We describe a simple two-dimensional array of plane mirrors operated by only two motors, which collects efficiently Sun light in order to produce electrical power at about the cost of oil. The system preserves the merits of previous

state-of-the-art solar power plants but is simpler and by far less expensive. A first prototype has been operated at the Physics Department of the University of Udine providing a power of 0.56 kW per m2 of mirror surface in mid November

Grassmann, H.

Prest, A.

English

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DOI 10.1393/ncc/i2009-10313-0IL NUOVO CIMENTO Vol. 31 C, N. 4 Luglio-Agosto 2008The linear mirror for solar energy exploitationA. Prest and H. GrassmannIsomorph srl(∗) - Visogliano 9R1, I-34013 Duino-Aurisina (Trieste), ItalyDipartimento di Fisica dell’Universita` di UdineVia delle Scienze 208, I-33100 Udine, Italy(ricevuto il 7 Gennaio 2009; approvato il 28 Gennaio 2009; pubblicato online il 12 Marzo 2009)Summary. — We describe a simple two-dimensional array of plane mirrors op-erated by only two motors, which collects efficiently Sun light in order to produceelectrical power at about the cost of oil. The system preserves the merits of previousstate-of-the-art solar power plants but is simpler and by far less expensive. A firstprototype has been operated at the Physics Department of the University of Udineproviding a power of 0.56 kW per m2 of mirror surface in mid November.PACS 42.79.Ek – Solar collectors and concentrators.PACS 84.60.-h – Direct energy conversion and storage.PACS 89.30.Cc – Solar power.PACS 89.20.Bb – Industrial and technological research and development.1. – State of the artNowadays there are several quite different techniques for exploiting solar energy. Solarpanels can be used for heating water. In winter at European latitudes these panels canheat water up to about 60 ◦C [1]. Electricity can be obtained from semiconductingphotovoltaic modules. Both these technologies are rather expensive. The cost of thephotovoltaic panel is typically 700 euro/(m2 of radiated area) [2], resulting in a price ofabout 40 to 50 cent/kWh.One can exploit solar energy by means of concentrating mirror systems [3]. Theycan provide heat at relatively high temperatures (up to about 1000 ◦C) and generatehot steam driving a turbine to produce electricity. At the same time they provide lowertemperature heat—that can be used for instance for heating buildings. However, existingmirror systems suitably concentrating solar light are even more expensive than solarpanels or photovoltaic modules. In addition, their operation is rather complex. As aconsequence their use up to now has been very limited [4].(∗) E-mail: http://www.isomorph.itc© Societa` Italiana di Fisica 557558 A. PREST and H. GRASSMANNFig. 1. – Pictorial view of a matrix of mirrors, reflecting Sun light onto a focal area.There are various ways of realizing a concentrating mirror system:1) Parabolic mirrors focus parallel Sun rays onto a common focal point. The advantageof parabolic mirrors is the simplicity of the system to control their motion—themirror simply has to point to the Sun. Their problem is the construction of theparabola. Large parabolic mirrors are particularly expensive [5].2) Parabolic “trough” systems are only particular versions of the parabolic mirror.3) Solar towers consist in an array of planar mirrors, each reflecting the Sun rays ontoan approximate focal point at the top of a tower. These systems are relatively easyto construct. However, their control system is very complex, the motion of each mir-ror being driven by two precision motors. This results again in a high system price.In this paper we describe a mirror system similar to a solar tower which allows ex-ploiting solar energy at a much lower cost. A pictorial view of such an array is shown infig. 1.2. – The linear mirrorThe linear mirror depicted in fig. 1 consists of four rows of mirrors, arranged in a ma-trix, and a focal area which collects the concentrated sunlight during the day. The systemis oriented so that the focal area points toward the South.In order to illustrate the principle of functioning(1) of this system, we begin consid-ering one of the four rows of the mirror matrix. The mirrors are mounted on axes whichform a plane normal to the incident Sun rays. We denote the orientation of each mirrorby means of the normal to its surface. This vector is referred to as “mirror vector” inthe following. This system is sketched as viewed along the axes in fig. 2.The row of mirrors is normal to the south direction (the south direction definesφsun = 0, as indicated in fig. 2). When for instance the Sun is in the south, we can(1) Demonstraive movies are available in the website www.isomorph.it/solutions/renewable-energies/solar-thermal/principle-of-functioningTHE LINEAR MIRROR FOR SOLAR ENERGY EXPLOITATION 559Fig. 2. – Top view