Wyniki 1-9 spośród 9 dla zapytania: authorDesc:"Andrzej SZAFRANIEC"

Modelowanie matematyczne procesów oscylacyjnych w napędzie elektrohydraulicznym o podatnej transmisji ruchu DOI:10.15199/48.2017.12.42

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Ważnym zagadnieniem analizy układów elektromechanicznych jest uwzględnienie nieustalonych procesów dynamicznych oraz oscylacyjnych [1], [2], [3], [9]. W przypadkach najprostszych, gdy wał napędu traktujemy, jako układ absolutnie sztywny [4], [6], [8], oscylacyjne procesy nieprawidłowo odzwierciedlają rzeczywiste przebiegi procesów fizycznych w napędzie. Związane jest to z tym, że w absolutnie sztywnym układzie mechanicznym niemożliwe jest uwzględnienie procesów rezonansowych oraz stanów bliskich rezonansu (dudnienie drgań), ponieważ w takich przypadkach nie występuje przekształcenie energii potencjalnej w kinetyczną i odwrotnie. Innymi słowami, w absolutnie sztywnym wale a priori niemożliwe jest zastosowanie niekonserwatywnej funkcji Lagrange’a w dziedzinie mechaniki [1]. W pracy niniejszej analizowany jest model matematyczny układu elektromechanicznego obciążonego pompą pionową. Zakłada się, że wał napędu nie należy do długich wałów, a dla zmniejszenia uderzeniowych momentów w napędzie zastosowano sprzęgło elastyczne. Przy takich założeniach do opracowania modelu układu elektrohydraulicznego wykorzystuje się teorię Eulera- Lagrange’a wykorzystując aparat zwyczajnych równań różniczkowych. Celem pracy jest modelowanie matematyczne nieustalonych procesów oscylacyjnych w rozbudowanym napędzie elektromechanicznym o hydrodynamicznym obciążeniu w postaci pompy pionowej w warunkach podatnej transmisji ruchu o parametrach skupionych. Rozwiązanie sformułowanego zadania wykorzystuje interdyscyplinarne podejście w tym zmodyfikowaną zasadę Hamiltona-Ostrogradskiego. Dla zastosowania wymienionej zasady należy opracować rozszerzony, niekonserwatywny lagrangian, drogą formowania czterech elementów tego ostatniego. Następnie wymieniony lagrangian podstawiamy w funkcjonał działania wg Hamiltona-Ostrogradskiego lub bezpośrednio w równania Eulera- Lagrange’a [7]. W pracy niniejszej a priori tworzymy równania stanu obiek[...]

Analysis of transient processes in a susceptible motion transmission pump drive system with asynchronous motor DOI:10.15199/48.2019.05.38

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Electromechanical drives take important place in the national economy. This is because the electromechanical drives execution of various types of complicated tasks, including hydraulic systems with vertical pumps [3], [4], [5], [7], [9]. In most cases, several pumps should be used to perform the tasks performed by the hydraulic system. Movement transmission of asynchronous pumping systems is complicated. The pump set transient states effective analysis requires mechanical sub-system consideration as susceptible system. The transient analysis can be performed as the case of transmissions with lumped parameters or transmission with distributed parameters. Modeling methods are significantly differing in both cases. An important element in modeling the hydraulic system is possibility to divide into two parts. In the first part there is no compensating battery and there are no units which would not comprise battery. The part is presented in figure 1. In this paper, the hydraulic unit mathematical model based on the interdisciplinary variational method [1] is created. This model consists of a vertical pump which is coupled with a deep-bar asynchronous motor with susceptible movement transmission. The movement transmission is implemented on the base of flexible elasticdissipative clutch with mechanical lumped parameters. The clutch transmits torque from the motor to vertical pump blades. The listed drives are parts of the electric unit. The electric unit cooperating with the reactive power compensation battery in the power system. In this case, the transient state processes are analyzed in the electrohydraulic- mechanical unit. This is the main goal of this work. The mathematical model of system In the general case, M drives are considered - figure 1. The mathematical model of the system uses the variation method presented in [1]. The variation of the functional activities should be determined and equate it to zero to obtain [...]

