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Energy 106 (2016) 790e801

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Energy

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Investigating the impact of weather variables on the energy yield andcost of energy of grid-connected solar concentrator systems

Eduardo F. Fern�andez a, b, *, D.L. Talavera b, Florencia M. Almonacid a, b, Greg P. Smestad c

a Centre for Advanced Studies in Energy and Environment, University of Jaen, Las Lagunillas Campus, Jaen, 23071, Spainb IDEA Solar Energy Research Group, University of Jaen, Las Lagunillas Campus, Jaen, 23071, Spainc Sol Ideas Technology Development, San Jos�e, CA, 95150-5729, USA

a r t i c l e i n f o

Article history:Received 25 December 2015Received in revised form10 March 2016Accepted 14 March 2016

Keywords:Energy yieldEnergy economicsLCOE (Levelised cost of electricity)HCPV (High concentrator photovoltaics)Solar resourceAtmospheric variables

* Corresponding author. Centre for Advanced StudieUniversity of Jaen, Las Lagunillas Campus, Jaen, 23071,

E-mail address: fenandez@ujaen.es (E.F. Fern�ande

http://dx.doi.org/10.1016/j.energy.2016.03.0600360-5442/© 2016 Elsevier Ltd. All rights reserved.

a b s t r a c t

This work connects the electrical performance and economics of High Concentrator Photovoltaic tech-nology beyond the cell and module levels. It analyses the impact of fundamental variables on thecalculated energy output and economics of a typical system for real-world solar power plants in fivelocations with diverse climatic conditions. It was found that there exists a nearly linear relationshipbetween the Final Energy Yield and the average direct normal irradiance, while the cell temperature andspectral AC energy losses ranged from 4.6% to 1.8% and 5.0%e2.4%. The LCOE (Levelised Cost of Electricity)calculations used these insights, together with the specific economic values for each location. The resultsshow that the locations with the higher annual energy yield tend to have the lower LCOE values. Inparticular, the LCOE ranged from 5.5 cV/kWh to 22.2 cV/kWh for a conservative scenario. However, thesites with the highest final yield do not necessarily present the lowest values of LCOE. The resultsemphasize the interrelationship between the instantaneous effects of cell temperature and spectrum onthe performance of the system, as well as the importance of considering the specific economic param-eters to estimate the LCOE at each location.

© 2016 Elsevier Ltd. All rights reserved.

1. Introduction

HCPV (High Concentrator Photovoltaic) technology represents apromising energy source to produce more cost-effective electricitycompared to conventional PV (Photovoltaic) technology byreducing the amount of expensive semiconductor material used forthe cell by using less expensive optical elements [1]. Currently, thistechnology is largely based on the use of high efficiency III-Vconcentrator MJ (multi-junction) solar cells consisting of severalp-n junctions, usually three, to increase the absorption of theincident solar spectrum, and thus maximize the efficiency of thesolar conversion device [2,3]. The most widely used opticalconfiguration consists of a POE (primary optical element), usuallyFresnel lenses, and a SOE (secondary optical element). The aim ofthe POE is to collect and concentrate the direct rays, while the aimof the SOE is to receive the light from the POE to homogenize theluminous power on the solar cell surface and improve the

s in Energy and Environment,Spain. Tel.: þ34 9543213520.z).

acceptance angle of the overall concentrator system [4,5]. An HCPVmodule is the fundamental unit of an HCPV system used to convertthe direct sunlight into electricity. It consists of a particular numberofMJ solar cells and concentrator optical units, and other peripheralcomponents necessary to generate electricity and dissipate the heatproduced by the high energy flux of concentrated sunlight [6].Passive cooling mechanisms are mainly used because of theirsimplicity and reliability [7e9]. Finally, a typical grid-connectedsystem consists of several modules interconnected in series andparallel mounted on a high-precision pedestal. This two-axis solartracker is connected to a high efficiency DC/AC inverter and the restof BOS (balance of system components) [10e12]. The tracker allowsfor the optical axis of the concentrator optics to bewithin <1� of thesolar disk. The efficiency of MJ concentrator cells, HCPV modulesand systems is increasing over time, and is expected to reach valuesup to 50%, 45% and 40%, respectively, within the next few years[13,14]. Moreover, the costs of electricity for this technology hasshown decreasing trends and has already shown promising resultsat locations with a high solar resource [15,16]. The comments aboveshow the great potential of this technology, as an alternative

Nomenclature

Amodule Area of the modules, m2

b0, b1 and b2 Coefficients for the inverter, dimensionlessd Nominal discount rate, %DEPy Annual tax depreciation, V/kWpDNI Direct Normal Irradiance, W/m2

DNIheat Portion of the direct normal irradiance transformedinto heat, W/m2

ds Annual dividend of the equity capital, %E Energy output, kWhf Instantaneous power correction function, W or

dimensionlessHCPVAOMAnnual operation and maintenance cost, V/kWpHCPVI Initial investment cost, V/kWpHCPVl Amount equal to the portion of the initial investment

financed with the loan, %HCPVs Amount equal to the portion of the initial investment

financed with equity, %i Annual inflation rate, %il Annual loan interest rate, %L Power conversion losses, dimensionlessLCC Life cycle cost of the system, V/kWpLCOE Levelised Cost of Electricity, V/kWhN Life cycle (useful lifespan) of the system, yearsNd Tax life for depreciation, yearsNl Loan duration, yearsNS Number of modules in series, dimensionlessNP Number of modules in parallel, dimensionlessP Power, Wpin Normalized inverter input power, dimensionlessPR Performance Ratio of the system (PR ¼ YF/SDNI), %PW [DEP(Nd)] Present worth of the tax depreciation, V/kWpPW[HCPVOM (N)] Present worth of operation and maintenance

cost, V/kWprd Annual degradation rate of the efficiency of the system,

%rO&M Operation and maintenance cost of the system,V/kWpRtotal Thermal resistance of the modules, �C/Wm�2

