CN102208274A - Optimization design method for cross section of iron core column of power transformer - Google Patents

Abstract

The invention discloses an optimization design method for the cross section of an iron core column of a power transformer, which comprises the following steps of: aiming at the structure of the cross section of the iron core column of the power transformer, firstly establishing a mathematical model of the cross section so as to carry out initial optimization design; then carrying out programming and solution on the mathematical model of the cross section; afterwards, carrying out further optimization design on the basis of a solution result; and finally, designing an oil duct by considering the heat dissipation of the cross section on the basis of the further optimization design so as to provide a final optimization design embodiment. The optimization design method has the advantages of enabling the design of the structure of the cross section of the iron core column of the power transformer to be more reasonable and effective, enabling the effective sectional area to be more excellent and achieve better optimization effect and higher utilization ratio, lowering manufacturing cost of the iron core, reducing more energy loss, having better heat dissipation performance, stronger practical applicability and the like.

Description

The Optimization Design of power transformer iron core column section

Technical field

The present invention relates to the technical field of Power Transformer Optimum Design, especially relate to the Optimization Design of power transformer iron core column section.

Background technology

For power transformer, iron core is important part, and it is the flux circuit of transformer, is again the supporting core of transformer.The iron core of power transformer is the shaped as frame closing structure, and the part of wherein overlapping winding is a core limb.Iron core has core type and shell-type two big basic structure forms, and wherein, the core type core structure is the core construction form that China transformer manufactory generally adopts.

In the design of power transformer, how the cross section of core limb is designed is a very important link.China's transformer manufacturing industry adopts the unified core type core structure Design drawing in the whole nation usually.Can according to knowhow for many years, each factory exists the query to existing design: improve and how to improve these designs, could both improve result of use, can reduce the cost of transformer simultaneously again.

The area of core limb effective cross-section, the geometric cross section product that equals multistage core limb is with the lamination coefficient, and the lamination coefficient is a constant.Wish during design that effective cross-section is big as far as possible, so both can save material, can reduce energy loss again.But not only to consider that the effective cross-section maximum gets final product, also should consider the requirement of manufacturing process, could apply to well in the practice like this, just can be promoted better.In addition, cause copper loss when electric current flows through because copper conductor can generate heat, unshakable in one's determination the magnetic line of force by the time can generate heat and cause iron loss.So in order to improve heat radiation unshakable in one's determination inner, the core limb diameter is cooling oil duct to be set more than 380 millimeters the time.Briefly, stay the horizontal blanking of 6 millimeters thick exactly between some adjacent stairstepping, be full of oil in the space, transformer when work oil circulates up and down and takes away heat in the iron core.Concrete oil duct number is chosen by industrial requirements, and the position of the oil duct of design should make its adjacent two parts core limb sectional area approximately equal of cutting apart.

The power transformer iron core post extensively has very wide application prospect in utilization at present.But also there are many defectives in the design of its core limb cross-sectional configuration, desirable not enough as its cross-sectional configuration design, net sectional area is big not enough, the minimizing low not enough, energy loss of high not enough, the unshakable in one's determination manufacturing cost of circular section utilance is many not enough, the thermal diffusivity processing is good not enough etc.

Summary of the invention

At the defective that exists in the above-mentioned prior art, the invention provides a kind of Optimization Design of power transformer iron core column section, this method can make its cross-sectional configuration design more reasonable, effective, makes advantages such as its net sectional area is more excellent, optimization better effects if, higher, the unshakable in one's determination manufacturing cost of utilance is lower, the minimizing energy loss is more, thermal diffusivity is better.

