• Energy Research

In this paper, a procedure for generating a family of parametrical broadband clear-sky models is described. The key element is the conversion of one or more model input variables into tunable mathematical parameters. The approach is tested on the PS model [Paulescu, M. and Schlett, Z., Theor. Appl. Climatol. 75, 203 (2003)], with the free parameter being the Ångström exponent (α). This allows us to fine-tune for conditions dominated by desert dust, urban-industrial, and mixed aerosols. We find that for an arbitrary set of data, the optimal value of the free parameter is not the same as its actual measured value (inserting the measured value in the model would result in a lower performance). We attribute this fact to the inaccurate nature of the base model. The optimal α value varies with the considered solar irradiance component, aerosol type and loading, and the error measure(s) used for assessing model accuracy. A set of recommended models for each aerosol type and loading class is given. The tabled values for the aerosol transmittance coefficients are also listed. A preliminary validation shows that the newly developed models are very reliable. The optimal version generally falls within a few percent of the results of REST2v5, a benchmark model in clear-sky solar irradiance estimation. While some established models outperform REST2v5 for certain aerosol types and for only one solar irradiance component, the new models prove competitive under most scenarios. Beyond showing the performance of the developed model family, these results hint at great potential of our approach.

It is entirely apparent that an accurate estimation of global horizontal solar irradiance (GHI) does not guarantee an accurate estimation of its fundamental components. This basic perception motivates the present study, which evaluates the ability of the clear-sky solar irradiance models to accurately partition GHI into beam and diffuse components. Diverging from the traditional perspective, the diffuse fraction is assessed as an appropriate quantifier for the fractional part of GHI estimated by a clear-sky solar irradiance model as being diffuse. Acting as a quantifier, the diffuse fraction has the merit of isolating the uncertainty induced by aerosols in estimating the diffuse solar irradiance. The results of evaluating various clear-sky solar irradiance models show that many models consistently experience similar errors under high atmospheric turbidity. A strong influence of the atmospheric aerosol loading on the dissimilarities between the accuracies in estimating diffuse fraction and the corresponding diffuse solar irradiance is noticed. Our analysis of uncertainties in estimating the diffuse solar irradiance appears naturally as a sum of two terms: one encapsulating the ‘intrinsic’ error of the model, as quantified through errors in global solar irradiance, and the other encapsulating the aerosol modeling errors, as quantified through errors in diffuse fraction. For small atmospheric aerosol loading, the intrinsic errors of the model are dominant, while for high atmospheric aerosol loading the accurate modeling of the aerosols effect on GHI becomes critical.

Abstract Recent progress in radiometry allows the development of diffuse fraction models based on data stored at high-frequency sampling. At the present only a handful of such models exist in the literature. In this paper, we present a new and simple model for estimating diffuse fraction developed on 1-minute resolution data. The new model (PB) is extensively validated on data from the Baseline Surface Radiation Network, for both diffuse fraction (kd) and direct normal irradiance (Gn). The results show that PB performs well compared to other similar models, despite its structural simplicity. kd is estimated with the best accuracy in locations with temperate climate (TM), the average (median) nRMSE of the tested TM stations being 18.38% (17.79%). The Gn estimates are found to be most accurate at arid locations (AR), the average (median) nRMSE over all tested AR stations being 17.29% (16.96%). We find that the performance of the models varies strongly as a function of the climate zone or when we switch between estimating diffuse and direct normal irradiance components, possibly changing the accuracy-based rankings among models, a fact which should be taken into consideration by users when selecting appropriate models.

The atmospheric aerosol loading may significantly influence the performance in solar power production. The impact can be very different both in space (even in short distance) and time (shortterm fluctuations as well as long-term trend). Aiming to ensure a high degree of generality, this study is focused on the aerosol impact on the collectable solar energy. Thus, the results are independent of solar plants characteristics. A new methodology for estimating the average daily,monthly, and yearly losses in the solar potential due to aerosols is proposed. For highlighting the loss in the overall solar potential, a new ideal scenario is defined as a reference for the atmospheric aerosol background. A new equation for computing the solar potential loss is proposed to adjust for possible biases. In a departure from similar studies, the analysis relies on ground measurements (BSRN and AERONET), always more accurate than remotely sensed satellite data. The seldom discussed impact of aerosol type is considered. As a general conclusion, the monthly and yearly reductions of the solar potential due to aerosols are estimated at 12 locations spread around the globe, amounting to losses of the solar potential ranging from 0.6% to as high as 7.2%.

