Materials
and processes for energy: communicating current research and technological developments (A. Méndez-Vilas, Ed.)
____________________________________________________________________________________________________
Evaluation of energy produced by grid-connected photovoltaic systems in
Porto Alegre - Brazil
C.H. Rossa ¹, J. B. Dias ¹ and G.A.M. Karnas ¹
1
Graduate Program in Mechanical Engineering, UNISINOS, Av. Unisinos, 950. São Leopoldo-RS, 93022-000. Brazil.
Using equations to estimate the incident radiation on clear days, the temperature values measured by the automatic station
A801 and implementation through command lines in Matlab, we propose in this paper a detailed analysis of the production
of electricity in grid-connected photovoltaic systems on specific sunny days of the year, such as solstices, equinoxes,
aphelion and perihelion, in the region of Porto Alegre, Brazil. The analysis was performed using the SB 3800 inverter, and
an array of 4 strings in parallel with 15 monocrystalline silicon modules connected in series, From the results, it is
suggested that the irradiance, however contributing to power generation, influences more than the air temperature to
increase the operating temperature of the cell, which leads to a decrease in system efficiency. Although it is a small
difference in energy production, the effective amount may be quantified.
Keywords Grid-connected photovoltaic systems, working temperature of the cell, cell efficiency
1. Introduction
From the perspective of becoming reality in Brazilian homes the use of solar photovoltaic grid-connected and studies
about the behavior of several installation configurations are needed to have an accurate estimate, mainly on the amount
of electricity to be produced. Many studies have been done by computer simulation [1,2], which aim to analyze and
estimate the behavior of several configurations of photovoltaic installations connected to the grid, as well as studies
related to the climate simulations [3], aiming to aggregate and increase the reliability of certain types of simulations.
This study examines possible differences in the production of electricity on certain days of the year, more specifically at
the solstices, equinoxes, aphelion and perihelion, for a determined spot on Earth's surface. Equations were implemented
in Matlab to calculate the radiation and irradiance and algorithms for reading the measured data of temperature
occurring on days specifically analyzed.
The program can easily simulate the production of energy to any location of the planet, as long as there are the
temperatures occurring in the area to be analyzed. In the present work, the analysis shown is in the region of Porto
Alegre - Brazil, located at latitude 30 ° S. We opted for an analysis of clear sky to estimate with more reliability the
energy production depending only on temperature and irradiance.
2. Calculating the incident radiation
2.1 Incident radiation on clear days
Obtaining the incident radiation on a clear day is one of the necessary data for the final calculation of the power
supplied to the grid. To do so, we used the equations and models presented by Duffie & Beckmann [4]. Considering that
the simulation is for days without cloud cover, the production of electrical energy depends only on the atmospheric
transmissivity τb, which calculates the percentage of radiation that reaches the modules, and is given by Eq. (1), adapted
from Hottel [5].
=
+
(1)
−
where the unknowns a0, a1 and k are dimensionless constants used to calculate the climate of the region, defined as
= 0,4237 − 0,00821(6 − )²
(2)
= 0,5055 − 0,00595(6,5 − )
(3)
= 0,2711 − 0,01858(2,5 − )²
(4)
and A is the altitude above sea level, given in kilometers, with appropriate limits of 2.5 km altitude. The values of r0, r1,
and rk are correction values, as defined by Hottel [2] and shown in Table 1.
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Materials
and processes for energy: communicating current research and technological developments (A. Méndez-Vilas, Ed.)
____________________________________________________________________________________________________
Table 1: Correction Factors for Climate Types (adapted from Hottel)
Climate Type
r0
r1
rk
Tropical
Midlatitude summer
Midlatitude winter
Subartic summer
0.95
0.97
1.03
0.99
0.92
0.99
1.01
0.99
1.02
1.02
1.00
1.01
In this study were used only the correction values for midlatitude summer and midlatitude winter, which correspond
to the location analyzed, 30 ° S, which lies between the Tropic of Capricorn and Antarctic polar circle. Midlatitude
summer is the period of the spring equinox to the autumnal equinox, and midlatitude winter, the autumnal equinox to
the spring equinox.
With the atmospheric transmissivity τb it is obtained the radiation that actually reaches the module in relation to the
angle it makes with the horizontal plane, through the Eq. (5)
(5)
=
where Gon is the solar radiation that arrives at the top of the atmosphere, given in W / m², in terms of a daily n, which
ranges from 1 to 365, and is obtained by Eq. (6)
=
(1,000110 + 0,034221
+ 0,001280
+ 0,000716
2 + 0,000077
2 )
(6)
where B sets the nth day by Eq. (7)
(7)
= ( − 1)
3. PV system proposed
3.1. Scheme PV system connected to grid
Fig.1 is basically the photovoltaic system proposed for the analysis.
