CN105845427B - Cross section of transformer core design method based on particle group optimizing - Google Patents
Cross section of transformer core design method based on particle group optimizing Download PDFInfo
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Abstract
The invention discloses the cross section of transformer core design method based on particle group optimizing, belong to transformer manufacture field, series unshakable in one's determination is determined with series corresponding relation unshakable in one's determination according to transformer fe core diameter first, pre-processed next to optimize every grade of folded thickness, then solution is optimized to folded thickness at different levels using particle swarm optimization algorithm, and then obtain final optimizing design scheme, cross section of transformer core tectonic sieving can be made more reasonable, increase operation rate, reduce the manufacturing cost and energy loss of transformer core, the present invention is due to the particle swarm optimization algorithm using fast convergence rate, and merged transformer fe core diameter and series corresponding relation unshakable in one's determination, this method is allowd quickly to try to achieve prioritization scheme.
Description
Technical field
The invention belongs to transformer manufacture field.
Background technology
Transformer is the visual plant in power system, and its designing quality is directly connected to the reliability of Operation of Electric Systems
With benefit.Although China in Recent Years Transformer Enterprise achieves preferable effect in terms of technology and scientific and technical innovation, to design
But more and more higher is required with optimization etc..Loss and the cost of transformer are reduced, is also implement China's energy-saving and emission-reduction policy important
Behave.
A critically important link is exactly the design of core section in power transformer design, cross section of transformer core it is big
The number of the small magnetic ducting capacity for determining transformer and flux loss.It can be seen from electromagnetic theory：The hold-in winding number of turn is constant,
Increase area of core section can reduce the magnetic flux density in iron core, reduce open circuit loss；When the selected close timing of magnetic flux, increase
Area of core section, can reduce coil turn, save copper material, reduce load loss.But simply increase core-diameter raising
Area of core section can make cost increase again, cause a large amount of wastes.Therefore, how to be improved in the case where core-diameter holding is constant
Its net sectional area, with very significant practical significance, so can both save material, volume be reduced, while damage can be reduced
Consumption, reduces saturation degree unshakable in one's determination, improves power supply quality.
The set unshakable in one's determination of transformer is in the coil of transformer inner circular, in order to sufficiently utilize the space in circular coil
And consider the reasonability of manufacture craft, the core section of transformer is usually disposed as multiple silicon steel sheets differed in size and constituted
Small rectangle stack up, make silicon steel sheet try one's best full of coil circular space in.Therefore, cross section of transformer core optimization is set
Meter general thinking be：First according to given specification unshakable in one's determination, silicon steel sheet series and every grade of folded thickness are determined using proper method,
Finally obtain the foundation that numerical procedure is manufactured as transformer core., can basis on the determination of series and folded thickness at different levels
Transformer fe core diameter is determined with series corresponding relation.On the other hand, particle swarm optimization algorithm is that a kind of new modern intelligence is excellent
Change algorithm, have the advantages that calculating speed is fast, good convergence, it directly can be encoded to real number, therefore be especially suitable for solving
Certainly cross section of transformer core folded thick optimization problems at different levels.The present invention is based on transformer fe core diameter and series corresponding relation and particle
Colony optimization algorithm optimizes design to core section, finally realizes that the efficient rapid Optimum of cross section of transformer core problem is asked
Solution.Due to the particle swarm optimization algorithm using fast convergence rate, and transformer fe core diameter and series corresponding relation are merged, made
Prioritization scheme can quickly be tried to achieve by obtaining this method.
The content of the invention
It is an object of the invention to provide a kind of cross section of transformer core design method based on particle group optimizing, this method is melted
Transformer fe core diameter and series corresponding relation unshakable in one's determination and particle swarm optimization algorithm have been closed, transformer core series has been carried out first
Solve, specification unshakable in one's determination is determined by being actually needed, series unshakable in one's determination is determined according to transformer fe core diameter and series corresponding relation；So
Core-diameter, series and the triangular mathematical modeling of area of section are based on afterwards, using particle swarm optimization algorithm to every grade of folded thickness
Solution is optimized, wherein being encoded using folded thickness at different levels as particle, penalty is introduced come processing constraints, passes through
Population iterative calculation finally tries to achieve optimal case.This method can cause power transformer iron core section in tectonic sieving more
Optimization is reasonable, makes that its utilization rate is higher, manufacturing cost is lower, it is stronger to reduce energy loss, practicality.
