RU2845627C1 - Method of controlling electric mode of arc furnace - Google Patents

Abstract

FIELD: electrical engineering.

SUBSTANCE: invention relates to electrical engineering and specifically to control of electric mode of electric arc furnace. In method of controlling electric mode of arc furnace instantaneous values of alternating currents of electrodes are measured by their number and first derivatives of currents of electrodes in time, as well as instantaneous values of phase secondary voltages of transformer, on the alternating current half-periods of the electrodes, calculating the current lead-to-arc inductance as the quotient from the division of the corresponding phase secondary voltage of the transformer by the value of said first derivative of the electrode current in time, determined at the initial moment of the corresponding half-period of this current, at operational short circuit on electrode determining active resistance R_i i-th phase of current lead to arc, calculating instantaneous values of voltage drop on arcs u_di and instantaneous values of arc resistance of i-th electrode r_di, on load alternating current half-periods determining dynamic characteristics of arc furnace as theoretical dynamic current-voltage characteristic (DCVC) of arc u_di=F(i_i), which is found as joint solution of system of equations, further, determining the arc resistance nonlinearity coefficient and plotting the arc resistance nonlinearity coefficient functional dependence on the arc time constant, then by the instantaneous values of the currents of the electrodes, the voltage drop on the arcs and the resistance of the arcs, constructing the actual DCVC of the arcs, calculating the actual coefficient of nonlinearity of the resistance of the arcs on the half-period as the ratio of the highest instantaneous value of the resistance of the arcs to its least value on the half-period, after that, finding the arcs time constant actual value according to its functional dependence of the arcs nonlinearity coefficient on the time constant.

EFFECT: enlarging functional capabilities of the method for fast control of power mode of arc furnace and improving adjustment accuracy of furnace power controller.

3 cl, 3 dwg, 1 tbl

Description

Field of technology to which the invention relates

The invention relates to the field of electrical engineering, namely to heating by electric discharges, and can be used in controlling the power of arc furnaces.

State of the art

A method for determining the resistance of a three-phase arc furnace is known, described in patent RU No. 2073248 "Method for determining the resistance of the subelectrode and interelectrode volumes and the reactive resistance of the phases of a three-electrode ore-reducing electric furnace" (published 10.02.1997, IPC G01R 27/00), according to which the line currents and phase voltages of a three-phase arc furnace are measured, signals proportional to the sine and cosine components of the first and third harmonics of the line currents, the effective values of the line currents, the sine and cosine components of the first and third harmonics of the phase voltages are isolated, and the inductive resistances of the power supply circuit and the active resistances of the arc are calculated using algebraic formulas.

The disadvantage of this method is that it is based on the assumptions of the uniqueness of the volt-ampere characteristic of the arc, which is approximated by a power series of the third order, which does not reflect the physical processes in the arc and leads to significant errors in determining the inductances and other parameters of the arc mode. The dynamic volt-ampere characteristic (DVAC) of the arc is ambiguous - its ascending branch differs significantly from the descending branch. Therefore, the approximation of the DVAC of the arc by a single-valued function, including a power series of the third order, is obviously incorrect and leads to errors.

A method for determining the time constant and differential resistance of a direct current electric arc is known, described in author's certificate SU No. 755471 "Method for determining the time constant and differential resistance of a direct current electric arc" (published 15.08.1980, IPC B23K 9/10). According to this method, the current of the power source is stabilized by connecting an inductance in series with the power source, a charged capacitor is connected in parallel to the arc, the voltage and current oscillations of the arc are damped, the transient process curve is recorded and the attenuation ratio and the natural frequency of the induced damped oscillations are determined from it, after which the time constant and differential resistance of the electric arc are determined using formulas.

The disadvantages of this method of determining the parameters of the electrical mode of the arc circuit are its low functionality and the inclusion of additional power elements in the arc power supply circuit, which is practically impossible in an operating arc furnace, and making changes to the arc burning mode, which contradicts the main technological task of the arc furnace - the maximum reduction of fluctuations in the electrical mode of the arc.

The closest in technical essence to the proposed invention is the method for monitoring the inductive-arc load mode described in the author's certificate SU No. 1086557 "Device for determining the electrical parameters of the current supply and arc voltages of a three-phase electric arc furnace" (published 15.04.1984, IPC H05B 7/144), in which line currents are measured and, at the moments of their transition through zero, the values of the derivatives of line currents over time and the values of phase voltages are measured, and the inductances of the power supply circuit are determined as the quotient of dividing the said values of phase voltages by the said values of the derivatives of current over time.

