Tracking and ground cover ratio

Tracking

PROGRESS IN PHOTOVOLTAICS: RESEARCH AND APPLICATIONS

Prog. Photovolt: Res. Appl. 2008; 16:703–714

Published online 7 August 2

*Correspondence to: L. NarCiudad Universitaria s/n, 28yE-mail: [email protected]

Copyright # 2008 John Wil

008 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/pip.847

Applications

and Ground Cover Ratio
L. Narvarte*,y and E. LorenzoInstituto de Energıa Solar, UPM, Ciudad Universitaria s/n, 28040 Madrid, Spain
Energy yield and occupation of land are two parameters that must be optimized when designing a large PV

plant. This paper presents the results of simulating the energy yield of flat panels for some locations and

different tracking strategies as a function of the ground cover ratio. Some interesting results for design

purposes, such as the optimal solar trackers depending on the land availability or the energy gains of every

tracking strategy, are shown. For example, the energy gains associated to one north–south axis tracking,

referenced to static surfaces, ranges from 18 to 25%, and from 37 to 45% for the two-axes tracker for

reasonable ground cover ratios. To achieve these results, a simulation tool with appropriate models to

calculate the energy yield for different solar trackers has been developed. Copyright # 2008 John Wiley &

Sons, Ltd.

key words: PV plants; grid-connected systems; tracking; ground cover ratio

Received 3 March 2008; Revised 24 June 2008

INTRODUCTION

Solar tracking has been used with PV flat modules for

more than 20 years.1 The available literature describes

several cases with good performance in terms of both

reliability and energy gains.2–15 Typical costs of PV

grid-connected systems at current Spanish market are

around 5s/Wp for static arrays (3s/Wp for PV

modules plus wiring, 0�5s/Wp for support structure

plus civil works, 0�5s/Wp for inverters and 1s/Wp for

others) and 6s/Wp for two-axes tracking (support

structure plus civil works are now 1, 5s/Wp). Then,

investment increase is about 20% while energy yield

increase is about 40%. This is why trackers are

flourishing in this market and also why this can

continue, meanwhile PV modules cost remains larger

than 0�8s/Wp. We estimate that about 70% of the

106MW installed during 2006 are combined with solar

varte, Instituto de Energıa Solar, UPM,040 Madrid, Spain.m.es

ey & Sons, Ltd.

trackers. A recent market survey16 has identified up to

22 companies offering a large variety of trackers.

When many PV generators are concerned, there is an

obvious relationship between land occupation and

energy yield; increasing land occupation reduces

mutual shading and, therefore, increases energy yield.

However, this is not without a price, because land-

related costs (land, wiring, fencing, civil works, etc.)

also increase. Hence, the study into the relationship

between land occupation and energy yield is a key

point in the design of large PV plants. At the IES-UPM,

we are often required to advise on practical questions

about the design of PV tracking plants: What is the

recommended tracker for a given terrain? What is the

recommended separation between trackers? etc. In

fact, answering such questions has been the main

motivation for this work.

This paper deals with the relationship between land

occupation and energy yield of flat panels for different

tracking possibilities: two axes, single vertical axis,

single horizontal axis and single tilted axis. As a matter

of reference, static surfaces are also considered. Thus,

tracking geometry has been reviewed and a simulation

exercise for different places has been carried out.

704 L. NARVARTE AND E. LORENZO

TRACKING GEOMETRY

The receiver position and the incident angle are

relevant parameters as far as tracking is concerned.

Tracking geometry descriptions can be found in the

available literature for many years. Those based on

matrix17 are particularly consistent but not very

intuitive and rather cumbersome when implemented

in software codes. That is why some authors have

developed equations directly relating position and

incident angles with a particular motion. However,

they were given with specific constraints. For example,

the classic book by Duffie and Beckman18 provides

useful equations but only for surfaces that rotate on

axes parallel to the surfaces. Hence, despite these

antecedents, there is a need to develop a set of

equations for arbitrarily oriented surfaces, also able to

take shading into account, and still easy to implement

in software codes.

