Viorel Badescu

Modeling Solar Radiation at the Earth Surface

The aim of this chapter is to describe algorithms for estimating the amount of solar energy incident at ground level on horizontal and inclined surfaces as well as on sun tracking surfaces. First, a general algorithm for estimating the solar irradiation on tilted surfaces is summarized. Next, models are presented for, respectively, the calculation of extraterrestrial radiation, quantification of the atmosphere effect on extraterrestrial solar radiation, calculation of solar irradiance on the horizontal plane, and transposing the result on tilted planes. Some of these models may be included within the procedures for forecasting the solar resource. Simple models may be used for straightforward prediction of solar irradiance and irradiation on horizontal surface under clear sky conditions. For more demanding applications, parametric models are the alternative. Basically, this is feasible by employing forecasted meteorological parameters as model inputs. For adjusting clear sky solar irradiance to the forecasted state of the sky, a survey of the required equations is presented.

Verification of some very simple clear and cloudy sky models to evaluate global solar irradiance

Several very simple clear sky and cloudy sky global irradiance models were tested under the climate and latitudes of Romania (Eastern Europe). The very simple clear sky models do not require meteorological data while the very simple cloudy sky models need only data on the total cloud amount. Three slightly more complex cloudy sky models which use additional meteorological inputs were also tested. The mean absolute error of the very simple clear sky models varies between 7 and 14% in July and between 12 and 19% in January. The best model originates from Western Europe. The performance of the very simple cloudy sky models is comparable to that of the more complicated ones. This is the main conclusion of the paper. Generally, their root mean square error varies between 35 and 45% in close agreement with results from the literature. Twelve classes of daily average cloudiness were defined. The model accuracy is better for the first six classes (with smaller cloud amount) and worse for the other six classes.

Weather modeling and forecasting of PV systems operation

The future of the energy mix paradigm.- Solar radiation measurements.- State of the sky assessment.- Stability of the radiative regime.- Modeling Solar Radiation at the Earth Surface.- Time series forecasting.- Fuzzy logic approaches.- Air temperature based models.- Outdoor operations of PV systems.- Forecasting the power output of PV systems.- Perspectives

Correlations to estimate monthly mean daily solar global irradiation: application to Romania

Seven existing relationships between monthly mean clearness index and the number of bright sunshine hours are tested under the climate and latitude of Romania. New (best-fit) correlations are derived. They use bright sunshine hour number or fractional total cloud amount as input. The dependence of the new sunshine-based regressions on month is stronger than their dependence on latitude. They generally underestimate the clearness index in the first half-year and overestimate it in the rest of the year. The accuracy of the new regression seems not to depend significantly on the year.

3D isotropic approximation for solar diffuse irradiance on tilted surfaces

A well known 2D approach of Liu and Jordan allows computing isotropic solar diffuse irradiance on a tilted surface. It is a 2D theory as the position of a sky element is characterized by a single (zenith) angle. A more realistic 3D model (that uses both zenith and azimuth angles to describe sky elements position) is developed in this paper for both isotropic diffuse irradiance and ground reflected irradiance incident on an arbitrary oriented surface. The 3D formula predicts a lower diffuse irradiance than the 2D relationship while the ground reflected irradiance is higher in case of the 3D model than in case of the 2D approach. In case of a small tilt angle, the 2D and 3D approximations predict comparable values, higher than the mean of the results obtained with a (reference) non-isotropic model. However, the 3D model is slightly more precise. When a larger tilt angle is considered, the 3D model predicts a few percent larger value than the mean of the values estimated by the reference model while the 2D model gives a significantly higher value.

First and second law analysis of a solar assisted heat pump based heating system

We propose a model for the heating system of an ecological building whose main energy source is solar radiation. The most important component of the heating system is a vapour compression heat pump. Both the first law and the second law were used to analyse the heat pump operation. The state parameters and the process quantities were evaluated by using, as input, the building thermal load. The second law analysis emphasised that most of the exergy losses occur during compression and condensation. Preliminary results show that the photovoltaic array can provide all the energy required to drive the heat pump compressor, if an appropriate electrical energy storage system is provided.

Degree-days, degree-hours and ambient temperature bin data from monthly-average temperatures (Romania)

This paper reports the implementation of the degree-day (degree-hour) method in Romania. The distribution of hourly average temperatures was represented analytically. The regression coefficients were obtained by fitting the distribution function to the existing meteorological data. Various temperature cumulative distribution functions have been produced and tested. From such functions, the degree-hour numbers can be calculated easily. Five models of computing degree-day numbers were tested. The most accurate method has been used to evaluate the heating degree-days for 29 Romanian localities.

Dynamic model of a complex system including PV cells, electric battery, electrical motor and water pump

The time dependent operation of several components of a PV pumping system (i.e. the PV cell, the PV array, the battery and the assembly electric motor—centrifugal pump) is modelled in this paper. The system has two main operating modes, which depend on the level of the incident solar global irradiance. The mathematical model consists of systems of seven or four ordinary differential equations, respectively, according to the operating mode. A computer simulation code is developed. Clear days with high incident solar irradiance and high cell temperature Tcell are characterised by lower PV efficiency, while the cell efficiency is larger on cloudy days, when the temperature Tcell is smaller. The sun-to-user efficiency is larger during the winter months. The battery acts as a buffer, as the main part of the electricity supplied by the PV array is used to drive the motor. The value of the PV cell series resistance Rs causes the battery to operate under two different regimes: when Rs is larger, the battery is over-discharged once or twice each month in the cold season. In case Rs is small, the battery is over-charged once per month in the warm season. The electric power used to drive the motor is rather constant during the year.

Improved model for solar cells with down-conversion and down-shifting of high-energy photons

A system for converting high-energy incident photons into photons of lower energy was proposed by Trupke et al (2002 J. Appl. Phys. 92 1668). In the present paper we re-analyse this system by using a more elaborate model. The main conclusions of this work are as follows. (1) When non-radiative recombination is neglected, our results confirm the findings of Trupke et al. Both the front and rear down-converter systems improve the performance of a single mono-facial solar cell. However, the present model shows that the conversion efficiency is smaller than estimated before. (2) When both the cell and the front (or rear) converter have the same low radiative recombination efficiency, their combination does not increase the cell conversion efficiency. (3) Adding a converter with a high (near unity) value of the radiative recombination efficiency to a solar cell shows beneficial effects. (4) In this case (i) for high-quality solar cells, the combination cell-rear converter provides a higher efficiency than the combination front converter-solar cell whereas (ii) for low quality solar cells, the front converter system performs better than the rear converter system. Conclusions (3) and (4) may be dependent on the details of the model adopted here.

Model of a thermal energy storage device integrated into a solar assisted heat pump system for space heating

Details about modelling a sensible heat thermal energy storage (TES) device integrated into a space heating system are given. The two main operating modes are described. Solar air heaters provide thermal energy for driving a vapor compression heat pump. The TES unit ensures a more efficient usage of the collected solar energy. The TES operation is modeled by using two non-linear coupled partial differential equations for the temperature of the storage medium and heat transfer fluid, respectively. Preliminary results show that smaller TES units provide a higher heat flux to the heat pump vaporiser. This makes the small TES unit discharge more rapidly during time periods with higher thermal loads. The larger TES units provide heat during longer time periods, even if the heat flux they supply is generally smaller. The maximum heat flux is extracted from the TES unit during the morning. Both the heat pump COP and exergy efficiency decrease when the TES unit length increases. Also, the monthly thermal energy stored by the TES unit and the monthly energy necessary to drive the heat pump compressor are increased by increasing the TES unit length.