## 3 Analysis of IM Loads Characteristics in Power System  
### IM Load Parameter Sensitivity Analysis  
This paper performs sensitivity analysis of the IM load parameters and their effect on the system voltage. Mentioned above in Section 2, the IM load model comprises six parameters; \(R_{s},~{}R_{r},X_{s},X_{r}\), and \(X_{m}\) are all in [p.u.] but \(H\) is in [second]. Figure 5 shows the time trajectories of bus voltages as the result of time-domain analysis considering the voltage recovery characteristics with regard to the changes in IM load parameters.  
Figure 4: Proportion of the ZIP and IM load.  
From Figure 5, one can notice that the bus voltage profiles are not very sensitive with regard to the changes in \(R_{s},\ R_{r},X_{s},X_{r},\) and \(X_{m}.\) On the other hand, the inertia constant \(H\) had an influence on the system voltage. When the \(H\) value is high, the fluctuation of the bus voltage becomes large; this means that the power system's voltage recovery ability is closely affected by \(H.\) The inertia constant \(H\) can be expressed as:  
\[H=\frac{\textit{Kinetic energy at synchronous speed}}{\textit{MVA power base}}=\frac{\frac{1}{2}\textit{I}\omega_{0}{}^{2}}{S_{base}} \tag{14}\]  
Figure 5: Bus voltage sensitivity analysis results of IM parameters. (**a**) \(R_{s}\); (**b**) \(X_{s}\); (**c**) \(R_{r}\); (**d**) \(X_{r}\); (**e**) \(X_{m}\); (**f**) \(H.\)  
where \(I\) is the moment of inertia; and \(S_{base}\) is the MVA power base. Although the inertia constant varies depending on the machine's capacity and type, the values range from 1 to 10 [second]. For a rotating load, the motor can be either directly connected or through a gear or belt drive [30]. The swing equations can be expressed as follows:  
\[\frac{2H}{\omega_{0}}\omega=T_{m}-T_{e} \tag{15}\]  
From the swing equations, Equation (5) of the IM model can be derived. It is noted that increasing load results in an increase of slip [23]. In the form of kinetic energy, the power system has its own energy level because several machines in the power system rotate with speeds close to \(\omega_{0}\). From the definition of the inertia constants with rated powers of individual generators, the kinetic energy level can be obtained as follows:  
\[KE_{sys}=\sum_{i=1}^{N}S_{ni}H_{si} \tag{16}\]  
where \(S_{ni}\) is the rated power of the generator; and \(H_{si}\) is the inertia constant of the synchronous generator \(i\). Not only synchronous generators, but also induction machines in service contribute to the kinetic energy. Then, the system kinetic energy \(KE_{sys}\) can be calculated as follows:  
\[KE_{sys}=\sum_{i=1}^{N}S_{ni}H_{si}+\sum_{i=1}^{N}IM_{ni}H_{mi} \tag{17}\]  
where \(IM_{ni}\) is the proportion of IM; and \(H_{mi}\) is the inertia constant of induction machines. When the system has a high IM proportion, the kinetic energy of the power system might be decreased, compared to cases only with synchronous generators. In high IM load concentrated regions, consumption of reactive power is high. As a result, the equivalent inertia of the system decreases, and this has a significant impact on the system's dynamical responses. In this paper, dynamic characteristic analysis is performed by the mean of changing \(H\) values as well as the proportion of IM loads.