Figure 1 describes the solar coordinates referred to a

system whose X, Y and Z axis are pointing,

respectively, to West, South and Zenith. It is not

difficult to deduce these coordinates in relation to solar

elevation, gS, and solar azimuth, cS, angles by

x ¼ cos gSsincS;

y ¼ cos gS coscS; z ¼ singS

(1)

At any given moment, the solar elevation and

azimuth angles are calculated from the equations

sin gS ¼ sin d sinfþ cos d cosf cosv (2)

and

coscS ¼ ðsin gs sinf� sin dÞ=ðcos gs cosfÞ (3)

s

s

z (Zenith)

x (West)

y (South)

Figure 1. Sun coordinates referring to the site

Copyright # 2008 John Wiley & Sons, Ltd.

where d, f and v are, respectively, the latitude, the

declination and the hour angles.

Single vertical axis

For a plane with a fixed slope, bGEN, rotated around a

vertical axis, the angle of incidence is minimized when

the surface azimuth and solar azimuth angles are equal.

Axis rotating angle, vID (‘ID’ means ideal value) and

incidence angle, uS, are easily determined from

Figure 2.

vID ¼ cS (4)

uS ¼ gS � bGEN (5)

Single horizontal axis

For a plane rotated around a horizontal axis and forming

a fixed angle with this axis, bGEN, the angle of incidence

is minimized when the axis, the line to the Sun and the

normal to the surface are on the same plane. Relevant

equations are determined from Figure 3.

tanvID ¼ x

z¼ cos gS sincS

singS

(6)

uS ¼ arc tany

ðx2 þ z2Þ1=2

" #� bGEN (7)

Single tilted axis

For a plane rotated around a single axis oriented to the

south and tilted an angle, bAXIS, and forming a fixed

angle with this axis, bGEN, the angle of incidence is

minimized, again, when the axis, the line to the Sun

and the normal to the surface are on the same plane. In

Figure 2. Vertical tracking: (a) plane of the line to the Sun

and the normal to the surface. (b) View of this plane showing

incidence angle


DOI: 10.1002/pip

Figure 3. Horizontal tracking: (a) plane of the line to the Sun

and the normal to the surface. (b) View of this plane showing

incidence angle

TRACKING AND GROUND COVER RATIO 705

order to deduce the relevant expressions, it is best to

refer the position of the Sun to the OX0Y0Z0 systemresulting from turning the previous OXYZ system just

an angle bAXIS around the X axis, as shown in Figure 4.

Then, the Sun coordinates at the new system are

given by

x0 ¼ x; y0 ¼ r cosðu þ bAXISÞ;

z0 ¼ r sinðu þ bAXISÞ(8)

where

r ¼ ðy2 þ z2Þ1=2 y u ¼ arc tanðz=yÞ (9)

Now, relevant expressions can be deduced through a

simple analogy with the previous case. Thus,

vID ¼ arc tanx0

z0

� �(10)

uS ¼ arc tany0

ðx02 þ z02Þ1=2

" #� bAXIS (11)

axis

axis

x = x’

y

y’

zz’

Figure 4. Meridian view of Y,Z and Y0,Z0axis


Two axes

Two-axes tracking is obtained when adding the

capability to rotate the receiving plane around a

second axis normal to the first one to a single axis

tracking. Then, this plane can always be kept normal to

the sun. The new angle, bGEN-TRAC, depends on the

first type of axis. When this is vertical (see Figure 2b)

bGEN�TRAC ¼ gS (12)

Similarly, Figure 3b leads to determining when the

first axis is horizontal

bGEN�TRAC ¼ arc tany

ðx2 þ z2Þ1=2

" #(13)

and when it is tilted

bGEN�TRAC ¼ arc tany0

ðx02 þ z02Þ1=2

" #(14)

SHADING

PV generators often include several trackers. Depend-

ing on the Sun’s position, partial shading between two

adjacent trackers may occur, mainly in the early

morning and late evening.

Single horizontal axis

Figure 5 shows the projection at the XZ plane of two

adjacent trackers, at a distance LEW (distance at the

EW direction), when shading occurs. Horizontal

shadow length, sEW, and shaded fraction, FSEW, are

given by

sEW ¼ 1

cosvID

and

FSEW ¼ max 0; 1� LEW

sEW

� �� (15)

Single tilted axis

Figure 6 shows a projection at the plane of the Y axis

and normal to the surface when shade in the NS

direction takes place. This figure applies to receptors

rotated around a horizontal axis and forming a fixed

angle, bGEN, with this axis, and also for receptors

rotated around a tilted axis, bAXIS, and coplanar with


DOI: 10.1002/pip

.

