Holomorphic Embedding Load-flow method: Difference between revisions

Revision as of 13:38, 7 February 2022

Revision as of 08:45, 7 November 2023

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HELM is grounded on a rigorous mathematical theory, and in practical terms it could be summarized as follows:

# Define a specific (holomorphic) embedding for the equations in terms of a complex parameter {{math|<var>s</var>}}, such that for {{math|<var>s</var>{{=}}0}} the system has an obvious correct solution, and for {{math|<var>s</var>{{=}}1}} one recovers the original problem.

# Given this holomorphic embedding, it is now possible to compute univocally [[power series]] for voltages as analytic functions of {{math|<var>s</var>}}. The correct load-flow solution at {{math|<var>s</var>{{=}}1}} will be obtained by analytic continuation of the known correct solution at {{math|<var>s</var>{{=}}0}}.

# Perform the analytic continuation using algebraic approximants, which in this case are guaranteed to either converge to the solution if it exists, or not converge if the solution does not exist (voltage collapse).