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13ПРИМЕНЕНИЕ АНАЛОГОВОГО РАСЩЕПЛЕНИЯ ФАЗ В СИСТЕМАХ МОДЕЛИРОВАНИЯ
ИНДУКЦИОННЫХ УСТРОЙСТВ
Тяпин А.А.
аспирант, Сибирский федеральный университет, г. Красноярск
Пантелеев В.И.
д.т.н, профессор, Сибирский федеральный университет, г. Красноярск
Кинев Е. С.
К.т.н., директор, ООО Тепловые электрические системы,
г. Красноярск Первухин М.В.
д.т.н, профессор, Сибирский федеральный университет, г. Красноярск
APPLICATION OF ANALOG PHASE SPLITTING IN INDUCTION DEVICE SIMULATION
SYSTEMS
Tyapin A.,
Postgraduate student, Siberian Federal University
Panteleev V., Professor, Siberian Federal University
Kinev E.,
Ph.D., director of Thermal Electrical Systems LLC
Pervukhin M.
Professor, Siberian Federal University
Аннотация
В статье предложено аналоговое устройство, предназначенное для модификации трехфазной системы напряжений в многофазную. Показана методика и результаты имитационного моделирования многофазных источников в симметричных и несимметричных режимах. Схемное решение предусматривает сохранение синхронизации многофазной системы с трехфазной в реальном времени. Использование виртуального пространства обеспечивает сопряжение аналогового схемного решения с произвольными программно-аппаратными средами моделирования. Отсутствие реактивных элементов в звеньях электронной цепи обеспечивает точность и быстродействие устройства. Режимы схемы исследованы в символической области и отображены на графиках мгновенных характеристик. Представленный модуль расщепления фаз может быть использован в сигнальных и в силовых цепях.
Abstract
The article proposes an analog device designed to modify a three-phase voltage system into a multiphase one. The technique and results of simulation of multiphase sources in symmetric and asymmetric modes are shown. The schematic solution provides for maintaining the synchronization of the polyphase system with the three-phase system in real time. The use of virtual space provides the interface of an analog circuit solution with arbitrary software and hardware simulation environments. The absence of reactive elements in the links of the electronic circuit ensures the accuracy and speed of the device. The modes of the circuit are investigated in the symbolic area and are displayed on the graphs of instantaneous characteristics. The presented phase splitting module can be used in signal and power circuits.
Ключевые слова: Многофазная электрическая цепь, симметричный режим, аналоговые электронные устройства, операционный усилитель, математическое моделирование, схемная модель.
Keywords: Multiphase electrical circuit, symmetric mode, analog electronic devices, operational amplifier, mathematical modeling, circuit model.
Introduction. When creating digital-to-analog models of electromechanical and electronic devices in software simulators, problems are possible when, along with the original three-phase power system, auxiliary multiphase ones are used [1, 2]. In this case, an important condition may be the phase synchronization of separate multiphase sources [3]. Various approaches to the construction of multiphase source circuits are possible. Depending on the chosen modeling system, direct programming of the mathematical model, or the use of circuit modeling tools, is possible. In simulators, the carrier of the program code is a set of virtual models in
the graphical interface. In linear invariant systems, both approaches are equivalent, since the computational errors are insignificant. In the physical simulation of electronic circuits, the results of the study of polyphase devices in simulators are easy to check and confirm empirically.
For harmonic functions, general expressions are valid, which determine the rules for addition and equivalent transformations of vector quantities [4, 5]. For complex voltage amplitudes in a compact form, you can write:
Um = {Re [Um ej(rat+p) ]2 + Im [Um ej(rat+p) ]2 }1/2, Re[U„ ei(rai+p) ] = Re[Um eiraeip ] = Um cos(rat + p)
Im[Um eiia+p) ] = Im[Um eirateip] = Um sin(rat + p)
The construction of a multiphase voltage system is possible by graphical programming of a new system or by modifying the finished circuit, by splitting each phase of a three-phase source into several. The division procedure can be performed using an idealized iner-tialess electronic module [6]. In any case, in the chosen modeling environment, a connected system of vectors is created for sources that simulate sinusoidal functions of time [7, 8].
Formulation of the problem. To interface the modeling technology and hardware equipment of the physical experiment, it is convenient to use the description of the models, formed in a tabular form using the program code. It is necessary to investigate the possibility of using a real electronic device as a means of division virtual signals from multiphase electrical sources. In this case, analog circuitry should be implemented as a set of discrete models encoded in matrix form and processed by numerical algorithms that form the basis for simulators of electrical and electronic circuits.
