Electric Circuit Theory Research Articles

Evaluation of habitat suitability and migratory paths of an endangered raptor, Steppe Eagle (Aquila nipalensis) in Iran

Understanding habitat suitability, the environmental variables limiting the distribution of species, and migratory paths are important issues for conservation of threatened bird species. Identifying areas important for birds and their overlap with conservation areas (CAs) can guide conservation managers in establishing new CAs. The Steppe Eagle (Aquila nipalensis) is a globally endangered winter visitor raptor in Iran. We used 164 occurrence records of Steppe Eagles and data on 12 environmental variables in Iran as input to ensemble modeling and electrical circuit theory models to identify, respectively, potential wintering areas and migratory paths between those wintering areas. Our results revealed that elevation, distance to rodents, mean diurnal range, distance to villages, and distance to cities were the most influential variables for habitat suitability in Iran. Potential wintering areas identified by our models were mainly located in the north and south of Iran and migratory paths connected these areas through the central plains. CAs covered about one-fifth of potential wintering areas. Conservation of the species within potential wintering areas and the migratory paths from northern to southern Iran is necessary for the survival of this endangered species in its entire distribution. Therefore, wildlife managers should pay increased attention to non-protected parts of potential wintering areas in order to establish new CAs and protect migration paths against threats. Our results pave the way for proper planning for the conservation of threatened raptors in Iran, particularly Steppe Eagle.

Evaluation of the effectiveness of incomplete phase pulse width modulation algorithms in the converter-electric motor system

Aim. This study evaluates the effectiveness of incomplete-phase algorithms for pulse width modulation of three-phase voltages in frequency control of electric drives, using integral current dispersion in the load as the criterion. Materials and methods. This study examines pulse width modulation processes in frequency-controlled electric drives, focusing on the converter-electric motor system. Methods from electric circuit theory are used, with proposed algorithms illustrated through drawings, and these drawing can be implemented in the matrix laboratory software. Results. The process of pulse width modulation in the converter-electric motor system is considered. It is demonstrated that to minimize the number of switching keys in the frequency converter, incomplete-phase pulse width modulation algorithms are beneficial. Expressions for local dispersion of the interphase current in single-phase and two-phase modulation are analyzed. An expression for local current dispersion in a three-phase bridge circuit load is derived, and the concept of integral current dispersion in a three-phase load is derived. Indicators for evaluating the effectiveness of algorithms for incomplete-phase pulse width modulation are proposed. Graphs the efficiency coefficient, characterizing incomplete-phase pulse width modulation with a minimum number of switching of key elements in the function of the amplitude coefficient and in the function of the relative frequency of modulation are constructed. Conclusion. The results aid in developing algorithms for controlling frequency converters in asynchronous electric drive systems.

Geometrical description and Faddeev-Jackiw quantization of electrical networks

In lumped-element electrical circuit theory, the problem of solving Maxwell's equations in the presence of media is reduced to two sets of equations, the constitutive equations encapsulating local geometry and dynamics of a confined energy density, and the Kirchhoff equations enforcing conservation of charge and energy in a larger, topological, scale. We develop a new geometric and systematic description of the dynamics of general lumped-element electrical circuits as first order differential equations, derivable from a Lagrangian and a Rayleigh dissipation function. Through the Faddeev-Jackiw method we identify and classify the singularities that arise in the search for Hamiltonian descriptions of general networks. The core of our solution relies on the correct identification of the reduced manifold in which the circuit state is expressible, e.g., a mix of flux and charge degrees of freedom, including the presence of compact ones. We apply our fully programmable method to obtain (canonically quantizable) Hamiltonian descriptions of nonlinear and nonreciprocal circuits which would be cumbersome/singular if pure node-flux or loop-charge variables were used as a starting configuration space. We also propose a specific assignment of topology for the branch variables of energetic elements, that when used as input to the procedure gives results consistent with classical descriptions as well as with spectra of more involved quantum circuits. This work unifies diverse existent geometrical pictures of electrical network theory, and will prove useful, for instance, to automatize the computation of exact Hamiltonian descriptions of superconducting quantum chips.

