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IMPROVING THE QUALITY OF ELECTRICITY OF A METALLURGICAL ENTERPRISE BY
BALANCING THE INDUCTION LOAD
Tyapin A.
Postgraduate student, Siberian Federal University
Krasnoyarsk, Russia Kinev E.
Candidate of technical sciences, Director Thermal Electric Systems LLC
Krasnoyarsk, Russia
Abstract
The article discusses the features of balancing the regime of a powerful two-phase induction equipment, as a means of improving the quality of electricity. Asymmetrical loading of a three-phase network worsens the power consumption mode and increases losses. When balancing in two phases, in conditions of compensation of the reactive power of the inductors, adjustable capacitive and inductive balancing elements are used. To calculate the changing load mode, a circuit model is constructed in the basis of controlled sources and a modified nodal analysis. The study of current consumption by phases was carried out by circuit simulation, using optimization and building vector diagrams of currents. In practice, in order to increase energy efficiency, it is recommended that the microcontroller mode control system be tuned according to the regulation characteristics.
Keywords: balancing device, induction load, power quality, steady mode, automatic control, vector diagrams, hybrid analysis, mathematical modeling.
Introduction. Powerful unbalanced load dramatically affects the quality of electricity in a three-phase network. At the same time, one of the factors complicating the use of induction heating can be considered the complexity of controlling the electrical modes of power supply systems and induction equipment when using asymmetric power consumers.
The fact is that the power supply of relatively powerful induction devices (ID) is often performed asymmetrically. It happens that their three-phase symmetrical design is either impossible for structural or technological reasons, or impractical for technical and economic indicators. The power of induction devices can range from hundreds of kilowatts to tens of megawatts. At the same time, the voltage in the windings does not exceed the level of standard values for plants distribution networks. Therefore, currents in linear or phase wires reach thousands of amperes. The connection of such powerful loads to a three-phase network causes a long asymmetric mode in currents and voltages, usually characterized by negative sequence currents [1]. The asymmetry of the power supply network sharply worsens the working conditions of electric machines and other equipment, up to accidents, causes additional losses, reduces the wire throughput [2].
In conditions of complete obviousness of the operating modes of the ID, in fear of a deterioration in the quality of the voltage, enterprises often switch from induction to gas heating. Despite the obvious harm to the environment, as well as the high cost of natural gas, gas heating technology has gained some popularity [3]. This is often due to a lack of necessary equipment and
staff qualifications. Often, the feasibility study of decisions taken is carried out without taking into account the components of the compensation for harm from gas burning and the component of energy saving from the use of high-tech control systems [4]. The feasibility study of the decisions made should be solved after overcoming the difficulties in applying effective and accurate calculation methods, as well as building flexible and accurate control systems for the electric modes of inductors.
Formulation of the problem. The article proposes an approach to the analysis and modeling of asymmetric modes of inductors according to three-line circuit diagrams, without using the method of symmetrical components and generalizing the characteristics [1, 2, 5].
The indicated approach to simulations requires detailing the presentation of rather large circuits, including cable sections of the distribution network, power transformers, induction devices, booster transformers, inductors, capacitor banks, frequency converters and other equipment. You may notice that the construction of such a system leads to the creation of models of enormous size, but the capabilities of modern computing tools allow us to solve such problems [6, 7]. Some difficulties of the indicated approach lie in creating a complex of correct, convenient models. Models should have a well-known algorithm of work in a single language space of a circuit simulator [7, 8]. Due to the cumbersomeness of the mathematical description, the symmetry of only a two-phase induction device is shown below and only some results are presented [9, 10].
Solution. The overall level of development of modern modeling systems in electrical engineering and electrical technology, in comparison with the past, seems very high [11, 12]. Improving software in the field of modeling at the turn of 2020 is associated with improving the quality of the interface, since computational methods and algorithms have achieved tremendous efficiency [7]. Specialized software has also reached a high level [6, 12]. However, unresolved applied problems remained in narrow areas [13].