Solution. The summation of harmonics and vectors in real time can be ensured by using a simple circuit
design, in the form of a device based on operational amplifiers (OA) [9, 10]. Let us consider a circuit solution applied to a linear circuit with an OA, which makes it possible to obtain multiphase voltage systems for a multiple number of phases, for example, a six-phase voltage from a three-phase primary source [11, 12]. A schematic diagram of the device for splitting the phases of the power supply is shown in Fig. 1.
For the condition of maintaining the full functionality of the linear electronic circuit, it does not matter in what form the implementation of the circuit is performed, in analog execution from physical modules, or by using discrete simulation models in the virtual space of the simulator [13]. The circuit is implemented on three inverting adders and allows you to obtain from the reference system of three-phase voltages another system of connected voltages, in the presence of a fixed phase shift + tc/6. If a three-phase symmetric system of EMF eA(t), eB(t), eC(t), modeled by sinusoidal sources Es1, Es2, Es3 operates at the inputs of the device, then at the outputs of the device model (Out4, Out5, Oufc) there is system of stresses md(0, ue(0, uf(0.
The effect of phase splitting is achieved by cross-summing the normalized voltage of one phase and a part of the instantaneous voltage of the other phase. For example, phase A instantaneous input voltage is added
to phase B instantaneous voltage from resistive divider R3/R4.
Fig. 1. Diagram of a device for splitting phases in a three-phase system
If these resistors are the same, then the division ratio is equal to two and with the instantaneous voltage of the source eA(t) = EAm sinrat at the input of the first OA, the sinusoid of the voltage of phase B is summed:
eB (t) / 2 = [eBm (t) / 2] • sin(ra t - 2k / 3).
The summation of voltages at the inputs of other OA is performed in a similar way. Upon transition to the complex plane, the addition of symbolic quantities (vectors) of different phases, conventionally selected unit and half amplitudes, occurs.
eD(t) = sin rat + sin(rat - 2k/3) = 0,866 cos(rat - 2k/3) = 0,866 sin(rat -k/6) ; eE (t) = sin(rat - 2k/3) +1 sin(rat - 4k/3) = 0,866 cos(rat - 4k/3) = 0,866 sin(rat - 5k/12);
eF(t) = sin( rat - 4k/3) + 1sin rat = 0,866 cos rat = 0,866 sin( rat -k / 2).
The addition of the vectors of the three-phase ref- analog solution allows a relatively simple circuit-tech-
erence voltage system according to the cross-linking nical method to obtain a connected multiphase voltage
scheme, in accordance with the written expressions, is system, synchronized with the network, with a dou-
shown in the vector diagram in Fig. 2, a. The use of an bling of the number of phases [14]. With the reverse
sequence of cross-connections, in the second channel of the splitter of phases A, B, C, a system of voltages -D, -E, -F is obtained, which, together with the original D, E, F, forms a six-phase voltage system D, synchronized with the reference, E, F, -D, -E, -F. Using the dual module shown in Fig. 1, a symmetric system with smaller stress shear angles can be obtained.
For a hybrid digital model built in a simulator and decoupled from the network, by analogy with a real three-phase system, you can apply another, for example, a virtual digital reference voltage system [16, 17].
An illustration of such a solution is shown using the example of a five-phase system in Fig. 2, b. The use in the same coordinates of the circuit model shown in Fig. 1, allows you to go to an idealized 10-phase system, reflected by the corresponding vector diagram (Fig. 2, b). If there is an interface, the construction of circuits is done in the graphic field [18]. At the same time, a description of the circuit model is formed in the format of the input language of the schematic and technical modeling system, as shown in table. 1.
Table 1
r 1 (1 5) 100k r 2 (5 6) 100k r 3 (2 4) 1k r 4 (4 0) 1k r 5 (4 5) 100k
r 6 (2 8) 100k r 7 (8 9) 100k r 8 (3 7) 1k r 6 (7 0) 1k r 10 (7 8) 100k
r 11 (3 11) 100k r 12 (11 12) 100k r 13 (1 10) 1k r 14 (10 0) 1k r 15 (10 11) 100k
da 1 (5 0 6) da 2 (8 0 9) da 3 (11 0 12) out 1 (6 0) out 2 (9 0)
es 1 0 1 1 50 0 es 2 0 2 1 50 -120 es 3 0 3 1 50 120 out 3 (12 0) out 4 (1 0)
The solution of systems of high-order linear equations in the used simulator is implemented using algorithms for the reduction of weakly filled matrices [19]. For the numerical solution of systems of nonlinear equations in the time domain, implicit algorithms for the analysis of discrete models of reactivities and non-linearities are used. Iterative calculations are performed in a module programmed using several computational
methods, including Adams-Moulton, Newton-Raphson and Gere [20, 21]. In dynamics, the modeling system makes it possible to solve rather large schemes using the method of state variables in the numerical analysis of equations using the Runge-Kutta method [22]. The order of the formed and solved systems of equations can be quite large and is often determined by several tens of thousands of nodes and branches.
