CN106990289B - A method of obtaining the reactance of electric melting magnesium furnace conductive cross arm - Google Patents

A method of obtaining the reactance of electric melting magnesium furnace conductive cross arm Download PDF

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CN106990289B
CN106990289B CN201710190797.XA CN201710190797A CN106990289B CN 106990289 B CN106990289 B CN 106990289B CN 201710190797 A CN201710190797 A CN 201710190797A CN 106990289 B CN106990289 B CN 106990289B
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conductive cross
geometric mean
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李国锋
由纪
王进君
王志强
王宁会
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Dalian University of Technology
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    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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Abstract

The present invention provides a kind of method for obtaining the reactance of electric melting magnesium furnace conductive cross arm, it mainly comprises the steps that and conductive cross arm section is considered as rectangle frame cross section first, and be divided into being made of several small rectangles, the geometric mean distance in the section is obtained using the geometric mean distance formula of complex figure;Followed by the single-phase conductive cross arm cross section geometric acquired away from the mutual geometric mean distance between three-phase, to obtain the mutual induction amount between the self-inductance of single-phase conductive cross arm and each phase, electric melting magnesium furnace conductive cross arm reactance is finally obtained according to reactance formula.Since conductive cross arm section is handled from geometric mean distance by complex geometry, and influencing each other between each phase is considered, so that its result is more accurate.The present invention is suitable for obtaining the reactance value of the electric melting magnesium furnace conductive cross arm of different materials, structure and space layout, and accuracy is higher.

Description

A method of obtaining the reactance of electric melting magnesium furnace conductive cross arm
Technical field
The present invention relates to the fields for obtaining metallurgical equipment reactance, and in particular to a kind of acquisition electric melting magnesium furnace conductive cross arm reactance Method.
Background technique
Produce magnesia and other products using electric melting magnesium furnace, to obtain good technical and economic requirements, it is electrical and The design parameter of electric furnace is crucial.And the design of the short net of electric melting magnesium furnace and production technology and equipment investment suffer from close pass System.Conductive cross arm is the key component in the short net of electric melting magnesium furnace, it is desirable that its light weight, good rigidity, reactance is small, repairs less, the service life It is long.It is not only used to clamp and support Electrode for remelting, and conveys electric energy as the conductor of connection electrode.According to studies have shown that Tens of thousands of amperes can achieve by the electric current of electric melting magnesium furnace conductive cross arm at present, can be generated the impedance of conductive cross arm is small again Biggish electric energy loss thereby reduces the effective power of electric melting magnesium furnace.Conductive cross arm impedance includes resistance and reactance two parts. Wherein, active component ratio shared in impedance is smaller, therefore the size of conductive cross arm reactance has been largely fixed electricity Can loss number, and then influenced the raising of electric melting magnesium furnace effective power.
The characteristics of electric melting magnesium furnace conductive cross arm is that electric current is big, and section is big, and appearance profile is complicated, and working environment is severe.At present To in the research of conductive cross arm reactance, being to carry out theoretical calculation using empirical equation mostly, often simplifies and conductive cross arm is cut The solution of face geometric mean distance has ignored influencing each other between three-phase conductive cross arm, causes estimation result deviation larger, is unfavorable for The subsequent prediction to electric melting magnesium furnace conductive cross arm electric energy loss.
The present invention provides a kind of methods for obtaining the reactance of electric melting magnesium furnace conductive cross arm, including obtain conductive cross arm section and answer Miscellaneous geometric mean distance, every phase self-inductance and mutual induction amount between phase and phase, more can accurately obtain the reactance value of conductive cross arm, with Just designer understands the electric energy loss situation of electric melting magnesium furnace conductive cross arm in advance, thus targetedly propose corrective measure, Achieve the purpose that reduce electric energy loss and improves electric melting magnesium furnace effective power.
