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Renewable Energy 31 (2006) 20422062

Design of grid connected PV systems considering

electrical, economical and environmental aspects:

A practical case

Alberto Ferna ndez-Infantesa, Javier Contrerasa,,

Jose L. Bernal-Agustnb

aE.T.S. de Ingenieros Industriales, University of Castilla-La Mancha, Avda. Camilo Jose Cela s/n.,

13071 Ciudad Real, SpainbDepartment of Electrical Engineering, University of Zaragoza, Calle Mar a de Luna, 3., 50018 Zaragoza, Spain

Received 5 August 2005; accepted 28 September 2005

Available online 2 November 2005

Abstract

This paper presents the complete design of a photovoltaic installation that may be either used for

internal electric consumption or for sale using the premium subsidy awarded by the Spanish

Government. Electric optimization strategies are detailed in the project, as well as the sizing of the

photovoltaic installation and economic and financial issues related to it. The project optimizes the

electricity demand, improving reactive power and studying the convenience of hourly discrimination

fees in addition to the design of the photovoltaic installation. A specific computer application for the

automated calculation of all relevant parameters of the installationphysical, electrical, economical

as well as ecologicalhas been developed to make the process of calculating photovoltaic

installations easier and to reduce the design development time. Moreover, the budget of the

photovoltaic installation is included, as well as its corresponding financial ratios and payback

periods. Finally, the conclusions reached in the technical and economic design of the installation areshown.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Photovoltaic energy; Power optimization; Renewable energies; Computer application

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www.elsevier.com/locate/renene

0960-1481/$ - see front matterr 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.renene.2005.09.028

Corresponding author. Tel.: +34 926 295464; fax: +34 926 295361.E-mail address: [email protected] (J. Contreras).
http://www.elsevier.com/locate/renenehttp://www.elsevier.com/locate/renene

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1. A brief history of the project

The project starts as a response to the inquiry placed by the High School Ojos del

Guadiana (Fig. 1) in Daimiel, Ciudad Real, Spain, to the Industrial Engineering School

at Ciudad Real to study the feasibility of a photovoltaic installation within their premises.Preliminary studies begin in September 2004 and the project is finished in March 2005.

Within these 6 months, the forecasted electric demand, the available surface to place the

solar arrays, overall funding, and other relevant data are exhaustively studied in order to

build a design according to the needs of the Centre. The main innovation of this project

resides in the development of a computer application to design the photovoltaic

installation connected to the grid. This application considers all relevant parameters,

allowing for an interactive design that takes into account all the electric, financial and

economic data simultaneously. In addition, we have reduced the development time and run

several sensitivity analysis studies to compare different solutions.

2. Proposals for optimizing the electricity consumption

The activities oriented to optimize the electricity consumption have produced the results

described in the following subsections.

2.1. Feasibility study of the electricity demand of the Centre

The results of the preliminary study of the electrical consumption confirm a worrying

increase in the demand: from 32,200 kWh and 23,200 kVArh in year 2000 to 44,070 kWhand 28,900 kVArh in 2004, as shown inFig. 2. In 2005, the trend is even sharper. With the

beginning of the construction of a new annex building equipped with 2 classrooms and a

library, demand forecasts are even bigger. The prediction of electric demand for 2005 is

48,100 kWh and 32,000 kVArh. Thus, we plan a strategy based on three key points to

reduce the electricity bill:

1. Optimization of the current electricity consumption studying the possibility of including

reactive compensation equipment and the convenience of signing for different hourly

price discrimination fees.

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Fig. 1. Computer simulation of the High School Ojos del Guadiana building in Daimiel, Ciudad Real, Spain.

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2. Reduction of the electric demand in the next years, proposing basic rules for savingenergy and the selection of new electrical equipment in the future.

3. Feasibility study of a photovoltaic installation connected to the low voltage network

that would cover part of the annual demand of the Centre with solar energy.

To calculate the demand for each bimonthly period, or even for a monthly period, is a

complex task, due to the presence of seasonality, with peaks during the months of January

and February (corresponding to the March invoice) and troughs during July and August,

in which the Centre is closed (September invoice). The most precise way to adjust all data is

to use a moving averages model of 6 periods (equivalent to 1 year).

To predict the electricity demand for 2005 we proceed to seasonalize and deseasonalizethe consumption data from 2000 to 2005, using the centred and non-centred 6-point

moving averages model [1]as shown below:

Pmt

Pt6it

Ti

6 , (1)

Pmct PmtPmt1

2 , (2)

IEt Tt

Pmct, (3)

where Tiis the demand in the bimonthly period i. Assuming that the active and reactive

energy consumptions for a 2-month period are known, we calculate the moving averages

values for 6 periods, as indicated in (1); later, we find the centred moving average value,

Pmci, from Pmiand Pmi1, as shown in (2). And from the moving averaged value centred

in period iand the demand of that period, we obtain the seasonality index of period Ti,

IEi, as shown in (3).

