## 6 Case Study
### Four-Units under a Wind Farm  
In the above simulations, the tested cluster shows a great stabilized power tracking ability under the proposed active power control strategy. However, the capacity of four tested units will be a limit that the wind farm usually contains much more units than the tested cluster, where the cluster mainly provides a middle layer between the wind farm and each unit. Thus, the wind farm is controlled as Figure 13 to test the regulation ability of the selected cluster ability. In the wind farm, the selected four units are selected as the tested cluster and the other 16 units form another conventional cluster. The wind farm power demand is split into two parts based on the maximum capacity of two clusters. The conventional cluster is controlled by following the PD strategy, and the tested cluster is controlled under the proposed strategy or the PD strategy to verify the influence of the tested cluster on the wind farm power output. The wind farm is tested under both step-change power demand and time-varying demand, and the farm power output are shown in Figures 14 and 15. Clearly, when the tested cluster is controlled under the proposed MPC strategy, the wind farm active power is improved in both tracking ability and output stability. The power output in Figure 15 tracks the power demand more quickly than the PD strategy. The wind farm power output under the step demand in Figure 14 also shows the effectiveness when the selected cluster is controlled by the proposed strategy and the conventional cluster follows the PD strategy. Although the power fluctuation from the conventional cluster still brings oscillations to the farm power output, the improvement is still significant. Figure 13: Wind farm control structure. To show the improvement in a intuitive way, the integrated absolute error (IAE) is selected as the quantitative index to show the above improvement when using the proposed strategy, which is calculated as follows:  
\[IAE=\int_{0}^{T}\left|e(t)\right|dt,\]  
in which \(e(t)\) is the tracking error between the power set-point and power output for the wind farm or the wind turbine cluster; \(T\) is the simulation time. The corresponding result is shown in Table 1.  
In Table 1, the IAE_step is the IAE index for the wind farm and wind turbine cluster under a step change set-point as shown in Figure 14, and IAE_TimeVarying is the result under the time varying power demand in Figure 15. Clearly, the improvement for a cluster level is significant, but when \begin{table}
\begin{tabular}{c c c} \hline \hline
**Object** & **IAE\_Step** & **IAE\_TimeVarying** \\ \hline Cluster\_4 PD & 6.75335 & 19.54523 \\ Farm\_4 PD & 13.4768788 & 51.32480 \\ Cluster\_4 MPC & 1.721556 & 10.02838 \\ Farm\_4 MPC & 9.477333 & 43.02592 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: IAE(integrated absolute error). Figure 14: Wind farm power output under a step changes power demand. Figure 15: Wind farm power output under a time varying power demand. considering the wind farm level, the capacity of the tested cluster is still a limit to further improve the wind farm power output. On the other hand, the proposed strategy mainly considers the active power distribution and frequency support under a cluster level. Essentially, it belongs to the secondary frequency modulation under the wind farm scheduling, which can be easily extended to primary frequency modulation only needs a suitable frequency-power droop curve for the cluster. However, it is not appropriate to choose a large-scale wind farm as a cluster and apply the proposed strategy directly. Under our simulations, the increase of the units number in the cluster will lead to the prolongation of the optimization problem solving time, and the problem caused by modeling deviation will also be serious. All 20 units of the wind farm are selected and tested under a step change set-point and the electric power output and frequency responses are shown as in Figures 16 and 17.