a b
Fig. 2. Representation of multiphase systems on the complex plane
In Fig. 2, and the phase EMF vector - E of the six-phase voltage system is plotted with a dotted line. The number of phases of a polyphase system of voltages obtained from an electronic splitter can be increased with other combinations of cross-connections and other settings. At the same time, in the analytical representation of the source voltages, the possibility of describing the system in a symbolic form is preserved, which makes it possible to apply the method of symmetric components [23, 24]. The presence of adjustable resistors R5, R10, R15 at the input of analog adders DA1 - DA3 provides the ability to change the amplitude of the output voltage, by adjusting the inverter transmission coefficient. In addition, the gain adjustment can be performed with a resistive voltage divider R2/R1, R7/R6, R12/R11.
For dynamic control of the transfer coefficients of inverting adders, it is possible to apply pulse models of parametric two-terminal devices with binary code control, implemented on the basis of resistive matrices [25 - 27]. Depending on the area of modeling, the results are obtained either as a set of established modes, or as
dynamic characteristics [28, 29]. In addition, the author's simulator provides for the study of the system in the frequency domain, with the analysis of the behavior of the models for stability. Instrumental errors of characteristics associated with the imperfection of DA elements are excluded for the proposed virtual device.
The results of modeling the instantaneous characteristics of the circuit mode with one phase splitter according to Fig. 1 are shown in Fig. 3. The instantaneous voltage curve of the first phase of the three-phase reference voltage source is marked with special symbols. For a three-phase system of input EMF of unit amplitude, a model of a three-phase system of output voltages is obtained, with a value of about Um = 0,8 B, with a phase shift by an angle tc/6. Obviously, in the considered circuit model, the phase angles do not depend on the frequency.
This property can be used in the construction of a hybrid software and hardware laboratory complex designed to study the modes of three-phase and multiphase circuits, including those at significant frequencies.
0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8 t, C 2
Fig. 3. Results of representation of three-phase systems in the time domain
To obtain a six-phase voltage [D, E, F, -D, -E, -F] = [D, E, F, G, H, I] use the macromodel circuit shown in fig. 4. Model Model declares the same part of the circuit, which has eight nodes to connect to the three-
phase source model. The macromodel circuit with a three-phase source connected by a star includes two models A2.1 and A2.2 [DA3-3FAZ.lin].
Fig. 4. Structure of a split-phase macromodel
The description of the head module of the circuit with two identical circuits of the phase splitter is presented in table. 2. Since the renumbering is automatic, the seven-node model [DA3-3FAZ.LIN (1 2 3 4 5 6 0)] is possible. The zero node in the header file corresponds to the node number 7 inside the virtual model. Output connection nodes (Out 1, 2, 3) are designed to control the initial system of voltages A, B, C. For the newly
synthesized phases D, E, F, G, H, I, outputs (Out 4-9) are used, and in the adopted numbering, they are indicated in antiphase. The author's simulator is focused on the tasks of modeling power circuits of induction devices. In addition to electromagnetic devices, the description includes macromodels of power inverters with a mathematical or schematic description of the control system.
Table 2
es 1 (0 1) 1 50 0 es 2 (0 2) 1 50 -120 es 3 (0 3) 1 50 120
out 1 (1 0) out 2 (2 0) out 3 (3 0) out 4 (4 0) out 5 (5 0) out 6 (6 0)
out 7 (0 7) out 8 (0 8) out 9 (0 9) model da3-3faz.lin (1 2 3 4 5 6 0)
model da3-3faz.lin (1 2 3 7 8 9) appc 0 0.06 rez 600
Models of electronic multi-pole components are traditional [7, 19]. Modeling tasks are described in batch files in ASCII code. When debugging the solution of complex multi-stage modeling problems, especially in the time domain, the built-in tools of the graphical interface are used. It is preferable to combine the work in the graphics field with the batch mode. Virtual connection of software modules and automatic renumbering of nodes make it relatively easy to change the
circuit configuration [13, 20]. The use of macromodels (Table 2) is convenient for constructing a compact description of circuitry models of complex circuits for multichannel multiphase devices.
The characteristics of the instantaneous voltage of the six-phase system, obtained using two sets of the splitter, are shown in Fig. 5. The characteristics of the first phase of the newly formed six-phase voltage system are highlighted with special symbols.
Рис. 5. Кривые мгновенного напряжения шестифазной системы
The presented device on an op-amp (Fig. 1) is convenient to use in the synthesis of analog macromodels of the control system of IGBT-inverters, in the power supply circuits of metallurgical induction machines [3, 23].
A simplified diagram of an electromagnetic melt stirrer based on a three-phase metallurgical linear induction machine (LIM) of a four-zone design, with windings in a triangle, is shown in Fig. 6.
