Field approaches are employed to develop a mathematical model of a power network section. The facility consists of two electric power subsystems described with ordinary differential equations and presented as concentrated parameter systems connected with a three-phase power supply line, presented as a distributed parameter system. The model of the electric power line is described with partial differential equations. Mathematically, the supply line model is described utilizing a mixed problem with explicitly indefinite boundary conditions. All electromagnetic state equations of the integrated system are introduced in their matrix-vector forms. The equation of the three-phase long supply line is expressed untraditionally as a system of two first-order differential equations as a function of long line voltage. Since the power supply line is part of the integrated system that includes two subsystems, the boundary conditions at the line’s start and end are implicitly defined, avoiding the traditional application of the Dirichlet first-type boundary condition. An expanded system of ordinary differential equations that describe physical processes in both the supply and loading subsystems is used to calculate the boundary conditions. To this end, third-type boundary conditions, or Poincaré’s conditions, serve to describe the wave equation of the electric power line. Such an integrated model of an electric power system helps analyse transient processes across the supply line when the electric power system is switched on and is single-phase short-circuited at the final point of the electric power line. A comparison of computer simulation results with well-known software packages shows a convergence of approx. 96%.

The paper examines the impact of the COVID-19 pandemic on human resource management processes in project-oriented companies. It is proposed to use formal transformations on groups of performers. The use of formal transformations will reduce the influence of the subjective factor and improve the quality of sustainability management decisions made when forming a project team. The formalization of the selection process of applicants and the distribution of work among the performers have been considered. The existing methods of forming a project team with functional redundancy are approximate. Methodological support for the process of forming a project team with functional redundancy, based on a logical-combinatorial approach, and allowing to form project teams under given constraints, is proposed. A method of forming a functionally redundant project team based on formal transformations of groups of performers has been developed. The use of the apparatus of symbolic sequences for the formation of a project team with functional redundancy is proposed. An example of using the proposed method when forming a command with functional redundancy is considered. It is shown that the use of this methodological support makes it possible to select the composition of the project team with the minimum number and the minimum value of the characteristic.

In the paper, the kinematic structure of the transmission shaft between the driving motor and the working mechanism is studied. The analysis is based on electrical and mechanical similarities. The equivalent circuits, typical for electrical systems, are defined for the transmission shaft concerned. Modelling of the transmission shaft based on a formal analogy between the transmission shaft and the electric transmission line is also proposed. The results of a computer simulation and experimental test are presented. The results confirm the high conformity of the proposed mathematical model with the physical object.

In remote locations, it is advisable to combine solar water pumping with electric energy storage and power supply for other forms of consumption. In such complex systems, individual subsystems feature their own local control, and the general automatic control of the system in different modes of its operation is carried out in accordance with an energy management strategy (EMS). In this paper, the functions of local and general control of the solar water pumping system with battery storage and external power supply are combined in the system of passivity-based control (PBC). The EMS is constructed in such a way that for all modes, only two PBC systems are developed, which are switched depending on the battery’s state of charge and the current levels of the two main disturbances—solar irradiation and electrical consumption. For each system, two control influence former (CIF) structures were synthesized and their operation was investigated by computer simulation. Despite the simplicity of CIFs’ implementation, due to the introduced interconnection and damping coefficients, such control allows the provision of the required voltage regulation with a static error up to 1%, sufficient quality of transients during disturbances and switching of the system structure, as well as system asymptotic stability.

Transition processes in a steel conductive strip are analyzed during its induction heating under a quasi-steady electromagnetic field. In particular, the temperature field in the strip is studied. A method of solving corresponding initial boundary problems in a two-dimensional mathematical model for differential equations of electrodynamics and heat conduction is developed. The Joule heat and the temperature are determined with a high level of accuracy. The defining functions are the temperature and component of the magnetic field intensity vector tangent to the bases and end planes of the strip. To find them, we use cubic approximation of the defining functions’ distribution along the thickness coordinate. The original two-dimensional initial boundary value problems for the defining functions are reduced to one-dimensional initial boundary value problems on their integral characteristics. General solutions for these problems are obtained using the finite integral transformation by the transverse variable and the Laplace transform of the integral by time. Integral characteristics’ expressions are represented as convolutions for functions that describe homogeneous solutions of one-dimensional initial boundary value problems and limiting values of defining functions on the bases and end planes of the strip. The change of temperature under a varying regime in the dimensionless Fourier time and temperature distribution over the strip cross-section in a steady state depending on the parameters of induction heating and the Biot number are numerically analyzed. Varying and constant temperature regimes of the strip under conditions of the near-surface and continuous induction heating are studied.

Information management, an important element of which is the information system, has a direct impact on the functioning of a company, including its competitive position. Information management is related to the shape of the organizational culture, represented, inter alia, by the context of trust, relationship, and communication. The shape of the organizational culture, including the functioning of the information system, is particularly influenced by factors (usually external) that appear in a sudden and unpredictable manner. This impact increases with the intensity and scale of their influence. The recent COVID-19 pandemic should undoubtedly be considered such a factor. As a result, many enterprises suddenly had to switch to remote work. The aim of this paper is to analyze the essence and recognize the impact of the forced transition to a remote form of work on trust as a shaping and effective factor in the functioning of the company’s information system. To achieve this goal, the results of qualitative research conducted by the authors during the period March 2020–February 2021 and quantitative research conducted in February 2021 were used. In connection with the conducted research, it was found that trust is a very important factor influencing the efficiency and quality of employees’ work. It was also found that the forced need to switch to remote work mode was a problem for most people. This was influenced by both the time of the pandemic, as well as technical and organizational problems. As a result of observations, own experiences, interviews, and a questionnaire survey, the authors state that the necessity to switch from traditional to remote work resulted in an increase in the costs of functioning of people, including employees.