At the present stage of development the industry is increasingly focusing on the problem of improving power quality. This primarily relates to single-phase loads, causing asymmetry of currents and voltages in the power supply system. It is obvious that a change in consumers' parameter settings and the emergence of new devices, both industrial and domestic, can make it impossible for economic and efficient operation of the entire electrical system and result in the rejection of a number of large industrial facilities projects. Such objects in the electrical system are: electric arc furnace, induction furnace, three-phase uneven loads, welding machines, etc. [1, p. 63].
In systems of power supply and control of the arc steel-smelting furnaces (ASSF) as all majorities of the existing control systems use an electric power expense as key parameter for transition from one stage of melting to another.
In the metal melting in ASSF process necessary to control the power of the arcs by changing the amount of energy introduced into the furnace [2, p. 188]. Active power arc in arc furnaces is adjusted by changing the secondary voltage of the furnace transformer, and at a constant voltage by changing the current in the electric circuit of the furnace. To maintain a phase current of a predetermined value and, accordingly, the arc power system is used automatically move the electrodes. The control system electric mode DSP usually runs a two-tier.
Much attention is paid to energy saving and quality of the electric power that is especially urgent for such power-intensive customers as arc electric furnaces. One of important problems of operation of arc electric furnaces is the asymmetry in distribution of power of an arc on phases leading in the accelerated wear of lining and reduction of average power of the furnace. Depending on an origin asymmetry is subdivided on [3, p. 104]:
– the constructional, caused by asymmetry forms of a short network or unequal parameters of wires. At the same time mutual inductivity and the given pure resistances are various for each phase;
– operational, caused by instability of burning of arcs both frequent collapses, and furnace charge relocation, especially during melting therefore currents of separate phases change from zero (an arc breakaway) and to current of operational short circuit.
Asymmetry of loading of the arc steel-smelting furnace causes appearance on buses of substations of power supply systems of asymmetry of tension that worsens quality of the electric power and leads to decline in production of profitability both electric furnaces, and the customers who are powered from the general with it buses of substations.
In case of design and operation of arc electrical furnace installations there is a need for calculations of asymmetry of currents and tension both for a choice of diagrams of electrical power supply, and for development of actions to symmetry of an operation mode of furnaces. The accounting of asymmetry allows to estimate in a complex processes in case of change of the mode and to select the best energetic mode, to receive more authentic results. Switching on in an electrical circuit of the furnace of reactive impedance of a short network substantially worsens electrical furnaces of characteristics and leads to loading of its sources big reactive power.
The problem of development of highly effective algorithms for calculations of the asymmetrical set modes is urgent in many cases. The carried-out analysis of various approaches to the solution of this task has shown that the most perspective in this area is the method of harmonious balance allowing to carry out calculations taking into account the interference of nonlinear loading and external electric network which is really taking place when results of calculation are adequate to numerical calculation of uniform system of the differential equations describing the alternating current main and nonlinear loading. Calculation is conducted separately on each harmonica with the subsequent use of a method of imposing. At such approach dependences of parameters of elements of electric network on frequency are rather just considered that causes difficulties when using other methods of calculation.
Calculations and the analysis of the asymmetrical operation modes of the furnace are necessary for the decision of many practical tasks: analysis of operation of automatic regulators of power, choice of the best parameter of regulation and creation of the most perfect type of the regulator; a choice of appropriate construction of a short network and development of actions for maintenance of equal capacities of all phases of the furnace; settings of relay protection and automatic regulators of the furnace, check of their sensitivity in case of different types of the asymmetrical short circuits of a circuit; analysis of operating characteristics of the furnace.
In the known classical methods of calculations of three-phase asymmetrical circuits of resistance of each of phases are accepted by the constants which aren't depending on current. Application of these methods for calculation of the asymmetrical circuits with arcs in which not resistance of arcs, but tension on arcs are constant are impossible.
For this diagram it is possible to write the following equations under the second law of Kirchhoff:
(1)
,
where 
; 
; 
— currents in circuit phases;
; 
; 
— conductivities in branches of phases; 
— tension offset of a neutral;
, 
, 
— phase EMFs of idling of windings of the lowest tension of the transformer;
; 
; 
inherent resistances of the current distributor;
, 
, 
− of resistance of arcs of each phase of the furnace.
