Space Based Solar Power

The Wikipedia's take on the topic is here https://en.wikipedia.org/wiki/Space-based_solar_power

Power Satellites Economics

In the absence of other forces such as legal requirements, power satellites compete in the energy market. Energy, particularly electrical energy, is the ultimate standard commodity. When a customer plugs in a toaster, energy is just there. At the end of the month, they pay the bill at the rate set by the state utility commission. One level up, the power companies are hemmed in by regulations that they buy (or make) the lowest cost electricity, with exceptions that they have to purchase certain amounts of renewable power.

Space based solar power is renewable. That should make it easier to sell power from space at a premium. However, governmental energy polity changes unpredictably over time. An alternative would be a "design to cost" where the target cost of power is low enough to get a large market share without government intervention. Competing on cost is the way discount suppliers of many commodities obtained a substantial market share. (Examples, Southwest Airlines, GIECO, Charles Schawb.)

Levelized cost of power

The formula for the levelized cost of electricity is here; https://en.wikipedia.org/wiki/Cost_of_electricity_by_source

The below spreadsheet assumes $1,600,000 per MW as the initial cost and 10% per year of the cost for maintenance. Power satellites run supplying base load, here assumed ~91% of the time, it may be higher.

The discount rate used in the model is 6.8%, same as the government uses for other sources. The accounting period is 20 years and no salvage value is assumed.

https://docs.google.com/spreadsheets/d/1wDvn369EudkYGsPK3jNt4FmBFpNFtt0ZwDZl_lt_SNM/edit#gid=1481425448

The ratio between the $1600/kW cost and the cost that comes out of the formula (~2 cents per kWh) is close enough to 80,000 to one. Electric power cost is proportional to the cost of a power satellite (or any power source that has no fuel cost) in this ratio for this discount rate and years of service.

The UK government has determined that 3.5% discount is proper for projects of this kind. Using 3.5%, the electric cost comes out at just over 1.5 cents per kWh and ~100,000 to one. Extending the accounting period to 30 years at 3.5% brings the cost of power down to 1.24 cents per kWh and a cost of power to cost of investment ratio to ~130,000 to one. It's a live spreadsheet, try your own numbers. A ratio of 80,000 to one is conservative.

To take market share from coal will require the cost to be less than 4 cents per kWh. Three cents per kWh allows a capital cost of $2400/kW.

The current model has this split out as $200/kW for the rectanna ($1 B for 5 GW), $900/kW for the cost of parts and minor labor in space and $1300/kW 6.5 kg/kW and $200/kg) for the cost of transport to GEO.

Power Satellite Types

Photovoltaic (PV)

Most designs for power satellites since the 1970s have been PV. PV has advantages, long experience powering communication satellites being important. However, PV suffers from relatively low efficiency (20%) and degradation from radiation. There are proposals by Forward and Holt on draining van Allen belt, http://en.wikipedia.org/wiki/HiVolt, however, just the presence of a substantial number of power satellites in GEO is expected to greatly mitigate the radiation from particles trapped in the Earth's magnetic field. (There are only about 3 kg of protons trapped in the belts.) There are PV cells that range up to 40% efficient, but they require concentrated light and cooling.

Thermal

Thermal (heat engines) power satellites are expected to range up to 60% efficient, similar to combined cycle plants on earth. This means they need about 1/3 of the light interception area, which reduces station keeping from light pressure. However, they also need radiator area that is about twice the sunlight interception area, (Bejan, 1997, pg 495, ref Bejan, A. Advanced Engineering Thermodynamics, 2nd ed. New York: Wiley, 1997.) Counting both sides of the radiator makes the exposed area for thermal and photovoltaic power satellites about the same.

Common considerations

Mass

The original studies done in the late 1970s came up with a mass of ~10 kg/kW. More recent realistic studies have averaged around 7 kg/kW. A few studies have proposed designs under one tenth of a kg/kW. Very light designs require a lot of station keeping against light pressure where designs in excess of 5 kg/kW can average the light pressure over a year. Because a substantial fraction of the construction cost is for transport to GEO, the mass of a power satellite is an important number as is the lift cost to GEO. This analysis will use 6.5 kg/kW. The number can be adjusted in the spreadsheets.

Energy transmission loss

How efficient is the transmission of the energy with the microwave beam?

For economic analysis, 50%. The loss chain might be a little better with technical improvements, but not much. It means you generate two kW in space for one kW on the rectenna bus. That's been assumed in all the analysis here.

Energy payback time

Most of the energy embedded in a power satellite come from the hydrogen

The fuel fraction to raise cargo from LEO to GEO is about 20% So 15 tons of cargo delivered to LEO will take 3 tons of hydrogen to deliver to GEO (with or without a stop at 12,000 km for construction).

Thus for 12 tons in GEO, the trip to LEO burn 59 tons in the Skylon and 3 tons for the LEO to GEO leg. I.e., ~62 tons for 12 tons delivered or ~5.17 tons of hydrogen per ton of cargo or 5.2 kg of LH2 for one kg of parts. It takes 6.5 to 7 kg of parts per kW installed. For a kW of capacity, it takes about 35 kg of LH2. The hydrogen has an energy content of ~50 kWh/kg plus it takes about 20 kWh/kg to liquify it. [[1]] The energy expenses to lift a kW of capacity to GEO is therefore 2400 kWh/kW installed. This would take 100 days to repay the energy after startup or a little over 3 months. For a first approximation, the embedded energy in the parts and the energy required to make LOX are so small in comparison to LH2 that they can be ignored.

Reliability

Electric power needs to be reliable. First, the power satellite size is only 5 GW. The target number is 3000 for 15 TW. There would be spares sending power to low priority loads that could be switched in less than a second to replace a higher priority failed one. Plus we would still have the grid to distribute electricity from the remaining powered rectennas, and for a long time, there would be other generation in the mix.

None the less, there are ways we could lose the whole fleet of them in an instant if they were not designed to deal with it. In 774 or 775 the Earth seems to have been hit with a fairly close gamma ray burst. Those are typically a few seconds, but it put a serious kink in the carbon 14 for the next growing season. Alternately, the earth could have been hit with an unprecedented solar flare. Such an event would take out the controls for any power satellite that did not have enough shielding around the control computers. The shielding needed against these 1000 year events is considerably more than the worst solar flares observed to date.

Unlikely as they are, GRB or intense high energy solar flares are a concern that requires mitigation and recovery strategies such as watch dog timers and hardened reboot memory. Radiation resistance is an argument in favor of rotating machines rather than PV.

A solar flare can be seen coming and outside workers would probably have time to reach shelter. A GRB would be over before the workers had a chance to move. Neither are serious problems for people behind cosmic ray shielding.

Transport Earth to LEO

SpaceX

SpaceX will not get the transport cost down low enough. It's got to be SSTO or possibly TSTO runway operations.

SpaceX _will_ eventually get the cost to GEO down by a full order of magnitude, a remarkable achievement. Unfortunately this won't do it for power from space, it takes _two_ orders of magnitude reduction. Musk knows this. It might be why he is so down on power satellites.

Skylon

Until Reaction Engines demonstrated their high performance precooler, there were no realistic SSTO proposals out there.

www.reactionengines.co.uk/space_skylon.html

www.reactionengines.co.uk/space_skylon.html