Space Power Resources, Manufacturing and Development Volume 11 Number 2 1992
SPACE POWER Published under the auspices of the Council for Social and Economic Studies EDITOR Andrew Hall Cutler, Space Engineering Research Center, The University of Arizona ASSOCIATE EDITORS Roger A. Binot, European Space Agency, The Netherlands Eleanor A. Blakely, Lawrence Berkeley Laboratory, USA Richard Boudreault, Consultant, Montreal, Canada Lars Broman, SERC, Sweden Gay Canough, Extraterrestrial Materials, Inc., USA Lucien Deschamps, Paris, France Ben Finney, University of Hawaii, USA Josef Gitelson, Academy of Sciences, USSR Peter Glaser, Arthur D. Little, Inc., USA Owen Gwynn, Mars Center for Exploration, Moffet Field CA. Praveen K. Jain, Northern Telecomm, Ottawa, Ont., Canada Dieter Kassing, ESTEC, The Netherlands Fred Koomanoff, DoE, Washington, D.C. Mikhail Ya. Marov, Academy of Sciences, Moscow, Russia Gregg Maryniak, Space Studies Institute, USA Michael Mautner, University of Canterbury, New Zealand Makoto Nagatomo, ISAS, Japan Mark Nelson, Institute of Ecotechnics, USA John R. Page, University of New South Wales, Australia Geoffrey Pardoe, Brunel Science Park, UK Gillian Pierce, Oxford University, UK Vladimir Prisnyakov, Dniepropetrovsk State University Tanya Sienko, NASDA, Tsukuba, Japan Ray A. Williamson, OTA/US Congress, USA Space Power: Resources, Manufacturing and Development is a quarterly, international journal for the presentation, discussion and analysis of advanced concepts, initial treatments and groundbreaking basic research on the technical, economic and societal aspects of: large-scale spaced- based solar power, space resource utilization, space manufacturing, space colonization, and other areas related to the development and use of space for the benefit of humanity. Papers should be of general and lasting interest and should be written so as to make them accessible to technically educated professionals who may not have worked in the specific area discussed in the paper. Editorial and opinion pieces of approximately one journal page in length will occasionally be considered if they are well argued and pertinent to the content of the journal. Submissions should represent the original work of the authors and should not have appeared elsewhere in substantially the same form. Proposals for review papers are encouraged and will be considered by the Editor on an individual basis. Editorial Correspondence: Dr. Andrew Hall Cutler can be reached by telephone at (602) 322- 2997, by Facsimile at (602) 326-0938 and by mail at 4717 East Fort Lowell, Tucson, AZ 85712, USA. Dr. Cutler should be consulted to discuss the appropriateness of a given paper or topic for publication in the journal, or to submit papers to it. Questions and suggestions about editorial policy, scope and criteria should initially be directed to him, although they may be passed on to an Associate Editor. Details concerning the preparation and submission of manuscripts can be found on the inside back cover of each issue. Business correspondence including orders and remittances for subscriptions, advertisements, back numbers and offprints, should be addressed to the publisher: The Council for Social and Economic Studies, 6861 Elm Street, Suite 4H, McLean, Virginia 22101. The journal is published in four issues which constitute one volume. An annual index and title-page is bound in the December issue. ISSN 0883-6272 © 1992, SUNSAT Energy Council
SPACE POWER Volume 11, Number 2, 1992 V. Badescu. Optimization of Stirling and Ericsson Cycles Using Solar Radiation 99 P.Q. Collins and R. Tomkins. A Method for Utilities to Assess the SPS Commercially 107 Yoshiki Yamagiwa and Makoto Nagatomo. An Evaluation Model of Solar Power Satellites Using World Dynamics Simulation 121 Fadhel M. Channouchi, Yves Cassivi & Renato G. Bosisio. Six-Port Junctions for the Control of Phased Array Antennas on Microwave Power Satellites 133 B.A. Osadin. Plasma Launchers for SPS’s 141 Anatoly S. Koroteev, Anatoly M. Kostylev, Vladimir S. Tverscoy Prospects for the Application of Solar Arrays with Concentrators in Near-Earth Orbits 149 Seth D. Potter. Microwave Power Transmission Using Tapered Beams 155 Lucien Deschamps. Space Power Systems for the Global Environment Age! 175 Rashmi Mayur. The Energy Crisis and SPS for the Third World’s Future! 183 t Presented at SPS Rio 92, Space Power Systems and Environment in the 21st Century, (Third International Symposium) Rio de Janeiro, June 4'h, 1992.
