Applied Energy 88 (2011) 5131–5142

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Applied Energy

journal homepage: www.elsevier .com/locate /apenergy

An approach to evaluate the energy advantage of two axes solar tracking systemsin Spain

Fernando Cruz-Peragón a, Pedro J. Casanova-Peláez b, Francisco A. Díaz a, Rafael López-García a,José M. Palomar a,⇑a Dep. of Mechanical and Mining Engineering, Escuela Politécnica Superior de Jaén, University of Jaén, Campus Las Lagunillas s/n, 23071 Jaén, Spainb Dep. of Electronic Engineering and Automatics, Escuela Politécnica Superior de Jaén, University of Jaén, Campus Las Lagunillas s/n, 23071 Jaén, Spain

a r t i c l e i n f o

Article history:Received 21 January 2011Received in revised form 8 July 2011Accepted 11 July 2011Available online 20 August 2011

Keywords:Solar trackingPhotovoltaic solar systemProfitabilitySpain

0306-2619/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.apenergy.2011.07.018

⇑ Corresponding author. Tel.: +34 953212368; fax:E-mail address: jpalomar@ujaen.es (J.M. Palomar).

a b s t r a c t

The present work shows an alterative method for determining the tracking energy advantage, defined asthe additional electrical energy produced by two axes tracking systems respect to fixed devices, in orderto analyze the economical profitability in Spain. For this purpose, 52 main cities of this country have beenanalyzed. The proposed methodology starts from irradiation data, combining diffuse models and daily–hourly relations. Different types of losses have been evaluated, and the electrical behavior of the systemshas been incorporated. Final annual energetic results demonstrate that two axes devices show a relevantenergy advantage (higher than 20%) for most of the national territory.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

During the last few years, photovoltaic solar systems havebecome one of the most popular renewable energy sources inSpain. Nevertheless, the high cost of these installations in relationto the generated electricity constitutes one of the main drawbacksof this technology. In this sense, one and two axes solar trackingsystems seems to be an attractive alternative compared to thosefixed systems since they make it possible to maximize the captureof solar energy [1–3], especially in Spain [4,5]. Previous analysesdemonstrate that considerable gain in the generated electricitycan be reached using this technology, in particular for two axessystems [6–11]. However, it is required to evaluate if additionaleconomic costs still guarantee the profitability of these systems.

The best way to evaluate solar systems is to use information ofsolar irradiance, measured throughout the time. Nevertheless, thisis only possible after a systematic and rigorous instantaneous mea-surement of the radiation at the location of study. In practice, thebig quantity of data makes its use impracticable, making it neces-sary to reduce the information volume. For this purpose, pyranom-eters or satellite images are commonly used to catch the globalirradiance on a horizontal surface (in the same way, it is possibleto measure the direct and diffuse components over horizontal sur-face in a certain place). Most available information of differentplaces in earth (for example, main Spanish cities), corresponds to

ll rights reserved.

+34 953212870.

monthly average daily radiation on horizontal surface HG (kJ/m2).This information has been obtained by integrating measurementsof global irradiance distribution over horizontal surface IG (kW/m2). In this sense, there exists different global irradiation databasesavailable, such as METEONORM (http://www.meteonorm.com)[12], European Atlas of solar irradiation [13], PVGIS (http://re.jrc.e-c.europa.eu/pvgis/) [14], or CENSOLAR [15]. However, some mis-matches between different sources are observed [16].

On the other hand, one major advantage of flat plate solar sys-tems (both thermal and photovoltaic) is the use of both compo-nents of the solar radiation (beam and diffuse). These componentscan be estimated from irradiance data and corresponding models[17].

The purpose of the current work is to quantify the additionalsolar gain of tracking system respect to fixed devices to demon-strate their economical viability in Spain. For this reason differentissues have been considered, such us irradiation data and modelsproviding instantaneous irradiances over horizontal, tilted andtracking surfaces, motion limits, shadows influence and efficiencyof the generation system (cells, inverters, etc.). Instantaneous re-sults have been integrated over the year, obtaining annual results.Different issues have been evaluated for one location (Jaén) over ayear for instantaneous data, validating the proposed procedure forthis location. In addition, some associated parameters have beenestimated to adopt a simplified methodology in all the territory.Thus, the analysis has been extended to most of the cities in Spain,and a practical range of gains along this national territory has beenobtained.

5132 F. Cruz-Peragón et al. / Applied Energy 88 (2011) 5131–5142

2. Materials and methods

2.1. 1- Experimental devices for measuring instantaneous data andmodels

To evaluate the robustness of the proposed method, some taskshave been carried out at a location corresponding to the city of Jaén(latitude: 37.5�N; longitude: 3.47�W, altitude: 570 m.). Data of irra-diance over horizontal surface for this location have been collectedand published by the investigation group MatRas (http://www.ujaen.es/dep/fisica/estacion3.htm) [18]. They employed a Kipp &Zonen CMP11 pyranometer placed over the roof of a building.

Several instantaneous diffuse models have been evaluated (thatwill be discussed later) in order to predict the irradiances over bothtilted and tracking surfaces, using instantaneous irradiance mea-surements over horizontal surface.

