Virtual Sensors for Estimating District Heating Energy Consumption under Sensor Absences in a Residential Building

District heating (DH) is an energy efficient building heating system that entails low primary energy consumption and reduced environmental impact. The estimation of the required heating load provides information for operators to control district heating systems (DHSs) efficiently. It also yields historical datasets for intelligent management applications. Based on the existing virtual sensor capabilities to estimate physical variables, performance, etc., and to detect the anomaly detection in building energy systems, this paper proposes a virtual sensor-based method for the estimation of DH energy consumption in a residential building. Practical issues, including sensor absences and limited datasets corresponding to actual buildings, were also analyzed to improve the applicability of virtual sensors in a building. According to certain virtual sensor development processes, model-driven, data-driven, and grey-box virtual sensors were developed and compared in a case study. The grey-box virtual sensor surpassed the capabilities of the other virtual sensors, particularly for operation patterns corresponding to low heating, which were different from those in the training dataset; notably, a 16% improvement was observed in the accuracy exhibited by the grey-box virtual sensor, as compared to that of the data-driven virtual sensor. The former sensor accounted for a significantly wider DHS operation range by overcoming training data dependency when estimating the actual DH energy consumption. Finally, the proposed virtual sensors can be applied for continuous commissioning, monitoring, and fault detection in the building, since they are developed based on the DH variables at the demand side.