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Optimization of Stirling and Ericsson Cycles Using Solar Radiation V. BADESCU+ SUMMARY A model is considered in this paper which consists of: (i) a source of radiation (the sun); and (ii) two energy converters. The first converters, an absorber, transforms the solar radiation into heat while the second one, a Stirling or Ericsson cycle engines, uses heat to produce mechanical work. Polarization coefficients were introduced to characterize the radiation emitted by the sun and the converter. The maximum conversion efficiency of sunlight into work was determined. Consideration of thermal equilibrium allowed a relationship between the polarization coefficients to he derived. Introduction It is well known that the higher the temperature a working fluid is heated to by a solar collector the lower the collector efficiency will be. However, heat engines are more efficient at higher heat supply temperatures. This indicates that any solar collector - heat engine combination will have an optimum operating temperature. The maximum global efficiency of such collector - engine combinations has been extensively studied. [ 1-9] The ideal case of a Carnot cycle engine has typically been described in the literature. Here I briefly study the case of Stirling and Ericsson cycle engines which might be used in actual space power applications. This has also been discussed by Howell and Bannerol, [3] as well as other authors who took different theoretical approaches. [10-12] The present approach is based on development of the model proposed by Landsberg and Baruch. [13] Power Generation and Conversion Efficiency Following Landsberg and Baruch, (13] I consider a system consisting of two large reservoirs - the pump (p) and the sink (s) - together with two converters. The first converter is the absorber (RI I) and it interacts with both the pump and the sink by interchange of isotropic radiation. In the RI I converter energy received as black body radiation at temperature T is received from the pump and transferred to the second converter - the heat engine (IIW) where it is partially transformed into mechanical work. When the sink docs not emit radiation the energy and entropy balance equations per unit area for the RI I converter arc: * Mechanica, Terniolechnica, Polytechnic Institute of Bucharest, Bucharest 79590 Romania.
where S*" is the entropy generated per unit area of the RI I converter. Similar balance equations may be written for the IIW converter: In (1-4) Ts and Tc are the ambient and converter temperatures while 4> and ip refer to energy and entropy fluxes respectively. The subscript pc denotes a flux from the pump to RI I and the subscript cs denotes a flux from RI I to the sink. The return flux from RI I to the pump is also considered (cp). RI I supplies the heat flux Q' to IIW. This heat flux is accompanied by the entropy flux which is the rate of entropy generation while the work produced and the heat transferred from IIW to the sink are W and Q. We may determine the power generated by manipulating equations 1-4: Considering isentropic black body radiation the total energy and entropy fluxes emitted by component i towards component j (i,j = p,c,s) are given by: [13]
where a is the Stefan-Boltzmann constant 1, = 1 or 2 is the polarization factor for polarized or unpolarized radiation and the B^ are geometric factors given by In equation 8 is the angle between the direction radiation is incident from and the normal to the surface of component i, while fl- is the solid angle subtended by component j when viewed from component i. BT denotes the value computed using equation 8 for the total solid angle accessible to the converter RH. The following relations apply:13 The model of Landsberg and Baruch [13] has been extended to cover the case where the radiation emitted by component i (i = p,c) is partially polarized. The flux Qj may be decomposed into a flux <Pipo1 of polarized radiation (1, = 1) and a flux $iunpo1 of polarized radiation (1; = 2) [14 pg. 163]. A polarization coefficient P; 6 [0,1] is defined so that: When P; = 1 the radiation emitted is completely polarized while P, = 0 corresponds to unpolarized radiation. Combining equations 6 and 11 the energy flux for partially polarized radiation is obtained:
The following notation is used here [13]: By substituting equations 6, 7, 11 and 12 into equation 5 and then using the relationships in equations 9, 10, 14 and 15 power can be obtained in a more useful form: Efficiency is best defined as [13]: Consider the entropy being generated in RI I. By eliminating Q' between equations [11 and [2] and combining equations 12-15 I obtain:
In order to calculate entropy generation in HW (the heat engine) the efficiency H„w is defined as: Equations 3, 4 and 21 can be combined to yield: Using equation 1 to eliminate Q' from equation 22 I derive: Landsberg and Baruch [13| did not take the rate of entropy generation SgHW into account in their analysis. These authors considered the converter I1W to be a reversible Carnot engine. In this case r)HW = 1 - a/b, and combining this with equation 23 we see that SgR" vanishes. It is now possible to draw some interesting conclusions regarding the case where the pump, sink, RI I and HW are in equilibrium. In this case the three T, are equal black body temperatures. Consequently, a=b= 1 and tjhw = 0. From equation 23 we can now calculate that Ss"w = 0 without further information. For RI I, equilibrium only obtains when SgRH = 0. Manipulating equation 20 we find that the condition must be fulfilled. If a hemispherical pump is considered, (r4 = 1) equilibrium only occurs when Pc = Pp.
Results and Discussion For an HW converter (the heat engine) operating on an air standard Stirling cycle, the efficiency tjhw can be put in the form: [3] and d is the fractional deviation from ideal regeneration, R is the gas constant, Cv is the heat capacity of the working fluid at constant volume, and V] and V2 are the specific volumes of the constant volume regeneration process for the cycle (V,/V2 is the overall compression ratio). Note that regeneration is perfectly efficient when d = 0 in equation 25, and tjhw reduces to the ideal Carnot cycle efficiency. For the Ericsson cycle, the efficiency 7)HW is also given by equation 24, but x has the following form where Cp is the heat capacity of the working fluid at constant pressure, ?! and P2 are the pressures at which the two isobaric regeneration processes take place, and the other symbols have been defined above (Further details for these cycles are available in the literature) [3]. In order to determine r; the power generated must be evaluated, which can be done by substituting equations 1 and 24 into equation 21:
conversion efficiency is then given by equations 12, 18 and 27. In order to maximize 77 with respect to b (=TC/Tp) the equation drj/db = 0 must be solved: Figure 1 shows that dependence of the maximum conversion efficiency pmax on the parameter x for different values of the polarization coefficient Pp, assuming BT = 2tf a = Tj/Tp = 300/6000 = 0.05 and r4 = 2.17 x 10’3 (this last value corresponds to concentrated solar radiation with a concentration ratio of 100). Suppose the radiation emitted by the converter is not polarized (Pc = 0). The influence of the parameterx is seen to be important. T7max is significantly dependent on P , especially at low values of x. Detailed discussion and numerical results will be published in a future paper.
