Development of a Model for Prediction of Solar Radiation

ENGINEERENGINEER - - Vol. Vol. XLVIII, XLVIII No., No. 03, 03 pp., pp. [19-25], [page 2015range], 2015 ©© TheThe Institution Institution of of Engineers, Engineers, Sri SriLanka Lanka

W. D. A. S. Wijayapala and D. H. K. Kushal

Abstract: Power generation from renewable energy sources such as wind, mini-hydro, solar etc is becoming increasingly popular due to environmental concerns. However, it is not possible to predict the energy generation of solar power plants in advance. Hence the power system operator has no information about the tomorrow‟s possible energy availability from these non-dispatchable power plants. The outcome of this study enables the system operator to predict the possible energy generation from solar power plants based on the weather forecasts and provide the system operator with predictions on energy generation and capacity of solar power plants connected to the grid. The predictions will enable to prepare the dispatch schedules accordingly.

In this study, the effect of the geographical and meteorological parameters for predicting daily global solar radiation at Sooriyawewa, Hambantota in Sri Lanka is investigated. A multiple linear regression was applied to explain the relationship among solar radiation and identified meteorological and geographical parameters such as cloud cover, sunshine duration, precipitation, open air temperature, relative humidity, wind speed, gust speed and sine value of declination angle. Variables in these equations were used to estimate the global solar radiation. Values calculated/predicted from models were compared with the actual measurements to validate the model.

Keywords : Solar Power, Solar Radiation, Prediction

The most important usage of this model is that 1. Introduction it can be used to predict the future solar

radiation available for power generation using Power generation from renewable energy weather forecast data. Then the electricity sources is becoming popular all over the dispatch control centre of the country can use world. Sri Lanka, a developing country located this information when preparing their future close to the equator, should consider solar dispatch schedules. energy as a source of power generation to the nation. Due to the geographical location close The accurate information of solar radiation to the equator, solar radiation is abundantly intensity at a given location is essential to the available throughout the year in most parts of development of solar energy-based projects the country. Therefore, proper utilization of and in the evaluation of the solar energy this resource would be beneficial both conversion systems‟ long-term performance. economically and environmentally. This information is used in the design, in financial analysis, and in the efficiency Measurements of solar radiation are important calculations of a project. Furthermore, monthly in developing solar energy devices to mean daily data are needed for the estimation supplement existing energy sources. This is of of solar power system‟s energy generation. Sri particular importance for a country like Sri Lanka as a country located in the equator belt Lanka where the sunshine is available in has the opportunity to utilize solar energy abundance. There are also other uses for such effectively, promoting a clean environment, information in quantitative ecological studies and developing renewable energy technologies as the source of energy used in photosynthesis in the country. The use of photovoltaic devices, and evapotranspiration. The solar radiation BScEng(Hons) (Moratuwa), climatology of the world has been extensively Eng. W.D.A.S Wijayapala, studied by numerous workers in the past. MEng(Moratuwa), Int.PEng(SL), CEng, FIE(Sri Lanka), Senior Lecturer, Department of Electrical Engineering, However, since solar radiation reaching the University of Moratuwa. earth's surface depends on factors such as Eng. D.H.K. Kushal, BScEng (Hons) (Ruhuna), cloud cover and turbidity which are not global MSc (Moratuwa), AMIE(Sri Lanka), Electrical Engineer, Central Engineering Consultancy Bureau. in nature, on-site radiation data are essential.

