0191 -9067/82/020133-11$03.00/0 Copyright ® 1982 SUNSAT Energy Council A PARAMETRIC STUDY OF MINIMAL COST SPS SYSTEMS A. W. LOVE Space Operations and Satellite Systems Division Rockwell International Seal Beach, California Abstract — In this study, a cost function for a single solar power satellite (SPS) system is developed using the recently defined magnetron-powered reference system as a model. By assuming a one-parameter Hansen distribution of microwave energy over the spacetenna, it is shown that the cost of delivered power is a function of only two variables. One is the Hansen parameter, h, while the other is the power density level at which the rectenna intercepts the power beam of the spacetenna. This simplification makes it possible to compute a family of curves of cost per kilowatt versus rectenna intercept level with h as a parameter. These curves all have minima and it is apparent that the current reference system, at $2110/kW, is not a minimum power cost system. For this particular system h is approximately 2.4 and the minimum in the cost function is actually $1990/kW. This 6% decrease in cost of power can be realized by making only one simple change in the design; the rectenna diameter must be decreased in order to intercept the power beam at the -8.3 dB level instead of the -13.6 dB level. Although the absolute minimum cost of power, about $1930/kW, occurs for uniform illumination of the spacetenna (h = 0), it turns out that the system with the least overall total cost occurs for h = 3.2, corresponding to a -27 dB sidelobe level. INTRODUCTION The solar power satellite (SPS) has three major and costly elements. The first is the very large array of photovoltaic cells in geostationary orbit which generate d.c. power from sunlight. The second is the spacetenna, in which the d.c. power is converted to RF and radiated by microwave beam to the Earth. The third element is the ground rectenna, which collects the microwave power in the beam, converts it to d.c. and then delivers it to a public utility grid. Although the distance R between the two antennas is very great, the rectenna nevertheless must collect a large fraction of the total power radiated by the spacetenna. Hence, rectenna diameter, DR, must be large enough to intercept a significant portion of the spacetenna's main beam. Thus DR = 2R0N, where 0N is the angle to the —N dB level of the spacetenna pattern (assumed circularly symmetric). But 20N = BX/Dt, where X is wavelength, DT is spacetenna diameter, and B is the beamwidth constant at the -N dB level. Combining these gives *This far-field relation will be equally valid in the near-field (i.e., Fresnel zone) providing the spacetenna is focused on the rectenna. Dk is actually the minor diameter of the rectenna in case it is not on the equator.
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