Conclusions The polarization coefficients Pp and Pc for black body radiation emitted by the pump and RH converter influence entropy generation in both RI I and HW (the absorber and the heat engine). When thermal equilibrium is considered, the polarization coefficients are not independent. The maximum efficiency r/max of the converter - heat engine combination is strongly dependent on the parameter x which is used to characterize the Stirling or Ericsson cycle (equations 25 and 26). The dependence of 7/mM on the polarization of the pump radiation is quite significant, especially at low values of x. REFERENCES [1] MUSER, H. (1957), Z. Phys., 118 pp. 380-390. [2] Castans, M. (1976) Rev. Geofis,. 35, pp. 227-239. [3] Howell, J.R. and Bannerot, R.B., (1977) Sol. Energy, 19, pp. 149-153. [4] DeVos. A. and Pauwels, H. (1981) Appl. Energy, 25. pp. 119-125. [5] JETER, S. M. (1981) Sol. Energy, 26, pp. 231-236. [6] Bejan, A., Kearney, D.W. and Dreith, F., (1981)7. Sol. Energy, 103, pp. 23-30. [7] HAUGHT, A.F. (1984)7. Sol Energy Eng., 106, pp. 3-15. [8] MANFRIDA, G., (1985) Sol. Energy, 34, pp., 513-515. [9] BADESCU V. (1989) Int. J. Energy, 14. pp. 237-239. [10] Selcuk, M.K. (1986) "Prediction of Performance of Paraboloid Dish Solar-Power Modules Using Graphical Methods,” in Solar Energy Utilization. Fundamentals and Applications (Eds. H. Yuncu, B. Kilki§), EIEI Printing Shop, Ankara, Turkey, pp. 543-563. [11] Constantinescu R., Costea, M., Mladin, C„ Brusalis, T., Petrescu, S. AND PETRESCU, V., (1988) Bull. Inst. Polytechn. Bucarest, seria Energetica, 50, pp. 59-67. [12] Petrescu, S„ Brusalis, T., Iordache, R., Costea, M. and Petrescu, V., (1989) Energetica, 37, pp. 358-363. [13] Landsberg, P.T. and Baruch, P. (1989)7. Phys. A, 22, pp. 1911-1926. [14] LANDAU, L AND LlFCHITZ, E. (1970) Theorie des Champs, Editions MIR, Moscow.
A Method for Utilities to Assess the SPS Commercially P.Q. COLLINS AND R. TOMKINS1 SUMMARY Most of the literature on satellite solar power stations (SPS) has considered the combined satellite-rectenna unit as a means of generating continuous power. This paper shows that by considering the rectenna as an independent facility owned and operated by a utility, the utility could use their existing expertise to estimate how much they would be prepared to pay for supplies of microwave power from space, thereby providing clear cost targets for space engineering companies. In addition a range of more flexible and more profitable modes of operation for the SPS can be analysed including provision of daytime power, provision ofpower to a rectenna from more than one satellite, and coordinated operation of a system of several satellites. Introduction For the SPS project, as for any new commercial venture, the concerns of potential customers are of primary importance. The customers for the SPS will be the major electric utilities of the world, and it is therefore essential to consider the SPS from their point of view. The concerns of electric utilities center, in turn, on the needs of their customers, and in particular on the pattern of demand for electricity. This is not constant, but fluctuates according to a number of regular patterns. First there is a daily cycle, whereby for most utilities the daytime level of demand lasts for some 16 hours and then falls by some 50% for the 8 hours of night-time. There is also an annual cycle, which for some utilities shows an average winter demand approximately 100% higher than the summer average; for other utilities the summer average is higher than the winter. There are also weekly cycles and short-term surges at peak demand periods during the day. In order to supply this power, utilities operate electricity generating capacity of different types, some providing continuous "baseload" power, some providing daytime power, and other capacity providing short-term "peak" supplies. The marginal cost per kilowatt-hour from each of these sources is different generally being lowest for baseload power and highest for short-term supplies. Most SPS studies have assumed that, because of the SPS’s high capital cost and the corresponding need to maximise its usage, each satellite would be used to transmit "baseload" power more or less continuously to a single rectenna. However, this assumption overlooks the fact that the value of electric power is not constant but varies during the day and over the year. + The Management School, London, United Kingdom.
