Mirrors in Space for Low-Cost Terrestrial Solar Electric Power at Night
see above what do they look like to you??
Lewis M Fraas
JX Crystals Inc, Issaquah, WA, USA
ABSTRACT
A constellation of 18 mirror satellites is proposed in a
polar sun synchronous dawn to dusk 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
that terrestrial site equivalent to the normal daylight sun
intensity extending the sunlight hours at that site at dawn
and 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 in 10 years, there will be
approximately 40 terrestrial solar electric field sites evenly
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 or power plant
capacity factor for a terrestrial solar electric power site can
thus be extended by about 30%. Assuming a launch cost
of $400/kg as was assumed in a recent NASA Space
Power Satellite study for future launch costs, the mirror
constellation pay back time will be less than 1 year.
BACKGROUND
The idea of using mirrors in space to beam sunlight
down to earth for terrestrial solar electric power generation
is not new. Dr. Krafft Ehricke first proposed this idea in
1978 (1, 2) as shown in figure 1 under the title Power
Soletta. Because of the simplicity of mirrors compared to
the complexity of the Space Power Satellite concept, his
idea was brilliant particularly for the time in which it was
first proposed.
Specifically, Ehricke proposed a constellation of
satellites in an orbit 4200 km in altitude beaming power
down to a 1200 sq km site in Western Europe. Deflecting
sunlight down to earth where it is then converted to
electricity is conceptually much simpler than converting it
to electricity in space and then microwave beaming it
down to earth and then converting it to electricity as per
the Solar Power Satellite concept.
The key physical limitation for this concept relates to
the size of the sun’s disc as viewed from earth. The sun’s
disc subtends an angle, θ, of 10 mrads. This means that
the minimum size of a sun spot produced on the earth’s
surface from a mirror in space at an altitude, A, is:
2A tan (θ/2) (1)
Applying this formula for a mirror in orbit at an altitude
of 4200 km gives a sun spot diameter on earth of 42 km
with a corresponding area of 1385 sq km. This explains
the 1200 sq km solar field size for the Power Soletta
concept. This also means that in order to produce an
intensity of sunlight on earth equivalent to the normal
daylight sun intensity, the area of the 3 mirrors shown
beaming power down in figure 1 would have to be 1385 sq
km and the area of the 10 mirror satellites in the
constellation in figure 1 would have to be 4617 sq km.
Unfortunately, the enormous task of placing this mirror
area in orbit was somewhat discouraging in 1978.
In addition, there are two other problems with this
concept as Ehricke proposed it. One problem is that this
orbit falls in the Van Allen radiation belt. A second
problem will reside with the size of the earth solar electric
power field and the resulting problem of then distributing
the power produced throughout Europe. Ehricke assumed
that the 1200 sq km solar field would produce electricity at
15% efficiency implying a 180 GW central power station
which then implies enormous distribution problems.
Figure 1: Power Soletta proposed by Dr. Krafft Ehricke
While this Power Soletta concept was intriguing, given
the problems just described, NASA has focused much
more attention over the subsequent years on the Space
Power Satellite (SPS) concept (3, 4). A recent version
(2003) of this SPS concept is shown in figure 2. This
Integrated Symmetrical Concentrator (ISC SPS) concept
is of interest here because it also utilizes mirrors (3, 4). As
shown in figure 2, in this concept, two sets of 36 mirrors
with each mirror approximately 0.5 km in diameter are
used to beam sunlight to a central PV converter platform
that then generates electricity and beams microwave
energy to an earth generating station. This satellite is
assumed to be located in Geosynchronous Orbit at an
altitude of approximately 36,000 km. The special 8 km
diameter earth receiver / generator station is assumed to
generate 1.2 GW of electricity.
There are also problems with this ISC SPS concept.
One problem is its complexity. More than just mirrors are
now required and it now no longer uses a potentially
existing terrestrial solar electric power station.
Figure 2: Integrated Symmetrical Concentrator Solar
Power Satellite NASA. Dimensions: 5 km x 15 km.
Within the context of mirrors in space, one promising
feature associated with the ISC SPS design is the
assumed use of 0.5 km diameter mirrors (figure 2). There
are also other recent developments related to mirrors in
space. A Japanese Ikaros Solar Sail satellite (figure 3) is
now en route to Venus (5) and L’Garde (6) is now
developing lightweight inflatable reflectors (figure 4).
Figure 3: Ikaros Solar Sail - Launched on 21 May 2010,
Ikaros is a solar sail currently en route to Venus (5).
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 x (1.3)10 = 900 GW of PV in fields world
wide. Furthermore, 5 GW terrestrial electric power
stations are now already being built (7).
