Time-dependent solar aperture estimation of a building: Comparing grey-box and white-box approaches

Abstract

This paper proposes a B-splines integrated method combining in-situ data with grey-box modeling to estimate buildings' dynamic solar gain more efficiently than the conventional white-box model and much more precisely than the classic grey-box model. Solar gain, referring to the overall indoor energy gain supplied by solar radiation, plays a vital role in the indoor energy balance. Estimating dynamic solar gain precisely is essential to building energy optimization, e.g., in model predictive control. However, in almost all existing grey-box modeling works, a constant solar gain factor (solar aperture; gA) is assumed to estimate dynamic solar gain, which almost certainly will result in solar gain prediction errors, especially in buildings with unevenly distributed windows. To fill this gap, this study presents an advanced B-splines integrated grey-box model, using customized B-splines to advance the constant gA assumption toward its nature of time-dependence and precisely characterize the dynamic solar gain conclusively. On-site measured datasets of a portable site office (PSO) representing a ‘simplified’ building, under two scenarios with windows fully or partially uncovered, serve as test cases. To verify the physical interpretation of outcomes estimated by the proposed method, based on the said test cases, the proposed B-splines integrated grey-box model is compared with a classic white-box simulation. It is concluded that the proposed method can reveal the main trends and key dynamic features of solar gain very well, but still has some limitations of quantifying ‘local’ details with acceptable variations. Nevertheless, given that the proposed method merely asks for a very limited amount of low-frequency data, the proposed method is considered as a much more effective alternative to the classic white-box simulation approach, which requires massive and often hard-to-collect input data.