在电力系统的一系列最优化问题中，如何综合地考虑潮流约束和各种稳定性约束，而又不影响计算速度，始终还是个难题。至于概率安全性评估的计算负担就更加难以想象。为了解决此类问题，本文提出了安全域（SR）的方法论，该方法论是在经典的逐点法基础上发展起来的全新方法论。天津大学自20世纪80年代开始并长期坚持安全域的研究，至今取得了如本文所述的一系列原创成果。本文所介绍的安全域主要是定义在功率注入空间上的，包括确保静态安全、暂态稳定、静态电压稳定和小扰动稳定的安全域。对于既定的网络拓扑（以及暂态事故的发生地点和清除过程）和系统元件参数，它们是唯一确定的，并且与运行状态无关。本文通过11个命题和相应的注释，简明而系统地介绍了这些电力系统安全域的基本概念、构成、动力学性质、拓扑学与几何学特征、实用边界的实用数学描述及其快速计算方法，以期为成体系地认知安全域方法学、开展后续研究与应用提供支持。在拓扑学与几何学特征方面，最重要的发现是，在功率注入空间上，在工程实际所关心的范围内，安全域的边界可用一个或少数几个超平面的并集表示。基于该特征，电力系统安全约束优化问题和概率安全性评估（风险分析）的计算时间可以按数量级减少。

How to comprehensively consider the power flow constraints and various stability constraints in a series of power system optimization problems without affecting the calculation speed is always a problem. The computational burden of probabilistic security assessment is even more unimaginable. In order to solve such problems, a security region (SR) methodology is proposed, which is a brand-new methodology developed on the basis of the classical point-wise method. Tianjin University has been studying the SR methodology since the 1980s, and has achieved a series of original breakthroughs that are described in this paper. The integrated SR introduced in this paper is mainly defined in the power injection space, and includes SRs to ensure steady-state security, transient stability, static voltage stability, and small disturbance stability. These SRs are uniquely determined for a given network topology (as well as location and clearing process for transient faults) and given system component parameters, and are irrelevant to operation states. This paper presents 11 facts and related remarks to introduce the basic concepts, composition, dynamics nature, and topological and geometric characteristics of SRs. It also provides a practical mathematical description of SR boundaries and fast calculation methods to determine them in a concise and systematic way. Thus, this article provides support for the systematic understanding, future research, and applications of SRs. The most critical finding on the topological and geometric characteristics of SRs is that, within the scope of engineering concern, the practical boundaries of SRs in the power injection space can be approximated by one or a few hyperplanes. Based on this finding, the calculation time for power system probabilistic security assessment (i.e., risk analysis) and power system optimization with security constraints can be decreased by orders of magnitude.