A new neural network model for evaluating the performance of various hourly slope irradiation models: Implementation for the region of Athens

The present study is divided into two parts. The first part deals with the comparison of various hourly slope irradiation models, found in the literature, and the selection of the most accurate for the region of Athens. In the second part the prediction of global solar irradiance on inclined surfaces is performed, based on neural network techniques.The models tested are classified as isotropic (Liu and Jordan, Koronakis, Jimenez and Castro, Badescu, Tian) and anisotropic (Bugler, Temps and Coulson, Klucher, Ma and Iqbal, Reindl) based on the treatment of diffuse irradiance. For the aforementioned models, a qualitative comparison, based on diagrams, was carried out, and several statistical indices were calculated (coefficient of determination R², mean bias error MBE, relative mean bias error MBE/A(%), root mean square error RMSE, relative root mean square error RMSE/A(%),statistical index t-stat), in order to select the optimal.The isotropic models of “Tian” and “Badescu” show the best accordance to the recorded values. The anisotropic model of “Ma&Iqbal” and the pseudo-isotropic model of “Jimenez&Castro”, show poor performance compared to other models. Finally, a neural network model is developed, which predicts the global solar irradiance on a tilted surface, using as input data the total solar irradiance on a horizontal surface, the extraterrestrial radiation, the solar zenith angle and the solar incidence angle on a tilted plane. The comparison with the aforementioned models has shown that the neural network model, predicts more realistically the total solar irradiance on a tilted surface, as it performs better in regions where the other models show underestimation or overestimation in their calculations.     

Impact of solar radiation variation on the optimal tilted angle for fixed grid-connected PV array—case study in Beijing

A key design parameter for fixed grid-connected photovoltaic (PV) arrays, the optimal tilt angle, does not only depend on the geographic location but is also directly affected by atmospheric conditions. In this paper, long-term variations of solar radiation (i.e. global solar irradiance, direct horizontal irradiance, diffuse irradiance, and ratios of direct and diffuse irradiance) in Beijing are considered to determine their effect on the optimal tilt angle for a fixed grid-connected PV array. We found that there is a declining trend in global solar irradiance over the past 55 years, mainly caused by the decreased direct horizontal irradiance. In contrast, the decline of diffuse irradiance is not obvious, leading to a considerable decrease in the direct irradiance ratio and consequent increase in the diffuse irradiation ratio. Likewise, the long-term optimal tilt angle shows a downward trend. Compared with the optimum in the 1960s, the optimal tilt angle has decreased by 2° in 2011–2015. These results suggest that the declining trend in the optimal tilt angle is mainly caused by the decrease in direct irradiance ratio, which is highly related to atmospheric conditions. Therefore, the design and construction of PV power stations must consider the variations of atmospheric conditions and solar irradiance to determine the optimal tilt angle.     

Optimum tilt angle and orientation for solar collector in Brunei Darussalam

One of the important parameters that affects the performance of a solar collector is its tilt angle with the horizontal. This is due to the fact that the variation of tilt angle changes the amount of solar radiation reaching the collector surface. A mathematical model was used for estimating the total (global) solar radiation on a tilted surface, and to determine the optimum tilt angle and orientation (surface azimuth angle) for the solar collector in Brunei Darussalam on a daily basis, as well as for a specific period. The optimum angle was computed by searching for the values for which the total radiation on the collector surface is a maximum for a particular day or a specific period. The results reveal that changing the tilt angle 12 times in a year (i.e. using the monthly-averaged optimum tilt angle) maintains approximately the total amount of solar radiation near the maximum value that is found by changing the tilt angle daily to its optimum value. This achieves a yearly gain in solar radiation of 5% more than the case of a solar collector fixed on a horizontal surface.     

