# 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  
This section provides a comparison between the fault level results obtained from the previous methods that utilized measurement-based Thevenin impedance estimation for fault calculation, and those obtained from the steady-state and the dynamic simulations. To simplify the comparison process, the different fault level calculation approaches used in this study are abbreviated in Table 4. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Bus** & **Scenario 1 (\(p=0\%\))** & **Scenario 2 (\(p=2\%\))** & **Scenario 3 (\(p=56\%\))** \\
**Num.** & & & \\ \hline Bus 5 & 979 & 924 & 794 \\ Bus 6 & 914 & 794 & 742 \\ Bus 8 & 958 & 779 & 395 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Fault level MVA obtained from the capacitor bank switching-based Thevenin impedance. As intended, this comparison aims to examine the extent to which the actual fault level can reflect the Thevenin impedance, hence the system strength in scenarios of high penetration of RESs. Figures 5-7, show the results obtained from measurement methods in comparison with the dynamic simulation in different penetration scenarios for bus five, six, and eight, respectively. Note that the steady-state simulation is based on IEC 60909 standards in which the fault current contribution of the PE-based RESs (i.e., PV and type-four wind) is accounted for as a current source. This contribution is added to the fault current of traditional SGs that is calculated based on the Thevenin equivalent method. The maximum values of the fault currents contribution to the PV system and the type-four wind generators are kept bounded by the maximum overrating capability of the converters (i.e., \(I_{\text{Max}}\)) around the rating current. In this study, a maximum fault current contribution of both installed RESs in the considered scenarios is set to 1.2 p.u. accordingly. It is worth mentioning that the actual fault current of the PE-based RESs during the faults may show different levels of contribution according to the severity of the fault and the measured voltage during the fault at the entry point connecting the RES to the grid. This also might be sensitive to the FRT and control strategy during the fault. In this research, for the dynamic simulation (RMS) purposes, the RESs are modelled and controlled in such a way to remain connected during the fault and to inject a reactive current proportional to the voltage dip seen by the RESs. \begin{table}
\begin{tabular}{c c} \hline
**Acronym** & **Method** \\ \hline LCTI & Load change-based Thevenin impedance \\ CSTI & Capacitor switching-based Thevenin impedance \\ IEC & Steady-state simulation based on IEC 60909 \\ Simulation & Dynamic simulation based on RMS \\ \hline \end{tabular}
\end{table} 
Table 4: Abbreviations of fault level calculation methods. Figure 5: Bus five fault level in different penetration scenarios. Similar to the measurement-based fault calculation methods (i.e., LCTI and CSTI), both steady-state and dynamic simulations have shown the declining trends of the fault level with the increased penetration of RESs. While all the methods converge to the dynamic simulation results with a marginal difference in scenario one (i.e., no RES), a big mismatch can be observed in scenario two and scenario three. This can be seen more in bus eight, which is located between the G2 and G3 where the RESs are introduced. Considering Figure 5, which presents the results obtained in bus five, both CSTI and IEC 60909 methods can lead to the same values of fault level which are matched with the dynamic simulations. However, the LCTI method has shown lower values of the fault level in scenarios one and two, hence a lower system strength. This means that the LCTI method does not account for the impact of the fault current contribution of the RESs.