Members:

Travis Smith
Darren Chan
Sam Cronin

Questions:

1.) Why isn't this project viable? Name two reasons.
2.) If the shuttle carrying the panels was already built and the panels could be shipped off immediately, wiping out much of the capital cost, would this be a worthwhile project to carry out? Explain with calculations shown.

Problems and Objectives

The efficiency of solar harvesters on earth is greatly impacted by the Earth's atmosphere; we have roughly 30% loss of the sun's radiant energy. We also encounter the issue with low duty cycle (<50%), since solar cells can only operate effectively when exposed to direct sunlight; during the night, we have effectively 0% efficiency.

We evaluate the feasibility of constructing solar panels on the moon and beaming the energy wirelessly back to Earth. The goal of this design is to increase renewable energy in the United States by increasing power production without using the limited space left on Earth. We will investigate:
  • The costs of putting solar panels on the moon
  • Maintenance costs
  • The efficiency of beaming the energy back to Earth (wireless power transmission)
  • Financial viability of this project

Technology: Solar Panels

A Stretched Lens Array Photovoltaic designed by NASA will be used [1]. This photovoltaic is based upon a GaAs triple–junction design which demonstrates a 45% efficiency under terrestrial laboratory conditions [1],though is expected to operate at 23% efficiency in space [8]. Laser collectors, based upon a similar design and demonstrating 56% laser to electricity conversion efficiency under terrestrial laboratory conditions, will be utilized [1,13].

General Safety Concerns

Even at low power levels laser beams can blind and/or kill people [2,4], hence multiple levels of safety protocol will be installed. The laser beams on the moon will feature a remote shutdown system in case of emergency. In addition, an automatic shutdown system will be installed in the laser in the event that the laser itself is severely damaged. Commands from Earth can override this automatic shutdown system. In addition, the lease of receiving plant on earth will be placed in an isolated location, such as the Yucca Mountain range in Nevada, in order to minimize civilian injury.

Issues with Orbits

A key problem with with project is that laser transmission requires a direct line of sight with the laser collector [2].
Because the Earth rotates faster than the moon, energy cannot be beamed to Earth 24/7 unless laser collectors were placed across the world. Due to loss in efficiency and increased logistics (primarily due to international law and logistics planning) associated with transporting energy halfway around the globe, this project assumes that only one laser collector exists in the world and that it exists in the Southwestern United States, an area that features clear skies for the better part of the year.

To somewhat alleviate this problem a satellite will be placed in geosynchronous orbit (GTO) over the laser collector. This satellite will be equipped with mirrors that will reflect incoming laser beams from the moon towards the collector facility on Earth. Since the satellite will be in GEO it will always be directly above the laser collector [3]. This solution also affords better control in directing the high powered laser beams at Earth, minimizing the chance of misdirected laser beam irradiation.

Benefits of Laser Technology

Laser beams are small enough that they will not interfere with satellite signals and radio waves, which are used for wireless communication on Earth [2]. In addition, laser beams are best suited for long range distance transmission, with distance having a negligible effect on the beam’s energy [5].

Financial Calculations


Cost Breakdown:

Much of the cost regards sending and installing the solar panels on the moon. The cost of sending the panels and technicians to the moon consists of $1.7 billion to construct the space shuttle and $450 million to launch [6]. The cost of the Stretched Lens Array Photovoltaics is assumed to be 85% cheaper than the cost of current GaAs high efficiency photovoltaics, which cost $50,000 per square meter [1,7]. The laser collector, laser, and satellite are quoted at $10 million [1], $500,000 [9], and about $5 million [8], respectively.

We assume that the annual maintenance and operation costs are approximately 1% of the capital cost, which is identical to most solar plants on Earth [11]. This estimate will be treated as a baseline figure because the costs can increase significantly if there is pressing need to make repairs on the moon multiple times a year.

Solar Panels

Laser collector

Laser Transmitter
$5E5
Send to Moon
$2.15E9
Cost of collector
$1.00E7


Cost of Panels + Installation (75% of cost)
$3.00E4
per m^2
M&O (1% of capital) per year
$1.00E5
Cost of Satellite
$5E6
M&O (1% of capital) per year
$2.15E7





In addition to the financial difficulties, another consideration is the temperature extremes on the moon, which range from 100 K to 400 K [12]. There is also an increased chance of meteor impact due to the lack of atmosphere on the moon relative to earth. These temperature fluctuations affect the efficiency of the solar panels by changing the width of the band-gap. In subsequent calculations it will be assumed that the efficiency of the solar panels is temperature independent.

From these cost approximations (assuming only a square meter of the moon was covered with solar panels), the initial capital cost is $2.17 billion. However it will take time to construct the panels and the space shuttle (we estimate 10 years), the capital cost changes to $4.26 billion assuming a 7% interest rate. The total annual cost of maintenance and operation is $21.6 million.

Because the panels degrade quickly in the span of 10 years, it is assumed that the solar panels will have a 20 year lifespan on the moon. Hence it is assumed that a 30 year loan is taken to pay for this project at 7% interest. Since no revenue will come in until year 11, the total annual cost (capital cost plus M&O) becomes $424 million. This value will increase as more solar panels are placed on the moon.

Capital Cost (year 1)
$2.17E9
Capital Cost (at year 11)
$4.26E9
Annual M&O Cost
$2.17E7
Interest Rate
7%
Years
20 (30 total)
CRF
0.094
U
$4.02E8




Total Annual Costs
$4.24E8
Total Incoming Electricity
74
kWh/year * m^2
Cost of Electricity
$5.69E6
per kWh

Energy Obtained from the Moon

Since a 30 year loan is taken and construction takes 10 years to accomplish, the panels will be generating electricity for 20 years. The moon is irradiated with 1000 W/m^2, though this number is a slight underestimation since the moon’s atmosphere is less substantial than Earth’s.

