Content uploaded by Xun Li
Author content
All content in this area was uploaded by Xun Li on Mar 18, 2017
Content may be subject to copyright.
Invited Paper
A novel design project for space solar power station
(SSPS-OMEGA)
Yang Yang, Yiqun Zhang
n
, Baoyan Duan, Dongxu Wang, Xun Li
Key laboratory of Electronic Equipment Structure Design, Xidian University, China
article info
Article history:
Received 9 September 2015
Received in revised form
25 November 2015
Accepted 19 December 2015
Available online 6 January 2016
Keywords:
Space solar power
Solar energy collection system
Microwave power transmission
Power-mass ratio
SSPS
abstract
The space solar power station (SSPS) capable of providing earth with primary power has
been researched for 50 years. The SSPS is a tremendous design involving optics,
mechanics, electromagnetism, thermology, control, and other disciplines. This paper
presents a novel design project for SSPS named OMEGA. The space segment of the pro-
posed GEO-based SSPS is composed of four main parts, such as spherical solar power
collector, hyperboloid photovoltaic (PV) cell array, power management and distribution
(PMAD) and microwave transmitting antenna. Principle of optics, structure configuration,
wired and wireless power transmissions are presented.
&2016 IAA. Published by Elsevier Ltd. All rights reserved.
1. Introduction
The SSPS concept was firstly introduced by Dr. Peter
Glaser in 1968 [1]. The basic idea is that sunlight is col-
lected and converted into electricity in space, and then
transmitted to the ground-receiving antenna via wireless
power transmission (WPT). It is a promising methodology
to provide earth with primary power.
Since the invention of SSPS concept, there have been
numerous research activities. As far as design project of
SSPS is concerned, a few innovative design concepts, such
as Reference model, Sun tower, Sun sail, JAXA models,
Tethered SPS, etc., have been proposed by the scientists and
engineers from the US, Japan and Europe [2,3,4,5].Typical
SSPS concepts can be divided into three kinds according to
their difference on focusing methodologies: such as non-
focusing, point-focusing and distributed focusing. The
NASA/DOE reference model [6], put forward in 1979, is a
typical one of non-focusing. The model consists of a single
large solar array about 50,000 m
2
in area, a microwave
transmitting antenna, and a high-power rotary joint
mechanism. The shortcoming is the excessive initial
investment. Another one is the Tethered Solar Power
Satellite [7,8], proposed by Japanese government METI and
USEF, a concept to reduce the system complexity and mass.
It is composed of a power generation/transmission panel of
2.0 km 1.9 km suspended with multi-wires deployed
from a bus system. The panel consists of 400 subpanels of
100 m 95 m. However, low efficiency and large fluctua-
tion on energy collecting curve are the obvious dis-
advantages. Typical concepts of point-focusing are Inte-
grated Symmetrical Concentrator (ISC) and Symmetrical
Two-stage Flat reflected Concentrator (STFC) [4]. ISC utilizes
large, symmetrically placed off-axis parabolic reflectors
whilst receiving surface being placed on the focal plane. By
integrating the PV cell array, microwave devices and
transmitters into sandwich structure and making use of
secondary reflectors, an improved concept named STFC was
proposed which is good for receiving a high degree of dis-
tribution uniformity and a suitable condensation ratio by
adjusting the parameters of the main reflectors, secondary
reflectors and receiving plane [9]. However, high-power
rotating mechanism and complicated control strategies are
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/actaastro
Acta Astronautica
http://dx.doi.org/10.1016/j.actaastro.2015.12.029
0094-5765/&2016 IAA. Published by Elsevier Ltd. All rights reserved.
n
Correspondence to: Xidian University, Mailbox 191, No. 2, South
Taibai Road, Xi'an 710071, China. Tel.: þ86 029 88203040.
E-mail address: yiqunzhang@xidian.edu.cn (Y. Zhang).
