Analytical Solution Strategy for Building Energy Dynamics With Stochastic Thermal Gains and External Temperature

Energy dynamics in buildings are inherently stochastic in nature due to random fluctuations from various factors such as heat gain (including the solar) and ambient temperature. This paper proposes a theoretical framework for stochastic modeling of building thermal dynamics as well as its analytical solution strategies. Both the external temperature and the heat gain are modeled as stochastic processes, composed of a periodic (daily) mean-value function and a zero-mean deviation process obtained as the output process of a unit Gaussian white noise passing through a rational filter. Based on the measured climate data, the indicated mean-value functions and rational filters have been identified for different months of a year. Stochastic differential equations in the state vector form driven by white noise processes have been established, and analytical solutions for the mean-value function and covariance matrix of the state vector are obtained. This framework would allow a simple and efficient way to carry out predictions and parametric studies on energy dynamics of buildings with random and uncertain climate effects. It would also provide a basis for the robust design of energy efficient buildings with predictive controllers.