Electric Circuit Theory Research Articles

Analysis of non-sinusoidal non-stationary modes of electric networks based on the wavelet transformation

Subject of research: methods for calculating and analyzing non-sinusoidal non-stationary modes of electrical networks.
 Purpose of research: development of a method for calculating active and reactive power, as well as the power of distortion of non-sinusoidal modes of electrical networks based on the theory of wavelet transform.
 Object of research: electrical networks and power supply systems containing a non-linear load, which is the cause of non-sinusoidal modes.
 Methods of research: packet wavelet transform of currents and voltages; theory of electrical circuits.
 Main results of research: The paper proposes the idea of using the wavelet transform for frequency decomposition of currents and voltages of non-sinusoidal non-stationary modes of electrical networks. Based on the wavelet coefficients, it is proposed to calculate the active, reactive power and distortion power of non-sinusoidal modes.

Development of a method for selective determination of the outgoing line and the distance to the place of occurrence of a single-phase earth fault

Subject of research: algorithms for selective determination of the outgoing line in the event of a single-phase earth fault; algorithms for determining the distance to the fault location.
 Purpose of research: development of an industrial frequency overlay method for determining the outgoing line with a single-phase earth fault. Development of an algorithm for determining the distance to the place of a single-phase earth fault by the method of standing waves.
 Object of research: electrical networks 6-35 kV.
 Methods of research: theory of electrical circuits, mathematical analysis and modeling; resonant modes; standing wave method.
 Main results of research: An algorithm for the selective determination of the outgoing line with a single-phase earth fault has been developed. An algorithm for determining the distance to the closure site by the standing wave method has been developed.

Development of an arc extinguishing reactor control system

Subject of research: the system of automatic control of the arc-extinguishing reactor.
 Purpose of research: development of an automatic control system of an arc-extinguishing reactor to improve the efficiency of the electrical network.
 Object of research: 6-35 kV electric networks with compensated neutral through an arc-extinguishing reactor.
 Methods of research: the main provisions of the theory of electrical circuits, mathematical analysis and modeling, numerical programming.
 Main results of research: The article proposes the idea of using the wavelet transform to organize software The article proposes a refined mathematical model of a distribution network with an arc-extinguishing reactor, which allows to increase the accuracy of determining network parameters, including the neutral offset voltage. The algorithm of the reactor settings according to the extreme method in the absence of a single-phase earth fault in a distribution network with a high natural asymmetry.

Разработка метода идентификации синхронного сопротивления турбогенератора и критериев выбора состава данных синхронизированных векторных измерений

To enhance power system dependability and efficiency, it is of great importance to obtain correct parameters of the models of key power system components such as a synchronous generator (SG). Technology of synchronized phasor measurements allows us to estimate the SG model parameters through measurements in power system steady states and transients states, without switching the SG off and conducting complex testing procedures. The theory of electric circuits and electric machines, theory of optimization and statistics, and matrix algebra are applied in this study. The developed parameter estimation method has been implemented in the MATLAB software. The method has been verified through real-world measurements captured by a phasor measurement unit installed at a large power plant in the United Power System. This paper presents an algorithm of the turbogenerator synchronous reactance estimation via a set of synchrophasor data taken under steady-state conditions. Also, the paper considers the criteria for an appropriate data array ensuring successful parameter estimation. An algorithm has been developed and implemented in MATLAB software package. To improve the parameter estimation accuracy, an algorithm has been proposed to modify a nominal value for the SG no-load excitation current depending on the heating of the field winding. The algorithm has been successfully tested out based on a set of steady state synchrophasor data captured for one of the turbogenerators in the Russian United Power System. The authors have developed and analyzed quantitative criteria to determine a set of measured parameters of steady-state modes, providing the most accurate results of the turbogenerator synchronous reactance. The developed algorithm allows accurate update of the turbogenerator synchronous parameters through synchrophasor measurements recorded in a steady state modes of electric power systems. Using the criteria for selecting phasor data, it seems possible to automate the process of generating a data array of measurement of various steady-state modes necessary for identification. The proposed procedure that considers the field winding temperature can be employed in math models to estimate SG transient and subtransient parameters based on phasor measurements in transient modes of electric power systems.