Analiza procesów nieustalonych w układzie napędowym z pompami pionowymi o podatnej transmisji ruchu DOI:10.15199/48.2019.08.06

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Analiza nieustalonych elektromechanicznych procesów oscylacyjnych w złożonych systemach dynamicznych przetwarzania energii jest ważnym aktualnym problemem elektrotechniki stosowanej. Tradycyjne schematy zasilania dla napędów elektrycznych o dużej i średniej mocy są od dawna znane, natomiast w przypadku szczegółowym elektromechaniczne przetwarzania energii jest analizowane w różnych aplikacjach [1-4]. Dlatego każdy konkretny układ napędowy powinien być analizowany za pomocą odpowiedniego modelu matematycznego. Jest całkiem oczywiste, że dokładność charakterystyk elektromechanicznych i elektrycznych układu napędowego zależy od stopnia adekwatności zastosowanych modeli. Tworzenie modeli matematycznych układów napędowych zwłaszcza średniej i dużej mocy zawierają bardzo złożone transmisje ruchu, które zawierają długie wały, różne sprzęgła elastyczne, przekładnie mechaniczne. Wykorzystanie takiej transmisji w jednym modelu matematycznym wymaga zastosowania skomplikowanego aparatu mechaniki stosowanej, opartego na teorii Lagrange'a z wykorzystaniem metod mechaniki analitycznej dla układów dyskretnych, a czasami systemów ciągłych. Należy zauważyć, że nie zawsze jest możliwe z wystarczającą dokładnością określić momenty obciążenia układów napędowych w postaci zaproksymowanych zależności. W takich przypadkach należy stworzyć nowe modele matematyczne uwzględniające rzeczywiste momenty obciążenia badanych napędów elektrycznych. W niniejszej pracy analizowane są stany nieustalone procesów elektromechanicznych w elektrycznym układzie napędowym, składającym się z N pompowych napędów asynchronicznych i M pompowych napędów synchronicznych, a także dodatkowego obciążenia zespołu, które reprezentowane jest przez gałąź obciążenia o charakterze rezystancyjno-indukcyjnym. Zakłada się, że wymienione elementy układu napędowego zasilane są przez uzwojenie wtórne transformatora o nieskończonej mocy. Analiza układu napędowego wymaga zastosowania[...]

Mathematical model of asynchronous pump drive with distributed mechanical parameters DOI:10.15199/48.2018.06.32

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The use of electric drives as of today is practically unlimited. The electric drive analysis should include a description of the phenomena related to: drive motor, system movement transmission, drive mechanism and the electric drive control system. Each of the system components is very important in the context of the task set up for the drive system. The paper proposes mathematical modeling of transient dynamic processes in a drive system, consisting of a deepgroove asynchronous motor, a complex movement transmission with mechanical distributed parameters and a vertical pump. Such systems are widespread in many industrial applications, for example in the water pumping systems for cooling turbine sets in power plants. In case of these drives, it is important that the system movement transmission consists of very long shafts between the motor and the vertical pump. Multiple energy conversion process complicates the analysis electro-mechanic-hydraulic. The process is complicated itself, and there are no mathematical models of vertical pumps integrated in the electromechanical part of the drive system [4], [6], [8], [9], [10], [13], [15]. In order to solve a similar problem at a high theoretical level, it should be assumed that the movement transmission of the elastic-dissipative drive will be analyzed as a continuum with mechanical distributed parameters. Therefore, the main emphasis in the work is put on the analysis of transient processes in the pumping system including long elastic elements. To solve this problem, the interdisciplinary method of variation was used. The method is based on the modification of the Hamilton-Ostrogradski principle [1], [2], [3], [5], [10]. The aim of the work is mathematical modeling of transient processes in complex pumping systems with long elements of flexible movement transmission based on interdisciplinary approaches. Mathematical model of system When analyzing the structure of the syst[...]