The field of energy forecasting has attracted many researchers from different fields (e.g., meteorology, data sciences, mechanical or electrical engineering) over the last decade. Solar forecasting is a fast-growing sub-domain of energy forecasting. Despite several previous attempts, the methods and measures used for verification of deterministic (also known as single-valued or point) solar forecasts are still far from being standardized, making forecast analysis and comparison difficult. To analyze and compare solar forecasts, the well-established Murphy-Winkler framework for distribution-oriented forecast verification is recommended as a standard practice. This framework examines aspects of forecast quality, such as reliability, resolution, association, or discrimination, and analyzes the joint distribution of forecasts and observations, which contains all time-independent information relevant to verification. To verify forecasts, one can use any graphical display or mathematical/statistical measure to provide insights and summarize the aspects of forecast quality. The majority of graphical methods and accuracy measures known to solar forecasters are specific methods under this general framework. Additionally, measuring the overall skillfulness of forecasters is also of general interest. The use of the root mean square error (RMSE) skill score based on the optimal convex combination of climatology and persistence methods is highly recommended. By standardizing the accuracy measure and reference forecasting method, the RMSE skill score allows-with appropriate caveats-comparison of forecasts made using different models, across different locations and time periods.

Abstract The relation between solar irradiation and sunshine duration was investigated from the very beginning of solar radiation measurements. Many studies were devoted to this topic aiming to include the complex influence of clouds on solar irradiation into equations. This study is focused on the linear relationship between the clear sky index and the relative sunshine proposed by the pioneering work of Angstrom. A full semi-empirical derivation of the equation, highlighting its virtues and liabilities, is presented. Specific Angstrom – type equations for beam and diffuse solar irradiation were derived separately. The sum of the two components recovers the traditional form of the Angstrom equation. The physical meaning of the Angstrom parameter, as the average of the clouds transmittance, emerges naturally. The theoretical results on the Angstrom equation performance are well supported by the tests against measured data. Using long-term records of global solar irradiation and sunshine duration from thirteen European radiometric stations, the influence of the Angstrom constraint (slope equals one minus intercept) on the accuracy of the estimates is analyzed. Another focus is on the assessment of the degradation of the equation calibration. The temporal variability in cloud transmittance (both long-term trend and fluctuations) is a major source of uncertainty for Angstrom equation estimates.

Abstract Passing clouds and the phenomenon of cloud enhancement (CE) can cause severe fluctuations in the incoming solar radiation. The modeling of PV systems’ operation is conditioned by the ability of forecasting and estimation models to capture such phenomena. In time-averaged datasets, these high-frequency events can be completely smeared out. Thus, it is important to study the impact of temporal smoothing on the accuracy of solar irradiance models. This paper focuses on empirical separation models. In the first part, the frequency of CE episodes in the measured data is analyzed, finding an exponential decrease with increasing data timescale. In the second part, the impact of temporal smoothing on the performance of separation models developed on 1-h or 1-min data is assessed. The results show that the aggregated nRMSE of the hourly models decreases from 37.7% to 28.6% between smallest and largest considered timescale. Under the same scenario, the nRMSE of the minute models decreases from 32.1% to 29.7%. Additionally, the hourly models tend to underestimate the measured diffuse fraction, the aggregated nMBE varying between –11.3% and –1.1%, while the minute models tend to overestimate the measured data, the aggregated nMBE ranging between 2.8% and 8.4%, as the averaging interval is increased. The performance of the models is found to have a strong dependence on climate type. No dominating model could be found. The models which perform most consistently are: (a) Yang2 and BRL-min in temperate climates, (b) BRL and PB in tropical climates, and (c) PB and BRL-min in arid climates.