Title :
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
fDate :
9/1/1994 12:00:00 AM
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;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
