Electrical loses in a photovoltaic system caused by the dispersion of electrical parameters have been

Transcription

1 PROGRESS IN PHOTOVOLTAICS: RESEARCH AND APPLICATIONS Prog. Photovolt: Res. Appl. 2005; 13: Published online 10 March 2005 in Wiley InterScience ( DOI: /pip.582 Applications Losses Caused by Dispersion of Optical Parameters and Misalignments in PV Concentrators I. Antón*,y and G. Sala Instituto de Energía Solar UPM, ETSI Telecomunicación. Ciudad Universitaria s/n, Madrid, Spain One factor greatly affecting the output power of a photovoltaic concentrator system and not found in conventional flat systems is optical mismatch, caused mainly by dispersion in the efficiencies of the optics and misalignments among collectors and modules. In these systems, there are many factors, besides the electrical performance of the PV modules, acting on the overall efficiency and thus on the power output: reflectivity and shape of the optics, cleanliness, misalignments, etc. They are less known than equivalent topics in flat arrays and usually the data come from medium-sized prototypes. Now we have the opportunity to study such factors on a big plant where components and the installation have been carried out by industry on a final user site. An analysis of the optical mismatch based on Gaussian distributions of the generated photocurrents will be presented in order to evaluate the power losses. A mathematical model is also proposed to calculate the main moments of the distribution from the experimental V I curve under concentrated light. Besides, a novel study of the transmission curves of a photovoltaic concentrator has been carried out and will be described throughout the paper. The series/parallel connection of the modules can affect the transmission curve in different ways, depending on the array voltage, and thus this effect must be considered for the definition of the acceptance angle of the system. Copyright # 2005 John Wiley & Sons, Ltd. key words: photovoltaic concentrator; mismatch; acceptance angle; transmission curve INTRODUCTION Electrical loses in a photovoltaic system caused by the dispersion of electrical parameters have been widely studied and reported on in literature. 1 5 In general, this type of loss is due to the series/parallel connection of devices whose electrical characteristics are not exactly the same. In the case of concentration systems there may also be dispersion in the light received by the photovoltaic receptors. 6,7 The origin is * Correspondence to: Dr I. Antón, Instituto de Energía Solar UPM, ETSI Telecomunicación. Ciudad Universitaria s/n, Madrid, Spain. y nacho@ies-def.upm.es Contract/grant sponsor: European Commission; contract/grant number: ENK5-CT Received 11 May 2004 Copyright # 2005 John Wiley & Sons, Ltd. Revised 22 July 2004

