Optimal Power Flow as a Polynomial Optimization Problem

Formulating the alternating current optimal power flow (ACOPF) as a polynomial optimization problem makes it possible to solve large instances in practice and to guarantee asymptotic convergence in theory. We formulate the ACOPF as a degree-two polynomial program and study two approaches to solving...

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Bibliographic Details
Published in:IEEE transactions on power systems 2016-01, Vol.31 (1), p.539-546
Main Authors: Ghaddar, Bissan, Marecek, Jakub, Mevissen, Martin
Format: Article
Language:English
Subjects:
Approximation methods
Asymptotic properties
Convergence
Data buses
Hierarchies
Inequalities
Linear matrix inequalities
Load flow
Mathematical programming
method of moments
numerical analysis
Optimization
Polynomials
Power flow
power system management
sparse matrices
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Summary:Formulating the alternating current optimal power flow (ACOPF) as a polynomial optimization problem makes it possible to solve large instances in practice and to guarantee asymptotic convergence in theory. We formulate the ACOPF as a degree-two polynomial program and study two approaches to solving it via convexifications. In the first approach, we tighten the first-order relaxation of the nonconvex quadratic program by adding valid inequalities. In the second approach, we exploit the structure of the polynomial program by using a sparse variant of Lasserre's hierarchy. This allows us to solve instances of up to 39 buses to global optimality and to provide strong bounds for the Polish network within an hour.
ISSN:0885-8950
1558-0679
DOI:10.1109/TPWRS.2015.2390037