CN107045284B - On-load voltage regulation construction method of transformer based on electro-fused magnesia furnace - Google Patents

On-load voltage regulation construction method of transformer based on electro-fused magnesia furnace Download PDF

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CN107045284B
CN107045284B CN201710218685.0A CN201710218685A CN107045284B CN 107045284 B CN107045284 B CN 107045284B CN 201710218685 A CN201710218685 A CN 201710218685A CN 107045284 B CN107045284 B CN 107045284B
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fused
temperature
sand
energy consumption
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CN107045284A (en
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张颖伟
栗振杰
邸天然
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Northeastern University China
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    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Abstract

The invention relates to a construction method of on-load voltage regulation of a transformer based on an electro-fused magnesia furnace, which comprises the following steps: analyzing the power demand with the electrode position and the voltage value as independent variables; establishing an optimization target according to the power requirement and the minimum unit energy consumption and the sand rate; solving an optimization problem, and determining the voltage value and action time of each filling stage; formulating an on-load voltage regulation scheme according to the voltage value and action time of each filling stage; the power requirement with electrode position and voltage values as arguments was analyzed as: taking electric arc heat as an internal heat source of the electric magnesium melting furnace temperature field model, and establishing an internal heat source electric arc and gas cavity conductive area model; and respectively carrying out data fitting on the relationship between the specific heat capacity c and the density rho of the magnesium oxide and the temperature to obtain the action relationship between the voltage and the voltage action time of each stage and the electrode lifting height and the temperature change. The method of the invention can lead the unit energy consumption of fused magnesia and the rate of fused weight and the sand coat of the fused weight to be superior to the prior constant current control strategy, and has important guiding significance for the production process of the fused magnesia furnace.

Description

On-load voltage regulation construction method of transformer based on electro-fused magnesia furnace
Technical Field
The invention relates to a fault detection and diagnosis technology, in particular to a method for constructing on-load voltage regulation of a transformer based on an electro-fused magnesia furnace.
Background
Magnesium is one of light metal elements widely distributed in the nature, and is a natural metal with important use value, and each country pays great attention to the development and utilization of magnesium resources. Is an extremely important strategic resource and plays a significant role in modern industry. The magnesite in China is very large in reserve, but the distribution area is small in range, the magnesite is mainly concentrated in provinces such as Shandong and Liaoning, Liaoning is very rich in magnesite resources, more than 10 mining areas are reserved according to geological exploration, the reserve is 25 hundred million tons, and accounts for 85% of the total reserve in China and 20% of the total reserve in the world. The Liaoning magnesite has relatively few impurities, high grade and great utilization value. Magnesite resources in Liaoning province are concentrated, mineral deposits are huge, the magnesite belt is larger like a large stone bridge in the Haicheng, the burial is shallower, the magnesite mine belt is very suitable for open-air large-scale mechanical exploitation, and the transportation industry is relatively convenient. The fused magnesia is also called fused magnesia, has a melting point of 2852 ℃ and a boiling point of 3600 ℃, and is a latticed magnesia. The fused magnesia has NaCl type crystal lattices, and the crystals of the fused magnesia have a face-centered cubic structure and have the characteristics of high hardness, high brittleness and the like. Because the fused magnesia has the excellent characteristics of high melting point, strong metal or slag corrosion resistance, strong slag resistance, thermal stability, oxidation resistance, complete structure, compact structure, wear resistance and the like, the fused magnesia is widely used in alkaline refractory materials in the metallurgical industry. Meanwhile, the material is widely used as an insulating material and a heat conducting material in the fields of chemical engineering, aerospace, optical instruments and the like. The use value and the performance of the fused magnesia are related to the purity of magnesia contained in the fused magnesia, and the quality fraction of the magnesia is generally adopted to measure the performance of the fused magnesia. The higher the mass fraction of magnesia, the larger the crystals in the fused magnesia, the higher the utility value. How to promote the magnesium oxide grade in the fused magnesia lump after melting in the actual fused magnesia smelting, reduce the energy consumption and improve the yield is a research hotspot and an effort direction of researchers.
According to statistics, in recent 20 years, in the accidents or faults of 110-500 kV transformers in China, the accidents and faults of the on-load tap-changer account for 19% and 18.5% of the accidents and faults of the transformers respectively; in 89 failures of a 500kV transformer, the on-load tap-changer accounts for about 30%. Therefore, a power supply and voltage regulation scheme for reducing power system accidents by adopting the on-load voltage regulation technology can be widely adopted in the power system.
The basic principle is that the change of the voltage ratio of the transformer is realized by adding or subtracting turns of the primary winding or the secondary winding. The voltage regulation method of the transformer is to arrange a tap on a winding on one side of the transformer, cut off or increase the turns of a part of the winding to change the turns of the winding, thereby achieving the polar voltage regulation method of changing the voltage ratio, and a circuit for extracting the tap from the winding for voltage regulation is called a voltage regulation circuit.
The voltage regulation mode of the transformer comprises on-load voltage regulation and no-load voltage regulation, and the main difference is that the voltage regulation transformer is provided with or not provided with a voltage regulation tap, and the voltage regulation mode of the on-load tap switch is on-load voltage regulation. By using the on-load tap changer, the tap of the high-voltage winding is changed to change the number of high-voltage turns for voltage regulation under the condition of ensuring that the load current is not cut off.
Therefore, the no-load voltage regulating transformer without the tap switch needs to be powered off for voltage regulation when the load changes, and the on-load voltage regulating transformer with the tap switch can realize on-load voltage regulation along with the change of the load under the condition of no power cut.
The production process of the fused magnesia at the present stage has the problems of low automation level, serious energy consumption, difficult control of product taste, complex chemical components of materials in a furnace, difficult control of chemical changes, difficult establishment of mechanism models and the like.
