Space Solar Power Systems
A Comprehensive Design Trade Study
Introduction
In this white paper, we propose to revisit the idea of space-based solar power systems (SSPS) by
conducting a comprehensive trade study which emphasizes current and emerging technologies.
SSPS received much attention in the 70’s but interest faded as it became clear that the then
current technologies could not produce an affordable system. Presently, however, there is
renewed attention to SSPS because of technological advances and the emergence of niche
markets associated with the US DoD and developing nations. The time is now ripe for an up-todate design trade off study with emphasis on a First Revenue System (FRS) that can serve to
validate the technology and surmount the economic obstacles to initial implementation of space
solar power.
The trade study will address seven elements of the design of SSPS:
1. Beam transmit science, and orbit/constellation design
- Laser vs. EB vs. EM microwave
2. SSPS satellite design
- Modular, expandable, controllable, etc.
3. Ground collector system
4. Database and software development
5. Full turnkey system integration
6. Weather control system
7. Interplanetary spacecraft power beam
The study team, led by Prof. David Hyland has deep experience in the physics and engineering
of large optics and RF systems, adaptive phased array technologies (optical to RF), large space
structure control (including high bandwidth vibration and figure control, and precision actuator
and sensor hardware), advanced trajectory design, constellation design, and formation flying. To
appropriately complement these strengths, the team is prepared to recruit collaborators from all
relevant institutions having expertise in such areas as software development, active/smart
materials, phased array transmitter manufacture, solar array manufacture and meteorology with
specialization in weather control.
In the following sections, we outline the nature of the seven study topics and sketch the principal
tradeoffs to be considered.
Beam transmit science, and orbit/constellation design
The science of transmitting electromagnetic radiation depends critically on the wavelength
regime being employed, and this in turn, when combined with the orbit parameters (esp. transmit
1
distance), strongly drives the overall dimensions (and cost) of the SSPS. Thus we link transmit
science and orbit/constellation design in this discussion. The following discusses design
constraints and trades relating to mainly to the transmitter, with some attention to the size of the
ground receiving station. Trades associated with the receiving apparatus are discussed in a later
section.
First, consider the relation between the transmitter size and the receiving station on the ground.
Given an operating wavelength,  , and a filled aperture or dense phased array of diameter DA ,
transmitting to the ground at distance z , the width of the irradiated spot on the ground, x , is
approximately:
x 
z
DA
(1)
For a system at geostationary (GEO) altitude (35,786 km) operating a wavelength 1 cm, Figure 1
shows the numerical relationship between receiver and transmitter size. If we simultaneously
minimize both dimensions by setting DA and x equal, Equation (1) yields DA  x  600m obviously a very large system.
Figure 1: Beam width on the ground vs. transmitter diameter for a GEO SSPS operating at 1cm.
2
However one cannot adjust DA and x arbitrarily such that their product satisfies (1). There is the
added constraint that the maximum power density on the ground must be at a safe level for
human exposure. “Safe” is typically thought to be no more than 20% of the solar insolation at the
Earth’s surface and at zenith (approximately 1050 W/m2). In this discussion we take the
maximum safe level, denoted by  max , to be 10%, or 105 W/m2. Roughly, this requirement is:
  DA 
2

 Pt  105W m
4  z 
2
max 
(2)
Where Pt is the total power transmitted. In this discussion, we assume a FRS collecting in the
neighborhood of 5 MW of total power. Note that  max could be less than this but that would
require x to be larger than necessary, and the cost and potential inconvenience of the receiving
station increases with size. Thus to reduce the receiving station size as much as possible we
choose the equality sign in Equation (2):
 D 
  A  Pt  105W m 2
4  z 
2
 max
(3)
Numerically, the relation given by Equation (3) is shown in Figure 2. To get the transmitter size
for which the maximum power density equals 105 W/m2 for the 5 MW GEO system at 1cm
wavelength, we solve for D A to get DA  1.850 km , and use (1) to obtain x  200m .
Figure 2: Power density at ground level vs. transmitter diameter for 1cm wavelength, 5MW FRS
at GEO
3
Note that combining (1) and (3) and solving for x , we get:
x 
 Pt
4  max
(4)
Thus, when the safety constraint is imposed, the receiving station size is independent of altitude.
