TY - JOUR
N2 - In the complex RLC network, apart from the currents flows arising from the normal laws of Kirchhoff, other distributions of current, resulting from certain optimization criteria, may also be received. This paper is the development of research on distribution that meets the condition of the minimum energy losses within the network called energy-optimal distribution. Optimal distribution is not reachable itself, but in order to trigger it off, it is necessary to introduce the control system in current-dependent voltage sources vector, entered into a mesh set of a complex RLC network. For energy-optimal controlling, to obtain the control operator, the inversion of R(s) operator is required. It is the matrix operator and the dispersive operator (it depends on frequency). Inversion of such operators is inconvenient because it is algorithmically complicated. To avoid this the operator R(s) is replaced by the R’ operator which is a matrix, but non-dispersive one (it does not depend on s). This type of control is called the suboptimal control. Therefore, it is important to make appropriate selection of the R’ operator and hence the suboptimal control. This article shows how to implement such control through the use of matrix operators of multiple differentiation or integration. The key aspect is the distribution of a single rational function H(s) in a series of ‘s’ or ‘s⁻¹’. The paper presents a new way of developing a given, stable rational transmittance with real coefficients in power series of ‘s/s⁻¹՚. The formulas to determine values of series coefficients (with ‘s/s⁻¹’) have been shown and the conditions for convergence of differential/integral operators given as series of ‘s/s⁻¹’ have been defined.
L1 - http://www.czasopisma.pan.pl/Content/113173/PDF/18_613-620_01006_Bpast.No.67-3_06.02.20.pdf
L2 - http://www.czasopisma.pan.pl/Content/113173
PY - 2019
IS - No. 3
EP - 620
DO - 10.24425/bpasts.2019.129659
KW - principle of minimum energy losses
KW - optimal and suboptimal control
KW - power series
KW - operators of multiple differentiation or integration
KW - decomposition of a rational function
A1 - Siwczyński, M.
A1 - Żaba, S.
A1 - Drwal, A.
VL - 67
DA - 30.06.2019
T1 - Energy-optimal current distribution in an electrical network – controlling by the differential or the integral systems
SP - 613
UR - http://www.czasopisma.pan.pl/dlibra/publication/edition/113173
T2 - Bulletin of the Polish Academy of Sciences Technical Sciences
ER -