Abstract
State-of-the-art Model Predictive Control (MPC) applications for building heating adopt either a deterministic controller together with a nonlinear model or a linearized model with a stochastic MPC controller. However, deterministic MPC only considers one single realization of the disturbances and its performance strongly depends on the quality of the forecast of the disturbances, which can lead to low performance. In fact, inadequate building energy management can lead to high energy costs and CO2 emissions. On the other hand, a linearized model can fail to capture some dynamics and behavior of the building under control. In this article, we combine a stochastic scenario-based MPC (SBMPC) controller together with a nonlinear Modelica model that is able to provide a richer building description and to capture the dynamics of the building more accurately than linear models. The adopted SBMPC controller considers multiple realizations of the external disturbances obtained through a statistically accurate model, so as to consider different possible disturbance evolutions and to robustify the control action. To this purpose, we present a scenario generation method for building temperature control that can be applied to several exogenous perturbartions, e.g.solar irradiance, outside temperature, and that satisfies several important stastistical properties, in contrast with simpler and less accurate methods adopted in the literature. We show the benefits of our proposed approach through several simulations in which we compare our method against the standard ones from the literature, for several combinations of a trade-off parameter between comfort and energy cost. We show how our SBMPC controller approach outperforms the standard controllers available in the literature.
Highlights
Energy consumed in buildings for heating, ventilation, and airconditioning (HVAC) purposes accounts for around half of total energy used in buildings [1–5]
We focus on a scenario-based Model predictive control (MPC) (SBMPC) algorithm that includes both a nonlinear system description through Modelica, while using a scenario generation method based on probability distributions obtained empirically, making it a very suitable tool for a building heating control problem
We have presented a stochastic SBMPC controller using a Modelica nonlinear model that can be applied to building heating in buildings and that overcomes the limitations of both deterministic and linear MPC approaches
Summary
Let us define a random variable X representing some time series process, e.g. external temperature, and the related multidimensional random variable X representing the distribution of X in a time grid of N time steps, i.e. X 1⁄4 1⁄2X1; . . . ; XN>. We will build the multivariate distribution of X, i.e. FðXÞ, so that by sampling from FðXÞ we can obtain M scenarios of X, i.e. x1; . When building FðXÞ, in order to satisfy the desired properties of scenario generation methods (see Section 1.1.2), several requirements need to be satisfied: FðXÞ should not be substituted by the N marginal distributions FðX1Þ; . FðXiÞ only represents the distribution of X at time step i but does not consider the correlation between X1; . The distribution FðXÞ should include any external dependency of X. If X represents the ambient temperature, FðXÞ needs to explicitly include the dependency w.r.t. factors like the solar irradiance I, i.e. FðXÞ :1⁄4 gðX; IÞ
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