# Relationship between Fault Level and System Strength in Future Renewable-Rich Power Grids
## 5 Results and Discussion
### Comparison Study Using the Adjusted IEEE Nine-Bus Test System
Likewise, the results obtained at bus six show that LCTI and IEC 60909 methods can converge with the dynamic simulation results opposing the LCTI method which underestimates the fault levels at high penetration of RESs (i.e., scenarios two and three) as shown in Figure 6. Based on that, it can be concluded that the LCTI may fail to represent the system strength at network buses. As shown in Figure 7, the fault level obtained from LCTI at bus eight provided underestimated values compared with the dynamic simulations. Unlike the results of bus five and six, a different behavior can be observed at bus eight. For instance, although the fault level obtained by CSTI matched those obtained from dynamic simulation in scenarios one and two, it failed to do so in scenario three, with 56% penetration of RESs. Note that  
Figure 6: Bus six fault level in different penetration scenarios. Figure 7: Bus eight fault level in different penetration scenarios. both LCTI and CSTI methods fail to match the dynamic simulation results in scenario three with a larger gap for the results of LCTI. The results of bus eight show that the measurement-based approaches assessed (LCTI and CSTI) reflect inaccurate system strength with high penetration of PE-based renewables. More specifically, they have shown lower system strength (i.e., higher Thevenin impedance) in comparison with what might be indicated from using the fault level results of the dynamic simulation. This also means that the CSTI method for fault level calculation is more sensitive to the location of the bus and the scenario of penetration of RESs. The closer the node to the RESs, the higher the mismatch between system strength indicated by the CSTI and the dynamic simulation. On the other hand, the steady-state simulation based on the IEC 6090 standards have shown the most accurate estimation of the dynamic simulation results regardless the scenario or the bus location. However, they might overestimate the actual fault level and the system strength at high penetration scenarios (scenarios two and three) depending on the location of the bus as shown in Figures 6 and 7. In order to provide a better insight, the fault level results obtained from all utilized methods have been validated against the dynamic simulations. In this regard, the absolute error percentages corresponding to each method have been calculated for scenarios one, two, and three, and are listed in Tables 5-7, respectively. As depicted in Table 4, both CSTI and IEC 60909 methods have registered marginal errors with an average of 1.03% and 3.53%, respectively. On the other hand, the LCTI has a big error gap, with an average of 33.86%. Note that the maximum error associated with LCTI method is 57.8% at bus eight. Table 5 shows that the error between the IEC 60909 method and the dynamic simulation is increasing, and that the maximum error at bus eight has increased from (6.5%, in scenario one) to (10.9%, in scenario two). Table 6 has revealed that all methods have increased error in scenario three when compared with the dynamic simulations. For example, very large errors have been registered at all the studied buses when using LCTI and CSTI \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Bus**} & **Dynamic** & \multicolumn{2}{c}{**LCTI**} & \multicolumn{2}{c}{**CSTI**} & \multicolumn{2}{c}{**IEC 6090**} \\ \cline{3-8}  & **Simulation** & **MVA** & **Error\%** & **MVA** & **Error\%** & **MVA** & **Error\%** \\ \hline Bus 5 & 960 & 729 & 24.1 & 914 & 4.8 & 855 & 10.9 \\ Bus 6 & 917 & 461 & 49.7 & 842 & 8.2 & 857 & 6.5 \\ Bus 8 & 792 & 244 & 69.2 & 742 & 6.3 & 768 & 3.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Fault level MVA obtained in scenario two.