Computational applications for the evaluation of buildings' energy performance (including their passive and active solar energy systems) require detailed information regarding incident solar radiation. As only global horizontal irradiance data is available for most locations, models are needed to derive from such global data, the diffuse radiation component. In this context, the present paper compares the predictive performance of six existing and one new diffuse fraction models for the location of Vienna, Austria

Mahdavi, Ardeshir

Vaziefeh, Ehsah

Epoka University

Proceedings of the 2nd ICAUD International Conference in Architecture and Urban Design  Epoka University, Tirana, Albania, 08-10 May 2014 Paper No. 200 200-1  A Comparative Performance Study of Diffuse Fraction Models  Based on Data from Vienna, Austria  Ehsan Vaziefeh and Ardeshir Mahdavi Department of Building physics and Building ecology Vienna University of Technology  Karlsplatz 13, 1040, Vienna, Austria em.vazifeh@gmail.com    ABSTRACT Computational applications for the evaluation of buildings’ energy performance (including their passive and active solar energy systems) require detailed information regarding incident solar radiation. As only global horizontal irradiance data is available for most locations, models are needed to derive from such global data, the diffuse radiation component. In this context, the present paper compares the predictive performance of six existing and one new diffuse fraction models for the location of Vienna, Austria.   KEYWORDS: Solar radiation, diffuse fraction model, clearness index, global horizontal irradiance, diffuse horizontal irradiance, Sun state.  1 INTRODUCTION Incident solar radiation has a significant impact on the thermal and visual performance of buildings. Thus, the amount of solar radiation and its diffuse and direct components must be known. Unfortunately, only the global horizontal irradiance is widely measured. Consequently, extensive research has been done to estimate components of global horizontal irradiance. Different models use different input data. Depending on the variables, approaches, and location, different predictive performance is achieved.  In the past, diffuse fraction model developers mainly used clearness index (ratio of global horizontal irradiance over horizontal extraterrestrial irradiance) as a model input to derive the diffuse fraction (ratio of diffuse horizontal irradiance to global horizontal irradiance). Clearness index gives information about the overall sky conditions. Small values denote overcast/dark skies, whereas higher values denote bright (not necessarily clear) skies. Diffuse fraction is generally lower when the clear index value is high. However, at very high clearness index values (higher than around 0.8 for Vienna) diffuse fraction might increase again (unobstructed sun, bright clouds). Clearness index does not yield on its own accurate results for diffuse fraction. Past research has thus involved the deployment of multiple input variables, resulting in rather complex models. Most of these models appear to perform satisfactorily only for locations whose data were used for model development, i.e., mostly northern hemisphere (Spencer 1982, Boland et al. 2001). Recent studies (Dervishi and Mahdavi 2012, Vazifeh et al. 2013) using measured data from Vienna, Austria documented a rather poor performance by the models.  200-2 2 METHOD 2.1 Data Data from the weather station of Building physics and Building ecology department of Vienna University of Technology was used for the present study. This data consists of hourly global and diffuse horizontal irradiance obtained from a sunshine pyranometer (Delta-T 2007). The monitored data was subjected to multiple quality checks. For instance, data for sun altitudes below 5 degrees was removed from the dataset. Moreover, hourly global horizontal irradiance less than 50 W.m-2 was excluded. Finally, hourly global horizontal irradiance data measured by sunshine pyranometer was compared with high precision pyranometer (Kipp & Zonen 2004). Thereby, instances where measured values were more than 5% apart were discarded.  2.2 Models description A brief description of the models (functions, variables) selected for the present study are shown in Table 1. Erbs et al. (1982) presented a piecewise polynomial model, which used only clearness index as a variable. Maxwell (1987), by applying a quasi-physical model, developed a model which used air mass and clearness index as variables. The model is called DISC (Direct Insulation Simulation Code), which generates direct beam irradiance. Reindl et al. (1990) applied four variables, namely clearness index, solar altitude, relative humidity, and temperature in a piecewise function. Skartveit and Olseth (1987) developed a simple hourly model using solar altitude. In subsequent work (Skartveit and Olseth ,1998) they presented a model, which considered