# A PMSG Wind Energy System Featuring Low-Voltage Ride-through via Mode-Shift Control
## 5 Simulation Results
### Case 1: 70% Symmetrical Grid Voltage Dip  
System performance has been investigated for a 70% three-phase symmetrical voltage sag occurring at the PCC at t = 0.6 and was cleared at t = 0.75 s (i.e., sag duration is 150 ms), and the results are demonstrated in Figure 7. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Parameter** & **Value** \\ \hline \(P_{w}\) & Turbine rated Power (MW) & 1.5 \\ \(V_{w}\) & Rated wind speed (m/s) & 13 \\ \(R\) & Turbine rotor diameter (m) & 54.4 \\ \(A\) & Swept area (m\({}^{3}\)) & 2324.27 \\ \(n\) & Number of blades & 3 \\ \(P_{gen}\) & Generator rated power (MW) & 1.5 \\ \(f_{gen}\) & Generator frequency (Hz) & 11.5 \\ \(p\) & Pole pairs of PMSG & 40 \\ \(v_{gen}\) & Generator phase voltage & 690 \\ Hz & Frequency & 11.5 \\ \(\omega_{r}\) & Mechanical angular frequency (rad/s) & 1.8 \\ \(I\) & Generator Inertia constant (M kg.m\({}^{2}\)) & 0.92 \\ \(T_{e}\) & Generator torque (M N.m) & 0.83 \\ \(\varphi_{f}\) & Permanent magnet flux linkage (V/rad/s) & 8 \\ \(L_{d}\) & d-axis inductance (mH) & \(4\times 10^{-3}\) \\ \(L_{q}\) & q-axis inductance (mH) & \(4\times 10^{-3}\) \\ \(R_{a}\) & Stator resistance (\(\Omega\)) & 0.000317 \\ \(C_{r}\) & Rectifier output capacitor (μF) & 5000 \\ \(f_{c}\) & Boost chopper and VSI switching frequency (Hz) & 5000 \\ \(L_{dc}\) & Boost chopper inductor (mH) & 10 \\ \(C_{dc}\) & DC-link capacitor (μF) & 6000 \\ \(V_{dc}\) & DC-link voltage (V) & 5500 \\ \(v_{grid}\) & Grid voltage (V) & 480 \\ \(f_{grid}\) & Grid frequency (Hz) & 50 \\ \(R\) & Grid filter resistance (\(\Omega\)) & 0.02 \\ \(L\) & Grid filter inductance (mH) & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Rated parameters of the WECS considered for simulation. During the dip incident, the MSC continues to extract maximum power from wind, while the GSC achieves DC-link voltage regulation and grid synchronization at unity power factor. Due to the drop in grid voltage \(v_{grid}\) to 0.3 p.u., the grid currents \(i_{grid}\) will rise accordingly to almost 1.2 of its rated value, while the active power injected into the grid \(P_{grid}\) is reduced significantly. At the generator side, the MSC does not sense or detect the sag incident; thus, the boost chopper current \(I_{b}\) will continue to track the chopper reference current \(I_{b}^{*}\) corresponding to the MPPT operation. MSC control is unaltered; therefore, no observed changes are indicated in the generator speed, torque, output line voltage \(v_{ab-gen}\), or its line current \(i_{a-gen}\), meaning the generator maximum power \(P_{gen}\) is still extracted. Due to the energy imbalance, the PMSG will inject its active power into the DC-link, causing a rise in the DC-link voltage \(V_{dc}\) that exceeds its rated value by almost 20%. In response to the DC-link voltage rise, the GSC \(d\)-axis current \(I_{d}^{*}\) controller command rises, to maintain the energy balance and deliver all the energy stored in the DC-link capacitor to the grid, thus hitting the grid current limitations. Meanwhile, grid reactive power \(Q_{grid}\) is maintained to zero due to unity power factor operation; thus, the \(q\)-axis current \(I_{q}^{*}\) controller command remains at zero. In real systems, grid current rise can hit the converter thermal limits, and this may destroy the power converters due to voltage and current stresses on the power modules. As the fault is cleared at t = 0.75 s, grid voltage \(v_{grid}\) recovers to 1p.u. DC-link voltage \(V_{dc}\) takes time for recovery as it is governed by the dynamics of the DC-link voltage control loop and the DC-link capacitor \(C_{dc}\) value. Grid currents and power return to pre-fault values and the system fully recovers at t = 1.45 s.  
To validate the proposed approach's effectiveness, the system is retested when swapping the control during the dip duration. Figure 8 shows the system response after applying the proposed control methodology for a similar 70% symmetrical voltage sag.