Therefore the two important constraints are Equation (4) and Equation (5) below, obtained by
solving (3) for D A :
DA   z
4max
 Pt
(5)
Let us pause to consider the implications of Equations (4-5). (4) shows that the receiver size of a
safe system is determined by the square root of the ratio of total power output to the allowable
power density on the ground. Otherwise the size is independent of wavelength and altitude or
transmit distance. Of course, the receiver equipment certainly is dependent on wavelength
regime. We can expect overall cost to depend on wavelength regime and rise at least as fast as
the area,  x  
2
Pt
max
, of the receiver station.
In contrast the transmitter size is proportional to the wavelength-altitude product, and the max
power density to total power ratio. A note on cost: The PIs experience with large RF or optical
systems shows that the cost of the aperture rises faster than the aperture area. A popular cost
model for large optics is that cost is proportional to the aperture diameter raised to the 2 23 power.
Figure 3 shows a more precise model with better fit to existing data. In any case existing models
show that cost rises faster than the square of the aperture size; or, according to Equation (5),
faster than the square of the altitude-wavelength product. Hence this product is a strong design
driver and our primary discussion of design trades must consider tradeoffs of both operating
wavelength and orbit design for the transmitters.
Consider the pros and cons of various wavelength regimes. The useful ranges are limited to those
wavelengths that are not strongly absorbed by the atmosphere. As Figure 4 shows, there are three
principal windows of atmospheric transparency: (1) The microwave and RF region between a
few centimeters and 10 meters, (2) the long wavelength IR range centered around 10 m, and (3)
the visible range around 0.5 m.
Starting with the longest wavelength range, the disadvantage as equation (5) shows, is the large
size of the transmitter required for a given altitude. If this regime is chosen, it is clearly desirable
to work in the low wavelength end of the microwave range, say approximately 1 cm. Here
transmitter hardware is of convenient size - neither very large as in RF nor microscopically
small, as in visible. Nevertheless, transmitters as a whole can be very large unless the transmit
distance ( z in Equation (5)) is considerably reduced.
The suitability of the microwave region for weather control depends on the possibility of heating
selected atmospheric constituents. Figure 4 shows absorption without the details of a multitude
4
M  M 0  M 1 D 2 1   f D 2   2f D 4  ...
D2
 M 0 M1
1  f D 2
Figure 3: Fabrication cost vs. primary mirror diameter, diffraction limited optics.
Figure 4: Absorption spectrum of the Earth’s atmosphere
5
Figure 5: Detailed absorption spectrum in the microwave range.
of absorption lines in the microwave band. The more detailed Figure 5 displays the absorption
lines. The frequencies can be tuned to excite a variety of molecules in the atmosphere such as
Oxygen or water vapor if one desires to heat an atmospheric region. When instead one wishes
undiminished transmission, the frequency can be detuned to avoid an absorption line.
A major advantage of this wavelength range is that the electromagnetic signals have frequencies
(recall   frequency  c  where c is the speed of light) that are low enough that they can be
digitized, processed, amplified, phase shifted, etc. This makes possible phased array technology
whereby power beams can be shaped and steered without the use of moving parts. Moreover, as
is discussed below, the effect on the transmitted beam of positioning errors due to structural
motion can be nulled entirely electronically and without moving parts or the use of force or
torque actuators that when used in closed-loop feedback control can result on instability (the
frequent consequence of control/structure interaction).
6
In the two lower wavelength regimes, the clear advantage is the smaller size of the necessary
transmitter structure for a given transmit distance. For our 5MW, GEO FRS, DA would be
 1.8m for the long wave IR and  9cm for mid-visible. The small size of these apertures raises
the problem that their components are too small. Also, for these small apertures, power densities
at the aperture can be high enough to require special cooling systems, as the PI’s experience with
the Zenith Star program attests. This is certainly the case if the system is scaled up to the
GigaWatt range. Moreover, in the long wave IR range, photonic detectors needed for wave front
control must be cooled to avoid very high dark count.
Another consideration is safety. The prescription that DA would be  1.8m for the long wave IR
and  9cm for mid-visible is based on using the formula, Equation (3), for the maximum power
density and then constraining it to be at a safe level. However at these short wavelengths, the
aperture diameter could be made much larger; thereby reducing the spot size and increasing the
power density in proportion to DA2 . A laser system that initially carries a small aperture with safe
power density could readily be altered, later, with an aperture 10 to 30 times larger, thus
  DA 

 Pt ) power densities one hundred to 1000 times the safe level. This
4  z 
constitutes a space weapon in contravention of international treaties. Such a metamorphosis of
microwave systems is entirely infeasible since safe aperture sizes, even down to lower altitudes,
are already tens to thousands of meters wide. The difficulty of weaponizing microwave systems
is possibly a decisive factor in their favor.
