## 6 Case Study
### Four-Units Cluster Robustness Test  
In the previous simulations, the unit available power is obtained based on the lookup table related to the measured wind speed. However, the predictive wind speed usually adopted in the real industrial field, which may introduce the external prediction error and disturbance to the cluster instructions. In order to testify the robustness of the proposed cluster-level active power control strategy, a bounded Gaussian white noise is added on the measured wind speed every few seconds, which will influence both the predictive available active power and the units' power set-point. The tested units are the same as in Section 4.4. The simulation result are shown as in Figures 6 and 7.  
The cluster power output in Figure 6 shows that the active power model predictive controller has better robustness than the conventional PD strategy. The additional random noise does influence the predicted available power and the proportional coefficient for each unit. Because of the open loop characteristic of the conventional strategy, the cluster power output cannot be guaranteed with no difference when tracking the set-point, and the deviations from the predicted available power will influence the active power output directly. As for the proposed model predictive controller, the predicted available power mainly provides a constrained feasible interval for each unit power set-point instead of adding the influence directly. The predicted error will be mitigated by the spare capacity of each unit in the cluster without causing any significant deviations of the cluster power output. The constrained feasible interval and power output for each unit in Figure 7 shows such a feature very clearly. In Figure 7, the blue curves are the generator active power output for four units, and the black curves are the constrained feasible intervals by the time-varying (19). Once the cluster power set-point changed, the feasible interval reaches its maximum range and gradually reduces if the cluster power set-point keeps still until meeting its minimum range after 30s. During the time-varying region, power output of units 3 and 4 are gradually increasing; meanwhile, units 1 and 2 cut out several power outputs to maintain the adequate spare regulation capacity after the fast tracking of  
Figure 6: Four-units cluster robustness test—cluster power output (measured wind speed with Gaussian white noise).  
power set-points. The comparison about the unit power output between the conventional strategy and the proposed strategy is shown in Figure 8.  
Moreover, the selected cluster is also tested under the irregular time-varying power set-point, where the cluster power output and each units power output are plotted in Figures 9 and 10. Obviously, the cluster power output under the proposed controller follows the set-point change quickly and almost coincides with the power set-point. In Figure 10, the slow time-scale units served as a mainstay under the frequent set-point change, and the fast time-scale units are giving full play of their own regulation flexility to support the cluster active power demand.  
Figure 8: Four-units cluster robustness test—comparison between the proposed strategy and the conventional strategy, sub-figures a, b, c, d are the active power output comparison between the proposed strategy and conventional strategy for wind turbine 1, 2, 3, 4 respectively.  
Figure 7: Four-units cluster robustness test—the active power output under the proposed controller for each wind turbine, sub-figures a, b, c, d are the active power output and the constraints under the proposed strategy for wind turbine 1, 2, 3, 4 respectively.