Sky conditions at Ilorin as characterized by clearness index and relative sunshine

Clearness index (K_T) and relative sunshine (S) are used to characterize the sky conditions at Ilorin, Nigeria (latitude: 8°32′N, longitude: 4°34′E, elevation: 375 m), a tropical location. Daily analysis shows that the majority of the days are relatively cloudy with hardly any very clear or overcast days. Based on monthly averaged K_T, the monthly variations of cumulative frequency of K_T, f, and prevalent climatic conditions, the annual sky conditions have been classified into six patterns: three patterns each for the two broad seasons, dry and rainy. The trend in the seasonal variation of S lends further credence to this six seasonal pattern. Determined cumulative frequency curves further confirm the assertion that Liu and Jordan’s generalized cumulative distribution curves (CDC) are not applicable to tropical locations hence available design procedures based on these curves should be reconsidered [Liu, B. Y. U and Jordan, R. C. (1960). The Inter-relationaship and characteristic distribution of direct, diffuse and total solar radiation. Solar Energy 4, 1–19]. An empirical expression relating monthly maximum clearness index (K_max) and the monthly average clearness index (K_T) is presented and recommended for tropical locations. Comparative analysis shows that a similar expression by Saunier et al. is also appropriate to this location while that of Hollands and Huget is quite inadequate. [Saunier G. Y., Reddy T. A. and Kumar S. (1987). On monthly probability distribution function of daily global irradiation values appropriate for both tropical and temperate locations. Solar Energy 38, 169–177; Hollands K. G. T. and Huget R. G. (1983) A probability density function for clearness index, with applications. Solar Energy 30, 195]. Furthermore, the values of the minimum clearness index (0.12–0.24) for Ilorin are noticed to be much higher than the generally accepted value of 0.05 for overcast sky conditions. The results are further compared, especially with those of Ideriah and Suleman [Ideriah, F. J. K. and Suleman, S. O. (1989). Sky conditions at Ibadan during 1975–1980. Solar Energy 43, 325–330.] and Akuffo and Brew-Hammond [Akuffo, F. O. and Brew-Hammond, A. (1993). The frequency distribution of global solar radiation at Kumasi. Solar Energy 50, 145–154.] for Ibadan and Kumasi, all in the West African sub-region. Although the locations are slightly different in agro-climatic conditions, results are found to be very comparable.     

Methods to estimate global and diffused luminous efficacies based on satellite data

This paper presents universal models and constant values to estimate luminous efficacies for each of global and diffused solar radiation on a horizontal surface. They are applicable to all sky conditions and are based on satellite derived data available via web servers. Solar radiation data from ten locations in Europe and North Africa was used to obtain three global and diffused functions for luminous efficacy (K) against solar altitude (α), cloud amount (C), and sky clearness index (k_t). All were used to estimate illuminance for the ten originating locations; for four locations based on satellite data; and for a further five based on measured data. A statistical assessment showed that the best models are K against α. Comparison between results from the proposed models and those produced using three published models for both cases, indicate that the former produce more accurate estimates of luminous efficacy. Constant values also showed very reliable results, especially for the diffused case. The satellite based approach makes daylight data available in locations remote from current measurement sites.     

Evaluation of clear-sky conditions in high altitude sites

The correct assessment of cloud conditions in any site is important for determining the characteristics of solar resource availability. The criterion proposed by Iqbal has been widely used for this purpose, through the classification of the daily clearness index K_t. However, evidence was found to suggest that this criterion may not be applicable to data measured in high altitude sites, because partially cloudy days are incorrectly classified as clear-sky days. This paper analyzes the cloudiness state of the sky by observing the values of the clearness index K_t and the clear-sky index K_c. These indices were obtained from reliable global solar irradiance data measured over a year in three places of Argentina located at different altitudes (25, 1200 and 3700 m.a.s.l). ESRA and ARG-P models were used to estimate daily clear-sky global solar irradiation values H_c. They also reveal that the most probable value of K_c which corresponds to an actual clear-sky day of a particular location and time depends on the model used to estimate the clear-sky global solar radiation values. Thus, it was confirmed that, unlike the index K_c, the Iqbal's criterion does not correctly classify the cloud cover status from data measured in high altitude sites (>1000 m.a.s.l.).     

