## 2 Literature Review
The superior economic performance of the proposed optimization framework was verified by comparing it with two conventional operational strategies. The optimal strategy demonstrated a reduction in the operating costs of approximately 8% over a two-month cooling period. Reference [47] evaluated a price-responsive MPC strategy for a solar thermal heating system integrated with TES for buildings with high occupancy variability. The coupled system supplies the building with heating through a low-temperature underfloor heating system. A case study was conducted on a university building in Nottingham, UK, with the objective of evaluating the feasibility of the proposed heating system, which is controlled by an MPC strategy. The MPC controller was designed to optimize the solar heating system's operation by dynamically adjusting to forecasted weather, occupancy, and solar availability, with the aim of balancing indoor comfort with energy efficiency. Finally, economic model predictive control (EMPC) [48] represents a variant of model predictive control used for optimizing economic revenues arising from controlled dynamical processes. It has established itself as a variant of standard MPC, departing from the latter in that arbitrary cost functions are allowed in the formulation of the stage cost. The reference [49] illustrated how the EMPC can be adapted to accommodate time-varying or parameter-varying costs. Several references have dealt with EMPC for energy management in residential buildings. In [50], an MPC utilizing artificial neural networks (ANNs) was implemented in a residential building. The ANN-MPC was successfully tested and demonstrated satisfactory performance in predicting the building's energy consumption. Subsequently, the controller was modified to function as an EMPC, with the objective of optimizing demand flexibility, defined as the ability to adapt energy demands in response to fluctuations in supply. The operational costs of energy usage were associated with this demand flexibility, which was represented by three flexibility indicators: the flexibility factor, the supply cover factor, and the load cover factor. The results of the day-long test demonstrated that these flexibility indicators were optimized when the EMPC controller's demand flexibility was compared to that of a conventional proportional-integral (PI) controller. Specifically, the flexibility factor ranged from \(-0.88\) to \(0.67\), the supply cover factor from \(0.04\) to \(0.13\), and the load cover factor from \(0.07\) to \(0.16\). To conclude, reference [51] examined the potential of the EMPC of complex residential energy systems with electric coupling to the public grid. The system under examination incorporates a battery energy storage system, photovoltaic power generation, an air-to-water heat pump, thermal energy storage, and a building model. The aforementioned power generation system provided energy for electric loads, as well as domestic hot water and space heating. Two algorithms for distributed MPC were developed, and their efficacy was evaluated in comparison to a common reference control concept and a centralized model predictive control approach. In order to facilitate a comparison of the annual operational costs, the current German energy prices and subsidies were incorporated into the economic calculation. The results demonstrated an enhanced performance of the developed approaches, with an 11.6% reduction in cost in comparison to the reference. This was achieved by increasing the heat pump seasonal performance factor by 3.4%, reducing the curtailment of electrical photovoltaic energy to 21.5% of the reference value and preventing the operation of the auxiliary heater. Furthermore, increased photovoltaic self-consumption by the heat pump resulted in a slight reduction in battery storage operation. In conjunction with the aforementioned monetary and energetic advantages, MPC increased comfort with regard to the violation of minimum limits for the comfort criteria. Finally, the issue of resilience is of particular concern.