C. Renno; F. Petito

Abstract

The potential of the concentrating photovoltaic technology has been evaluated from the thermal point of view in this paper. A model of a concentrating photovoltaic thermal system （CPV/T） was presented in order to size it and to evaluate its energy performance when it is used to satisfy the electric， heating and cooling loads referring to a domestic application. The choice and sizing of the CPV/ T system components is first of all considered. The triplejunction cells and the reflective optics with parabolic mirror concentrators of point-focus type assembled with a dual axis tracker， are adopted in order to obtain a high concentration system； an active cooling system of the photovoltaic cells is also considered. The CPV/T system allows recovering thermal energy at high temperature for the absorption heat pump working. The model analyzed the CPV/T system working in terms of： cell efficiency， module electric and thermal efficiency， thermal and electric energy provided by the cell and module， cell and cooling fluid temperatures. So， the simulation process allows realizing an energy analysis and defining the best configuration of the CPV/T system， evaluating its energy convenience in comparison with a traditional system under different working conditions.

Key words： Concentrating photovoltaic； CPV/T system； Domestic application

INTRODUCTION

The photovoltaic systems allow obtaining electric energy with competitive costs if compared to traditional systems； in the last years the concentrating photovoltaic systems （CPV） have been greatly developed （Kurtz， 2009； Mokri & Emziane， 2011）. In the CPV systems the solar light is concentrated by means of optical devices that allow decreasing the solar cells area proportionally to the concentration factor （C）； C is the ratio between the primary concentrator area and that of the solar cell（Zahedi， 2011）. A concentration system consists of three parts： receiver， focusing optics and solar tracker. The receiver is the component that includes both the solar cell and the heat dissipation system. The focusing optics allows the sunlight concentration on the receiver. Since the concentration systems work with the sunlight direct component， the receiver and the focusing optics require the use of a single axis or dual axis solar tracker in order to optimize the incident radiation at any moment. About the optics there are two basic solutions. The first is the refractive by means of the Fresnel lenses （Zhai et al.， 2010）. The second solution considers the parabolic concentrators， consisting essentially of mirrors able to concentrate the radiation on the cells without reproducing the light source image； moreover， a secondary optics could be used to increase the concentration and enhance the radiation focus （Vossier et al.， 2012； Brogen， 2004）. As for the solar cells use in the last years the triple junction cells are more adopted. They have a voltagecurrent characteristic which increases logarithmically with the concentration level （Cotal et al.， 2009）. They are also less influenced by the temperature increase， as the lower percentage decrease of the open circuit voltage shows； hence， efficiencies over 30% are experimentally achieved （Zhai et al.， 2010）. There are various types of concentration systems， which depend on the type of sunlight focus and receiver， and classified， according to the concentration factor， in plants at low， medium and high concentration. The advantages obtained with the concentration are evaluated in many studies in terms of electrical performance. In （Brogen， 2004） a low concentration system with parabolic concentrators is discussed. In （Li et al.， 2011） the possibility to use arrays of cells with high performance such as GaAs instead of traditional cells is studied， concentrating the light with a linear reflector and adopting heat recovery systems in order to obtain both higher electric performance and thermal energy. The thermal energy can be recovered by the solar cells both by means of active systems using a cooling fluid and with passive cooling systems that use the natural convection mechanism （Zahedi， 2011）. An active mechanism of heat transfer is important either to cool the cells or to obtain exploitable thermal energy. In （Kribus et al.， 2006） a CPV/T system of small dimensions has been analyzed， based on a parabolic concentrator which reflects the light on a single cell. This system provides a particular mechanism of heat transfer which allows extracting heat from the cells and transfers it to the cooling fluid； the thermal efficiency is about 60% with an electric efficiency higher than 20%. The thermal energy available can be used not only for the heating and sanitary hot water， but also to get cooling. In （Mittelman et al.， 2007） a CPV/ T system has been linked to a single stage LiBr/H2O absorption heat pump， realizing so a solar cooling system. It is important to use an apparatus that allows both to chase the solar radiation and the right location of the pipes where the heat transfer fluid flows without occupying too much space （Mousazadeh et al.， 2009）. In particular， in this paper a model built in Matlab （Matlab R2007b， 2007） is presented in order to evaluate the electric， heating and cooling performances of a CPV/T system usable in a domestic application. A reflective optics with parabolic mirror concentrators of point-focus type and a triplejunction （InGaP/InGas/Ge） cell mounted on a dual axis tracker， are used to obtain a high concentration system. A CPV/T system， differently from traditional photovoltaic systems， allows recovering thermal energy at high temperature； hence， a coupling between a CPV/T system and an absorption heat pump （AHP） allows satisfying the cooling demands. The model allows both to size the CPV/ T system components， evaluating also the direct normal irradiance， and to compare from the energy point of view the CPV/T system with a traditional system.