2
producing (  max 
Regarding beam shaping and steering, the frequencies in these regimes cannot be digitized or
processed so as to provide beam control without moving parts. Beam control must rely on shape
sensors and actuators with closed-loop control as in adaptive optics. This, in turn, brings in the
complexities of control/structure interaction which we will discuss in the section on SSPS
satellite design below. A disadvantage to the use of these regimes is that, as Figure 4 shows,
there is substantial atmospheric absorption. The Figure only shows absorption for zenith, i.e. for
the minimum optical thickness. At lower elevations, the increased absorptivity can markedly
reduce transmission efficiency. By the same token however, larger absorption means greater
capability to heat atmospheric constituents – an advantage for weather control.
Above we have considered the qualitative advantages and drawbacks of the various wavelength
regimes available to SSPS. Recalling Equation (5), the aperture size, and overall cost are
strongly driven by the product of wavelength and transmit distance. Thus it is appropriate to
discuss the trades associated with orbit/constellation design for a given operating wavelength.
The simplest and most obvious choice is to put the SSPS at geostationary orbit. Solar radiation is
essentially uninterrupted and beam pointing is basically static. However, the enormous transmit
distance is possibly the single most important factor underlying the large initial investment
required to field an FRS. If, for example, the transmit distance for our 5MW, 1 cm FRS were 700
km, the transmit aperture would be reduced to  35m (compared with 1.8 kilometers at GEO).
The most meaningful size reduction would be the MEO altitudes in the vicinity of 2000km. To
7
achieve this size reduction advantage, a more complex orbit design and power transmission
program employing more than one satellite are necessary.
First, power collection satellites need to be stationed at a sun synchronous orbit to ensure
continuous collection. Such orbits use the J 2 -induced precession of the argument of perigee to
maintain the orbit plane at a fixed orientation with respect to the sun (obviously in this case at
maximum angle of incidence). The orbit inclination, I, is given by:
cos i    a 12352km 
72
   P 3.795 Hrs.
73
a  orbit radius (circular orbit assumed) in km
(6.a-c)
P  orbit period in hours
For example, for an orbit altitude of ~ 2200km , we have 11 orbits per day and a maximum
latitude of ~ 740 . Since these orbits are at high inclination, there may be necessary an additional
set of relay satellites in low inclination orbits to transfer the power to selected ground stations. A
simple STK orbit analysis shows that only four such satellites would be necessary to relay power
continuously to four ground stations, i.e. for each ground station, at least one of the relays would
be within the accessible elevation at all times. Regarding the program of power delivery, many
alternatives could be considered: (1) as already mentioned, one could deliver power continuously
to one ground station, or (2) deliver power intermittently to a ground station, or (3) deliver power
intermittently to several ground stations. In the case of intermittent delivery, one might use a
superconducting power storage ring to maintain power supply continuity during off periods, or
one could employ a power grid concept, coordinating and reinforcing other power sources by
integrating the SSPS into the overall power grid. All of these possibilities need to be explored
and evaluated quantitatively.
Some quantitative estimates of the reduction in necessary aperture size when a formation of
several, N s , satellites are used to beam power to the same location at distance z can be obtained
by using Equation (5) and assuming that the power density on the ground adds incoherently
(because the satellites are certainly many wavelengths distant from one another), and imposing
the requirement that the total power density be in the safe range ( max  105.0W m2  N S ):
DA   z
4 105
 Pt N S
(7)
Assuming our example 5MW, 1cm FRS, Figure 6 shows the aperture diameters as functions of the
transmit distances for N s from one to ten. For example, for a ten satellite formation the aperture
diameter for transmit distance of 700km is only slightly more than ten meters.
