Разработка модели переходных процессов в трансформаторе при емкостном характере нагрузки

This thesis deals with the functional behavior of a salient pole synchronous generator during two kinds of short-circuits. In particular, we studied the case of short circuit in the supply of the excitation winding of the synchronous machine when it is connected to an infinite bus and either the rotor speed was absolutely constant, or a simple PI- Controller maintained the synchronous speed equal to the synchronous. Additionally, the case of an internal fault in the stator winding for the two cases mentioned above was investigated. The electromagnetic torque and the magnetic flux density in each case were calculated and studied, as well as the stator and rotor currents, including the damper cage, and the short-circuit current in the faulty loop of the stator winding. Firstly, it is described in detail the way in which the salient pole synchronous generator was modeled and it is analyzed the method by which the faults are modeled in both stator and rotor and the way these faults were simulated, in the finite element program. Additionally, it is presented the way in how the areas of the model are defined, the equations that were solved through finite element software, in order to extract the results, the definition of the boundary conditions and finally it is described the finite element method, which was applied to this specific model. The case of a short circuit in the supply of the field winding while the stator of the synchronous machine is connected to the grid and the rotor speed is held constant and equal to the synchronous one, is examined. During this fault the magnetic flux, the electromagnetic torque and all the stator and rotor currents are measured in detail. Useful conclusions about the behavior of the machine throughout this kind of short-circuit were derived, all the electromagnetic magnitudes were recorded and an assessment of the generator behavior during this transient phenomenon is made. Similarly, the same type of fault is analyzed, but the speed of the rotor is maintained constant through a speed controller. It is observed that the behavior of the machine and all the electromagnetic magnitudes are quite different compared to the previous case. In this dissertation is examined the behavior of the hydrogenerator in the case of an inter-turn short circuit in the stator winding, while it is connected to the grid with a constant rotor speed. Specifically, it is examined the currents in the rotor and the stator winding for a short circuit between turns that belong to the same or to different phases. The short circuit current is calculated and it is presented the way that it affects quantitative and qualitative the stator phase currents. It is also analyzed the damper currents and it is studied their behavior during the short circuit. The speed controller alters the behavior of the synchronous generator and all the electromagnetic magnitudes of this machine are analytically calculated, resulting significant conclusions on how the faulty loop affects these quantities, while it is set out the role of the participating phases in this short-circuit. Finally, a brief comparison of the way that the number of the shorted turns affects the behavior of the simulated machine in the case of an inter-turn stator fault, while it is connected to the grid with a fixed number of the rotor revolutions. Specifically, it is analyzed the stator and rotor currents and the electromagnetic torque, for the cases that the short-circuited turns belong either to the same or to different phases, but with different number of shorted turns. It is concluded that a key role in determining the electromagnetic magnitudes during this fault has the number of the short-circuited turns and not the number of the phases that are involved in the short circuit.

