Current and voltage wave‐form optimization with non‐linear deformations for real voltage sources

Abstract

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.

Reactive T-topology four-terminal-network compensator for multiharmonic current

“…From the minimum current condition under the active-power constraint (formula 1) [3,4], we obtain the value of the equivalent conductivity G e [1,2,5]; thus, from the EMF's point of view, the entire system reduces to a resistance equal to 1 G e , which in turn amounts to impedance Z opt in series with inner impedance Z s (see Fig 3).…”

The steady-state impedance operator of a linear periodically time-varying one-port network and its determination

“…The optimization problem (30), (31) can be solved using the Lagrange multipliers method in a specific manner similar to that presented in (Siwczyński, 1995;Siwczyński and Kłosiński, 1997a;1997b). Lagrange's functional is…”

“…The description of an LPTV system by means of a CPO was introduced for the first time by Siwczyński to implement a new numerical operator method for nonlinear systems analysis described in (Siwczyński, 1987). Later, CPOs were used in algorithms of optimal operational condition determination of real voltage sources with periodically time-varying or non-linear inner impedance and load one-port networks (Siwczyński et al, 1993;Siwczyński, 1995;Siwczyński and Kłosiński, 1997a).…”

“…The CPO identification method applied resembles the algorithm called the smooth periodic escape (SPE), used to design time-varying compensator networks (Siwczyński, 1995;Siwczyński and Kłosiński, 1997a;1997b). The derivation and properties of the identification scheme were presented in (Kłosiński, 2005;2006;2007).…”