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3 Bulletin of the Polish Academy of Sciences. Technical Sciences

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Application of L1-impulse method to the optimization problems in power theory

Siwczyński M., Jaraczewski M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2010

Vol. 58, nr 1

197-207

In optimization power theory we can distinguish the three approaches: -the theory of instant power values -the theory of average power values (integral power) -the theory of instant.average power value. The theory of instant power uses the instant power and signals values i.e. p(t) = u(t)i(t) whereas the theory of average power uses the energy or average power terms i.e. P = (u(t), i(t)) (the dot the product of signals). This inequality causes numerous optimization problems, among which the norm of the current minimization is the most important one. The mathematic methods used in these theories derive from the theorems of signals and instant power modulation. This article deals only with the average power theory which uses the L1 impulses as an alternative to the Fourier series method. This technique is efficient when the energy is transmitted with highly distorted periodic signals.

The L1-impulse method as an alternative to the Fourier series in the power theory of continuous time systems

Siwczyński M., Jaraczewski M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2009

Vol. 57, nr 1

79-85

The Fourier series method is frequently applied to analyze periodical phenomena in electric circuits. Besides its virtues it has many drawbacks. Fourier series usually have slow convergence and fail for fast changing signals, especially for discontinues ones. Therefore they are suitable to describe only quasiharmonic phenomena. For strongly nonsinusoidal signal analysis we propose the L 1-impulse method. The L 1-impulse method consists in an equivalent notation of a function belonging to L 1 as a sum of exponential functions. Such exponential functions have rational counterparts with poles in both sides of imaginary axis. With the L 1-impulse functions we can describe periodical signals, thus we get the homomorfizm between periodical signals and a rational functions sets. This approach is especially adapted to strongly deformed signals (even discontinues ones) in linear power systems, and thanks to that we can easily calculate optimal signals of such systems using the loss operator of the circuit. The loss operator is exactly the rational function with central symmetry of poles [1]. In this paper the relation between the L 1-impulse and the Fourier series method was presented. It was also proved that in the case of strong signal deformation the L 1-impulse method gains advantage.

The Poincare theorem in linear circuit synthesis

Siwczyński M., Jaraczewski M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2007

Vol. 55, nr 1

49-58

The paper deals wit h linear circuits synthesis wit h periodic parameters. It was proved that the time-varying voltages and currents of inner branches of such circuits can be calculated using linear recursive equations wit h periodic coefficients if signals on port are given. The stability theorem of periodic solution was formulated. Hereby described the synthesis problems appear when compensation of power supply systems is considered.