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International Conference on Renewable Energies and Power Quality (ICREPQ’17) Malaga (Spain), 4th to 6th April, 2017 Renewable Energy and Power Quality Journal (RE&PQJ) ISSN 2172-038 X, No.15 April 2017 ARIMA Method Applied to Solar Predictability Marcello Anderson F. B. Lima1, Paulo C. M. Carvalho1 Deivid Matias de Freitas1 Josileudo R. Leite2, Luiz J. de Bessa Neto2, Gessica Kelly Laureano Rodrigues2 1Department of Electrical Engineering Federal University of Ceará, Fortaleza, Brazil e-mail: marcello@ifce.edu.br, carvalho@dee.ufc.br, deivid_ce@oi.com.br 2Department of Oil and Gas Federal Institute of Education, Science and Technology, Tabuleiro do Norte, Brazil e-mail: josileudorodrigues@hotmail.com, luizbessa2015@hotmail.com, gessicakelly07@gmail.com Abstract. Studies in recent years show the great population growth and the need for energy demand, and the search for sources that cause less impact to the environment. In this scenario, emerged renewable energy sources, including solar, which has been increasing in several countries, especially in Brazil, but a disadvantage of this energy is present up intermittently. The characteristics of solar energy makes it unpredictable, so the balance between production and consumption of it is difficult for operators. Currently there are several mathematical models applied predictability of solar radiation on the earth's surface, among them stand out the methods of Artificial Neural Networks (ANN), and Regression models and Self-Regressive (SR). This work suggests the adaptation of ARIMA method, which are modern techniques for high precision using correlations between data collected in different periods, allowing the description systematically both stationary behavior in the non-stationary of the series in intermittent renewable electricity sector, aiming to make predictions of solar irradiance from data obtained through an anemometer station located in Maracanaú - CE. Key words. ARIMA method, solar irradiance, renewable electricity. 1. Introduction With the population growth of recent years, where esteemed that the world population will exceed 11 billion in 2100 [1]. While the population should have an estimated increase of 121% by 2030, energy consumption has increased 219% [1]. Along with population growth and increasing energy demand, another factor that is gaining prominence is the search for ways to minimize impacts to the environment, where there are impacts caused by use of non-renewable fossil fuels such as oil, and high consumption renewable resources such as the use of forest timber and fishing activities. The sources that stand out are solar and wind power, which has remarkable growth in global energy matrix, where in 2015, 147 new renewable energy gigawatts are now generated in the world [2]. In the case of solar energy, it has been highlighted in several countries. In moderate scenario, it is expected that solar will be responsible for about 11% of the world supply of electricity in 2050, data from the International Energy Agency (IEA), which corresponds to values close to 5,000 TWh. Despite its high cost, solar energy is still prominent among renewable energy, an example is Germany, which in 2014 generated 18.8% of solar energy in the world, followed by China which generated 15.7% and Italy which yielded 12.7% [3]. The renewed energy has been growing in recent years in Brazil, thanks to natural resources, such as high solar irradiance, mainly in the Northeast, which has the highest overall index, so solar energy has great prominence [3]. In 2018, Brazil will is among the 20 countries with the highest solar power generation, considering the power already contracted and the scale of the expansion of other countries according to the Ten Year Plan for Energy Expansion (PDE 2024), expected still that by 2050, 18% of the country's homes will have solar power generation [3]. The substantial increase in the share of renewables in the global energy matrix has caused impacts on electricity generation that need to be studied, known and where necessary prevented. Current models used in Brazil for the expansion planning and operation need to be revisited to reflect this new reality [4]. The Brazilian electric system, hydroelectric base in the near future will have a large installed capacity of solar parks and wind farms, which bring different characteristics of the current generating capacity, as the short-term variability in generation and greater unpredictability. Photovoltaic solar energy although it is a source of abundant energy, it has the disadvantage of presenting up intermittently, that is, not concentrated and difficult to capture in comparison with hydroelectric power by being subject to climate variability, mainly due to performance of the clouds and the movement of the planet. So to be harnessed, are studies demanded that allow better understand their regional availability, temporal variability and predictability [5]. The