First assume that 1 m^2 worth of solar panels are placed on the Moon’s equator on the side that always faces the Earth. Assuming the Earth does not block incoming solar radiation at any point during the Moon’s orbit due to the large distance between the two bodies, the solar panels are effectively operational for half the moon’s orbit, as shown in Figure 1, because solar panels work at their best when sunlight is perpendicular to the panel’s surface and do not function when the sunlight is parallel to their surface.

FIGURE 1: How the position of the moon (in radians) affects the efficiency of the solar panels, whereby at 0 and pi radians sunlight is parallel to the solar panels (0% efficient) and at 3pi/2 radians sunlight is perpendicular to the panels (full efficiency). No electricity is generated at pi/2 radians because incoming sunlight is coming from behind the solar panels [15].
external image ciLUgyvtPTcGWSCyoVy0a9vP0_fWmwM3zWY5rlwjII3bWNkK4KpZ7HD7nck4kltFgFVu9nfDKbDrZ5jos064z66BtifXENlNJBmwrVsKBntgUWnMs_SCHPah

Assuming a linear increase in solar panel efficiency with changing lunar position, then over the course of seven days the efficiency of the solar panels is:

Efficiency=(23-0 %)/(7-1 day) x =3.8% (x), where x is the number of days since 0% efficiency

Average efficiency (daily)=sum of efficiencies over 14 days divided by 14=(2 (0+3.8+7.6+11.4+15.2+19+22.8) )/14=11.4%

Efficiency of Transmission (Sun to Moon to Earth)

From the above calculation, the average daily efficiency of the solar panels is 11.4%. Transmission of energy by laser beam thru space is approximately 100% efficient. Laser beams, unfortunately, are small enough that scattering and absorption in the atmosphere is likely [5,13]. It is estimated that only half the power of the laser beam will reach the laser collector [4] and that the laser collector is 60% efficient [1]

Average Total Efficiency (daily): 0.114 (1) (0.50) (0.60)=3.4%

However, due to conflicting orbits, energy can only be beamed to earth 25% of the time, representing a 75% loss in efficiency. As a result, the total efficiency is 0.85%, meaning that only an additional 8.5 W will be beamed to earth each day. Over the course of a day this represents an additional 0.204 kWh supplied to the Grid (just enough energy to fully charge 4 laptops). And this is at top efficiency, which will only get worse with time.

(8.5 J/s) (86400 s/day) (1 kWh/3.6E6 J)=0.204 kWh

In addition, solar panels are expected to degrade (lose 25% efficiency every decade) due to solar irradiation and extreme temperature changes [10]. As a result the 0.204 kWh per day is expected to decrease with time.

Figure 2: Energy Diagram
external image 3CsvjaeFUNusAxfPkIjx4CUnDwWHcl1_XsdZK3L6ANzNa2Fa4eBbwKGnwlSCoKv3MjMUbPt4D4tQlq45OuBZo5xR_Y3KaUujqYHHEdVchFelxuMV01nfjE1w

Cost of Electricity

The cost depends on the number of solar panels placed on the moon’s surface, as shown in Figure 3. Assuming one space shuttle and one trip to the moon is required the cost of electricity reaches a $75/kWh minimum once 10 million square meters of the moon are covered. This cost is expected to double over two decades as the efficiency of the panels worsens due to particle irradiation and extreme temperature changes. The capital cost of such a venture is estimated at $594 billion, which is about 4% of the 2010 USA GDP [14].

Figure 3:It is assumed that only one space shuttle will be built and that only one trip to the moon will be required to install the solar panels. This approximation becomes unrealistic as the surface required increases beyond several tens of square meters.
ScreenHunter_153 Jun. 04 10.20.jpg

Conclusions

Overall this project is not a feasible means of supplying energy to Earth primarily due to poor systematic efficiency (which is expected to worsen over time) and the high cost of the solar panels. While costs can be somewhat reduced by building more laser collector facilities across the world and placing more satellites in orbit above those collectors, the cost is not expected to fall near the $0.15/kWh price of Californian electricity without drastic improvements in photovoltaic technology, space transport, and energy beaming.

References

[1] www.stretchedlensarray.com/Papers/SPSLaser.pdf
[2] http://en.wikipedia.org/wiki/Wireless_power
[3] http://www.polaris.iastate.edu/EveningStar/Unit4/unit4_sub3.htm
[4]http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/16855/1/99-0263.pdf
[5]http://www.academia.edu/1561057/Feasibility_of_Wireless_Power_Transmission
[6]http://www.space.com/17556-giant-nasa-rocket-space-launch-cost.html
[7] http://gcep.stanford.edu/pdfs/2wh9Q1Alh3q2zMOQRKD4MQ/MikeMcGehee_SolarEnergy101.pdf
[8] http://www.nationaldefensemagazine.org/archive/2010/July/Pages/MilitaryLookstoSmallSatellites.aspx
[9]http://peswiki.com/index.php/Wireless_power_transmission_satellite
[10]https://web.engr.oregonstate.edu/~yokochia/wiki/uploads/Documents/ch10%20space%20based%20systems.pdf
[11] http://en.wikipedia.org/wiki/Solar_power
[12]http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html
[13]http://www.rand.org/content/dam/rand/pubs/technical_reports/2011/RAND_TR898.pdf
[14]http://www.particle.com/wp-content/uploads/downloads/2012/02/WP-MET-ONE-Long-Life-Lasers-in-Optical-Particle-Counters-US.pdf
[15]http://energyworksus.com/solar_power_incident_angle.html