The disadvantage of this technical solution is its low functionality due to its inapplicability for dynamic control of the energy regime of an arc furnace in real time.

Disclosure of the essence of the invention

The technical task of the proposed invention is to implement high-speed control of the energy regime of an arc furnace by determining its characteristics in real time, taking into account the electrodynamic processes occurring in it.

The technical result consists in expanding the functional capabilities of the method for high-speed control of the energy regime of an arc furnace.

This is achieved by the fact that in a known method of monitoring the electrical mode of an arc furnace, in which the instantaneous values of alternating currents of the electrodes are measured in the arc furnace by their number and the first derivatives of the electrode currents over time, as well as the instantaneous values of the phase secondary voltages of the transformer, on half-periods of the alternating current of the electrodes, the inductance of the current lead to the arc is calculated as the quotient of dividing the corresponding phase secondary voltage of the transformer by the value of the said first derivative of the electrode current over time, determined at the initial moment of the corresponding half-period of this current, during an operational short circuit on the electrode, the active resistance is determined i -th phase of current supply to the arc according to the formula

Where , - secondary voltages of the transformer of the i -th phase and the current of the i -th electrode in case of operational short circuit on the i -th electrode;

T is the period of alternating current of the electrodes, equal to two consecutive half-periods;

t - time;

calculate instantaneous values of voltage drop on arcs and instantaneous values of arc resistance of the i -th electrode according to the formulas:

Where instantaneous values of voltage drop on arcs and phase secondary voltages of the transformer of the i -th phase;

- the mentioned inductance of the i -th phase of the current supply to the arc;

- instantaneous value of the current of the i -th electrode,

on half-periods of alternating current loads determine the dynamic characteristics of the arc furnace, as the theoretical dynamic volt-ampere characteristic (DVAC) of the arc , which is found as a joint solution to the system of equations:

Where - arc time constant, set in the range from 0.1 to 10 ms,

- theoretical counteracting electromotive force of the arc, then, based on the joint solution of the said system of equations, the coefficient of nonlinearity of the arc resistance is determined as the ratio of the largest instantaneous value of the arc resistance to its smallest value on the half-period of the electrode current and a functional dependence of the coefficient of nonlinearity of the arc resistance on the arc time constant is constructed, then, based on the instantaneous values of the electrode currents, the voltage drop on the arcs and the arc resistance, the actual TWO-DAY arcs are constructed, the actual coefficient of nonlinearity of the arc resistance on the half-period is calculated as the ratio of the largest instantaneous value of the arc resistance to its smallest value on the half-period, after which the actual value of the arc time constant is found based on the said value of the arc resistance of each i -th electrode according to formulas (2, 3):

Where instantaneous values of voltage drop on arcs and phase secondary voltages of the transformer of the i -th phase;

- the mentioned inductance of the i -th phase of the current supply to the arc;

- instantaneous value of the current of the i -th electrode.

Theoretical dynamic volt-ampere characteristic (DVAC) of the arc are found as a joint solution to the system of equations (4):

Where - arc time constant, set in the range from 0.1 to 10 ms,

- theoretical counter-electromotive force of the arc;

by setting the values of the arc time constant in the range from 0.1 to 10 ms and the theoretical counteracting electromotive force of the arc, for example, according to the expression:

Where And - the voltage drop across the arc of the i -th electrode at the maximum value of the electrode current in the positive half-period and, accordingly, at the minimum value of the electrode current in the negative half-period. The specified range of values of the arc time constant corresponds to the arc combustion conditions typical for arc furnaces of various purposes.

Based on the joint solution of the mentioned system of equations (4), a family of theoretical TWO-DAY equations is constructed . On the half-periods of the alternating current of the load, the dynamic characteristics of the electrical mode are determined as the ascending (line C'B'OAfC in Fig. 2) and descending (line CBdOA'C' ) branches of the theoretical dynamic volt-ampere characteristic of the arc (DVAC - solid line). DVAC is constructed in the coordinates of the voltage drop on the arc u _d and the arc current i and the dependences of the resistance arcs from current i -th electrode, similar to that shown in Fig. 2 for one of the values of the arc time constant . The theoretical coefficient of nonlinearity of arc resistance is determined as the ratio of the greatest instantaneous value of arc resistance to its smallest value on the half-period of the electrode current, and the dependence of the coefficient of nonlinearity of arc resistance on its time constant is plotted (Fig. 3).