Acta Astronautica 121 (2016) 51–58
needed for both ISC and STFC. The ALPHA (Solar Power
Satellite via Arbitrarily Large Phased Array) [10],proposed
by John C. Mankins, is a hyper-modular design of dis-
tributed focusing. Thousands of individually pointed light
weight thin-film mirrors redirect sunlight to a high-
efficiency photovoltaic array. Typical concepts are sum-
marized and compared in Table 1 .
2. SSPS-ALPHA concept
Biomimetic and hyper-modular design have been
introduced in the architectural design of the ALPHA, a
concept which is thought to be the first practical and one
of the most advanced SSPS. The basic concept is to form an
exceptionally large space platform from an extremely large
number of small, high modular elements using the idea of
cooperative behavior.
2.1. Architecture
Fig. 1 shows the basic architecture of the space segment
of the ALPHA, which is comprised of three major func-
tional elements: (1) a large sandwich structure with
antenna surface toward earth. (2) a solar energy collecting
system involving a large number of individually reflectors
mounted on a non-moving primary structure; and (3) a
truss structure that connects these two.
2.2. Principles of optics
Operating in the GEO, the sandwich structure is always
pointing toward earth. A large number of flat reflectors
that act as individually pointing “heliostats”[14] are
steered to reflect the sunlight into the PV cell array. Fig. 2
illustrates the structure of the reflectors and its opera-
tional principle.
Some schemes of the ALPHA have been proposed
varying from the different approaches to the primary
structure configurations, the newest one among which is
the 2013 version [10]. The main reflector is created by
Table 1
Typical SSPS concepts.
Reference model [11] Sun tower [12] Solar disc [4] ISC [4] Sun Sail [4] Tethered- SSPS [8] ALPHA [13]
Year 1979 1995 1997 1998 1999 2001 2012
Organization NASA/ DOE NASA NASA NASA ESA METI/ USEF Artemis
Orbit GEO LEO GEO GEO GEO GEO GEO
Power (GW) 5 0.1–0.4 1–10 1.2 0.275 0.75 2
Frequency (GHz) 2.45 5.8 5.8 2.45 2.45 5.8 2.45
Mass (MT) 30,0 00–50,000 20 00–7000 80 00–70,000 35,00 0 3750 3800 25,260
*
Focus Non Point Non Point Non Non Distributed
Modularity Monolithic Modular Monolithic Modular Modular Modular Modular
*
The data is from the ALPHA DRM 5/Case_4B, a mature full-scale SSPS with 2 GW power for commercial markets, which might to be realized at least
30 years.
Fig. 1. Basic architecture of the ALPHA concept.
HexFrame
HexBux
Interconnects
Reflectors
Sandwich Sunlight
Reflectors
Fig. 2. Structure and adjustment of the reflectors.
Y. Yang et al. / Acta Astronautica 121 (2016) 51–5852
rotating a sigmoid curve [15] and secondary reflector is a
hyperboloid. The introduction of the secondary reflector
could enhance the effective area of receiving energy and
sunlight collecting efficiency. Part of sunrays are reflected
by the main reflector whilst others being firstly reflected
by the main mirrors and then secondly reflected by the
secondary mirrors.
Concerning the ALPHA, distributed focusing and
adjustment for reflector modules in place of integral
adjustment have been utilized. Therefore, the reflector
modules are needed to be adjusted individually in differ-
ent attitude control strategies. For example, ALPHA
DRM_5/Case_4B [13], representing large-scale GEO-based
SSPS platform, as many as 4,662 reflector modules are
required real-time adjustment, which would certainly
results in mirror interference and complicated control.
Moreover, the effective projected area of sunlight on
the reflectors varies from the incident angle, which would
be less than the geometric area of the reflectors. Therefore,
part of sunrays emitting to the aperture of the reflectors
could not be reflected to the PV cell array. The phenom-
enon could be described as ‘light leaking’, as is shown in
Fig. 3.
