## 4 Fault Current Limiting Devices
### Non-Superconducting FCL  
#### 4.1.1 Inductive Type FCL: Non-Controlled FCL  
In [26], a cost-effective topology of a non-controlled FCL, to improve the FRT capability of the DFIG, has been studied. The non-controlled FCL is placed in the rotor side, which is shown in Figure 5a. Its configuration is similar to a three-phase bridge type FCL. The limiting inductance is a non-superconductor (NSC), which is cost-effective from an industrial point of view. Regarding the location of the FCL, inserting the NSC either in the stator side or in the rotor side has different impacts. When the non-controlled FCL is located in the stator side, regarding (9) and (10), the value of back-EMF voltage and the transient inductance of the rotor are changed as follows:  
\[\overset{\rightarrow}{V}_{0r}=\frac{L_{m}}{L_{s}+a^{2}L_{FCL}}\frac{d \overset{\rightarrow}{\psi}_{s}}{dt} \tag{9}\]\[\sigma_{L1-FCL}=1-\frac{L_{m}^{2}}{(L_{s}+a^{2}L_{FCL})L_{r}} \tag{10}\]  
Figure 5b shows the variation of the leakage coefficient by changing the FCL's impedance. As it is clear by (9), by increasing the inductance of the FCL in the stator side, the value of rotor back-EMF voltage decreases. Therefore, the RSC has a good controllability in order to counteract the stator flux oscillations. However, the absolute value of the leakage coefficient significantly decreases and damps by increasing the FCL's inductive impedance. In fact, there is the possibility that the rotor transient over-current is not restricted to an acceptable range. It should be mentioned that, by locating the FCL in the stator side, the stator voltage is resumed to some extent. By placing the FCL in the rotor side, the leakage coefficient is expressed as follows:  
\[\sigma_{L4-FCL}=1-\frac{L_{m}^{2}-a^{2}L_{FCL}L_{s}}{L_{s}L_{r}} \tag{11}\]  
When the inductive FCL is located in the rotor side, the variation of the leakage coefficient is also shown in Figure 5b. In order to find out the variation of the leakage coefficient, some points should be considered. For the inductive FCL located in the rotor side, any impedance value lower or higher than the intersection point of curves could result in good rotor transient over-current limitation. Otherwise, the FCL could have an inverse impact on limiting the rotor transient over-current. As a result, if the inductive FCL is going to be in the rotor side, its impedance should be lower or higher and far away  
Figure 5: (**a**) The non-controlled inductive fault current limiter [26]; and (**b**) the leakage coefficient variation, with the FCL inductance variation in the stator and the rotor sides.  
than from the intersection point of the curves in order to achieve a good current limitation capability. However, it should be noted that, from limiting the rotor transient over-current perspective, the inductive FCL in the rotor side is more effective than placing the FCL in the stator side. Furthermore, it should be noted that the rotor back-EMF voltage remains unchanged and, consequently, a rather high electromagnetic torque oscillation might occur due to the weak controllability of the RSC on the stator flux linkage. In addition, there is no possibility to restore the stator voltage.