## 4 Impact of Wind Penetration and Correlation  
The IEEE Reliability Test System (IEEE-RTS) [16] was used in this study to investigate the effect of various factors on the reliability indices of a WIPS obtained using multi-state wind models. The IEEE-RTS has 32 generating units ranging from 12 MW to 400 MW capacities with a total installed capacity of 3405 MW. The system LOLE of IEEE-RTS is 9.44 h/year. The system peak load is 2850 MW. The details of load data are provided in [16] from which the daily and hourly load models can be obtained. A Computer program called SIPSIREL [17] was used to calculate LOLE values in this study. The LOLE of the IEEE-RTS decreases after adding wind generation to the system. The LOLE values obtained for the various correlation between the two wind farms, and to different wind penetration levels are summarized Table 1.  
The impact of wind correlation on the WIPS reliability is shown in Figure 7 by applying a 27-state wind capacity model to the IEEE-RTS with 20% wind penetration. The total wind capacity in this case is 850 MW from two wind farms of equal installed capacities connected to the system.  
It can be seen in Figure 7 that the system LOLE increases with the value of the correlation coefficient between the two wind farms, and vice-versa. Correlation between wind farms is therefore an important consideration in developing an appropriate wind model for reliability studies.  
The multiple-state wind capacity model was simplified by gradually reducing the number of states from 27 to 5. The LOLE for the same system was evaluated for the different wind correlation values as described in the previous study. The WIPS LOLE for different number of states in the wind capacity model are shown in Figure 8. It can be observed from Figure 8 that he LOLE results obtained using a reduced number of states in the wind model can have remarkable error. The error rapidly increases as  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Correlation**} & \multicolumn{4}{c}{**Penetration**} \\ \cline{2-5}  & **5\%** & **10\%** & **15\%** & **20\%** \\ \cline{2-5}
0 & 8.1065 & 6.9114 & 5.9108 & 5.0427 \\
0.25 & 8.1121 & 6.9442 & 5.9772 & 5.1453 \\
0.5 & 8.1186 & 6.9803 & 6.049 & 5.2543 \\
0.75 & 8.1231 & 7.0133 & 6.1161 & 5.3572 \\
1.0 & 8.1263 & 7.044 & 6.1798 & 5.4549 \\ \hline \hline \end{tabular}
\end{table}
Table 1: LOLE values for RTS varying correlation and penetration.  
the NoS is reduced below 10 in this study. The results obtained from 27-state model are considered to be the most accurate in this study.  
The impact of wind penetration on the LOLE accuracy obtained using different number of states in the wind model was also studied considering 5%, 10%, 15% and 20% wind penetration in the IEEE-RTS. The correlation between the wind farms was taken to be 0.5 in this case. The WIPS LOLE for the varying number of states in the wind capacity model at the different wind penetration levels are shown in Figure 9.  
It can be seen from Figure 9 that the error in LOLE increases as the NoS is reduced. The increase in error is less significant at low wind penetration, and very significant at high penetration. It can be inferred from Figure 9 that the determination of an appropriate NoS in the wind capacity model also depends upon the wind penetration level in a power system.  
Figure 8: Variation in LOLE results with the NoS in the wind model at different wind correlations.  
Figure 7: Variation in LOLE with peak load for different correlations.