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中文摘要：
对关键元件单调性进行了机理分析和相关论证。结合运行圆和极限圆概念，对输电元件有功限值进行了修正。在此基础上，分三种情况由浅入深地对电力系统中的关键元件单调性进行了研究：（1）在直流潮流基础上，考虑进正弦函数的非线性，建立了数学模型，对输电元件输送有功功率与节点注入之间的函数单调关系以及关键元件单调性的存在性进行了严格的数学证明，并给出了估计单调区间的算法；（2）再考虑进电阻参数，即损耗的影响，论证了有损情况下，输电元件有功流依然是节点注入的单调函数，而且关键元件单调性依然成立，但是单调区间与无损耗时相比会根据r/x的大小发生偏移；（3）定性的讨论了电压水平和无功功率对有功功率关键元件单调性的影响。最后结合5节点系统算例对上述三种情况进行了比较验证。
英文摘要：
The mechanism and the related certification of crucial element and its monotone proposed in Part Ⅰ is analyzed. Based on the concepts of operating circle and limiting circle, the limiting value of active power flow in transmission elements is amended. Under a given operation mode, the crucial element＇s monotone of power systems is studied from the simple to the more complex in three situations as following. Firstly, on the basis of DC power flow model, taking the sine nonlinearity into consideration, the monotone relationship between active power flow in transmission elements and injective active power, and the existence of crucial element＇s monotone are proven mathematically. And then, an algorithm is proposed to find the monotone interval in which the crucial element＇s monotone maintains. Secondly, taking resistance, namely power losses, into consideration, the monotone relationship between active power flow in transmission elements and injective active power, and the existence of crucial element＇s monotone continue to maintain. Comparing with the no-loss situation, the monotone interval shifts according to the value of r/x when the loss is considered. Thirdly, the impact of voltage level and reactive power on the crucial element＇s monotone is discussed qualitatively. A comparison test with 5-bus system is following, in which the certification about the above three situations is done.
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