Fig. 1 Scheme photovoltaic system connected to grid
Table 2 shows in detail the characteristics of the proposed PV system.
Table 2: Characteristics of the PV system
46
Cell Technology
Monocrystalline silicon
Module
number of modules per string
Number of strings
Total power at standard condition (kWp)
BP 585
15
4
5.1
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3.2. DC/AC inverter
The simulation was performed using an inverter rated power 3800 W. The inverter efficiency is calculated by the by
Eq. (8)
inv=
(1 + 1) +
(
)
(
(
(
/
)
/
)
(8)
where Pmppt is the power in maximum power point, considering the efficiency of MPPT follower equal to 1, the
inverter input. Pinv is the nominal power of the inverter and the constant k0, k1 and k2 are constant adjustment obtained
experimentally and are worth 0.0187, 0.0368 and 0.0440, respectively.
4. Energy delivered to the grid
The electricity delivered to the grid is calculated by integrating the power into alternating current generated throughout
the day, according to Eq. (9)
(9)
=
and is given in kWh. Pca corresponds to the alternating current power supplied to the grid.
4.1. Temperatures
The energy generated by the photovoltaic modules also depends on the operating temperature of the cell. As the
analyzed region lacks a typical meteorological year (TMY), we used temperatures recorded hourly, available on the
website of the National Institute of Meteorology (INMET). The data are from the A801 automatic station, located in
Porto Alegre, Brazil. The analyzed data cover the period from August 31, 2012 to January 4, 2013. During this period,
we obtained values of radiation and were selected only the days that graphically would present sunny days radiation
characteristic without any presence of clouds. Some of the days analyzed presented curves very close to those expected
for sunny days. In such cases, to resolve any doubts, we analyzed the database of images obtained from satellite GOES
12, available at the website of CPTEC / INPE, at times when the curve had some questionable information. If there was
some cloud comprising the region analyzed, both in the visible and infrared band, the day was discarded. From this
sample we obtained 40 days under the conditions prescribed. Temperatures are arranged in a spreadsheet, with each
column representing a day to be analyzed, read automatically when the program is run.
5. Simulation and analysis of the energy produced at the solstices, equinoxes, aphelion
and perihelion
On sunny days, the expected result is that in the winter there is less production of electricity, due to the apparent
inclination of the Sun. Near the solstices, aphelion and perihelion occurs, the point where the Earth is further or closer
to the Sun, respectively. For this, we chose to analyze data mainly near the solstices and these points especially in the
trajectory of the Earth, because, indirectly, if the distance of the Earth around the Sun was significant, there should be a
considerable difference in energy production.
In addition to the modules previously specified, as well as the temperatures, the analysis was done with the modules
inclined at 30 ° to the horizontal plane. This angle corresponds to the latitude site. We opted for this inclination to
obtain power equally throughout the year, so that the apparent position of the Sun changes also 23.5 ° to the normal
vector of each module. The modules are pointed at the geographic north (azimuth 180°), aligned with the local meridian
north-south.
5.1. Winter solstice
For this analysis, data from the same automatic station A801, Porto Alegre, were obtained. These, specifically, in order
to catch a recurring temperature from a sunny winter day in the region. The most recent data obtained from a sunny day
near the winter solstice was June 22, 2010. Fig. 2 illustrates the characteristic curve generated by the simulation, where
we can see, from largest to smallest peak of the four curves, the maximum power generated by the panel, the power
supplied to the network, the total radiation and incident irradiance on the modules.
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Materials
and processes for energy: communicating current research and technological developments (A. Méndez-Vilas, Ed.)
____________________________________________________________________________________________________
Fig. 2 Total radiation (Rad Total), irradiance in the modules (irradiância), Power generated (Pot max gerada), power supplied to the
grid (Pot Fornecida) for the day June 22, 2010. The y-axis is radiation and power (Radiação [W/m²] Potência [W]) and x-axis is time,
in hours (tempo [h]). The vertical blue lines represent the times of sunrise and sunset on the day.
The curves radiation and irradiance appear flatter to be visible at the same graph as the curves of power. Note that the
curve of the irradiance on the module follows the growth curve total radiation as well as the other curves, but they do
not touch each other, because the focusing sunlight is being inclined at approximately 23° below the normal each
module, near the winter solstice. Although the permittivity increases the air throughout the day, as the sun moves away
from the horizon, with a peak just over 50% at noon local, the power delivered to the grid becomes smaller than the
power generated mainly at this time, when it shows an increase in the efficiency of the inverter, which occurs when the
power generated value approaches the value of the inverter rating. Fig. 3 illustrates, respectively, the efficiency curve of
the inverter and atmospheric permittivity for this day.
a)
b)
Fig. 3 a) inverter efficiency curve for that day and b) atmospheric permittivity, with 23 km of visibility, for the day June 22, 2010.
