A REVIEW OF SOLAR IRRADIANCE PREDICTION TECHNIQUES L. Martín 1, L. F. Zarzalejo 1, J. Polo 1, B. Espinar 2 and L. Ramírez 1

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1 A REVIEW OF SOLAR IRRADIANCE PREDICTION TECHNIQUES L. Martín 1, L. F. Zarzalejo 1, J. Polo 1, B. Espinar 2 and L. Ramírez 1 1 Departamento de Energía. CIEMAT / MEC. España. Av. Complutense 22, Madrid, Spain. 2 Plataforma Solar Almería / MEC. España. P.O. BOX 22, Tabernas, 04200, Almería, Spain. Keywords: FORECAST, PREDICTION, SOLAR RADIATION, SATELLITE IMAGES Contact Details: Luis Martín Pomares Departamento de Energía. CIEMAT / MEC. España. Av. Complutense 22, Madrid, Spain. Phone: Fax: luis.martin@ciemat.es Abstract: Until now most of the efforts in the developing of solar energy has been made to utilize solar energy efficiently, although only minimal resources have been directed toward forecasting the incoming energy. Spanish government has approved recently a new Royal Decree 436/2004, which sets up a lasting financial regime based on a method for calculating retribution that, predictably, allows faster progress implementing solar power. The power plants integration within the electric grid makes up a new stage where it is needed to estimate the power generation in the short term to optimize resources management, preventing load reduction scenarios and bringing forward possible black-outs of the power supply. This paper makes a review of the solar irradiance forecasting methods researches until now which are based basically on statistical techniques. 1. Introduction The sun can be considered as a huge fusion nuclear reactor, which consists of different gases which are retained inside by gravitational forces. The energy as electromagnetic radiation is produced by the fusion reactions in the inner layers, basically the kernel, and is transferred to the external layers to be radiated to the space. The solar energy reaches the earth in the form of electromagnetic radiation. It is the main source of energy and produces all the main processes on earth: dynamic in the atmosphere, the oceans and in general life on earth. There are several human uses from this resource: solar water heating, water detoxification, water desalinization, electric power energy generation from solar thermal power and photovoltaic energy, agricultural applications, etc.

2 Solar thermal power and photovoltaic energy have a huge developing potential in near future, supported on the Kyoto protocol agreements from different countries and on the retribution system which different countries are promoting. In Spain, Royal Decree 436/2004, which minimizes investment risk to promoters, opens new perspectives to solar energy development. It is planned to have 500MW of solar power plants by 2010, and as a remark in 2005 it is expected that more than 50 power plants begin construction in the near future. Besides a report Published (1) by Greenpeace presents a future demand stage and generation with renewable energies of electricity in Spain in The conclusion of this study is that future energy demand can be supplied more than 8 times with solar energy. Figure 1 shows results from this study. Figure 1. Electrical energy generation with renewable energies sources Although considerable effort has been made to utilize solar energy efficiently, from industrial revolution expecting fossil fuels would run out in the future, only minimal resources have been directed toward forecasting the incoming energy. Even that the necessity to have forecasting models that allow optimize the integration of solar thermal power and photovoltaic within different sources of electric power generation will grow up as they gain recognition as a resource in the next year. Indeed royal decree 436/2005, says, All facilities with power upper than 10MW should communicate to the network distributor a prevision of electric energy in each one of the scheduling periods of the market of electric energy generation. The prevision should be communicated for each period of the day hourly, almost 30 hours the beginning of the day....

3 Summing up there is a basic need to characterize and predict incoming solar radiation to be used as a energetic resource. Next sections describe prediction techniques for different temporal horizons. 2. Forecasting techniques Prediction methods can be divided basically in numeral weather prediction (NWP) techniques, based on parameterization of physical phenomenon in atmosphere dynamics and statistical methods (2). Some statistical forecasting methods operate without information from dynamic circulation models. This pure methods are defined as classics, reflecting its prominence in the period where information from NWP more where unavailable. This methods are used in the present for short term prediction and medium-long term prediction, where information from NWP is unavailable with enough resolution or frequency (3). Other important application from statistical methods in weather prediction is in conjunction with NWP methods. Statistical forecasting models are used to improve the dynamic prediction model outputs over some quantities (probabilities) or locations not represented in included this one (3). The generic prediction can be divided in three categories: short term prediction which prediction horizon is between one hour and one week in advance, medium term prediction which goes from 1 week to one year and long term prediction which is longer than one year. It should be pointed that thanks to higher resolution in satellites like Meteosat Second Generation (MSG) from EUMETSAT it is now possible to develop nowcasting techniques (very short range prediction which horizon prediction is less than one hour). As an example, MSG products are cloud mask, cloud height, cloud temperature, All this products are produced by SAF, Satellite Application Facility, centres which belong to the national weather services that are part of the EUMETSAT consortium. More information can be found at Depending on the specific necessities from different users they will request a different prediction horizon. For example, for designing a solar energy system or back-up energy system it would be more useful a climatic prediction than a prediction from day to day. Nevertheless, once the system is operational a daily forecasting of incoming energy is more useful than climatic estimation (4). Works developed in solar irradiance forecasting framework are based basically in statistical method and short term horizons. Next sections describe the most important ones.

