Models used for forecasting, control and optimisation within the Smart-Energy Operating System can be described as grey-box models. In the digital twin context, these models are optimised for real-time operations and, most importantly, for assimilating information from available sensors into the model parameters (red dash line in the figure below). Grey-box models used in digital twins act as simplified models of the associated system - for instance, that of a building, wastewater treatment plant, heat pump.
Grey-box models in data-driven digital twins of energy systems
Developing a digital twin typically requires a large number of equations and relations. This implies a large number of parameters that may not be easy to identify. The grey-box modelling framework bridges the gap between purely data-based approaches (black-box) and physics-based approaches (white-box). By combining information from physics with information from sensors, it enables model improvements and hidden states of the system to be revealed.
Grey-box models vs white- and black-box models
Unlike classical digital twins that are represented through static 3D models, the grey-box approach allows for a data-driven digital twin that facilitates assimilation of near real-time information from sensors into the model descriptions, leading to improved forecasting, control and optimisation.
Grey-box models are often formulated as Hidden Markov Models through discretely observed stochastic differential equations. Stochastic elements of grey-box models provide a coherent description of the uncertainty originating from sensors, model approximations and unrecognised explanatory variables. For models, this feature is important as it allows for self- and auto-calibration as well as built-in real-time adaptation to system changes.
Grey-box modelling has been successfully deployed in many applications related to energy systems, smart cities and buildings. Grey-box models are suitable for scenario generation and can be used as input to decision making under uncertainty using methods such as stochastic programming.
In BIPED, the approach will be used to derive suitable models for relevant parts of the energy system in Aarhus. As an example, a starting point may be a rather simple model of the water flow and heat loss related to the district heating use in a house. Here, we will take advantage of some of the most fundamental relations between load, flow and temperature differences in the district heating system. By integrating stochastic approaches, comprehensive digital twin models for the thermal dynamics, including heat consumption of buildings, can then be created.
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