A Comprehensive Review of Solving Selective Harmonic Elimination Problem With Algebraic Algorithms

Selective harmonic elimination pulsewidth modulation (SHEPWM) is an effective way to eliminate low-order harmonics in high-power applications. However, one of the biggest challenges of SHEPWM is to solve the selective harmonic elimination (SHE) equations, which are composed of some nonlinear transcendental equations. Over the past few decades, algebraic algorithms have shown a considerable ability to solve SHE equations, specifically for obtaining all exact solutions. Much research has been published about algebraic algorithms, struggling to solve more switching angles, solving different mathematic models of SHEPWM, and so on. This article comprehensively reviews existing algebraic algorithms, including elementary symmetric polynomials, power sums, Newton's identities, resultant elimination method, Wu's method, Gröbner-basis-based method, Chudnovsky algorithm, polynomial homotopy continuation algorithm, and real-time implementation by algebraic algorithms. The principle operation of these methods is summarized, and their performance is analyzed in terms of execution time, solving ability, and applicability for different mathematical models.