A method for calculating the Lyapunov exponent spectrum of DC‐DC converter feeding with a switching constant power load

Abstract

Nonlinear dynamic behaviors such as the bifurcation and chaos of DC‐DC converters with switching constant power load are studied in this paper. Based on the consideration of constant power load switching, a discrete iterative mapping model of the system including the switching process is established, and its Lyapunov exponent spectrum algorithm is derived. The main procedure of the algorithm is as follows: Firstly, the system is divided into six smooth segments, and the zero‐time discontinuous mapping of the load and mode switching is introduced. Secondly, the local mapping of each smooth segment and the zero‐time discontinuous mapping of the switching phase are used to construct the composite Poincaré mapping of the system by the chain rule, and then the discrete iterative mapping model of the system is established. Finally, the Lyapunov exponent spectrum algorithm of the system is derived based on the model to determine the type of nonlinear dynamic behavior of the system. This algorithm overcomes the problems of the existing methods, which lead to inaccurate results due to the neglect of the switching process, and achieves the purpose of accurately describing the dynamic characteristics of power electronic circuits. The simulation and experimental results have verified the validity of the proposed model and algorithm. © 2020 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Discrete Modeling and Period-Adding Bifurcation of DC–DC Converter Feeding Constant Power Load

“…To verify the effectiveness of the proposed discrete model and validate PABS analysis, an experimental setup of a buck converter feeding an SCPL was constructed in the laboratory, shown in Fig. 3 [17]. The phase portraits of iL(t)-uC(t) and the time waveform of uC(t) under several P0 values were measured with the experimental platform, as shown in Figs.…”

“…On the basis of the modeling method of the impact oscillator [15,19,21,023], the discrete mapping of the switched evolution process for a DC-DC converter feeding an SCPL was derived in detail in our previous work [17]. Thus, the discrete mapping of the switched evolution process is used directly and rewritten as [17,19,20] k Ck…”

“…To establish the discrete model of the system, the SMs and LMs of the system in a switching period must be exactly determined in advance. Previous studies [14,17] have shown that these SMs and LMs can be exactly determined by comparing the initial values of uC to the boundary voltages of the system. Therefore, deriving the boundary voltages is of importance for the discrete modeling of the system.…”

“…To overcome the problem that the equivalent model of CPL is only applicable to the equilibrium point in abovegiven models and the modeling difficulty of the switched evolution processes of power electronic system, a discrete model including the switched evolution process for DC-DC converters feeding switched CPLs (SCPLs) is established in this work. Here, the so-called SCPL is a CPL that may exhibit switching behaviors such as hopping, removal, or cut-in under different conditions [17], e.g., a constant power electrical brake system [18].…”