In order to solve the problems of the technologies described above, realize that general thought of the present invention is: at first, it is set up Mathematical Modeling carry out the initial optimization design; Then, its model is programmed find the solution; Then, on the basis of solving result, it is carried out further optimal design; At last, on the basis of further optimal design, consider that its thermal diffusivity carries out the oil duct design, provides final optimal design embodiment.Its concrete steps are as follows:

1) it is carried out the initial optimization design, set up the target function of its Mathematical Modeling

Because the effective cross-section of core limb is big more, it is many more to save material, and energy loss is few more, and then its target function is the net sectional area maximum of core limb, is:

$\max S=k\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i{y}_i---\left(1\right)$

S represents the net sectional area of core limb, and k represents lamination coefficient, x _i(i=1,2 ... n) width of expression i level silicon steel sheet, y _iThe thickness of representing i level silicon steel sheet, n represents progression.

2) set up the constraints of Mathematical Modeling

1. because the width of silicon steel sheet generally is taken as 5 multiple, then have:

x _i=5 * lx (i), lx (i) are integer (2)

2. Fig. 1 is the core limb schematic cross-section, mid portion is the 1st grade, upwards be the 2nd, 3,4 successively ... the first half of level, be downwards the 2nd, 3,4 successively ... the latter half of level, know by Pythagorean theorem, half of i level width square with the 1st grade of half square sum to the thickness of i level, smaller or equal to the core limb circumradius square, so constraint is arranged: (d represents diameter)

${\left(\frac{x_i}{2}\right)}^2+{\left(\underset{j=1}{\overset{i}{\mathrm{\Σ}}}\frac{y_j}{2}\right)}^2\≤{\left(\frac{d}{2}\right)}^2---\left(3\right)$

3. be 26 millimeters owing to generally requiring the thickness minimum of the first order, the width minimum of silicon steel sheet is 20 millimeters, then has:

y ₁≥26，x _n≥20 (4)

4. because require the width of i level bigger, then have than the width of i+1 level:

x _i＞x _i+1 (5)

5. since the Breadth Maximum of silicon steel sheet and the gross thickness of silicon steel sheet can not then have greater than the external diameter of a circle of core limb:

$x_1<d,\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i<d---\left(6\right)$

6. by the manufacture process requirement restriction, the selection of core limb progression adopts the progression of the core limb that is drawn by engineering experience to choose with reference to principle generally speaking, and its principle is: the core limb diameter is at 80-195mm, and requiring progression is the 5-7 level; The core limb diameter is at 200-265mm, and requiring progression is the 8-10 level; The core limb diameter is at 270-390mm, and requiring progression is 11 grades; The core limb diameter is at 400-740mm, and requiring progression is the 12-14 level; The core limb diameter is more than 760mm, and requiring progression is more than 15 grades.Then have:

$n\left\{\begin{array}{cc}5\&le;n\&le;7& d\&Element;\left[\mathrm{80,195}\right]\\ 8\&le;n\&le;10& d\&Element;\left[\mathrm{200,265}\right]\\ n=11& d\&Element;\left[\mathrm{270,390}\right]\\ 12\&le;n\&le;14& d\&Element;\left[\mathrm{400,740}\right]\\ n\&GreaterEqual;15& d\&Element;[760,\&infin;)\end{array}\right.---\left(7\right)$

3) set up Mathematical Modeling and carry out the initial optimization design

The target function of Mathematical Modeling in the top step (1) and the constraints in (2) are combined, can be set up following non-linear mixed-integer programming model:

$\max S=k\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{y}_i$

4) Mathematical Modeling that initial optimization is designed is programmed and is found the solution

The sum of series width and the thickness at different levels in the maximum of utilizing lingo Optimization Software programming to find the solution above-mentioned mathematical programming problem just can to draw the long-pending maximum in its core limb geometric cross section, core limb net sectional area, corresponding core limb cross section.

5) on the solving result basis of initial optimization design, it is carried out further optimal design

For the solving result of above initial optimization design, because its just locally optimal solution that solves can utilize the neighborhood searching method that it is sought more excellent separating further to this.

The thought of this method is: on the basis of the locally optimal solution that solves, earlier to its each level width x _iDefine it and move neighborhood; Then at x _iMobile neighborhood in carry out neighborhood searching according to target call, select one " preferably move ", make it be better than present feasible solution; Again with this initial point, again it is carried out more excellent search subsequently as search next time; Like this up to each being moved till institute in the neighborhood searched a little the last optimal solution that hunts out of selecting again.This can utilize mathematical software Mathematica that it is programmed to find the solution and obtain its more excellent separating.