1. CPV/T SYSTEM

The CPV/T system （Figure 1） simulated in this paper uses solar energy concentrated to satisfy the different energy demands related to a domestic application. This system uses a reflective optics that consists of small parabolic concentrator mirrors， of point-focus type in order to obtain a high concentration system， that reflect the light on triple-junction cells InGaP/InGaAs/Ge（Indium-Gallium Phosphide/ Indium-Gallium Arsenide/ Germanium） placed at a certain distance among them on a plate where the cooling fluid flows in pipes suitably sized. The system is completed with a mechanism of dual axis tracker； in particular， in the system considered a rotating frame on which the concentrators are placed to follow the sun， is presented. This frame is then raised or lowered to follow the solar elevation through an actuator. Referring to a domestic application， in order to optimize the space occupied， the CPV/T system is modular and each module consists of 90 cells. Hence， using square cells with side of 9 mm， a concentration level up to 900x is reached and each concentrator is represented by a parabolic surface of area 0.073 m2. The calculation of the module total size takes into account the optics used， the cells area and their number， and the concentration factor. Moreover， the cells arrangement that constitute the module is important. After geometric considerations， it has been determined that the module that occupies less space is related to a cells layout of rectangular type， where the cells are positioned on multiple parallel rows， compared to other types of layout （rhomboid， circular， etc...）. In order to reduce the number of cells in series and not to affect the module performance， the 90 cells have been arranged in six parallel rows each of which consists of 15 units. In order to calculate the space occupied by each module， it is necessary to know the cell size and the concentration factor in order to determine the concentrator area from which it is possible to evaluate the concentrator side； hence， a side equal to 0.27 m is obtained. Assuming 15 cells in series and a distance between the cells equal to half of the concentrator diameter， the module total length is equal to 5.94 m （Figure 1）. The module width， equal to 2.43 m， is calculated in a similar way and takes into account the distances between the six rows in order to allow the tubes mounting of the cooling fluid； hence， the single module occupies a total area of 14.43 m2. Related to south Italy sites， the CPV/T system generally consists of two modules which occupy a total area of about 30 m2. In Figure 2 a scheme of the CPV/T system， used to meet the energy demands related a domestic application， is shown. The concentrating photovoltaic modules are linked to a tank working as a hot water storage. The mains water is mixed to obtain a glycol solution and reaches the tank where is sent to the CPV/T system for its cooling. In Figure 2 a single stage absorption heat pump （AHP）， which receives thermal energy from the CPV/T system for its working， is presented. The scheme presents either a traditional boiler able to integrate thermal energy or an inverter able to convert the direct current obtained by the CPV/T system into alternating current. A grid-connected system is also considered； it is possible to integrate the electricity from the network and to give the surplus energy back to it.

The model of the CPV/T system described above requires the definition of the main exogenous and endogenous variables. The first are non controllable external variables（solar radiation， atmospheric conditions， environment temperature）， but they can be evaluated and parameterized in order to simulate the different working conditions of the CPV/T system. The second represent the system internal variables that characterize its working. In order to analyze the system proposed under various operating conditions， the main system variables （optics， cell size， concentration factor and loads） have been suitably varied. The CPV/T system model has been realized in Matlab and subdivided into several steps （Figure 3）. The first phase analyzes the model input data （optics， cell size， geographic location， etc..）. Subsequently the main variables （cell temperature， cell efficiency， etc..） which characterize the CPV/T system working are parameterized， and， finally， the model results（thermal energy， electric energy， module efficiency， etc..） are determined.

2.1 Model Input Data

It is necessary first of all to determine the site where to install the CPV/T system； latitude， longitude and altitude of several Italian sites （ENEA） have been included in the model.

Moreover， the average values of cloud cover have been considered in the evaluation of the direct normal irradiance （Desiato et al.， 2006） and calculated in oktas on a statistical basis of thirty years. Other input data are the optics type adopted and the cells data （area and number） that constitute the single module.