The highest and lowest values of arc resistance are determined, for example, from a graph of its changeon the half-period of the load current shown in Fig. 2. The highest and lowest values of arc resistanceis also defined as the tangent of the angle of inclination of the rays drawn from the origin of coordinates tangent to the ascending and descending branches of DVAX. In particular, for a positive half-period (the first quadrant in Fig. 2), the greatest value of the arc resistance is taken to be equal to the tangent of the angle of inclination of the ray (dotted line) drawn from the origin of coordinates tangent to the ascending branch of DVAX or (which is the same) equal to the ratio of the ordinate of the pointAto its abscissa. The smallest value of the arc resistance is taken to be equal to the tangent of the angle of inclination of the ray drawn from the origin of coordinates tangent to the descending branch of DVAH or (which is the same) equal to the ratio of the ordinate of the pointINto its abscissa. For a negative half-period (third quadrant), the greatest value of the arc resistance is taken to be equal to the tangent of the angle of inclination of the beam drawn from the origin of coordinates tangent to the descending branch of DVAH or (which is the same) equal to the ratio of the ordinate of the pointA'to its abscissa. The coordinates of the pointA(A') are also determined by the position of the corresponding local maximum of arc resistance (curvein Fig. 2). The smallest value of arc resistance is taken to be equal to the tangent of the angle of inclination of the beam drawn from the origin of coordinates tangent to the descending branch of DVAH or (which is the same) equal to the ratio of the ordinate of the pointB(B') to its abscissa. The coordinates of the pointB(B') are also determined by the position of the corresponding local minimum of arc resistance (curve). The theoretical coefficient of nonlinearity of arc resistance in a half-period is determined as the quotient of dividing the largest instantaneous value of active arc resistance by its smallest instantaneous value.

For half-periods of the electrode current, the actual TWO arcs are constructed based on the instantaneous values of the electrode currents and the instantaneous values of the voltage drop on the arcs, and the actual dependence of the instantaneous value of the arc resistance on the electrode current is constructed. The actual coefficient of nonlinearity of the arc resistance on a half-period is calculated as the ratio of the greatest instantaneous value of the arc resistance to its smallest value on a half-period. Based on the mentioned functional dependence of the theoretical coefficient of nonlinearity of the arc resistance on the arc time constant, the actual value of the arc time constant on a half-period is found, for which the instantaneous value of the electrode currents and instantaneous values of the secondary phase voltages of the transformer were measured.

As an example, Fig. 3 shows a graph of the dependence of the theoretical arc nonlinearity coefficient on its time constant, and the table below shows the values of the inductance of the current supply to the arcs of the industrial arc steel-making furnace DSP-120. The table shows the values of the arc time constant determined by the proposed method.

Table. Determination of the inductance of the circuit at different arc time constants

Time constant Inductance of the circuit Relative error 0.5 ms 1.748⋅10 ^-5 H 2.8% 2.5 ms 1.709⋅10 ^-5 H 0.55% 5.0 ms 1.705⋅10 ^-5 H 0.31%

The control of the arc furnace mode is carried out by determining its dynamic characteristic as the reactive power of the arc of the i -th electrode proportional to the area limited by the actual dynamic TWO-DAY arc , on two consecutive half-periods of the change in the electrode current, with a proportionality coefficient equal to which is calculated using the formula

The indicated area is limited by the ascending and descending branches of the dynamic volt-ampere characteristic of the arc, that is, by the line C'B'OAfCdOA'C' in Fig. 2.

The arc furnace mode is controlled by determining its dynamic characteristic as the reactive power of the i -th phase proportional to the area limited by the graph of the dependence of the instantaneous value of the phase secondary voltage of the transformer on the current of the corresponding electrode on two consecutive half-periods of the change in the electrode current, with a proportionality coefficient equal to which is calculated using the formula

During the melting process, all furnace operation parameters: currents, voltages, resistances, and power and its components continuously change randomly within wide limits and at a changing rate. Monitoring the above dynamic characteristics in real time of arc furnace operation: the nonlinearity coefficient of arc resistance and its time constant, reactive power of arcs and phases - allows optimizing the settings of the automatic power regulator and reactive power compensation system.

Thus, by determining the theoretical dynamic volt-ampere characteristic (DVAC) of the arc , determining the nonlinearity coefficient of arc resistance and constructing a functional dependence of the nonlinearity coefficient of arc resistance on the arc time constant, the proposed method implements control of the dynamic characteristics of an arc furnace - the functional dependence of the nonlinearity coefficient of arc resistance on the arc time constant.

By constructing actual TWO arcs and calculating the actual coefficient of nonlinearity of arc resistance in a half-period, the proposed method implements high-speed control of the dynamic characteristic of an arc furnace - the coefficient of nonlinearity of arc resistance.