The x-axis is the same for both graphics. In a), y-axis is efficiency (Eficiência) and in b) is coefficient
The total energy supplied to the grid that day, as calculated by Eq. (9) was 18,484 kWh.
5.2 Terrestrial aphelion
Near the winter solstice, around July 4, occurs a larger distance of the Earth in relation to the Sun. In astronomical
terms, the difference is subtle. The Earth is distant approximately 152 million kilometers from the sun that day. The
incident irradiance on the modules is larger than the one obtained on the winter solstice, since the modules are inclined
at 30 ° in relation to the ground, and in aphelion the sun is at a smaller angle to the normal of the modules, with a
smaller declination and least away from the celestial equator. However, the energy produced that day was 18,223 kWh,
slightly lower than the one produced on the winter solstice. Although the distance of the Earth was higher this day, it is
noteworthy that this day specifically showed milder temperatures than that day represented on the winter solstice, while
still cold, with air temperatures ranging from 12-25 °C, compared with the winter solstice, which ranged from 4.5 to
14.9 ° C. It is known that the cell efficiency drops with the increasing temperature, and this probably contributed to the
lower energy production. Fig. 4 illustrates the behavior of the curve for that day, showing a lower power output in the
previous analysis where the power curve is provided below the lines of 3 kW. The legend at the Fig 4 and others
graphics is the same as the previous graphic.
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and processes for energy: communicating current research and technological developments (A. Méndez-Vilas, Ed.)
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Fig. 4 curve for the 4th of July 2010, showing the maximum power generated by the PV panel at noon above 3 kW, above occurred
on the winter solstice.
5.3 Summer solstice
The air temperature data for that day are December 22, 2012, obtained from the nearest summer solstice for sunny days.
The air temperature ranged from 17.8 to 27.1 ° C that day. Fig. 5 shows the maximum power generated by photovoltaic
panel above 3.5 kW.
Fig. 5 Total radiation, incident irradiance, maximum power generated by the PV panel and power supplied to the grid curves for the
day December 22, 2012.
It is noted that in the graph of Fig. 5 the limits of the total radiation curve are beyond the limits of the other curves.
This is partly because the sun at this time rises and sets behind the imaginary line connecting the cardinal points east
and west, illuminating the back of the modules. When the incidence starts in front of the modules, as represented by the
curve trend of irradiance, the power generation begins. The maximum power generated by the modules exceeds 3.5 kW.
The energy generated that day was 24.942 kWh, about 25% more than that generated at the winter solstice.
5.4 Terrestrial perihelion
The energy generated at perihelion was 24,752 kWh, slightly below the generated on the summer solstice. It was found
that the working temperature of the cell at perihelion remained most of the day with values approximately 4 ° C higher
temperature compared to the summer solstice, which contributed to lower production of energy by the system in this
day compared to the summer solstice. The radiation to this day, although in a smaller incident angle to the normal of the
PV panel, not to mention the close proximity of the Earth in relation to the Sun, it was pretty much the same occurred
on the solstice. The differences are small, and in this case, the temperature increasing turned out to have the most
significant power loss of the panel.
5.5 Equinoxes
Regarding the solar positioning, it is expected that the energy is produced on the equinoxes is approximately the same.
The energy produced on the autumn equinox was 24.637 kWh, and on the spring equinox, 23.583 kWh. The air
temperature on the autumn equinox evaluated ranged from 20.9 ° C to 30.4 ° C. On the other hand, the vernal equinox
evaluated ranged from 9.2 ° C to 21.3 ° C. The apparent position of the Sun is the same at the equinoxes and the
generation should be the same, if it depended only on this factor. It was also found that the temperature on the spring
equinox was lower overall than the autumnal equinox, which should result in greater production of energy. Thus, we
assessed the two periods on the same temperature, in order to make that only the irradiance is relevant in the generation
and operating temperature of the cell. Table 3 illustrates the power produced in each equinox and the temperature held
for that day.
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Materials
and processes for energy: communicating current research and technological developments (A. Méndez-Vilas, Ed.)
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Table 3: Evaluation of the energy produced on the equinoxes in range of original temperatures
Equinox
Tmin~Tmax (°C) Produced Energy (kWh)
Spring
Autumn
9.2~21.3
20.9~30.4
23.583
24.637
It was evaluated the autumn equinox with the air temperature on the day of the vernal equinox. The energy produced
was 0,337 kWh higher than the normal temperature produced in fall, and 1,391 kWh higher than the one produced in
the spring. In the spring equinox, we evaluated the temperature obtained for the autumn equinox. The energy produced
was 0,720 kWh less than that produced in the original temperature, and less than 1,774 kWh produced in the fall. Table
4 shows the reversal of temperatures between equinox, and the respective energies produced in each.
