Look at the sky. Ask yourself: Has the sheep eaten the flower, Yes or no? And you will see how everything changes. Antoine de Saint Exupéry.

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2 Look at the sky. Ask yourself: Has the sheep eaten the flower, Yes or no? And you will see how everything changes Antoine de Saint Exupéry Page 1

3 INDEX NOTE Report Title Selection and performance quantification of the most appropriate Clear Sky Model for the forecasting of solar radiation at the Reunion Island Curriculum International Master PM3E Year 2013 Author Mickaël Edon Company Réuniwatt No. of Employees < 50 Address 14, rue de la Guadeloupe Sainte Clotilde France Company Tutor Dr Sylvain Cros Function/Position R&D Engineer School Tutor Dr C. Mangwandi Keywords Variable renewable energy, Photovoltaic production forecasting, Clear Sky model, Atmospheric parameters, Solar irradiation, validation of ground measurement, Detection of clear sky moments. Summary The thesis is focused on solar irradiance forecasting methods and more specifically on clear sky models (CSM). CSMs with many inputs are often the most accurate but their performance remains very sensitive to local climate conditions. Moreover, availability of some inputs is not always guaranteed at every location. The objective of the thesis is the selection and performance quantification of the most appropriate CSM for the forecasting of solar radiation at the Reunion Island. Appendices I. Model input data summary II. Model error (official and literature) III. Process organigram IV.a Detail of results, table IV.b Detail of results, correlograms Page 2

4 CONTENTS CONTENTS ACKNOWLEDGMENTS 4 EXECUTIVE SUMMARY 5 LIST OF FIGURES 6 LIST OF TABLES 6 1 INTRODUCTION ON ENERGY AT A WORLD S SCALE ENERGY SYSTEM ON THE RÉUNION ISLAND AN ISLAND WITH GREAT POTENTIAL FOR SOLAR PHOTOVOLTAIC ENERGY REUNIWATT, AN INNOVATIVE COMPANY SCOPE: CHOOSING THE MOST APPROPRIATE CLEAR SKY MODEL 10 2 INTRODUCTION TO CLEAR SKY MODEL CLEAR SKY ATMOSPHERIC EFFECTS ON THE IMPORTANCE OF USING AN APPROPRIATE CLEAR SKY MODEL CHOICE OF MODELS TO ANALYSE MODEL_ MODEL_ MODEL_3 ERREUR! SIGNET NON DEFINI. 2.7 MODEL_ METHODOLOGY GROUND MEASUREMENTS SELECTION OF CLEAR SKY MOMENTS SOURCE OF ATMOSPHERIC PARAMETERS ASSESSING MODEL PERFORMANCE DEALING WITH GROUND MEASUREMENT UNCERTAINTIES 24 4 MODEL PERFORMANCE SUMMARY OF RESULTS RESULTS COMPARISON WITH THE LITERATURE 29 Page 2

5 CONTENTS 4.3 SELECTION OF THE MOST APPROPRIATE MODEL 31 5 CONCLUSION 33 BIBLIOGRAPHY 34 APPENDICES 37 I. MODEL INPUT DATA SUMMARY 38 II. MODEL ERROR (OFFICIAL AND LITERATURE) 39 III. PROCESS ORGANIGRAM 40 IV.A DETAIL OF RESULTS, TABLE 41 IV.B DETAIL OF RESULTS, CORRELOGRAMS 44 Page 3

6 Acknowledgments ACKNOWLEDGMENTS This MSc. thesis has been carried out at Reuniwatt, at the Reunion Island, and supervised by Sylvain Cros, Earth Observation and Climate Business Intelligence Expert. I wish to express my sincere appreciation to Sylvain for his enthusiastic support and excellent supervision within both Clear Sky Models and computer science. Particular thanks to Nicolas Schmutz, founder of Reuniwatt, for having welcomed me within this vibrant and ambitious company. I am also very much grateful to Nicolas for having inviting me to participate to the 1) International conference on solar forecasting in an insular context 2) Journées Européennes du Solaire 3) Rencontre avec le monde économique dans le cadre du débat national sur la transition énergétique. Besides, I will bring back home a very good memory of our lunches at La Jonque. I wish to Nicolas, and to the rest of Reuniwatt team, a complete success in the development of Soleka and future projects contributing to the energy autonomy of this lovely and unique island which is La Réunion. I would also like to thank the all staff of Reuniwatt for making me feel welcome and contributed to a fruitful, creative and innovative atmosphere. Working here, with such enthusiastic colleagues, has been a really positive and enriching experience to me. Finally, I would also like to take this opportunity to express my gratitude to the great ME3 (extended) family: for being the most diverse yet most integrated group of extraordinary talent I ve ever had the chance to be part of. Industry Thesis Advisor Dr Sylvain Cros Earth Observation and Climate Business Intelligence Expert Reuniwatt Academic Thesis Advisor Dr C. Mangwandi Queen s University Belfast United Kingdom Cover page photo: Mickaël Edon Page 4

7 Executive summary EXECUTIVE SUMMARY As part of solar irradiance forecasting, there is a need for values of solar radiation under clear sky conditions. Uncertainty of solar irradiance under clear sky can affect significantly the forecast results accuracy. Clear sky models can compute this value, by using few or many inputs. Clear sky models (CSM) with many inputs are often the most accurate but their performance remains very sensitive to local climate conditions. Four models have been tested in this study: Model_1: A physical model requiring detailed inputs. Model_2: An empirical model Model_3: A physical model requiring simplified inputs. Model_4: A very new physical model using detailed atmospheric radiative transfer features. The performance quantification has been established by using ground measurements in Sainte Marie (Réunion Island) covering 658 days, and during clear sky moments determined by the Perez et al. method. Atmospheric parameters were retrieved from the Aeronet database. The study has revealed that, unlike what is often agreed in the literature, a model accuracy does not always depend on its number of inputs. Model_3, which require much less inputs than Model_2 and Model_1, have given more accurate results. Using more local atmospheric input, even on a daily basis, has not been effective for improving accuracy. Model_4 was built with less approximation on atmospheric radiation phenomena; and is the most accurate in this study. Model_3 is the most operational model, requiring the smallest number of atmospheric parameters and yet it shows very satisfactory performance. Therefore, the most appropriate model to use, as part of solar radiation forecasting, would be Model_4. Model_3 would be the most appropriate one if there was a need for a clear sky model with small computation resources. Index words: Variable renewable energy, Photovoltaic production forecasting, Clear Sky model, Atmospheric parameters, Solar irradiation, Validation of ground measurement, Detection of clear sky moments. Page 5

