Convex Relaxations in Power System Optimization: Convex Relaxation of AC OPF (7 of 8)

Convex relaxations of the AC power flow equations have attracted significant interest in the power systems research community in recent years. This collection of videos provides a brief introduction to the mathematics of AC power systems, continuous nonlinear optimization, and relaxations of the power flow equations.

Combining results from the previous videos, this video revisits the AC Optimal Power Flow problem and illustrates how a simple convex relaxation can be developed for this non-convex problem. This is followed by a brief overview of different relaxations and a discussion of the challenges that convex relaxations face in accurately representing power losses on lines and power flow around cycles in a network. Special cases when a convex relaxation also provides a feasible solution to AC Optimal Power Flow are discussed, as well as more challenging cases where simple convex relaxations may fail.

A citable abstract of this lecture series is available here: https://arxiv.org/abs/1807.07227

References in the video:
https://ieeexplore.ieee.org/document/...
https://ieeexplore.ieee.org/document/...
https://ieeexplore.ieee.org/document/...
https://ieeexplore.ieee.org/document/...
https://ieeexplore.ieee.org/document/...
https://ieeexplore.ieee.org/document/...

https://ieeexplore.ieee.org/document/...
https://ieeexplore.ieee.org/document/...
https://arxiv.org/abs/1411.0359
https://github.com/power-grid-lib/pgl...

LA-UR-18-26156