The continuous addition of the materials in the fused magnesia furnace is equivalent to the change of the load under the current voltage, and at the moment, if the voltage is properly adjusted along with the increase of the seasoning times, the crystallization quality of the fused magnesia can be improved and the skin sand rate can be reduced under the condition of relatively low energy consumption.
Disclosure of Invention
Aiming at the defects of low automation level, serious energy consumption and the like in the production process of fused magnesite in the prior art, the invention aims to provide the on-load voltage regulation construction method of the transformer based on the fused magnesite furnace, which can ensure that the unit energy consumption and the fused lump skin sand rate of the fused magnesite are superior to those of the existing constant current control strategy.
In order to solve the technical problems, the invention adopts the technical scheme that:
the invention relates to a construction method of on-load voltage regulation of a transformer based on an electro-fused magnesia furnace, which comprises the following steps:
analyzing the power demand with the electrode position and the voltage value as independent variables;
establishing an optimization target according to the power requirement and the minimum unit energy consumption and the sand rate;
solving an optimization problem, and determining the voltage value and action time of each filling stage;
and formulating an on-load voltage regulation scheme according to the voltage value and action time of each filling stage.
Analyzing the power demand with electrode position and voltage values as arguments comprises the steps of:
taking electric arc heat as an internal heat source of the electric magnesium melting furnace temperature field model, and establishing an internal heat source electric arc and gas cavity conductive area model;
and analyzing the relationship between the electrode position, the voltage value and the temperature according to the heat source arc and gas cavity conductive area model, respectively performing data fitting on the relationship between the specific heat capacity c and the density rho of the magnesium oxide and the temperature to obtain a temperature-specific heat and temperature-density relationship change curve, expressing the temperature-density relationship change curve into a temperature-voltage relationship expression, and obtaining the action relationship between the voltage, the voltage action time, the electrode lifting height and the temperature change in each stage.
Before the internal heat source arc and gas cavity conductive area model is established, the following assumptions are made for the arc model: the arc is in a steady state; the anode, namely the surface of the molten pool, has no deformation; the arc and gas cavity conductive area is processed into a cylinder; the gas medium in the cavity is air; the arc plasma is optically thin, i.e. the self-absorption part in the plasma radiation loss is neglected; the arc heating power is equivalent to the product of the arc voltage drop and the current.
The action relation of voltage, voltage action time, lifting height and temperature change in each stage is as follows:
→ represents a proportional relationship, T0And TiIs a constant value, T0The temperature of the molten magnesium oxide is set between 2800-iIncreasing the electrode temperature for adding raw material, T being the current temperature value, Δ TiThe duration of the voltage in the phase, D (T) is a high-order function of the temperature T in the phase, the value of T is represented by TiChange to T0And i is the number of times of filling of the fused magnesia furnace, and is the rising height value factor of the material layer at the stage.
Establishing an optimization target by using the minimum unit energy consumption and the minimum sand coat rate, wherein the optimization target comprises unit energy consumption optimization target construction and fused weight sand coat rate optimization target construction, and a multi-target optimization model of a batch voltage control strategy in the following form is provided by a unit energy consumption optimization target function and a sand coat rate optimization target function:
wherein T isstartFor arcing voltage, the voltage U within the entire smelting batchiFor optimizing decision variables of decision mathematical model, Umax,UminUpper and lower limits, f, of the secondary side voltage of the transformer, respectively1Is the unit energy consumption of fused magnesia in the batch time of 0 to delta mt, f2Is the skin sand rate, U, in 0 to Δ mt batch time1,...,UmIs the batch voltage,. DELTA.tiDuration of melting, mMgO(T)The quality of the skin sand in the fused weight, i, is the number of times the fused magnesia furnace is filled.
The unit energy consumption optimization target is constructed as follows:
the quality of the fused magnesia in the fused weight is as follows:
mMgO(T)=ρMgO·VMgO(T)
the density of the fused magnesia in the fused weight is rhoMgO(T)=3580kg/m3
And if the secondary phase voltage is U, calculating the unit energy consumption of the fused magnesia in the batch time of 0-delta mt according to the following formula:
wherein, UiIs the voltage value from (i-1). delta.t to i.delta.t in the batch time, Umax,UminThe upper limit and the lower limit of the secondary side voltage are respectively determined by the field process; i is the number of times of filling of the fused magnesia furnace, VMgO(T) fused magnesite unit volume, f, of T ∈ (1200, + ∞)1Is the unit energy consumption of fused magnesia within 0 to delta mt batch time, delta tiDuration of melting, UiIs the voltage value from (i-1). DELTA.t to i.DELTA.t in the batch time, RiIs the equivalent resistance of the molten pool, mMgO(T)Quality of the sand in the fused weight.
The melting lump skin sand rate optimization target is constructed as follows:
the quality of the sand in the fused weight is as follows:
mwaste(T)=ρwaste·Vwaste(T)
cooled meltThe density of the sand in the lump is rhowaste=3000kg/m3
The sand coat rate can be calculated by the following formula:
mwasteis the quality of the sand in the fused weight, Vwaste(T) fused magnesite unit volume m when T ∈ (0,1200)MgO(T)Quality of the sand in the fused weight.
Solving the optimization problem as follows:
and solving the multi-objective optimization problem to obtain a set of solutions, namely a Pareto non-inferior optimal solution set, and selecting a proper solution from the obtained Pareto non-inferior optimal solution set as the Pareto optimal solution set of the batch current control strategy by adopting a particle swarm algorithm.
The on-load voltage regulation scheme is formulated according to the voltage value and action time of each filling stage as follows: in the Pareto optimal solution set of the batch current control strategy, a chart of voltage change along with a material mixing process and voltage action time change along with a packing process is drawn to show the change of the voltage value required along with the increase of the material mixing times and the change of the action time required under a certain voltage along with the increase of the material mixing times, two on-load voltage regulation design schemes with lowest unit energy consumption and lowest sand coat rate and a compromise solution are respectively selected, and the voltage is regulated according to the production requirement.
