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中文摘要：
在一定条件下，发电、负荷有可追寻的变化趋势，这样复杂电网运行必然存在明确的物理规律，在运行中实时寻求这一规律及其变化趋势的快速方法，对电网调度、控制、监视等功能实现具有重要意义。在前人研究的基础上，结合不均匀性和单调性的概念，提出了电网关键元件具有单调性的思想。以有功的传输为研究对象，定义了运行模式、输电通路、关键元件及其单调性等概念。建立了输电元件有功流与网络输送有功总流之间的函数关系，讨论了灵敏度在关键元件单调性研究中的应用。以简化直流潮流为例阐明关键元件单调性的存在性。最后结合5节点系统算例对本文思想进行了验证。论文分为三个研究系列：一是概念和基础部分；二是机理与证明部分：三是应用部分。
英文摘要：
The trend of power generation and load is clear under certain conditions. So there is explicit physical law in the operation of complex power grid. It is of great importance for the dispatch, control and supervision of power systems to find the law in real-time. Based on the previous studies, the idea of acrucial element having monotone is proposed as the combination of monotone and non-homogeneous. Taking the transmission of active power as a research object, the concepts of operation mode, transmission path, crucial element and its monotone are defined. The relationship between active power flow in transmission element and total active power flow transferred in power grid is founded, and then crucial element＇s monotone is discussed with sensitivity theory. The existence of monotone is analyzed qualitatively considering the DC model. Finally, taking the 5-bus system as an example, the results verify the proposed idea. This Part Ⅰ forms the basic idea of crucial element and its monotone. The following Part Ⅱ will analyze the mechanism of the proposed idea in depth.And then the Part Ⅲ will discuss the applications of the proposed idea in power systems. This project is supported by National Natural Science Foundation of China（No.50677036 and No.50377021）.
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