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13FOUR-ZONE LINEAR INDUCTION MHD MACHINE WITH POWER FROM THREE-PHASE IGBT-
INVERTER
Tyapin A.
Siberian Federal University, Krasnoyarsk, Russia
Kinev E.
Thermal Electrical Systems LLC, Krasnoyarsk, Russia
Abstract
Linear induction MHD machines with a low-frequency power supply inverter form a complex of electromagnetic mixing of liquid aluminum in smelting furnaces. The article discusses some classification features and characteristic features of four-zone inductors of a longitudinal magnetic field with three-phase power. To calculate the operating parameters of a linear induction MHD machine, a nonlinear multiphase model of a magnetic circuit was used. As a result of an iterative calculation, the distribution of the integral magnetic fluxes in the tooth zone of a flat inductor is obtained, and vector diagrams of electromagnetic regime parameters are constructed. The study shows the main directions of optimization of the low-pole induction machine mode to obtain the best current distribution in the windings and to estimate the equivalent linear current load. According to the results of the analysis, the main tasks and the sequence of stages of their solution were formulated when developing energy-efficient induction MHD machines of a longitudinal magnetic field.
Keywords: Induction MHD machine, inductor of longitudinal magnetic field, electromagnetic stirrer, running magnetic field, multiphase magnetic circuit model, vector magnetic flux diagram, three-phase power supply system, frequency inverter.
For stirring metal melts in furnaces, linear induction machines of transverse and longitudinal magnetic fields are used [1, p.3]. The cost of each technical solution, along with the technological and energy efficiency of induction machines and power sources, is a decisive factor in the decision to modernize production or to develop design solutions for the new construction of smelting furnaces [2, p. 37]. As induction machines for stirring aluminum alloys in mixers and furnaces, in addition to the transverse field inductors, high-tech shortened inductors of the longitudinal field are used [3, p.26]. Among the simplest flat induction MHG machines, two constructive solutions can be distinguished, which determine the type of machine, according to the number of force inducing windings (inducing zones). These design features appropriately characterize the polarity of the inductor and the magnitude of the synchronous velocity of the traveling magnetic field in the melt [4, p.64]. The following designations are used as design parameters in the description:
2p - is the number of poles of the inductor; Z - is the number of teeth of the core; q - is the number of grooves of the core per pole and phase;
a - is the phase zone of the inductor; m - is the number of phases of the multi-phase winding of the inductor. A - working gap.
In the classical induction MHD machine of a longitudinal magnetic field there can be three or four windings (a three-zone or four-zone inductor). In addition, the power supply of induction machines can be provided in a three-phase or two-phase version [5, p.86]. Thus, when developing inductors and evaluating their effectiveness, four main options should be considered for constructing shortened low-pole induction machines of a longitudinal magnetic field.
1. Four-zone inductor with a three-phase power supply.
2p = 4/3, Z = 5, q = 1, m = 3, a = 60°.
2. Four-zone inductor with two-phase power supply.
2p = 2, Z = 5, q = 1, m = 2, a = 90°.
3. Three-zone inductor with a three-phase power supply.
2p = 1, Z = 4, q = 1, m = 3, a = 60°.
4. Three-zone inductor with a two-phase power supply.
2p = 3/2, Z = 4, q = 1, m = 2, a = 90°.
The traditional approach to the development of linear induction metallurgical machines includes a number of stages, among which engineering calculations can be distinguished [2, p.25], the development of winding switching circuits, mathematical modeling and optimization of the electromagnetic field, melt hydrodynamics and thermal calculation, design, manufacturing and test. Each stage is implemented in a specific sequence with the use of appropriate mathematical, software, hardware, technical and other equipment [6, p.50]. Already on the basis of engineering calculation, the basic characteristics of the machine are determined, which are then refined by the results of mathematical modeling of the field [7, p.29]. However, despite careful calculation and the transition to the use of powerful software environments, some integral parameters, such as magnetic waves of the dentate zone, are not readily available for perception, evaluation, and timely adjustment [8, p.69]. Therefore, it seems appropriate, prior to the stage of mathematical modeling of the electromagnetic field, to refer to the calculation and modeling of the induction device by the methods of the theory of circuits. By reviewing the magnetic and electrical equivalent circuit of the inductor and generating the appropriate mathematical models, you can get additional information about the modes, which will allow you to more consciously refer to the evaluation of the differential parameters of a linear induction machine and outline ways to achieve the best result.
