CAJ | 학술논문

拓扑结构切换、占空比控制方法和非线性元件均可使电力电子系统具有非线性特性，因此其小干扰稳定问题属于微分方程周期轨的稳定问题。由于状态空间平均法误差较大、难以预测分叉，而数值仿真法物理概念不清晰，因此，提出了基于梯形积分法的非线性电力电子系统周期轨稳定性分析方法。利用梯形积分法描述系统占空比方程和每阶段的非线性状态方程，由隐函数求导法和链式求导法计算周期轨Poincar6映射的雅可比（Jacobiarl）矩阵，提出了系统稳定裕度指标，建立了基于周期轨Poincar6映射的非线性电力电子系统小干扰稳定性分析方法。该方法能够克服小干扰稳定传统分析方法的困难，揭示非线性电力电子系统失稳的动力系统机制。仿真分析验证了算法的有效性。
탁복결구절환、점공비공제방법화비선성원건균가사전력전자계통구유비선성특성，인차기소간우은정문제속우미분방정주기궤적은정문제。유우상태공간평균법오차교대、난이예측분차，이수치방진법물리개념불청석，인차，제출료기우제형적분법적비선성전력전자계통주기궤은정성분석방법。이용제형적분법묘술계통점공비방정화매계단적비선성상태방정，유은함수구도법화련식구도법계산주기궤Poincar6영사적아가비（Jacobiarl）구진，제출료계통은정유도지표，건립료기우주기궤Poincar6영사적비선성전력전자계통소간우은정성분석방법。해방법능구극복소간우은정전통분석방법적곤난，게시비선성전력전자계통실은적동력계통궤제。방진분석험증료산법적유효성。
Topological structure switching, duty ratio control method and nonlinear components can all make power electronics systems have nonlinear characteristics, so small signal stability of nonlinear power electronic systems belongs to stability of periodic orbit of differential equations. State space averaging method has difficulty to predict bifurcation or the prediction has lower accuracy, while numerical integration method has not clear physical concept, so this paper presents an analysis method of periodic orbit stability based on trapezoidal integration method. Trapezoidal integration method was applied to describe the duty ratio equation and nonlinear state space equation of each stage. Jacobian matrix of the Poincare mapping was calculated by implicit function derivative method and chain derivative method, and the stability margin was presented. Thus the analysis method of small signal stability for nonlinear power electronic systems was established based on Poincare mapping of periodic orbit. The presented method can overcome the difficulty of traditional analysis method of small signal stability and reveal the instability mechanism of dynamical system for nonlinear power electronic systems. Simulation analysis verified the validity of the algorithm.