Computation of multiple solutions of load-flow equation by simplicial subdivision homotopy method

1989 ◽  
Vol 109 (3) ◽  
pp. 59-67
Author(s):  
Kohshi Okumura ◽  
Akira Kishima ◽  
Takeshi Fujita
Keyword(s):  
Multiple Solutions ◽  
Flow Equation ◽  
Homotopy Method ◽  
Load Flow ◽  
Simplicial Subdivision

Application of the homotopy method to load flow solution-finding all the multiple solutions

1985 ◽  
Vol 9 (3) ◽  
pp. 263-272 ◽  
Author(s):  
J.F. Chen ◽  
C.E. Lin ◽  
C.T. Pan ◽  
C.L. Huang
Keyword(s):  
Multiple Solutions ◽  
Homotopy Method ◽  
Load Flow ◽  
Flow Solution

Structure, singular points and existence of multiple solutions in load flow analysis

1980 ◽  
Vol 100 (3) ◽  
pp. 107-115 ◽  
Author(s):  
Yousuke Nakanishi ◽  
Kenji Yamada ◽  
Hiroshi Nagasawa ◽  
Shini'Chi Iwamoto ◽  
Yasuo Tamura
Keyword(s):  
Multiple Solutions ◽  
Flow Analysis ◽  
Load Flow ◽  
Singular Points ◽  
Load Flow Analysis

scholarly journals Computational issues of solving the 1D steady gradually varied flow equation

2014 ◽  
Vol 62 (3) ◽  
pp. 226-233 ◽  
Author(s):  
Wojciech Artichowicz ◽  
Romuald Szymkiewicz
Keyword(s):  
Differential Equation ◽  
Multiple Solutions ◽  
Energy Equation ◽  
Variable Number ◽  
Flow Equation ◽  
Flow Profile ◽  
Initial Condition ◽  
Initial Value ◽  
Step Method ◽  
Critical Stage

Abstract In this paper a problem of multiple solutions of steady gradually varied flow equation in the form of the ordinary differential energy equation is discussed from the viewpoint of its numerical solution. Using the Lipschitz theorem dealing with the uniqueness of solution of an initial value problem for the ordinary differential equation it was shown that the steady gradually varied flow equation can have more than one solution. This fact implies that the nonlinear algebraic equation approximating the ordinary differential energy equation, which additionally coincides with the wellknown standard step method usually applied for computing of the flow profile, can have variable number of roots. Consequently, more than one alternative solution corresponding to the same initial condition can be provided. Using this property it is possible to compute the water flow profile passing through the critical stage.

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