8 List of figures LIST OF FIGURES FIGURE 1 1 ENERGY SCHEMA OF THE REUNION ISLAND... 8 FIGURE 1 2 DISTRIBUTION BY POWER RANGE OF THE INSTALLED PV CAPACITY IN 2010 (DARK BLUE = NUMBER OF INSTALLATIONS; LIGHT BLUE = INSTALLED CAPACITY)... 9 FIGURE 2 1 CLEAR SKY ATMOSPHERIC EFFECTS FIGURE 2 2 RADIATION REDUCTION THROUGH ATMOSPHERIC EXTINCTION PROCESSES (SOURCE: C. HOYER KLICK: INTRODUCTION TO SOLAR RESSOURCE ASSESSMENT FIGURE 2 3 AIR MASS EFFECT FIGURE 2 4 LOSSES ON INCIDENT IRRADIATION ON A TYPICAL PV CELL (SOURCE: TECHNIQUES DE L INGENIEUR) FIGURE 2 5 ACCURATE AND INACCURATE MODELLED GHI FIGURE 2 6 ACCURATE AND INACCURATE CLEAR SKY INDEX FIGURE 3 1 SOLAR REFERENCE CELL USED FOR THE GROUND MEASUREMENTS FIGURE 3 2 IRRADIATION MAP AT SAINT MARIE, IN [WH/M2], FROM 19 AUG 2010 TO 07 JUN FIGURE 3 3 EXTRA TERRESTRIAL IRRADIATION, MODELLED AND MEASURED IRRADIATION DURING ONE DAY FIGURE 3 4 KC, KT AND KT' FIGURE 3 5 SOLAR ELEVATION ANGLE H AND AIR MASS (AM). THE DASHED LINE SHOWS FIRST FILTER ON H> FIGURE 3 6 CLEAR SKY MOMENTS FOR H>15 AND 0,65<KT'<= FIGURE 3 7 RELATIVE RMSE OF MODELLED/MEASURED IRRADIATION VERSUS KT' FIGURE 3 8 WATER VAPOUR BETWEEN 2007 AND 2012 IN SAINT DENIS, AERONET DATABASE FIGURE 3 9 INTERPOLATED AOD AT 700NM BETWEEN 2007 AND 2012 IN SAINT DENIS, AERONET DATABASE FIGURE 3 10 MONTHLY AVERAGE OF THE LINKE TURBIDITY FACTOR AT THE REUNION ISLAND, SOURCE: CONFIDENTIAL FIGURE 4 1 MEASURED AND MODELLED IRRADIANCE OF ALL MODEL ON A RELATIVELY CLEAR SKY DAY FIGURE 4 2 CORRELOGRAM OF ALL MODELS (GHI MINUTE) FOR H>15 AND 0,65<KT'<= FIGURE 4 3 MODEL RESULTS FOR MINUTE VALUES AND SOLAR ELEVATION ANGLE > 15 AND 0,65<KT'<=1. THE BLUE DASHED LINE INDICATES THE ASSUMED 5,2% UNCERTAINTY LIMITS. THE RED DASHED LINE INDICATES THE ASSUMED 2% TYPE B UNCERTAINTY LIMITS FIGURE 4 4 MODEL RESULTS FOR HOURLY VALUES AND SOLAR ELEVATION ANGLE > 15 DEG AND 0,65<KT'<=1. THE BLUE DASHED LINE INDICATES THE ASSUMED 5,2% UNCERTAINTY LIMITS. THE RED DASHED LINE INDICATES THE ASSUMED 2% TYPE B UNCERTAINTY LIMITS FIGURE 4 5 ACCURACY VERSUS OPERATIONALITY FOR EACH MODEL LIST OF TABLES TABLE 3 1 VERIFICATION OF THE APPLICABILITY OF THE ÅNGSTRÖM S LAW TABLE 4 1 RESULTS FOR GHI MODELLED PER MINUTE STEP. FILTERS: 0,65<KT <=1 AND H>15 ON AT LEAST, ONE CONTINUOUS HOUR TABLE 4 2 RESULTS FOR GHI MODELLED PER HOURLY STEP. FILTERS: 0,65<KT <= 1 AND H>15 AND AT LEAST ONE CONTINOUS HOUR TABLE 4 3 ORIGINAL MODEL OUTPUT AND MODIFICATION TO THE MODELS Page 6

9 Introduction 1 INTRODUCTION 1.1 ON ENERGY AT A WORLD S SCALE Our societies are facing a growing need for energy since the industrial revolution, and particularly since the Post World War II era. The world total primary energy consumption amounted TWh in 1971 and TWh in 2009 [1]. Energy production, Green House Gas (GHG) emissions and climate change are strongly correlated [2]. The energy sector accounted for 68% of the global GHG emissions in On current trends, the world is on track for a warming of +6 C by the end of the century. Because our world s energy system is mostly based on finite fossil resources, the energy price increases along with the growing energy demand. The recent geopolitical events, such as the 2009 gas supply disruption to the EU, showed that the energy security is an increasing concern. From the climate/environmental, economic and energy security point of view, it is now obvious that it is vital to change the world s energy system. Despite these clear reasons for a change, investments in fossil fuel technologies are still greater than investments to best available sustainable energy technologies [1]. The potential of the various forms of renewable energies have not yet been fully appreciated. By using these technologies, together with changed behaviour, it is acknowledged that the long term increase of the mean global temperature can be limited to +2 C [2]. Using sustainable energy technologies would deliver benefits of enhanced energy security and sustainable economic development, while also reducing human impact on the environment. The sun offers mankind virtually unlimited energy potential. Solar photovoltaic has been the fastest growing energy technology over the period Installed capacity was equal to 1,5 GW in 2000 and 65 GW in 2011 [3]. This energy s potential is significant; according to optimistic scenarios [4], solar photovoltaic energy could account for 20% of the global electricity generation in By disregarding externalities associated with the use of fossilfuel for energy production, solar photovoltaic is very close to being cost competitive, especially in sunny countries. 1.2 ENERGY SYSTEM ON THE RÉUNION ISLAND La Réunion is a French insular department situated in the Indian Ocean (21 South, 55 East). It has an area of 2512 km 2 and its population equals inhabitants. Like most islands, La Réunion is strongly dependant to fossil fuels (coal, refined gas and diesel) for its transportation and energy sectors. In terms of primary energy consumption, this dependency is about 90% (Figure 1 1 [5]). Page 7

10 Introduction FIGURE 1 1 ENERGY SCHEMA OF THE REUNION ISLAND La Réunion used to be energy autonomous some thirty years ago although the rapid population growth and greater use of air conditioning has led to a bigger use of coal in the electricity production as it accounts for 48,7% in The island is not interconnected with any surrounding islands. It is also located in a cyclonic area, which imposes more constraints on eg. solar and wind farm designs. In 2002, the regional administration set the objective of energy autonomy, all sectors included, at the horizon of 2030 [6]. This island possesses various exploited renewable energy sources for its electricity production. These are hydro (20,1%); sugar cane biomass (10%); solar photovoltaic, wind energy, biogas (3,7%). There are also projects to exploit wave energy, geothermal energy and ocean thermal energy. During the last years, the grid operator has been facing a great increase of variable renewable energy source in its capacity mix, mostly due to solar photovoltaic. As a consequence, the regulatory limit of 30% of instantaneous production by variable energy sources has been attained in Increasing the capacity of variable renewable energy in the network decreases its stability. The management of the equilibrium production/consumption is also more complex. Consequently, beyond this limit the grid operator is authorised to disconnect any photovoltaic plant whose nominal power is greater than 3 kilowatt peak (kwp). As seen on Figure 1 2, it impacts a small number of installations but most of the total capacity. The nominal power, in kilowatt peak, of a photovoltaic module is its maximum power. In order to increase this share, the Energy Regulation Commission (CRE) has published in 2012 a request for quotation making storage and solar production forecasting compulsory for new solar plants. Page 8

11 Introduction FIGURE 1 2 DISTRIBUTION BY POWER RANGE OF THE INSTALLED PV CAPACITY IN 2010 (DARK BLUE = NUMBER OF INSTALLATIONS; LIGHT BLUE = INSTALLED CAPACITY) 1.3 AN ISLAND WITH GREAT POTENTIAL FOR SOLAR PHOTOVOLTAIC ENERGY Solar photovoltaic has a great role to play in order to meet the objective of energy autonomy. Its capacity has increased very sharply during the last years (42 MWp installed in 2009; 89 MWp in 2010 [5]). In 2011, the feed in tariff and tax incentive dropped so the regional administration decided to promote solar photovoltaic with an energy cheque [7]. In 2013, the installed photovoltaic capacity is 153 MW, 90% of which is in the industry sector. Because the space is limited on the island, there are projects where agriculture farm and photovoltaic farm are combined [8]. In order to increase the solar photovoltaic capacity, while keeping power grid stable and service reliable, forecasting and storage will be necessary compounds of future systems at La Réunion. A production prevision will be needed one day before in order to plan the needed production capacity mix. The prediction will be refined up to six hours before and a thirty minute prevision will allow anticipating steep ramp in the production capacity. Storage will be a necessary compound in order to smoothen the production variability of photovoltaic systems; it can also help to transfer energy during the peaks of consumption; and it can help the grid operator to maintain network stability [9]. Page 9

