  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.
