## 3 Analysis of IM Loads Characteristics in Power System
### Voltage Recovery Characteristics of IM Loads  
Typically, the IM loads can be categorized based on their capacity (large and small) and load type. It might be desirable to model IM loads with both small and large motors, with significantly different parameters depending on their sizes [9; 44]. When only considering the parameters for large IM loads, the corresponding load portion can be regarded as being too large, so the system's margin seems to be high. When only taking into account those for small IM loads, the industrial IM load might be too small, so the simulation results seem to be more critical than the real system's behavior. For this reason, dynamic characteristic analysis is needed, considering the intermediate values for the parameters, and the values used in this paper are as shown in Table 1.  
The IM loads are about 60% to 70% of the total load for a typical power system, but applying this IM portion can provide critical simulation results. In simulation, the most widely used portions are 40% or 50%. In this paper, based on the above-mentioned data, it is recommended that the range of the IM portion is from 30% to 50% to get reliable simulation results. This paper also reflects the characteristics of \(H\) regarding power system stability. Table 2 shows the results of the analysis on the voltage recovery characteristics depending on the proportion of the IM loads and the H parameter changes. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(R\)s & \(X\)s & \(R\)r & \(X\)r & \(X\)m & \(H\) \\ \hline
0.043 & 0.074 & 0.025 & 0.051 & 3.14 & 0.4–1.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of induction motor loads. When the applied proportion of IM loads was 30% or 40%, it can be seen that the voltage recovery characteristics were similar, regardless of the change of \(H\). When the proportion of IM loads was 50% and the \(H\) value was increased, voltage instability occurred. The power system voltage did not recover due to the generator angle stability problem. A low value of \(H\) becomes a severe situation, but a high value of \(H\) makes the situation of the systems less severe. When the IM loads suffer a sustained low voltage, they consume excessive reactive power. According to the results, the equilibrium point of the system did not exist. In addition, if fault clearing was not quickly applied, the kinetic energy of the IM load was increased and the voltage could not be recovered. This short-term voltage instability problem is greatly affected by the proportion of IM loads. If the proportion is low, the voltage recovery is fast, but if the proportion is high, the voltage recovery might be slow, or the system might experience voltage collapse [30]. Figure 6 shows the results of the effect of IM load proportion on the system behaviors, assuming that the proportion of IM loads is about 30-50%. From Figure 6, in the case of an IM proportion of 30%, the bus voltage was stabilized after the fault was cleared. The IM load speed successfully has been recovered to a normal speed, and the IM loads are reaccelerated. In the case of an IM proportion of 40%, the stalling of IM loads occurred after the fault. For the high IM load condition, motors could not reaccelerate. The IM load speed did not recover to the normal speed due to the fact that the IM mechanical and electrical torque curves did not intersect, and the IM slip exceeded the unstable equilibrium point. In the case of an IM proportion of 50%, the voltage instability happened by the stalling of the IM loads after the fault. IM load speed dropped due to the increase in the total transmission impedance. As a result, IM stalling caused voltage collapse because of the post-fault equilibrium point not existing.