Solar Cells in Concentrating Systems and Their High temperature Limitations

Transcription

1 Solar Cells in Concentrating Systems and heir High temperature Limitations A hesis Submitted in Partial Satisfaction of the Requirements for the Degree of Bachelor of Sciences in Physics at the University of California, Santa Cruz by arn A. Yates September 3, 003 Ali Shakouri Clemens Heusch echnical Advisor Supervisor of hesis, David Dorfan Chair, Department of Physics

2 able of Contents Abstract 1 Introduction heory i. he p-n junction. 6 ii. he p-n junction under an applied bias. 7 iii. Solar cell principles. 9 Summary of Related Papers i. hermally Affected Parameters of the Current-Voltage Characteristics of Silicon Photocell. E. Radziemska, E. Klugmann 13 ii. he Effect of emperature on the Power Drop in Crystalline Silicon Solar Cells. 0 iii. emperature Dependence of the Spectral and Efficiency Behavior of Si Solar Cell Under Low Concentrated Solar Radiation. M. A. Mosalam Shaltout et al. 3 Derivation of Power Conversion Formula 7 Verification of Power Conversion Formula 34 Experiment 36 i. Apparatus. 36 ii. Data Collection. 37 iii. Data. 37 iv. Data Analysis. 39 v. Conclusions. 4 Conclusion 44 References 46 Acknowledgements 47

3 3 Abstract A mathematical model of power conversion vs. illumination for a solar cell is presented. Heating of the solar cell under illumination and temperature dependent properties are taken into account. his model is designed for use in the construction of solar concentrating devices and takes into account reflection losses, efficiency, loss of efficiency due to heat, and thermal resistance of the cell. Experimental results on the thermal resistance of a cell are also presented.

4 4 Introduction Current means of energy production all have environmental drawbacks. hese drawbacks include the damming of rivers, the creation of nuclear waste, and the pollution associated with fossil fuels. Compounded with these problems is the dependence on other nations for oil that can lead to global conflict, and the fact that the supply of fossil fuels is quickly being depleted. It is apparent that an alternative source of energy must be developed. A potential solution to this problem can be found in the production of solar electricity. It has been calculated that approximately one kilowatt per square meter falls on the earth during the day [1]. Putting this energy to use would diminish the demands put on the environment and reduce the reliance on other sources of energy. Photovoltaic technology was developed in 1954 [], but it has not caught on as a widely used source for the production of electricity. his is because the cost of solar panels compared to the amount of power they produce makes their purchase uneconomical for most buyers. Significant gains have been made in the cost per watt ratio since the 1970 s reducing the price from $70 per Watt to under $4 per Watt today []. However, this ratio needs to be reduced further before photovoltaic technology becomes a viable resource. At present, there are two types of photovoltaic cells that dominate the market. he most widely used are silicon cells, which constitute 86% of the current market [4]. Single crystalline cell technology is well developed because it uses the same manufacturing techniques that are used in the electronics semiconductor industry. In this process, a single silicon crystal is grown and then sliced into wafers. his produces identical cells

5 5 that are up to 15 percent efficient []. However, the process is very time consuming and expensive. A less expensive technique is the production of polycrystalline silicon cells. In this process molten silicon is poured into molds and allowed to cool, then sliced into wafers similar to those in the single crystal method. Many small silicon crystals are formed in the mold instead of one large one as in the single crystalline cell. his results in the efficiency of the polycrystalline cell being lower, between 11 and 14 percent []. hin film semiconductors make up the remaining 14% of the PV market [3]. In this process, a thin film of semiconductor material, most often amorphous silicon, is deposited on an inexpensive substrate such as glass. his is a fast process and uses much less material because the silicon layer is only one micron thick []. hin film has no crystalline structure, which results in efficiencies of only six to seven percent. he low cost of production makes up for the poor efficiency, and thin films may be the future of the photovoltaic market. More efficient cells have been developed, but due to their high price, they are used mainly in research or in space. he most promising high-efficiency cell is the multijunction cell. Multi-junction cells are several layers of photovoltaic cells stacked on top of one another. Each successive layer has a lower band gap energy, allowing for the absorption of a wider range of the spectrum. Boeing holds the current record for the efficiency of a multi-junction cell at 34. percent [4]. his is more than twice the efficiency of cells currently on the market, and efforts are being made to increase the efficiency up to 40 percent [4]. It would not be practical to build a solar panel out of multi-junction cells because they are so expensive. However, a solar concentrating system utilizing multi-junction cells could be cost effective.