To valuate the final results and establish the efficiency losses forthe whole generation system, electrical generation data for a littletracking system has been used. This device incorporates a littleamorphous photovoltaic cell, storing data along a year. The systemtakes into consideration the knowledge associated to mechanical,electrical and control tasks, such as other devices [19,20]. Althoughthere are experiences to align the device with sensors [21], herethe alignment has been done following the sun polar coordinatesat each time.

2.2. General procedure

Monthly average daily radiation over horizontal surface HG data[15] have been used as a starting point for this analysis. From thesedata, global irradiation over tilted surface can be obtained usingcertain diffuse models and associated relations:

(a) One of the most widely known and used isotropic model inthis work is the Liu and Jordan model [22], which assumesan uniform distribution of the diffuse radiation on the celes-tial hemisphere. This model underestimates the value of thediffuse radiation in clear skies, while it works very well forcovered days. In any case, the whole estimated irradiation isbelow the real value within a 3% [23,24].

(b) On the other hand, anisotropic models consider a bigger dif-fuse component in the circumsolar zone that comes directlyfrom the direction of the solar beams. [25–30]. From theanalysis of different methodologies, it has been observedthat the Reindl anisotropic model [26] is quite useful inlatitudes similar to those into the Spanish territory [24].

In any case, the use of both diffuse models makes it possible toestablish the upper and lower limits in which results can be reli-able. They will define the most favorable scenario (with maximumannual radiation values) and the most unfavorable one (with min-imum annual radiation values).

Fig. 1 summarizes the general adopted methodology.The first step (see Fig. 1) consists of determining both the max-

imum annual solar exposure FS (kWh m�2 year�1) and their corre-sponding surface tilt bop, using both isotropic and anisotropicdiffuse models. The long-term established procedure that appearsin the literature for determining the incoming solar energy in atilted surface has been carried out [26,31–33]. Different inclina-tions have been also considered (with surface azimuth angle cop

equal to zero, that is, oriented to the south), and the correspondingannual irradiation have been evaluated. The maximum valuedetermines the optimum surface slope bop at each place for theconsidered diffuse model. Subsequently, an average generationefficiency for fixed system geF is applied to FS, in order to obtainthe energetic response of the system F (kWh m�2 year�1). This va-

lue constitutes the reference datum to evaluate the trackingimprovements.

On the other hand, the yearly tracking response J (kWh m�2

year�1) is analyzed for the tracking device. It is obtained by integrat-ing instantaneous daily results. The ratio between J and F constitutesthe fractional gain in the energy production of a tracking system inrelation to an optimum fixed one. In a percentage basis, the trackingadvantage DJ (%) is defined as follows:

DJð%Þ ¼ 100 � J � FF

� �ð1:aÞ

Additionally, a maximum tracking advantage DJ0 can be defined in asimilar way to Eq. (1.a) if no restrictions in the yearly response ofthe system are considered J0 (kWh/year). It will be discussed next.

DJ0ð%Þ ¼ 100 � J0 � FF

� �ð1:bÞ

2.3. Tracking analysis

Fig. 2 summarizes de procedure for the daily instantaneousevaluation of a tracking system. All the parameters have been dis-tributed into different vectors (with length N). In order to establishdata along the day of study, all of them have been related to a timevector T corresponding to time steps of 1 min.

Initially, the global irradiance GG0 (kW/m2) and their compo-nents (beam GB0, diffusive GD0 and reflected GR0) over the surfaceof a tracking system surface are evaluated considering that the an-gle of incidence h of the beam component is always equal to 0� dur-ing the solar time (that is, assuring maximum beam irradiance).

For this purpose, the hourly–daily relations have been considered[34] by determining the hourly irradiation Hj

G (kJ m�2 h�1) from dai-ly solar exposures over horizontal surface HG (kJ m�2 day�1), foreach hour j, such as Eq. (2) shows:

HjG ¼ rj

GHG; rjG ¼

p24ðaþ b cos xjÞ

cos xj � cos xs

sin xs �xs cos xj

a ¼ 0:409þ 0:5016 sinðxs � p=3Þ;b ¼ 0:6609� 0:4767 sinðxs � p=3Þ

ð2Þ

In this equation, xj corresponds to the sun hour angle and the sun-set hour angle is denoted by xs. The same expression has also beenused to determine an instantaneous distribution of the global irra-diance along the day on a horizontal surface IG (kW/m2). Results in-ferred by integrating the obtained curve agree with HG.

Subsequently, Erbs et al. correlation [35] makes it possible tofind the diffuse component of irradiation ID, using the clearness in-dex kt at each time. The beam component IB is then obtained fromthe difference between IG and ID:

ID=IG ¼

1:0� 0:09kt for kt 6 0:220:9511� 0:1604kt þ 4:388k2

t � 16:638k3t

þ12:336k4t for 0:22 < kt 6 0:8

0:165 for kt > 0:8

8>>><>>>:

IG ¼ ID þ IB

ð3Þ

In addition, the two previous diffuse models (both isotropic andanisotropic ones) have been applied to these instantaneous data.They determine the incoming irradiance on the tracked surfaceGG0 (with instantaneous tilt angle b and surface azimuth angle c)[20]:

GG0 ¼ GB0 þ GD0 þ GR0 ð4Þ

in which each component is denoted as follows:

GB0 ¼ IB � RB; with RB ¼cos hsinaS

ð5Þ

LOCATION INITIAL DATA

ANDMODELS

EXPOSURE AND GENERATION

DAILY DATA OVER HORIZONTAL

SURFACE

IRRADIATIONHG, HB, HD (kJ/m2)

IRRADIANCEIG, IB, ID (kW/m2)

GEOMETRIC CONSIDERATIONS

AND TRACKER LIMITS

RESULTS(Data integration)

OPTIMUM FIXED SYSTEM, F

TRACKING RESPONSES, J

ANNUAL GENERATION

COMPARISON

INSTANTANEOUS ANALYSIS (Fig. 2)

LONG-TERM EXPRESSIONS

Fig. 1. General analysis procedure developed for a particular location.