3. The OMEGA design project
Optics, mechanics, electromagnetism, thermology,
control, and other disciplines are all concerned in the SSPS
design. In general, improvement of one performance
would lead to a decline in another performance. For
instance, the sandwich structure eliminates the wired
power transmission via long electric cables, nevertheless,
difficulty on thermal control is greatly increased [16].
Taking main factors which make great influences on SSPS
performance in design stage, a novel concept is proposed.
The novel concept has some technical advances over some
previous concepts, such as no need of integral adjustment
on main reflector, low demand on thermal control, wired
power transfer from PV array to transmitting antenna in
short distance and low-mass connection structure
between main reflector and transmitting antenna.
The SSPS-OMEGA [17] (Space Solar Power Station via
Orb-shape Membrane Energy Gathering Array) concept
can be described as a modular, spherical system concept in
which sunlight is collected with the main reflector and
power is generated in a series of PV cell array. The elec-
tricity is delivered into the microwave devices with the
electric cables and conductive joints. Fig. 4 provides a
summary diagram of the OMEGA concept.
3.1. Principles of optics
The focusing mode of spherical reflector is line-
focusing. Fig. 5 illustrates the light propagation process
in a two-dimensional plane. On the basis of geometrical
optics, the incident light paralleling to the z-axis is
reflected by the reflecting surface and converges to the
region from R/2 to R, where Ris the spherical radius. Mis
the boundary point, the incident light reflecting only once
could arrive the focusing region if x-coordinate of the
intersection of the x-axis and the direction vector of sun-
light x
in
Að0;Rcos 301Þwhilst two or more times of
reflecting being needed if x
in
AðRcos 301;RÞ.
As presented in Fig. 5,ifx
in
AðRcos 301;RÞ, two or more
times of reflecting will be needed. On the one hand, the
Points of junction
Cables
Module Basic elements
Full size
Primary
Sub-array
Secondary
Sub-array
PV cell
Electric
cables
Sliding slice
Pulleys
Sliding rail
Conductive
joint
Thin-film
reflector
modules
Fig. 4. Summary diagram of the SSPS-OMEGA concept.
Reflector
PV cell
Reflector
PV cell
Sunlight Sunlight
Before adjustment After adjustment
Fig. 3. Illustration of the ‘light leaking’.
Y. Yang et al. / Acta Astronautica 121 (2016) 51–58 53
reflectivity of a thin-film is impossible to achieve 100% for
its physical properties. On the other hand, surface preci-
sion of multiple reflection area is of high requirement for
efficient light propagation, which certainly would increa-
ses the manufacturing difficulty. Therefore, removing the
multiple reflection area to ensure the efficient utilization
of the reflector is available, which certainly would reduce
the area and quality of spherical reflector to some extent,
as is shown in Fig. 6 . It must be pointed out that this paper
deals with the region of one-time reflecting, if the surface
accuracy and reflectivity meet the requirements, can the
areas of two or more times reflecting be persisted.
3.2. Approaches to the spherical reflector
Two kinds of approaches are promising to the realiza-
tion of spherical reflector.
3.2.1. Semi-transparent and semi-reflecting thin film
Semi-transparent and semi-reflecting thin film is
promising for the realization of the spherical reflector.
Sunlight could pass through one side of the thin film
whilst being reflected by the other side. In this case, the
size of the main reflector should be recalibrated on the
premise of invariant received power, and the radius can be
calculated as:
R
r
¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
W
Cη
r
η
t
η
c
ðπþ4R
0
π
=6
sin
2
φdφÞ
v
u
u
tð1Þ
where η
t
and η
r
are the transmissivity and reflectivity of
the thin film, respectively. η
c
is the average solar energy
collection efficiency. Cis the power density of space solar
power. Wis the received power required by the system
design.