To overcome some difficulties in a detailed representation of asymmetric induction equipment, the author's software was used in the work, which can be replaced by a modern, advanced circuitry simulator. An example of a general view of a single-phase inductor
for heating aluminum ingots is shown in Fig. 1. According to technological requirements, a pair of inductors can be included in the distribution network. When connected to different phases, the induction load becomes two-phase and, in order to equalize the currents consumed by the installation in three phases, usually resort to the mode balancing procedure [14, 15].
A sharp difference in the consumed currents by phases leads to a voltage distortion that significantly exceeds the limits established by GOST and worsens the operating modes of the rest of the workshop equipment [16]. With significant unit capacities of inductors, it is difficult to overestimate the importance of balancing an asymmetric load, and the uniformity of the distribution of power of inductors into three phases ac-uires special relevance.
Fig. 1 Inductors for aluminum extrusion
Power balancing devices usually include special balancing devices (BD) based on static capacitor banks, electromagnetic chokes, frequency inverters and other electronic modules, as well as setting up the power supply system of inductors in a mode close to current resonance [2, 9].
The scheme for including a two-phase induction load in a three-phase distribution network is shown in Fig. 2. Inductors ID1, ID2 are connected between the phases AB and BC and are shunted by the bat1, bat2 capacitor banks. To account for losses in the capacitance, the inclusion of resistors in the model circuit is provided.
Fig. 2 Diagram of a two-phase ID with a balancing element
An inductance or capacitance is used as the balancing devices. Naturally, both balancing elements must be able to regulate, therefore, bends are provided in the throttle. Due to lower losses, the use of a capacitor bank is preferred.
The purpose of the elements C1 and C2 in the local compensation of the reactive power of each inductor by transferring the induction device to a mode close to the resonance of the currents. To adjust the parameters of the device in the course of changing the load mode, an automated control system (ACS) is used. To create an algorithm for the automation, control curves are used that take into account the nature and depth of the load change. In addition to the condition of symmetry of
phase currents, the calculation of the regime in the article is complicated by the technological requirement for the power of inductors. In the calculations, a twofold increase in the current in one of the inductors, relative to the other, should be ensured.
The impedance and reactance of the investigated inductor are equal to rid = 0.039 Ohm; xid = 0.174 Ohm (with L1 = 5.539 10-4H). Natural power factor cos 9n = 0.219; the current in the inductor has a value of Iid = 2130 A. The active power consumed by the inductor is equal to Pid = 177 kW. For the resonance mode at cos 9id = 1, the capacitance of the capacitor bank of the compensating device (C1 = 16183 ^F) was determined
at the beginning of heating at a temperature T = 20°C and the steady-state mode was calculated.
It is possible to recall the condition of resonance of currents in parallel branches (Fig. 2) and show the
Im[Y 31 ] = ImY 32 ],
resonance characteristics during adjustment and load changes in the parameters of the elements.
C< =
L<
R2 + (L <<
(1)
Estimated characteristics are easier to obtain by circuit simulation using controlled models. The results should be taken into account when analyzing the mode of balancing, as well as when describing the sequence of operations in the executable algorithm of the control controller.
The curves of changes in the operating parameters of the ID are shown in Fig. 3 and 4. When changing the depth of load control^ [2, 17], the curves shown inFig.
2,20 0.9
1l.c 1
2,10 0.7
2,05 0,6
2.00 0.5
1.95 0.4
1,90 0,3
•i,kA' ! ! ' ' | _ ■ 1 1 1 1 1 Lt*
• •O^j 1 _ 1 i Jf ii
r---t ~ i i ---)- 1 1 -OsJ IS* t ~ s.
t 1 I ~ t 1 ' 1 ¡SLi'
-¿ft. JT 1 vt 1 i yr - 1 "T-- -i-'c-
-----1. ... 1.
0.2 0.3 0.4 0,5 0.6 ?„
Fig. 3 Adjustment characteristics
0.8
3. It should be noted that the practical range of parameters during heating is relatively small, since the inductor current varies by 8-10 %. The curves shown in Fig.
4, correspond to capacity regulation. Taking into account the internal resistance of the bat1,2 for each inductor, the intrinsic resonance shifts (Fig. 4) with some increase in the capacity of the compensating battery up to 16.2 mF.