Since the algorithm based on moving averages condenses all the data of the year in a few

values, we use linear interpolation for year 2005 to approximate more accurately. Fromavailable data of the JanuaryFebruary periods for the years 20002004, we extrapolate

the same data for the year 2005, and the same process is repeated for all bimonthly periods.

With the actual data from 2000 to 2004 and the first forecast for 2005 we proceed to

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0

10000

2000030000

40000

50000

60000

kWh/kVArh

Active Energy Reactive Energy

2000 2001 2002 2003 2004 2005

Year

Fig. 2. Annual development of the electricity demand of the Centre and future trend obtained using interpolation.

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calculate the seasonality indexes for each of the periods. Once this is done, we order theseasonality indexes in columns and we calculate the seasonality indexes corresponding to

each of the bimonthly periods, so that the sum of all of them is equal to 6, which is the

number of periods considered in a yearly cycle. With this we obtain the factors to weigh the

linear estimation for the complete year (obtained from the overall consumption data in

previous years, as shown inFig. 3). In this way, we obtain the weighted demand for each of

the bimonthly periods. To approximate the demand profile even more, we have distributed

the result for each bimonthly period between the two months, using a smooth distribution

function that considers the number of working days of the month.

2.2. Compensation of reactive energy

The compensation of reactive energy may result in a 4% bonus in the electricity bill, as

opposed to the current 5% penalty, if it were possible compensate between 90% and 98%

of the total reactive energy demand. Currently, for every billing period, the average value

of the power factor cos j is given by

cos j Eaffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

E2aE2r

q , (4)

where Ea and Er are the values of the active and reactive energy demands, respectively,during the billing period.

Using Eq. (5) we can calculate the penalty or the bonus applied by Spanish law; it is

limited to 47% in case of penalty, and to 4% in case of bonus:

kr% 17ffiffiffiffiffiffiffiffiffiffiffiffiffi

cos2 jp 21. (5)

In our calculations we specifically take this fact into account for the year 2005. Later, we

compare the bills with and without compensation to obtain the annual savings.

Likewise, we calculate the reactive power of the equipment necessary to compensate the

reactive demand, based on the total amount of the demand (with the exception of a baselevel demand of the entire year, which is consumed by static equipment and concentrated

within the daily 8 h with the highest demand). Thus, a piece of equipment of 17.5 kVAr

should meet the demand 100% of the time, smaller units ranging from 12.5 to 15 kVAr

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Cos

0

2000

4000

6000

8000

10000

12000

Jan-00 May-00 Sep-00 Jan-01 May-01 Sep-01 Jan-02 May-02 Sep-02 Jan-03 May-03 Sep-03 Jan-04 May-04 Sep-04 Jan-05

kVAh/kVArh

0.00

0.20

0.40

0.60

0.80

1.00

1.20

Active Energy Reactive Energy Cos

Fig. 3. Development of the active and reactive electricity demands of the Centre, showing seasonalities.


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may be unable to meet the demand sometimes, and the compensation would not be

optimal (98% of reactive demand).

2.3. Reduction of electricity consumption

We present a series of actions for the following years, especially for 2005, where the

demand shows a marked trend to increase. The suggested actions are fundamental to keep

a certain level of independence with respect to the future incomes obtained from

photovoltaic generation. The actions can be reduced to the following ones:

Rational use of energy. Replacement of obsolete equipment of high consumption whenever possible. Progressive renewal of current lighting equipment by new equipment with reflectors and

electronic ballasts.

Discarding the use of electricity for heating (furnaces, convectors, accumulators, etc.),only allowing it for heat pumps and refrigerators.

Adaptation of the computer equipment: selection of moderate consumption feeders andLCD-type screens.

Publicity campaign oriented to the students promoting consumption moderation andenvironmental consciousness in public and in private.

Periodic reporting of the energy savings results.

3. Photovoltaic installation design method

Once the convenience of having a solar photovoltaic installation has been decided, we have

to consider the limited economic funds available to the Centre. Thus, instead of choosing a

traditional design based on power from generators and inverters we seek a more flexible design

method that takes into account all the parameters that can have an influence on: performance,

production, financial data, available subsidies, remuneration for selling electricity, taxes

applied to the remuneration, annual quota in concept of repayment once the electricity sales

income is discounted, etc. This custom-made concept is the most innovative feature of this

project;Fig. 4reflects the main differences between both design philosophies.

