A convex relaxation approach for the optimized pulse pattern problem

@article{Wachter2021ACR,
  title={A convex relaxation approach for the optimized pulse pattern problem},
  author={Lukas Wachter and Orcun Karaca and Georgios Darivianakis and Themistoklis Charalambous},
  journal={2021 European Control Conference (ECC)},
  year={2021},
  pages={2213-2218}
}
Optimized Pulse Patterns (OPPs) are gaining increasing popularity in the power electronics community over the well-studied pulse width modulation due to their inherent ability to provide the switching instances that optimize current harmonic distortions. In particular, the OPP problem minimizes current harmonic distortions under a cardinality constraint on the number of switching instances per fundamental wave period. The OPP problem is, however, non-convex involving both polynomials and… 

Figures and Tables from this paper

Algebraic perspectives on signomial optimization
Signomials are obtained by generalizing polynomials to allow for arbitrary real exponents. This generalization offers great expressive power, but has historically sacrificed the organizing principle
On the theory and applications of mechanism design and coalitional games in electricity markets
TLDR
A new preemptive model is formulated that allows us to obtain stable benefits immune to deviations and achieves minimal stability violation with a tractable computation.

References

SHOWING 1-10 OF 32 REFERENCES
Model predictive pulse pattern control
Industrial applications of medium-voltage drives impose increasingly stringent performance requirements, particularly with regards to harmonic distortions of the phase currents of the controlled
Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization
In the first part of this thesis, we introduce a specific class of Linear Matrix Inequalities (LMI) whose optimal solution can be characterized exactly. This family corresponds to the case where the
DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization
TLDR
DSOS and SDSOS optimization are introduced as linear programming and second-order cone programming-based alternatives to sum of squares optimization that allow one to trade off computation time with solution quality.
Approximate dynamic programming via sum of squares programming
TLDR
It is shown that a recently introduced method, which obtains convex quadratic value function approximations, can be extended to higher order polynomial approximation via sum of squares programming techniques.
Sum of Squares Programs and Polynomial Inequalities
How can one find real solutions (x1, x2)? How to prove that they do not exist? And if the solution set is nonempty, how to optimize a polynomial function over this set? Until a few years ago, the
Relative Entropy Relaxations for Signomial Optimization
TLDR
A hierarchy of convex relaxations is described to obtain successively tighter lower bounds of the optimal value of SPs through the observation that the relative entropy function provides a convex parametrization of certain sets of globally nonnegative signomials with efficiently computable nonnegativity certificates via the arithmetic-geometric-mean inequality.
Newton Polytopes and Relative Entropy Optimization
TLDR
The question of certifying nonnegativity of signomials based on the recently proposed approach of Sums-of-AM/GM-Exponentials (SAGE) decomposition is studied, and the results represent the broadest-known class of nonconvex signomial optimization problems that can be solved efficiently via convex relaxation.
An Introduction to Polynomial and Semi-Algebraic Optimization
This is the first comprehensive introduction to the powerful moment approach for solving global optimization problems (and some related problems) described by polynomials (and even semi-algebraic
Global Optimization with Polynomials and the Problem of Moments
TLDR
It is shown that the problem of finding the unconstrained global minimum of a real-valued polynomial p(x): R n to R, in a compact set K defined byPolynomial inequalities reduces to solving an (often finite) sequence of convex linear matrix inequality (LMI) problems.
...
...