6) on the basis of further optimal design, consider that its thermal diffusivity carries out the oil duct design, provides final

The optimal design embodiment

Further also should consider its thermal diffusivity after the optimal design.Because can generating heat, copper conductor causes power loss (abbreviating copper loss as) when electric current flows through; Unshakable in one's determination the magnetic line of force by the time also can generate heat and cause power loss (abbreviating iron loss as).To this, in order to improve heat radiation unshakable in one's determination inner, the core limb diameter is cooling oil duct to be set more than 380 millimeters the time.Briefly, stay the horizontal blanking of 6 millimeters thick exactly between some adjacent stairstepping, be full of oil in the space, transformer when work oil circulates up and down and takes away heat in the iron core.

Concrete oil duct number is generally by choosing with reference to principle that engineering experience draws, and its principle is: when the core limb diameter was 380-410mm, 6mm oil duct number was 0 in the semicircle; When the core limb diameter was 420-500mm, 6mm oil duct number was 1 in the semicircle; When the core limb diameter was 510-690mm, 6mm oil duct number was 2 in the semicircle; When the core limb diameter was 700-840mm, 6mm oil duct number was 3 in the semicircle.

Simultaneously, the position of oil duct should make its adjacent two parts core limb sectional area approximately equal of cutting apart.

To this, can carry out the oil duct constraint to it, utilize the C Programming with Pascal Language to find the solution then, just can provide final optimal design embodiment.

Description of drawings

Fig. 1 is the core limb schematic cross-section

Fig. 2 is the core limb sectional view that carries out after oil duct designs

Embodiment

The specific embodiment of finishing according to technical scheme provided by the invention below in conjunction with accompanying drawing and inventor; the present invention is described in further detail; but present embodiment is not limited to the present invention; every employing similarity method of the present invention and similar variation thereof all should be listed protection scope of the present invention in.

The specific embodiment of the invention provides the Optimization Design that circumscribed circle diameter is 650 millimeters a power transformer iron core column section, and its concrete implementation step is:

1) it is carried out the initial optimization design, set up the target function of its Mathematical Modeling

Because the effective cross-section of core limb is big more, it is many more to save material, and energy loss is few more, and then its target function is the net sectional area maximum of core limb, is:

$\max S=k\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{y}_i---\left(1\right)$

S represents the net sectional area of core limb, and k represents lamination coefficient, x _i(i=1,2 ... n) width of expression i level silicon steel sheet, y _iThe thickness of representing i level silicon steel sheet, n represents progression.

2) set up the constraints of Mathematical Modeling

1. because the width of silicon steel sheet generally is taken as 5 multiple, then have:

x _i=5 * lx (i), lx (i) are integer (2)

2. Fig. 1 is the core limb schematic cross-section, mid portion is the 1st grade, upwards be the 2nd, 3,4 successively ... the first half of level, be downwards the 2nd, 3,4 successively ... the latter half of level, know by Pythagorean theorem, half of i level width square with the 1st grade of half square sum to the thickness of i level, smaller or equal to the core limb circumradius square, so constraint is arranged: (d represents diameter)

${\left(\frac{x_i}{2}\right)}^2+{\left(\underset{j=1}{\overset{i}{\mathrm{\&Sigma;}}}\frac{y_j}{2}\right)}^2\&le;{\left(\frac{d}{2}\right)}^2---\left(3\right)$

3. be 26 millimeters owing to generally requiring the thickness minimum of the first order, the width minimum of silicon steel sheet is 20 millimeters, then has:

y ₁≥26，x _n≥20 (4)

4. because the width of i level is bigger than the width of i+1 level, then have:

x _i＞x _i+1 (5)

5. since the Breadth Maximum of silicon steel sheet and the gross thickness of silicon steel sheet can not then have greater than the external diameter of a circle of core limb:

$x_1<d,\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i<d---\left(6\right)$

6. limit by manufacture process requirement, the selection of core limb progression adopts the progression of the core limb that is drawn by engineering experience to choose with reference to principle generally speaking, can be chosen as according to its principle: when the core limb diameter was 650mm, between 400-740mm, requiring progression was the 12-14 level.Then have:

12≤n≤14 (7)

3) set up Mathematical Modeling and carry out the initial optimization design

The target function of Mathematical Modeling in the top step (1) and the constraints in (2) are combined, can be set up following non-linear mixed-integer programming model:

$\max S=k\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{y}_i$

4) Mathematical Modeling that initial optimization is designed is programmed and is found the solution

Utilizing the programming of lingo Optimization Software to find the solution above-mentioned mathematical programming problem can get: the long-pending maximum in core limb geometric cross section is 320739.8 square millimeters, the maximum of core limb net sectional area is the 320739.8k square millimeter, the progression in corresponding core limb cross section is 14 grades, and can obtain width at different levels and thickness.

5) on the solving result basis of initial optimization design, it is carried out further optimal design

For the solving result of above initial optimization design, because its just locally optimal solution that solves can utilize the neighborhood searching method that it is sought more excellent separating further to this.

The thought of this method is: on the basis of the locally optimal solution that solves, earlier to its each level width x _iDefine it and move neighborhood; Then at x _iMobile neighborhood in carry out neighborhood searching according to target call, select one " preferably move ", make it be better than present feasible solution; Again with this initial point, again it is carried out more excellent search subsequently as search next time; Like this up to each being moved till institute in the neighborhood searched a little the last optimal solution that hunts out of selecting again.

Because if excessive then its amount of calculation of mobile neighborhood with excessive, search time with long, only moving up and down a unit quantity with it here is that example is carried out more optimal design to it.Utilize mathematical software Mathematica that it is programmed and can obtain its more excellent separating after finding the solution: the long-pending maximum in core limb geometric cross section is 320753.1 square millimeters, the maximum of core limb net sectional area is the 320753.1k square millimeter, activity coefficient unshakable in one's determination (circular section usage factor) is 96.66%, about 93% of the activity coefficient of designing than the current national criteria design drawing unshakable in one's determination that adopts by China transformer manufacturing industry unshakable in one's determination (circular section usage factor) has improved about 3%; The progression in corresponding core limb cross section is 14 grades, and can obtain width at different levels and thickness is:

The 1st grade, width is 640mm, and thickness is 113.578mm;

The 2nd grade, width is 620mm, and thickness is 81.614mm;

3rd level, width are 595mm, and thickness is 66.4851mm;

The 4th grade, width is 570mm, and thickness is 50.7327mm;

The 5th grade, width is 540mm, and thickness is 49.3911mm;

The 6th grade, width is 510mm, and thickness is 41.1878mm;

The 7th grade, width is 475mm, and thickness is 40.7172mm;

The 8th grade, width is 435mm, and thickness is 39.2795mm;

The 9th grade, width is 395mm, and thickness is 33.2267mm;

The 10th grade, width is 350mm, and thickness is 31.5104mm;

The 11st grade, width is 300mm, and thickness is 28.9056mm;

The 12nd grade, width is 245mm, and thickness is 25.4308mm;

The 13rd grade, width is 180mm, and thickness is 22.5209mm;

The 14th grade, width is 105mm, and thickness is 16.8833mm;

6) on the basis of further optimal design, consider that its thermal diffusivity carries out the oil duct design, provides final optimal design embodiment

Further also should consider its thermal diffusivity after the optimal design.Because can generating heat, copper conductor causes power loss (abbreviating copper loss as) when electric current flows through; Unshakable in one's determination the magnetic line of force by the time also can generate heat and cause power loss (abbreviating iron loss as).To this, in order to improve heat radiation unshakable in one's determination inner, the core limb diameter is cooling oil duct to be set more than 380 millimeters the time.Briefly, stay the horizontal blanking of 6 millimeters thick exactly between some adjacent stairstepping, be full of oil in the space, transformer when work oil circulates up and down and takes away heat in the iron core.Concrete oil duct number is generally by choosing with reference to principle that engineering experience draws, and can be chosen as according to its principle: when the core limb diameter was 650mm, between 510-690mm, 6mm oil duct number should be 2 in the semicircle.Simultaneously, the position of oil duct should make its adjacent two parts core limb sectional area approximately equal of cutting apart.