2 342 I. ANTÓN AND G. SALA in the optical systems and the tracking process, and may give rise to much more significant power losses than those found in conventional systems. One of the most surprising effects of a concentration system is what is known as the misalignment effect. Fixing alignment errors of the optics and displacements due to weight and wind cause an apparent widening of the system s transmission curve, which is defined as the generated photocurrent of the array versus the angle of deviation from the perfect pointing position. This widening is only apparent and has no effect on a greater acceptance of the system. Indeed the reverse is true. It could give rise to significant power losses, depending on the angular acceptance of the system, of the magnitude of the aforementioned misalignments and the precision of the aiming system. These effects have not been widely studied in the past, to a large extent due to the limited experience of large concentration systems. Experience from the EUCLIDES-THERMIE plant in Tenerife, the largest concentration plant in Europe, has served to highlight this. As a result of this experience, new aspects found in the characterisation of this system are studied and described in this article, especially those related to the dispersion of optical parameters. REVISION OF THE EUCLIDES CYLINDRICAL PARABOLIC CONCENTRATOR The EUCLIDES concentrator is a concentration system for silicon cells, based on parabolic troughs, widely accepted in the past in thermal solar systems, but of insufficient quality for photovoltaic applications. The design and manufacture of better quality parabolic mirrors for photovoltaic applications 8 has been one of the main achievements of the EUCLIDES project. The EUCLIDES prototype, 24 m in length, was developed and installed in Madrid in a project subsidised by the JOULE II programme, 9 providing successful results. 10 After that, a 480 kw plant was installed in Tenerife, of a size capable of providing indication of the real cost of the technology, difficulties in carrying out real projects and the viability of the subsystems The EUCLIDES installation in Tenerife has been subsidised within the framework of the European JOULE-THERMIE programme, and in its day it was the largest photovoltaic concentration installation. The size of the plant is a trade-off between the funds available and a minimum volume for an industrial project which would allow precise data to be obtained in order to identify design and mounting problems, as well as identifying the real costs. The installation consists of 14 EUCLIDES arrays with a nominal power of 480 kw p. The main objective of this project was to transfer an already tested technology to an industrial-scale prototype. The identification of providers and subcontractors for the manufacture of components and tools stand out as significant objectives, as well the evaluation of the system. From the point of view achieving these objectives we can assert that the project was a success, especially if westicktotherealresult obtaining acost 12 of 445 s/w p, which shows that the objective of overall cost of 35 s/w p is possible for annual productions of 10 MW p. The EUCLIDES-THERMIE plant in Tenerife A EUCLIDES array such as those installed in the Tenerife plant (Figure 1) is a 382 photovoltaic concentration system, 84 m in length and with a collection surface of 250 m 2. Two rows of parabolic mirrors, with a total of 140 mirrors per system, are mounted on an iron structure designed to carry out sun tracking around a N S axis. The technology of the mirrors is based on acrylic silvered film laminated on aluminium sheet which is later shaped in a perfect mould and fixed by means of ribs. The photovoltaic receptor modules, manufactured by BP Solar, are located in the focus of the parabolic mirror, making up two parallel lines in the direction of the axis of the array. Each module is made up of 10 buried contact cells 14 series connected and a bypass diode. The cooling of the modules is passive by means of an aluminium heat-sink upon which the module is stuck. The iron structure only has three supports, one in the centre and two at the extremes. 15 The central support consists of a wheel which transforms the linear movement of a sliding bar to a circular one by means of steel cables. The bar is connected to a turning screw which is linked to a motor with gears.

3 LOSSES IN PV CONCENTRATORS 343 Figure 1. Photograph of the EUCLIDES system installed in the Tenerife plant The tracking system combines the open-loop strategy, by means of calculated coordinates, and the closedloop strategy, with an adaptative learning system which uses the output current of the system as optimisation signal Connection to the electrical grid is made by means of a 68 kva inverter, to which two EUCLIDES lines are connected in parallel. In the Tenerife plant, the 138 modules of each array are connected in series to provide an operating voltage of 750 V, as required by the plant owner in order to avoid the need for a transformer at the inverter output. STUDY OF THE DISPERSION THROUGH OPTICAL CAUSES A EUCLIDES array consists, therefore, of 140 mirrors and 138 modules. The structure of the system has been designed for severe conditions for position errors of less than 2 mm over an aperture of 2 m both in manufacture and mounting. 15 The EUCLIDES mirrors have an interesting facility of individual alignment. This allows the mirrors to be adjusted one by one until the focus of the light is focused in the centre of the receiver. This operation is carried out with the array tracking the sun. Given that the rigidity of the structure is very large this adjustment becomes definitive, as the structure does not deform after mounting and installation. Although the visual effect after an adjustment is very encouraging, the V I curves obtained in a an array show a false parallel resistance, which is nothing more than a demonstration of a dispersion in the generated photocurrent of the 138 modules. 18 The modules were classified before their installation, for which the initial dispersion of the photocurrent of the modules belonging to the array itself is around 1%. The remaining dispersion is attributed to the misalignment between each mirror and its receptor and also to the dispersion in the optical efficiency of the mirrors. Effect of the bypass diodes The bypass diodes have two basic functions. The first is to protect the modules from overheating through hotspot effects. 19 The second is to lessen the power losses as a result of the dispersion of generated photocurrents. In the following we will see how the dispersion in the amount of light received by the modules affects the V I curves. When the array is biased at a point (v, i), only those modules whose photocurrent I L is greater than the array current at point i will be forward biased. Those modules which are receiving less light and whose value I L

