# Relationship between Fault Level and System Strength in Future Renewable-Rich Power Grids
## 5 Results and Discussion
### Fault Level Results from the Capacitor Switching-Based Thevenin Impedance  
This part utilizes the capacitor switching events to collect required sets of measurements for estimating the Thevenin impedance of the system seen at three different buses (five, six, and eight). This is achieved by registering the steady-state voltages before and after switching on the capacitor bank at the studied nodes as detailed in Section 3.2. By using both the voltages with the reactive current injected by the capacitor bank, the Thevenin impedance can be calculated as previously described in (6). To do so, a 50 MVAr capacitor bank is switched on at each of the studied buses where the system strength represented by the Thevenin impedance is estimated. A voltage step change occurs, and the RMS positive sequence voltage is monitored without considering the impact of the transient and the inrush current. Table 3 lists the values of the calculated fault level at those buses by employing the estimated Thevenin impedances using (2). As shown in Table 3, it can be noted that the calculated values of the fault level are different from those calculated using the load change-based Thevenin impedance given in Table 2.  
This difference is not significant in scenario one (\(p=0\%\)) but it is getting larger with the increased penetration of RESs in scenarios two and three. For instance, the fault level at bus five witnessed a decline from its original value of 934 MVA in scenario one (i.e., \(p=0\%\)), down to 924 MVA and 794 MVA in scenario two (i.e., \(p=22\%\)), and scenario three (i.e., \(p=56\%\)), respectively. Similarly, the fault level at bus six has decreased from 914 MVA in scenario one down to 794 MVA and 742 MVA in scenarios two and three, respectively. Unlike the load change-based method, the calculated fault level at bus six does not show the same sensitivity to the high penetration of RESs, and those results in scenario two and scenario three are almost the same. On the other hand, the calculated fault level at bus eight has shown the highest sensitivity to the RES penetration scenario with the highest level of decline severity.  
Taken together, these results show that the application of capacitor bank switching for estimating the Thevenin impedance, hence the fault level, is not only more sensitive to the location of the bus, but also to the RES penetration scenario. This might be attributed to the different sensitivity of the bus voltage to the local reactive current change other than the case of load change-based method, where both the active and reactive current are both changed for all loads simultaneously.  
Generally, it can be noted that these two methods can estimate different values of Thevenin impedance and the fault level, hence, different system strength. To an extent, the difference might be marginal at the base scenario (i.e., scenario one, \(p=0\%\)), but this might be significant otherwise. For better evaluation and to provide a more accurate conclusion, the fault levels obtained from these methods are compared with the values obtained from the IEC 60909 standards and the dynamic simulations (i.e., RMS simulations), which is expected to be the most accurate one, in the next section.