Abstract. 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.Key words: periodically time-varying networks, operational calculus, stability, synthesis, optimization. L 1 -impulses and periodic signalsThe L 1 -impulse is an absolutely summable signaland its periodic extension is a T -period functioñwhere p ∈ Z (integers). Series (1) always converges. It results from the fact that every L 1 -impulse is majorised by an exponential signal:where a, b, c, d -positive numbers, 1(t) -step function. Applying the formula (1) to the (2) we getfor t ∈ [0, T ).The inner product of the L 1 -impulses is defined as followsand the linear operator Hwhere L ∞ -space of bounded signals, R -real numbers. The special case of the (5) operator is the convolution operatorIt results that the sequence of two convolution operators act as L ∞ into L ∞ mapping, which means at the same time thatThus the convolution of the L 1 impulses produce also the L

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The article deals with the search for the signals of the real source current or the real source voltage with the help of the ||i ‐ i0|| or ||u0 ‐ u||→ min criteria. At the same time there, one must know the power flux between the source and the receiver. The problem is solved by means of a certain Hilbert space where a special square functional is minimized. Both the inner impedance operator of the source and the receiver operator are non‐linear. The article presents a simple computational algorithm for a two‐terminal circuit, in particular for the circuit consisting of a saturated choking coil and a diode element. This algorithm can be applied to a special class of two‐terminal circuits, i.e. the circuits recognized as linear in case of small signal increase. The optimal current is calculated until it is fixed. This way, one gets a periodic steady state. The algorithm in question is always locally convergent, but the global convergence is difficult to prove. However, many numerical experiments indicate the global convergence. Presents the results in the form of computer plots.

The simple digital filters are not sufficient for digital modeling of systems with distributed parameters. It is necessary to apply more complex digital filters. In this work, a set of filters, called the digital function filters, is proposed. It consists of digital filters, which are obtained from causal and stable filters through some function transformation. In this paper, for several basic functions: exponential, logarithm, square root and the real power of input filter, the recursive algorithms of the digital function filters have been determined The digital function filters of exponential type can be obtained from direct recursive formulas. Whereas, the other function filters, such as the logarithm, the square root and the real power, require using the implicit recursive formulas. Some applications of the digital function filters for the analysis and synthesis of systems with lumped and distributed parameters (a long line, phase shifters, infinite ladder circuits) are given as well.

Abstract. The source reactive-current compensation is crucial in the energy transmission efficiency. The compensator design in a frequencydomain has already been widely discussed and examined. This paper presents results of a study on how to design reactive compensators in a time-domain. It is the first time the reactive compensator has been designed in a time domain. The example of a compensator is presented.