Analytical solutions for power flow equations based on the multivariate quotient-difference method

Chengxi Liu, Claus Leth Bak, Yongli Zhu, Kai Sun

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

Abstract

This paper proposes a method of obtaining the approximate analytical solutions for power flow equations based on the multivariate quotient-difference method. The power flow solutions for different operating conditions can be directly obtained by scaling multiple symbolic variables in the analytical solutions, such that the power injections or consumptions of selected buses or groups of buses can be independently adjusted. This method first uses the multi-dimensional holomorphic embedding method to derive the power flow solutions in the form of multivariate power series. Then, the multivariate quotient-difference method is applied to transform multivariate power series (MPS) to multivariate Padé approximants (MPA) to expand the radius of convergence (ROC), so that the accuracy of the derived analytical solutions can be significantly increased. This method can adapt to many online applications, since the analytical solution can be derived offline and evaluated online by only plugging values into the system symbolic variables according to actual operating conditions. This proposed method is validated in detail on the IEEE 39-bus New England power system considering independent load variations in multiple regions.
Original languageEnglish
Title of host publicationProceedings of 2019 IEEE Milan PowerTech
Number of pages6
PublisherIEEE Signal Processing Society
Publication dateJun 2019
Article number8810702
ISBN (Electronic)9781538647226
DOIs
Publication statusPublished - Jun 2019
Event2019 IEEE Milan PowerTech - Milan, Italy
Duration: 23 Jun 201927 Jun 2019

Conference

Conference2019 IEEE Milan PowerTech
CountryItaly
CityMilan
Period23/06/201927/06/2019

Keywords

  • Analytical solution
  • Multi-dimensional holomorphic embedding method
  • Multivariate quotient-difference method
  • Power flow calculation

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