Abstract
This paper introduces a non-linear grey-box (GB) model based on stochastic differential equations that describes the heat dynamics of a school building in Denmark, equipped with a water-based heating system. The building is connected to a local district heating network through a heat exchanger. The heat is delivered to the rooms mainly through radiators and partially through a ventilation system. A monitoring system based on IoT sensors provides data on indoor climate in the rooms and on the heat load of the building. Using this data, we estimate unknown states and parameters of a model of the building’s heating system using the maximum likelihood method. Important novelties of this paper include models of the water flow in the circuit and the state of the valves in the radiator thermostats. The non-linear model accurately predicts the indoor air temperature, return water temperature and heat load. The ideas behind the model lay a foundation for GB models of buildings that use different kinds of water-based heating systems such as air-to-water/water-to-water heat pumps. Such GB models enable model predictive control to control e.g. the indoor air climate or provide flexibility services.
Highlights
The use of fossil-based energy sources does not belong in a sustainable future [1]
This paper introduced a physically inspired stochastic differential equations (SDEs)-based nonlinear model to describe the complex heat dynamics of a school building with water-based heating
We model the thermostats in the radiators using a Sigmoid function to describe the level of water flow through the radiators
Summary
The use of fossil-based energy sources does not belong in a sustainable future [1]. Society must shift to energy sources where CO2-emissions lie within the planetary boundaries; i.e. we need to use resources that are renewable [2]. Complex building energy performance models based exclusively on physical equations, known as white–box models, are often used for providing simulations. This has many advantages: First, SDEs provide a natural method to model physical phenomena as they are formulated in continuous-time They include probabilistic uncertainty that accounts for modelling approximations, unrecognised exogenous variables, and uncertainty related to the provided input variables. They lay a solid foundation providing predictions of the system behaviour and for model-based optimal control, to predict system behaviour It is well-know that solutions to Ordinary Differential Equations (ODEs) are functions of time, and this implies that an ODE modelling framework assumes that we are able to predict the exact evolution in time of the states. Optimal control theory based on SDEs is well-established in the literature with numerous examples of applications, e.g. for control of glucose concentration in humans [20], building thermal control [21], and operation of waste-water treatment plants [22]
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