The invention has the following beneficial effects and advantages:
1. the construction method of the invention shows through calculation results that theoretically the provided on-load voltage regulation design scheme can enable the unit energy consumption of fused magnesia and the rate of fused weight skin sand to be superior to the existing constant current control strategy, and the on-load voltage regulation design scheme has important guiding significance for the production process of the fused magnesia furnace.
2. The method changes the original constant current control strategy into voltage transformation and regulation, changes the constant voltage transformer into an on-load voltage regulation transformer, takes the minimum unit energy consumption of the fused magnesite as an optimization target, and regulates the position of an electrode, the voltage value and the action time of the voltage so as to meet the requirements of power and temperature distribution in the electrode lifting process and achieve better smelting and crystallization effects.
Drawings
FIG. 1 is a schematic view of the arc and gas cavity region involved in the method of the present invention;
FIG. 2 is a flow chart of the method of the present invention;
FIG. 3 is a graphical representation of the specific heat capacity of magnesium oxide as a function of temperature in accordance with the method of the present invention;
FIG. 4 is a graphical representation of the density of magnesium oxide as a function of temperature in accordance with the method of the present invention;
FIG. 5 is a flow chart of a particle swarm algorithm involved in the method of the present invention;
FIG. 6 is a graph of Pareto curves for a current control strategy to which the method of the present invention relates;
FIG. 7(a) is a bar graph of voltage as a function of packing process for strategy 1 in accordance with the method of the present invention;
FIG. 7(b) is a bar graph of voltage on-time as a function of packing process for strategy 1 in accordance with the method of the present invention;
FIG. 8(a) is a bar graph of voltage as a function of packing process for strategy 2 in accordance with the method of the present invention;
FIG. 8(b) is a bar graph of voltage on-time as a function of packing process for strategy 2 in accordance with the method of the present invention;
FIG. 9(a) is a bar graph of voltage as a function of packing process for strategy 3 involved in the method of the present invention;
FIG. 9(b) is a bar graph of voltage on-time as a function of packing process for strategy 3 involved in the method of the present invention.
Detailed Description
The invention is further elucidated with reference to the accompanying drawings.
The invention provides an on-load voltage regulation design aiming at the problem of high energy consumption of an electro-fused magnesia furnace. Analyzing the relation among voltage, power and temperature, analyzing heat transfer, resistance and the like in the furnace on the premise of meeting the smelting power and temperature, finding the relation between the voltage and the temperature, finally solving the voltage value of each stage, and verifying the energy conservation of the method through calculation of single-ton energy consumption and sand ratio.
As shown in fig. 1, the method for constructing the on-load voltage regulation of the transformer based on the electro-fused magnesia furnace of the invention comprises the following steps:
analyzing the power demand with the electrode position and the voltage value as independent variables;
establishing an optimization target according to the power requirement and the minimum unit energy consumption and the sand rate;
solving an optimization problem, and determining the voltage value and action time of each filling stage;
and formulating an on-load voltage regulation scheme according to the voltage value and action time of each filling stage.
The invention provides an improved design aiming at the constant-voltage constant-current control strategy that the transformer of the original fused magnesia furnace keeps the input power of the fused magnesia furnace unchanged from the power point of view, when each batch achieves the target smelting effect, if the target smelting effect can be achieved in each batch, the electrode is lifted, materials are added, and the power is adjusted by changing the voltage, so that the requirements of the temperature and the smelting quality required by smelting are met, no excess energy is wasted, and the energy consumption of single ton is reduced.
The internal heat source in the smelting process of the electro-fused magnesia furnace is mainly divided into arc heat generated between the tail ends of the three electrodes and the surface of a molten pool and resistance heat generated when current flows through the molten pool. Among them, arc heat is the main heat source (about 97% of input electric energy) for preparing fused magnesia single crystal. The internal heat release mechanism of the electric arc is extremely complex, the high-temperature plasma spreads heat to the periphery, the heat convection phenomenon is generated by the interaction of the high-temperature plasma and the surrounding magnesium oxide raw materials, the air cavity exists, the electric arc burns in the formed air cavity, part of electric arc heat is transferred to the materials around the air cavity (about 15% -20% of electric arc heat), and a small part of electric arc heat transfers the heat to the surface of the air cavity in a heat radiation mode (about 7% of electric arc heat). Meanwhile, the graphite electrode cathode electric arc plasma jet penetrates through the air cavity at a high speed to reach the surface of the anode molten pool, the impact force generated on the surface of the anode molten pool is very violent, and the flow characteristics of the electric arc plasma jet are difficult to obtain through experiments. From the above analysis, the amount of heat actually transferred to the surface of the molten pool accounts for about 65% to 70% of the electric heat of the arc.
During the operation of the electric magnesium melting furnace, the internally generated alternating current arc is unstable, the shape of the arc is related to the magnitude of the input current, and the arc voltage is very sensitive, which often causes the root of the arc to move irregularly on the surface of the cathode at the end of the electrode, so that the arc becomes bent or twisted and dispersed and unstable, and the shape of the anode spot on the surface of the molten pool is also changed. This makes the physical phenomena involved in the arc itself extremely difficult to determine, and it becomes extremely difficult to calculate the internal heat generation rate of a three-phase ac magnesium melting furnace. For simplification, the invention neglects the resistance electric heat of the melting pool with less heat in the furnace, and takes the arc heat with the main heat as the internal heat source of the temperature field model of the electric smelting magnesium furnace to make the following assumptions: the arc is in a steady state; no deformation of the anode (surface of the molten pool); the arc and gas cavity conductive area is processed into a cylinder; the gas medium in the cavity is air; the arc plasma is optically thin, i.e. the self-absorption part in the plasma radiation loss is neglected; the arc heating power is equivalent to the product of the arc voltage drop and the current.
Based on the above assumptions, the internal heat source arc and gas cavity conductive area model is shown in fig. 2.
