# Stability Analysis of Buck Converter Based on Passivity-Based Stability Criterion
## 5 Simulation Validation
### Simulation of the Improved Control Strategy for the Buck Converter with CPL  
Figure 11 shows the dynamic performance comparison waveform of the system using traditional control and improved control when the load power changes suddenly. It can be seen that the system overshoot is reduced by 4.3 V under the improved control strategy, which has been significantly improved. The comparison shows that the improved control strategy improves the dynamic characteristics of the system. Different control strategies of the Buck converter were investigated. The simulation waveforms of input voltage \(v_{\text{s}}\), the bus voltage \(v_{\text{dc}}\) and the inductor current \(i_{\text{L2}}\) are shown in Figure 12 when the desired value of the DC bus voltage increases. The corresponding simulation of waveforms of the Buck converter at the time when the desired value of bus voltage decreases is shown in Figure 13. At this time, the voltage loop proportionality coefficient \(k_{\text{p1}}\) is 0.3, the integration coefficient \(k_{\text{i1}}\) is 300, the current loop proportionality coefficient \(k_{\text{p2}}\) is 0.05, the integration coefficient \(k_{\text{L2}}\) is 200, and \(k_{\text{F}}\) = 0.003 in the improved control. Figure 11: Comparison waveform under load disturbance. (**a**) Traditional control; (**b**) improved control. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Traditional Control** & **Improved Control** \\ \hline \multirow{5}{*}{Parameters} & \(R_{\text{d2}}=0.01\) & \(R_{\text{d2}}=0.01\) \\  & \(k_{\text{p21}}=0.015\) & \(k_{\text{p21}}=0.015\) \\ \cline{1-1}  & \(k_{\text{k21}}=200\) & \(k_{\text{k21}}=200\) \\ \cline{1-1}  & \(k_{\text{p22}}=0.002\) & \(k_{\text{p22}}=0.002\) \\ \cline{1-1}  & \(k_{\text{k22}}=0.5\) & \(k_{\text{k22}}=0.5\) \\ \cline{1-1}  & & \(k_{\text{F}}=0.001\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Control parameters of the Buck converter. Figure 12: Simulation waveforms of the Buck converter with a DC bus voltage increase. (**a**) Traditional control; (**b**) improved control. As shown in Figure 12a, when the Buck converter adopts the traditional control strategy, the maximum offset of the system bus voltage compared with the steady state value is 12 V, the overshoot is 15% and it is stabilized at 80 V after 0.16 s of oscillation after the bus voltage is increased from 60 V to 80 V, and the maximum offset of the system inductance current compared with the steady-state value is 5A and it is stabilized at 3A after 0.16 s of oscillation. When the Buck converter adopts the improved control strategy, the system waveform is shown in Figure 12b, where the bus voltage is stabilized at 80 V and 0.06 s. After a sudden increase in the bus voltage expectation value from 60 V to 80 V the bus voltage stops overshooting. The system inductor current has a maximum offset of 2.5A compared with the final steady-state value and is stabilized at 3A after 0.06 s.  
As shown in Figure 13a, when the Buck converter adopts the traditional control strategy, the bus voltage desired value suddenly decreases from 80 V to 60 V compared with the steady-state value, where the maximum offset of the system bus voltage is 15 V and stabilizes at 60 V after 0.2 s of oscillation, and the system inductor current falls to 0A, after which the oscillations converge and stabilize at 4A after 0.2 s of oscillation. When the Buck converter adopts the improved control strategy, the system waveforms are shown in Figure 13b. The system voltage is stabilized at 60 V after 0.06 s of oscillation and no overshooting after a sudden decrease in the desired bus voltage from 80 V to 60 V, and the system inductor current falls to 1.5A and converges and finally stabilizes at 4A after 0.06 s.  
Therefore, compared with the traditional control strategy, when the Buck converter adopts the improved control strategy, the stability margin of the system is improved, and when the system is subjected to perturbation, it can quickly recover to the steady state with better dynamic performance.