The optimisation of the angle of inclination of a solar collector to maximise the incident solar radiation

Irradiation data, recorded on vertical surfaces facing north, south, east and west and on a horizontal surface every ten minutes during daylight hours from January–December 1992 in Valencia, Spain, have been compared with estimated solar irradiation from inclined-surface models. Results show that Hays model most accurately reproduces the variation in irradiation on all vertical surfaces.Hays model has been used to find the hourly variation in the optimum tilt angle for a South-facing solar collector in Valencia, Spain, and also to calculate the yearly average of this angle. This method has been compared with the results provided by another model that uses average monthly values of daily irradiation derived from the same experimental data, to calculate average monthly values of the optimum tilt angle. The results show that the method involving monthly averages is more accurate and easier to work with.     

Solar radiation on tilted south oriented surfaces: validation of transfer-models

Three transfer-models in use for estimating solar radiation on tilted surfaces are tested. A 12 year series of hourly global, diffuse, and reflected solar irradiation measured with horizontal pyranometers as well as hourly global solar irradiation measured with tilted south oriented pyranometers is available. One model uses daily irradiation, the other two use hourly irradiation. The models converting hourly solar irradiation on a horizontal surface to a tilted surface yield better results than that using daily irradiation. The best results are gained if pairs of hourly global and diffuse solar irradiation are available. The root mean square errors exceed 10% only if the sky is covered by more than 85% with clouds or if the solar elevation angle is less than 10°.     

Determining seasonal optimum tilt angles,solar radiations on variously oriented,single and double axis tracking surfaces at Dhaka

The performance of a solar radiation conversion system is affected by its orientation and tilt angle with the horizontal plane. This is because both of these parameters change the amount of solar energy received by the surface of solar system. Three mathematical models- the Isotropic, the Klucher and the Perez model for the point source with parameters optimized for a variety of climatic conditions have been employed to determine hourly and seasonal optimum tilt angles. Theoretical optimum tilt angles (10° for Mar–Sep and 40° for Oct–Feb) were compared with measured data for Nov 2007 to Oct 2008 at Dhaka. The anisotropic Perez model showed least rmse of 0.09 for monthly tilt factor estimation. This model was also used for theoretical study of solar radiation on variously oriented, single axis and double axis tracking surfaces.     

Study of models for predicting the diffuse irradiance on inclined surfaces

Solar irradiance data on various inclined surfaces at different orientations are important information for active solar-system analyses and passive energy-efficient building designs. In many parts of the world, however, the basic solar irradiance data for the surfaces of interest are not always readily available. Traditionally, different mathematical models have been developed to predict the solar irradiance on various inclined surfaces using “horizontal” data. Alternatively, the diffuse irradiance of a sloping plane can be calculated by integrating the radiance distribution generated with a sky radiance model. This paper presents the evaluation of two slope irradiance models, namely, the Perez point-source model (PEREZSIM) and the Muneer model (MUNEERSIM), and two sky-distribution models, namely, the Perez all-weather model (PEREZSDM) and the Kittler standard-sky model (KITTLERSDM). Three-year (1999–2001) measured average hourly sky radiance and horizontal sky diffuse irradiance data were used for the model assessment. Statistical results showed that all four models can accurately predict the solar irradiance of a 22.3° (latitude angle of Hong Kong) inclined south-oriented surface, indicating the good predictive ability for modelling an inclined surface with a small tilted angle. In general, the KITTLERSDM and PEREZSIM show the best predictions for vertical solar irradiance at this location, followed by the PEREZSDM, then the MUNEERSIM.     

An assessment of a revised Olmo et al. model to predict solar global radiation on a tilted surface at Beer Sheva,Israel

A model to convert horizontal solar global radiation to that on a tilted surface is presented. It is based upon a relatively simple model proposed by [Olmo FJ, Vida J, Foyo I, Castro-Diez Y, Alados-Arboledas L. Prediction of global irradiance on inclined surfaces from horizontal global irradiance. Energy 24 (1999) 689–704]., which requires only measurements of horizontal solar radiation but was found to produce significant errors when tested with data from another site. The present model assumes the availability of databases for at least two of the three solar radiation types, viz., global, beam and diffuse. The horizontal global radiation is converted to that on a tilted surface by applying the Olmo model to the diffuse component, whereas the beam component is converted by using the geometrical relationship between the two surfaces. The original Olmo anisotropic radiation correction factor is now assumed to be a function of sky conditions. The solar radiation databases were converted to subsets corresponding to clear, partially cloudy and cloudy sky based upon clearness index values. The three anisotropic correction factors were determined by fitting to a 12-months database. The present model was then tested by applying it to a second database consisting of 24-months not involved in the model development. It was found to give better results than three highly regarded more complex models.     

