Open AccessSustained oscillations and bifurcations in three‐phase voltage source converter tied to AC grid
Author(s) -
Ma Rui,
Yang Ziqian,
Cheng Shijie,
Zhan Meng
Publication year - 2020
Publication title -
iet renewable power generation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.005
H-Index - 76
eISSN - 1752-1424
pISSN - 1752-1416
DOI - 10.1049/iet-rpg.2020.0204
Subject(s) - hopf bifurcation , control theory (sociology) , physics , oscillation (cell signaling) , inductance , instability , saturation (graph theory) , phase locked loop , bifurcation theory , bifurcation , voltage , mathematics , mechanics , phase (matter) , nonlinear system , quantum mechanics , computer science , chemistry , biochemistry , control (management) , combinatorics , artificial intelligence
Recently large‐scale integration of power‐electronic‐based devices has made system‐level oscillations occur frequently, which posed a big challenge for modern power grids. Previous studies mainly treated sustained oscillations under the framework of (linear) small‐signal stability and/or by incorporating the impact of current saturation, but seldom considered system non‐linearity like phase‐locked‐loop. In this study, the authors established a sixth‐order non‐linear model for a three‐phase voltage‐source converter tied to AC grid, and studied its dynamics completely from non‐linear system theory and signal analysis technique, with all parameters including current controllers, phase‐locked‐loop, line inductance, and grid voltage. They found that the operation point usually becomes unstable by Hopf bifurcation, and the sustained oscillations are possible only for super‐critical Hopf bifurcation. Based on these observations, sustained periodic oscillation should be treated as a limit cycle even without saturation. With saturation, some other phenomena have also been found, such as saturation‐induced instability and saturation‐restricted oscillation. In addition, they discovered that for sustained oscillations, the usual purely sinusoidal three‐phase currents exhibit the form of sin [ 2 π f 1 t + c sin ( 2 π f d qt ) ] or cos [ 2 π f 1 t + c sin ( 2 π f d qt ) ] , where f 1 ( f d q ) denotes basic (modal oscillation) frequency with c a constant. This work could provide an improved understanding of sustained oscillations and associated system dynamics in an overall perspective manner.