3.2.2. Rotation mechanism
Another simple approach is to make use of the rotation
mechanism. Thousands of reflector modules are mounted
on a support structure and rotated individually. While
operating in the orbit, the reflector modules facing the
sunlight are rotated to maintain their individual normal
vector being perpendicular to the direction vector of the
sunlight. The adjustment of the main reflector is shown in
Fig. 7.
Typically, the radius can be expressed as:
R
r
¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
W
Cη
r
η
c
ðπþ4R
0
π
=6
sin
2
φdφÞ
v
u
u
tð2Þ
Theoretically, both the scale of main reflector and its
mass would be decreased. Actually, as the use of control
mechanism, the analysis of optical path, energy collecting
efficiency, as well as the radius and mass of main reflector
are all variables to be analyzed in greater detail.
3.3. Orbit
Orbits, such as low earth orbit (LEO), geostationary
earth orbit (GEO), sun synchronous orbit (SSO), etc., have
been evaluated for SSPS. Table 2 summarizes a technical
comparison of the LEO and GEO.
As is described in Table 2, SSPS in LEO presents better
performance than that in GEO for its size, mass, cost, etc.
while multiple systems would be needed to provide con-
tinuous power to target area. However, SSPS is expected to
supply earth with baseload power and SSPS in GEO has
0X
Z
Incident sunlight
30°
60°
R
M
Fig. 5. Illustration of light path in 2D.
O
X
Z
Y
Interception part
Sunlight
Fig. 6. Illustration of multiple reflection area.
Sunlight Reflectors
PV cell
Fig. 7. Attitude control of the reflectors.
Y. Yang et al. / Acta Astronautica 121 (2016) 51–5854
very simple attitude control. Therefore, GEO has been
chosen by most SSPS concepts, also by the OMEGA
concept.
3.4. Solar power generation
High efficiency GaAs solar cell array is expected for the
proposed project. A hyperboloid-based shape is designed
for the PV cell array to obtain better performance on
energy distribution uniformity and a suitable condensa-
tion ratio. The array is rotated at constant angular velocity
to collect solar power continuously with an orbital period
of 24 h. Theoretically, in addition to the shadow region, the
receiving power of PV cell array fluctuates little, as is
shown in Fig. 8.
3.5. Power management and distribution (PMAD)
Fig. 9 indicates the transmission process of the direct
current (DC) from the PV cell array to the microwave
devices. DC would be transmitted into the microwave
devices via the electric cables, sliding slice and conductive
joint. Line contact has been introduced between the slice
and rail to reduce the friction, also pulleys for guarantee-
ing mechanical connection strength. As solar cells and
transmitting antenna are not designed in sandwich
structure, the difficulty on heat dissipation would be
reduced, and allowable concentration ratio of PV cell array
increased. Compared to the design schemes with electric
cables connection, such as Sun tower (ground-receiving
power is 100–400 MW, the maximum cabling connecting
length is as long as 15 km [18]), the maximum cabling
length of the proposed project will be in 3.5–4.5 km scale
for design reference mission which is capable of 2 GW
power supply on the ground.
3.6. Wireless power transmission
There are two fundamental approaches for wireless
power transmission: one that uses a coherent microwave
beam at specific frequencies, and the second using a laser.
The advantage of using a laser is extremely short wave-
lengths, which enables very small transmitting antenna
and receiving antenna. Moreover, the very low efficiency
of key components and inability to pass readily through
haze or cloud cover results in its unavailability for SSPS. By
comparison, microwave power transmission (MPT) has
greater component efficiency. Furthermore, low cloud
penetration loss and relatively mature technology enable
its potential for application for SSPS. Therefore, great
efforts have been made in the study of MPT whilst most
concepts using microwave beam for power transmission
[4,5], the OMEGA concept included. Moreover, several
experiments implemented by the US and Japan have
confirmed the validity of MPT for SSPS [10,19,20].
