CN111639440B - Method for constructing ultrahigh-power electric arc furnace model - Google Patents
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- CN111639440B CN111639440B CN202010516489.3A CN202010516489A CN111639440B CN 111639440 B CN111639440 B CN 111639440B CN 202010516489 A CN202010516489 A CN 202010516489A CN 111639440 B CN111639440 B CN 111639440B
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Abstract
The invention relates to a method for constructing an ultrahigh-power electric arc furnace model, which comprises the following steps: step S1, establishing a power balance equation of the ultra-high power electric arc furnace according to the law of energy conservation; step S2, establishing a deterministic arc model of the arc furnace according to the power balance equation of the ultra-high power arc furnace; the method comprises the steps of S3, modulating static arc voltage by adopting a low-frequency chaotic signal generated by an asymmetric nonlinear resistor Chua' S circuit, and constructing an uncertainty model reflecting the randomness of the operation of the electric arc furnace load, and S4, constructing a novel alternating current electric arc furnace simulation model for the research of the low-frequency non-stationary inter-harmonic wave according to the uncertainty model reflecting the randomness of the operation of the electric arc furnace load and the certainty model reflecting the randomness of the operation of the electric arc furnace load. The invention can accurately reflect the operation characteristics of the ultrahigh power electric arc furnace under the actual industrial application, can reveal the emission characteristics of the low-frequency non-stationary inter-harmonic of the ultrahigh power electric arc furnace, and reflects the influence of the operation of the ultrahigh power electric arc furnace equipment on the stability of a power distribution network.
Description
Technical Field
The invention relates to the research field of an ultrahigh-power electric arc furnace, in particular to a construction method of an ultrahigh-power electric arc furnace model for low-frequency non-stationary inter-harmonic research.
Background
With the rapid development of modern arc smelting and ultrahigh power supply technology, ultrahigh power electric arc furnaces are increasingly widely applied in the metallurgical industry. Although the application of the ultra-high power arc furnace can shorten the melting time, improve the production efficiency, reduce the energy loss and save the production cost, the influence of non-stable inter-harmonics and high-power impact generated by the loads on the power quality of the power distribution network is more and more serious. For example, when a certain ultrahigh power electric arc furnace user (100-ton electric arc furnace) is in production, not only can the equipment of a precision casting company connected to the same 35kV bus be damaged, and the generator of a power generation enterprise has the problems of stator vibration, local heating abnormity and the like, but also the problems of frequent starting of multiple sets of protection of the connected 110kV transformer substation can be caused, and the main transformer generates serious noise when carrying a load.
At present, research and analysis conducted at home and abroad on the low-frequency non-stationary inter-harmonic emission characteristics of ultra-high-power arc equipment are few, some expert and scholars at home and abroad conduct research and analysis on an arc furnace model for voltage fluctuation research and the mutual influence mechanism of inter-harmonic and voltage fluctuation, and the relevant model of the arc furnace is established based on a random theory or a chaos theory mostly from the randomness of the arc.
Disclosure of Invention
In view of this, the present invention provides a method for constructing an ultra-high power arc furnace model for low-frequency non-stationary inter-harmonic research, which can accurately reflect the operation characteristics of an ultra-high power arc furnace in practical industrial applications, reveal the emission characteristics of the low-frequency non-stationary inter-harmonic of the ultra-high power arc furnace, and reflect the influence of the operation of the ultra-high power arc furnace on the stability of a power distribution network.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for constructing an ultrahigh power electric arc furnace model comprises the following steps:
step S1, establishing a power balance equation of the ultra-high power electric arc furnace according to the law of energy conservation;
step S2, constructing a deterministic arc model of the electric arc furnace according to a power balance equation of the ultra-high power electric arc furnace;
s3, modulating static arc voltage by adopting a low-frequency chaotic signal generated by an asymmetric nonlinear resistor Chua' S circuit, and constructing an uncertainty model reflecting the randomness of the load operation of the electric arc furnace;
and step S4, constructing and obtaining a novel alternating current electric arc furnace simulation model for low-frequency non-stationary inter-harmonic research according to the deterministic arc model of the electric arc furnace and the uncertain model reflecting the load operation randomness of the electric arc furnace.