This article discusses some results of the calculation of the electromagnetic mode of a linear induction
machine, which has the classification features of a four-zone inductor of a longitudinal magnetic field with a three-phase power supply [3, 5, 8].
A sketch of the design of a flat induction MHD machine in four-zone design is shown in Fig. 1. Four groups of windings 1, designated wl, w2, w3, w4 with
disk double-thread coils of insulated copper bus are located on a core 2 from steel and are separated by teeth 3, which act as magnetic field concentrators. In the inductor circuit implemented AXZCBYXA. The encoding of the circuit characterizes the inverted phase of the inductor [3, p.32].
1 - Wl W2 w3 W4 N \3,
1_ ----- XI VL
|i4
Figure 1
The windings of four-zone induction machines of the simplest configuration can include a star with a neutral wire (Fig. 2, a) or a triangle (Fig. 2, b) in the circuit. There are other ways to include sections of inductive windings, however, their common property is the need
to invert one of the phases to create the desired phase shift a =2^/3, which ensures the condition of low polarity of the shortened machines, similar to splitting the windings into groups.
Figure 2
6
a
Due to the asymmetry of the magnetic system of the shortened inductors of the longitudinal magnetic field, the connection of the windings as a triangle is more preferable. In the triangle provides more stability and the best energy performance. Obviously, when the windings in the star are connected, the amount of current in the neutral wire may be excessive, especially when the steel core is saturated. However, the star connection is forcedly considered as working because it provides the best control characteristics of the inverter, due to the possibility of separate phase control, however, it is accompanied by difficulties in overcoming extreme currents in the neutral due to the constructive
asymmetry of the inductor core. The cause of the asymmetry is the large influence of mutual inductance between the phases and the transfer of power between adjacent windings [9, p.211].
A simplified model of the distribution of dentate magnetic fluxes is shown in Fig. 3, a. The scheme of connection of three-phase windings AZB is implemented. The vector diagram of the magnetomotive forces is shown in Fig. 3, b. The diagram shows the equivalent combination of AYC. Taking into account the additional section of the four-zone inductor, the inverted phase gives the AZBX connection scheme for the standard phase shift a = 2jt/3.
Figure 3
6
a
The transition from a three-zone configuration of a three-phase inductor to a four-zone one can be considered an improvement if the overall dimensions of the process pit at the furnace and the non-magnetic plate allow, since the distribution of the magnetomotive
forces obtained in this case provides a significantly larger raster of toothed magnetic fluxes.
For metallurgical inductors of medium size, the characteristic operating parameters of the inverter can be as follows. Line voltages up to 0,4 kV are ensured
by smooth acceleration of the frequency converter at steady state currents up to 300 Amps with asymmetry up to 50%. A characteristic feature of induction machines of the longitudinal field should be considered extremely low values of the natural power factor [3, p.27]. Most induction machines have a significant inductance. Moreover, with a peak power consumption of 250 kVA inductor of average size, the active power consumed for losses and cravings, often does not exceed 45-50 kW. With the value of cos^ = 0.05 - 0.1 induction load, the frequency converter in the distribution network of an industrial enterprise serves as a source of a huge number of higher harmonics in the spectrum up to the fiftieth and even higher [8, p.70]. Thus, the need to use an isolating transformer inlet of
the inductor, which acts as a filter, becomes quite obvious. In this case, the frequency converter serves as a means of compensating reactive power [10, p.55].
One can notice the characteristic feature of the considered class of MHD machines with three-phase power, which consists in the transformation of the original balanced three-phase system of connected current vectors into a system with pronounced asymmetry. The graphical representation of the sweep of the magnetomotive forces (Fig. 4) makes it possible to understand that a given system with shifts a = 2^/3 turns out to be not only asymmetrical, but also unbalanced, since its cross section at any time does not give zero the sum of the instantaneous values of the functions of time [3, p.31].
Figure 4
The use of the inverted phase in the winding w2 leads to certain consequences that should be taken into account when constructing electromagnetic stirring complexes for melts. One of the significant consequences is an increased level of inductor vibration at a frequency of 1 Hz, as well as increased mechanical forces of currents and fields acting on the power and design elements of a transistor inverter. Presented in Fig. 4 amplitude-phase distribution of the magnetizing forces F1 - F4 is used when programming the multiphase circuit model, discussed below.
