Modelling of Sequential Optimal Power Flow by Piecewise Linear Convexificated Quadratic Approximations

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Original languageEnglish
Title of host publication2018 International Conference on Power System Technology, POWERCON 2018 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages87-92
Number of pages6
ISBN (electronic)9781538664612
ISBN (print)978-1-5386-6462-9
Publication statusPublished - 2018
Event2018 International Conference on Power System Technology, POWERCON 2018 - Guangzhou, China
Duration: 6 Nov 20189 Nov 2018

Abstract

Formulating Optimal Power Flow Problems is well- known since the 1960s, but solving those problems to global optimality is challenging until today, due to the nonconvex characteristic of the embedded functions and the huge number of variables and constraints.To handle nonconvexities they have to be eliminated or convexificated. Nonlinear equality constraints are always nonconvex and can be eliminated by inserting them or their inverse function into the objective functions and into all constraints. In this paper the power equation is expanded by a distributed slack, inverted end eliminated as described.The optimization in this paper is done by sequentially solving quadratically constrained quadratic programs (SQCQP). The remaining nonconvex parts of the objective function and the constraints of each QCQP are identified by principal axis transformation and analysis of eigenvalues and then convexificated by piecewise linearization.Thus, a mixed-integer convex quadratically constrained quadratic problem results, which can be solved fast and reliably with e.g., CPLEX or Gurobi. The high accuracy of the convexficated quadratic approximations and fast convergence of the sequential approach is shown in case studies.

Keywords

    convexification, distributed slack, optimal power flow, principal axis transformation, sequential quadratic programming

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Cite this

Modelling of Sequential Optimal Power Flow by Piecewise Linear Convexificated Quadratic Approximations. / Leveringhaus, Thomas; Breithaupt, Timo; Garske, Steffen et al.
2018 International Conference on Power System Technology, POWERCON 2018 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2018. p. 87-92 8601613.

Research output: Chapter in book/report/conference proceedingConference contributionResearchpeer review

Leveringhaus, T, Breithaupt, T, Garske, S & Hofmann, L 2018, Modelling of Sequential Optimal Power Flow by Piecewise Linear Convexificated Quadratic Approximations. in 2018 International Conference on Power System Technology, POWERCON 2018 - Proceedings., 8601613, Institute of Electrical and Electronics Engineers Inc., pp. 87-92, 2018 International Conference on Power System Technology, POWERCON 2018, Guangzhou, China, 6 Nov 2018. https://doi.org/10.1109/powercon.2018.8601613
Leveringhaus, T., Breithaupt, T., Garske, S., & Hofmann, L. (2018). Modelling of Sequential Optimal Power Flow by Piecewise Linear Convexificated Quadratic Approximations. In 2018 International Conference on Power System Technology, POWERCON 2018 - Proceedings (pp. 87-92). Article 8601613 Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/powercon.2018.8601613
Leveringhaus T, Breithaupt T, Garske S, Hofmann L. Modelling of Sequential Optimal Power Flow by Piecewise Linear Convexificated Quadratic Approximations. In 2018 International Conference on Power System Technology, POWERCON 2018 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2018. p. 87-92. 8601613 doi: 10.1109/powercon.2018.8601613
Leveringhaus, Thomas ; Breithaupt, Timo ; Garske, Steffen et al. / Modelling of Sequential Optimal Power Flow by Piecewise Linear Convexificated Quadratic Approximations. 2018 International Conference on Power System Technology, POWERCON 2018 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2018. pp. 87-92
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