Nonlinear Modal Analysis of Transient Behavior in Cascade DC–DC Boost Converters

Abstract

This paper deals with the transient characteristics of the cascade DC–DC Boost converter under a large disturbance by using nonlinear modal series method. Based on the power balance principle, a nonlinear averaged model is derived to describe the nonlinear dynamics of the cascade converter. And then, the modal series method is described in detail and the second order approximate solutions are derived by this method. Furthermore, the simulation results and the theoretical analysis demonstrate that there are plenty of modal interactions, particularly the stronger second order modal interactions, which can affect the transient behavior significantly in the disturbed transient process. The modified approximate solutions considering the dominant nonlinear interaction modes of some state variables are subsequently obtained. In addition, by selecting appropriate system parameters, we can improve the transient behavior of the system under disturbance so that the amplitude and duration of the oscillation can be effectively reduced to satisfy the requirements of the system tolerance during the transient process. Moreover, the dominant oscillation modes of each state variable are also studied, which will help us improve the understanding of the salient transient behaviors in DC–DC cascade converters with disturbance. Finally, PSpice circuit experiments are performed to verify the above theoretical and numerical results.

Flatness-Based Decentralized Adaptive Backstepping Control of Cascaded DC–DC Boost Converters Using Legendre Polynomials

“…A simple structure to own a wide voltage conversion ratio is connecting the boost converters in a cascade form due to the reliability and good scalability (Zhang et al 2018;Do 2012). However, the cascaded boost converters suffer from a variety of nonlinear interactions, non-minimum phase nature and uncertainties such as parameter variations, DC supply and sudden load changes (Zhang et al 2017;Shoja-Majidabad and Hajizadeh 2020). The interactions between the converter modules may cause the overall system instability and switching stress (Yang et al 2009).…”

“…In the frequency domain, Middlebrook suggested an impedance criterion that the cascaded system can be stable if the magnitude of the source converter output impedance be far smaller than the load converter input impedance (Middlebrook 1976). In this regard, the cascaded modules can be decoupled, which causes the interaction terms ignorance (Zhang et al 2017). Due to the conservative property, the Middlebrook impedance criterion is tough to satisfy in practice.…”

“…A multi-cascaded buck converters time-domain stability is reported in Li et al (2018). In Zhang et al (2017), bifurcation phenomena and stability regions of the cascaded boost converters are investigated. A nonlinear modal series method is proposed to improve the transient behavior of the cascaded modules in the presence of uncertainties.…”

Modeling and analysis of complex dynamics for dSPACE controlled closed‐loop DC‐DC boost converter

“…The synchronization and anti‐synchronization of chaotic systems with application to boost converter in simulation were described by R. Sakthivel et al L. Cheng et al introduced a circuit‐oriented geometrical approach in predicting subharmonic oscillation of VMC switching converters . The transient characteristics of the cascaded boost converter under a large disturbance by using nonlinear modal series method were reported by H. Zhang et al The nonlinear phenomena like chaos and other periodic motion, which are influenced by system parameters, topological structure, load, and pulse period in a single‐stage boost converter were discussed by R. Zhang et al B. S. Tekpeti et al studied the design and modeling of boost converter for photovoltaic systems in simulation …”

“…Although the considerable amount of works has already been done by previous researchers, some important portions of the dynamics study of converters are still uncovered. It has been observed from the aforesaid literatures that the most of the prior researchers have been used state space averaging (SSA) method for converter modeling, has been implemented using integral controller for closed‐loop operation etc.…”