# Assessing the Impact of an EV Battery Swapping Station on the Reliability of Distribution Systems
## 6 Numerical Study
### Analysis on the Performance of Sampling Methods Adopted  
For comparing the performance of LHS-based sequential simulation and traditional SMCS, this procedure uses LHS and SRS to sample the EV traffic flow, empty batteries' SOC, and system failure status in each period. For SMCS, traditional techniques sampling from the probability distribution through random or pseudo-random numbers are used. Among them, SRS is widely used. The SRS \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**System** & **Load Point** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** \\ \hline SAIFI (time/c-y) & 0.6886 & LAIFI (time/c-y) & 0.7570 & 0.7634 & 0.5063 & 0.5457 & 1.3822 & 0.7068 & 0.4111 & 1.3711 \\ \hline SAIDI (h/c-y) & 3.1099 & LAIDI (h/c-y) & 2.4107 & 2.5219 & 1.8284 & 3.4009 & 4.4924 & 4.7184 & 1.7280 & 4.2596 \\ \hline SEENS (MWh/y) & 43.0769 & LEENS (MWh/y) & 0.6952 & 0.8277 & 0.8488 & 0.7184 & 0.9877 & 2.8633 & 1.2140 & 0.9496 \\ \hline  & & Load point & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 \\ \hline  & & LAIFI (time/c-y) & 1.0679 & 0.5379 & 0.6446 & 0.4157 & 0.3197 & 1.3223 & 1.8200 & 1.2038 \\ \hline  & & LAIDI (h/c-y) & 3.3914 & 4.5208 & 3.6350 & 2.0565 & 1.6042 & 4.0237 & 7.0081 & 3.7127 \\ \hline  & & LEENS (MWh/y) & 0.7849 & 0.6867 & 0.8038 & 0.4413 & 0.6590 & 0.9235 & 1.3962 & 0.8897 \\ \hline  & & Load point & 17 & 18 & 19 & 20 & 21 & 22 & 23 & 24 \\ \hline  & & LAIFI (time/c-y) & 1.0709 & 0.7528 & 1.0276 & 0.8544 & 0.7459 & 0.3049 & 0.5059 & 0.3150 \\ \hline  & & LAIDI (h/c-y) & 5.8087 & 3.8259 & 4.5517 & 4.9074 & 3.1179 & 1.5383 & 2.4164 & 1.6049 \\ \hline  & & LEENS (MWh/y) & 1.8367 & 1.2501 & 1.3919 & 1.4557 & 0.8581 & 0.4977 & 3.8711 & 2.3218 \\ \hline  & & Load point & 25 & 26 & 27 & 28 & 29 & 30 & 31 & 32 \\ \hline  & & LAIFI (time/c-y) & 1.4059 & 1.0244 & 1.5301 & 0.4140 & 0.9340 & 0.5422 & 0.3185 & 0.6284 \\ \hline  & & LAIDI (h/c-y) & 4.4512 & 4.1157 & 4.2341 & 1.8990 & 6.3910 & 2.3520 & 1.6136 & 3.7638 \\ \hline  & & LEENS (MWh/y) & 1.0108 & 0.8667 & 0.9000 & 0.7452 & 4.2011 & 4.3137 & 1.2378 & 0.6287 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Calculation of system reliability indexes under the disorderly charging strategy. Figure 10: Load profile of a BSS under orderly and disorderly charging schemes. technique is completely random, and any given sample may fall anywhere within the input distribution range. The LHC involves the stratification of the input probability distribution. Stratification divides the cumulative curve into equal intervals of cumulative probability levels (0 to 1.0). Then, it randomly samples from each interval or creates \"stratification\" of the input distribution. It samples the values in each interval and then sorts them, so that the correlation between each sample is minimized. In order to compare the difference between the two sampling methods, we list the row correlation between samples when the two sampling methods are used. For EVs, row correlation refers to the correlation between the time of arrival of different visited vehicles in a day and the initial SOC; for system components, it is the correlation between the failure states of different components. It can be seen from the Table 8 that when using LHS, the row correlation between samples is very small. Studies have proven that the correlation of smaller sample rows will bring greater accuracy [29]. Similarly, Figure 11 plots the convergence of the simulation results when using different sampling methods. It can be seen from the figure that the procedure of LHS-based sequential simulation converges faster than SMCS, the number of iterations is reduced, and the simulation time is shortened. This is because in the case of the same sampling times, the sampling coverage of LHS is larger and can better reflect the true probability distribution of random variables, so that the difference between the results of each iteration is reduced.