A convex relaxation approach for the optimized pulse pattern problem

TL;DR

This paper introduces a convex relaxation method for the optimized pulse pattern problem in power electronics, providing global optimality guarantees and demonstrating strong performance for problems with up to 50 switching instances.

Contribution

It extends polynomial optimization techniques to solve the non-convex OPP problem with global convergence guarantees using semi-definite programming and relative entropy relaxations.

Findings

Method converges to the global optimal solution.

Effective for problems with up to 50 switching instances.

Outperforms existing local solvers in accuracy.

Abstract

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 trigonometric functions. In the existing literature, the OPP problem is solved using off-the-shelf solvers with local convergence guarantees. To obtain guarantees of global optimality, we employ and extend techniques from polynomial optimization literature and provide a solution with a global convergence guarantee. Specifically, we propose a polynomial approximation to the OPP problem to then utilize well-studied globally convergent convex relaxation hierarchies, namely, semi-definite programming and relative entropy relaxations. The resulting hierarchy is proven to converge to the global optimal solution. Our method exhibits a strong performance for OPP problems up to 50 switching instances per quarter wave.