## 5 Appropriate Wind Capacity Model Considering Wind Correlation and Penetration  
Table 1 presented the reliability evaluation results considering different wind penetrations in the IEEE-RTS at different correlations between the two wind farms connected to the system. The results were obtained using a 27-state wind capacity model. Similar studies were carried out using wind capacity models with reduced number of states. Reducing the number of states in the wind model simplifies the evaluation process at the cost of accuracy in the results. The errors in the WIPS LOLE obtained using reduced wind models at different wind penetrations and wind farm correlations were calculated using the Table 1 results obtained from the 27-state model as the reference. The results are shown in Figure 10.  
It can be seen in Figure 10 that the error in LOLE results generally increases as the number of states in the wind capacity model is reduced. The error is insignificant up to a certain NoS reduction, and then increases sharply as the NoS are further reduced. The error resulting from a reduced NoS is very sensitive to the wind penetration level. The errors increase rapidly as wind penetration increases and the number of states are reduced for model simplification. This is an important observation since the wind penetration in many WIPS around the world is expected to substantially increase within the next decade. Figure 10 also shows the impact of wind correlation on the LOLE errors obtained by using a reduced wind capacity model. At low wind penetration, the wind farm correlation does not really affect the LOLE errors as the NoS is reduced to simplify the wind model. The effect of correlation on the errors produced by NoS reduction is however significant at high wind penetration. The error increases as the correlation coefficient between the wind farms is decreased, and vice versa. The effect of correlation on the LOLE errors can be significant if relatively low NoS are used in the wind model at reasonable wind penetrations in the foreseeable future. Figure 9: Variation in LOLE results with the NoS in the wind model at different wind penetrations. Highly accurate results are usually not desired in a practical world if the methodologies to obtain the results are difficult to apply. An easy to use method that provides results with reasonable accuracy is more suitable for real life application. A wind capacity model with the minimum number of states that produces reasonable accuracy should therefore be used in WIPS reliability evaluation. An evaluation model that can provide system LOLE results within an error of 0.1 h/year would be considered appropriate model in practice. The minimum NoS to simplify a wind capacity model can therefore be deduced from Figure 10.  
Table 2 shows the appropriate wind capacity model at three different wind penetration levels. The wind capacity models recommended in Table 2 were applied to the IEEE-RTS considering wind penetrations of 10%, 15% and 20% from two wind farms with zero wind correlation. It is shown in Figure 10 that the error is highest when correlations between sites are zero. The LOLE of the IEEE-RTS without considering wind penetration is 9.44 h/year, which is relatively higher than the NERC recommended criterion of 0.1 day/year. This criterion is equivalent to about 1 h/year [18]. The \begin{table}
\begin{tabular}{c c} \hline
**Penetration Level** & **Minimum NoS** \\ \hline up to 10\% & 7 states \\ up to 15\% & 9 states \\ up to 20\% & 11 states \\ \hline \end{tabular}
\end{table} 
Table 2: NoS for wind capacity model. Figure 10: Error produced by using reduced number of states in the Wind Capacity model. peak load of IEEE-RTS was reduced up to 90% to get LOLE values close to 1 h/year. The WIPS LOLE at the three wind penetration levels were calculated for a range of system loads between 90% and 100% of the IEEE-RTS peak.