EFFECTS OF THE SEASONAL SUNLIGHT VARIATION
ON PREDICTIONS OF THE SOLAR-AEOLIC POTENTIAL
FOR POWER GENERATION
Eduardo B. Marafiga
Federal University of Santa Maria,
Santa Maria, Rio Grande do Sul, Brasil
bonuncielli@gmail.com
Abstract - This study discusses theyearly seasonal influence on
sunlight time series to predict oscillations of the solar potential
for generation of electricity and thermal energy along with its
implications on climate changes. It is confirmed that there has
been a decrease of 1% in the average variation of insolation
from 1961 to 2011 and a trend of lower rates in all seasons. Both
the predicted and measured data have demonstrated the
possibility of a reduced insolation or sustained lower levels in
the coming quarters in most months, with likely direct
consequences on climate change and, in those forms of power
generation dependent on the climatic stability.
Index Terms - Seasonality, time series, forecasting, Box-Jenkins
Models, X11-ARIMA.
I. INTRODUCTION
Energy systems are subject to climate changes in theiruse
and production in different forms.When related to renewable
energy sources,climate changes play a major role. Climate
change and its direct consequences for humanity have been
a major concern for the scientific community in the past
decade specially after the crisis that inpactedJapan in 2011
and threatened the use of nuclear power as a way to meet
Japanese energy needs.
If there are missing data of solar radiation, reduced
number of radiometric stations, and discontinuities in the
collection of wind speed, temperature, sunlightand other
relevant data related toclimate prediction in Brazil, who can
guaranty how long the best location for a wind or solar plant
remains the best solution among the options available? It can
be added to this the constant climate change, numerous
forest fires, rampant deforestation, monocultures, increased
pollution, both on the continent and sea and irregular
insolation, among other factors, that change the foundation
dynamics for location of current solar and wind power
generation.
Hydroelectric power plants are heavily dependent on the
climatic variations affected by the cyclic increase or
decrease of rainfall for extended periods which can endanger
the power generation system which isthe case of Brazil.
Due to the fact that voices of the organized society have
been weak and faltering so far, nature itself gives its reaction
against this state of mankind’s neglect and abuse of natural
resources, demanding that preventive, fast and effective
actions be taken under the serious threat of irreversible and
global destruction[1].
Regarding the variations in solar brightness either due to
its cycles or cloud formations, it impacts on the amount of
solar radiation for electricity generation and heating from
Felix A. Farret, PhD, IEEE Member,and Nirvan H.
Peixoto,
Federal University of Santa Maria
Santa Maria, Rio Grande do Sul, Brasil
solar collectors. The wind regime defines the potential for
wind power generation which in turn is linked to climate
changes. Thus, it is of utmost importance for all planetary
lifeto better comprehend the influence of the sun on human
activities.
According to the [2] a recomended minimum of 30 years
of climate information is needed to serve as a reference for
climate change and variability studies (WMO, 2004). Based
on information from the solar historical series, prediction
models can be adjusted to the series being analyzed to
predict heat stroke on the estimation anywhere on the planet
of the behavioral trend of this variable where components
such as trend, seasonality and cycle need to be estimatedonce
it is available a reasonable number of local measurements
over the years.
When analyzing seasonal changesor othertrend
influencing factors, it must be observed how seasonality may
or may not affect power generation in different months along
the year or in each month of different years.How to consider
an atypical point in the series or extreme value affects
somehow in the climate orif that was just an isolated event.
Moreover, time series of insolation can serve as a guide
forresearchers when itinforms periods of higher efficiency in
energy production and some estimation about what may
happen in a short-term period. Furthermore, it can provide
very useful information for planning and location of future
altenative-energy generation sites such as wind, hydro and
solar power as well as to serve as a support for other areas of
research. In this context, this paper discusses the seasonal
influence on the time series of insolation, in order to predict
the potential of solar power generation and its implications
on climate changes.
