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Research Papers

# Improved Accuracy Models For Hourly Diffuse Solar Radiation

[+] Author and Article Information
T. Muneer

Applied Energy Group, School of Engineering, Napier University, 10 Colinton Road, Edinburgh, United Kingdomt.muneer@napier.ac.uk

S. Munawwar

Applied Energy Group, School of Engineering, Napier University, 10 Colinton Road, Edinburgh, United Kingdoms.munawwar@napier.ac.uk

J. Sol. Energy Eng 128(1), 104-117 (Jan 31, 2005) (14 pages) doi:10.1115/1.2148972 History: Received June 17, 2004; Revised January 31, 2005

## Abstract

Solar energy applications require readily available, site-oriented, and long-term solar data. However, the frequent unavailability of diffuse irradiation, in contrast to its need, has led to the evolution of various regression models to predict it from the more commonly available data. Estimating the diffuse component from global radiation is one such technique. The present work focuses on improvement in the accuracy of the models for predicting horizontal diffuse irradiation using hourly solar radiation database from nine sites across the globe. The influence of sunshine fraction, cloud cover, and air mass on estimation of diffuse radiation is investigated. Inclusion of these along with hourly clearness index, leads to the development of a series of models for each site. Estimated values of hourly diffuse radiation are compared with measured values in terms of error statistics and indicators like, $R2$, mean bias deviation, root mean square deviation, skewness, and kurtosis. A new method called “the accuracy score system” is devised to assess the effect on accuracy with subsequent addition of each parameter and increase in complexity of equation. After an extensive evaluation procedure, extricate but adequate models are recommended as optimum for each of the nine sites. These models were found to be site dependent but the model types were fairly consistent for neighboring stations or locations with similar climates. Also, this study reveals a significant improvement from the conventional $k-kt$ regression models to the presently proposed models.

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Copyright © 2006 by American Society of Mechanical Engineers
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## Figures

Figure 1

Geographical location of the sites under study

Figure 2

k-kt regression analysis for Bracknell quality controlled database. Dashed curve represents linear fit (R2=0.855), thick solid line is for quadratic polynomial fit (R2=0.893), and thin solid line for cubic polynomial fit (R2=0.903).

Figure 3

Scatter plot of crude data for Fukuoka with the defining curves (k¯±2.0σk) enveloping only the quality data (91.2% of the total data)

Figure 4

k-kt plot of quality-controlled Chennai database: (a) prior to diffuse radiation correction, (b) postdiffuse radiation correction

Figure 5

Error histograms of calculated diffuse radiation of selectively chosen eight models for Mumbai

Figure 6

Error histograms of calculated diffuse radiation of selectively chosen eight models for Gerona

Figure 7

Evaluation of given models by means of presently developed accuracy scoring system. (a) India, (b) Japan, (c) Spain, (d) UK.

Figure 8

Calculated vs measured k-kt plot for Bracknell. Light- and dark-colored data points represent actual and calculated values, respectively. Solid black curve is the locus of quadratic k-kt regression.

Figure 9

The above plots show a significant improvement in the estimation of diffuse radiation from the basic k-kt model through an intermediate (k-kt, SF) to the eventual models selected as optimum. (a) Pune, (b) Fukuoka, (c) Gerona, (d) Bracknell.

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