On fire risk reduction when operating individual households

The article aims to elaborate a technical means for reducing fire occurrence in internal electrical networks of individual households. General scientific methods of numerical analysis, electric circuit theory, and prediction theory were used. It was determined that the operating mode of the electric network under study is characterized by a significant unbalanced power consumption due to the asymmetry and non-sinusoidality of phase currents caused by the occurrence of additional symmetrical components of forward, reverse, and zero sequences. Additional heat losses increase significantly and lead to overheating of the neutral conductor, thus intensifying fire risks. On the basis of measurements and the authors’ software, a simulation modeling of integration of the developed balancing device into the investigated network was carried out. The conducted analysis found that the developed device can reduce additional heat losses and fire risks by over 90%. Using statistical methods of forecasting, regression analysis in particular, a preventive long-term assessment of the level of additional power losses was conducted. Autoregressive equations for predicting the parameter of additional power losses at a certain probability level were derived. MATLAB graphic editor technologies and Excel software were used to visualize changes in the studied indicators. The results can be used by construction companies when designing the internal electrical network of individual households, as well as for researchers developing approaches to reducing additional losses of electrical energy.

Предел передаваемой мощности в системе тягового электроснабжения

Objective: the concept of the limit of power flow is widely used in general industrial power engineering to compare different ways of amplifying an electric network. In this paper, it is proposed to use it to evaluate the operation of traction networks of railways. Setting the traction power load is used in several simulation development of an express methodology for comparing various ways to enhance traction power supply is an urgent task. Methods: the paper uses mathematical modeling methods based on the theory of electrical circuits. The MATLAB software package was used as a modeling tool. Results: expressions are obtained for calculating the maximum transmitted power depending on the length of the substation zone. The dependence of the transmitted power on the minimum voltage on the current collector, the equivalent resistance of traction substations for DC sections, is analyzed. For alternating current sections, the dependence of the transmitted power on the power factor of the traction load is analyzed. The conclusion is made about the relevance of increasing the power factor of an alternating current electric rolling stock. Practical importance: the proposed technique will allow you to quickly assess the effect of using various methods of strengthening the traction power supply system.

Экспериментальное определение внешних характеристик тяговых подстанций переменного тока для выбора параметров активных устройств системы тягового электроснабжения

Objective: to develop a method of experimental determination of external characteristics of alternating current traction substations for selection of parameters of active devices of traction power supply system. Methods: finding of equivalent currents of phases of a step-down transformer using the theory of linear electric circuits; statistical methods, including: construction and approximation of external characteristics of regression analysis methods, construction of theoretical and experimental law of distribution of equivalent current of traction load and determination of current quantile for a given confidence probability. Results: advantages and disadvantages of methods of simulation modeling of traction power supply system as applied to determination of parameters of active devices are shown, possibilities of experimental method are given. A detailed description of the conducted experiment is given, connection schemes of measuring devices and vector diagrams of currents and voltages are shown. The main stages of the proposed methodology for selecting the parameters of the booster transformer are outlined. Calculation formulas for determining the equivalent phase currents are presented, the external characteristic for the selected traction substation is constructed. The theoretical and experimental distribution law of the equivalent current of the traction load was constructed and the quantiles of the equivalent current were determined, which amounted to 400 A at a confidence level of 0.968. The maximum required value of volt additive for the selected traction substation and the law of volt additive voltage control for the booster transformer were determined. Practical importance: the proposed methodology of selecting the parameters of active devices of traction power supply system based on the experimental determination of external characteristics of traction substations will allow to determine more accurately the energy performance of booster transformers. It is supposed to improve the methodology by processing the results of synchronous measurements of currents and voltages at neighboring traction substations feeding the inter-substation zone. This will make it possible to expand the possibilities of application of active devices of the traction power supply system and improve the algorithms of booster transformer operation, including taking into account the operation of controlled reactive power compensation devices.

Grounding resistance model considering propagation time between grounding electrodes

The velocity of electric field in the soil is sufficiently lower than that in the air. Conventional grounding resistance models based on an electric circuit theory ignore the propagation time between grounding electrodes (GEs). If the GEs are connected using an aerial lead conductor, the propagation time along the lead conductor is apparently different from that along a grounding conductor (GC) in the soil. The propagation time of mutual grounding resistance between GEs should be considered in accurate lightning surge analysis. This paper proposes a simulation model of the mutual grounding resistance considering the propagation time between GEs.