Model Problems on Oscillations of Mechanical and Biological Membranes

Various models of membrane oscillations emerging in the theory of elasticity of mechanical systems, biomechanics of the internal ear of vertebrata, and in the theory of electrical circuits are discussed in the article. The considered oscillations have different natures, but their mathematical models are described using similar initial boundary value problems for the second-order hyperbolic equation with the nontrivial boundary condition. The differential equations in these problems are the same. Thus, for example, the model of voltage distribution in the telegraph line emerges for the one-dimensional equation of oscillations. The model of oscillations of a circular homogeneous solid membrane, a membrane with a hole, and the model of gas oscillations in a sphere and spherical region emerge for the two-dimensional and three-dimensional operators, but take into account the radial symmetry of oscillations. The model problem on membrane oscillation can be considered as the problem on ear drum membrane oscillations. The unified approach to reducing the corresponding problems to the initial boundary value problem with zero boundary conditions is suggested. The technique of formulating the solution in the form of a Fourier series using eigenfunctions of the corresponding Sturm–Liouville problem is described.

Analysis of I-V on Basic Electrical Circuit Using Ni Multisim App in Apply Physics

Utilization of the NI Multisim application is useful for designing a circuit, starting with designing schematic circuits and analyzing and simulating. Increasing the use of technology so that it is very much needed in physics learning at the Polytechnic of Maritime Sciences on electrical circuit material. This study aims to measure and characterize I-V currents in an electrical circuit by comparison with laboratories and multisim applications. Research activities were carried out using the I-V Current and Voltage comparison analysis method using theory in the manual formula, practice with the circuit kit, and NI Multisim simulation by building a circuit scheme on circuit composition namely resistance, voltage source, and using voltage measuring instruments and current measuring instruments which are all regulated in such a way concerning the theory of electric circuits. The results of this study are that there is a difference in the total resistance value between the values in the circuit kit module practice with the use of Multisim. But the difference is very slight with an error of about 1% for series circuits, and about 4.4% for parallel circuits. Voltage values in series circuits using NI Multisim circuit kits and applications have differences with errors ranging from 0 to 3.3 %. The comparison of the voltage values in direct measurements of the circuit kit and the NI Multisim simulation has the lowest error of 0% and the highest of 20% at the 6V source in R2.

THE RESONANT AMPLIFIER OF THE ACTIVE ELECTRICAL POWER WITH ADDITIONAL VOLTAGE SOURCE. SUGGESTIONS, ANALYSIS, NUMERICAL ESTIMATES

The problem of increasing energy saving in industry leads to the need to develop new technical devices. The paper presents and analyzes the circuit of the resonance amplifier of active electric power, evaluates the characteristics of electromagnetic processes for the fundamental substantiation of the operation of real devices based on this circuit. Mathematical analysis of electromagnetic processes taking place was carried out using strict methods of the theory of electric circuits. The advantages of this scheme in comparison with similar previous proposals are shown. The device includes four active-reactive circuits that are inductively connected. The first of them is an input circuit with a harmonic signal source that needs to be amplified. The second circuit generates enhanced reactive power in the "voltage resonance" mode. The third circuit with an additional voltage source provides reactive power output from the second circuit in the "resonance of currents" mode without adverse effects on amplification processes. The fourth circuit, inductively connected to the third circuit, contains an output load - a resistor that simulates the allocation of active power. On the basis of the analysis and numerical evaluation of the characteristics of the processes taking place in the proposed scheme of the resonance amplifier of active electric power, its basic efficiency is shown. The calculations of the experimental model made it possible to formulate recommendations for the selection of circuit elements of a working resonant amplifier with a high efficiency for low-impedance output loads. The considered real parameters of the device make it possible to minimize the dissipation of the energy of converted electrical signals and to increase the amplification factor of the electric power of harmonic currents and voltage by choosing the element base. The obtained results can be considered as practical recommendations for the creation of real devices for amplifying active electric power for use in various industries.

