Comparison of Different Models for Estimation of Global Solar Radiation in Jharkhand ( India ) Region

In this paper with the help of different empirical models we have estimated the value of monthly average global solar irradiation for Ranchi (23.3500 ̊N, 85.3300 ̊E), a tropical location. The values of monthly average global solar radiation are calculated using the regression constants in the models (both linear and quadratic) suggested by: AngstromPrescott, Rietveld, Ogleman, Akinoglu, Glover, Gopinathan and Sangeeta et al. All the regression models are investigated, validated and compared. On comparison it was observed that the quadratic models are overall more accurate for calculating the Global Solar Radiation for the Jharkhand region, but the Angstrom-Prescott model as well shows better variance for most of the months. The calculated data from these models is compared with the data provided by MNRE [1]. GSR values are important parameters for designing any Solar Power Systems as the whole solar power generation is directly proportional to the amount of global solar radiation. The calculated and measured data are simulated using MATLAB.


Introduction
Solar energy technologies offer a clean, renewable and domestic energy source and are essential components of a sustainable energy future.The amount of global solar radiation and its temporal distribution are the primary variable for the use of solar energy.Development of a solar energy research program must always start with a study of solar radiation data at a site or region of interest [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].Unfortunately, the measurement of these parameters is made only in a few meteorological stations, especially in developing countries, for both historical and economical reasons.For places where it is not directly measured, solar radiation can be estimated by using models and empirical correlations.Therefore, there have been numerous investigations on the examination of the relationship between global radiation and sunshine duration for which data are available in a greater number of meteorological stations [2].However, the computational complexity and associated time and input data requirements discourage many researchers and users from basing their calculations of energy, irradiation on models which have strong links to the fundamental radiative equations rather they are encouraged by simplicity and expediency of cal-culations using empirically based methods [3].It can be observed from Figure 1 shows that the solar energy potential of India is one of the highest in the world as the tropic of cancer passes through it [4].But the true potential is yet to be utilized because of lack of data.It is worth pointing that regression models are used for prediction or estimation, data description, parameter estimation and control.

Model of Analysis (Table 1)
To calculate the monthly mean daily radiation on a horizontal surface in absence of atmosphere H o a number of approaches had been made here is based on Duffi and Beckman [5].The value of H o is thus calculated as shown in Equation ( 1 where

Angstrom-Prescott Model
Among the different empirical models, the most popular is the regression equation of the Angstrom [6,7] type.The regression constant a and b depend on φ (latitude) and seasonal variation.

Rietveld Model
Rietveld [8] examined several published values of a and b and noted that a is related linearly and b hyperbolically to the mean value of S such that this equation is believed to be applicable anywhere in the world and yields superior results for cloudy conditions, for S < 0.4.

Glover Model
Glover and McCulloch [11] attempted to introduce latitude dependency to one of the Angstrom-Prescott coefficients and presented the following

Gopinathan Model
Gopinathan [12] proposed a and b are related to three parameters, the latitude, the elevation and the sunshine hours. 

Comparison of Models
The various models discussed above are used to calculate the extra-terrestrial radiation and the Global Solar Radiation.The calculated values are show in Table 2.In Figure 2 and Table 3, the comparison of different linear models with measured data provided by MNRE for Ranchi for the year 2008 is shown.In Figure 3, the comparison of quadratic models with measured data is shown.In Figure 4, the variation of H g (GSR) in all proposed models is compared and it is observed that the quadratic models have more accuracy than the linear models with the exception of Angstrom-Prescott and Riveted for the months of June-October.

Conclusion
When all the values of H g for different linear models are compared in Figure 2, it is seen that the Angstrom-Prescott model shows more accuracy than rest of the linear models, while quadratic models are compared in       models.Though it can be seen that Rietveld model show greater accuracy during June-October period i.e. during the monsoon.Thus observing all the factors Ogleman, Akinoglu and Angstrom-Prescott models are proposed for measuring the Global Solar Radiation for the Jharkhand region.Thus we can conclude that the quadratic models are more accurate than the linear models for calculating the Global Solar Radiation in Jharkhand region.

Fig- ure 3 ;
it is observed that Ogleman and Akinoglu models have shown more accuracy with respect to other linear

Figure 2 .
Figure 2. Comparison of different models with measured data.

Figure 3 .
Figure 3.Comparison of quadratic models with measured data.

Figure 4 .
Figure 4. Comparison of all models with measured data. ) et al. proposed the use of a correlation which relates the global solar radiation to S in a quadratic form as