Seasonality in functional connectivity: A case study with the American marten in Forillon National Park

AbstractProtected areas are essential tools for reducing loss of global biodiversity. To fulfill their ecological functions, protected areas must be connected to their surroundings, a requirement that is difficult to meet in landscapes intensively disturbed by anthropogenic activities. Therefore, protecting movement corridors at the edges of protected areas is crucial, especially for species with broad habitat needs, such as the American marten (Martes americana). However, habitat selection and space use patterns are dynamic processes, so we could expect that functional connectivity would vary temporally in response to changing environmental conditions and levels of human activities. In this study, we aimed at predicting the location of movement corridors for the American marten in Forillon National Park and its periphery during two contrasted periods (snow‐free: May–November; snow‐covered: December–April). We used “seasonal” resource selection functions to identify core areas (interpreted as circuit “nodes”) and CircuitScape to delineate movement corridors between them based on the electrical circuit theory. Habitat selection patterns differed between periods, with martens avoiding open areas, high elevations and road proximity during the snow‐free period, while avoiding areas closer to secondary roads but selecting areas closer to primary roads and housing structures during the snow‐covered period. Consequently, the location of movement corridors differed partially between periods. Functional connectivity was favored by the presence of forest patches for both periods, while being constrained by open environments, especially during the snow‐free period. Our study highlights the importance of modeling functional connectivity at fine temporal scales in order to provide movement corridors that fulfill the requirements of a species at each period of its annual cycle.

Modeling Excitable Cells with Memristors

This paper presents an in-depth analysis of an excitable membrane of a biological system by proposing a novel approach that the cells of the excitable membrane can be modeled as the networks of memristors. We provide compelling evidence from the Chay neuron model that the state-independent mixed ion channel is a nonlinear resistor, while the state-dependent voltage-sensitive potassium ion channel and calcium-sensitive potassium ion channel function as generic memristors from the perspective of electrical circuit theory. The mechanisms that give rise to periodic oscillation, aperiodic (chaotic) oscillation, spikes, and bursting in an excitable cell are also analyzed via a small-signal model, a pole-zero diagram of admittance functions, local activity, the edge of chaos, and the Hopf bifurcation theorem. It is also proved that the zeros of the admittance functions are equivalent to the eigen values of the Jacobian matrix, and the presence of the positive real parts of the eigen values between the two bifurcation points lead to the generation of complicated electrical signals in an excitable membrane. The innovative concepts outlined in this paper pave the way for a deeper understanding of the dynamic behavior of excitable cells, offering potent tools for simulating and exploring the fundamental characteristics of biological neurons.

On reliability and quality of functioning of power grids (as exemplified by the branch of PJSC Rossetti Volga – Samara Distribution Networks)

The analysis of the electric energy transmission through the distribution electric networks of the branch of PJSC Rosseti Volga — Samara Distribution Networks over the period of 2018 – 2022 was carried out. The structure of the company is considered, the characteristics of the main elements of the power grids under study are given, the balance of the electric energy transmission in and out of the company's networks is estimated. Based on the information published in public media on the accident rate in the company's power grids, assessment was made of the number of emergency situations that occurred over the period under study, assessment of the duration of interruptions in power supply to consumers, as well as the amount of undersupplied electric energy caused by these interruptions. The influence of the seasonal component on the number of emergencies during the period under study is considered. Based on the 2022 data, the analysis of the main causes of damage to components of power grids and the classification of failures are presented, their main characteristics over the period in question are considered. The percentage ratio of the number of failures for the most characteristic reasons to the total number of shutdowns over the period under study was established, and the classification of the number of emergency shutdowns according to the degree of undersupply of electrical energy was made. General scientific methods, numerical methods of analysis, methods of the electrical circuit theory were used in the study. 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 power supply reliability.