Mathematical modelling of transient processes in power systems considering effect of high-voltage circuit breakers DOI:10.15199/48.2019.01.13

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Gas circuit-breakers are used in high-voltage electrical grids [1]. Air-break circuit-breakers are part of some solutions. However, operation of these breakers involves a range of shortcomings, including: the need to operate compressors, considerable noise at the time of commutation, and large size [1]. These defects are absent from circuit-breakers of another type, where operating gas is replaced with sulphur hexafluoride - SF6. Its physical and chemical properties are better than of air since it does not react with materials of the breaker fittings, is not toxic or cause fire hazards. It is far smaller than equivalent air-break circuit-breakers. SF6 circuit-breakers are used both in new power facilities and in modernised power switching stations on a mass scale. ABB circuit-breakers using SF6 are the most common in highvoltage electrical grids.LTB 362-800 (T) E4 high-voltage circuit-breaker by ABB is analysed in this paper, quite common in the European countries. Each phase of the breaker consists of two modules connected in series. Each module comprises two pairs of contacts in parallel, to which capacitors are connected in order to distribute voltage more evenly. It is known [2] the time of arc burning in a circuit-breaker is affected by mechanical processes, in particular, the distance between contacts, dependent on the rate of their disconnection. Note gas pressure in the compression boxes, required to extinguish the arc, is generated only by mechanical means, without extra compression equipment [3]. Such circuit-breakers should have expanded drives to move contacts of the mechanism in order to overcome pressure in the circuit-breaker box, on the one hand, and to ensure necessary rate of contact movement in normal operation of a circuit-breaker. The fact pressure generated operates in the direction opposite to contacts’ movement, which gives rise to parasitic oscillations, is an important point in operation of [...]

Mathematical modelling of transient processes in power supply grid with distributed parameters DOI:10.15199/48.2018.01.05

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One of the key elements of energy systems is long power supply line with distributed parameters. All the power supply line relations are functions of time coordinate vs. spatial coordinate, this enforces use of complicated apparatus of applied mathematics while forming equations of line state, in particular, use of nonlinear differential equations with ordinary and partial derivatives. A very important issue concerning the analysed system is the fact that the power supply line is usually a component of one and only national energy system, which makes it necessary to establish very complicated boundary conditions for integration of telegraphers’ equations showing relations between voltage and current in any point of the power supply line at any moment of time. In most countries, power supply lines transmit direct and alternate current depending on the requirements. Direct current lines are used to transmit electricity to distant places at high rated voltage [3], [9]. However, electricity is transmitted most often using three-phase lines of alternate current [8]. The reason for this is simply the fact that electricity receivers requiring alternate current are most frequently accessible. Paper [4] presents design of mathematical model of two- and threewire power supply line, wherein analysis of processes of high voltage line 500 kV were made. With use of ATPEMTP software, high voltage lines’ breakdowns were studied. Practical approach to analysis of transient electromagnetic states occurring in power supply line are described in paper [6]. The authors present assumptions and requirements concerning modelling of separate elements of electric power systems (the energy system) in an innovative way. This article presents mathematical model of electric power system designed on the basis of interdisciplinary approaches. The main element of the system is power supply line with distributed parameters, linking two local [...]

The mathematical model of the drive system with asynchronous motor and vertical pump DOI:10.15199/48.2018.01.34