Further, the power balance equation specifically includes:
p＝p 1 +p 2 (1)
in the formula: p is the input power of the electric arc furnace; p is a radical of 1 Converting power to electric arc furnace energy; p is a radical of 2 Is the dissipation power in the smelting process of the electric arc furnace.
Further, the step S2 is specifically:
step S21, the mathematical expression of the input power p and the arc conductance of the arc furnace is
p＝i 2 /g (2)
In the formula: i is the arc instantaneous input current; g is the arc conductance of the ultra-high power arc furnace;
p 1 for converting power to energy in ultra-high power electric arc furnaces, the magnitude of which is related to the energy accumulated in the arc, i.e.
p 1 ＝dQ/dt (3)
In the formula: q is the energy accumulated in the arc column; t is time;
step S22, derived from the Sakah equation
dQ＝k 2 g β dg (4)
p 2 Representing the external dissipated power of the ultra-high power arc furnace, the magnitude of which is related to the arc conductance, i.e.
p 2 ＝k 1 g α (5)
In the formula: k is a radical of 1 And alpha is a constant coefficient, and the size of the constant coefficient is related to the type of the electric arc furnace.
Step S23, the deterministic arc model described by the differential equation obtained by substituting the formulas (4) to (7) into the formula (3) is
In the formula: k is a radical of 1 、k 2 M and n are parameters to be determined, n ═ α - β, and m ═ β -1.
Further, the parameter k to be determined 1 、k 2 M, n and eta are determined by comparing the simulation voltage with the actual measurement voltage by using the actual measurement current data as input and the simulation voltage of the electric arc furnace as output through a least square method, a genetic algorithm or a particle swarm algorithm.
Further, the step S3 is specifically:
low-frequency chaotic signal v generated by using asymmetric nonlinear resistor Chua's circuit choat The static arc voltage u is modulated, i.e.
In the formula: u. of arc Calculating a simulation value of the arc voltage; eta is a proportionality coefficient between the chaotic signal voltage and the arc static voltage; v. of choat Is the output voltage of the asymmetric nonlinear Chua's circuit.
Further, in the step S4, a novel ac arc furnace simulation model for low-frequency non-stationary inter-harmonic research is established in Matlab/Simulink environment.
Compared with the prior art, the invention has the following beneficial effects:
the invention can accurately reflect the operation characteristics of the ultrahigh power electric arc furnace under the actual industrial application, can reveal the emission characteristics of the low-frequency non-stationary inter-harmonic of the ultrahigh power electric arc furnace, and embody the influence of the operation of the ultrahigh power electric arc furnace equipment on the stability of the power distribution network; the method is suitable for the simulation research of the power quality problem of the ultra-high power electric arc furnace; the method can be used for simulation research on low-frequency non-stationary inter-harmonic, reactive power shock and other problems of the ultra-high power electric arc furnace.
Drawings
FIG. 1 is a mathematical model of an ultra high power electric arc furnace constructed in accordance with an embodiment of the present invention;
FIG. 2 is a block diagram of parameter identification according to an embodiment of the present invention;
FIG. 3 is an arc furnace model in a Matlab/Simulink environment in accordance with an embodiment of the present invention;
FIG. 4 is a Chua's circuit in a Matlab/Simulink environment in an embodiment of the present invention;
FIG. 5 is an asymmetric nonlinear resistor in a Matlab/Simulink environment in an embodiment of the present invention;
FIG. 6 is a schematic diagram of a Chua's circuit in an embodiment of the present invention;
FIG. 7 is a comparison graph of the primary side simulated calculated voltage and the measured voltage of the electric furnace transformer in one embodiment of the present invention;
FIG. 8 is a graph of the V-I characteristic of a 100 ton ultra high power electric arc furnace simulated in accordance with an embodiment of the present invention;
FIG. 9 is a graph illustrating low frequency non-stationary inter-harmonic and harmonic content analysis of simulated arc voltage of an arc furnace load using DFT analysis in accordance with an embodiment of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
Referring to fig. 1, the present invention provides a method for constructing an ultra-high power arc furnace model, comprising the following steps:
step S1, establishing a power balance equation of the ultra-high power electric arc furnace according to the law of energy conservation;
step S2, establishing a deterministic arc model of the arc furnace according to the power balance equation of the ultra-high power arc furnace;
s3, modulating static arc voltage by adopting a low-frequency chaotic signal generated by an asymmetric nonlinear resistor Chua' S circuit, and constructing an uncertainty model reflecting the randomness of the load operation of the electric arc furnace;
and S4, constructing a novel alternating current electric arc furnace simulation model for low-frequency non-stationary inter-harmonic research in a Matlab/Simulink environment according to the deterministic arc model of the electric arc furnace and the uncertain model reflecting the randomness of the load operation of the electric arc furnace.
