## 4 Results and Discussion
### Influence of Battery Size  
While the system is not running, the electricity demand must be fulfilled by relying either on the grid or on the batteries. In this section, the role of electricity storage is investigated, which has the potential to make the CHP-system more flexible and possibly grid-independent. In their analysis, [PERSON] [17] did not account for batteries and assumed that the excess of electrical energy could be only injected into the grid. In the present analysis, the electric generator and the batteries are assumed to be ideal, meaning that no conversion losses are taken into account and that the energy stored in the batteries does not decrease due to the long storage time. These factors could quantitatively reduce the benefits shown in this section; however, they do not change the qualitative trends found here, which are the real focus of this study. In Figure 8, the influence of battery size on the daily operative cost at full-load is shown. In Figure 8, the operative cost for an SFH with one, two, and three occupants is plotted for different battery sizes. Similarly, an MFH with up to three families is taken into account in Figure 8. It can be seen that even a small battery, up to 1 KWh, contributes to rapidly decreasing the costs. In fact, batteries allow a direct reduction of the electricity bought from the grid. The advantage of installing a battery strongly depends on the electricity prices. If buying 1 KWe from the grid costs more than selling it, which is usually the case, a battery could be convenient. In fact, it is more convenient to store the excess energy instead of selling it at a low price and buying eventually at a higher price when needed. However, this advantage saturates when the battery size exceeds the needs of the building. It can be seen that small advantages are obtained for batteries larger than 1.5 KWh and that no further advantage is obtained over 2 kWh. In fact, beyond this size, the battery is so large that it is never completely charged. The installation cost, however, depends on size. For these reasons, a battery between 1.5 and 2 kWh is recommended for CHP systems that wish to be electrically independent and for reducing the operative costs. The costs of a battery system vary with storage type and size. The average price of the main battery types in 2018 is reported in Table 2. It can be seen that the total project cost can vary between USD 469/kWh and USD 928/kWh [24]. The prices reported are expected to decrease by about 20-40% in 2025; also, the price per kWh generally decreases if larger systems are installed. Given their commercialization start in the early 1990s, Li-ion batteries are prevalent across a variety of industries, such as the electric automobile industry and the consumer electronics market, mainly in the MW range, due to their high specific energy, power, and performance. There have been successful deployments of Li-ion systems built for grid support up to several MW. Lead-acid and sodium-sulfur batteries are used across a wide variety of applications, but are not typically found in small, portable systems. Sodium metal halide batteries have primarily been introduced into the electrical storage market for  
Figure 8: Influence of battery size on daily cost, for different house occupancies for SFH (**a**) and number of families per MFH (**b**). Climate Zone 5, setting WSB, tank 800 L, full-load. EV usage; the battery sizes have a capacity range of between a few kWh and a few MWh and have a high level of scalability and flexibility. Due to their flexibility, sodium metal halide batteries are capable of being used across a large variety of applications, including EVs and public transportation, residential and commercial buildings, renewable generation smoothing, and others [25]. For their suitability and reliability in the small-grid kWh power range, sodium metal halide batteries were selected and implemented in this analysis.