## 4 Numerical Applications  
### System Description and Basic Data  
In this paper, RBTD-BUS 6 is applied to verify the validity of the optimization model and method proposed in this paper. The single line diagram of the test system is shown in Figure 5. In this distribution network, the installed capacity of the conventional generator is 300 MW. The IEEE-RTS [38] load demand distribution is utilized in this study, and the peak load is 550 MW. The hourly wind speed data are taken from the historical wind speed data of Prince Albert in Canada, from years 2001 to 2012 [39]. In addition, the conventional generator availability is generated using a Monte-Carlo simulation. The system includes 51 nodes and 40 load nodes. The distribution network is connected to the main grid by connection lines through node 35. Figure 5 demonstrates the single line diagram of the distribution network. In the studies, the energy storage devices are centrally installed in the distribution network. The proposed model is implemented in IBM ILOG CPLEX 12.2 on a Dell M4600 laptop with Intel Core i7-2820 QM CPU 2.30 GHz RAM 8 GB. In the application, the candidate location nodes for the energy storage system are finite, and the installation of energy storage is centralized. In the power system planning, the installation location of the energy storage system is unverified. This paper analyzes the application of energy storage by the following four cases in detail to demonstrate that the improvement of system reliability differs when the energy storage system is installed at different locations. Four cases are designed, and the comparison is discussed in the following section. * Case 1: The energy storage devices are located near the distributed generation (DG); in this case, it is located at the wind  
Case 3: The energy storage system is installed at load point 40 (LP40). This installation point is also the end of the distribution system (just like the load point 30); however, these two installation points have different electrical distances from the wind power. The comparison results can tell the energy storage system planner the influence of the electrical distance from the wind power on the reliability improvement of the energy storage system. * Case 4: The energy storage system is installed at line point 45 (LP45). This installation point is a reference point for the other cases. Figure 6 indicates the daily output power of the generators in distribution network. Figure 6b shows the daily output of wind generation. The power system daily load profile was modeled with a single-step model, and the daily load profile is shown in Figure 6c. Figure 6d shows the hourly load profile pattern, and only the active load demand is given in the figure. In the period from 9:00 to 23:00, there is high load demand, which constitutes the daily peak load hours. During the period from 2:00 to 7:00, there is a lower load demand. In this case, as foreseeable, the energy storage charge power occurs when the available capacity of distribution network is lower than the load demand; otherwise, it is the energy storage discharge power. As Figure 6 shows, from 1:00 to 10:00, the output power of the wind power generator is less and the wind power generator is in the outage state. Although the load demand is less during this period, the output power of energy storage is large enough to fill the gap caused by the wind power  
Figure 6: Daily power of the devices in the distribution network. (**a**) Daily output power of the fuel generator; (**b**) daily wind power; (**c**) output power of energy storage at LP30; (**d**) daily load demand and available capacity. Therefore, the energy storage discharges power during the period. Furthermore, during the period of 12:00-22:00, the output power of the wind turbine works at the rated operating condition most of the time. During this period, the wind power can supply a greater load demand; although the load demand is high, the energy storage system works at the charging power status.