Summary of the invention
The purpose of the present invention: to solve deficiency present in the domestic and international prior art and method, the invention discloses one kind The method for obtaining the reactance of electric melting magnesium furnace conductive cross arm has many advantages, such as that process is clear, be easily understood and result is accurate, is suitable for not The acquisition of the electric melting magnesium furnace conductive cross arm reactance value of same material, structure and space layout.
To achieve the above object, concrete scheme of the invention is as follows:
A method of the reactance of electric melting magnesium furnace conductive cross arm is obtained, is mainly included the following steps:
Step 1 obtains conductive cross arm from geometric mean distance
The conductive cross arm of the electric melting magnesium furnace is hollow rectangular conductor, and frame and bracket are special metal materials, When obtaining the conductive cross arm reactance, section can be considered as rectangle frame, rectangular shaped rim section is divided into multiple small rectangles to ask The section from can all there is mutual geometric mean distance between geometric mean distance, rectangle and rectangle, which is considered as each The distance between rectangle geometric center.
After electric melting magnesium furnace conductive cross arm section is divided into several small rectangle compositions, it can be schemed from geometric mean distance according to complexity Shape geometric mean distance acquires.When a figure is made of the part n, it can be made of according to formula (1) each from geometric mean distance Partial acquires from geometric mean distance and mutual geometric mean distance:
Wherein, g is entire conductor rectangular section from geometric mean distance, unit mm;gkkFor the small rectangle after any decomposition From geometric mean distance, can be acquired according to formula (2), unit mm;gkiThe mutual geometry between small rectangle after decomposing for any two is equal Away from unit mm;Sk、Si、SnIt is the small rectangular area after arbitrary decomposition, unit mm2
gkk=k (a+b) (2)
Wherein, gkkIt is single small rectangle from geometric mean distance, unit mm;A is the length of rectangle, unit mm;B is rectangle Width, unit mm;K is coefficient of alteration.
Step 2 obtains conductive cross arm mutual induction amount
The reactance that conductor is acquired according to the mutual inductance between the self-induction of the conductor of acquisition itself and adjacent conductor, works as conductor When length is much larger than the mutual geometric mean distance between conductor, the mutual inductance simplified between straight equal long conductors is calculated according to formula (3):
Wherein, mutual inductance of the M between two phase conductors, unit mm;μ0For the space permeability of conductor;L is conductor length, single Position mm;D is the mutual geometric mean distance between two flat straight conductors, unit mm.
Step 3 obtains conductive cross arm self-inductance
When conductor length much larger than conductor from geometric mean distance when, the mutual inductance formula that simplifies between two parallel conductors In, if by mutual geometric mean distance d be changed to independent conductor from geometric mean distance g, mutual inductance formula is self-induction formula, i.e., according to formula (4) conductive cross arm self-inductance is obtained:
Wherein, L is the self-induction of conductor, unit mm;μ0For the space permeability of conductor;L is conductor length, unit mm;G is Conductor from geometric mean distance, unit mm.
Step 4 obtains conductive cross arm reactance
According to formula (5) and formula (6) through the above steps in the self-inductance and between phase and phase of conductive cross arm that obtains Mutual induction amount, the side phase reactance value and middle phase reactance value of conductive cross arm can be acquired respectively.
The formula of side phase reactance:
The formula of middle phase reactance:
According to above step, proposed by the present invention is a kind of method for obtaining the reactance of electric melting magnesium furnace conductive cross arm, is related to Conductive cross arm geometric mean distance, every phase self-inductance and the acquisition of mutual induction amount between phase and phase, more can accurately acquire conduction The reactance value of transverse arm reduces the electric energy loss of electric melting magnesium furnace for corrective measure and improves active power providing foundation.This method is suitable The acquisition of electric melting magnesium furnace conductive cross arm reactance for different materials, structure and space layout, it is simple and practical, there is higher application Value.
Detailed description of the invention
Fig. 1 is the single-phase conductive cross arm sectional view of electric melting magnesium furnace provided by the invention.