2.2 Direct Normal Irradiance The direct normal irradiance （DNI） determination is the starting point to realize a correct sizing of the CPV system. For this purpose it is important to consider the main angles in the model necessary to calculate the air mass and the direct normal irradiance incident on the surface（Technical standard UNI， 1983）. Moreover， it is necessary to consider the impact that the weather conditions have on the direct normal irradiance determination differently from the diffuse irradiance. Once known the daily light hours， the total daily irradiance can be evaluated together with the monthly and yearly irradiance. By means of HRA both the solar elevation hour by hour and the zenith angle（θz=90°–α） are defined and represent the input parameters to calculate the air mass （Kasten and Young， 1989）： that defines the path of light in the atmosphere compared to the path that it would perform if the sun was at its zenith. Once known the air mass value， the direct normal irradiance， calculated in a determined hour， can be obtained （Laue， 1970）：

The irradiance is calculated knowing the daily light hours that can be obtained through the hour angle of the astronomical sunset （ωs） （Technical standard UNI）. Because at dawn HRA=-ωs and at sunset HRA=ωs the direct irradiance previously calculated can be changed by means of the cloud cover factor （c_n）：

The irradiance thus calculated will take into account the further losses due to the surface inclination also with a tracking system. The Table 1 shows the monthly trend of the direct normal irradiance for several Italian cities.

2.3 Cell Efficiency And Temperature

The factors evaluation that most influence the working conditions of the CPV/T system are closely interconnected； in fact it is necessary to know the cell temperature to calculate its efficiency. The temperature determination is complex because of the illumination characteristics and the cell construction technology. Although there are not equations that uniquely express the cell temperature in terms of the concentration factor （C）， it is possible to refer to some experimental results （Luque et al.， 1998）. Hence， it is possible to express the cell temperature in this way： where To is the environment temperature， Voc （Tc， C） is the open circuit voltage function of the cell temperature and concentration factor， Voc（To，Co） is the open circuit voltage function of the environment temperature and concentration factor equal to 1， β（C） is the voltage thermal coefficient. This expression is not usable as it requires the knowledge of parameters that can be only empirically obtained. It is possible， therefore， to consider some experimental diagrams of the variables examined （Steiner et al.， 2011）. The open circuit voltages depend on the cell temperature that represents the unknown. This can be overcome considering a relation deduced graphically （Cotal et al.， 2009） where Voc depends only on the concentration factor：

The voltage thermal coefficient depends also on C and

is calculated as （Steiner et al.， 2011）：

Once known the cell temperature， the cell efficiency can be determined. Also in this case it is not possible to define a theoretical equation between the quantities examined， but it is possible to use some experimental diagrams （Steiner et al.， 2011） which show the efficiency decrease when the concentration factor increases at the same cell temperature. Hence， the cell efficiency is calculated as：

2.4 Electric and Thermal Energy

The electrical energy theoretically produced by a single cell， using a concentration system with biaxial motion， is equal to （Kribus et al.， 2006； Mittelman et al.， 2007）： where Gdir，r represents the direct irradiance previously calculated and， considering a non ideal tracking system， a factor f equal to 0.9 is considered. The system optical efficiency with parabolic concentrator mirrors is equal to（Brogen， 2004）： where τ and ρ represent the transmission and reflectivity coefficients of the mirrors； the value 0.98 is the ratio between the areas of the photovoltaic cell and the concentrator. In order to determine the electric energy actually delivered by the cell， the power thermal coefficient （kt）， which indicates the percentage decrease of the electricity supplied by the system at a given operating temperature， has to be defined kt=1+σt.（Tc-25） where σt is the temperature coefficient dependent on cell type and manufacturer； analyzing many data sheets a σt value equal to -0.16% has been chosen. Hence， the electrical energy actually delivered by the cell is equal to Pc，r = kt.Pc.

To calculate the module electric energy， it is necessary to

consider the cells number that constitute it and its efficiency（ηmod） fixed equal to 0.9 （Kribus et al.， 2006）. This value takes into account the coupling in series of the cells along a line， considering the possibility that a cell can operate at a efficiency lower than the nominal one. Hence， the electric energy delivered by the module is equal to：

The value obtained has to be reduced taking into account the parasitic current losses generated in the module， defined as （Kribus et al.， 2006）： where ppar is a loss factor depending on the radiation and equal to 0.023 （Kribus et al.， 2006）. So， considering the inverter efficiency （ηinv） fixed equal to 0.9 （Mittelman et al.， 2007） and cells linked in series， the actual electric energy provided by module is equal to： where the concentrating photovoltaic module overall efficiency （ηpv） considers all the system losses and is equal to （Kribus et al.， 2006）：

Moreover， the solar rays which act on the triplejunction cell determine its heating and thermal energy dispersion because of radiative and convective phenomena（Mittelman et al.， 2007）： where εc is the cell emissivity equal to 0.85. The actual thermal energy is equal to the difference between the theoretical total thermal energy and the radiative and

convective losses generally included in the range 1÷ 3%（Kribus et al.， 2006）.

