A worldwide comparison of the annual yield between conventional c-Si photovoltaic (PV) technology and high concentrated photovoltaic (HCPV) technology is presented. The idea of this paper is to find the most appropriate locations for HCPV systems in terms of the annual energy produced when comparing to fixed tilt PV systems and two-axis oriented PY systems. For estimating the annual energy generation, the method of the Performance Ratio is used. For some locations with high annual direct normal irradiation values, which are distributed around the world, HCPV systems are found to be more advantageous than fixed tilt PV systems. World maps showing this comparison are presented.
1. Introduction and Description of the Technology
In this paper, we analyze the energy produced by three different kinds of photovoltaic plants: high concentration HCPV systems equipped with high efficiency multijunction solar cells (MJ) on a two-axis tracker, c-Si latitude tilt inclined fixed panels oriented to the south (in the Northern Hemisphere) and oriented to the north (in the Southern Hemisphere), and c-Si panels two-axis oriented. We also compare the energy produced by these HCPV systems with both kinds of c-Si systems mentioned above. For all the cases, we only analyze the annual AC energy produced by grid-connected systems. The inputs for these calculations are (a) annual irradiation data from the NASA database and (b) Performance Ratio values from real PV and HCPV power plants.
Conventional c-Si photovoltaic (PV) technology is nowadays worldwide used for harvesting solar energy into electricity with a cumulative installed capacity of around 180 GW in the year 2014, mostly grid-connected [1]. For fixed PV systems, the optimum tilt angle has been studied, being the simplest rule of inclining the panels according to the latitude for areas between 45°S and 45°N [2]. The annual input energy for fixed tilt c-Si PV systems is the global irradiation on a fixed tilt plane, HA [kW·h/m^{2}·year], and for c-Si PV two-axis tracking systems is the global normal irradiation, H2X,A [kW·h/m^{2}·year].
High concentrator photovoltaic (HCPV) systems are intended to decrease the cost of the photovoltaic electricity generation through the reduction of the use of semiconductor material which is substituted by sunlight concentrating optical devices made of cheaper common materials (glass, plastic, etc.) [3].
HCPV systems are usually equipped with high efficiency III–V triple-junction solar cells. Each of these subcells is responsible for the photocurrent generation corresponding to different wavelength ranges of the solar spectrum, which are determined by the energy band gap of each subcell. Hence, the efficiency of a multijunction (MJ) solar cell is higher than that for a cell used in conventional c-Si PV modules because, among other reasons, MJ solar cells utilize a broader total wavelength range for the energy conversion [4, 5]. Moreover, MJ solar cells have a higher potential of efficiency ratio than conventional solar cells of c-Si PV modules that is given by the thermodynamic limit, which grows with the number of junctions of the MJ solar cell [6]. As an example, considering a HCPV module of 1000x concentration ratio of an area of 1 m^{2}, the total area of MJ solar cell would be only 10 cm^{2}, which can be a square cell of less than 3.2 cm side. For achieving such concentrating ratios, efficient and optimized optical designs that concentrate direct sunrays have to be implemented. Since HCPV systems concentrate direct sunrays, it is preferable to install them in those regions with the highest annual direct irradiance levels (DNIA, measured in kW·h/m^{2}). High performance optical systems in HCPV modules usually collect and concentrate direct sunrays onto the small solar cell in two optical stages that are implemented by the elements often known as POE (primary optical element) and SOE (secondary optical element). Fresnel lenses are usual POE elements and concentrate direct sunlight whereas a wide variety of prisms are often used as SOE in order to homogenize the irradiance distribution over the solar cell as well as to increase the acceptance angle of the system, which decreases as the concentration ratio increases [7]. HCPV modules are typically mounted on a high accuracy pedestal two-axis tracker in order to align the optics with the sunrays. The higher the acceptance angle of the concentrating optics of the HCPV module is, the lower the accuracy requirements of the tracker system are [8, 9].
2. Calculation of the Annual Yield for Grid-Connected Systems
The estimation of the energy yield of grid-connected photovoltaic systems depends on the atmospheric parameters, on its location, on the electrical characteristics of the photovoltaic generator, and on its angle of inclination and orientation. Moreover, it is necessary to consider a series of losses referred to the generator to calculate the energy generated, as it has been pointed in some studies [10]. Particularly the dependency of the electrical efficiency of the generator with the temperature [11], mismatch effects, tolerance losses, losses due to soiling, and so forth have to be considered. So, the energy yield estimation methods for grid-connected systems are usually based on the experimental values of the parameters involved in the mathematical expressions used.
