CN111579940A - Electric arc furnace modeling and harmonic wave analysis method and system - Google Patents
Electric arc furnace modeling and harmonic wave analysis method and system Download PDFInfo
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Abstract
The invention provides an electric arc furnace modeling and harmonic wave analysis method and system. The electric arc furnace modeling method comprises the following steps: setting reasonable sampling time for actually measured voltage and current data of each stage in the smelting process of the electric arc furnace, respectively sampling to obtain the waveforms of the voltage and the current and each subharmonic vector value, and acquiring the actual distribution of the electric arc voltage and the electric arc; establishing a nonlinear time-varying resistance model, namely a static model, of the arc resistor; identifying parameters in the nonlinear time-varying resistance model of the electric arc furnace based on a particle swarm algorithm, and calculating parameters of the equivalent resistance model of the electric arc furnace; because the rapid irregular change of the arc length is the main factor of the voltage and current distortion of the electric arc furnace, three small signals, such as a random signal, a Gaussian noise signal and a chaotic signal, are superposed with the arc length static model according to the modulation principle, the modulation parameters of each signal are adjusted, and a simulation model which can reflect the smelting external characteristics of the electric arc furnace is deduced.
Description
Technical Field
The invention relates to the field of electrical control, in particular to an electric arc furnace modeling and harmonic analysis method and system.
Background
The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.
The alternating current electric arc furnace is one of important devices of modern iron and steel enterprises, has outstanding economic benefit and widely exists in the metal smelting industry. In the smelting process of the electric arc furnace, the change of electric arc current is irregular in the operation process due to the operation characteristics of the electric arc furnace, the distortion of three-phase current in a power grid is serious, the obvious three-phase imbalance phenomenon occurs, electric arc short circuit and short circuit frequently occur, current impact is caused, a large amount of harmonic current is generated, active power and reactive power are changed violently, and negative influence is generated on the safe and stable operation of a power system. With the continuous increase of the capacity and the number of the electric arc furnaces, the electric arc furnaces become common harmonic sources, the quality of electric energy of a power grid is deteriorated, the working efficiency of equipment is influenced, and the loss of the equipment is increased, so that the accurate modeling of the electric arc furnaces has important significance for harmonic analysis evaluation and harmonic current suppression.
At present, the harmonic modeling of the electric arc furnace has been studied, and the common method can be summarized into two main types, namely a controllable power supply model and a load model, wherein the controllable power supply model is used for replacing the electric arc furnace by a voltage source with the same waveform as the electric arc voltage, and the controllable power supply model is used for studying the external impedance characteristic of the electric arc furnace load and calculating and deriving an arc resistance analytical expression on the basis of theories such as ohm's law, energy balance equation and the like. The inventor finds that the types of electric arc furnaces applied in the industry are more and different in tonnage, and the parameters of a simulation model of the electric arc furnaces are difficult to accurately determine; in addition, the existing model is difficult to accurately reflect the external characteristics of time-varying property, chaos, randomness and the like expressed in the electric arc furnace smelting. An alternating current electric arc furnace is one of important equipment of modern iron and steel enterprises, is widely used in the metal smelting industry, is used as an important nonlinear harmonic source, and can inject a large amount of nonstationary random harmonics into a power grid in the smelting process, so that the voltage distortion of the power grid is aggravated, the voltage flicker and other electric energy quality problems are caused, the safe and stable operation of a power system is threatened, and immeasurable economic loss is brought to users.
Disclosure of Invention
In order to solve the above problems, a first aspect of the present invention provides an arc furnace modeling method, which establishes a model that can consider the influence of the rapid irregular change of the arc length on the arc voltage and current distortion and perform arc furnace model parameter identification through measured data, thereby improving the accuracy of a simulation model and providing a model determination method with strong versatility.
