# Relationship between Fault Level and System Strength in Future Renewable-Rich Power Grids
## 5 Results and Discussion
### Fault Level Results from the Load Change-Based Thevenin Impedance  
This section calculates the fault level at the nodes of interest in the IEEE nine-bus test system using the estimated Thevenin impedance from using the load step change method described in Section 3.1. This has been achieved by scaling the loads at three different levels up to 105%, 110%, and 115% of their original values simultaneously. It is worth noting that both the active (P) and the reactive (Q) power of the loads have been changed correspondingly. Two sets of measurements for both the current and the voltage at each node of interest have been collected before and after the load change at a steady state, neglecting the transient. Three values of the Thevenin impedance are obtained using (5). The corresponding values of the fault level are calculated using (2), and are then averaged. Note that this has been repeated for each scenario of penetration of RESs as listed in Table 2.  
It can be seen from Table 2 that the fault level results are marginally affected by the value of the load step change as they are almost converging to the same values for all buses, more specifically in scenarios one and two. However, the impact of the load step change might be more tangible in the third scenario where the penetration of RESs is the highest. This can be observed at bus eight, which is closer to the displaced SGs at G2 and G3. In other words, the sensitivity of the application of load change method for estimating the Thevenin impedance, and in turn the fault level, is location-dependent and it might be notably affected by the scenario of the penetration of RESs. As expected, a remarkable decrease in the fault level, and in turn the increased Thevenin impedance, can be observed by increasing the penetration level of RESs. For instance, the fault level at bus five has witnessed a decline from its original value of 934 MVA in scenario one (i.e., \(p\) = 0%), down to 717 MVA and 334 MVA in scenario two (i.e., \(p\) = 22%), and scenario three (i.e., \(p\) = 56%), respectively.  
Similarly, the fault level at the other buses show a remarkable decline with more severity. For example, the fault level at bus six has decreased from 729 MVA in scenario one down to 478 MVA and 244 MVA in scenarios two and three, respectively. On the other hand, the highest decline in fault level was registered at bus eight, where the fault level decreased from 806 MVA in the base scenario (i.e., scenario one, \(p\) = 0%), down to 482 MVA and 143 MVA in scenarios two and three, correspondingly. This variable sensitivity of the fault level in different buses can be attributed to the fact that these nodes are located at different locations meaning that they have distinct electrical distances from the generation centers, which is also affected by the RE  
\begin{table}
\begin{tabular}{c c c c} \hline
**Load** & **Bus** & **P [MW]** & **Q [MVAr]** \\ \hline Load A & Bus 5 & 125 & 50 \\ Load B & Bus 6 & 90 & 30 \\ Load C & Bus 8 & 100 & 35 \\ \hline \end{tabular}
\end{table}
Table 1: Load distribution in IEEE nine-bus test system.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline  & \multicolumn{4}{c}{**Scenario 1 (\(p\) = 0\%)**} & \multicolumn{4}{c}{**Scenario 2 (\(p\) = 22\%)**} & \multicolumn{4}{c}{**Scenario 3 (\(p\) = 56\%)**} \\ \cline{2-11}
**Bus** & **105\%** & **110\%** & **115\%** & & **105\%** & **110\%** & **115\%** & **105\%** & **110\%** & **115\%** & **Average** \\
**Num.** & **Load-** & **Load-** & **Load-** & **Load-** & **Load-** & **Load-** & **Load-** & **Load-** & **Load-** & **Load-** & **Load-** & **Average** \\  & **ing** & **ing** & **ing** & **ing** & **ing** & **ing** & **ing** & **ing** & **ing** & **ing** & **ing** & **ing** \\ \hline Bus 5 & 937 & 934 & 930 & 934 & 719 & 717 & 713 & 717 & 334