3.6.1. Microwave frequency and dimension of transmitting
antenna
As far as the scale of the SSPS is concerned, the size of
the transmitting antenna and ground-receiving antenna
are key points, which determine the system scale and cost.
On the basis of radio wave theory [21], the beam collection
efficiency (BCE) between transmitting and receiving
antennas can be calculated by,
η¼1e
τ
2
ð3Þ
τ¼ffiffiffiffiffiffiffiffiffi
A
t
A
r
pλLð4Þ
where A
t
,A
r
,λand Lare aperture area of the transmitting
antenna, aperture area of the receiving antenna, wave
length, and distance between these two antennas,
respectively.
Table 2
Illustration of orbits for SSPS.
Altitude Size Mass Cost Efficiency Attitude control
LEO Low Low Low Low High Complex
GEO High High High High Low Simple
Fig. 8. Variation of solar collection with local time.
PV cell
Sliding slice
Pulleys
Sliding rail
Conductive joint
Electric cables
Fig. 9. Diagram of the PMAD system.
Y. Yang et al. / Acta Astronautica 121 (2016) 51–58 55
It is obvious that the shorter wave length, or higher fre-
quency means smaller aperture are of the antenna on given
BCE. In contrast, efficiency of circuits, semiconductors, and
tubes decreases with increasing frequency. For MPT to the
surface of the earth, a limited range of microwave frequencies
is suitable. Frequencies at 2.45 GHz, 5.8 GHz and 35 GHz are
within the microwave radio windows of the atmosphere. In
view of the technical maturity in 20–30 years based on
potential progress of the microwave devices, the heat dis-
sipation and the cost, frequency at 5.8 GHz is promising for
the WPT of the OMEGA concept.
As is seen in Fig. 10,field regions can be divided into
reactive near-field region, radiating near-field (Fresnel)
region, and far-filed region, under the condition that
RrR
1
,R
1
rRrR
2
, and R4R
2
, respectively, where
R
1
¼0:62 ffiffiffiffiffiffiffiffiffiffiffi
D
3
t
=λ
q,R
2
¼2D
2
t
=λ, and D
t
is the largest dimen-
sion of the transmitting antenna.
For small angle of beam divergence, the receiving
antenna should be in Fresnel region while Lo2D
2
t
=λ. As far
as the proposed project is concerned, the altitude of the
orbit is L¼36000km, the frequency is 5.8 GHz (the cor-
responding wave length is 5.17 cm), the receiving antenna
is located in the Fresnel region while D
t
Z965m. Therefore,
the diameter of the proposed transmitting antenna is
about 1 km scale.
3.6.2. Ultra-large antenna plane assembly and integration
Transmitting antenna of the OMEGA requires a dia-
meter of about 1 km at 5.8 GHz which is considerably
larger in size and weight than conventional onboard
antennas for other microwave applications, such as com-
munications [22]. Moreover, total number of the antenna
elements is about 5.2 million with antenna element spa-
cing of 0.75
λ
¼3.88 cm. Therefore, it is impossible to form
such a large aperture in a single aperture, therefore,
modular design and sub-array is a promising way to deal
with the problem. As is presented in Fig. 11, the modules,
which consist of several basic elements, compose a pri-
mary sub-array which is a basic unit of a secondary sub-
array. Several groups of secondary sub-arrays consist of
the full size antenna plane.
3.6.3. Beam forming
Accuracy of beam forming is very important in
increasing the BCE, which is one of the key indexes of WPT
system. Traditionally, the profile of the microwave inten-
sity for the transmitting antenna has been premised 10 dB
Gaussian commonly in the past and current SSPS models
to concentrate the microwave beam power in the main
lobe, that is the optimal WPT tapering [23] is found to be
“quasi-Gaussian”distribution. However, the feeding net-
work is complicated to fabricate and maintain, owing to its
“smooth nature”of “quasi-Gaussian”distribution [24].A
novel method has been proposed by our group by use of
uniformly excited, unequally spaced planar array synth-
esis, which shows better performance on enhancing BCE
and reducing sidelobes [24].