In this way, our automated calculation of the solar photovoltaic installation generates

numerous advantages compared to a traditional design method:

It considers many more parameters, in fact, more than 60. It allows for a better-adjusted design where we can alter parameters such as power,

surface, orientation, production of energy, profitability, etc.

Fast sensitivity analysis of influential parameters. Faster design process with many scenarios that reflect particular needs. For a quick modification of the parameters we link our application to a database that

includes the main features of the most popular photovoltaic panels and inverters; by

typing the code and the number of units, the application collects all data necessary to

proceed with the calculations.

The main factors considered in our computer application that affect the performance of

the photovoltaic generators are described in following subsections.

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3.1. Solar irradiation data variability

While theAtlas of Solar Radiation in Spain provides the most optimistic data, the most

conservative data come from theNASAweb site[2], showing a standard deviation of 3.6%

and a variability greater than 7%. We use data fromNASA Surface Meteorology and SolarTables (SSE). As shown in Table 1 obtained from [3], it can be observed that actual

readings obtained in the same place by different sources provide results that vary around

10%. Thus, we consider adequate using the most pessimistic available data.

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Fig. 4. Diagram comparing the traditional design process versus our flexible calculation method.

Table 1

February and yearly averages of the daily horizontal global irradiation in Algiers, according to different sources

Information source February Gd(0) (kWh/m2) Yearly average (kWh/m2)

CDER 3.03 4.23

Capde rou 3.20 4.60Censolar 3.00 4.37

NASA 2.90 4.45

Meteonorm 3.00 4.52


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3.2. Losses due to shading over the PV panels

They can be due to distant shading (trees, posts, nearby buildings, etc.) if shadows

interpose between the sun and the panels during the day, or due to direct shading, if there

are several rows of panels arranged in the same horizontal plane.Losses can be important, because of that, the location must be carefully chosen to avoid

distant shading as much as possible, whereas, to avoid direct shading, we can opt to split

each row of panels arranged in the same plane, or to elevate them on an inclined surface.

To estimate losses due to distant shading we use the method proposed by the Institute for

diversification and energy savings(IDAE)[4] of Spain, by superposing the profile of visible

obstacles observed from the installation point to a graph of solar trajectories (see Fig. 5).

Each sector of the graph has an associated loss coefficient that varies according to the

orientation and the slope of the panels. We calculate each of the sectors intercepted by the

shading profile and we add up the corresponding coefficients obtained from a table,

depending on the orientation and slope of the panels. This results in a loss percentage for a

particular location. This is the only loss contribution that is not automated in our

program; Fig. 5 shows that there are no obstacles in the solar trajectory and losses are

negligible (0.2%).

On the other hand, losses due direct shading are estimated to be around 2% [4]. Lower

values cannot be considered for a flat-grounded placement, even if the distance between

two consecutive rows is greater than the one shown in (6), such that

dmin hvertical

k , (6)

where coefficientkis calculated as [tan(611latitude)]1. The latitude of the location is 391

050 N; therefore coefficient k is: [tan(611391050)]1 [tan(211550)]

1 2.4855.

We obtain the height of the panel, according to its dimensions and optimal slopes, from

Eq. (7). Also, we can deduce the minimum spacing between rows of modules using Eq. (8).

hverticalLmodsinb hsup, (7)

dmin kLmod sinb hsup 2:4855 1:593sin30:67 0

ffi2:55m, 8

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Fig. 5. Superposition of the solar trajectories diagram to a panoramic view of the roof for shading calculation.


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where b is the inclination angle that turns out to be 30.671, as shown in Section 3.4. See

Fig. 6for a pictorial description of the calculations.

3.3. Losses due to electric conductors

These losses are important in DC, when the voltage is low. It is crucial to conveniently

size the conductor sections so that the voltage drop is less than 1.5%. It is also important:

to place the generators close to the inverters, to work at the maximum DC voltage that the

panels and the inverters can withstand, to increase the conversion performance, and to

reduce ohmic losses. Depending on the conductor section considered, our computerapplication calculates losses due to voltage drop in DC.

3.4. Slope, orientation and glass surface reflexivity of the PV panels

Usually, if the PV panels are not perfectly oriented to the south (azimuth 01 in the

northern hemisphere), their orientation can originate a considerable loss of efficiency.

Likewise, the slope of the panels should be changed two to four times a year to maximize

the solar absorption, since the optimum slope in the summer is not the same as the

optimum one in the winter.