There are different methods [12] to calculate the energy generated by a photovoltaic grid-connected system. The method based on the Performance Ratio (PR) is one of the most used methods. The IEC standard 61724 [13] defines that the annual electricity generated by a conventional fixed PV system with panels optimally inclined over the horizontal and permanently oriented southwards can be estimated using the next equation: (1)YPV=PRHoptAGSTC,where YPV is the final annual AC energy yield in a conventional fixed grid-connected system [kW·h/kWp·year], HoptA is the annual global irradiation on optimally inclined plane [kW·h/m^{2}·year], and GSTC is the global irradiance in standard test conditions [1 kW/m^{2}].
The Performance Ratio (PR) coefficient (nondimensional) describes the relation between the final energy output real and theoretical one of a photovoltaic installation. Therefore, PR is a measure of the quality of a photovoltaic installation and shows the proportion of energy that is available at the output after subtracting the energy losses in the system. The higher the PR is, the more efficient the grid-connected PV installation is. It is impossible to achieve a PR = 100% because of the unavoidable losses. A high efficiency grid-connected PV power plant can achieve a value of PR = 80% [14]. The International Energy Agency [15] has analyzed the performance of different PV systems and it concludes that the range of PR values is quite wide, from a minimum of 40% to a maximum of 85% (see Figure 1). Specifically, for grid-connected systems installed since the year 1996 the average value is 74%. The PR value in a conventional fixed grid-connected PV system usually ranges from 70% to 80%. Based on the experience in this kind of systems [16–20], we have used a value of 78% for grid-connected PV systems of high efficiency and a value of 75% for standard systems. In addition, a value of PR = 78% has been also taken for c-Si PV two-axis grid-connected systems in this work based on the analyses previously cited.
Histogram of the annual Performance Ratio for PV systems [15].
The annual electricity generated by a HCPV system can be estimated using the following equation: (2)YHCPV=PRDNIADNISTC,where YHCPV is the final AC annual energy yield in a HCPV system [kW·h/kWp·year], DNIA is the annual direct normal irradiation [kW·h/m^{2}·year], and DNISTC is the direct normal irradiance at standard test condition [1 kW/m^{2}]. The definition of the final AC annual energy yield for c-Si PV two-axis tracking systems can be expressed as (3)Y2XPV=PRH2XAGSTC,where the annual global normal irradiation on a plane two-axis oriented, H2XA [kW·h/m^{2}·year], can be expressed besides as(4)H2XA=DNIA+DiffuseA,where DiffuseA is the annual diffuse radiation [kW·h/m^{2}·year].
The value of PR in a typical HCPV system ranges from 76% to 91% in general as shown in Table 1 and is analyzed in some examples: case of SolFocus [22], case of Amonix [23], case of Daido Steel study concerning the spectral influence on the Performance Ratio [24], and case of Semprius [25]. Based on the analysis of these data and arguing similarly to the c-Si PV case, we have used a value of 82% for high efficiency systems and a value of 80% for standard systems.
Performance Ratio (PR) for some HCPV power plants [21].
Company/location
DNIA (kW⋅h/m^{2}⋅year)
YHCPV (kW⋅h/kWp⋅year)
PR (%)
Soitec/Touwsrivier
2447
1878
76–81
SolFocus/Puertollano (ISFOC)
1861
1914
88.7
Magpower/Portugal
1978
2113
91
Semprius/NREL
2446
2079
85
Solar Systems/Hermannsburg
2464
2104
85.4
The solar irradiation annual data used for the calculations were taken from the NASA database [26] and have a resolution of 1° for latitude and longitude. Although DNIA data were available, HoptA were not used for the calculations of this study. Instead of HoptA, data of annual global irradiation on latitude tilt plane were used. The optimum inclination of the fixed PV panel does not match the latitude tilt angle, so a brief analysis of the error of this approximation is shown in the next section.
