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The University of Southampton
CORMSIS Centre for Operational Research, Management Sciences and Information Systems

"Tight-and-Cheap Conic Relaxations for Optimal Power Flow and Optimal Reactive Power Dispatch " -- talk by Miguel Anjos (University of Edinburgh) Event

16:00 - 18:00
14 November 2019
Room 3043, Building 2, Southampton Business School, University of Southampton, Highfield Campus, SO17 1BJ

For more information regarding this event, please email Dr Christine Currie at .

Event details

The classical alternating current optimal power flow (ACOPF) problem is highly nonconvex and generally hard to solve. Computational speed and global optimality are key needs for practical OPF algorithms. In practice, an OPF may be computed up to every few minutes to validate a market outcome or other operational aspects. Convex relaxations of ACOPF, including conic, convex quadratic, and linear relaxations, have recently attracted significant interest. The semidefinite relaxation is the strongest among them and is exact for many cases. However, solving large-scale semidefinite optimization problems remains a challenge.

We present a conic optimization approach to ACOPF that combines semidefinite optimization with the reformulation-linearization technique (RLT) to obtain a Tight-and-Cheap Relaxation (TCR) of ACOPF. TCR is tighter than the second-order cone relaxation and nearly as tight as the standard semidefinite relaxation. We show conditions under which TCR is exact and can provide a global optimal solution for the ACOPF problem, theoretically and computationally. Computational experiments using standard test cases with up to 6515 buses (nodes) show that the time to solve TCR is up to one order of magnitude lower than for the chordal relaxation, a semidefinite relaxation technique that exploits the sparsity of power networks.

We also consider the optimal reactive power dispatch (ORPD) problem. This is an extension of ACOPF where discrete control devices for regulating the reactive power, such as shunt elements and tap changers, are introduced. We model the ORPD problem as a mixed-integer nonlinear optimization problem, and apply the tight-and-cheap approach to it. We show that this relaxation, combined with a round-off technique, leads to near-global optimal solutions with very small optimality gaps. This is an improvement over the (nonconvex) continuous relaxation of ORPD. We report computational results on realistic test cases with up to 3375 buses.

Some power system applications that require solving OPFs are multi-period because of evolving factors such as market prices or demand behaviour. We propose a multi-period TCR for the multi-period ACOPF problem, and report computational experiments using test cases with up to 500 buses showing that this new relaxation is promising for power system applications.

This is joint work with Christian Bingane and Sébastien Le Digabel.


Speaker information

Professor Miguel Anjos, University of Edinburgh, is a Licensed Professional Engineer in the province of Ontario, Canada. He received the B.Sc. degree in 1992 from McGill University, the M.S. in 1994 from Stanford University, and the Ph.D. degree in 2001 from the University of Waterloo. He was appointed Lecturer in Operational Research at the University of Southampton, then Professor of Management Sciences at Waterloo, cross-appointed to Electrical and Computer Engineering. Prior to joining the University of Edinburgh, he was Professor in the Department of Mathematics and Industrial Engineering of Polytechnique Montreal. His research interests are in the theory, algorithms, and applications of mathematical optimization. He is particularly interested in the application of optimization to problems in power systems management and smart grid design, including hydropower operation and maintenance planning, electricity markets, energy storage systems, unit commitment, capacity expansion, and demand response. His research has been published in journals such as the IEEE Transactions on Power Systems, the IEEE Transactions on Smart Grid, Mathematical Programming, the SIAM Journal on Optimization, and the European Journal of Operational Research.

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