Figure 4: Inflatable Reflector Development at L’Gaarde
One problem for solar generated electricity is that the
solar energy available to a 1-axis tracking solar power
station on earth on average is only about 7 kW hours per
m2
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. Ehriche chose the mirror orbit at 4200 km
because he wanted to provide solar electric power all
night. Is there another better orbit choice where the
mirrors can be utilized for 24 hours per day? For
reference, figure 5 shows the concept of a sun
synchronous orbit.
Figure 5: Diagram showing the orientation of a Sunsynchronous
orbit (green) in four points of the year. A
non-sun-synchronous orbit (magenta) is also shown
for reference.
CONCEPT: MIRRORS IN DAWN TO DUSK LEO SUN
SYNCHRONOUS ORBIT
Now imagine 18 mirror satellites in a sun synchronous
orbit at an altitude of approximately 1000 km as shown in
figure 6. There are several immediate benefits that result
from this MiraSolar satellite constellation configuration.
First, applying equation 1, the illuminated sunlight
spot size on the earth is now only 10 km in diameter
instead of the 42 km spot size associated with the Power
Soletta configuration. Furthermore, the size of each mirror
satellite now required to produce a solar intensity
equivalent to daylight sunlight is now only 10 km as well.
This 10 km mirror satellite size is comparable in size to the
5 km x 15 km ISC NASA SPS satellite size. As we will
show in a later section, the size of this earth based electric
power station is now approximately 5 GW instead of the
Power Soletta sized 180 GW station.
Figure 6: A 18 mirror satellite constellation 1000 km
high is in a dawn/dusk sun synchronous orbit around
earth. North is up. The mirror satellites are evenly
spaced in latitude at the equator by 20 degrees.
In this paper, we shall assume this 18 satellite
constellation will be available to an array of ground solar
electric stations distributed around the world. As already
noted, 10 years from now, there will be 900 GW of solar in
the world. All of this will not be in central power fields but
if we assume that 1/3 of the 900 GW is or could be, then
there will be 300/5 = 60 available solar ground stations.
These stations will be located in sunny parts of the world
near population centers. Table 1 presents a partial list of
potential sites. Here, we shall assume that over the
course of 24 hours as the world turns, 40 of the potential
60 future sites depending on the weather for that day will
be selected to receive additional sun beam energy in the
early morning and early evening hours. Our goal is then
to calculate the additional energy this collection of sites
can produce and to compare that revenue stream with the
potential mirror constellation cost in order to calculate a
pay back time for this mirror constellation.
Table I: Tentative Solar Electric Power Ground Sites
1.) LA, San Diego, S. Ca.
2.) Hawaii
3,) Albuquerque
4.) Phoenix
5.) Las Vegas
6.) El Paso
7.) Alaska
8.)Calgary
9.) Denver
10.) Kansas City, St. Louse
11.) Miami
12.) Boston, N.Y., N.J.
13.) Mexico City
14.) Panama
15.) Rio de Janeiro
16.) Brasilia
17.) Lima Peru
18.) Buenos Aires
19.) Madrid
20.) Rome
21.) Berlin
22.) Istanbul
23.) Moscow
24.) South Africa
25.) Saudi Arabia
26.) Bombay
27.) Calcutta
28.) Bangkok
29.) Manila
30.) Taiwan
31.) Sydney
32.) Tokyo
33.) Beijing
34.) Tibet Plateau
35.) Inner Mongolia
36.) Cairo
37.) Delhi
38.) Perth.
SLANT RANGE AND 1-SUN EQUIVALENT HOURS
In addition to the sun’s disc size which determines the
satellite and earth station sizes as per equation (1), there
is another important equation that relates the solar
intensity at the ground site to the slant range to the
satellite in view at the earth station. The sun beam
intensity will decrease with the slant angle, θ, and slant
range, R, as per equation (2).
I=Io cos(θ)/R2
(2)
Referring to figure 7, θ = 0 and R = A when a mirror
satellite is vertically over head.
This slant range equation is important for calculating
the effective one-sun beam energy available per day to
each ground site. One-sun beam energy will be
calculated in kWh / m2
.
Figure 7: N is up here.
The circle represents the
earth’s surface at a 35o
latitude. As the world
turns, the target ground
station moves up and the
slant angle and slant
range increase. 15o
represents 1 hour. When
the slant angle is 45o
, the
earth has turned 13o
or
60x13/15 = 52 minutes.
In order to estimate the available sun beam energy
per day, we first look at the north-south (NS) dimension
and then the EW dimension.
