Literature Review. Chapter Introduction

Transcription

1 Chapter 2 Literature Review 2.1 Introduction Almost all the renewable energy sources originate entirely from the sun. The sun s rays that reach the outer atmosphere are subjected to absorption, scattering, reflection and transmission processes through the atmosphere, before reaching the earth s surface. Solar radiation data at ground level are important for a wide range of applications in meteorology, engineering, agricultural sciences, particularly for soil physics, agricultural hydrology, crop modeling and estimation of crop evapo-transpiration, as well as in the health sector, in research and in many fields of natural sciences. A few examples showing the diversity of applications may include: architecture and building design (e.g. air conditioning and cooling systems); solar heating system design and use; solar power generation and solar powered car races; weather and climate prediction models; evaporation and irrigation; calculation of water requirements for crops; monitoring plant growth and disease control and skin-cancer research. The solar radiation reaching Earth s upper atmosphere is rather constant in time. But the radiation reaching some point on Earth is random in nature due the gases, clouds and dust within the atmosphere which absorbs and/or scatters radiation at different wavelengths. Obtaining reliable 21

2 radiation data at ground level requires systematic measurements. However, in most countries the spatial density of actinometrical stations is inadequate. For example, the ratio of weather stations collecting solar radiation data relative to those collecting temperature data in the USA is approximately 1: 100 and worldwide the estimate is approximately 1:500 (Viorel Badescu[67]). Even in the developed countries there is a dearth of measured long-term solar radiation and daylight data. 2.2 Existing Estimation models Radiative Transfer Model In radiation, the energy is transmitted by electromagnetic waves emitted by the atoms and molecules inside the hot body. Stefan in 1879 found experimentally that, at a given temperature T ºK, the total energy E, radiated by a body is given by, E = σ T 4 (2.1) where σ is a constant ( Wm -2 K -4 ), called Stefan-Boltzmann constant. Sun is the star at the center of the solar system. Its surface temperature is about 5778 ºK. For all theoretical purposes, sun is considered as a black body radiating energy in all direction. As per Stefan s relation this amounts to 6,31,82,037 Wm -2 at the sun s surface. With, radius of Sun, R= km and of distance of Earth from Sun, r= km, solar radiation striking the top of the earth s atmosphere, referred as solar constant Io would be given by the relation, 22

3 (2.2) which is equal to 1360 Wm -2. The solar constant is the amount of energy received at the top of the Earth's atmosphere on a surface oriented perpendicular to the Sun s rays at the mean distance of the Earth from the Sun. The earth revolves around the sun in an elliptical orbit. This leads to variation of extraterrestrial radiation flux. This value on any day of the year can be calculated from the equation, (2.3) where, n is the day of the year. To specify the position of a point on the surface of the earth, one should know the latitude λ (horizontal lines) and longitude φ (vertical lines) of the point. Figure 2.1 shows various geometrical parameters related to sunearth relations. The angular displacement of the sun from the plane of the earth s equator is termed as the declination of the sun, δ. This angle varies between º to º as the earth performs its yearly circum-navigation around the sun. The hour angle, ω is an angular measure of time and is equivalent to 15º per hour. It varies from -180º to +180º. 23

4 λ Figure 2.1 Measuring longitude, declination and hour angle (Courtesy: Duffie and Beckman[68]) Before the expression for global solar radiation is established, it is necessary to understand the following parameters, h = Elevation angle, measured up from horizon θ Z = Zenith angle, measured from vertical and A = Azimuth angle, measured clockwise from north The above useful angles are represented in figure

5 If θz called as the zenith angle, is the angle between an incident beam of flux I and the normal to a plane surface, then the equivalent flux falling normal to the surface is given by, (2.4) Figure 2.2 Measuring elevation angle, zenith angle and azimuth angle (Courtesy: Sukhatme[69]) For a horizontal surface, we can show that, sin sin cos cos cos (2.5) The hour angle corresponding to sunrise or sunset, ωs on a horizontal surface can be found from above equation by substituting the value of 90º for the zenith angle. Thus, cos tan tan (2.6) Then instantaneous global solar radiation on a horizontal surface is computed as, 25