Fig. 4 Resonance curves
The unbranched section current is denoted by I(X, C), the inductor current is denoted by Il(X, C), and the capacitor bank current is Ic(^, C). It should be noted that taking into account the increase in the temperature of the equipment, a change in operating parameters is noticeable. For example, taking into account the nonideal reactivity leads to some inequality of the current modules of the inductor and capacitor bank (Fig. 4). In practice, there are fluctuations in the voltage of the network, so the discrepancy between the parameters can be even more significant, and the balancing procedure can slightly move the inductor mode from the resonance of the currents, so the control device must accordingly process the dynamics of the process. In the
algorithm of the control system, some inertia and a region of insensitivity to changes in operational characteristics should be provided. Additional information for describing the balancing procedure is obtained from the vector diagrams (Fig. 7, 8) of the settings of the operating parameters that are generated by the results of mathematical modeling.
As the main calculation method, a modified nodal analysis has been programmed in the software environment for mathematical modeling of induction devices [7, 10, 16]. A generalized expression of a computational method converted to a symbolic region is given below:
yii
Ykk
a
11
Akk
b
kk+1
b
nn
7kk+1
7
7nn
v
17
VkY
I1Z
lnZ
X J ky
X EnZ
(2)
We can briefly dwell on the structure of the elemental basis used to generate circuit models processed by nodal analysis. Most modern circuitry simulators built using a computing core based on modified nodal analysis use a similar basis [11]. Unlike simulators, the
software described here provides direct access to the textual description of the models generated in the ASCII code, by analogy with the Ansys modeling system model files, and to the numerical results of machine analysis.
A simplified mathematical formalization of the elemental basis used in constructing circuit models and modeling is presented below. The description of the idealized capacitive element (Fig. 5, a) is formed in the form of a matrix and presented, either in the time or in the frequency domain, in the form of a symbolic image.
The capacitive element is denoted by the Latin letter C. A schematic image of the element C with the numbering of the connection nodes is shown in Fig. 6 a. The schematic image of the element L with shown in Fig. 6 b.
a b
Fig. 5 Elemental basis of mathematical models
When forming a system of modified nodal equa- dies below for the Y- and Z-branches generated in the tions manually, one should use the capacitance element time domain.
Vm(t ) " Vn(t ) - 1J ic(t )dt = 0 ,
- Vm(t ) + Vn(t )+1J ic(t )dt = 0.
(4)
m 0 0
n 0 0
ic -1 1
1J dt
"Vn(t )" "0"
Vn(t ) = 0
_ ic(t ) _ 0
C
In complex form, the component equations are written similarly
U C = Vm - Vn =-j
'œCic
или
- V + V - j
' m ' n J
■ ic = 0.
œ C
(4)
(5)
Corresponding matrix expressions describing reactive elements in the computational space have dimensions of the second and higher order
m jœ c - jœ c "0"
n - jœ c jœ c _ Vn _ 0
или
0 0 0 0 -1 1
ic 1
-1
j
1
œ c
"Vm " "0"
Vn = 0
ic 0
(6)
m
n
m n
m
n
m
n
c
For the mathematical model of a capacitive element, it can be represented both in the form of a Z-branch (resistance -1//©C) and in the form of a Y-branch (conductivity jœC).
Vm(t ) - Vn(t ) - Ld • iL (t ) = 0,
For modified nodal equations, inductive element dies for Y- and Z-branches are also formed on the basis of component equations.
- Vm(t ) + Vn(t ) + Ld ■ iL (t ) = 0 .
(7)
Bringing the equation into a matrix generalized expression, we obtain a universal stamp suitable for conversion to a hybrid calculation method
m n / ^
0 0 1
0 0 -1
-1 1 Ld dt _
Quite similarly to capacitance, component equations can be formulated in complex form: Ul = ^m - V = j®L • il ИЛИ - Vm + Vn + j®L • iL = 0 .
"Vn(t )" "0"
Vn(t ) = 0
_ iL (t) _ 0
(8)
And, accordingly, get a matrix expression for reactivity
m 1
7 œL 1
œL
J
1
œL 1
œL
V " "0"
0
n IL
0 1 Vm
0 -1 V
1 JœL IL
(10)
n
m
m
m
n
n
L
For the mathematical model of inductance, it is possible to represent both in the form of a Z-branch (resistance jraL) and in the form of a Y-branch (conductivity -1/jrnL). The list of bipolar, three-pole, four-pole circuit elements, models and macromodels in the language basis is described in the literature [8, 11, 18] and is integrated into the software structure. The presented matrix expressions have no special features and are automatically integrated into the general description of the circuit model generated by performing computational procedures.