RESEARCH OF STRUCTURAL AND MECHANICAL PROPERTIES OF MEAT AS AN OBJECT OF PROCESSING IN MEAT COMMINUTOR

Reliable assessments of the state of modern energy show the relevance of scientific and technical developments aimed at solving its problems. In this regard, the use of resonance phenomena in electrical circuits with active-reactive elements acquires particular significance. Their various combinations open up exceptional opportunities for creating fundamentally new efficient energy sources. This article discusses a resonant active electrical power amplifier containing a sequence of several electrically connected active-reactive circuits, which, depending on the purpose, are excited in the voltage resonance or current resonance mode. An equivalent circuit is proposed for the proposed resonant amplifier of active electrical power, represented by two blocks, each of which consists of a sequence of inductively coupled active-reactive circuits excited at the same frequency. Calculations are presented showing the theoretical justification for the performance of the proposed scheme. The analysis of ongoing electromagnetic processes was carried out using well-known methods of the theory of electrical circuits without involving any hypotheses about the physics of resonance phenomena. It is shown that in the proposed amplifier circuit, the first block amplifies the reactive power of the harmonic signal with a high conversion coefficient, the second, with a slight gain, converts the reactive power of the harmonic signal into active power. The results of calculations are presented, illustrating the functional dependence of the integral gain on the main characteristics of the output resonant circuit. Numerical estimates of the main characteristics of the proposed circuit showed that with an appropriate choice of its parameters, high values of the output characteristics are possible, so the gain can reach a value of ~ 48. The significance of the results obtained for practice lies in their use for formulating recommendations for the creation of real efficient sources of electrical energy, the principle whose actions are based on the use of natural resonance phenomena.

A DC fault current fast-computing method of MMC-HVDC grid with short circuit protection equipment

The multi-terminal modular multi-level converter-based high voltage direct current (MMC-HVDC) grid with short circuit protection equipment (SCPE) is so complex that it is difficult to estimate its fault current and analyze the performance of SCPE by conventional time-domain numerical calculation method, it meets three big obstacles. This paper has made significant progress in overcoming these obstacles. 1). By applying the modern electrical circuit theory, a systematic formulation of the differential equation set for fault current calculation is developed to avoid a lot of complex and cumbersome matrix manual calculations. 2). A novel Y-Delta transformation in the s-domain is proposed to develop an eliminating virtual node approach for a complex MMC-HVDC grid, including the ring, radial, and hybrid topologies. 3). It is difficult to solve the equivalent circuit of MMC-HVDC grid with SCPE since SCPE is a time-variable-nonlinear circuit. A canonical voltage source model of SCPE is established to transform the time-variable-nonlinear circuit into a piecewise linear circuit. Based on the three significant progresses, a DC fault current fast-computing method of MMC-HVDC grid with SCPE is put forward to deal with all kinds of MMC-HVDC grids with several kinds of SCPEs. Then, the performance of several kinds of SCPE is analyzed and compared by this method. Consequently, the proposed DC fault current fast-computing method is a new powerful tool to estimate the fault current of MMC-HVDC grid and analyze the performance of SCPE.

Simulation of Kirchoff's Law In Ni-Multisim Application to Determining the Current on a Circuit

The increasingly rapid development of technology has given rise to simulation methods used in circuit specifically in dynamic electricity. One of them is the NI-Multisim application which is useful for determining current and voltage values efficiently and effectively with a circuit design that is built first in the application. Research activities were carried out by simulating Khirchoff's law on NI Multisim by building a circuit scheme based on the circuit composition, namely resistance, voltage source and using voltage measuring instruments and current measuring instruments which are all arranged in such a way by referring to electrical circuit theory. The results of this research are that there is a difference in the total resistance value between the values in the circuit kit module practice and the use of Multisim. However, the difference is very small with an error of around 7.83% for the series-parallel circuit. The current value for each resistance which is connected in a mixed manner can be seen that the practical and theoretical values have an error value of 0% to 24.24% respectively located at R3 at the 6V voltage source and R2 at 12V. The current in I3 is equal to the sum of the current in I2 and the current in I1 for each specified voltage variation. The measurement values with the Khirchoff kit module are different from the NI Multisim simulation, but the differences are still relatively small, ranging from 6% to 28%.