6 6 Solar concentrators have been in use since as early as 1 BC, when it was reported that Archimedes used mirrors to concentrate sunlight onto invading Roman ships, setting them on fire [5]. Whether or not this is true, it is evident that the principles behind solar concentration have been known for some time. Concentrators make it possible to focus solar radiation falling on a large area onto a very small area. his increases the intensity of the sunlight, leading to greater power falling on the area of focus. he solar intensity or concentration ratio, denoted by the letter C, is determined by the ratio of the area of incident sunlight to the area that it is focused on [6]. Concentration ratios in the thousands have been achieved [5]. he use of concentrators creates the potential for the production of less expensive solar panels using high efficiency mono-crystalline or multi-junction cells. In general the materials used to build concentrators are less expensive than photovoltaic cells. he concentrator takes up most of the area of a concentrator system, and only a small amount of photovoltaic material is needed. Concentrator panels could reduce the cost per watt ratio to the point where solar power is an economical alternative. At present there are many different types of concentrators that could be used in a photovoltaic system. hese concentrators can be divided into two different groups: reflecting concentrators and lenses. In the former group the most common concentrators are flat plate mirrors, spherical and parabolic mirrors, and cylindrical trough collectors. he most prominent lens is the Fresnel lens. It was developed in 18 for use in lighthouses and can achieve high concentration ratios [7]. ewer lenses such as Aspheric lenses and IR (ransmission, total Internal reflection, Refraction) lenses can be used together to achieve concentration ratios of over 300 while being only cm thick [8].

7 7 he use of concentrators is not free of problems. Most concentrators rely on being directly focused on the sun; any deviation causes a severe drop in the concentration ratio. Some of the collected power must be used to run a tracking system. Also, though it seems that the power converted by a solar cell would increase indefinitely with increasing illumination, that is not the case. As the intensity of illumination increases, the solar cell heats up. It is a well-documented fact that the efficiency of solar cells decreases as the temperature of the cell increases. he loss in efficiency is about 10% for every 5 K increase in temperature [9], although the exact loss in efficiency depends on the specific cell. his paper concerns the presentation of a mathematical model of power conversion vs. illumination. he model takes into account the thermal resistance, efficiency, and loss of efficiency due to an increase in temperature of the cell. It also considers reflection losses. his model could be useful in the designing of solar concentrator systems. It shows that there is a maximum power conversion point beyond which any increase in illumination causes a decrease in converted power. he model also reveals the importance of using cells with low thermal resistance in concentrator systems. Basic solar cell theory will be reviewed, including a discussion of p-n junctions, a derivation of the diode current, and the production of electron-hole pairs leading to the photocurrent. his is followed by a summary of papers related to temperature effects on solar cells. he results of an experiment to test the thermal resistance of a solar cell are presented in the final section.

8 8 heory he p-n Junction In order to understand how a solar cell works, it is necessary to understand p-n junctions. A p-n junction is formed when an n-type semiconductor is put together with a p-type semiconductor. See Figure 1 he n-type semiconductor is doped with donor atoms that have more electrons than the surrounding material, and the p-type semiconductor is doped with acceptor atoms that have fewer electrons than the surrounding material. Atoms in the p-type semiconductor with fewer electrons than the surrounding material are said to have holes. hese holes are thought of as positive entities much like electrons in that they can move throughout the material and contribute to the current. When a hole and an electron meet, they essentially annihilate each other; this is called recombination. Figure 1: p-n Junction (electrons are depicted as filled circles, holes are depicted as empty circles, negatively charged donor atoms in the p-side and positively charged acceptor atoms in the n-side are also shown.) Putting an n-type semiconductor together with a p-type semiconductor creates an electron/hole concentration gradient. his concentration gradient causes a diffusion current with electrons diffusing to the p-side and holes diffusing to the n-side. he area in

9 9 which this diffusion takes place is called the depletion region. When electrons from the n- side diffuse to the p-side they meet with holes and recombine leaving negatively charged donor atoms on the p-side. he holes from the p-side diffusing to the n-side create positively charged donors on the n-side. he ionized donors create an internal electric field in the depletion region [10], [11]. See Figure. he Electric field in the region works as a barrier preventing more electrons from diffusing from the n-side to the p-side. Only those electrons with a high enough energy to overcome the field can make the transition. In equilibrium there is no net current so the diffusion current and the drift current (due to the internal electric field) cancel each other. Figure : Creation of Internal Electric Field he p-n Junction Under an Applied Bias When a potential is applied across a p-n junction, it can either increase or decrease the internal electric field. If the negative side of the potential is connected to the p-side, then the electric field is increased. his is called a reverse bias. Alternately, a forward bias, where the positive side of the potential is connected to the p-side, results in the reduction of the internal field. When the internal field is decreased by a forward bias the number of electrons on the n-side that have enough energy to cross the depletion

10 10 region to the p-side increases by a factor of exp ( ev k ). Here e is the charge of the electron, V the applied voltage, k the Boltzmann coefficient, and absolute temperature. he resulting electron current from the n-side to the p-side is e0 small electron current I e0 I exp ( ev k ) from the p-side to the n-side. his is due to the very few electrons (minority carriers) in the p-side. hus the total electron current is:. here is a ev k ( e ) I e = I e0 1 1 he same relation holds for the hole current from the p-side to the n-side. A forward bias results in a hole current: ev k ( e ) I h = I h0 1 where I h0 is the equilibrium hole current. Putting equations 1 and together gives the total current, also known as the diode current: where ev k 0 I = I + I = I ( e 1) 3 e h I = I e + I h0 I 0 is sometimes called the dark current [1].