Investigating different diffuse solar radiation models to analyse solar radiation on inclined surfaces in Oman

In this paper, a detailed analysis of the solar radiation on horizontal and tilted surfaces for six locations in Oman is presented. The locations are (from North to South): Majis/Sohar, Sur, Fahud, Masira, Marmul, and Salalah. These locations spread over Oman and cover different types of landscape. The method is validated through the use of measured data. The effect of tilt angle and orientation on the incident solar radiation is presented along with optimum surface tilt angles and directions for maximum solar radiation collection in these six locations. The solar radiation models used in this paper show good agreement with measured data. The results presented in this paper are extremely useful for quick estimation of solar radiation for calculations of buildings’ cooling load and solar collector system performance. This can be easily extended for other locations with similar landscapes and geographical conditions.     

General models for optimum tilt angles of solar panels: Turkey case study

This paper deals with finding the optimum tilt angle of solar panels for solar energy applications. The optimization of tilt angles was performed using solar radiation data measured for eight big provinces in Turkey. The optimum angle for tilted surfaces varying from 0° to 90° in steps of 1° was calculated by searching for the values of which the daily total solar radiation was at a maximum for a specific period. It was found that the optimum tilt angle changed between 0° and 65° throughout the year in Turkey. It was seen that the optimum tilt angle reached a minimum of 0° in June and July and, the monthly average daily total radiation at this angle was generally at a maximum. In addition, the optimum tilt angle increased during the winter months and reached a maximum in December in all provinces. Likewise, general correlations were developed to estimate the optimum tilt angle of solar collectors used in Turkey and their accuracies were compared on the basis of statistical error tests of Mean Bias Error (MBE), Root Mean Square Error (RMSE), t-statistic (t-stat) and correlation coefficient (r).     

Determining optimum tilt angles and orientations of photovoltaic panels in Sanliurfa, Turkey

The performance of a photovoltaic (PV) panel is affected by its orientation and its tilt angle with the horizontal plane. This is because both of these parameters change the amount of solar energy received by the surface of the PV panel. A mathematical model was used to estimate the total solar radiation on the tilted PV surface, and to determine optimum tilt angles for a PV panel installed in Sanliurfa, Turkey. The optimum tilt angles were determined by searching for the values of angles for which the total radiation on the PV surface was maximum for the period studied. The study also investigated the effect of two-axis solar tracking on energy gain compared to a fixed PV panel. This study determined that the monthly optimum tilt angle for a PV panel changes throughout the year with its minimum value as 13° in June and maximum value as 61° in December. The results showed that the gains in the amount of solar radiation throughout the year received by the PV panel mounted at monthly optimum tilt angles with respect to seasonal optimum angles and tilt angel equal to latitude were 1.1% and 3.9%, respectively. Furthermore, daily average of 29.3% gain in total solar radiation results in an daily average of 34.6% gain in generated power with two-axis solar tracking compared to a south facing PV panel fixed at 14° tilt angle on a particular day in July in Sanliurfa, Turkey.     

Model evaluation and optimum collector slope for a tropical country

Various models proposed in the literature, viz. the Beam method, proposed by Morse & Czarnecki; two methods proposed by Liu & Jordan, using hourly values and average daily values of solar radiation: and Klucher's method are compared in this paper using measured hourly values of global and diffuse radiation on a horizontal surface and the total radiation on a tilted surface. It was observed that the model proposed by Klucher estimates the radiation more consistently with the experimental observations for clear as well as cloudy sky conditions.