3.6.4. Beam control
Precise beam control is necessary in the proposed
system. The required beam control accuracy of MPT system
may be achieved using a very large number of power-
transmitting antenna elements, and by limiting the total
phase errors over the antenna array to a few degrees to
realize the 0.0005 degree beam control, corresponding to
2 arc seconds [4]. Moreover, 6 or 8 cables pre-stressed are
designed for OMEGA concept to keep the antenna stability,
as is described in Fig. 12. However, if the antenna is
required for some other use, the attitude of the antenna
can be controlled by adjusting the length of the cables.
4. System analysis
The OMEGA concept is proposed for providing base
load power into terrestrial markets. Therefore, system
scale and cost are key factors which should be taken into
consideration. In view of efficiency of the key components,
such as PV cell, microwave power tubes and rectenna at
current state which are available for mass production, the
system would be a tremendous project with excessive
R
2
R
1
D
Reactive
near-field region
Rediating near-field (Fresnel) region
Far-field region
Fig. 10. Field regions.
Module Basic elements
Full size
Primary
Sub-array
Secondary
Sub-array
Fig.11. Illustration of the ultra-large antenna plane.
Y. Yang et al. / Acta Astronautica 121 (2016) 51–5856
investment. Accordingly, the realization is hardly possible
via current technologies. The OMEGA is proposed for
supplying 2 GW power into earth’s grid, which might be
for realization around 2050. Without consideration of
environmental adaptability in space, transportation and
inventions of revolutionary devices, Table 3 provides a
preliminary analysis on system efficiency at current state
and for the OMEGA.
From the data in Table 3, with current technologies, the
spherical solar power collector is estimated for effectively
collecting solar power at least 22.4 GW. The system is
estimated in 8–10 km scale, which is unlikely for realiza-
tion both for technological maturity and cost. Never-
theless, advanced technologies are promising for its reali-
zation. Table 4 summarizes the estimated system scale,
efficiencies of wired and wireless power transmission and
system mass of the OEMGA, which might be realized
around 2050.
5. Conclusion
SSPS-OMEGA project has been investigated in a con-
ceptual study level. Both principles of optics, structure
configuration, wired and wireless power transfer are dis-
cussed in the manuscript. This project has several advan-
tages, as summarized below:
(1) Compared to previous concepts with need of whole
adjustment on main reflector, the proposed concept
decreases the energy consumption for adjustment.
(2) PV cell array and transmitting antenna are designed in
separate parts, which is propitious to heat dissipation.
(3) Solar energy collection has low fluctuation with the
local time, which is profitable for continuous and
stable energy supplying.
(4) The transmitting antenna is connected to the main
reflector through long span cables, which could reduce
the mass of connecting mechanism.
(5) The maximum cabling length of the proposed project
could be reduced as about 4 times as that in the
Tethered SSPS.
The findings of this study have important reference
value. However, the implementation of this elegant con-
cept is far from realization on account of low maturity for
key technologies and high cost. Furthermore, as a con-
ceptual study, many key points should be studied in detail.
Therefore, further studies need to be carried out to enable
the OMEGA concept:
(1) The energy distribution, system mass and scale are
necessary to be further studied via structure
optimization.
Fig. 12. Connection between the reflector and antenna.
Table 4
The OMEGA scale preliminary results (2 GW @ Earth).
Specification Mass (MT)
Spherical collector Specific mass goal is 0.051 kg/m
2
, including thin-film reflector and skeleton frame. 957
Solar power generation GaAs, efficiency goal is 60% and power/mass ratio goal is 300 0 W/kg 1903
PMAD Superconducting cables, specific mass goal is 15 kg/m. 59
Transmitting antenna Specific mass goal is 25 kg/m
2
, including solid-state transmitters, power division network, phase shifters,
antenna elements and support structure.