T Income tax rate, %Tair Air temperature, �CTC Cell temperature, �C

WACC Weighted average cost of capital, %YF Final energy yield, kWh/kWp

Greek lettersd Temperature coefficient of maximum power, %/�Cε Air mass coefficient of maximum power, %4 Aerosol optical depth coefficient of maximum power, %hinverter Efficiency of the inverter, %

Subscripts and superscripts* Values at reference conditions550 550 nm (AOD)AC Alternating current electricityDC Direct current electricityDNI Direct Normal Irradianceinverter Inverter of the systemmodule Module of the systemnominal Nominal power (inverter)o Peak power (system)Sb Spectral direct normal irradianceTc Cell temperatureU Umbral value

AbbreviationsAERONET Aerosol Robotic NetworkAM Air MassAOD Aerosol Optical DepthBOS Balance of SystemCDM Clean Development MechanismCEAEMA Centro de Estudios Avanzados en Energía y Medio

AmbienteCSTC Concentrator Standard Test ConditionsEQE External Quantum EfficiencyHCPV High Concentrator PhotovoltaicsMJ Multi-junction (solar cell)PMMA Poly(methylmethacrylate) (Fresnel lens)POE Primary optical elementPV PhotovoltaicsSMARTS Simple Model of the Atmospherics Radiative Transfer

of SunshineSOE Secondary optical element

E.F. Fern�andez et al. / Energy 106 (2016) 790e801 791

renewable power source, to play an important role in the globalenergy market [17].

Despite such excellent potential, different barriers must still beeliminated to increase the confidence of investors, and thus topromote the market expansion of concentrator technology as areal alternative to traditional PV. Among all of them, the followingtwo main concerns can be cited [18]: on the one hand, the un-derstanding of the performance of HCPV systems when operatingin real world conditions is clearly lower than conventional PVsystems [19,20]; on the other hand, the cost of electricity andbankability of HCPV technology needs to be more thoroughlystudied [15,21].

The electrical modelling of HCPV devices is inherently differentandmore complex than conventional PV devices. As in other types ofPV technology, the energy output of HCPV is mainly determined bythe irradiance, temperature and spectrum [19]. However, forinstance, HCPV only collects the direct component of the irradiancedue to the use of optical devices and the thermodynamic connections

between concentration ratio and acceptance angle. Moreover, thisaspect has demonstrated to be, by far, the most relevant variable todetermine the performance of HCPV systems in the outdoors [20]. Atthe same time, the energy output ofMJ solar cells is strongly affectedby the spectral changes produced by the time-varying atmosphericparameters [22,23], due to the series connection of several subcellswith different energy gaps [24]. Therefore, the input spectrum alsoplays a crucial role in determining the energy output of HCPV mod-ules or systems [25,26]. The currentevoltage characteristics of MJsolar cells are also affected by temperature [27,28]. Under real-worldworking conditions, the operating cell temperature of HCPV systemsis also affected by the weather variables [29]. So, the performance ofHCPVmodules or outdoor systems is also going to be determined bytheir cell operating temperature [30]. However, the measurementand/or estimationof the cell temperature is a complex task due to thefact that the MJ cells mounted on HCPV modules are surrounded byseveral peripheral elements [31]. During recent years, the HCPVcommunity has devoted large efforts to develop tools tailored to the

E.F. Fern�andez et al. / Energy 106 (2016) 790e801792

specific features of HCPV technology [32,33], and has attempted toquantify the impact of the parameters described above on the per-formance of HCPV deviceswhen operating in a deployed installation[19,20,22,23,26,34e36]. Despite this, themajorityof these studies arelimited to the cell or module level, and there is a clear lack of studiesconcerning the analysis of the impact of the variables on the energyperformance of complete HCPV systems found in solar power plants[21,37e39].

At the same time, the cost of electricity is directly affected by theenergy output of HCPV systems under real conditions. Hence, dueto the lack of studies about this issue and because HCPV is a rela-tively new technology, there is also an important lack of studiesabout the cost of electricity of this emerging technology [40,41]. Areport analysing the LCOE (Levelised Cost of Electricity) of twosystems at two locations with different irradiation levels in Ger-many was presented by the Fraunhofer ISE [42]. An analysis of theLCOE of two systems at two locations with different irradiationlevels in USA was also presented by SolFocus Inc. [43]. A morecomplete analysis of the LCOE of a typical HCPV system covering allthe irradiation levels of Spain has recently been presented byTalavera et al. [15].

The goal of this paper is to relate the calculated electrical per-formance of a representative HCPV system deployed at several lo-cations to its corresponding LCOE. We analyse the performance andquantify the temperature and spectral losses in the AC energyoutput of a typical HCPV system at locations with disparate climateconditions. We then analyse the LCOE and quantify the tempera-ture and spectral impacts on it using economic scenarios relevant tothose locations. To our knowledge, these types of analyses have notpreviously been undertaken using this approach. For the estimationof the AC energy output, we use a typical HCPV system studiedexperimentally, together with a model previously introduced byFernandez et al. [38]. For the analysis of the cost of electricity, weshall use the LCOEmethod, since it is the most widely used methodto describe and compare both renewable and conventional en-ergies, as considered in the literature [15,16].