In order to achieve the purpose, the invention adopts the following technical scheme:
an electric arc furnace modeling and harmonic analysis method comprises the following steps:
s1: setting sampling time for voltage and current data of each stage in the smelting process of the electric arc furnace, respectively sampling to obtain the waveform and each subharmonic vector value of the voltage and the current, and acquiring the actual distribution of the voltage and the current of the electric arc;
s2: establishing a nonlinear time-varying resistance model of the arc resistance;
s3: identifying parameters in the non-linear time-varying resistance model of the electric arc furnace based on a particle swarm algorithm, calculating model parameters in the non-linear time-varying resistance model of the electric arc furnace, obtaining an electric arc time-varying resistance expression, and fitting a change curve of an electric arc equivalent resistance in the smelting process of the electric arc furnace;
s4: superposing three small signals, namely a random signal, a Gaussian noise signal, a chaotic signal and the like, with the arc length static model, and adjusting the modulation parameters of the signals to obtain a modulated arc length random fluctuation model;
s5: according to the steps, establishing an electric arc furnace model based on a PSO algorithm and arc length modulation;
s6: and calculating the voltage and current values of each harmonic wave in the smelting process of the electric arc furnace, and performing harmonic wave analysis.
In order to solve the above problems, a second aspect of the present invention provides an electric arc furnace harmonic modeling system comprising:
the data acquisition module is used for sampling the actually measured voltage and current data of each stage in the smelting process of the electric arc furnace, and further performing Fourier analysis respectively to obtain the waveform distribution of the voltage and the current and each subharmonic vector value;
the nonlinear time-varying resistance module of the electric arc furnace is used for obtaining a static model of equivalent resistance of the electric arc furnace;
the model parameter identification module is used for identifying parameters in the non-linear time-varying resistance model of the electric arc furnace through a particle swarm algorithm, calculating model parameters in the non-linear time-varying resistance model of the electric arc furnace, obtaining an electric arc time-varying resistance expression and fitting a change curve of electric arc equivalent resistance in the smelting process of the electric arc furnace;
the arc length modulation module is used for superposing three small signals, namely a random signal, a Gaussian noise signal, a chaotic signal and the like, with the arc length static model, and adjusting the modulation parameters of all the signals to obtain a modulated arc length random fluctuation model;
and the harmonic analysis module is used for calculating the distortion degree of each harmonic voltage and current in the electric arc furnace smelting process according to the change of the equivalent resistance of the electric arc in the electric arc furnace smelting process.
In order to solve the above problems, a third aspect of the present invention provides a computer-readable storage medium, which establishes a model that can consider the influence of the rapid irregular change of the arc length on the arc voltage and current distortion and perform arc model parameter identification through measured data, thereby improving the accuracy of a simulation model and providing a model determination method with strong versatility.
In order to achieve the purpose, the invention adopts the following technical scheme:
a computer-readable storage medium, having stored thereon a computer program which, when being executed by a processor, carries out the steps of the method for arc furnace modeling and harmonic analysis as set forth above.
In order to solve the above problems, a fourth aspect of the present invention provides a computer device, which establishes a model that can consider the influence of the rapid irregular change of the arc length on the arc voltage and current distortion and perform the arc model parameter identification through the measured data, thereby improving the accuracy of the simulation model and providing a model determination method with strong versatility.
In order to achieve the purpose, the invention adopts the following technical scheme:
a computer apparatus comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the steps of the method for arc furnace modeling and model parameter identification as described above when executing the program.
The invention has the beneficial effects that:
(1) the invention establishes a model which can consider the relation between arc length fluctuation and arc voltage and current distortion degree and can determine parameters in the model according to the actual operation condition of the arc furnace, thereby improving the accuracy of the simulation model and providing a model determination method with stronger universality;
(2) according to the modulation principle, the arc length modulation is carried out by utilizing random signals, Gaussian noise signals and chaotic signals, so that the typical external characteristics of the electric arc furnace can be reflected;
(3) the method carries out model parameter estimation through the particle swarm algorithm, and can carry out dynamic model parameter adjustment according to the application type, nameplate parameters and actual operation conditions of the electric arc furnace; the method accurately evaluates the harmonic waves of the electric arc furnace, can improve the stability of a power grid, reduce harmonic current, improve the quality of electric energy, and improve the economical efficiency, the stability and the like of the operation of the electric power system.