In three-phase electrical networks during the operation of power supply systems, damage to electrical equipment and difficult modes of operation are possible. Damage associated with insulation failure, rupture of wires and cables of power lines, personnel errors when switching, lead to a short circuit between the phases or on the ground. At a short circuit in a closed circuit there is a big current, voltage drop on elements of the equipment increases that leads to the general decrease in voltage in all points of a network and disturbance of work of consumers. Complex modes of operation of electrical networks occur, as a rule, as a result of accidents or after emergency shutdowns of equipment, with subsequent overloads and voltage deviations from the nominal values. And although these modes have been considered acceptable for some time, they create the preconditions for various types of damage and disorders in the operation of power grids. To ensure normal operation of electrical networks and prevent the development of accidents, it is necessary to respond quickly to changes in the mode of operation of the electrical network, immediately separate damaged equipment from serviceable and, if necessary, turn on a backup power supply. These functions are performed by relay protection and automation devices. Principles of operation of relay protection devices. 1. Current protection. Short circuits are accompanied by a sharp increase in current that exceeds the value predetermined by the calculation, which will perform simple relay protection devices that can control the value of currents. Separate the maximum current protection, which acts to disconnect the damaged network element with a time delay and current cut-offs, which operate without a time delay. The difference between them is in the choice of how to ensure selectivity. The currents controlled by the relay protection device can be measured in phases (through current transformers), or individual components of phase currents can be measured (currents of direct, reverse and zero sequences. This method is based on the method of symmetrical components). Current types of protection are divided with control of power direction (directional) and without control (non-directional). Current protection works on the principle of operation not only in case of damage to one of the network elements, but also to adjacent ones. Therefore, current protection is referred to as protection with relative selectivity. 2. Differential protection. The basis of the principle of differential protection is the comparison of homogeneous, instantaneous values at the ends of the protected element of the network (transformer, busbar section, generator, overhead line). Usually compare currents in magnitude and phase. Differential protection by its principle works only in case of damage to the protected element of the network, so it is performed without time delay and differential protection is called protection with absolute selectivity. 3. Remote protection. In the event of short circuits in the electrical network is not only a sudden increase in current, but also a sharp decrease in voltage, ie a decrease in resistance. The advantage of relay protection devices based on this principle is that the resistance to the fault does not depend on the current and voltage, but only on their ratio. This allows protection at short-circuit currents less than the nominal for electrical equipment. Single-phase earth faults account for about 70% of all damage to electrical equipment. According to the Rules of technical operation in the event of a single-phase short circuit to "ground" in 6-35 kV electrical networks, relay protection devices must act either to turn off the equipment or to "signal". At the enterprises with special working conditions and the increased risk of damage of the equipment and defeat of people by action of an electric current protection against single-phase short circuits on the earth operates on shutdown with the minimum endurance of time. Thus, after the analysis of the modes of operation of power supply systems, the importance of using switching devices of relay protection to ensure normal operating conditions of electrical networks and prevent accidents is confirmed. Also, the use of relay protection devices must be justified for each individual electrical equipment according to the principles of operation and characteristics of the proper functioning of the switching apparatus. In case of emergencies, namely single-phase earth faults, 6-35 kV electrical network operation modes and operation of single-phase earth fault protection are performed according to various technical parameters, depending on the type and connection scheme of the neutral of this power system.

The influence of arrangement, dimensions, and magnetic permeability of the magnetic flux shunts on the flux distribution, leakage reactance as well as axial electromagnetic forces acting on the transformer yokes, is studied in this paper using finite elements method and a simple modeling. By using magneto-static analysis and finite element method, the flux distribution in the 2D model of a core-type three phase power transformer was calculated, and then the leakage reactance of the transformer windings is calculated using the magnetic stored energy method. By calculating the leakage reactance, the short circuit current amplitude and therefore the flux distribution in short circuit conditions and axial electromagnetic forces on the transformer windings were obtained. By studying the different models including magnetic flux shunts, the effect of the arrangement, geometric dimensions as well as the magnetic permeability of the magnetic flux shunt on the leakage reactance and the net axial forces acting on the transformer yokes were studied and some interesting results were obtained. It is shown that the variation of these parameters in the transformer model has the significant effect on the leakage reactance and net axial force acting upon the transformer yoke, for instant, for certain value of the magnetic shunt length, the net axial force acting upon yoke has its maximum value.

Under short circuit condition, the oil immersed distribution transformer will endure combined electro-thermal stress, eventually lead to the mechanical damage of the inner winding of distribution transformer, therefore it is necessary to study the short circuit ability of the oil immersed distribution transformer. In this paper, the typical current waveform of the distribution transformer under the short-circuit condition is analyzed theoretically. The short circuit fault simulation model of distribution transformer is built on the MATLAB/Simulink simulation platform, the short circuit waveform of the single phase, double phase and three phase short circuit is obtained. Further on the ANSYS simulation platform, three dimensional solid modeling of the three-phase five column transformer is carried out, the harmonic and transient field are applied to analyze the magnetic field distribution of the key components in distribution transformer under the short circuit condition, the internal cause of large short-circuit force in the winding of the distribution transformer under the short circuit condition is analyzed to certain extent. The results of the modeling and simulation show that the three phase short circuit current is larger than the single-phase and bi-phase short circuit current. Its value is 1.45 times the normal running current, which is the gradual damping asymmetrical short-circuit current. Magnetic induction intensity is in-homogeneous in the circumferential direction of the core column, and the degree of in-homogeneity varies along height. The magnetic density distribution under the short circuit condition is more than 6 times as much as the the normal condition. From the point of view of simulation modeling, short circuit ability of the oil immersed distribution transformer is analyzed, distribution characteristics of short circuit current and magnetic field of oil immersed distribution transformer under short circuit condition have been obtained, the theoretical reference value of the state characteristics and protection measures of oil immersed distribution transformer under the overload condition can be provided.