2. Concentrator system description

The HCPV system used in this study is located at the CEAEMA(Centre for Advanced Studies in Energy and Environment) of theUniversity of Jaen in southern Spain (N 37�2703600, W 03�2801200).The HCPV modules of the generator are made up of 25 triple-junction lattice-matched GaInP/GaInAs/Ge solar cells inter-connected in series, PMMA (poly(methylmethacrylate)) Fresnellenses as a POE (primary optical element) and refractive truncatedpyramids as the SOE (secondary optical elements). The moduleshave an optical efficiency of 85%, a geometric concentration of 550xand use passive cooling based on an aluminium plate to maintainthe temperature of concentrator solar cells within their optimaloperating range (50e80 �C). Fig. 1 (left) shows a schematic of asingle receiver of the modules, while Fig. 1 (right) shows the EQE(external quantum efficiency) of the MJ solar cells and trans-mittance of the PMMA Fresnel lenses. As can be seen in Fig. 2 (top),the generator is formed by three modules connected in series andthree branches in parallel. The modules are mounted on a two-axistracker designed for point focus concentrators. The trackingmechanism of the system, in open loop to the irradiance and closedloop with the position, allows a high accuracy to be reached e anerror lower than 0.1�. The array is connected to a high efficiencysingle-phase transformerless inverter with a high maximum DC/ACconversion of 96.6% and a Europeanweighted efficiency of 95% (seeFig. 2 bottom). The main electrical characteristics of the wholeHCPV system are shown in Table 1. This systemwas installed at theCEAEMA in 2011, and the main electrical parameters and

atmospheric variables were recorded daily every minute since thattime. Further details regarding the characteristics, performance andexperimental set-up used to carry out the evaluation of the systemcan be found in a previous work [38]. It is worth mentioning thatthe features of the modules [6], as well as the electrical configu-ration [44], represent the most wide-spread HCPV system nowa-days. Thus, the results of this work can be consideredrepresentative of the current HCPV technology.

3. Model for estimating the energy yield

The energy yield of the HCPV system is estimated using themodel previously introduced and experimentally validated byFernandez et al. [38]. That model has been summarized andadapted to the goals and purpose of the present study. Themodelling approaches and required input parameters for themodelare outlined below in order to help the reader understand thediscussion of the results shown in Sections 4 and 5.

The power output of an HCPV module is mainly determined bythe DNI (direct normal irradiance), cell temperature (Tc) andspectral distribution of the direct normal irradiance (Sb) as [46]:

Pmodule ¼ fDNI$fTc$fSb (1)

The impact of DNI on the power can be estimated as a linearfunction of DNI as [24,47]:

fDNI ¼P*

DNI*$DNI (2)

where the superscript “*” refers to the values at referenceconditions.

The influence of temperature can be evaluated with a lineartemperature coefficient (d) as [30,31]:

fTc ¼ 1� d$�TC � T*c

�(3)

Among the different methods to estimate the cell temperature[33], it is appropriate to predict the value of Tc from atmosphericparameters as [29]:

Tc ¼ Tair þ Rtotal$DNIheat (4)

where Tair the air temperature, Rtotal the thermal resistance of themodule and DNIheat the portion of DNI transformed into heatestimated as [48,49]:

DNIheat ¼ DNI � Pmodule

Amodule(5)

The AM (air mass) and aerosol optical depthe usually evaluatedat 550 nm e (AOD550) have proved to be the relevant parameters toquantify the impact of the input solar spectrum on the long-termperformance of HCPV devices [25,34]. This influence can be eval-uated with the following simple mathematical relationship [20,50]:

fSb ¼ ð1� ε$ðAM � AMUÞÞð1� 4$�AOD550 � AOD550;U

�(6)

where ε and d are the air mass and aerosol optical depth co-efficients, and AMU and AOD550,U are the umbral air mass andaerosol optical depth at which the power output begins to beinfluenced by AM and AOD550.

The DC power (PDC) delivered by the complete generator can beestimated considering its electrical configuration as:

Fig. 1. Left: Schematic diagram of an HCPV solar converter (generator) unit. Right: External quantum efficiency of the multi-junction solar cells and transmittance of the Fresnellenses of the HCPV modules [3,38].

0%

20%

40%

60%

80%

100%

0 0.2 0.4 0.6 0.8 1

η inv

erte

r

PDC/Pnominal

Fig. 2. Top: Electrical configuration of the HCPV system. Bottom: Efficiency of theinverter as a function of the input DC power [38].

Table 1Electrical characteristics of the HCPV system considered in this study under CSTC(concentrator standard test conditions) (1000 W/m2, 25 �C, AM1.5D) [45].

Parameter Value

Short-circuit current (A) 7.2Open-circuit voltage (V) 228Current at the maximum power point (A) 6.9Voltage at the maximum power point (V) 195Maximum power (kW) 1.35

E.F. Fern�andez et al. / Energy 106 (2016) 790e801 793

PDC ¼ NSNPPmoduleð1� LDCÞ (7)

where NS and NP are the number of modules in series and parallelrespectively, and LDC the additional DC losses of the HCPV generatorsuch as shadowing, mismatch, soiling, wiring or misalignment.

The evolution of the instantaneous efficiency of the inverter(hinverter) is mainly determined by the input DC power of the arrayand can be simulated as [51,52]:

hinverter ¼PACPDC

¼ 1� Linverter (8)

where PAC the AC power of the system and Linverter the losses in theDC/AC conversion of the inverter given by Ref. [53]:

Linverter ¼b0 þ b1pin þ b2p2in

pin(9)

where b0, b1 and b2 are specific coefficients of the inverter thatquantify the different DC/AC conversion power losses and pin is thenormalized inverted input power defined as:

pin ¼ PDCPnominal

(10)

where Pnominal is the nominal power of the inverter.With the comment above, the AC power output of the whole

HCPV system can be predicted as:

PAC ¼ PDCð1� LinverterÞð1� LACÞ (11)

where LAC is the additional losses produced in the AC part of thesystem such as the non-ideal performance of the inverter in the DC/AC conversion or downtime. Thus, the AC energy produced for adesired period of time T can be estimated as:

EAC ¼ZT

PACdt (12)

and the so-called final energy yield as:

Table 3Annual average values of the main atmospheric parameters (note that only valueswith DNI higher than 10 W/m2 have been used to estimate the means of the vari-ables) and simulated annual energy yield of the HCPV system for each siteconsidered.