4 2.1. Short term prediction of solar irradiance In this forecasting horizon is where there are more works published. In the next paragraph will be described most important ones following a chronological order of appearance and ordering in different techniques Model Output Statistics (MOS) In 1979, National Weather System from United States (NWS) (5) used the MOS technique to develop a solar irradiance prediction system relating daily solar irradiance observed to forecast output produced by one of the NWS numerical weather prediction models. The equations tested with independent data produced forecasts with mean absolute errors of 0.74, 0.80 y 0.89 kwh m 2 for advance periods of 1, 2 y 3 days, respectively. The mean absolute error for forecasts based on the expected climatic value was 1.04 kwh m 2. Table 1. Mean absolute error (5) Prediction Mean absolute error (MAE) kwh m 2 MOS 1 day 0.74 MOS 2 days 0.80 MOS 3 days 0.89 Prediction based on climatic value 1.04 Baker y Casper (6) developed and tested three types of regression equations for objectively forecasting the percent of extraterrestrial radiation (I 0 ) received in three different locations: Bismark, ND, Madison, WI, y Chicago, IL. For the first type of equation, the relationship between MOS forecasts of precipitation and the observed insolation was determined. For the second type of equation, a MOS approach was used to relate the observed insolation to relative humidity forecasts from numerical weather prediction model. The third type of equation was similar to the second except that the observed relative humidity was related to the insolation rather than to predicted relative humidity. Verification results for 24 hours forecast indicated that third technique was best. In terms of the percent of percent of extraterrestrial radiation root mean square error for this method was Falconer (7) from mean precipitation obtained a reduction irradiance coefficient by effect of clouds, which was 0.85±0.15 for days with scattered clouds and 0.55±0.25 for days with broken clouds. He didn t present any independent test verifications of his method in his report.

5 In 1979, the National Oceanic and Atmospheric Administration (NOAA) proposed a new system that World provide solar energy forecasts for the conterminous United Status. Using the MOS technique to predict solar irradiance for 1 and 2 days in advance. To develop equations was used 1 year of data from 34 stations from NOAA Solar Radiation Network. Two Basic approaches for producing the insolation forecasts were tested. For the first they derived the clear sky index to obtain the solar irradiance. For the second one the derived equations to predict the insolation amount directly. In addition, two types of equations were developed for each approach. Single-station equation type and regionalized equation type for 6 regions in the USA. The verification process showed that regionalized equations obtained from clear sky index gave best results. Mean absolute error in terms of extraterrestrial radiation was 10% for a 24 periods and 13% for a period of 60 hours. Although the MOS approach worked well for the 34 stations used to develop equations, there was no way to determine how well the equations would work in locations where insolation data were unavailable. This way NWS (8) developed and tested a MOS approach bases on second order equations. The relation between global radiation from 30 stations from NOAA Solar Radiation Network and MOS cloud cover and dew point predictions to develop an unique equation for all stations. To develop the model data from 1977 January to 1978 December was used. As can be seen in Table 2 errors for MOS predictions are considerably lower than predictions based on persistence (prediction is the same as observed data the day before) or expected climate value. The correlation between observed and predicted data is much higher for MOS predictions. Table 2. Verification for MOS forecasting (9) Statistic error 24h statistical forecast 24h persistence Climatic stimate 48 hour prediction 48 hour persistence Mean forecast value Mean observed value Mean absolute error Root mean square error (RMSE) Correlation of the forecasts and observations Richard Perez (10) Developer a model to predict solar irradiance using predictions of sky cover, SK, from National Weather Service (NWS). From relation between cloud index, CI, and global irradiance,, he established a lineal relation for sky cover which can be express as: clear sky = g( SK)

6 where clear-sky is global irradiance under clear sky conditions and g(sk) is a function from sky cover predicted. Figure 2.1 shows relation between SK index and observed that relation isn t totally lineal. clear sky index. It can be Figure 2. Relation between SK prediction for 4-8 hours and global irradiance index observed (10). For this reason it is used two new types of expressions to model the relationship. First one was proposed by (11) to relate sky cover index and index from the following expression: clear sky 3,4 ( 1 0,75( N 8) ) = where N is the sky cover observed over surface defined in octas. Resides, Perez establish a new empiric adjust between SK and index, obtaining new coefficients to define the relation in the following way: clear sky 3,4 ( 1 0,75( N 8) ) =

