Abstract In this article, the linear dynamic analysis of AC generators modeled as RLC circuits with periodically time-varying inductances via Floquet’s theory is considered. Necessary conditions for the dynamic stability are derived. The harmonic balance method is employed to predict the transition curves and stability domains. An approximate expression for the Floquet form of solution is constructed using Whittaker’s method in the neighborhood of transition curves. Numerical verifications for the obtained theoretical results are considered. In accordance with the experimental results, a satisfactory agreement is relatively achieved with the closed experimental literature of the problem.

中文翻译：

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线性动态 RLC 电路的 Floquet 分析

摘要 本文考虑了通过 Floquet 理论建模为具有周期性时变电感的 RLC 电路的交流发电机的线性动态分析。推导出动态稳定性的必要条件。采用谐波平衡法来预测过渡曲线和稳定域。Floquet 形式的解的近似表达式是在过渡曲线的邻域中使用 Whittaker 方法构建的。考虑对所获得的理论结果进行数值验证。根据实验结果，与问题的封闭实验文献相对达到了令人满意的一致性。