A Describing Function-Based Stability Analysis Method for Cascaded DC-DC Converters

• Published in: IEEE open journal of the Industrial Electronics Society Vol. 3; pp. 484 - 495
• Main Authors: Li, Hong, Liu, Qian, Zhang, Zhipeng, Liu, Chen, Li, Zhong, Yang, Zhichang, Zheng, Trillion Q.
• Format: Journal Article
• Language: English
• Published: New York IEEE 2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Analytical models; cascaded DC-DC converters; DC-DC power converters; describing function; Design parameters; Impedance; Links; Mathematical models; Power system stability; Pulse duration modulation; Pulse width modulation; Stability analysis; Stability analysis method; Stability criteria; Switches; Voltage converters (DC to DC)
• ISSN: 2644-1284; 2644-1284
• DOI: 10.1109/OJIES.2022.3191906

The parameters of DC-DC converters in a cascaded converters system are often set up separately, which may cause instability or even breakdown of the whole system. The traditional Middlebrook impedance stability criterion and Nyquist criterion are based on the small-signal model, where the nonlinear links are ignored or linearized, which, however leads to inaccurate modeling, and the difficulty for analytically obtaining stability range. In this paper, the nonlinear links, i.e., pulse width modulation links, of cascaded DC-DC converters system are first modeled by the describing function (DF); then, a novel stability analysis method for the cascaded DC-DC converters system is proposed by combining the impedance analysis method, Nyquist criterion and DF to accurately determine the stability range of the cascaded converters system. Since the DF method is only used into single converter so far for stability analysis, a source/load converter equivalent method is proposed in this paper to apply DF method into the cascaded converters. To this end, the two-stage cascaded boost converters systems with and without considering the parasitic parameters are taken as examples to conduct the simulation and experiment for verifying the correctness and the accuracy of the proposed DF-based stability analysis method. This work provides an analytical method to determine not only the stable and unstable ranges but also the critical stability range of the cascaded system, as well as provides a reference to quantificationally design the control parameters.