4 344 I. ANTÓN AND G. SALA is less than the array current i, will be in reverse biased (i.e., the bypass diode is forward biased) and therefore will take away power from the array. The number of forward biased modules N varies with the bias point of the array, increasing with voltage. The characteristic curve of the array satisfies the following equation: vðiþ ¼ X I Lk >i V m ðiþ X I Lk <i V d ði I Lk Þ ð1þ where the first term expresses the contribution of the forward biased modules V m ðiþ and the second, the bypass diodes contribution V d ði I Lk Þ. In typical configurations of conventional PV arrays, with lower voltage, it is appropriate to assume that the short-circuit current of the array corresponds to the best illuminated module. On the other hand, in a EUCLIDES array, given the large number of modules and the relationship of 10 cells per diode, things are very different. With the array in short-circuit, the number of forward biased modules NðI sc Þ must compensate for the power which falls on the rest of the bypass diodes, according to the following equation: NðI sc ÞV mp ¼ ½N t NðI sc ÞŠV ð2þ where we have assumed that the modules are biased at the maximum power point (MPP), being V mp ¼ V mparray =N t and N t the number of modules in series; and that the voltage of the bypass diodes is V 06 V for the typical intensity values, obtained from the data sheet. For the case of the EUCLIDES array, the value of N at short-circuit point is 19 or 20. This means that there are 20 modules whose photogenerated current is greater than the short-circuit current of the array. A one-quadrant V I curve does not provide any information on those better illuminated modules. Pseudo-parallel resistance caused by optical mismatch The presence of the bypass diodes together with an elevated dispersion in the photocurrents of the modules brings about a significant slope in the V I curve, similar to that originated by a low parallel resistance. 18 The light dispersion in the modules is due to several statistically uncorrelated effects: dirt, misalignments, edge effects of the mirror, flaws, etc. We will, therefore, assume that the illumination currents of the modules follow a Gausian distribution ð<i L >; I Þ. We will obtain the average value <I L > of the distribution from the V I curve. At the maximum power point the number of forward biased modules is ideally the total number of modules N t, while the short-circuit point is NðI sc Þ (Figure 2). The point in the curve V I which corresponds to the average value of the current is that which satisfies the following equation: Vð<I L >Þ¼ 1 2 V mparray 1 NðI scþ N t NðI sc Þ The variance of the Gaussian distribution 2 can be obtained from the number of forward biased modules at the short-circuit current of the array, calculated in Equation (2), and the properties of the Gaussian distribution: 1 NðI scþ ¼ 1 ð Isc p N t ffiffiffiffiffi 2 1! exp ði <I L >Þ di Equation (4) provides a simple relationship between the average value, obtained from the experimental V I curve and Equation (3), and the variance of the distribution, which for the particular case of a EUCLIDES array is: ð3þ ð4þ I sc ¼ 1058 þ<i L > ð5þ

5 LOSSES IN PV CONCENTRATORS 345 Figure 2. Number of modules forward biased throughout the I V curve of an array Figure 3. Experimental V I curve of a EUCLIDES array (1) compared with a PSPICE simulation (2) with a population of generated photocurrents following a Gaussian distribution (see inset table); PSPICE simulation for the case of zero photocurrent dispersion (3); number of active modules as a function of the array voltage (4) Figure 3 shows an experimental V I curve of a EUCLIDES array and the statistical distribution of the light obtained with the previous equations. In order to contrast its validity, simulations have been carried out using PSPICE (software for simulation of analog circuits), by introducing a population of 138 modules whose generated photocurrents follows the obtained Gaussian distribution.

