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Issue 18
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Thermal Power Satellites

Keith Henson

hkeithhenson@gmail.com

 

 


ABSTRACT

Researchers have studied power from space for decades but the studies have fallen short on competitive cost. This paper is a new approach to the economics, which finally resolves the cost problem, undercutting the price of electricity from coal. This approach out-competes most other sources of electric power, excepting hydro, which is limited. It seems to be a better solution than peaking plants, and that leads to hydrogen production from off peak power and low cost replacement of petroleum products. This solution is partly in the transportation systems and partly in the design of the power satellites. As an alternate concept to photovoltaic (PV), this paper is concerned with transport cost, thermal power satellite mass, the cost of energy and some description of the construction. The satellites use a 2.45 GHz microwave beams to get the energy to the ground and deliver five GWe. We assume 60% efficient, use mirrors to concentrate sunlight and use boilers, turbines and condensing radiators to make electricity. The main working fluid would be water or SCCO2, and they would use a topping cycle, perhaps potassium vapor and a main cycle of steam or supercritical CO2 to reach 60% efficient. We present an initial design and with mass estimates for the major parts of a power satellite: concentrators, boilers and steam generators, turbines and other rotating parts, generators, frame, radiators and the transmitter. Radiator design is considered in detail since this part is unique to power satellites. Power satellites, both photovoltaic and thermal, offer the possibility of electricity from space at less than the cost of electricity from coal. For this to happen, power satellites must cost less than $2400/kW. This cost requires a specific mass of no more than 6.5 kg/kW for a transport cost to GEO of $200/kg.

 

Introduction to Thermal Power Satellites

Power-satellite designs published over the past thirty years have all been photovoltaic (PV). This paper describes an alternative:  low exhaust-temperature steam turbines. Sunlight focuses into boilers, vapor spins turbines and large surface area radiators cool the turbine exhaust. There are two advantages thermal satellites have over PV. Turbines do not degrade over time from radiation (1) and thermal power satellites are three times as efficient as PV. This means a thermal power satellite would need one third of the light interception area of a PV power satellite. This paper is a preliminary design of a thermal power satellite and estimates the masses of the parts needed to build them. The mass limit is constrained by the economics to gain market share.

 

Power Satellites, Frequency and Size (Microwave Optics)

The scale of this design is 10 GW in space and, due to transmission losses, 5 GW delivered to the grid on the ground (2). The analysis assumes 2.45 GHz for the microwave link. That is the frequency used in microwave ovens and the same as the original designs investigated in the 1970s. Reevaluating this proposal for 5.8 GHz will not change the total mass lifted to space if the goal is to quit burning fossil fuels. 

 

Thermal cycles and efficiency

On Earth, rivers, the ocean or the atmosphere carries waste heat away from a thermal power plant. In space, the only choice is radiation into 'deep space' (3).
Consequently, a thermal power satellite design must include radiators, and very large ones given the scale of the power plants. A reasonable target is an efficiency of 60%, about the same as a modern combined cycle natural gas-fired plant on earth. Sixty percent would require radiating 6.7GW of low temperature heat for a plant rating of 10GW. Efficiency is not a direct economic concern (sunlight is free), but a substantial fraction of the mass is in the waste heat radiators that scale with the waste heat, and that is a concern. High efficiency will reduce the size (and mass) of the sunlight interception area and the area of the radiators.

Sixty-percent-efficient thermal cycles are not practical with single-stage steam (Rankine) cycles. The power satellite will need at least two cycles and two or three working fluids. The topping cycle considered here is potassium operating between 840°C and 595°C (1113 K and 868 K) cycle (Chambers, 1964) (4). The Carnot efficiency for an ideal heat engine between these temperatures is 22%. At 75% of Carnot, the output would be around 15%. The condensing potassium would heat water or supercritical CO2 (SCCO2) to 550 C. The low temperature end would be 20°C or 32°C respectively. At present, the heat radiation part of the cycle does not seem to have working fluid options other than low-pressure steam.