Moreover, the SPS has technical capabilities that make a system of satellitesand rectennas capable of more flexible modes of operation which are of much greater value to electricity supply companies, and therefore potentially more profitable to satellite operators. Supplying baseload power narrows the scope for the SPS operation, and ignores a major part of the systems’s potential value. It also sets the most demanding cost targets for the SPS, since it would be in competition with other base-load plans with the lowest operating costs. Alternative Assessment Method An important feature of the SPS project is that it involves two distinct industries, space engineering and electricity supply, whose fields of expertise are both essential to the project, but very different. One possibility for overcoming this difficulty is to treat the ground segment and the space segment as two separate investment projects: Thus a utility would construct, own and operate a rectenna integrated into its power supply grid but a different organisation would own the satellite and be responsible for its operation and maintenance. The utility would then purchase microwave ’fuel’ from the satellite company. Such a division of the overall system would have considerable similarities to the operation of international satellite telecommunications: INTELSAT commissions, purchases and operates telecommunications satellites, and leases channels to its users who construct, operate and control their own Earth terminals. It would also be similar to the new, non-integrated structure of the electricity sector in the United Kingdom, where a number of local distribution companies purchase electricity from a range of generators. Cost targets for the space segment could be found as follows. Utilities would estimate the cost to them of installing and operating a rectenna in their grid, and would calculate what additional price it would be economic for them to pay for microwave ‘fuel’ under different conditions. This would then provide the targets for the satellite company’s costs. The evaluation of the SPS proposal would be much enhanced by the direct involvement of utilities. However, the prospect of financing an extremely large capital investment in a field with which they arc unfamiliar is not attractive to utilities. One advantage of the approach outlined above is that the technological and economic uncertainties concerning the rectenna are much less than those relating to the space segment. Most of the major technologies involved in the rectenna lie within utilities’ existing fields of expertise, and so they could become independently involved from a very early stage. Rectenna Cost Contribution Every rectenna would, to a considerable extent, be unique both in the civil engineering requirements of the site and in its electrical connections to the existing grid. However, the method proposed above can be demonstrated in a simplified
form. The annual cost, C, to a utility of operating a rectenna can be expressed as: These cost elements can be broken down further: The capital recovery factor depends on the required rate of return on assets and their lifetime (see Table 1), and the rectenna capital cost is the sum of the site acquisition and preparation cost, the support structure cost, the receiving antenna cost, the power conditioning and grid interface cost and additional storage cost. Using equation (1) we can use cost estimates from the literature in order to calculate what would be an economic ‘fuel’ cost. Denman el al. (1) estimated the rectenna capital cost at $3000m in 1977 dollars, which converts to approximately $600/kw (assuming US inflation of 5%/year since then, and an exchange rate of $ 1.90:£l). The correct rate of return on capital is a matter of debate, and so we consider the two cases of 5% and 10% (which are the past and present values of the required rate of return for UK nationalised industries) and a rectenna lifetime of 30 years. The operation and maintenance costs include a number of elements. The figure of 3% per annum of capital cost assumed here is that used by Cottrill (2) for other renewable energy sources. Table 2 shows the cost of operating a rectenna on these assumptions.
Microwave "Fuel" Price In 1988/89 the average operating cost for the CEGB’s power stations was 3.53p/kWh [3], Future power stations may be of the combined cycle gas turbine type of advanced coal combustion technologies. James Capel [8] estimates the variable operating costs of such plants to be in the range 1.3-1.5 p/kWh, which implies an operating cost of around 3.0 p/kWh. Hence if the SPS were to be competitive with modern a coal-fired plant, the utility could pay up to 1.96p/kWh (ie 3.00-1.04) for microwave ‘fuel’ if the rectenna capital cost were £600/kW, the discount rate 10% and the load factor 90%. Alternatively, at 70% load factor, £400/kW capital cost and 5% discount rate, the utility could pay 2.38p/kWh. For the SPS to be economically viable its overall cost of electricity should be competitive with the alternatives. However, the criterion for being suitable to provide baseload power is that its operating costs should be competitive with other baseload plants - which is a more stringent condition. In the UK, nuclear power stations have the lowest running costs; the estimated generation cost for a new PWR power station is given by Jones & Woite as 0.98 p/kWh (1989 prices), [9]. Table 3 shows the maximum price which could be paid for microwave ’fuel’ if this target were to be met by a rectenna. It is thus possible that the SPS could become competitive as an energy source but not be high enough in a utility’s merit order to provide baseload power. In this case the expected flexibility of the power output of the SPS could be valuable in allowing the rectenna to perform two-shift operations. Although the rectenna would not achieve a high load factor, the satellite supplying it could still do so if it were to transmit microwave power to other rectennas some distance away around the globe, thereby acting as a peakload power source at several locations.
Value of Flexibility Following this approach, it can be seen that significant economic benefits would arise if SPS systems were designed: 1. to allow a satellite to switch some or all of its transmitted power between two or more "rectennas" according to the pattern of demand on the rectennas, and 2. to allow rectennas to receive microwave power from one or more satellites simultaneously. The combination of these enhancements would permit the achievement of a high load factor on the satellite (which represents some 80% of the total cost) while utilising the rectennas to which it delivered power at lower load factors for the provision of daytime and peak load power, for which the cost to utilities is substantially more than for base-load power. That is, since the capital costs of both satellite and rectenna dominate their operating costs, the contribution of both segments to the cost of SPS power is dependent on the load factors at which they are operated, the space segment being substantially more important. Thus, provided that the load factor on the space segment can be kept high by delivering power to more than one rectenna in succession during the day rectennas could be operated profitably even at relatively low load factors. Figure 1 illustrates the additional flexibility of rectenna operation that this permits: A particular system might not be competitive as a baseload power source even if both satellite and rectenna were operated at the maximum load factor of 0.9, and it might not be economic if operated with a load factor of only 0.67 (typical for daytime demand) on both satellite and rectenna. The system could nevertheless provide daytime power profitability with a load factor on the rectenna as low as 0.6 if the satellite load factor was 0.9. The shaded area illustrates the range of load factors over which the system could be both profitable and competitive for supplying daytime power. Thus in a given case, an SPS might be uncompetitive as a base-load power source, but be attractive as a source of daytime and peak power. In order to exploit
this potential fully, a mature SPS system should not comprise equal numbers of satellites and rectennas but should contain more rectennas than satellites, at least some of which should provide power intermittently to several different rectennas. The operation of rectennas at low load factors would be more attractive the lower was the capital cost per kilowatt of the rectenna. The potential benefits of more flexible power supply therefore constitute an additional incentive to design low cost-per-kilowatt rectennas. A promising means of reducing the rectennas cost per kilowatt would be to use rectennas designed to receive power from two or more satellites simultaneously [4], The cost of a rectenna capable of handling the output of two satellites would be between 132% and 145% of the cost of a single capacity rectenna [5]. Consequently a rectenna uprated to double its initial capacity would be economical to operate at lower load factors. Flexible SPS Operation There are several different ways in which the potential flexibility of a system of SPSs could be utilised to follow the loads at different rectenna sites as they vary over the time of day or year.