Equivalent circuits in nanopore-based electrochemical systems

Single-nanopore membranes constitute physical models for biological ion channels and are also central to electrochemical energy transducers, logical circuits in sensors and actuators, and converters in bioelectrical interfaces. The membrane potential, defined as the electrical potential difference established between two different ionic solutions separated by the membrane, is crucial for the electrical coupling of nanofluidic concentration cells to electronic components such as load capacitors and resistors. Here we analyze, theoretically and experimentally, the validity of basic principles governing electric circuit theory such as the Thévenin equivalent circuit, the additivity of voltages and resistances, and the Millman theorem in nanopore-based concentration cells. To this end, we consider a wide range of practical conditions with respect to salt concentrations, nanopore asymmetry, electrical capacitances, and series and parallel arrangements. Additionally, we investigate the scaling of the single pore results to the multipore case. The results obtained suggest that basic circuit models offer approximate tools to guide the analysis of the nanofluidic concentration cells.

Study of subharmonic oscillation processes in ferroresonance circuits

The article presents a general theory of the analysis of subharmonic oscillations at a frequency of 25 Hz in three-phase Ferro resonance circuits with common magnetic conductors. The abbreviated equations are obtained by averaging with the corresponding phases. From the condition of the existence of a periodic solution, the phase and amplitude ratios of the excited oscillations are determined, which differ from threephase circuits with a separate ferromagnetic element. In steady-state mode, the excitation conditions and the area of existence are determined depending on the parameters of the circuit, the bias current and the applied action. The stability of the solution of the initial system of nonlinear second-order differential equations is also studied by analysing the roots of the characteristic equation using a qualitative method. In the theory of nonlinear electrical circuits, the analysis of the physical processes occurring in threephase Ferro resonance circuits during the excitation of second-order subharmonic oscillations is of particular importance in the design and creation of various converter devices.

Modeling of dynamic modes of a generalized pumping station with an asynchronous electric drive of centrifugal pumps

Transportation of large volumes of liquid to distribution pipelines is provided by transit facilities - main pipelines and pumping stations, which consume significant amounts of electricity and are of strategic importance. The requirements for continuity, reliability, safety, fault finding, and diagnosis of existing, as well as requirements for the design of new strategic objects, are usually regulated by national legislation. The possibility of conducting physical experiments to analyze the modes of operation of such complexes is significantly limited by the inadmissibility of interrupting their functioning, as well as technical and financial risks. The use of a hybrid model consisting of a digital model of the power equipment and a physical model of the control system makes it possible to solve this problem. In this work, attention is focused on the digital model of power equipment. Based on the system approach and the principle of electrohydrodynamic analogy, a formalized mathematical model of the generalized system of asynchronous centrifugal pump units of a multi-unit pumping station with asynchronous electric drive of centrifugal pumps was created. The use of the principle of electrohydraulic analogy made it possible to apply the basic principles of the theory of electric circuits to form the equations of the hydraulic subsystem. The achieved formalization makes it possible to automate the formation of equations to obtain a model of an object of a specific configuration. The use of pump parameters in the model, which depend on the geometry of the internal elements, the speed of the impeller, and the physical properties of the liquid, makes it possible to investigate the impact of emergency and operational deviations of the equipment characteristics on the operating modes both at the level of individual modules and at the level of the pumping station as a whole. The obtained mathematical model was verified by adapting it to the pumping station of the given configuration. A computer simulation of several operational and emergency modes of operation of a pumping station with four hydraulically connected pumps was carried out. The scope of use and ways of improving the developed model are proposed, as well as the direction of further research

CALCULATION OF POWER TRANSFORMER INDUCTANCE MATRIX

Practical calculations of electric equipment and electric networks are performed using equivalent circuits. Without taking into account saturation phenomena, electromagnetic processes in a power transformer are described by a system of linear equations, which can be represented in matrix form. The transformer inductance matrix contains self and mutual winding inductances, whose values for one phase are determined directly from the passport data containing the results of no-load and short circuit experiments. Mutual inductances between phases depending on the type and size of the magnetic core are not usually given in the transformer documentation. It does not allow to simulate the operating modes that differ from the steady state with uniform phase load.
 
 The purpose of the work is to develop an algorithm for calculating elements of the power transformer inductance matrix according to its passport data and magnetic circuit parameters.
 
 The scientific novelty lies in use of information about magnetic circuit type and size to determine elements of the inductance matrix.
 
 Materials and methods. Methods of linear electric and magnetic circuit theory are used in the work.
 