Simulation and model validation of a horizontal shallow basin solar concentrator

Salt removal from drainage water is becoming increasingly important for sustainable irrigated arid land agriculture, where inadequate drainage infrastructure exists. Solar evaporation and concentration systems are currently in development in California for this purpose. The thermal behavior and evaporation rates of a horizontal shallow basin solar concentrator were modeled for design purposes and investigated experimentally in order to validate the model. Three different evaporation rate models were evaluated and compared. Measured and predicted peak brine temperatures differed by as much as 5 °C when using prescribed literature coefficients without calibration. Model prediction was improved by calibration so that peak brine temperature deviated less than 3 °C when tested against independent data sets.Minimum root mean square error was used to calibrate the mass transfer coefficient and absorptance of the collector surface for solar radiation, which are the main factors affecting the heat transfer associated with the solar concentrator. Calibrated collector surface absorptance for solar radiation declined while mass transfer coefficients were increased from reported literature values. Under calibration, the absorptance of the collector surface was adjusted from 0.8 to 0.61, and mass transfer coefficients estimated by Newell et al. [Newell, T.A., Smith, M.K., Cowie, R.G., Upper, J.M., Cler, C.L., 1994. Characteristics of a solar pond brine reconcentration system. Journal of Solar Energy Engineering 116 (2), 69–73] from 1.36 × 10⁻⁶(1.9 + 1.065V) to 1.70 × 10⁻⁶(1.84 + 1.0V) kg m⁻² s⁻¹ mm Hg⁻¹, by Manganaro and Schwartz [Manganaro, J.L., Schwartz, J.C., 1985. Simulation of an evaporative solar salt pond. Industrial & Engineering Chemistry Process Design and Development 24, 1245–1251] from 0.0208(1 + 0.224V) to 0.0233(1 + 0.214V) kg m⁻² h⁻¹ mm Hg⁻¹, and by Alagao et al. [Alagao, F.B., Akbarzadeh, A., Johnson, P.W., 1994. The design, construction, and initial operation of a closed-cycle, salt-gradient solar pond. Solar Energy 53 (4), 343–351] from 2.8 + 3.0V to 3.0 + 3.33V W m⁻² °C⁻¹. The calibrated models were tested using an independent data set. Maximum deviation between measured and predicted brine temperatures differed by less than 3 °C. The measured and predicted peak evaporation rates were between 1.2 and 1.4 kg m⁻² h⁻¹.The calibrated Newell model was used to predict the monthly productivity and daily maximum evaporation rates at Five Points, California for the year 2004. The productivity from April to September and from March to October was 80.7% and 94.3% of the total annual productivity, respectively.     

Total suspended particles and solar radiation over Cairo and Aswan

Measurements were carried out at Cairo (30.05°N, 31.17°E) and Aswan (23.58°N, 32.47°E) in Egypt for three years (1990–1992) by the Egyptian Meteorological Authority. The measurements were done using an Eppley ultraviolet radiometer to measure the global ultraviolet solar radiation (UV), Eppley pyranometers to measure the global solar radiation (G) and the pyrgeometers with silicon dome from Eppley to measure the atmospheric infrared radiation (IR). The clearness index (K_t) and the diffuse fraction (K_d) for both regions have been calculated. Finally the total suspended particles for Cairo and Helwan and their interaction with the solar radiation has been found.     

Equations for estimating global solar radiation in data sparse regions

The knowledge of the amount of solar radiation in an area/region is very essential in the field of Solar Energy Physics. In this work two equations are put forward for estimating global solar radiation from common climate variables in data sparse regions. The first is the Hargreaves equation, R_s=0.16R_aT_d^0.5 where R_a is the extraterrestrial solar radiation and T_d is the temperature difference (maximum minus minimum), while the second is the Angstrom equation, R_s=R_a(0.28+0.39n/N) where n and N are the measured sunshine hours and the maximum daylight duration respectively. The global solar radiation estimated by the two equations for three sites, Owerri (5°28′N, 7°2′E), Umudike (5°29′N, 7°33′E) and Ilorin (8°32′N, 4°46′E), located in different climate zones of in Nigeria, West Africa, are in agreement with those of earlier workers and that from Photovoltaic Geographic Information System (PVGIS) project. The implication of this in solar photovoltaic applications has been stressed.     