DEVELOPMENT OF A TESTER FOR DIAGNOSTICS OF CABLE LINES STATE WITH XLPE INSULATION

Link for citation: Konev A.A., Khakimyanov M.I. Development of a tester for diagnostics of cable lines state with XLPE insulation. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2023, vol. 334, no. 9, рр. 216-223. In Rus. Relevance. The moral and physical deterioration of cable lines voltage of 6–10 kV in our country ranges from 40 to 80 %. At the same time, up to 63 % of all accidents in electrical equipment are due to cable line failures. Recently, cables with cross-linked polyethylene insulation have been actively used, for the diagnosis of which special approaches are required. Therefore, the issues of developing high-voltage test facilities for diagnosing the state of insulation of electrical equipment are quite relevant. The authors proposed an original design of a high-voltage test facility that allows generating both direct voltage and alternating voltages of industrial and ultra-low frequencies. A feature of the device is the use of a multifunctional integrated electromagnetic component in it, which combines the functions of both an inductor and a capacitor. The use of this component allows reducing the dimensions and weight of the test facility. The main aims of the research are to develop a design of a high-voltage test facility and to study its characteristics; build a mathematical model and get dependency graphs. Objects: cables with XLPE insulation, high voltage test facilities. Methods: theory of electrical circuits, mathematical modeling, program for mathematical and engineering calculations Mathcad, MATLAB Simulink. Results. The authors proposed the original design of a high-voltage test facility, which makes it possible to generate both direct voltage and alternating voltages of industrial and ultra-low frequencies. The simulation of the installation was carried out. A method for calculating high-voltage test facilities is proposed.

FEATURES OF THE ORGANIZATION OF LABORATORY WORKS IN THE STUDY OF PHYSICS OF ELECTRICAL PHENOMENA USING SOFTWARE SIMULATORS

The article shows the possibility of convenient use of software simulators of electric circuits in performing laboratory works in physics, theory of electric circuits and signals, and the basics of electronics. An example of studying Kirchhoffʼs laws in the NI Multisim 14 simulator as one of the simplest in terms of interface but very powerful in terms of capabilities is considered. The choice of NI Multisim is due to the fact that it is de-facto one of the industrial standards in the real design of electronic devices. Thus, students are introduced to not an educational software simulator for modeling electrical phenomena, but to industrial software that they may have to deal with as future electronics designers.The article describes the structure of a typical mini-project (laboratory work) on the study of Kirchhoff's laws, and shows that this approach to organizing training is related to the specifics of teaching students majoring in 172 – “Telecommunications and Radio Engineering”, 123 – “Computer Engineering” and 125 – “Cybersecurity”.As a result, students acquire the skills to develop and test models of electrical circuits with visualization of the results obtained, learn to use the methods of solving systems of linear equations acquired in the course of mathematics in practice.
 Keywords: educational technologies of distance learning; simulation of electrical circuits; analysis of processes in electrical systems; use of NI Multisim 14 software package for educational purposes; laboratory works in physics and electronics; Ohm’s law; Kirchhoff's laws; virtual learning environment.

Physics in deformable spacetime: Physical laws emerging from the surface minimality principle and the masses of particles

