### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 465-475 |

Number of pages | 11 |

Journal | IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications |

Volume | 49 |

Issue number | 4 |

DOIs | |

State | Published - Apr 2002 |

### Fingerprint

### Keywords

- Harmonic elimination
- Newton identities
- Orthogonal polynomials
- Padé approximation
- Pulsewidth modulation (PWM)
- Single-phase inverters
- Symmetric functions

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications*,

*49*(4), 465-475. https://doi.org/10.1109/81.995661

**Solving the optimal PWM problem for single-phase inverters.** / Czarkowski, Dariusz; Chudnovsky, David V.; Chudnovsky, Gregory V.; Selesnick, Ivan.

Research output: Contribution to journal › Article

*IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications*, vol. 49, no. 4, pp. 465-475. https://doi.org/10.1109/81.995661

}

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

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

UR - http://www.scopus.com/inward/record.url?scp=0036540892&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036540892&partnerID=8YFLogxK

U2 - 10.1109/81.995661

DO - 10.1109/81.995661

M3 - Article

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

SN - 1549-8328

IS - 4

ER -