6 sin sin cos cos cos (2.7) Thus, monthly averaged global radiation denoted by Ĥ o, is obtained by integrating over the day length as follows: Ĥ sin sin cos cos cos (2.8) Now, where, t is in hours and ω is in radians. (2.9) Hence, (2.10) Substituting in the above equation, Ĥ sin After simplification, we obtain, sin cos cos cos (2.11) Ĥ sin sin cos cos sin (2.12) Equation (2.12) could be used for calculating the monthly averaged global radiation at extra-terrestrial plane called extra-terrestrial radiation (ETR). As shown in figure 2.3, the atmosphere scatters and absorbs some of the Sun's energy that is incident on the Earth's surface. Scattering of radiation by gaseous molecules (e.g. O 2, O 3, H 2O and CO 2), is called Rayleigh scattering. Almost half of the radiation that is scattered is lost to outer space. The remaining half is directed towards the Earth's surface from all directions as 26

7 diffuse radiation. Absorption of solar radiation is mainly by oxygen and ozone molecules in the atmosphere. Reflected Figure 2.3 Plane of earth receiving the component of beam, diffuse radiations from extraterrestrial radiation. (Courtesy: Rai[70]) Clouds reflect a lot of radiation and absorb a little. The rest is transmitted through atmosphere which helps regulating the surface temperature. The fraction of the total solar radiant energy reflected back to space from clouds, scattering and reflection from the Earth's surface is called the albedo of the Earth-atmosphere system, is roughly 0.3 for the Earth as a whole. Figure 2.3 also shows that a plane on the Earth's surface receives: Beam (or direct) radiation coming straight through the atmosphere to hit the plane (very directional); Diffused radiation scattered in all directions in the atmosphere and then some arrives at the plane on the Earth s surface (not directional); 27

8 Reflected radiation beam and diffused radiation that hits the Earth's surface and is reflected onto the plane. The amount of solar radiation energy reflected, scattered and absorbed depends on the condition of atmosphere that the incident radiation travels through as well as the levels of dust particles and water vapor present in the atmosphere. The latter is usually difficult to judge. The distance travelled through the atmosphere by incident radiation depends on the angle of the Sun Empirical Models The utility of existing weather data sets is greatly expanded by including information on solar radiation. Radiation estimates for historical weather can be obtained by predicting it using either a site-specific radiation model or a mechanistic prediction model. A site-specific model relies on empirical relationships of solar radiation with commonly recorded weather station variables. Although a site-specific equation requires a data set with actual solar radiation data for determining appropriate coefficients, this approach is frequently simpler to compute and may be more accurate than complicated mechanistic models. These simple, site-specific equations, therefore, may be very useful to those interested in sites near to where these models are developed. In the following sections, various such site-specific models are discussed Sunshine based models The fundamental Angstrom-Prescott-Page[4,5,6] model, is the most commonly used and is given by, 28

9 (2.13) where H is the monthly averaged daily global solar radiation, Ho is the monthly averaged daily extraterrestrial radiation; S o is the day length, S is the maximum sunshine duration. a and b are empirical coefficients which vary depending upon the site. Page[5] has given the coefficients a=0.23 and b=0.48, for Angstroms- Prescott-Page model, which is believed to be applicable anywhere in the world. For Turkey, Tiris et al.[71] gave a=0.18 and b=0.62. Bahel et al[72]., suggested a=0.175 and b= for Saudi Arabia. Louche et al.[73], presented a model for French Mediterranean site with a=0.206 and b= Monthly specific correlations with S/So and λ (latitude) are given by Dogniaux and Lemoine[74] for Europe. Rietveld[75] examined several published values of a and b coefficients and noted that a is related linearly and b hyperbolically to the appropriate mean value of S/S o. Soler[76] applied Rietveld s model to 100 European stations and gave the specific monthly correlations. Zabara[77] modified the Angstroms expression for Greece and expressed the a and b coefficients as a third order function of (S/So), as under (2.14) (2.15) Kilic and Ozturk[78] calculated the a and b empirical coefficients for Istanbul as, a = Z cos (λ-δ), b= cos (λ-δ), where Z is the altitude of the site. 29