It can be noted that behind each passive element there is a second or third order model, and a fifth and higher order model corresponds to each controlled source, so the order of the resulting system of equations is very high. However, for machine analysis methods, the dimension of systems of equations is not critical. The circuit model of the induction installation according to Fig. 2 is shown in fig. 6.
In the circuit model (Fig. 6), designs of controlled sources are used to diagnose operational parameters in the steady state, as well as in transition mode, in the analysis of dynamics and phase characteristics. In the same model, if necessary, study the frequency characteristics. Application of the described mathematical support of calculations allows one to obtain numerical arrays of solutions for a set of steady-state modes of induction devices. Despite the linear nature of the analysis problem, to obtain a symmetric distribution of the currents Ii, I2, I3 in phases, for a given ratio of 1/2, the currents of the inductors L4 and L5 (Fig. 6) have to use an iterative calculation.
The number of design options is significant and the approximation to the desired result is performed using the optimization procedure. For two variants of the initial conditions (Il4 = 2Il5, 2Il4 = Il5), two source data files are generated from the model of a two-phase induction installation (Fig. 6).
Fig. 6 Simplified diagram of a two-phase ID model with a balancing inductor
The procedure for solving the circuit optimization problem using executable modules of the application software package [11, 12] can be characterized by the following sequence of manipulations. In the English-language directory of the root directory, group executable, service, command modules, as well as the necessary libraries. In the circuit modeling module, a modified nodal analysis method is programmed based on topological and component equations using sparse matrix densification subsystems, as well as a state variable method for several implicit methods of numerical integration [8].
A genetic algorithm with local search is programmed in the optimization module [25, 27, 28]. A
text file with a description of the model is formed in the ASCII code [19]. The control program is built to solve the problem in several stages. Start of the control module, launches the computing project and imports the model. The analysis module performs the calculation of the i-stage and generates a file with the results of the calculations. File markup allows you to cyclically write and read the results of subsequent steps. At each stage, the results are evaluated in the optimization module, where a new evolutionary calculation task is formed, and the result file is kept open during the entire computing session. The criterion for completing the optimization is the fulfillment of the given condition for the equality of the symmetrized currents [I(ES0 = I(ES2) =
I(ES3)] according to the model (Fig. 6) and the current distribution between the inductors L4 and L5 (Ii and I2 given by the proportion 1/2) )
The results of the optimization calculation of the regime of a two-phase induction installation with a balancing choke in the final version are unloaded in a table
form. The results of the calculation of the first productive stage are presented in the form of a vector diagram in Fig. 7. The calculation was performed according to the model (Fig. 6).
Fig. 7 Vector diagram (VD) of a two-phase ID with a balancing choke
A brief description of the generated vector diagram for the obtained symmetric mode of the two-phase induction installation is presented below.
When using inductive BD, a lagging angle 8 of current Ica is obtained, relative to voltage U№ close to -tc/2. Own losses in the inductor determine the degree of difference of the current angle from 90 degrees. And the losses in compensating capacities determine the difference between the angles ai, 0,2 of the currents of the bati, bat2 from 90 degrees. The diagram is constructed in such a way that in each of the vertices of the symmetrical triangle of linear stresses there are corresponding vector expressions of the Kirchhoff law for the node. The reliability of the mode balancing, with different compensation of the reactive power of the inductors, can be easily checked according to the first Kirchhoff law for any node of the initial circuit (Fig. 2).
The equivalent symmetric mode is characterized by the same phase consumption (Ia = Ib = Ic) with a lagging power factor (9a = 9b = 9c « tc/3). The load of two inductors during balancing by the choke in the obtained version is distributed asymmetrically. In the shown in fig. 2 sequences of switching on the inductors IDi and ID2, the power of the first inductor (element L4 in Fig. 6) is twice the power of the second L5. The
numerical values of the operating parameters are formed in the tables and are also shown in the vector diagram (Fig. 7). According to the VD, the power of the first inductor can be approximately estimated at 0.8 MVA.
