# Dynamic Energy Consumption Modeling for HVAC Systems in Electric Vehicles
## 4 Results and Discussion
### Constant Speed Driving Condition and the Influence of Precooling Phase  
The adoption of a precooling phase gives advantages in terms of comfort conditions inside the vehicle together with a lower battery electric consumption during the driving. In order to evaluate the effective advantages, the cases with and without the precooling phase are compared in this section. Table 3 shows the common conditions imposed as input in both cases, while Table 4 shows the different assumptions made in order to compare the two different solutions. In the first case, the car undergoes a precooling phase from 0 to \(t_{0}\) = 1200 s with the HVAC system on, and a second period from \(t_{0}\) to \(t_{1}=3600\) s when the user is inside the car and drives at an average velocity of 20 km/h. In the second case, the car is not cooled before the user arrival, and the simulation starts when the user enters the car. In order to compare this second case with the previous one, the second case ends at 2400 s and the average velocity of the vehicle is equal to 20 km/h. In both simulations, the initial temperature inside the vehicle cabin is 40 \({}^{\circ}\)C. \begin{table}
\begin{tabular}{l c c c} \hline
**Description** & **Case** & **Simulation** & **Measurements** \\ \hline High pressure & 1 & 14.8 & 15.5 \(\pm\) 0.5 \\ Low pressure & 1 & 2.1 & 2.0 \(\pm\) 0.2 \\ High pressure & 2 & 14.4 & 15.0 \(\pm\) 0.5 \\ Low pressure & 2 & 2.3 & 2.0 \(\pm\) 0.2 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison between mean simulated and measured pressures (bar). Figure 6: Evaporating and condensing pressure obtained for case 1 (**left**) and for case 2 (**right**). The results are shown in Figure 7 for the case with the precooling phase and in Figure 8 for the case without. In the figures, \(\dot{Q}_{true}\) represents the thermal power exchanged in the evaporator. From this variable, we determine the coefficient of performance (COP) of the cycle, which is variable, with a maximum value of 3.6. Figure 7 shows that once the user enters the vehicle (dotted line), the temperature inside the cabin has already reached the comfort set point. More precisely, after almost 14 min, \(T_{cab}\) reached the set-point value (\(T_{sp}\)) and the system started the on-off cycle. This means that for all of the driving period, the HVAC system works only to keep the temperature inside the vehicle cabin at the comfort temperature. On the contrary, without the employment of the precooling phase, when the user enters the vehicle, the temperature \begin{table}
\begin{tabular}{l c} \hline
**Input Encoding** & **Values** \\ \hline Simulation time & 3600 s \\ Average vehicle velocity (t \(<t_{0}\) ) & 0 km/h \\ Average vehicle velocity (t \(>t_{0}\) ) & 20 km/h \\ \hline Without Precooling & \\ \hline Simulation time & 2400 s \\ Average vehicle velocity & 20 km/h \\ \hline \end{tabular}
\end{table} 
Table 4: Different settings between the two cases. Figure 7: Thermal loads and cabin temperature obtained in the case with precooling. A dashed line is drawn in correspondence with 1200 s.  
inside the vehicle is equal to the maximum temperature (i.e., 40 \({}^{\circ}\)C) and the HVAC system must continue to work until it reaches the comfort temperature before starting the on-off cycle (as shown by Figure 8). Regarding the energy consumption of the batteries (\(E_{el,batt}\)), the analysis can be made as follows. In the case of the precooling phase, the energy absorbed from the batteries during the driving period can be calculated as the integral of the power absorbed from the compressor (\(P_{el}\)) over the time interval \(\Delta t=t_{1}-t_{0}\):  
\[E_{el,batt}=\int_{t_{0}}^{t_{1}}\delta(t)P_{el}dt \tag{45}\]  
where \(\delta(t)\) is a function equal to 1 when the system is \"on\" and equal to 0 when the system is \"off\". In our specific case, Equation (45) gives a value of 0.65 kWh.