In this embodiment, the power balance equation specifically includes:
p＝p 1 +p 2 (1)
in the formula: p is the input power of the electric arc furnace; p is a radical of 1 Converting power to electric arc furnace energy; p is a radical of formula 2 Is the dissipation power in the smelting process of the electric arc furnace.
In the embodiment, the determination of the energy conversion power and the dissipation power of the arc furnace is an important factor influencing the modeling of the arc furnace, and the embodiment establishes a static model suitable for the research of the ultra-high power arc furnace starting from the expression of the conversion power and the dissipation power, and specifically comprises the following steps:
step S21, the mathematical expression of the input power p and the arc conductance of the arc furnace is
p＝i 2 /g (2)
In the formula: i is the arc instantaneous input current; g is the arc conductance of the ultra-high power arc furnace;
p 1 for converting power to energy in ultra-high power electric arc furnaces, the magnitude of which is related to the energy accumulated in the arc, i.e.
p 1 ＝dQ/dt (3)
In the formula: q is the energy accumulated in the arc column; t is time;
step S22, derived from the Sakah equation
dQ＝k 2 g β dg (4)
p 2 Representing the external dissipated power of the ultra-high power arc furnace, the magnitude of which is related to the arc conductance, i.e.
p 2 ＝k 1 g α (5)
In the formula: k is a radical of 1 And alpha is a constant coefficient, and the size of the constant coefficient is related to the type of the electric arc furnace.
Step S23, the deterministic arc model described by the differential equation obtained by substituting the formulas (4) to (7) into the formula (3) is
In the formula: k is a radical of 1 、k 2 M and n are parameters to be determined, n ═ α - β, and m ═ β -1.
Referring to fig. 2, in the present embodiment, the parameter k to be determined 1 、k 2 M and n, determining by using the least square method, genetic algorithm or particle swarm algorithm, taking the measured current data as input, taking the simulation voltage of the electric arc furnace as output, and comparing the simulation voltage with the measured voltage.
In this embodiment, the step S3 specifically includes:
low-frequency chaotic signal v generated by using asymmetric nonlinear resistor Chua's circuit choat The static arc voltage u is modulated, i.e.
In the formula: u. of arc Calculating a simulation value of the arc voltage; eta is a proportionality coefficient between the chaotic signal voltage and the arc static voltage; v. of choat Is the output voltage of the asymmetric nonlinear Chua's circuit.
In this embodiment, referring to fig. 5, the zaa circuit based on the asymmetric nonlinear resistor in this embodiment includes a linear inductor L, a variable linear resistor R, and two linear capacitors C 1 And C 2 And an asymmetric nonlinear resistance controlled by a voltage. Wherein i L For the current through the inductance L, i r For flowing through an asymmetric nonlinear resistance N r Current of U C1 、U C2 Respectively represent capacitances C 1 And C 2 The terminal voltage of (c). The basic principle of the circuit is that three interacting balance points are formed by using asymmetric nonlinear resistors, so that an asymmetric double-scroll chaotic attractor is generated. According to kirchhoff's law of current and voltage, i L 、U C1 、U C2 As the state variable of the system, a Chua's circuit dynamic state equation based on asymmetric nonlinear resistors is obtained, namely
In the formula: g is 1/R; i.e. i r Represented by the volt-ampere characteristic of asymmetric nonlinear resistance, and the mathematical expression is
In the formula: g a 、G b 、G c Respectively represent three-segment slopes of a current-voltage characteristic curve of the asymmetric nonlinear resistor, and G b ≠G c 。
Referring to fig. 9, for the analysis of the low frequency non-stationary inter-harmonic and harmonic content after the DFT analysis method is used to analyze the simulated arc voltage of the arc furnace load, the total harmonic distortion rate of the voltage obtained by simulation is 30.27%, while the actual distortion rate is 30.64%, and the error between the two is only 0.37%. The voltage fluctuation obtained from the simulation was 1.80%, whereas it was actually 1.64%, and the error between the two was only 0.16%. The ultrahigh-power electric arc furnace model for researching the low-frequency non-stationary inter-harmonic waves, which is obtained by the embodiment, can accurately reflect the operation characteristics of the ultrahigh-power electric arc furnace under actual industrial application, can reveal the emission characteristics of the low-frequency non-stationary inter-harmonic waves of the ultrahigh-power electric arc furnace, and reflects the influence of the operation of the ultrahigh-power electric arc furnace on the stability of a power distribution network.
