Design of Tracking PV Systems With a Single Vertical Axis

PROGRESS IN PHOTOVOLTAICS: RESEARCH AND APPLICATIONS

Prog. Photovolt: Res. Appl. 2002; 10:533–543 (DOI: 10.1002/pip.442)

Design of TrackingPhotovoltaic Systemswith a Single Vertical AxisE. Lorenzo1,*,y, M. Perez2, A. Ezpeleta3 and J. Acedo4

1Instituto de Energıa Solar, ETSI Telecomunicacion, Ciudad Universitaria, s/n, 28040, Madrid, Spain2Alternativas Energeticas Solares, Pol Industrial La Nava, 1, 31300, Tafalla, Naavarrsa, Spain3Energıa Hidroelectrica Navarra, C/Yanguas y Miranda, 1, 31002, Pamplona, Spain4Ingeteam SA, C/Pintor Maeztu, 2, 31008, Pamplona, Spain

Solar tracking is used in large grid-connected photovoltaic plants to maximise solar

radiation collection and, hence, to reduce the cost of delivered electricity. In particu-

lar, single vertical axis tracking, also called azimuth tracking, allows for energy gains

up to 40%, compared with optimally tilted fully static arrays. This paper examines the

theoretical aspects associated with the design of azimuth tracking, taking into

account shadowing between different trackers and back-tracking features. Then,

the practical design of the trackers installed at the 1�4MW Tudela PV plant is pre-

sented and discussed. Finally, this tracking alternative is compared with the more

conventional fully stationary approach. Copyright # 2002 John Wiley & Sons, Ltd.

INTRODUCTION

Solar tracking remains an interesting option for PV generation, especially when medium/large grid-

connected PV plants are concerned. High reliability and low maintenance requirements have been

demonstrated in several practical projects.1–2 The Toledo PV Plant, for example, where a 1000-m2

tracking system has been in routine operation since July 1994, with 100% availability. This can be interpreted

as a mean time between failures below 60 000 h, which speaks for itself.

Single, horizontal, North–South-oriented axis structures associated with flat-plate modules represent by far

the most extended tracking solution in current PV plants.2–4 Because of their inherent lack of shadowing in the

North–South direction, single tracking devices can drive large surfaces and, owing to the horizontal axis posi-

tion, associated wind loads tend to be relatively low. It involves a particularly simple and robust mechanical

construction, which is a major advantage of this type of tracking. Coming back to the Toledo PV plant, its

tracker is formed of four 250-m2 surfaces, each powered by a single 0�25-HP standard AC motor. North–South

oriented horizontal single axis tracking also plays a major role in solar thermal electric technology. In particular,

it has been selected for the famous LUZ-developed power plants,5 totalling 2�3� 106 m2 aperture area, which

began operation in southern California in 1984.

However, the horizontal axis position limits energy collection by the tracking surface. This depends on the

solar climate and latitude site, �, and can be quantified by comparison with the energy collected by an ideal two-

axis tracking, which represents the largest solar radiation potential for a particular location. Table I presents

Published online 17 September 2002 Received 31 December 2001

Copyright # 2002 John Wiley & Sons, Ltd. Revised 16 March 2002

* Correspondence to: E. Lorenzo, Instituto de Energıa Solar, ETSI Telecomunicacion, Ciudad Universitaria, s/n, 28040, Madrid, Spain.y E-mail: [email protected]

Contract/grant sponsor: EC; contract/grant number: NNE5/1999/547.

Applications

some examples calculated on a yearly basis. This table has been compiled from solar radiation data contained in

the H-World database,6 except for the case of Tudela, where radiation data has been provided by the Regional

Meteorological Services of Navarra. Although it does not affect the central message of this paper; it is worth

mentioning that significant data differences are found for the same location, when consulting different sources

of solar radiation data.