During the development of linear induction MHD machines, the main geometrical dimensions of inductors are determined already at the stage of engineering calculation [2, p.81]. At the next step, the electromagnetic field is simulated, the basic operational characteristics are evaluated, and the inductor linear load current
is calculated. As the experience of creating an MI showed, immediately after determining the magnetizing forces of the windings, it is necessary to thoroughly diagnose the electromagnetic mode of a three-phase inductor, evaluate the distribution of power characteristics, which are then relatively easy to optimize by several criteria and get the best distribution of serrated magnetic fluxes, creating the greatest tractive effort in the melt [ 8, p.72].
Analysis of the distribution of the integral magnetic fluxes in the yoke and the teeth of induction MHD machines is conveniently performed using numerical simulation of the multiphase magnetic circuit mode [8, p.70]. A simplified fragment of the spatial circuit model of a nonlinear three-phase magnetic circuit is shown in Fig. 5.
Figure 5
The order of construction of a detailed nonlinear It is possible to briefly discuss the element base of the model of a three-phase magnetic circuit and the deter- computational model [11, p. 121], in which the con-mination of its parameters are considered in [3, 8, 11]. trolled sources of the magnetic field kF serve as a key
link. Their use was made possible thanks to the principle of the formal analogy of electric and magnetic circuits [11, 12]. As a prototype for sources of magnetizing force controlled by magnetic flux, an analogue is used - voltage source [12, p.457], controlled by current (VSCC), the matrix description of which allows integrating it into software environments of widely used circuit simulators. The use of copyright software, which is effectively used for modeling electronic devices, allowed us to construct high-order nonlinear mathematical models into which the circuit components were imported (Fig. 5). An example of a schematic image and a matrix description controlled by the flux of a source of magnetizing force is shown below.
The integration of the matrix description of the controlled source (CS) into the nodal analysis algorithm is performed automatically according to the detailed description of the circuit model in the ASCII code. Naturally, for each new circuit model of an induction installation, it is necessary to form the corresponding computational project, grouping the necessary decision and auxiliary modules in a separate directory, connecting the necessary libraries and using computer-aided computing, for example Fortran [13].
As a means of designing circuit models of magnetic circuits for induction devices, in addition to the resistive element Rm [H-1], four active controlled elements FU, FF, FU, FF are used, similar to the models of the standard element basis of electrical circuits.
Four-pole primary links have the letter designation. FU is a source of magnetic voltage (Fig. 6, a), voltage controlled (analogue of SVCV); FO - a source of magnetic voltage (Fig. 6, b), controlled by a magnetic flux (analogue of SVCF); OU - source of magnetic flux (Fig. 6, c), controlled by magnetic voltage (analogue SFCF); OO - a source of magnetic flux (Fig. 6, d), controlled by a magnetic flux (analogue SFCV). Unfortunately, both the elements described and their electrical counterparts have not found wide application in practice, although it is their capabilities that provide direct access to the numerical values of the regime parameters when modeling the behavior of induction installations in phase space. Apparently the reason for their relatively rare use was the incomplete evidence of mathematical models of controlled sources obtained using component equations and some of the complexity of their interfacing with the traditional method of calculating electrical and magnetic circuits using topological equations.
Below are examples of circuit models and a matrix mathematical model of a controlled source of magnetizing force (analogue of SVCF) in the basis of extended nodal equations. The structure of the description of the controlled source has the following form: [FO <num> g, h, r, n, k]. Indices i, j - denote the input nodes CS, r, n - output nodes CS, k - transfer coefficient.
Schematic images of controlled sources are shown in Fig. 6
Figure 6
The mode of transmission of a controlled source (analogue of SVCF) is determined by the expression:
"2(0 = Vr(t) - Vn(t) = k • ®x(t)
(4)
where: U2(t) is the output scalar magnetic voltage of the source [A], F1 (t) is the instantaneous value of the input magnetic flux of the source [Wb], V(t) is the scalar magnetic potential of the node [A], k = R is the transfer coefficient source is a transient magnetic resistance.
For nonlinear resistive elements, the description of the table-type web-ampere characteristics is provided, allowing only an unambiguous representation of non-linearity, for example, based on the main magnetization curve of electrical or structural steel. Description of the mathematical model used to build an algorithm for analyzing circuits with a controlled source FO. The input
stream is directed from node g to node h, the input magnetic voltage is zero, the output magnetic voltage is directed from node r to node n against the source, the output stream and source of magnetizing force is directed from node n to node r.