Fig. 2 is electric melting magnesium furnace three-phase conductive cross arm section provided by the invention layout drawing.
Fig. 3 is electric melting magnesium furnace conductive cross arm two-dimensional simulation illustraton of model provided by the invention.
Specific embodiment
The present invention is described in detail for son combined with specific embodiments below:
This example is to obtain the reactance of its conductive cross arm part by taking the short web frame of 5000kVA electric melting magnesium furnace, parameter as an example. Conductive cross arm use copper-steel composites structure, internal layer steel thickness 10mm, outer layer copper thickness 6mm, the entire a height of 290mm of rectangle frame width × 340mm.Three-phase conductive cross arm length is 6.376m.Since the electric current by conductive cross arm is flowed through from attached layers of copper mostly, so Approximately think that rectangle frame is only made of copper product, thus can be divided into section the width of numerous small rectangles to be selected as 6mm.
Step 1 obtains conductive cross arm from geometric mean distance
As shown in Figure 1, electric melting magnesium furnace conductive cross arm section is divided into the small rectangle that 16 width are 6mm first.According to public affairs Formula (1) obtain conductive cross arm from geometric mean distance need to acquire each small rectangle area, from geometric mean distance and each rectangle it Between mutual geometric mean distance.Wherein each small rectangle is acquired according to formula (2) from geometric mean distance.From figure 1 it appears that conductive horizontal There are the rectangles of two kinds of different parameters in numerous rectangles that arm section divides.As rectangle length a=82mm, width b=6mm, B/a ≈ 0.073 consults and compares related data from table 1, and the value of b/a is closer to 0.05, so approximately taking k= 0.22346, therefore have g11=g22=g33=g44=g99=g (10) (10)=g (11) (11)=g (12) (12)=0.22346 × (82+6)=19.66448mm;As rectangle length a=72.5mm, width b=6mm, b/a ≈ 0.083 is consulted from table 1 With comparison related data, the value of b/a is closer to 0.1, so approximately taking k=0.2236, therefore has g55=g66=g77= G88=g (13) (13)=g (14) (14)=g (15) (15)=g (16) (16)=0.2236 × (72.5+6)=17.5526mm.
b/a k b/a k
0.000 0.22313 0.50 0.22360
0.025 0.22333 0.55 0.22358
0.05 0.22346 0.60 0.22357
0.10 0.22360 0.65 0.22356
0.15 0.22366 0.70 0.22355
0.20 0.22360 0.75 0.22354
0.25 0.22369 0.80 0.22353
0.30 0.22368 0.85 0.22353
0.35 0.22366 0.90 0.22353
0.40 0.22364 0.95 0.223525
0.45 0.22362 1.00 0.223525
Table 1
