GRONWALL定理在消除铁磁谐振分析中的应用

The Application of Gronwall Theorem in the Analysis of the Elimination of Ferroresonance

唯一稳态消谐法是近年出现的消除非线性系统谐振新的分析方法.该方法的基本思想是如果非线性系统存在一个非谐振的正常解,并且该系统具有唯一的稳态,则此时对应的条件就是系统不发生谐振的条件.该文将这一方法应用在中性点接地电力系统铁磁谐振的分析中,以GRONWALL定理为工具,得到了相应的消谐条件.文章的结果表明,消除谐振的条件可以用一个矩阵的稳定性条件来决定,并用数值模拟进行验证,结果正确,同时也说明唯一稳态消谐法有效性.

Unique steady state elimination method is a new method for eliminating resonance in nonlinear system presented recently.Its basic idea is that if there is a normal（non-resonance） solution for the system,and the steady state of the system is unique,then the corresponding conditions are those for eliminating resonance.In this paper,this new method is applied to analyze the elimination of ferroresonance in neutral grounding power system by zero-sequence resistor.Based upon Gronwall theorem,the conditions for eliminating this ferroresonance are obtained,which can be determined by the stability conditions of some constant matrixes.The conclusions of this paper have been proved to be correct by numerical simulation,and the result has shown the effectiveness of unique steady state elimination method.