Hourly solar irradiance forecasting based on machine learning models

Transcription

1 th IEEE International Conference on Machine Learning and Applications Hourly solar irradiance forecasting based on machine learning models Fateh Nassim MELZI IRT SystemX, Palaiseau, France Taieb TOUATI, Allou SAME and Latifa OUKHELLOU Université Paris-Est, IFSTTAR, COSYS, GRETTIA, F Marne-la-Vallée, France (taieb.touati, allou.same, Abstract In recent years, many research studies are conducted into the use of smart meters data for developping decisionmaking tools including both analytical, forecasting and display purposes. Forecasting energy generation or forecasting energy consumption demand are indeed central problems for urban stakeholders (electricity companies and urban planners). These issues are helpful to allow them ensuring an efficient planning and optimization of energy resources. This paper investigates the problem for forecasting the hourly solar irradiance within a Machine Learning (ML) framework using Similarity method (SIM), Support Vector Machine (SVM) and Neural Network (NN). These approaches rely on a methodology which takes into account the previous hours of the predicting day and also the days having the same number of sunshine hours in the history. The study is conducted on a real data set collected on the Paris suburb of Alfortville. A comparison with two time series approaches namely Naive method and Autoregressive Moving Average Model (ARMA) is performed. This study is the first step towards the development of the hourly solar irradiance forecasting hybrid models. I. INTRODUCTION Nowadays, there is a growing interest on renewable energies. This trend is likely to continue with the need to address environmental issues and thanks to the decreased costs and technological advances of the renewable energy sources. Within this context, public stakeholders involving electricity suppliers, distribution network operators and city managers have to face a rapide increase in electricity demand, to diversify the sources of energy production and to be able to balance production, supply and demand. For these purposes, smart meters are increasingly used and the amount of data they collect are analysed. The aim is to build decision-making tools in order to be able to plan the electricity requirements depending on current and emerging needs. Therefore, photovoltaic energy is among the top three renewable energy used world wide. However, due to the fact that the output power depends on solar irradiance and weather conditions, one of the challenge to face to make this kind of energy production more attractive relies on the ability to develop advanced and precise irradiance solar measurements, modeling and forecasting. In so doing, a better planning and scheduling of different types of generation plants can be achieved. Considering the specific problem of solar irradiance forecasting, a variety of methods and tools can be handled depending on the relevant temporal and spatial prediction horizons as well as on the contextual variables available to make this prediction. Multivariate time series or machine learning methods can thus be developed to tackle this problem. This paper investigates the opportunity to explore three machine learning techniques namely: Similarity method, Support Vector Machine (SVM) and Neural Network (NN), in order to perform the hourly solar irradiance forecasting. These methods rely on a methodology which takes into account the previous hours of the predicting day and also the days in the history having the same number of sunshine hours. A comparison with two time series methods specifically: Naive method and Autoregressive Moving Average Model (ARMA) is performed. Experiments are carried out on a real data set collected over twelve years on the Paris suburb of Alfortville and provided by Reuniwatt company 1. The remainder of the paper is organized as follows. A review of related work is provided in Section II. The solar irradiance data set used throughout our study is described in Section III. The hourly forecasting methods are presented in Section IV. Experimental results are detailed and discussed in Section V. Section VI concludes the paper and gives some perspectives of further works. II. STATE OF THE ART Global horizontal irradiance (GHI) forecasting is the key step in the majority of photovoltaic prediction systems, thus an increase of interest among researchers is observed. The GHI forecast gives a more precise modeling and forecasting for solar power. Various solar irradiance forecast methodologies have been developed for different time horizons up to 24h [1]. We can divide the models into two main groups: statistical models and numerical weather predictions models. Statistical models stand on the analysis of historical data and are divided into two categories namely Time series models and Machine learning models. Neural networks (NNs) are considered as a reference method for solving complex problems in various fields and this is the reason why applications of NNs in the field of solar forecasting is mentioned in several scientific works [2], [3], [4]. In fact, the scope of historical data on meteorological databases and the fact that NNs are intrinsically data driven approaches make them very attractive for the /16 $ European Union DOI /ICMLA

