Electrical Engineering and Power Engineering

Estimation of the minimum level of higher harmonics in the single-phase-to-ground fault current in compensated 6–10 kV networks

A. E. Shamrai — 2025-12-26

Purpose Development of a model for a compensated 6–10 kV network and a methodology for selecting its element parameters based on estimating the minimum level of higher harmonics in the single-phase-to-ground fault current.

Methodology. To estimate the minimum level of higher harmonics in single-phase-to-ground fault current currents, a generalized model of a compensated 6–10 kV cable network and its constituent elements, implemented in the Matlab system with the Simulink extension package, was used. The generalized model of the compensated 6–10 kV cable network and its element parameters were obtained based on a statistical analysis of data from the power supply systems of cities and industrial enterprises.

Findings. The main requirements for the equivalent calculation scheme of a 6–10 kV cable network for estimating the minimum level of higher harmonics in the single-phase-to-ground fault current were formulated, and the ranges of variation and average values of its parameters were determined. The developed mathematical model of the 6–10 kV cable network accounts for the main factors determining the minimum level of higher harmonics in the single-phase-to-ground fault current. Based on the results of computational experiments performed on the mathematical models of 6–10 kV cable networks, it was established that to ensure the required sensitivity, single-phase-to-ground fault protection devices based on the use of higher harmonics must have a primary pickup current of no more than 0.1A.

Originality. A model of a compensated 6–10 kV network was developed, which allows clarifying the sensitivity requirements for single-phase-to-ground fault protection systems based on the use of higher harmonics, thereby enhancing their operational efficiency.

Practical value. Based on the mathematical model, a methodology for selecting its element parameters is proposed, which utilizes the estimation of the minimum level of higher harmonics in the single-phase-to-ground fault currents.

Methodology for modeling steady state thermal behavior of current-carrying systems of electrical and electronic apparatus

O.V. Blyznіakov — 2025-12-26

Purpose. Develop a procedure for constructing models of the stationary thermal behavior of current-carrying systems of electrical and power electronic apparatus.

Methodology. The development of the procedure was carried out using methods of analysis and synthesis of current-carrying systems of apparatus, as well as classical methods to solve differential equations.

Findings. Structural analysis of the current-carrying systems of real electrical and power electronic apparatus has shown that they contain a certain set of typical current-carrying components, namely, conductors of invariable cross-sectional area (rods of a certain length or semi-infinite ones); contacts of various types, power semiconductor devices. These components have a certain mathematical model that establishes their boundary parameters: temperatures and heat flows in a stationary thermal behavior. Using the property of temperature field continuity, it is possible to construct a mathematical model of a current-carrying system of a rather complex structure, which contains the foregoing current-carrying components.

Originality. A methodology has been developed for constructing mathematical models of the stationary thermal behavior of current-carrying systems of apparatus that contain various current-carrying components: conductors, contacts, and power semiconductor devices.

Practical value. The proposed methodology enables us to construct a mathematical model of the current-carrying system of the apparatus, which, in turn, makes it possible to determine its stationary thermal behavior with consideration of the system configuration.

PI controller for speed control of separately excited DC motor supplying from dual buck converter

Omar T. Tawfeeq — 2025-12-26

Purpose. The primary objective of this revision is to adjust the speed and overall performance of a separately excited direct current motor by implementing a traditional controller route that incorporates a Proportional-Integral (PI) controller. The objective of the present scheme is to verify the precise functionality of the motor by means of the dynamic regulation of the two input currents, which are sourced from two separate direct current (DC) power supplies. The objective of the present study is to apply the PI controller to achieve stable and effective performance, especially under variable load conditions, thereby reducing oscillations in speed and enhancing the motor's response to dynamic vagaries. This tactic has been demonstrated to enhance the motor's flexibility, rendering it particularly well-suited for scenarios that demand high-precision motion control. The research demonstrates the efficacy of the PI controller in preserving optimal operational parameters, thereby enhancing energy efficiency and system dependability.

Methodology. The design methodology of the Proportional-Integral (PI) controller is based on exact principles, with the aim of improving motor operation by defining the model controller parameters. This method guarantees the optimal system performance by means of successful adjustment of current inputs, with the objective of minimizing fluctuations and enhancing response stability. The tuning procedure involves the selection of appropriate proportional and integral gains, with a view to maintaining a balance between speed control and dynamic flexibility. The efficacy of the PI controller is enhanced by systematic parameter optimization, resulting in improved efficiency, reduced steady-state error, and enhanced transient response. Consequently, the controller is well-suited for applications that demand precise motor control.

