# Considering the Life-Cycle Cost of Distributed Energy-Storage Planning in Distribution Grids
## 5 Case Studies
### Case Study Results  
The ESS pre-selected candidate configuration nodes in the low-voltage distribution system are presented in Figure 5, and the parameters of the GA and the SA are shown in Table 1. ESS configuration locations and corresponding minimum configuration capacities, in the first-stage optimization, are shown in Figure 7. The output power of the ESS and voltage variation of each typical nodes are separately presented in Figures 8 and 9. As shown in Figure 7, three installation nodes were selected from eight pre-selected nodes, and the installation capacity of node 3 was 3,712 kW\(\cdot\)h, the installation capacity of node 81 was 3,206 kW\(\cdot\)h, the installation capacity of node 84 was 1,519 kW\(\cdot\)h, after the first-stage optimization. According to the results shown in Figures 8 and 9, the scheduling of the ESS, after the first-stage optimization, could effectively solve the voltage issues with a minimum power output of the ESS. In this condition, when the PV output was large, during the day, the voltage magnitudes of some nodes which was close to the PV, exceed the upper limit. So, the ESS operated to absorb energy from the network to pull the voltage level back to the safety limit. When the loads increased during night, the voltage of some nodes that were close to demand would have exceeded the lower limit. So, the ESS operated to emit energy to the network, as sources to keep the voltage level in the safety limit. In addition, the output power of the adjacent battery 2, three were operated, coordinately, to stabilize voltage fluctuations caused by load 2 and PV2, with the consideration of the charging/discharging energy balance of a day. In order to improve the ESS utilization and the system economy, battery 2 and 3 could be combined as battery 2' and battery 0 was presented as battery 0', with same output as battery 0. The first-stage optimization was repeated to determine the optimal power and capacity, with the updated installation sites. As in Figure 10, the results showed that the optimized capacity  
Figure 8: Power output of the three planned ESSs. Figure 9: Voltage profiles of each typical node before (**a**) and after (**b**) the ESS configuration. after the merging of the adjacent batteries was obviously reduced and Figure 11 showed the output power of the ESS, after merging. The second optimization stage was based on the result of the first stage, then the rated capacity and rated power of the ESS, of a day, could be determined by the method shown in Figure 4. The rated power and rated capacity is shown in Table 2. The lifetime and average annual cost of the ESS, before and after the second optimization stage are shown in Table 3, according to the results, although the optimization capacity of the ESS in the second stage was larger than the results calculated by the first stage, the lifetime expectancy was accompanied by capacity growth. The capacity of the ESS expansion extended its lifetime, so the average annual cost was substantially lower than the first stage. The average annual costs of battery 0' and battery 2' had dropped by 32.4% and 58.3%, separately, and the total average annual cost of the ESS had dropped by 47.3%. According to Reference [28], the total average annual cost of the ESS could be converted as per kW\(\cdot\)h, by Equation (29). \[COE=\frac{C_{sys}+C_{rep}+C_{FOM}+C_{VOM}+C_{dis}}{\sum\limits_{i=1}^{24}\mu_{ D}C_{E}|P_{ESS,i}(t)|\cdot\Delta t\cdot 365} \tag{29}\]  
where \(COE\) is the cost per kW\(\cdot\)h of ESS. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Installation Site** & **Node 3** & **Node 81** \\ \hline Rated capacity(kW\(\cdot\)h) & 4950 & 4703 \\ Rated power(kW) & 750 & 500 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Configuration results of the second-stage optimization. Figure 11: The power output of the ESSs after merging. Figure 10: Capacity comparison before and after the adjacent ESS merging. In Figure 12, battery 0\" and battery 2\" are used to represent the battery 0' and battery 2', after the second-stage optimization.