characteristics of solar generation makes it unpredictable, that is, not fully controllable by the human being, transforming thus the balance between generation and consumption of electricity a challenging task for operators. Therefore, the higher the share of this source in the global energy matrix, the greater the stochasticity and short term intermittency in electricity generation and minimize these impacts has become an important subject of study [6]. Currently, there are several mathematical models that allow to simulate the solar radiation reaching the Earth's surface. However, to make such predictions, should take into account the processes that occur when solar radiation interacts with the atmosphere. Among the factors that attenuate solar radiation the presence of clouds is the most important or even the only, in the case of specific regions such as the Northeast. The attenuation caused by the same process is a stochastic nature, which makes its prediction a complex task [7]. In this sense, there have been employed various techniques in order to provide solar radiation at the earth's surface, among them include the use of Artificial Neural Networks (ANNs), which are systems in parallel distributed and constituted by processing units capable of modelling from simple to the most complex problems and, once trained, can make predictions and generalizations instantly [7]. Another commonly used technique for predicting solar irradiance in the medium and long term, are the regression models and self-regressive (ARs) with coefficients that vary over time. This method consists in constructing a matrix L(i,k) of 52 rows by 24 columns, where each row corresponds to one week of the year and each column at a time of day. Thus, it is concluded that in this model there is a self-regressivity first order in the determination of estimates, i.e., the amount of radiation in the preceding time has significance for the calculation of the radiation over the next hour. The images obtained from satellites have also been continuously used to make estimates and predictions of solar radiation in the medium term, because of its excellent spatial and temporal resolution. In this type of prediction, it is considered that there is a linear relationship between the cloudiness index, which refers to the fraction of the partly covered by the sky at a given moment with the transmissivity of the atmosphere, by which is the ratio of terrestrialsolar radiation and the alien [8]. The global irradiance on Earth, is then calculated by combining these weather features with solar radiation calculation model for the conditions of a day with clear skies. However, the satellites have some limitations such as the high cost of implementation and high duration of the acquisition of two images, which makes it impossible to make predictions very short time, or for time scales of less than 30 minutes [7]. Furthermore, the use of this technology is not the most appropriate when you want to run a forecast at the local level. In the mid of 1970, the statistical George Box and Gwilym Jenkins, developed a methodological body, called ARIMA (Self-Regressive Integrated and Moving Averages) to identify, assess and diagnose dynamic time series models, in which the time variable plays a role key. An important part of this methodology was designed in order to release the investor of economic models specification task, leaving the very time of the variable data in the study, indicating the characteristics of the underlying probabilistic structure [9]. The ARIMA's models are highly accurate modern techniques that use correlations between data collected in different times and could describe systematically both stationary behaviour as the non-stationary of the series [10]. Thus, it can be said that this is a flexible modelling methodology that forecasts based on these models are made from the current and past values of the time series. The ARIMA method has been regularly used in the administrative and food sector to manage, control and estimates of commodity prices in shops, malls and large restaurants, with a high margin of efficiency and reliability. Moreover, it has been used in stationary time series for forecasting and indication of prices of cattle prices in the state of Paraná, in Brazil, aiming assist sectors involved in beef cattle to achieve a future price reference that enables management efficient market risk as well as the decision-making process, cost management and definition of the best marketing strategies [11]. This work suggests the adaptation of ARIMA method in intermittent renewable electricity sector, aiming to make predictions of solar irradiance and wind speed from data obtained through an anemometer station located in Maracanaú - CE, located 18 km from Fortaleza, considered the largest industrial center of the state. 