Findings. The PI controller design increases separately the excited dc motor stability and regulates its speed.

Originality. This research introduces a modified control routine for a dual buck DC-DC converter, whereby one converter supplies power to the armature motor circuit, while the second provides power to the flux circuit. The originality of the work lies in the application of a devoted control system on the second converter, which has been built to adjust the flux current. It is evident that by controlling the flux current, the controller enhances the magnetic field stability.

Optimization of automatic control systems for DC electric drives using nonlinear correction devices

O.V. Savchenko — 2025-12-26

Purpose of the work. The purpose of this work is to study a nonlinear correction device for an automatic control system for a DC electric drive, which provides an approach to the optimal operating mode according to the criterion of speed and accuracy, while simultaneously determining the stability conditions and limits of the system's performance.

Research methods. The work uses mathematical modeling, the theory of optimal control based on the minimax principle, the harmonic linearization method for stability analysis, as well as numerical methods to determine the optimal parameters of the phase-leading link. Structural diagrams of DC electric drives and models with relay characteristics were used, which made it possible to study the influence of nonlinear correction on the dynamic properties of the system.

Results. In the process of research, a structural diagram of a DC electric drive with a nonlinear regulator, including a phase-leading link and relay elements, was constructed. A method for approximating the optimal control law using the minimax principle is proposed, which ensures minimization of deviations from the optimal regime in a wide range of input amplitudes. Dependencies between the parameters of the phase-leading link and the magnitude of the system error deviation are established, which made it possible to formulate criteria for selecting its time constants. Analytical expressions for estimating the signal switching moment are obtained, the normalized relations between the amplitude and the switching time are constructed, which determine the quality of the control process. It is shown that the proposed nonlinear corrector allows to reduce the time of the transient process and reduce the error magnitude without a significant increase in overshoot. The analysis of the system stability using the harmonic linearization method made it possible to determine the critical values of the gain coefficients and self-oscillation frequencies. It is established that the presence of a nonlinear corrector significantly affects the dynamic characteristics and at the same time narrows the limits of stability. The constructed graphs of the critical gain and self-oscillation frequency depending on the nonlinear link parameter allowed us to determine clearly the areas of stable and unstable operation of the DC electric drive. Thus, the results confirm that the use of a nonlinear correction device provides an increase in the system speed and a decrease in the error, but requires consideration of a compromise between the quality of regulation and the margin of stability.

Scientific novelty. The work substantiates a new approach to the synthesis of DC electric drive control systems based on nonlinear dynamic correction. The application of the minimax principle for approximating the optimal control law is proposed and its effectiveness in a wide range of input influences is shown. For the first time, a comprehensive analysis of the relationship between the parameters of the nonlinear link and the system stability limits is carried out.

Practical value. The results of the work can be used in the design of electric drives operating in modes with high requirements for speed and regulation accuracy. The proposed approaches contribute to the creation of more effective control algorithms that take into account the trade-off between speed, accuracy, and system stability.

Enhancement of mathematical models for AC electromechanical converters

M.D. Hizenko — 2025-12-26

Purpose. Development of mathematical models of electromechanical AC converters invariant to the speed of rotation of the coordinate system using as state variables of electromechanical converters the modules of the resulting vectors of three-phase variables and their phase shifts relative to each other for the development of new structures of automated asynchronous electric drives.

Methodology. Mathematical modeling methods for electromechanical systems, numerical methods for solving systems of first-order differential equations for the development of mathematical models of AC electromechanical converters invariant to the rotational speed of the coordinate system.

Findings. The reviewed mathematical models of electromechanical converters made it possible to reproduce their steady-state and dynamic processes with the same accuracy as models in Cartesian coordinates. The use of phase shifts of the resulting vectors relative to each other as state variables for the electromechanical converter allowed for the derivation of mathematical models in which all variables are limited in magnitude and have constant values in the steady-state mode, regardless of the coordinate system's rotational speed. Studies performed using the proposed models indicate that the vector and circular diagrams, which are traditionally used for analyzing the steady-state modes of electromechanical converters, characterize the angular position of some vector variables with an accuracy of a multiple of 2πK.

Originality. The proposed mathematical model of AC electromechanical converters is invariant to the rotational speed of the coordinate system, which allows the use of the modules of the resulting vectors of three-phase variables and their phase shifts relative to each other as state variables of electromechanical converters.