INSTANTANEOUS ANALYSIS FOR DAY ‘n’

τ = T (j)

TSTOP (j) = 0?

γ (j) = γ (j-1) ; β (j) = β (j-1)

γ (j) , β (j)

MOTION LIMITS

INCIDENCE ANGLE DETERMINATION, θ

COMPONENTS ONTO TILTED SURFACE

SHADES EVALUATION

END

θ (j)GB0(j), GD0(j) , GG0(j)

GG(j)

j = N?

YES

j = j+1NO

j = 1INSTANTANEOUS SOLAR DAILY DATA

Vectors with length ‘N’:IB(τ), ID(τ), IG(τ), αS(τ),

γS(τ), T, TSTOP

IB(j), ID(j) , IG(j)

αS(j), γS(j)

TSTOP (j) YES

NO

ELECTRICAL BEHAVIOUR

W(j)

PLATES EFFICIENCY, AUXILIARIES

DAILY DATA INTEGRATION

Jday(n)

Fig. 2. General procedure of instantaneous evaluation of solar irradiation over a tracking surface.

F. Cruz-Peragón et al. / Applied Energy 88 (2011) 5131–5142 5133

EAST WEST

γ

NORTH

β

αS

γS

EAST WEST

NORTH

γ (+)

γL (-) γL (+)

βL

Fig. 3. Two axes tracking system scheme.

5134 F. Cruz-Peragón et al. / Applied Energy 88 (2011) 5131–5142

GR0 ¼ IG � FR; with FR ¼ r � 1� cos b2

ð6Þ

GD0 ¼ ID � FD; ð7Þ

FD;Isotropic ¼1þ cos b

2ð8:aÞ

FD;Anisotropic ¼ ðkb � RB þ ð1� kb � FD;isotropicÞÞ � ð1þ f � sinð0:5 � bÞ3Þ

with f ¼

ffiffiffiffiIB

IG

s; kb ¼

IB

I0

ð8:bÞ

where the location latitude u, the angle of incident radiation h, sur-face azimuth angle c, declination d and extraterrestrial irradiance I0

(kW/m2) are additional variables to be considered in the analysis.Their instantaneous values can be easily obtained using expressionsavailable in the literature [32]:

cos h ¼ sin d sin / cos b� sin d cos / sin b cos c

þ cos d cos / cos b cos x

þ cos d sin / sin b cos c cos xþ cos d sin b sin c sinx ð9:aÞ

c ¼ signðxÞ � cos�1 cos hZ sinu� sin dsin hZ cos u

� ��������� ð9:bÞ

d ¼ 23;45 sin 2p � 284þ n365

� �ð9:cÞ

I0 ¼ ISN � cos h ð9:dÞ

The solar zenith angle is denoted as hZ. In addition, the reflectancecoefficient r (dimensionless) is required to estimate the reflectedirradiance. It will take a value of 0.2. Finally, the solar constant ISN

can vary during the year, taking values between 1.31 and1.39 kW/m2 [32].

These data correspond to values with no restrictions associatedto the device. However, several restrictions sources may appear:

2.3.1. Motion limitsThe maximum exposure considers that the surface azimuth an-

gle of the system c is always equal to the solar azimuth cS, as wellas the surface slope b (deg) is equal to 90� � aS (deg). Where aS

(deg) is the solar altitude angle at each time. However, themechanical configuration of the system does not make it possibleto reach these limits [36]. In this case, according to the maximumsurface azimuth angle |cL| and maximum tilt angle bL of the system,there exist some tracking positions (near sunset and sunrise) inwhich the angle of incidence is different from 0�. It occurs when|cS(s)| > |cL| and aS(s) < 90� � bL. As an example, Fig. 3 shows ascheme of a previous designed mechanical system [12].

2.3.2. Time steps motionAn ideal solar tracking process consists on following the solar

motion instantaneously along the time. Nevertheless, mechanicalconfigurations, control devices and actuators make the systemmoving by steps, with no motion time periods. In this case, it isnecessary to determine the energy losses for different time stepsaccording to the daily sun path. In this sense, a time stop vectorTSTOP has been included into the analysis. It contains only zerosand ones values. The values j into this vector will be equal to 0when the system must stay blocked and 1 if it is moving. The dis-tribution of values equal to 1 into this vector depends on the timeintervals in which the system must be blocked.

2.3.3. Shadow lossesThe geometric configuration of the solar field implies that some

plates over one individual tracker receive shadows from others ateach moment. Thus, annual integrated global losses between 2%and 6% appear [37]. Geometric considerations must be consideredin the instantaneous analysis (described in Fig. 3), in order toestablish an initial evaluation of shadow losses [38–40]. The high-est influence in partial shadowing is always produced by the near-est 3 sets [37], such as Fig. 4 shows. Distances X, Y and Z, andsurface width L and height H will be the main geometric character-istics associated to this study. A simplified method to analyze theshadow problem is to evaluate a typical squared distribution(X = Y), in horizontal position (Z = 0) and observe what happensthroughout the solar day, modifying separation distances betweentrackers, considering unitary height H = 1 [41].