12 Introduction 1.4 REUNIWATT, AN INNOVATIVE COMPANY This MSc. thesis is carried out with Reuniwatt. Reuniwatt is a young and innovative company, settled in Reunion Island, France, in the Indian Ocean. Reuniwatt s development is based on three core activities: Photovoltaic production forecasting Deployment of networks of communicating smart sensors. Climatic data recording. Climatic database management Energy mix expertise Being deeply involved with the university world and performing R&D on solar forecasting, Reuniwatt has developed, together with the Université de la Réunion, the project Soleka [10]. This project is also laureate 2013 of the Concours National d Aide à la Création d Entreprise de Technologies Innovantes, a national competition for companies with innovative technologies. Soleka is a tool intended to ease the insertion of variable energy in the energy mix. Soleka will allow forecasting the production of solar photovoltaic plant thirty minutes to one day ahead. This will help the electric grid operator to manage the balance production / consumption and to secure the electricity supply on the whole island. Soleka will also model the photovoltaic production in order for the production companies to size their storage system. Reuniwatt is developing innovative solutions that will contribute to the energy autonomy of the Reunion Island; and accompany its customers in the realisation of their industrial investments that introduce cleaner processes. 1.5 SCOPE: CHOOSING THE MOST APPROPRIATE CLEAR SKY MODEL Solar irradiance forecasting methods can be described as the prediction of cloud behaviour over a specific area. This information is then combined with the value of solar radiation under clear sky conditions for the same area at the same forecast time. Uncertainty of solar irradiance under clear sky can affect significantly the forecast results accuracy. Atmospheric radiative transfer models can compute this value. The inputs are varying from one model to another. The simplest models just take into account the solar elevation, while more detailed ones may include other inputs such as concentration of atmospheric components (aerosols, water vapor, ozone), elevation of the site, barometric pressure or ground albedo, in order to better model atmospheric transmittance. Clear sky models (CSM) with many inputs are often the most accurate but their performance remains very sensitive to local climate conditions. Moreover, availability of some inputs are not always guaranteed at every locations. The objective of the study is the selection and performance quantification of the most appropriate CSM for the forecasting of solar radiation at the Reunion Island. Page 10

13 Introduction to clear-sky model The study is organized with the following tasks: bibliography study identifying the most relevant and promising CSMs CSM input data collection of the specific area. Assessment of CSM performance by comparing their outputs to instrumental measurements. 2 INTRODUCTION TO CLEAR SKY MODEL 2.1 CLEAR SKY ATMOSPHERIC EFFECTS The extra terrestrial solar radiation arriving to Earth is a relatively stable characteristic. Due to the elliptical shape of earth s orbit, it varies by +/ 3% around its average value, the extraterrestrial constant which is equal to 1,367 kw/m 2. This radiation arrives as a beam on top of earth s atmosphere [11] and it is absorbed and scattered while passing through the different layers of the atmosphere [12]. Absorption means that the energy is taken up by matter while scattering means that radiation is deviated from straight propagation. As seen on Figure 2 1, up to 30% of the incoming extra terrestrial solar radiation is lost by absorption and up to 25% of the total irradiation is scattered back to space [13]. FIGURE 2 1 CLEAR SKY ATMOSPHERIC EFFECTS Page 11

14 Introduction to clear-sky model The amount of radiation that reaches the ground is called the global radiation. It is composed of two components, the beam and diffuse compound (2 1). The diffuse compound, a fraction of the total diffused extra terrestrial radiation, is between 5 and 22% of the global component [14]. (2 1) Absorption occurs from different components at different spectral range. As seen in Figure 2 2, the ozone has two small absorption band near 290 nm and 600 nm. Water vapour absorbs strongly in the infrared part of the solar spectrum. Carbon dioxide is another strong absorber of infrared radiation. There are two kinds of scattering effects: Rayleigh scattering and Mie scattering. The Rayleigh scattering is the scattering of electromagnetic radiation by particles which are much smaller than the wavelength of the radiation. The Mie scattering is the scattering by particles whose diameter is of about the same dimension as the wavelength or larger. Rayleigh scattering is quite exclusively a function of Air Mass while the Mie scattering depends on local conditions. The Mie scattering has a strong forward pattern. The atmospheric gases have a significant absorption band in the visible spectrum. These gases are mostly biatomic oxygen O 2 and biatomic N 2, which accounts for 20,95% and 78,09% of the atmospheric gases respectively [15]. FIGURE 2 2 RADIATION REDUCTION THROUGH ATMOSPHERIC EXTINCTION PROCESSES (SOURCE: C. HOYER KLICK: INTRODUCTION TO SOLAR RESSOURCE ASSESSMENT The amount of scattering and absorbing depends on the length of the path through the atmosphere, which is expressed as the Air Mass (AM). It is simply the ratio of the actual path length to the path length when the sun is directly overhead. As seen in Figure 2 3, the Air Mass can be calculated from the solar zenith angle. A photovoltaic cell can only convert a theoretical maximum of 54% of the incident irradiation [16]. As per Figure 2 4, 18% of the incident energy in the infra red part is lost. The high Page 12

15 Introduction to clear-sky model energy photons generate heat which leads to another loss on the ultra violet and visible band. This loss accounts for 28% of the total incident irradiation. Therefore, the useful incoming irradiance on a photovoltaic cell is varying due to scattering by aerosols and absorption by water vapour. FIGURE 2 3 AIR MASS EFFECT FIGURE 2 4 LOSSES ON INCIDENT IRRADIATION ON A TYPICAL PV CELL (SOURCE: TECHNIQUES DE L INGENIEUR) 2.2 ON THE IMPORTANCE OF USING AN APPROPRIATE CLEAR SKY MODEL Solar photovoltaic is the fastest growing source of renewable energy and the greatest project requires considerable financial investments [17]. The knowledge of clear sky irradiation reaching the ground is a key parameter in the field of solar radiation modelling and evaluation. Because equity investors evaluates projects based on the return on investment, magnitude of capital cost and perceived risk [18], the solar resource needs to be as accurately characterised as possible as it has a direct impact on the plant design and power output predictions. As an example, reducing the solar resource uncertainty by about 1% can allow the project to take on 1% more debt, and therefore reduce the capital cost of the owner. For a 50 MW project, valued at USD , it means that the loan can be increased by about USD [18]. R&D is being done at the Réunion Island in order to develop guaranteed PV systems, which includes production forecasting and storage. Forecasting the solar resource means that clear sky irradiation and cloud coverage need to be estimated as precisely as possible. The clear sky index Kc (refer to 3.2 for its definition), which is proportional to the cloud coverage, is predicted by various means and used with a clear sky model in order to predict the incoming irradiation on e.g. a PV farm: the modelled irradiation is the product of the clearsky index by the clear sky irradiation. The following Figure 2 5 and Figure 2 6 illustrate the importance of using an accurate model: an inaccuracy on the clear sky model has the same impact as over or under estimating the clear sky index. Therefore, the accuracy of the clearsky model used has an impact on the accuracy of the predicted irradiation. Page 13