Glass surface reflexivity protects the panels from the accumulation of dirt in the surface;a dirty glass reflects a percentage of energy that increases with the divergence of the

incidence angle with respect to a perpendicular line to the glass surface plane (a glass

reflects more light and looks dirtier when you observe it from the side). This causes the

panels to reflect part of the direct radiation and the majority of the diffuse radiation

available. Rain can solve this problem, but in the summer season the efficiency of the

radiation is significantly reduced unless the surface of the panels is cleaned on a regular

basis.

We use Eq. (9) to calculate the optimal slope [5]:

bopt 3:7

0:69f, (9)where bopt is the inclination angle that optimizes the incident radiation over the panel

surface for a year, and f is the latitude of the location point. The optimal angle that is

obtained from Eq. (9) is 30.671.

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Fig. 6. Minimum spacing between two consecutive rows of panels as a function of the geometric parameters.


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Provided the optimal angle and the annual irradiation over a horizontal surface, (Ga(0)),

it is possible to calculate the value of the annual irradiation for the optimal anglebopt using

Gabopt

Ga0

14:46104 bopt1:19104 b2opt

. (10)

Finally, we calculate the incident effective annual irradiation over the generators surface,

denoted byGeffb; a, using Eqs. (11) and (12) proposed in[5], including orientation, slope,and reflexivity due to dirt on the surface of the glass

Geffb; a

Gabopt g1b bopt

2 g2b bopt g3, (11)

gig1ijaj2 g2ijaj g3i; i 1; 2; 3, (12)

wherea is the azimuth, and the coefficientsg1i,g2i,g3idepend on the degree of dirtiness ofthe panel. For a medium-dirtiness case, the values of these coefficients correspond to the

ones shown inTable 2.

3.5. Efficiency of the inverters

Despite being electrical equipment of high performance in DC/AC conversion, they

never reach 100% efficiency [6]; they reach their optimum performance in the range of

8596% efficiency for power values close to the nominal rating, while for the generation of

small amounts of powerin conditions of cloudiness, start-ups, sunrise and sunsetthe

efficiency can diminish considerably. Spanish law [7] makes the use of inverters with aminimum efficiency at 25% of the nominal power compulsory, which means selecting good

equipment turns out to be fundamental. Also, the monitoring of the point of maximum

power and the adaptation to the variable conditions of generation involves a small loss of

power during normal operation conditions. For single-phase inverters, the sum of all the

losses can be about 820% of the total energy generated, depending on the quality of the

equipment. The data provided by the manufacturers for each model is included in the

database of the computer application; we also consider a loss factor by monitoring the

Maximum Power Point (MPP) and the start-up/shutdown of the inverters.

3.6. Actual power produced by the PV panels

It is usually lower than the nominal value in catalogues [8]. Spanish law[7]establishes

that the power, measured in standard conditions, cannot be lower than 90% of the

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Table 2

Coefficients used in (11), with 97% transmittance due to dirt

Tdirty0=Tclean0 0:97

Coefficients i 1 i 2 i 3

gi1 8 109 3.8 107 1.218 104

gi2 4.27 107 8.2 106 2.892 104

gi3 2.5 105 1.034 104 0.9314


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nominal power value in catalogues. A breach of contract could be reason for refund

(almost all the manufacturers freely replace the panels if they do not comply with the

specification of the 90% of power), but one must consider that the standard conditions:

1000 W/m2, 25 1C in the surface of the cells and spectral distribution 1.5 AM, in which the

nominal power is measured, do not correspond to the real working conditions.To reach a temperature of 25 1C in the cells of the panel, it is necessary that the ambient

temperature is, approximately, 5 1C. Provided that the ambient temperature is usually

greater than this value, there can be a decrease in the power delivered by the panels because

the open circuit voltage and the maximum power voltage diminish when the temperature

increases with respect to the nominal condition (25 1C). However, the current delivered by

the panel does not significantly depend on the temperature. Therefore, the power delivered

by the panels is usually lower than the nominal one.

Our computer application considers the nominal power minus 10%, or the maximum

percentage guaranteed by the manufacturer, if it were smaller. Then, it is multiplied by a

variable coefficient[8]that takes into account: (i) the average temperature at noon for each

month in the considered location and (ii) the decrease of power due to temperature, as

explained above.

The relation between the power output of the panels and the nominal power of the PV is

calculated in

Preal Pnom 100devnom%

100

100 DP 25Tcell

100

, (13)

where devnom (%) is the maximum deviation of power guaranteed by the provider [W], DP

is the power variation for each degree increase in the temperature with respect to the 251

Cnominal value [W/1C], and Tcell is the average temperature of the cell during operating

conditions (atmospheric temperature while the sun is at its zenith plus an empirical

increment between 8 and 20 1C, depending on the climate).