11 11 Solar Cell Principles When photons of a high enough energy are incident on a semiconductor, they create an electron-hole pair. his can be understood by looking at the energy band diagram of a semiconductor. Figure 3 shows the three distinct energy bands of electrons in a semiconductor. Valence band states are fully occupied by electrons and the first empty band (conduction band) is separated by a band gap. Electrons in the valence band can not be involved in conduction. his is due to the Pauli exclusion principle, since there are no low lying empty energy states for the electrons in the valence band to move to under and electric field. When electrons acquire a sufficient amount of energy, they can enter the conduction band. When a photon with an energy greater than the band gap is incident on a semiconductor, it gives an electron in the valence band enough energy to move to the conduction band. Both the electron in the conduction band and the hole that has been created in the valence band can be involved in the conduction of a current under an electric field [1]. Figure 3: Band Diagram and Electron-Hole Pair Production A solar cell can be constructed by putting a very thin, heavily doped n-type layer on top of a thicker p-type layer. As can be seen in Figure 4, the depletion region is mostly on the p-side. Light is absorbed through the n-type layer. Because the n layer is so thin,

12 1 most photons penetrate into the depletion region, or the p-side before creating an electron-hole pair. When an electron-hole pair is created in the depletion region the electric field moves the electron into the n-side and the hole into the p-side. his gives the previously neutral n-side a negative charge and the previously neutral p-side a positive charge. When a load is connected to the cell, the electron can travel through the circuit, do work, and recombine with the hole. Figure 4: Electron-Hole Pair Behavior in Solar Cell If the light penetrates into the neutral p-side, then there is no electric field to separate the electron-hole pair. Instead the electron and the hole diffuse at random through the material and recombine if they meet. he average time between pair production and recombination for an electron is τ e. In this time, the electron diffuses a mean distance of L e = D e τ e where e D is the diffusion coefficient in the p-side. If the electron-hole pair is created within L e of the depletion region, then the electron can

13 13 diffuse to the depletion region and be moved by the electric field over to the n-side. For this reason it is important for the diffusion length L e to be as long as possible. he same process takes place for electron-hole pairs created in the n-side. In silicon, the diffusion length is longer for electrons than it is for holes. his is why the thin top region is n-type, and the thicker region is p-type. When an illuminated solar cell is short-circuited, a current flows through the circuit in the opposite direction of the diode current. his current is a result of electronhole production in the solar cell and is called the photocurrent I ph. he photocurrent is directly proportional to the intensity of light. If the cell is in a circuit with some resistance, then there is a voltage across the junction. his voltage acts like a forward bias and results in a diode current through the cell. he total current is then [11]: ev k ( e ) I = I I ph A typical IV curve for a solar cell can be seen in Figure 5. he Fill Factor(ff) of a solar cell is a measure of the quality of the cell. It is defined as: I mppvmpp ff = 6 I V SC OC where I mpp and V mpp are the current and the voltage at the maximum power point on the IV curve, I SC is the short circuit current, and V OC is the open circuit voltage.

14 14 Figure 5: A typical IV curve for a solar cell under illumination. MPP is the maximum power point of the cell. he efficiency of a cell is the ratio of the maximum converted power P C to the input power P I : P C η = 7 P I Converted power is the product of the current and voltage at the maximum power point so equation 7 can be rewritten as [10]: ff I SC OC η = 8 P I V

15 15 Summary of Related Papers Paper 1) hermally Affected Parameters of the Current-Voltage Characteristics of Silicon Photocell (00) E. Radziemska, E. Klugmann Energy Conversion & Management his paper presents a comprehensive explanation of the temperature effects on silicon solar cells. It gives experimental results showing a slight increase in short circuit current with increased temperature and a large decrease in open circuit voltage with increased temperature. Radziemska and Klugmann show that the product I SCVOC degrades by 0.8 % for every 1 K increase in temperature. hey assert that temperature losses account for 7.6 % of PV conversion losses in a working power plant. his paper introduces the following main temperature effects. Series Resistance A solar cell in a circuit with some load resistance can be represented by the equivalent circuit shown in Figure 6. he voltage across the load is: V L = V I r 9 ph L s where I L is the current through the load.

