A novel methodology for map-based model fitting: A case study with a Dual Source Heat Pump experimental dataset

Abstract

[EN] This paper presents a new methodology to adjust map-based models to experimental data and reports the main results of a comprehensive experimental campaign of a Dual Source Heat Pump (DSHP) prototype. The prototype tested incorporates variable speed components (compressor, circulation pumps, and fan). The novelty of this prototype lies in its ability to select two possible heat sources: air or ground. Thus, it can operate as a geothermal or aerothermal heat pump, as well as a chiller, thanks to the additional capacity to reverse the cycle. Thanks to this hybrid approach, several advantages can be obtained compared to conventional equipment, such as higher efficiency, the requirement of smaller borehole heat exchangers, or the absence of defrost cycles. In a prior study, polynomial models were developed to accurately characterize the DSHP¿s performance (i.e., condenser and evaporator capacities and electrical energy consumption). These models were obtained considering the external variables to the unit as independent variables to facilitate their applicability using variables commonly measured in real installations. Due to the complexity of heat pump performance, which in current equipment can be influenced by up to 5 or 6 independent variables, the search for suitable polynomial models required the availability of a complete working map including more than 3000 working points. Thus, this previous work developed these models based only on simulation results. In this sense, this paper concludes the development of these models by focusing on two critical issues concerning empirical model development. The first aspect involves determining the minimum number and location of testing points needed to define the experimental sample for the model adjustment. The reported experimental data were obtained by analyzing the most suitable experimental design methodology to create the experimental matrices in each operating mode of the DSHP. The second aspect focuses on the final adjustment of models using experimental data. A novel fitting approach for empirical models is introduced in the last part of this study. The developed methodology enables the integration of simulation and experimental results for the final fitting of empirical models through a two-step adjustment. The first step involves analyzing and defining polynomial functionals from the complete working maps generated by simulation. Subsequently, in a second step, the polynomial models are refitted to a suitable experimental sample using the methodology presented in this work. The latter allows for the increase of the accuracy of the models and the minimization of experimental costs. This novel approach ensures a robust characterization of systems with many independent variables using a minimum amount of experimental data. Significant benefits can be obtained from its application, such as the reduction of experimental cost and an increase in the model¿s accuracy through an effective combination of both experimental and simulated information. Furthermore, it can be considered of general applicability to other engineering problems where the characterization of physical systems influenced by a high number of independent variables is required.