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on the other hand, is suitable for rural recorded in a number of weather stations all electrification, water pumping, over the country for a fairly long period of telecommunication towers, solar thermal time is available with the meteorological devices, etc. Given these many possible uses of department of Sri Lanka. Other than that solar energy, it is important to know the global agricultural research centres also maintain solar radiation distribution throughout the records of sun shine hours. Availability of year for interested regions.[1] data records for a longer time period is very much important for researches of this nature. Even though the climate of the country is most In order to propose a model to predict solar favourable for solar energy utilization, the radiation, it is necessary to identify the factors distribution of the solar radiation is not well that affect the solar radiation that would be known. The most important parameter for available on earth‟s surface. [2] [3] solar energy applications is the average global Factors affecting Solar Radiation solar radiation of which measurements are not  Distance from the sun. available at every location.  Duration of daily sunlight period.  Solar elevation or inclinations of the solar In places where no measured data are rays to the horizon. available, a common application has been to  Transparency of the atmosphere towards determine this parameter by appropriate heat radiation correlations which are empirically established  Output of solar radiation. using the measured data. Several empirical models have been used to calculate solar The first three of these factors are intimately radiation, utilizing available meteorological, connected with revolution of earth. It is to be geographical and climatological parameters noted here that the earth revolves about the such as sunshine hours, air temperature, sun in an elliptic orbit and makes one complete latitude, precipitation, relative humidity, and revolution in 365 days; simultaneously it spins cloudiness. Models to estimate solar radiation about itself and complete one rotation in every based only on sunshine hours are available for 24 hours. The average distance to earth from Sri Lanka. the sun is 149.5 million km. The duration of daylight also varies with the latitude and The main objectives of this study is season. Longer the daylight duration, greater determination of factors affecting the solar is the insolation received [4]. radiation reaching the earth‟s surface and development of a model to predict solar Several empirical models to estimate solar radiation based on the identified parameters of radiation are found in literature and those which forecasts are available. models utilize available meteorological, geographical and climatological parameters In order to achieve the main objective, the such as sunshine hours, air temperature, following methodology was formulated. latitude, precipitation, relative humidity, and cloudiness [5].  Identification of the parameters that affect the solar irradiance. The most commonly used parameter for  Collecting data on the parameters that are estimating global solar radiation is sunshine measured in Sri Lanka. duration. It is obvious that sunshine duration  Performing Regression analysis. is a parameter which indicates the amount of  Obtaining a model to predict solar solar radiation available at the earth‟s surface radiation. rather than a factor that affects the radiation  Validating the proposed model. reaching the earth‟s surface.

2. Methodology Parameters such as relative humidity, precipitation, wind speed, and gust speed can Monthly average daily global solar radiation cause impacts on the atmosphere through data is essential in the design and study of which the radiation reaches the earth‟s surface. solar energy conversion devices. For this The presence of clouds in the sky is very purpose there are some proposed models for common in Sri Lanka throughout the year. Sri Sri Lanka by researchers. Many of the models Lanka being closer to the equator where the developed to estimate solar radiation are based trade winds tend to converge causing on the sunshine hours. Sunshine hour data development of low pressure cells helps the

