Gossen’s first law in the modeling for demand side management: a thorough heat pump case study with deep learning based partial time series data generation

Gossen’s First Law describes the law of diminishing marginal utility. This paper aims to further verify the proposed hypothesis that Gossen’s First Law also holds in the modeling for Demand Side Management (DSM) with a thorough heat pump case study. The proposed hypothesis states that in general the complexity-utility relationship in the field of DSM modeling could be represented by a diminishing marginal utility curve. On the other hand, in data based modeling, when utilizing a large dataset for validation, the data integrity is critical to the reliability of the results. However, the absence of partial time series data may occur during the measurement due to missing sensors or IT related issues. In this work, an extensive real-world open dataset of a ground source heat pump is utilized for the case study. In the raw data, one key variable namely the flow rate is missing. Thus, three different algorithms based on machine learning and deep learning architectures namely Random Forest (RF), Long Short-Term Memory (LSTM) and Transformer are applied to predict the flow rate by utilizing an open loop forecasting. The raw data are first pre-processed with a time interval of one hour and then used for training, validation and forecast. Furthermore, a modified persistence model as the baseline is also defined. The predicted flow rate using LSTM yields the lowest error of 7.47 $$\%$$ nMAE and 10.56 $$\%$$ nRMSE respectively. The forecast results are then utilized in the following step of modeling of a heat pump use case. With the introduced quantification method for complexity and a modified version for utility, we further verify the proposed hypothesis with a longer time horizon of 7 days.