# Dynamic Energy Consumption Modeling for HVAC Systems in Electric Vehicles
## 2 Materials and Methods
### The HVAC Model
#### 2.1.1 Evaporator  
The thermal power balance in the evaporator can be modeled using the following equation:  
\[\dot{Q}_{eva,ref}(p_{eva})=\dot{Q}_{eva,\Delta T_{ml}}(p_{eva})\,, \tag{5}\]  
where \(\dot{Q}_{eva,ref}\) is the thermal power to the refrigerant and \(\dot{Q}_{eva,\Delta T_{ml}}\) is the thermal power of the air side calculated using the mean logarithmic temperature difference [15]:  
\[\dot{Q}_{eva,ref}=m_{ref}(h_{ref,out}-h_{ref,fin})\,, \tag{6}\]  
and  
\[\dot{Q}_{eva,\Delta T_{ml}}=f_{eva}(UA)_{eva}\Delta T_{ml}\,. \tag{7}\]  
In Equation (6), \(\dot{m}_{ref}\) is the refrigerant mass flow rate, while \(h_{ref,out}\) and \(h_{ref,in}\) are the enthalpies of the refrigerant fluid, respectively, at the inlet and outlet of the evaporator. In Equation (7), \(f_{eva}\) is a correction factor which depends on the evaporator typology, \((UA)_{eva}\) is the product between the global heat transfer coefficient of the evaporator and the heat transfer area (see Equation (11)) and \(\Delta T_{ml}\) is the mean logarithmic temperature difference [15]. The mean logarithmic temperature difference requires knowledge of the air and refrigerant temperatures at the inlet and outlet of the evaporator. The air temperature at the evaporator inlet is defined by the ventilation operation condition: indoor temperature set point (in case of recirculation) or external temperature (in case of outdoor air). The air temperature at the outlet of the evaporator (\(T_{air,out}\)) can be calculated from the following equation:  
\[\dot{Q}_{eva,air}=\dot{Q}_{eva,air,sen}+\dot{Q}_{eva,air,lat}=\dot{m}_{ref}(h _{ref,out}-h_{ref,in})\,, \tag{8}\]  
where the sensible and latent heat are obtained by  
\[\dot{Q}_{eva,air,sen}=\frac{\dot{V}_{air}p_{air}}{3600}c_{p,air}(T_{air,in}-T_ {air,out})\,, \tag{9}\]  
and  
\[\dot{Q}_{eva,air,lat}=\frac{\dot{V}_{air}p_{air}}{3600}r\Delta x\,, \tag{10}\]  
where \(r\) is the water latent heat of vaporization (2430 kJ/kg [16]) and \(\Delta x\) is the air humidity difference between inlet and outlet air flow. The evaporator model is the most complex component in the air conditioning system. This block allows calculation of the thermal load due to refrigerant evaporation, evaluation of the evaporating pressure and change in the physical properties of the refrigerant. The input data are the physical state of the refrigerant (the pressure of the refrigerant fluid is then updated inside the evaporator element), the temperature inside the vehicle at the last iteration, the set-point temperature (\(T_{sp}\)), the air flow rate and the geometry of the evaporator (or at least its global heat transfer coefficient, \(U_{eva}\)). In our case, the selected evaporator is made up of flat tubes made of louvered finned microchannels. If the global heat transfer coefficient is not known in advance, it is possible to calculate it from knowledge of the evaporator geometry and the heat transfer mechanism. Then, due to the high conductivity and small thickness of the tubes, the expression of \((UA)_{eva}\) can be simplified as follows [15]:  
\[(UA)_{eva}=\frac{1}{h_{ref,eva,h_{ej}}+\frac{1}{h_{hi,eva}A_{ej}}}\,, \tag{11}\]  
where \(h_{ref,eva}\) and \(h_{hi,eva}\) are the heat transfer coefficients on the refrigerant and air side, respectively, while \(A_{ej}\) and \(A_{ej,o}\) are, respectively, the inner and outer surfaces of the evaporator. Several correlations proposed in the literature were tested for the determination of the heat transfer coefficient on the refrigerant side, \(h_{ref,eva}\)[17; 18]. As suggested by [PERSON] et al. (2012) [17], among the several tested correlations, the correlation proposed by [PERSON] and [PERSON] (2003) [19] was chosen.