Energy balance
The window’s immediate energy balance is equal to incident solar energy minus the heat loss through the window, taking into account the position of the sun and the orientation and slope of the window. The incident solar energy is defined as the combination of direct and diffuse solar radiance reaching the window and the window’s solar energy transmittance (g-value). Direct solar radiance is corrected for the slope of the window and the position of the sun, which defines the angle of incidence on the window. The angle of incidence is calculated by the method described in European Solar Radiation Atlas [ESRA]. Diffuse solar radiance is corrected for the scattering effect of the sky by the method described in “Modelling daylight availability and irradiance components from direct and global irradiance” by Richard Perez et.al. Diffuse radiance includes reflected radiance from the earth, corrected for the slope of the window. Heat loss is defined as the product of the window’s insulating property (U-value), its area and the difference in internal and external temperatures.
Predicted conditions
Predicted conditions are based on weather data from a Danish reference year. For each month, 11, 12 and 13 hours were used to calculate an average temperature, solar radiance and cloud cover at noon. Those average values were used to divide the days of each month into five categories of cloud coverage: 5 – completely overcast: 4 – completely to partially overcast; 3 – partially overcast; 2 – partially overcast to clear skies; 1 – clear skies. Subsequently, averages were determined for temperature and solar radiance for categories 1, 3 and 5 called Sunny, Cloudy and Overcast. This enabled the determination of weather data in the middle of the day for three of those categories for every month of the year. Categories 2 and 4 were excluded to dismiss transitional periods. It is also an option to choose the category Night which for each month 23, 24 and 1 hours was used to calculate an average temperature.
Real time
Real time data is gathered near the building from a weather station where external temperatures and global vertical horizontal solar radiation are measured. External temperatures are entered directly into the calculation model whereas global radiance is divided into direct and diffuse contributions for each window with the methodology described in [Duffie & Beckman].
The indoor temperatures are not measured and instead it was assumed that for external temperatures equal to or less than 20 °C the internal temperatures are 21°C. For any other external temperatures, the assumption was made that the internal temperatures are 1°C higher than the external temperature.
References:
[DRY] H. Lund and J. M. Jensen “Design reference year, dry - et nyt dansk referenceår” Technical Report lfv-281, Laboratoriet for varmeisolering, Danmarks Tekniske Universitet, 1995.
[Duffie&Beckman] J. A. Duffie and W. A. Beckman “Solar Energy thermal processes”, John Wiley & Sons.
[ESRA] K. Scharmer and J. Greif “European Solar Radiation Atlas” Les Presses.
[Perez] R. Seals, J. Michalsky, R. Perez, P Ineichen and R. Stewart “Modeling daylight availability and irradiance components from direct and global irradiance” Solar Energy, 44:271–289, 1990.