A simplified model exploration research of new anisotropic diffuse radiation model
Graphical abstract
The specific process of measured diffuse radiation data
Introduction
Accurate solar radiation data is essential for design, simulation, performance evaluation of solar energy system [1], [2]. Which is also affect the building cooling load and air-conditioning equipment selection, meanwhile, diffuse radiation is also the key problem in calculating solar radiation [3], [4]. The diffuse radiation on the inclined plane is very significant for solar thermal use and photovoltaic power generation; however, meteorological station cannot provide these data [5], [6], [7], [8]. Therefore it is urgent to develop a theoretical model to calculate diffuse radiation on an inclined surface through diffuse radiation on a horizontal surface.
The research of the diffuse radiation models can be divided into three generations [9]. The first generation models are isotropic diffuse radiation models, represented by the Liu and Jordan model [10]. These diffuse radiation models are only suitable for cloudy days, which cannot be applied to partially cloudy days and clear days.
The second generation models are generally based on modification of the first generation models, which are suitable for partially cloudy and sunny weather. The typical models include Temps and Coulson model [11], Klucher model [12], Hay model [13], Skartveit and Olseth model [14] and Reindl model [15]. The second generation models have relatively simple forms and better practical values, but they do not have clear physical meaning and are lower accuracy because they are only adjusted based on isotropic models.
The third generation are anisotropic diffuse radiation models which are obtained by building the diffuse radiation integral equation, and the typical models are Perez model [16] and Muneer model [9], [17]. Muneer model [9], [17] is developed from Steven and Unsworth model [18] which is gained by integrating Moon and Spencer model [19]. The radiation distribution index is a core indicator of these models, which has a significant impact on accuracy of diffuse radiation calculation. Perez model [16] is strictly set up in accordance with the definitions of the radiation intensity and the solid angle. The source of diffuse radiation is divided into three regions, including the circumsolar region, sky horizontal region and sky dome region based on the radiation intensity. The model assumes each region is isotropic, and the diffuse radiation from these three regions is solved by integration respectively. However, the distributions of diffuse radiation in the sky dome region are actually not isotropic in the Perez model. Many observations and studies [11], [18], [20], [21], [22] show that diffuse radiation from a region located at 90 degree angles with the Sun (hereinafter referred to as orthogonal diffuse radiation) is weakened. Therefore, a new anisotropic diffuse radiation model (NADR model) was proposed to solve this problem in our previous paper [23]. The source of diffuse radiation is divided into four regions by NADR model, including the circumsolar region, orthogonal region, sky horizontal region and sky dome region. It can effectively make up the defect of isotropic assumption of orthogonal regions in the Perez model.
The calculation process of the Perez model is complex, especially for solving solid angles occupied by the circumsolar region and horizontal region, lots of variables need to be solved. For irregular buildings, more parameters need to be solved, and operations are carried out for a long time. With the increased volume and complex structure, complexity and calculation time will be further increased. Therefore, it is necessary to simplify the model reasonably in the premise of not significantly reduced accuracy. Complex parameters (fraction of the circumsolar region which can be seen by horizontal and diffuse radiation from the sky horizontal region) in Perez model are simplified to get a simplified Perez model [24], which is easier to solve the diffuse radiation on the inclined surface. The reason why the simplified Perez model has been used in energy simulation software EnergyPlus is reasonable and effective simplification. The solving process of Perez model and its simplified model are shown in Figs. 1 and 2. Based on the reasonable simplification on the basis of new anisotropic diffuse radiation model (NADR model), a new simplified anisotropic diffuse radiation model (NSADR model) is put forward in this paper.
Section snippets
NADR model description [23]
According to the space distribution characteristics of the diffuse radiation, the sky is divided into four parts, including: circumsolar region (radiation intensity is ), orthogonal region (radiation intensity is ), sky horizontal region (radiation intensity is ) and sky dome region (radiation intensity is ). There is no significant gradients in the interior of each regions. However, there are significant gradients among these regions. The diffuse radiation of each region is
Recombine of NADR model
According to the definition of diffuse radiation on horizontal surface and tilted surface, Eq. (1) can be rewritten as Eq. (2).where the superscripts i, c, q and h refer to the diffuse radiation from sky dome region, circumsolar region, orthogonal region and sky horizontal region, respectively. Diffuse radiation on a horizontal surface is the sum of the diffuse radiation from these four region (Eq. (3)).
Eq. (4)
Testing scheme and measuring instrument
Solarimeter SL100 and SL200 (KIMO) are used to measure global solar radiation and beam solar radiation. The measuring range and accuracy of SL100 and SL200 are shown in Table 2. The measurement range and accuracy of SL100 and SL200 are the same, except that the amount of data stored. SL100 is used to measure global solar radiation on a horizontal surface and tilted surface. SL200 is used with shading cylinder and sun tracking device to measure direct normal solar radiation. These pyranometers
Evaluation and discussion
Typical existing diffuse radiation models, NADR model and NSADR model are comparatively analyzed based on the diffuse radiation data measured on different orientations 90° tilted surfaces, and then the results are shown in Table 4.
Table 4 shows when calculating the diffuse radiation on tilted surfaces, the accuracy of calculating results of the second generation models (Temps and Coulson model, Klucher model, Hay model, Skartveit and Olseth model and Reindl model) is not necessarily better than
Conclusion
In summary, the following conclusions are available by simplifying the NADR model:
- (1)
The accuracy of the existing models and new models are compared based on the measured value of the diffuse radiation. The results demonstrate that for existing models, Perez model and its simplified model are relatively accurate. However, the accuracy of these two existing models are lower than NADR model and its simplified model (NSADR model), because Perez model and its simplified model do not consider the
Acknowledgments
The authors gratefully acknowledge the support of the National Natural Science Foundation of China (Grant Nos. 51508372; 51278349 and 51208363), the Opening Funds of State Key Laboratory of Building Safety and Built Environment (Grant No. BSBE 2015-09), Doctor Scientific Research Foundation of Tianjin Chengjian University, University Students Innovation and Entrepreneurship Training Program (Grant No. 201510792010) and Soft Task Item of Construction Committee (Grant No. 2015-Soft 7).
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