Drawings
FIG. 1 is a flow chart of an electric arc furnace modeling process according to an embodiment of the present invention.
Fig. 2 is a comparison graph of arc resistance before and after parameter identification according to an embodiment of the present invention.
Fig. 3 illustrates an arc length modulation process according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of an asymmetric nonlinear resistor chua's circuit according to an embodiment of the present invention.
Fig. 5(a) is a waveform diagram of a chaotic signal generated by a zaa circuit according to an embodiment of the present invention.
Fig. 5(b) is a waveform diagram of a chaotic signal generated by a zaa circuit after an initial value is up-regulated by 5% according to an embodiment of the present invention.
FIG. 6(a) is a waveform diagram of an arc furnace arc voltage simulation provided by an embodiment of the present invention.
FIG. 6(b) is a waveform diagram of an arc furnace arc current simulation provided by an embodiment of the present invention.
Fig. 7(a) is a waveform diagram of primary side three-phase voltages of a transformer according to an embodiment of the present invention.
Fig. 7(b) is a waveform diagram of primary side three-phase current of the transformer according to the embodiment of the present invention.
FIG. 8 is a graph of A-phase voltammetry of an electric arc furnace according to an embodiment of the present invention.
Detailed Description
The invention is further described with reference to the following figures and examples.
It is to be understood that the following detailed description is exemplary and is intended to provide further explanation of the invention as claimed. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
As shown in fig. 1, the method for modeling an arc furnace and analyzing harmonics according to the present embodiment includes:
s101: an experiment measuring platform is established, experiment measurement is carried out on the load of the electric arc furnace, Fourier analysis is carried out on actually measured voltage and current data of each stage in the smelting process of the electric arc furnace respectively, each subharmonic vector value of the voltage and the current is obtained, and distribution of the voltage and the current of the electric arc is obtained through Fourier function fitting.
The method comprises the steps of carrying out experimental measurement on electric arc furnaces of different types, obtaining voltage and current data in normal operation, then carrying out synchronization processing on the measured data, and obtaining harmonic phasor values of each time of voltage and current through Fourier analysis.
S102: and establishing a nonlinear time-varying resistance model of the arc resistance according to ohm's law and an arc related theory.
S103: and calculating all parameters required in the non-linear time-varying resistance model of the electric arc furnace according to the measured voltage, current waveform and each subharmonic vector value of the electric arc furnace.
Based on the physical characteristics of the interior of the alternating-current arc, according to the arc theory and the ohm law, the equation satisfied by the arc is simplified and approximated, factors such as the power factor of the arc furnace, the smelting temperature and the arc current phase angle are calculated, and a time-varying resistance model which can accurately reflect the arc impedance characteristics is obtained, and a specific expression is
Where F (L (t)) reflects the effect of arc length on arc resistance,
l (t) is an arc length random variation expression; the parameters to be identified are A, B, C' and (D + θ). R represents a time-varying resistance.
The main task of the identification of the parameters of the model of the electric arc furnace is to find an optimal set of parameter vectors λ so as to minimize the value of the objective function of the predetermined error, the objective function F of the errorfitnessUsually, a non-negative function is chosen, and the sum of the squared errors of the discretized arc voltage is taken in the present invention:
wherein U isiIs the actual measured value of the arc voltage,
n is the number of samples measured in S101 for the model calculation value of the arc voltage.
Then, 4 model parameters such as A, B, C and (D + θ) in the nonlinear time-varying resistance model of the arc furnace were calculated based on the particle swarm optimization using the arc current as an input and the arc voltage as an identification. The specific steps are as follows:
1) inputting: the method comprises the steps of arc current I, arc voltage U, arc resistance R and initial values of parameters to be identified.