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on the other hand, is suitable for rural recorded in a number of weather stations all formation of clouds. When clouds are present, Relative Humidity Jul 2011 to electrification, water pumping, over the country for a fairly long period of water droplets effectively absorb the energy MD (r), % Dec 2012 telecommunication towers, solar thermal time is available with the meteorological from downward radiation. Thus, inclusion of devices, etc. Given these many possible uses of department of Sri Lanka. Other than that cloud cover data as an explanatory variable to Wind speed (W), SPP Jul 2011 to solar energy, it is important to know the global agricultural research centres also maintain the model for cloud transmittance is necessary m/s Dec 2012 solar radiation distribution throughout the records of sun shine hours. Availability of to achieve better predictions. Gust speed (G), Jul 2011 to year for interested regions.[1] data records for a longer time period is very SPP m/s Dec 2012 much important for researches of this nature. Since the declination angle (δ) explains the Even though the climate of the country is most In order to propose a model to predict solar sun‟s location in the sky, it affects the amount In order to find a model to estimate the solar favourable for solar energy utilization, the radiation, it is necessary to identify the factors of solar radiation available to a particular radiation, selected eight parameters are distribution of the solar radiation is not well that affect the solar radiation that would be location of the earth at a particular considered as explanatory variables. Then, known. The most important parameter for available on earth‟s surface. [2] [3] time[4][6].Therefore, the sine value of the investigations were made to find relationship solar energy applications is the average global Factors affecting Solar Radiation declination angle (sin δ) is taken as an between those parameters and the solar solar radiation of which measurements are not  Distance from the sun. explanatory parameter in the model proposed radiation. For this purpose multiple linear available at every location.  Duration of daily sunlight period. in this study. regression analysis was performed. In the  Solar elevation or inclinations of the solar Declination Angle (δ) can be defined as follows process of applying multiple linear regression, In places where no measured data are rays to the horizon. (Duffie and Beckman, 1991): out of eight parameters, one variable is available, a common application has been to  Transparency of the atmosphere towards selected and came out with eight equations 8 determine this parameter by appropriate heat radiation ( C1) for the selected explanatory variable. correlations which are empirically established  Output of solar radiation. Where, n = Julian day of the year using the measured data. Several empirical Similarly, two variables are selected out of the models have been used to calculate solar The first three of these factors are intimately 8 Data collection eight parameters and twenty eight ( C2) radiation, utilizing available meteorological, connected with revolution of earth. It is to be numbers of equations are obtained. This geographical and climatological parameters The daily data for computations were collected noted here that the earth revolves about the process is repeated for 3, 4,5,6,7 and 8 number such as sunshine hours, air temperature, from July 2011 to December 2012 for sun in an elliptic orbit and makes one complete of variables. latitude, precipitation, relative humidity, and Hambantota, Sri Lanka. Data for Solar revolution in 365 days; simultaneously it spins cloudiness. Models to estimate solar radiation Radiation, Sunshine Duration, Cloud cover, about itself and complete one rotation in every 8 8 In the above process total of 255 ( C1 + C2 + based only on sunshine hours are available for Precipitation, Ambient Temperature, Relative 24 hours. The average distance to earth from 8 8 8 8 8 8 C3 + C4 + C5 + C6 + C7 + C8) number of Sri Lanka. Humidity, Wind Speed, Gust Speed were the sun is 149.5 million km. The duration of equations are obtained [7] [8]. collected from Meteorological daylight also varies with the latitude and The main objectives of this study is Department(MD)of Sri Lanka and from an season. Longer the daylight duration, greater In mathematics, the coefficient of determination, determination of factors affecting the solar existing Solar Power Plant (SPP) at 2 is the insolation received [4]. denoted by R is a number that indicates how well radiation reaching the earth‟s surface and Hambantota where regular measurements are data fit a statistical model. Out of the 255 development of a model to predict solar made. Several empirical models to estimate solar equations, model with the highest R2 value is radiation based on the identified parameters of radiation are found in literature and those Table 1 - Data for Hambantota and collected selected as the best model which explains the which forecasts are available. models utilize available meteorological, source solar radiation reaching the earth‟s surface. geographical and climatological parameters In order to achieve the main objective, the Parameter/Measure Available such as sunshine hours, air temperature, Source The parameter, maximum Gust Speed (G) is following methodology was formulated. ment Period latitude, precipitation, relative humidity, and not easily available as a forecast or a cloudiness [5]. Solar Radiation (H), Jul 2011 to measurement. Therefore, in addition to the 8  Identification of the parameters that affect SPP MJ/m2 Dec 2012 variable model, seven other models are the solar irradiance. The most commonly used parameter for selected again based on higher R2 values  Collecting data on the parameters that are Jul 2011 to estimating global solar radiation is sunshine Cloud Cover (C), % MD avoiding G. Nov 2012 measured in Sri Lanka. duration. It is obvious that sunshine duration  Performing Regression analysis. is a parameter which indicates the amount of Jul 2011 to 3. Comparison Techniques  Obtaining a model to predict solar solar radiation available at the earth‟s surface Sunshine Hours (n), MD Oct 2011 & radiation. rather than a factor that affects the radiation h Feb 2012 to There are numerous research in literature  Validating the proposed model. reaching the earth‟s surface. Aug 2012 which deal with the assessment and comparison of the daily solar radiation Precipitation (p), Jul 2011 to Parameters such as relative humidity, SPP estimation models. The most popular 2. Methodology mm Dec 2012 precipitation, wind speed, and gust speed can statistical parameters are the Mean Bias Error cause impacts on the atmosphere through (MBE) and the Root Mean Square Error Monthly average daily global solar radiation Open Air Temp. SPP Jul 2011 to which the radiation reaches the earth‟s surface. o (RMSE). In this study, to evaluate the accuracy data is essential in the design and study of (Ta), C Dec 2012 of the estimated data from the models solar energy conversion devices. For this The presence of clouds in the sky is very described above, statistical tests on MBE, purpose there are some proposed models for common in Sri Lanka throughout the year. Sri Sine value of Jul 2011 to RMSE and Mean Percentage Error (MPE) were Sri Lanka by researchers. Many of the models Lanka being closer to the equator where the Declination Angle Calculated Dec 2012 carried out. For better data modelling, these developed to estimate solar radiation are based trade winds tend to converge causing (sin δ), o statistics should be closer to zero. The Nash– on the sunshine hours. Sunshine hour data development of low pressure cells helps the