The major motivation for the development of other one-axis tracking alternatives is to overcome this limita-

tion, while keeping the mechanics fairly simple. This is the case for the 1�4 MW PV plant installed in Tudela

(Spain), which is formed of 400 azimuth trackers. This type of tracker rotates around its vertical axis, in such a

way that the azimuth of the receiver surface is always the same as the Sun’s azimuth, while its tilt angle remains

constant. Calculation of the solar radiation collected by ideal tracking is rather straightforward, the basic rules

are well defined in classical books on solar radiation.7 Some results in Table I show that azimuth tracking repre-

sents an energy collection increase, in comparison with horizontal axis tracking, of about 10%. It can also be

seen that the advantages of tracking energy increase for both latitude and clearness index. In the case of Tudela,

the energy collected by an ideal azimuth tracker is about 40% higher than that corresponding to an optimally

tilted static surface.

When several trackers are arranged together, mutual shadows give rise to a design optimisation problem. The

lower the spacing between adjacent trackers, the lower is the gross land occupation and, therefore, the lower the

land-area-related costs (land, civil works, wiring, etc.). On the other hand, the larger the impact of shadowing,

the greater is the detrimental effect on the electricity generation of the PV plant. This paper first examines the

theoretical aspects of this problem, by relating the collection of energy to the relevant design parameters,

namely, the tilt angle � and the aspect relation (length/width) b of the single tracked surfaces, and the spacing

between adjacent trackers in North–South and East–West directions, lNS and lEW, respectively. The so-called

Back-tracking8 features are also considered as a mean of reducing shadowing impact. Then, a cost-optimisation

exercise is performed for the particular case of the recently installed 1�4 MW Tudela PV plant, and some general

conclusions are outlined.

GEOMETRY OF SHADOWING

Let us consider a set of azimuth trackers arranged as shown in Figure 1. Note that the ground cover ratio (GCR),

defined as the ratio of total PV module area to total gross land area, is given by:

GCR ¼ b

lNS lEWð1Þ

Table I. Yearly solar energy collection in several locations

Location �(�) Clearness indexa Ga0b, (kW h m�2) Two-axis/Ga0

c Horizontal/Ga0d Azimuth/Ga0

e Static/Ga0f

Medellin 6�2 0�469 1708 1�22 1�18 1�08 1

Morelia 19�7 0�410 1470 1�20 1�14 1�08 1

Cayro 30�6 0�637 2040 1�54 1�40 1�44 1�04

El Paso 31�5 0�689 2190 1�63 1�46 1�50 1�06

Tudela 42�1 0�596 1680 1�63 1�43 1�56 1�10

Freiburg 48 0�428 1100 1�42 1�26 1�36 1�07

St Petersburg 59�5 0�453 942 1�72 1�43 1�64 1�18

Ice-Island 80 0�580 900 2�71 1�94 2�5 1�67

aRatio (global horizontal/extraterrestrial) irradiation.bGlobal horizontal irradiation.cRatio (two axis tracking/horizontal) irradiation.dRatio (one North–South horizontal axis tracking/horizontal) irradiation.eRatio (one azimuth axis tracking/horizontal) irradiation.fRatio (optimally tilted static/horizontal) irradiation.

534 E. LORENZO ET AL.

Copyright # 2002 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2002; 10:533–543

Figure 2 shows the solar angular coordinates: solar azimuth S, and solar altitude �S; and the incidence angle of

the beam radiation on the tracking surface �S. Straightforward geometrical considerations lead to:

�S ¼ �

2� �S � � ð2Þ

East–West shadowing

Depending on the Sun’s position, partial shadowing between two adjacent trackers may occur, mainly in the

early morning and late afternoon. Figure 3 shows a case of shadowing in the East–West direction. The horizon-

tal projections of two adjacent tracked surfaces and their corresponding mutual shadowing are presented in

Figure 3(a), and additional geometrical details are given in Figure 3(b). Note that shadowing occurrence

requires two simultaneous conditions. First, the shadow should point to the adjacent tracker and, second, its

length should be large enough to reach it. This can be described by introducing a parameter FSEW, being 1 when

ideal tracking leads to shadowing occurrence and 0 otherwise. Thus:

ðLEW cos SÞ < 1 and ðLEW sin SÞ < s ¼ s1 þ s2 ) FSEW ¼ 1 ð3Þ

Figure 1. Design parameters of a tracking field: (a) tilt angle �; (b) aspect relation b; (c) spacing between

adjacent trackers in North–South and East–West directions, lNS and lEW

Figure 2. (a) Solar coordinates: azimuth S, and elevation �S; (b) incidence angle of the beam radiation �S

SINGLE-AXIS TRACKING PV SYSTEMS 535


where

s1 ¼ b cos � and s2 ¼ b sin � cot �S ð4Þ

Because of the finite dimensions of the PV field, East–West shadowing unavoidably occurs at in some times

during the year ( S ! �=2 and �S ! 0, close to sunrise at the equinoxes). When shadowing occurs, it can be

avoided by moving the surface’s azimuth angle away from its ideal value, just enough to get the shadow border-

line to pass through the corner of the adjacent surface (Figure 4). The new surface’s azimuth, 0, is given by:

0 ¼ S � FSEW AC ð5Þ

where AC is the azimuth correction angle, which can be found by analysing the triangles SS1S2 and T1S2T2.

From the first:

s ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis2

1 þ s22 þ 2s1s2 cos AC

qð6Þ

Figure 3. East–West shadowing in ideal tracking. Horizontal projection of: (a) trackers and shadows; (b) a meridian plane

Figure 4. Surface azimuth necessary to avoid East–West shadowing 0



sin S2 ¼ s2

ssin AC ð7Þ

1 ¼ �

2� S þ AC � S2 ð8Þ

and from the second:

bT2 ¼ �

2þ S2 ð9Þ

sin bT2 ¼ lEW sin 1 ð10Þ

The solution of the system formed by Equations (6–10) leads to the value of AC. It is worth noting that:

� ¼ �

2) AC ¼ cos�1ðlEW cos SÞ ð11Þ

which represents a maximum limit for the AC value for the general case. Because such a maximum always

avoids shadowing, it can be used as a rough approximation to the general case.

This non-ideal tracking mode is called back-tracking, and has sometimes been implemented in horizontal

single-axis tracking.8–9 Figure 5 shows the evolution of the surface’s azimuth at an equinox. One can note that

the surfaces begin each day facing South, and gradually rotate towards the East, to avoid shadowing, until some

time in the morning, when they reverse direction and rotate West to minimise the beam incidence angle. Then,

there is no difference between ideal and back-tracking strategies, until the low afternoon Sun’s elevation and

ideal tracking strategy would produce shadowing again. Once more the back-tracking reverses direction and

gradually returns to face the South.

North–South shadowing

Figure 6 shows the horizontal projection and a tracked surface with its corresponding shadow for a general case.

North–South shadowing requires, first, that the shadow falls behind the front line of the rear trackers row, and,

second that shadow points toward some tracker, and not towards the free space among them. A conservative

approach (reasonable for low lEW values) consists of assuming that shadowing occurs just when the first

Figure 5. Surface azimuth angle plotted against solar time



condition is fulfilled. This can be described by defining a parameter FSNF, being 1 when North–South shadow-

ing occurs and 0 otherwise. Thus:

lNS < s sin 1 þ sin 0 ) FSNS ¼ 1 ð12Þ

ENERGY PRODUCED BY THE PV PLANT

For simplicity, let us consider that all the solar cells of a single-tracked surface are associated in series, that the

cell size is negligible compared with the surface size, and that the PV field is large enough to neglect border

effects. Note that in the hypothetical situation of only beam radiation, the simple shadowing event would annul

the output of the whole PVarray. Thus, neglecting the albedo, the electrical power from the PV field is given by:

P ¼ �A�FSNS Bð�; 0Þ þ Dð�; 0Þ

�ð13Þ

where � and A are the global efficiency of the PV plant, and Bð�; 0Þ and Dð�; 0Þ are the beam and diffuse

irradiances incident on the tracked surfaces. The annual electrical energy produced by the PV plant, EPV, is

given by the integral of P over the whole year, and is easily calculated from widely available horizontal solar

radiation data, following classical procedures to translate from horizontal to inclined surfaces.10

In particular, we have developed an hourly-based software application that uses as input the twelve monthly

mean values of the horizontal global daily irradiation. It considers the diffuse global correlation proposed by

Collares Pereira and Rabl,11 the Liu and Jordan method12 to estimate hourly irradiation values from the daily

irradiation, and the model proposed by Hay and McKay13 to estimate the circumsolar and isotropic components

of the diffuse solar radiation. Then, the circumsolar radiation has been treated as beam radiation for considera-

tion of shadowing. On the other hand, we have estimated the global efficiency of the PV plant by considering

separately each phenomenon that affects its behaviour, as indicated by the following expression:

� ¼ ��TC �AL �INV ð14Þ

where �* is the efficiency of the PV array under standard test conditions (STC), �TC takes into account the

dependence of the efficiency on the operating temperature of the solar cells,14 �AL takes into account the angular

reflection losses at the PV module surface,15 and �INV considers the DC-to-AC conversion losses.16

Figure 6. North–South shadowing; horizontal projection of a tracker and its shadow



In this way, a value for annual energy production can be calculated for each PV field configuration, i.e., for

each set of �, b, lEW and lNS values, given the characteristics of the PV modules and the inverter composing the

PV plant. Obviously, the largest possible energy yield corresponds to the case of only one tracked surface,

which excludes mutual shadowing and allows for fully ideal tracking. Just for this case, Figure 7 shows the

relative variation of the energy yield, as a function of the angle of inclination of the tracked surface, for several

locations. It can be seen that, irrespective of the site, a maximum occurs for an inclination close to the latitude

plus 10�. It is very interesting that the sensitivity of the annual capture of energy for the inclination angle is very

low. A value of approximately 0�4% loss for each degree of deviation from the optimum value is roughly indi-

cative of the situation. A descriptive empirical expression is:

EPVð�ÞEPVð�optÞ

��l¼1

¼ a0 þ a1ð� � �optÞ þ a2ð� � �optÞ2 ð15Þ

where � is the site latitude, �opt ¼ �þ 10�; a0 ¼ 1; a1 ¼ 0�32 � 10�2, and a2 ¼ �10�4. It is interesting to note

that, because the product �A is scarcely related to the inclination angle, such functions are essentially

independent of the PV module and inverter type. Hence, they describe not only the energy produced by the

PV field, but also the energy collected by the PV array.

OPTIMAL DESIGN

A rough approximation to the produced energy unit cost CE can be made by assuming that it is a linear function

of the ratio between the total investment cost and the yearly energy yield. Furthermore, the total investment cost

can be divided into a term related to the gross land area (wiring, civil works, fencing, land, etc.) and another

term independent of it (PV modules, tracking structures, inverters, etc.). Thus:

CE ¼ a

EPV

ð p1 p� þ lEW lNS NT p2Þ ð16Þ

where p1 is the cost per unit of peak power of the PV system excluding land, p* is the STC power of the PV

array, p2 is the land area related cost per unit area, NT is the number of trackers composing the PV field, and a is

a parameter accounting for the evolution of the economy (discount rate, inflation, etc.). The cheapest concei-

vable energy cost corresponds to the hypothetical case of only an optimally tilted ideal tracker and no land

occupation. It is worth using this case as a reference. Thus:

CE

CREFE

¼ EREFPV

EPV1 þ 1

GCR ��GSTC

p2

p1

� �ð17Þ

Figure 7. Relative yearly energy production of ideal one-axis trackers plotted against tilt angle for several locations



This ratio represents the relative unit energy cost associated with a particular PV field configuration, and is

particularly well suited to judge the merit of its design.