16 Introduction to clear-sky model As part of a guaranteed PV system, the size of storage is directly proportional to the error in forecasting thus, reducing the error on clear sky irradiation has a positive impact on the storage size (internal communication). FIGURE 2 5 ACCURATE AND INACCURATE MODELLED GHI FIGURE 2 6 ACCURATE AND INACCURATE CLEAR SKY INDEX Along with the model accuracy, its operability is equally important. If a model is to be industrially used, the high demand of atmospheric input parameter may be expensive and uneasy to use. Therefore, an appropriate model depends on its use and can be a compromise between both. The study aims at answering what is the most appropriate model to use for solar forecasting on the Réunion Island, from the accuracy and operability point of view. 2.3 CHOICE OF MODELS TO ANALYSE There are numerous Clear Sky models [19]. The simplest ones aim at calculating the radiation that arrives on a specific location at a given time. Therefore the minimum parameters that are needed by a clear sky model are the solar elevation angle, the date and solar constant. More complexes models can include up to 8 atmospheric parameters, such as the aerosols and the water vapour [20]. Whilst the inputs needed vary from one model to another; the output are either irradiation (Wh/m 2 ) or irradiance (W/m 2 ). The GHI (Global Horizontal Irradiance) is given along with the beam (BHI) and diffuse (DHI) compound. In this study, four models are selected according to three criteria: (i) they must be easily operational (ii) their quality needs to be recognized (iii) it must be already used in large scale processes. The four models chosen have all different approaches to modelling radiation. They are the following: Model_1: This model is well tried and easy to use; it is currently used by research laboratories and Reuniwatt at the Réunion Island. Page 14

17 Introduction to clear-sky model Model_2: This model has a good precision with the use of aerosol and water vapour parameters and is also widely used in the solar energy research community. Model_3: This model has 3 simple inputs data and was used in the of a long term solar radiation database over Europe. Model_4: This is a very new model. Atmospheric radiation computations are made with less approximation than the others models, and it is usable with an integrated aerosol and water database. Input data for each model can be classified as: astronomical; geographical; surface data; meteorological (column integrated); quantities related to atmospheric turbidity. A table summarizing the model input data is available in Appendices I. 2.4 MODEL_1 The Model_1 is a simplified clear sky model for direct and diffuse insolation on horizontal surfaces. The Model_1 is built from three different codes. In each of these codes, a multilayered atmospheric model is constructed with defined atmospheric parameters. Once the atmosphere is modelled, each code is used to calculate the radiative transfer at a given location and time. This model was written in an excel spreadsheet by its author, and translated into a Matlab script by Reuniwatt. 2.5 MODEL_2 Model_2 was developed to design a new scheme converting meteorological stationary satellite images into solar irradiance map. In the Model_2, the irradiance is calculated based on radiative transfer models (RTM) and the Lambert Beer relation. The main input parameters are the atmospheric water vapour column [cm] and atmospheric aerosol optical depth [cm] [21]. The ozone content is taken constant at 340 Dobson units. The Model_2 is empirical; it is calculated from analytical expressions rather than RTM calculations. In this model, the aerosol optical depth (AOD) is taken for the whole broadband. 2.6 MODEL_3 The Model_3 was created to build a solar energy atlas at continental scale. The Model_3 is composed by two sets of models, one giving the irradiance and one giving hourly irradiation. Just like the Model_2, the Model_3 is also used to estimate solar radiation at ground level from satellite images [14]. The model is based on the Rayleigh optical depth (or thickness) parameterization and the Linke turbidity coefficient at air mass 2. The input parameter is the Linke turbidity [22]. This describes the optical thickness of the atmosphere due to both the absorption by the water vapour and the absorption and scattering by the aerosol particles relative to a dry and clean atmosphere. It summarizes the turbidity of the atmosphere, and hence the attenuation of the direct beam solar radiation [23]. The Model_3 model has been Page 15

18 Methodology checked against the previous model that were used for similar usages and was found the most robust and accurate [14] [24]. 2.7 MODEL_4 Model_4 is a very new fast clear sky and fully physical model that replace empirical relations or simpler models used before [25] [26]. It uses the recent results on aerosol properties, and total column content in water vapour and ozone produced by a global mapping initiative of these parameters. The comparison with state of the art clear sky models showed that Model_4 surpasses them, especially regarding RMSE and correlation coefficient. 3 METHODOLOGY 3.1 GROUND MEASUREMENTS In order to quantify the performance of each model, irradiation data during clear sky periods is needed at the site where modelling of daily irradiation is performed. Measured and modelled irradiation can be correlated together only they cover the same time periods and location. In this study, data covering 658 days / starting the 19 th August 2010 / with a 1 minute resolution, are available for Sainte Marie, in the North of the island (Lat 20,8925; Lon 55,5361). These irradiance data (in [W/m 2 ]) have been measured with solar reference cell (Figure 3 1) and converted afterwards to irradiation values (in [Wh/m 2 ]). The solar reference cell has been calibrated with a thermopile pyranometer on the Reunion Island. The following Figure 3 2 shows the irradiation map of these data. FIGURE 3 1 SOLAR REFERENCE CELL USED FOR THE GROUND MEASUREMENTS Page 16

19 Methodology FIGURE 3 2 IRRADIATION MAP AT SAINT MARIE, IN [WH/M2], FROM 19 AUG 2010 TO 07 JUN SELECTION OF CLEAR SKY MOMENTS Identifying clear sky moments is not an easy task because there is no objective definition of a true clear sky moment. There are different methods used to identify clear sky moments [27]. These are based on cloud cover and/or sunshine fraction, while others are based on a combination of sky clarity indices, or the Linke turbidity. Keeping cloudless sky based on cloud cover is not a good method due to the wide scattering of clouds. Furthermore, these data are not available for this study. A combination of these methods will bring the most accurate results. In this study, the detection of clear sky moments is based on modified clearness indices K t. The clearness index K t does not depend upon a clear sky model. It allows characterizing the insulation conditions at a given point of time when only the global component is known. It depends on the extra terrestrial irradiance G 0 and the solar elevation angle h. The clearness index K t is the ratio of incoming solar irradiation over the extra terrestrial irradiation; it is defined as per [28]. The clearness index is a measure of the transparency of the total atmosphere.. (3 1) The clearness index K t depends on the solar elevation angle and tends to be under estimated for low solar elevation angle. In order to be used as a reliable sky condition descriptor, it can be corrected with the formula from Perez et al. (1990) [28], which uses the Air Mass AM. The modified clearness index, K t is defined as: Page 17

20 Methodology,.,,,, (3 2) The clear sky index k c is a very usefull parameter for solar forecasting. It is used to represent the clearness of the sky, ie, how much irradiation reaches the ground at a certain time (GHI site ), compared how much it would be if the sky was clear (GHI cs ), it is therefore an indicator on cloud coverage: (3 3) The following Figure 3 3, Figure 3 4 and Figure 3 5 show the different irradiation, indexes, solar elevation angle and Air Mass during a typical day, with a clear sky in the morning and clouds forming in the afternoon. FIGURE 3 3 EXTRA TERRESTRIAL IRRADIATION, MODELLED AND MEASURED IRRADIATION DURING ONE DAY FIGURE 3 4 KC, KT AND KT' FIGURE 3 5 SOLAR ELEVATION ANGLE H AND AIR MASS (AM). THE DASHED LINE SHOWS FIRST FILTER ON H>15 Page 18