LEW

.1

id

SEW

iz

x

FSE

Figure 5. Two horizontal trackers as projected at the XZ

plane when shading occurs

1

b

β·


this axis. In other words, this figure applies when only a

tilt angle, bGEN or bAXIS, differs from zero. Tracker

length and distance, both in the NS direction, are

respectively b and LNS. Then, horizontal shade length,

sNS, and shaded fraction, FSNS, are given by

sNS ¼ b cos bþ sin b

tanB

� �(20)

tanB ¼ ðx2 þ z2Þ1=2

y(21)

FSNS ¼ max 0; 1� b � LNSsNS

� �� (22)

In these equations b can represent, both, bGEN or

bAXIS.

It can be observed that the following value of LNS

LNS ¼ b cos bþ sin b � tanðfþ dMÞð Þ (23)

just avoids shade at noon for all the days throughout the

year, where dM is the maximum declination angle

throughout the year (dM¼ 23.58).

LNS

b

sNS

B

y

b.FSP

GEN or AXIS

Figure 6. Two horizontal (or tilted) one-axis trackers as

projected at the plane of the Yaxis and normal to the surface,

when shading in the NS direction occurs


Single vertical axis

Let us consider a set of vertical trackers arranged as

shown in Figure 7.

Figure 8 shows a case of shading in the East–West

direction. The horizontal projection of two adjacent

tracked surfaces and their corresponding mutual

shading are presented in Figure 8a, while the meridian

projection is presented in Figure 8b. Note that

incidences of shading require two simultaneous

conditions. First, the shadowmust point to the adjacent

tracker and, second, its length must be large enough to

reach it. Shadow length and shaded fraction are given,

respectively, by

sEW ¼ s1 þ s2 ¼ b cos bGEN þ b sin bGENcotgS (24)

and

FSEW ¼ FS1 � FS2 (25)

where

FS1 ¼ max 0;s� LEW � sincS

s

� �and

FS2 ¼ max 0;1� LEW � coscS

1

� � (26)

Figure 9 shows a case of shade in the North–South

direction. Strictly speaking, effective shading requires

lEW

lNSN

Figure 7. Parameters of a field with single vertical axis

trackers: tilt angle bGEN; aspect relation b; spacing between

adjacent trackers in North–South and East–West directions

lNS and lEW


DOI: 10.1002/pip

Figure 8. East–West shadow in ideal single vertical axis

tracking. Projections at (a) Horizontal plane (b) Vertical

plane of the line to the Sun

Figure 9. North–South shade in vertical single axis tracking.

Projections at (a) Horizontal plane (b) Vertical plane of the

line to the Sun


two different conditions: First, the shade borderline

must reach the front of the rear trackers and, second,

shade must impinge on a tracker and not only on the

empty space between two trackers. However, a

reasonable approximation, in particular for relatively

low LEW values (let us say, LEW< 3) consists of only

considering the first condition. Then,

FSNS ¼ max 0; 1� s0

sNS

� �� (34)

where

s0 ¼ LNS � sincS

sinðp=2� cSÞ(35)

Two axes

Shade considerations already taken into account for

vertical axis trackers can also be applied for two axes

trackers, when considering that the tilt angle is now the

complementary to the Sun’s elevation angle.


ENERGY YIELD CALCULATION

There are a number of software tools available to

simulate the energy yield of PV grid-connected

systems.19–23 However, none of them can deal with

all of the possible tracking strategies. Hence, we have

developed our own code, comprising the following steps:

1. O
btaining solar radiation site information (the 12
monthly averages of the daily horizontal global

irradiation, the daily maximum ambient tempera-

ture and the daily minimum ambient temperature)

from available databases.

2. P
reparation of horizontal (both global and diffuse
component) irradiance sequences (it can be

selected hourly or minute time intervals).

3. D
etermination of the position of the Sun and the
receiving surface, and the incidence angle.

4. D
etermination of shade.
5. T
ransposition from horizontal to inclined irradi-
ance values.

6. C
alculation of the losses of dirty PV modules.

DOI: 10.1002/pip

Table I. Models used to simulate the energy yield of a grid-connected PV plant

Step Comment/Reference

1 Solar irradiation site information PVGIS database (for solar radiation)24 and NASA database

(for ambient temperature)25

2 Irradiation to irradiance (horizontal) First, solar radiation components are calculated by means of the Global—

diffuse (Kt, Kd) correlation described by Erbs.26 Second, irradiance

values are derived from those of the daily irradiation, as described by

Collares-Pereira and Ralb.27

3 and 4 Geometry As described in the previous section

5 In-plane irradiance Anisotropic properties of the diffuse solar radiation are considered as

described by Hay and McKay.28

6 Degree of cleanliness and incidence

angle effects

Incidence angle effects are considered in relation with the degree of

cleanliness, as described by Martin and Ruiz.29

7 Shading effects It is considered that a shadow only affects the direct and circumsolar

(a part of the diffuse) components of the solar irradiance.