The above description is only a preferred embodiment of the present invention, and all equivalent changes and modifications made in accordance with the claims of the present invention should be covered by the present invention.
Claims (3)
1. A construction method of an ultrahigh power electric arc furnace model is characterized by comprising the following steps:
step S1, establishing a power balance equation of the ultra-high power electric arc furnace according to the law of energy conservation;
step S2, establishing a deterministic arc model of the arc furnace according to the power balance equation of the ultra-high power arc furnace;
s3, modulating static arc voltage by adopting a low-frequency chaotic signal generated by an asymmetric nonlinear resistor Chua' S circuit, and constructing an uncertainty model reflecting the randomness of the load operation of the electric arc furnace;
step S4, constructing and obtaining an alternating current electric arc furnace simulation model for low-frequency non-stationary inter-harmonic research according to the deterministic electric arc model of the electric arc furnace and the uncertainty model reflecting the randomness of the load operation of the electric arc furnace;
the power balance equation specifically includes:
p＝p 1 +p 2 (1)
in the formula: p is the input power of the electric arc furnace; p is a radical of 1 Converting power to electric arc furnace energy; p is a radical of 2 The external dissipated power of the electric arc furnace;
the step S2 specifically includes:
step S21, the mathematical expression of the input power p and the arc conductance of the arc furnace is
p＝i 2 /g (2)
In the formula: i is the arc instantaneous input current; g is the arc conductance of the ultra-high power arc furnace;
p 1 for converting power to electric arc furnace energy, the magnitude of which is related to the accumulated energy of the arc, i.e.
p 1 ＝dQ/dt (3)
In the formula: q is the energy accumulated in the arc column; t is time;
step S22, derived from the Sakah equation
dQ＝k 2 g β dg (4)
p 2 Indicating the dissipated power to the outside of the arc furnace, the magnitude of which is related to the arc conductance, i.e.
p 2 ＝k 1 g α (5)
In the formula: k is a radical of 1 α is a constant coefficient, the magnitude of which is related to the arc furnace type;
step S23, the deterministic arc model described by the differential equation obtained by substituting the formulas (4) to (5) into the formula (3) is
In the formula: k is a radical of 1 、k 2 、 m And n n ═ α - β, m ═ β -1 for the parameters to be determined;
low-frequency chaotic signal v generated by using asymmetric nonlinear resistor Chua's circuit choat The static arc voltage u is modulated, i.e.
In the formula: u. of arc Calculating a simulation value of the arc voltage; eta is a proportionality coefficient between the chaotic signal voltage and the arc static voltage.
2. The method of claim 1, wherein the parameter k to be determined is the parameter k 1 、k 2 M, n and eta are determined by comparing the simulation voltage with the actual measurement voltage by using the actual measurement current data as input and the simulation voltage of the electric arc furnace as output through a least square method, a genetic algorithm or a particle swarm algorithm.
3. The method for constructing the model of the ultra-high power electric arc furnace of claim 1, wherein the step S4 is implemented by establishing a simulation model of the alternating current electric arc furnace for low-frequency non-stationary inter-harmonic research in Matlab/Simulink environment.
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| US7391218B2 (en) * | 2005-03-11 | 2008-06-24 | Honeywell International Inc. | Method and apparatus for generalized arc fault detection |
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| DE102009043639A1 (en) * | 2009-09-29 | 2011-03-31 | Sms Siemag Aktiengesellschaft | Method and apparatus for controlling the production of a foamed slag in a metallic melt |
| CN103631985A (en) * | 2013-09-02 | 2014-03-12 | 国家电网公司 | Simulation impedance model of electric arc furnace piecewise linearity |
| CN109768553A (en) * | 2019-01-08 | 2019-05-17 | 上海羲源电气科技有限公司 | High-tension network harmonic absorption and network pressure vibration suppression device |
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