Overview

Grey box and black box MPC models, and many other data-based algorithms are trained using measurement data. Many algorithms exist for doing so, which are often positioned under the umbrella of ‘artificial intelligence’. During the training period, an algorithm attempts to learn how model inputs (e.g. control setpoints, outdoor temperature or heating power) affect model outputs (e.g. building temperature and heating cost). The algorithm can only learn from the observed behavior and for models with many inputs and outputs it becomes increasingly hard to distinguish what the influence is of each input on each output. In practice, this means that grey-box and black-box models are often quite simple, e.g. by assuming that the whole building has the same temperature. The degree of accuracy can be increased somewhat by including physical knowledge in the model equations. This has led to an increasing interest in grey-box modelling. The limited complexity limits the optimisation potential that the optimisation algorithm can work with, and model errors due to simplifications can lead to unsatisfactory performance. E.g. when one room requires heating and another requires cooling, a problem may occur. The MPC may choose not to cool and not to heat, since the heating and cooling loads cancel each other out in a simple model where both rooms are represented using a single room.

At the other extreme there exist white-box models. The white box philosophy is that there is no need to train what we already know. This is why we have engineering faculties! There exists an entire academic discipline about building energy simulation that has developed mathematical models for modelling important physical processes within buildings. These models use physical knowledge such as the building geometry in generic component models. The resulting component models are combined into a system model. Here too, the level of detail can be chosen, which affects the time required to implement the model and to perform computations using that model. Granted, these models are not perfect, they serve as a good starting point and benchmark for the building behavior. See for instance below for a heat pump validation exercise that was part of our development work, which shows a nearly perfect match between measurements and the model!