2 scientific community. Most publications are moving towards the hour ahead solar forecast, as it is the prevalent operational forecast solicited by most of the utility companies in the insular grids field. However, Mellit et al. [5] proposed a multiplayer model for a daily irradiance forecasting, using as inputs both the mean daily irradiance and the mean daily temperature. Another popular machine learning method is the Support Vector Machines (SVMs) [6]. The use of these techniques in the field of solar energy is relatively recent [7], [8], [9]. Li et al. [10] compared SVMs regression and Hidden Markov Models [11], in order to forecast short-term solar irradiance. The algorithms have been implemented under three different weather conditions with the same datasets. Li et al. developed a Matlab interface, the weather forecasting platform to enhance solar forecasting. The spectrum of methods used in irradiance forecasting, can range from machine learning methods to linear statistical methods like the Autoregressive model (AR) and the Autoregressive moving average model (ARMA) [12]. These methods are efficient for predicting the future value of auto-correlated time series data. The popularity of the ARMA method within the scientific community lies in its capacity of extracting interesting statistical tools, in addition to the adoption of the well known Box-Jenkins method [13]. To set up an ARMA model, a necessary condition is the stationarity of the time series [14]. Ji et al. [15] use the Augmented Dickey-Fuller (ADF) test to measure the stationarity of the time series. As the original solar irradiance data is not stationary (daily and annual seasonalities), a pre-processing is essential. Lauret et al. [16] proposed a bechmarking of several machine learning techniques and an AR model. In order to make the solar irradiance times series stationary, they used the Bird clear sky model [17] to normalize the data. More recently, David et al. [18] used the same pre-processing to forecast solar irradiance with recursive ARMA-GARCH models. Besides its benefits on stationarity, this data normalization facilitates the learning process for Machine learning methods. In this paper, we focus on forecasting the hourly solar irradiance using three machine learning techniques which take into account the previous hours of the predicting day, and also the days in the history having the same number of hours of sunshine. III. DATA SET PRESENTATION A. Description of the Data Set The available data set consists of an hourly solar irradiance of the Paris suburb of Alfortville provided by Reuniwatt company 2. The Irradiance expressed in Watts/m2 is collected for a duration of 144 months (1st January 2004 to 31st December 2015). The data set is represented by a time series X having a dimension (D T ), where D is the number of days (4383 days) and T =24is the number of measurements recorded every day. It is worth noting that no missing values are detected in X. Figure 1 shows the daily solar irradiance curves for the year At first glance, we can distinguish three parts in each day: the first one represents the night before 2 the sunrise, the second is the part of the day between the sunrise and the sunset, while the third one corresponds to the night after the sunset. As it can be expected, the durations of these parts vary from one period to another in the year depending on the seasonal fluctuations. We explore the data through the elementary statistics presented in the next section. Fig. 1: Daily solar irradiance curves during the year 2015 B. Elementary Statistics Elementary statistics are first applied to have an overview on the data. Figure 2 represents the evolution of the number of hours of sunshine over the 12 years (from 2004 to 2015). We remark that the progression of the number of hours of sunshine is the same from one non-leap year to another and even for the leap years. These observations will help us in the forecast process detailed in the next section. When we focus on each type of year, Figure 3 shows the distribution of the number of hours of sunshine during the years 2012 and 2015 corresponding to a leap and non-leap years respectively. We find that the year is divided into 9 groups of days according to their number of hours of sunshine during the day. This number varies between 9 and 17 hours. Figure 4 represents the average irradiance profiles for each group during the year As it can be expected, the more the number of hours of sunshine is high, the greater the level of irradiance is. This is explained by the presence of the sunny days during the hot periods when the days are long, and contrary for the cloudy days during the cold periods. Using these information, in the next section, we will focus on forecasting hourly solar irradiance. Fig. 2: Evolution of the number of hours of sunshine over 12 years 442