21 Methodology In order to keep only moments with a clear sky, K t values are first filtered for h > 0. When the sun is below the horizon, the measured GHI may not be equal to 0 but, because AM is calculated with h, it would not be possible to calculate K t. Furthermore, K t values for h comprised between 0 and 15 are not kept in order to eliminate all risks of errors caused by shading of obstacles just above the horizon. This has the consequence of systematically excluding the very data point that are usually modelled with the lowest accuracy and therefore, the performance assessment results are on the optimistic side [20] [19]. Then, K t values are filtered for 0,65 < K t 1 in order to only keep clear sky conditions, as per the Perez et al. method [28]. These limits are arbitrary but coherent with other classifications. At last, only measurements fulfilling these conditions and covering at least one continuous hour are kept. After following this methodology, 17,3% of the period covered by the 658 days filtered for h > 15, are kept and are considered to have clear sky conditions. These moments can be seen in red in Figure 3 6. The incoming irradiation doesn t have a single value for a given solar elevation angle because it depends on atmospheric parameters, which have a seasonally pattern, as explained in 3.3. FIGURE 3 6 CLEAR SKY MOMENTS FOR H>15 AND 0,65<KT'<=1 However, there are researchers that oppose the use of clear cut K t value for defining clearsky moments because each researcher tend use his/her own values depending on the location and the month of the year [29]. To confirm the pertinent usage of the Perez et al. method, the RMSE of modelled and measured data was plotted for various K t (Figure 3 7). Refer to 0 for explanation on the RMSE index definition. The preliminary results with the Model_4 and a threshold of 0,65 < K t 1 are very good. This gives confirmation that the clear sky data kept in this study are of good quality and prove the validity of the Perez et al. method for the clear sky measured data. Page 19

22 Methodology FIGURE 3 7 RELATIVE RMSE OF MODELLED/MEASURED IRRADIATION VERSUS KT' 3.3 SOURCE OF ATMOSPHERIC PARAMETERS Irradiance is affected by astronomical, geographical and atmospheric parameters. The first two classes can be obtained easily; they have a big impact on the predicted irradiance but can be known very accurately. On the contrary, atmospheric parameters have large effects. The Aerosol Optical Depth (AOD) (or thickness) has the greatest impact, and then come Water Vapour (WV). The challenge in getting accurate parameters is that they changes rapidly over both time and space, and are difficult to predict [20]. The aerosol optical depth or optical thickness (τ) is defined as the integrated extinction coefficient over a vertical column of unit cross section. In other words, it is the degree to which aerosols prevent the transmission of light by absorption or scattering of light; therefore it has no unit. The water vapour is defined as the amount of water which would be obtained if all the water vapour in a specified column of the atmosphere were condensed to liquid; therefore its unit is in cm 3 /cm 2 or g/cm 2 [30]. The Linke turbidity basically describes the attenuation of the solar radiation in terms of a clean and dry atmosphere, and allows for an accurate and efficient way to describe the solar radiation during a cloud free day [31]. It is defined as the number of clean and dry atmospheres that would be necessary to produce the same attenuation of the extra terrestrial solar radiation that is produced by the real atmosphere [32]. Atmospheric parameters are obtained thanks to the AErosol RObotic NETwork (AERONET) database. The AERONET programme is a federation of ground based remote sensing aerosol network established by the NASA, and PHOTONS (Univ. of Lille 1, CNES, and CNRS INSU) [33]. Atmospheric measurements that cover the studied period are retrieved from their database. They were done in Saint Denis, which is just a few kilometres away where the irradiance measurements were made, thanks to a multiwavelength sunphotometer measurements were made between the May 2007 and October The downloaded parameters are of level 2 in terms of quality assurance criteria [34]. Page 20

23 Methodology The Linke turbidity is available online. Monthly climatic values are given for a specific latitude and longitude. The data available for Saint Denis do not include the AOD at 700 nm, which is needed by the Model_2 simplified. This AOD is evaluated thanks to the AOD at 500 and 550 nm [21], thanks to the Ångström s Law: ( 3 4) Where, Τ λ is the AOD at the wavelength λ, β is the Ångström turbidity coefficient. It represents the aerosol vertical quantity in the atmosphere, α is the wavelength exponent. It is linked to the size of particles and varies between 0 (for big particles) and 4 (for aerosol with the size of molecules). Part of the AOD at 380 and 500 nm, which are needed are also missing. Consequently, these data are inter/extrapolated with the same method. A verification is made when possible to verify the accuracy of this method with the Aeronet data. The following Table 3 1 validates the inter/extrapolation made to fill holes in the database: the results found are sufficiently good in comparison with the models sensitivity to these atmospheric parameters variation. The Model_1 and Model_2 are fed with daily, monthly average and climatic monthly average atmospheric data. The monthly values are calculated from the daily ones if at least the data 75% of the month. The climatic monthly averages are found by averaging all the data available between 2007 and 2012 for a given month. TABLE 3 1 VERIFICATION OF THE APPLICABILITY OF THE ÅNGSTRÖM S LAW Interpolation at AOD500 Number of data Correlation coefficient 0,997 Variance of the difference of the 2 time series 1,4E 05 mean difference 0,002 Relative mean error (mean difference / mean AOD500) 3,35% Relative variance (variance / mean AOD500) 0,02% Extrapolation at AOD380 Number of data Correlation coefficient 0,995 Variance of the difference of the 2 time series 3,3E 05 mean difference 0,001 Relative mean error (mean difference / mean AOD380) 0,89% Relative variance (variance / mean AOD380) 0,04% The Box and Whiskers plots (Figure 3 8 and Figure 3 9) show the variation of the water vapour and the AOD at 700 nm between 2007 and The water vapour shows a clear seasonal pattern, with higher value during the austral summers. The AOD at 700 nm is relatively constant through the years, with very small peaks during the austral springs. Page 21

24 Methodology FIGURE 3 8 WATER VAPOUR BETWEEN 2007 AND 2012 IN SAINT DENIS, AERONET DATABASE FIGURE 3 9 INTERPOLATED AOD AT 700NM BETWEEN 2007 AND 2012 IN SAINT DENIS, AERONET DATABASE The Linke turbidity is retrieved with on a monthly step. Figure 3 10 shows the variation of this factor throughout the year: FIGURE 3 10 MONTHLY AVERAGE OF THE LINKE TURBIDITY FACTOR AT THE REUNION ISLAND, SOURCE: CONFIDENTIAL Page 22

25 Methodology The concentration of water vapour in the atmosphere has a strong seasonal pattern, with a peak during the austral summer. This is due to a higher average irradiation which causes more evaporation. The variation of concentration of aerosol in the atmosphere is due to several factors [35]. These are of anthropogenic sources such as agricultural, industrial, airtransportation, etc. and of natural sources such as dust storms, sea salt particles, etc. The peak of aerosol concentration at the Réunion Island is due to slash and burn in Madagascar during the dry season [36]. 3.4 ASSESSING MODEL PERFORMANCE Accuracy indicators are needed in order to compare two times series against each other, such as measured and modelled values. Various indicators are used in the literature [20] [19]; the most common being the Mean Bias Error (MBE) and the Root Mean Square Error (RMSE). They are defined as: And, (3 5) (3 6) Where: n is the number of couples of eg. measured and predicted values, is the mean value of these measured and predicted values, is the difference between the measured and the predicted value, The RMSE of a pairwise difference of two time series can serve as a measure on how far on average the error is from zero. The MBE is the mean difference between the two time series. The relative RMSE and MBE, in percentage, give a value of the correlation between two time series which is easier to compare with other models. The correlation coefficient is another useful accuracy indicator. It is a statistical measure of how well the model approximates the real data points. It is defined as: (3 7) Where, is the average of the first time series, and is the average of the second one. Correlograms are also used to visually check the correlation quality between two time series. A correlogram is a scatter plot with each pair of the time series plotted on X and Y. A higher Page 23