2) And (3) circulation: the position and velocity of each sample point is set and updated step by step.
3) Calculating FfitnessAnd comparing with the historical optimal value, if the current value is more optimal, updating the parameter value by using the current value, and storing the calculated A, B, C' and (D + theta) and other 4 model parameters.
4) The position and velocity of each particle is updated.
5) And ending the loop and outputting the parameter to be identified.
In order to verify the model parameter method provided by the invention, a model parameter value taking method based on comparison of results obtained by formula derivation and empirical analysis calculation is adopted, the values of the model parameters of the nonlinear time-varying resistance of an electric arc furnace are compared, and specific results are shown in a table 1:
TABLE 1
| Parameter(s) | Initial value | Calculated value |
| A | 0.1806 | 0.1812 |
| B | 0.0978 | 0.0986 |
| C’ | 0.000577 | 0.000569 |
| (D+θ) | -2.7 | -2.61 |
The comparison result of the arc resistance waveforms obtained by the two model parameter value taking methods is shown in fig. 2.
S104: according to the external characteristics characterized in the smelting process of the electric arc furnace, arc length modulation is carried out by adopting random signals, Gaussian noise signals and chaotic signals, and corresponding modulation coefficients are set.
According to the theory of electric arcs and related experience in the smelting process of the electric arc furnace, the effect of the arc length on the arc resistance in the smelting process of the electric arc furnace can be represented by the following expression:
in the formula, rcIn terms of arc radius, l (t) represents the random fluctuation of arc length, which is expressed by equation 4:
L(t)＝L0+0.5L1·(1+sin wt) (4)
L0minimum arc length in operation, L1The maximum variation of the arc length, i.e. the difference between the maximum and minimum values. The selection range of w is usually between 1Hz and 30Hz, which is the range most sensitive to voltage flash of human eyes, and the invention takes w as 15 Hz. The rapid irregular change of the arc length is the main reason causing the arc voltage and current distortion, and in order to enable an arc furnace simulation model to represent the typical external characteristics of the arc furnace in operation, the invention uses three small signals to modulate the arc length.
Referring to fig. 3, in particular, it includes:
(1) establishing an arc length static fluctuation model;
(2) establishing a random signal generating circuit, and carrying out arc length modulation by using a random signal;
(3) establishing a Gaussian noise signal generating circuit, and performing arc length modulation by using the Gaussian noise signal;
(4) establishing a chaotic signal generating circuit, and performing arc length modulation by using the chaotic signal;
(5) obtaining a modulated arc length random fluctuation model;
the main step (1) comprises
Establishing an arc length static fluctuation model, wherein the specific expression is as follows:
L(t)＝L0+0.5L1·(1+sin wt) (4)
wherein L is0Minimum arc length in operation, L1The maximum variation of the arc length, i.e. the difference between the maximum and minimum values. The selection range of w is usually between 1Hz and 30Hz, which is the range most sensitive to voltage flash of human eyes, and the invention takes w as 15 Hz.
The main step (2) comprises
Establishing a random signal generating circuit, wherein the specific expression is as follows:
singal-1＝a·sin wt (5)
where a is the modulation factor of the random signal.
The arc length is modulated by superposing small signals, the adopted small signals are actually a.sin wt, and 1 represents an initial expression of the modulated arc length, namely the expression (5).
The random signal can reflect the quasi-periodicity and the existing low-frequency harmonic component in the operation of the electric arc furnace, and f is 10Hz in the invention. According to the superposition theorem, the random signal is added into the arc length for modulation, and the modulated arc length expression is as follows:
L1(t)＝L(t)·(1+asin wt) (6)
the main step (3) comprises
Establishing a Gaussian noise signal generating circuit, wherein the specific expression is as follows:
wherein b is a modulation factor of the random signal,
is a random number module.
