# Optimal Power Dispatch of an Offshore Wind Farm under Generator Fault
## 5 Case Study
### Case 3: Comparison of Fault Handling  
Generally, when a fault occurs on WT, the WF operator selects a specific fault-handling method according to the fault alarm. However, there are only two general methods: one is to let the faulty WT run in the original state, which is marked as M1, and the other is to directly shut down the faulty WT, which is marked as M2. In Case 3, the wind speed and \(P_{\text{dem}}\) were set to 12 m/s and 17 MW. Assuming the fault occurred on the WT2, \(R_{\text{th}}\) changed from 0.003 K/W-0.006 K/W. According to the thermal model in Section 3, the temperature rise of the generator at full load (\(TR\)) was 96 K and the corresponding power limit was 3.53 MW. We compared the two fault handling methods in PDS with ODS. The result is shown in Tables 4 and 5 and Figures 13 and 14. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{2}{c}{**ODS**, \(k2=0\)} & \multicolumn{2}{c}{**ODS**, \(k2=4\)} \\ \cline{2-5}  & \(P\) **(MW)** & \(P^{\prime}\) **(MW)** & \(P\) **(MW)** & \(P^{\prime}\) **(MW)** \\ \hline \(P_{\text{dem}}\) & 17.00 & 16.00 & 17.00 & 16.00 \\ \hline WT1 & 5.00 & 4.82 & 5.00 & 5.00 \\ WT2 & 4.17 & 4.25 & 4.17 & 4.17 \\ WT3 & 2.81 & 2.01 & 2.81 & 2.51 \\ WT4 & 2.61 & 1.51 & 2.61 & 2.21 \\ WT5 & 2.41 & 3.41 & 2.41 & 2.11 \\ \hline \(P_{\text{WF}}\) & 17.00 & 16.00 & 17.00 & 16.00 \\ \(\text{r}(\mathbf{P},\mathbf{P^{\prime}})\) & 0.8161 & & 0.9987 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of power fluctuation in Case 2. Figure 12: Comparison of power fluctuation in Case 2: (**a**) power references in ODS (\(k2=0\)); (**b**) power references in ODS (\(k2=4\)). When M1 was taken, the faulty WT continued to operate as normal. Therefore, the temperature rise increased from 96.00 K to 100.95 K due to the increase of \(R_{\text{th}}\). Long-term over-temperature operation will reduce the lifetime of the coil isolation and the efficiency of the generator. In ODS, the faulty turbine was down-regulated to the power limit. The result shows that both PDS and ODS can track the power demand very well. However, the temperature rise of the faulty WT exceeded 96 K in PDS. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{2}{c}{**PDS**} & \multicolumn{2}{c}{**ODS**} \\ \cline{2-5}  & \(\mathbf{P_{\text{r}}}\) (MW) & \(\mathbf{P}\) (MW) & \(\mathbf{P_{\text{r}}}\) (MW) & \(\mathbf{P}\) (MW) \\ \hline WT1 & 3.87 & 3.87 & 5.00 & 5.00 \\ WT2 & 3.62 & 3.62 & 3.53 & 3.53 \\ WT3 & 3.25 & 3.25 & 3.01 & 3.01 \\ WT4 & 3.13 & 3.13 & 2.81 & 2.81 \\ WT5 & 3.13 & 3.13 & 2.64 & 2.64 \\ \hline \(P_{\text{WF}}\) & 17.00 & 17.00 & 17.00 & 17.00 \\ \hline \(\Delta\theta\)(K) & \multicolumn{2}{c}{100.95} & \multicolumn{2}{c}{96.00} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of power and temperature rise in Case 3, M1. Figure 13: Comparison of power and temperature rise in Case 3, M1: (**a**) power reference and power output in PDS; (**b**) power reference and power output in ODS; (**c**) temperature rises of the faulty WT in PDS and ODS; (**d**) power output of the WF. When M2 was taken, the faulty turbine was shut down. Therefore, the temperature rise of the generator became zero. This method can protect the WT from further damage. However, the power output of WF decreased to 16.13 MW. The sudden drop of the WF power will also have a bad effect on the grid. It can be seen that PDS and the general fault-handling methods can only choose one option from power production and fault protection. However, an efficient trade-off can be obtained through ODS.