# Minimization of the Decoupling Circuit (DC-Link) in Induction Motors
## 3 Results  
This section presents simulation results to validate the capacitance equation developed in this work, considering the selected critical operating case when the highest energy return occurs. This occurs when the motor accelerates from 0% to 100% of its rated speed at maximum load in the shortest possible time, using the established design specifications (Table 4) for the three-phase full-bridge inverter with SPWM modulation using a modulation index of 0.9 and a switching frequency of 3300 Hz. These specifications contribute to establishing the operating limits of the critical case mentioned and thus delimit the analysis of the system behavior through the graphs and results presented in this paper. The schematic diagram of the system is shown in Figure 11.  
In this work, because it works with a multiphase DC boost converter (five phases), the switching frequency of each phase is 50 kHz, so the output presents a signal with a frequency of 250 kHz, which compared to the switching frequency of the inverter designed (3.3 kHz) is considerably higher, so the behavior of the waveform concerning the switching of the converter does not interfere significantly with the objective of the analysis of the power flow between the decoupling capacitor and the inverter, addressed in this article. To carry out the validation of the minimum required capacitance equation obtained in this work, presented at the end of the previous section, the following steps are performed:  
1. Average values of K-parameters are proposed to be used in (19). 2. Voltage ripples are proposed and used in (19) together with the K parameters obtained in the previous step and minimum required capacitance values are obtained. 3. The simulation of the complete system is carried out using the minimum required capacitance values obtained. 4. The voltage ripples are obtained by simulation using the minimum capacitance value obtained previously. 5. The error percentage between the values initially proposed and the values obtained using (19) is calculated. Firstly, to obtain the K parameters of (19), different 3 HP motors were simulated, considering the selected application and critical case. The obtained values are presented in Table 5.  
The average value of these parameters \(K\) in the case study is used in the capacitance equation of (19), resulting in (20), (21), and (22):  
\[K_{dc}=2.947 \tag{20}\]  
\[K_{4}=1.439 \tag{21}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline DC source & 320 V \\ Modulating signal frequency & 60 Hz \\ Carrier signal frequency & 3300 Hz \\ Modulation index & 0.9 \\ Power load (Motor) & 3 HP \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Design specifications used. Figure 11: Schematic system diagram. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**3 HP Induction Motor** & \multicolumn{3}{c}{**Proportionality Factors**} \\ \hline  & \(K_{DC}\) & \(K_{4}\) & \(K_{6}\) \\ Motor 1 & 43/14 & 10/7 & 17/14 \\ Motor 2 & 2.96 & 1.4 & 1.19 \\ Motor 3 & 2.85 & 1.48 & 1.24 \\ Motor 4 & 2.91 & 1.45 & 1.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: \(K\) parameters obtained. \[K_{6}=1.213 \tag{22}\]  
Emphasizing that the obtained values belong to the critical case selected and to the proposed application. Subsequently, different voltage ripples are proposed to verify the good performance of the capacitance equation developed. Table 6 shows different proposed voltage ripples and the minimum capacitances obtained using these values in (19). The calculated capacitance under the different proposed voltage ripples is implemented in the complete system. Figure 12 shows the voltage ripples obtained using the different capacitance values calculated with the developed equation. The purpose is to compare the initially proposed voltage ripples with those obtained using the minimum required capacitance equation developed in this work, to obtain a percentage error between them.