8 PV array output power PV array efficiency is considered to be linearly related to solar cell temperature.

The constant coefficient depends on the solar cell technology. For most

Si-x modules, the value of �0�5% per 8C is appropriate.

9 Inverter output power Inverter efficiency is considered to vary with load ratio as described by Schmid

and Schmidt.30 This model involves the determination of three dimensionless

parameters characterising the full behaviour of the inverter. These parameters

are here previously determined from the efficiency information provided by

inverter manufactures for several load ratios: typically

5,10,20, 50 and 100%. In this work we have used Ki0¼ 0�004461;Ki1¼ 0�01473;Ki2¼ 0�02093 which correspond to an inverter with a European efficiency¼ 96%.

10 Transformer efficiency versus output power Transformer losses are the sum of the so called stand-by losses and wiring losses

The latter is related to the square output power. Transformer manufactures

provide characteristic information.


7. C

Copy

alculation of the losses of PV modules in the

shade.

8. C
alculation of the PV array output power.
9. C
alculation of the inverter output power.
10. C
alculation of the low voltage/medium voltage
transformer output power.

Table I sets out brief explanations for each step.

It is worth mentioning that soiling impact can be

very significant when dry climates are concerned, as it

is the case in most of Spain. Our code paid particular

attention to this fact, supported by Reference 29 at step

6. This not only allows soiling impact on PV modules

cover transparency to be into consideration but also

soiling impact in angular reflection losses.

SELECTED CASES

Although there are a large variety of trackers, the

tracking strategies considered in this paper are the most

extended ones on the current market: two axes, one

vertical axis, one north–south horizontal axis and one

north–south horizontal axis tilted 208. We have also

right # 2008 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2008; 16:703–714

DOI: 10.1002/pip

.

considered, as a reference, the case of a static surface

with an optimal tilt, that is the tilt that maximizes the

annual incident irradiation.

The output power of a PVarray can be described by

P ¼ P� G

G� ð1� bðTc � T�c ÞÞ (36)

where Tc¼ TaþKG, P� is the nominal power of PV

generator, G�¼ 1000W/m2, G is the irradiance on the

PV generator’s surface, K and b are characteristic

parameters of the solar cell technology, and Ta is the

ambient temperature. The good behaviour of this rather

simple approximation to the power output of PV

modules has been validated by recent studies.31

Here we assume that shading affects the direct and

circumsolar components of the incident irradiance, and

not the isotropic components. Hence,

GBS ¼ Bþ Diso þ Dcircumsolar þ R

GAS ¼ ðBþ DcircumsolarÞð1� FSÞ þ Diso þ R

whereGBS andGAS represent the irradiance before and

after shading consideration respectively, and B, D and

R respectively, are the direct, diffuse and reflected

components of the irradiance.

File 1

File 2

+ -Vertical axis


For a given shaded fraction FS, defined as the ratio

between the shaded area and the total area of a PV

generator surface, the power reduction SI, depends on

the particular electric PV system layout (mainly solar

cells series and parallel association, bypass-diode

disposition and inverter arrangement). Whatever be the

case, it encompasses two extremes:

File 3

Horizontal axis

(a) T

Copy

he most optimistic is when the power reduction is

just equal to shaded fraction (SI¼FS).

(b) T
hemost pessimistic is when the mere existence of
any shade fully avoids power (FS> 0! SI¼ 1).

Figure 10. Electrical layout of a PV generator considered

here
This paper analyses these two extremes and the case
detailed in Figure 10, which can be often found in real

PV plants: the PV generator carried by a tracker is

made by the parallel association of three rows, each

made up of the series association of a certain number of

PVmodules. Thus, each time one row gets shaded output,

power reduces by one third. (0<FS< 1/3! SI¼ 1/3;

1/3�FS< 2/3! SI¼ 2/3; 2/3�FS� 1! SI¼ 1).

