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.

本文介绍了一种基于随机微分方程的非线性灰盒 (GB) 模型，该模型描述了丹麦一所配备水基供暖系统的学校建筑的热动态。该建筑通过热交换器连接到当地的区域供热网络。热量主要通过散热器和部分通过通风系统输送到房间。基于物联网传感器的监控系统可提供有关房间内室内气候和建筑物热负荷的数据。使用这些数据，我们使用最大似然法估计建筑物供暖系统模型的未知状态和参数。本文的重要创新之处包括电路中的水流模型和散热器恒温器中阀门的状态。非线性模型准确预测室内空气温度、回水温度和热负荷。该模型背后的想法为使用不同类型的水基供暖系统（如空气对水/水对水热泵）的建筑的 GB 模型奠定了基础。这种 GB 模型使模型预测控制能够控制例如室内空气气候或提供灵活性服务。