There are other candidates for topping cycles. They include helium Brayton cycle, MHD and thermionic (the latter featured in the original Boeing studies). Alkali-metal thermal-to-electric converters (AMTEC) are another option.

Using SCCO2 instead of water for the main thermal cycle is worth investigating. Due to the high density of CO2, SSCO2 turbines are much smaller than steam turbines. They are much lighter and the efficiency is high (45%). The high temperature end (550°C) is a good match for condensing potassium. The cold temperature end of a SCCO2 cycle is ~ 32°C. A low delta T heat exchanger could transfer the low-grade heat to water and low-pressure steam. The heat exchanger would have similar specifications to the ones proposed as pre-coolers on SABRE engines. The steam and fog would circulate through the radiator tubes at ~20°C. Steam turbines are highly developed legacy technology with very low risk. Exhausting them directly into the radiator tubes saves the mass of heat exchangers; however, the mass of SCCO2 turbines and heat exchangers may be less than the mass of the steam turbines.

Estimated thermal power satellite efficiency at 60% is “justified” because ground-based systems reach that. In the space environment, it might be better or worse. However, we need a starting number for a rough analysis. Efficiency and power determine the collector area and radiator area.

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Optical path and Sunlight Collectors/Mirrors

Other design considerations are the light paths. The concentrating mirrors must point at the sun and the microwave transmitter must point to the earth. If the radiator and power generation system stays pointed to the earth, we can avoid the cost and mass of a rotating joint for conductors. Instead, we rotate the light path. All recent power-satellite designs rotate the light path.

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Figure 1. Thermal Power Satellite showing reflector-concentrators, support structures, radiators and transmitter. Not shown:  boilers, frame structure, turbines and generators. Artist Anna Nesterova.

For 60% efficient and 10 GW out, the input thermal energy to the boilers will be 16.7 GW, The radiator will need to dispose of 6.7 GW of low-grade heat. The solar collecting area will be 16.7 GW/1.365 GW/km2 or 12.2 km2 plus an increment (10-15 %?) for less than unity reflection and heat reradiated from the boilers. We will assume the mass of the structure holding the mirrors and the mirrors to be 0.5 kg/m2 or 500 tons per km2. The reflector surface might be stretched aluminized plastic. It should mass no more than 0.1 kg/m2. The intent is to concentrate light by more 1000 times (1000 suns).

Construction of the support structure could use channel beams. They would be roll formed from thin Invar sheet metal of near-foil thickness. (Invar is a low thermal expansion, 35% nickel alloy.) Spot welding may be the simplest way to join sheet metal beams. We can use other materials for power satellite structure, for example, sunlight-cured graphite/epoxy. Invar’s advantage (in the long run) is that it is available from M-type asteroids.

The design analyzed here has the radiator laid out like the proposed cooling for a laser propulsion system. (Henson K. , 2014) (5) Radiator tubes are in pairs, turbines sending spent steam down a radiator tube where it condenses. The condensate goes into the adjacent steam generator as feed water. The large and small ends alternate for tapered tubes.

The radiator tubes occupy an area a little larger than a 3-km square. The solar concentrators are over the leading and trailing edges of the radiator. To get the energy input needed they need to intercept ~12.2 km2 of sunlight. There are six of them (3 on the north leading edge and 3 on the south trailing edge). They need two km2 per collector (2.2 km2 with loses and reradiation). The diameter as a circle would be 1.7 km. The reflectors would be elliptical at 1.7 by 2.4 km mounted at 45°. The sub unit facets would be a few tens of meters in size. They would act as moveable, long focal length, off-axis parabolic concentrators. The concentration ratio would be over 1000 to get the high temperature needed for the topping cycle.