This method was used for predicting the year round radiation availability on (i) a fixed collector inclined at an optimum tilt, (ii) a partially tracking collector in which the slope is fixed but following the sun's azimuth angle, and (iii) a fully tracking collector. In this analysis, measured values of hourly global and diffuse solar radiation on a horizontal plane for four widely separated Indian stations, viz. Delhi (28°38′N), Poona (18°29′N), Calcutta (22°36′N), and Madras (13°8′N) as per India Meteorological Department classification for climatic analysis, have been used.

With the model proposed, the radiation availability on different slopes for all the twelve months of the year for a fixed and partially tracking collector have been evaluated and optimum tilts for various seasons of a year for different solar energy applications for all the four Indian stations have been determined. For a typical winter month at New Delhi in the semi-arid zone of India, a fixed collector, a partially tracking collector and a fully tracking collector receive 60, 80 and 95% more radiation compared to that received on a horizontal plane respectively. Another observation is that the variation of the insolation received on inclined surfaces is not at all sensitive to the angle of tilt in the neighbourhood of the optimum angle of operation.     

PV-GIS: a web-based solar radiation database for the calculation of PV potential in Europe

Solar radiation is a key factor determining electricity produced by photovoltaic (PV) systems. This paper presents a solar radiation database of Europe developed in the geographical information system, and three interactive web applications providing an access to it. The database includes monthly and yearly average values of the global irradiation on horizontal and inclined surfaces, as well as climatic parameters needed for an assessment of the potential PV electricity generation (Linke atmospheric turbidity, the ratio of diffuse to global irradiation, an optimum inclination angle of modules to maximize energy yield). In the first web application, a user may browse radiation maps and query irradiation incident on a PV module for different inclination angles. The second application simulates daily profiles of irradiance for a chosen month and module inclination and orientation. The third web application estimates electricity generation for a chosen PV configuration. It also calculates optimal inclination and orientation of a PV module for a given location. The database and the applications are accessible at http://re.jrc.cec.ev.int/pvgis/pv/imaps/imaps.htm.     

A study on the intercepted insolation as a function of slope and azimuth of the surface

Monthly average daily global radiation on surfaces tilted towards the equator and also inclined at various azimuth angels are estimated for three locations in the Southern African region from reported global and diffuse radiation on a horizontal surface. The anisotropic model suggested by Hay is used in obtaining daily radiation at various slopes and orientations. Total annual radiation data are also computed for various tilt and azimuth angles and optimum tilt and azimuth angels corresponding to maximum insolation are obtained for winter, summer and annual collection. The optimum tilt and orientation reported here show some variation from those reported earlier by other investigators and the results are discussed.     

A new methodology to optimise solar energy extraction under cloudy conditions

The orientation and tilt position of the solar panel affect the amount of solar radiation that falls on the panel surface over the course of the day and indeed the year. The choice of tilt angle for a solar panel is fundamental to its efficient operation because incorrectly positioning the solar panel leads to an unnecessary loss in potential power. In the past, much work has been done by authors to determine the optimum tilt angle by applying existing models to their locations. This approach has been successful in climates with the most favourable solar potential, where greater than 90 percent of the solar radiation arrives as direct beam radiation. The accuracy of these models in these locations has been attributed to the low presence of cloud cover and the consequential dominance of the beam radiation portion of the global radiation. Countries located above 45°N however, (Northern Europe), require a different approach to optimising the tilt angle as they receive the least amount of direct radiation with approximately half arriving as diffuse radiation, due to frequent, heavy cloud cover. This paper reviews existing methods and describes a means of predicting the solar radiation in a frequently overcast climate and proposes a method for choosing the optimum tilt angle in such a climate. The effect of different load profiles on the optimum tilt angle is also investigated. The solar radiation model is then used to predict the solar radiation for Cairo, Egypt to show that the model has a global application and is not limited to frequently overcast climates.     