The area of each small rectangle is as follows:
S1=S2=S3=S4=S9=S10=S11=S12=6 × 82=492mm2
S5=S6=S7=S8=S13=S14=S15=S16=6 × 72.5=435mm2
Mutual geometric mean distance between each small rectangle is approximately considered the distance between geometric center, and it is as follows to obtain data:
G12=g21=g23=g32=g34=g43=g9 (10)=g (10) 9=g (10) (11)=g (11) (10)= 82mm;
G13=g24=g31=g42=g9 (11)=g (10) (12)=g (11) 9=g (12) (10)=164mm;
G14=g41=g9 (12)=g (12) 9=246mm;
G15=g4 (16)=g51=g8 (12)=g9 (13)=(16) 4 ≈ 291.900mm of g (12) 8=g (13) 9=g;
G16=g4 (15)=g61=g7 (12)=g9 (14)=g (11) (12)=g (12) 7=g (12) (11)=g (14) (15) 4 ≈ 308.680mm of 9=g;
G17=g4 (14)=g6 (12)=g71=g9 (15)=(15) 9 ≈ 340.401mm of g (12) 6=g (14) 4=g;
G18=g4 (13)=g5 (12)=g81=g9 (16)=(16) 9 ≈ 383.374mm of g (12) 5=g (13) 4=g;
(12) 4 ≈ 375.729mm of g19=g4 (12)=g91=g;
G1 (10)=g29=g3 (12)=g4 (11)=(12) 3 ≈ 327.951mm of g92=g (10) 1=g (11) 4=g;
G1 (11)=g2 (10)=g2 (12)=g39=g3 (11)=g4 (10)=g93=g (10) 2=g (10) 4=g (11) (12) 2 ≈ 295.601mm of 1=g (11) 3=g;
G1 (12)=g2 (11)=g3 (10)=(12) 1 ≈ 284mm of g49=g94=g (10) 3=g (11) 2=g;
G1 (13)=g48=g59=g84=g95=g (12) (16)=g (13) 1=g (16) (12) ≈ 254.581mm;
G1 (14)=g47=g69=g74=g96=g (12) (15)=g (14) 1=g (15) (12) ≈ 183.6mm;
G1 (15)=g46=g64=g79=g97=g (12) (14)=g (14) (12)=(15) 1 ≈ 114.538mm of g;
G1 (16)=g45=g54=g89=g98=g (12) (13)=g (13) (12)=(16) 1 ≈ 55.150mm of g;
G25=g3 (16)=g52=g8 (11)=g (10) (13)=g (11) 8=g (13) (10)=(16) 3 ≈ of g 210.641mm;
G26=g3 (15)=g62=g7 (11)=g (10) (14)=g (11) 7=g (14) (10)=(15) 3 ≈ of g 233.339mm;
G27=g3 (14)=g6 (11)=g72=g (10) (15)=g (11) 6=g (14) 3=g (15) (10) ≈ 273.929mm;
G28=g3 (13)=g5 (11)=g82=g (10) (16)=g (11) 5=g (16) (10)=(13) 3 ≈ of g 325.791mm;
G2 (13)=g38=g5 (10)=g83=g (10) 5=g (11) (16)=g (13) 2=g (16) (11) ≈ 280.627mm;
G2 (14)=g37=g6 (10)=g73=g (10) 6=g (11) (15)=g (14) 2=g (15) (11) ≈ 218.287mm;
G2 (15)=g36=g63=g7 (10)=g (10) 7=g (11) (14)=g (14) (11)=(15) 2 ≈ of g 164.496mm;
G2 (16)=g35=g53=g8 (10)=g (10) 8=g (11) (13)=g (13) (11)=(16) 2 ≈ of g 130.313mm;
G56=g65=g67=g76=g78=g87=g (13) (14)=g (14) (13)=g (14) (15)=g (15) (14)=g (15) (16)=g (16) (15)=72.5mm;
G57=g68=g75=g86=g (13) (15)=g (14) (16)=g (15) (13)=g (16) (14)= 145mm;
G58=g85=g (13) (16)=g (16) (13)=217.5mm;
G5 (13)=g8 (16)=(16) 8 ≈ 398.575mm of g (13) 5=g;
G5 (14)=g6 (13)=g7 (16)=g8 (15)=(16) 7 ≈ of g (13) 6=g (14) 5=g (15) 8=g 364.117mm;
G5 (15)=g6 (14)=g6 (16)=g7 (13)=g7 (15)=g8 (14)=g (13) 7=g (14) 6=g (14) (16) 6 ≈ 341.778mm of 8=g (15) 5=g (15) 7=g;
G5 (16)=g6 (15)=g7 (14)=g8 (13)=g (13) 8=g (14) 7=g (15) 6=g (16) 5= 334mm;
Above data is substituted into above-mentioned formula (1) can acquire conductive cross arm from geometric mean distance g ≈ 183.812mm.