of a horizontal slice of the array. Plane mirrors are mounted on axes “A”and rotate around them during the day. The angle of the mirror normal relative to south, whichequals the angle between mirror and array, is denoted φ. The focal area has approximately thesame size as the mirror.adjust (in φ) each of the mirrors in such a way that all mirrors in a row reflect theSun rays onto a common focal area, as indicated in fig. 2. When the Sun is in a dif-ferent direction, the focal area remains fixed in space while the mirrors are rotated byΔφmirror = 1/2φsun. In this way, the reflected Sun light of this median row will point tothe focal area during all day.Several mirrors above (and below) the median row can be mounted on each axis, inorder to increase the concentrating power of the system: this is sketched in fig. 3, whichshows a vertical array of mirrors on one of the axes (normal to the incident Sun rays).This mirror system would be very cheap, due to the simplicity of its construction.However, if we consider rotating the mirrors around their axes in order to follow the Sunduring the day, as sketched in fig. 2, we observe that its optical properties are inadequateas discussed in the following.We assume that each mirror is tilted up-down and left-right by the appropriate amountas to reflect the Sun rays onto the focal area when the Sun is in the south direction(φsun = 0). We shall call this “the ideal case”. When the Sun is in a different direction,Fig. 3. – Side view of a vertical (normal to the Sun rays) slice of the mirror array. Most mirrorshave an inclination η with respect to the axis A, so that when the mirrors are rotated in φduring the day the reflected rays are not normal to the vertical axis “A”.560 A. PREST and H. GRASSMANNthe focal area remains fixed in space while the mirrors are rotated by Δφmirror = 1/2φsun.As discussed before, for those mirror vectors which are normal to the axis to which theyare mounted, the reflected Sun light will point to the focal area during all day. However,most mirrors would not be normal to their axes and tilted in the vertical direction asillustrated in fig. 3.If now the mirrors are rotated according to Δφmirror = 1/2φsun during the day, themirrors with η = 0 will not reflect the light on the focal area precisely. We expressthe deviation of the reflected rays from the ideal case by considering the angle in spacebetween the real reflected ray and the ideal ray (pointing precisely to the focal area).We label the projections of this angle as Δφ on the Sun plane and Δθ in the conjugatedirection. The deviations Δφ and Δθ will of course be 0 for mirrors without inclination(η = 0), and will increase with η being larger for larger inclinations. In order to illustratethe problem we show in figs. 4 and 5 these deviations for a number of mirror inclinations.For simplicity only mirrors in the vertical slice at the centre of the array have beenconsidered, for which φmirror = 0 when the Sun is south, at φsun = 0.We see that for an inclination η = 15◦ the deviations Δφ and Δθ will be as much as 4◦and 6◦ respectively, for a Sun angle of φsun = 70◦(2). If we therefore rotate all axes andmirrors by means of a single motor, according to Δφmirror = 1/2φsun, the reflections fromthe various mirrors would deviate from the focal area by less than about 6◦. Since mirrorsat small inclinations would have deviations smaller than 6◦ and since even the mirrors atlarge η will have smaller deviations then 6◦ during most of the day, this mirror system(which would be very easy to construct) would already have a significant efficiency andpossibly be of practical use. In the following we shall illustrate how by simple means wecan reduce these deviations to 1◦ or less and achieve a system of excellent light collectionefficiency. Noticeably, this limit has great practical impact because large systems withmechanical tolerances much below 1◦ would be expensive to build.2.1. Making the mirror array approximately linear by means of linear operations. –Figure 6 shows a simple way of correcting the Δφ deviations. Each mirror is mountedon an axis of its own and is rotated by means of a lever. The levers are all connectedto a common axis of control, which is rotated by a motor. By appropriately choosingthe length of each lever we can move the mirror axes at a speed different from therotation speed of the axis of control. This allows reducing the deviation in Δφ to a fairapproximation.In order to reduce Δθ we use a system as is shown in fig. 7. Now, when the mirror ismoving to left or right (in φ), it is also changing its inclination at the same time. Thisallows compensating some of the Δθ deviation.We consider again the same mirror positions as in calculating the distributions offigs. 