Statistical properties of hourly global radiation

A model is described which generates synthetic daily sequences of hourly radiation values, on the horizontal plane, for any location, with the daily clearness index K_t as input. The model assumes that for each K_t and solar hour the probability density of the hourly clearness index k_t is (simply) a truncated Gaussian function. A first-order autoregressive model is fitted for the k_t variable, normalised using parametrisations for the time-dependent average and standard deviation values. Values generated by this ARMA (1,0) model can then be transformed backwards to generate synthetic sequances of k_t values. Using a diffuse fraction correlation and a tilted radiation model, the horizontal global data can be transformed to any desired plane, thus providing solar system designers with the necessary hourly data for the accurate sizing of every type of solar system, including stand-alone, high solar fraction and passive ones.     

Global, direct and diffuse solar irradiance in Riyadh, Saudi Arabia

The regression coefficient of the well-known Angstrom correlation are determined for Riyadh city (the capital of Saudi Arabia) longitude 46° 14′E 24°55′N The relationship of the daily and monthly variation of the fraction of the diffuse solar irradiation to extrateresstrial and the clearness index are obtained. The variation of the values of the average daily global solar radiation against the month of the year is reported. The value of K_n defined as the ratio of direct normal Insolation, H_bn measured in Riyadh to direct normal solar extraterrestrial radiation with the K_T and K_d were obtained. The daily diffused ratio and the daily clearness index are shown as a function of the month of the year.     

Global solar irradiance in Cordoba: Clearness index distributions conditioned to the optical air mass

The biological and photochemical effects of solar radiation and solar energy applications make it really important to characterize the variability of this component. In view of the fact that the clearness index indicates not only the level of availability of solar radiation but also the changes in atmospheric conditions in a given location, since the classic Liu and Jordan study, many papers have dealt with its statistical distribution. Specifically, Tovar et al. [Tovar J, Olmo FJ, Alados-Arboledas L. Solar Energy 1998;62(6):387–393] proposed a model to represent the probability density distributions of the instantaneous clearness index conditioned to the optical air mass from measurements recorded in Granada (Spain). In this work, we have proved the applicability of this model in a different location, Cordoba (Spain), finding that the parameters for fitting the model depend on both the optical air mass and the geographic and climatic conditions.     

Cumulative distribution curves of daily clearness index in a southern tropical climate

Most previous works, involving the analysis of the statistical properties of solar radiation, have considered places situated in the Northern Hemisphere, generally at latitudes above 30°. In this work, the cumulative distribution curves for 23 sites located in the Southern Hemisphere, in the tropical and inter-tropical regions of Brazil, between the Equator and 30° latitude were calculated, trying to enlarge the available information on the statistical properties of solar radiation towards locations in sub-equatorial regions of the world. Results are compared with four distinct models of daily cumulated distribution functions , proposed by Bendt et al., Hollands and Huget, Saunier et al., and Babu and Satyamurty. A first comparison shows that the function proposed by Saunier et al. is well adjusted to our experimental data for the greater part of the Brazilian locations, except for places with temperate climates, in which the Hollands and Huget model, with the maximum clearness index equal to 0.864, as proposed by these authors, is superior. By substituting the maximum clearness index 0.864 of the Hollands and Huget model for a local maximum, as obtained experimentally in this work, results improve considerably. This study ratifies the conclusions previously obtained by other authors such as Saunier et al., and Babu and Satyamurty on the non-universal character of the Liu and Jordan cumulative distribution functions (CDFs).     

An analysis of thermal and solar zone radiation models using an Angstrom–Prescott equation and artificial neural networks

The correlation between the clearness index and sunshine duration is useful in the estimation of the solar radiation for areas where measured solar radiation data are unavailable. Regression techniques and artificial neural networks were used to investigate the correlations between daily global solar radiation (GSR) and sunshine duration for different climates in China. Measurements made during the 30-year period (1971–2000) from 41 measuring stations covering 9 thermal and 7 solar climate zones and sub-zones across China were gathered and analysed. The performance of the regression and the ANN models in the thermal and solar zones was analysed and compared. The coefficient of determination (R²), Nash–Sutcliffe efficiency coefficient (NSEC), mean bias error (MBE) and root-mean-square error (RMSE) were determined. It was found that the regression models in both the thermal and the solar climate zones showed a strong correlation between the clearness index and sunshine duration (R²=0.79–88). There appeared to be an increasing trend of larger MBE and RMSE from colder climates in the north to warmer climates in the south. In terms of the thermal and solar climate zone models, there was very little to choose between the two models.     