3. Optimum Tilt Angle and Error Estimation
In Figure 2, the optimum tilt angle for a fixed panel in the North Hemisphere oriented to the south as a function of the latitude for some different locations (around 30 locations) in Africa and Europa is shown. These optimum angle values are taken from the PVGIS [27]. The strait line represents the panel’s tilt angles that coincide with the angle of latitude, that is, the tilt angles corresponding to the annual global irradiation on fixed PV panels data used in our study. We can distinguish three parts in the graph of Figure 2. For latitudes between 15° and 35° the latitude tilt angle is a good approximation to the optimum angle. For latitudes between 0° and 15° the optimum angle is few degrees higher than that of the latitude. For latitudes higher than 35° the optimum angles are clearly lower (up to 10° less) than the latitude angles. The highest deviation in terms of annual irradiance by taking the optimum tilt angle versus the latitude tilt angle is 30 kW·h/m^{2}·year for these 30 locations analyzed. Note that this is not an exhaustive analysis of this issue, since only around 30 locations have been considered in order to have an approach to the error of this approximation. The standard deviation for these data corresponds to around 8 kW·h/m^{2}·year, which corresponds to ca. 0.4% of relative standard deviation. Therefore we can conclude that this approximation is justified for the purpose of the study presented in this work.
Optimum inclination angle for fixed PV panels in comparison with latitude tilt angle.
4. Calculation Results and Conclusions
Figure 3 represents the global final AC annual yield of a HCPV system, YHCPV, when considering a PR = 0.82. The values obtained are in the range of 600 to 2400 kW·h/kWp·year. The regions with higher values of YHCPV are, obviously, those with higher values of DNIA, typically around 2400 kW·h/m^{2}·year. They may correspond to areas with very much fewer clouds, typically arid zones.
Map of global annual AC final yield, YHCPV, measured in kW⋅h/kWp for a HCPV power plant. A Performance Ratio (PR) of 0.82 was considered for the calculation.
Africa is the continent with overall higher values of YHCPV and the more remarkable regions (with maximums of 2400 kW·h/m^{2}·year) in this continent are
Libyan Desert,
Ténéré Desert (south central Sahara),
Sahara Desert in general.
Another African desert region with high values is the Namib Desert, with values of around 2300 kW·h/m^{2}·year. The areas near to those deserts cited above are also of interest for HCPV due to their relative high values of YHCPV. The Arabian Peninsula also shows relative high values of YHCPV that are in the range of 1800–2200 kW·h/m^{2}·year. In the Mediterranean zone the HCPV yield is around 1600 kW·h/m^{2}·year, representing the European highest yield values. Asiatic regions near the parallel 35°N at the west of the Gobi Desert and in the desert itself are also of interest for HCPV due to their relative high yield values. In Oceania, the northwest zone of Australia shows the highest values of HCPV yield, which are near to 2200 kW·h/m^{2}·year. In North America, the western regions of Mexico and southwestern USA, where there are some deserts, are the most preferable for HCPV, reaching yield values up to around 2200 kW·h/m^{2}·year. Cuba and some other Caribbean islands reach yields values of 2000 kW·h/m^{2}·year. In South America, The area of Atacama Desert and its surroundings shows very high yield values up to 2400 kW·h/m^{2}·year.
In Figure 4 the global final AC annual yield map for conventional c-Si PV inclined over the horizontal according to the latitude, YPV, is shown. A value of PR = 0.78 was applied for this calculation. This map is similar to that for HCPV technology but with some differences. The maximum yield, YPV, value is not higher than 2000 kW·h/m^{2}·year, less than in the case of YHCPV. The regions with higher yield values are very similar to those of the YHCPV map (Figure 3) like, for example, in the case of all the deserts previously cited.
Map of global annual AC final yield, YPV, measured in kW⋅h/kWp for a conventional c-Si PV power plant latitude tilt oriented. A Performance Ratio (PR) of 0.78 was considered for the calculation.
Moreover, the global final AC annual yield map for c-Si two-axis tracking systems, Y2XPV, is plotted in Figure 5, where a value of PR = 0.78 was considered. In this case, the values are clearly higher than in the case of those of the map of Figure 3 (YHCPV map) for all regions. This is an important conclusion that can be explained due to the fact that a c-Si PV two-axis tracking system utilizes not only the direct normal irradiation, which is the case of the HCPV systems, but also the diffuse radiation, DiffuseA.
Map of global annual AC final yield, Y2XPV, measured in kW⋅h/kWp for a conventional c-Si PV power plant two-axis oriented. A Performance Ratio (PR) of 0.78 was considered for the calculation.