2. Literature review In the last decades has found several lines of research on the application of ARIMA method in energy planning sector, estimates for electricity generation costs and electricity consumption. Priority is thus to minimize the alternative/intermittent sources of energy forecasting errors, diversify the global energy mix. Search by means of this method adaptation to the electrical system to the variability of solar photovoltaic generation, as well as facilitate the integration of renewable technologies variables efficiently in terms of electricity production costs. One of the first scientific papers to adapt the ARIMA method on temporary electricity series, aiming to provide financial figures for electricity consumption with a day in advance, was published in 2003 by the Spanish researcher Javier Contreras. The table I presents a summary of the works found in the world regarding the adaptation of the ARIMA method[7-12]-[20]. Table I. - Literature of review AUTHORS APPLICATION METHOD GENERATION SOLAR Melo, 2016 Forecast of solar potential in the Brazilian Northeast ARIMA Yes Hussain; Alili, 2016 Forecast solar daily in Abu Dhabi ARIMA Yes Colak et al, 2015 Forecast solar of multiple periods ARIMA Yes Passos, F., 2015 Forecast of consumption of electricity ARIMA Yes Christo, E., 2013 Forecast of electric charges ARIMA Yes Silva, T., 2012 Forecast of electric charges ARIMA Yes Mohamad,A. 2012 Forecast of demand of electricity ARIMA Yes Wu; Chan, 2012 Forecast solar monthly ARIMA Yes Jesus, T., 2008 Forecast of consumption of electricity ARIMA Yes Contreras, 2003 Forecast of renewable electric resource ARIMA Yes 3. ARIMA method of adaptation to forecast solar and wind data To achieve greater flexibility in real time series assembly with a greatly reduced number of parameters, it is advantageous and include both Autoregressive Moving Average. Thus, there is a ARMA combination which is given by the estimation of the regression of dependent variable Y depending on the lags of the variable itself Y, indicated by “p” autoregressive terms, according to the random error, indicated by “q” terms moving average, with the model indicated as ARMA. Thus, the ARMA (1,1) model can be written as (1) [12]. 1 1 1 1 0 Yt Yt pYt p Ut Ut qUt q (1) wherein Δ is the difference operator. However, most of the time series is naturally non- stationary, then the model application requires processing thereof by differences to make them through the stationary method ARIMA (p, d, q) in equation (2) [21]. 0 t t tB z B dz B a at where: 1 2 2 1 2 2 1 1 p p q q B B B B B B B B ϕ(B) is the autoregressive operator; It is stationary, where ϕ(B) = 0 are outside the unit circle. φ(B) = φ(B)∇d is the generalized autoregressive operator; It is a non-stationary operator d of the φ(B) = 0 equal to unity, that is, unit roots of d. θ(B) is the moving average operator; inverted, that is, where roots θ(B) = 0 they are outside the unit circle. When d = 0, this one model is a stationary process. The stationarity and invertibility requirements apply independently, and, in general, the operators φ(B) and θ(B) will not be of the same order. However, many series have a seasonal component and it may be necessary to model these in order to obtain a more reliable model. In this sense, SARIMA models were developed (Seasonal ARIMA), which are seasonal ARIMA models. Such a model is represented in equation (3) as SARIMA (p, d, q) (P, D, Q)s, where s is the period corresponding to seasonality, Φ(Bs) are seasonal coefficients autoregressive; ϕ(B) are the coefficients of the seasonal moving averages and (1-Bs)D is the order difference operator D of seasonal differentiation [12]. 1 1 Bs B Bs d Bs D Xt Bs B Zt The ARIMA methodology for modeling a process consisting of four steps according to [15] be seen in figure 1 below [21]-[22]. I - Identification of the model II - Parameter estimation III - Diagnostic checking IV - Forecasting No (Return to Step 1) Yes (Go to Step 4) Fig. 1. Steps ARIMA methodology (p, d, q). a) Identification: the first step consists in obtaining the appropriate values for p, q and d. For this, one can employ the correlogram and partial correlogram, which are graphical representations of the autocorrelation function (CAF) and Partial Autocorrelation Function (FACP) against the size of the gap. The aim is to get the index (p, d and q) in which the series has stationarity; b) Estimation: It is estimated model parameters, which can be done by means of least squares or non-linear estimation method; c) Diagnostic check: it is checkedwhether the estimated model fits the data well. One way to do this check is to see if the model residuals are white noise. If so, whether to accept the model. Otherwise, the process must be restarted in order to identify another model; d) Forecast: the model is used to make forecast. The ARIMA processes have the general characteristic of their predictions revert to the mean when the forecast horizon increases. In this sense, the potential for prediction of these models is limited to short-term horizons. With the aim of obtaining the solar data were considered information obtained from the