Gaussian noise signal can reflect randomness in the operation of the electric arc furnace, and the sampling time t is 10-4And s. According to the superposition theorem, the Gaussian noise signal is added into the arc length for modulation, and the modulated arc length expression is as follows:
the main step (4) comprises
Establishing a chaotic noise signal generating circuit, wherein the specific expression is as follows:
singal-3＝c· (9)
wherein c is the modulation coefficient of the random signal and is the chaotic signal.
The chaotic signal can reflect the chaos in the operation of the electric arc furnace, the chaotic signal in the invention is generated by an asymmetric nonlinear resistor Chua's circuit, and the schematic diagram of the circuit is shown in an attached figure 4. The chaotic signal is taken as the generation of an asymmetric nonlinear resistor Nr controlled by voltage in figure 4, and the current value of an inductor L at the initial moment is changed, so that a capacitor C1、C2And obtaining the required chaotic signal by the voltage value at the initial moment.
In order to prove the sensitivity of the chaotic signal generated by the chaotic system in the attached figure 4 to initial conditions, the parameter values of the energy storage element of the Chua's circuit can be changed, the initial parameter settings are all adjusted up by 0.5%, and the simulation waveforms obtained before and after adjustment are shown in the attached figures 5 and 6. The results show that the deviation of the two simulation waveforms occurs within 0.3s, which indicates that the signal is applied to the modeling of the electric arc furnace, so that the model can show chaos and is consistent with the actual operation state of the electric arc furnace.
According to the superposition theorem, the chaotic signal is added into the arc length for modulation, and the modulated arc length expression is as follows:
s105: and according to the steps S101-S104, establishing the arc furnace model, calculating the parameter values of each electric element of the arc furnace simulation electric system according to the actual electric power supply system of the arc furnace, and completing system construction.
S106: and carrying out electric arc furnace harmonic analysis, calculating voltage and current values of each harmonic in the electric arc furnace smelting process through Fourier analysis, and analyzing the influence of the voltage and current values on the power quality of the power grid.
The calculation accuracy of the arc resistance value and each subharmonic voltage value of the time-varying resistance model after the model parameter identification and the arc length modulation used in the embodiment and the traditional nonlinear time-varying resistance model is compared. Fig. 2 shows a comparison graph of real-time variation waveforms of arc resistance of two models, and table 2 shows a comparison between each harmonic voltage content value and an actual value of the two models:
TABLE 2
Therefore, compared with the traditional model, the simulation precision of the 2 to 7 harmonic waves of the model after parameter optimization and arc length modulation is obviously improved, and the operation of the electric arc furnace can be better simulated.
The types and the tonnage of the electric arc furnaces applied in the modern smelting industry are various, and table 3 shows the comparison of the accuracy of the calculated value and the measured value of each harmonic voltage value of three common alternating current electric arc furnaces such as a steel furnace, a calcium carbide furnace, an iron alloy furnace and the like, so that the method provided by the invention has strong universality and can be applied to the harmonic analysis research of various electric arc furnaces.
TABLE 3
By using the model provided in this embodiment, a 40t arc furnace model is established, and the parameters of each element of the electrical system are as follows:
1) a power supply: phase voltage of 10kV and frequency of 50Hz
2) High-voltage transmission line: r1＝1.258Ω，X1＝3.156Ω
3) A transformer: s-400 kVA, RF＝0.620mΩ，XF＝7.12mΩ
4) Short network: r2＝2,1mΩ，X2＝6mΩ
The change curves of the arc voltage and the arc current in the smelting process are shown in fig. 6(a) -6 (b), the change curves of the three-phase voltage and the three-phase current on the primary side of the transformer are shown in fig. 7(a) -7 (b), and the volt-ampere characteristic curve of the phase A load of the electric system of the electric arc furnace is shown in fig. 8. As can be seen from the attached drawing, the arc furnace has great contribution to the distortion rate of the voltage and the current of the power grid, the three-phase current and the voltage have serious unbalance, and the THD can reach more than 5.5 percent; the volt-ampere characteristic curve of the electric arc furnace obtained by simulation is integrally matched with the load characteristic curve of a typical electric arc furnace, and obvious randomness and time variation are presented; the asymmetry of the positive and negative half periods conforms to the characteristics of the electric arc furnace when the anode and the cathode alternate and conforms to the dynamic characteristics of electric arc furnace steel making. The simulation result of the model is basically consistent with the actual measurement result, and the result is more accurate than that of the traditional model.