4 and 5. We also use the same values for the inclination η, but now the inclinationof the mirror is achieved by a support system according to fig. 7. The length of the leversis optimised. As a result we get the Δφ and Δθ deviations as shown in figs. 8 and 9.Now the Δφ deviation for a mirror with inclination η = 15◦ is much less than 1◦, tobe compared to 4◦ as observed in fig. 4.For η = 15◦ the deviation in Δθ is less than 1◦ to be compared to  6◦ in fig. 5.(2) For angles larger than φsun = 70◦ the effective area of the array exposed to the Sun is lessthan 34% (cos(70◦) = 0.34). A coverage of ±70◦ results in an exposure of 12 h∗140◦/180◦ = 9.3hours per day.THE LINEAR MIRROR FOR SOLAR ENERGY EXPLOITATION 561Fig. 4. – For a vertical slice of mirrors at the centre of the array, deviation of the reflected lightray from the ideal direction for different inclination angles η. The mirrors rotate around an axisnormal to the Sun rays.2.2. Aberrations of light from non-central mirrors. – In figs. 8 and 9 we have calculatedthe deviations for mirrors of a vertical slice at the centre of the array. The correspondingdistribution for the uppermost and outmost mirror of the system shown in fig. 1 is shownin fig. 10. Compared to central mirrors, the focal quality is somewhat decreased but thedeviations are still within ∼ 1◦.3. – Measurement of the power transfer in a linear mirror with 20 mirrorelementsA prototype of the linear mirror of size 4m · 2m, consisting of an array of 50 mirrorshas been constructed. Due to financial constraints for the time being we have mountedFig. 5. – For a vertical slice of mirrors at the centre of the array, deviation of the reflected lightray from the ideal focal point for different inclination angles η. The mirrors rotate around anaxis normal to the Sun rays.562 A. PREST and H. GRASSMANNFig. 6. – A common axis of control rotates by φ1, causing a mirror to rotate by a different angle,φ2.only 20 of the 50 mirrors, as shown in fig. 11. The orientation of the mirror systemtowards the Sun was regulated by hand, using a gauge mirror. The oven of the systemconsists of a tin container of size 55 cm · 55 cm · 1 cm. It was painted with a black colouras used for painting car motors. The container was filled with 4.3 litres of water (thecontainer widened to a width of more than 1 cm when filled with water). The irradiatedcontainer is shown in fig. 11. The oven had no isolation at all.The goal of the experiment is to determine the increase in water temperature as afunction of time. The heat capacity of water is known (4.180 kJ/(kg·K)), as well as themass of the water (4.3 kg). Therefore the temperature increase per time gives a measureof the radiation energy absorbed by the water volume (the mass of the iron container is8.0 kg, which is larger than the mass of the water, but the specific heat of iron is muchless than that of water, so that the energy absorbed by the iron container can be ignoredin this context).Fig. 7. – The axis of rotation of the mirror is not normal to the Sun rays anymore. It is inclinedby η relative to “A”, while the mirror is inclined by 2η with respect to its axis.THE LINEAR MIRROR FOR SOLAR ENERGY EXPLOITATION 563Fig. 8. – For a vertical slice of mirrors at the centre of the array, deviation Δφ of the reflectedlight ray for mirrors with corrected rotation. Note that the x and y scales are the same as infig. 4.3.1. Description of the experiment . – The measurement was performed on November16th 2008, at noon time. A digital thermometer was used with high temperature resistantsensors. At time t = 0 the measurement started and the mirrors were turned onto theoven. Since there was only one person for operating the mirror system and for readingthe thermometer, the start of the measurement at t = 0 and the activation of the mirrorswere not perfectly coincident, for which reason the measurement at t = 0 will be reportedin the following, but it will not be used for a quantitative evaluation. Figure 12 shows thetemperature measured in the water volume with time. The temperature increase dependson two effects: first, there is the energy absorbed by the oven, causing an increase inwater temperature. Second, heat will be lost to the environment. In order to estimate theloss of heat energy to the environment we have switched the linear mirror off (rotatingFig. 9. – For a vertical slice of mirrors at the centre of the array, deviation Δθ of the reflectedlight ray for mirrors with corrected rotation.564 A. PREST and H. GRASSMANNFig. 