26 Methodology RMSE value will give a thicker line while a higher MBE will give the line a positive or negative shift. The more accurate a model is, the smaller the RMSE and MBE are. A MBE can be corrected unlike the RMSE, which is a value intrinsic to the model performance and its input parameters. A good value for a RMSE or a MBE depends on different aspects. First the time step chosen for the modelling is very important, modelling irradiation every minute will bring a higher accuracy than modelling it every hour, which involve averaging steps. The filters used have an impact too. The quality of the measured irradiation and the chosen clear sky moments is also very important since it is meant to be a reference for the model. In this study, a more stringent filtering on K t allows increasing the quality of the clear sky moments kept. The choice of filters on e.g. the solar elevation angle can have a positive impact, as stated in 3.2. There are different thresholds for defining good RMSE and MBE values in the literature. (Badescu, 2011) defines a good calibration with global hourly irradiation if 5%<MBE<5% and RMSE<15%. (Gueymard, 2011) ranks models with a MBE equal to ±2% and RMSE equal to ±5% as best ones. These thresholds are valid for irradiance value and solar elevation angle greater than DEALING WITH GROUND MEASUREMENT UNCERTAINTIES Assessing a model performance would ideally be done against a reference source of measurement which is error free. In reality, both modelled and measured data series are uncertain and must still be compared together. This is why some researchers prefer to use the terms of difference with the MBD and RMSD indicators rather than MBE and RMSE, as chosen in this study. Not being able to appreciate these uncertainties can lead to false conclusion. For example, if the mean difference between a model A and the reference measurements are 1% whereas it is 3% for model B, it is tempting to conclude that model A is more accurate than model B. It is likely to be exact although the opposite conclusion would have been reached if it has been established that the measurements themselves had a systematic difference of 2% compared to the value of the measurand [20]. The measurements used in this study are obtained from a solar reference cell. This sensor is a pertinent tool for measuring irradiance on a solar PV farm since both exhibit a matching response which varies with climatic and astronomic parameters [18]. A solar reference cell measures a spectrally corrected irradiance (i.e. usable fuel for PV systems as per Figure 2 4). The cell used in this study, of the solar reference cell gives a broadband irradiance value [37] which is therefore directly comparable with broadband models. The total measurement uncertainty is the combination of both the basic calibration and field measurement uncertainties. As said in 3.2, the solar reference cell has been calibrated for the local light spectrum with a thermopile pyranometer. The pyranometer has a total expanded uncertainty (95% confidence interval) of about 4,3% on broadband resource data [38]. The Page 24

27 Model performance uncertainty of the solar reference cell is known to be below 3% [37]. Therefore, it is now possible to calculate the total uncertainty with the composed uncertainty formula [39]: 2 2 ( 3 8) Thus, the total uncertainty for field measurement is equal to 5,2%. Part of this total uncertainty consists of a systematic type B uncertainty. It represents a bias that cannot be corrected in general. In this study, it is assumed to be equal to 2% [20]. 4 MODEL PERFORMANCE 4.1 SUMMARY OF RESULTS All models were tested with various atmospheric parameters as explained in 3.3, and over different time step, one minute and one hour. Figure 4 1 illustrates on a relatively clear sky day, the 4 th of September 2010, the difference in modelling the GHI by the different models. Model_3 appears to be the least accurate during that day although it is not when looking at it over many clear sky moments. A great number of measurements reduces the influence of anomalies. FIGURE 4 1 MEASURED AND MODELLED IRRADIANCE OF ALL MODEL ON A RELATIVELY CLEAR SKY DAY The following Figure 4 2 is a correlogram showing all models correlations on one scatter: Page 25

28 Model performance FIGURE 4 2 CORRELOGRAM OF ALL MODELS (GHI MINUTE) FOR H>15 AND 0,65<KT'<=1 It shows that Model_4 performs very well in this study; it has the thinnest plot. The increasing plot thickness with the GHI is due to the fact that errors are greater on greater values. Model_3 is also performing well, with a small over estimation of the irradiation for higher irradiation values. The Model_2 seems to have the thickest plot although it performs better than Model_1 for lower irradiation values. A detail of the correlograms is given in the appendices. Model_4 is used differently from other models. It has input data which are different from other model, which may explain its superiority. The following Table 4 1 gives the results for a GHI modelled every minute, and with filters on 0,65<K t 1 and h>15. The Table 4 2 is the same as the previous table except that the simulations are made on an hourly basis. The details of results are available in the Appendices. TABLE 4 1 RESULTS FOR GHI MODELLED PER MINUTE STEP. FILTERS: 0,65<KT <=1 AND H>15 ON AT LEAST, ONE CONTINUOUS HOUR. Model Mean value at site [Wh/m2] MBE [Wh/m2] Relative MBE [%] RMSE [Wh/m2] Relative RMSE [%] Correlation coefficient Number of measurements Model % % Model2_cte % % Model2_Daily % % Model2_Monthly % % Model2_MonthlyClim % % Model1_cte % % Model1_Daily % % Model1_monthly % % Model1_monthlyClim % % Model % % Page 26

29 Model performance Table 4 1 shows the number of measurements is in the same range for all models thus their results can be directly compared. All the simulations present a correlation coefficient above 0,98; which can be considered as a very satisfactory value. Model_4 is the most accurate model; it has the lowest relative MBE, the lowest relative RMSE and the highest correlation coefficient. Model_3 comes just behind with values of relative MBE and RMSE close to Model_4. The Model_2 and Model_1, which are used with daily, monthly averaged and climatic monthly averaged atmospheric parameters are coming behind with a relative RMSE above 5%. Using daily parameters does not give Model_1 and Model_2 a significant advantage compared to e.g. Model_3, which uses monthly averaged atmospheric parameters. It is worth noting that the relative RMSE of Model_2 is not reduced by using daily parameters compared to monthly parameters. Model_1 exhibits contrary trends. This could be due to the fact that the Model_2 is an empirical model and is more sensitive to noise in its input parameters. As explained in 2.4, Model_1 is a radiative transfer model, based on physical equations. The use of varying atmospheric parameters, coming from the Aeronet database, does improve the model accuracy so much compared to the use of constant parameters. All the models have a negative bias in these simulations, meaning they all over estimate the irradiation. TABLE 4 2 RESULTS FOR GHI MODELLED PER HOURLY STEP. FILTERS: 0,65<KT <= 1 AND H>15 AND AT LEAST ONE CONTINOUS HOUR. Model Mean value at site [Wh/m2] MBE [Wh/m2] Relative MBE [%] RMSE [Wh/m2] Relative RMSE [%] Correlation coefficient Number of measurements Model % % Model2_Daily % % Model2_Monthly % % Model2_MonthlyClim % % Model1_Daily % % Model1_monthly % % Model1_monthlyClim % % Model % % All models have been tested on an hourly basis for several reasons, one being the calculation time required. Table 4 2 shows that Model_4 is still the best performing model in terms of relative RMSE and correlation coefficient. Model_3 has a relative RMSE 1% greater although its relative MBE is a little less than 2% better. The Model_2 Simplified, which was slightly better than Model_1 on a minute basis, is now less accurate on an hourly basis. This leads to the fact that ranking of models may depend upon the time step chosen. All models are less accurate on an hourly basis. It is worth noting that the number of measurements has fallen drastically from the minute step simulations to the hourly ones. The sampling size (called number of measurements in the above table) is an important factor when calculating a model accuracy and when comparing two, or more, models together. As part of a model performance quantification, values which are less accurately Page 27

