Influence of Solar Radiation Models in the Calibration of Building Simulation Models

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1 Influence of Solar Radiation Models in the Calibration of Building Simulation Models J.K. Copper, A.B. Sproul 1 1 School of Photovoltaics and Renewable Energy Engineering, University of New South Wales, Kensington, NSW, 2052 ABSTRACT This study investigates the methods used to obtain solar radiation data, in the absence of experimental data, for use in calibrating building simulation models to measured energy consumption. Two global and two diffuse/direct irradiance models are presented and compared to experimental data for Melbourne, Australia. In the case where experimental global irradiance data is available, values are used as input into various models to obtain diffuse and direct irradiance. In the absence of experimental data, the approach taken is to estimate global irradiance with a separate model and then feed these values into the diffuse/direct models. The errors associated with both of these approaches are investigated by comparing the modelled diffuse and direct irradiance values with known experimental data for Melbourne, Australia over a period of a number of years. For the approach where global irradiance is estimated from a model, the resulting direct and diffuse data was found to differ significantly from the experimental data. Further this paper investigates the influence that these differences in irradiation models have on building simulation programs. Our initial results for a standard building model indicate that these differences in irradiation values cause differences in the prediction of sensible cooling loads exceeding 30%. Hence, it was concluded that caution should be taken when using estimated values of irradiance if attempting to calibrate a building simulation model to measured energy data. Keywords Radiation, global, direct, diffuse, building, simulation INTRODUCTION Calibration of building simulation models involves comparisons of measured energy consumption to simulated thermal performance and energy data of buildings over a defined time period. Weather data for these simulations must have hourly records of temperature, humidity, wind speed and both direct and diffuse solar radiation. The Australian Climatic Data Bank consists of hourly records over numerous years of these climatic variables, however it only contains data up to 2004 (ACADS-BSG 2006). Up to date data for temperature, humidity and wind speed for most locations are measured and freely available. However for most locations irradiance values are not recorded or only global irradiance is inferred from satellite information (Ridley, Boland et al. 2010). To overcome this lack of experimental data a number of mathematical relations have been developed to estimate irradiance. The global radiation models developed by Bird (Bird and Hulstrom 1981), Kasten (Kasten and Czeplak 1980) and the model used to develop the International Weather files for Energy Calculation (IWEC) (Thevenard and Brunger 2002) were developed using a two step process where the level of irradiance is first calculated under clear sky conditions and then adjusted to take into account the effects of cloud cover. Other models have also been developed which estimate global radiation based on relations to meteorological weather parameters like temperature, Solar2010, the 48 th AuSES Annual Conference

2 humidity, wind speed and cloud cover. The most common of which is a model developed by Zhang and Huang (Zhang, Huang et al. 2002). Similarly, a number of relations have been developed to estimate diffuse and direct horizontal irradiance based on known values of global irradiance, the most recent from Ridley et al. (Ridley, Boland et al. 2010) and Zhang (Zhang 2006). The accuracy of using global or diffuse radiation models singularly have been reported for numerous locations across the globe. However only a selection of analyses have been reported discussing accuracies of feeding global irradiance estimates into diffuse/direct models. Thevenard et al, mentioned that there should be a very legitimate concern about piling up models as they did for the production of IWEC files (Thevenard and Brunger 2002). Unfortunately Thevenard et al. only presented comparative results between experimental and modelled global irradiance and did not present a comparison for diffuse and direct irradiances. Zhang and Huang presented comparative results for diffuse irradiance for two locations in China after superimposing the Watanabe diffuse model (Watanabe, Urano et al. 1983) on the outputs of their global radiation model (Zhang, Huang et al. 2002). They reported that the goodness of fit, between measured and estimated daily diffuse irradiance, achieved good but not great results with coefficient of determination values (R 2 ) of and Results for the correlation between estimated direct and measured direct values were not presented. Another study conducted by Krarti et al. (Krarti and Seo 2006) investigated two model combinations for the location of Tunisia. The results showed that the average monthly root mean squared errors (RMSE), calculated from hourly modelled and experimental values, ranged between 38 and 126 W/m 2. These errors are large in proportion to the measured hourly diffuse values which predominantly fell below 300 W/m 2. Again the results were not presented for the direct component of irradiance. A small number of journal articles have been written discussing the accuracies of using estimates of diffuse and direct irradiance in building energy simulations. Al- Anzi et al, continued the work of Krarti et al. and developed TMY weather files to determine the impacts of solar model selection on building energy analysis for Kuwiat (Al-Anzi, Seo et al. 2008). In this case the authors re-solved the coefficients of the model to measured data for the location under study, improving the accuracy of the global model estimates. The study simulated a 7 story office building with three irradiance scenarios; the experimental irradiance values, and the two combined model scenarios of Krarti et al. The results indicated that percentage errors on an annual basis, due to combining models, ranged between 0 to 9.3%. However, it should be noted that the percentage errors reported on an annual basis were significantly lower than reported errors in monthly irradiance estimates, due to cancellation effects of over and underestimation of global irradiance in different months. In this paper the predictions of four combinations of global and diffuse/direct models have been compared against six years of experimental irradiance data for Melbourne. The second part of this paper presents the simulation results from a building model using one year s worth of experimental irradiance data in comparison to the simulation results when estimated values of irradiance are used as input. SOLAR RADIATION ANALYSIS The solar data used within this study was sourced from the Australian Bureau of Meteorology (BOM), for the six years from 2000 to 2005, both years inclusive. The 2