 Results. The proposed algorithm for calculation of power transformer inductance matrix includes three stages: calculation of self and mutual inductances for one phase; construction of an equivalent circuit for a magnetic circuit and calculation of magnetic fluxes in order to take into account the mutual influence of windings on various phases; assembly of the inductance matrix of three-phase transformer. A method is proposed for constructing the transformer inductance matrix with an arbitrary type of magnetic circuit, phases and windings quantity. The method involves preliminary calculation of the coefficient matrix that characterizes the magnetic circuit and depends mainly on its type and, to a less, on the ratio of geometric dimensions in rods and yokes. The coefficient matrix can be calculated in advance and used to determine the inductance matrix of a wide range of transformers.
 
 Conclusions. 1. The passport data of the transformer do not allow to model transformer operation at unbalanced load validly. 2. An algorithm for determining the inductance matrix of transformers has been developed. 3. A method for compilation of a transformer inductance matrix with an arbitrary type of magnetic circuit, the number of phases and windings is introduced. The practical significance of the algorithm is determined by the simplicity of algorithmizing, as well as by the possibility of using it in computer simulation of electrical circuits with transformers, for example, using the modified nodal analysis method.

COMPLEX DESIGNING ALGORITHM FOR SPACECRAFT ENERGY-CONVERTING EQUIPMENT

Introduction. The complication of the spacecraft payload requires the use of non-standard circuits. The analysis of scientific and technical publications shows that there is no formalized methodology for spacecraft energy-converting equipment designing. Reviewed publications consider some design algorithms taking into account one (efficiency) or two criteria (efficiency, weight and size characteristics). At the same time, the issues of ensuring trouble-free operation of energy-converting equipment are not sufficiently considered which leads to rejection of most part of proposed circuitsolutions and reduces developer efficiency.
 
 The research purpose is to form a spacecraft energy–converting equipment designing algorithm, taking into account the reliability, efficiency and relative power coefficient requirements.
 
 Materials and methods. The main provisions of the electrical circuit theory and the theory of technical systems reliability were used. All calculations were carried out in Mathcad 15.0.
 
 Research results. The article step-by-step discusses the design process using the example of boost and buck voltage converters. It is shown that taking into account the reliability requirements leads to a decrease of weight and size indicators (due to the additional mass of redundant elements) and efficiency (due to power losses on redundant elements). Converters with an AC-current node based on a double active bridge (active front end bridge inverter) and add-voltage circuits are considered. It can be seen that the use of converters with AC-current node in spacecraft energy-converting equipment is complicated because of low reliability or high weight and size meters.
 
 Conclusions. A converter circuit must ensure operation in the event of a single failure of a random power element. At the same time, scheme with a minimum number of power elements have the greatest prospects for application. A converter energy characteristic must be evaluated after ensuring the reliability.

Linear generator for power supply to on-board consumers of high-speed magnetically levitated carriages

Background: Maglev transport is a promising mode of transport that can provide passenger and freight transportation at speeds of up to 400-500 km/h, and in the longer term – up to 1000 km/h. Active research in this area is being conducted in China, Japan, and the USA. Currently, in China and Japan, speeds of 450-500 km/h have been achieved for commercial transportation, and promising programs have been adopted for the construction of high-speed maglev tracks and the creation of rolling stock. At such speeds, one of the pressing problems is the problem of contactless energy transfer for on-board consumers located on the carriage, because it is very difficult to ensure reliable contact current collection at speeds of 450-500 km/h and above.
 Aim: development of the design, calculation and analysis of the characteristics of a linear generator of electrical energy for contactless power transfer to the moving crew of high-speed magnetically levitated transport.
 Materials and methods: to calculate the external magnetic field of the linear generator inductor and the EMF induced in the receiving coil of the crew, methods of electromagnetic field theory and electrical circuit theory were used; calculation algorithms are implemented in the Visual Basic for Applications software environment.
 Results: a design was proposed and the calculation of the external magnetic field of an inductor with transposition of conductors was performed; to increase the EMF induced in the receiving coil of the crew, it is proposed to give the receiving coil a double 8-shape; the most rational inter-circuit distance of the linear generator inductor has been established; the nature of the change in the magnetic flux penetrating the receiving coil when the vehicle moves, and the magnitude of the emf induced in the receiving coil are determined.
 Conclusion: the results can be used in the development of rolling stock for promising high-speed maglev transport systems.

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.