非线性系统的多项式近似表示及电力系统应用(Ⅰ)——理论篇  

Polynomial approximation of a nonlinear system and its application topower system (Ⅰ):Theoretical justification

作　　者：孙玉娇[1] 刘锋[1] 梅生伟[1] 

机构地区：[1]清华大学电机系电力系统国家重点实验室,北京100084

出　　处：《电机与控制学报》2010年第8期19-23,30,共6页Electric Machines and Control

基　　金：国家自然科学基金资助项目(50823001,50977047)

摘　　要：提出了一种利用多项式近似系统研究一般非线性系统平衡点及稳定性的新方法。多项式近似系统在平衡点求解上与一般非线性系统相比具有以下优势:1)实根个数或其上界可估计;2)目前对多项式全部实根的求解算法已有深入研究,许多系统采用合适的算法可实现全部实根的求解。本文利用半张量积方法给出了一般非线性系统的多项式近似表达,并在理论上证明,在足够高的近似阶数下,多项式近似系统与原系统平衡点可任意接近,且其不稳定平衡点类型可保持不变。这一工作为利用多项式近似系统研究原系统平衡点性质和进行稳定性分析奠定了理论基础。This paper proposes a novel method to study the equilibrium points （EPs） and the stability of a general nonlinear system by using its polynomial approximate system which has some advantages in the aspects： 1 ） the number or the max number of a polynomial system＇ s real roots can be estimated; 2） there are many deep researches in solving polynomial systems＇ real roots, and all of the real roots can be solved for some polynomial systems if appropriate algorithms are adopted. This paper applies the semi- tensor product method to calculate the polynomial approximation of a general nonlinear system. And theo- retical analysis reveals that the EPs of the polynomial approximate system can be arbitrarily close to that of the original system if the approximation order is high enough. Moreover, their types can keep unchanged This result lays a theoretical foundation for us to study the EPs＇ properties and the stability analysis of a general nonlinear system by using its polynomial approximate system.

关 键 词：半张量积 电力系统 多项式系统 平衡点 稳定域 

分 类 号：TM711[电气工程—电力系统及自动化] TM712