A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Shukla, K. N.; Rangnekar, Saroj; Sudhakar, K. Article Comparative study of isotropic and anisotropic sky models to estimate solar radiation incident on tilted surface: A case study for Bhopal, India Energy Reports Provided in Cooperation with: Elsevier Suggested Citation: Shukla, K. N.; Rangnekar, Saroj; Sudhakar, K. (2015) : Comparative study of isotropic and anisotropic sky models to estimate solar radiation incident on tilted surface: A case study for Bhopal, India, Energy Reports, ISSN 2352-4847, Elsevier, Amsterdam, Vol. 1, pp. 96-103, http://dx.doi.org/10.1016/j.egyr.2015.03.003 This Version is available at: http://hdl.handle.net/10419/187817 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. 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Sudhakar b a Electrical & Electronics, Lakshmi Narain College of Technology, Bhopal-462021, India b Department of Energy, Maulana Azad National Institute of Technology, Bhopal-462051, India article info a b s t r a c t Article history: The purpose of this study is to compare the different empirical models used for estimation of solar Received 15 January 2015 radiation on tilted surface. For this, three isotropic and same number of anisotropic sky models were Received in revised form employed by using average monthly mean value of solar radiation on daily basis at Bhopal, local climatic 4 March 2015 condition, located in central region of India. The tilt angle was fixed at 23.26, N (latitude of Bhopal). The Accepted 22 March 2015 models results were compared with ground measured data from one sample statistical test. It was found Available online 21 April 2015 that Hays and Davis model (HD) estimated the highest amount of incident solar radiation in the whole year whereas Badescu model (BA) established the lowest among all isotropic as well as anisotropic models. Keywords: Isotropic Finally, Badescu model (BA) was preferred for estimation of solar radiation incident on tilted surface with Anisotropic smallest statistical errors among all models and closed agreement with measured data. Empirical models ' 2015 The Authors. Published by Elsevier Ltd. Solar irradiances This is an open access article under the CC BY-NC-ND license Tilted surface (http://creativecommons.org/licenses/by-nc-nd/4.0/). Statistical test 1. Introduction parameters, such as sunshine duration, cloud cover, humidity, maximum and minimum ambient temperatures, and wind speed Solar radiation data are the best source of information for esti- (El-Sebaii et al., 2010). mating average incident radiation necessary for proper design and Wu et al.(2007) used the metrological data from 1994 to 2005 the assessment of solar energy conversion systems (Sabziparvar, of Nanchang station (China) to predict daily global solar radiation 2008). There are several forms of solar radiation data, which could from sunshine hours, air temperature, total precipitation and dew be used for a variety of purposes in the design and development point. Wu et al.(2007) and Bulut and Buyukalaca(2007) recently of solar energy systems (Jakhrani et al., 2012). Daily data is of- proposed a simple model for estimation of monthly average of ten available and hourly radiation can be estimated from available daily global solar radiation on horizontal surface for 68 provinces daily data. The availability of more comprehensive solar radiation of Turkey with a high accuracy (Bulut and Buyukalaca, 2007). Janjai data is invaluable for the design and evaluation of solar-based con- et al.(2009) proposed a model for calculating the monthly average version systems. Particularly, the basic solar radiation data for the hourly global radiation in the tropics with high aerosol load using surfaces of interests are not readily available in most developing satellite data. This model was employed to generate hourly solar countries (Li et al., 2008; El-Sebaii et al., 2010). Because of not being radiation maps in Thailand (Janjai et al., 2009). able to afford the measuring equipments and techniques involved. It is rather important to determine the beam and diffuse components of total radiation incident on a horizontal surface. Therefore, it is necessary to develop methods to estimate the solar Once these components are determined, they can be transposed radiation on the