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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
The HELM load flow algorithm was invented by Antonio Trias and has been granted two US Patents.<ref name="patent-7519506">
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A detailed description was presented at the 2012 IEEE PES General Meeting
The method is founded on advanced concepts and results from [[complex analysis]], such as [[Holomorphic function|holomorphicity]], the theory of [[algebraic curve]]s, and [[analytic continuation]]. However, the numerical implementation is rather straightforward as it uses standard linear algebra and [[Padé approximant|Padé approximation]]. Additionally, since the limiting part of the computation is the factorization of the admittance matrix and this is done only once, its performance is competitive with established fast-decoupled loadflows. The method is currently implemented into industrial-strength real-time and off-line packaged EMS applications.
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