3 data included on an hourly basis, global horizontal, direct normal and diffuse radiation in MJ/m 2. Non solar data for the same time period was obtained including temperature, dew point temperature, wind speed, wind direction and cloud cover. Processing of the raw data was undertaken to exclude missing or erroneous values. The data cleaning process removed an entire day s worth of hourly data when any one individual hourly parameter of temperature, humidity, radiation etc was missing or had a high level of uncertainty or appeared to be clearly erroneous. For each hourly experimental data point, an estimated value of irradiance was generated via the chosen irradiance models. Hourly estimated values and their difference from the experimental data were computed. Results for mean bias deviation (MBD), root mean squared deviation (RMSD) and the coefficient of determination (R 2 ) were calculated based on the cleaned data set which contained hourly data points (roughly equivalent to 4.6 years). With regards to irradiance model selection, this paper s focus is on the Zhang and Huang global model (Zhang, Huang et al. 2002), due to its employment in EnergyPlus (US-DOE 2010), and the BRL diffuse model (Ridley, Boland et al. 2010) as it included Australian data in its development and calibration. For a comparison the results of the Kasten global model (Kasten and Czeplak 1980), which was partially used by ASHRAE to generate the IWEC weather files, will also be presented as will be the direct/diffuse model developed by Zhang (Zhang 2006). Model coefficients were not resolved for the location of this study; all model coefficients used were as presented in their respective publications, except the coefficients for the Zhang and Huang model were taken from those proposed by Seo and Huang (Seo, Huang et al. 2008). These coefficients were chosen over the coefficients presented by Zhang and Huang as there was an improvement in the model fit for Australian locations. RADIATION MODEL RESULTS A graphical validation of the two diffuse/direct models plotted against experimental irradiances for Melbourne is presented in Figure 1. Mean bias deviation (MBD) values presented in Table 1 indicate that the BRL model overestimates diffuse radiation and underestimates direct radiation, while the Zhang model achieves the reverse statistics. Together the graphs and the statistics show that both models have a good fit to the measured data set, even though in the case of the Zhang model the coefficients were solved to fit Chinese data. Figure 1: BOM experimental data with BRL and Zhang model estimates 3

4 Table 1: Diffuse and direct irradiance statistics for BRL and Zhang model estimates against BOM experimental data Figure 2 presents graphically the estimates of global irradiation from the Zhang and Huang and Kasten models in comparison to the measured global irradiances for Melbourne. Table 2 presents the statistics for these comparisons. The statistics and scatter plots indicate that both models achieve almost identical linear correlations, with R 2 values of and The results also indicate that the Zhang and Huang model overestimates the amount of global radiation with a MBD of 20 W/m 2 whilst the Kasten model only slightly underestimated with a MBD of -1 W/m 2. Although the Kasten model achieved a better MBD it is evident from Figure 2 that the Kasten model was unable to appropriately model high levels of global irradiance. Figure 3 illustrates this further by presenting the diffuse fraction and clearness index relationship of the combined global and BRL diffuse model estimates, in comparison to the experimental data. The results show that the Kasten global radiation model is unable to appropriately replicate clear sky conditions, i.e. periods of zero to low cloud cover with low levels of diffuse radiation and high levels of direct radiation. The Zhang and Huang global model does not appear to have the same problem. Figure 2: BOM global irradiance in comparison to Zhang and Huang and Kasten model estimates Table 2: Global irradiance statistics for model estimates against BOM data 4

