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With the increasing integration of decentral renewable energy systems in the residential sector, the opportunity to enhance the control via model predictive control is available. In this article, the main focus is to investigate the objective function of the model predictive controller (MPC) of an integrated thermal-electrical renewable energy system consisting of photovoltaics, solar thermal collectors, fuel cell along with auxiliary gas boiler and electricity grid using electrical and thermal storage in a single-family house. The mathematical definition of the objective function and the depth of detailing the objectives are the prime focus of this particular article. Four different objective functions are defined and are investigated on a day-to-day basis in the selected six representative days of the whole year for the single-family house in Ehingen, Germany with a white-box simulation model simulated using TRNSYS and MATLAB. Using the clustering technique then the six representative days are weighted extrapolated to a whole year and the outcomes of the whole year MPC implementation are estimated. The results show that the detailing of the mathematical model, even though is time and personnel consuming, does have its advantages. With the detailed objective function J#, 9% more solar thermal fraction; 32% less powerto-heat at an expense of 32% more gas boiler usage; 6% more thermal system effectiveness along with 10% increased total self-consumption fraction with 16% decrease in space heating demand, 492 kWh more battery usage and 66% reduced fuel cell production is achieved by the MPC in comparison to the status quo controller. Except for the effectiveness of the thermal system with increased gas boiler usage, which occurs due to less power-to-heat, the detailed objective function in comparison to the simple mathematical definition does evidently increase the smartness of the MPC.

Configuring the Objective Function of A Model Predictive Controller for An Integrated Thermal-Electrical Decentral Renewable Energy System