This paper aims at a methodology to determine especific
aspects of solar potential applicable to any point on the
planet, but using especific data from the Rio Grande do Sul
State (Brazil’s south). In particular, it is discussed
seasonality targeting the variations of solar potential for
generation of electric and thermal powers. It is presented
also some time series models for the analysis of insolation
using daily data, transformed into monthly averages,
covering a period between January 1961 and December 2008
to confirm a prediction for 2012 and its comparison with the
data measured in the 2008-2011 period.
II. MATERIALS AND METHODS
Data from 30 meteorological insolationstations, located
in nine regions of the Rio Grande do Sul state were used as
platykurtic (kurtosis value <3) relative to the normal
distribution curve, Figure 1.
Fig. 1. Histogram of the insolation series (insolation x frequency
distribution).
The Jarque-Bera Normality test was carried out with the
objective of offering credibility to the statistic tests, due to
to the fact that they are based on the normal distribution of
the residual term. The tested hypothesis were:
H0: Assymetry = 0 and kurtosis = 3, thus, the serie is considered normal;
H1: Assymetry ≠ 0 and kurtosis ≠ 3, thus, the serie is considered not normal.
It can be observed that the variable does not follow a normal
distribution, given that the calculated value of 5.39 is lower
than the standard number 5.99, this can be observed in
Figure 1.
According to Figure 2, this insolation series does not
show a clear trend, but only major variations over the years.
As the series presents a wide variation in their stability, a
different series is proposed to perform the studies on series
seasonality. The graph of the autocorrelation function for the
first difference (Figure 3) suggests some seasonal effects.
The study of seasonality with time series according to [7] has
two objectives: the analysis of the seasonality itself and
removal of seasonality from the series for later study about
other aspects. This series was subjected to several Friedman
and Kruskal Wallis tests for verification of stable
seasonalities. The results of these tests are shown in Table 1
where it can be seen that the series has a stable seasonally in
the variation of sunlight.
11
10
9
8
Insolação (h)
described in Table 1. The Rio Grande do Sul (RS) state is
located in the extreme south of Brazil, between latitudes
from 27° to 34°S and longitude from 50° to 57°W. These
datawere provided by the following organizations:
Agrometeorology Labof theState Foundation of
Agropecurary Research (FEPAGRO-RS), the National
Institute of Meteorology, INMET, and the Weather
artnership Stationfrom Pelotas/EMBRAPA, UFPel/INMET.
For an improved data processing, the daily information were
transformed into monthly averages totaling 48 years of
information.
When working with enviromental data it is not rare to
find incomplete or poorly historical data series, especially
when it comes to very large time periods, as is the case in
this study.
According to [3] incomplete series should be treated as
time series using the Box-Jenkins models which is based on
identifying models from the time series behavior constituting
a fast and efficient tool for analysis of data series [4 - 5].
When using a time series the researcher aims to study the
generating process of the series to make predictions on the
basis of its past values and to describe the possible behavior
of the seriesin the future. This study can be performed in the
time domain by means of autocorrelation functions.The
ADF test was carried out to determine if the series is
stationary or not. The series were not stationary, but became
stationary after the first diference.
A time series analysis using univariant models have two
main objectives: firstly, to identify the relevant features and
properties of the series and according to that, establish the
forecast to beused to fill gaps in the series with lack of
information. However, one has to be very careful not to
exceed 12 months and a temporal interpolation following the
technique discussed in [6]. These models can be expressed
by Auto-Regressive (AR) and Moving Averages (MA)
models or by the union of these models. The observations
were spaced at equal time intervals and they have at least 50
previous observations to allowan application of this
methodology.
Regarding seasonality, the results contributed to reveal
the series showing the overall behavior of the variable, so
that the decisions were scientifically based, getting the best
plan and allowing a rational allocation and optimized results.
