TY - JOUR

T1 - Solving the optimal PWM problem for single-phase inverters

AU - Czarkowski, Dariusz

AU - Chudnovsky, David V.

AU - Chudnovsky, Gregory V.

AU - Selesnick, Ivan W.

N1 - Funding Information:
Manuscript received December 13, 1999; revised January 20, 2001. This work was supported in part by the National Science Foundation under CAREER Grant CCR-987452. This paper was recommended by Associate Editor H. S. H. Chung.

PY - 2002/4

Y1 - 2002/4

N2 - In this paper, the basic algebraic properties of the optimal PWM problem for single-phase inverters are revealed. Specifically, it is shown that the nonlinear design equations given by the standard mathematical formulation of the problem can be reformulated, and that the sought solution can be found by computing the roots of a single univariate polynomial P(x), for which algorithms are readily available. Moreover, it is shown that the polynomials P(x) associated with the optimal PWM problem are orthogonal and can therefore be obtained via simple recursions. The reformulation draws upon the Newton identities, Padé approximation theory, and properties of symmetric functions. As a result, fast O(n log 2 n) algorithms are derived that provide the exact solution to the optimal PWM problem. For the PWM harmonic elimination problem, explicit formulas are derived that further simplify the algorithm.

AB - In this paper, the basic algebraic properties of the optimal PWM problem for single-phase inverters are revealed. Specifically, it is shown that the nonlinear design equations given by the standard mathematical formulation of the problem can be reformulated, and that the sought solution can be found by computing the roots of a single univariate polynomial P(x), for which algorithms are readily available. Moreover, it is shown that the polynomials P(x) associated with the optimal PWM problem are orthogonal and can therefore be obtained via simple recursions. The reformulation draws upon the Newton identities, Padé approximation theory, and properties of symmetric functions. As a result, fast O(n log 2 n) algorithms are derived that provide the exact solution to the optimal PWM problem. For the PWM harmonic elimination problem, explicit formulas are derived that further simplify the algorithm.

KW - Harmonic elimination

KW - Newton identities

KW - Orthogonal polynomials

KW - Padé approximation

KW - Pulsewidth modulation (PWM)

KW - Single-phase inverters

KW - Symmetric functions

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U2 - 10.1109/81.995661

DO - 10.1109/81.995661

M3 - Article

AN - SCOPUS:0036540892

SN - 1057-7122

VL - 49

SP - 465

EP - 475

JO - IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

JF - IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

IS - 4

ER -