On the continuation-path uniqueness of homotopy enhanced power flow method for general distribution networks with distributed generators

The integration of renewable energies requests smart power grids to be capable of supporting various power flow patterns, and thus urgently needs the development of smart and robust power flow solvers. However, there are several great challenges, as the problem of power flow divergence and the issue of multi-solution. Homotopy methodology is commonly utilized to deal with these issues. This paper proposes a set of sufficiently conditions for the uniqueness of power flow solution, by showing the uniqueness of continuation path in a homotopy method, which can serve as the condition for controlling when to apply the costly global-searching techniques for finding multiple power flow solutions. Theoretical results are illustrated by simulations on the IEEE 1123-bus distribution network with distributed generation.

[1]  Jen-Hao Teng,et al.  Modelling distributed generations in three-phase distribution load flow , 2008 .

[2]  R. Ramakumar,et al.  An approach to quantify the technical benefits of distributed generation , 2004, IEEE Transactions on Energy Conversion.

[3]  Lennart Söder,et al.  Distributed generation : a definition , 2001 .

[4]  D. Shirmohammadi,et al.  A three-phase power flow method for real-time distribution system analysis , 1995 .

[5]  Tsai-Hsiang Chen,et al.  Distribution system power flow analysis-a rigid approach , 1991 .

[6]  J. Yorke,et al.  Finding zeroes of maps: homotopy methods that are constructive with probability one , 1978 .

[7]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[8]  Tzong-Mou Wu,et al.  A study of convergence on the Newton-homotopy continuation method , 2005, Appl. Math. Comput..

[9]  E. Allgower,et al.  Introduction to Numerical Continuation Methods , 1987 .

[10]  Loring W. Tu,et al.  An introduction to manifolds , 2007 .

[11]  L. T. Watson,et al.  Globally convergent homotopy methods: a tutorial , 1989, Conference on Numerical Ordinary Differential Equations.

[12]  Ronnie Belmans,et al.  Distributed generation: definition, benefits and issues , 2005 .

[13]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[14]  G. Joós,et al.  Models for Quantifying the Economic Benefits of Distributed Generation , 2008, IEEE Transactions on Power Systems.

[15]  J. Yorke,et al.  A homotopy method for locating all zeros of a system of polynomials , 1979 .

[16]  Yasuaki Inoue,et al.  An efficient algorithm for finding multiple DC solutions based on Spice oriented Newton homotopy method , 2001, ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196).