The Seasonality and Seasonal Factor (St): describes the
periodic fluctuations of a constant length, repeated at fixed
periods. The period length is denoted by "S", associated in
most cases, to climate changes. Seasonality is a component
of hard estimationin a historical series. Sometimes, it is
necessary to reconcile the conceptual question of the
phenomenon under study with statistical issues.
For a better understanding of the series in this paper is
performed a descriptive statistical analysis of insolation as a
support for the inferences to be investigated in order to
determine the behavior of the variables during the analytical
period and to check the contents of conditional
heteroscedasticity in the series (volatility).
The coefficient of average variation was considered
representative since this value expressed a percentage far
below 50% and can be used for further estimations. By
analyzing the asymmetry and kurtosis it was observed that
the asymmetry is non-zero and a kurtosis of 2.56
indicatesthat the insolation number shows a distribution
7
6
5
4
3
2
Período (1961 - 2008)
Fig. 2. Original Historical Series of Monthly Insolation (period x
insolation).
Fig. 3. Correlogram of Insolation Series
Table 1. Tests to check seasonality.
Test F
stableseasonality
Fp-valor
972.3880.0000
Test
stableseasonality
Kruskal
T1p-valor
332.1670.0000
Friedman
test
p-valor
0.0001
Note: significances adopted stable seasonality of 0.1% (0.001), Kruskal
Wallis 1% (0.01).
Thus, correction of the seasonal variations are of
particular importance in the analysis of economic
fluctuations since it allows an evaluation in the series
variation due to a trend change, which may require an
intervention, or a mere cyclical variation, in which will be
adjusted automatically.
The inclusion of the X11 ARIMA model is key when the
seasonal structure changes rapidly and randomly. As the
series is extended, the filters applied to extreme observations
are similar to those applied to central observations, which,
according [8], minimizes the magnitude of the seasonal
revision factors in terms of mean square error. So X11ARIMA is an iterative procedure to yield estimations for the
successive application of filters.
III. PRINCIPLES OF THE METHOD X11 AND X11ARIMA
The seasonal adjustment in the time series ZZt is to
decompose it into two unobservable components, the
seasonal and non-seasonal aspects. The seasonal component
can not be decomposed into other components such as the
trend, the cycle and erratic components. The seasonal
adjustment is to isolate the seasonal component from other
series components.
The X11 method consists of successive filtering by
applying linear filters based on the premise that the original
series can be decomposed into four components (1): the
trend (T), which reflects the behavior of the variable over
time; cycle (C), which translates the oscillating long term
movement; seasonality (S), which refers to oscillations
around the year trend to lower frequency; erratic or residual
component (I), reflecting the irregular movements,
explained by random or unknown causes, which are referred
to movements not explained by the previous components for
which is assumed a random behavior. When these
components are independent of the time series they may be
related additively as (1):
Tt + Ct + St + It
The X11 method uses the principle of this simple
algorithm, using selected moving averages and tested in the
estimation
of
components
through
computer
interactions.The X11-ARIMA procedure consists of:
 Modeling the original series by an integrated
autoregressive moving average process (ARIMA) of
the Box-Jenkins;
 Extrapolate the unadjusted observations at each end of
the ARIMA model series that best fit the behavior of
the original series in terms of prediction;
 Seasonally adjusted extended series, with the use of
filters by the Census X11 method.
The insolation series used in this study shows a clear
seasonal fluctuation (Fig. 3). The purpose of seasonal
decomposition in general is to derive estimations of
seasonality, trend/cycle and irregular components that make
up the series.
The graphs in Figure 4 show the adjusted seasonally of
trend and cycle, where it is proven the absence of both. The
dotted line shows the trend/cycle components and the solid
line, the final seasonally adjusted series. Clearly, there is a
variability range set around the estimated trend/cycle.
Fig. 4. Seasonal Adjusted Series.
