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A General Recipe for Relaxations of PP
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Classroom Contents
Polynomial Optimization Applied to Power Network Operations
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- 1 Intro
- 2 Polynomial Programming
- 3 A General Recipe for Relaxations of PP
- 4 Sum-of-square Relaxations for PP
- 5 Overcoming the size blow-up
- 6 Sparse Relaxations of PP Polynomial Optimization Problem
- 7 SOCP-based Hierarchy for PP
- 8 Motivation
- 9 Proposed Solution Methods
- 10 Application - AC Optimal Power Flow
- 11 Challenges - AC Optimal Power Flow
- 12 ACOPF: Parameters
- 13 ACOPF: Formulation
- 14 ACOPF: Quadratic PP
- 15 Optimal Power Flow - Duality
- 16 Sparsity of the SDP relaxation: 39 Buses
- 17 OPF - Results
- 18 Uncertainty in Power Systems
- 19 ACOPF as a non-convex quadratic optimization problem
- 20 Adjustable Robust ACOPF
- 21 Affine equalities
- 22 Algorithm to solve (ARP)
- 23 Details of piecewise-affine approximations
- 24 Numerical experiments: instances with 30 to 118 buses
- 25 Conclusions