For the geometry in figure 1, the mirrors never eclipse each other. At noon and midnight, they appear from the direction of the sun to be stacked over each other. Each reflector rides in a hoop track supported by structural beams down to the radiator plane. It would take about 80 km of beam using four support beams per hoop. Eight-meter-wide channel beams roll formed from 0.1 mm aluminum sheet 10 meters wide would mass about 2.7 tons per km or 216 tons.

The one-km transmitting disk always points to the earth. The large-scale holder for the mirror segments ride on circular tracks to follow the sun. The focal point would be on a boiler on the edge of the heat radiators. Each concentrator focuses sunlight into the number of radiator tubes divided by six boilers. The individual mirror segments are mobile. They shift focus from boiler to boiler as the boilers and radiator plane rotate under (or above) them.

At 500 tons per km2, reflectors and support structures would mass ~6100 tons.

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Figure 2. Showing boilers, turbines, radiator tubes, reflectors and steam compressors. Artist Anna Nesterova.

 

Boilers and Steam Generators

Solar boilers in space would not have fireside corrosion (no oxygen). Thus, they could operate at a higher temperature compatible with a potassium topping cycle. Boilers on Earth are very heavy. They use kilometers of thick boiler tubing. The large area of tubes is required to get relatively low heat fluxes out of atmospheric-pressure hot gases. Higher heat fluxes cause burn though. Based on a potassium-vapor topping cycle, primary boilers in space should not be very heavy; the pressure of the potassium should not exceed three atmospheres (6). They could even be “glassed in,” letting concentrated sunlight go through a pressure-supporting window into a flow of vapor from the cold end to the hot cavity (7). The outer reaches of the boiler light funnel could be cooled with boiler feed water, saving the mass of feed water heaters.

After passing through a topping turbine, the low-pressure potassium vapor condenses on steam generator tubes. The potassium vapor provides an excellent heat source at a uniform temperature. This avoids the runaway burnout problem that afflicts boilers at high heat rates. A 0.5-GW, nuclear-heated potassium topping cycle analyzed in 1964 had 200 tons of steam tubing inside the potassium condenser. Lighter designs may be possible, but here we will use 1000 tons for the potassium boiler and 4000 tons for the potassium condensers/steam generators. These can use five times the ΔT in standard power plants.

Turbines

Thermal designs usually involve turbines. Ten GW requires a lot of turbines. The largest turbine/generator sets constructed to date are 1.75 GW. They are far too heavy to consider moving into space in one piece.

A better estimate for specific mass might be a GE90 turbine engine for a Boeing 777. That turbine puts out 75 MW with a mass of ~7500 kg or 0.1 tons per MW. Given a 15-ton shipping limit, a turbine could put out 150 MW at this specific power. It would take ~66 turbines of this scale to generate 10 GW. Ten thousand MW of turbines at 0.1 tons/MW would mass 1000 tons. We modeled various numbers, from 60-240 of steam (and potassium-vapor) turbines.

Generators

The generators may be heavier than the turbines. An existing example is an aircraft 400-Hz generator, 40-50 KVA that massed 15 kg, or .3 kg/kW, or 300 tons per GW (8). Using higher than 400-Hz may reduce generator mass. Generator voltage does not usually exceed 20 kV to avoid corona insulation damage.  Both the losses in the connection to the transmitter and the internal breakdown in the generator windings need consideration.

Superconducting generators will be somewhat lighter and, if we use superconductor wiring, they may be acceptable. We will assume the generator and power cables to the transmitter to mass 3000 tons with the understanding that this may be off either way. (A study of power transmission between the generators and the transmitter came in at 1280 tons for a design with a 75 MW I2R loss.)

Radiators

The ratio of collector-intercept area to radiator area optimizes (minimum total area) with a radiator area of about twice the collector. (Bejan, 1997, pg 495) Counting both sides of the radiator, the projected area is about the same. For 6.7 GW spread over 24.4 km2, the thermal radiation is ~273 W/m2. From the Stefan–Boltzmann law, the temperature for this radiation rate is cooler than useful for steam cycles (i.e., below freezing).