10 For Spain, Almorox and Hontoria[19] proposed the exponential model as, exp (2.16) Togrul et al.[49], proposed variations in correlations for Ealzig, Turkey, as a function of sunshine duration ratio. Akinoglu and Ecevit[79] obtained the correlations in a second order polynomial equation for Turkey as (2.17) Bahel[80] developed a worldwide correlation based on bright sunshine hours and global radiation data of 48 stations around the world. The model is given by, (2.18) Bahel et al.[72] suggested the following model for Saudi Arabia, (2.19) Samuel s[81] model for Srilanka is given as under, (2.20) Raja and Twidell[82], for Pakistan offered the following model, cos (2.21) Model including a logarithmic term is given by Newland[83]for South China as, 30

11 (2.22) Temperature based models Bristow and Campbell[25] suggested the following model for India as 1 exp (2.23) Hargreaves et al.[26] reported a simple model based on temperatures as. (2.24) Allen[27] suggested self calibrating model that is function of the daily extraterrestrial radiation, mean monthly maximum and minimum temperatures as. (2.25) For China, Chen at al.[30], presented the following model (2.26) For six stations in India, S.S. Chandel et al.[84] model is 7.9 sin exp Cloud observation based models (2.27) Black[33], using data from many parts of the world, proposed the following quadratic equation 31

12 (2.28) by clouds. where C is the monthly average fraction of the daytime sky obscured Badescue[37] suggested the following models for Romania, (2.29) (2.30) (2.31) Supit and Kappel[85] proposed the following model 1 (2.32) Multiple parameter based models For various places in Sudan, Elagib and Mansell[86] have suggested the following models (2.33) (2.34) (2.35) (2.36) (2.37) 32

13 Abdalla[87] modified these equations for Baharin as, (2.38) (2.39) where PS is the ratio between mean sea level pressure and mean daily vapor pressure. Trabe and Shaltout [88]suggested the model for Egypt as, (2.40) where V, is the water vapor pressure. Gopinathan[14] introduced a multiple linear regression equation of the form, (2.41) Dogniaux and Lemoine[74] proposed the following correlation for Europe, where the coefficients of the Angstrom-Prescott-Page model seem to be a function of the latitude of the site, (2.42) For South Western Nigeria, Ojosu and Komolafe[89] proposed the following equation, (2.43) Ododo et al.[90] proposed two new models for Nigeria as under (2.44) 33

14 (2.45) Garg and Garg[91] proposed the model for India as below (2.46). where For Zimbabwe, Lewis [46] gave following models log log (2.47) log log log (2.48) ln (2.49) ln (2.50) ln (2.51) Ertekin and Yaldiz[48] estimated the monthly average daily global solar radiation by multiple linear regression model based on nine variables, as follows (2.52) where TS Soil Temperature, P Precipitation and E Evaporation. Chen et al., [30] presented the following models for China, sin (2.53) sin (2.54) 34

15 (2.55) sin (2.56) Nadir Ahmed Elagib, Sharief Fadul Babiker and Shamsul Haue Alvi[47], have given new empirical models for estimating the monthly averaged daily global solar radiation from commonly measured meteorological parameters such as relative humidity and temperature, at Bahrain. These models are, Ĝ (2.57) Ĝ (2.58) Ĝ (2.59) Satellite Observation Model The accurate knowledge of solar radiation at the earth s surface is of great interest in solar energy, meteorology, and many climatic applications. Ground solar irradiance data is the most important data required for characterizing the solar resource of a given site but the spatial density of such measuring meteorological stations is far low because of economic reasons. In this context, satellite-derived solar radiation estimation has become a valuable tool for quantifying the solar irradiance at ground level for a large area. Thus derived hourly values have proven to be at least as good as the accuracy of interpolation from ground stations at a distance of 25 km (Zelenka et al.[92]). Several algorithms and models have been developed during the last two decades for estimating the solar irradiance at the earth surface from 35