Of course, the cost per satellite also depends on the solar array area. This is still huge and
unaffected by orbital distance. Technologies relating to solar array efficiency, and
manufacturability are discussed in a later section, whereas here we consider estimates of overall
size. For our 5 MW, 1cm FRS example, if we assume very optimistically an end-to-end
efficiency of 25%, the total solar array area would have to be 14,631m2 . It may be that total cost
8
rises faster than area to the first power of the area, so that there is some meaningful tradeoff
between a single large FRS and a cluster of smaller spacecraft. Figure 7 shows the array area per
satellite in a multi-satellite formation versus the number of satellites for the 5MW example. As in
the case of the transmit aperture, the incremental cost of each satellite can be reduced to a modest
level, making incremental investment more feasible. This kind of tradeoff must be pursued in the
study.
SSPS Satellite Design - Manufacturability, and Controllability
In this section, we concentrate on the tradeoffs associated with the design of SSPS satellites. This
study will assess the wide variety of satellite concepts proposed to-date as illustrated in Figure 8.
Of course, the spacecraft configuration is deeply dependent on the wavelength regime, the orbit
concept, the solar array technology and the transmit science.
Figure 6: Aperture diameters as functions of the transmit distances for N s from one to ten.
9
Figure 7: Total solar array area for each satellite vs. the number of satellites in the formation.
Considering the implications of the wavelength regime, we again note that in the LW IR and
visible regimes, signal frequencies are too high for the direct electronic control of beam direction
and shaping and reliance must be put on high bandwidth mechanical actuators and motion
sensors interconnected with a closed loop feedback controller as depicted in Figure 9. Motion
sensors and actuators may be optical or electronic or utilize active materials such as piezoelectric
material or SMAs, but the difficulties with closed loop control are common to all. In the small
wavelength regimes, the transmitter aperture is more compact but the optical tolerances on beam
pointing and primary mirror figure control are far more stringent – demanding accuracies in the
nanometer range. This implies very high gain control laws involving extreme sensitivity to
system modeling errors, and the ever-present possibility of closed-loop instability.
The PI has enormous experience in the dynamics and control of large optics in the visible range.
On the Zenith Star program (SDI) he led the advanced systems group of Harris Corporation in its
support of the Prime Contractor (Martin Marrietta) for carrying out the end-to-end system
simulation and performance evaluation. This was complemented by numerous advanced control
theory studies, specialized vibration control actuator and sensor developments, and large space
structure laboratory control experiments hosted by NASA and AFRL. His experience in large
optics control culminated in the ACTS project, an NRO program involving a competition among
Harris Corporation, TRW and Lockheed to suppress optical errors in a large test bed. This work
is detailed in Appendix 1. Very tight tolerances on pointing, defocus and wavefront error –
10
Figure 8: A wide variety of SSPS spacecraft configurations will be evaluated in this study.
Disturbances
System
Dynamics
Actuator forces
and torques
Actuator
dynamics
Optical
element
deformation
/vibration
Actuator commands
Sensor
measurements
of optical
element
position errors
Dynamic
feedback
control
Figure 9: Block diagram of high gain, closed-loop optical structure control.
11
similar to what might be required for an optical FRS – necessitated up to 40 dB suppression of
the response of over 150 vibration modes. The superior Harris Corporation design was successful
in these objectives by virtue of the capability to design a robust controller accounting for the
system dynamics with a 300 state space model. Figure 10, from Appendix 1 shows the open-loop
versus closed-loop of the wavefront errors in the primary mirror. Due to the symmetries of the
structure, each of the large peaks represents the resonance response of some 14 individual
vibration modes. Despite this success it must be remarked that the ACTS program experience
showed that high gain closed loop control of large optics can be nearly as complex and expensive
as the front-end optics technology itself. Our experience strongly motivates the hierarchy of
control approaches shown in Figure 10. The recommendation is to start with the simplest
Figure 10: Open- and closed-loop response wavefront errors obtained from the ACTS test bed in
the most effective control system design.
possible solution (potentially designing the system so that it does not need structural control at
all), then moving to passive damping, then inherently energy dissipative positive-real control,
and finally accepting high gain closed-loop control as the last and most complex resort.
Next, let us consider systems in the microwave regime, starting from a reasonably conventional
concept proposed by the NRL (and similar to our 5MW example). The system requires the
12
phased array to point at nadir while the reflector/solar array assemblies track the sun. This will
produce torques and necessarily induce vibrations in what is a very large and flexible structure.