Note that ageing and degeneration of the modules causes them to slightly decrease their

performance each year: due to UV irradiation, severe temperature changes have a

cumulative effect over the electrical production.

4. Final design of the grid connected PV installation

Once all data described in Section 3 are considered, we proceed to obtain the overall

electricity production for each monthly period, according to the longitude and latitude

data obtained, using Eq. (14) [5].

Emonth Pnom Geffect

G

FShadow Feff

kWh

month

, (14)

where Pnom is the nominal power, as indicated by the manufacturer of the photovoltaic

panels in standard conditions, Geffect is the effective annual incident irradiation over the

panel surface considering the orientation angle and the panel slope, G is the value of the

irradiation for whichPmaxis measured: 1000 W/m2, 25 1C,FShadowis a factor that considersthe losses due to shading in the panel, Feffis an efficiency factor including the losses in the

inverter, the losses in the generators at temperatures greater than 25 1C, and the voltage

drops in the lines.

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With all this, Feffoscillates between 0.7and 0.9 for a standard installation, and mainly

depends on the quality of the equipment selected. IfFeffwere lower than 0.7 it would imply

a deficient performance of one or several components.

The optimal dimension of the photovoltaic installation that meets all High School

requirements is a plant composed of 72 modules, each module with a peak production of160 peak power or Wp (total production is 11,520 Wp). The plant is arranged in 12 groups

of 6 modules, where each group produces 960 Wp. The modules are connected in series and

operate at 210 V and 4.55 A in nominal rate. Every 3 groups of 6 modules are also

connected to the inverter through a pair of wires, so each pair of wires (4 pairs in total)

operates at 210 V, 13.65 A and 2880 W (nominal rate). SeeFig. 7for details. The panels are

oriented to the south forming an angle of 11.231with respect to the main orientation of the

roofs of the building. The modules are manually mounted on inclinable supports to

maximize the electric power generation. The optimum slope in case of fixed supports is

30.671, as calculated in Eq. (9).

As shown inFig. 8, the generation plant is connected to 3 single-phase inverters; two of

them withstand 2600 W during nominal operation, and the other one withstands 4600/

5200 W. The latter can be connected either to 5 or to 6 basic groups of 6 photovoltaic

modules to reduce total investment without modifying the optimal performance

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Fig. 7. Arrangement and connections of the photovoltaic modules.


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conditions. Each inverter comes with its own electrical protections and is connected to oneof the phases (R, S, T) of the low voltage grid, delivering power ranging from 9800 to

10,400 W. To ensure the optimal protection of the electrical equipment and the inverters

from their environment, they are located within a 1.50 2.50 m brick-made shelter placed

beside the High Schools gym, conveniently insulated against rain and humidity and

adequately ventilated. SeeFig. 9 for an overall 3D view of the installation, including the

inverters shelter, andFig. 10for a detailed view of the solar panels.

The power ratio (PGenerator=PInverters) is near 1.10. The efficiency of the inverters istypically 94% (maximum efficiency is 96%). The section of the cables has been enlarged by

design to reduce DC losses, and the location of the power lines and inverters has been

chosen to reduce the distance to the MV/LV transformer substation. The lines from themodules to the inverters are aerial, whereas the three-phase line to the main grid is buried

underground.

The electrical production of the installation would approximately meet 29% of the

estimated demand for 2005, as shown in Fig. 11, but it would have met 43% of it in the

year 2000, 42% in 2001, 35% in 2002, and 32% in 2003. That is why it is equally important

to take actions to also reduce the electric consumption, as detailed in Section 3.2. The

calculation of the photovoltaic power production is automated in our computer

application from data inputs.Fig. 12compares the forecast of the photovoltaic generated

energy versus the forecast of electrical demand of the High School per month. The energy

produced per kWp in such conditions is about 1207 kWh per year. This data is far from theoptimistic forecasts of many photovoltaic manufacturers, who predict values between 1300

and 1500 kWh per year. Note that our installation is optimized for normal operation and

does not have shading effects [9].

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Fig. 8. One-line diagram of the proposed photovoltaic plant.


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5. Environmental analysis

The final design has resulted in an electric power plant composed of photovoltaic

modules based on polycrystalline silicon technology with a peak power of 11,520 Wp and 3

single-phase inverters, one of 5200 W and two of 2600 W, totaling 10,400 W in nominal

operation. Each inverter injects its current to one of the phases (R,S,T) of the low voltage

grid. The area of each photovoltaic module is 1.26 m

2

(1.16 m

2

of active area) so that the 72projected modules add up to a collector area of 90.57 m2, whose active area is

approximately 83.61 m2.