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Sutcliffe equation (NSE) was also selected as 3.4 Nash–Sutcliffe Equation an evaluation criterion. A model is more n 2 efficient when NSE is closer to 1. However, Ʃ ( Hi,meas- Hi,calc) these estimated errors provide reasonable 1 NSE = 1 - criteria to compare models but do not n 2 objectively indicate whether a model‟s Ʃ ( Hi,meas– Hmeas) estimates are statistically significant. The t- 1 statistics allows models to be compared and at the same time it indicates whether or not a Where Hi,meas is the mean measured global model‟s estimate is statistically significant at a radiation and n the number of data pairs. A particular confidence level. Therefore t-test of model is more efficient when NSE is closer to the models were also carried out to determine 1. statistical significance of the predicted values by the models. [5] [12] 3.5 t-Statistic Test

3.1 Mean Bias Error t-statistic is defined as (Walpole and Myers, 1989) n 1 1/2 2 MBE = Ʃ (Hi,calc- Hi,meas ) (n-1) (MBE) n 1 t =

(RMSE)2 - (MBE)2 th Where Hi,meas, Hi,calc are the i measured value and ith calculated value of daily solar radiation. n is the number of data pairs. The smaller the value of t, the better is the performance of the model. This test provides information on long-term performance. A low MBE value is desired. A 4. Development of the Models negative value gives the average amount of underestimation in the calculated value. One As mentioned earlier, multiple linear drawback of this test is that overestimation of regression analysis was performed to find the an individual observation will cancel relationship between selected parameters to underestimation in a separate observation. the solar radiation.

The response variable is set as solar radiation 3.2 Mean Percentage Error (H) and the other variables as sunshine hours

n (n), cloud cover (C), precipitation (p), open air 1 Hi,calc- Hi,meas *100 temperature (Ta) ,sine value of the declination MPE (%) = Ʃ 1 Hi,meas angle (sin δ), relative humidity (r), wind speed n (W), gust speed (G) as explanatory variables.

Out of the many models developed, following A percentage error between −10% and +10% is 8 models were found to be with acceptable considered acceptable. accuracy levels as validated in the following

sections. 3.3 Root Mean Square Error  Model 1 - H versus C, n, p, Ta, sin δ, r, W,G n 1/2 1 2 RMSE = Ʃ (Hi,calc- Hi,meas) H = - 19.3 - 0.0413 C + 0.645 n - 0.0480 p n 1 + 1.53 Ta - 4.88 sin δ - 0.0596 r - 0.029 W + 0.114 G The value of RMSE is always positive, representing zero in the ideal case. The  Model 2 - H versus C, n, p, Ta, sin δ, r, W normalized root mean square error gives information on the short term performance of H = - 19.3 - 0.0389 C + 0.662 n - 0.0396 p + 1.54 Ta - 4.91sin δ - 0.0588 r + 0.169 W the correlations by allowing a term by term comparison of the actual deviation between  Model 3 - H versus C, n, p, Ta, sin δ, r the predicted and measured values. The H = - 21.0 - 0.0374 C + 0.664 n - 0.0440 p smaller the value, the better is the model‟s + 1.61 Ta - 4.49 sin δ - 0.0529 r performance.

