## 1 Introduction
### Control Methods of Heat Pumps Integrated into Ventilation Systems  
One distinctive feature of HVAC systems is their technologically defined yet constantly stochastic energy demand throughout the year, the day, and sometimes even within hours. The operation modes of heat pumps need to be adjusted depending on the continuously changing ambient temperature. Additionally, decisions must be made regarding the outdoor air temperature at which the highest nominal indicators can be achieved while maintaining system functionality at other temperatures.  
Based on the thermodynamic dependencies of fluids, under steady-state conditions, all of the system's state points within the cycle of the heat pump can be defined on the basis of three values of enthalpy at the outlets of the evaporator, compressor, and condenser, along with one pressure or temperature value (corresponding to one of those three enthalpies). To calculate heat transfer quantities, the refrigerant mass flow rate is required. This degree of freedom is a hydrodynamic rather than a thermodynamic variable and cannot be captured in the _p-h_ diagram of the cycle. Therefore, the heat pump cycle has a total of four thermodynamic degrees of freedom. [PERSON] and [PERSON] [14] presented a case of optimizing these degrees of freedom to reduce the amount of destroyed exergy. It has been theoretically proven that optimization could increase the COP of the refrigeration system by 52.5%. However, optimal operational points of the cycle can be achieved by simultaneously adjusting the system's high and low pressures.  
[PERSON] and [PERSON] [15] examined the possible degrees of freedom in the vapor compression cycle from the component perspective. They defined five controllable degrees of freedom: compression work, expansion valve permeability, optimal heat transfer in two heat exchangers, and the \"active charge\" in the cycle. \"Active charge\" refers to the mass accumulated in the process equipment, mostly in two heat exchangers. [PERSON] and [PERSON] [15] suggested controlling the amount of \"active charge,\" which indirectly determines the \"pressure level\" in the cycle. However, others, when optimizing and controlling vapor compression cycle systems, essentially ignored this degree of freedom. Additionally, in this work [15], three out of the five identified degrees of freedom are constrained for technical reasons, leaving the problem of 2 degrees of freedom, where the size of condensation sub-cooling and evaporation superheating is optimized.  
In practice, most control methods present the refrigerant mass flow rate and the pressure or temperature of the evaporator to the control system operation. The enthalpies of the condenser and evaporator outlets depend on heat transfer indicators and environmental conditions. The refrigerant flow rate can be controlled by a variable-speed compressor. The state of the evaporator is controlled by a variable-opening expansion valve. This provides two control degrees of freedom. The position of the expansion valve that ensures the required evaporator conditions must depend on a specific operating mode of the refrigerant flow rate (or compressor speed). Most control methods studied by researchers aim to simulate one or both of the abovementioned degrees of freedom, while more advanced controllers focus on manipulating these variables through optimization of the objective function, such as reducing exergy destruction, maximizing the COP, or maintaining heating or cooling loads.