16 16 r s Vph rj RL VL Figure 6: Electrical model of a solar cell. r j is the junction resistance, rs is the series resistance, and resistance. R L is the load When the temperature of the cell increases, it causes an increase in the series resistance r s. his is due to the fact that the mobility of charge carriers, µ, is inversely proportional to the temperature: 3 µ 10 As the temperature rises, there is increased carrier scattering on lattice vibrations (phonons) and impurities. his decrease in mobility causes a decrease in the conductivity and an increase in the series resistance. In the normal operating range of a solar cell, 300 to 380 K, this increase in very small.

17 17 Short Circuit Current An increase in the temperature of a solar cell results in a slight increase in the short circuit current. he short circuit current from a solar cell is the photocurrent. At a given wavelength of light the photocurrent is: I ph ( λ) = e 11 η λ λ where λ is the number of photons at that wavelength, and ηλ is the efficiency of the solar cell at that wavelength, also known as the spectrum response. he power of irradiation is: hc P λ = λ 1 λ Combining this with equation 11 gives: I ph Pλ λ ( λ) = ηλe 13 hc In order to find the total photocurrent equation 13 must be integrated over all wavelengths that are absorbed by the solar cell. A photon must have an energy greater

18 18 than the bandgap of the solar cell in order to contribute to the photocurrent. his introduces a maximum photon wavelength λ 1. he total photocurrent is then: I ph = e hc λ 0 η P λdλ 1 λ λ 14 As the temperature of a solar cell increases, the bandgap approximation, the bandgap follows the equation: Eg decreases. o a linear E g deg ( ) = Eg (300K) + ( 300K) 15 d For silicon 4 de g d =.3 10 ev/k. his decrease in the bandgap allows photons with longer wavelengths, lower energy, to be absorbed by the solar cell. For example, an increase in temperature of 80 K raises the limiting wavelength by 19 nm. As a result, the short circuit current of the cell is increased. his is offset by the fact that increasing temperature decreases the built in voltage of a p-n junction. he built in voltage for a p-n junction is: k D V 0 = ln 16 e A ni

19 19 where A and D are the number of acceptor and donor atoms respectively that the junction has been doped with, and n i is the intrinsic carrier concentration of the junction. In silicon, n i follows the equation: 3 16 η = exp( E k) 17 i go In a silicon cell where A 16 = 10 3 cm and D 15 = 10 3 cm, an increase in temperature from 300 to 380 K causes the built in voltage to decrease from 0.66 V to 0.35 V. his decrease in the built in voltage allows thermally agitated charge carries to cross over the p-n junction in both directions. he voltage is also much less effective at separating electron-hole pairs. Due to these two factors, there is less build-up of excess charge, negative on the n-side, positive on the p-side, and the short circuit current is decreased. Open Circuit Voltage An increase in temperature reduces the open circuit voltage. As the bandgap decreases with increasing temperature, more electrons are able to move into the conduction band. he extra electrons in the conduction band and the holes in the valence band lead to an increase in the dark current. It is simple to show that an increase in the dark current results in a decrease in the open circuit voltage. he output current of a solar cell is: I = I ph ev k ( e ) I 0 1

20 0 Under open circuit conditions, the output current is zero, so the photocurrent and diode current must be equal: ev k ( e ) I = I ph his can be rearranged to give: V kt I ph = V = ln + 1 e I 0 OC 19 As can be seen from equation 19, an increase in dark current with increasing temperature leads to a lower open circuit voltage. Dark current is related to the temperature by this proportionality: E g I 0 exp 0 k Experimental Results hese theories were tested on a Siemens type 5, photovoltaic cell. he cell was placed on a thick copper plate to control the temperature and illuminated with a solar simulating halogen lamp. Data was taken on the open circuit voltage and short circuit

21 1 current at various temperatures. Figures 7 and 8 are the graphs that resulted from this research. From these graphs, it was found that the open circuit voltage decreased by 0.38 K, and the short circuit current increased by % K 1. he paper reported that % 1 the product I decreased by 0.8% K 1 [13]. SCVOC Figure 7: emperature dependence of the open circuit voltage for the Siemens Solar cell. Figure 8: Short circuit current vs. temperature of the Siemens solar cell.

22 Paper ) he Effect of emperature on the Power Drop in Crystalline Silicon Solar Cells (003) E. Radziemska Renewable Energy his paper presents data showing a decrease in maximum output power of a silicon solar cell of 0.65% K 1, a decrease in maximum output power of a silicon solar module of 0.66% K 1, and a decrease in module efficiency of 0.08% K 1. Experimental Results Data was recorded from a single-crystalline silicon solar cell illuminated by a halogen lamp. A thick copper plate, which was heated by an electric heater, was used as a base for the cell to ensure a stable temperature. Four MOSFEs were used to monitor the temperature of the cell. Data was also taken from an ASE-100DGL-SM solar module illuminated by the sun. A water cooling system was used on the module, and the temperature was measured using a copper-constantan thermocouple. Figure 9 is a graph of the output power vs. voltage for the single-crystalline silicon cell at different temperatures. A dramatic drop in maximum output power can be seen with each increase in temperature. Figure 10 is a graph showing how the maximum power degraded with temperature. It was determined from the graph that the maximum power decreased by 0.65% K 1.