It must be considered that shades only affects the reception ofthe beam constituent of radiation in the related surface. Neverthe-less, the diffuse part is always captured from the sky, although in aless quantity. In relation to the reflected constituent, this can beconsidered as negligible, due to the obstacles surrounding the sys-tem in study.

2.3.4. Plates efficiencyIt is well known that power generation in a photovoltaic panel

drops as the inner temperature increases. Therefore, it is necessaryto consider the losses of the system and compare them with opti-mized fixed systems (with maximum annual energetic gain). Thisanalysis starts from a thermal study of the system. It considers heattransfer parameters [42,43] next to current–voltage correlations ofthe photovoltaic panel [44–46]. From the plate model equations,the plate temperature can be calculated at each moment. Never-theless, the great quantity of cells typologies, and the panel charac-teristics and configurations, make it difficult to perform a genericstudy. In this case, several aspects must be remarked:

(d.1) Taking as a reference a typical efficiency for 25 �C, everyincreased degree implies an efficiency fall between 0.4%and 0.5% (between 1–2 %, in other cases). [47,48].

X

Y

TRACKER ON STUDY

Azimuth angles

(a)

(c)

(b)

SUN

South

East

L

Projected shadows

γγs

West

Z

TILT ANGLE, θ

SOLAR ANGLE, h

H

TRACKER ON STUDY

Projected shadow

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

SURFACE WIDTH L, (m)

HEI

GH

T H

, (m

)

Fig. 4. Geometric considerations for shadow losses determination at one point of the tracker path: (a) Ground view; (b) front view; (c) shadow over surface.

F. Cruz-Peragón et al. / Applied Energy 88 (2011) 5131–5142 5135

(d.2) In a fixed system (south positioned) a high value of theincident angle (corresponding to a low value in the beamcomponent), considerably increases the efficiency. Differ-ences can reach up to 25% during the sunset and the sun-rise [43]. Nevertheless, these differences disappearquickly, as the beam component increases.

(d.3) In addition, for an incident angle close to 0�, the cell tem-perature increases considerably (up to 70� in conven-tional cells) while the efficiency decreases. Nevertheless,the relative differences are small (up to 10%) [43].

Thus, the minimum efficiency is reached for high temperaturesand high beam component. It is only 10% lower when considering atypical conditions scenario. In a fixed system, this condition isreached around the solar midday, and a similar situation (withhigher incident angle and less beam component of radiation) is re-peated during most of the solar time. Thus, the difference betweenfixed and tracking systems will be always less than 10%. In anycase, the distribution of the efficiency along the day has been ob-tained from the reviewed literature, following the tendencies thatappear in Fig. 5.

The first source (time step motion of item a) must be incorpo-rated to the GG0 determination. Thus, the second and third sources,that is, those indicated in items (b and c), imply that the globalirradiance GG can be achieved and always will be less than GG0.Subsequently, the effectiveness of the system ge (see item d)

defines the instantaneous electrical production W. These instanta-neous data must be integrated, providing a value of the energy re-sponse from the device Jday(n) (kWh m�2 day�1) for the day n instudy, as Fig. 2 shows. The addition of all these final daily valuealong the 365 days of the year provides the annual energy responseof the tracked surface J (kWh m�2 year�1).

The method is validated for a particular location in the next sec-tion. From this analysis it will be possible to obtain several param-eters that can be used in a simplified methodology that can beextended for all the cities analyzed in the current work.

3. Detailed local results for one location

The global procedure previously described will be detailed forone particular location: Jaén. The historical Database CENSOLARprovides a value of 5.8 GJ/m2 for yearly irradiation, while the inte-gration of the instantaneous measurements along 2008 of MatRasgroup is 5.2 GJ/m2 (difference around 10%). This analysis has beencarried out for instantaneous data along the year.

3.1. Optimum tilt for fixed system

Following the steps described above, the established procedureshave been carried out [32,33] for different tilts in order to deter-mine the optimum inclination for a fixed system with a maximum

SOLAR TIME (hours)

EFECTIVENESS RELATED TO TYPICAL VALUE FOR FIXED SYSTEMEFECTIVENESS RELATED TO TYPICAL VALUE FOR TRACKED SYSTEM

EFFI

CIE

NC

Y R

ATIO

(d

imen

sion

less

)

1

0.9

1.25

MIDDAY SUNSETSUNRISE

Fig. 5. Efficiency ratio tendencies for a photovoltaic system along a day.

5136 F. Cruz-Peragón et al. / Applied Energy 88 (2011) 5131–5142

annual energetic capturing. The maximum value of yearly energycollection corresponds to 30� tilt. In any case, variations of expo-sures with tilts between 20� and 40� are below 1% of the maximumvalue. There exists a 3� difference between the optimum slope forannual evaluation considering isotropic model (30�), and the eval-uation considering anisotropic model (33�).

3.2. Two axis tracking without restrictions

To improve the energetic optimization, the theoretical limit oc-curs when the incidence angle of the radiation is always zero. Eq.(2) has been used to determine the irradiance distribution alongthe day for horizontal surface.