Practical value. The proposed mathematical models make it possible to obtain the amplitude values of the vector variables, their angular position relative to one another, instantaneous cosφ values (and so on), without additional calculations.

Systematic methodology for calculating transient processes in linear electric circuits by the classical method

D.R. But — 2025-12-26

Purpose. Traditionally, transient calculations by classical method were performed only in linear electrical circuits containing no more than two reactive elements. If the number of reactive elements was three, the problem became significantly more complicated, and with a larger number, the problem could not be solved at all. A systematic methodology for calculating the transient process by the classical method in linear electrical circuits containing several reactive elements is proposed.

Methodology. Methods of integrating ordinary differential equations, matrix methods, computer programming, theory of electrical circuits.

Findings. The paper proposes a systematic method for calculating the transient process in linear electrical circuits containing more than two reactive elements using the classical method. This is achieved by dividing all variables into groups: derivatives of state variables, state variables, and dependent variables. Each group of variables constitutes a separate vector. By matrix transformations, The differential-algebraic equations of state are converted into normal form by matrix transformations. This made it possible to find the roots of differential equations. The constants of integration were also found by matrix transformations.

Originality. In existing textbooks, the classical method of calculating transients in linear electrical circuits is limited to considering circuits containing no more than two independent reactive elements, because with a larger number of reactive elements, the problem becomes dramatically more complicated. This work removes this limitation.

Practical value. A computer program has been developed to calculate the transient process in a linear electrical circuit containing three independent reactive elements. The program can be modified to simulate more complex circuits with more reactive elements. Analytical methods for calculating transients can be used to estimate the error of calculations using approximate methods, such as numerical methods. Analytical methods allow obtaining an exact solution in analytical form, which is described by mathematical expressions. The obtained mathematical expressions of the solution results allow better perform their research.

Analysis of linearization limit conditions and automated synthesis of the output voltage regulator of a PWM-buck converter in MATLAB/SIMULINK

O.A. Plakhtii — 2025-12-26

Purpose. Determination of the transfer function of the output voltage regulation of buck converters as a function of the PWM duty cycle, determination of the constraints and conditions for convergence of transient processes in the linearized and pulsed model of the buck converter, as well as presentation of a method for automated calculation of PI and PID controller parameters using the Matlab/Simulink tool.

Methodology. Electrical theory, automatic control theory, analytical calculations in MathCad and simulation modeling in Matlab.

Findings. The results of the study of linearization and determination of the transfer function of the output voltage regulation of a step-down pulse converter (buck converter) as a function of the pulse duty cycle in pulse-width modulation are presented. The transfer function of a buck converter with PWM is determined and the limitations of this linearization are determined, namely, the condition for the adequacy of the linearized model of the buck converter is the limitation of the input signal value, i.e. the pulse duty cycle in PWM, less than 1. The method of automatic calculation of the parameters of P, PI, PD and PID controllers is presented according to the criterion of forming a transient process of a satisfactory form by using the “PID controller” block in Matlab/Simulink. The presented method of automatic calculation of the coefficients of controllers in the automatic control system (ACS) structures works exclusively with linearized models, and does not allow calculations for pulse and nonlinear models. For the defined linearized model and the corresponding transfer function of the buck converter, the PI coefficients of the output voltage regulator are determined. The results of the analytical calculation of the instantaneous function of the buck converter output voltage as part of the automated output voltage control system, which is obtained by inverse Laplace transformation of the inverse function of the automatic control system, are presented. The results of the modeling of the buck converter output voltage on the linearized model (transfer function) and the simulation model in Matlab/Simulink are also presented. The results of the analytical calculation and the two methods of computer modeling gave identical results, which indicates the adequacy of the linearization performed and the satisfaction of the method of automatic calculation of the regulator parameters according to the criterion of forming a transient process of a satisfactory form according to the parameters of the transient process time and the value of overshoot.

Originality The conditions for convergence of transient processes of the buck converter output voltage regulation in the structures of automatic control systems for linearized and pulsed models have been determined, which allows obtaining a real transient process of the desired form, which corresponds to the previous analytical calculation.

Practical value. The presented transfer functions and the method of automatic synthesis of PID parameters of the output voltage regulator of the buck converter in Matlab/Simulink can be used in the development of power semiconductor converters and allows to simplify the synthesis process of regulators in automatic control systems.