To this, can carry out the oil duct constraint to it in conjunction with Fig. 2 (wherein blackstreak partly is oil duct), suppose that 2 oil ducts in the semicircle are located at p level and p+1 inter-stage, q level and q+1 inter-stage respectively, and p＜q, then have:

p+1＜q+1＜n (9)

$\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{S}_i\&ap;\frac{1}{2}\underset{i=p+1}{\overset{q}{\mathrm{\&Sigma;}}}{S}_i,$ $\frac{1}{2}\underset{i=p+1}{\overset{q}{\mathrm{\&Sigma;}}}{S}_i\&ap;\frac{1}{2}\underset{i=q+1}{\overset{n}{\mathrm{\&Sigma;}}}{S}_i,$ $\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{S}_i\&ap;\frac{1}{5}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{S}_i---\left(10\right)$

For the design of its oil duct, directly it is considered how to increase therein oil duct under the core limb net sectional area maximum case that can obtain in front.To this, the inventor has carried out the C Programming with Pascal Language and has found the solution, and the main thought of its algorithm is in the value that all p, q can get, find out can make wait the symbol both sides to make difference in the oil duct constraints approximately to take absolute value again after, the p that the conduct of its difference minimum is asked, q value.X as a result with previous calculations _iAnd y _iAs the initializaing variable that calculates, establishing the maximum secting area error is E _Max(initial value is 1000).

Utilization C language to its programme find the solution after, obtain p=1, q=4, E _Max=3583.Promptly insert oil duct the 1st grade and the 4th grade, the position of oil duct be between the 1st grade and the 2nd grade and and the 2nd grade width equate, between the 4th grade and the 5th grade and and the 5th grade width equate.

Claims (1)

1. the Optimization Design of power transformer iron core column section is characterized in that, carries out according to the following steps:

1) it is carried out the initial optimization design, set up the target function of its Mathematical Modeling

Because the effective cross-section of core limb is big more, it is many more to save material, and energy loss is few more, and then its target function is the net sectional area maximum of core limb, is:

$\max S=k\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{y}_i---\left(1\right)$

S represents the net sectional area of core limb, and k represents lamination coefficient, x _i(i=1,2 ... n) width of expression i level silicon steel sheet, y _iThe thickness of representing i level silicon steel sheet, n represents progression.

2) set up the constraints of Mathematical Modeling

1. because the width of silicon steel sheet generally is taken as 5 multiple, then have:

x _i=5 * lx (i), lx (i) are integer (2)

2. Fig. 1 is the core limb schematic cross-section, mid portion is the 1st grade, upwards be the 2nd, 3,4 successively ... the first half of level, be downwards the 2nd, 3,4 successively ... the latter half of level, know by Pythagorean theorem, half of i level width square with the 1st grade of half square sum to the thickness of i level, smaller or equal to the core limb circumradius square, so constraint is arranged: (d represents diameter)

${\left(\frac{x_i}{2}\right)}^2+{\left(\underset{j=1}{\overset{i}{\mathrm{\&Sigma;}}}\frac{y_j}{2}\right)}^2\&le;{\left(\frac{d}{2}\right)}^2---\left(3\right)$

3. be 26 millimeters owing to generally requiring the thickness minimum of the first order, the width minimum of silicon steel sheet is 20 millimeters, then has:

y ₁≥26，x _n≥20 (4)

4. because the width of i level is bigger than the width of i+1 level, then have:

x _i＞x _i+1 (5)