23 3 Figure 9: Output power vs. voltage of a single-crystalline silicon solar cell at various temperatures. Figure 10: emperature dependence of the maximum output power. Graphs of both the current vs. voltage and power vs. voltage for the solar module at different temperatures can be seen in Figures 11 and 1. It is apparent that the module suffers from the same loss of output power with increased temperature that the cells do. Parameters collected from the data presented in Figures 11 and 1 can be found in able 1. hese numbers can be used to show that the

24 4 maximum power output drops by 0.66% K 1 and that the efficiency decreases by 0.08% K 1. Figure 11: Current vs. voltage and output power vs. voltage of the solar module at 5 C. Figure 1: Current vs. voltage and output power vs. voltage of the solar module at 60 C.

25 5 U OC (V ) I ph (A) P m (W ) FF η (%) = 5 C = 60 C able 1 Radziemska suggests that the temperature of the module could be lowered by decreasing the heat produced by: -non-active absorption of photons, which do not generate pairs, -recombination of electron-hole pairs, -photocurrent (Joule s heat generated during the current flow in the series resistance of the p-n junction) and parasitic currents [14]. Paper 3) he emperature Dependence of the Spectral and Efficiency Behavior of Si Solar Cell Under Low Concentrated Solar Radiation (000) M.A. Mosalam Shaltout, M.M. El-icklawy, A.F. Hassan, U.A. Rahoma, M. Sabry Renewable Energy his paper presents data on the behavior of solar cell efficiency and maximum power output at different temperatures under various levels of illumination. Data was taken at light concentrations between 1 and 5 suns. hese concentrations were chosen to mimic low cost static concentrators, such as parabolic and v-trough concentrators. he

26 6 authors believe these concentrators to be very promising due to the fact that they do not need tracking systems and can be used with low cost, one-sun solar cells. Experimental Results he data was taken on a monocrystalline solar cell illuminated by a variable intensity halogen lamp. Cell temperature was controlled by a large serpentine of brass that was cooled by a water circulator. he following graphs (Figures 13 and 14) show how the maximum power of the cell varied with temperature and illumination. It is interesting to note in Figure 13 that at higher illuminations, the temperature had a much larger influence on the maximum power than at lower illuminations. Also, that at 90 C there is only an 8 % difference between the maximum power at 4010W / m and at 81 W / m. In Figure 14, when the cell is at 85 C, a large increase in the illumination causes a relatively small increase in the maximum power. Figure 15 is a graph of the cell efficiency vs. back cell temperatures. It shows that an increase in temperature always leads to a decrease in cell efficiency. he change in cell efficiency with temperature is more dramatic as the illumination level goes up. Mosalam Shaltout et al. all concluded that one-sun solar cells could be used in solar concentrating devices with low concentration ratios. Beyond a certain temperature, there is no use for increased illumination. hey believe that the optimum concentration ratio for one-sun solar cells is around 4 times or 3000 W/m [15].

27 7 Figure 13: Decrease of cell maximum power with temperature at different illuminations. Figure 14: Maximum power variation of the cell with illumination at three cell temperatures.

28 8 Figure 15: Efficiency behavior of the cell with temperature at five illuminations.

29 9 Derivation of Power Conversion Formula he following model was created for this paper, in an attempt to understand the effects that increased temperature has on concentrating systems. he increase in a cell s temperature under illumination is a function of the thermal resistance of the cell R and the amount of power that is involved in heating the cell P H. he relation is: = P R 1 H where is the change in temperature. here are three factors that govern the amount of power that is involved in heating the cell. hese factors are the power incident on the cell P I, the percentage of light that is reflected off the surface of the cell α, and the efficiency of the cell η E. he power transmitted past the surface coating of the cell is: P P ( 1 α) = I where P is the transmitted power. his is the power that can be converted into electricity by the cell. It is also the power that goes into heating the cell. ransmitted power that is not converted into electricity is absorbed as heat. he equation governing this relation is: P H P ( E = 1 η ) 3