The embodiment of the invention also provides an electric arc furnace modeling and harmonic wave analysis system. The method comprises the following steps:
the data acquisition module is used for sampling the actually measured voltage and current data of each stage in the smelting process of the electric arc furnace, and further performing Fourier analysis respectively to obtain the waveform distribution of the voltage and the current and each subharmonic vector value;
the nonlinear time-varying resistance module of the electric arc furnace is used for obtaining a static model of the equivalent resistance of the electric arc according to ohm's law and the electric arc correlation theory;
the model parameter identification module is used for carrying out parameter identification on the nonlinear time-varying resistance model of the electric arc furnace according to the actually measured voltage and current data through a particle swarm algorithm to obtain a simulation model with higher fitting degree with the electric arc furnace;
the arc furnace arc length modulation module is used for modulating the rapid irregular change of the arc length by utilizing small signals, so that the simulation model represents the external characteristics of the arc furnace smelting process, and meanwhile, the three-phase unbalance simulation analysis of the arc furnace is carried out by adjusting the modulation coefficient in the module;
the harmonic analysis module is used for calculating the distortion degree of each harmonic voltage and current in the electric arc furnace smelting process according to the change of the equivalent resistance of the electric arc in the electric arc furnace smelting process;
in another embodiment, a computer readable storage medium is also provided, having stored thereon a computer program which, when executed by a processor, carries out the steps in the arc furnace modeling and harmonic analysis as shown in fig. 1.
In another embodiment, there is also provided a computer apparatus comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the steps in arc furnace modeling and harmonic analysis as shown in fig. 1 when executing the program.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of a hardware embodiment, a software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by a computer program, which can be stored in a computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), or the like.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (19)
1. An electric arc furnace modeling and harmonic analysis method is characterized by comprising the following steps:
s1: setting sampling time for voltage and current data of each stage in the smelting process of the electric arc furnace, respectively sampling to obtain the waveform and each subharmonic vector value of the voltage and the current, and acquiring the actual distribution of the voltage and the current of the electric arc;
s2: establishing a nonlinear time-varying resistance model of the arc resistance;
s3: identifying parameters in the non-linear time-varying resistance model of the electric arc furnace based on a particle swarm algorithm, calculating model parameters in the non-linear time-varying resistance model of the electric arc furnace, obtaining an electric arc time-varying resistance expression, and fitting a change curve of an electric arc equivalent resistance in the smelting process of the electric arc furnace;
s4: superposing three small signals, namely a random signal, a Gaussian noise signal, a chaotic signal and the like, with the arc length static model, and adjusting the modulation parameters of the signals to obtain a modulated arc length random fluctuation model;
s5: according to the steps, establishing an electric arc furnace model based on a PSO algorithm and arc length modulation;
s6: and calculating the voltage and current values of each harmonic wave in the smelting process of the electric arc furnace, and performing harmonic wave analysis.
2. The method of claim 1, wherein the step S1 includes:
the method comprises the steps of carrying out experimental measurement on the load of the electric arc furnace, carrying out Fourier analysis on actually measured voltage and current data of each stage in the smelting process of the electric arc furnace respectively to obtain each subharmonic vector value of the voltage and the current, and obtaining the actual distribution of the voltage and the current of the electric arc furnace through Fourier function fitting.