The estimated electrical efficiency of the modules is approximately 13.5%, losses related

to orientation, slope and dirt of the modules are estimated around 6.88%, losses due to

indirect shading are negligible and direct shading losses are around 2%. In addition, power

losses due to temperature are around 4.42%, assuming that the cells surface temperature is

12 1C higher than the monthly average temperature when the sun is at its zenith. Power

losses due to voltage drops are estimated around 1%, due to oversized cable sections. All

things considered, the power plant generates an average of 1.287 MWh each month, as

shown in detail inTable 3.On average, 1.158 MWh are injected to the grid per month, considering all types of

losses, with an 85% efficiency factor. Compared to the thermal data, the electric

production is equivalent to the combustion of 1.195Tons of Oil Equivalents(TOE) or 1.708

Tons of Coal Equivalents (TCE), even after assuming a 100% efficiency factor in

generation, transformation and distribution of the electric power. Considering a more

realistic scenario and assuming that:

(1) The electricity would be generated from a combined cycle or an equivalent technology

whose efficiency factor could be around 50% on the average.

(2) A 95% efficiency factor in each successive voltage adjustment: from 12,000 V-

250,000 V, from 250,000 V-20,000 V and from 20,000 V-380 V.

(3) Additional losses of 5% in low voltage distribution, then, we would have an

approximate overall efficiency factor of 40%.

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Fig. 9. 3D view of the installation showing the DC circuit and the location of the inverters shelter.


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August 3%

July 4%

June 4%

May 3%

April 3%

March 2%

February 2%

Forecast 71%

September 3%October 2%

December 1%November 1%

January 1%

Fig. 11. Monthly PV generation forecast vs. annual electric demand of the Centre.

Fig. 10. 3D detail view of the solar panels arrangement on the roof.


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So, to generate the same electric power using fossil fuel [10], it would be necessary toburn up to 2.934 TOEor up to 4.197 TCEevery year, even without considering the cost

and power needed to extract, refine and deliver the fuel, which would increase prices even

more.

All of this implies that, throughout a life-span of 25 years for the entire installation, the

photovoltaic modules would produce the same power as 73.35 tons of oil or 104.93 tons of

coal, with the subsequent reduction in emissions of CO2, NOX and SOX. So, the

consideration of the environmental impact changes the global appreciation of the

installation [11], especially if we take into account the relatively small dimensions and

the power produced in the plant.

6. Complete budget of the PV installation: economic and financial case studies

We show inTable 4the complete budget of the PV installation.

Current legislation in Spain[12]regarding the production of electrical energy originated

from renewable energy sources, waste and cogeneration, allows all the energy generated by

the PV system to be injected into the grid. In addition, the energy consumed by the PV

system can be bought back at a much lower price than the one paid to the PV system for its

production.

For installations with less than 100 kW of installed power, the energy tariff is establishedat 575% of the average electric tariff, or the reference tariff (updated yearly) for the first 25

years of the installation, decreasing to 460% in the following years.

We carry out two different economic and financial case studies using the methodology

in [10]. In the first case study we assume that the investment is financed through a loan

of 90% of the total value, and the remaining 10% comes from the Centres own funds. In

the second case study, the investment is completely financed with external funds from

a loan that covers the part of the investment that is not subsidized by the Spanish

Government[13].

Next, we present the financial parameters:

Required investment without Value Added Tax (VAT): 64,577 h. VAT: 16% (10,332 h). Taxes not related to subsidies are 8472 h, they are refundable a

year later.

ARTICLE IN PRESS

0

1000

2000

3000

4000

5000

6000

7000

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

[kWh/mon

th]

PV Generation

Electric Demand

Fig. 12. Monthly PV generation forecast vs. monthly electric demand of the Centre.


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ARTICLE IN PRESS

Table3

Averagesola

rirradiation,

temperature-relatedlosses,generatedandgrid-delivered

powerandincomefromelectricitysalesoftheproposedinstallation

(aminussign

indicatespositiveearnings)

Month

IrradiationG

eff

(b,a

)(kWh/m2

month)

Temperature

lossescoefficient

Photovoltaic

gen.power

(kWh/month)

Griddelivered

power(kWh/

month)

Economic

remunerationa

(h)

Electricitybill

(h)

Monthly

differencea

(h)

