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March 24, 2012

Mirrors in Space for Low-Cost Terrestrial Solar Electric Power at Night

A proposal to only launch ultra thin and light inflatable mirrors (no power conversion, no energy storage, no lasers or masers to transmit the power etc...) and have them redirect sunlight to ground based solar farms at night. Efficiency is the ground based systems efficiency. Can be done at lower orbit 600 miles up with 12 or more satellites. Helps ground based solar get around the storage issue at night. Again best to do it to desert locations without clouds. Also away from places that want to do astronomy or have other impacts of turning the night into day. Just need to get astronomy into space and away from the light. Again get past a critical mass of space based power capability and infrastructure so that it is easy to make 500 MW of lasers for boosting skylon space planes to drive down costs to get to space.

A constellation of 12 or more mirror satellites is proposed in a polar sun synchronous orbit at an altitude of approximately 1000 km above the earth. Each mirror satellite contains a multitude of 2 axis tracking mirror segments that collectively direct a sun beam down at a target solar electric field site delivering a solar intensity to said terrestrial site equivalent to the normal daylight sun intensity extending the sunlight hours at said site by about 2 hours at dawn and 2 hours at dusk each day. Each mirror satellite in the constellation has a diameter of approximately 10 km and each terrestrial solar electric field site has a similar diameter and can produce approximately 5 GW per terrestrial site. Assuming that approximately 50 terrestrial solar electric field sites are evening distributed in sunny locations near cities around the world, this system can produce more affordable solar electric power during the day and further into the morning and evening hours. The typical operating hours for a terrestrial solar electric field site can thus be extended from approximately 8 hours per day by 50% to approximately 12 hours per day. Assuming a cost of electricity of 10 cents per kWh and a projected launch cost to orbit of $1500/kg for the SpaceX Falcon Heavy launch vehicle, the cost of this mirror constellation system should be recovered in approximately 2.7 years from the additional solar electricity sales.

The proposal looks at recent developments to improve upon a 2001 ISC SPS design that would achieve 1.2 GW. The 2001 design assumed use of 0.5 km diameter mirrors. There are recent developments related to mirrors in space. A Japanese Ikaros Solar Sail satellite is now en route to Venus and L’Garde is now developing lightweight inflatable reflectors.

The proposed system is cheaper because it does not convert to electricity. It is only mirrors that shown on ground based solar farms at night

Ikaros inflatable solar cells

Inflatable Reflector Development at L’Gaarde. Inflatable antenna design matures in the form of this new 7 meter rigidifiable inflatable antenna structure. The torus and struts on this spectacular configuration rigidify shortly after deployment. The resulting reflector is thermally stable, stiff, and well damped, with a low error for high gain space applications. The entire reflector assembly stows in the small round structure visible above the simulated hexagonal spacecraft. It inflates and rigidifies to the configuration seen.

Another promising recent development is the large and growing use of solar cells in terrestrial fields to generate electricity. As of 2011, the total world wide solar electricity generation reached 65 GW and this is growing at a rate of 30% per year. At this rate, in 10 years, there should be 65 exp(10x0.3) = 1300 GW of PV in fields world wide.

Furthermore, 5 GW terrestrial electric power stations are now already being built.
One problem for solar generated electricity is that the sun only shines on average for about 8 hours per day. With mirrors in space, sunlight can be potentially provided during night time hours. However, a challenge is to invent a method whereby mirrors are provided in space for night time solar electric power simply and affordably.




One of the unfortunate features of the 1000 km orbit altitude is the period of rotation for each satellite around the earth. The orbit period is 105 minutes. This problem is resolved because the mirrors on each satellite are allowed to turn as directed to maintain solar illumination on a given location for approximately 105/12 = 8.75 minutes after which the next satellite in the constellation can then continue to illuminate that assigned location.

This constellation is potentially viable now because of the rapid growth in solar
installations around the world. However, it is assumed here that a political decision will be required to implement this MiraSolar constellation concept and its actual implementation will then take approximately 10 years. By that time, we assume that there will be approximately fifty 5 GW ground solar electric generating locations distributed around the world with approximately 5 available in each 30 degree longitudinal increment such that 10 of the 12 mirror satellites will always be directing sunlight down to a station for 24 hours each day. If in fact there are 50 x 5 GW = 250 GW of solar ground stations available 10 years from now, that will still be only 250/1300 = 20% of the projected solar electric power production in 2022.


10 km diameter satellite mirror array shown with 1 km mirror elements to simplify the drawing. Smaller mirror elements can be used such as the 0.5 km mirror elements proposed for the ISC Space Power Satellite. Even smaller mirrors can be used with more mirror elements then required. The optimum mirror size would require more detailed design study.


Mirror element section with detail


Economics - Revenue and Cost estimates

Even assuming the projected launch costs with SpaceX Falcon Heavy, the payback time is 2.7 years. It could be less with reusable launch vehicles and frequent standard launch procedures.