3. The method of claim 1,
in step S2, the non-linear time-varying resistance model of the arc furnace has the following specific expression:
wherein F [ L (t) ] reflects the influence of arc length on arc resistance, and L (t) is an arc length random variation expression; the parameters to be identified are A, B, C' and (D + θ); r represents a time-varying resistance, and ω represents an angular velocity.
4. The method of claim 3,
in step S3, the identifying the parameters in the arc furnace nonlinear time-varying resistance model includes:
s31: setting an error objective function FfitnessComprises the following steps:
wherein U isiIs the actual measured value of the arc voltage,
calculating a value for the model of the arc voltage, n being the number of samples measured in step S1;
step S32: a, B, C' and (D + theta) 4 model parameters in the arc furnace nonlinear time-varying resistance model are calculated based on a particle swarm algorithm by taking the arc current as an input quantity and the arc voltage as an identification quantity.
5. The method of claim 4, wherein the step of S32 includes:
1) inputting: the method comprises the following steps of (1) arc current I, arc voltage U, arc resistance R and initial values of parameters to be identified;
2) and (3) circulation: setting the position and speed of each sample point, and gradually updating;
3) calculating FfitnessComparing the current value with the historical optimal value, if the current value is more optimal, updating the parameter value by using the current value, and storing A, B, C' and (D + theta) 4 model parameters obtained by calculation;
4) updating the position and speed of each sample particle;
5) and ending the loop and outputting the parameter to be identified.
6. The method of claim 5, wherein S4 specifically comprises:
1) establishing an arc length static fluctuation model;
2) establishing a random signal generating circuit, and carrying out arc length modulation by using a random signal;
3) establishing a Gaussian noise signal generating circuit, and performing arc length modulation by using the Gaussian noise signal;
4) establishing a chaotic signal generating circuit, and performing arc length modulation by using the chaotic signal;
5) and obtaining a modulated arc length random fluctuation model.
7. The method of claim 6, wherein the arc length static fluctuation model is established in step 1) by the following specific expression:
L(t)＝L0+0.5L1·(1+sin wt)
wherein L is0Minimum arc length in operation, L1The maximum variation of the arc length, i.e. the difference between the maximum and minimum value, w is chosen to be in the range of 1Hz to 30 Hz.
8. The method of claim 6, wherein step 2) comprises:
establishing a random signal generating circuit, wherein the specific expression is as follows:
singal-1＝a·sin wt
wherein a is the modulation coefficient of the random signal;
the random signal reflects quasi-periodicity and low-frequency harmonic components in the operation of the electric arc furnace, f is 10Hz, the random signal is added into the arc length for modulation, and the modulated arc length expression is as follows:
L1(t)＝L(t)·(1+a·sinwt) 。
9. the method of claim 6, wherein step 3) comprises:
establishing a Gaussian noise signal generating circuit, wherein the specific expression is as follows:
wherein b is a modulation factor of the random signal,
is a random number module.
Gaussian noise signal reflects randomness of the electric arc furnace in operation, and sampling time t is 10-4s, adding the Gaussian noise signal into the arc length for modulation, wherein the modulated arc length expression is as follows:
10. the method of claim 6, wherein step 4) comprises:
establishing a chaotic signal generating circuit, wherein the specific expression is as follows:
singal-3＝c·
wherein c is the modulation coefficient of the random signal and is a chaotic signal;
the chaotic signal is generated by an asymmetric nonlinear resistor Chua's circuit, the chaotic signal is added into the arc length for modulation, and the expression of the modulated arc length is as follows:
11. a computer readable storage medium having stored thereon a computer program, characterized in that the program, when being executed by a processor, realizes the steps in the electric arc furnace modeling and harmonic analysis method as claimed in any one of the claims 1-10.
12. A computer apparatus comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor, when executing the program, implements the steps in the electric arc furnace modeling and harmonic analysis method as claimed in any one of claims 1-10.