16 satellite images (Gautier et al.[93]; Tarpley[94]; Hay[95]). All of them can be generally grouped into physical and pure empirical or statistical models (Noia et al.[96]). Statistical models are simpler, since they do not need extensive and precise information on the composition of the atmosphere, and rely on simple statistical regression between satellite information and solar ground measurements. On the contrary, the physical models require input of the atmospheric parameters that model the solar radiation attenuation through the earth s atmosphere. On the other hand, the statistical approach needs ground solar data and such models suffer from lack of generality. Satellites observations of the earth can be grouped, according to its orbit. In polar orbiting satellites, with an orbit of about 800 km have high spatial resolution but a limited temporal coverage. The geostationary satellites, orbiting at about km, can offer a temporal resolution of up to 15 minutes and a spatial resolution of up to 1 km. Most of the methods (Shafiqur Rehman and Saleem Ghori, [97]) for deriving solar radiation from satellite information make use of geostationary satellite images. The solar radiation absorbed at the earth surface may be expressed as a function of surface albedo (ρ) and incident solar irradiation (IG). 1 (2.60) Therefore, the solar radiation on the earth surface may be expressed as: where, (2.61) I o is the extraterrestrial irradiation ETR= 1360 Wm -2 E a is the absorbed energy 36

17 IS is the radiation measured by the satellite s radiometer. Above equation is thus the fundamental equation for all the models aiming at deriving solar radiation from satellite images. The use of satellite images to estimate the solar radiation has, in fact, noticeable advantages, in particular the following are worth to mention: Satellites collect information for large extensions of ground at the same time, which allows identifying the spatial variability of solar radiation at ground level. When the relevant information is available from satellite images, they can be superimposed on the corresponding images of that area. It is possible to study the time evolution of values in an image pixel or in a certain geographic area. Satellites images allow the analysis of the solar resource in a potential emplacement that has no previous ground measurements ANN Model An Artificial Neural Network (ANN) is an interconnected structure of simple processing units. The functionality of ANN can graphically be shown to resemble that of the biological processing elements called the neurons. Neurons are organized in such a way that the network structure adapts itself to the problem being considered. The processing capabilities of this artificial network assembly are determined by the strength (weightage factor) of the connections between the processing units. Haykin[98] states that: A neural network is a massively parallel distributed processor that has a natural propensity for storing experiential 37

18 knowledge and making it available for use. It resembles the brain in two respects: 1. Knowledge is acquired by the network through a learning process; 2. Interconnection strengths between neurons, known as synaptic weights or weights, are used to store knowledge. During the last two decades, ANN has proven to be excellent tools for research, as they are able to handle non-linear interrelations (non-linear function approximation), separate data (data classification), locate hidden relations in data groups (clustering) or model natural systems (simulation). Naturally, ANN found a fertile ground in solar radiation research. A detailed survey about the applicability of ANN to various Solar Radiation topics is given below. Mohandes et al.[59] performed an investigation for modeling monthly mean daily values of global solar radiation on horizontal surfaces; they adopted a back-propagation algorithm for training several multi-layer feedforward neural networks. Data from 41 meteorological stations in Saudi Arabia were employed in this research: 31 stations were used for training the neural network models; the remaining 10 stations were used for testing the models. The input nodes of the neural networks are: latitude (in degrees), longitude (in degrees), altitude (in meters) and sunshine duration. The output of the network is the ratio of monthly mean daily value of the global solar radiation divided by extraterrestrial radiation received at the top of the atmosphere. The results from the 10 test stations indicated a relatively good agreement between the observed and predicted values. Along the same line is the research by Mohandes et al.[99], in another research for simulating monthly mean daily values of global solar radiation (the output of 38

