# Wide-Area Protection System for Radial Smart Distribution Networks
## 2 Fault Current Contribution of DFIGs  
Among various types of DERs, wind energy is a leading option, accounting for 900 GW out of the total 3372 GW (\(\sim\)27%) of installed capacity of renewable energy sources in 2022 [26]. Wind power generators use different technologies such as Traditional Asynchronous Machines (TAMs), Permanent Magnet Asynchronous Machines (PMAMs), and DFIGs. TAMs are not widely used due to stability issues during wind speed and load fluctuations. PMAMs, on the other hand, connect to the main network via power electronic converters, which makes their fault contribution behavior dependent on the converter configuration and settings, similar to photovoltaic farms that have been extensively studied [27; 28].  
DFIGs are being increasingly used in the green energy industry due to their high efficiency and flexibility [29; 30; 31]. In the vision of protection analysis, the behavior of DFIGs is like Asynchronous Machines (Ams) where the short circuit current is reliant to the machine impedances, machine rating, and rotor slip. As in Ams, the rotor is spinning close to the synchronous speed; the slip effect can be neglected. Furthermore, the rotor and stator resistances can also be neglected due to their low value, and the short circuit current (\(i_{s}\)) is calculated using (1) [32; 33]:  
\[\overset{\rightarrow}{i_{s}}=\frac{\sqrt{2}V_{s}}{\text{j}\omega_{s}L_{s}^{ \prime}}\Big{[}1-(1-\sigma)e^{\text{j}\omega_{s}t}\Big{]} \tag{1}\]  
where \(\sigma\) is the leakage factor which can be derived from (2):  
\[\sigma=1-\frac{L_{m}^{2}}{L_{s}L_{r}} \tag{2}\]  
where \(L_{s}^{\prime}\) is the stator transient inductance. The assumption of neglecting machine resistances results in a non-decaying component in the stator current (first part of the term inside the bracket in (1)) that is indeed decaying with the stator transient time constant (\(T_{s}^{\prime}\)),and the second term inside the bracket is the result of the rotor DC component that is also decaying with the rotor transient time constant (\(T_{r}^{\prime}\)). Hence, the short circuit current is in the following form:  
\[\overset{\rightarrow}{i_{s}}=\frac{\sqrt{2}V_{s}}{j\omega_{s}L_{s}^{\prime}} \left[e^{-t/T_{s}^{\prime}}-(1-\sigma)e^{j\omega_{s}t}.e^{-t/T_{r}^{\prime}}\right] \tag{3}\]  
Detailed calculations can be found in [32; 33].  
During short circuit faults, large currents flow through the rotor and stator windings of DFIGs, and as shown in Figure 1, these large currents can damage the back-to-back converter of the machine whose ability to withstand thermal damage is much lower than machine windings. To avoid breakage of the converter and maintain the grid requirements relating to fault ride through capability, crowbar resistances are installed on the rotor circuit and are switched on during faulty conditions. In this case, the maximum short circuit current of the machine is determined based on the following:  
\[i_{s,\ max}=\frac{1.8V_{s}}{\sqrt{X_{s}^{\prime 2}+R_{cb}^{2}}} \tag{4}\]  
The value of the crowbar resistances can be achieved by the following rules:  
1. The crowbar resistance shall be large enough to limit the fault current value passing through rotor circuit;
2. The crowbar resistance shall be small so as to not cause a high magnitude of voltage during fault conditions, because voltages above the DC link rating can cause large currents on the blocking diodes of the converter, resulting in an unacceptable charge of the DC link. Furthermore, a voltage that is too high can cause isolation breakage of the rotor windings and the converter.