30 Model performance modelled have a greater impact on the results accuracy if the sampling is small. This effect has been verified when filtering data on more stringent clear sky conditions: keeping clearer clear sky moments and thus reducing drastically then number of measurements has a negative impact on the model accuracy results. Another reason why the hourly simulations give less accurate results than the minute ones is because the clear sky moments are calculated using irradiation of site measurements with a minute step which are, on average, considered as a clear sky. There could be the case of one hour considered having clear sky conditions with short moments with a significant cloud coverage, or longer moments with a very light cloud coverage. On average, the irradiation over one hour can be great enough so that this hour is considered as a clear sky. This source of error can potentially lower the quality of the overall clear sky moments. When increasing the lower threshold on the clearness index k t to 0,7; all models show better results on both relative MBE, RMSE and on the correlation coefficient. By doing so, the number of measurements does not decrease a lot; consequently there is no negative impact on the results. The following Figure 4 3 and Figure 4 4 shows on a diagram the relative MBE and RMSE as presented in Table 4 1 and Table 4 2. FIGURE 4 3 MODEL RESULTS FOR MINUTE VALUES AND SOLAR ELEVATION ANGLE > 15 AND 0,65<KT'<=1. THE BLUE DASHED LINE INDICATES THE ASSUMED 5,2% UNCERTAINTY LIMITS. THE RED DASHED LINE INDICATES THE ASSUMED 2% TYPE B UNCERTAINTY LIMITS. Page 28

31 Model performance FIGURE 4 4 MODEL RESULTS FOR HOURLY VALUES AND SOLAR ELEVATION ANGLE > 15 DEG AND 0,65<KT'<=1. THE BLUE DASHED LINE INDICATES THE ASSUMED 5,2% UNCERTAINTY LIMITS. THE RED DASHED LINE INDICATES THE ASSUMED 2% TYPE B UNCERTAINTY LIMITS. The blue and red dashed line show the limits below which the uncertainties from the measurements would prevent to compare a model with another, as explained in RESULTS COMPARISON WITH THE LITERATURE The next step is to compare the results from the different simulation with the available data in the literature. They are few publications where various models have been tested on different sites. Each model, when introduced to the scientific community, comes with publications that justify its creation and describe its performance. A table detailing the model error (official and literature) is available in the Appendices. When performing results comparison with the literature, it must be defined which value can be compared with which value. One can only compare values which are comparable. As seen in Table 4 3, the models used in this study have different output, either irradiance or irradiation, and different time steps. The scripts of the models having hourly irradiance as an output have been modified so that they model the irradiance every minute. Once every model gives irradiance value every minute, it has been considered that these values do not change over one minute, and thus the value could be read as an irradiation value if divided by 60. In the same way, the irradiation values of a model having a one minute step can be read as irradiance values if multiplied by 60. The comparison of correlation accuracy of two or more models in irradiation and having the same time step is possible as long as the sampling size and other parameters are similar. Page 29

32 Model performance TABLE 4 3 ORIGINAL MODEL OUTPUT AND MODIFICATION TO THE MODELS Model Original output Original step New output after modifications on the model's script Model_1 Irradiance [W/m2] 1 min 1 min / 1 hour irradiation [Wh/m2] Model_2 Irradiance [W/m2] 1 hour 1 min / 1 hour irradiation [Wh/m2] Model_3 Irradiation [Wh/m2] 1 hour 1 min / 1 hour irradiation [Wh/m2] Model_4 Irradiance [W/m2] 1 min / 15 min / 1 hour / 1 day 1 min / 1 hour irradiation [Wh/m2] Comparison of results obtained with Model_4 are in accordance with its official performance, as found in [25]. Its correlation coefficient is greater than the official minimum 0,95; and both its RMSE and MBE are below the official maximum, for the global irradiation. Comparison of results obtained with Model_3 and its official performance is not directly possible since its accuracy is given for the diffuse irradiation only [14]. The comparison results obtained with Model_1 and its official performance is also not possible since its accuracy is given in comparison with other models [11]. The official performance of the Model_2 is given in relation to the original Model_2 [40] [21]. The best Relative RMSE of Model_2, obtained with monthly parameters, is within the model official performance. The comparison made by the creators of Model_2 on one site gave a relative RMSE of 4% and no bias. Since Model_2 is has up to 1% difference on the RMSE; the 4,52% calculated can be compared with the official 5,04%. Model_2 has officially no bias; in this study it has been calculated to 1,25%, on the best simulation. Three publications have been found with quantification of clear sky model performance. In the first one [20], Model_1 and Model_3 have been tested on 5 different sites having different altitude and on different test period. Regarding Model_3, The relative MBE calculated in this study is better than those of [20]; and the relative RMSE is better for 3 of the 5 sites. Regarding Model_1, the relative MBE found in this study are smaller although the relative RMSE is 1% behind when comparing to the worst site. Comparing Model_1 and Model_3 is a first confirmation of the quality of the results obtained here since their performance is in the same range in both studies. In the next publication [22], Model_1, Model_3 and Model_2 have been tested against 16 independent data banks. The comparison of Model_1 s performance in both studies shows similar results on the relative MBE and RMSE. The comparison of Model_3 and Model_2 s performance shows that they are performing better in this study than in the one of this publication. In the third publication [41], the same models have been compared with ground measurement in the tropics. There is no information regarding the temporal resolution nor on the filter used. In comparison, Model_2 has a better relative MBE and RMSE in this study than in the publication. This is also true for Model_3. The relative RMSE of Model_1 in this study is better than the one on the publication although its relative MBE is slightly behind. Page 30

33 Model performance Some authors choose to rank model against each other and does not provide numeric results. In this study,[19], 54 clear sky models are used to compute global irradiation and compared with ground measurements made in Romania. Model_3 and Model_2 are ranked best models while Model_1 is ranked second best model. 4.3 SELECTION OF THE MOST APPROPRIATE MODEL The selection of the most appropriate model depends which accuracy is required and how much operational a model is when used in e.g. forecasting. The following Figure 4 5 shows graphically the performance of each model, from the accuracy and operationality point of view. However, it is important to emphasise on the fact that Model_4 needs only one parameter with its actual coding automatically connected with its input parameters. The model itself requires many more parameters, including daily atmospheric parameters. FIGURE 4 5 ACCURACY VERSUS OPERATIONALITY FOR EACH MODEL In this graph, the results are taken from Table 4 1. Model_4 appears to be clearly the most appropriate model since it has the lowest relative MBE and RMSE. Model_3 is not far behind in terms of accuracy, and it has the best operationality if disregarding the fact that Model_4 is used on its current format. The Model_2 and Model_1 need a higher number of input parameters, which reduces their operationality. Both have a relative RMSE which is in the same range but greater than for Model_3. The different computations with Model_1 place him in the opposite corner of Model_4, making it the least accurate and operational of the four models. The computational time is another aspect to take into account when electing a model. Computing Model_4 and Model_3 have been very fast, even with a temporal resolution of a minute. Computing Model_1 took a little longer; in the order of 15 min for a temporal Page 31

34 Model performance resolution of a minute. At last, computing Model_2 was the longest; in the order of 1,5 hour for a temporal resolution of a minute. Page 32

