## 4 Simulation Results
For each system configuration, and for every \"n\" of the N simulations, the annual Total Savings Cost (TSC) [4; 8] is calculated as follows:  
Figure 9.5  
The evaluation of the optimal configuration is based on the Discounted Payback Period (DPP) method. The DPP is the time in which the initial cash outflow of an investment (\(I_{0}\)) is expected to be recovered from the cash inflows generated by the investment [1; 32]. The advantage of this approach is that it considers the present value of money through discounting the cash inflows. The value of the DPP, for each configuration of the hybrid system installed, is calculated as follows:  
Figure 9.6  
where \(k\) is the interest rate (%), \(I_{0}\) is the hybrid system installation cost (at the year zero); \(CF_{(y)}\) is the cash flow at the year \(y\) defined as:  
Figure 9.7  
TSC in Equation (10) is assumed to be equal to the mean value of the TSC for N simulations and for each configuration system. Simulation results, shown in Tables 2 and 3, evidence that, for both sizes of the PV system, the DPP grows with the increase the capability of the ESS. Lower DPPs can be observed for a PV-Generator size equal to 2 kW. \begin{table}
\begin{tabular}{c c c c c c} \hline
**PV** & **ESS** & **ESS** & **ESS** & **ESS** & **ESS** \\
**PV** & **4 kWh** & **5 kWh** & **6 kWh** & **7 kWh** & **8 kWh** \\ \hline
1 kW & 5556 & 6256 & 6956 & 7656 & 8356 \\
2 kW & 6556 & 7256 & 7956 & 8656 & 9356 \\ \hline \end{tabular}
\end{table} 
Table 1: Initial investment cost (\(I_{0}\)) (\(\xi\)). \begin{table}
\begin{tabular}{c c c c c c} \hline
**PV (kW)** & **ESS (kWh)** & **Io (\(\xi\))** & **k (\%)** & **TSC (\(\xi\)/y)** & **DPP (year)** \\ \hline
1 & 4 & 5556 & 3 & 586.04 & 11.3 \\
1 & 5 & 6256 & 3 & 598.06 & 12.7 \\
1 & 6 & 6956 & 3 & 603.81 & 14.3 \\
1 & 7 & 7656 & 3 & 606.66 & 16.1 \\
1 & 8 & 8356 & 3 & 608.97 & 17.9 \\ \hline \end{tabular}
\end{table} 
Table 2: Analysis of the Discontinued Payback Period (DPP) for the configurations 1 kW/4–8 kWh. The most advantageous configuration of the hybrid system is therefore shown in Table 4.  
In view of market developments in the electronic components for renewable energy and energy storage systems, future scenarios, where the initial investment cost decreases to 20%, 40%, 60%, or 80% of the current cost, are considered [32]. Figure 21 shows the DPP for these feature scenarios for each configurations of the hybrid system. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**PV (kW)** & **ESS (kWh)** & **Io (€)** & **k (\%)** & **TSC (€/y)** & **DPP (year)** \\ \hline
2 & 4 & 6556 & 3 & 747.10 & 10.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimal configuration hybrid PV-storage system for case study  
Figure 21: DPP versus Investment (% of \(l_{0}\)) in future scenarios for different configurations: (a) 1 kW/4–8 kWh; and (b) 2 kW/4–8 kWh. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**PV (kW)** & **ESS (kWh)** & **Io (€)** & **k (\%)** & **TSC (€/y)** & **DPP (year)** \\ \hline
2 & 4 & 6556 & 3 & 747.10 & 10.3 \\
2 & 5 & 7256 & 3 & 757.04 & 11.5 \\
2 & 6 & 7956 & 3 & 762.66 & 12.7 \\
2 & 7 & 8656 & 3 & 766.15 & 14.0 \\
2 & 8 & 9356 & 3 & 767.88 & 15.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Analysis of the Discontinued Payback Period (DPP) for the configurations 2 kW/4–8 kWh. It is useful to compare these results with those related to other energy management models. Specifically, in [26], the proposed system provides for control of shiftable loads and people presence-windows states, without considering the PV-battery hybrid system. The EMS proposed in this paper, combining the control strategies for shiftable loads and storage system with renewable energy, achieves a better management in terms of energy savings and end-user comfort.