The ratio YHCPV/YPV is plotted for each location when considering PRHCPV = 0.82 and PRPV = 0.75 in Figure 6. The green color denotes ratio values lower than 1 and red colors are for ratio values higher than 1. The areas corresponding to latitudes much higher than 50° in absolute value, which is near the polar circles and beyond, are not of interest due to their relative low levels of YHCPV. This figure shows the more and the less preferable locations for a HCPV plant in terms of the electrical energy than can be produced in a year compared to a PV plant latitude tilt oriented.
Ratio YHCPV/YPV considering PRHCPV = 0.82 and PRPV = 0.75.
For some regions, the energy produced by HCPV plants and PV plants latitude tilt oriented is quite similar. Those are the regions in which the ratio YHCPV/YPV is in the range 0.9–1.1. These regions correspond majorly to southeast of Brazil, eastern USA, equatorial zones in central Africa, southern India and southwestern China, and the surroundings to the parallel +50° north across Asia and America. The more interesting regions for locating a HCPV plant, taking into account its advantage for producing energy referred to a PV plant latitude tilt oriented, are the desert regions cited previously: deserts in California and surroundings (USA), Atacama (Chile), western Sahara and Namib (Africa), and western deserts in Australia. These desert zones correspond to ratio values of 1.3; that is, there the energy yield of a HCPV plant is 30% higher than for a PV one. The zones surrounding the cited deserts are also of high interest for HCPV installations compared to PV. There are also large extensions suitable for HCPV that achieve 1.2 ratio values like
Sahara desert (central and western),
southwestern Africa,
Arabian Peninsula,
Mediterranean regions from the Iberian Peninsula to Israel,
the area from Turkey to Pakistan and from Pakistan to Uzbekistan,
Mongolia and western China,
western USA and Mexico,
north Chile and middle Argentina,
Australia, excepting the northern and southern zones relative to the desert regions.
The less favorable regions for HCPV are also clearly visible in dark green in this map and correspond to ratio values of 0.7; that is, a PV plant would produce 30% more energy yearly than a HCPV one. These regions correspond to equatorial regions overall: in South America and in Africa, more seriously in the western areas for both cases, and in the southern Asiatic and Oceanic archipelagos. Also in eastern China the irradiance conditions are disadvantageous for HCPV. Northern Europe is also unfavorable for HCPV. These more disadvantageous regions for HCPV have in common high presence of humidity in the atmosphere in the form of clouds majorly, when averaging during a whole year in comparison to sunny regions.
A more restrictive case for HCPV technology is shown in Figure 7, in which the Performance Ratio is imposed to be PRHCPV = 0.80 and PRPV = 0.78. In fact, this is the same as analyzing the ratio DNIA/HoptA, that is, the ratio between the usable energy for HCPV systems and c-Si PV systems, since the other terms in the definitions equations (1) and (2) have the same numerical value in this specific case. This map is very similar to the previous one (Figure 6). The main difference is that the ratio values are closer to 1, which leads to the result that the usable energy for HCPV systems only deviates 30% over that of PV systems in some deserts (Libya, Egypt, Namib, and Atacama). Nevertheless, there are wide regions in which the usable energy for HCPV systems is 20% higher than for c-Si PV systems.
Ratio YHCPV/YPV considering PRHCPV = 0.80 and PRPV = 0.78.
Finally, the ratio YHCPV/Y2XPV comparing HCPV systems with c-Si PV two-axis systems is plotted in Figure 8. This ratio is <1 for all the regions since as explained before the incoming useful energy for a c-Si PV two-axis system is always greater than for HCPV systems because of the diffuse radiation that the c-Si panels convert into electricity. From this map of Figure 8, it can be observed that the annual final AC yield is very similar for HCPV systems compared to that for c-Si PV two-axis systems in some regions spread worldwide that correspond to the highest values of YHCPV. However, the efficiency of HCPV systems is higher than that of c-Si systems, and this contributes to reduce costs. Bearing this in mind, this issue should be deeply analyzed in a future research work in order to better select the best technology for each specific region.
Ratio YHCPV/Y2XPV considering PRHCPV = 0.82 and PR2XPV = 0.78.
Based on this analysis, it can be concluded that the use of HCPV, c-Si PV, or c-Si PV two-axis tracking technology depends on the region considered. There are regions worldwide in which the energy yield of HCPV technology is higher than in c-Si PV technology and vice versa. Moreover, the energy yield of HCPV systems is always lower than that of c-Si PV two-axis tracking systems; however, HCPV systems need less surface because of their higher efficiency and power density. For those reasons, the implementation of each specific technology has to be carefully analyzed for the area of interest.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgments
This work is part of the Project ENE2013-45242-R supported by the Spanish Economy Ministry and by the European Regional Development Fund/Fondo Europeo de Desarrollo Regional (ERDF/FEDER).
