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Simulation of the saturation process of a current transformer with a load

The article deals with the mathematical basis and simulation of the saturation processes of current transformers with aperiodic components of short-circuit currents. Saturation processes of current transformers can affect the correct operation of the protections. At power plants, in particular atomic ones, the number of current transformers is several hundred with different loads, lengths of supply cables and the implementation of relay protection. At the same time, the determination of the time to saturation is essential for the construction of circuits and principles of construction of relay protection systems and automation of power plants. The dynamic processes in the primary and secondary circuits of current transformers in dynamics are considered in detail. A mathematical description of the dynamic processes of a current transformer in the nominal mode and during a short circuit in its primary circuit is given. The substantiation of the expediency of using the hypothesis of a rectangular magnetization characteristic in simplified calculations of saturation processes is given. The possibility of using the characteristics of magnetization in the test protocols available in practice in the no-load mode to simulate saturation processes has been demonstrated. Simulation of current transformers for the no-load experiment and power supply of the current transformer from the secondary side, as well as during its operation under conditions of a short circuit on the primary side and a known load on the secondary side is carried out. Thus, with the help of a computer experiment, it is possible to take the current- voltage characteristics and transfer them to the model with the saturation of current transformers already in the short-circuit mode. The efficiency of dynamic simulation of current transformers is shown. The software implementation of the model is performed by means of structural simulation in the MatLab package, based on the solution of equations of matrix structures and emulation of parallel computations. It was found that with the adequacy of the model and the real current transformer with the involvement of information from the no-load mode, the determination of the magnetization time from the aperiodic current components from the model is much easier than the analysis by other existing methods. They require detailed design details of the current transformer and the magnetic properties of the steel. Read more...

Modeling the process of self-starting of electric motors for auxiliary needs of a nuclear power plant to accelerate it and minimize various disturbances

The article proposes a solution to the problem of accelerating the processes of self-starting of asynchronous electric motors of pumping equipment with the help of simulation computer modeling tools to reduce the negative impact on the power supply circuit of the auxiliary needs of a nuclear power plant. The features of the run-down transient processes and the interaction of machines of various capacities in the autonomous circuit that occurs after they are turned off, the subsequent transition to a backup power source, and the emerging effects during self-start are considered. It is shown that the most severe mode of such a transition occurs as a result of the operation of automatic switching on of the reserve and disconnection of working power sources by technological protections or actions of operational personnel at the operational level of operating voltage and nominal or close to it load sections. The analysis of emerging modes is carried out using models developed in the MatLab computer mathematics system with a built-in electrical application. The features of the processes of run-down and subsequent self-starting at various favorable and unfavorable moments of time and the magnitude of the mismatch between the voltages of the network and the resulting autonomous circuit are demonstrated. The models make it possible to obtain a reliable mathematical description of the electromagnetic and mechanical processes of motors in a complex electromechanical system of several motors, to measure the instantaneous voltage differences between the network and the run-down circuit, and to predict the optimal time to turn on the backup power source. The results of the studies carried out on the models are the development of recommendations on the technology for monitoring voltage and circuit mismatches for the same phases, the assessment of the root-mean-square deviation of these mismatches and the effective search for the moment of re-enabling the backup source to improve the technological modes of nuclear power plants. Read more...

Neural network analysis method of heat treatment processes of pelletized phosphate ore raw materials

Currently, there is an acute problem of waste disposal of mining and processing plants, which accumulate in significant volumes in the territories adjacent to them and pose a serious threat to the environment. In this regard, the creation of technological systems for processing ore waste and the improvement of their information support represent an urgent area of research. An example of such a system is a complex chemical and energy technology system for the production of yellow phosphorus from waste apatite-nepheline ores. The purpose of the study was to develop a model for collecting data on the parameters of the processes of heat treatment of pelletized phosphate ore raw materials in such a system, as well as a method for identifying dependencies between these parameters. The identification of dependencies in the information support of the yellow phosphorus production system will improve the quality of its functioning in terms of management criteria, energy and resource efficiency. To achieve this goal, the tasks of choosing a mathematical concept for the basis of the method being developed, constructing an algorithm and creating software implementing this method, conducting model experiments were solved. The method is based on the use of deep recurrent neural networks of long-term short-term memory, which have a high generalizing ability and are used in solving problems of regression and classification of multidimensional time sequences, in the form of which, as a rule, the parameters of a chemical and energy technology system are presented. The method is implemented as an application created in the MatLab 2021 environment. The application interface allows you to interactively conduct experiments with various sets of input and output parameters to identify the relationship between them, as well as change the hyperparameters of neural networks. As a result of the application, a repository of trained neural networks is created that simulate the relationships found between the specified parameters of the technological system and can be applied in decision support systems, management and engineering. Read more...