In this work, the study was focused on how deformable spacetime gives rise to physical laws, particularly quantum and special relativity. It was shown that both the Lorentz factor and quantum mechanics can emerge from the dynamical behavior of minimal surfaces in deformable spacetime, where the Möbius transformations prevail rather than the Lorentz transformations. The motion of deformable surfaces under minimality conditions creates a helicoidal pattern, a minimal surface with a metric designated by AdS (anti-de Sitter) space. Its isometry is a catenoid of which metric belongs to dS (de Sitter) space. When the two ends of the helicoid join it becomes a Möbius strip with multi-twists (i.e. windings), the so-called Möbius helicoid. It represents the most elementary mass with the attributes of charge and spin. It was shown that the number of windings increases with velocity according to the Lorentz factor. In other words, the Lorentz factor emerged from the transformation equations between the helicoid and catenoid, and both of them are isometric minimal surfaces. This fact serves as a means of transforming the metrics of the two isometric surfaces in AdS and dS spaces. There is an intimate relation between helicoidal motion, Möbius helicoid, and the Lorentz transformations. The zitterbewegung behavior of Dirac electron can be explained by the internal dynamics of the Möbius helicoid. Instead of using electromagnetic theory which led to the birth of special relativity, one can use the electrical circuit theory for deformable surface dynamics. A master equation was derived by using the resistive, capacitive, and inductive properties of deformable spacetime. The electromagnetic wave, Schrödinger, Klein–Gordon, Dirac, quantum telegrapher, and quantum torsion equations could be easily obtained from this master equation by making some simplifying assumptions for the parameters involved. The existing torsion due to helicoidal motion modifies the energy/mass equation (i.e.E=mc2) of special relativity. The Higgs potential can be obtained from the dynamic potential term of the master equation. Deformable space–time allows the emergence of a rich number of physical laws and relations. The masses of particles were calculated using the Möbius helicoid model for the very elementary structure of mass. The mass of a particle can be visualized as a three-dimensional network of helicoids with relatively higher stability. The stability is particularly associated with the phase changes of the catenoidal structure of the Möbius helicoid and the torsional vibrational modes of windings. Both the phase (or shape) change and/or the increase of the vibrational energies of windings produce a new configuration that represents a new particle. The masses of 187 particles were determined from this mechanism with an accuracy of ±3 MeV. It turned out that excitation energy states which could be expressed in terms of prime number multiples of a precursor mass play an important role in providing relatively higher stability.

Spectral method of electrical circuits accelerated simulation with thyristors

Purpose. The development of transient processes calculation method in electric circuits with thyristors based on the use of functions approximation by orthogonal polynomials.
 Methodology. Functions approximation by orthogonal polynomials, numerical methods of differential equations integration, matrix methods, programming, theory of electric circuits.
 Obtained results. The method of solution function polynomial approximation of integro-differential equations of state, which describes the transient processes of an electric circuit with thyristors, is used in this paper. The used method showed the advantages over other known methods in increasing the accuracy and reducing the simulation time of transient electrical processes by more than 6 times.
 Findings. The solution is approximated by a series of Chebyshev polynomials. The integro-differential equations of state are transformed into linear algebraic equations for special depiction of the solution functions. The depiction of functions of true currents in the equivalent circuit is interpreted as direct currents. Such a schematic model creates visibility for a researcher performing simulation of transient electrical processes.
 Practical value. The proposed methods discover the possibility of using the apparatus of direct current electric circuits’ theory for transient processes in complex schemes modeling with thyristors.

ВИЗНАЧЕННЯ ОПОРУ ЗАЗЕМЛЮВАЛЬНИХ ПРИСТРОЇВ ПІДСТАНЦІЙ 330(220) кВ

In the electric power industry of Ukraine, the main system-forming objects are power transmission lines and substations with 330(220) kV switchgear. The most powerful sources of danger at substations are short circuits on the busbars, a direct lightning strike or the operation of overvoltage limiters and arresters.The purpose of the article is to develop a method for determining the resistance of the grounding system of substations with open switchgear 330(220) kV, aimed at increasing accuracy, taking into account the most influential independent factors. The provisions of the theory of experiment planning, the theory of electric circuits, mathematical modeling in the package Grounding 1.0, LiGro and Microsoft Excel were used to conduct the research. In the paper, a comparative analysis of the known formulas for determining the resistance of the grounding system is carried out: the formula of the GOST 12.1.30-81 standard, Ohlendorf-Laurant, Laurent and Neumann, Schwartz, Sverak formulas, as well as the formula of the international standard IEEE Std 80-2013. The results of multifactorial experiments to determine the dependence of the resistance of the grounding system on its area, the size of the grid cell, the perimeter of the cross-section of the grounding, the equivalent specific resistance of the soil, the short-circuit current and the depth of the grid location are given. A graphical comparison of the results of determining the resistance according to the considered formulas was carried out. In the paper, the method of determining the parameters of grounding system of 330(220) kV substations was further developed, aimed at ensuring standardized values of the resistance of the grounding system and the ground potential rise using formulas obtained from the results of multifactorial experiments. The results obtained in the work will make it possible to reduce the probability of damage to the insulation of 6-10 kV cables, as well as cables of secondary circuits from low-frequency and high-frequency (pulse) voltages when large currents flow into the grounding system in the mode of a single-phase short-circuit to the ground in electrical grid with a grounded neutral. References 9, tables 2, figures 6.