Introduction (problem statement and relevance). The article describes a physical model of a road train with active drive of semi-trailer wheels. The results of research tests of the physical model are given, with the help of which the adequacy of the mathematical models of dynamics of the road train as a part of a truck tractor and semi-trailer with active wheel drive is evaluated. The purpose of the study is estimation of efficiency of the technical solutions aimed at increase of vehicle passability and maneuverability.Methodology and research methods. In the course of the study the method of analysis of results of tests of the operating active road train scaled mock-up, the method of comparative analysis of the results of mathematical and physical modelling have been used. Scientific novelty and results. The performed studies confirmed correlation of the physical and mathematical modelling results, as well as indicated that the use of physical modelling serves as an efficient method to obtain an objective assessment of operational properties of the designed road train. The article considers constraints and limitations of using a scalable vehicle to study its dynamics. Matters of model parameters validity, conditions for dynamic similarity, and physical modelling results for active road train dynamics are given.Practical significance. Physical modelling of a (full-)scale sample using a scaled model reduces the costs and time when developing an active road train with new technical solutions, and increases reliability of the results obtained through the mathematical and physical modelling.

This paper presents an improved generalized physical model for photovoltaic, PV cells, panels and arrays taking into account the behavior of these devices when considering their biasing existing in direct and reverse modes. Existing PV physical models generally are very efficient for simulating influence of irradiation changes on the short circuit current but they could not visualize the influences of temperature changes. The Enhanced Direct and Reverse Mode model, named EDRM model, enlightens the influence on the short-circuit current of both temperature and irradiation in the reverse mode of the considered PV devices. Due to its easy implementation, the proposed model can be a useful power tool for the development of new photovoltaic systems taking into account and in a more exhaustive manner, environmental conditions. The developed model was tested on a marketed PV panel and it gives a satisfactory results compared with parameters given in the manufacturer datasheet.

The intermediate band (IB) solar cell offers a route to higher efficiency solar cells by inserting a band into the band gap of large band gap material. Theoretically, the open circuit voltage of the IB solar cell is close to that of the high band gap regions, and the current is increased through the addition of the intermediate band. However, experimental results have shown a decrease in the open circuit voltage, and a small increase in the short circuit current. We explain the decrease in Voc, as well as the small increase in Jsc though a thermodynamic and physical model. These models show that both these results are consistent with the absence of multiple quasi-Fermi levels. Because of the importance of realizing multiple quasi-Fermi levels, the definitive proof of this effect is critical in demonstrating the viability of the intermediate band, but show that demonstrated indicators of an intermediate band may be caused by other physical mechanisms. Instead, a key indicator of a quasi-Fermi level separation not explained by non-idealities are the features associated with the intermediate band quasi-Fermi level crossing the intermediate band energy level, demonstrated by shifting peak energies.

This article proposes a new rotor interturn short circuit (RISC) fault analysis model for the electromechanical property study in synchronous generators. The specific novelty of this model lies in two aspects: First, It considers that most generators exist static air-gap eccentricity (SAGE), so it analyzes the RISC fault under normal and SAGE, making the model more versatile, and second, it takes into account not only the short circuit degree, but also the short circuit position, consequently it is more universal. By feeding the number of short circuit turns (denotes the short circuit degree), the angle between the two slots, where the short circuit takes place (denotes the short circuit position) and the detailed parameters of the generator into the model, the developing tendency of the key magnetic flux density (MFD)-based parameters can be conveniently predicted. The advantages of the proposed model primarily lie in the universality and the calculation speed. It can quickly evaluate the generator operating conditions. The phase current and the electromagnetic torque are selected in this article as the representatives of the electrical parameter and the mechanical parameter, respectively. Two-dimensional finite element analysis and experimental studies validate the proposed model.