Supply of Daytime Power by a Satellite to more than one Rectenna A satellite supplying daytime power to a rectenna would be unloaded between the hours of approximately 10 p.m. and 6 a.m. local time at the rectenna. It would therefore be free to transmit power to other rectennas during this period each day. Transmission to other rectennas sited in different time zones from the primary rectenna would permit the transmission of daytime power to these rectennas during the night-time load period of the primary rectenna. Time zones are typically 15 degrees of longitude in East-West extent, and consequently, assuming similar daily load curves, rectennas separated by more than 15 degrees of longitude could differ by one or two hours in the timing of their load curves, while rectennas separated by more than 30 degrees could differ by two or three hours. Thus a satellite at the same longitude as its primary rectenna might deliver three hours of daytime power to a rectenna some 30 degrees West of primary rectenna from 7 p.m. to 10 p.m. at the rectenna (i.e. 10 p.m. to 1 a.m. local time at the satellite) plus three hours daytime power to a rectenna some 30 degrees East of the primary rectenna from 6 a.m. to 9 a.m. local time at the rectenna (ie 3 a.m. to 6 a.m. local time at the satellite) in addition to supplying full daytime power to the primary rectenna 6 a.m. to 10 p.m. as illustrated in Figure 2. When power is transmitted from a satellite to a rectenna with a longitude offset from the satellite, the area over which the microwave beam is spread at the ground increases. For a longitude offset of 30 degrees the area of the rectenna increases by some 50% (depending on the latitude of the rectenna) over the area of a rectenna delivering equal power with zero longitude offset. This would increase the cost of the rectenna by some 25% [5]. Following this schedule, the satellite would thus save both plant capacity and fuel costs for the full daytime load period of the utility operating the primary rectenna, as well as providing three hours’ daytime fuel saving for each of the other two utilities. The load factor on the satellite would of the order of 0.9, which is the target for the SPS space segment [6], while that on the rectennas would be 0.67, 0.125 and 0.125 respectively. In order to be economic for the utilities operating the secondary rectennas, these would each have to receive power from some other satellite for some part of the day in order to increase their overall load factors. If, for instance, each of the secondary rectennas had similar arrangements with two other satellites, the load factors could reach 0.37, which might be economic for a rectenna uprated to receive power from multiple satellites [5], Back-up Supplies and Grid Interlinking The antenna design that has to date been considered most appropriate for the SPS is a phased-array antenna. Such systems have the technical capability to alter the direction of the transmitted microwave beam in a very short time: Radar transmitters with power outputs of the order of 100 kW currently switch their beam direction in time periods of less than 1 millisecond. Consequently, even allowing
for the very much larger power output of the SPS it should be technically possible to switch the direction of the power transmission from one rectenna to another within a few seconds. In practice, constraints on doing this are likely to arise within the ground segment of the system, both in the maximum rate of change of power flow than can be tolerated with an electricity grid, and in the maximum rate of change of load that is experienced by utilities. The most rapid changes in power flow that occur in a typical grid result from the sudden loss of the output of a power station. Hence, provided that the arrangement was economically attractive, an SPS might be used to provide periods of standby power supply to one or more utility grids, covering both loss of output and rapid increases in load. If the grid to which an SPS was currently delivering power contained sufficient storage and/or steady capacity to replace the SPS output at very short notice, the SPS could at the same time provide backup power to another grid, enabling several grids to share their standby and reserve capacity with several SPS delivering power to a number of different grids, this flexibility could substitute in part for the use of long distance transmission cables between the grids.
