弹性支持扁拱动力稳定性分析和变压器内线圈短路动稳定分析

Dynamic Stability of Shallow Arch With Elastic Supports—Application to the Dynamic Stability Analysis of Inner WindingS of Transformer During Short-Circuit

本文采取脉冲载荷激励下弹支扁拱弹性动力稳定性的理论模型分析电力变压器内线圈短路动稳定问题.首先导出了脉冲载荷激励下弹支扁拱非线性运动积分微分方程级数解,给出了各平衡位置(奇点)的局部稳定(不稳定)性证明,导出弹支扁拱抗跳跃失稳的稳定性充分条件、判别公式和临界载荷;其次导出了短路载荷与脉冲载荷的相当关系,考虑内线圈各线匝(铜条)短路电动力到内线匝的传递,给出了内线圈短路动稳定临界电动力计算公式和动稳定判别方法;最后作出与实验结果的比较和算例.

In this paper, the dynamic stability of shallow arch with elastic supports subjected to impulsive load is studied as a theoretical model to investigate the dynamic stability problem of inner windings of power transformer under short-circuit condition. Firstly, the series solutions representing the equilibrium configurations of shallow arch are obtained by solving the corresponding nonlinear integrodifferential equation, the local stability of each equilibrium configuration is then discussed, and the sufficient condition for stability of the shallow arch system as well as the critical load against snapthrough are given. After the equivalent relation of short-circuit load to impulsive one, and the electrical forces transfer pattern between the coils of inner windings are assumed, the results of the shallow arch model are applied to the case of the inner windings of transformer such that the formulas for computing critical electromagnetic force and the dynamic stability criterion of the inner windings are established. Finally, examples are offered and the theoretical results well agree with the experimental ones.