In this paper, the radial and axial forces due to inrush and short circuit currents on both inner and outer surfaces of low voltage (LV) and high voltage (HV) windings are calculated. Static and dynamic aspects of these forces which are related to the variation of forces versus winding height and time are analyzed. Power transformer in the start-up mode and under short circuit fault is modeled using two-dimensional (2D) time stepping finite element method (TSFEM). This approach leads to the precise determination of the required signals including current, magnetic flux density, radial and axial forces. Calculated forces are analyzed significantly to compare impacts of the mechanical forces due to inrush and short circuit currents on the windings of the transformer. Three-dimensional (3D) TSFEM is utilized to evaluate aforementioned forces and compare with 2D TSFEM results. In the 3D TSFEM, geometrical and physical characteristics of the all components of the transformer, nonlinearity of the core materials and distribution of the primary and secondary windings are taken into account. 2D TSFEM results are verified by 3D TSFEM results.

THE PURPOSE. Consider the issue of the presence of distortions in the form of sinusoidal voltage and current in autonomous electrical power systems with electrical propulsion systems, built on the principle of the unified electric power system. Compare the results of the study of voltage distortion for electrical power systems with electrical propulsion systems of various structures and give recommendations for their application.METHODS. For research, unified electric power systems with DC electrical propulsion systems on the Yeysk ferry and alternating current on the asymmetric icebreaker Baltika are considered. The possibilities of programming with frequency control of modern drives of rudder propellers with AC motors are analyzed.RESULTS. Oscillograms of voltages and currents of generators were obtained using thyristor converters and inverters to control electrical propulsion systems in various modes. Significant ripples and distortions of the sinusoidal voltage and generator currents were noted when thyristor converters are used to power DC propulsion electric motors. Also, small deviations from the sinusoidal form of the ship's network voltage were recorded when inverters were used to control AC propulsion motors as part of rudder propellers.CONCLUSION. The issue of ensuring the quality of electricity produced in autonomous electrical power systems of sea vessels is of great relevance and importance. To ensure the best results, it is advisable to use azimuthing podded drive with AC electric motors, the rotation speed of which is implemented by inverter frequency converters with a DC link.

The article presents the results from investigating the power plant generator voltage circuit segment physical model made using two high-voltage voltage transformers. A possible algorithm for monitoring the state of voltage transformer insulation in the power plant generator voltage circuit, which is intended for predicting insulation malfunctions, is studied on the basis of a physical modeling approach. Malfunctions resulting from a short circuit fault in the high-voltage winding of type ZNOL single-phase instrument voltage transformers with the grounded neutral caused by gradual degradation of their cast insulation are investigated on the physical model. The short circuit fault is modeled by short-circuiting the transformer’s primary winding taps. Also, the effect the short-circuiting of turns in the primary high-voltage winding of one transformer has on the currents in the primary windings and voltages in the secondary windings of both devices is considered. The results from experimental investigation into the electrical characteristics of the generator voltage network segment’s physical model have confirmed that there is a growth of current in the transformer primary winding at a constant output voltage at the secondary winding. This is necessary for validating the algorithm of detecting a short circuit fault development process in the high-voltage winding. It has been experimentally shown that the effect of the instrument transformer output voltage remaining constant in short-circuiting part of primary winding turns with the secondary winding operating in the no-load mode still takes place also when the voltage transformer shifts to operate under nonlinear magnetic core magnetization conditions, as was expected from the numerical simulation results. The results from analyzing the effect the secondary winding load has on the transformer operation mode are presented. A numerical assessment of the effect the load resistance has on the instrument voltage transformer output voltage with taking into account the presence of short-circuited turns in its primary winding has shown that there is a correlation between the measured characteristic of the network phase (phase voltage) and the state of the transformer high voltage winding insulation. This correlation can supplement the list of cases with incorrect operation of relay protection devices.

