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A quasi analytical procedure for determining the optimum commutation angles of PWM converters

Quasi analytische Bestimmung der optimalen Steuerwinkel für pulsbreitenmodulierte Frequenzumrichter

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Contents

A method for calculating the optimum commutation times for PWM converters is proposed. The method is mainly analytical and leads to a simple, fast calculation procedure. The time behaviour of any variable, electrical or non electrical, which is considered to be the most characteristic of the behaviour of the system, can be optimized. The validity of the analytical approach is subject to some hypotheses which are often verified in practice. The computation power required by the method is so limited that, in the majority of cases, a minicomputer can be used.

Übersicht

Man beschreibt ein meist analytisches Verfahren für die Berechnung der optimalen Steuerwinkel für pulsbreiten-modulierte Frequenzumrichter. Durch dieses Verfahren wird es möglich, den Zeitverlauf der bedeutendsten elektrischen und nichtelektrischen Größen des Systems zu optimieren. Das Rechnungsverfahren beruht auf meistens erfüllten Annahmen; auf Grund seiner einfachen und schnellen Durchführung braucht man in den meisten Fällen nur Minicomputer zum Zweck.

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Abbreviations

\(f_f = \frac{{\omega _f }}{{2\pi }}\) :

fundamental frequency

x(t) :

modulated wave (input wave)

y(t) :

variable to be optimized (output wave)

f *(ω):

transfer function

f *(ω):

f *(ω) amplitude

Φ*(ω):

f *(ω) phase

f(n):

f *(ω) evaluated only in correspondence with (ω) f integer multipliers

a n :

x(t) Fourier coefficients relative to the terms cos (nω f t)

b n :

x(t) Fourier coefficients relative to the terms sin (nω f t)

a ′ n ,b ′ n :

asa n ,b n , but relative toy(t)

y d (t) :

required output wave-form

a d (n), b d (n) :

y d (t) Fourier coefficients

y s (t) :

deviation function (defined asy(t)−y d (t))

a s (n), b s (n) :

y s (t) Fourier coefficients

ω * :

rms value ofy s

σ:

asω * except for some constants

α i :

commutation angles

m 1 :

commutations number in the first half of the period

m :

number of independent commutations in the period

α ij ,δ ij x ij :

auxiliary variables dependent on theα i

V k :

numerical values relative to the links imposed onx(t)'s,y(t)'s harmonics

\(\hat Y_{n,} \hat X_n \) :

peak values ofy(t) andx(t) harmonic of ordern

Y n ,X n :

rms values of ordern harmonics ofy(t) andx(t)

μ j :

Lagrange multipliers

z :

number of constraints relative tox(t)'s harmonics

References

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Authors and Affiliations

  1. Istituto di Elettrotecnica ed Elettronica, Università di Padova, Via Gradenigo 6A, Padova, Italy

    P. Tenti

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  1. P. Tenti
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Research supported by Italian Research Council (C.N.R.)

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Tenti, P. A quasi analytical procedure for determining the optimum commutation angles of PWM converters. Archiv f. Elektrotechnik 62, 343–350 (1980). https://doi.org/10.1007/BF01579004

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  • DOI: https://doi.org/10.1007/BF01579004

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