Thus we must consider the second level of the hierarchy of control in Figure 11 in order to
suppress the deformations that produce displacements of the phased array elements from their
nominal positions. This may indeed imply the need to deal with the response of many modes of
the structure. But unlike the optical or LW IR cases, microwave has the advantage that the
relatively lower frequency signals can be processed and manipulated so that the phased array
gains are able to cancel out the errors without feeding back forces on the structure. This is the
Build a Large
Space Structure?
Consider a formation of
small satellites
Closed-Loop Control of
Component Relative
positions?
On-board disturbance
sources?
Consider substituting
knowledge for control –
Using electro/optical means
Adopt “quiet” technologies to
the maximum extent
Isolate Sensor from Disturbances:
Passive  Active
Passive Structural Damping
For Accessible Disturbances:
Feedforward cancellation
Feedback control: Positive Real
(inherently robust) control strategy
High Gain (Non-passive) Feedback Control:
On-Line ID, Adaptive/Intelligent Control
Figure 11: Recommended hierarchy of Large Space Structure control approaches
13
Figure 12: The NRL 5 MW SSPS concept
Phased Array Gain
Disturbances
System
Dynamics
Actuator forces
and torques
Actuator
dynamics
Undistorted
radiation
pattern

Array
element
deformation
/vibration
Actuator commands
Sensor
measurements
of array element
position errors
Electronic
phase
adjustment
Dynamic
feedback
control
Figure 13: Microwave phased arrays can null the effects of structural vibration electronically.
14
strategy of “substituting knowledge for control using electro/optical means” mentioned in Figure
10. The block diagram of this approach is shown in Figure 13. In contrast to optical systems,
microwave phased arrays can cancel the effects of structural deformation without feeding back
forces into the structure. Instead, sensor measurement of array deformation (knowledge) is used
to adjust the array gains so that the phase changes in the emitted field amplitude due to
deformation are cancelled. This eliminates the complexity and potential instability of a closedloop controller (shown in pink in Figure 13), as well as the need for complex actuation devices.
The system is inherently stable because the feedback loop is eliminated and the structure is itself
inherently energy dissipative and stabile.
The capabilities of phased array technology for beam steering and beam forming should be
mentioned here. The basic idea of phased arrays is illustrated in Figure 14, while the analytical
theory of optimal beam forming is given in Appendix 2. The figure shows a collection of phased
arrays where each array is a battery of small antennas. The AC input to each antenna is
modulated by a separate phase shift (electronic time delay), and an amplifier (electronic gain).
The phase shifts and amplifier gains to all the array antenna elements are collectively referred to
as the array gain. If the constituent antennae are separated by a fraction of a wavelength, the
whole array produces a continuous wavefront that can be shaped at will. For example, by
properly choosing the array gains, the beam can be directed as desired, and its direction can be
changed essentially instantaneously without any mechanical slewing motion. Even more, as the
theory of Appendix 2 explains, given enough array elements, any desired radiation pattern on the
ground (including multiple beams to disparate reception stations) can be created through entirely
electronic means. Given a desired radiation pattern, Appendix 2, develops an explicit solution for
the optimum array gains.
Of great relevance to SSPS satellite design and its eventual cost are the technologies of the solar
cells and the individual phased array antenna elements. First, solar cell technologies will be
reviewed over a broad spectrum, where the significant tradeoffs are efficiency versus cost and
manufacturability. At one extreme are the laboratory devices that explore the limits of efficiency,
as illustrated in Figure 15. These cells are one-at-a-time creations that achieve ever greater levels
of efficiency. However the ability to produce them in quantity is presently nonexistent. At the
other end of the scale are printed solar cells, as shown in Figure 16. Here lithography and related
techniques are employed to manufacture massive numbers of solar cells on a flexible substrate.
The drawback, however is that efficiencies are low – only a few percent. Still, with
improvements in efficiency, these techniques could revolutionize the construction of very large
in-space solar arrays.
A similar trend toward quantity production is evident for phased array antennas. The old arrays
featured cumbersome transmitters that had to be individually mounted on the back-plane
structure. Significant advance in manufacturability was made with the advent, in the 70’s, of
microstrip antennas, also known as printed antennas or patch antennas. A single emitter element
consists of a metal “patch” on top of a grounded dielectric substrate (see Figure 17). Thanks to
steady progress, at the present time large phased array antennas can also be printed on flexible
substrates. A recent example is shown in Figure 18.