19 the model is the ratio of monthly mean daily value of the global solar radiation divided by extraterrestrial radiation outside the atmosphere). They retained the same input parameters as measured above (latitude, longitude, altitude, sunshine duration) but they added a new one, namely, the month number. They made use of the same data sets, which were also separated into the same training and testing sub-sets. In this research, they use Radial Basis Functions (RBF) neural networks technique (Wassereman[100]; Bishop[101]) and compare its performance with that of the MLP as used in their previous study (Mohandes et al. [59]). The comparative performance of both the RBF and MLP networks was tested against the independent set of data from 10 stations by using the mean absolute percentage error as the testing statistic. The test has indicated mixed results for individual stations but, overall, RBF performs better than MLP. In a more recent endeavor, Mellit et al.[102] studied wavelet network architecture and its suitability in the prediction of daily total solar radiation. Wavelet networks are feed-forward networks using wavelets as activation functions and have been used successfully in classification and identification problems. This architecture provides a double local structure which results in an improved speed of learning. The objective of this research was to predict the value of daily total solar radiation from preceding values; in this respect, five structures were studied involving as input various combinations of total daily solar radiation values. The meteorological data that have been used in this work are the recorded solar radiation values during the period extending from 1981 to 2001 from a meteorological station in Algeria. Two datasets have been used for the training of the network. The first set includes the data for 19 years and the second dataset comprises data for one year (365 values) which is selected from the database. In both cases, the data for the 39

20 year 2001 are used for testing the network. The validation of the model was performed with data which the model had not seen before and predictions with a mean relative error of 5% were obtained. This is considered as an acceptable level for use by design engineers. 2.3 Study of drawbacks, limitations and ideas to overcome In this section, limitations on the existing empirical models (detailed in 2.2.2) are discussed Sunshine Based Models All these models contain the term S/So. Linear models, polynomial models, exponential models, trigonometric models and logarithmic models presented and as given in for different parts of the world which need the measured data of S/S o. Estimation models are developed with known values of S/S o. Sunshine duration can be recorded by an instrument called sunshine recorder. The instrument is needed to be kept on the horizontal earth surface under the sun. As the instruments are costly; measurements and recording is laborious, generally such facility is made available with primary meteorological stations of any country. For example, India has only 18 primary stations and many secondary stations. The main limitation is actual measurement by instruments. If the arrangements for measurement of sunshine duration are being made, it is possible to measure the global solar radiation with pyranometer instrumentation set-up at the station. Therefore it is necessary to look for other meteorological parameters, which are easily and economically measurable. Such parameters could be - maximum ambient temperature, minimum ambient temperature, relative humidity, cloud coverage, precipitation, wind speed etc. 40

21 2.3.2 Ambient Temperature Based Models These models, few of them are given in , generally use the data Tmax and Tmin. Quadratic, exponential and logarithmic models have been proposed by various researchers for different parts of the world. Measuring and recording ambient temperature is an easy task. In India, there are more than 451 stations recording the daily maximum and minimum temperatures along with other meteorological data. Measuring and recording ambient temperature is easy and economical; it serves as an important parameter, on which the solar radiation estimation models could be developed. Global solar radiation comprises of two components direct radiation and diffuse radiation. Maximum ambient temperature is not the indicator of maximum solar energy received and vice versa. The ambient temperature might be high due to green house effect on a cloudy sun day. Thus the temperature based models may suffer from under such condition which is a major drawback. Hence dependability on only this parameter is in question Cloud Observation Based Models Few researchers have presented the estimation models based on the cloud observations as discussed in Cloud coverage (C) is done in eight stages. For a non-cloudy clear sun day, C=0. A fully cloudy day counts C = 8. It is difficult to derive the value of C for a partially cloudy day. Hence the models based on cloud observations heavily depend on the value of C. Judgment of C calls for expertise in the weather technology field. An experienced weather specialist will be able to judge the suitable value of C, on the cloud observations. 41

22 Multiple Parameter Based Models Researchers around the world have presented the multiple parameter estimation models. Few such models are discussed in These parameters include sunshine duration, mean ambient temperature, relative humidity, longitude, latitude, mean sea level and soil temperature etc. The models with these parameters developed for specific area (region) cannot be extended to the other areas, without relaxing on estimation accuracy. Hence a need arises to choose the parameters which are constant with time and all seasons, but represent the global radiation variation on earth surface. Geographical parameters such as longitude, latitude, mean sea level are constants for a site. A model integrating these geographical parameters and few meteorological parameters such as temperature and relative humidity would be an ideal solution to estimate global solar radiation. 2.4 Model Validation and Comparison As outlined in the Handbook of Methods of Estimating Solar Radiation (1984), a dataset to be used for the validation and comparison must: be randomly selected; be independent of models being evaluated; span all seasons; be selected from various geographical regions; be sufficiently large to include a spectrum of weather. 42