Analyzing the power demand with electrode position and voltage values as arguments comprises the steps of:
taking electric arc heat as an internal heat source of the electric magnesium melting furnace temperature field model, and establishing an internal heat source electric arc and gas cavity conductive area model;
and analyzing the relationship between the electrode position, the voltage value and the temperature according to the heat source arc and gas cavity conductive area model, respectively performing data fitting on the relationship between the specific heat capacity c and the density rho of the magnesium oxide and the temperature to obtain a temperature-specific heat and temperature-density relationship change curve, expressing the temperature-density relationship change curve into a temperature-voltage relationship expression, and obtaining the action relationship between the voltage, the voltage action time, the electrode lifting height and the temperature change in each stage.
In this embodiment, a curve (as shown in fig. 3) of the specific heat capacity c of magnesium oxide along with the change of temperature and a curve (as shown in fig. 4) of the density of magnesium oxide along with the change of temperature are obtained by analyzing the relationship between the temperature and the power of the material layer, the influence factors of the resistance and the temperature value of the raw material layer during the melting process, and the power dissipation during the melting process, wherein:
the relationship between the temperature difference of each material layer and the action power and time is as follows:
T0after each layer of filler is smelted, adding raw materials and simultaneously increasing the temperature of a material layer in front of an electrode, namely the set temperature target value of each layer of smelting, and taking the MgO melting point value approximately; t is1,T2…TnThe initial temperature of the material layer after the electrode is increased at the same time for just adding the material layer each time. Power per layer of electrodeTime of action Deltati,PυTo dissipate power, each time the filler is spaced, the power dissipation can be assumed to be the same.
The factors influencing the temperature value of the green layer after addition of the green material are: 1. the preheating temperature of the raw material layer and the conduction temperature of the raw material layer are influenced by the thickness of the filler; 2. the heat conduction temperature of the lower high-temperature molten material layer to the raw material layer; 3. the arc heat temperature generated by the three-phase electrode; 4. after the electric arc, the resistance of the raw material layer molten pool generates heat temperature.
In the invention, the power dissipation analysis in the smelting process is as follows:
there are 3 forms of power dissipation in the melting process of an electro-fused magnesia furnace. During the smelting process, 2 dissipation forms, namely convective heat transfer and thermal radiation, exist inside the molten pool. Magnesium oxide has high viscosity and relatively low convective heat transfer quantity, and the convective heat transfer and thermal radiation heat in a molten pool can be assumed to be negligible. The heat exchange between the electrode surface and the outside is less, and the heat is ignored. The outer surface of the furnace shell and the furnace opening simultaneously carry out convection heat exchange and thermal radiation heat exchange with the surrounding environment, and thermal radiation heat transfer cannot be ignored due to high temperature. Here, the conversion of the radiation term into the composite heat transfer coefficient is equivalent to a surface convection heat transfer coefficient, which is expressed by the following formula:
the equivalent convective heat transfer coefficient obtained by the formula is:
wherein, the emissivity of the outer surface of the furnace shell is taken as the normal emissivity 0.8 of the oxidation steel plate at 600 ℃; σ is the Stefan-Boltzmann constant; t iswThe temperature of the outer surface of the furnace shell; t iseAt ambient temperature, 313.15K (30 ℃) is used.
In this example, the convective heat transfer coefficient h at the furnace shell was set to 15W/(m)2K), the convective heat transfer coefficient h at the furnace mouth is taken as 25W/(m)2·K)。
The influence factors of the temperature of the material layer at the position are as follows: the initial temperature at that location, as well as the height of each lift, the voltage value and the application time at that location.
The temperature is taken as a target, and after the target temperature is reached, the power of the electrode is maintained or reduced to achieve the energy-saving effect.
When the magnesium powder in the smelting layer is in a molten state after smelting is finished, the raw material layer is newly filled, the heat absorption temperature at the bottom of the raw material layer rises suddenly, the melting layer cannot be obviously reduced, and the heat loss can be ignored. Although the green layer endothermically rises in temperature, the entire green layer does not immediately melt into a molten state. The purpose of the smelting is that both layers reach a molten state and become magnesium oxide in a molten state with consistent state.
Assuming two substances A and B, the mass of which is M (A) and M (B), the specific heat of which is C (A) and C (B), and the temperature of which is T (A) and T (B), respectively, and assuming that the temperature after mixing is T, the heat absorbed or released by A is equal to the heat released or absorbed by B, and the formula of heat balance is written:
M(A)C(A)[T(A)-T]=M(B)C(B)[T-T(B)]
if heat loss exists, the equilibrium temperature T' is less than T, and the heat loss is as follows:
Q=[M(A)C(A)+M(B)C(B)][T-T']
the temperature of the whole green layer does not rise so much within a few seconds of charging the green material, and since most of the energy of magnesium oxide in the molten state of the bottom layer and the heat generation of the electrode are eventually transferred to the green material of the upper layer, it is considered that the temperature of the green material rises endothermically from the initial temperature.
The heat source comprises two parts, wherein one part is magnesium oxide in a lower layer molten state for contact heat transfer, the other most part is arc heat generated by a three-phase electrode, part of the heat is conducted to the furnace wall by furnace mouth air convection, and the furnace wall is conducted to the furnace wall and radiated to the ambient air, the heat convection heat of the furnace mouth air convection is small and negligible, the main heat is dissipated to the furnace wall for conduction heat, the heat dissipation accounts for ξ% of the power supply, and the power of the magnesium oxide in a lower layer molten state to magnesium oxide raw materials in an upper layer is the mu of all high-temperature materials in the lower layeriAnd (4) doubling.