Previous work (Henson, Drexler 1979) found that non-condensing radiator tubes should be in a loop heated on both ends to avoid the mass of return headers. Also from that work, a minimum mass radiator has a square outline. It uses reflectors between the radiator tubes to avoid them blocking each other’s view of deep space. The square outline helps keep the radiator perimeter short (it needs a sunshade all around).

We made a conceptual advance while working on cooling for space-based laser propulsion. The idea is to condense the low-pressure working fluid (steam) only partway to prevent "water logging" the radiator tubes and high fluid mass. It turns out from spreadsheet studies that the vapor pressure of steam falls faster than radiation from the Stefan-Boltzmann law. Stefan-Boltzmann law is dependent on T4 so this was a surprise. However, in the relevant temperature range (0-100 C), the tube-wall mass plus the mass of steam falls faster than radiation. This results in the odd situation that a colder radiator has less mass per kW than a hotter one. Practical considerations are tube length and pressure drop. There is a minimum wall thickness to resist micrometeoroids.

The walls may need to be thicker to resist micrometeoroids, but for this stage of the analysis, we assume 1/10th mm Spectra with a mass of 0.1 kg/m2. A certain number of micrometeoroid punctures per hour will have to be tolerated and locators for holes and repair mechanisms included. The design considerations tentatively favor a radiator temperature of 18-22°C. This is nearly ideal for steam-turbine exhaust.

At 20°C and an emissivity of 0.95, the radiation rate is ~400 W/m2 and the length for 28-meter diameter tubes is 186 km. The radiator outline would be 3.1 km in each direction using 60 tubes spaced at 3.65 times the radius of the tubes. The radiator has 16.75 square km of surface, and the walls would mass 1675 tons.

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A better approach than straight tubes is to make the radiator tubes taper at the same rate the steam condenses. Steve Nixon suggested this during design discussions. We later found that tapered, condensing radiator tubes for both steam and potassium vapor were extensively investigated by Carbide Union for the AEC (Fraas, 1968) (9).

Tapering makes the tubes longer while keeping the steam/water mass per unit length and the flow velocity constant. Depending on the taper ratio, the tube length increases by about 1.5 times for the same area. (This is a truncated cone vs a cylinder of the same area.) The radiator has to present the same area to the sky regardless of the number of tubes or their size. The mass breakout is 1675 tons for wall material and 1200 to 3300 tons for steam/water depending on tube diameter (from 11 to 28 m).

 

Pressure Drop and Number of tubes

Larger numbers of smaller tubes have smaller masses of steam and water in them. They also have a higher-pressure drop over the length of the tube. This also depends on the condensation ratio. The pressure drop for 90%-condensing, 11-meter tapered tubes three km long is around 3.5% of the internal pressure. For 95% condensing (giving a smaller exit end) the pressure drop increases to 11.5%. It is not clear how much pressure drop is acceptable. Nor have we determined the optimal number of tubes. Large numbers save steam/water mass at the cost of complexity from larger numbers of turbines and generators. This analysis uses 240 11-meter tubes and 2900 tons for the radiator mass.

Frame

The boilers, steam generators, turbines, electrical generators and radiators need a frame to keep them oriented. At a mass of 100 tons per km and 12 km, the frame would mass 1200 tons. Anna Nesterova did an animation of a roll former bending coils of sheet metal into two construction cubes, then using the cubes to create a frame. https://www.youtube.com/watch?v=H0PDV43Sg_8

Transmitter

The Boeing 1979 study gave a number of 6400 tons (10). A more recent SolarHigh study (incomplete) came in at 5900 (11). Tentatively this analysis will assume 6,000 tons for the transmitter mass estimate.