Due to the fact that according to the method the actual value of the arc time constant is found according to its mentioned functional dependence on the arc nonlinearity coefficient, the proposed method implements high-speed control in real time of the dynamic characteristic of the arc furnace - the arc time constant taking into account the electrodynamic processes occurring in them. This expands the functional capabilities of the method of high-speed control of the energy mode of the arc furnace and allows to increase the accuracy of the furnace power regulator adjustment.

Calculation on two consecutive half-periods of alternating current of the electrode area limited by the actual TWO arcs, multiplied by a coefficient equal to The proposed method implements high-speed control of the dynamic characteristic of the arc furnace - the reactive power of the arc. This also expands the functional capabilities of the method of high-speed control of the energy mode of the arc furnace and allows symmetrizing the energy mode of the furnace by electrodes.

Due to the fact that on two consecutive half-periods of alternating current the electrode is calculated as multiplied by a coefficient equal to area limited by the graph of the dependence of the instantaneous value of the phase secondary voltage of the transformer on the current of the corresponding electrode, in the proposed method, high-speed control of the dynamic characteristic of the arc furnace - the reactive power of the phases is realized. This expands the functional capabilities of the method of high-speed control of the energy mode of the arc furnace and allows to increase the speed of the furnace reactive power compensation system.

Control of the arc time constant allows to adjust the dynamic characteristics of the automatic power regulator so as to reduce overshoot and eliminate self-oscillations of the electric mode of the arc furnace. Control of the reactive power of arcs and phases allows to adjust the dynamic characteristics of the systems of power symmetry by electrodes and reactive power compensation. As a result, the use of the proposed method will improve the use of the installed power of the transformer, increase the active power and productivity of the arc furnace, improve its electromagnetic compatibility with the power grid.

The use of the invention makes it possible to expand the functional capabilities of the method for high-speed control of the energy regime of an arc furnace.

Claims (14)

1. A method for monitoring the electrical mode of an arc furnace, in which instantaneous values of electrode currents are measured by their number and the first derivatives of electrode currents over time, as well as instantaneous values of phase secondary voltages of a transformer, in half-periods of alternating current of the electrodes the inductance of the current lead to the arc is calculated as the quotient of dividing the corresponding phase secondary voltage of the transformer by the value of the said first derivative of the electrode current over time, determined at the initial moment of the corresponding half-period of this current, in the event of an operational short circuit on the electrode the active resistance is determined i -th phase of current supply to the arc according to the formula: , Where: , - secondary voltages of the transformer of the i -th phase and the current of the i -th electrode during operational short circuit on the i -th electrode; T is the period of alternating current of the electrodes, equal to two consecutive half-periods; t is time; calculate instantaneous values of voltage drop on arcs and instantaneous values of arc resistance of the i -th electrode according to the formulas: Where: instantaneous values of voltage drop on arcs and phase secondary voltages of the transformer of the i -th phase; - the mentioned inductance of the i -th phase of the current supply to the arc; - instantaneous value of the current of the i -th electrode; characterized in that on the half-periods of alternating current the loads determine the dynamic characteristics of the arc furnace as theoretical dynamic volt-ampere characteristic (DVAC) of the arc , which is found as a joint solution to the system of equations: Where: - arc time constant, set in the range from 0.1 to 10 ms, - theoretical counteracting electromotive force of the arc, then, based on the joint solution of the said system of equations, the coefficient of nonlinearity of the arc resistance is determined as the ratio of the greatest instantaneous value of the arc resistance to its smallest value on the half-period of the electrode current and a functional dependence of the coefficient of nonlinearity of the arc resistance on the arc time constant is constructed, then, based on the instantaneous values of the electrode currents, the voltage drop on the arcs and the arc resistance, the actual TWO-DAY arc characteristics are constructed, the actual coefficient of nonlinearity of the arc resistance on the half-period is calculated as the ratio of the greatest instantaneous value of the arc resistance to its smallest value on the half-period, after which the actual value of the arc time constant is found based on the said functional dependence of the coefficient of nonlinearity of the arcs on the time constant. 2. The method according to paragraph 1, characterized in that the dynamic characteristic of the arc furnace is determined on two consecutive half-periods of the alternating current of the electrode as the reactive power of the arc, which is calculated as the area limited by the actual TWO arcs, multiplied by a coefficient equal to 3. The method according to paragraph 1, characterized in that the dynamic characteristic of the arc furnace is determined on two consecutive half-periods of the alternating current of the electrode as the reactive power of the phase, which is calculated as the area limited by the graph of the dependence of the instantaneous value of the phase secondary voltage of the transformer on the current of the corresponding electrode multiplied by a coefficient equal to 1⁄2π.