5 Figure 3: Experimental BOM diffuse irradiance data in comparison to estimated data from the BRL diffuse model (i) with the Zhang and Huang global model as input (left) and (ii) with the Kasten global model as input (right). The results from combining diffuse/direct models with global irradiance models caused a doubling of the differences when compared to diffuse and direct estimates calculated from experimental global irradiances. For all models considered, Table 3 shows that the root mean square deviation increased to an average of 91 W/m 2 for diffuse radiation and 268 W/m 2 for direct radiation. This is in comparison to the case presented in Table 1 where irradiance estimates were calculated from experimental values of global radiation, with a RMSD of 46 W/m 2 for diffuse and 120 W/m 2 for direct irradiance. This increase in model uncertainty is visually presented in Figure 4, where the outputs of the BRL diffuse model is plotted against the BOM experimental data. Overall the results indicate that the differences caused by the choice of diffuse/direct model are less significant than the differences caused by global model selection. Based on these results the Zhang and Huang global model in conjunction with the Zhang diffuse model appears to achieve the least biased results. Table 3: Diffuse and Direct irradiance statistics for combined model estimates against experimental data 5

6 Figure 4: Experimental BOM diffuse irradiance data in comparison to estimated data from the BRL diffuse model (i) with experimental BOM global irradiance as input (left) and (ii) with the Zhang and Huang global model as input (right). BUILDING SIMULATION ANALYSIS The following section presents the results of a simulation study investigating the impacts that irradiance data has on the outputs of a building simulation model. For this analysis one year s worth of experimental BOM irradiance data was used as a reference data set. DesignBuilder, which utilises the EnergyPlus simulation engine, was used to obtain the thermal modelling results presented within this section (DesignBuilder 2010). The EnergyPlus simulation platform was chosen for its ability to be able to model numerous building types and thermal energy systems. Weather files compatible with EnergyPlus were generated with the use of EnergyPlus auxiliary weather generator program (US-DOE 2010). The only difference between the weather files were the inputs for global, direct and diffuse irradiance. A weather file was developed for each of the four model combinations as well as one based on the experimental irradiance data from the BOM. This section presents the simulated sensible heating and cooling loads for a building model of a standard house run under each of the irradiance scenarios. Building Model A simple single storey project style home design was used for this simulation analysis. House 4, from Appendix A.2., in the Australian Building Codes Board (ABCB) study investigating building improvements to raise house energy ratings from 5.0 stars, was selected (ABCB 2009). Figure 5 presents the floor plans for this building. This house has a conditioned floor area of 197m 2, is modelled with no eaves and has a total window to wall ratio (WWR) of 27%. The breakdown of WWR per surface orientation is 27% North, 34% East, 25% South and 29% West. Table 4 presents the material construction details as modelled in DesignBuilder/EnergyPlus. 6

7 Figure 5: Floor plan for House 4 from Appendix A.2 of ABCB study (ABCB 2009) Table 4: Material summary for simulated building Building Element Material U-Value (W/m 2.K) Wall Brick Veneer/Airgap/Plaster Ceiling Plaster/249mm Glass Wool (rolls) Insulation/Plywood Roof Clay tile/airgap/roofing felt Floor Kit/Bath Concrete slab/tile Floor Bed/Living Concrete slab/underlay/carpet Window Single Clear 3mm/Wooden Frames / SHGC Simulation Results Figure 7 presents the monthly sensible heating and cooling loads for all model combinations and for the weather file generated from the BOM experimental irradiances. The graphs show that on a monthly basis, use of irradiance estimates from the combined models is able to pick up the trend in sensible heating and cooling. It should be noted that the level of differences in predicted sensible cooling is larger than the difference in sensible heating. Table 6 presents the average daily statistics and the annual heating and cooling load. Again the results indicate that a closer match occurs for sensible heating then for sensible cooling. This result is an artefact of the level of errors in prediction at the irradiance level, where differences in direct irradiance estimates are 1.5 times larger than for diffuse irradiances. This becomes important in the calculation of building cooling loads which depend on the level of direct irradiance entering a building. 7

8 Figure 7: Simulation results for sensible heating (left) and sensible cooling (right) utilising the BOM experimental irradiance values in comparison to the four model combination results. Table 6 also presents the coefficient of variation of the root mean square error (CV(RMSE)) which indicates the overall level of uncertainty of a models outputs. In the case of sensible cooling, CV(RMSE) annual results vary between 36.7% and 38.4%. This level of error is higher than the threshold limit for acceptance within global measurement and verification guidelines (Nexant 2008). These guidelines set the threshold at 30% for CV(RMSE) calculated based on hourly results and 15% for CV(RMSE) calculated based on monthly results. The results of CV(RMSE) on a monthly basis for this work, calculated based on daily simulation results, vary between 15% and 200% for sensible cooling whilst for sensible heating the values fall below 7% except for the month of November. This month corresponds to the month with the highest levels of differences in direct irradiance estimations. Overall the results indicate that the difference in the prediction of sensible cooling loads is high and this should be considered if weather files based on combined model estimates of irradiance are to be used for calibrating a building simulation model to measured energy data. Table 6: Simulation statistics for sensible heating and sensible cooling loads calculated from combined model irradiances against BOM experimental irradiances SUMMARY AND CONCLUSION Two global and two diffuse/direct radiation models were evaluated in combination against experimental data from the BOM for the city of Melbourne, 8

