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 -