ENGINEER 22  Model 4 - H versus C, n, p, Ta, sin δ, W

 Model 4 - H versus C, n, p, Ta, sin δ, W to predict day after tomorrow‟s (Day number H = - 22.3 - 0.0401 C + 0.662 n - 0.0435 p + 1.49 Sutcliffe equation (NSE) was also selected as 3.4 Nash–Sutcliffe Equation 3)to radiationpredict day using after today‟s tomorrow‟s predictions (Day numberon day H = -T 22.3a - 5.43 - 0.0401 sin δ +C 0.155+ 0.662 W n - 0.0435 p + 1.49 an evaluation criterion. A model is more n after3) radiation tomorrow's using explanatory today‟s predictions variables. on Then, day efficient when NSE is closer to 1. However, 2 Ta - 5.43 sin δ + 0.155 W after tomorrow's explanatory variables. Then, Ʃ ( Hi,meas- Hi,calc) tomorrow (on day number 2) one can compare these estimated errors provide reasonable 1 tomorrowthe predicted (on dayfigure number with the2) one actual can andcompare also NSE = 1 -  Model 5 - H versus C, n, Ta, sin δ, r, W n criteria to compare models but do not  Model 5 - H versus C, n, Ta, sin δ, r, W the predicted figure with the actual and also 2 predict the radiation for day number 3 based objectively indicate whether a model‟s Ʃ ( Hi,meas– Hmeas) H = - 21.5 - 0.0381 C + 0.672 n + 1.64 Ta- 5.07 onpredict day numberthe radiation 2‟s data. for Onday day number number 3 based3 one H = - 21.5 - 0.0381 C + 0.672 n + 1.64 Ta- 5.07 estimates are statistically significant. The t- 1 sin δ - 0.0696 r + 0.193 W canon day compare number the 2‟s actual data. Onvalue day with number predicted 3 one sin δ - 0.0696 r + 0.193 W statistics allows models to be compared and at radiationcan compare values the prediactualcte valued based with on predictedboth day  the same time it indicates whether or not a Where Hi,meas is the mean measured global Model 6 - H versus C, n, sin δ, p, Ta numberradiation 1 values and day predi numbercted based 2.Comparison on both day of radiation and n the number of data pairs. A  Model 6 - H versus C, n, sin δ, p, Ta model‟s estimate is statistically significant at a H = - 23.6 - 0.0386 C + 0.664 n - 0.0472 p + 1.56 actualnumber and1 and predicted day number radiation 2.Comparison values inof particular confidence level. Therefore t-test of model is more efficient when NSE is closer to actual 2 and predicted radiation values in H = -T 23.6a - 4.99 - 0.0386 sin δ C + 0.664 n - 0.0472 p + 1.56 MJ/m are shown in Table 3 to Table 10 for the 1. 2 the models were also carried out to determine Ta - 4.99 sin δ MJ/mdeveloped are models.shown in Table 3 to Table 10 for the statistical significance of the predicted values developed models.  Model 7 - H versus C, n, Ta, sin δ, r 3.5 t-Statistic Test by the models. [5] [12]  Model 7 - H versus C, n, Ta, sin δ, r Table 3 - Validation of the model 1 with 8

H = - 23.7 - 0.0364 C + 0.673 n + 1.73 Ta- 4.58 variablesTable 3 - (C,Validation n, p, Ta, sin of δ,the r, W,model G) 1 with 8 H = - 23.7 - 0.0364 C + 0.673 n + 1.73 Ta- 4.58 3.1 Mean Bias Error t-statistic is defined as (Walpole and Myers, sin δ - 0.0643 r variables (C, n, p, Ta, sin δ, r, W, G)

sin δ - 0.0643 r

1989)

 ) from from 2 Model 8 - H versus C, n, sin δ, Ta

1 1/2  ) from from 2 Model 8 - H versus C, n, sin δ, Ta

2 ted from ted from 2’s data 3’s data MBE = Ʃ (Hi,calc- Hi,meas ) (n-1) (MBE) H = - 27.1 - 0.0379 C + 0.673 n + 1.68 Ta- 5.20 1’s data

ted from ted from (MJ/m 1 H = - 27.1 - 0.0379 C + 0.673 n + 1.68 Ta- 5.20 1’s data 2’s data 3’s data Radiation n t = sin δ Measured day day day 2 2 (MJ/m Radiation Measured Predic Predic (RMSE) - (MBE) sin δ Predicted day day day th Predicted Predic Predic Where Hi,meas, Hi,calc are the i measured value The statistical performance of developed and ith calculated value of daily solar radiation. modelsThe statistical was investigated performance by using of MBE,developed MPE, Day1 16.27 19.35 Day1 16.27 19.35 n is the number of data pairs. The smaller the value of t, the better is the RMSE,models NSE,was investigatedt- statistic and by Rusing2 and MBE, the results MPE, RMSE, NSE, t- statistic and R2 and the results Day2 20.22 19.36 21.28 performance of the model. are summarized in Table 2. Day2 20.22 19.36 21.28 This test provides information on long-term are summarized in Table 2. Table 2 - The results of statistical analyses of Day3 23.99 19.37 21.29 22.47 performance. A low MBE value is desired. A 4. Development of the Models Table 2 - The results of statistical analyses of Day3 23.99 19.37 21.29 22.47 models negative value gives the average amount of models Table 4 - Validation of the model 2 with underestimation in the calculated value. One