Fig. 6 shows an example for a particular day of the year. Themeasured instantaneous irradiance over a horizontal surface to-gether with additional predicted values for other conditions hasbeen presented. At that day, the midday solar angle is around56�. Thus, the tracker tilt at this time is about 34�, very similar to30� defined for a fixed system, and consequently they provide verysimilar results (in fact, the irradiance on the cells of the tracker isslightly higher than for the case of a fixed system). It demonstratesthat Eq. (2) can be used to infer the instantaneous irradiances.

Once data along the year (with both clear and cloud sky days),have been evaluated, the average annual exposure of a tracked sys-tem regarding to the optimum fixed one without restrictions, isaround 30% higher with an isotropic model. On the other hand,

−6 −4 −2 0 2 4 60

100

200

300

400

500

600

700

800

900

1000

SOLAR TIME FROM MIDDAY (h)

Irrad

ianc

e (W

/m2 )

Horizontal (measured)2−axes tacking30° tiltHorizontal (modelled)

Fig. 6. Measured instantaneous irradiance over horizontal surface (from MatRasgroup), modelled irradiance form daily irradiation and predicted irradiance fortilted (30�), tracking surface (anisotropic diffuse model) and (26/03/2009).

an anisotropic model provides up to 38%. As plate efficiency is con-sidered with the same value as for fixed system, the lower and theupper limits for the maximum tracking advantage DJ0 correspondto those values.

3.3. Motion restrictions

Geometric and mechanical limitations of the tracking systemcould make not possible to reach certain positions, making the an-gle of incidence to be different from zero in these cases. Therefore,it is necessary to evaluate how these limits affect to the incomingsolar energy. An analysis of different combinations of cL and bL forthe tracker has been evaluated, resulting in the incoming energeticlosses shown in Fig. 7. For example, for |cL| > 95�, and bL > 60�, an-nual losses lower than 1% can be assured. This procedure has beenrepeated in two additional cities, with maximum and minimumlatitudes into the country: Oviedo (43.22�N, 5.50�W) and LasPalmas (28.06�N, 15.25�W). Results are very similar, demonstrat-ing that Jaén represents a typical city to evaluate this kind of losses.

3.4. Tracking strategy

For any control system, it is always required to analyze differenttime intervals in which the tracker will remain blocked. It impliesthat the angle of incidence of direct radiation differs from zero,resulting in a lower solar isolation, which decreases as the stop

50 60 70 80 90 100 11040

45

50

55

60

65

70

75

80

85

90

MAXIMUM AZIMUTHAL ANGLE (degrees)

MAX

IMU

M T

ILT

(deg

rees

)

1

1

1

2

2

2

33

33

4

4

44

66

6

6 6

88

8

8 8

10

1010 10

13

Fig. 7. Energetic irradiation losses (%) derived from angle limitations of both axes inJaén for a tracking system.

1.5 2 2.5 3 3.518

20

22

24

26

28

30

32

34

36

38

Sola

r cap

turin

g ga

in o

ver 3

0° ti

lted

surfa

ce (%

)

L = H L = 1.2 H L = 1.4 H L = 1.6 H L = 1.8 H L = 2 H Maximum

DISTANCE BETWEEN TRACKERS (m)

Fig. 9. Percentage of capture gains (respect to an optimum fixed system) consid-ering the shadow effect using an anisotropic model for a tracker with unitary height(H = 1 m) and a squared field distribution.

F. Cruz-Peragón et al. / Applied Energy 88 (2011) 5131–5142 5137

intervals increase. The incoming losses depending on each newstrategy must be evaluated. Thus, Fig. 8 shows instantaneous irra-diances on the tracker surface for different stop times: 1, 5, 10, 15,20, 30 and 60 min.

As a result of integrating the instantaneous data throughout ayear, the global energetic capture and losses due to this conceptcan be obtained giving relative results that are always below 0.5%.

Again, this analysis has been extended to both cities with extremelatitudes within the country: Oviedo and Las Palmas, observing verysimilar results. Thus, several considerations can be remarked:

(i) Losses are almost identical in the three analyzed cities,which leads to consider the analysis in Jaén as very signifi-cant. Thus, results can be extrapolated to the rest of thecountry.

(ii) Stop interval times below 10 min do not introduce signifi-cant differences.

(iii) Incoming radiation losses higher than 1% are only possiblewith stop intervals of 30 min or more.

(iv) The most useful stop time strategy consists on reducing theintervals as the solar time reaches the midday.

3.5. Shadow losses

Shadow analyses must reflect what exposure can be obtainedconsidering different configurations, width–height relations (L–H)in the tracking systems and their separation. In those cases withhigh separation distances, exposures correspond to those resultswithout restrictions (for example, 38% for anisotropic model inJaén). If geometric parameters associated to separation are modi-fied (X and Y), the gain percentages can be estimated, such asFig. 9 shows.

A comparison between both scenarios (isotropic and aniso-tropic models) shows that reliable distances correspond to thosewith 8–10% losses (exposure gains related to optimum fixed sys-tems of 28–30%). More detailed studies will be the goal for a futurework. In this analysis, an average global gain is needed to estimatethe influence of this kind of losses in the whole final annual result.