30 30 his relation shows that the higher the efficiency of the cell is, the less power there will be to heat the cell. Putting equations and 3 together gives: P H P I ( E = 1 α)(1 η ) 4 Combining this expression with the relation for the increase in temperature results in: = P R I ( 1 α )(1 η E ) 5 With this known, it is then possible to determine how the efficiency of the cell changes with illumination. Solar cell efficiency follows the equation: η = η η µ 6 E where η E is defined more precisely as the efficiency of the cell under increased illumination, η is the efficiency of the cell under normal illumination (one sun) at a given temperature, and µ is the percentage decrease in efficiency with increased temperature. his relation is made more complex by the fact that is itself a function of the efficiency. Plugging equation 5 into equation 6 gives: η E = η η µ P R I 1 α)(1 η ) ( E Pulling η out in front and multiplying out results in:

31 31 η E [ 1 µ R ( 1 α ) P + η µ R ( α ) P ] = η 1 I E I his can be rearranged and solved for η E : η E 1 µ R (1 α) P 1 µ R (1 α) PI η I = 7 Once this has been found, it is then possible to create a relation for the power converted based on a given illumination. As mentioned above, the power available to the cell to convert into electricity is P. Multiplying this by the efficiency gives the converted power: P C = ηe P = ηe PI ( 1 α) or P C P (1 α)[1 µ R (1 α) P ] 1 µ R (1 α) PI η I I = 8 where P C is the converted power. A graph of this function using standard values for α µ R,,, and η can be seen in Figure 16. he intercepts are at P I = 0 and 1 P I =. µ R (1 α)

32 3 Figure 16 illustrates how the increasing temperature of the solar cell effects the converted power. Up to a certain point, an increase in illumination causes an increase in converted power. However, there is a point at which the efficiency becomes so poor, due to the rise in temperature, that any increase in illumination causes a decrease in converted power. he point at which this occurs represents the maximum power that a cell can convert. P C ( w / cm ) Figure 16: Power Converted vs. Power Incident P I ( w / cm ) ( α. 06, η =.1, µ =.004, R = cm K / w = )

33 33 Finding the Maximum Power Conversion Point he maximum power point P mpc can be found by taking the derivative of equation 8 with respect to incident power, setting it equal to zero, and solving for P I. his yields a quadratic, which, when solved gives two answers for the maximum power point: P mpc [ 1± ( 1 η ) ] 1 1 = 9 η µ R (1 α) his equation can be simplified by using the expansion ( 1 η ) 1 η η... Plugging the expansion into equation 9 gives: P mpc η 1 µ R 1 1 ( ) 1 ± 1 η η 1 α 8 30 he answer in which the addition sign is used shows the maximum power point to the right of the positive intercept. his answer is non-realistic. he correct answer is the one in which the minus sign is used: P mpc η... µ R ( 1 α ) 8 31

34 34 It can be seen that the ratio of the maximum power point to the positive intercept is just slightly greater than one half. Varying Efficiency and hermal Resistance It is interesting to look at the effect that a change in either the efficiency or the thermal resistance has on the converted power. his is illustrated in Figure 17. Curve 1 is a graph of equation 8 using the same values as in Figure 16. Curve was created by doubling the efficiency used to create Curve 1 and holding everything else constant. Curve 3 was created by reducing the thermal resistance used in Curve 1 by one half and again keeping everything else constant. As would be expected an increase in efficiency greatly increases the power converted at a given illumination. More interesting is the fact that a decrease in thermal resistance can also cause a large gain in power at increased illuminations. And, if working with very high levels of illumination, decreasing the thermal resistance is more important than increasing the efficiency of the cell. hese results could be very useful in constructing a solar concentrating panel.

35 35 P C ( w / cm ) P I ( w / cm ) Figure 17: Change in P curve by varying C η and R. For Curve 1 the parameters used were: α. 06, η =.1, µ =.004, R = 1.95 cm K / w. For Curve all the parameters remained = constant except for the efficiency, which doubled to η =. 4. Curve 3 was produced using the same parameters as Curve1 except that the thermal resistance was cut in half to R =. 975.

36 36 Verification of Power Conversion Formula he power conversion vs. illumination model can be verified using data from a working concentrator system. he following data was taken from a parabolic dish concentrator that is part of a power plant at White Cliffs, Australia. Light from the dish was focused on the receiver at a concentration of about 340 times. he receiver consisted of 384 series-connected HEDA31 silicon solar cells from SunPower Corporation. A water cooling system was used to keep the receiver from overheating. Pictures of the concentrating dish and the receiver can be seen in Figures 18 and 19. Figure 18: Parabolic concentrator power plant.

37 37 Figure 19: he receiver consisting of 384 series connected cells. Power Incident on Receiver Module Efficiency emperature Coefficient P 5.6W / cm I η 6.5 % µ K Reflection α % hermal Resistance R cm K / W Area of Receiver A 576 cm able : Data from parabolic concentrator at White Cliffs. Plugging these numbers into equation 8 predicts that the receiver should convert 33.5 watts. his is very close to the recorded value for converted power of 3448 watts [16]. It is a difference of 6.5 %.