15
w4V  V w4 ei4
Gain
ei4
Time delay
4
w4
Satellite Aperture
w1 V0
d4
w1
1
V
d3
d1
w3
3
w2
2
w5
5
d2
d5
Individual transmitter aperture,
area  A
Assumption: The individual transmitter apertures all have
immediate neighbors with spacing d  A and d<  2
Figure 14: A formation of phased array apertures.
Figure 15: Progress in solar cell efficiencies, 1976 to 2008.
16
This solar panel printer can make 33 feet of solar cells per minute
By Sarah Laskow
University of Melbourne
Whatever oil and gas true believers want to think, the world is doing this solar power thing. It’s
getting cheaper and cheaper to make solar panels, and the panels are getting more and more
effective. For example: A team in Australia just built a gigantic printer that spits out solar cells
at a rate, Gizmodo reports, of about 33 feet every minute.
Figure 16: Progress in flexible solar cell production
Figure 17: Microwave patch antennas
17
Figure 18: (left) Schematic layout of a 4X4 Phased Array system with multilayer interconnection
scheme. (right) Photograph of a fully developed 4X4 system consisting of a three-layer circuit.
(D. Phan, X. Xu, et al. IEEE Antennas &Wireless Propagation Letters, Vol.12, 2013, pp.170-3.)
Figure 19: The 41 meter diameter Echo 2 relay communications satellite.
18
Very large structures in space are few in number and do not exist in the sizes typical of
conventional SSPS designs. They are typically of the truss-panel type, or the more sophisticated
tensioned cable/compressed strut construction. Very few structures are precision structures in the
sense that they can sustain very precise geometry and component alignment. The development of
efficient printed solar arrays and higher power printed microwave antennas with the ability to
reside on flexible sheets would be a significant breakthrough for SSPS structures. At least in
part, they could be folded up for launch and then inflated on-orbit. This would reduce or avoid
altogether the necessity of construction in orbit.
The above discussion raises a number of possibilities that should be explored in the trade study.
One might envision the development of a multi-functional material consisting of tough, flexible
sheets upon which solar cells interspersed with phased array antennas are printed. This material
would be used to fabricate the entire SSPS satellite as an inflatable. One could imagine that the
simplest realization would be an inflated sphere as epitomized by the old Echo relay satellites
(see Figure 19). This, by the way, is an elegant example of a truly large space structure. As for
Echo, the balloon would be packed in a spherical canister that conforms to the launch vehicle
payload envelope. Once on orbit its pressurized gas supply would be turned on for inflation. The
resulting spherical symmetry means that the system can gather solar power from any angle
without any slewing motion. Likewise, the microwave antenna can direct the beam in any
direction by adjusting its electronic gains, and without dynamic motion. The system operation
would generate no disturbances, and disturbances that do occur can be nullified by the gain
adjustment algorithm. Following the successful trial of the FRS, the SSPS system can be
augmented by deploying more, or larger “power stars”.
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Ground Collector System
The overall efficiency η of the Space Solar Power System (SSP) can be broken down into three
segments.
(8)
Here,
is the efficiency of conversion from solar energy to transmission wave
is the efficiency of propagation of power from space to Earth
is the efficiency of reception and conversion to useful power on Earth
In the previous sections, the transmission and the propagation efficiencies were discussed. In this
section the efficiency of ground reception of wireless power transmission from space to Earth is
discussed.
As discussed previously, the two most preferred modes of transmission are at Laser frequency or
Microwave frequency. The power received at the earth station in the form of laser beam or radio
frequency (RF) waves have to be converted to direct current (DC) power for storage and long
distance transmission. The conversion efficiency of RF to DC at high power is currently less than
70 % but is expected to increase to 80%. The laser beam conversion efficiency to DC is also
expected to increase to 60% in the near future.
In the case of RF power, there are two efficient methods available to convert RF to DC. The first
technology is an array of rectennas, each comprising of a receiving antenna, a low pass filter, a
rectifying circuit and an output smoothing filter.
Figure 20: Block diagram of a single rectenna
The diode type rectenna was used to first demonstrate wireless power transmission by Brown in
the year 1964. Since then semiconductor research has produced Schottky diode rectennas with
efficiency as high as 80%. Although for the high power transmission required for the SSP, an
array of rectenna will be needed at the receiving end. The efficiency of the array is not as high as
a single Rectenna (80%) but less than 70%.