The law of conservation of energy of a material layer in the smelting process is as follows:
cmΔTi=cm(T0-Ti)=PiΔti+PωΔti-PυΔti=(Pi+Pω-Pυ)Δti(i=1,2,...,n)
since the temperature rise of the raw material is almost the same after each charging of raw material, T can be assumed1=T2=......=Tn
The lift electrode height after each fill is h, ∈ [0,1.5 ] if seasoning and lift height are discretized into h]Is a proportional parameter, i.e. the lift electrode height is not constant after each filling. At this time, the articleThe mass m of the material is also variable, and is changed into m after the ith filling and the lifting electrodei
Simplified calculation of power dissipation of electric smelting magnesium furnace
Pi,Pω,PυThere is a very complex non-linear relationship, and for the sake of simplicity, the heat dissipation is about ξ% of the power supply, ξ is 15, and the heat transfer power of the bottom molten magnesium oxide to the upper magnesium oxide raw material is mu of all the high-temperature materials in the lower layeriMultiple, muiWhich varies with increasing mass of the underlying material, arc heat remains a major source of heat generation considering that the underlying molten magnesium oxide crystallizes slightly as the temperature decreases, but the temperature as a whole is above the crystallization temperature 2800 ℃.
The above equation can be simplified to:
(3) relationship between electrode position and voltage value and temperature
And respectively carrying out data fitting on the relationship between the specific heat capacity c of the magnesium oxide and the temperature of the density rho, and finding out the approximate mathematical relationship between the specific heat capacity of the magnesium oxide and the density and the temperature.
Matlab data fitting is carried out on the relation between the specific heat capacity c of the magnesium oxide and the temperature to obtain the functional relation between the specific heat capacity c and the temperature, wherein the temperature is thermodynamic temperature and is K.
c=7.1600×10-12T5-1.5826×10-8T4+2.1469×10-5T3
-0.0174T2+7.7637T-236.2925
The quality of the raw material layer is m ═ rho.2pi.r2The density ρ of magnesium oxide varies with temperature;
fitting Matlab data on rho to obtain a functional relation between rho and temperature, wherein the temperature is thermodynamic temperature and is in K.
ρ=-1.0089×10-15T7+2.9182×10-12T6+4.6440×10-9T5
-4.4374×10-6T4-0.0026T3+0.9171T2-176.2532T+17004
According to the above calculation formula, the equivalent resistance of the molten poolAn equivalent power of
Bonding of
In the above formula, take g (ρ)h)=0.005Ωm,g(ρr)=10-6Ω m, the action relationship of voltage, voltage action time, elevation height and temperature change in each stage can be deduced as follows:
equation (3.21) shows that under the same expected temperature T change condition, the product of voltage and action time is different due to different electrode height lifting. → represents a proportional relationship, T0And TiIs a constant value, T0The temperature of the molten magnesium oxide can be set between 2800-iAnd increasing the temperature after the electrode is added with the raw material, wherein T is the current temperature value. Δ tiThe duration of the voltage in the phase, D (T) is a high-order function of the temperature T in the phase, the value of T is represented by TiChange to T0. Is the rise height value factor of the material layer at the stage.
D (T) discussion of temperature as a function of time in this stage: namely the influence of the current temperature T and the influence of temperature changes on the crystallization.
It can be seen from equation (3.21) that temperature is affected by voltage and time of application. The voltage and the voltage acting time can be adjusted only by finding out the reasonable temperature change condition of the electric magnesium melting furnace. While equation (3.21) has two variables and μiAnd, the value can be set constant, i.e., the filler height is constant. Mu.siDirectly influences the voltage UiSize.
μiThe value depends on the influence of the lower layer on the upper layer, and the value of mu is known from the literatureiThe value of (a) is between 2% and 8%. Setting different mu of each stage according to the smelting processi
Aiming at the change situation of the temperature T along with the time, when the temperature change rate is unstable and is small and large, the material heat absorption process is easy to be uneven, namely, the energy consumption affects the material melting effect, therefore, the melting material temperature in the furnace is expected to be changed uniformly, wherein a temperature function with the T linear change as much as possible, a temperature and time change function in the form of a linear function and the T are taken0=2500。
In the invention, the establishment of an optimization target by using the minimum unit energy consumption and the minimum sand coat rate comprises the establishment of a unit energy consumption optimization target and the establishment of a fused lump sand coat rate optimization target, and a multi-target optimization model of a batch voltage control strategy in the following form is provided by a unit energy consumption optimization target function and a sand coat rate optimization target function:
wherein T isstartFor arcing voltage, the voltage U within the entire smelting batchiFor optimizing the decision variables of the decision mathematical model equation (3.28), Umax,UminRespectively the upper and lower limits of the secondary side voltage.
The unit energy consumption optimization target is constructed as follows:
the control of the unit energy consumption of fused magnesia products is an important index for evaluating the process level of the fused magnesia industry, and the unit energy consumption is the electric energy consumed by producing one ton of fused magnesia. The electric magnesium melting industry has the defects of high power consumption, severe power consumption pressure and power grid pollution. Reducing the specific energy consumption of fused magnesite is a major objective pursued by factories. In this chapter, an optimization objective function of fused magnesia unit energy consumption is established by taking input voltage as a decision variable, and when field smelting is finished, the temperature of the interface between the skin sand and the fused magnesia is 1200 ℃ on average. Therefore, the temperature field in the furnace is divided into the following two regions according to the solution result of the temperature field:
(a) a sand-skin area: t is from (0,1200) DEG C;
(b) electric smelting of the magnesia zone: t ∈ (1200, + ∞) DEG C.
Based on the temperature field simulation solving result, respectively counting the unit volumes of the skin sand and the fused magnesia in the two area ranges as follows:
let the density of fused magnesia in the cooled fused weight be rhoMgO(T)=3580kg/m3And then the quality of the fused magnesia in the fused weight is as follows:
mMgO(T)=ρMgO·VMgO(T)
if the secondary phase voltage is U, the unit energy consumption of fused magnesite in the batch time of 0 to Δ mt can be calculated by the following formula:
wherein, UiIs the voltage value from (i-1). delta.t to i.delta.t in the batch time, Umax,UminThe upper and lower limits of the secondary side voltage are determined by the field process.
