METHOD FOR VOLTAGE CONTROL IN CHARGE CIRCUIT OF ELECTRIC DISCHARGE INSTALLATIONS WITH TWO CAPACITORS UNDER NONZERO INITIAL CONDITIONS

Purpose. To analyze the transient processes in the charge circuit of electric discharge installations with two capacitors, taking into account the change in the initial conditions of such processes (initial voltage on the capacitors and the initial current in the charge circuit) as well as to develop the method for charge voltage control of such installations using purposeful change of these initial conditions. Methodology. We have applied the concepts of theoretical electrical engineering, the principles of theory of electrical circuits, and mathematical simulation in the software package MathCAD 12. Results. We have obtained analytical expressions and graphical dependencies establishing a quantitative relationship between the value of the maximum charge voltage of an electric discharge installation and the values of the initial voltage on its capacitors and the initial current in the circuit. This allows us to propose the method for the charge voltage control of electric discharge installations with two reservoir capacitors, using a purposeful change in their initial voltages and initial current in the charge circuit. Originality. For the first time, we have found that the charge voltage of the installation can be controlled using two influence mechanisms – either changing the initial current in the charge circuit (by interrupting the transient process of the first capacitor charge at a certain time) or using a nonzero initial voltage on the charged second capacitor. In this case the charge voltage can be varied by 2 times. Practical value. The use of this method makes it possible to obtain discharge pulses of complex shape in the technological load, since the maximum charge voltages of the first capacitor and second one can differ by a factor of 1.5

APPLICATION OF VYSHNEGRADKY'S DIAGRAMS FOR TRANSIENT ANALYSIS IN ELECTRIC DISCHARGE INSTALLATIONS WITH STOCHASTIC LOAD

Purpose. To analyze the transient processes in the discharge circuit of reservoir capacitor of electric discharge installations at a change in the circuit configuration during the discharge as well as to determine the appropriate circuit parameters for which the discharge process described by the third-order differential equation remains a damped oscillatory process. Methodology. We have applied the concepts of theoretical electrical engineering, the principles of theory of electrical circuits, theory of automatic control systems and mathematical simulation in the software package MathCAD 12. Results. We have obtained the analytical expressions and graphical dependencies that allow us to determine a relationship between the value of the element parameters of the discharge circuit of installations with an additional active-inductive chain and the character of the transient discharge process without solving a third-order differential equation. Originality. Using Vyshnegradsky's criteria and their graphical representations in the form of diagrams, we have proposed the procedure for determining the inductance value in additional chain shunting the capacitor of electric discharge installation in order to avoid the undesirable aperiodic discharge transient process in the stochastic load. Practical value. The use of this approach makes it possible to determine the ranges of the expedient change in the additional inductance at different load resistances for the realization of transient process required by the technology – the oscillatory discharge of the reservoir capacitor trough the load

Моделювання та аналіз електротеплових процесів в установках індукційної термообробки алюмінієвої жили силових кабелів

Introduction. The development of the electric power industry is directly related to the improvement of cable lines. Cable lines meet modern requirements for reliability, they are increasingly used. Problem. Currently, power cables with an aluminum multi-conductor core, which requires heat treatment - an annealing process at the stage of the technological manufacturing process, are widespread. This process makes it possible to desirably reduce the electrical resistance of the wire and increase its flexibility. For effective use of induction heating during annealing of an aluminum core, it is necessary to determine the optimal frequency of the power source of the inductor. Considering the long length of the inductor and the large number of its turns, the numerical calculation of the electromagnetic field, which is necessary for calculating the equivalent electrical parameters of the turns of the inductor and its efficiency, requires significant computer resources. The goal is to develop a computer model for calculating electro-thermal processes in an induction plant for heating (up to the annealing temperature) an aluminum core of a power cable moving in the magnetic field of a long multi-turn inductor, as well as obtaining frequency dependences of the equivalent R, L parameters of such an inductor and determining the optimal the value of the frequency of the power source, which corresponds to the maximum value of the electrical efficiency of the inductor. Methodology. The mathematical model was developed to analyze the coupled electromagnetic and thermal processes occurring in a core moving in a time-harmonic magnetic field of an inductor at a constant speed. The differential equations for the electromagnetic and temperature fields, taking into account the boundary conditions, represent a coupled electro-thermal problem that was solved numerically by the finite element method using the Comsol software package. For a detailed analysis of the electromagnetic processes in the inductor, an additional problem was considered at the level of the elementary cell, which includes one turn of the inductor and a fragment of the core located near this turn. Results. According to the results of the calculation of the electromagnetic field in the area of the elementary cell, the equivalent electrical parameters of one turn of the inductor and the entire multi-turn inductor were calculated depending on the frequency of the electric current. The frequency dependences of the electrical efficiency of the inductor were calculated. Originality. Taking into account the design features of the inductor (its long length and large number of turns), the method of multiscale modeling was used. Electro-thermal processes in the core were studied at the macro level, and the distribution of the electromagnetic field and electric current density in the cross-section of the massive copper turn of the inductor was calculated at the micro level – at the level of an elementary cell containing only one turn of the inductor. The frequency dependences of the equivalent R, L parameters of the inductor, taking into account the skin effect, the proximity effect, and the geometric effect, were obtained, and the quantitative influence of the electric current frequency on these effects was studied. Practical value. The dependence of the electrical efficiency of the inductor on the frequency of the power source was obtained and it was shown that for effective heating of an aluminum core with a diameter of 28 mm, the optimal value of the frequency is in the range of 1–2 kHz, and at the same time the electrical efficiency reaches values of ηind = 0.3–0.33, respectively.У роботі досліджено електромагнітні та теплові процеси в установках індукційного нагрівання алюмінієвої жили силових кабелів та умови реалізації технологій її відпалювання. При математичному моделюванні вказаних процесів ураховано такі конструктивні особливості індуктора, як його значна довжина і відповідно велика кількість його витків, що викликало необхідність використати метод мультимасштабного моделювання. При цьому на макрорівні розраховувались електротеплові процеси в жилі, що рухалась у магнітному полі індуктора, а на мікрорівні (тобто на рівні елементарної комірки, що має лише один виток індуктора) визначався розподіл електромагнітного поля та густини електричного струму в перерізі масивного мідного витка індуктора з урахуванням особливостей його конструкції. На обох рівнях у роботі використовувався чисельний метод скінченних елементів, реалізований в пакеті програм Comsol. За результатами розрахунку електромагнітного поля на рівні елементарної комірки, отримано частотні залежності еквівалентних R, L параметрів індуктора із урахуванням скін-ефекту, ефекту близькості та геометричного ефекту. Досліджено кількісний вплив частоти електричного струму на ці ефекти та отримано залежність електричного ККД індуктора від частоти джерела електроживлення. Показано, що для ефективного нагрівання алюмінієвої жили діаметром 28 мм оптимальне значення частоти знаходиться в діапазоні 1–2 кГц, в якому електричний ККД може досягати значень ηind = 0,3–0,33