5. since the Breadth Maximum of silicon steel sheet and the gross thickness of silicon steel sheet can not then have greater than the external diameter of a circle of core limb:

$x_1<d,\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i<d---\left(6\right)$

6. by the manufacture process requirement restriction, the selection of core limb progression adopts the progression of the core limb that is drawn by engineering experience to choose with reference to principle generally speaking, and its principle is: the core limb diameter is at 80-195mm, and requiring progression is the 5-7 level; The core limb diameter is at 200-265mm, and requiring progression is the 8-10 level; The core limb diameter is at 270-390mm, and requiring progression is 11 grades; The core limb diameter is at 400-740mm, and requiring progression is the 12-14 level; The core limb diameter is more than 760mm, and requiring progression is more than 15 grades.Then have:

$n\left\{\begin{array}{cc}5\&le;n\&le;7& d\&Element;\left[\mathrm{80,195}\right]\\ 8\&le;n\&le;10& d\&Element;\left[\mathrm{200,265}\right]\\ n=11& d\&Element;\left[\mathrm{270,390}\right]\\ 12\&le;n\&le;14& d\&Element;\left[\mathrm{400,740}\right]\\ n\&GreaterEqual;15& d\&Element;[760,\&infin;)\end{array}\right.---\left(7\right)$

3) set up Mathematical Modeling and carry out the initial optimization design

The target function of Mathematical Modeling in the top step (1) and the constraints in (2) are combined, can be set up following non-linear mixed-integer programming model:

$\max S=k\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{y}_i$

4) Mathematical Modeling that initial optimization is designed is programmed and is found the solution

The sum of series width and the thickness at different levels in the maximum of utilizing lingo Optimization Software programming to find the solution above-mentioned mathematical programming problem just can to draw the long-pending maximum in its core limb geometric cross section, core limb net sectional area, corresponding core limb cross section.

5) on the solving result basis of initial optimization design, it is carried out further optimal design

For the solving result of above initial optimization design, because its just locally optimal solution that solves can utilize the neighborhood searching method that it is sought more excellent separating further to this.

The thought of this method is: on the basis of the locally optimal solution that solves, earlier to its each level width x _iDefine it and move neighborhood; Then at x _iMobile neighborhood in carry out neighborhood searching according to target call, select one " preferably move ", make it be better than present feasible solution; Again with this initial point, again it is carried out more excellent search subsequently as search next time; Like this up to each being moved till institute in the neighborhood searched a little the last optimal solution that hunts out of selecting again.This can utilize mathematical software Mathematica that it is programmed to find the solution and obtain its more excellent separating.

6) on the basis of further optimal design, consider that its thermal diffusivity carries out the oil duct design, provides final optimal design embodiment

Further also should consider its thermal diffusivity after the optimal design.Because can generating heat, copper conductor causes power loss (abbreviating copper loss as) when electric current flows through; Unshakable in one's determination the magnetic line of force by the time also can generate heat and cause power loss (abbreviating iron loss as).To this, in order to improve heat radiation unshakable in one's determination inner, the core limb diameter is cooling oil duct to be set more than 380 millimeters the time.Briefly, stay the horizontal blanking of 6 millimeters thick exactly between some adjacent stairstepping, be full of oil in the space, transformer when work oil circulates up and down and takes away heat in the iron core.

Concrete oil duct number is generally by choosing with reference to principle that engineering experience draws, and its principle is: when the core limb diameter was 380-410mm, 6mm oil duct number was 0 in the semicircle; When the core limb diameter was 420-500mm, 6mm oil duct number was 1 in the semicircle; When the core limb diameter was 510-690mm, 6mm oil duct number was 2 in the semicircle; When the core limb diameter was 700-840mm, 6mm oil duct number was 3 in the semicircle.

Simultaneously, the position of oil duct should make its adjacent two parts core limb sectional area approximately equal of cutting apart.

To this, can carry out the oil duct constraint to it, utilize the C Programming with Pascal Language to find the solution then, just can provide final optimal design embodiment.

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