Location DNI (W/m2) Tair (�C) AM AOD550 YF (kWh/kWp)

Solar Village 694 28.8 3.0 0.35 2072Alta Floresta 608 27.7 2.8 0.28 1829Frenchman Flat 704 18.4 3.3 0.07 2302Granada 623 19.1 3.3 0.15 1964Beijing 390 15.7 3.4 0.82 1003

E.F. Fern�andez et al. / Energy 106 (2016) 790e801794

YF ¼ EACPo

(13)

where Po is the peak power of the system.The procedure above takes into account all the main parameters

that affect the performance of an HCPV system by using simplemathematical relationships. Moreover, the model is entirely afunction of atmospheric variables that can be obtained or calcu-lated from atmospheric stations or databases in order to facilitateits application for long-term analysis at any desired site. Table 2shows the values of the coefficients of the model for the systemas previously presented by Fern�andez et al. [38]. It should bepointed out that some of the equations above have been refor-mulated when compared to those found in the reference [38], forinstance those for fDNI, fTc and fSb. The definition of these functions,in conjunctionwith the rest of equations of themodel shown in thissection, are the key to understanding the impact of the atmosphericparameters on the energy yield and LCOE of the system.

2600

4. Energy yield

The annual energy produced by the system described in Section2 has been estimated for the following 5 locations:

� Solar Village (Saudi Arabia): lat. N 24�5402500, long. E 46�2304900

� Alta Floresta (Brazil): lat. S 09�5201500, long. W 56�0601400

� Frenchman Flat (USA): lat. N 36�4803200, long. W 115�5600600

� Granada (Spain): lat. N 3700905000, long. W 03�3601800

� Beijing (China): lat. N 39�5803700, long. E 116�2205100

As previously considered by Fern�andez et al. [25,34]. These sitesrepresent worldwide regions over different continents with diverseclimate conditions. Hence, it is possible to evaluate the perfor-mance of the HCPV system in a wide range of working conditions.Table 3 gives the average values of the relevant weather parametersin order to show the atmospheric characteristics of each location.

The procedures to obtain the input parameters required by themodel presented in Section 3 are essentially the same as previouslydescribed and experimentally validated by the authors [3]. The inputparameters used in this work are simulated, while they were ob-tained fromanatmospheric station in thepreviouswork [38]TheDNIwas simulated using the SMARTS (Simple Model of the AtmosphericRadiative Transfer of Sunshine) [54] as discussed by Fern�andez et al.[25,34,46]. The air mass was estimated from the sun's position [55]while the daily time-series of aerosol optical depth at 550 nm wasgathered from the AERONET (Aerosol Robotic Network) database[56]. Finally, the time-series of the air temperature was modelledfrom the maximum, minimum and average values obtained from

Table 2Values of the coefficients obtained from outdoor monitored data for estimating theenergy yield of the HCPV system considered.

Coefficient Value Unit

Rtotal 0.059 �C/Wm�2

d 0.12 %/�Cε 4.11 %4 32 %AMU 2.06 DimensionlessAOD550,U 0.25 DimensionlessLDC 4.41 %b0 0.010 Dimensionlessb1 0.023 Dimensionlessb2 0.023 DimensionlessLAC 2.11 %

NASA (National Aeronautics and Space Administration) data sets [57]using the Erbsmodel [58,59]. Once the inputswere available, the finalenergy yield of the system was obtained integrating the AC powerevery 10min for thewhole year. AMATLAB™ programming codewasdeveloped and used to carry out all the calculations. These results areshowninTable3. In addition, inorder tohavea senseof theaccuracyofmethodology used in this work, appendix I has also been included tocompare the simulated and actual values of the annual energy outputof the HCPV system under study. From this it is concluded that theresulting methodology is of good quality, with an error in the esti-mation of the annual energy yield of the HCPV system of less than 3%.

4.1. Impact of cell temperature and spectrum

As described above, Table 3 shows the annual energy yield of theHCPV under study using the model described in Section 3 and theobtained input parameters. As expected, the highest values ofannual yield are produced for the locations with the highest DNIvalues. It was found that there exists a nearly linear relationshipbetween the Final Energy Yield, YF, and the average DNI at thevarious locations. However, the increase of the annual yield withthe annual average DNI is not perfectly linear (see Fig. 3). This canbe explained due to the different impact of cell temperature andspectrum at each location produced by their diverse weather con-ditions, as shown in Table 3. In order to clarify this issue, Table 4shows the annual average impact of direct normal irradiance, celltemperature and spectrum to better understand the impact of theweather variables listed.

Figs. 4 and 5 show the effect of cell temperature and spectrum,respectively, on the annual energy output at each site. The effect ofcell temperature has been estimated as:

DYF;Tc ¼�YFðDNIÞ � YFðDNI; TcÞ

YFðDNIÞ�$100 (14)

Solar Vilalge

Alta Floresta

Frenchman Flat

Granada

Beijing

800

1000

1200

1400

1600

1800

2000

2200

2400

350 400 450 500 550 600 650 700 750

Y F(k

Wh/

kWp)

Annual average DNI (W/m2)

Fig. 3. Final energy yield (YF) versus annual average DNI (direct normal irradiance) ateach location.

