Electrical circuits with state-feedbacks are addressed. It is shown that by suitable choice of the gain matrices of state-feedbacks it is possible to obtain the closed-loop system matrices with nilpotency indices equal to two and their state variables are linear functions of time. The considerations are illustrated by linear electrical circuits.
One of the main problems of electrical power quality is to ensure a constant power ?ux from the supply system to the receiver, keeping in the same time the undisturbed wave form of the current and voltage signals. Distortion of signals are caused by nonlinear or time varying receivers, voltage changes or power losses in a supply system. The wave-form of the voltage of the source may also be deformed. This study seeks the optimal current and voltage wave-form by means of an optimization criteria. The optimization problem is de?ned in Hilbert space and the special functionals are minimized. The source inner impedance operator is linear and time-varying. Some examples of calculations are presented.
Along with the increase in the use of nonlinear electronic devices, e.g. personal computers, power tools and other electrical appliances, the requirements for uninterruptible power supplies are constantly growing. This paper proposes a method and deep analysis of results viable for checking how single-phase uninterruptible power supplies (UPSs) cope with nonlinear circuits under varying power loads in terms of electric energy quality.Various classes of single-phase UPS systems with different topologies were tested, for instance line-interactive and double conversion (online) single-phase UPS devices. Furthermore, measurements were carried out in view of a power source – loads were supplied both from a power grid and UPS built-in battery. Juxtaposition of the obtained results such as a THDU, THDI (Total Harmonic Distortion) percentage ratio of input/output voltage and current, a power factor and crest factor volume etc. of the tested UPS systems indicated major differences in their performance during laboratory tests.
Minimum energy control problem for the fractional positive electrical circuits is formulated and solved. Sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by an example of fractional positive electrical circuit.