Land occupation is established by the so called

Ground Cover Ratio, GCR, defined as the ratio

between PV array area to total ground area. For

simplicity, we have restricted our analysis to the

following cases:

– s
ingle vertical axis (with b¼ location latitude) and
two-axes individual trackers are all square (b¼ 1)

Figure 11. Evolution of yearly energy yield in Almerı

the optimistic shading case and assuming

right # 2008 John Wiley & Sons, Ltd.

and equally spaced over the ground (LNS¼ LEW¼ L;

GCR¼ 1/L2)

– s
ingle pure horizontal axis is understood as infinitely
large (GCR¼ 1/LEW)

– s
ingle tilted axis is three times longer than wide
(b¼ 3) and LNS is selected to avoid shading in this

direction fully, which is close and avoids shading at

the noon winter solstice. It can be shown that

this condition leads to LNS¼ b(cos bþ sin

b � tan(þ dM)), where F is the location latitude

and dM the maximum value of the declination angle

(dM¼ 23�58) (GCR¼ b/(LNS � LEW)).

a for the tracking strategies considered here, for

a constant dirtiness degree of 3%


DOI: 10.1002/pip

Table II. Yearly energy yield for the tracking strategies considered here and the optimistic shading case for some GCR

values and referenced to the case of an optimally tilted static surface

1/GCR Fixed tilt N–S N–S (08 208) N–S (208 08) Azimuthal Two-axes

1 1 1�037 0�662 0�6662 1 1�177 1�142 1�179 1�048 1�0613 1 1�233 1�270 1�292 1�219 1�2424 1 1�253 1�317 1�332 1�283 1�3225 1 1�263 1�338 1�351 1�320 1�3746 1 1�268 1�351 1�361 1�338 1�4037 1 1�271 1�357 1�367 1�349 1�4248 1 1�274 1�362 1�371 1�356 1�4379 1 1�275 1�365 1�373 1�361 1�44810 1 1�277 1�368 1�376 1�365 1�455


Finally, it must be noted that when shading occurs, it

is possible to avoid it by moving the surface angles

away from their ideal values, just enough to get the

shadow borderline to pass over the border of the

adjacent tracker. This is called ‘back-tracking’, and is

in fact implemented in some commercial products.

However, ‘back-tracking’ will be dealt with in a future

paper.

RESULTS

As a representative example, Figure 11 shows the

evolution of the yearly energy yield for the tracking

Figure 12. Evolution of yearly energy yield in Alm

the realistic shading case and assumin


strategies considered here, as calculated for Almerıa,

for the optimistic case and assuming a constant degree

of dirtiness of 3% (Normal transmittance¼ 0�97).Table II details the numerical results for some GCR

values, referring to the case of an optimally tilted static

surface. Outstanding facts are:

– T

erı

g

here is like a ‘surrounding curve’ describing the

relationship between maximum energy yield and

GCR.

– T
his contour curve roughly, coincides with horizon-
tal tracking for 1< 1/GCR< 2, with a north–south

tracking axis tilted 208 for 2< 1/GCR< 4 and with

two-axes tracking for 1/GCR> 4.

a for the tracking strategies considered here, for

a constant dirtiness degree of 3%


DOI: 10.1002/pip

Table III. Yearly energy yield for the tracking strategies considered here together with the realistic shading case for some

GCR values and referenced to the case of an optimally tilted static surface

1/GCR Estatico N–S N–S (08 208) N–S (208 08) Azimuthal Two-axes

1 1 0�917 0�486 0�4692 1 1�109 1�015 1�062 0�905 0�8873 1 1�195 1�199 1�230 1�103 1�0934 1 1�227 1�271 1�292 1�201 1�1995 1 1�243 1�306 1�321 1�253 1�2696 1 1�252 1�324 1�337 1�283 1�3117 1 1�259 1�336 1�348 1�305 1�3478 1 1�263 1�345 1�355 1�320 1�3719 1 1�266 1�350 1�359 1�332 1�39110 1 1�269 1�354 1�363 1�339 1�405


– W

Co

hen comparing them with static surfaces (1/

GCR¼ 2), energy gains associated to practical

trackers range from 18–25% (horizontal axis, 1/

GCR¼ 2–4) to 37–45% (two axes, 1/GCR¼ 5–10).

– S
ingle vertical axis provides 96% of the energy
provided by two-axes tracking (1/GCR¼ 5).