Table 4Annual average impact of direct normal irradiance, cell temperature and spectrumfor each site considered (note that only values with DNI higher than 10 W/m2 havebeen used to estimate the means of the variables).

Location fDNI (W) fTc fsb

Solar Village 104 0.96 0.90Alta Floresta 91 0.97 0.91Frenchman Flat 106 0.97 0.93Granada 93 0.98 0.93Beijing 58 0.99 0.75

0%

5%

10%

15%

20%

25%

Solar Village Alta Floresta Frenchman Flat Granada Beijing

∆YF,

Sb

Fig. 5. Annual energy spectral losses of the HCPV system for the five locationsconsidered. See Tables 3 and 4 to better understand the impact of spectrum on theoutput of the system at each location.

E.F. Fern�andez et al. / Energy 106 (2016) 790e801 795

while the effect of spectrum has been estimate as:

DYF;Sb ¼�YFðDNIÞ � YFðDNI; SbÞ

YFðDNIÞ�$100 (15)

As can be seen, the cell temperature AC energy losses range from4.6% to 1.8%. Solar Village presents the highest losses due to thehigh DNI and Tair values, while Beijing presents the lowest lossesdue to the lowDNI and Tair values. Regarding the spectral AC energylosses, they range from 5.0% to 2.4%, except in Beijing. This locationshows extreme spectral losses (21%) due to its extremely highAOD550 values. Frenchman Flat presents the lowest AOD550 valuesand similar AM values compared with Granada (see Table 3).However, the minimum spectral losses are produced at Granada.This can be explained, because this location has lower DNI values,and therefore the input DC power and efficiency of the invertervalues are slightly lower. Therefore, the contribution to the annualAC energy losses of AM and AOD550 are lower. This effect isexplained below in more detail.

It can also be concluded that cell temperature and spectral ACenergy losses are similar (except in the case of Beijing); the celltemperature losses range from 4.6% to 2.8% Solar Village and thespectral losses range from 5.0% to 2.4%. This conclusion seemscontrary to what is usually assumed, since the spectrum isconsidered to have a larger impact than cell temperature on theperformance of HCPV devices [3]. In order to explain this finding,Figs. 6e9 show an example of the instantaneous impact on theoutput of cell temperature, spectrum, direct normal irradiance, aswell as the efficiency of the inverter, for a summer andwinter day atthe Granada site. The same behaviour was found for the five loca-tions analysed, with instantaneous cell temperature losses between0.9 and 1, and instantaneous spectral losses between 0 and 1. Basedon these results, it may be stated that the spectral losses are higherthan the thermal losses, as widely considered. However, the

0%

1%

2%

3%

4%

5%

Solar Village Alta Floresta Frenchman Flat Granada Beijing

∆YF,

Tc

Fig. 4. Annual energy cell temperature losses of the HCPV system for the five locationsconsidered. See Tables 3 and 4 to better understand the impact of cell temperature onthe output of the system at each location.

maximum thermal loses are produced at midday and duringsummer (see Fig. 6), when the contribution to the annual final yieldis at maximum (see Fig. 8). In contrast, the maximum spectrallosses are produced at sunrise and sunset and during winter (seeFig. 7) when the contribution to the annual energy yield is at aminimum (see Fig. 8). Moreover, the efficiency of the inverter isminimum at sunset and sunrise, and is maximum at midday (seeFig. 9). This means that the efficiency of the inverter is at a mini-mum when the higher spectral losses are produced, and is at amaximum when the higher cell temperature losses are produced.This explains why the effect of cell temperature and spectrumproduce similar AC annual energy losses even though the instan-taneous impact of the spectrum produces higher losses within thesystem. The comment above also highlights the importance oftaking into account the coupling between the instantaneous effectof cell temperature and spectrum on the performance of the sys-tem, as well as the DC power of the generator and the efficiency ofthe inverter, to accurately estimate the temperature and spectrallosses in the energy output of a real grid-connected HCPV system.

5. Cost of energy

In the previous section, the annual energy yield and the impactof cell temperature and solar spectrum on the annual energyoutput for the HCPV system have been analysed. Their values in-fluence the cost of electricity of the HCPV system. So, in this section,the LCOE (Levelised Cost of Electricity) method has been applied toestimate the costs of energy of the system, and also to analyse the

0.94

0.96

0.98

1

1.02

1.04

4 6 8 10 12 14 16 18 20

f Tc

Sun hour (h)

July 15th

January 15th

Fig. 6. Instantaneous impact of cell temperature vs. sun hour, or solar time, for twoexample days at Granada.

0

0.2

0.4

0.6

0.8

1

1.2

4 6 8 10 12 14 16 18 20

f Sb

Sun hour (h)

July 15th

January 15th

Fig. 7. Instantaneous impact of spectrum vs. sun hour, or solar time, for two exampledays at Granada.

0

20

40

60

80

100

120

4 6 8 10 12 14 16 18 20

f DNI(

W)

Sun hour (h)

July 15th

January 15th

Fig. 8. Instantaneous impact of direct normal irradiance vs. sun hour, or solar time, fortwo example days at Granada.

0

0.2

0.4

0.6

0.8

1

1.2

4 6 8 10 12 14 16 18 20

η inverter

Sun hour (h)

July 15th

January 15th

Fig. 9. Instantaneous efficiency of the inverter vs. sun hour, or solar time, for twoexample days at Granada.