19,634
Attitude control Propulsion system with propellant. 400
Total 22,953
Table 3
The OMEGA system efficiency preliminary results (2 GW @ Earth).
Current state The OMEGA
Efficiency Power
(GW)
Efficiency Power
(GW)
Photoelectric
efficiency
0.30 22.4* 0.60 5.14*
DC-RF efficiency 0.50 6.73 0.85 3.09
Amplitude error 0.99 3.37 0.99 2.62
Phase error 0.98 3.33 0.98 2.59
Quantization error 0.99 3.27 0.99 2.54
Antenna aperture
efficiency
0.98 3.23 0.98 2.52
Propagation loss 0.98 3.17 0.98 2.47
Beam collection
efficiency
0.92 3.11 0.92 2.42
Rectenna efficiency 0.70 2.86 0.90 2.22
DC 2.00 2.00
dc-dc efficiency 18.2% 47.4%
Y. Yang et al. / Acta Astronautica 121 (2016) 51–58 57
(2) The specific number, structure, connecting point, and
pre-stressed force of the cables are all variables to be
analyzed in greater detail.
(3) Attitude control and vibration suppression of the
proposed concept should be implemented for its
stable operation.
(4) The influence caused by the carbon fiber frame and
thin film of the main reflector on the BCE and beam
pointing remains to be intensively studied.
(5) Field-coupling model [25] involving optics, mechanics,
electricity, thermology and electromagnetic field
should be studied thoroughly to improve system
performance.
Acknowledgments
The research was supported by the National Natural
Science Foundation of China under Grants no. 51405361,
No. 51490660 and in part by the Fundamental Research
Funds for Central Universities under Grant no. SPSZ011401.
References
[1] P.E. Glaser, Power from the sun: its future, Science 162 (1968)
857–861.
[2] Committee for the Assessment of NASA's Space Solar Power
Investment Strategy, Aeronautics and Space Engineering Board,
National Research Council, Laying the Foundation For Space Solar
Power: An Assessment of NASA’s Space Solar Power Investment
Strategy, National Ational Academy Press, Washington, D.C, 2001.
[3] J.D. Rouge, Space-based solar power: as an opportunity for strategic
security, National Security Space Office, 2007.
[4] URSI inter-commission working group on SPS, URSI white paper on
solar power satellite (SPS) systems and report of the URSI inter-
commission working group on SPS, URSI, 2007.
[5] N. Shinohara, Wireless Power Transfer via Radiowaves (Wave Ser-
ies), ISTE Publishing and John Wiley & Sons, Inc., Great Britain and
United States, 2014.
[6] J.C. Mankins, New directions for space solar power, Acta Astronaut.
65 (2009) 146–156.
[7] S. Sasaki, K. Tanaka, S. Kawasaki, N. Shinohara, K. Higuchi,
N. Okuizumi, K. Senda, K. Ishimura, The USEF SSPS study team,
conceptual study of SSPS demonstration experiment, Radio Sci. Bull.
310 (2004) 9–14.
[8] S. Sasaki, K. Tanaka, K. Higuchi, N. Okulzumi, S. Kawasaki,
N. Shinohara, K. Sendac, K. Ishimurad, A new concept of solar power
satellite: tethered-SPS, Acta Astronaut. 60 (2006) 153–165.
[9] X.L.Meng,X.L.Xia,C.Sun,G.L.Dai,Optimaldesignofsymmetricaltwo-
stage flat reflected concentrator, Sol. Energy 9 3 (2013) 334–344.
[10] J.C. Mankins, The Case for Space Solar Power, first ed. Virginia
Edition Publishing, Houston, 2014.
[11] G.M. Hanley, Satellite power systems (SPS) concept definition study,
NASA Contractor Report 3318, 1980.
[12] J.C. Mankins, A technical overview of the “Sun Tower”solar power
satellite concept, Acta Astronaut. 50 (2002) 369–377.