Revenue - Assumptions
1.) 12 mirror satellite constellation in sun synchronous orbit at 1000 km above earth.

2.) The sun’s disc diameter viewed from earth is 10 mrad. This implies that the solar spot size on earth from a mirror in orbit at 1000 km will be 1000 x tan(10 mrad) = 10 km.

3.) Assume each of the mirror satellites has a diameter of 10 km.

4.) Solar intensity = 1.36 kW/sq m = 1.36 GW per sq km. If mirrors are at 45 degrees
deflecting sunlight 90 degrees toward earth, the beam intensity directed at earth will be 0.95 GW/sq km. The area of the mirrors on each satellite is π x 25 sq km = 78.5 sq km. The energy in the sunlight beamed down toward earth will be 75 GW. Assuming atmospheric attenuation of 1/1.36, the intensity on earth will be 0.7 GW/sq km.

5.) Assuming that an already installed PV array on earth uses 20% efficient modules and has a ground coverage ratio of 50% and occupies an area with a diameter of 10 km equal to the sun beam size, then that ground station will produce 0.7 GW/sq km x 0.1 x 78.5 sq km = 5.5 GW.

6.) Now assume that in the year 2022 there are 50 ground stations distributed around the world that the 12 satellite constellation will serve and that the constellation gives 2 hrs of sunlight to each station in the morning and 2 hrs to each station in the afternoon for a total of 4 hrs of sunlight per day per station.

7.) Combined, the 50 earth stations will produce 5.5 x 50 = 275 GW. The total energy
produced from the sun beamed satellite constellation will then be 275 GW x 4 x 365 hrs per year = 400,000 GWh /yr = 4 x 10^11 kWh/yr.

8.) Assume that the price for electricity is $0.1 / kWh, then the annual revenue will be $4x10^10 per yr = $40 billion per yr.

Mirror Satellite Mass – Inputs
1.) The mirror weight on the Ikaros solar sail is 45 g/sq meter. This implies a mirror weight of 45 metric tons (MT) per sq km.

2.) The Ehricke Power Soletta study assumed a mirror weight of 75 MT per sq km.

3.) Mass of mirror element, L’Garde estimate: dish of diameter 16.5 meters could be built for mass of 15 kg. This is 70 MT per sq km.

4.) I shall assume 75 MT per sq km which means that each MiraSolar satellite will weigh about 6000 MT or 6x10^6 kg.

Mirror Satellite Cost
1.) It all depends on launch cost to reach LEO orbit (Not GEO).

2.) The ISC SPS study assumed $400 per kg.

3.) SpaceX web site for Falcon Heavy says $80 million for 53 ton. This is $1,500 per kg.

4.) Cost will come down with reusable vehicles and frequent standard launches. I shall assume $900 per kg.

5.) Each MiraSolar sat will then cost $5.4 B and the constellation will cost $65 B.

Dr Lewis Fraas is the inventor of MiraSolar

Dr. Fraas has been active in the development of Solar Cells and Solar Electric Power Systems since 1975. He led the research team at Boeing that demonstrated the first GaAs/GaSb tandem concentrator solar cell in 1989 with a world record energy conversion efficiency of 35%. He has over 30 years of experience at Hughes Research Labs, Chevron Research Co, and the Boeing High Technology Center working with advanced semiconductor devices.

Dr. Fraas joined JX Crystals in 1993, where he has led the development of advanced solar cells and concentrated sunlight systems. At JX Crystals, he pioneered the development of various thermophotovoltaic (TPV) systems based on the new GaSb infrared sensitive PV cell. In 1978 while at Hughes Research Labs, he published a pioneering paper proposing the InGaP/GaInAs/Ge triple junction solar cell predicting a cell terrestrial conversion efficiency of 40% at 300 suns concentration. This 40% efficiency has now been achieved and this cell is the predominant cell today for space satellites. It is now entering high volume production for terrestrial Concentrated Photovoltaic (CPV) systems.

Dr Fraas holds degrees from Caltech, Harvard, and USC. At Caltech, he studied Physics with Prof. Richard P. Feynman. Dr. Fraas has written over 150 technical papers, over 50 patents, and a book entitled Path to Affordable Solar Electric Power & The 35% Efficient Solar Cell (2005).

JX Crystals is a spin-off from the Boeing Company with licenses for key patents on IR sensitive Gallium Antimonide photovoltaic cells. JXC broadened the usefulness of GaSb cells to include not only efficiency boosting aerospace solar cells but also Thermo PV cells and TPV Combined Heat and Power systems. JXC has established a strong patent position in TPV technology and is currently seeking investors and strategic partners to develop a 1.5 KWe residential home cogeneration system that can supply heat, hot water and electricity from natural gas or propane. JXC has an international patent position on a novel, low cost Solar PV module design and has started manufacturing product in China for 500 kW projects there in 2006 and then for the Global Market

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