E.F. Fern�andez et al. / Energy 106 (2016) 790e801796

impact of cell temperature and input spectrum in these costs.Following the procedure introduced in previous works [15,60], thisparameter can be calculated as:

LCOE ¼ LCC

YFKdð1�KN

d Þ1�Kd

(16)

where the factor Kd is (1 � rd)/(1 þ d), where rd is the annualdegradation rate of the efficiency of the HCPV system, d is thenominal discount rate, N is the life cycle of the HCPV system andLCC is the normalized life cycle cost of the system. The annual final

yield (YF) is assumed to remain constant over the life cycle of thesystem. The values for LCC can be estimated as:

LCC ¼ HCPVI þ PW½HCPVOMðNÞ� � PW½DEPðNdÞ�$T (17)

This parameter mainly depends on the initial investment cost ofthe system (HCPVI), the present worth of the operation andmaintenance cost (PW[HCPVOM(N)]) and the present worth of thetax depreciation (PW[DEP(Nd)]) (Nd is the period of time overwhich an investment is amortized for tax purposes and T is theincome tax rate period.).

The initial investment cost may be financed through long-termdebt or/and by means of equity capital. In the case where it isfinanced through a loan (debt) and the remainder by means of anissue of stocks (equity capital), it may be expressed as:

HCPVI ¼"HCPVl$

ilð1� TÞ1� ð1þ ilð1� TÞÞ�Nl

$PVIFðNlÞ#

þhds$HCPVs$PVIFðNÞ þ HCPVs$qN

i(18)

The first term in brackets of Equation (18), related to the loanHCPVl, is an amount of the initial investment cost that is borrowedat an annual loan interest (il) to be paid back in Nl years. This cor-responds to the loan duration, where the impact of taxation onfinancing is taken into account (tax deduction applies to interestpayments of loan). In this term, the present value interest factor isdenoted as PVIF(Nl), and is related to the nominal discount rate (d)by PVIFðNlÞ ¼ q$ð1� qNl Þ=ð1� qÞ, where q ¼ 1/(1þ d). The secondterm of Equation (18) corresponds to the issue of stocks HCPVs, withan annual payback in the form of dividends (ds) that must be paid infull at the end of the life cycle of the system. It is worth mentioningthat Equation (18) is only valid if the selected value of d is equal tothe WACC (weighted average cost of capital) of the investment (thecost of the chosen financing). As shown above, d is involved in thecalculation of the present value interest factors.

The present worth of the operation and maintenance cost dur-ing the life cycle of the system can be written as:

PW½HCPVOMðNÞ� ¼0@HCPVAOMð1� TÞ$

KPV$�1� KN

PV

�1� KPV

1A (19)

where HCPVAOM is the annual operation and maintenance cost,assumed constant over the life cycle of the system, KPV is a factorthat considers the annual escalation rate of the operation andmaintenance cost of the system (rO&M), so KPV ¼ (1þ rO&M)/(1þ d).

Finally, the present worth of the tax depreciation that corre-sponds to the impact of taxation, is taken into account by assumingthat the tax depreciation is deductible. In this case, the tax depre-ciation is assumed linear over the period time for which the HCPVsystem investment is amortized for tax purposes. Therefore, thisterm is expressed, bearing in mind that it represents a saving in thecash outflow, as:

PW½DEPðNdÞ� ¼ DEPy$PVIFðNdÞ (20)

where DEPy is the annual tax depreciation of the HCPV system. Theconsideration of a linear tax depreciation implies thatDEPy ¼ HCPVI/Nd.

It should be highlighted that the weighted average cost of cap-ital is the cost that must be paid by the owner or investor of theproject for the use of capital sources in order to finance the in-vestment. Organizations typically use the value of the organiza-tion's weighted average cost of capital as nominal discount rate

0

5

10

15

20

25

30

900 1200 1500 1800 2100

LCO

E (c

€/kW

h)

Ini al investment cost (€/kWp)

Solar Village

Alta Floresta

Frechman Flat

Granada

Beijing

Fig. 10. LCOE (Levelised Cost of Electricity) versus initial investment cost (HCPVI) at

E.F. Fern�andez et al. / Energy 106 (2016) 790e801 797

[61]. Following this strategy, in this work it is assumed that d isequal to WACC for the estimation of LCOE.

Table 5 lists the values of the parameters involved in the esti-mation of the LCOE using Equation (16) for the five locationsconsidered. The reasoning that leads to the selection of the pa-rameters shown in this table is described below. It is important tomention that the procedure above has been formulated in terms ofHCPV technology. However, the same methodology can be appliedto estimate the LCOE of any type of solar energy or photovoltaicsystem.

The annual energy yield as a function of the atmospheric vari-ables was presented in the previous section for the five sitesconsidered. This is affected by the intrinsic degradation that themodules suffer throughout their lifetime. Therefore, the annualyield of the HCPV system is assumed to decrease every year. In thiswork, an annual degradation rate of 0.5% has been considered[62,63]. Finally, the time horizon of this cost analysis has been set to30 years as previously considered by Talavera et al. [15].

The initial investment cost of the HCPV system is derived fromthe learning curve for HCPV technology. This curve describes thecost reduction as a function of the accumulated experience in themanufacturing and in the use of a particular technology. Previousstudies [15,16] analysed the cost of the initial investment during theperiod 2013e2020. As previously described, this initial investmentcost may be financed by means of debt or/and equity capital. In thisstudy, taking into account that commercial banks are generallyaccepting higher leverage in stable economies with secure propertyrights [64], it has been assumed that 70% of this amount is bor-rowed as a loan, while the remaining investment amount (30%) iscontributed from equity capital, for the cases of Spain and the USA.For the remaining countries, the share of equity and debt for theproject is assumed to be 50%, as recommended by the CDM (CleanDevelopment Mechanism) Executive Board [65]. Regarding theloan, this amount is borrowed at an annual interest that is specificfor each country. An average value for the period 2009e2013 hasbeen considered for each specific location [66] and the loan term of20 years has been considered for all of them. With regard to theequity capital, the annual payment of dividend is assumed to bespecific for each country. As in the previous case, an average valuefor the period 1900e2000 has been considered for each location[67] and they will be payable completely at the end of the life of thePV system.

