Optimal power flow formulations and their impacts on the performance of solution methods

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Abstract

In this paper, we study four equivalent mathematical formulations of the Optimal Power Flow (OPF) problem and their impacts on the performance of solution methods. We show how four mathematical formulations of the OPF problem can be obtained by rewriting equality constraints given as the power flow problem into four equivalent mathematical equations using power balance or current balance equations in polar or Cartesian coordinates while keeping the same physical formulation. All four mathematical formulations are implemented in Matpower. In order to identify the formulation that results in the best convergence characteristics for the solution method, we apply MIPS, KNITRO, and FMINCON on various test cases using three different initial conditions. We compare all four formulations in terms of impact factors on the solution method such a number of nonzero elements in the Jacobian and Hessian matrices, a number of iterations and computational time on each iteration. The numerical results show that the performance of the OPF solution method is not only dependent upon the choice of the solution method itself, but also upon the exact mathematical formulation used to specify the OPF problem.

Original languageEnglish
Title of host publication2019 IEEE Power and Energy Society General Meeting, PESGM 2019
PublisherIEEE
Number of pages5
Volume2019-August
ISBN (Electronic)9781728119816
DOIs
Publication statusPublished - 2019
Event2019 IEEE Power and Energy Society General Meeting, PESGM 2019 - Atlanta, United States
Duration: 4 Aug 20198 Aug 2019
http://www.pes-gm.org/2019/

Conference

Conference2019 IEEE Power and Energy Society General Meeting, PESGM 2019
Abbreviated titlePESGM 2019
CountryUnited States
CityAtlanta
Period4/08/198/08/19
Internet address

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