Figure 6 allows an examination of the sun beam
energy in the NS time dimension. Figure 6 is a view
looking in the direction of the sun with the earth’s NS axis
up and with the satellite sizes and altitude in real
proportion relative to the earth’s size. All 18 satellites are
continuously circling the earth with a period of 105
minutes. So, at a given earth ground site, the time interval
for one satellite overhead to be replaced by the next will
be 5.8 minutes. When a satellite is directly overhead, by
design, the power at the ground site will be 1-sun or 1
kW/m2
. However when a satellite is not overhead as for
example with a view angle of 45o
, applying equation 2, the
cosine loss will be 0.7 and the range loss will be down by
a factor of 2. However, because there will be 2 satellites
available for beaming power, this factor of 2 loss can be
avoided. So, the power available at the ground site will
continuously oscillate on a 5.8 minute period between 1
and 0.7 kW/m2
.
Next turning to the power variation at a ground site as
the earth slowly turns. Figure 7 gives a representative
case. Three different latitude slant ranges are shown in
this figure. When a satellite is directly overhead, the
power is again 1 kW/m2
. However, when the earth has
turned 30 minutes (7.5o
), the slant range has increased to
1,230 km which means that the power at the site falls to
0.67 kW/m2
. Here, we shall assume that the solar ground
stations, be they silicon PV or trough CSP, are using 1-
axis EW tracking so that there is no cosine loss in the EW
direction. One can continue this process of estimating
power vs time out to 1 hour or 15o
. The average is
approximately 0.7 kW/m2
over the 1 hour period so that
the sun beam energy is then 1 hour x 0.7 kW/m2
. Given
that satellites are in view at a given ground site both
before and after the peak times and both in the early
morning and the early evening, the daily available sun
beam energy is about 2.8 hours x 0.7 kW/m2
per solar
ground station.
ECONOMICS
The primary reason why this MiraSolar concept is
interesting is its very attractive economics. In table II, first
the revenues are calculated and then the costs are
calculated.
Referring to the calculation of revenues first, there are
two key assumptions. First note that while the assumed
overhead ground power density is 1 kW/m2
or 1 GW/km2
,
the average power density is assumed to be 0.7 kW/m2
or
0.7 GW/km2
(Item 4 in revenue assumptions in table II).
The power produced per ground station of 5.5 GW follows
from this assumption.
The second key assumption is that the daily energy
available at each ground station is 2 hrs x 0.7 kW/m2
(Item 6 in revenue assumptions in table II). This is less
than the 2.8 hours x 0.7 kW/m2 per solar ground station
just calculated for the figure 7 example in order to be
conservative and because there will be variation from site
to site with latitude and weather conditions.
From these two key assumptions and assuming $0.1
per kWh, the annual revenues work out to be $16 billion.
Next referring to the satellite mass calculation,
fortunately, there are three consistent sources of
information here from the original Soletta study and the
Ikaros satellite and L’Garde studies.
Table II: Revenue and Costs Projections for MiraSolar
Satellite Constellations
Revenue - Assumptions
1.) 18 satellites in dawn/dusk orbit 1000 km above earth.
2.) The sun’s disc diameter viewed from earth is 10
mrad. This implies solar spot size on earth from a
mirror up 1000 km equal 1000xtan(10 mrad) = 10 km.
3.) Assume each mirror satellites has diameter of 10 km.
4.) Solar intensity = 1.37 kW/sq m = 1.37 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 each
satellite is π x 25 sq km = 78.5 sq km. The energy in
the sunlight beamed down toward earth = 75 GW.
Assuming slant range losses, the average 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 40
ground stations distributed around the world that the
18 satellite constellation will serve and that the
constellation gives 1 hr x 0.7 kW/m2 of sunlight to
each station in the morning and 1 hr x 0.7 kW/m2 to
each station in the afternoon for a total of 2 hrs x 0.7
kW/m2 of sunlight per day per station.
7.) Combined, the 40 earth stations will produce 5.5 x 40
= 220 GW. The total energy produced from the sun
beamed satellite constellation = 220 GW x 2 x 365 hrs
per year = 160,000 GWh /yr = 1.6 x 10^11 kWh/yr.
8.) Assume that the price for electricity is $0.1 / kWh,
annual revenue $1.6x10^10 / yr = $16 billion per yr.
Mirror Satellite Mass – Inputs
1.) The mirror weight on the Ikaros solar sail (7.5 micron
thick plastic) is 6g / sq m = 6 metric tons (MT) per sq
km (5).
2.) The Echo I satellite used 12.5 micron mylar with 0.2
micron Al as a mirror weighing 10 MT per sq km (2).
