Details
| Original language | English |
|---|---|
| Title of host publication | 2018 International Conference on Power System Technology, POWERCON 2018 - Proceedings |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 87-92 |
| Number of pages | 6 |
| ISBN (electronic) | 9781538664612 |
| ISBN (print) | 978-1-5386-6462-9 |
| Publication status | Published - 2018 |
| Event | 2018 International Conference on Power System Technology, POWERCON 2018 - Guangzhou, China Duration: 6 Nov 2018 → 9 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
ASJC Scopus subject areas
- Energy(all)
- Energy Engineering and Power Technology
- Engineering(all)
- Electrical and Electronic Engineering
- Mathematics(all)
- Control and Optimization
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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 proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - Modelling of Sequential Optimal Power Flow by Piecewise Linear Convexificated Quadratic Approximations
AU - Leveringhaus, Thomas
AU - Breithaupt, Timo
AU - Garske, Steffen
AU - Hofmann, Lutz
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
KW - convexification
KW - distributed slack
KW - optimal power flow
KW - principal axis transformation
KW - sequential quadratic programming
UR - http://www.scopus.com/inward/record.url?scp=85061707643&partnerID=8YFLogxK
U2 - 10.1109/powercon.2018.8601613
DO - 10.1109/powercon.2018.8601613
M3 - Conference contribution
SN - 978-1-5386-6462-9
SP - 87
EP - 92
BT - 2018 International Conference on Power System Technology, POWERCON 2018 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2018 International Conference on Power System Technology, POWERCON 2018
Y2 - 6 November 2018 through 9 November 2018
ER -