BrunisholzM.A snapshot of global PV markets—1992–2014BreyerC.SchmidJ.Global distribution of optimal tilt angles for fixed tilted PV systemsProceedings of the 25th European Photovoltaic Solar Energy Conference and ExhibitionSeptember 2010Valencia, SpainLuqueA.SalaG.Luque-HerediaI.Photovoltaic concentration at the onset of its commercial deploymentCotalH.FetzerC.BoisvertJ.KinseyG.KingR.HebertP.YoonH.KaramN.III-V multijunction solar cells for concentrating photovoltaicsZubiG.Bernal-AgustínJ. L.FracastoroG. V.High concentration photovoltaic systems applying III-V cellsLétayG.BettA. W.EtaOpt—a program for calculating limiting efficiency and optimum bandgap structure for multi-bandgap solar cells and TPV cellsProceedings of the 17th European Photovoltaic Solar Energy ConferenceOctober 2001Munich, GermanyBuljanM.Mendes-LopesJ.BenítezP.MiñanoJ. C.Recent trends in concentrated photovoltaics concentrators' architectureMuñozE.VidalP. G.NofuentesG.HontoriaL.Pérez-HiguerasP.TerradosJ.AlmonacidG.AguileraJ.CPV standardization: an overviewInternational Electrotechnical CommissionRodrigoP.RusC.AlmonacidF.Pérez-HiguerasP. J.AlmonacidG.A new method for estimating angular, spectral and low irradiance losses in photovoltaic systems using an artificial neural network model in combination with the Osterwald modelSkoplakiE.PalyvosJ. A.On the temperature dependence of photovoltaic module electrical performance: a review of efficiency/power correlationsRus-CasasC.AguilarJ. D.RodrigoP.AlmonacidF.Pérez-HiguerasP. J.Classification of methods for annual energy harvesting calculations of photovoltaic generatorsInternational Electrotechnical Commission (IEC)SMA Solar Technology AGPerformance ratio. Quality factor for the PV plantPerfratio-UEN100810ClavadetscherL.NordmannT.Cost and performance trends in grid-connected photovoltaic systems and case studiesŠúriM.HuldT. A.DunlopE. D.OssenbrinkH. A.Potential of solar electricity generation in the European union member states and candidate countriesRuiz-AriasJ. A.TerradosJ.Pérez-HiguerasP.Pozo-VázquezD.AlmonacidG.Assessment of the renewable energies potential for intensive electricity production in the province of Jaén, southern SpainDrifM.PérezP. J.AguileraJ.Univer Project. A grid connected photovoltaic system of 200 kWp at Jaén University. Overview and performance analysisRansomeS. J.WohlgemuthJ. H.SolarB. P.kWh/kWp dependency on PV technology and balance of systems performanceProceedings of the 29th IEEE Photovoltaic Specialists ConferenceMay 2002142014232-s2.0-0036957797MondolJ. D.YohanisY. G.SmythM.NortonB.Performance analysis of a grid-connected building integrated photovoltaic systemProceedings of the ISES Solar World CongressJune 2003Göteborg, SwedenTalaveraD.Pérez-HiguerasP.Ruíz-AriasJ.FernándezE.Levelised cost of electricity in high concentrated photovoltaic grid connected systems: spatial analysis of SpainKingC.Site data analysis of CPV plantsProceeding of the 35th IEEE Photovoltaic Specialists Conference (PVSC '10)June 2010Honolulu, Hawaii, USA3043304710.1109/pvsc.2010.56142362-s2.0-78650084150KennethS.Analysis of five years of field performance of the Amonix high concentration PV systemProceedings of the Power-Gen Renewable Conference2006Al HusnaH.ShibataN.SawanoN.Impact of spectral irradiance distribution and temperature on the outdoor performance of concentrator photovoltaic systemKingB.RileyD.HansenC.ErdmanM.GabrielJ.GhosalK.HCPV characterization: analysis of fielded system dataNASASurface meteorology and solar energy data information2015European CommissionPVGIS: PV Potential Estimation Utility, Photovoltaic Geographical Information System, July 2015, http://re.jrc.ec.europa.eu/pvgis/apps4/pvest.php