Besides, for a three-wire three-phase circuit fairly following ratio:
. (2)
«Star triangle» diagrams, «triangle star» and «triangle triangle» when calculating are provided by conversion of the active or passive triangle to the equivalent circuit «star star» (fig. 1).
Let's consider a case when it is necessary to provide an identical operation mode of the furnace on current in phases. From a system of equations (1) and (2) we will express currents in phases through the made tension and resistance of a circuit. Let's enter the following parameters:
, (3)
, (4)
,(5)
Solving jointly the equations (1)-(5) we will receive the following system:
,
,(6)
.
This system of equations allows to calculate the diagram concerning currents in circuit phases.We calculate arc resistance in each phase by these formulas. Further we check the calculated value resistance with the previous value. If a difference of less admissible error, we quit a cycle of check of resistance. We write result in in advance prepared array of results. Further we calculate arc resistance for the following value of current of a circuit. Calculation of the symmetric operation modes for power, tension and resistance of an arc happens on a similar algorithm.
The arc steel-smelting furnaces used in metallurgical industry are characterized as receivers with rezkoperemenny loading. In the course of their operation generation of currents of the higher harmonics, essential asymmetry of tension, throws of reactive power is watched. The specified phenomena lead to oscillations of tension in power lines that negatively affects both operation of other customers of the electric power, and operation of the most arc furnace. Use of the static thyristor compensators (STC) allows to increase throughput of power lines, to restrict temporal overvoltage, to reduce losses, to improve tension curve sinusoidalnost in different operation modes of a network. The filter-compensating circuits) which are set up definitely allow to compensate harmonicas of the higher orders. Generation of reactive power in filter-compensating circuits happens discretely therefore for receiving the smooth regulation of reactive power together with filter-compensating circuits the thyristor and reactor group (TRG) is used. Besides, application of TRG allows to increase stability of system and to damp oscillations of power. Regulation of parameters of system in STC is made incremental, balancing of system there by is carried out. In given work is also considered functional scheme, in accordance with which is realized controlof STC.
The compensation level of reactive power is defined by a voltage amplitude which is compared to the setting value and by means of the PI-regulator the adjusting signal arriving on TRG and filter-compensating circuits is worked out.
The required voltage stabilization level is as a result carried out. The unit of distribution performs function of division of a signal of control into switching on of the corresponding filter-compensating circuits and choice of a necessary angle of regulation of TRG.Determination of parameters of the PI-regulator by a classical method difficult owing to the fact that their variation strongly depends on operation modes of the arc furnace.
In [4, p. 489] it is shown that even for a reduced model of STC considering more than possible combinations of switchings of the reactor and the furnace transformer, the system of equations of electrical and non-linear circuits turns out very difficult and poor-selling in practice.
One of options of implementation of the adaptive PI-regulator. In this regulator by means of a circuit of back coupling are considered as the response characteristics of the thyristor influencing the moment of switching on filter-compensating circuits, and reactive impedance of constant-error behavior of 
, STC defining an angle of regulation of TRG[5, p. 25].
Use of the offered model of system of electrical power supply of ASSF in the presence of STC gives the chance to estimate influence on figures of merit of an electrical network of parameters and operation modes of ASSF, and also to consider own characteristics of a network influencing control algorithms STC. Weakening of influence of not stationarity of the ASSFs parameters on figures of merit of a power line can be reached by creation of system of regulation of STC on the basis of the modern microprocessor technique [6, p. 81].
In this paper for solving these problems were used the theory of electrical circuits, methods, and symmetrical components of phase coordinates, the calculation of probability characteristics and indicators of asymmetry, mathematical and computer models of asymmetric modes DSP operation. In developing the model used Matlab and Simulink package.
For achievement of a goal in a research the following results are received:
– analysis of the various types of short chains and identify the nature of their asymmetry; possible ways to eliminate structural and operational asymmetry;
– developed a mathematical model for calculating the unbalance of currents, voltages and power transfer in phases of three-phase current supply system in electric arc furnaces;
– proposed power system model arc furnaces in the presence of STC on the basis of modern microprocessor technology;
– developed software packages to meet the challenges of research and computer models of asymmetric modes of operation of electric arc furnaces.
References:
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- Kochkin, V. I. Use of static compensators of reactive power on electrical networks of power supply systems and the enterprises / V. I. Kochkin, O. P. Nechayev. — M.: NTs ENAS publishing house, 2002. — 248 pages.
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