January

68.0

0

1.027

665.4

9

598.9

4

288.3

5

560.5

8

272.2

3

February

85.5

7

1.015

827.4

9

744.7

4

358.5

4

673.8

5

315.3

0

March

138.3

2

1.001

1319.05

1187.1

5

571.5

4

575.8

5

4.3

2

April

159.4

1

0.990

1504.27

1353.8

4

651.7

9

463.3

6

188.4

3

May

195.7

6

0.971

1811.78

1630.6

0

785.0

3

423.4

7

361.5

6

June

211.4

9

0.941

1895.86

1706.2

8

821.4

6

381.2

9

440.1

8

July

238.0

1

0.904

2050.85

1845.7

7

888.6

2

263.4

5

625.1

7

August

210.9

4

0.902

1813.59

1632.2

3

785.8

1

192.5

9

593.2

2

September

159.4

1

0.923

1401.71

1261.5

4

607.3

5

417.7

4

189.6

1

October

104.9

8

0.966

966.5

7

869.9

2

418.8

1

537.1

8

118.3

7

November

67.0

9

1.001

639.7

7

575.8

0

277.2

1

589.7

2

312.5

1

December

56.7

8

1.022

553.1

1

497.8

0

239.6

6

441.0

7

201.4

1

Total

1695.7

9

15,4

49.5

5

13,9

04.5

9

6694.1

7

5520.1

5

1

174.0

2

Monthly

average

141.3

2

0.97

1287.46

1158.7

2

557.8

5

460.0

1

97.8

4

aWithoutVAT.


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Depreciation period of the investment: 20 consecutive years. Total electrical power produced by the photovoltaic modules: 11,520 Wp. Inverter estimated production: 10,400 W. Photovoltaic estimated production: 13,904 kWh/year. Electric reference tariff (ERT): 0.083728 h/kWh, as shown in the Official State Bulletin

of Spain, BOE (12/31/2004).

Electric remuneration (h/kWh): 575% of the ERTduring 25 years; 460% of the ERTuntil the end-of-life of the installation.

EURIBOR interest rate for a 6 months loan (%): 2.5% yearly. Period to pay back the subsidized loan: 7 years. Amount of the subsidized loan: 57,494 h (90% of total investment minus the total value of a

diesel-engine alternator which could generate the same power for 8000h of use/year). Non-recoverable subsidy given by IDAE: 20% of the subsidized amount, or 11,499 h. Inter-annual inflation: 2.5%. Inter-annual energy inflation: 2%. Self-financed investment: 6457 h. VATreturn: 8472 h. Period to return the VATof the installation: 7 years. Economic Activity Tax (EAT): 0.7212 h/installed kWp; nevertheless, the installation

would be free of this tax since it would not reach 37.24 h (corresponding to a 51 kWp

installation).

State taxes: 35% of net profit (excluding depreciation of equipment+VAT). Estimated maintenance costs: 0.018 h/generated kWh. Insurance cost to cover defective equipment: 0.4% of the installation value each year. Investment required to generate an equivalent amount of electric power using a diesel-

engine alternator: 801 h for a 1.74 kW engine working 8000 h/year.

Depreciation of the equipment: Although it is expected that the photovoltaic modulescan be operative after 25 years of use, its salvage value is 0 h.

Considering all the costs involved, earnings from electricity sales (after taxes) for thetwo studied cases are shown as follows.

Scenario 1: mixed financing: 10% self-funding,90% external funding.

Internal rate of return (IRR): 14.65%. Payback period: 6 years and 6 months.

ARTICLE IN PRESS

Table 4

Complete budget of the PV installation

Description Total (h)

Photovoltaic modules, supports and accessories 49,720.08

DC circuit, connection to the grid and grounding 883.70

Inverters and related devices 6980.95

Civil engineering project work 2593.80

Labor costs and equipment installation 2060.30

Civil engineering project management work 1805.36

Total 64,044.41


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Aggregate profit: 110,916.80 h. Net Present Value (NPV): 73,696.31 h. Costbenefit ratio: 0.46 in 10 years, 1.24 in 15 years, 2.08 in 20 years, and 2.85 in 25

years.

Scenario 2: 100% external financing.

Internal rate of return (IRR): 16.00%. Payback period: 7 years and 2 months. Aggregate profit: 109,561.07 h. Net present value (NPV): 73,079.76 h. Costbenefit ratio: 0.42 in 10 years, 1.20 in 15 years, 2.05 in 20 years, and 2.82 in 25 years.

In the second case study, the cash flow is basically the same as in the first one; only the

development of the income varies: the aggregate profit during the payback period (first 7

years) is less positive compared to the first case. Also, the IRR has a higher value because

the interest of the loan (subsidized by IDAE) is not affected by inflation; in addition, the

interest of the consumer credit does not affect the NPVand the aggregate profit value,

since high interest rates of up to 20% have been tested without significant variation in the

aggregate profit.

