A complete solution to the harmonic elimination problem

By John N. Chiasson, Leon M. Tolbert, Keith McKenzie, Zhong Du. IEEE transactions on power electronics, 2003

317 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/dffbc95f9efd7a4a215ad103027fbe29966a7a7a

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In Control and Systems Engineering

In Electrical and Electronic Engineering

Citations in the corpus

Elimination of harmonics in a multilevel converter with nonequal DC sources (2005, methodology): “Work was reported in [1] and [2] that presented a method to compute the switching angles for the H-bridges in a cascaded converter using the mathematical theory of resultants.”
A unified approach to solving the harmonic elimination equations in multilevel converters (2004, background): “3(a), it has been shown in [4], [5] that this is possible only for modulation indices between approximately 0.”
Selective harmonic control: a general problem formulation and selected solutions (2005, methodology): “the more restrictive quarter-wave symmetric problem including standard iterative approaches [15], [16], elimination theory [17], minimization techniques [18], [19], or genetic algorithms [24].”
A Generalized Formulation of Quarter-Wave Symmetry SHE-PWM Problems for Multilevel Inverters (2009, methodology): “The theory of resultants and its performance for a multilevel staircase waveform was reported in [6], in which it is shown that the transcendental equations characterizing the harmonic content can be converted to polynomial equations and the latter can be solved to get the complete solution using th”
On applying a minimization technique to the harmonic elimination PWM control: the bipolar waveform (2004, methodology): “In [6], the method of resultants has been proposed.”
Selective Harmonic Elimination With Groebner Bases and Symmetric Polynomials (2016, methodology): “In [31] and [32], the resultant elimination theory is introduced to convert the SHE equations to an equivalent triangular form”
Unified Selective Harmonic Elimination for Cascaded H-Bridge Asymmetric Multilevel Inverter (2018, methodology): “For the algebraic methods, such as the resultant elimination method [27], [28] and the Groebner bases method [29], as their huge computation burden, the symmetric polynomials [30], [31] are usually used to reduce the degrees of the polynomials and then cut down the computation burden.”
A Review of Architectures and Concepts for Intelligence in Future Electric Energy Systems (2015, methodology): “The transcendental equations characterizing the harmonic content can be converted in polynomial equations, which can be then solved using the method of resultants from elimination theory [50], [51].”
Elimination of harmonics in multilevel inverters with non-equal DC sources using PSO (2008, methodology): “13 depicts the variation of the %THD versus m for the study cases under consideratio of the %THD are better or at leas obtained from other techniques [5].”
A Five-Level Symmetrically Defined Selective Harmonic Elimination PWM Strategy: Analysis and Experimental Validation (2008, background): “, the three-level or unipolar waveform) [7].”
A Groebner Bases Theory-Based Method for Selective Harmonic Elimination (2015, methodology): “In [20], [21], the SHE equations are converted to the polynomial equations by using the multiple-angle formulas and the variables substitution, then the resultant elimination theory is introduced to transform the polynomial equations to their equivalent triangular form, finally, it can be solved by ”