9 Australia. In addition, a simple simulation analysis was performed to determine how the level of differences in irradiance estimates carried over into the prediction of annual energy use for a simple project home style house. The results of the irradiance analysis suggested that although individually global and diffuse solar radiation models achieve good correlation to measured data, combining the results of global and diffuse/direct models leads to poor results, particularly in the prediction of direct irradiance. Similarly, the results of the simulation analysis indicated that no matter which combination of solar radiation models was chosen the overall level of uncertainty in the prediction of sensible cooling loads exceeded 30%. Such a level of uncertainty lead to the conclusion that caution should be taken if combined model estimates of solar radiation are used in building simulation models that are to be calibrated and compared against real performance energy data. In the case where no irradiance data is available and a combination of models must be used to predict diffuse and direct irradiance, then the Zhang and Huang global model with the coefficients presented by Seo et al. in conjunction with the Zhang direct model achieved the least biased results of the models investigated. Although only two global radiation models and one location were presented in this paper, other models have been tested and future publications will expand on this work. DEFINITIONS The following definitions are extracted from the U.S. Department of Energy Measurement and Verification Guidelines for Energy Projects (Nexant 2008). CV(RMSD) Coefficient of variation of the root mean squared deviation (error). This value indicates the overall uncertainty in the prediction of a model/simulation. The lower the CV(RMSD) the better the calibration. ( )= MBD Mean bias deviation (error). The MBD indicates how well the results predicted by a model compare to the measured data. Positive values indicate that the model over predicts actual values; negative values indicate that the model under predicts actual vales. However it is subject to cancellation errors, where the combination of positive and negative values serves to reduce the MBD. = ( ) RMSD Root mean squared deviation = ( )2 Where M is the measured (experimental) data point, S is the simulated (estimated) data point and N is the total number of data points in the sample. REFERENCES ABCB (2009). Building improvements to raise house energy ratings from 5.0 stars. A. B. C. Board, Constructive Concepts and Tony Issacs Consulting. ACADS-BSG. (2006). "The Australian Cimatic Data Bank." from 9

10 Al-Anzi, A., D. Seo, et al. (2008). "Impact of Solar Model Selection on Building Energy Analysis for Kuwait." Journal of Solar Energy Engineering 130(2): Bird, R. E. and R. L. Hulstrom (1981). "Direct insolation models." Journal of Solar Energy Engineering 103: DesignBuilder (2010). DesignBuilder Simulation Software. London, DesignBuilder Software Ltd., Kasten, F. and G. Czeplak (1980). "Solar and terrestrial radiation dependent on the amount and type of cloud." Solar Energy 24(2): Krarti, M. and D. Seo (2006). "Comparative analysis of three solar models for Tunisia." ASHRAE Transactions 112: Nexant, I. (2008). M & V Guidelines: Measurement and Verification for Federal Energy Projects Version 3.0. U. S. DOE. Boulder, CO, Federal Energy Management Program. Ridley, B., J. Boland, et al. (2010). "Modelling of diffuse solar fraction with multiple predictors." Renewable Energy 35(2): Seo, D., J. Huang, et al. (2008). "Development of Models for hourly solar radiation predictions." ASHRAE Transactions 114: Thevenard, D. J. and A. P. Brunger (2002). "The development of typical weather years for international locations: Part I, Alogorithms." ASHRAE Transactions 108: US-DOE (2010). EnergyPlus Energy Simulation Software, U.S. Department of Energy, Watanabe, T., Y. Urano, et al. (1983). "Procedures for seperating direct and diffuse insolation on a horizontal surface and prediction of insolation on tilted surfaces." Transactions, No.330, Architectural Institute of Japan, Tokyo, Japan. Zhang, Q. (2006). "Development of the typical meteorological database for Chinese locations." Energy and Buildings 38(11): Zhang, Q., J. Huang, et al. (2002). "Development of typical year weather data for Chinese locations." ASHRAE Transactions 108(2): BRIEF BIOGRAPHY OF PRESENTER Jessie Copper is a PhD student in the field of energy efficiency and building simulation at the school of Photovoltaics and Renewable Energy (SPREE) at UNSW. She received her Bachelor of Engineering in Photovoltaics and Renewable Energy in 2004, and went on to work for BP Solar as a Process Engineer and R&D device scientist until

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