[13] J.C. Mankins, SPS-ALPHA: the first practical solar power satellite via
arbitrarily large phased array, Artemis Innovation Management
Solutions LLC, September 2012.
[14] M. Renzi, C.M. Bartolini, M. Santolini, M.,A. Arteconi, Efficiency
assessment for a small heliostat solar concentration plant, Int. J.
Energy Res. 39 (2015) 265–278.
[15] M. Humphrys, Continuous Output –the sigmoid function, URL
〈http://computing.dcu.ie/humphrys/Notes/Neural/sigmoid.html〉.
[16] P. Jaffe, J. Mcspadden, Energy conversion and transmission modules
for Space Solar Power, Proc. IEEE 106 (2013) 1424–1437.
[17] Y. Yang, B.Y. Duan, J. Huang, X. Li, Y.Q. Zhang, J.Y. Fan, SSPA-OMEGA: a
new concentrator for SSPS, Chin. Space Sci. Technol. 34 (2014) 18–23.
[18] W. Seboldt, Space-and earth-based solar power for the growing
energy needs of future generations, Acta Astronaut. 55 (2004)
389–399.
[19] W.C. Brown, E.E. Eves, Beamed microwave power transmission and
its application to space, IEEE Trans. Microw. Theory Tech. 40 (1992)
1239–1250.
[20] T. Ishikawa, Y. Kubo, J. Yoshino, N. Shinohara, Study of beam forming
for microwave power transmission toward Solar Power Satellite
with advanced phased array system in Kyoto University, in: Pro-
ceedings of the IEEE International Symposium on Antennas and
Propagation Antennas and Propagation, 2013, pp. 2225–2226.
[21] N. Shinohara, Beam control technologies with a high-efficiency
phased array for microwave power transmission in Japan, Proc.
IEEE 101 (2013) 1448–1463.
[22] T. Takano, A. Sugawara, S. Sasaki, System considerations of on board
antennas for SSPS, Radio Sci. Bull. 311 (2004) 16–20.
[23] G. Oliveri, L. Poli, A. Massa, Maximum efficiency beam synthesis of
radiating planar arrays for wireless power transmission, IEEE Trans.
Antennas Propag. 61 (2013) 2490–2499.
[24] X. Li, J.Z. Zhou, X.L. Du, Planar arrays synthesis for optimal wireless
power transmission, IEICE Electron. Express 12 (2015) 1–6.
[25] B.Y. Duan, Electromechanical Coupling Of Electronic Equipments:
Theory, Method and Application, Science Press, Beijing, 2011.
Glossary of acronyms
ALPHA: Arbitrarily Large Phased Array
BCE: Beam collection efficiency
DC: Direct current
DOE: Department of Energy
ESA: European Space Agency
GEO: Geostationary Earth Orbit
GHz: Gigahertz
GMT: Greenwich Mean Time
GW: Gigawatts
ISC: Integrated Symmetrical Concentrator
JAXA: Japan Aerospace Exploration Agency
kg: Kilogram(s)
km: Kilometer(s)
kW: Kilowatts
LEO: Low Earth Orbit
METI: Ministry of Economy, Trade and Industry
MPPR: Modular Push-me/Pull-you Robotic (Arm)
MPT: Microwave Power Transmission
mT: Metric Tons
MW: Megawatts
NASA: National Aeronautics and Space Administration
OMEGA: Orb-shape Membrane Energy Gathering Array
PAC: Propulsion / Attitude Control
PMAD: Power management and distribution
PV: Photovoltaic
SPG: Solar Power Generation
SSPS: Space Solar Power Station/Space Solar Power Satellite
STFC: Symmetrical Two-stage Flat Reflected Concentrator
USEF: Ministry of Economy, Trade and Industry
WPT: Wireless Power Transmission
Y. Yang et al. / Acta Astronautica 121 (2016) 51–5858