2.5 Fluid Outlet Temperature

The CPV/T system model allows also the calculation of the fluid outlet temperature （Tf，out）， usually water and glycol， used to cool the cells and to provide thermal energy to a domestic application. In particular， the sun rays focused on the triplejunction cell allow the heating of the absorber plate， placed immediately below the cells （Figure 1）. The polymeric insulating material is used in order to avoid heat loss. The equation that regulates the exchange between the cell and plate is （Kribus et al.， 2006）：

from which the plate temperature can be obtained once calculated the real thermal power. Once considered the system CPV/T dimensions and the conductivities values of the substrate between the cell and cooling plate and assuming a homogeneous and isotropic model， a K value has been determined. In order to satisfy the sanitary hot water， heating and cooling demands related to a domestic application， it is necessary to determine Tf，out. This temperature has been calculated assuming that the absorber plate temperature （Tp） is uniform （Kribus et al.， 2006）. Considering the first law and the design equation of a heat exchanger， the following equation is obtained：

where Tout and Tin are the outlet and inlet fluid temperatures and UA is the global conductance. Hence， the outlet fluid temperature is equal to：

3. ENERGY ANALYSIS RESULTS

The model has allowed a daily， monthly and annual results evaluation in order to identify the main technical characteristics necessary for the realization of the most efficient CPV/T system. The main input variables of the simulation process are： installation site， optics type， cells size， cells number of the module and concentration factor. In particular， in the CPV/T system simulation two types of optics have been considered： Fresnel lenses and parabolic mirror concentrators of point-focus type. In the simulation the cells size has been varied between 1 cm2 and 1.5 cm2 in the system with lenses， and between 8 mm2 and 9 mm2 with mirrors； the concentration factor has been varied in the range 600x and 900x and the cells number per module between 60 and 120. The model has allowed to realize simulations in all Italy and to define the optimal concentration system， especially in southern Italy where the CPV/T system is resulted more convenient. The energy demands of a house are determined related to the site considered. 80 and 200 m2 houses inhabited by 2 to 6 people have been considered. The average annual electric demand varies between 19 and 30 kWh/m2. For example， an electric consumption of about 2820 kWh/ year has been estimated for a house of 100 m2 inhabited by 4 people in Rome. The calculation related to the sanitary hot water is based on the f-chart method （Klein and Beckman， 1993）； considering an average index of 75 liters/day per person， 300 kWh of thermal energy per month are on average required. Energy consumption for heating and cooling depends on the site considered and their evaluation has been carried out monthly. For example， the energy required for heating during the winter months is on average equal to about 1800 kWh per month in Palermo； as for the cooling the AHP cooling peak power is 7 kW， with monthly average requirements of cooling energy of about 1100 kWh per month. The model presented allows varying both the input conditions and the load for different time intervals （yearly， monthly， daily， hourly） and to size， then， the CPV/T system according to the site and energy demands. The annual simulation has allowed evaluating both the most suitable optical device and optimal cells number able to satisfy the electric and thermal energy demands and to obtain low module size and high fluid outlet temperature necessary for the AHP working. The yearly simulation results represent the input of the monthly simulation that has allowed evaluating the high potential of the CPV/T system in southern Italy and not in northern Italy， and the concentration factor able to satisfy the electric energy demand with a low modules number. In particular， from northern to southern Italy， the modules number required decreases from three to two in order to satisfy the electric load. Related to the optics used， the concentrator mirrors allow obtaining electric energy about 10% higher than the refractive optics because of the Fresnel lens chromatic aberration for high concentration factor values. Moreover， the electric and thermal monthly efficiencies obtained from the model have been compared with small differences with those reported in （Kribus et al.， 2006） in the same working conditions considering a fluid outlet temperature of about 90°C； the module electric efficiency decreases with the concentration factor differently from the thermal efficiency（Figure 4）. The CPV/T system structure with two modules of 90 cells is the best solution to satisfy on average the energy demands （electricity， heating and cooling） in southern Italy. In particular， the Figures 5 and 6 show the electric and thermal energy produced in Milan and Palermo by a single module when the cells number and the concentration factor vary. The electric and thermal energy production increases when the concentration factor and number of cells increase， with absolute values higher in Palermo. The CPV/T systems satisfy the cooling demands adopting an absorption heat pump （AHP）； the fluid outlet temperature increases with the concentration factor. The choice of the cells number that constitute the module has to be a good compromise between the electric and thermal energy demands and the fluid temperature values of about 90°C to make possible the AHP use. Coupling CPV/T and AHP， the cooling capacity is equal to Q. r=Q.