The data for the inflation rate has been obtained from the av-erages from historical data for each country in the period2009e2013 [68e70]. The influence of the tax rate for the organi-zation or taxpayer and its variations depending on each country'sregulations have also been considered. In this analysis, the value of

Table 5Values of the factors assumed for the calculation of LCOE on HCPV systems for the five locaand electricity yields are all normalized per unit of power (kWp).

Factors Location

Solar village Alta floresta French

YF 2072 1829 2302HCPVI 900e2100HCPVAOM 2rd 0.5rO&M Equal to iT 20 34 40i 4.5 5.6 1.6d 11.2 21.7 5.5il 6.9 38.5 3.3Nl 20ds 15.3 18.1 10N 30

the income tax rate is assumed specific for each country [71e73].The method used in the tax depreciation is based on a generalmethod, using amaximum linear coefficient of 5%, with a tax life fordepreciation of 20 years for all countries [74,75]. The nominaldiscount rate, which is considered equal to the weighted averagecapital of cost, is not constant and will vary depending on thecapital resources chosen to finance the initial investment.

The normalised annual operation and maintenance costs of theHCPV system are considered as an annual fixed percentage (2%) ofthe normalized initial investment cost of the HCPV system [76].Additionally, these costs will also be influenced by an annualescalation rate, which was set equal to the value of the annualinflation rate for each country, so rO&M ¼ i.

5.1. Impact of cell temperature and spectrum

Fig.10 shows the Levelised Cost of Electricity of the HCPV systemunder study using the procedure described above. In addition,Table 6 shows some of the main economic parameters involved inthe estimation of the LCOE for the five locations considered. InFig.10, the LCOE values at each location are plotted versus the initialinvestment cost, since it has been demonstrated to have the largestimpact, together with the annual energy yield. Other factors such asnominal discount rate, operation and maintenance cost and the lifecycle of the HCPV system have been shown to have a moderateeffect on the LCOE, while tax rate and power degradation rate havebeen shown to have an almost negligible influence [15,77]. As canbe seen, the locations with the higher annual energy yield tend tohave the lower LCOE values. In particular, the lowest LCOE

tions. It should be noted that the values presented here referring to costs, incentives

Units

man Flat Granada Beijing

1964 1003 kWh/kWpV/kWp%%/year%/year

30 25 %1.7 2.7 %5.1 9.8 %4.3 5.9 %

years7.6 13.4 %

years

each location.

Table 6Example of the main economic parameters involved in the estimation of the Levelised Cost of Electricity for the five locations under study. An initial investment cost of1800 cV/kWp has been assumed.

Location LCC (V/kWp) PW[HCPVOM(N)] (V/kWp) PW[DEP(Nd)] (V/kWp)

Solar Village 2039 381 141Alta Floresta 1816 154 138Frenchman Flat 1751 381 430Granada 1941 477 335Beijing 1924 336 194

Solar Village

Alta Floresta

Frenchman FlatGranada

Beijing

0

5

10

15

20

25

30

900 1100 1300 1500 1700 1900 2100 2300

LCO

E (c

€/kW

h)

YF (kWh/kWp)

Fig. 11. LCOE (Levelised Cost of Electricity) versus annual energy yield (YF) at eachlocation. An initial investment cost of 1800 cV/kWp has been assumed.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Solar Village Alta Floresta Frechman Flat Granada Beijing

ΔLCO

E Sb

(c€/

kWh)

Fig. 13. Impact of spectrum on the LCOE (Levelised Cost of Electricity) of the HCPVsystem for the five locations considered. An initial investment cost of 1800 cV/kWp hasbeen assumed.

E.F. Fern�andez et al. / Energy 106 (2016) 790e801798

corresponds to Frenchman Flat, with values ranging from 2.7 cV/kWh to 6.6 cV/kWh, while the highest LCOE corresponds to Beijingwith values ranging from 10.6 cV/kWh to 24.7 cV/kWh. It should bealso highlighted that a higher annual energy yield does not imply alower value of LCOE, as can be clearly seen in Alta Floresta. Thislocation has an annual energy yield of 1829 kWh/KWp, higher thanBeijing (1003 kWh/KWp) but its LCOE is slightly higher. This ismainly due to its high value of nominal discount rate (22.7%)compared to the values of this parameter for the rest of the loca-tions. Therefore, it is important to note that the sites with thehighest final yield do not necessarily present the lowest values ofLCOE, as clearly shown in Fig. 11. These results highlight theimportance of considering the specific economic parameters thatare involved in the estimation of the LCOE for the location understudy.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Solar Village Alta Floresta Frechman Flat Granada Beijing

ΔLCO

E Tc

(c€/

kWh)

Fig. 12. Impact of cell temperature on the LOCE (Levelised Cost of Electricity) of theHCPV system for the five locations considered. An initial investment cost of 1800 cV/kWp has been assumed.

