Improved Approximate Minimum Degree Ordering Method and Its Application for Electrical Power Network Analysis and Computation  

作　　者：Jian Guo Hong Liang Songpu Ai Chao Lu Haochen Hua Junwei Cao 

机构地区：[1]Beijing National Research Center for Information Science and Technology,Beijing 100084,China [2]Department of Electrical Engineering,Tsinghua University,Beijing 100084,China [3]College of Energy and Electrical Engineering,Hohai University,Nanjing 211100,China

出　　处：《Tsinghua Science and Technology》2021年第4期464-474,共11页清华大学学报（自然科学版（英文版）

基　　金：supported in part by the National Key Basic Research and Development Program of China(No.2017YFE0132100);the Tsinghua-Toyota Research Fund(No.20203910016);the BNRist Program(No.BNR2020TD01009)。

摘　　要：Electrical power network analysis and computation play an important role in the planning and operation of the power grid,and they are modeled mathematically as differential equations and network algebraic equations.The direct method based on Gaussian elimination theory can obtain analytical results.Two factors affect computing efficiency:the number of nonzero element fillings and the length of elimination tree.This article constructs mapping correspondence between eliminated tree nodes and quotient graph nodes through graph and quotient graph theories.The Approximate Minimum Degree(AMD)of quotient graph nodes and the length of the elimination tree nodes are composed to build an Approximate Minimum Degree and Minimum Length(AMDML)model.The quotient graph node with the minimum degree,which is also the minimum length of elimination tree node,is selected as the next ordering vector.Compared with AMD ordering method and other common methods,the proposed method further reduces the length of elimination tree without increasing the number of nonzero fillings;the length was decreased by about 10%compared with the AMD method.A testbed for experiment was built.The efficiency of the proposed method was evaluated based on different sizes of coefficient matrices of power flow cases.

关 键 词：Approximate Minimum Degree and Minimum Length(AMDML) electrical power network analysis elimination tree numerical solution ordering method 

分 类 号：TM711[电气工程—电力系统及自动化]