35 Conclusion 5 CONCLUSION As part of solar irradiance forecasting methods, which includes the prediction of cloud behaviour over a specific area, the solar irradiance under clear sky conditions is needed for the same area at the same forecast time. Both are combined and therefore, their errors need to be both minimized. Uncertainty of solar irradiance under clear sky can have a significant impact on the forecast results accuracy. There are more or less complex clear sky models, requiring various set of input parameters and empirical or physical. Four models were retained in this study: Model_4, Model_3, Model_2 and Model_1. The scope of this study was to quantify the performance of each one, the impact of atmospheric parameters when used with a different averaging, and the impact of computing irradiation with a different temporal resolution. The scope was ultimately the selection of the most appropriate model for the forecasting of solar radiation the Réunion Island. The study included a bibliography research in order to select the most relevant and promising models, followed by their script modification in order to have similar output. Next, the required atmospheric parameters were collected from the different database for the area of Sainte Marie, where the ground measurements have been performed. After this step was completed it was possible to assess each clear sky model performances. For that purpose, specific scripts were developed in order to automatize all the computations. The process included atmospheric data reshaping, executing the model on the studied period, filtering to keep the clear sky moment only and quantifying the model accuracy against ground measurements. As part of the study, the error on the ground measurement has been estimated and the models were then comparable between each other. This study has revealed that, unlike what is often agreed in the literature, the model accuracy does not only depend on its number of inputs. Model_3, which require much less inputs than Model_2 and Model_1, have given more accurate results. Using more local atmospheric input, even on a daily basis, has not been effective for improving accuracy. The use of daily parameters from the Aeronet database have not brought much better results than compared to using e.g. monthly ones. In the future, it would be interesting to conduct these simulations with other database. The data used by the model Model_4 can be downloaded online [42] and thus, it would be very interesting to try them with Model_1 and the Model_2. Model_4 is the model which is the most operational, on its current format, and the most accurate in this study, therefore it is the most appropriate one to use as part of solar radiation forecasting. If there was a use for a clear sky model without an internet connection, then Model_3 would be the most appropriate one. Page 33

36 Bibliography BIBLIOGRAPHY [1] I. E. Agency, Energy Technology Perspectives [2] T. Barker, Climate Change 2007 : An Assessment of the Intergovernmental Panel on Climate Change, no. November, pp , [3] IEA, Home > Topics > Solar (PV and CSP).. [4] Solar Energy Perspectives. OECD Publishing, [5] A. R. de l Energie Réunionaise, Bilan énergétique 2010 de l île de la Réunion [6] Observ ER, Systèmes Solaires, Le journal des énergies renouvelables, Spécial île de la Réunion. [7] La Région Réunion met en place le chèque énergie.. [8] ferme agri-solaire AKUO.. [9] U. de L. R. Laboratoire PIMENT, Intégration des EnR intermittentes aux réseaux insulaires, 2013, p. Journées Européennes du Solaire. [10] Reuniwatt, Reuniwatt. [Online]. Available: [11] Confidential reference [12] J. D. Spelling, Solar Power Technologies Solar Fundamentals. [13] Enermena, Advanced CSP teaching material, chapter 2 Solar radiation. [14] Confidential reference [15] Nasa, Earth Fact Sheet.. [16] Techniques de l ingénieur, Électricité photovoltaïque - Principes, vol. 33, no. 0, pp. 0 15, [17] REN21, Renewables 2010 Global Status Report p. 15. [18] PV Magazine. [19] V. Badescu, C. a. Gueymard, S. Cheval, C. Oprea, M. Baciu, A. Dumitrescu, F. Iacobescu, I. Milos, and C. Rada, Computing global and diffuse solar hourly irradiation on clear sky. Review and testing of 54 models, Renewable and Sustainable Energy Reviews, vol. 16, no. 3, pp , Apr Page 34

37 Bibliography [20] C. a. Gueymard, Clear-sky irradiance predictions for solar resource mapping and large-scale applications: Improved validation methodology and detailed performance analysis of 18 broadband radiative models, Solar Energy, vol. 86, no. 8, pp , Aug [21] Confidential reference [22] P. Ineichen, Comparison of eight clear sky broadband models against 16 independent data banks, Solar Energy, vol. 80, no. 4, pp , Apr [23] Confidential reference [24] Confidential reference [25] Confidential reference [26] Confidential reference [27] S. Younes and T. Muneer, Clear-sky classification procedures and models using a world-wide data-base, Applied Energy, vol. 84, no. 6, pp , Jun [28] P. Ineichen, Five satellite products deriving beam and global irradiance validation on data from 23 ground stations, no. February, [29] A. Lanetz, Inter-comparison of different methods for estimating clear-sky global radiation for the Negev region of Israel.. [30] NASA, Aerosol Optical Thickness.. [31] F. Mavromatakis and Y. Franghiadakis, Direct and indirect determination of the Linke turbidity coefficient, Solar Energy, vol. 81, no. 7, pp , Jul [32] W. E. A. and N. S. Awadalla, The linke turbidity factor and Angstrom coefficient in humid climate of Bahrain. [33] AERONET.. [34] B. N. Holben, I. Slutsker, A. Smirnov, A. Sinyuk, J. Schafer, D. Giles, O. Dubovik, and U. S. T. De Lille, AERONET s Version 2. 0 quality assurance criteria, [35] J. Xu, Z. Wang, G. Yu, W. Sun, X. Qin, J. Ren, and D. Qin, Seasonal and diurnal variations in aerosol concentrations at a high-altitude site on the northern boundary of Qinghai-Xizang Plateau, Atmospheric Research, vol , pp , Feb [36] Dr. Chatrapatty BHUGWANT, TD M2 PRO GUE; MODULE: POLLUTION DE L AIR, [37] Confidential reference Page 35

38 Bibliography [38] L. Dunn, M. Gostein, and K. Emery, Comparison of pyranometers vs. PV reference cells for evaluation of PV array performance, th IEEE Photovoltaic Specialists Conference, pp , Jun [39] G. Todoran, Global Measurement Uncertainty, vol. 49, no. 3, pp , [40] Confidential reference [41] S. Janjai, K. Sricharoen, and S. Pattarapanitchai, Semi-empirical models for the estimation of clear sky solar global and direct normal irradiances in the tropics, Applied Energy, vol. 88, no. 12, pp , Dec [42] Confidential reference Page 36

39 Appendices APPENDICES I. MODEL INPUT DATA SUMMARY II. MODEL ERROR (OFFICIAL AND LITERATURE) III. PROCESS ORGANIGRAM IV. DETAIL OF RESULTS, TABLE V. DETAIL OF RESULTS, CORRELOGRAMS Page 37

40 Appendices I. MODEL INPUT DATA SUMMARY Model Name Model_1 Model_3 Model_2 Model_4 Year Confidential Confidential Confidential Confidential Institution Confidential Confidential Confidential Confidential Example of application Confidential Confidential Confidential Confidential Input data Geographial site elevation, h [m] surface albedo, ρg [ ] Atmospherical (surface) barometric pressure, p [mb] temperature, T [ C] relative humidity, RH [ ] Atmospherical (column integrated) total ozone abundance, Uo [atm cm] total nitrogen dioxide abundance, Un [atm cm] precipitable water, w [cm] Quantities related to atmospheric turbidity horizontal visibility, V [km] atmospheric transparency, k [ ] Linke turbidity coefficient, Tl [ ] broadband aerosol optical depth, τa [ ] aerosol optical depth at 700 nm, τa700 Ångström's wavelength exponent, α Ångström's turbidity coefficient, β aerosol single scattering albedo, ωa Total REQUESTED INPUTS (BESIDE ASTRONOMICAL PARAMETERS SUCH AS DATE, ZENITH ANGLE AND SOLAR CONSTANT) Page 38

41 Appendices II. MODEL ERROR (OFFICIAL AND LITERATURE) Confidential Page 39

42 Appendices III. PROCESS ORGANIGRAM Page 40