3.6. Generation energetic losses

From the tracker installation, some results have been presentedin Figs. 10 and 11. Fig. 10a shows the measured results for one dayobtained using the tracking system (March 25, 2009). In this figure,

11.7 11.75 11.8 11.85 11.9 11.950.409

0.4092

0.4094

0.4096

0.4098

0.41

0.4102

0.4104

0.4106

0.4108

Irrad

iatio

n (k

W/m

2 )

SOLAR TIME (hour)

1 minute5 minutes10 minutes15 minutes20 minutes30 minutes

Fig. 8. Instantaneous incident irradiances over surface for several stop timeintervals of the tracker in Jaén in a particular day in December.

data have been compared with those measured on horizontal sur-face and diffuse models for the tracking strategy, considering a0.14 reference value of effectiveness in the electrical generationsystem (ge) for that particular day. This value has been achievedin order to adjust the generation with the model as much as possi-ble. Results demonstrate that an anisotropic model is closer toevaluations than an isotropic model for that particular case. The ra-tio between the instantaneous efficiency and that referenced valuege varies as Fig. 10b shows.

On the other hand, Fig. 11a and b shows results in a middaywhen the system remained in horizontal position due to wind(April 25, 2009), with a reference value of effectiveness of 0.12 inthat particular day. In both cases, the integration of curves in Figs.10b and 11b provides a mean relative efficiency loss of 20%.

After evaluating multiple days with reliable results, these rela-tive efficiency losses vary from 2% to 7.5%, with a mean value of 5%.

3.7. Global results. Towards a simplified methodology

Table 1 summarizes the prediction of gains and losses due tothe different sources considered for the case of Jaén.

If the analyzed procedure is extended to a number of localities,it is possible to obtain an idea of the potential of the tracking sys-tem. In addition, there are some aspects that are not necessary tobe repeated: both stop timing and motion limits can be adoptedin order to assure always losses below 1%, as Table 1 shows. Thus,their influence can be removed from the analysis. In this way, anindividual analysis can be done considering the long-term evalua-tion for fixed system (providing a F value), next to the tracking sur-face behavior without restrictions. For this particular case a vectorcontaining all those daily gains J0day and a yearly value J0 withoutrestrictions can be obtained. It gives a maximum tracking advan-tage DJ0 (%) previously defined (see Eq. (1.b)).

However, shades and generation losses can also be assumed asthose indicated in Table 1. All these losses can be easily inferred inan easy way and their mean values can be adopted for all the casesto study. Then, the final tracking advantage DJ can be obtainedfrom DJ0 considering the percentage losses indicated in Table 1.It implies that it is necessary to modify the initial procedure de-scribed in Figs. 1 and 2 as Fig. 12 shows.

Nevertheless, no instantaneous data are known, and the proce-dure must start with monthly average daily radiation on horizontalsurface HG (kJ/m2). The hourly/instantaneous solar estimation for

−6 −4 −2 0 2 4 60

50

100

150(a)

(b)

SOLAR TIME FROM MIDDAY (h)

Elec

trica

l Pow

er G

ener

atio

n (W

/m2 )

Horizontal and ηe=0,14

Tracking and ηe=0,14

Real measurements

−5 0 5

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

Rel

ativ

e Ef

ficie

ncy

(dim

ensi

onle

ss)

SOLAR TIME FROM MIDDAY (h)

Fig. 10. Generation (a) and efficiency tendencies (b) for a tracking photovoltaicsystem along a day (25/03/2009).

0 1 2 3 4 5 6 70

20

40

60

80

100

120(a)

(b)

SOLAR TIME FROM MIDDAY (h)

Elec

trica

l Pow

er G

ener

atio

n (W

/m2 )

Horizontal and ηe =0.12Real measurements

0 1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

1.2

SOLAR TIME FROM MIDDAY (h)

Rel

ativ

e Ef

ficie

ncy

(dim

ensi

onle

ss)

Fig. 11. Generation (a) and efficiency tendencies (b) for a tracking photovoltaicsystem along a day (25/04/2009).

5138 F. Cruz-Peragón et al. / Applied Energy 88 (2011) 5131–5142

the mean day of each month of the year incorporates the meanbehavior for all the days for that particular month. Jain et al. [49]obtained horizontal instantaneous irradiance from daily values.They inferred better fitting results than expression in Eq. (2), butits use cannot be generalized. Thus, expressions in Eq. (2) are quiteaffordable [34]. In any case, the values correspond to average irra-diation, integrated from a large amount of instantaneous measure-ments along the time (usually during some years). In addition, theadopted models consider statistical analyses from all these data[17,32]. It means that models account for the weather conditionsfor both cloudy and clear days.

In this sense, the analysis without restrictions has been re-peated for the case of Jaén, starting now from published HG values[15]. Although final annual irradiation is slightly different for bothcases, the main task to remark is that the difference between thegain ratios is below 1%. For the case of an anisotropic model, DJ0

was obtained from instantaneous data, providing a value of38.5%, while when using monthly average daily radiation the value

Table 1Summarizing of results in Jaén compared with optimum fixed system.

Diffuse model 2-axes DJ0(%) Motion limits losses (%) Time stops losses (%)

Isotropic 30 <1a <1a

Anisotropic 38

a These values are related to the case of a tracking system without restrictions.

was 37.97%. It demonstrates that the proposed procedure can beefficiently used when employing monthly average daily radiationvalues.

