# Stability Analysis of Buck Converter Based on Passivity-Based Stability Criterion
## 1 Introduction
On the basis of the large signal method, numerous advanced nonlinear control techniques have been developed [17], such as the sliding mode method (SMM) [18], predictive methods [19], fuzzy methods [20; 21] and so on. These methods have received a great deal of attention for their simple structure and high robustness. The comparative analysis of the model, implementation complexity and performance of this method are shown in Table 1. It can be seen that the nonlinear control techniques have better performance; however, the model and complexity are more complex than in the traditional methods. Passivity is a more general condition of boundedness, which is applicable to open dynamical systems. The boundedness of passive systems still holds if the passive system interconnects with other passive systems. The Passivity-Based Stability Criterion (PBSC) was proposed for the DC power distribution system based on the passivity of the bus impedance [22]. It stated that if the overall bus impedance is passive, then the system is stable. Furthermore, the PBSC has the characteristic of passivity, as the system obtained by a parallel connection or negative feedback connection of two passive systems is also passive and stable. Therefore, the passivity and stability of the whole system can be ensured by designing each subsystem in the DC microgrid as a passive module [23]. Since there is no power flow assumption, the PBSC is also applicable when the power flow changes. To date, the PBSC has been applied to stability analyses in multiple scenarios. Reference [24] takes multi-bus medium-voltage DC distribution systems as the research object, applies the PBSC to analyze the passivity of each interacting bus impedance in medium-voltage DC systems, proposes a new technology to evaluate the total line impedance damping of the system and designs positive feedforward (PFF) control to ensure that the Nyquist profile of the bus impedance is included within the boundary of the specified allowable impedance region. Reference [25] takes voltage source converters as the research object, applies the PBSC to \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Advanced Control** & **Model** &
\begin{tabular}{c} **Implementation** \\ **Complexity** \\ \end{tabular} & **Performance** \\ \hline Sliding mode method & Averaged & High & Good \\ Predictive methods & Averaged & High & Good \\ Fuzzy methods & Averaged & High & Good \\ PID methods & Simple & Moderate & Averaged \\ PI methods & Simple & Simple & Common \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparative analysis of the control methods. analyze the input admittance passivity of voltage source converters and increases the filter resistance to make the system input admittance passive. Reference [26] takes multiple parallel converters in offshore wind farms as the research object, applies the PBSC to evaluate the overall system stability and reduces the resonance risk of LCL filters by adding active damping technology based on virtual resistors. Reference [27] focuses on civilian DC systems with bidirectional power flow, applies PBSC to analyze the passivity of the system and adopts feedforward control to make the input admittance of the Buck converter passive. Reference [28] applies generalized PBSC to a dual-component DC power load power system to achieve stability in interconnected power systems. Reference [29] applies PBSC to a closed-loop system of a row of cyclically controlled vehicles and improves the passive stability of the system through feedforward and feedback methods. Reference [30] applies PBSC to the grid-connected system of controlled active and reactive power injection devices by modifying the existing controller to make the system passive. In order to reduce the complexity when analyzing the stability of the system, the passivity-based stability criterion (PBSC) is proposed to improve the stability analysis of the DC microgrid.