Figure 4 shows the different components plotted (ranked)
by month in which is seen the pure series behavior, in this
case without the effect of trend, which was almost
nonexistent, and seasonality, therefore, it is the actual
behavior of the series. In Figure 5 can be observed the
behavior of seasonality for different years and different
months. Thus, decisions can be taken in the best way,
making sure that a given instant of time will influence the
series of ascending or descending order.
(1)
Fig. 5. Seasonal behavior in different years and months.
By evaluating the model in Figure 6, is noticeable that
the adjusted series has a better behavior. Therefore, it was
used forthe necessary inferences because the effects due to
the series external behavior were quantified and adjusted.
Fig. 6. Original and Adjusted Seasonal Series (IN-Sunstroke)
IV. RESULTS AND DISCUSSION
The results in the seasonality charts are displayed in
Figure 5 with forecasts from 2009 to 2012, compared with
data measured in the period from 1961 to 2011 (fifty years),
Table 2. According to these charts, it is observed that out of
the 12 months of the year, nine months presented a lower
mean variation of insolation. In August, apparently remained
without an increase nor decrease in the average change for
the same period under study. In the months of March and
November showed percentual increases in the average
variation of insolation. This finding was for the whole period
1961-2011.
In analyzing the results of the seasonal behavior for
different years and different months in Figure 5 and Table 2,
it appears that in January and February showed less
insolation during the entire period with a tendency to a slight
decrease for the coming years or it should remain without
significant changes. In March is without any significant
increase. In April, despite showing an index of increase
between 1991 to 2011, the variation was low (-0.70%)
compared to the entire period of the study from 1961 to 2011.
The variation in insolation has kept without changes within
the incoming periods. In the months of May, June and July,
showed a decrease in insolation with opportunities to
maintain this trend of decrease or remain unchanged in their
indexes. In August showed a negative index in the period,
but with a tendency to remain without significant changes.
In September shows a decrease with the possibility of
continuing with low values in the coming periods. In the
analyzed period, in October did not change despite having
demonstrated a negative average between 1981 and 2011 (4.17%), that should remain in the average without negative
or positive changes. In November showed an increasing
trend in the series under study and should remain with
positive results for the coming years. However, in December
has showed a negative average change in the analysed period
and should continue so for the coming years without
showing any positive index variations or remaining without
significant changes.
Table 2.
Average change in solar brightness at different times (measured data).
January
February
March
April
May
June
July
August
September
October
November
December
Δ1961 a
1980
-2.15%
0.00%
-1.06%
4.33%
-8.21%
-5.03%
-2.93%
-6.83%
7.12%
2.01%
5.60%
-0.37%
Δ1971 a
1990
-1.3%
-4.16%
9.22%
-15.97%
-2.15%
-6.32%
0.59%
1.96%
-8.46%
6.67%
-4.27%
-1.00%
Δ1981 a
2000
-6.02%
-8.83%
-9.57%
-0.96%
-2.19%
0.21%
-5.78%
-0.97%
-2.14%
-16.34%
-2.09%
-9.32%
Δ1991
a 2011
6.26%
10.3%
5.28%
9.77%
-5.42%
-2.40%
5.15%
2.13%
-1.12%
7.99%
4.00%
5.48%
Average
variation
-0.80%
-0.67%
0.96%
-0.70%
-4.49%
-3.38%
-0.74%
-0.92%
-1.15%
0.08%
0.81%
-1.30%
As the final graph of the irregular unmodified seasonality
(ratios), and the irregular modified to the extreme seasonality
of Figure 5, some atypical points or outliers may be related
to the ENSO phenomenon (El Niño Southern Oscillation) or
may have been affected by weather influences in a ascending
or descending series order. The ENSO is a phenomenon of
atmospheric-ocean interaction associated with impairment
of normal patterns of the sea surface temperature [9], as
related to the case study. It appears that during summer and
spring, the ENSO sunshine effects are more prominent in
Rio Grande do Sul. In most events, El Niño coincides with
lower insolation values and La Niña with higher insolation
indices.