basis of the more readily available meteorological over tilted surfaces, and hence, the short as well as the long term data (El-Sebaii et al., 2010). performances of tilted flat plate collectors, photovoltaic modules Several models have been developed to estimate the amount of and other solar devices can be estimated. Many authors have global solar radiation on horizontal surfaces using various climatic presented empirical correlations to estimate the monthly average daily diffuse radiation on a horizontal surface. El-Sebaii and Trabea (2003) proposed correlations for estimating horizontal diffuse ∗ Corresponding author. radiation in Egypt by correlating .Hd=Hg / and .Hd=Ho/ with KT and E-mail address: [email protected] (K.N. Shukla). .S=Smax/ (El-Sebaii and Trabea, 2003). Solanki and Sangani(2008) http://dx.doi.org/10.1016/j.egyr.2015.03.003 2352-4847/' 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4. 0/). K.N. Shukla et al. / Energy Reports 1 (2015) 96–103 97 proposed a new method which may be used for estimating Hb Nomenclature on the basis of calculation of the elevation angle constant (") for a given location and time (Solanki and Sangani, 2008). Ozan and HN : Monthly Average daily extraterrestrial solar radia- o Tuncay(2009) proposed artificial neural-network using satellite 2 tion (kWh=m -day) data were also used to estimate monthly mean daily average of 2 ISC: Solar constant 1:367 kW=m horizontal direct and diffuse radiation in different cities of Turkey N: Day of the year (Ozan and Tuncay, 2009). HN : Monthly average daily global solar radiation g Furthermore, meteorological stations usually measure solar 2 (kWh=m -day) global and diffuse radiation intensities on horizontal surfaces. a; b: Angstrom constants (for Bhopal a D 0:26, b D 0:05) Measured solar radiation data on tilted surfaces are rarely s: Monthly average daily hours of bright sunshine available. Consequently, the solar radiation incident on a tilted (hours) surface must be determined by converting the solar radiation Smax: Monthly average of the maximum possible daily intensities measured on a horizontal surface to that incident on hours (day length) of bright sunshine the tilted surface of interest in order to design the system size and N 2 Hd: Monthly average daily defused radiation (kWh=m - estimate its long term performance. day) It is generally known that in the northern hemisphere, the KT : Monthly average clearness index optimum collector orientation in south facing (γ D 0) and N HT : Total incident solar radiation on tilted surface the optimum tilt depend upon the latitude and the day of the (kWh=m2-day) year. In winter month, The optimum tilt is greater (usually N 2 HT ;b: Beam radiation on tilted surface (kWh=m -day) latitude C 15) whilst in summer months the optimum tilt is less N 2 HT ;d: Defused radiation on tilted surface (kWh=m -day) (usually latitude − 15). There are many papers in the literature N HT ;r : Ground reflected radiation on tilted surface which make different recommendations for the optimum tilt based (kWh=m2-day) only on the latitude Sudhakar et al.(2013). In practice the collector N Hb: Monthly average daily beam radiation on horizontal plate is usually oriented south facing and latitudinal fixed tilt angle surface (kWh=m2-day) which is set to maximize the average energy collected over a year N Rb: View factor for beam radiation (Ahmad and Tiwari, 2009). N Rr : View factor for ground reflected radiation Total radiation incident on a tilted surface consists of three com- N Hd;iso: Isotropic diffused radiation ponents: beam radiation, diffuse radiation and ground reflected ra- N Hd;cs: Circumsolar component of diffused radiation diation. The beam radiation on a tilted surface can be computed by N Hd;hz: Horizon brightening component of diffused solar the relatively simple geometrical relationship between the hori- radiation zontal and tilted surfaces. The ground reflected radiation can be N estimated with good accuracy with the aid of an isotropic model Hgm: Metrological ground measured global solar radia- tion at horizontal surfaces (kWh=m2-day) using a simple algorithm. This is not the case regarding the diffuse N component, since diffuse radiation has no define or (singular) angle Hgmt: Metrological ground measured tilted global solar of incidence on a horizontal surface.