Modeling red deer functional connectivity at a regional scale in a human-dominated landscape

Ecological connectivity is a key attribute of landscapes and indicates how landscapes facilitate or impede movement. It is an essential criterion to consider in the design of green infrastructures (GIs) when landscape planners and managers deal with population viability, which in part depends on the movement capacities of organisms. Our goal is to inform about the conservation value of land parcels to maintain or enhance connectivity. For this, we developed a red deer functional connectivity model at a regional scale. We focused our study on this large mammal species inhabiting the Greater Geneva agglomeration between Switzerland and France. Our study site is dominated by forested mountains and lowlands, which are highly fragmented by human infrastructures and agricultural lands. We used GPS location data from 15 red deer to parameterize the habitat resistances with a multivariate analysis. To predict connectivity at the regional scale, we used local expert knowledge to design a graph-based landscape. Then, we used electric circuit theory with Circuitscape software to detect pinch points and map corridors, using the set of resistances parameterized with experimental data and the putative core areas and links identified with the help of expert knowledge. We obtained a map that highlights suitable regional habitat patches and corridors or connectivity pinch points potentially used by red deer between the mountains and the lowlands, ratifying the importance of the transfrontier collaboration while implementing the GI. The obtained results are used to assist landscape managers and planners in their effort to include functional connectivity in the prioritization of the GI across the region.

Assessment of electric energy transport reliability (as exemplified by JSC "Rosseti Siberia Tyvaenergo" power networks)

Analysis of electric energy transport by power distribution networks of JSC Tyvaenergo over the period of 2017 – 2022 has been carried out. The structure of the company is considered, the characteristics of the main elements of the studied electric networks are given, the balance of the transmission of electric energy in and out of the company's networks is estimated. Based on the information published in open sources on the rate of accidents in the company's electrical networks, an estimate has been made of the number of emergency situations that occurred during the period under study. The duration of interruptions of power supply to consumers, as well as the amount of undersupply of electric energy caused by those interruptions, has been estimated. The influence of the seasonal component on the number of emergencies during the period under study is considered. Based on the data for the last quarter of 2022, analysis of the main causes of damage to elements of electrical networks has been carried out. The classification of failures is made, their main characteristics for this period are considered. The percentage ratio of the number of failures for the most characteristic reasons to the total number of outages during the period under study has been established. A technical tool is proposed to improve the reliability in conditions of unbalanced power consumption. General scientific methods, numerical methods of analysis, methods of the theory of electrical circuits were used in the research. To visualize the results of the analysis, the technologies of the MATLAB graphics editor were used. The results obtained may be of interest to the heads of power grid companies, as well as researchers and engineers engaged in research in the field of reliability of power supply.

Features of the Relaxation Process in an RC Circuit under the Influence of a Sinusoidal Voltage

The article is devoted to the study of the properties of the relaxation process in a nonlinear electrical circuit under the sinusoidal voltage influence. Electronic devices and processes the operation of which is based on relaxation principles are sources of specific series of pulses, the monitoring of which allows one to draw conclusions about the technical parameters of these devices and processes. The occurrence of a series of partial discharges in a high-voltage device can serve as an example. An essential factor of partial discharges is their multiplicity both in time and in space, which are dispersed in an a priori unknown number of defects. The aim is to determine the number of defects and to perform appropriate grouping of the entire set of partial discharges by defects. Internal deterministic correlations derived as a result of solving the problem and presented in terms of the classical theory of electrical circuits should be regarded as a key to solving the problem that was set forth. Analytical correlations for the deterministic component of partial discharges in potential electrical insulation defects are revealed. The obtained correlations characterize the time intervals between individual discharges inside the insulation defect. These time intervals are uniquely related to the defect parameters and can serve as a basis for identifying this defect against the background of other partial discharges. As an example, the result of mathematically modeling a relaxation process with the specified parameters is given.

