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该文作为3篇系列文章的第1篇，首先介绍所做工作的理论工具--非线性奇异摄动系统的慢不变流形理论和电力系统稳定域边界理论；利用电力系统的经典二阶模型，推导电力系统的奇异摄动模型；以此奇异摄动模型为基础，利用慢不变流形理论阐述具有多时间尺度特性的电力系统呈现各种失稳模式的数学机理和条件；最后，给出电力系统弱连接的定义，并从理论上分析紧急情况下从系统弱连接上进行解列控制的合理性。“,”ABSTRACT:As the first one of the series of three papers, this paper firstly introduced the theoretical tools-the slow invariant manifold theory of nonlinear singularly perturbed systems and power system stability region boundary theory. The perturbation model of power system was derived using the classical 2nd model. Based on the above perturbation model, the mathematical mechanism and condition of all kinds of instability patterns for power systems with multi-time scales was elaborated. Finally, the definition of power system weak-connection was given and the rationality of conducting islanding control on the weak-connections of power system under emergency circumstances was analyzed theoretically.