The Tudela PV plant

Table II summarises the required input data for the optimisation design of the Tudela PV plant. The most

obvious criterion is to seek to lower the unit energy cost, i.e., to select the configuration leading to the minimum

value of the ratio described by Equation (17). A simple approach consists of the successive optimisation of each

configuration parameter. In this way, an inclination equal to �opt is first selected. Figure 8 shows the cost ratio as

a function of b and lEW, for a given lNS. It is noticeable that the lowest b gives the lowest the energy cost. How-

ever, there are practical limits to b. On the one hand, values lower than b’ 0�5 imply lengthy pedestal structures,

which are inherently unstable in strong winds. On the other hand, all the PV modules of a single series string

should be installed in the same tracker to avoid mismatching losses.

In our case, the pre-established DC nominal voltage of the PV field (450 V) requires each string to be formed

by 36 PV modules, for which 8 different arrangements can be imagined: 1� 36, 2� 18, 3� 12, 4� 9, 6� 6,

9� 4, 12� 3 and 18� 2. Moreover, each arrangement can adopt two different physical dispositions, depending

on the PV module side chosen as the length. Hence, 16 values for b, ranging from 0�012 to 81�7, are possible.

We have finally selected a 3� 12 arrangement leading to b¼ 0�5675, which is shown in Figure 9.

Coming back to Figure 8, it can be seen that the optimum value of lEW is about 2�3. Now, Figure 10 shows the

variations of the cost ratio as a function of lNS, for � ¼ �opt; b ¼ 0�5676 and lEW ¼ 2�3. The ratio (EPV/EREFPV ) is

also shown. Again, an optimum lNS value around 2�3 is observed. Hence, the strict optimum design corresponds

to a GCR’ 0�1, which is much larger than usual values in common PV fields, and has adverse aesthetic

implications (trackers too sparsely placed), which can not be neglected in highly visible demonstration

Table II. Input data for the design of the Tudela PV plant

Latitude(�) 42�1Reference year, m¼ 1 � � �12

Global horizontal daily irradiation (W h m�2 1826, 3184, 4637, 5777, 6611, 7183, 7494, 6489, 5000, 3247, 2118, 1582

Maximum daily temperature (�C) 6�9, 7�4, 12�6, 15�4, 19�4, 24�6, 26�1, 28�0, 21�0, 13�7, 9�5, 9�1Minimum daily temperature (�C) 0�7, 1�0, 3�6, 5�4, 9�1, 12�7, 13�0, 14�6, 11�2, 7�0, 3�3, 3�2PV module dimensions (mm) 1222� 538

PV array STC efficiency (%) 13�3Inverter efficiency parameters16 k0¼ 0�01, k1¼ 0�025, k2¼ 0�05

Cost parameters p1¼ 6�6 s/Wp; p2¼ 6 s/m2

Figure 8. Relative energy production (dashed lines) and cost ratio (dotted lines) plotted against East–West spacing; tracking

aspect relation b is used as parameter



projects, such as the present case. Because of this, we also have analysed other less land-consuming alternatives.

Fortunately, they are largely favoured by the low sensitivity of the unit energy cost to the GCR. The same is

true for the energy yield. For example, the figures of merit for the optimal case are (CE/CREFE )¼ 1�166 and

(EPV/EREFPV )¼ 0�923, while for lEW¼ 1�547 and lNS¼ 2�012, the values are (CE/CREF

E )¼ 1�2436 and

(EPV/EREFPV )¼ 0�85 and GCR¼ 0�182. In other words, selecting this case implies a 6�7% energy cost increase,

but a 41% reduction of the total occupied land. We have finally selected this case because it adapts particularly

well to the available terrain. Figure 11 shows a general view of the plant. Table III presents the yearly perfor-

mance parameters for this case, as estimated by the model. The corresponding performance ratio,17 defined as

the ratio between the final yield and the on-plane irradiation, is 0�82, which is rather optimistic when comparing

it with current experimental values. The reason lies in the different losses not considered by the model: wiring,

dirt, mismatching, supplied PV power below nominal values, etc. Together, they will probably amount to an

11% energy production decrease, leading to a performance ratio of about 0�73.