study "CHARACTERIZATION AND PREDICTION OF SOLAR POTENTIAL: CASE STUDY FOR PARNAÍBA (PI) Maracanaú (CE) and PETROLINA (PE)" Authorship [12]. Thus, we performed a study of information The study of solar data was done with information obtained in northeast Brazil, more precisely in Maracanaú - CE. The city was chosen due to this being one of the three sites with tower data collection belonging to CNPq project "wind potential forecast aiming optimal integrated operation of generating electricity units: a case study for the Northeast of Brazil", which finances the study presented. By way of (2) (3) information, the other two municipalities included in the project are Parnaíba (PI) and Petrolina (PE) [12]. The equipment installed in the station used to obtain the observed data have an acquisition system NRG Symphonie-plus, which enables data storage at 10 min intervals (obtained by arithmetic means from data processed every 2 s). The parameters recorded directly by the datalogger, are stored in MMC type memory cards (Multi Media Card), with capacity of 32 M, which ensures a range of more than one year of recorded data [12]. The present equipment at the weather station can be seen by Figure 2. Fig. 2. Datalogger NRG Symphonie-plus installed. Source: Adapted of [17]. This study made use of the XLSTAT software, as this is modulated to Microsoft Excel for data entry and presentation of results, but the calculations are performed with the components of own software independently. We used this tool for achieving solar forecast data, since it takes on characteristics of an automatic statistics software. The XLSTAT generates the confidence limits based prediction graph is also shown graphically validation media (sized) and the average prediction as a straight line in the graph. Figure 3 shows the main elements of the graph produced by the software [12]. Fig. 3. Explanation of the XLSTAT forecast charts. Source: Adapted of [12]. Thus, after analysis of data were carried 23970 4485 hourly averages between 5:00 am to 17:00 and forecast solar irradiance data 10 in 10 minutes by selecting 42 days and obtaining 3318 data. These surveys are formed as time series and therefore for their predictions, require specific statistical methods for their treatment. As seasonality is a characteristic present in data time series solar irradiance, characterization and prediction is made using the seasonally low solar irradiance component, the atmospheric transparency index, Kt. The use of this component is justified by the fact of providing results more accurate and reliable forecasts, low interference from components trends present in temporal data series, the forecasting process. The forecasts made in this study using the ARIMA method, exponential smoothing method in Simple mode (AES) and the method of Moving Averages [23]. Thus, after the selection of monthly time series for each time band period information collected it was carried out analysis of 23 series time corresponding to the 5:00 hours of tracks to 17:00 hours every day of the period of may 2012 to April 2013. Analyzed by XLSTAT looked at the range of twelve months each series and obtained from the series generates a graph for each series. Thus, there were the forecast of 546 hours of solar irradiance. 4. Results and discussions The behavior of prediction of solar resource, with a comparison between the predicted and observed values of irradiance solar, can be seen by Figure 4, which shows the values in W / m² obtained forecasts acquired by ARIMA method, and the irradiance solar measured by the anemometer station. Were realized forecasts of 546 hours of solar radiation were performed. Fig. 4. Comparison between the solar irradiance measured and observed. It appears that the forecast of solar irradiance are monitoring the characteristic behavior of solar availability throughout the day, but it is clear that situations of climate interference, such as rainfall and periods cloudy for example, were not understood and anticipated by the method ARIMA forecasting. Yet the method was able to present values close to forecasts and observations at different times of the analysis period. Recalling that the night period was disregarded for predictions because they are null values. For situations where the values obtained from the time series of anticipation method ARIMA did not follow satisfactory way the solar irradiance values observed, there is a highlight for the time 156 of the forecast, where the predicted value for the solar resource availability for this time was 24.54 W/m² and the observed value was 0.76 W/m², presenting as the biggest difference between predicted and observed values for all 546 hours forecast, causing a large overestimation of the amount available solar resource for time analysis. The smallest difference in predicted and observed values was found in time 318 with the predictive value of 683.79 W/m² and observed value of 683.23 W/m². The greatest value of solar irradiance observed was 996.54 