Step 2 obtains conductive cross arm mutual induction amount
Electric melting magnesium furnace conductive cross arm is in factory's actual arrangement, due to separated by a distance bigger between three-phase, each phase Between mutual geometric mean distance be approximately considered the distance between geometric center.The three-phase conductive cross arm of 5000kVA electric melting magnesium furnace is cut Face layout drawing is as shown in Figure 2.Mutual geometric mean distance between each phase available in figure:
gAB=gBC=629mm
gAC=900mm
The straight mutual inductance waited between long conductors is obtained according to formula (7):
Wherein, mutual inductance of the M between two phase conductors, unit mm;μ0For the space permeability of conductor;L is conductor length, single Position mm;D is the mutual geometric mean distance between two flat straight conductors, unit mm.
Under normal circumstances, the length l of electric melting magnesium furnace conductive cross arm is significantly larger than the mutual geometric mean distance d between conductor.Therefore, two Mutual inductance formula can be reduced to formula (3) between phase conductive cross arm.It is conductive horizontal that above data is substituted into formula (3) available each phase Mutual inductance value between arm.
MAB=MBC≈2.565×10-6H
MAC≈2.112×10-6H
Step 3 obtains conductive cross arm self-inductance
In mutual inductance formula between two straight grade long conductors, if mutual geometric mean distance d is changed to oneself of independent conductor Geometric mean distance g, mutual inductance formula are self-induction formula.Under normal circumstances, the length l of electric melting magnesium furnace conductive cross arm is significantly larger than conductor From geometric mean distance g.Similarly, conductive cross arm self-inductance formula can be reduced to formula (4).The conductive cross arm acquired is equal from geometry Away from formula (4) are substituted into the other data provided in example, each phase conductive cross arm self-inductance can be obtained.
Conductive cross arm is from inductance value are as follows:
Step 4 obtains conductive cross arm reactance
The mutual inductance value from inductance value and between phase and phase of the every phase of the conductive cross arm acquired above is substituted into formula (5) and formula (6), the reactance value of the conductive cross arm side phase and middle phase that can acquire is as follows:
Conductive cross arm side phase reactance value are as follows:
XA=XC≈5.631×10-4Ω
Phase reactance value in conductive cross arm are as follows:
XB≈4.920×10-4Ω
In order to verify the accuracy for the electric melting magnesium furnace conductive cross arm reactance value that this method obtains, established in Maxwell The 2D model of conductive cross arm, and the inductance of the model is emulated, simulation model is as shown in Figure 3.This conductive cross arm In the simulation process of inductance, has chosen when A, B, C three-phase current reach maximum value and emulated respectively in magnetostatic field, obtained The simulation value of corresponding inductance.For example, according to the rated current that conductive cross arm passes through in 5000kVA electric melting magnesium furnace actual production Value, wherein a phase current values are set as 22248A, remaining biphase current is set as -11124A.Boundary condition is the balloon of default Boundary.Material properties are set as copper.Emulation obtains the self-inductance and mutual induction amount between phase and phase of conductive cross arm, will be above-mentioned Value substitute into formula (5) and formula (6) can acquire conductive cross arm side phase and middle phase reactance value.
Based on the above results, the theoretical value of electric melting magnesium furnace conductive cross arm reactance and simulation value are summarized in table 2.
Table 2
Since electric melting magnesium furnace operating condition is extremely complex, as long as the acquisition of usual conductive cross arm reactance is managed in engineer application Requirement of engineering can be met in an order of magnitude by value and simulation value.By by gross data in table 2 and emulation data comparison, two Person's result is almost the same, and this method can be very good to meet Practical Project demand.
The above embodiments are only used to illustrate the technical solution of the present invention., rather than its limitations;Although referring to aforementioned each reality Applying example, invention is explained in detail, those skilled in the art should understand that: it still can be to aforementioned each Technical solution documented by embodiment is modified, or equivalent substitution of some or all of the technical features;And These are modified or replaceed, the range for technical solution of various embodiments of the present invention that it does not separate the essence of the corresponding technical solution.