The potential for short-term flexibility of power delivery could be exploited most fully if satellites had two transmitting antennas with the capability to transmit two power beams simultaneously of which the power levels could be varied smoothly. Technically it would be possible to vary the output of an SPS continuously, but whenever power was being delivered at less than the maximum rate possible, some of the system capacity would be being wasted. The use of a satellite with two antennas, of which the combined capacities exceeded the capacity of the satellite, would enable the power output of the two antennas to be adjusted inversely. In this way the load factor on the satellite could be kept at its maximum, and the power delivered to the two rectennas be adjusted to match best the requirements of the two utilities. Figure 3 illustrates a possible pattern for sharing of the output of an 8 GW satellite between two 5 GW antennas. (An alternative means of transmitting two microwave beams from a single satellite has been proposed by Arndt and Kerwin [7] who have described single antennas capable of transmitting two and four microwave beams at an overall cost of power very similar to that of single beam antennas. However, the efficiency of power transmission falls off as the separation between rectennas increases, which would greatly restrict the scope for long distance power switching). The cost per kilowatt of an 8 GW satellite with two 5 GW transmitting antennas would be some 12% more than the cost of a 5 GW system [5]. This margin
might be compensated for by the greater flexibility of delivery and the potential for somewhat higher satellite load factors due to the possibility of shutting down one antenna for maintenance work while maintaining more than a 60% power output from the other antenna. Seasonal SPS Capacity Sharing A major opportunity for sharing the output of a satellite between two rectennas results from the fact that the periods of maximum demand on different electricity grids arise during different seasons of the year. (For instance, the maximum demand on some American electricity grids arises during the summer when the demand for cooling is highest, while in Northern Europe the maximum demand arises during the winter). Consequently a single satellite could be operated in such a way as to supply baselaod power to one rectenna during the winter months and to supply the same to another rectenna during the summer. In this way each rectenna would achieve a load factor of approximately 0.45 (ie 50% of 0.9). If each rectenna also received six hours of daytime fuel-saving supplies for approximately half the year, they would achieve overall load factors of 0.57. Such a winter/summer peak delivery pattern would make a convenient match with the fact that for three weeks either side of the equinoxes (March 21s' and September 23rd) geostationary satellites are eclipsed for a few minutes around midnight. Thus, by concentrating some of the planned outages for necessary maintenance into these periods, an SPS would be able to achieve higher load factors during the months of maximum demand. This potential for sharing capacity on a seasonal basis between two widely separated utility grids is a capability that is unique to the SPS. Coordinated Operation of a Global SPS System As the number of satellites and rectennas in a global system increased, the average longitude offset between them would decrease, and the scope for economising on satellite capacity through coordinatedoperation of satellites would increase. Such arrangements would be facilitated by some formation of long-term supply agreements between several different utilities. A computer model has been used to estimate the scale of savings that might be achievable in practice through the coordinated switching of power between several satellites and rectennas. Optimal Operation of SPS Systems In order to study the potential benefits of switching power supplied from satellites between several rectennas according to the changing pattern of demand during the day, a system of sixteen rectennas was selected, sited at major population centres around the world. For this exercise, assumptions were made about demands to be served at peak and off peak-times (see Table 4). A critical parameter in determining the relative profitability of supplying peak or base load power from an SPS is the ratio of the marginal costs of power at peak and
base load periods. We have not attempted to forecast the marginal costs at the various locations next century, but have merely taken a ratio of 2:1 as representatives. On this assumption, if satellites were used to provide power only during the daytime period, the duration of which is commonly sixteen hours, they would earn 33% more than if used to provide base load power. Similarly, if a set of satellites were used to supply equal amounts of base and peak power, average satellite revenues per kWh would be 16.5% more than if supplying only base load demand. If the capacity of SPSs to switch the direction of their microwave beams is to be fully exploited, less satellite capacity should be employed than the total rectenna capacity. A set of thirteen satellites, with capacities ranging from 8.4 GW to 12.4 GW, with a total capacity of 130 GW, were allocated positions in geostationary orbit, to serve the sixteen rectennas with total peak demands of 180 GW. Costs at other demand centres in Table 4 are assumed to vary plus or minus 20% from the U.K. A linear programming model was formulated to determine the allocation of power from satellites to rectennas in order to maximise the total revenue earned by the satellites. It was assumed that the revenue to a satellite would be the same as the marginal cost to a utility of alternative supply. The formulation is as follows:
where Py = ratio of power transmitted from satellite i to power received at rectenna j; and S, = capacity of satellite i. The need for the Pij factors exists since more power must be transmitted from the satellite than is received at the rectenna, and as the longitude offset between a satellite and rectenna increases, the area of the "footprint" of the microwave beam on the ground increases. (In practice it would be possible to receive the entire beam, at the expense of increasing the area of the rectenna concerned). Satellites were permitted to deliver power to rectennas with longitude offsets of up to approximately 40 degrees. The above L.P. was solved for four typical hours in a 24 hour cycle (01.00, 07.00, 13.00 and 19.00 GMT), to give an optimal switching pattern for the microwave beams. The model solution achieved a 15% average revenue increase over the 1:1 daytime only case and a 53% increase over the 1:1 baseload case. The average satellite load factor achieved was 0.80, compared to 0.67 in the corresponding 1:1 case. Average rectenna load factors were 0.53 compared to 0.67 in the 1:1 case. Although this model was very simplified, the potential for optimising the operation of a flexible system is clearly substantial. A range of more complex L.P. models can also be formulated with various objectives, such as to select the optimal sizes and optimal locations of satellites, as well as the optimal pattern of power transmission over typical 24 hour cycles. Conclusion It could be very valuable if electric utilities were to contribute to the appraisal of the SPS to a greater extent than they have in the past. A particularly valuable form that such a contribution could take would be for one or more utilities to evaluate the cost of designing and constructing a rectenna linked into their distribution grid, and of operating it as one component of their power station "mix". This would enable utilities to calculate the value which they would place on supplies of microwave "fuel", and hence what price it would be profitable for them to pay for deliveries of microwave "fuel" to their rectenna. This would create a market for microwave power from space, and set cost targets for the designers of the SPS space segment. Space engineering companies would then compete to supply microwave power of the appropriate technical specification on the most competitive terms.