Table 4: Evaluation of the energy produced on the equinoxes, with temperature ranges exchanged
Equinox
Tmin~Tmax (°C) Produced Energy (kWh)
Spring
Autumn
20.9~30.4
9.2~21.3
22.863
24.974
In relation to fall, the reduction on the air temperature caused the panel to produce more, because the system
efficiency increases with the decrease of air temperature due to the lowering of the module’s temperature. The
difference is significant in comparison with the spring. Under the same temperature, there was an increase in energy
production. This happens because in the autumnal equinox the Earth is closest to the Sun, in relation to the opposite
equinox, as calculated by the Eq. (6).
For the autumn equinox, Gon = 1377.8 W / m², while for the spring equinox, Gon = 1356.7 W / m². This value ranges
from 1321 to 1415 W / m² over the year, and happens because Earth's orbit is elliptical, causing the Sun occupying one
of the foci of this ellipse.
Evaluating the vernal equinox to the temperature of the autumn equinox, there was a drop in production, according to
the amounts set out above. Again, the temperature incrementing contributed for the decreasing of cell efficiency
compared with the temperature held at vernal equinox, and compared with the fall, a greater decrease was due to the
great distance back from the earth. One factor is interesting to note was the greater influence of the variation of these
different irradiance in comparison with the temperature. It is necessary, in this case, to observe the Eq. (10)
=
+
[
(10)
]
where Tc is the operating temperature of the cell, the air temperature Ta, Ga irradiance and NOCT the normal operating
temperature of the cell, which is regarded 47 ° C for the evaluated cell. One can easily verify that the increase in air
temperature or irradiance, increases the cell operating temperature. As the typical values of irradiance increasing are
much higher than the temperature rise, although the reason that multiplies the value of irradiance has low value, the
temperature variation ends up, in this case, being less influential on the increase of the cell’s working temperature than
the variation on irradiance.
6. Final remarks
Simulating the production of electricity in photovoltaic systems connected to the grid on sunny days brings the
advantage of analyzing the behavior of a hypothetical facility in its detail, in relation to the apparent position of the sun,
something somehow impossible with the implementation of AMT, although this brings a more realistic view of the
location in the climatic context. In solving engineering problems, commonly, it is assumed an approximate view at
certain points where the proximity of values makes the difference slight in a larger context. Thus, little is approached, in
the context of photovoltaic solar energy, the differences in energy production discussed here. These, on the equinoxes,
were not higher than 8%. It was verified that the irradiance has more significant influence on the efficiency of the
installation compared to the air temperature for the simulated cases, except the comparison between the summer solstice
and perihelion, where production was lower at perihelion in relation to summer solstice, due to the reported in Section
5.4. This difference shows that specifically more irradiance not always results in a higher production, as the operating
temperature of the cell increases with increasing irradiance, together with the increase of the air temperature. It was
evident that the Earth-Sun distance influences the production of electricity, though barely noticeable. Although there are
extensive literature on the amount of solar energy intercepted by the Earth throughout the year, showing the little
difference, there was no certainty about the perception of difference in a photovoltaic installation.
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6.1 Suggestion for future work
Many analysis can be made from this program or similar, taking into account other places and temperatures, as well as
different technology PV modules, inverters and types of installation configurations. Here, it was decided to maintain an
installation type with the same configuration and analyze different seasons. The analysis was performed using
monocrystalline silicon cells, widely used for having a higher efficiency of electric power generation, among the
technologies available in the market. To determine whether there were significant differences generating at different
times with different cells in the same configuration would be interesting as well as analyzing a minimum installation
area for the occurrence of the same difference, since it is assumed that, to obtain the same performance, it is necessary
to modify the installed area of photovoltaic modules.
References
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fotovoltaicos. IV Congresso Brasileiro de Energia Solar e V Conferência Latino-Americana da ISES
[2] Filho J F P, Macedo, W N, Pinho J T. Aprimoramento de Ferramenta Computacional para Análise e Projeto de Sistemas
Fotovoltaicos Conectados à Rede Elétrica. IV CEBENS. V Conferência Latino-Americana da ISES.
[3] Luiz E W, Martins F R, Pereira E B, Schuch N J. Determinação de um Ano Meteorológico Típico para Florianópolis - SC.
CBMET – 2012.
[4] Duffie J A, Beckmann W A. Solar Engineering of Thermal Processes. Ed. 3. New Jersey. John Wiley & Sons. 2006
[5] Hottel H C. A Simple Model for Estimating the Transmittance of Direct Solar Radiation Through Clear Atmospheres. 1976.
Vol 18. pp 129-134.
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