THE APPLICABILITY OF SEVERAL DIFFUSE SOLAR RADIATION MODELS TO THE CYPRIOTE ENVIRONMENT

Solar radiation measurements at one location in Cyprus are used to test the applicability of several theoretical and empirical models which compute diffuse radiation on a horizontal surface. Two types of correlation tests were used [1]: the first correlates the ratio of diffuse-to-global solar radiation with the “clearness index” K_T; and the second correlates the ratio of diffuse-to-global solar radiation with the fractional sunshine.

Therefore, the selected models for discussion are compared and tested for their applicability to one location in die eastern Mediterranean basin in general, on the basis of statistical error tests. A comparative study of the models shows that Page's model [3], based on the first type of correlations and Hay's one [13] based on the second type of correlations, are equally accurate for the greater Cypriote environment. Finally, two statistical equations are proposed for estimating diffuse radiation for solar energy applications in the greater environment of Cyprus.     

Estimation of global solar irradiation on horizontal and inclined surfaces based on the horizontal measurements

Solar radiation data are essential in the design of solar energy conversion devices. In this regard, empirical models were selected to estimate the global solar radiation on horizontal and inclined surfaces. The hourly solar radiation data measured at the study area during the period of 2004-2007, were used to calculate solar radiations using selected models. The selected models were compared on the basis of statistical methods. Based on the results, a new model, H/H_o = 0.19490 + 0.4771(n/N) + 0.02994 exp(n/N) has been developed, based on Kadir Bakirci linear exponential model. This is highly recommended to estimate monthly mean daily global solar irradiation, on a horizontal surface. Further, a model to convert horizontal solar global radiation to that of radiation on a tilted surface is also presented. It is based upon a relatively simple model proposed by Olmo et al. which requires only measurements of horizontal solar radiation. The developed model appears to give excellent results and has the advantage of being relatively simple for applications. The present work will help to improve the state of knowledge of global solar radiation to the point where it has applications in the estimation of global solar radiation, both on horizontal and inclined surfaces.     

Measurement of solar-energy (direct beam radiation) in Abu Dhabi, UAE

This paper presents actual measurements of direct solar radiation in Abu Dhabi (24.43°N, 54.45°E) with the existing meteorological conditions encountered during the measurement throughout the year. High resolution, real-time solar radiation and other meteorological data were collected and processed. Daily and monthly statistics of direct solar radiation were calculated from the one-minute average recorded by a Middleton Solar DN5-E Pyroheliometer. The highest daily and monthly mean solar radiation values were recorded as 730 and 493.5 W/m², respectively. The highest one-minute average daily solar radiation was recorded as 937 W/m². In addition to direct beam radiation, the daily average clearness indexes, surface temperature variations, wind speeds and relative humidity variations are discussed. When possible, direct beam radiation and some meteorological data are compared with corresponding data of the 22-year average of NASA's surface meteorology and solar-energy model. The measured data (direct beam radiation and meteorological) are in close agreement with the NASA SSE model with some discrepancy.     

Practical models to estimate horizontal irradiance in clear sky conditions: Preliminary results

The Argentinean Northwest (ANW) is a high altitude region located alongside Los Andes Mountains. The ANW is also one of the most insolated regions in the world due to its altitude and particular climate. However, the characterization of the solar resource in the region is incomplete as there are no stations to measure solar radiation continuously and methodically. With irradiance data recently having been measured at three sites in the Salta Province, a study was carried out that resulted in a practical model to quickly and efficiently estimate the horizontal irradiance in high altitude sites in clear sky conditions. This model uses the altitude above sea level (A) as a variable and generates a representative clearness index as a result (k_t-R) that is calculated for each site studied. This index k_t-R is then used with the relative optical air mass and the extraterrestrial irradiance to estimate the instantaneous clearness index (k_t). Subsequently, the index k_t-R is corrected by introducing the atmospheric pressure in the definition of relative optical air mass proposed by Kasten. The results are satisfactory as errors in the irradiance estimations with respect to measured values do not exceed 5% for pressure corrected air masses AM_c < 2. This model will be used in a feasibility study to locate sites for the installation of solar thermal power plants in the ANW. A prototype of a CLFR solar power plant is being built in the INENCO Campus, at the National University of Salta.     