Figs.12 and 13 show the effect of cell temperature and spectrum,respectively, on the Levelised Cost of Electricity at each siteconsidering an initial investment cost of 1800 cV/kWp (conserva-tive scenario [15]). The effect of cell temperature has been esti-mated as:

DLCOETc ¼ LCOEðDNI; TcÞ � LCOEðDNIÞ (21)

while the effect of spectrum has been estimated as:

DLCOESb ¼ LCOEðDNI; SbÞ � LCOEðDNIÞ (22)

As can be seen, the impact of cell temperature on the LCOEranges from 0.17 cV/kWh (Frenchman Flat) to 0.80 cV/kWh (AltaFloresta). Regarding the impact of spectrum, the LCOE ranges rangefrom 0.16 cV/kWh (Frenchman Flat and Granada) to 0.94 cV/kWh(Alta Floresta), without considering Beijing. The high AC energyspectral losses produced at this location lead to an extreme increasein its LCOE (4.37 cV/kWh). This demonstrates the importance ofselecting locations with adequate weather characteristics to avoidsignificant increases in the cost of electricity produced by thespectral effects. It is worthmentioning that higher temperature andspectral AC energy losses do not necessarily produce a higher in-crease on the LCOE. This can be clearly observed comparing SolarVillage and Alta Floresta (see Figs. 4 and 5). Solar Village has highercell temperature and spectral losses than Alta Floresta, but the in-crease on the LCOE produced by these effects is lower. This can beexplained by taking into account that the higher the LCOE, thehigher the impact of temperature and spectral AC energy losses.Finally, the outcome of this work clearly indicates that the effect ofcell temperature and spectrum on the energy yield needs to beconsidered in the analysis of the costs of the electrical generation ofan HCPV system, since it could drive significant variations in theestimation of the LCOE.

Table AI.1Simulated and experimental values of the final energy yield (YF) and PR (perfor-mance ratio) of the HCPV system under study at the Granada AERONET site. Theexperimental data for the validation of the methodology used in this work haspreviously been presented by Fern�andez et al. [38] (note that cloudy days have beenremoved in the estimation of the energy yield at each location by using the dataprovided by MODIS Daily Level-3 data source as previously considered [78,79]).

Parameter Simulated Experimental

YF (kWh/kWp) 1964 1912PR (%) 84 86

E.F. Fern�andez et al. / Energy 106 (2016) 790e801 799

6. Conclusions

We have utilized the connections between the performance andeconomics of HCPV (High Concentrator Photovoltaic) technology toexplore the cost of electricity of complete HCPV systems deployedin real-world settings. A typical state-of-the art systemwas studiedexperimentally at the Centre for Advanced Studies in Energy andEnvironment (CEAEMA) of the University of Jaen in Spain. Usingexperimental results for this system, its annual energy productionhas been estimated for deployment at five representative locationswith diverse climatic conditions. The model used widely availabledata from meteorological and satellite databases.

The cell temperature and spectral AC energy losses were foundto range, respectively, from 1.8% to 4.6% and from 5.0% to 2.4%(except in the case of a highly polluted location). It can beconcluded that the cell temperature and spectral AC energy lossesare similar for the selected locations, contrary to what is oftenassumed. Analysis of the cell temperature and spectral AC energylosses led to the conclusion that it is the interrelationship betweeninstantaneous cell temperature and input solar spectrum that af-fects the overall performance of the system.

Regarding the LCOE (Levelised Cost of Electricity), it was found,as expected, that locations with the higher annual energy yieldtend to have the lower LCOE values. Sites with the highest finalyield do not necessarily present the lowest values of LCOE, becauseof the importance of the specific economic parameters that areinvolved in the calculation of the LCOE, and the impact of celltemperature and spectrum. Values ranging from 2.7 cV/kWh to24.7 cV/kWh were obtained.

It may be concluded that at sunny locations with annual averageDNI over 650 W/m2, installations are expected to produce energyyields above 2000 kWh/kWp. Moreover, for a conservative scenariowith an initial investment cost of under 1800 cV/kWp, the LCOE forstate-of-the-art HCPV solar power plants can be below 10 cV/kWhfor many locations in the world. This highlights the ability of HCPVtechnology to produce large amounts of energy at competitiveprices. Thus, this study supports the idea that HCPV can be a viablepower source at locations with a favourable solar resource andeconomic scenario. This work can therefore serve as a guide forfurther technical development of HCPV technologies, as well as forpolicy makers seeking to create economic conditions for their rapiddeployment. Our analysis can be extended to include multiplemodules and trackers in an HCPV array for a full solar power plant.This would allow for an estimation of the economics as a function ofdeployment scale.

Acknowledgements

This work is part of the project ENE2013-45242-R supported bythe Spanish Economy Ministry and the European Regional Devel-opment Fund/Fondo Europeo de Desarrollo Regional (ERDF/FEDER). Eduardo F. Fern�andez is supported by the Spanish Ministryof Economy and Competitiveness through the Juan de la Cierva2013 fellowship.

Appendix I

As described, themathematical model, as well as the proceduresused to simulate the required input parameters, have been previ-ously validated to estimate the electrical output of HCPV devices[38]. Despite this, a comparison between the simulated andexperimental data for the HCPV system considered at the GranadaAERONET site is presented in this appendix. It is important tomention that the system is located close to the Granada ground-based photometer of the AERONET data source. From among all

the experimental years available, the data recoded during 2011 hasbeen selected for the following two (main) reasons:

1. This year has the lowest (<2.5%) annual irradiation differencecompared with the values obtained from statistical analysis orsatellite measurements (Photovoltaic Geographical InformationSystem, PVGIS and Solar Radiation Data, SODA).

2. This year has not been used to fit the coefficients of the modelshown in Table 2.

This year was also selected in a prior work [38] to validate themathematical model described in Section 3 for the same two rea-sons as mentioned above. However, in that prior work, the inputparameters to estimate the annual energy yield of the systemweregathered from an atmospheric station, while in this case they aresimulated. Despite this, the methodology used in this work shows ahigh quality. There is a difference lower than 3% in the estimation ofthe annual energy yield and of around 2.5% in the estimation of thePR (performance ratio), as shown in Table AI.1.

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