38 38 Experiment At this point, with the resources available, it is not possible to do a test of the power conversion equation (equation 8) presented in the previous section. Instead the following experiment was run in order to test the thermal resistance of a small solar panel. his experiment was conducted because manipulation of the power conversion equation pointed out the importance of the thermal resistance. Measurements of the panels fill factor and efficiency are also presented. Apparatus he solar panel used in this experiment was a Radio Shack Sola 6 volt, 50 ma panel. It consisted of twelve 0.5 volt silicon cells wired in series. he cells were housed in a black plastic container with a clear plastic anti-reflection cover. Positive and negative wires protruded from one end of the panel. he wires were connected to a 0-1 k Ω variable resistor. A brass plate was used as a base for the solar panel. here were ype E, Omega Engineering, IC. thermocouples mounted on the inside bottom of the solar panel and on the brass plate. he two Constantan ends of the thermocouples were soldered together so that the thermocouples measured the temperature difference between the solar panel and the brass plate. GB Instruments GD-11 multimeters were used to measure the value of the resistance, the voltage across the resistor, the current through the resistor, and the voltage difference between the two ends of the thermocouples. A sun meter was

39 39 used to measure the intensity of the incident sunlight. Also used were a Jameco solderless breadboard, a screwdriver, thermal grease, and black plumbers tape. Data Collection Data collection began by setting the solar panel mounted on the brass plate and the light meter out in the sun. o data was recorded until the temperature difference between the solar panel and the plate was stable. When the temperature was stable, the intensity of the sunlight was measured, and the open circuit voltage and short circuit current of the solar panel was recorded. he panel was then connected to the variable resistor, which was set at a low resistance. Multimeters were connected in both parallel and series with the resistor to measure the voltage drop and the current. he resistance was then increased in small increments with measurements of the current and voltage taken at each increment. At each resistance the intensity of the light was recorded to ensure that it not vary too drastically. Data L (kfc) V (mv ) R (Ω) (ma) hermocouple I I σ Volts σ V

40 able 3 In this table L is the intensity of the light; the unit of measurement is footcandles. he error in the intensity is σ L = kfc. V hermocoup le is the voltage generated by the thermocouple due to the temperature difference between the solar panel and the

41 41 brass plate. here was an error in the temperature data of σ = mv. he area of the B solar panel is: ± m Data Analysis In order to find the fill factor, efficiency, and thermal resistance of the panel, the data for the intensity of the light had to be converted into incident power in watts, and the amount of power incident on the panel had to be calculated. Also the power delivered to the resistor had to be found. he conversion for foot-candles is: 1 fc = watts m the voltage. hese values can be found in able 4.. Converted power is simply the product of the current and P ( watts / m ) (watts) P I PI σ (watts) P C σ PC

42 he error on P is.81 able 4 and P C was the power that the solar panel converted. watts / m. P I was the power incident on the solar panel, In order to find the fill factor and the efficiency, it is necessary to know the voltage and the current at the maximum power point. he maximum power point can be found by plotting the converted power vs. the voltage. See Figure 0. From this graph, the voltage at the maximum power point can found. he current at the maximum power point can then be found from a graph of the current vs. voltage. See Figure 1. he current at the maximum power point is I = ± ma, and the voltage is mpp V = 3.41 ± V. Using these numbers, the short circuit current, the open circuit mpp voltage, and equation 6 gives a fill factor of ff = ± he efficiency can then

43 43 be found using equation 8, the fill factor, and the incident power at the maximum power point PI = 9.40 watts. his yields an efficiency of η = ± he thermal resistance of the panel can be found using equation 1. A ype E thermocouple table shows that a -0.9mV voltage difference corresponds to a he error on is as large as 0.5 K. his gives a thermal resistance of of 1 K ± m K / W or 6.59 ± cm K / W. Figure 0: power vs. voltage

44 44 Figure 1: current vs. voltage Conclusions he value calculated for the fill factor of is very low compared to expected results of Also, the efficiency of the panel 1.49 % is very low. A typical amorphous silicon solar cell has an efficiency between 6 % and 9%. he low efficiency of this panel is a result of the fact that only about half of the area of the panel is covered in solar cells. his automatically cuts the efficiency of the cell in half. Another factor leading to the low efficiency is the reflection of incident light off the plastic cover.

45 45 he experiment to calculate the thermal resistance was very rough, and more precise equipment would be needed in order to get an accurate result. he largest inaccuracy involved the measuring of the temperature with the thermocouples. he multimeter used to measure the voltage difference only made measurements down to a tenth of a millivolt, this made the use multimeters capable of measuring microvolts. data very vague. Subsequent experiments should he data for the incident power was also inexact. his is because no estimation was made of how much light the clear plastic cover reflected. It is reasonable to include the loss of power due to reflection in the measurement of the efficiency of a panel so that value should not have been affected. However, the thermal resistance value is lower than it would be if light reflection had been taken into consideration. Experiments should be run on a wide range of solar cell packages to test their thermal resistance. In these experiments, it should be possible to estimate reflection losses by placing the solar panel s plastic cover over the light meter. Also, various heat sinks should be used to see if there is any effect on the thermal resistance.