According to the formula, the unit energy consumption optimization objective function is determined by the batch voltage U1,...,UmAnd the mass m of fused magnesia in the fused weightMgO(T)And (6) determining. Wherein m isMgO(T)Determined by the temperature field distribution in the furnace. Under the condition that the secondary total resistance is basically unchanged, the temperature field distribution in the furnace is only influenced by the voltage and the smelting time delta t. Therefore, the unit energy consumption is only influenced by the voltage and the smelting time delta t.
The melting lump skin sand rate optimization target is constructed as follows:
the fused mass skin sand rate is the mass percentage of the skin sand in the fused mass in the whole fused mass. The purpose of the electric melting magnesia is to obtain the purified magnesia with high quality and large crystallization after the magnesite ore or light burned magnesia powder containing magnesia with lower purity is melted by high temperature electric arc, cooled, mixed and crystallized. Therefore, the method reduces the sand coat rate of the fused mass, improves the yield and the quality of the fused magnesia, and is an important index for measuring the process level of the fused magnesia industry. The definition of the coat sand rate function for the fused mass is set forth below.
According to the literature, the unit volume of the sand area is counted to be V based on the simulation solving result of the temperature fieldwaste(T)
Let the density of the sand in the cooled fused weight be rhowaste=3000kg/m3And then the quality of the sand in the fused weight is as follows:
mwaste(T)=ρwaste·Vwaste(T)
the sand coat rate can be calculated by the following formula:
in the above formula, mMgO(T) and mwasteThe magnitude of the values between (T) is traded off for this, the magnitude of which is influenced by the temperature field distribution in the furnace. The temperature field distribution in the furnace is only affected by the voltage change and the melting time delta t of each batch. Therefore, mMgO(T) and mwasteThe magnitude of the value of (T) is also affected only by voltage variations. Therefore, as with unit energy consumption, the fused mass coat sand rate optimization objective function is only influenced by the voltage and the smelting time change.
In the invention, the solving optimization problem is as follows:
and solving the multi-objective optimization problem to obtain a set of solutions, namely a Pareto non-inferior optimal solution set, and selecting a proper solution from the obtained Pareto non-inferior optimal solution set as the Pareto optimal solution set of the batch current control strategy by adopting a particle swarm algorithm.
The multi-objective optimization problem is different from the single-objective optimization problem, the multi-objective optimization problem usually obtains a set of solutions, the single-objective optimization problem is only a determined unique optimal solution, and the multi-objective optimization problem is called a Pareto non-inferior optimal solution set. And the optimal solutions of each Pareto in the set cannot be compared with each other, namely, each Pareto optimal solution in the set can make one objective function optimized while the other objective function deteriorated. An appropriate solution is selected from the solved Pareto non-inferior optimal solution set to serve as an optimal solution of the final multi-objective optimization problem[17,18]. For Pareto dominant definitions:
1) pareto governs: the vector u is equal to (u)1,…,un) Dominant vector v ═ v1,…,vn) Let u > v, if and only if:
2) pareto optimal or non-inferior solution: weighted decision vector x*For Pareto optimal solution, if and only if:
a set formed by all Pareto optimal solutions is called a Pareto non-inferior optimal solution set, and an area formed by target vectors corresponding to each non-inferior optimal solution in the solution set is called a Pareto front end.
(2) Brief introduction to particle swarm optimization based on multiple targets
And (3) performing particle swarm optimization based on multiple targets, namely PSO algorithm. It is a method for solving optimization problems by finding characteristics from the behavior of the biological population.
In PSO, an optimization problem is considered to be a flock of birds foraging in the air, then "food" is the optimal solution to the optimization problem, and each foraging "bird" flying in the air is a "Particle" (Particle) that is searched in the solution space in the PSO algorithm.
A random population of particles is initialized with a random solution and then an optimal solution is found by iteration. In each iteration, the particle updates itself by tracking two "extrema":
one is the best solution found by the particle itself, i.e., the individual extremum (pbest), and the other is the best solution (gbest), i.e., the global extremum, achieved by all particles in the entire population during the past search.
Finding these two best solutions is followed by the most important "acceleration" process in PSO, where each particle constantly changes its velocity in the solution space to "fly" as much as possible towards the regions pointed to by pbest and gbest.
Assuming a search is performed in an N-dimensional space, the information of particle i can be represented by two N-dimensional vectors to indicate x, where the position of the ith particle can be representedi=(xi1,xi2,…xiN)TVelocity vi=(vi1,vi2,…viN)T
After finding the two optimal solutions, the particles can update their velocity and position according to the following formula:
is the velocity of particle i in dimension d in the kth iteration;is the current position of particle i in the d-th dimension in the k-th iteration; 1, 2, 3 …, M: the size of the population. The particle swarm algorithm flowchart is shown in fig. 5.
In the invention, an on-load voltage regulation scheme is formulated according to the voltage value and action time of each filling stage as follows: in the Pareto optimal solution set of the batch current control strategy, two on-load voltage regulation design schemes, namely lowest unit energy consumption and lowest sand coat rate, are respectively selected and solved, and a graph of the change of a plurality of batches of voltages along with the material mixing process and the change of the voltage action time along with the filling process is obtained to show the change of the voltage value required along with the increase of the material mixing times and the change of the action time required under a certain voltage along with the increase of the material mixing times, and the voltage is regulated according to the production requirement.