The potential to transmit large amounts of power across very long distances at short notice is a unique feature of the SPS. The exploitation of this capability would permit more profitable operation of a system of SPS units than the provision of base load power, by achieving high load factors on the space segment while delivering daytime power from the ground station linked to local utility grids. Further studies aimed at determining and assessing in more detail the satellite and ground system specifications necessary to achieve these capabilities would therefore be desirable. Decoupling the load factors achieved on space segments from the load factors achieved on rectennas, which are determined by different technical and market influences, permits the operation of each to be optimised. In particular it facilitates the achievement of higher load factors on the satellite than on the rectenna. These are desirable both because the satellite has a much higher capital cost than the rectenna, and because the value of daytime and peak electricity (that is, power with a lower load factor than base-load power) has greater value to utilities than baseload power. REFERENCES [1] DENMAN, O.S. ET AL. (1978), "A Microwave Power Transmission System from Space Satellite Power," Proc. 13th IECEC, SAE, pp 62.8 [2] Cottrill. J.E., (1979). "Economic Assessment of the Renewable Energy Sources," Future Energy Concepts, IEE Conf. Pub. No 171, pp 427-32. [3] Central Electricity Generating Board, (1989), Statistical Yearbook. [4] GELSTHORPE, R.V. and Collins, P.Q., (1980), "Increasing Power Input to a Single SPS Rectenna by using a Pair of Satellites," Electronic Letters, 16,9, 311-313. [5] COLLINS, P.Q., (1985) "Economics of Satellite Solar Power Stations," PhD Thesis, London University. [6] U.S. Dept, of Energy and NASA, (1978), "SPS Ref. System Report," DOE/ER-0023. [7] ARNDT, G.D., AND KERWIN, E.M., (1982), "Multiple Beam Microwave Systems for the Solar Power Satellite," Space Solar Power Review, 3, 4, 201-315. [8] James Capel & Co. (1990), "The New Electricity Industry," May. [9] JONES P.M. and Woite G., (1990), "Cost of Nuclear and Conventional Baseload Electricity Generation," IIASA Bulletin, June.
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An Evaluation Model of Solar Power Satellites Using World Dynamics Simulation YOSHIKI YAMAGIWA1 & MAKOTO NAGATOMOft SUMMARY A world dynamics simulation model including solar power satellites (SPS) is proposed for the purpose of analyzing the effect of SPS on the Earth’s environment. The model consists of the Earth section which is based on Forrester’s WORLD-2 model, and the SPS section which is based on energy cost analysis referring to the chemical and traffic industries on Earth. Both sections of the model are connected through the energy investment in SPS from the Earth and the energy return from SPS to the Earth. The simulation results indicate that a relatively small amount of energy investment in SPS would be effective in improving the Earth’s environment in the future. Introduction Recently, the influence of human activitieson the Earth’s environment, such as the exhaustion of resources, pollution of the air, the greenhouse effect, etc., have increased significantly. Such influences were predicted by the world dynamics models of Forrester [1] and Meadows’ team at MIT [2] about twenty years ago. Figure 1 shows a basic simulation result of a modified version of Forrester’s WORLD-2 model. The natural resources and pollution subsystems in the model were modified as described later, but this simulation result is almost the same as that of the original model. This figure shows that the population, the capital and the quality of life on Earth reach their peak values in the early years of the next century, and decline there after, due mainly to the depletion of resources if economic growth on Earth continues at the present rate and if energy production depends on fossil fuels found on Earth. For such "limits to growth" in the closed Earth system, space industrialization, which makes it possible to get energy and natural resources from outer space, will provide the world dynamics model with new boundary conditions and provide a new solution. In this study, a satellite power system, especially using solar power satellites (SPS) [3], is selected as representative of space industrialization because; 1) it is a basic element of space industrialization that will need to come first; 2) the quantitative characteristics of SPS-related activities can be estimated from existing industrial statistics; 3) the value of electricity generated can easily be evaluated as a return on investment. In this study, a world dynamics simulation model including SPS is proposed for evaluating the effect of SPS on the Earth’s environment. College of Engineering, Shizuoka University, 3-5-1 Johoku, Uamamatsu-shi, 432 Japan. + ' Institute of Space and Astronautical Science, 3-1-1 Yoshinodai, Sagamihara, 229 Japan.