– T
ilting the PV modules over the horizontal axis
leads to very similar results as tilting the axis over

the horizontal.

– N
orth–south axis tilted 208 and single vertical axis
show very similar results when 1/GCR!1.

– N
orth–south axis tilted 208 provides the same
energy yield as two-axes tracking when 1/GCR¼ 4,

4, and it represents 90% of the maximum energy

Figure 13. Evolution of yearly energy yield in Al

for the pessimistic shading case and assu

pyright # 2008 John Wiley & Sons, Ltd.

yield of a practical tracker (two-axes with 1/

GCR¼ 10).

Figures 12 and Table III, and Figure 13 and Table IV

detail the results of a similar exercise but for the

previously called realistic and pessimistic cases,

respectively. In order to make the reader’s task easier,

Figure 14 puts together the three cases corresponding

to two-axes tracking. It can be seen that the same

comments for the optimistic case apply here with some

additional remarks:

– T

me

mi

he contour curve is made up of the same tracking

strategies, but the more pessimistic the shading case,

rıa for the tracking strategies considered here,

ng a constant dirtiness degree of 3%


DOI: 10.1002/pip

Table IV. Yearly energy yield for the tracking strategies considered here and the pessimistic shading case for some GCR

values and referenced to the case of an optimally tilted static surface

1/GCR Estatico N–S N–S (08 208) N–S (208 08) Azimuthal Two-axes

1 1 0�576 0�436 0�4292 1 0�952 0�713 0�784 0�692 0�6843 1 1�109 1�034 1�088 0�968 0�9504 1 1�170 1�167 1�202 1�101 1�0835 1 1�201 1�230 1�257 1�176 1�1736 1 1�219 1�267 1�287 1�221 1�2267 1 1�231 1�290 1�307 1�254 1�2718 1 1�240 1�306 1�320 1�276 1�3049 1 1�246 1�318 1�329 1�296 1�33210 1 1�251 1�326 1�336 1�310 1�351

Co


the wider the portion of the contour occupied by the

north–south tracking axis tilted 208.
– E nergy gains referenced to static surfaces (1/
GCR¼ 2) decrease, ranging from 11% (horizontal

axis, 1/GCR¼ 2) to 40% (two axes, 1/GCR¼ 10)

for the realistic case, and from �5 to 35% for the

pessimistic case.

– W
hen comparing with the optimistic shading case
(1/GCR¼ 5) for the two-axes tracking, the energy

yield of the realistic case is the 92% and the pessi-

mistic case is the 85%.

Finally, Table V sets out the results of extending the

simulation exercise for the realistic case to several

Figure 14. Comparison of yearly energy yield in A

cases consid


Mediterranean places. It can be noted that, despite

relatively large variations in latitude and clearness

index, the previous comments essentially remain the

same. It is worth to note that these results can be

different than the ones given by other available tools. It

is not easy to determine the causes of these differences

due to the details of the internal models of these tools

are out of the knowledge of the authors of this paper.

For example, the impact of shadows in the output

power of PV modules is highly dependant of the

shading case, as it has been shown. The model to

characterize the degree of cleanliness of PV modules

and the incidence angle effects can also explain some

of these differences.

lmerıa for the two-axes tracking, for the shading

ered here


DOI: 10.1002/pip

Table V. Yearly energy yield for the tracking strategies considered here and the realistic shading case for some GCR values

and referenced to the case of an optimally tilted static surface. Comparison of some Mediterranean locations

Location Lat (8) Kt N–S N–S (08 208) N–S (208 08) Azimuthal Two-axes

1/GCR 2 5 10 2 5 10 2 5 10 2 5 10 2 5 10

Sevilla 37�5 0�587 1�12 1�25 1�28 1�02 1�31 1�36 1�06 1�33 1�37 0�91 1�26 1�35 0�89 1�27 1�41Toledo 39�8 0�571 1�11 1�25 1�28 0�99 1�31 1�36 1�04 1�32 1�37 0�90 1�26 1�36 0�89 1�27 1�41Tel-Aviv 32�1 0�552 1�16 1�28 1�31 1�09 1�32 1�36 1�12 1�34 1�37 0�96 1�26 1�32 0�94 1�28 1�40Crete 35�3 0�546 1�15 1�28 1�30 1�06 1�32 1�36 1�09 1�33 1�36 0�96 1�27 1�34 0�94 1�28 1�40Alger 36�7 0�537 1�13 1�25 1�28 1�03 1�31 1�35 1�07 1�32 1�36 0�92 1�26 1�34 0�90 1�27 1�40Larisa 39�6 0�498 1�14 1�26 1�27 1�02 1�31 1�35 1�06 1�31 1�35 0�95 1�27 1�35 0�93 1�28 1�40Toulouse 43�6 0�492 1�10 1�22 1�24 0�94 1�28 1�34 0�99 1�29 1�33 0�89 1�25 1�35 0�87 1�25 1�39


