## 4 Simulation and Hardware-in-the-Loop Results
### Simulation Studies
#### 4.1.1 Long-Term (One Day) Simulation  
First, a simulation of one day of wind profile was performed. In this study, simplified model of the WT and PMSG were used to expedite the simulation. The wind profile used in this study is shown  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Wind Turbine** & **Values** \\ \hline Nominal wind speed & 12 m/s \\ Nominal output power & 2.0 MW \\ Air density & 1.225 kg/m\({}^{3}\) \\ Wind turbine radius & 35.5 m \\ Nominal rotor speed & 25.88 rpm \\ Stator resistance of PMSG & 0.821 m\(\Omega\) \\ Armature inductance of PMSG & 1.5731 mH \\ Flux linkage of PMSG & 7.8264 V.s \\ Machine side switching frequency, \(f_{M,s}\) & 1.5 kHz \\ DC link voltage reference, \(V_{DC}\) & 1450 V \\ \hline \hline \end{tabular}
\end{table}
Table 1: Wind turbine and permanent magnet synchronous generator (PMSG) Parameters.  
Figure 4: Wind turbine system with a control loop, including the proposed de-loading method.  
in Figure 5. Figure 6 shows the maximum power available and the de-loaded power. The dotted line represents the WT power achieved by rotor speed only. The WT power obtained by coordinating between rotor speed and pitch angle is presented by the dashed line. It is clear that both approaches provide the same amount of reserve power (\(\Delta P\)). In this study, the reserve is fixed at 0.3 MW for all wind profiles.  
Although every method gives the same reserve, the rotor speed is different, as shown in Figure 7. The rotor speed is increased by involving the pitch angle. This is because of the higher pitch angle that results in lower torque of the WT. Therefore, to maintain the same reserve, the rotor speed is increased. As a result, the quadrature current of the PMSG (\(I_{q}\)) is reduced, as shown in Figure 8. In this simulation, we controlled the current of the direct axis to be zero. Therefore, the only current that appears in the losses is the current of the q-axis. From Figure 8, it is clear that with a \(0^{o}\) pitch angle, the current is higher for whole period considered in this simulation. Current produced by the proposed approach reduces the power losses in the stator of the machine and the conduction losses of the switch, as given in (6) and (7). In Figure 9, the pitch angle is represented using the dashed line.  
The proposed strategy has the ability to utilize a wind speed forecast and predict the optimal solution. In this case, one can combine the optimal operating point of the current and future state in order to minimize the operation of the pitch angle. For the same wind profile, one model included the wind forecast and the other model did not consider the wind prediction in the decision. The pitch angle changed 82 times for the model without a forecast. In contrast, in the case where there was a wind forecast, the pitch angle changed 64 times, as shown in Figure 10. In both cases, the power produced by the WT was the same.  
Figure 5: Wind profile (long-term simulation).  
Figure 6: Mechanical power for the maximum power point tracking (MPPT) and de-loaded scenarios.  
Figure 8: Stator current (\(I_{q}\)).  
Figure 7: Rotor speed of a wind turbine (WT).  
Figure 9: Pitch angle (\(\beta\)).