It can be noted that the disadvantage of the obtained symmetrical ID mode is the relatively large inductive currents consumed in phases. This corresponds to a relatively small value of the power factor cos 9 = 0.5 of the induction installation, requiring additional compensation. Nevertheless, the goal of balancing the ID during machine search is achieved. With the corresponding replacement of the description of the inductive balancing element L6 in the model (Fig. 6) with the capacitive c6, a new source data file is formed and the next stage of the computational project is executed. The results of the optimization calculation of the two-phase ID mode with a balancing capacitor bank are presented in the form of a vector diagram in Fig. 8.
The vector diagram is generated according to the scheme of a two-phase induction installation shown in Fig. 2 using the expression of the first Kirchhoff law for nodes. The current of the balancing element connected between phases A and c is designated Ica.
Fig. 8 Vector diagram of a two-phase ID with balancing capacity
For a capacitive balancing device (bat), currents in phases acquire a leading angle 8 of current Ica, relative to voltage Uca, close to +rc/2. The supporting vectors for constructing the VD are the reactance currents Ibati and Ibat2. They also have close to +90 degrees, ahead of the angles ai and a2. The angles are fixed relative to the linear voltages Uab and Ubc.
Judging by the diagram, the equivalent symmetric mode of the modified version of the circuit (Fig. 2) is also characterized by the same phase consumption (IA = Ib = Ic C), but with a capacitive power factor (9a = 9b = 9c) of a relatively small value (~0.5). Thus, a symmetric distribution of currents in phases during the optimization search is achieved. When balancing the inductors in a three-phase network with a capacity, the load of two inductors is also distributed asymmetrically. As shown in fig. 2 sequences of switching on the inductors IDi and ID2 the power of the first inductor (Fig. 8) is twice as low as the power of the second.
The reliability of the mode balancing, with different compensation of the reactive power of the inductors, can be easily checked according to the first Kirchhoff law for any node of the initial circuit (Fig. 2).
T - T - T - 0
Tab TL1 TEK1 — 0 ,
T - T - T — 0
Tbc TL2 TEK2 — 0 '
Ta + T ca T ab — 0 , Tc + Tbc-Tca — 0 ,
T
+ Tab -Tbc — 0 .
It should be noted that even in the presence of perfect modeling systems and multivariate calculations, it is not possible to detect a regime with a symmetric current distribution in the circuit of a complex multicom-ponent two-phase installation without using the optimization search procedure. Therefore, when building a real-time AcS, you should use the appropriate software modules for calculating the model mode and optimization. Another possible solution may be the approach to programming the microcontroller for a specific circuit model of the ID and the chosen optimization method.
Conclusion. The article discusses the means of balancing the regime of two-phase induction equipment, designed to improve the quality of electricity in the network. With asymmetric loading of a three-phase power supply system in two phases, adjustable reactive elements are used for balancing. In contrast to the practice of calculating the generalized parameters of the system and symmetrical components, when modeling and tuning the microcontroller control system of the local installation, it is proposed to use the current operational characteristics of regulation. A schematic model is constructed in the basis of a modified nodal analysis. To reduce the complexity of solving the problem, balancing the current consumption in phases was performed by circuit simulation, using optimization and building vector diagrams. The use of simulation and optimization software allows you to calculate the symmetrical modes of other induction plants with an arbitrary nature of the load distribution between the inductors, for varying degrees of reactive power compensation.
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AUTOWAVES IN HIGH ENTROPY COATINGS CuTiZrCrNi
Yurov V.
Candidate of Physical and Mathematical Sciences, Associate Professor, Karaganda State University named after E.A.Buketov,
Karaganda, Kazakhstan Shelpyakov B.
Candidate of Technical Sciences, Associate Professor, Karaganda State University named after EA.Buketov
Karaganda, Kazakhstan Guchenko S.
PhD student, Karaganda State University named after EA.Buketov
Karaganda, Kazakhstan Twardovsky A.
Engineer, Karaganda State University named after EA.Buketov