Fig. 6. Scheme of an electromagnetic stirrer based on a three-phase LIM
Since the inductor is distinguished by significant asymmetry, in addition to electronic components operating in the key mode, in the simulation system, it is necessary to apply a model of an electromagnetic device with inductive couplings. As the results of the study of the electromagnetic field show, the ferromagnetic steel of the core, weighing up to 1 ton, in different sections of the magnetic circuit turns out to be in different degrees of saturation. Due to the uneven distribution of the linear current load (105 A/m), the circuit model has to be idealized to a certain extent. It should be noted that typical inverter power supply circuits in several cases are unsuitable for asymmetrical flat linear induction machines with more than 3 working probes and windings [14, 30]. In such conditions, it is natural to use multiphase inverters and corresponding models. When referring to the systems of circuit simulation of analog digital devices, it may turn out to be quite a suitable solution proposed in the module shown in Fig. 1.
The study of the modes of power circuits with the use of a simulator turns out to be extremely necessary with the complication of the power supply system due to an increase in the number of inductor windings and phase zones, the transition to multiphase power supply, as well as the use of dual power supplies. The issue of using a multiphase transistor inverter with pulse currents as a power supply unit requires a separate thorough study.
An example of circuitry for connecting a power module (1) of a transistor multi-phase inverter used for a six-zone (2) inductor is shown in Fig. 6. The flat inductor LIM, made six-phase, has an increased length and is used mainly in systems for pumping or dosing melt [31], as a rule, at powers not exceeding 50 kW. When modeling the electromagnetic modes of its power supply system, the presented phase splitting module is used, which provides a symmetrical system of connected voltages of the source.
Fig. 7. Connecting the power module of the transistor inverter to the six-zone LIM
Taking into account the current trend in the use of programmable electronics and means of microcontroller control of the power unit, it can be noted that the parameters of a multiphase communication system of voltages of a transistor power supply are subject to a program description. If there is a condition for synchronizing the controller with the industrial network in the technology of building the program code, you can use
the principle of the analog splitting link (Fig. 1) for a discrete numerical model of the control system. It is convenient to use the proposed simulation model of the phase splitter when simulating analog and discrete-analog power supply systems for induction heating equipment [32] and other multiphase induction devices [33]. The presence of adequate macromodels of operational amplifiers in simulators, for example MATLAB and
Simulink and LabVIEW, allows using the proposed circuit directly [13, 16, 18], bypassing the stage of generating component systems of equations [20].
Conclusion. It is advisable to use the proposed device for simulation modeling in hybrid software and hardware systems, where it is necessary to obtain a connected system of multiphase voltages or currents, synchronized with the leading three-phase electrical network, in a schematic and technical way. The advantage of the device can be considered the absence of instrumental errors characteristic of electronic modules built on real operational amplifiers, as well as its speed, since there are no reactive elements in the circuit. For the case of using a microcontroller system during programming, it is necessary to replace the circuitry solution with a model of the system of equations, while maintaining the connection to the network through the complex of sensors of the information-measuring device.
The proposed device can be used both in signal circuits and in power circuits designed to control the modes of analog and digital-analog devices, apparatus, induction machines and electric drives, as applied to any system of circuit simulation.
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РАЗРАБОТКА ТЕХНОЛОГИИ ПРОИЗВОДСТВА ЛЕЧЕБНО-ПРОФИЛАКТИЧЕСКОГО ПРОДУКТА НА ОСНОВЕ РАСТЕНИЯ АМАРАНТ
Фатхуллаев А.,
Кандидат технических наук, доцент Ташкентский государственный аграрный университет,
Искандаров З.С., Доктор технических наук, профессор, Ташкентский государственный аграрный университет,
Абдумаликов И.Р., докторант
Ташкентский государственный аграрный университет,
Сайдуллаева Ю. Т. магистрант
Ташкентский государственный аграрный университет
DEVELOPMENT OF A TECHNOLOGY FOR THE PRODUCTION OF A THERAPEUTIC AND PROPHYLACTIC PRODUCT BASED ON THE AMARANTH PLANT
Fatkhullaev A.,
Candidate of Technical Sciences, Associate Professor Tashkent State Agrarian University, Iskandarov Z., Doctor of Technical Sciences, Professor, Tashkent State Agrarian University,
Abdumalikov I.,
doctoral student Tashkent State Agrarian University, Saydullaeva Yu. undergraduate Tashkent State Agrarian University
Аннотация
Включение лечебно-профилактического продукта на основе амаранта в рацион питания человека, открывает безопасный немедикаментозный путь регулирования функций отдельных систем организма, позволяет максимально удовлетворить физиологические потребности в пищевых веществах людей, страдающих различными заболеваниями, а также ускорит выведение из организма продуктов обмена веществ.
