## 7 Impact of Ramp Rate and Failure Rate on CGRR  
The impacts of generating unit ramp rates and the failure rates on the CGRR index provide important information for a power system operator to optimally schedule generating units in system operation. This is investigated by analyzing the IEEE-RTS operating schedule given in Table 5 to serve a load of 1995 MW. As mentioned earlier, a total of 13 generating units were committed from priority loading order to meet the N-1 criterion, and the units were loaded based on the economic load dispatch. Four different cases were considered to investigate the impact of ramp rates and failure rates on the CGRR index. The IEEE-RTS data given in Table 4 constitutes the base case, or Case 1. The failure rates of the committed units are doubled in Case 2. The ramp rates of the committed units are doubled in Case 3, while keeping the failure rates the same as that in the base case. Both the ramp rates and the failure rates are doubled in Case 4. The CGRR was evaluated for the four cases and shown in Figure 2.  
Figure 2 shows that CGRR increases significantly as the failure rate of the committed unit is increased. It can be seen that the CGRR increases in similar proportion when the failure rate is doubled  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Evaluation Method** & **CGRR** \\ \hline Analytical & 0.00270118 \\ MCS & 0.00270114 \\ \hline \hline \end{tabular}
\end{table}
Table 6: A comparison of the CGRR results of the example IEEE-RTS operating condition.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Priority** & **MCR** & **Min. Capacity** & **Ramp Rate** & **Fail. Rate** & \multicolumn{3}{c}{**Cost Parameters (\$/h)**} \\ \cline{5-10}
**Order** & **(MW)** & **(MW)** & **(MW/min)** & **(occ/yr)** & **a** & **b** & **c** \\ \hline
1–4 & 50 & 0 & 10 & 4.42 & 0.000 & 0.500 & 0.00000 \\
5–6 & 400 & 200 & 0 & 7.96 & 216.576 & 5.345 & 0.00028 \\
7 & 350 & 150 & 9 & 7.62 & 388.25 & 8.919 & 0.00392 \\
8–10 & 197 & 80 & 6 & 9.22 & 301.223 & 20.023 & 0.00300 \\
11–14 & 155 & 60 & 5 & 9.13 & 206.703 & 9.271 & 0.00667 \\
15–17 & 100 & 40 & 3 & 7.30 & 286.241 & 17.924 & 0.00220 \\
18–21 & 76 & 25 & 2 & 4.47 & 100.439 & 12.145 & 0.01131 \\
22–26 & 12 & 5 & 1 & 2.98 & 30.396 & 23.278 & 0.13733 \\
27–30 & 20 & 6 & 4 & 19.50 & 40.000 & 37.554 & 0.18256 \\
31–32 & 50 & 0 & 10 & 4.47 & 0.000 & 0.500 & 0.00000 \\ \hline \hline \end{tabular}
\end{table}
Table 4: IEEE-RTS generating unit data.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline
**Unit \#** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** \\ \hline MCR & 50 & 50 & 50 & 50 & 400 & 400 & 350 & 197 & 197 & 155 & 155 & 155 \\ Loading & 50 & 50 & 50 & 50 & 400 & 400 & 302 & 80 & 80 & 80 & 151 & 151 & 151 \\ Reserve & 0 & 0 & 0 & 0 & 0 & 0 & 48 & 117 & 117 & 117 & 4 & 4 & 4 \\ RM & 0 & 0 & 0 & 0 & 0 & 0 & 48 & 60 & 60 & 60 & 4 & 4 & 4 \\ \hline \hline \end{tabular} Note: All data in MW.  
\end{table}
Table 5: A sample operating condition of the IEEE-RTS under study.  
from case 1 to Case 2. The CGRR increases over four times when the failure rate is doubled from Case 3 to Case 4. Figure 2 shows that the CGRR is highly sensitive to the ramp rate of a committed unit that carries an operating reserve. It can be seen that the CGRR was reduced more than 100 times when the ramp rates of the units were doubled from Case 1 to Case 3. It should be noted that the ramp rate of the base load generators that do not carry any spinning reserve have no impact on the risk index. This study illustrates that the impact of these parameters should be evaluated prior to making unit commitment and dispatch decisions.