Holomorphic Embedding Load-flow method: Difference between revisions

Revision as of 20:50, 15 October 2015

Revision as of 12:58, 27 February 2016

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With this choice, at {{math|<var>s</var>{{=}}0}} the right hand side terms become zero, (provided that the denominator is not zero), this corresponds to the case where all

the injections are zero and this case has a well known and simple operational solution: all voltages are equal and all flow intensiti esintensities are zero. Therefore, this choice for the embedding provides at s=0 a well known operational solution.

Now using classical techniques for variable elimination in polynomial systems<ref>B. Sturmfels, "Solving Systems of Polynomial Equations”, CBMS Regional Conference Series in Mathematics 97, AMS, 2002.</ref> (results from the theory of [[Resultants]] and [[Groebner basis#Elimination property|Gröbner basis]] it can be proven that equations ({{EquationNote|1}}) do in fact define {{math|<var>V(s)</var>}} as holomorphic functions. More significantly, they define {{math|<var>V(s)</var>}} as [[algebraic curves]]. It is this specific fact, which becomes true because the embedding is holomorphic that guarantees the uniqueness of the result. The solution at {{math|<var>s</var>{{=}}0}} determines uniquely the solution everywhere (except on a finite number of branch cuts), thus getting rid of the multi-valuedness of the load-flow problem.