The uneven load of the electric drive of sucker-rod pumping units causes an increase in the consumption of reactive power, which requires compensation. This article discusses the issue of calculating the processes in sucker-rod pumping units in the case of individual compensation of the reactive power. Mathematical models for calculating the process of changing the capacity of cosine capacitors for reactive power compensation in the starting and steady-state modes of the electric drive of the sucker-rod pumping unit, which are characterized by the periodically varying load and moment of inertia, have been developed. The calculation is based on a mathematical model of the induction motor that takes into account the saturation of the magnetic path and the skin effect in the bars of the deep-bar rotor. The created mathematical model can be used to regulate the capacitance of the capacitors connected to the induction motor in order to reduce the reactive power consumption.

The dynamics of power systems is often analyzed using real-time simulators. The basic requirements of these simulators are the speed of obtaining the results and their accuracy. Known algorithms (backward Euler or trapezoidal rule) used in real-time simulations force the integration time step to be reduced to obtain the appropriate accuracy, which extends the time of obtaining the results. The acceleration of obtaining the results is achieved by using parallel calculations. The paper presents an algorithm for mathematical modeling of the dynamics of linear electrical systems, which works stably with a relatively large integration time step and with accuracy much better than other algorithms widely described in the literature. The algorithm takes into account the possibility of using parallel calculations. The proposed algorithm combines the advantages of known methods used in the analysis of electrical circuits, such as nodal analysis, multi-terminal electrical component theory, and transient states analysis methods. However, the main advantage over other algorithms is the use of the method based on average voltages in the integration step (AVIS method). The attention was focused on the presentation of the scientifically acceptable general principle offered to mathematical modeling of dynamics of linear electrical systems with parallel computations. However, the evidence of its effective application in the analysis of the dynamics of electric power and electromechanical systems was indicated in the works carried out by the team of authors from the Institute of Electrical Engineering UTP University of Science and Technology in Bydgoszcz (Poland).

In recent years, the idea of the operation of energy systems (power systems, heating systems) has changed significantly. This paper is an overview of locally balanced energy systems without the use of fossil fuels. The paper justifies the concept of local energy balancing in a new energy system that does not use fossil fuels (coal, natural gas, and crude oil), based on European Union guidelines and formal documents as well as the literature on the subject. In this context, the issue of local energy self-sufficiency, utilizing renewable energy sources, as well as the concept of local smart grids based on innovative market mechanisms are raised. Attention is also paid to technical issues with regard to locally balanced energy systems, in particular photovoltaic sources and energy storage. Challenges related to the use of electrical protection in networks with many sources of energy are described. In such networks, the power flow is not in one direction only. Moreover, the selection of protections is problematic due to the distribution of short-circuit currents. Additionally, earth fault currents in such networks may be distorted, and this negatively affects the operation of residual current devices. The basic nomenclature describing locally balanced systems has been sorted out as well. Finally, possible future research paths in the field of creating locally balanced systems without the use of fossil fuels are presented.

The main issue in this paper is the real-time simulator of a part of a power grid with a wind turbine. The simulator is constructed on the basis of a classic PC running under a classic operating system. The proposed solution is expected and desired by users who intend to manage power microgrids as separate (but not autonomous) areas of common national power systems. The main reason for the decreased interest in real-time simulators solutions built on the basis of PC is the simulation instability. The instability of the simulation is due to not keeping with accurate results when using small integration steps and loss of accuracy or loss of stability when using large integration steps. The second obstacle was due to the lack of a method for integrating differential equations, which gives accurate results with a large integration step. This is the scientific problem that is solved in this paper. A new solution is the use of a new method for integrating differential equations based on average voltage in the integration step (AVIS). This paper shows that the applied AVIS method, compared to other methods proposed in the literature (in the context of real-time simulators), allows to maintain simulation stability and accurate results with the use of large integration steps. A new (in the context of the application of the AVIS method) mathematical model of a power transformer is described in detail, taking into account the nonlinearity of the magnetization characteristics. This model, together with the new doubly-fed induction machine model (described in the authors’ previous article), was implemented in PC-based hardware. In this paper, we present the results of research on the operation states of such a developed real-time simulator over a long period (one week). In this way, the effectiveness of the operation of the real-time simulator proposed in the paper was proved.

Currently used methods of simulation of doubly fed induction machines (DFIM), especially in real-time simulators (where a relatively large calculation step is used and high adequacy is required), do not provide the required adequacy, especially in rotor electrical circuits. In order to increase the adequacy of reproducing of electrical processes occurring in the circuits of the wound DFIM rotor, this paper presents a proposal and a verification of a new method of real-time simulation. The new method of mathematical modeling of electrical circuits uses voltage averaging at the calculation step. This method was supplemented by prediction of the machine’s rotor angle, which significantly increases the degree of adequacy of reproducing physical quantities present in DFIM, especially in the machine’s rotor. This method allows real-time simulation of electrical systems with a relatively large calculation step (of the order of 200 µs), while maintaining an appropriate degree of adequacy.

This paper presents decomposition method of mathematical model of electric power system and implementation its in digital system with GPU. The electric power system model can be used for real-time simulation of electromagnetic transients. The article presents the results of experimental research of calculation time for two different digital systems using both the CPU and GPU.