where Py = ratio of power transmitted from satellite i to power received at rectenna j; and S, = capacity of satellite i. The need for the Pij factors exists since more power must be transmitted from the satellite than is received at the rectenna, and as the longitude offset between a satellite and rectenna increases, the area of the "footprint" of the microwave beam on the ground increases. (In practice it would be possible to receive the entire beam, at the expense of increasing the area of the rectenna concerned). Satellites were permitted to deliver power to rectennas with longitude offsets of up to approximately 40 degrees. The above L.P. was solved for four typical hours in a 24 hour cycle (01.00, 07.00, 13.00 and 19.00 GMT), to give an optimal switching pattern for the microwave beams. The model solution achieved a 15% average revenue increase over the 1:1 daytime only case and a 53% increase over the 1:1 baseload case. The average satellite load factor achieved was 0.80, compared to 0.67 in the corresponding 1:1 case. Average rectenna load factors were 0.53 compared to 0.67 in the 1:1 case. Although this model was very simplified, the potential for optimising the operation of a flexible system is clearly substantial. A range of more complex L.P. models can also be formulated with various objectives, such as to select the optimal sizes and optimal locations of satellites, as well as the optimal pattern of power transmission over typical 24 hour cycles. Conclusion It could be very valuable if electric utilities were to contribute to the appraisal of the SPS to a greater extent than they have in the past. A particularly valuable form that such a contribution could take would be for one or more utilities to evaluate the cost of designing and constructing a rectenna linked into their distribution grid, and of operating it as one component of their power station "mix". This would enable utilities to calculate the value which they would place on supplies of microwave "fuel", and hence what price it would be profitable for them to pay for deliveries of microwave "fuel" to their rectenna. This would create a market for microwave power from space, and set cost targets for the designers of the SPS space segment. Space engineering companies would then compete to supply microwave power of the appropriate technical specification on the most competitive terms.
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