The use of the passivity-based control (PBC) properly fits stability problems related to multilevel converters. Two approaches for

the PBC design have been proposed and will be reviewed in the present paper. Particularly the second is developed by splitting the system into n subsystems and controlling them independently. The partition of the multilevel converter is done on the basis of energy considerations. The main advantage of the second approach is the separate control of the different DC-links and a flexible loading capability.

With the continuous increase of output power ratings, multi-phase (multichannel) interleaved power factor corrector (IPFC) is gradually employed in domestic and commercial inverter air-conditioners. IPFC can solve several main problems, such as power rating increase, power device selection, input current ripple reduction as well as inductor on-board mounting. But for a multi-phase IPFC, the key problem is that it should show rapid dynamic responds and good current sharing capability, so in this paper the aim is to improve the dynamic performance and current sharing capability by means of passivity control theory. Considering the power circuit topology of a four-phase IPFC, an EL (Euler-Lagrange) mathematical model is established when the IPFC operates in continuous conduction mode (CCM). Then the passivity of the four-phase IPFC is proved, and the passivity-based controller using the state variables feedback and damping injection method is designed. The proposed control scheme, which is easy to control and needs no proportion integral controller, has strong robustness on disturbance from singlephase AC input voltage, the load as well as the parameters of the employed devices. Even in wide-range load condition, the mains current has a fast dynamic response and the average output voltage almost keep unchanged. As a result, the main functions of the four-phase IPFC are implemented including nearly unitary power factor and constant DC output voltage. Meanwhile, the four-phase IPFC acquires an excellent current sparing effect after using passivity-based controller. The above analysis has been proved with simulated results by means of MATLAB/SIMULINK and experimental results, showing that the passivity-based IPFC controller has superior performances and feasibility.

The LLC resonant converter is a widely used DC/DC converter that offers the benefit of enabling soft switching compared to classical DC/DC converters. However, traditional PI control strategy based on a linear model has drawbacks such as slow dynamic response and poor anti-interference performance. To overcome the shortage, a passivitybased control strategy based on the Euler–Lagrange (EL) model is proposed in this paper to improve the dynamic performance of the half-bridge LLC resonant converter. In addition, the stability of the system based on the proposed strategy is analyzed and verified. Further, the effectiveness and performance of the proposed strategy is verified in the simulation by comparing with the traditional PI controller. Finally, a prototype was built to verify the dynamic performance of the LLC resonant converter based on the proposed control strategy.