W/m² while the highest value of planned solar irradiance was 769.26 W/m². The lowest solar irradiance observed was 0.57 W/m² while lower value provided to solar irradiance was 3.15 W/m². The forecast did not get results faithful regarding climate variations over the hours, but managed to make a good accompaniment of natural variations of amplitudes in the course of hours. The Figure 5 shows the comparison between the data obtained from the forecasts obtained by ARIMA method for solar irradiance measurements and for the first 24 hours of forecast. The separation of this period facilitates viewing and comparing the predicted and measured values. Fig. 5. Comparison between measured solar irradiance and observed for the first 24 hours of forecast. The behavior of the errors can be viewed by Figure 6. In the image prediction with ARIMA method presents a clear tendency to overestimate the availability of wind resource. Fig. 6. Error solar of forecast. The forecast with the highest proportional difference between irradiance values measured solar and collected was carried out at the time 156, where it obtained the mistake of 3.115, 2%. In other six situations the errors were also higher than 1.000%, specifically in 442 hours with 1.918,18%, 456 with 1.354,7%, 520 with 1.815,93%, 539 with 1.384,82%, 540 with 2.968,12% and 546 with 1.310,41%. The Figure 7 shows the combination of the collected solar irradiance and the forecast errors. Fig. 7. Comparison between the collected solar irradiance and the forecast errors. In hour 144 there was greater underestimation solar resource availability, where obtained a forecast of error of -86.04% forecast. The smallest difference in predicted and observed values was found in time 318,with the of forecast value showing 0,08% of error. Finally, the average error of the solar forecast was of 82,14% and the mean of the errors module is of 91.86%. For a better understanding of the behavior of forecast errors, a separation of hours the prediction was made, related to Increasingly, demonstrating their respective scope of departure from the ideal, wind and solar prediction. Thus, it is possible to separate negative and positive errors and understand the amount of hours that was among the tracks of -5% a 5% e -10% a 10%. The figure show the separation hours predictability of errors for this one resource. Fig. 8. Hours of sun forecast in relation to forecasting errors The Predictability of solar resource obtained a total of underestimation of 179 hours, 367 hours of positive error and no null error. Related to the departure from the ideal forecast for the error range of -5% a 5% of error, a total of 61 hours remained within the range and 127 hours for the range of -10% to 10% error. The forecast ranged of - 86,04% to 3,115,2%. 5. Conclusions The Brazilian energy matrix, composed mostly of electricity from hydraulic resource, must be diversified due to the non implementation of new large hydroelectric plants. From this fact, management methodologies and potential analysis of implementation of complementary sources for the electrical grid should be developed. Due to the high availability of solar resource, northeast Brazil presents itself as a contributor to expanding the diversification of the Brazilian energy matrix. This potential contribution can best be exploited provided that adequate investment and technical policy be developed for understanding the impacts caused by the implementation of alternative energy sources in the energy matrix of the country. The generation intermittency characteristic solar source must be worked towards developing techniques that can reduce the additional costs to the production of electricity; of these costs is related to the expected availability of solar and wind resources due to climatic factors. The forecast solar irradiance could follow the irradiance behavior throughout the day, but could not foresee climate variations such as cloud cover and rain. The value found in solar forecast of errors module was of 91,86%, however, the large previously presented forecast errors occurred in situations with low solar irradiance, more precisely at sunrise or sunset. This characteristic minimizes the forecast errors, because precisely the moment where the solar forecast errors were higher, a possible electricity production system from the sun resource would be at a time of low energy production, resulting in less impact the energy matrix. References [1]. United Nations. “World Population Prospects The 2015 Revision Key Findings and Advance Tables”, New York, 2015, pp. 2-3. [2]. A. Zervos. “Renewables 2016: Global Status Report”, Paris (2016). pp 30-32. [3]. A. V. Filho. “Ten Year Plan for Energy Expansion 2024.”, MME, Brasilia 2015, pp.38-232. [4]. G. A. Cavados, “A introduction of the impact analysis of intermittent sources in brazilian electricity sector: case study of The Region Northeast”, COPPE- UFRJ, Rio de Janeiro 2015, pp 1-3. [5]. 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