基于模态分析和虚拟支路法的串联谐波谐振分析

串联谐振与并联谐振共同组成谐振问题的两个重要分支。模态分析为解决谐振问题提供了新思路。该文指出，由于串联谐振的发生与回路阻抗的密切关系，利用模态分析法(简称模态法)解串联谐振问题时应使用回路阻抗矩阵，而非节点阻抗矩阵。阐明分析串联谐振时，网络拓扑结构不断改变的实质。提出一种结合模态分析和"虚拟支路法"来分析网络回路阻抗矩阵以获得串联谐振频率及相关支路信息的方法。该方法继承模态法解谐波谐振问题的优点并对之是补充和完善，使模态分析与目前通用的频谱分析并列，成为可完整解决谐振问题的方法。测试系统研究和实际应用均证明该文所提出方法的正确性和适用性。研究结果可作为分析谐波谐振问题的基本方法，还可用于滤波器装置的谐振频率校验。

Series Resonance Analysis Based on Modal Analysis and Dummy Branch Method

Both parallel resonance and series resonance are the two important parts of harmonic resonance problem. Modal analysis brings us new way for harmonic resonance problem. This paper points out loop impedance matrix should be used for studying series resonance problems by modal analysis, not node impedance matrix, due to the affinity between series resonance and loop impedances. It is illuminated that network frame changes constantly while analyzing series resonance phenomenon. A novel method combined modal analysis and dummy branch method is proposed for obtaining series resonance frequency and corresponding branch information through analyzing loop impedance matrix. This method inherits modal analysis and perfects it, making which as the coordinate method with frequency scan that can solve harmonic resonance problem completely. The results of tests and practical application show the correctness and effectiveness of this method. The results of this paper can be used as the basic method for harmonic resonance problems and also for the checkout of resonance frequency for filters.