7 Verification of model is tested with surface data and with values estimated from satellite images for different temporal forecasting periods. Table 3 synthesize the estimation results from three models. Table 3. Comparison of the models Lineal approximation to sky cover index (A), Kasten & Czeplak (B) and Best Fit Formula (C) (12) Satellite Ground Prediction horizon Relative mean bias error Root mean square error A B C A B C < 4 hours -36% 22% -2% 51% 42% 35% 4 8 hours -33% 30% 4% 49% 46% 34% 8 26 hours -35% 35% 5% 57% 59% 46% hours -35% 32% 4% 59% 58% 48% < 4 hours -41% 12% -10% 52% 32% 32% 4 8 hours -38% 21% -3% 52% 40% 34% 8 26 hours -39% 27% -1% 54% 47% 38% hours -40% 22% -4% 56% 44% 40% Results show from equation 3 that parameters surface observed sky cover index and satellite sky cover index are different Forecasting techniques with satellite images Satellite data are a high quality source for irradiance information because of excellent temporal and spatial resolution within short term forecasting horizon. Its utility is based basically on the strong impact of cloudiness on surface irradiance, so the description of temporal development of the cloud situation is essential for irradiance forecasting. There are several publication related to solar energy forecasting from satellite images (13) (14) (15) (16) (17), which belongs to the energy meteorology group from Oldenburg University in Germany. Cloud index images from Heliosat methods (18) derives a cloud measure from satellite images and obtain solar surface irradiance incoming. To predict the future clear sky index two main approaches are used: motion vector field (19) and neural networks.

8 Figure 3. Mean RMSE of píxel intensities (14). In Figure 3 can be observed a comparison of both methodologies. Motion Vector fields have better performance for all prediction horizon. Figure 4. Prediction estimation for a location and for a region 35kmx45km (13).

9 Estimation results from predictions are shown in Figure 4. For high values of solar irradiance the error is within 10% for a forecasting horizon of 30 meanwhile if the horizon is of 6 hours the error grows to 25% Forecasting techniques passed on spectral analysis and artificial intelligent techniques From the appearance in the last 20 years of advance mathematical techniques in the field of signal processing and neurocomputación it is possible to identify from solar irradiance data information that it isn t obvious at first sight. It is possible to do a signal study in frequency domain relating the time domain and decompose the signal in basic frequencies thanks to Wavelet analysis. In (20) it is proposed to decompose a time series data of various years solar irradiance daily data in 4 components and use them to train four neural networks. The outputs from these neural networks (NN) in frequency domain will be passed to temporal domain with inverse wavelet transform, so we can obtain solar irradiance predicted. In the Table 4 can be shown a comparison of predicted estimation based on neural networks with/without pre-processing signal with wavelet transform. Table 4. Predictions error based on NN with/without wavelet analysis (20) Medium and long term prediction of solar irradiance Medium and long term prediction is based in past climatic data and in day by day climatic data. Past climatic data, for example, can be used to determine the probability of 3, 4 or 5 consecutives days of cloudy weather. In general, predictions based on past climatic data assume that the meteorological patterns are somehow regular. This kind of assumption will not be useful for resource evaluation seasonally or annually because climatic condition can fluctuate considerably, instead they will be useful to estimate meteorological conditions averaged over the lifetime of a solar energy system that will usually deviate only slightly from the mean value (21).

10 3. Future works In a first phase the work to develop will be centred on daily solar irradiance. Preprocessing of signals with wavelet analyses (22-24) to obtain the signals expressed in different basic frequencies is the technique with best results to date. From this irradiance signals it is possible to apply different techniques (temporal series or neural networks) to predict signals. Finally, solar daily irradiance prediction will be obtained reconstructing the signal with inverse wavelet transform. A way to model the sequential and stationary properties of solar irradiance signal mapped into several time-frequency domains is using stochastic process analysis. It is based on analyzing past data to determine, from this information, the statistical properties that can be used to predict future signal. Other way to model and forecast signal is using neural networks as it is done in (22-24). However several improvements can be applied like the use of other kind of neural networks like self-organising networks (Kohonen maps) that uses rules of competitive learning. The main characteristics of this kind of networks: Belongs to the category of competitive learning networks or Self- Organized Features Maps (SOFMs) that is unsupervised learning. They have a two layer architecture (only one layer of connexion), lineal activation networks and unidirectional flux information (cascade networks). The entrance units receive continues normalized data, and the weights of the connexions are modified with data from out layer. After learning period, each entrance pattern will activate only one output unit. Besides it is possible to use as input data in the neural network surface irradiance data forecasted from NWP from European Centre Medium Weather Forecasting (ECMWF). Other way to fed the networks is using a model which relates with concentric rings cloud index values with satellite images from Meteosat-8 to a particular location. From satellite images it will be possible as it is done in (13) use different techniques to model temporal development of the cloud situation from motion estimation with segmentation techniques, considering clouds as whole group and not estimating the movement of each square as it is done in (13). Additionally rotation and scaling matrix can be obtained as it is done in graphic information field. For long term solar irradiance prediction it would be interesting used statistical techniques like EOF analysis to relate different atmospheric oscillation patterns, NAO (North Atlantic Oscillation), ENSO (El Niño-Southern Oscillation), with expected solar irradiance.