Simulation modeling of the adaptive speed identifier of an induction motor of a sintering machine

By means of simulation computer modeling, an effective variant of constructing an identifier for the speed of an asynchronous motor of an electromechanical system of a sintering machine is analyzed. The mathematical and algorithmic basis of the adaptive speed identifier (ASI) of an induction motor with a squirrel-cage rotor (ACIM) is given. Using the developed mathematical description of ASI with a reference model and using the apparatus of Lyapunov functions, an adequate computer simulation model was created. Compared with the existing methods for constructing identifiers in sensorless asynchronous electric drives, the proposed version of the ASI allows taking into account the discrete nature of the supply voltage of the ACIM at the output of the frequency converter with pulse-width modulation (PWM) of the output voltage and changing a larger number of equivalent circuit parameters. The stability of the speed identification process is provided in a wide range, sufficient to stabilize the speed of the trolleys according to the requirements of the technological process of sintering machines. As a result, the accuracy of speed identification in static and dynamic modes of operation of the electric drive increases. Simulation confirmed the operability of the proposed version of the identifier, proposed options for setting the AIS components. Universal, important for practical application results have been obtained, which allow both to build a high-precision system for identifying the ACIM speed in general and to refine the setting of the coefficients of the proposed version of the identifier in particular. An important property of the developed version of the ASI is its operability without loss of accuracy at near-zero and zero speeds of rotation and close to the nominal load torque on the ACIM shaft. In this regard, the practical application of the developed version, in addition to the drive of the sintering machine, is also possible in high- precision positioning systems for electric drives for various purposes. Read more...

Dynamic simulation modeling of the excitation system of synchronous generators of stationary diesel generator sets for emergency power supply of a nuclear power plant

In the article, using MatLab dynamic simulation modeling, a study was made of the excitation systems of powerful synchronous generators of stationary diesel generator sets, which are the main sources of emergency power supply for nuclear power plants. The optimal structural complexity mathematical model of a synchronous machine in relative units and orthogonal synchronous coordinate system is used. A comprehensive simulation of diesel generator sets was carried out with the reproduction of both the dynamics of the automatic control system for excitation of a synchronous generator and the diesel engine control system. The simulation takes into account the features of starting a diesel generator to accelerate a synchronous machine, its initial excitation from a battery. Particular emphasis is placed on the study of self-excitation modes through a transformer connected to the stator circuit of the generator and a thyristor rectifier with an excitation winding as a load, as well as parallel operation with the power system. As a result, the processes of starting a diesel generator set in idle mode, effective self-excitation, autonomous operation of the generator at idle, and applying a load to the generator up to the values of permissible overload were simulated. The work of all channels of the control system is shown, including the signals of the regulators of the automatic control system and mechanical variables that are inaccessible in practice. The adequacy of the developed model is proved by comparison with a real physical experiment when testing a diesel generator at a nuclear power plant. The possibility of using the model developed in MatLab as a virtual test site for testing a diesel generator set and a computer simulator for specialized engineering personnel of a nuclear power plant is demonstrated. Read more...

Structural modeling of existing and improved control algorithms for thyristor switching devices of uninterruptible power supply units for auxiliary needs of nuclear power plants

The article analyzes the operation of thyristor automatic switching devices for uninterruptible power supply units of nuclear power plants. They are part of the emergency power supply system for auxiliary electrical equipment with a rated voltage of 0.4 kV. In such a reliable power supply system for especially responsible consumers, alternative networks and backup sources are necessarily used. Typically, groups of consumers for auxiliary needs of nuclear power plants are powered from the inverter network, so that in the event of a shutdown of the backup bypass network, these loads continue to be powered by the uninterruptible power supply unit. It incorporates a charger – a controlled rectifier, a battery pack and a transistor inverter. The transition from one network to another in any direction must be “shockless” in order to avoid the operation of the protections of uninterruptible power units and other electrical protections of the reliable power supply system. If there are failures in the algorithms or their irrational organization, the processes of transition between networks may be accompanied by a violation of uninterrupted power supply or phase-to-phase short circuits. A structural simulation model has been created in the MatLab computer mathematics system for testing transition algorithms for various phase shifts of networks and transition directions. The algorithm of transition between networks for uninterruptible power units of one of the manufacturing companies that supplied equipment to nuclear power plants was analyzed. A safer optimal algorithm for controlling network switching with phase-by-phase control of the current drop in the disconnected network is proposed. The proposals are supported by the results of computer simulations. Read more...

