Polynomial Optimization Applied to Power Network Operations

Explore polynomial optimization techniques applied to power network operations in this 52-minute lecture from the Fields Institute's Optimization: Theory, Algorithms, Applications series. Delve into topics such as polynomial programming, sum-of-square relaxations, and sparse relaxations for polynomial optimization problems. Learn about the AC Optimal Power Flow problem, its challenges, and proposed solution methods. Examine the application of these techniques to power systems with uncertainty, including adjustable robust ACOPF and piecewise-affine approximations. Gain insights from numerical experiments conducted on power network instances ranging from 30 to 118 buses. Presented by Bissan Ghaddar from Western University, this talk provides a comprehensive overview of advanced optimization methods for tackling complex power network operational challenges.

Intro
Polynomial Programming
A General Recipe for Relaxations of PP
Sum-of-square Relaxations for PP
Overcoming the size blow-up
Sparse Relaxations of PP Polynomial Optimization Problem
SOCP-based Hierarchy for PP
Motivation
Proposed Solution Methods
Application - AC Optimal Power Flow
Challenges - AC Optimal Power Flow
ACOPF: Parameters
ACOPF: Formulation
ACOPF: Quadratic PP
Optimal Power Flow - Duality
Sparsity of the SDP relaxation: 39 Buses
OPF - Results
Uncertainty in Power Systems
ACOPF as a non-convex quadratic optimization problem
Adjustable Robust ACOPF
Affine equalities
Algorithm to solve (ARP)
Details of piecewise-affine approximations
Numerical experiments: instances with 30 to 118 buses
Conclusions