surface albedo and variability index. Boland et al. (2001) highlighted the shortcomings of existing models for the southern hemisphere. They developed a logistic model deploying clearness index as a variable. Lauret et al. (2010), by adding more variables to the Bolands’ logistic function, improved the model’s performance. All models, including a newly developed model for Vienna (see section 2.3 below), were implemented in the Matlab programming environment (MATLAB 2010). In case of Erbs et al., Reindl et al. and Boland et al. models, applicable coefficients of the models were calibrated, i.e., adjusted to achieve best fit to the empirical observations (Vienna data, 2013). To compute solar altitude, a procedure document in Reda and Andreas 2008 was used. Table 1 Models overview Model Function Variables Erbs et al. 1982 Polynomial    Maxwell 1987 Exponential   , mair Reindl et al. 1990 Polynomial   , sinα, T, φ Skartveit and Olseth 1998 Polynomial   , α, σ3 Boland et al. 2001 Logistic    Lauret et al. 2010 Logistic   , K ,AST, α, ψ   2.3 A diffuse fraction model for Vienna The distribution of clouds significantly affects the magnitude of solar radiation reaching the building surface. A normal weather station does not give information about cloud cover and distribution. Consequently, simple diffuse fraction models must rely on standard variables such as temperature, humidity, and global horizontal irradiance. A potential relationship between such variables and the diffuse fraction may be captured via statistical analysis of the measured data. With regard to Vienna data, we noticed that the correlation between clearness index and diffuse fraction can be improved, if multiple discrete ranges of global horizontal irradiance are differentiated. Therefore, for each bin of global  200-3 horizontal irradiance, linear least square regression was employed to fit the model to the data (observed values of diffuse fraction for the Vienna location in the year 2013). From 14 initial variables, six promising ones were selected. These variables are clearness index, daily clearness index (average of hourly clearness index day), solar altitude, relative humidity, temperature, and sun state. Sun state is a boolean variable: It equals to one in case of unobstructed sun, otherwise it is zero. Sun state and clearness index have the highest impact on diffuse fraction. Sun state data was imported from the pyranometer. The selected variables and their definitions are given in Table 2. The coefficients derived from least square regression are included in Table 3. Note that the values of temperature and relative humidity had a rather limited influence on the resulting diffuse fraction results.   Table 2 Variables being used in the present paper model Variable Symbol Formulation Solar altitude α  α       Clearness index              Daily clearness index              Temperature T                 Relative humidity RH RH/100 Sun state SS SS   Table 3 Coefficients for the proposed Vienna model as a function of the global horizontal irradiance (GHI) range   0<GHI<100  100<GHI<200  200<GHI<300  300<GHI<400  400<GHI<500  500<GHI<600  600<GHI<700  700<GHI<800  800<GHI<900  900<GHI<1000 1 0.88 0.796 0.487 0.535 0.098 0.392 0.442 0.526 0.329 2.97 SS -0.39 -0.529 -0.53 -0.574 -0.47 -0.632 -0.644 -0.649 -0.742 -2.325   0.33 0.349 -0.45 -0.244 -0.561 -1.27 -0.755 0.192 -0.011 -0.484    -0.004 -0.089 0.193 0.118 0.453 0.287 0.162 -0.174 0.502 -1.365    0.044 0.231 0.331 0.37 0.566 0.387 0.496 0.451 0.610 -0.199 T 0.071 0.018 0.075 0.067 0.198 0.22 0.079 0.049 0.136 -0.562 RH -0.001 0.0257 0.035 0.0018 0.071 0.115 0.077 0.2076 0.0794 0.407      200-4 2.4 Evaluation criteria A number of statistical measures (see equations 1 to 6) were used in order to evaluate the performance of the models, namely Median of the absolute percentage error (MeAPE), Median of the bias error (MeBE), Root mean square error (RMSE), Mean bias error (MBE), Mean absolute error (MAE), and Coefficient of variation of RMSE (CVRMSE).                                    (1)                                (2)                      (3)                        (4)                          (5)                          (6) Here,   ,       are predicted diffuse horizontal irradiance and measured diffuse hoizontal irradiance respectively. In addition to the above statistics, the percentage of results with a specific Relative Error (RE) range was displayed in terms of a cumulative distribution function (CDF). This function demonstrates the percentage of the results, which fall within a certain relative error range.  3 RESULTS AND DISCUSSION Figure 1 shows the value of the selected statistics for all models both for the year 2013 (whose data was used for model calibration) and 2011 (whose data was used solely for model verification. Figure 2 shows the cumulative distribution function (percentage of results with a specific Relative Error) for all models depicted for 2013 (left) and 2011 (right) data. As these Figures suggest, the Vienna model generally performs best. Whereas in the case of the Vienna model roughly 80% of the results show RE values less than 20%, only about 60% of the results of other models display the same error level.         