6 346 I. ANTÓN AND G. SALA One of the causes of the power loss is the possible existence of inverse modules at the maximum power point, which is not determined by the worst illuminated module, as is the case without bypass diodes. For the curve in the figure, both the statistical value NðI mp Þ and the PSPICE simulation indicate the existence of four reverse biased modules at MPP, which represent 3% of the power. Series/parallel connections The 138 modules of an array are series connected. The main reason is the high current that is generated by a EUCLIDES cell, more than 40 A at nominal operating conditions. The connections in the system are dimensioned for this value (wires, connectors, tabs, etc.). If all the modules were connected in parallel the losses caused by mismatch would be significantly reduced. It would bring about an increase in power of the array of 8% according to the PSPICE simulations for the conditions shown in Figure 3. But it would lead to unmanageable currents (5700 A for the case of 138 modules in parallel) and power losses caused by voltage drops in the wires and connectors. Two rows connected in parallel of 69 modules each is assumable from the point of view of the current but offers an improvement of just 13%. A total series connection is preferred, however, in order to obtain an operating voltage of 750 V, thus avoiding the need for a tri-phase transformer at the outlet of the inverter, together with its associated power loses. ANALYSIS OF THE POWER LOSSES IN THE SYSTEM Study of the characteristic V I curve For the EUCLIDES Tenerife plant, significant power losses associated with dispersion in the generated photocurrents caused by optical mismatch have been found, with values of 13 22% for the 14 arrays. The effect of misalignments and optical dispersion exerts a great influence on the final power of the system. The study and the quantification of those effects has provided very useful information in order to reduce the power losses associated, by introducing the necessary modifications into the system and for future redesigns. We shall define an ideal curve of an array as that whose mismatch losses are zero. In order to establish the ideal V I curve of a EUCLIDES array each type of mirror was characterised with the same receiver at wellknown irradiance and temperature conditions (B 0, T 0 ). The ideal curve of an array of that mirror technology is obtained by multiplying the voltage of the curve by the number of modules that make up an array (138) and extrapolating them to the required light and temperature conditions (B, T). This is curve (1) in Figure 4. Comparing the ideal curve with an experimental measurement of an array (curve 3) a slight loss is observed in I sc as opposed to the ideal curve. The losses in I sc are due to an overall loss of efficiency with respect to the optimal value, caused by dirt on the mirrors and receivers. No permanent degradation has been detected for the mirrors during the checking period of the plant. However, the arrays require frequent cleaning owing to the high winds and dryness of the area. The resulting power losses for the case study are 33%, a day after cleaning the array. Curve (2) of Figure 4 represents the ideal V I curve without optical dispersion with the same value of I sc as the experimental one. In this way we have discounted the losses associated to cleanliness for that specific day. If we compare them, the maximum power is 213% less in the case of dispersion (curve 3) than in the ideal curve (2). The table in the figure collects the power values obtained from the previous curves. Causes of optical dispersion There are several causes of optical mismatch of a statiscally uncorrelated nature. These can be grouped into two categories. In the first place, those that affect the optical quality and therefore the efficiency of each single mirror, such as dirt, localised defects, errors in the manufacturing process affecting the parabolic shape and the defects in the edges of the mirror. The other group of causes are related to the misalignments in the relative position between each mirror and its receptor. This could be due to a lack of positioning adjustment of the mirrors and to the torsion of the structure as a result of the wind and weight loads.

7 LOSSES IN PV CONCENTRATORS 347 Figure 4. Experimental V I curve of a EUCLIDES array of the Tenerife plant, compared with ideal curves The effects of the edges of the mirrors must be carefully studied. In a EUCLIDES array there is a discontinuity between mirrors, whose separation is on average 4 mm. The dispersion in this separation and damage incurred during their mounting and repair process could cause very significant power losses because the shadowing caused by edge damages affects mainly the extreme cells. Since cells are connected in series in the module, the current is given by the worst illuminated one. This effect could be reduced by increasing the number of bypass diodes in the module. For example, a module consisting of series connected sub-modules of two cells in parallel with a bypass diode per pair of cells, would reduce significantly the electrical losses caused by the edge effect of the mirrors. Understanding whether the cause of the optical dispersion is a problem of misalignment or of dispersion in the optical efficiencies is of vital importance in the search for solutions and for the improvement in future designs of the system. Carrying out systematic measurements on the individual efficiencies of the mirrors making up an array once the modules have been connected is a very complex problem. We will try to deal with this problem in this study. The optical transmission of the system vs the array bias The transmission curve is the ratio of the whole light reaching the receiver versus the total light cast on the collector at angle. In concentrator systems, it is experimentally measured by advancing the position of the system to the sun and, while the focus of light advances over the receiver, registering the generated photocurrent as a function of the sun s angular position. 20 Assuming that the cells have been designed for the concentrator system and there is no significant series resistance effect at the short-circuit point, the generated photocurrent can be obtained with the short-circuit current of the receiver. The acceptance angle of a concentrator system,