Claims (3)

1. a kind of method for obtaining the reactance of electric melting magnesium furnace conductive cross arm, which is characterized in that mainly comprise the steps that step 1, Conductive cross arm is obtained from geometric mean distance
The conductive cross arm of the electric melting magnesium furnace is that section is considered as by hollow rectangular conductor when obtaining the conductive cross arm reactance Rectangle frame, which is divided into multiple small rectangles acquire the section from geometric mean distance, and according to complex geometry The geometric mean distance formula of figure, when a complex figure by n part form when, it can be according to formula (1) from geometric mean distance By being acquired from geometric mean distance and mutual geometric mean distance for each component part:
Wherein, g is the rectangular section of entire conductor from geometric mean distance, unit mm;gkkFor small rectangle after any decomposition from Geometric mean distance can acquire, unit mm according to formula (2);gkiThe mutual geometric mean distance between small rectangle after being decomposed for any two, Unit mm;Sk、Si、SnIt is the small rectangular area after arbitrary decomposition, unit mm2
gkk=k (a+b) (2)
Wherein, a is the length of rectangle, unit mm;B is the width of rectangle, unit mm;K is coefficient of alteration;
Step 2 obtains conductive cross arm mutual induction amount
The reactance that conductor is acquired according to the mutual inductance between the self-induction of the conductor of acquisition itself and adjacent conductor, works as conductor length When much larger than mutual geometric mean distance between conductor, the mutual inductance simplified between straight equal long conductors is obtained according to formula (3):
Wherein, mutual inductance of the M between two phase conductors, unit mm;μ0For the space permeability of conductor;L is conductor length, unit mm; D is the mutual geometric mean distance between two flat straight conductors, unit mm;
Step 3 obtains conductive cross arm self-inductance
When conductor length much larger than conductor from geometric mean distance when, in the mutual inductance formula that simplifies between two parallel conductors, such as If by mutual geometric mean distance d be changed to independent conductor from geometric mean distance g, mutual inductance formula is self-induction formula, i.e., is obtained according to formula (4) Obtain conductive cross arm self-inductance:
Wherein, L is the self-induction of conductor, unit mm;μ0For the space permeability of conductor;L is conductor length, unit mm;G is from several He Jun is away from unit mm;
Step 4 obtains conductive cross arm reactance
The self-inductance of the conductive cross arm obtained through the above steps according to formula (5) and formula (6) and mutual inductance between phase and phase Amount, can be obtained the side phase reactance value and middle phase reactance value of conductive cross arm:
The formula of side phase reactance:
The formula of middle phase reactance:
Wherein, XA、XCFor the side phase reactance value of conductive cross arm, XBThe middle phase reactance value of conductive cross arm;F is frequency;LA、LBFor each phase Self-inductance;MAB、MAB、MABFor the mutual induction amount between each phase conductive cross arm.
2. the method according to claim 1 for obtaining the reactance of electric melting magnesium furnace conductive cross arm, it is characterized in that: the conductive cross arm The section divide the small rectangle number be two or more.
3. the method according to claim 1 for obtaining the reactance of electric melting magnesium furnace conductive cross arm, it is characterized in that: can be by the conduction Mutual geometric mean distance g between small rectangle described in any two after the frame section decomposition of transverse armki, it is considered as each rectangle geometry The distance between center.
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Citations (1)

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Publication number Priority date Publication date Assignee Title
CN203148191U (en) * 2012-08-30 2013-08-21 树赢(国际)控股西安装备有限公司 Low-impedance energy-saving composite conductive transverse arm

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Publication number Priority date Publication date Assignee Title
CN203148191U (en) * 2012-08-30 2013-08-21 树赢(国际)控股西安装备有限公司 Low-impedance energy-saving composite conductive transverse arm

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Analysis of power consumption in a submerged arc furnace for MgO single crystal production;Zhen Wang等;《2010 International Conference on Electrical and Control Engineering》;20101231;第433-436页 *
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