200-5       Figure 1: Comparison of the models in terms of various statistics for the calibration (2013, white bars) and verification (2011, dark bars) periods.  -20 -10 0 10 20 30 Vienna Laurent et al. Boland et al. Skartveit and Olseth Reindl et al. Maxwell Erbs et al. MBE (W/m2) 0 10 20 30 40 Vienna Laurent et al. Boland et al. Skartveit and Olseth Reindl et al. Maxwell Erbs et al. MAE (W/m2) 0 20 40 60 80 Vienna Laurent et al. Boland et al. Skartveit and Olseth Reindl et al. Maxwell Erbs et al. RMSE (W/m2) 0 10 20 30 40 50 Vienna Laurent et al. Boland et al. Skartveit and Olseth Reindl et al. Maxwell Erbs et al. CVRMSE (%) -5 0 5 10 Vienna Laurent et al. Boland et al. Skartveit and Olseth Reindl et al. Maxwell Erbs et al. MeBE (%) 0 5 10 15 20 Vienna Laurent et al. Boland et al. Skartveit and Olseth Reindl et al. Maxwell Erbs et al. MeAPE (%)  200-6   Figure 2: The cumulative distribution function (CDF) of the relative errors for all models for the calibration (Left: 2013 data) and verification (Right: 2011 data) periods.  4 CONCLUSION The performance of six existing diffuse fraction models was assessed using data collected in Vienna, Austria. In case of three of these models, applicable coefficients were calibrated (using data from 2013) to achieve the best possible fit to the empirical data. Nonetheless, none of these models displayed a satisfactory performance when their predictions were evaluated against observed data from 2011. In about 60% of the cases, the RE values were above 20%. A newly developed detailed empirically-based model for Vienna performed significantly better. However, the performance of this model has not been assessed for data from other locations. Ongoing and future research shall further explore the potential for development of models that could satisfy the twofold criteria of wide geographic applicability and acceptable accuracy.   5 ACKNOWLEDGEMENTS The research presented in this paper was supported in part a fund from Seventh EU Framework Program-ICT "CAMPUS 21" (Project-Nr: 285729).  REFERENCES Boland, J., Scott, L., Luther, M. 2001. Modeling the diffuse fraction of global solar radiation on a horizontal surface. Environmetric, 12, pp.103-116. Dervishi, S., Mahdavi, A. 2012. Computing diffuse fraction of global horizontal solar radiation: A model comparison. Solar Energy, Vol. 86 1796–1802.  Delta-T Devices Ltd (2007). User manual of sunshine Pyranometer type SPN1. Erbs, D.G., Klein, S.A., Duffie, J. A. 1982. Estimation of the diffuse radiation fraction for hourly, daily and monthly-average global radiation. Solar Energy, Vol. 28. pp. 293-302. 0 10 20 30 40 50 60 70 80 90 1000102030405060708090100Relative Error (%)PR (%)  Erbs et al.MaxwellReindl et al.Skartveit and OlsethBoland et al.Lauret et al.Vienna model0 10 20 30 40 50 60 70 80 90 1000102030405060708090100Relative Error (%)PR (%)  Erbs et al.MaxwellReindl et al.Skartveit and OlsethBoland et al.Lauret et al.Vienna model 200-7 Kipp & Zonen. 2004. CM3 pyranometer instruction manual. Lauret, P., Boland, J., Ridley, B. 2010. Derivation of a solar diffuse fraction model in a Bayesian framework. Case Studies in Business, Industry and Government Statistics 1, Vol. 3 pp: 108-122. Maxwell, E. L. 1987. A quasi-physical model for converting hourly global horizontal to direct normal insolation. Report SERI/TR-215-3087, Solar Energy Institute, Golden, CO. MATLAB 2010. MATLAB Statistics Toolbox Release 2010a. The MathWorks, Inc., Natick, Massachusetts, United States. Reindl, D.T., Beckman, W.A., Duffie, J.A. 1990. Diffuse fraction correlations. Solar Energy, Vol. 45 (1) pp:1-7. Reda, I., Andreas, A. 2008. Solar Position Algorithm for Solar Radiation Applications. Technical report. NREL Report No. TP-560-34302. 55 pp. Skartveit, A., Olseth, J.A. 1987. A model for the diffuse fraction of hourly global radiation. Solar Energy, 38:271-274. Skartveit, A., Olseth, J.A., Tuft, M.E. 1998. An hourly diffuse fraction model with correction for variability and surface albedo. Solar Energy, 63(3):173-183. Spencer, JW. 1982. A comparison of methods for estimating hourly diffuse solar radiation from global solar radiation. Solar Energy Vol. 29. - pp. 19-32. Vazifeh, E., Dervishi, S., Mahdavi, A. 2013. Calculation models for the diffuse fraction of global solar radiation. CESBP Conference, Vienna, Austria. 587-590.            200-8  

A Comparative Performance Study of Diffuse Fraction Models  Based on Data from Vienna,  Austria

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A Comparative Performance Study of Diffuse Fraction Models Based on Data from Vienna, Austria

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