Calculation models for the diffuse fraction of global solar radiation Department of Building Physics & Building Ecology Vienna University of Technology Department of Building Physics & Building Ecology, Vienna University of Technology 1 / 15
Application of solar energy in building industry Building performance simulation applications Photovoltaic cells Solar-thermal collectors Source: http://lerablog.org/technology/green-tech/advantages-of-solar-power-for-you-and-your-home/ Department of Building Physics & Building Ecology, Vienna University of Technology 2 / 15
Why do we need Diffuse fraction models? most weather stations provide global irradiance data High price of measurement instruments http://www.brighton-webs.co.uk/energy/modelling_solar_panels.htm Department of Building Physics & Building Ecology, Vienna University of Technology 3 / 15
Comparison of diffuse fraction models Models Function Input variables Erbs te al (1982) Polynomial k t Maxwell (1987) Exponential k t, m air Reindl (1990) Polynomial k t, sin α, T a, ϕ Perez (1991) Exponential Boland et al (2008) Logistic k t BRL (2010) Logistic k t, AST, α, K t, φ Department of Building Physics & Building Ecology, Vienna University of Technology 4 / 15
Measured data Department of building physics, Vienna, Austria Global horizontal irradiation Diffuse horizontal irradiation Temperature Relative humidity Department of Building Physics & Building Ecology, Vienna University of Technology 5 / 15
Solar measurement equipment http://www.tempcon.co.uk/kipp-and-zonen-cmp3-pyranometer Department of Building Physics & Building Ecology, Vienna University of Technology 6 / 15
Data quality control D <5% G <5% Data for year 2011 http://www.azosensors.com/equipment-details.aspx?equipid=251 http://www.tempcon.co.uk/kipp-and-zonen-cmp3-pyranometer http://eko-eu.com/products/photovoltaic-evaluation-systems/solar-monitoring-stations/ms-321lr-sky-scanner Department of Building Physics & Building Ecology, Vienna University of Technology 7 / 15
Statistical study MeAPE (Median of the Absolute Percentage Error) MeBE (Median of the Bias Error) MBE (Mean Bias Error) RMSE (Root Mean Square Error) CV (RMSE) (Coefficient of Variation of RMSE) Cumulative distribution of the relative error Department of Building Physics & Building Ecology, Vienna University of Technology 8 / 15
Comparison of the models based on different statistics Model RMSE (W/m2) CV(RMSE) (%) MeAPE (%) MeBE MBE (%) Boland 49.61 34.62 18.67-0.0002-11.18 BRL 53.83 37.57 19.19-0.0484-19.18 Erbs 50.72 ASHRAE 2002, for models' performance > 30 10< acceptable, 35.39 suggests, measure 18.28 of the -0.0488 MBE should be within ±10 % and -18.66 Maxwell 56.87 CV(RMSE) 39.68 should be within 22.49 ±30 % (for -0.0460-12.26 hourly measurements). Perez 57.84 40.36 16.67-0.0551-22.96 Reindl 53.58 37.31 19.87-0.0305-14.25 Department of Building Physics & Building Ecology, Vienna University of Technology 9 / 15
Percentage of results with errors within discrete Relative Error ranges (from ±5 to ±40) Model ±5 ±10 ±15 ±20 ±25 ±30 ±35 ±40 Boland 19.0 32.1 43.7 52.4 59.5 64.6 68.9 72.3 BRL 24.3 37.0 45.0 51.0 57.0 62.1 66.0 69.3 Erbs 24.5 37.2 45.5 52.3 58.0 63.0 67.0 71.3 Maxwell 15.6 28.8 38.0 45.9 54.3 61.0 67.1 72.4 Perez 21.4 38.4 47.6 54.5 60.9 65.6 70.4 74.2 Reindl 23.0 33.3 42.9 50.1 57.4 63.4 68.2 71.7 Department of Building Physics & Building Ecology, Vienna University of Technology 10 / 15
Percentage of results with errors within discrete Relative Error ranges (from ±5 to ±40) Department of Building Physics & Building Ecology, Vienna University of Technology 11 / 15
Conclusion The results indicate subpar performance by all models There is considerable uncertainty in the relationship between diffuse fraction and clearness index (especially for k t values between 0.3 and 0.7). Future studies shall address the possibility of developing more accurate predictive models for the Vienna location Department of Building Physics & Building Ecology, Vienna University of Technology 12 / 15
The measured values of diffuse fraction of global horizontal irradiance (Vienna) as a function of the clearness index Department of Building Physics & Building Ecology, Vienna University of Technology 13 / 15
Conclusion The results indicate subpar performance by all models There is considerable uncertainty in the relationship between diffuse fraction and clearness index (especially for k t values between 0.3 and 0.7). Future studies shall address the possibility of developing more accurate predictive models for the Vienna location Department of Building Physics & Building Ecology, Vienna University of Technology 14 / 15
Thank you for your attention Department of Building Physics & Building Ecology, Vienna University of Technology 15 / 15