# Considering the Life-Cycle Cost of Distributed Energy-Storage Planning in Distribution Grids
## 5 Case Studies
### Case Study Results
The costs of the ESSs were effectively reduced after the second-stage optimization. The fixed and variable operation and maintenance costs which were related to the operating power, did not change after the second-stage optimization. Before the second-stage optimization, the replacement costs for battery 0' and battery 2' were 45.9% and 67.3% of the overall ESS cost, respectively, while the capital investments were 28.7% and 18%, respectively. After the second-stage optimization, the largest share of the overall ESS cost became the capital investment which were 55.6% and 62.5%, for battery 0\" and battery 2\", respectively. The proportion of the replacement cost and the disposal cost were greatly reduced to 12.6% and 14% of the overall cost of battery 0\" and battery 2\". Due to the decrease of the replacement times, the proportion of disposal costs of battery 0\" and battery 2' changed from 4.5% to 0.9% and 5.1% to 0.7%, separately. In the second-stage optimization, the discount rate, which was the interest rate, the converted values of the future assets into the present value was considered. The investment cost of the whole project cycle was counted, to the first year, by using the net present value (NPV), then the uniform annual value method was used to average it to each year of the project cycle. In this study, NPV was defined as the sum of the present values of the incoming and the outgoing cash flows, over a period of time, and the uniform annual value method was the present value of the annual cash flow, calculated on the average of the cash flow of the investment scheme, and the period (years) of its utility. In this way, the capacity expansion of the ESS led to the increase of capital costs but reduced the times of replacement. The replacement costs were also affected by the prolongation of lifetime, therefore, decreasing the cost of the first year of the project derived by the NPV. The overall replacement cost could be deducted significantly. The economic characteristic of the ESS is shown in Figure 13, as the capacity grew and lifetime extended, the economics of the ESS tended to improve. There were fluctuations that occurred along with the increase in capacity and life, the reason was that the lifetime of the battery had been prolonged with the capacity increases, but the times of battery replacement remained the same, during the project life cycle. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Optimization Stage** & **Installation Site** & **Lifetime/year** & **Average Annual Cost/\%** \\ \hline First stage & Node 3 & 4 & 5,238,677 \\  & Node 81 & 2 & 7,081,373 \\ \hline Second stage & Node 3 & 16 & 3,541,137 \\  & Node 81 & 16 & 2,951,720 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Lifetime and the average annual cost of the ESS. Figure 12: Life-Cycle Cost (LCC) per kW-h comparison before and after the second-stage optimization. The results indicated that the proposed planning method in the distribution networks could optimize the ESS installation site and capacity, and improve the economic efficiency of the ESS by increasing the energy storage capacity, extending its service life, and reducing the annual cost in the condition of ensuring the safe operation of the system.