Holomorphic Embedding Load-flow method: Difference between revisions

Revision as of 22:54, 10 January 2013

Revision as of 12:23, 30 July 2013

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The '''Holomorphic Embedding Load-flow Method''' ('''HELM'''<ref group="note">HELM is a trademark of Gridquant Inc.</ref>)''' is a solution method for the [[Power flow study|power flow]] equations of electrical power systems. Its main features are that it is

[[Direct method (computational mathematics)|direct]] (that is, non-iterative) and that it mathematically guarantees a consistent

selection of the correct operative branch of the multivalued problem, also signalling the condition of voltage collapse when there is no solution. These properties are relevant not only for the reliability of existing off-line and real-time applications, but also because they enable new types of analytical tools that would be impossible to build with existing iterative load flows (due to their convergence problems). An example of this would be decision-support tools providing validated action plans in real time.

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corresponds to the correct operative solution, when it exists; and it signals the non-existence of the solution when the conditions are such that there is no solution (voltage collapse). Additionally, the method is competitive with the FDNR method in terms of computational cost. It brings a solid mathematical treatment of the load-flow problem that provides new insights not previously available with the iterative numerical methods.

== Methodology and Applicationsapplications ==

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

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This makes HELM particularly suited for real-time applications, and mandatory for any EMS software based on exploratory algorithms, such as contingency analysis, and under alert and emergency conditions solving operational limits violations and restoration providing guidance through action plans.

== Holomorphic Embeddingembedding ==

For the purposes of the discussion, we will omit the treatment of controls, but the method can accommodate all types of controls. For the constraint equations imposed by these controls, an appropriate holomorphic embedding must be also defined.

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A more detailed discussion about this procedure is offered in Ref.<ref name="helmpaper" />

== Analytic Continuationcontinuation ==

Once the power series at {{math|<var>s</var>{{=}}0}} are calculated to the desired order, the problem of calculating them at {{math|<var>s</var>{{=}}1}} becomes one of [[analytic continuation]]. It should be strongly remarked that this does not have anything in common with the techniques of [[Homotopy#Applications|homotopic continuation]]. Homotopy is powerful since it only makes use of the concept of continuity and thus it is applicable to general smooth nonlinear systems, but on the other hand it does not always provide a reliable method to approximate the functions (as it relies on iterative schemes such as Newton-Raphson).

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These properties confer the load-flow method with the ability to unequivocally detect the condition of voltage collapse: the algebraic approximations are guaranteed to either converge to the solution if it exists, or not converge if the solution does not exist.

== See also ==

* [[Power flow study]]

* [[Power system simulation]]

== Notes ==

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== References ==

{{Reflist}}

== See also ==

* [[Power flow study]]

* [[Power system simulation]]

{{DEFAULTSORT:Power Flow Study}}