20
Figure 21: A grid of rectennas for microwave power reception and conversion to DC power.
[Source: Propagation group, Georgia Tech University]
CONVERSION EFFICIENCY OF ARRAY OF RECTENNA
The power received at the antenna can be expressed as a function of the power density, the
receiving antenna gain and the wavelength of propagation.
(9)
Here,
is the input power to the rectenna
21
is the power density
is the antenna gain
is the wavelength of the signal
The equation (9) establishes the fact that the input power to the rectenna is directly proportional
to the square of the wavelength. This suggests that for the same input power density, the area
required to obtain a fixed input power to the rectenna is higher for the laser frequency as
compared to the RF frequency. This has also been discussed in the previous section where the
dependency of the ground receiver size was shown to be a function of the frequency of power
transmission.
81
82
80
80.5
Input 78
Power to Rectenna (dBm)
Input Power to Rectenna (dBm)
80
76
74
79.5
72
79
70
78.5
60
70
80
90
Power Density (W/m 2)
(a)
100
110
68
20
40
60
80
100
Wavelength (m)
120
140
(b)
Figure 22: (a) Input power to Rectenna as a function of power density for G=1 and frequency
2.45 GHz. (b) Input power as a function of wavelength of the signal for power density 100
W/m2.
To recall, the maximum safe level power density is 105 W/m2. Figure 22 a) plots the input power
to the rectenna for power density varying from 60 to 105 W/m2 at an operating frequency of
2.45GHz. The power input to the rectenna is of the order of tens of kWatts.
The conversion efficiency of rectenna is a nonlinear function of the input power. The
relationship between the input power to an array of rectennas connected in series or parallel and
the output DC voltage is nonlinear. For example, it is reported in the literature [1] that at 2.45
GHz dual-diode rectenna, the following nonlinear model relates the input power with the output
DC voltage .
(10)
22
Here,
(11)
(12)
Hence, the output DC power can be calculated using the output voltage and the load resistance.
Note that the output DC power of a larger rectenna array can be optimized by choosing the
optimal interconnections and load resistance.
Cyclotron Wave Convertor (CWC) is another device that efficiently converts RF to DC. The
CWC offers a more robust equipment as compared to diode based rectenna array that are
susceptible to breakdown at high power. The figure 23 shows the block diagram of a CWC
device and figure 24 shows a CWC device developed by the Moscow State University.
Figure 23: Block Diagram of a CWC device.
23
Figure 24: A version of the CWC tested at the Moscow State University
The CWC is a microwave vacuum tube that converts high power microwave to DC. In this
device, the microwave energy is used to provide a cyclotron rotation to a beam of electrons. A
change in magnetic field converts the energy of rotating electron beam to longitudinal
acceleration resulting into an electron beam in the shape of a spatial helix. The initial design of
CWC could demonstrate only 50-60% conversion efficiency. Recently, the TORIY Corporation
and the Moscow State University have demonstrated 70-83% conversion efficiency for 10-20kW
input power.
In summary, the conversion efficiency of the microwave to DC can be optimized to be as high as
80% by further design and development at the chosen frequency of microwave power
transmission for SSP.
---------------------- To be completed below-------------------------1. Laser power conversion to DC
2. Power Storage
3. Power Distribution
The laser power transmission requires photovoltaic cells to convert laser light to DC. Solar
rectenna are
The second design factor that affects the design of the ground station is the visibility of the
power transmission satellite to the ground station. If the Space based solar power is to be used as
the majority of the power provider, then the output of the ground station or a group of ground
station in an area must be continuous. With due placement of the satellites in the Earth orbit, the
continuous production of the power can be ensured. However, can the transmission of this
powerto a single ground station or a group of ground stations in an area be continuous?
Depending on the power transmission profile, the energy storage design at the ground station
will change. Considering that… amount of power
24
Power consumption in KiloWatt-Hour for different countries as of January, 2012. [Data Source:
CIA World Factbook]
References:
[1] Takhedmit, Hakim, Laurent Cirio, Odile Picon, and J-D. Lan Sun Luk. "An accurate linear electrical model
applied to a series and parallel 2.45 GHz dual-diode rectenna array." In Antennas and Propagation (EUCAP), 2012
6th European Conference on, pp. 2510-2513. IEEE, 2012.
25