## 7 Results and Discussion
### Effect of the Thermal Inertia  
To evaluate the effect of thermal inertia and its potential in the battery energy storage system, several simulations of the effect on the HVAC and TES system have been carried out in different houses with different levels of insulation and thermal inertia. To study this effect, we have used different thermal inertia coefficients, which were calculated from that of the studied dwelling, initially reducing it by 25% and 12.5% and then increasing it by 12.5% and 25%. For simplicity, only the analysis carried out for the winter period is included.  
In Figure 27, it is observed that higher thermal mass results in less frequent and smaller operational cycles for the HVAC system. This is because the additional thermal mass effectively buffers temperature fluctuations, reducing the regulation effort required and leading to more efficient energy consumption. Conversely, lower thermal mass causes faster temperature fluctuations, forcing the HVAC system to respond more frequently and at higher power levels, resulting in larger energy consumption spikes.  
Table 1 presents the cumulative energy consumption variation in one week for the different thermal masses compared to the case study. It clearly shows that higher thermal mass results in lower cumulative energy consumption over time. This is because the system requires less effort to maintain thermal stability. Conversely, lower thermal mass results in higher cumulative consumption, because the system works harder to compensate for rapid temperature changes.  
In summary, higher thermal mass reduces temperature fluctuations and cumulative HVAC energy consumption, improving overall system efficiency. On the other hand, lower thermal mass increases the frequency of HVAC system response and cumulative energy use, as the system's ability to buffer temperature changes is significantly reduced.  
Similarly, in less insulated houses, the TES responds quickly to changes in thermal load, which can be beneficial in applications requiring the rapid delivery of heat or cooling. However, this quick response makes the system less stable in the face of demand fluctuations. Additionally, a TES with low thermal mass undergoes more frequent charge and discharge cycles, which increases system wear and reduces its lifespan. Furthermore,  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Thermal Mass Variation** & **Consumption Variation** \\ \hline \(-\)25.0\% & +33.8\% \\ \hline \(-\)12.5\% & +14.5\% \\ \hline +12.5\% & \(-\)11.3\% \\ \hline +25.0\% & \(-\)20.3\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Cumulative energy consumption variation in one week for different thermal masses.  
Figure 27: Effect on the HVAC consumption for different thermal inertias.  
its ability to retain thermal energy over extended periods is diminished, making it less effective in long-term storage applications.  
Conversely, a TES with high thermal mass better buffers temperature fluctuations, providing a more stable and consistent energy delivery. Although this reduces the system's ability to respond quickly to abrupt changes in demand, it minimizes the frequency of charge and discharge cycles, thereby improving system durability and reducing operational costs. Moreover, greater thermal mass allows for the internal temperature to remain stable over prolonged periods, making it ideal for applications where thermal stability is crucial, such as renewable energy storage or the climate control of large buildings.