Estimating dynamic solar gains from on-site measured data: An ARX modelling approach

Abstract

On-site measured data in combination with statistical methods is used more and more to assess the actual performance of a building and to develop simplified models that can be used in model predictive control, fault detection, and optimization of energy grids. Most of the methods are based on a simplified heat balance of the building. For this heat balance, solar gains, referring to the part of energy supplied by the sun, are a vital factor. Gauging solar gains and their time dependency in practice is, however, challenging. Most models assume the solar aperture of the building as an invariable property, although it is highly dependent on the sun position during the time of the day and year. In this study a statistical modeling method, based on in-situ measurement data, is developed to estimate the time-varying solar gains more precisely. The method integrates basis splines (B-splines) into an ARX model (Auto-regressive with eXogenous input). Verified by white-box model simulation outcomes, it is demonstrated that this B-splines integrated ARX modelling approach can reflect the key information of the dynamic features ofthe solar gainsto a large extent. Most importantly, only a limited size of in-situ measurement data of high-frequency is required in this method, indicating its good efficiency in dynamic solar gain estimation.