23 Considering the above points in mind, generally the researchers investigate the goodness of the model based on a set of statistical parameters such as MPE, MAPE, MBE and MABE, RMSE, r and R 2. These statistical testing terms are defined in the following sections Statistical Errors In statistical literature, the performance of model is generally evaluated in terms of statistical errors, such as the mean percentage error (MPE), mean absolute percentage error (MAPE), mean bias error (MBE), mean absolute bias error (MABE) and root mean square error (RMSE). These errors are defined below (Grewal [103]): 100 (2.62) 100 (2.63) (2.64) (2.65) (2.66) where H im is the i th measured value, H ie is the i th estimated value and k is the total number of observations. In calculating the MPE values, the percentage errors in individual estimates are summed to calculate the mean. The MAPE gives the absolute value of the percentage errors. The MBE provides information on long term performance. A low MBE is always desirable. A positive value gives the 43

24 average amount error of over estimation of an individual observation, which will cancel an underestimation in a separate observation. The RMSE test gives information on the short term performance of the correlations by allowing a term by term comparison of the actual deviation between the estimated and measured values. The smaller the value of RMSE, the better is model s performance. Thus RMSE is a meaningful measure to compare the selected estimation models Correlation Coefficient, r Correlation coefficient indicates the strength and direction of a linear relationship between two random variables. In general, its statistical usage refers to departure of two variables from independence. The Pearson s correlation coefficient r, of series X and Y is r = ( x xa )( y ya ) 2 ( x x ) ( y y ) a a 2 (2.67) where, x and y are the series elements while xa and ya are the series averages. The correlation coefficient is interpreted as low, medium or high depending on the value of r, as given in the Table 2.1. Table 2.1 Interpretation of Correlation Coefficient Correlation Coefficient, r Low Medium High Positive 0.10 to to to 1.00 Negative 0.29 to to to

25 2.4.3 Coefficient of Determination, R 2 Coefficient of determination is computed as the square of correlation coefficient i.e. r 2. Once r has been estimated for any fitted model, its numeric value may be interpreted as follows. For instance, if for a given regression model r = 0.9, it means that R 2 = It may be concluded that 81% of the variation in Y has been explained by the model under discussion, leaving 19% to be explained by other factors Measure of Uncertainty Standard deviation is a widely used measurement of variability or diversity used in statistics and probability theory and serve as a measure of uncertainty. It shows how much variation or 'dispersion' there is from the 'average' (mean or expected value). A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data (x1, x2, x3, x4, x5,.) is spread out over a large range of values. The two variations of standard deviations are given below, To estimate the standard deviation from the sample of entire population of data, is given by, (2.68) To estimate the standard deviation from the entire population of the data, is given by, (2.69) The above methods of model validation and comparison are widely used to benchmark the performance of the estimate models under discussion. 45

26 discussed. In the next section, the basis of benchmark of performance of models is 2.5 Benchmark of Performance Design of solar thermal and PV conversion systems require several types of data. The main categories of data often requested by users are shown in table 2.2. It is known fact that, uncertainty in economic analysis of solar energy systems is directly proportional to the uncertainty in solar resource data. Researchers[3] show that the relative uncertainty in life cycle savings is especially sensitive in cases of high capital cost or low auxiliary energy cost. Many technologies depend on resources of global solar radiation data on a tilted surface. However, tilt conversion models generally begin with resources on a horizontal surface; the most commonly measured and modeled parameter. Keeping in the mind that the difficulties and involved costs to have the measured data of global solar radiation for large number of locations for a country, International Energy Agency (IEA) [104] report on the validation of solar radiation models declared,. There is little to recommend sunshine based models. Even though the Angstrom equation can be easily tuned to a location s climatic conditions by simple regression, it requires the existence of radiation data in the first place to produce the prediction equation. Further it concluded that, present solar radiation estimation models and measurements are rather comparable, with absolute measurement uncertainties in the order of W/m 2 (2.5% to 10.0%) in hemispherical measured global solar radiation data. 46