As mentioned earlier, multiple linear

1 1 Table 4 - Validation ofa the model 2 with seven variables(C, n, p, T , sin δ, r, W)

drawback of this test is that overestimation of regression analysis was performed to find the t (%) 1 1 seven variables(C, n, p, Ta, sin δ, r, W) 2

NSE NSE x 10 x 10 MBE MBE t an individual observation will cancel (%)

RMSE R

relationship between selected parameters to Model

MPE (%) rom NSE NSE ) x 10 x 10 MBE MBE 2

RMSE R underestimation in a separate observation. Model the solar radiation. MPE (%) rom )

2 2’s data 1’s data 3’s data

The response variable is set as solar radiation 1 1.06 2.292 0.770 69.5 2.20 6.94 (MJ/m

3.2 Mean Percentage Error 1’s data 2’s data 3’s data Radiation (H) and the other variables as sunshine hours Measured day day 1 1.06 2.292 0.770 69.5 2.20 6.94 day (MJ/m Radiation Measured Predicted from Predicted f Predicted from n (n), cloud cover (C), precipitation (p), open air 2 -0.11 2.298 0.077 69.3 1.64 6.93 day day day 1 Hi,calc- Hi,meas Predicted from Predicted f Predicted from *100 temperature (Ta) ,sine value of the declination 2 -0.11 2.298 0.077 69.3 1.64 6.93 MPE (%) = Ʃ Day1 16.27 18.79 1 Hi,meas angle (sin δ), relative humidity (r), wind speed 3 1.17 2.307 0.843 69.1 2.26 6.90 n Day1 16.27 18.79 (W), gust speed (G) as explanatory variables. 3 1.17 2.307 0.843 69.1 2.26 6.90 Day2 20.22 18.80 21.33 Out of the many models developed, following 4 -0.33 2.303 0.235 69.1 1.54 6.91 Day2 20.22 18.80 21.33 A percentage error between −10% and +10% is 4 -0.33 2.303 0.235 69.1 1.54 6.91 8 models were found to be with acceptable Day3 23.99 18.81 21.35 22.37 considered acceptable. 5 -1.00 2.307 0.098 69.0 1.62 6.90 accuracy levels as validated in the following Day3 23.99 18.81 21.35 22.37 5 -1.00 2.307 0.098 69.0 1.62 6.90 sections. 3.3 Root Mean Square Error 6 1.00 2.310 0.721 69.0 2.19 6.89 Table 5 - Validation of the model 3 with six 6 1.00 2.310 0.721 69.0 2.19 6.89  Tablevariables 5 - (C,Validation n, p, Ta, sinof theδ, r) model 3 with six n 1/2 Model 1 - H versus C, n, p, Ta, sin δ, r, W,G 7 0.40 2.316 0.284 68.8 1.88 6.88 variables (C, n, p, Ta, sin δ, r) 1 2

7 0.40 2.316 0.284 68.8 1.88 6.88 Ʃ (Hi,calc- Hi,meas) 2’s 3’s RMSE = 1’s )