3 (a) (b) Fig. 3: (a) Distribution of the number of hours of sunshine during a leap year (2012); (b) non-leap year 2015 Irradiance (W/m2) Number of hours Time (hour) Fig. 4: Average solar irradiance profiles for each group IV. FORECASTING METHODS In this section, we are interested in the two main categories of forecasting methods to predict the hourly solar irradiance. On the one hand, there are the times series models. On the other hand, we find machine learning techniques. They are succinctly described in the following. A. Time series models In this part we consider two time series approaches namely: Naive method and Autoregressive Moving Average model (ARMA), in order to forecast one hour ahead solar irradiance. These methods are described in the following. a) Naive method: is a simple forecasting method which is often used as benchmark to evaluate the performance of other prediction methods. It assumes that the predicted value is equal to the last observed one. In our case, the prediction of the solar irradiance at the hour h is expressed as follows: îr h = ir h 1, (1) where h =2,...,H, such as H =24. b) Autoregressive Moving Average (ARMA): is a linear stochastic process which describes a weakly stationary process through two polynomials. This model is a useful tool for forecasting time series. If X t N is a time series, ɛ t N a white noise, and L the lag operator then an ARMA(p,q) model can be written: Φ(L)X t =Θ(L)ɛ t, (2) where Φ and Θ are polynomials of degrees p and q respectively. Times series forecasting models needs stationarity [19] to be effective. Using the ADF-Test, we found that the solar irradiance time series is not stationary. In order to stationarize them, we use an analogue model to the one used by Lauret et al. [16]. More precisely, we compute the clear sky index k, which is the quotient of the measured irradiance X and the irradiance under a clear sky X clear as the following: k = X/X clear. (3) X clear is the output of the McClear model [20], available on the SoDa website 3. To forecast the clear sky index, we propose a unified number of predicting hours H by days in each month to guarantee a measured solar irradiance for the both time series. This filtering method removes about 1% of the annual total solar energy. H is variable for each month and bounded by a morning and an evening hours as illustrated in TableII. Month Morning hour Evening hour January 9 15 February 9 16 March 8 17 April 8 17 May 7 19 June 6 20 July 6 20 August 7 19 September 7 18 October 7 17 November 8 16 December 9 15 TABLE I: Morning and evening hours for each month The forecast is obtained by modeling the clear sky index time series through an ARMA(3,1) model

4 k h = α α i k h i + β ɛ h 1 (4) The solar irradiance at hour h is given by: where h =2,...,H. îr h = k h X h clear, (5) B. Machine Learning Models In this part, we target to forecast the hourly solar irradiance, using three machine learning techniques namely: Similarity method (SIM), Support Vector Machine (SVM) and Neural Network (NN). These methods are succinctly described in the following. The use of these methods relies on a methodology which takes into account the previous hours of the forecasting day, and also the days in the history with the same number of hours of sunshine as the one to be predicted. As described in section 3 (b), the number of hours of sunshine during the days is known both for leap and non-leap years. To forecast the hourly solar irradiance, we focus only on predicting the last H 1 sunshine hours, where H {9, 10,..., 17}. Each hour h =2,...,H is forecasted by using a model with h 1 inputs (previous hours). The methodology is described in Figure 5. E = {x h i,yh i }n is the training data set used to train the models, where n is the number of days with the same number of hours of sunshine as the day to predict. x h i is a vector with h 1 past values. The length of x h i is variable according to the forecasted hour h. yi h corresponds to the solar irradiance value at h. Similarly, (x h,y h ) is the test observation. For our study, we present now the methods that we have retained. ( wi h =exp 1 ( x h x h i )) 2 Cσ(x h,x h i ), (6) where σ is the standard deviation and C is constant fixed at The predicted value of the irradiance at the hour h is calculated as follows: îr h = n wi h yi h. (7) d) Support Vector Machines (SVMs): were invented by Cortes and Vapnik [21], in order to solve the discriminant and the regression problems. This machine learning technique aims at maximizing the margin between the hyperplane and the data, and at the same time, minimizing the empirical risk (as a cost function). In regression and time series forecasting applications, good performances were obtained [22]. For our application, the prediction of an input test case x h is given by: îr h = n α i f(x h,x h i )+b, (8) where f denotes the radial basis function, and b is a bias parameter. e) Neural Networks (NNs): A NN is a mathematical model that is inspired of the biological neural networks operation [23]. To define a non linear parameterized mapping from an input x i to an output y i, we design a NN that uses h 1 inputs, we fix the number of hidden neurons to 10 and we consider one single output (hour to forecast). The forecast of the input test variable x h is given by the following equation: îr h = m j=1 h 1 w j f( w ji x h + b 1 )+b 2, (9) the m hidden neurons are associated to the tangent hyperbolic function f. The weights w j, w ji and the biases b 1, b 2 are estimated during the training phase. It can be noticed that the number of hidden neurons can be optimized to improve the test performances of the model, which would be the subject of future investigation. Fig. 5: Methodology applied to forecast hourly solar irradiance using machine learning techniques c) Similarity method (SIM): is a simple method which is based on the comparison between the actual observation and the past observations in the history in order to forecast the future one. This method takes into account the hypothesis that the future following two similar observations are expected to be comparable. To evaluate how close is the test input variable x h with the past observations x h i in the history, a weight wi h is attributed to each observation x h i as follows: V. RESULTS AND DISCUSSION Two years of data (2014 and 2015) are considered to evaluate the performances of the models. The leave-one-out cross validation method is used, meaning that the training is performed on the n 1 past observations and the test is performed on the n th observation. This operation with different training and test sets is repeated n times, from 1st January 2015 to 31st December A statistical error indicator, namely the Normalized Root Mean Square Error (NRMSE) is computed to evaluate the accuracy of each model. This indicator is computed by determining the Root Mean Square Error (RMSE): 444