4. Global estimation results along the country

Therefore, the indicated procedure has been carried out for allthe main cities in Spain (52). There are three locations that belongto island territories, and two national cities into African continent(next to Morocco). The other 47 cities are distributed into the pen-insular territory. Thus, the geographical locations approach can beseen in Fig. 13.

Annual results from integration of instantaneous daily data canbe observed and compared throughout the DJ0 term in Fig. 14.

There are some conclusions that it is possible to extract fromFig. 14: optimum tilt for fixed systems implies an exposure respectto horizontal surface that ranges between 5% and 20%. However, a

Generation losses (%) Shadow losses (%) Annual generation global gain (%)

5 4 218 25

CAPTURINGDAILY DATA OVER HORIZONTAL

SURFACE

LOCATION (a)

(b)

INITIAL DATA AND

MODELS

IRRADIATIONHG, HB, HD (kJ/m2)

IRRADIANCEIG, IB, ID (kW/m2)

GEOMETRIC CONSIDERATIONS

INTEGRATION RESULTS WITHOUT

RESTRICTIONS

OPTIMUM FIXED SYSTEM, F

TRACKING RESPONSES, J0

MEAN ηeF

MEAN VALUES OF LOSSES (See Table 1)

INSTANTANEOUS ANALYSIS

WITHOUT RESTRICTIONS

LONG-TERM EXPRESSIONS

Instantaneous-daily relations

MAXIMUM TRACKING ADVANTAGE ΔJ0

TRACKING ADVANTAGE ΔJ

INSTANTANEOUS ANALYSIS DAY ‘n’

INCIDENCE ANGLE DETERMINATION, θ (j)

COMPONENTS ONTO TILTED SURFACE

θ (j)

GB0(j), GD0(j) , GG0(j)

GG

j = N?

YES

j = j+1NO

j = 1

INSTANTANEOUS SOLAR DAILY DATA

Vectors with length ‘N’:IB(τ), ID(τ), IG(τ), αS(τ),

γS(τ), T, TSTOP

IB(j), ID(j) , IG(j)

αS(j), γ S(j)

DATA INTEGRATION

END

J’day(n)

Fig. 12. Modified evaluation procedure for tracking analysis: (a) global procedure; (b) daily energetic assessment without restrictions.

F. Cruz-Peragón et al. / Applied Energy 88 (2011) 5131–5142 5139

tracking system implies an exposure that ranges between 27% and40% (anisotropic model), or between 22% and 33% (isotropic mod-el). These differences vary between 5% and 8% depending on thediffuse model. Therefore, three different scenarios can be deduced:

pessimist, associated with the isotropic model; optimistic, associ-ated to the anisotropic model, and in addition, an average or mod-erate scenario with intermediate values between the two previousones.

FRANCE

PORTUGAL

MEDITERRANEAN SEA

CANTABRIC SEA

MOROCCO

CEUTA

MELILLA

36º N

38º N

40º N

42º N

0º 4º W 8º W

28º N

18º W 16º W 14º W

ATHLANTIC OCEAN

CANARY ISLANDS

BALEARS ISLANDS

Fig. 13. Locations on study have been marked with points.

20

25

30

35

40

45(a)

(b)

28 30 32 34 36 38 40 42 44LATITUDE (degrees)

OPT

IMU

M T

ILT

(deg

rees

)

Linear approach to isotropic model response Linear approach to anisotropic model response

05

101520253035404550

28 33 38 43

LATITUDE (degrees)

ΔJ0 (

%)

FIXED vs. HORIZONTAL (ANISOTROPIC) FIXED vs. HORIZONTAL (ISOTROPIC) TRACKING vs. FIXED (ANISOTROPIC) TRACKING vs. FIXED (ISOTROPIC) AVERAGED SCENARIO TRACKING-FIXED

Fig. 14. Annual results without restrictions along the country: (a) Optimum slopefor fixed systems; (b) maximum tracking energy advantage.

13

15

17

19

21

23

25

27

28 33 38 43LATITUDE (degrees)

ΔJ (%

)

TRACKING vs. FIXED (ANISOTROPIC) TRACKING vs. FIXED (ISOTROPIC) AVERAGED SCENARIO TRACKING-FIXED

ADDITIONAL COSTS

TENDENCY OF MODERATE SCENARIO

Fig. 15. Final results for tracking advantage.

5140 F. Cruz-Peragón et al. / Applied Energy 88 (2011) 5131–5142

In all the cases, tendencies follow exponential laws. These trendsare not related only to the latitude. Cities placed in the coastal topband of the country next the Cantabric Sea, originate worse results,not only for its latitude, but for the minor irradiation that takesplace in them, principally diminished by the proximity to the seaand a major rainfall. It has not been reflected so drastically in thePyrenean area (French border) with similar latitudes.

The main conclusion is that for a moderate scenario, two axestracking systems assure a 30% of gain over a fixed system in the

major of the country. In an optimistic scenario (anisotropic model),it can be assured that this limit would reach a 35% value.

All the losses related to the limitations of the system (motionlimits, control, shadows, etc.) have been incorporated into the pre-vious results without restrictions, obtaining an estimation of theelectric production. Thus, in Fig. 15 it can be observed all these sit-uations throughout DJ, depending on latitude of the cities.