27 Therefore any model capable of estimating the global solar radiation with estimate errors within 10% could be acceptable. Few reported model uncertainties surveyed by different researchers around the globe are summarized in table 2.3. It is observed that the errors are in the range of 5% to 20%. Mainly these models are developed for few numbers of stations, hence the inherent property of site-specific nature is observed. The increase in errors indicates the limiting capability of the model. Hence for the model to become really global, the errors in estimates will rise. Therefore IEA states that, the challenge for the solar radiation measurements and estimation models in the 21 st century is to reduce the uncertainty in measured data, as well as develop more robust models (i.e., fewer input parameters and smaller residuals, under a wide variety of conditions). Table 2.2 Radiation data formats required by solar energy system designers and planners Type of data Time resolution Application Hemispherical (Global) Seasonal/ daily Glazing energy balance Illuminance (Sunshine) Seasonal/ daily Day-lighting Hemispherical tilt (Global) Monthly/ annual Fixed flat plate Hemispherical tracking (Global) Monthly/ annual Tracking flat plate Direct normal (Beam) Monthly/ annual Focusing/ concentrating system Monthly mean daily total (Global) Monthly/ daily Sizing and design specifications, economics Monthly mean (Global) Monthly Sizing and design specifications, economics Daily profiles (Global) Hourly System simulation, modeling and rating year hourly power (Global) Hourly System lifetime performance and economics Daily profiles power (Global) Sub-hourly System responses to clouds, etc. 47

28 Table 2.3 Summary of quoted uncertainties for various solar radiation models Radiation component Reference/ Model RMSE Comments Direct and hemispherical all sky Maxwell 1998[105] 5.2 % (direct) 3.0 % (hemi) Annual mean daily total; 33 US measurement data Direct, clear sky Gueymard, 1995[106] ±10.0% Mean of 17 best of 22 models for Canada Direct from hemispherical, all sky Perez 1992[107] 8.5% Five models; 18 US and European sites All sky hemispherical Skartvei et al. 1997[108] 11.0% Five models; 4 European sites All sky hemispherical Gul et al. 1998[16] 8.0% Three models; 12 UK stations All sky hemispherical from satellite Zelenka et al. 1999[92] 20% 31 Swiss, 12 US measurement stations 2.6 Layout of the Thesis Chapter 1 presents the motivation and background behind the present research work detailing the global energy concerns and discussing diverse efforts being taken towards solution. Solar energy option and available assessment methodologies are studied in short. The limitations and drawbacks of existing methods are briefly discussed. The chapter ends with the concept statement of the present thesis. In chapter 2, the detailed theory of various methods of assessment of solar radiation is discussed. The radiative transfer model explains how the extra-terrestrial radiation is computed. Typical models based on sunshine duration, temperature, cloud observations and multi-parameter inputs are detailed in the empirical models section. Discussions on how the solar radiation is estimated using satellite data is done. How artificial neural 48

29 network (ANN) technique is used for assessing the solar radiation is discussed. The detailed study of drawbacks and limitations of the above four methodologies is made, indicating the ideas to overcome these drawbacks. Methods of model validation and comparison and benchmarking the performance of estimation models are detailed in brief. Chapter 3 covers the study and analysis of the existing empirical models. Two existing models are presented with the results, tests against site variations and establishing their limiting capabilities. The limiting capabilities of these existing models lead to the necessity of a global or site-independent model for estimating the solar radiation. In chapter 4, new models are proposed, with several possible variants. These models are implemented and studied for their effectiveness. Identifying the competent model(s) among various proposed models is the objective of this chapter. The chapter concludes by giving the validation analysis of models which are identified. In chapter 5, the proposed models are evaluated and revalidated with artificial neural network (ANN) model and the comparative study of proposed numerical models and ANN models is carried out. Salient observations are recorded in the chapter 6 as conclusions. This chapter also discusses the scope for research that could be carried out further. 49