5 RMSE = 1 H (îr h ir h ) H 1 2, (10) h=2 where îr h and ir h are the hourly forecasted and measured irradiance respectively. H 1 is the number of hours to be predicted. Then we compute the NRMSE which is expressed by: NRMSE = RMSE, (11) īr where īr represents the mean measured irradiance corresponding to H 1 hours. Irradiance (W/m2) Irradiance (W/m2) Measured Naive ARMA SIM SVM NN Time (hour) (a) Measured Naive ARMA SIM SVM NN Time (hour) (b) Fig. 6: (a) Measured and forecasted values for a sunny day; (b) cloudy day Error indicator Models Naive ARMA SIM SVM NN NRMSE TABLE II: Normalized Root Mean Square Error for the hourly forecasting models After applying the five forecasting models, Figure 6 represents the measured and forecasted values using these methods for a sunny and a cloudy days respectively. For a sunny day (see Figure 6 (a)), we remark that the predicted values with ARMA, SIM, SVM and NN have well agreement with the measured ones. Especially, the forecasted solar irradiances of the three machine learning techniques are very close to the observed values comparing to the ARMA model. About the Naive method, the forecasted values are one hour lagged comparing to the measured ones. However, for the cloudy day (see Figure 6 (b)), the predicted values of the whole used models, follow the variations and the fluctuations of the measured irradiances, with a different adjustment. This difference is significant for Naive and SIM compared to the remaining methods. Our proposed models are accurate to forecast the sunny days without intermittency and less efficient in predicting the days with changeable weather. In the case of forecasting the cloudy days, it would be useful to integrate the meteorological variables (humidity, wind, temperature,...) in the models to increase their performances. Comparing the statistical error indicators of the five models (see Table II), we remark that ARMA, SIM, SVM and NN give better performances than the benchmark method (Naive). We observe also, that the NRMSE of ARMA is equal to that obtained by SVM and it is better than the SIM one. In this study, the best forecasting method is the NN with a NRMSE of The machine learning techniques can be more accurate by augmenting the training period. These performances are due to the methodology applied, which takes into account the previous hours of the forecasting day, and also the days having the same number of sunshine hours in the history. To perform a global evaluation of the models, we represent in Figure 7 the evolution of the NRMSE of the four forecasting methods according to the days of the year For certain extremely bad weather condition, machine learning techniques present a limitation in the forecasting comparing to ARMA. For example, during February 20th 2015, the machine learning techniques SIM, SVM and NN give a high NRMSE values: 1.627, and respectively, however ARMA obtains an acceptable NRMSE of To remedy this problem and take benefit from either machine learning and times series models, hybrid models could be a solution to extract full characteristics of solar irradiance. VI. CONCLUSION In this paper, an hourly solar irradiance forecasting methods have been used through three machine learning techniques, namely Similarity method (SIM), Support Vector Machine (SVM) and Neural Networks (NN). These methods rely on a methodology, which takes into account the previous hours of the forecasting day, and also the days in the history having the same number of sunshine hours. The study is conducted on a real data set collected on the Paris suburb of Alfortville. A comparison with two time series methods is performed, namely Naive method and Autoregressive Moving Average Model (ARMA). The proposed models give a satisfactory results during a sunny days and lesser accuracy for a cloudy days, thus it would be useful to integrate a meteorological variables (humidity, wind, temperature,...) to improve models performances. To take benefit from either machine learning and times series approaches, hybrids models could be a solution to extract full characteristics of solar irradiance. As future works, combination between hybrid models and meteorological variables are to be studied and investigated to improve the reliability for the extremely bad weather. 445

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