The number of (equilibrium) steady-state solutions of models of power systems

Author

Guo, S.X. ; Salam, F.M.A.

Author_Institution

Dept. of Electr. Eng., Michigan State Univ., East Lansing, MI, USA

Volume

41

Issue

9

fYear

1994

fDate

9/1/1994 12:00:00 AM

Firstpage

584

Lastpage

600

Abstract

We use powerful analytical tools and modern techniques from algebraic geometry to infer the number of (equilibrium) steady state solutions of models of power systems. The theorems developed also infer the upper bound on the number of solutions of the full-fledged (equilibrium) steady-state equations for various levels of detailed models of power systems. Sufficient conditions are provided which determine the precise number of complex solutions to the load flow. The sufficient conditions are cast in terms of properties of the admittance matrix of the power grid. Consequently, these sufficient conditions are placed on the topology (configuration) of the given power network. When the sufficient conditions are not satisfied, the determined precise number becomes an upper bound on the number of solutions

Keywords

approximation theory; electric admittance; load regulation; matrix algebra; modelling; polynomials; power system interconnection; power systems; admittance matrix; algebraic geometry; analytical tools; complex solutions; equilibrium steady state solutions; excitation system; load flow; polynomials; power grid; power network; power system modelling; steady-state equations; sufficient conditions; topology; upper bound; Admittance; Equations; Geometry; Load flow; Power system analysis computing; Power system modeling; Solid modeling; Steady-state; Sufficient conditions; Upper bound;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.317957

Filename

317957