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Mathematical modelling of transient electrodynamics processes occurring in complex drive systems is an assignment that has not been completed yet. It is well known that in the aforementioned systems, sophisticated physical processes occur in the course of which electromagnetic energy is transformed into mechanical energy, which is next turned into hydraulic energy. In complex electromechanical-hydraulic high power system, either incorrect or inaccurate description of means of energy transformation may result with drive system failure. This article describes mathematical modelling of transient dynamic processes of system comprising deep groove asynchronous motor which is coupled with vertical pump [10] by means of a fixed shaft. Such system is characterized by multiple transformation of energy, which makes analysis of electromechanical-hydraulic processes a complex issue. The very process itself is complicated by nature. Additionally, no one has yet designed mathematical model of vertical pumps integrated in electromechanical part of drive system [2], [3], [7], [9]. In consequence, in order to complete the above described assignment a comprehensive interdisciplinary knowledge in three scientific fields is required: electrical engineering, applied mechanics and hydrodynamics. For aforementioned complex systems it is recommended to apply interdisciplinary modelling methods, which significantly expands research capabilities [1], [5]. This method uses modified integral Hamilton-Ostrogradsky’s principle by expanding Lagrange function with two components: dispersion forces energy and non-potential energy of external forces. It should be noted that expanded Lagrange function is obtained by analytical method. This article aim is to design a mathematical model of complex drive system comprised of deep groove asynchronous motor coupled with vertical pump, and to analyse transient electromechanical-hydraulic processes. Mathema[...]

Analysis of transient processes in a power supply system of concentrated and distributed parameters based on variational approaches DOI:10.15199/48.2018.12.33

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Application of mathematical apparatus to modelling of electrical power systems is virtually the most effective method. This approach finds extensive applicability in the case of power systems including long supply lines. Such a system generally consists of widely different parts: power plants, switching stations, supply lines, compensation systems, and a number of other elements [1]. Long power supply lines are key parts in electricity processing and transmission. High voltage lines between local power systems constitute inter-system connections. Fault currents, dependent inter alia on capacitances between wires, and leakage currents, which depend on electric charges on wire surfaces (corona discharge), must be considered in these lines. Current in line wires generates an alternating magnetic field that induces along a selfinduction SEM line. In addition, voltage between the line wires is not constant either. To address current and voltage variations along the line, it must be assumed each infinitely short wire section exhibits resistance and inductance, with capacitance and conductance between wires of that section. In other words, the line should be treated as a distributed parameters system [2]. In view of these conditions, use of ordinary and partial differential equations, including the telegraph equation, is recommended for analysis of transient processes in power systems. Their solution is not a problem. Both analytical and numerical methods are employed (D’Alembert’s, Fourier’s, reticulated, and other methods.) Finding boundary conditions for the telegraph equation as parts of the only system of general differential equations of a power system is the most complicated problem in analysis of transient processes in power systems, on the other hand. The theory of applied mathematics says Dirichlet first type, Neuman second type, and Poincaré third type boundary conditions serve to solve boundary probl[...]

Reducing the dissymmetry of load currents in electrical networks 0,4/0,23 kV using artificial neural networks DOI:10.15199/48.2019.11.56

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The problem of the quality of electric energy plays a prominent role in development strategies of virtually every state. In European countries, it is believed that if the electricity losses exceed 7 - 9%, then such a transfer of electric energy is inefficient. Therefore, a need has emerged to develop new methods and measures of reducing the losses and improving the indicators of electric energy quality. Numerous studies on the analysis of voltage up to 0,4/0,23 kV in rural networks operating modes [1 - 3] showed that current dissymmetry is due to of municipal and household workload, most of which consists of casual switching, single-phase power-consuming equipment that is non-uniformly distributed over the phases. Knowledge of current values of asymmetry in a network allows specifying its additional power losses comparing to the symmetrical mode and the possibility of applying measures to reduce the losses [2]. The changing load of single-phase residential consumers of electricity is erratic and it is very difficult to predetermine its value at any given time. Boundaries of load change can only be established with a certain probability [4, 5, 6]. Technical and economic characteristics of the network performance deteriorate sharply in single-ended mode: energy losses increase and the voltage deviation from the nominal [7, 8]. Lifetime of asynchronous motors attached to a network also declines sharply. Furthermore, there are a number of adverse electromagnetic effects, both in the network and in the load. Therefore, losses of active energy, resulting in non-uniformity of phase load lines 0,4/0,23 kV and consumer transformers 6-10/0.4 kV, may increase by more than a third compared with the losses that would have occurred with a uniform load [3]. Analyzing two types of asymmetry, systematic, which is caused by a constant uneven phase load over time, and probable, which is determined by randomly varying loads in time, one fir[...]

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