It is available a phase-coordinate model for the single-phase transformer with mid-tap on the secondary side. This model allows the representation of 120 V single-phase loads on each section of the secondary of the lighting transformer in a three-phase transformer bank that supplies a four wire delta system. However, the available model represents the entire transformer's impedance in the secondary winding. It differed from the traditional equivalent transformer's circuit, which always represents some portion of the impedance in the primary winding. The presented work develops a new phase-coordinate model for the single-phase transformer with mid-tap on the secondary side to be used in Power Flow and Short-circuits programs. The new model is general and adaptable to be used with transformers with interlaced and non interlaced secondary windings. The developed model is proved with examples of the literature showing a good agreement with the available model for the Power Flow Studies, and a great disagreement for the Short Circuit Studies.

Various transformer models can be used to analyze fault conditions occurring in the power system. In this paper, several transformer models and their influence on the fault current course at different types of short circuits are investigated. Therefore, the 3-ph ideal transformer, the 3-ph saturable transformer (with and without saturation consideration), and the label-entered transformer (BCTRAN) were selected to compare the short-circuit current results. Faults such as 1-ph short-circuit, 2-ph metal short-circuit, 2-ph ground short-circuit and 3-ph short-circuit were considered. The results were compared with the methodology given in standard STN EN 60909-0 (33 3020).

In several cases, substations have become incapable of supporting faults due to increase in short-circuit levels. Fault current limiters (FCLs) are a potential solution for this problem. Among several FCL topologies presented in the literature, the saturated iron core superconducting fault current limiter (SIC-SFCL) has shown promising results in real tests in substations. In this context, this article presents the impacts of different kinds of short circuit on the SIC-SFCL device. To reproduce various types of fault, the SIC-SFCL is modeled in a 3-D framework considering both ferromagnetic and superconducting nonlinearities. Moreover, the proposed 3-D finite-element method model can couple the SIC-SFCL to the electric power system, also representing the electrical grid and the protection systems. For this investigation, the dc-bias superconducting coil’s normalized current density and the iron cores’ magnetic flux density are examined in light of different kinds of short circuit. The simulations are compared with measurements in a bench prototype, showing a maximum error of 16.5%. Furthermore, different types of short circuit are investigated and compared, which is possible only using a 3-D model. The highest limitation occurs in the phase-to-phase short-circuit case. In the dc circuit of the SIC-SFCL, the highest transient period happens in the single-phase short circuit. Finally, the phase-to-phase fault presents the highest dc current during the transient.

This paper is concerned with calculating the electromagnetic forces in the windings of distribution transformers with different shapes of coils. The electromagnetic forces as well as the magnetic flux density and their distribution were analyzed and calculated using Finite Element Method (FEM). The Finite Element models of the distribution transformers with non-linear magnetic characteristics for the iron core are built using FEM software "ANSYS". In this paper, the static analysis method is based on two-dimensional models, and these models have been solved by using the formula for the magnetic vector voltage (A). Three types of three-phase distribution transformers were adopted, each with a capacity of 250 kVA and a voltage ratio is 11/0.416 kV. These types of transformers with different shapes of coils are stack core transformer with oval coil, wound core transformer with rectangular coil, and stack core transformer with cylindrical coil. The results obtained from the FEM analysis agreed with the design calculations which depend on the conventional design formulas. The most important contributions of this study are to building two-dimensional models for different types of distribution transformers. Calculating electromagnetic forces in transformers winding during short circuit conditions in different coil shapes. Studding the effect of the shape of the coils on the calculation of the electromagnetic forces in them. This work can save time, effort, and cost for transformer manufacturers in calculating the electromagnetic forces, also using this model for the virtual test leads to avoid the risk, and efforts spent to do the real short-circuit test.