Holomorphic Embedding Load-flow method: Difference between revisions

Revision as of 19:01, 17 March 2021

Revision as of 19:03, 17 March 2021

Line 23:

== Background ==

The [[power-flow study|load-flow]] calculation is one of the most fundamental components in the analysis of power systems and is the cornerstone for almost all other tools used in [[power system simulation]] and [[Energy management system|management]]. The load-flow equations can be written in the following general form:

Line 37 ⟶ 36:

* A. F. Glimn and G. W. Stagg, "Automatic Calculation of Load Flows", ''Power Apparatus and Systems, Part III. Transactions of the American Institute of Electrical Engineers'', vol.76, no.3, pp.817–825, April 1957.

* Hale, H. W.; Goodrich, R. W.; , "Digital Computation or Power Flow - Some New Aspects," ''Power Apparatus and Systems, Part III. Transactions of the American Institute of Electrical Engineers'', vol.78, no.3, pp.919–923, April 1959.</ref>

, which has poor convergence properties but very little memory requirements and is straightforward to implement; the full [[Newton–Raphson method]]<ref>W. F. Tinney and C. E. Hart, "Power Flow Solution by Newton's Method," ''IEEE Transactions on Power Apparatus and Systems'', vol. PAS-86, no.11, pp.1449–1460, Nov. 1967.

straightforward to implement; the full [[Newton–Raphson method]]<ref>W. F. Tinney and C. E. Hart, "Power Flow Solution by Newton's Method," ''IEEE Transactions on Power Apparatus and Systems'', vol. PAS-86, no.11, pp.1449–1460, Nov. 1967.

* S. T. Despotovic, B. S. Babic, and V. P. Mastilovic, "A Rapid and Reliable Method for Solving Load Flow Problems," ''IEEE Transactions on Power Apparatus and Systems'', vol. PAS-90, no.1, pp.123–130, Jan. 1971.</ref>

which has fast (quadratic) iterative convergence properties, but it is computationally costly; and the Fast Decoupled Load-Flow (FDLF) method,<ref name="FDLF">B. Stott and O. Alsac, "Fast Decoupled Load Flow," ''IEEE Transactions on Power Apparatus and Systems'', vol. PAS-93, no.3, pp.859–869, May 1974.</ref>

Line 55 ⟶ 53:

== Methodology and applications ==

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.

Line 66 ⟶ 63:

== Holomorphic embedding ==

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.