CONCLUSIONS

A comprehensive set of equations describing the Sun’s

tracking geometry and a complete procedure to

calculate the energy yield of a flat PV module grid-

connected system have been presented. Based on

these, the relationship between the yearly energy gains

and land occupation has been analysed for several

tracking strategies. The outstanding results are as

follows:

– T

Co

here is a ‘surrounding curve’ describing the

relationship between maximum energy yield and

GCR, made up of three different tracking strategies;

horizontal tracking for 1< 1/GCR< 2, north–south

axis tilted 208 tracking for 2< 1/GCR< 4 and two-

axes tracking for 1/GCR> 4. When more pessi-

mistic shading models are used, the contour curve

remains but the portion of the contour occupied by

the north–south axis tilted 208 tracking is wider.

– T
he energy gains associated to practical trackers
referenced to static surfaces (1/GCR¼ 2) has been

calculated. For the optimistic shading case, these

gains range from 18–25% (horizontal axis, 1/

GCR¼ 2–4) to 37–45% (two axes, 1/GCR¼ 5–10).

– T
ilting the PV modules over the horizontal axis
leads to very similar results as tilting the axis over

the horizontal.

– T
he influence of the shading model is more import-
ant when the land occupation in larger. As a practical

example (1/GCR¼ 5), and taking the optimistic

shading case as a reference for the two-axes track-

ing, the energy yield of the realistic case is 92% and

the pessimistic case is 85%.

The extension of this simulation exercise to several

European places has shown that despite the relatively


large variations in latitude and clearness index, the

previous results are applicable.

REFERENCES

1. Wenger HJ, Jennings C, Iannucci JJ. Carrisa Plains PV

power plant performance, Conference Record of the

Twenty First IEEE, Photovoltaic Specialists Conference,

1990.

2. Lorenzo E, Maquedano C, Valera P. Operacional results

of the 100 kWp tracking PV plant at Toledo-PV project.

Proceedings of the 13th European PV Solar Energy

Conference, Nice, 1995; 2433–2436.

3. Jennings C, Farmer B, Townsend T, Hutchinson P,

Gough J, Shipman D. PVUSA—The first decade of

experience. Proceedings of the 25th IEEE PVSC,

Washington, 1996; 1513–1516.

4. Alonso-Abella M, Chenlo F, Vela N, Chamberlain J,

Arroyo R, Alonso F. Toledo PV plant 1 MWp—10 years

of operation. Proceedings of the 20th European PV Solar

Energy Conference, Barcelona, 2005; 2454–2457.

5. Illiceto A, Previ A. Progress report on ENEL’s 3�3 MWp

PV plant. Proceedings of the 12th PV Solar Energy

Conference, Amsterdam, 1994; 1167–1170.

6. Stern M, West R. Development of a low cost integrated

15kWAC solar tracking sub-array for grid-connected PV

power system applications. Proceedings of the 25th

IEEE PVSC, Washington, 1996; 1369–1372.

7. Ito M, Kato K, Komoto K, Kichimi T, Sugihara H,

Kurokawa K. Comparative study of fixed and tracking

system of very large-scale PV (VLS-PV) systems in the

World deserts. Proceedings of the 19th European PV

Solar Energy Conference, Paris, 2004; 2113–2116.

8. Klotz F, Schroeder S,MohringH. Light weight PV-louvres

for building integration. PV-Light EU-Project (FP5

NN�2001-550). Proceedings of the 19th European PV

Solar Energy Conference, Paris, 2004; 3154–3157.

9. Kimber A,Mitchell L. Performance evaluation standards

for large grid-connected PV systems in the United States


DOI: 10.1002/pip


and Germany. Proceedings of the 20th European PV

Solar Energy Conference, Barcelona, 2005; 3229–3232.