Information flow theory: Circuit network approach

With the rapid development of the idea of integration and cooperation and the proliferation of information systems and technology in supply chains, the importance of information, and its management are becoming more and more evident. In this chapter, we explore how the instruments used in a circuit network be applicable to a supply chain network. We borrow the laws developed in electric circuit theory and conceptually explain the relationship and open discussion on how to apply it for future researchers.

Monitoring spatiotemporal impacts of changes in land surface temperature on near eastern fire salamander (Salamandra infraimmaculata) in the Middle East

Persistence and coexistence of many pond-breeding amphibians depend on seasonality. Temperature, as a seasonal climate component, affects numerous physical and biological processes of pond-breeding amphibians. Satellite-derived land surface temperature (LST) is the radiative skin temperature of the land surface, which has received less attention in spatiotemporal seasonal habitat monitoring. The present study aims to evaluate the increasing and decreasing effects of LST trends at two levels: (1) habitat suitability and connectivity; (2) individual population sites and their longitudinal distribution (with increasing longitude).Habitat suitability modeling was conducted based on an ensemble species distribution model (eSDM). Using electrical circuit theory, the connectivity of interior and intact habitat cores was investigated. An average seasonal LST was prepared separately for each season from 2003 to 2021 and entered into Mann-Kendall (MK) analysis to determine the spatiotemporal effects of LST changes using the Z-Score (ZMK) at two confidence levels of 95 and 99%. Based on the results, in winter, 28.12% and 70.70% of the suitable habitat were affected by an increasing trend of LST at 95% and 99% confidence levels, respectively. The highest spatial overlap of the decreasing trend of LST with the suitable habitat occurred in summer and was 6.4% at the 95% confidence level and 4.2% at the 99% confidence level. Considering population site at 95% confidence interval, the increasing trend of LST was calculated to be 20.2%, 9.5%, 4.2%, and 6.3% of localities in winter, spring, summer, and autumn, respectively. At the 99% confidence level, these percentages reduced to 8.5%, 3.1%, 1%, and 1%, respectively. During winter and summer, based on the results of the longitudinal trend, an increasing trend of LST was observed in sites. Localities of Hatay and Iica village in Turkey experienced seasonally asynchronous climate change regimes. The approach used in this study allowed us to create a link between the life cycle and seasonal changes on a micro-scale (breeding sites) and macro-scale (distribution and connectivity). Findings of this paper can be effectively used by conservation managers to preserve S. infraimmaculata's metapopulation.

Issues of electric energy transport reliability (on example of JSC Krasnoyarskenergosbyt)

Analysis has been performed of the transmission of electric energy through the power distribution networks of PJSC Krasnoyarskenergosbyt over the period of 2016 – 2022. The structure of the company is considered, the characteristics of the main elements of the studied power networks are given, the degree of wear of the main electrical equipment is estimated. Based on the information from public media on the level of accidents in the company's power networks, an estimate has been made of the number of emergencies that occurred during the study period, the share of self-healing failures in the total amount of damage has been determined. The duration of interruptions of power supply to consumers, as well as the amount of undersupply of electric energy caused by these interruptions, has been estimated. The influence of the seasonal component on the number of emergencies during the study period is considered. Based on the data for the first half of 2022, the analysis of the main causes of damage to the elements of electrical networks has been performed. The classification of failures is made, with their main characteristics over the period under study considered. The possibility of using various methods of forecasting the reliability level of the power networks under consideration is evaluated. The results of the analysis of the use of statistical and cybernetic methods of preventive assessment of undersupply of electrical energy are presented. Based on the comparison of the results obtained, it is concluded that statistical methods are the most effective. The research uses general scientific methods, numerical methods of analysis, methods of the theory of electrical circuits, theories of mathematical statistics, data interpolation and forecasting. To visualize the results of the analysis, the technologies of the MATLAB graphics editor were used. The results obtained may be of interest to the heads of power grid companies, as well as researchers and engineers engaged in research in the field of reliability of power supply.