To conclude,Fig. 13depicts the annual cash flow for scenarios 1 and 2, which is almost

identical in both cases.Figs. 14 and 15present the development of the annual incomes for

scenarios 1 and 2, respectively.

7. Conclusions

After calculating the dimensions of the PV installation, the estimated power production,

the total budget and two financial case studies, these are the main conclusions that we have

reached:

The installation requires an initial investment several times greater than the costof diesel-engine alternator equipment that can generate the same amount of power in

1 year.

Economic incentives, like subsidies for part of the investment, and the chance to sell allthe electricity generated at 6 times its market price, are required to make a photovoltaic

installation profitable.

An even greater investment is necessary to generate the electricity required to meet thedemand of the Centre completely only using photovoltaic energy, since the installation

can only meet 30% of the annual electrical demand. Nevertheless, the income from sales

of the electricity generated is greater than the amount of the electricity bills.

Developing an installation of this type promotes the use of environmentally conscioussources of energy and motivates students to use renewable energies.

With the subsidized loans given by the IDAE, the installation becomes viable in areasonable period (nearly 8 years) and generates profits from the beginning; these profitscan be used to partially pay the Centres electric bills. Once the investment has been

repaid, the annual earnings from PV electric generation can fully compensate the

electricity bill, which would allow for considerable budget savings.

ARTICLE IN PRESSA. Fernandez-Infantes et al. / Renewable Energy 31 (2006) 20422062 2059

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The remuneration given to PV electric generation in Spain (575% of the ERTestablished by law for a 25 years period) allows making a profit from the investment in

the long term. Also, non-recoverable subsidies reduce the payback period. The actual

cost of this remuneration scheme represents just 2% of the special electricity taxes,

approximately 0.08% of the electricity bill, whereas the nuclear moratorium tax almost

absorbs 40%, or 1.6% of the electricity bill. The aggregate profit in the long term, 2025 years, doubles the initial value of the

installation. The NPV is also positive and the IRR guarantees that an increase in

inflation will not affect the profitability of the installation.

ARTICLE IN PRESS

-10000

-5000

0

5000

10000

15000

0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Years

Economic ActivityTax

Financing installments

VAT

Electricity income

1

Fig. 13. Annual cash flow components for scenarios 1 and 2.

-8000

-6000

-4000

-2000

0

2000

4000

6000

0 4321 5 9876 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Years

Fig. 14. Annual income development for scenario 1 (mixed financing: 10% self-funding, 90% external-funding).


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The durability of the equipment guarantees optimal operation for 25 years, exceptaccidents, for which a specific insurance can be purchased until the installation is totally

repaid in about 8 years, just after the subsidized loans are fully repaid.

Finally, the remuneration obtained from the sale of PV-generated electricity canproduce profits that can both repay the necessary loans to get the installation started

and also the electricity bill, even if the electric consumption remains constant during thefollowing years.

References

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[4] Technical conditions for PV installations connected to the grid [in Spanish]. Report available from the

publication services of the Institute for Diversification and Energy Savings, Spain. http://www.idae.es, 2002.[5] Lorenzo E. Energy collected and delivered by PV modules. In: Luque A, Hegedus S, editors. Handbook of

photovoltaic science and engineering. West Sussex, UK: Wiley; 2003. p. 90570.

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[7] Royal Decree 1663/2000 on the connection of photovoltaic installations to the low voltage network [in

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[8] Caaman o E. Grid connected photovoltaic buildings: characterisation and analysis. PhD thesis, Polytechnic

University of Madrid, Superior Technical School of Telecommunication Engineers, Madrid, Spain, 1998 [in

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[9] Caaman o E, Lorenzo E. Photovoltaics in grid-connected buildings: energy flow and economic aspects. Prog

Photovoltaics: Res Appl 1995;3:13543.[10] Bernal-Agustn, JL, Dufo-Lopez, R. Economical and environmental analysis of grid connected photovoltaic

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ARTICLE IN PRESS

-2000

-1000

0

1000

2000

3000

4000

5000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Years

Fig. 15. Annual income development for scenario 2 (100% external financing).

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[12] Royal Decree 436/2004 establishing the methodology for the update and systematisation of the legal and

economic regime of the activity of production of electrical energy in special regimes [in Spanish]. March 12,

2004. Available athttp://www.boe.es

[13] Line of financing ICO-IDAE for renewable energies and power efficiency projects [in Spanish], 2005.

Available athttp://www.idae.es

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