Study on dominant path of power grid under a given operation mode Part II: Proof in DC power flow systems

The related concepts of dominant path introduced in part I give a novel idea to analyze complex power grid with a simple method. In this paper of part II, based on the analysis of DC power flow, the concepts of operation mode vector, structure matrix, eigenmatrix and extended PTDF are proposed. And a mathematical proof of dominant path´s monotone is given with the extended concept of PTDF. Finally, taking a 5-bus system as a test, it gives the solving process of every related matrix and vector.