Energy Analysis of the Development of SPS To make a model of SPS to apply the world dynamics model to, the energy cost and the relation between output power and mass of an SPS are analyzed. As an energy cost of the SPS itself, the energy to produce solar cells, which dominates the total SPS energy cost, is estimated per unit output power based on Tajima’s study [4]. According to this data, a square solar cell of Si with 10cm sides which has output energy of 2.1 kWh/year requires an energy of 8.77 kWh for production with current technology. This output energy is the value on the ground where a solar energy availability of 20% is assumed, allowing for the diurnal cycle and inclement weather. On the other hand, in space, the availability is almost 100% because the solar cell can generate electric power continuously during the greater part of the year, and the intensity of the sunlight increases to a value about 1.75 times larger than that on the ground. So, the output power in space is about 2.1 W and the energy to produce the solar cell per output power is approximately 15 MJ/W. This value is about two orders of magnitude lower than assumed in Herendeen’s study in 1979 [5], and shows how much the energy cost of solar cells
have improved during the last 10 years. Tajima also estimated that production energy would decrease to 5.25kWh for solar cells with an output power on Earth improved to 2.8 kWh/year in the future. It follows that the production energy for solar cells will decrease to a value of about 7 MJ/W in future. The GaAs solar cell is not considered because of its high cost. The production energy of other elements of the SPS are also ignored in this study. The relation between output power and mass for the totally assembled SPS in orbit is the most important parameter for defining the quantitative SPS model. According to the DOE/NASA reference system, the solar panel weighs 25,000 tons and generates 7.5 GW of electrical power in space, and so achieves a specific power of 300 W/kg [3], This value would apply to the most advanced totally assembled SPS in the future. The ratio of output power to mass for a completely assembled SPS including the power transmitting system of the reference design in the DOE/NASA study is 100 W/kg [3]. This value also applies to the future prospect, but it is already reported that 100 W/kg has been achieved using silicon crystal cells [6], So this seems to be a realistic value for the SPS, and 100 W/kg is adopted as the present value of the ratio of output power to mass for a completely assembled SPS in the present. These results are summarized in Table 1. Rocket propulsion is the only practical way to put space systems in orbit. The energy which is necessary to put an SPS in orbit using rocket propulsion is much greater than the theoretical value of the energy given by orbital mechanics. So, in addition to the energy cost of the SPS itself, the energy cost of rocket propulsion is analyzed as an energy cost of the SPS transportation system. Three elements are considered as the cost of the transportation system, the chemical energy of the propellants, the production energy for the propellants, and the energy for vehicle manufacture. It is assumed that SPS will be established in geosynchronous orbit (GEO) and chemical propulsion will be used for transportation of the SPS.
The chemical energy of the propellants (liquid hydrogen and oxygen) is given by chemical reaction theory. Since one mole of hydrogen reacting with oxygen generates about 68 kcal of energy, which is 286 kJ, the energy per mass of hydrogen is 143 MJ/kg. For a typical launch vehicle, the payload mass in GEO is approximately 1% of the initial mass of the launch vehicle, and about 80% of the initial mass of the vehicle is for the propellants, whose fuel fraction is 1/7. The mass of liquid hydrogen required for launching 1 kg of payload into GEO is taken to be about 10kg. Thus, the chemical energy to be consumed in putting a unit mass of payload (SPS) into GEO is estimated to be 1430 MJ/kg. The production energy for propellants is based on Mann’s study [7], According to his study, the electrical energy required for the production of hydrogen gas is about 120 kWh/lOOOscf, that is, 192 MJ/kg. In addition to this energy, 2.5 to 3 kWh of electrical energy are required to get a liter of liquid hydrogen, which corresponds to 128-154 MJ/kg. Thus the total energy required for the production of liquid hydrogen is about 350 MJ/kg. The energy cost for production of liquid oxygen is one order of magnitude lower than that for the production of liquid hydrogen and so is ignored in this study. So, the production energy of propellants per unit mass of SPS is about 3500 MJ/kg. Current launch vehicles are designed to carry expensive spacecraft completely assembled on Earth. On the other hand, space vehicles which will carry SPS to orbit can be more appropriately compared to ocean-going vehicles than to missiles. So, the industry to build cargo launch vehicles is considered to resemble the shipbuilding and automobile industries, and the energy cost will be better reflected by the industrial statistics of the existing mechanical engineering industry.
In this study, the energy cost of launch vehicle manufacture is estimated by referring to data for the aluminum and iron & steel industries [8]. According to the data for aluminum in 1984, the energy for production of the raw material is about 40 MJ/kg, and the energy for manufacturing general machinery or electrical machinery from raw materials is about 20 MJ/kg from the data for the iron and steel industry. Therefore, the specific energy per mass for launch vehicles is taken as approximately 60 MJ/kg, and the specific energy per mass of payload (SPS) in GEO is taken as 1200 MJ/kg since the ratio of vehicle dry mass and SPS mass in GEO is about 20. In this study, it is assumed that the launch vehicle is disposable and the energy for vehicle manufacture is 1200 MJ/kg for simplicity. However, each launch vehicle could be reusable, and then this energy would be significantly lower than that value, since it could be divided by the number of flights. World Dynamics Simulation Model With SPS The system diagram of the model in this study is shown in Fig. 2. The Earth section of the model is based on Forrester’s WORLD-2 model [1], although the natural resources and pollution subsystems in the model were modified [9],
In the original WORLD-2 model, the natural resources are not specified and it is assumed that the total quantity of natural resources will last for 250 years at the rate of resource usage in 1970. In this study, fossil fuels (oil: NRO, coal: NRC and natural gas: NRG) are adopted as natural resources (NR) on Earth for comparison with energy from space. Their quantity is calculated in the natural resource unit equivalent to about 10 barrels of oil in the same way as in the original WORLD-2 model. Other energy resources on Earth, such as electricity generated by water, wind, nuclear fission, etc., are not considered in this study, because energy produced from them is one order of magnitude smaller than that from fossil fuels at present. In the original WORLD-2 model, the pollution is also not specified, but it is assumed that the quantity of pollution is one pollution unit per person in 1970. In this study, the CO2 level in the air (which is closely related to the consumption of fossil fuels) is adopted as pollution (POL). The CO2 level is determined by CO2 production with the consumption of fossil fuels, and CO2 absorption by oceans and forests. The absorption rate of CO2 is given as a parameter in this study.
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