Other known problems

Earth eclipses power satellites in GEO twice a year for as much as 70 minutes. It typically takes 10 minutes for the steam in a tube to condense completely, and less than a minute more for the condensed water to freeze. Restarting when the power satellite comes out of eclipse is a problem that needs attention. Rotating the between tube reflectors to block outgoing radiation while in eclipse may be a solution.

Tentative major elements mass budget

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Total 25.7 kt, 79% of a 32,500 ton target (6.5 kg/kW). The remaining 6.8 kt needs to cover items such as station-keeping engines, a 600-km gravity gradient “space anchor”), controls and miscellaneous structure. A thermal power satellite may exceed the target mass, but probably not by a large amount. 
To the best of my knowledge, this is the first power-satellite proposal for undercutting coal since G.K O’Neill’s Science article (12) in 1975. There he proposed to produce energy at less than the cost from coal. O’Neill based his proposal on material mined from the moon and not on cargo brought up from the earth.

It should be clear to the readers that bringing a thermal power satellite project to the point of implementation will take considerable effort. That is, it will take thousands of engineers instead of one retired electrical engineer and a few friends. Still, even the largest projects have to start somewhere.

SunFlower Alternate Design

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Figure 3 showing mirrors, radiator tubes and transmitter ©Mafic Studios

Kris Holland and Anna Nesterova animated the transportation and construction details of  a radial thermal power satellite for the SunSat 2015 contest. The design consists of a central boiler and turbines exhausting into 120 radial tubes.  The radial radiator tubes are single ended, about 1800 meters long, with the outer end 29 meters in diameter.  There are concentric 10-meter internal tubes that carry the turbine exhaust steam out to the end of the radiator tubes.  The steam then returns to the hub in the anular space while condensing.

This design has a modest penalty (about 14%) over a design with parallel tubes and reflectors.  This is due to the radiator tubes partly blocking the view of the sky for each other.  In compensation, a radial design may need less structural mass for the frame.

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Figure 4, Looking into the boilers. Turbines, generators are around the hub. ©Mafic Studios

The rest of the design, potassium boilers, steam generators, turbines, generators and transmitter are closely similar in mass.  The mirrors passively focus sunlight on a circular ring boiler around the center of the “flower.”  It is a lot less complicated to keep the sunlight focused into the ring as it rotates under the mirrors than it is to switch among the many boilers in previously analyzed design.  Determining the relative merits of this designs as well as a comparison with PV designs is a work in process.

Economics

The fact that electricity is a commodity forces power satellites to compete with coal. Coal has similar operational characteristics (base load). The price of electricity from coal, about four cents per kWh, sets the maximum price for electricity from space. The price of electricity from space should be enough lower than that from coal (say three cents per kWh) to capture a large market share. A large market share is required to justify the initial investments (and to get the Skylon costs down). A previous paper (Henson, 2014) discussed an approach to get the transport cost to GEO down to $200/kg (13). The allowable capital cost is $2400/kW for three cents per kWh. The current estimate for the cost of parts and the rectenna is $1100/kW leaving $1300/kW for transport to GEO. At $200/kW and $1300/kW, the maximum specific mass is 6.5 kg/kW or a five GW power satellite can mass no more than 32,500 tons if it is to deliver 3 cents per kWh electricity. After 47 years of study, we finally found one way to get the cost of power satellites down to where they make economic sense.

Conclusion

The reason to build power satellites is to displace coal with lower-cost, renewable, space-based solar power. The rough analysis in this article has found that a target mass of ~32,500 tons is reasonable for a thermal power satellite and electricity from satellites can be sold for less than that from coal.

The analysis depends on methods (Skylon, ground-powered LEO to GEO) that reduce the cost of cargo to GEO to $200/kg and a lightweight thermal cycle to convert sunlight into electricity. From this preliminary analysis, it seems probable that thermal power satellites would cost about $2.4 B/GW. Built in the thousands they would displace fossil fuel with low cost electricity and low cost synthetic hydrocarbon fuels. They would provide renewable energy on the ground for less than coal. The question now:  Should thermal power satellites be subjected to a more detailed analysis? It would be useful for the political world to have a large-scale replacement for fossil fuels available that does not destroy the economy.