Measurements and models for total solar irradiance on inclined surface in Athens, Greece

This article presents a comparative assessment of tilted irradiation models, using hourly measurements of total solar irradiation on a surface tilted 50 degrees and oriented south in Athens. Detailed measurements on inclined surfaces are carried out at the National Observatory of Athens and are unique in Greece. Twelve sky diffuse submodels are used with four albedo submodels to estimate the global irradiation on the tilted surface from data on the horizontal plane. Root mean square errors (rmse) and mean bias errors (mbe) are used to determine the intrinsic performance of each diffuse tilt/albedo submodel combination. GUEYMARD, HAY, REINDL, and SKARTVEIT-OLSETH diffuse tilt submodels are found to have the best overall performances, in conjunction with either one of three albedo submodels (constant albedo, seasonally varying albedo, and anisotropic albedo). The PEREZ model's performance was below expectations, probably due to the particular atmospheric environment of Athens. The anisotropic and seasonally varying albedo submodels do not improve the performance of the four better diffuse tilt models (compared to their performance using an albedo fixed at 0.2) for the moderately tilted surface investigated in this article.     

Estimation of the hourly solar irradiance on a horizontal surface

Experimental measurements for the hourly solar irradiance on a horizontal surface are carried out in Makkah and Jeddah, Saudi Arabia. A semiempirical formula to predict the hourly global solar irradiance is obtained using standard least squares fitting technique. The obtained formula coincides extremely well with experimental data recorded in Jeddah, Makkah, Sanaa (Yemen) and Hong Kong for various months of the year.     

Global,direct and diffuse solar radiation on horizontal and tilted surfaces in Jeddah,Saudi Arabia

The measured data of global and diffuse solar radiation on a horizontal surface, the number of bright sunshine hours, mean daily ambient temperature, maximum and minimum ambient temperatures, relative humidity and amount of cloud cover for Jeddah (lat. 21°42′37′′N, long. 39°11′12′′E), Saudi Arabia, during the period (1996–2007) are analyzed. The monthly averages of daily values for these meteorological variables have been calculated. The data are then divided into two sets. The sub-data set I (1996–2004) are employed to develop empirical correlations between the monthly average of daily global solar radiation fraction (H/H₀) and the various weather parameters. The sub-data set II (2005–2007) are then used to evaluate the derived correlations. Furthermore, the total solar radiation on horizontal surfaces is separated into the beam and diffuses components. Empirical correlations for estimating the diffuse solar radiation incident on horizontal surfaces have been proposed. The total solar radiation incident on a tilted surface facing south H_t with different tilt angles is then calculated using both Liu and Jordan isotropic model and Klucher’s anisotropic model. It is inferred that the isotropic model is able to estimate H_t more accurate than the anisotropic one. At the optimum tilt angle, the maximum value of H_t is obtained as ∼36 (MJ/m² day) during January. Comparisons with 22 years average data of NASA SSE Model showed that the proposed correlations are able to predict the total annual energy on horizontal and tilted surfaces in Jeddah with a reasonable accuracy. It is also found that at Jeddah, the solar energy devices have to be tilted to face south with a tilt angle equals the latitude of the place in order to achieve the best performance all year round.     

Optimum Tilt Angle for Solar Collectors

A solar collector is required to absorb solar radiation and transfer the absorbed energy into a heat transfer fluid with a minimum of heat loss. In assessing the performance of a collector, it is therefore important not only to determine its ability to absorb solar radiation but also to characterize its heat losses. The ability of a collector to absorb solar radiation is largely determined by its optical and geometric properties. One of the important parameters that affect the performance of a solar collector is its tilt angle with the horizontal. This is due to the fact that the variation in tilt angle affects the amount of solar radiation reaching the collector surface. In this study, a mathematical model is used to estimate the total (global) solar radiation on a tilted surface and to determine the optimum tilt angle for a solar collector in Izmir, Turkey. Total solar radiation on the solar collector surface with an optimum tilt angle is computed for specific periods. It is found that the optimum tilt angle changes between 0° (June) and 61° (December) throughout the year. In winter (December, January, and February) the tilt should be 55.7°, in spring (March, April, and May) 18.3°, in summer (June, July, and August) 4.3°, and in autumn (September, October, and November) 43°. The yearly average of this value was found to be 30.3° and this would be the optimum fixed tilt throughout the year.