Computer program for modeling the technical quality indicators of inductors of linear asynchronous electric motors

The determination of indicators of the technical quality of electric motors, as well as their modeling, are in demand in the organization, final control of the technical quality of products, in the procedures for diagnosing and monitoring the technical condition of electrical equipment during operation. A large role in substantiating the criteria for the technical quality of electric motors and developing methods for their determination is given to computer modeling. Along with rotating electric motors, linear asynchronous electric motors (LAEM) are increasingly being used in technical systems. Criteria and test methods developed for rotating electrical machines are not adequate to the specifics of the LAEM. As applied to LAEM inductors, a method is proposed for assessing the technical quality indicators of three-phase inhomogeneous inductors with a non-uniform distribution of magnetic properties along the magnetic circuit. The method is based on the impulse effects of a voltage source on the LAEM inductor. A mathematical model, an algorithm and a program for modeling the technical quality indicators of LAEM inductors that implement the proposed method have been developed and presented. The program is written using its own interpreted programming language of the Maple software product and requires the user to enter the parameters of an electrical device. At the output, the user automatically receives an image of the Green’s matrix, oscillograms of phase currents based on the results of three experiments, and numerical values of quality indicators. The simulation results indicate that the proposed method can serve as a tool for the technical control of inductors, and also that the developed technical quality criteria, mathematical model, algorithm and program allow modeling and evaluating the technical qualities of LAEM inductors both during final tests and during monitoring the technical condition of the device during operation. Read more...

Mathematical model for the design of linear asynchronous electric motors and its software implementation

Mathematical models are the main tool for the layout design of linear asynchronous electric motors. Existing design models of linear asynchronous electric motors assume that the device is powered from a source of multiphase symmetrical positive sequence current, which excludes from consideration the asymmetry of the inductor phase currents and the associated reduction in traction force. This approach is not flexible enough, since the operation of linear asynchronous electric motors in a wide range of movement speeds assumes a functional relationship between the current asymmetry coefficient and the movement speed. The study developed a mathematical model for design purposes that implements the functional relationship between the current asymmetry coefficient and the speed of movement. The mathematical model represents 13 linear equations linking geometric dimensions, current loads, electromagnetic field characteristics and mechanical forces with the speed of the secondary element of the electric motor. The current load of an electric motor has a variable degree of ellipticity depending on the speed of movement. An algorithmic study of the mathematical model was carried out and corresponding software modeling tools were developed. The proposed program algorithm, containing two subroutines, is implemented using the Maple symbolic computing software package. In order to expand the range of users, the software model is additionally implemented in C++. In this case, the functional dependence of the asymmetry coefficient of the exciting current wave on the speed of movement is implemented in the form of an iterative procedure for the case of connecting the winding of the linear asynchronous electric motors inductor to a source of symmetrical three-phase voltage according to the “triangle” circuit. Using the example of a three-phase linear asynchronous electric motors, the electromagnetic and mechanical characteristics of the electric motor were simulated. It was stated that the influence of current asymmetry on the mechanical characteristics of the linear asynchronous electric motors is small and is expressed in the region of high speeds. This makes it possible, in design tasks for the layout of an electric motor, to use models that involve powering the linear asynchronous electric motors from a symmetrical current source or to introduce a fixed asymmetry coefficient into them. Read more...

Application of mathematical modeling apparatus to the problem of diagnosing the state of the mechanical circuit of an asynchronous electric motor

The research is aimed at improving the reliability of complex technical systems, including a component such as an asynchronous electric motor, by monitoring their current state. The general objective of the study is to substantiate the possibility of using such a factor as the stator current vector, the oscillations of which are taken as an observable parameter, to diagnose a fault in the mechanical circuit of an electric motor. To substantiate the legitimacy of such a decision, a mathematical modeling apparatus was used with a computational experiment. For this purpose, the purpose and conditions for its implementation were preliminarily formulated, which made it possible to obtain a sufficient evidence base. The mathematical model of an asynchronous electric motor is supplemented with pulse load functions in the form of Fourier series, represented by rectangular alternating and constant sign pulses, the repetition frequency of which is equal to the rotational speed of the electric motor shaft. To conduct a computational experiment, a problem-­oriented algorithm and a Maple program were developed. An original feature of the mathematical model, algorithm and program is the linking of the load torque with the angle of rotation of the rotor, which is typical for damaged mechanical circuits of asynchronous electric motors. Using a mathematical model, the effects on a serial asynchronous electric motor of load torque pulses from a damaged bearing are revealed, as well as the effects of torque pulses from periodic impacts occurring in a damaged mechanical circuit. In both cases, oscillations of the modulus of the stator current vector were recorded, coinciding with the rotor rotation frequency. The results of the computational experiment indicate that stator current fluctuations make it possible to reliably judge the state of the mechanical circuit of the electric motor. The research materials can be used by operating organizations to create systems for instrumental monitoring of the current technical condition of a fleet of asynchronous electric motors. Read more...