## 3 Test and Results
### Simulation Results  
In order to investigate the effectiveness of the proposed MILP-based algorithm, two representative results are compared from different points of view. For the sake of a clearer representation, sample cases for Summer and Winter (May 16, 2013 and January 1, 2013) are both analyzed to evaluate operational behavior of optimization strategies. \begin{table}
\begin{tabular}{c c} \hline \hline
**Input Parameters** & **Value** \\ \hline Capital Cost of PV unit (\$/kW) & 500 \\ Replacement Cost of PV unit (\$/kW) & 500 \\ Maintenance Cost of PV unit (\$/kW) & 25 \\ Capital Cost of ESS unit (\$/kWh) & 90 \\ Replacement Cost of ESS unit (\$/kWh) & 90 \\ Maintenance Cost of ESS unit (\$/kWh) & 3 \\ Real Discount Rate & 0.05 \\ Project Lifetime (years) & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Economic input parameters for PV and ESS units. Figure 8: Dynamic pricing of buying energy from a grid. The power balance of the hybrid system comprising of the power drawn from the grid (buy), the power injected to the grid (sell), battery charging and using values, PV-used power, and electricity demand of end-user are depicted in Figures 9 and 10 for winter and summer days, respectively. At the beginning of the evaluated period, it is seen that the injected power to the grid has increased and reached the maximum value during 01:00 and 02:00 for the winter case. The SoE of the battery is 4 kWh (initial SOE) and it is utilized in selling power as well as covering demand. However, the demand should be provided by only a grid due to low SOE and low buying electricity prices in summer cases as shown in Figure 10.  
At 03:00 and 05:00, the charging power of the battery increases for both case studies due to lower demand and relatively low electricity prices. The power consumption rises at 17:00-20:00, which is to be covered by one of the optimally sized sources for decreasing the total costs. As also seen in Figure 11, the battery presents a good opportunity leading to the possibility of charging at low-priced periods and discharging at peak-demand periods. Therefore, it can be indicated that the existence of a battery in the  
Figure 10: Power balance of the proposed hybrid system for a sample summer case. Figure 9: Power balance of the proposed hybrid system for a sample winter case. hybrid system provides operational flexibility and the charging/discharging periods of this dynamic component are determined by the developed algorithm considering objective function maximization. The PV power production begins at nearly 08:00, reaches its maximum value (0.16 kW) at 12:00 and finishes at 18:00 for the winter case as illustrated in Figure 12. It is evidently clear that the amount of PV production is not enough for even supplying of the load consumption and as a result injecting power to the grid is zero. On the other hand, the summer case starts earlier than the winter case at 07:00, reaches nearly 0.8 kW value at 14:00 and ends at 21:00 as shown in Figure 13. The battery discharging is utilized to meet the high power consumption at 11:00 without transferring power from the grid due to relatively higher prices. Therefore, the algorithm gives a signal to utilize distributed generation instead of the grid after an economical decision-making process. Figure 11: Battery charging and discharging power along with state of energy variation for sample winter case. Figure 12: The PV system power decomposition for sample winter case. During the period from 12:00 to 16:00, even though a certain part of the demanded power can be matched with battery apart from PV, the system decides to use the energy of battery even after 17:00 as the buying prices are becoming higher in peak a period that makes sense to explain this condition. However, it is not right to say the same things for the summer case. Within these periods, high power generation supplies the demand and charges the battery as well as injects available power to the grid.