Component equations of a controlled source of magnetizing force are:
"2(t) = kR • ^i(t), Vr(t)-Vn(t) = kR • 0i(t), Vn(t) - Vr(t) + kR • 0i(t) = 0, Vh(t ) - Vg(t ) = 0.
The system of extended nodal equations for the controlled source of the magnetizing force FO is made up taking into account the control and controlled branches.
6
a
B
r
g h r n 01 02
g ' 0 0 0 0 1 0 " \Vg(t) 1 \0
h 0 0 0 0 -1 0 Vh(t) 0
r 0 0 0 0 0 -1 Vr(t) 0
n 0 0 0 0 0 1 Vn(t) 0
01 -1 1 0 0 0 0 01(t) 0
02 0 0 -1 1 kR 0 02 (t)_ 0
(5)
The presented expression has no features [12] and is automatically embedded in the general description of the circuit model (Fig. 5) generated when performing computational procedures. It can be noted that behind each controlled source in a multiphase model there is a matrix stamp of the sixth and higher order, therefore the order of the resulting system of equations is quite high. However, for machine-oriented methods of analysis, the dimension of systems of equations is of decisive no
importance [12, p.23]. Multivariate iterative calculation according to fig. 5 of the circuit model made it possible to determine the magnetic fluxes in the teeth and the yoke, which create the pull force of the induction machine in the melt and the loss in the steel core. The results of the simulation of a multiphase magnetic circuit are obtained in the form of tables with numerical data and displayed on a vector diagram, as shown in Fig. 7, a.
Figure 7
6
a
The diagram shows the combination of magnetizing forces and magnetic fluxes of five teeth, creating a raster of about 330 electrical degrees. The result obtained confirms that for the considered type of a low-pole induction machine, with a three-phase power supply, the raster of O1-O5 streams expanded to 11^/12 was obtained. It should be noted that in order to increase the uniform distribution of magnetic fluxes (Fig. 7, b) along the teeth, it is necessary to provide a method for redistributing the linear current load between the windings. The arrangement of the vectors Oh, O21, O31, O41, Osi presented on the vector diagram (Fig. 7, b) is considered quasi-optimal and is obtained by adjusting the magnetizing force of the windings. Increasing the
number of turns or increasing currents in the phases of the inverter create additional magnetizing forces, such as AF2 and AF3, to create optimized values of F20 and F30. More precisely, the settings and angle correction modes 811, 822, 844, 855 are determined after the formation of a set of optimization requirements. At the next stage, may to switch to mathematical modeling of the electromagnetic field using modern software [14].
The block diagram of the transistor frequency converter intended for power supply of induction machines of metallurgical purpose is shown in fig. 8.
Figure 8
Module 1 is a semi-controlled rectifier designed to charge a capacitor battery.
Module 2 is a DC link with a bipolar structure and provides the energy balance of the inverter.
Module 3 is the input power link of the inverter, designed to form a modified multiphase sinusoidal current and control the inductor magnetic field.
Practical measures to develop power supplies for linear induction machines of different configurations should take into account not only the number of phases, but also the actual operational characteristics of the inductors. And first of all it is necessary to take into account the extremely high asymmetry of currents in phases. It should be noted that the results presented here should be considered as a first approximation and a generalized statement of one problem in the development format of an induction MHD machine of the above configuration.
Conclusion. When building energy-efficient induction MHD machines, several interrelated problems should be solved.
Creating an effective winding switching circuit, controlling the number of poles and the speed of a traveling magnetic field should also be considered as a task in the field of research into flat induction machines of a longitudinal magnetic field. The study of the features of the electromagnetic field of an induction machine, as well as the methods of controlling the redistribution of magnetic flux, relates to the field of mathematical modeling and optimization of the inductor magnetic system. Evaluation of the effectiveness of the effect of inductors on the molten metal and the change in its characteristics when the operating characteristics change is the essence of the magnetohydrodynamic problem. In addition, it should be understood that standard three-phase frequency inverters of an asynchronous electric drive are not suitable for supplying metallurgical equipment, the modes of which are sharply asymmetric, extremely reactive and reversible. Therefore, when building complexes of different dimensions intended for electromagnetic stirring of the melt, it is necessary to create a series of economical and reliable power sources for induction machines operating at the edge of
the frequency range, with a different number of phases and various circuitry of windings. Each of the above problems for the whole variety of designs of induction MHD machines of a longitudinal magnetic field must be devoted to a separate article.
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