In this embodiment, the changes of 20 batches of voltages obtained by the three designs of on-load voltage regulation with the seasoning process and the changes of the voltage action time with the filling process are shown in fig. 7(a) -7 (b), fig. 8(a) -8 (b), and fig. 9(a) -9 (b). 7(a) -7 (b) are bar graphs of a scheme that minimizes specific energy consumption but maximizes sand rate; 8(a) -8 (b) are two bar graphs of a scheme that results in the lowest sand coat rate but the highest specific energy consumption; FIGS. 9(a) -9 (b) ensure moderate sand and skin rate and specific energy consumption. The abscissa of the bar chart is the frequency of filling, the ordinate (a) is changed along with the change of the voltage value required by the increase of the frequency of seasoning, and the ordinate (b) is changed along with the change of the required action time under the voltage shown in the bar chart (a) along with the increase of the frequency of seasoning.
In this embodiment, by MATLAB simulation, a batch voltage non-inferior solution target vector set after 200 iterations is obtained as shown in fig. 6, and the number of solutions meeting the conditions in the final Pareto optimal solution set is 68. And selecting a proper solution in the Pareto optimal solution set according to actual production requirements.
The change of 20 batches of voltages and the change of voltage action time with the packing process, which are obtained by designing 3 schemes for load voltage regulation, are shown in fig. 7(a), 7(b), 8(a), 8(b), 9(a) and 9(b), and a proper optimal solution is selected to determine the voltage and the voltage action time of each batch.
In the invention, an on-load voltage regulation scheme is formulated according to the voltage value and action time of each filling stage.
In the furnace starting stage, the establishment of a molten pool is carried out, the materials are required to be melted quickly, and the forming time of the molten pool is required to be short. And the arc power is required to be large and the resistance power of the molten pool is required to be small in the process, so that the secondary voltage of the transformer is required to be higher. As can be seen from fig. 7(a), 7(b), 8(a), 8(b), 9(a) and 9(b), the voltage value at this stage is high and the operation time is relatively short.
In the melting phase, not only is it required that the material be melted quickly, but it is also required that a suitable bath depth be maintained. The maintenance of the depth of the molten pool requires that the resistance power of the molten pool is proper, if the electric arc power is too large, the burning-off can be generated, and if the electric arc power is too small, the material smelting is slow, so that the proper electric arc voltage is required. This stage was filled 20 times for about 8 hours. As can be seen from fig. 7(a), 7(b), 8(a), 8(b), 9(a) and 9(b), the voltage value at this stage is high and the action time is short.
In the ending stage, the electric arc power is required to be small in the ending stage, the resistance power of the molten pool is required to be large, so that the constant temperature of the molten pool is ensured, the raw materials above the molten pool are sintered and sealed, and the raw materials are prevented from entering the molten pool to pollute products. For this purpose, the secondary voltage of the transformer is reduced in the final phase. The last batch layer covers the heat of the furnace mouth, and the batch layer is heated by using the waste heat.
The calculation of the single-ton energy consumption and the sand-skin ratio proves that the method can produce higher-quality fused magnesium crystals under the unit energy consumption.
Compared with the on-load voltage regulation, the constant current control strategy has the advantages that under the condition that the current of the existing process is constantly equal to 10000A, the unit energy consumption of fused magnesia in a complete furnace is 1735.3KWh/t, and the skin sand rate of a fused weight is 37.2552%. The optimized Pareto optimal solution is concentrated, and the unit energy consumption and the sand rate of only partial solution are superior to the two indexes in the existing production process. The method reduces the unit energy consumption of fused magnesia and the rate of fused lump skin sand, and improves the yield of fused magnesia, which is the aim pursued by fused magnesia enterprises in production. Therefore, solutions with unit energy consumption and sand rate superior to those of the two indexes in the Pareto optimal solution set selected by the on-load voltage regulation in the prior art are used as candidate solution sets of the on-load voltage regulation, and 12 solutions meet the requirement. Two on-load voltage regulation control strategies with the lowest unit energy consumption and the lowest sand coat rate and an optimal compromise solution with the unit energy consumption and the sand coat rate between the unit energy consumption and the sand coat rate are selected from 12 solutions respectively and are listed in a table 3.1.
TABLE 3.1 control strategy comparison
Table 3.1Control strategy comparison
As can be seen from the data in the table, in the whole production process of the three electric smelting magnesiums based on-load voltage regulation, the unit energy consumption is lower than that of the electric smelting magnesia produced under the existing process conditions, and simultaneously, the skin sand rate of the smelting lump is reduced compared with that of the existing process. The unit energy consumption of the on-load voltage regulation design 1 is the lowest, but the sand coat rate is the largest, and the sand coat rate of the on-load voltage regulation design 2 is the lowest, but the unit energy consumption is the largest. The unit energy consumption and the sand rate of the on-load voltage regulation design 3 are relatively moderate.
If the decision maker aims at reducing the energy consumption as the first consideration target, the on-load voltage regulation design 1 can be selected as the production scheme of the electro-fused magnesia furnace. Compared with a 10000A constant current control strategy in the existing production process, the unit energy consumption of the fused magnesia in the on-load voltage regulation design 1 is reduced by 9.6546% compared with the existing production process, and the sand coat rate of the fused lump is reduced by 0.2406%. If the decision maker aims to reduce the sand-skin ratio as the first consideration, the on-load voltage regulation design 2 can be used as the production scheme of the electro-fused magnesia furnace. Compared with the existing constant current control strategy, the unit energy consumption of the strategy 2 is reduced by 0.4770% compared with the existing constant current control strategy, and the coat sand rate of the fused mass is reduced by 18.37%. If a producer wants to have a compromise between the two, and simultaneously considers the minimum sand rate and the minimum unit energy consumption, the on-load voltage regulation design 3 can be selected as a production scheme, the unit energy consumption is reduced by 2.2700%, and the sand rate is reduced by 5.016%.
The invention changes the constant voltage transformer into the on-load voltage regulating transformer, takes the minimum unit energy consumption of the fused magnesite as an optimization target, regulates the position of the electrode, the voltage value and the action time of the voltage, and regulates the voltage regulating range and the value regulating amplitude of the fused magnesite furnace so as to meet the requirements of power and temperature distribution in the electrode lifting process.

