustrate this, we have plotted in figures C.2 and C.3 the total visibility angles and times for different altitudes. As these factors are strongly dependent on the maximum admissible elevation angle of the rectennas, we have evaluated 4 cases where the elevation angles range from 15° to 60° (in increments of 15° between each curve). In figure C.2, the total visibility angle is a measure of the orbital arc where the spacecraft is able to beam power to one rectenna. These arcs are very small in LEO (10° to 50°), but they grow rapidly as we get closer to GEO (continuous visibility between the spacecraft and the receiving site). Similarly, the total visibility time (figure C.3) is very short for LEO (only a few minutes). If we look at these curves, a LEO does not seem interesting since only a small amount of the total power produced by the spacecraft could be transmitted on a single rectenna (if no energy storage device is used aboard the satellite). But as we will see further, we can overcome this negative element by multiplying the rectennas along the trace of the orbit. Then we could collect all the energy beamed by the satellite at each revolution (but with reduced illumination of the spacecraft by the Sun as compared to higher orbits). However, if we want to use many rectennas for an entire coverage of the orbit, we must be aware of some physical limitations such as the maximum elevation angle between the beam and the rectenna and also the deflection of the beam from the antenna (figures C.4, C.5 and C.6). Actual technical limitations are roughly 60° for the elevation angle and 30° for deflection (these parameters depend on the technology used, and they will certainly improve in the future). We can see that these constraints are almost impossible to meet in LEO with less than 10 rectennas. The construction cost of the rectennas is a major part of total cost of the project and it needs to be carefully optimized in relation with the cost of the other main element of the infrastructure, i.e. the spacecraft. We do not possess enough information about the real costs of these elements and we will not be able to do a realistic and precise estimation. But we can assume, for instance, that for the rectennas, the construction cost will be nearly proportional to the total area. As we know how to estimate the area of the rectenna required to collect the power from a satellite at a given altitude, we can sum up the total receiving area needed for a entire coverage of the orbit vs altitude (figure C.7; figure C.8 is focusing on LEO).
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