H = - 19.3 - 0.0413 C + 0.645 n - 0.0480 p ed 2

n 1 8 0.80 2.322 0.573 68.6 2.09 6.86 1’s 2’s 3’s ) ed

2 + 1.53 Ta - 4.88 sin δ - 0.0596 r - 0.029 W + 0.114 8 0.80 2.322 0.573 68.6 2.09 6.86 data data data G (MJ/m data data data Predicted Predicted Predicted Radiation Measur from day from day from day The value of RMSE is always positive, from day 5. Validating the models (MJ/m Predicted Predicted Predicted Radiation Measur representing zero in the ideal case. The  Model 2 - H versus C, n, p, Ta, sin δ, r, W 5. Validating the models from day from day from day normalized root mean square error gives This study developed models to predict the This study developed models to predict the Day1 16.27 18.98 information on the short term performance of H = - 19.3 - 0.0389 C + 0.662 n - 0.0396 p solar radiation using eight explanatory Day1 16.27 18.98 + 1.54 Ta - 4.91sin δ - 0.0588 r + 0.169 W variables.solar radiation Using theusing model eights it is explanatorypossible to the correlations by allowing a term by term Day2 20.22 18.99 21.56 variables. Using the models it is possible to comparison of the actual deviation between  estimate today‟s (Day number 1) solar Day2 20.22 18.99 21.56 Model 3 - H versus C, n, p, Ta, sin δ, r estimate today‟s (Day number 1) solar the predicted and measured values. The radiation using today‟s measurable Day3 23.99 19.00 21.57 22.52 H = - 21.0 - 0.0374 C + 0.664 n - 0.0440 p radiation using today‟s measurable Day3 23.99 19.00 21.57 22.52 smaller the value, the better is the model‟s explanatory variables and also to predict + 1.61 Ta - 4.49 sin δ - 0.0529 r explanatory variables and also to predict performance. tomorrow‟s (Day number 2) solar radiation tomorrow‟susing today‟s (Day predictions number 2)for solar tomorrow‟s radiation explanatoryusing today‟s variables. predictions Similarly, for it tomorrow‟sis possible explanatory variables. Similarly, it is possible 23 ENGINEER Table 6 - Validation of the model 4 with six Table 10 - Validation of the model 8 with variables (C, n, p, Ta, sin δ, W) four variables (C, n, Ta, sin δ)

)

1’s data 2’s data 3’s data (MJ/m Radiation Me asured 1’s data 2’s data 3’s data day day day Predicted from Predicted from Predicted from Measured Predicted from day Predicted from day Predicted from day Day1 16.27 18.51 Day1 16.27 18.66 Day2 20.22 18.52 21.05 Day2 20.22 18.67 21.13 Day3 23.99 18.53 21.06 22.09 Day3 23.99 18.69 21.14 22.12

Table 7 - Validation of the model 5 with six variables (C, n, Ta, sin δ, r, W) 6. Recommendations and Conclusion

2’s 3’s 1’s )

2 The study was based on data collected from an

existing solar power plant at Sooriyawewa and data data data the Automated Weather Station (AWS) of (MJ/m Predicted Predicted Predicted Radiation Measured from day from day from day from day from day meteorological department of Sri Lanka. Multiple linear regressions was applied on the Day1 16.27 18.79 data set and several models were obtained which describe the daily solar radiation from Day2 20.22 18.80 21.25 other identified parameters. (sunshine hours, precipitation, cloud cover, ambient Day3 23.99 18.81 21.26 22.29 temperature, sine of declination angle, relative humidity, wind speed and gust speed).

Table 8 - Validation of the model 6 with five The proposed models gave acceptably high R2 variables (C, n, p, Ta, sin δ) values as well as other statistical indicators.

Therefore, it is possible to consider these

)

2 proposed models provide sufficiently accurate

predictions for solar radiation. 1’s data 2’s data 3’s data (MJ/m Radiation Measured day day day An effort was not made to compare between Predicted from Predicted from Predicted from the models because intention was to develop Day1 16.27 18.72 models based on parameters for which predictions are available for a given site. It Day2 20.22 18.73 21.29 could be observed that effects of sunshine hours, cloud cover, ambient temperature and Day3 23.99 18.74 21.30 22.27 declination angel on the solar radiation are more significant in all the models.

Table 9 - Validation of the model 7 with five Sri Lanka being an island small in size (65,000 variables (C, n, Ta, sin δ, r) km2) and small latitudinal extent (< 4°), the

model may form the basis for more

) comprehensive solar radiation prediction 2

models for other areas in Sri Lanka [2]. 1’s data 2’s data 3’s data (MJ/m Radiation Measured day day day In order to further improve the accuracy of the Predicted from Predicted from Predicted from results, it is recommended to collect data for a Day1 16.27 18.92 longer period of time to build models described in this paper. Day2 20.22 18.93 21.41

