## 4 Results and Discussion
### Multi-Phase Under Voltage Load Shedding Scheme Strategy
Figure 7 shows that the bus voltage recovery depends on LSA and LST. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & **Phase-1** & **Phase-1** & **Phase-2** & **Phase-2** & **Phase-3** & **Phase-3** \\  & **LSA (\%)** & **LST (second)** & **LSA (\%)** & **LST (second)** & **LSA (\%)** & **LST (second)** \\ \hline  
**\({}^{3}\) & 60 & 0.3 & 40 & 0.6 & & \\ \hline \hline \end{tabular}  
* \({}^{1}\) Time step: 0.5 s/\({}^{2}\) Time step: 0.4 s/\({}^{3}\) Time step: 0.3 s/\({}^{4}\) Phase 2, 3 time step: 0.5 s/\({}^{5}\) Phase 2, 3 time step: 0.4 s.  
\end{table} 
Table 4: Case study for selection of LSA and LST. From Figure 7, one can notice that when applying case A and B for the MUVLS scheme, voltage instability occurs. For these cases, the full deployment time is 1.5 s. Although load shedding is applied in phase 1, the LST is long, so that the kinetic energy of the IM load is significantly increased, resulting in voltage instability. Case C increased the LSA in phase 1 despite the longer LST, and the final LST was applied within 1 s after the fault, resulting in stable voltage recovery. It can be seen that as the initial LSA decreased, the importance of fast load shedding increased. Cases D-U show the result of voltage recovery, but it can be seen that the phase-2 and phase-3 LSA and LST do not affect the voltage recovery. As a result, it can be seen that phase-1 LSA and LST significantly impact the voltage recovery. The selected LSA and LST of the MUVLS control strategy based on Case S, which has the lowest LSA and the fastest LST per phase in the above results. Figure 7: Results of bus voltage recovery depends on load shedding amount (LSA) and load shedding time (LST). (**a**) Scenario 1: Set the LST in a constant time step in phase 1, 2 and 3; (**b**) Scenario 2: Set phase 1 LST to 0.3 s and phase 2 and 3 to set LST in scenario 1; (**c**) Scenario 3: In scenario 2, in the setup, set the phase 2 and 3 LST to the time step set from phase 1. The decision for load shedding is usually made by system operators, based on pre-established practical criteria. However, the existing UVLS scheme does not consider the dynamics of IM loads. When severe faults are applied to the systems, motor stalling might happen due to the reduced rotation speed of IMs. Because the existing UVLS scheme only considers the ZIP model in dynamic analysis, the effect of motor stalling on voltage recovery cannot be reflected by the scheme. For systems with a high portion of IM load, voltage reduction below a certain level after disturbances might cause voltage instability or DVR. To reduce load interruption, in this situation, adequate countermeasures should be taken, such that the controlled load shedding schemes and countermeasures should be carefully determined, considering the dynamical behaviors of IM loads. Comparison results of bus voltage recovery for existing schemes and the proposed scheme are shown in Figure 8.  
When designing UVLS schemes, proper determination of LSA and LST is essential. Practically, LSA is selected by steady-state analysis, and LST by dynamic analysis. The existing UVLS scheme for the Korean power system is based on the chosen LSA, and it sheds the whole control amount at the first phase. However, this might be excessive. In addition, the approach is based on the premise that there is no transient instability or transient behavior in system voltage. To ensure short-term voltage stability, therefore, LSA and LST need to be determined by both steady-state and dynamic analysis. As the situation of the power system changes in real time, if the MUVLS is applied, the LSA can be reduced compared to the existing scheme. The LSA and LST can be properly determined using the MUVLS strategy, lowering shedding amount for a better performance of voltage recovered.