8 348 I. ANTÓN AND G. SALA Figure 5. Short-circuit and power transmission curves of a EUCLIDES array compared with transmission curves of the most misaligned individual collector receiver sets defined as the angle formed by the incident light beam and the normal to the collector aperture plane for which 90% of the incident light is transmitted to the receiver, is obtained from the transmission curve. Nevertheless, this is valid only for a single collector receiver as we shall explain in the following paragraphs. The shortcircuit transmission curve on an array is affected by the series/parallel connection of the modules and thus information of angular transmission cannot be deduced from it. A consequence of the misalignments is a widening of the short-circuit transmission curve in the array with respect to an individual collector receiver. The misalignment between the individual collector receiver sets causes an angular shift in their transmission curves (Figure 5). As explained, at the short-circuit current of the array there are NðI sc Þ modules with better generated photocurrent. Therefore, the short-circuit transmission curve of the array is the envelope of the NðI sc Þ best illuminated modules, which is the origin of the aforementioned widening. Taking this into account, the transmission curves of the individual collector receiver sets have been shifted in order to fit the transmission curve of the whole array, providing a maximum displacement between the extreme collector receivers of 055. We can say, therefore, that the entire 138 mirror modules are found within the range of In Figure 5 the transmission curves of the most shifted collector receivers have been drawn. The transmission curve can be obtained not only at short-circuit point, but at any array bias, although it would not provide information on the amount of light transmitted to the receiver. The most significant is the transmission curve at the maximum power point, which provides information of the power transmission as a function of the relative angular position of the sun. In order to illustrate this, transmission measurements were taken of a EUCLIDES concentrator for different array bias, shown in Figure 6. As the voltage of the array increases, so does the number N of forward biased modules. The transmission curve of the array at any voltage is the envelope of the transmission curves of the best illuminated N modules, which are those forward biased at that bias point. The result is a significant reduction in both the absolute value and the width of the transmission curve as the voltage of the array increases. Comparing the power transmission curve, as opposed to the short-circuit curve, the reduction is appreciated. If we consider the transmission curves, the precision of the aiming system for a short-circuit current greater than 95% of the maximum must be 05. However, for the output power to be greater than 95% of the maximum, its precision is much more demanding and its value is situated at about 015. The conclusion is that only the power transmission curve provides true information of the acceptance angle of the system.

9 LOSSES IN PV CONCENTRATORS 349 Figure 6. Experimental measurements of the transmission curves of a EUCLIDES array at different bias points. Comparison between the short-circuit current and MPP current transmission of the system Going back to Figure 5, it can be appreciated that the power transmission of the array coincides with the intersection of the transmission curves of the most misaligned collectors, although with a lower peak value. The reason is that at the maximum power point, the majority of the modules are forward biased, so the power transmission is the lower envelope, i.e., the intersection of the individual transmission curves. The peak value is different because we have assumed in this study that all the mirrors have the same optical efficiency, and therefore the same maximum value of their transmission curves, but the reality is far from this approximation. The current at the maximum power point is 20% lower than the short-circuit current, while the intersection of the theoretical curves predicts losses of only 3%. Therefore, the main responsible cause of the losses is not the misalignment, but the dispersion in the optical efficiencies of the mirrors. A mirror with lower optical efficiency provides transmission curves of a lower relative peak value, and on occasions, asymmetric. Consequently, the intersection of the transmission curves of the individual collector-receiver sets, i.e., the power transmission curve, already has a lower peak value. That is, the effect of the misalignments increases the losses caused by dispersion in the optical efficiencies of the mirror. This study is of special relevance because it is the usual practise in concentrator systems to use the shortcircuit transmission curves in order to calculate the acceptance of the system. This is valid for an isolated collector receiver set, but not for a system with interconnected modules. On contrary, it is a transmission curve at the maximum power point which provides the information on the acceptance of the complete system and establishes the precision requisites for the aiming system. Study of a secondary stage From the beginning of the design of a EUCLIDES concentrator the convenience of a secondary stage (Figure 7) has been studied. Given the high optical quality of the Madrid prototype mirrors, we opted not to install it in the Tenerife plant. However, in the Tenerife plant the mirrors are larger and the angular acceptance lower, so the possibility of installing a secondary stage remained open and it has been necessary to study the convenience of it. The installation of secondaries has been carried out on one of the arrays at the Tenerife plant. It has two significant advantages: in the first place, an increase of 4% in the light intensity was achieved, since a significant amount of light is collected by the secondary from areas of the mirror with less acceptance angle. They can also contribute to a greater uniformity of light throughout the array since this improvement is more significant in the