 

Endnotes

1) Forward and Holt proposed a way to drain the Van Allen belts. http://www.tethers.com/HiVOLT.html Even without deliberate efforts, the presence of large structures in GEO will soak up the particles and decrease the radiation exposure.
2) Space Solar Power Satellite Alternatives and Architectures. slide 32
3) Earth is also in space. Radiation is the way Earth ultimately gets rid of waste heat.
4) A Potassium-Steam Binary Vapor Cycle for Nuclear Power Plants.
5) Dollar a Gallon Gasoline.
6)A Potassium-Steam Binary Vapor Cycle for Nuclear Power Plants.
7) Mass Flow Solar Energy Receiver “A receiver for collecting solar energy at high temperatures with low reradiation losses . . .” http://www.freepatentsonline.com/4033118.pdf
8) Westinghouse Engineer, Volumes 31-32
9) Design Studies of Condensers and Radiators for Cesium and Potassium Rankine Cycle Space Power Plants.
10) Solar Power Satellite System Definition Study. P. 34
11) Personal communication from Hubert Davis, 2013-solar-high-master-draft-for-swri-1-2.ppt slide 15. File available from author
12) Space Colonies and Energy Supply to the Earth, Gerard K. O’Neill Science, 5 Dec. 1975 Volume 190, Number 4218.
13) Too late, to animate for the contest, or even fully analyze, Steve Nixon proposed a disk shaped tug with the engines on one edge and the cargo packed in close to the disk. This avoids the center-of-gravity problems with an empty tug, requiring the tugs to come back in pairs from GEO. The implications for gravity gradient and thermal problems have been recognized but not analyzed. It also may make personnel transport more difficult. The disk presents a somewhat smaller target for the serious problem of space debris. Overall, we should look into it when resources are available.


 

REFERENCES

 

1.Bejan, A. Advanced Engineering Thermodynamics, 2nd ed. New York: Wiley, 1997.


2.Chambers, W.R., Fraas, A.P., Ozisik, M.N. A Potassium-Steam Binary Vapor Cycle For Nuclear Power Plants. Oak Ridge TN: Atomic
Energy Commission, 1964.


3. Davis, Hubert Dickinson, Talay, R., Woodcock, G. 2013 Update to Space-Based Solar Power. Austin, Texas, 2013.


4. Fraas, A. P. Design Studies Of Condensers And Radiators For Cesium And Potassium Vapor Cycle Space Power Plants 0rnl-Tm
2081. Oak Ridge, TN: Atomic Energy Commission, 1968.


5.Henson, K., Drexler, K.E. "Gas Entrained Solids: A Heat Transfer Fluid for Use in Space." Space Manufacturing Facilities 3. Princeton: AIAA, 1979. 141-147.


6. Henson, K. "Solving economics, energy, carbon and climate in a single project." Technologies for Sustainability (SusTech), 2014 IEEE
Conference. Portland: IEEE, 2014. 203-208.


7. Henson, K. "Dollar a Gallon Gasoline." The Energy Collective. April 2, 2014.

 

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Contents
Issue No. 18:
SunSat Design Competition

Fall 2013- Fall 2015


The Three 2013-2014 Prize Winning Entries

First Place Winner – Team Rajiv Gandhi University: HelioAstra

Second Place Winner – Team Solar Maximum LLC: Sun-Synchronous Orbits

Third Place Winner – Team University of North Dakota: Nano SSP Satellite

The Three 2014-2015 Prize Winning Entries

First Place Winner – Team CAST: Multi-Rotary Joints SPS

Second Place Winner – Team SunFlower: Thermal Power Satellite

Third Place Winner – Team Martian: SPS Test Bed (In process of publication)

Contributors

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