Особенности моделирования воздушных и кабельных участков линий электропередачи 110–750 кВ при использовании фазного координатного базиса

Power system steady state and transient analysis require correct modeling of overhead transmission lines and cables operating at 110–750 kV. The key difficulties to model sections of overhead and cable lines are caused by complex conductor geometry, their transposition, as well as grounding schemes of ground wires of overhead lines and screens of underground cables. The paper covers various aspects of 110–750 overhead line and cable modeling that must be taken into consideration to obtain a reliable mathematical model in a phase domain. Modern software does not provide a universal solution to determine line parameters. The 110–500 kV cable line modeling issues have not been worked out properly and require careful analysis of specialized foreign literature. Thus, the task to develop the algorithms of calculating the parameters of overhead and cable power lines is relevant, taking into account the various configuration options of these lines which are possible in operational practice. To derive overhead transmission line and cable line models, electric circuit theory and matrix algebra methods have been used. The ATP/ATPDraw and MATLAB/Simulink software environment has been used to investigate what tools are available to determine line parameters, as well as to verify some of the calculation results. Analysis has been carried out to reveal the options available in the ATP/ATPDraw and MATLAB/Simulink software to compute line parameters in a phase domain. An algorithm has been developed and verified to calculate overhead line parameters regardless of the number of parallel circuits. The key features of the calculation of the matrix of linear resistances of overhead power transmission lines are outlined. The main features of modern cable lines operating at 110–500 kV are also described. The paper presents various cable layouts possible in real-field conditions, as well as provides expressions that allow obtaining correct impedances and admittances for a system of cable line conductors. Study of the options of various software tools dedicated to overhead line parameter calculation in a phase domain has revealed that these tools cannot be deemed universal to represent an overhead line of whatever configuration. However, the developed algorithm is universal as it allows computing line parameters regardless the ground wire grounding approach. The expressions presented in this paper consider various layouts of 110–500 kV cable lines that could be encountered in the Russian power system.

THE DIFFERENT APPROACHES TO THE TRANSFORMATION OF REACTIVE POWER INTO AN ACTIVE POWER

The relevance of the development of modern problems of the electric power industry in connection with the depletion of the planet’s natural resources is undeniable and initiates the development of new physical and technical solutions with the practical use of known natural phenomena. The method of this work is to propose, justifying the expediency of a possible scheme of a resonant converter of reactive power into activity and conducting an analysis of the electromagnetic processes occurring in them. The proposed schemes combine the presence of resonant parallel and resonant circuit complexes. The difference is in the way they are implemented. For the data of the joint circuit, the feature is the presence of two inductively coupled active-reactive circuits, but different in the ways of creating resonance conditions. For a circuit without an additional power source, it is shown that the successful implementation of resonance conditions is possible by choosing the appropriate element base. For a circuit with an additional source of harmonic voltage, it is shown that for a suitable setting it is possible to completely eliminate the negative influence of the converter circuit on the source of reactive power. Calculations for the experimental model show that with the appropriate selection of the element base, it is possible to obtain a conversion factor of ~ 1.0 with a minimal effect on the current in reactive power sources. Given the calculated ratios, the mathematical apparatus of the theory of electric circuits was used to substantiate the principle possibility of resonant transformation of electrical energy. Thus, methods of calculating the characteristics of transient processes in closed circuits with active-reactive elements. For the first time, with the justification of practical power, we offer the possibilities of the scheme of resonant transformation of reactive power into active power, and an analysis of the electromagnetic processes occurring in them is carried out. The proposed work was initiated by the current needs of the electric power industry, caused by the depletion of natural resources and the rapidly growing needs of the world economy. The results of the work illustrate the practical possibilities of creating real schemes for converting reactive electricity into active electricity.