10. – Δφ and Δθ deviations for the outmost and uppermost mirror on the corner of themirror array of fig. 1.its mirrors sidewards), as shown in fig. 12: at the time intervals (b,c) and (d,e) the ovenwas not heated. For the time interval (b,c) (and a temperature of 53 ◦C) a decrease intemperature cannot be noted. For the time interval (d,e) (and a temperature of 75 ◦C) aslight decrease in temperature can be observed, indicating a relatively larger loss of heatenergy at this higher oven temperature.As mentioned above, the measurement suffers from a systematic uncertainty at aroundt = 0, so we use for the analyses the time from point (a) and later. In the time intervalbetween (a,b) (from t = 1.35min to t = 4.26min) the temperature increased from 36.8 ◦Cto 52.0 ◦C. This means that the heat energy of the oven increased at a rate of 1.6 kW.For the time interval (e,f) we find instead an increase of heat energy at a rate of 1.3 kW,due to the higher temperatures and the correspondingly higher heat loss. The meantemperature in the interval (a,b) is 44.4 ◦C and in the interval (e,f) it was 69.6 ◦C. Theambient temperature was about 15 ◦C. The temperature difference between oven andenvironment was therefore larger for the measurement (e,f) by a factor of 2.4 comparedto the measurement (b,c). Assuming that the heat loss to the environment increasedFig. 11. – Left: mirror array of 20 elements with oven. Right: view of the oven with the waterboiling (taken from behind the mirrors). The white paper fixed below the oven serves for readingthe signal from the gauge mirror needed for regulating the system.THE LINEAR MIRROR FOR SOLAR ENERGY EXPLOITATION 565Fig. 12. – Temperature of the water (in degree Celsius) as function of time.with ΔT at least linearly, we conclude that in the interval (a,b) the heat loss was atleast 0.2 kW (while it was 0.5 kW at (e,f)). That means that the oven absorbed between1.6 kW and 1.8 kW of heat power during the experiment from the mirrors.Since the 20 mirrors (of 40 cm · 40 cm each) have a total area exposed to the Sun of3.2m2, a total power of 1.8 kW corresponds to a power of 0.56 kW for each m2 of mirrorsurface. Given that the experiment was performed in mid November, this value is atleast satisfying, since it corresponds about to the primary radiation density at the Earthsurface at this time of the year.About one hour after having reached 100 ◦C the water had evaporated and thetemperature in the oven increased continuously up to 200 ◦C.These numbers indicate that the completed device with 50 mirrors should be ableto make 1 litre of water boil within about 1 minute and it should be able to reachtemperatures well above of 300 ◦C—sufficient for operating a heat engine.4. – ConclusionsWe have presented in this paper a very simple system of mirrors, which are operatedby only two motors, and which are able to project Sun rays onto a common focal areawith a precision of about 1◦ during most of the day [6]. Such a system should bevery easy to build and should therefore be very cheap. We estimate that a cost ofabout 200 euro/m2 should be achievable. This focusing system has been patented (patentno. PCT/EP2008/002661). A small size prototype has been tested providing a power of0.56 kW per m2 of mirror surface in mid November.In the focal area one can heat air, water, vapour or similar media, and dependingon the specifications of the system temperatures up to several hundred degrees Celsiusshould be easily obtained. This allows providing high temperature steam for electricityproduction and heat of easy practical use. Due to the high temperatures to be achieved,the heat would not only be well suited for heating buildings directly, but would also berelatively easy to be stored or to be used in industrial processes like air conditioning orbio-ethanol production.Finally, we note that we presented only a very first step into a new technology, whichpresumably leaves much room for further future improvements. Due to its low cost,its versatility and the possibility to store the produced energy, the system would allowsignificant savings of oil and coal. The system should be of major interest in regions566 A. PREST and H. GRASSMANNclose to the equator, but it should be competitive also in more northern (or southern)Countries like Germany or Canada.∗ ∗ ∗We thank G. Bellettini for many interesting discussions and for having encouragedus to proceed in this new and challenging field. His comments have improved the qualityof this paper. We also thank R. Fritsche for his input and advice.REFERENCES[1] Solar water heating technical bulletin, Vol. 3, http://www.sunearthinc.com/Evacuated%20Tubes%20v.%20Flat%20Plate%20Collectors.pdf.[2] Photovoltaic industry statistics, http://www.solarbuzz.com/StatsCosts.htm.[3] http://en.wikipedia.org/wiki/Solar thermal collector.[4] Trieb F., Langniß O. and Klaiß H., Solar Energy, 59 (1997) 89, Elsevier Science Ltd,doi:10.1016/S0038-092X(97)80946-2, Retrieved on 2007-03-30.[5] Overview of solar thermal technologies, http://www.hcs.harvard.edu/~hejc/papers/Solar Jan07/solar thermal overview.pdf, pg. 3.[6] http://www.isomorph.it/solutions/renewable-energies/solar-thermal.

The linear mirror for solar energy exploitation

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The linear mirror for solar energy exploitation

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