13. An electric arc furnace modeling and harmonic analysis system, comprising:
the data acquisition module is used for sampling the actually measured voltage and current data of each stage in the smelting process of the electric arc furnace, and further performing Fourier analysis respectively to obtain the waveform distribution of the voltage and the current and each subharmonic vector value;
the nonlinear time-varying resistance module of the electric arc furnace is used for obtaining a static model of equivalent resistance of the electric arc furnace;
the model parameter identification module is used for identifying parameters in the non-linear time-varying resistance model of the electric arc furnace through a particle swarm algorithm, calculating model parameters in the non-linear time-varying resistance model of the electric arc furnace, obtaining an electric arc time-varying resistance expression and fitting a change curve of electric arc equivalent resistance in the smelting process of the electric arc furnace;
the arc length modulation module is used for superposing three small signals, namely a random signal, a Gaussian noise signal, a chaotic signal and the like, with the arc length static model, and adjusting the modulation parameters of all the signals to obtain a modulated arc length random fluctuation model;
and the harmonic analysis module is used for calculating the distortion degree of each harmonic voltage and current in the electric arc furnace smelting process according to the change of the equivalent resistance of the electric arc in the electric arc furnace smelting process.
14. The system of claim 13,
the non-linear time-varying resistance model of the electric arc furnace has the specific expression as follows:
wherein F [ L (t) ] reflects the influence of arc length on arc resistance, and L (t) is an arc length random variation expression; the parameters to be identified are A, B, C' and (D + θ); r represents a time-varying resistance, and ω represents an angular velocity.
15. The system of claim 13,
the model parameter identification module is used for identifying parameters in the nonlinear time-varying resistance model of the electric arc furnace and comprises the following steps:
setting an error objective function FfitnessComprises the following steps:
wherein U isiIs the actual measured value of the arc voltage,
calculating a value for the model of the arc voltage, n being the number of samples measured in step S1;
a, B, C' and (D + theta) 4 model parameters in the arc furnace nonlinear time-varying resistance model are calculated based on a particle swarm algorithm by taking the arc current as an input quantity and the arc voltage as an identification quantity.
16. The system of claim 13, wherein in the electric arc furnace arc length modulation module,
establishing an arc length static fluctuation model, wherein the specific expression is as follows:
L(t)＝L0+0.5L1·(1+sinwt)
wherein L is0Minimum arc length in operation, L1The maximum variation of the arc length, i.e. the difference between the maximum and minimum value, w is chosen to be in the range of 1Hz to 30 Hz.
17. The system of claim 16, wherein in the electric arc furnace arc length modulation module,
establishing a random signal generating circuit, wherein the specific expression is as follows:
singal-1＝a·sinwt
wherein a is the modulation coefficient of the random signal;
the random signal reflects quasi-periodicity and low-frequency harmonic components in the operation of the electric arc furnace, f is 10Hz, the random signal is added into the arc length for modulation, and the modulated arc length expression is as follows:
L1(t)＝L(t)·(1+a·sinwt) 。
18. the system of claim 16, wherein in the electric arc furnace arc length modulation module,
establishing a Gaussian noise signal generating circuit, wherein the specific expression is as follows:
wherein b is a modulation factor of the random signal,
is a random number module.
Gaussian noise signal reflects randomness of the electric arc furnace in operation, and sampling time t is 10-4s, adding the Gaussian noise signal into the arc lengthModulation, wherein the expression of the arc length after modulation is as follows:
19. the system of claim 16, wherein in the electric arc furnace arc length modulation module,
establishing a chaotic signal generating circuit, wherein the specific expression is as follows:
singal-3＝c·
wherein c is the modulation coefficient of the random signal and is a chaotic signal;
the chaotic signal is generated by an asymmetric nonlinear resistor Chua's circuit, the chaotic signal is added into the arc length for modulation, and the expression of the modulated arc length is as follows:
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