Day3 23.99 18.94 21.42 22.37

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Table 6 - Validation of the model 4 with six Table 10 - Validation of the model 8 with variables (C, n, p, Ta, sin δ, W) four variables (C, n, Ta, sin δ) References

) [1] Dave Renne, Ray george, Bill Marion, Chris

2 Gueymard, Donna Heimiller, “Solar Resource asured 1’s data 2’s data 3’s data Assessment for Sri Lanka and Maldives, (MJ/m Radiation Me

1’s data 2’s data 3’s data National Renewable Energy Laboratory, U.S. day day day

Predicted from Predicted from Predicted from Department of Energy NREL/TP-710-34645,

Measured Predicted from day Predicted from day Predicted from day 2003. Day1 16.27 18.51 Day1 16.27 18.66 [2] Punyawardena, B.V.R., and Don Kulasiri, Day2 20.22 18.52 21.05 “Stochastic Simulation of Solar Radiation from Day2 20.22 18.67 21.13 Sunshine Duration in SriLanka”, Centre for Day3 23.99 18.53 21.06 22.09 computing and biometrics, Lincoln University, Day3 23.99 18.69 21.14 22.12 Research paper No. 96/06, September, 1996.

[3] Peiris, T. S. G. and Thattil, R. O., “An Table 7 - Validation of the model 5 with six „Alternative‟ Model to Estimate Solar variables (C, n, Ta, sin δ, r, W) 6. Recommendations and Radiation”, COCOS 10, 26-34, Department of Conclusion crop science, University of Peradeniya, Sri Lanka,

1’s 2’s 3’s )

2 The study was based on data collected from an 1994-1995.

existing solar power plant at Sooriyawewa and data data data the Automated Weather Station (AWS) of [4] Harlan, H., Bengtson, Solar Energy (MJ/m Predicted Predicted Predicted Radiation Measured Fundamentals, Course No. M04-018. from day from day from day from day meteorological department of Sri Lanka. Multiple linear regressions was applied on the [5] Inci Turk Togrul, “Estimation of Solar Day1 16.27 18.79 data set and several models were obtained Radiation from Angstroms Coefficients by which describe the daily solar radiation from using Geographical and Meteorological Data Day2 20.22 18.80 21.25 other identified parameters. (sunshine hours, in Bishkek, Kyrgystan”, Isi Billimi ve Teknigi precipitation, cloud cover, ambient Dergisi 29,2,99-108, Chemical Engineering Day3 23.99 18.81 21.26 22.29 temperature, sine of declination angle, relative Department, Engineering Faculty, Afyon Kocatepe humidity, wind speed and gust speed). University, 2009

Table 8 - Validation of the model 6 with five The proposed models gave acceptably high R2 [6] Scharmer, K., and Greif, J., “European Solar Radiation Atlas, Vol 1: Fundamentals and variables (C, n, p, Ta, sin δ) values as well as other statistical indicators. Maps”, Paris, 2000.

Therefore, it is possible to consider these

)

2 proposed models provide sufficiently accurate [7] Bose, A., Multiple Linear Regression, BIMTECH,

predictions for solar radiation. October 2009. 1’s data 2’s data 3’s data (MJ/m Radiation Measured day day day An effort was not made to compare between [8] Allin Cottrell, Regression Analysis: Basic Concepts, Predicted from Predicted from Predicted from the models because intention was to develop 2011. Day1 16.27 18.72 models based on parameters for which predictions are available for a given site. It [9] Muzathik, A. M., Nik, W. B. W., Ibrahim, M. Z., Samo, K. B., Sopian, K., and Alghoul, M. Day2 20.22 18.73 21.29 could be observed that effects of sunshine A., “Daily Global Solar Radiation Estimate hours, cloud cover, ambient temperature and Day3 23.99 18.74 21.30 22.27 Based on Sunshine Hours” , International declination angel on the solar radiation are Journal of Mechanical and Materials Engineering more significant in all the models. (IJMME), Vol. 6, No. 1.75-80, Malaysia, 2011.

Table 9 - Validation of the model 7 with five Sri Lanka being an island small in size (65,000 variables (C, n, Ta, sin δ, r) km2) and small latitudinal extent (< 4°), the

model may form the basis for more

) comprehensive solar radiation prediction 2

Day3 23.99 18.94 21.42 22.37

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