Claims (7)

1. A transformer on-load voltage regulation construction method based on an electro-fused magnesia furnace is characterized by comprising the following steps:
analyzing the power demand with the electrode position and the voltage value as independent variables;
establishing an optimization target according to the power requirement and the minimum unit energy consumption and the sand rate;
solving an optimization problem, and determining the voltage value and action time of each filling stage;
formulating an on-load voltage regulation scheme according to the voltage value and action time of each filling stage;
the action relation of voltage, voltage action time, lifting height and temperature change in each stage is as follows:
→ represents a proportional relationship, T0And TiIs a constant value, T0The temperature of the molten magnesium oxide is set between 2800-iIncreasing the electrode temperature for adding raw material, T being the current temperature value, Δ TiThe duration of the voltage in the phase, D (T) is a high-order function of the temperature T in the phase, the value of T is represented by TiChange to T0I is the number of times of filling of the electric smelting magnesium furnace; mu.siFor varying factors, UiIs the phase voltage;
the method comprises the following steps of establishing an optimization target by using the minimum unit energy consumption and the minimum sand coat rate, wherein the unit energy consumption optimization target is established, the fused lump sand coat rate optimization target is established, and a multi-target optimization model of a batch voltage control strategy in the following form is provided by a unit energy consumption optimization target function and a sand coat rate optimization target function:
wherein U ismax,UminUpper and lower limits, f, of the secondary side voltage of the transformer, respectively1Is the unit energy consumption of fused magnesia in the batch time of 0 to delta mt, f2Is the skin sand rate, U, in 0 to Δ mt batch time1,...,UmIs the batch voltage,. DELTA.tiFor the duration of the melting process, mMgO(T) is the quality of the skin sand in the fused weight, and i is the filling frequency of the fused magnesia furnace.
2. The on-load tap changing construction method of a transformer based on an electro-fused magnesia furnace according to claim 1, wherein analyzing the power demand with the electrode position and the voltage value as independent variables comprises the steps of:
taking electric arc heat as an internal heat source of the electric magnesium melting furnace temperature field model, and establishing an internal heat source electric arc and gas cavity conductive area model;
analyzing the relationship between the electrode position, the voltage value and the temperature according to the model of the internal heat source arc and the gas cavity conductive area, respectively performing data fitting on the relationship between the specific heat capacity c and the density rho of the magnesium oxide and the temperature to obtain a change curve of the relationship between the temperature and the specific heat and the relationship between the temperature and the density, expressing the change curve into a relational expression of the temperature and the voltage, and obtaining the action relationship of the voltage, the voltage action time, the electrode lifting height and the temperature change in each stage.
3. The on-load voltage regulation construction method of the transformer based on the electro-fused magnesia furnace according to claim 2, characterized in that: before the internal heat source arc and gas cavity conductive area model is established, the following assumptions are made for the arc model: the arc is in a steady state; the anode, namely the surface of the molten pool, has no deformation; the arc and gas cavity conductive area is processed into a cylinder; the gas medium in the cavity is air; the arc plasma is optically thin, i.e. the self-absorption part in the plasma radiation loss is neglected; the arc heating power is equivalent to the product of the arc voltage drop and the current.
4. The on-load voltage regulation construction method of the transformer based on the electro-fused magnesia furnace according to claim 1, characterized in that the unit energy consumption optimization objective is constructed as follows:
the quality of the fused magnesia in the fused weight is as follows:
mMgO(T)=ρMgO·VMgO(T)
the density of the fused magnesia in the fused weight is rhoMgO(T)=3580kg/m3
And if the secondary phase voltage is U, calculating the unit energy consumption of the fused magnesia in the batch time of 0-delta mt according to the following formula:
wherein, UiIs the voltage value from (i-1). delta.t to i.delta.t in the batch time, Umax,UminThe upper limit and the lower limit of the secondary side voltage are respectively determined by the field process; i is the number of times of filling of the fused magnesia furnace, VMgO(T) fused magnesite unit volume, f, of T ∈ (1200, + ∞)1Is the unit energy consumption of fused magnesia within 0 to delta mt batch time, delta tiFor duration of melting, RiIs the equivalent resistance of the molten pool, mMgOAnd (T) is the mass of the sand in the fused mass.
5. The on-load voltage regulation construction method of the transformer based on the fused magnesia furnace according to claim 1, characterized in that the fused weight sand coat rate optimization target is constructed as follows:
the quality of the sand in the fused weight is as follows:
mwaste(T)=ρwaste·Vwaste(T)
the density of the sand in the cooled fused weight is rhowaste=3000kg/m3
The sand coat rate can be calculated by the following formula:
mwasteis the quality of the sand in the fused weight, Vwaste(T) fused magnesite unit volume m when T ∈ (0,1200)MgOAnd (T) is the mass of the sand in the fused mass.
6. The on-load voltage regulation construction method of the transformer based on the electro-fused magnesia furnace according to claim 1, characterized in that the problem of solving optimization is as follows:
and solving the multi-objective optimization problem to obtain a set of solutions, namely a Pareto non-inferior optimal solution set, and selecting a proper solution from the obtained Pareto non-inferior optimal solution set as the Pareto optimal solution set of the batch current control strategy by adopting a particle swarm algorithm.
7. The on-load voltage regulation construction method of the transformer based on the electro-fused magnesia furnace according to claim 1, which is characterized in that:
the on-load voltage regulation scheme is formulated according to the voltage value and action time of each filling stage as follows: in the Pareto optimal solution set of the batch current control strategy, a chart of voltage change along with a material mixing process and voltage action time change along with a packing process is drawn to show the change of the voltage value required along with the increase of the material mixing times and the change of the action time required under a certain voltage along with the increase of the material mixing times, two on-load voltage regulation design schemes with lowest unit energy consumption and lowest sand coat rate and a compromise solution are respectively selected, and the voltage is regulated according to the production requirement.
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