11 4. References (1) José Luis García Ortega, Alicia Cantero. Renovables 2050: Un informe sobre el potencial de las energías renovables en la España peninsular (2) Jose Manuel Gutiérrez, Rafael Cano, Antonio S.Cofiño, Carmen M.Sordo. Redes probabilísticas y neuronales en las ciencias atmosféricas. Universidad de cantabria; INM; (3) Daniel S.Wilks. Statistical methods in the atmospheric sciences. Academic Press; (4) Hulstrom RL. Solar user needs for forecasts and satellite mapping of insolation. Proc First Workshop on Terrestrial Solar Resource Forecasting and on the Use of Satellites for Terrestrial Solar Resource Assessment 1981; (5) Jensenius JS, Jr., G.M.Carter. Specialized Agricultural Weather Guidance for South Carolina. TDL Office Note 1979;79(15):16. (6) Baker DG, M.A.Casper. Subjective forecasting of received solar radiation. Proc First Workshop on Terrestrial Solar Resource Forecasting and on the Use of Satellites for Terrestrial Solar Resource Assessment 1981;8-11. (7) Falconer P. A methodology for Forecasting Morning, Afternoon, and Daily Totals of Normal Incidence Solar Radiation at Ground Level under Clear or Partly Cloudy Skies. ASRC 1981;Publication 805:31. (8) Jensenius JS, Jr. Automated forecasts of daily global solar energy. Progress in Solar Energy 1983 Jun 1; (9) Jensenius JS, Jr. Automated forecasts of daily global solar energy. Progress in Solar Energy 1983 Jun 1; (10) Richard Perez, Kathleen Moore, Steve Wilcox & David Renné, Antoine Zelenka. Forecasting Solar Radiation - Preliminary evaluation of an approach based upon the national forecast data base (11) Kasten F., G.Czeplak. Solar and Terrestrial Radiation dependent on the Amount and type of Cloud. Solar Energy 1979;24: (12) Richard Perez, Kathleen Moore, Steve Wilcox & David Renné, Antoine Zelenka. Forecasting Solar Radiation - Preliminary evaluation of an approach based upon the national forecast data base (13) Elke Lorenz, Annette Hammer, Detlev Heinemann. Short term forecasting of solar radiation based on satellite data

12 (14) Annette Hammer, Detlev Heinemann, Carster Hoyer, Elke Lorenz. Satellite based short-term forecasting of solar irradiance - comparison of methods and error analysis (15) Detlev Heinemann, Elke Lorenz. Short-term forecasting of solar radiation: A statistical aproach using satelite data (16) Detlev Heinemann. Forecasting of solar irradiance (17) Annette Hammer, Detlev Heinemann, Elke Lorenz, Bertram Lückehe. Short-term forecasting of solar radiation based on image analysis of meteosat data (18) Cano D., Monget J.M., Albussion M., Guillard H., Regas N., Wald L. A method for the determination of global solar radiation from meteorological satellite data. Solar Energy 1986;37:31-9. (19) Ramus Larsen. Estimation of visual motion (20) Shuanghua Cao, Jiacong Cao. Forecast of solar irradiance using recurrent neural networks combined with wavelet analysis. Applied Thermal Engeneering (21) Jensenius JS. Insolation Forecasting (22) Cao JC, Cao SH. Study of forecasting solar irradiance using neural networks with preprocessing sample data by wavelet analysis. Energy 2006;In Press, Corrected Proof. (23) Cao S, Cao J. Forecast of solar irradiance using recurrent neural networks combined with wavelet analysis. Applied Thermal Engineering 2005 Feb;25(2-3): (24) Mellit A, Benghanem M, Kalogirou SA. An adaptive wavelet-network model for forecasting daily total solar-radiation. Applied Energy 2006 Jul;83(7):