# A PMSG Wind Energy System Featuring Low-Voltage Ride-through via Mode-Shift Control
## 7 Discussion
Thus, the grid current is maintained within the system nominal values for safe power converters' operation. However, power imbalance occurs due to the mismatch between the generator shaft mechanical torque \(T_{m}\) and its electromagnetic developed torque \(T_{e}\) as per the synchronous generator swing equation demonstrated in (39) [50]:  
\[T_{m}-T_{e}=T_{a}=J\ \omega_{gen} \tag{39}\]  
where \(T_{a}\) is the rotor accelerating torque, \(J\) is the moment of inertia and \(\omega_{gen}\) is the generator angular speed of rotation. Hence, energy mismatch and speed deviation can be represented by (40):  
\[(P_{m}-P_{e})dt=\frac{1}{2}\ J\ \Big{(}\omega_{gen,\ {\mathit{fault}}}^{2}- \omega_{gen,\ {\mathit{rated}}}^{2}\Big{)} \tag{40}\]  
where \(P_{m}\) is the generator input mechanical power ignoring the rotational losses, \(P_{e}\) is the generator electrical output power ignoring electrical losses, \(\omega_{gen,\ {\mathit{rated}}}\) is the rated generator speed (before fault occurrence), \(\omega_{gen,\mathit{fault}}\) is the shaft speed during fault and \(t_{fault}\) is the fault duration in msec [35,51]. Assuming maximum energy mismatch when \(P_{grid}\approx 0\) (grid voltage dip \(<50\%\)), the maximum generator speed during fault \(\omega_{gen,\ {\mathit{max}}}\) can be calculated using (41):  
\[\omega_{gen,max}=\sqrt{\frac{2P_{gen}t_{fault}}{J}+\omega_{gen,\ {\mathit{rated}}}^{2}} \tag{41}\]  
For simulation work, the value of fault duration \(t_{fault}\) is set to 150 msec, corresponding to the maximum permissible fault duration without tripping the wind turbine as per the Eon-Netz grid code requirements shown in Figure 1a. Thus, theoretically, for the considered 1.5 MW turbine, combined mechanical system inertia is chosen as \(J=5\) Mkgm\({}^{2}\)[52]. Given that \(\omega_{gen,rated}=1.8\) rad/s, the expression (41) gives \(\omega_{gen,max}=1.824\) rad/s corresponding to 1.24 rad/s and a speed increase of 0.24 rpm. Using these values, it is noted that the PMSG speed increase is 1.36% above the rated value owing to the inherit characteristic of the large turbine and generator inertia. These results demonstrate that the concept of storing energy in the rotating mass can be applied to real WECS. Compared to other energy storage techniques, no power is being dissipated as in the chopper-controlled crowbar method and no additional hardware is needed as in systems that use super capacitors or batteries [51]. In addition, the stored energy during the fault can be injected once again to the grid upon grid voltage recovery. Moreover, it is a safe approach since most commercial wind turbines are equipped with an overspeed capability, which offers overspeed protection at 130% above nominal speed [7]. It is worth mentioning that the above calculations depend on the grid dip profile and length, i.e., if the fault duration is too long, the generator may cross the overspeed capability limit. If this scenario happens, pitch mechanism can be employed to trip the turbine. For the correlated experimental prototype and using the experimental values found in Table 4, similar calculations' procedure yields to \(\omega_{gen,max}=105.5\) rad/s when \(t_{fault}\) is set to 60 msec compared to \(\omega_{gen,rated}=94.24\) rad/s. Thus, the speed increase is 107.45 rpm corresponding to 10.66% increase, which is still within machine-safe speed limits. To sum up, Table 6 compares the features of the considered PMSG versus the popular DFIG one. Moreover, it lists merits and limitations of the applied MSC topology, versus the popular active front-end one, as well as showing the superiority of the proposed swap control. Finally, simulation-set-up results as well as those of the correlated experimental prototype verify the effectiveness of the proposed swap scheme.