10. Lorenzo E, Perez M, Ezpeleta A, Acedo J. Design of

tracking photovoltaic systems with a single vertical axis.

Progress in Photovoltaics: Research and Applications

2002; 10: 533–543.

11. Guelbenzu E, Cueli A, Lagunas A. 1,2 MW photovoltaic

plant with sun tracking on all generation systems. Pro-

ceedings of the 19th European PV Solar Energy Con-

ference, Paris, 2004; 2258–2261.

12. Zdanowicz T, Rodziewicz T, Zabkowska M. Effective-

ness of the sun tracking option during different insola-

tion periods. Proceedings of the 19th European PV Solar

Energy Conference, Paris, 2004; 2580–2583.

13. Sureda F, Salas J, Gil J, Niesing H, Cantos S, Vidal J.

FSA SystemTM: an autonomous small scale power sys-

tem for distributed generation based on PV with an

effective demand side management. Proceedings of

the 20th European PV Solar Energy Conference, Bar-

celona, 2005; 2228–2230.

14. Comsat M, Calin R, Visa I, Duta A, Meester B. A

tracking system design for PV panels. Proceedings of

the 20th European PV Solar Energy Conference, Bar-

celona, 2005; 2212–2215.

15. Luque-Heredia I, Moreno J, Quemere G, Cervantes R,

Magalhaes P. SunDogTM STCU: a generic sun tracking

control unit for concentration technologies. Proceedings

of the 20th European PV Solar Energy Conference,

Barcelona, 2005; 2047–2050.

16. Siemer J. Market survey on tracking systems. A market

offering many choices. Photon International October

2007; 114–140.

17. Collins GW II. The Foundations of Celestial Mechanics.

Case Western Reserve University, 2004. URL http://

ads.harvard.edu/books/1989fcm.book/

18. Duffie JA, Beckman WA. Solar Engineering of Thermal

Processes. John Wiley & Sons, Inc.: New York, 1991.

19. PV Design Pro, Maui Solar Energy Software Corpor-

ation. Haiku. USA.

20. Menicucci D, Fernandez J. User’s manual for

PVFORM: a photovoltaic system simulation program

for stand-alone and grid-interactive applications, SA-


ND85-0376. Sandia National Laboratories, Albuquer-

que, 1988.

21. Wenger H, Gordon J. PVGRID: a user-friendly PC

software package for predicting utility-intertie photo-

voltaic system performance, ISES SolarWorld Congress,

Denver, 1991.

22. Marion B, Anderberg M. PVWATTS—An online per-

formance calculator for grid-connected PV systems.

Proceedings of the ASES Solar 2000 Conference, Madi-

son, 2000; 119–121.

23. Eicker U, Pietruschka D, Schumacher J, Fernandes J,

Feldmann T, Bollin E. Improving the energy yield of PV

power plants through internet based simulation, monitor-

ing and visualisation. Proceedings of the 20th European

PV Solar Energy Conference, Barcelona, 2005; 2670–

2673.

24. Available at http://re.jrc.ec.europa.eu/pvgis/apps/rad-

month.php

25. Available at http://eosweb.larc.nasa.gov/sse

26. Erbs et al. Estimation of the diffuse radiation fraction for

hourly, daily and monthly-average global radiation.

Solar Energy 1982; 28: 293–302.

27. Collares-Pereira M, Ralb A. The average distribution of

solar radiation—Correlation between diffuse and hemi-

spherical and between daily and hourly insolation

values. Solar Energy 1979; 22: 155–164.

28. Hay JE, McKay DC. Estimating solar irradiance on

inclined surfaces: a review and assessment of method-

ologies. International Journal of Solar Energy 1985; 3:

203–240.

29. Martin N, Ruiz J. Calculation of the PV modules angular

losses Ander field conditions by jeans o fan analytical

model. Solar EnergyMaterials and Solar Cells 2001; 70:

25–2538.

30. Schmid J, Schmidt H. Inverters for photovoltaic systems,

5th Contractor’s Meeting of the PV Demostration Pro-

jects. Ispra, 1991; 122–132.

31. Fuentes M, Nofuentes G, Aguilera J, Talavera DL,

Castro M. Application and validation of algebraic

methods to predict the behaviour of crystalline silicon

PV modules in Mediterranean climates. Solar Energy

2007; 81: 1396–1408.


DOI: 10.1002/pip

Documents

Tracking and ground cover ratio