3.) Mass of mirror element, L’Garde estimate (6): 2
membrane dish of diameter 16.5 meters, mass of 15
kg = 70 MT / sq km. This would be 35 MT for single
membrane.
4.) Assume goal 20 MT per sq km for each MiraSolar
satellite. Then each weighs about 1600 MT or 6x10^6
kg.
Mirror Satellite Cost
1.) It all depends on launch cost for LEO orbit (Not GEO).
2.) The ISC SPS study (4) assumed $400 per kg.
3.) SpaceX Falcon Heavy (8) = $1,100 per kg.
4.) Air Force Lab revolutionary approach (9) = $250 / kg
5.) MiraSolar sat (4) cost $0.6 B; constellation (4) $11 B.
6.) MiraSolar sat (8) cost $1.8B; constellation (8) $32 B.
7.) MiraSolar sat (9) cost $0.4 B, constellation (9) $7 B.
Payback time range: (4) 0.7 year; (8) 2 years,
(9) 0.5 years.
The major uncertainty lies with launch cost. There
are 3 different LEO launch cost references. There is the
near term Falcon Heavy (8) or an estimate used in the
NASA SPS study (4) assuming more frequent launches or
a revolutionary system proposed in an Air Force Research
Lab study (9). Given that launch costs should be less
with reusable launch vehicles and frequent standard
launch procedures, the NASA estimate of $400 per kg will
be used here. With this assumption, the payback time is
0.7 years.
MIRA SOLAR SATELLITE DESCRIPTION
Given that the economics looks very promising, we
now turn to a preliminary description of a MiraSolar
satellite.
Figure 8 shows a view of the earth and two MiraSolar
satellites looking along the NS axis with the satellites
simplified and their sizes exaggerated for illustrative
purposes and figure 9 shows a blow up of figure 8.
Figure 8: A view of the earth and two MiraSolar
satellites looking down the NS axis with the satellites
simplified and their sizes exaggerated for illustrative
purposes. The NS axis is perpendicular to the page.
Figure 9: The mirror satellites may consist of a large
3-axis inertial stabilized frame with multiple mirrors
that can rotate individually. The frame is aligned
along the N-S polar axis and fixed at a 45 degree angle
relative to the suns illumination. As shown here, in
the evening on the left, the mirrors are aligned with
the frame. The mirrors can rotate in both the NS and
EW axes and can always direct solar illumination
approximately perpendicular to the earth’s surface. In
the morning on the right, the mirrors are
approximately perpendicular to the frame as shown.
The mirrors on each satellite are allowed to turn as
directed to maintain solar illumination on a given
location for approximately 105/18 = 6 minutes after
which the next satellite in the constellation can then
continue to illuminate that assigned location. This
drawing is illustrative and not to scale.
A 10 km diameter satellite is still very big. The mirror
satellites may consist of a large 3-axis inertial stabilized
frame with multiple mirrors that can rotate individually. As
shown in figure 8, the frame is aligned along the N-S polar
axis and fixed at a 45 degree angle relative to the suns
illumination. In figures 8 and 9, only two mirror elements
are shown for simplicity although in actuality, there will be
many more mirror elements per satellite. The mirror
elements can rotate in both the NS and EW axes and can
always direct solar illumination approximately
perpendicular to the earth’s surface and in fact
approximately edge on to the orbit direction.
Figure 10 shows an alternate gravity stabilized mirror
satellite configuration.
Figure 10: The mirror satellites can be gravity
stabilized as illustrated. Here, the mirror satellites are
very simplified and exaggerated in size simply to
illustrate a concept.
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 105/18 = 6 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 forty 5 GW ground solar
electric generating locations distributed around the world
with approximately 7 available in each continent. If in fact
there are 40 x 5.5 GW = 220 GW of solar ground stations
available 10 years from now, that will still be only 220/900
= 24% of the projected solar electric power production in
2022.
How might a large mirror satellite be built? As noted
in figure 11 in a preferred embodiment, there will be a
large number of mirror elements held relative to each
other in a large frame. In an example case where the
satellite is in an orbit at 1000 km, the mirror satellite will be
approximately 10 km in diameter. These dimensions are
approximate. For example the altitude of the orbit may be
chosen in the range from approximately 500 to 2000 km
with the satellite size then varying as per equation (1).
The size of the mirror elements can also be varied. One
possible mirror element might be similar in size to the
mirror elements assumed for the ISC SPS at 0.5 km in
diameter. Smaller mirror elements may be more
appropriate.
Figure 11: A 10 km diameter satellite mirror array is
shown with 1 km diameter mirror elements to simplify
the drawing.