DISCUSSION

We fully understand the reader’s surprise when realising that, after the two rather tedious tasks of developing a

full behaviour model for the PV plant, and performing a cost optimisation exercise, our final design differs from

Figure 9. Selected tracker for the Tudela PV plant: (a) front; (b) back. The driven mechanism can be observed

Figure 10. Relative energy production (dashed line) and cost ratio (dotted line) plotted against North–South spacing



the optimal one, and attaches importance to aesthetic considerations. We also understand the tendency to

believe that the usefulness of the model presented is restricted to clarifying the geometry of back-tracking

for azimuth tracking, and to estimating the energy performance of the PV field. However, the model can be

used to study other relevant problems, such as the sensitivity of the design to economic factors, and the

comparison of tracking with conventional static alternatives.

For the first point, and because PV modules and tracking structures are expected to become cheaper in

the future, we have analysed the variation of the optimal GCR with respect to the ratio p2/p1. Table IV shows

the corresponding results. Roughly, a five-fold increase in cost ratio is translated into a two-fold decrease of the

required area. It is worth mentioning that the particular circumstances of the Tudela PV project have led to very

low p2 and high p1, i.e., to a rather low p2/p1ratio. In our opinion, p2/p1 close to 1�3 is a more representative value

for possible commercial PV plants.

For the second point, we have performed a similar design optimisation exercise for a hypothetical PV field

composed of fully static conventional support structures, and also operating in Tudela. For the same values of p1

and p2, the result is an optimal GCR¼ 0�38, but the corresponding energy cost ratio (CE=CREFE ) is 1�48.

Compared with the actual tracking plant, the static PV plant would require only about 60% of the land, but

the energy cost would be 28% higher.

Figure 11. General view of the Tudela PV field

Table III. Estimated annual energy performance of the Tudela PV plant

Model estimates

Horizontal irradiation (kW h m�2) 1680

On-plane irradiation (kW h m�2) 2366

Effective on-plane irradiation (kW h m�2)* 2235

Array DC energy yield (kW h kWp�1) 2100

PV plant AC final yield (kW h kWp�1) 1941

Performance ratio 0�82

More realistic estimates

Other losses (%) 11

PV plant final yield (kW h kWp�1) 1728

Performance ratio 0�73

*Considering shadowing and reflection losses.

Table IV. Optimal GCR versus different economic scenario

p2/p1* Optimal GCR

0�9 0�10

1�3 0�12

4�5 0�18

*In units of (currency/m2)/(currency/Wp).



CONCLUSIONS

This paper has discussed the theoretical aspects of azimuth tracking, including shadowing and back-tracking.

From them, a model capable of analysing the relation between the configuration of tracking PV plants (tilt

angle, aspect relation and spacing) and their energy performance and energy cost have been also presented.

This model has been used on the design of the 1�4 MW PV plant, recently installed in Tudela (Navarra,

Spain). The finally selected value of the GCR is 0�182, and the expected yearly energy yield is about

1700 kW h kWp�1. The comparison with conventional static arrangements shows that azimuth tracking land

requirements are about 40% larger than conventional static arrangements, but the corresponding energy cost

can be significantly reduced, providing the tracking structure’s cost is kept close to the static structures.

Acknowledgements

This work has been supported by the European Commission, under contract NNE5/1999/547. The authors

would like to acknowledge the helpful collaboration of all the persons involved in this project. The Diputacion

Foral de Navarra has been kind in providing the radiation data.

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Design of Tracking PV Systems With a Single Vertical Axis

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