Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Holomorphic Embedding Load-flow method
open-in-new
<p>The Holomorphic Embedding Load-flow Method (HELM) is a solution method for the <a href="/facts/Power-flow_study/QbMNhIbM">power-flow</a> equations of electrical power systems. Its main features are that it is <a href="/facts/Direct_method_(computational_mathematics)/uKMAJhEh">direct</a> (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-flow methods (due to their convergence problems). An example of this would be <a href="/facts/Decision_support_software/HPeJMlRM">decision-support tools</a> providing validated action plans in real time. </p><p>The HELM load-flow algorithm was invented by Antonio Trias and has been granted two US Patents. A detailed description was presented at the 2012 IEEE PES General Meeting and subsequently published. The method is founded on advanced concepts and results from <a href="/facts/Complex_analysis/hgCoQlH0">complex analysis</a>, such as <a href="/facts/Holomorphic_function/kVzthtEf">holomorphicity</a>, the theory of <a href="/facts/Algebraic_curve/LnWsPmDP">algebraic curves</a>, and <a href="/facts/Analytic_continuation/aBCuEgvt">analytic continuation</a>. However, the numerical implementation is rather straightforward as it uses standard linear algebra and the <a href="/facts/Pad%25C3%25A9_approximant/cR5BjAb8">Padé approximation</a>. 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 <a href="/facts/Energy_management_system/0G3BCYnY">EMS</a> applications. </p>