ESTIMATING THE DIFFUSE FRACTION OF HOURLY GLOBAL SOLAR RADIATION IN SOUTHERN AFRICA

Several years of hourly diffuse and global radiation data, reported for five Southern African locations, are used to establish a relationship between hourly diffuse fraction D_h/G_h and the hourly clearness index (K_T). This relationship is compared to the correlations established by Orgill and Hollands (Solar Energy, 19, 357, 1977) and by Bruno (Solar Energy, 20, 97, 1978) and also to a set of measured data from one location in South Africa. The remarkable agreement between the present model and the measured data suggests the wide applicability of the correlation to locations in the Southern African region. However, there is no agreement between the measured diffuse radiation fraction and those estimated from the models suggested by Orgill and Hollands and by Bruno. The developed correlation is also tested for its applicability to Lesotho by calculating hourly diffuse irradiation for one station in the country and comparing them with available data.     

Development of both-side junction silicon space solar cells

This paper reports the recent results of improving the radiation hardness of silicon solar cells, which is SHARP and NASDA's project since 1998 (Tonomura et al., Second World Conference on Photovoltaic Solar Energy, 1998, pp. 3511–3514). Newly developed 2×2 cm² Si solar cells with ultrathin substrates and both-side junction (BJ) structure showed 72.0 mW (13.3% efficiency) maximum output power at AM0, 28°C after 1 MeV electron irradiation up to 1×10¹⁵ e/cm² and the best cell showed 72.5 mW (13.4%) maximum output power. These solar cells have p–n junctions at both front and rear surfaces and showed less radiation degradation and better remaining factor than previous solar cells.     

Modeling the hourly solar diffuse fraction in Taiwan

Using the data for global and diffuse radiation in Tainan, Taiwan, for the years of 2011 and 2012, respectively, four correlation models with five predictors: the hourly clearness index (k_t), solar altitude, apparent solar time, daily clearness index and a measure of persistence of global radiation level, are constructed to relate the hourly diffuse fraction on a horizontal surface (d) to the clearness index. Two models use a single logistic equation for all k_t values, Eqs. (6), (7), and the other two models use a set of piece-wise linear equations for four k_t intervals, Eqs. (8), (9). The proposed models are compared respectively with the fourteen models available in the literature, in terms of the four statistical indicators: the mean bias error, the root-mean-square error, the t-statistic and the Bayesian Information Criterion, using the out-of-sample dataset for Tainan, Taiwan. It is concluded from the analysis that the proposed piece-wise linear models perform well in predicting the diffuse fraction, while the performances of the proposed logistic models are more case-dependent. Among those fourteen models considered in this study, the models developed by Erbs et al., Chandrasekaran and Kumar, and Boland et al. have competitive performances as the proposed piece-wise linear models do, when applying to the prediction of diffuse fraction in Tainan, Taiwan.     

A model for determining the global solar radiation for Makurdi,Nigeria

An empirical model for determining the monthly average daily global solar radiation on a horizontal surface for Makurdi, Nigeria (Latitude 7°7′N and Longitude 8°6′E) was developed using the Angstrom–Page equation. The solar radiation (W/m²), hours of bright sunshine and cloudiness were measured hourly from 0600 H to 1800 H daily for 18 months. The constants ‘a’ and ‘b’ of the Angstrom linear type equation were determined by plotting the clearness index (H/H_o) against the possible sunshine hours (n_s/N) to obtain the line of best fit. The constant ‘a’ was obtained from the intercept of the line on the y-axis while the constant ‘b’ was obtained from the slope of the line. The developed model for determining the global horizontal solar radiation at the location was H = H_o [0.17 + 0.68(n/N)] with a coefficient of correlation of 0.78. The mean bias error and root mean square error that were used to test the performance of the constants were 0.17% and 1.22% respectively. The measured solar radiation was compared with the solar radiation predicted by the model and no significant difference was found between them using F-LSD at P ≤ 0.05.     

Solar radiation attenuation in solar tower plants

With the advent of the first commercial solar power tower plants with a rated power in the 10–20 MW range, scale-up to larger 20–50 MW commercial plants is being considered (Lata et al., 2010, Herring, 2009) in the vast arid regions of the sunbelt. In the case of single-tower plants, the heliostat field size grows considerably and the heliostat–receiver slant range distances are often over 1 km. Solar radiation attenuation over these distances cannot be neglected and must be taken into consideration during plant design. The measurement of the atmospheric attenuation is not an easy task and the use of spectral atmospheric transmission models is necessary. We used the MODTRAN (MODerate resolution atmospheric TRANsmission) code to study the solar radiation attenuation at different slant range distances in different scenarios: rural atmosphere on a clear day (visibility 23 km) and rural atmosphere on a hazy day (visibility 5 km).