Economical approaches indicate there exist a 15–20% additionalcosts in tracking systems compared to fixed ones, due to higherinvestments, as well as other costs associated with the operationand maintenance of the plant (usually related to the electricity pro-duction). Thus, locations with an energy advantage DJ higher than20% (see Fig. 15) can experience a better profitability if a trackingsystem is considered instead of a fixed one.

It can be observed that two axes tracking systems can be in 37of the 52 main cities in Spain. Nevertheless, there are seven citieswhere these systems are not recommended in any case: A Coruña,Orense, Oviedo, Santander, Bilbao, Vitoria, San Sebastián. There arefive additional cities, where some uncertainties also appear: Barce-lona, Gerona, Lugo, Pamplona, Las Palmas and Pontevedra. Ten ofthese cities correspond to the North coastal band of the country,

F. Cruz-Peragón et al. / Applied Energy 88 (2011) 5131–5142 5141

while two of them belong to the highest latitudes in the Mediter-ranean zone. Moreover, Las Palmas belongs to the Canary Islandswith low latitude (28.2�). A high humidity and rainfall because ofthe proximity to the sea, next to the locations latitude could bethe main reasons for non-advisable installations in these locations.Results illustrate that in most of the national territory two axestracking systems seems to be profitable. Obviously, a more detailedanalysis in a higher number of locations must be done if gains mustbe quantified.

5. Conclusions

This work demonstrates that two-axes tracking systems can as-sure an economic viability respect to fixed ones in most of theSpanish national territory. There are some areas where highhumidity, rainfall and latitude combine making not recommend-able these solutions.

In any case, this work is a starting point to define a further de-tailed economic analysis. For this purpose, it is necessary to addsome technical details to the present model, such as different fieldconfigurations and systems separation (in order to optimize theshadow losses) and detailed instantaneous thermal–electricalmodel of the plates. It is also necessary to evaluate the investmentcosts in detail, by evaluating different market solutions, and incor-porating the ground field price, in order to reduce the additionalinvestment costs band (as Fig. 14 shows). At this point, investmentdecision criteria can be adopted, such as the Internal Rate of Return(IIR) of Payback Period (PB), searching the optimum one for a givensurface size and separation distances between systems into thetrackers field.

Acknowledgments

The authors thank to the University of Jaén (Project Desarrollo yoptimización mecánica de un sistema de seguimiento solar de dos ejespara el aprovechamiento energético del olivar jiennense, Code RFC/PP2006) for technical help and financial supports provided. It hasmade it possible to carry out the presented analyses.

Appendix A. Symbols

a, b coefficients to rjG determination (see Eq. (2))

F annual electricity to the grid (kWh m�2 year�1) for fixedsystem

FS maximum annual solar irradiation (kWh m�2 year�1) for afixed system

f1 function to approach GB0

f2 function to approach GD0

f3 function to approach GR0

GB0 vector of beam component of irradiance (W/m2) on atracked system

GD0 vector of diffusive component of irradiance (W/m2) on atracked system

GG0 global irradiance vector (W/m2) considering only motionlimits restrictions for a tracker system

GG global irradiance vector (W/m2) for a tracker system, con-sidering motion limits, shadow losses and plates efficiency

GR0 vector of reflected component of irradiance (W/m2) on atracked system

H surface height (m)HG monthly average daily radiation on horizontal surface

(kJ m�2 day�1)Hj

G hourly irradiation (time ‘j’) from HG (kJ m�2 h�1)IB beam component of irradiance over horizontal surface

(kW/m2)ID diffusive component of irradiance over horizontal surface

(kW/m2)

IG global irradiance over horizontal surface (kW/m2)I0 extraterrestrial irradiance (kW/m2)ISN solar constant (kW/m2)J annual electricity to the grid (kWh m�2 year�1) for a track-

ing deviceJ0 annual electricity to the grid (kWh m�2 year�1) for a track-

ing device without restrictionsJday daily electricity to the grid (kWh m�2 year�1) for a tracking

deviceJ0day daily electricity to the grid (kWh m�2 year�1) for a tracking

device without restrictionskt instantaneous clearness index (dimensionless)L surface width (m)N length of vector T (number of componentsrj

G ratio of hourly total to daily total radiationT time vector for daily analyses (from sunrise to sunset)TSTOP time stop vector for daily analyses (from sunrise to sunset).

Indicates when the tracker changes its position along thetime

W electrical production of a tracked system (W/m2)aS solar altitude angle (deg)b instantaneous tilt for a tracking system (deg)bL maximum tilt that a tracking system reaches (deg)bop optimum tilt for a fixed system to assure maximum solar

capturing (deg)c surface azimuth angle (deg)|cL| absolute value of maximum surface azimuth angle that

tracking system reaches (deg)cS solar azimuth angle (deg)ge average electricity generation efficiency for a tracked sys-

tem (dimensionless)geF average electricity generation efficiency for a fixed system

(dimensionless)h angle of incidence of radiation (rad)hZ zenith angle (rad)x sun hour angle (rad)xS sunset hour angle (rad)u latitude angle (deg)d declination (deg)r reflectance coefficient (dimensionless)DJ0 maximum tracking advantage: annual relative gain in elec-

trical production of a tracking system without restrictionsrespect to a fixed one (%)

DJ tracking energy advantage: annual relative gain in electri-cal production of a tracking system respect to a fixed one(%)

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