In a preferred embodiment, each mirror element will
be independently rotatable in 2 axes. Figure 12 shows
one potential mirror element configuration. In figure 12, N
is up. In this example, there are EW motors attached to
the main frame at the S end of each mirror element. Each
of these EW motors attaches to a mirror yoke that secures
each mirror element at the E and W edges of each mirror
element. There is also a NS motor attached to the yoke
and the mirror frame as shown for each mirror element.
Near each of these motors, there are relatively small solar
cell arrays that supply power to these motors so that the
mirror can be rotated around both the EW and NS axes as
directed by a beam direction controller also shown.
The fabrication of the mirror elements must also be
considered. They will need to be very light weight.
Fortunately, this problem has been addressed first in the
original Ehricke NASA study and most recently in the
Ikaros and L’Garde projects. Figure 13 suggests one
possible way a mirror element might be fabricated and
deployed.
3-Axis
Stabilized
Main Frame
PV Array for
N-S Drive
N-S Drive
Motor
Beam Point
Control
Mirror
Mirror
Yoke PV Array and E-W Drive Motor
Figure 12: Each mirror satellite will contain a very
large number of mirror elements each of which can be
individually pointed at the center of an earth target
solar field.
Figure 13: Possible mirror element with inflatable rim
for deployment.
SUMMARY
Table III provides a summary comparison of key
parameters contrasting the MiraSolar system with the ISC
SPS concepts. In this table, the cost comparisons are
done using the ISC SPS assumed launch cost of $400 per
kg so that the 2 systems can be compared on an equal
cost basis.
Figure 14 highlights the Advantage of the MiraSolar
concept over the ISC SPS concept by simply noting what
is not needed for the mirror concept. The elements no
longer needed are the solar converter, the special ground
station, the microwave power beaming, and the heat
management. The low cost of just the structure
component from figure 14 is very consistent with the low
cost fast payback time conclusions from table III.
Table III: Space power system comparisons
Parameter MiraSolar ISC SPS
Orbit 1,000 km 36,000 km
# Satellites 18 1
Mirror Area per Sat 78 sq km 12.8 sq km
Total Mirror Area 1404 sq km 12.8 sq km
24 hr/day Earth
Power
220x2/24
= 18.3 GW
1.2 GW
Cost ($400/kg) $11 B $14 B
$ per 24 h GW $0.6 B/GW $11.7 B/GW
Earth Station Size 5.5 GW 1.2 GW
Referring to table III, note that the cost of the
MiraSolar in $ per W is 5 times less than the SPS.
However, also note that in both cases, this cost per W is
for a system based on 24 hours of power per day. While
for the SPS this power is at one ground site, for the
MiraSolar case, the ground sites are to be built anyway
and the 24 hours is from the point of view of the space
mirror system.
How will the space mirror system affect the cost of
solar energy in cents per kWh? This question can be
answered as follows. Assume that the 220 GW ground
solar stations will be built for a complete installed system
cost of $2.2 per W (DOE projection for 2016) and that they
will be paid off over a period of 10 years. The cost will be
$2.2x220 B = $0.48x10^12 and over 10 years, they will
produce 7x365x10x220 GWh = 5,621,000 GWh =
5.6x10^12 kWh. So, the cost of solar energy without the
space mirrors is 8.6 cents per kWh. With the space
mirrors, the cost of solar energy will be (484+11 = $495 B)
/ 9x365x10x220 GWh. The production hours will increase
from 7 to 9. The solar energy cost is now reduced to 6.7
cents per kWh and of course there is now more energy at
peak demand times in the evening. Both of these
numbers are less than the projected energy cost for the
SPS of 16.8 cents per kWh from figure 14.
The advantages of the MiraSolar constellation can be
summarized as follows:
1.) The economics works because the mirrors in space
are always available 24 hours per day.
2.) For the terrestrial power producing sites, capacity
factor is increased by 9/7 = 1.28 or more for high
latitudes at almost no additional cost.
3.) Ultimate simplicity.
4.) Each mirror sat in LEO is no bigger than the 5 km x
15 km NASA ISC in GEO.
5.) While expensive, its cost is spread over 10 years.
6.) Could catch public’s imagination.
7.) Combines the national space exploration program
with the world wide energy future.
How does one begin? One could start with a
controlled pointing mirror element in orbit for a moon beam
passing over the various Disney amusement parks around
the world for entertainment every evening.
ACKNOWLEDGEMENTS
The author would like to thank Mark O’Niell and
Geoffrey Landis for their valuable comments and
suggestions.
Figure 14: Technology Contributions to Energy Costs
for MOD High Concentration ISC. Only structure is
required for MiraSolar.
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