Regarding Figure 7, which compares the seasons for the
1980s, 1990s and 2000, it appears that there were a 10%
decrease in summer insolation between the decades of1980
and 1990, and an increase of 7% was observed again in the
2000sbut still with an average 4% lower than the 1980s
decade. The same happened in the other three seasons. The
autumn season in the 1980-1990 decadeshas presenteda
decrease of 5% andan increase of 2% between the 1990-2000
decades resulting in a deficit of 3%. A winter witha 2%
decrease betweenthe 1980 to 1990,recovering -1% in the
2000s decade The spring presented a decrease of 7%
between the 1980s and 1990s decades with a 5% increase
from 1990 to 2000, resulting in a negative index of 2%.
It can be observed that in the decade of 1990 there was a
decrease in sunlight in all seasons of the year when
compared to the decade of 1980 and the first decade of 2000.
By analysis, it cannot be confirmed that it is an isolated case
or not.
Fig.7.Comparison between different seasonal periods.
Again, it is observable that there is a decay in different
seasons in the periodof analysis with the possibility of
remaning low values in some or all stations in the coming
decades. This demonstrates the possibility that in the
analyzed 1980s and 1990s series, there has been a more
intense browning than in other decades, which may also be
related to the phenomenon known as "global dimming".
In the decade of 2000 to 2011, the insolation rates rise
again but with smaller average changes from the previous.
There is the possibility that this decay has manifested
significantly much earlier, from the 70 or 80, as seen in Table
2. These results are consistent with other published studies
on global blackout that occurred worldwide, but with
different intensities and periods according the studied
regional coordinates. Works such as [10] also found a trend
of reduced insolation in Rio Grande do Sul and shown that
the daytime cloudiness would have increased in the region
within the period 1960-2005 along the four seasons.
V. CONCLUSION
According to the results of measured and predicted
insolation studied in this work, there is an indication that
may occur in the future decrease in its mean for most
summer and winter seasons. The energy consumption in
these two seasons are higher than the other two seasons,
autumn and spring, in southern Brazil. If this trend is
confirmed, these results may represent a significant
reduction in the natural potential to generate solar energy in
photovoltaic systems connected to the grid or residential
electric generation and in the conversion of solar energy into
heat. Another fact is the consequences that could arise from
climate variations related to the lower levels of insolation
over the region that may affect the planning of human
activities such as agriculture and livestock as well as the
generation of electricity using the hydropower potential.
Also, the data series to obtain the results discussed so far
have used both the Kruskal Wallis test as well as by the
Friedman test. Once proven its existence in these studies, it
is set the X11-ARIMA model on the time series of insolation
for the study case of Rio Grande do Sul, Brazil. This
methodology aims to make predictions about the solar
potential as close as possible to reality in a given region of
the planet, since the result of seasonally adjusted series
followed satisfactorily a trajectory within a significance
level of 5%.
It was observed in the studied case, that in the period
1961 to 2011 there was a decrease in insolation (sunshine) in
most months resulting in an average change of 1%.It was
also found a decrease in insolation at higher rates in the
period of 1980-2000 probably related to the phenomenon of
global dimming and the phenomena or ENOS. It is estimated
that in the coming decades the rates of heatstroke will keep
these lower rates with the possibility of a decrease during
few months in most seasons. A possible entry into a cold
PDO phase can lead to an intensified ENSO phenomena
resulting in a no encouraging climate change, especially for
the Brazilian hydroelectric energy sector that periodically
depends on rainfalls.
As a final conclusion,it is strongly suggested that the
variation inthe insolation cycles be taken into account in
preliminary studies to decide on the location and energy
planning for installation of wind farms, solar (PV or solar
thermal) and hydroelectric power plants. The mean changes
of insolation can be up to 4% depending on the season month
and therefore may cause an overestimation or under
estimation of predictions if only short periods of data were
used.
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Disponível
em
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