In the paper the squared voltage-current functionals are minimized, which represent the global power losses in the network. In that way it is possible to find the voltage-current distributions on the net without the use of immitance operators and basing only on the Kirchhoff laws. Farther the individual branch parameters are defined in the syntheses process. Many optimal power analysis examples are also shown to illustrate the thesis included in the paper.

The purpose of this research work is to study the issues of the protection of 6–10 kV lines and access ways overvoltage in the electrical networks of modern enterprises of high-energy intensity, as well as the search for real technical opportunities to improve the protection of power lines directly in conditions of their operation. The methodology of this scientific research is based on a combination of methods of system analysis of the principles of the functioning of electric networks of energy-intensive enterprises with an analytical study of the fundamental aspects of ensuring the protection of 6 to 10 kV lines and access ways from overvoltage. The results of the conducted scientific research indicate the relevance of the issues of ensuring the protection of lines and electrical networks of energy-intensive enterprises from overvoltage and the need to develop special technical devices to ensure the proper level of such protection in real conditions. The results and conclusions of this research work are of significant importance for developers and designers of electric networks of enterprises with increased energy capacity, as well as for employees of various power supply systems who, by their occupation, face the tasks of servicing electric networks, which include lines and access ways with specified operating voltage parameters and ensuring the proper level of safety and practical use of these electric networks of energy-intensive enterprises.

Spectral properties of nonnegative and Metzler matrices are considered. The conditions for existence of Metzler spectrum in dynamical systems have been established. An electric RL and GC ladder-network is presented as an example of dynamical Metzler system. The suitable conditions for parameters of these electrical networks are formulated. Numerical calculations were done in MATLAB.