46 46 Conclusion Concentrating systems could make solar technology an economical source of energy production. A concentrating system utilizes less photovoltaic material and is therefore less expensive to produce than a conventional solar panel. However, concentrating systems suffer from a loss of power due to the effect that increased temperature has on a solar cell. As the temperature of a solar cell increases the open circuit voltage, efficiency, and output power of the cell decrease. With this in mind, a mathematical model of power conversion vs. illumination has been created. his model shows that beyond a certain illumination, the power converted by a cell decreases. he model can be used to calculate the illumination at which a maximum level of power is converted. Manipulation of the power conversion model shows that the thermal resistance of a cell can greatly affect the amount of power a cell converts at increased levels of illumination. Great attention should be paid to decreasing the thermal resistance of solar cells used in concentrating systems. As a result of these findings, an experiment has been carried out to determine the thermal resistance of a typical solar panel. he experiment suffered from a lack of appropriate equipment; however, a rough measurement of the thermal resistance was made. he cell s thermal resistance, along with a measured value for the efficiency of the cell, and some typical values for efficiency loss with increased temperature, and reflection losses can be plugged into the power conversion model. See Figure. he model predicts that a Radio Shack Sola 6 volt, 50 ma panel will produce a maximum power of 0.14 w / cm at an illumination of 0.5 w / cm.

47 47 P C ( w / cm ) P I ( w / cm ) Figure : Power conversion curve for a Radio Shack Sola 6 volt, 50 ma panel. ( α. 06, η =.0149, µ =.004, R = cm K / w ) = Future research should focus on a confirmation of the power conversion model using solar simulators capable of producing the adequate concentration ratios. If verified, the presented model would allow an optimal match to be made between concentrating system and solar cells. his would ensure the most efficient use of the available material, and bring solar technology closer to being an economical source of energy production.

48 48 References 1. Welford, W. Winston, R. (1998) he Optics of onimaging Concentrators. (Academic Press, ew York). Perihelion (00) (Solar Electric Light Fund) 4. Hettelsater, D. (00) Photovoltaic echnology Overview. University of California, Santa Cruz. 5. Hathwar, M. (001) Photovoltaic echnology Cheremisinoff, P. Regino,. (1978) Principles and Applications of Solar Energy. (Ann Arbor Science Publishers, Inc., Ann Arbor, Michigan) 7. Hsieh, J. (1986) Solar Energy Engineering. (Prentice-Hall, Inc., Englewood Cliffs, ew Jersey) 8. Anicin, B.A. Babovic, V.M. Davidovic, D.M. (1989) Fresnel Lenses. American Journal of Physics 57. 4, Mulligan, W. erao, A. Daroczi, S. Chao Pujol, O. Cudzinovic, M. A Flat-Plate Concentrator: Micro-Concentrator Design Overview. (SunPower Corporation, Sunnyvale, California) 10. Radziemska, E. Kleugmann, E. (00) hermally Affected Parameters of the Current-Voltage Characteristics of Silicon Photocell. Energy Conversion and Management Hettelsater, D. (00) Solar Cell Lab. University of California, Santa Cruz 1. Kasap, S.O. (00) Principles of Electrical Engineering Materials and Devices, Second Edition (Mc Graw Hill) 13. Hook, J.R., Hall, H.E. (000) Solid State Physics, Second Edditon. (John Wiley & Sons) 14. Radziemska, E. (003) he Effect of emperature on the Power Drop in Crystalline Silicon Solar Cells. Renewable Energy Mosolam Shaltout, M.A., El-icklawy, M.M., Hassan, A.F., Rahoma, U.A., Sabry, M. (000) he emperature Dependence of the Spectral and Efficiency Behavior of Si Solar Cell Under Low Concentrated Solar Radiation. Renewable Energy Verlinden, P.J., erao, A., Smith, D.D., McIntosh, K., Swanson, R.M., Ganakas, G., Lasich, J.B. Will We Have a 0%-Efficient (PC) Photovoltaic System? (SunPower Corporation, Sunnyvale, CA)

49 49 Acknowledgements I am deeply grateful to professor Ali Shakouri for his guidance and patience with me throughout the duration of this project. His continued faith in me, as I struggled to complete this project, was extremely helpful. he direction and assistance of Clemens Heusch was also very valuable. Finally, I must thank my mother, who simply would not allow her son to wallow on in procrastination. Her help and motivation are the reason this project was completed.