10 350 I. ANTÓN AND G. SALA Figure 7. Optics of the EUCLIDES concentrator with a secondary stage Figure 8. Individual mirror collector transmission curves with and without secondary stage lower-quality mirrors and consequently reduces the optical mismatch. The second great advantage is the increase in the angular acceptance and therefore, a potential reduction in the losses due to misalignments. The transmission curve of a single collector receiver is shown in Figure 8 both with and without a secondary stage. For the case of mismatch losses in the array of around 20%, the presence of a secondary step would reduce them to 106%, including the aforementioned increase of light. In Figure 9, V I curves of the same array with and without the secondary stage have been plotted and compared with the ideal curve (1). For that particular case, optical mismatch loss of 221% is found with a single-step collector (curve 2), which is significantly reduced up to 101% with the secondary stage (curve 3). When the light increase provided by the secondary stage is discounted (4), a new V I curve with the same short-circuit current than curve (2) is obtained in which the power losses are reduced only to 136%. This last figure represents the losses caused by the dispersion in the optical efficiencies, while the difference of up to 101% is related to angular misalignments, whose effect is reduced by the widening of the transmission curves and the acceptance angle increase with the secondary stage. Another significant result is that the increase in power is higher than in current, owing to the reduction in the number of reverse biased modules at the maximum power point, and therefore, to the consequent voltage increase at this point, as can be appreciated in the table of Figure 9.

11 LOSSES IN PV CONCENTRATORS 351 Figure 9. Experimental V I curves of a EUCLIDES array under real operating conditions (850 W/m 2,T room ¼ 27 C, T cel 94 C), with and without a secondary stage and compared with the ideal curve (theoretical) under the same conditions CONCLUSIONS The analysis of power losses in a large concentration system, especially those of optical and mechanical nature, have turned out to be especially complex. Optical mismatch causes a higher dispersion in generated photocurrents than in conventional PV plants and it has been necessary the use of statistical models for their comprehension. The presence of bypass diodes every ten cells has proven to be insufficient to lessen the elevated photocurrent dispersion losses that might arise in a concentration system. One of the original aspects presented in this article is the study of the transmission curves of a concentrator system based on the short-circuit current and the power, and the apparent widening in the short-circuit current transmission caused by the electrical connection of modules and the misalignments between mirrors and modules. For that reason only the power transmission curves of an array provide true information on the angular transmission of the optical system and the accuracy requirement of the aiming system. The installation of a secondary stage, that has been carried out in a EUCLIDES line at the Tenerife plant, has produced good results in order to lessen the losses in the system associated to optical mismatch. From this study it can be deduced that the dispersion in mirror optical efficiencies, mainly caused by the edges of the mirrors, is responsible for these losses, although the collector misalignments also contribute to and increase the effect of the optical dispersion. The presence of a secondary stage and the associated widening of the angular transmission curves is offered as a solution to this problem and to increase the optical efficiency of the optical system, basically in the area of the mirror of lower acceptance. Nevertheless, the secondary stage must be evaluated economically, considering the increase in available energy and its market price. It seems with considering, in future designs, the possibility of including the secondary stage in the module. The small increase in cost

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