To achieve the above object, the present invention uses following technical scheme：Cross section of transformer core based on particle group optimizing
Design method, comprises the following steps：
Optimal design method for cross section of transformer core based on particle group optimizing, it is characterised in that comprise the following steps：
Step 1：Series unshakable in one's determination is determined with series corresponding relation unshakable in one's determination according to transformer fe core diameter, the series unshakable in one's determination is closed
It is that formula is as follows：
As D ∈ (a1, a2) N=n can be obtained1；
As D ∈ (a2, a3) N=n can be obtained2；
As D ∈ (a3, a4) N=n can be obtained3；
As D ∈ (ai, ai+1) N=n can be obtainedi；
In the Series Relations formula unshakable in one's determination：
D--- inputs core-diameter；
ai--- the critical value of core-diameter span；
N--- outputs series unshakable in one's determination；
ni--- series numerical value unshakable in one's determination；
Step 2：The number of cross section of transformer core is set up according to the functional relation of area of core section and silicon steel sheet stack thickness
Learn model；
The functional relation of the area of core section and silicon steel sheet stack thickness is as follows：
The constraints of the area of core section and the functional relation of silicon steel sheet stack thickness is as follows：
ti＞ 0；
The functional relation and the area of core section and silicon steel sheet stack of the area of core section and silicon steel sheet stack thickness are thick
In the constraints of the functional relation of degree：
D--- core section diameters；
di--- the stack thickness of preceding i layers of silicon steel sheet；
bi--- the width of i-th layer of silicon steel sheet；
ti--- i-th layer of silicon steel sheet thickness；
S--- area of core sections；
Limit control is 0 outside the given diameter of iron core；
Step 3：MATLAB mathematical modeling softwares are installed in PC, transformation is inputted in the MATLAB mathematical modelings software
The specifications parameter of device；
Core section is drawn using particle swarm optimization algorithm according to following steps in the MATLAB mathematical modelings software
Long-pending maximum and the numerical value of silicon steel sheet stack thickness, and write in the MATLAB mathematical modelings software according to following steps
Software program principal function：
A. particle coding directly is carried out to folded thickness at different levels first：[t1, t2..., tn], wherein tnIt is n-th grade of silicon steel sheet
Folded thickness, tnFor real number；
B. the position of particle initial search point and its speed are typically randomly generated in allowed limits, each particle
Pbest coordinates be set to its current location, and calculate its corresponding individual extreme value, the individual extreme value is individual extreme point
Fitness value, and the optimal particle of whole neighborhood is exactly maximum in individual extreme value in the particle neighborhood, records this optimal example
The particle sequence number of son, and Pgd is set to the current location of the particle, to evaluate each particle, calculate the fitness value of particle：
If the individual extreme value current better than the particle, Pbest is set to the position of the particle, and more new individual extreme value；Such as
Fruit particle optimal in the individual extreme value of all particles in the neighborhood of the particle is better than current Pgd, then Pgd is set into this
The position of particle, records the sequence number of the particle, and updates Pgd functional value, more new particle；
Particle cluster algorithm is according to following particle relational expression come the speed of more new particle and position：
Vi=Vi+c1×rand×(Pid-Xi)+c2×rand×(Pgd-Xi)；
Xi=Xi+Vi；
In the particle relational expression：
Vi--- i-th of particle present speed；
Xi--- i-th of particle current location；
C1, c2--- Studying factors, also referred to as aceleration pulse；
Uniform random number in the range of rand--- [0,1]；
Pid--- particle individual extreme value；
Pgd--- the maximum individual extreme value of particle neighborhood；
C. introduce penalty O and carry out the situation that treatment conditions exceed prescribed limit, when folded thick sums at different levels are advised beyond unshakable in one's determination
During lattice, mono- larger penalty value of penalty term O is given；Penalty relational expression is as follows：
WhenWhen,
In the penalty relational expression：
D--- core section diameters；
ti--- the silicon steel sheet stack thickness of i-stage；
D. optimization object function is set up, the characteristics of being minimized according to particle swarm optimization algorithm and the constraints are built
Vertical object function relational expression：
In the object function relational expression：
Y------ object functions；
S------ area of core sections；
O------ penalties；
Step 4：Emulated in the MATLAB mathematical modelings software, simulation result is analyzed, from receipts
Hold back in speed and convergence process that these aspects are contrasted to the average value and variance of the solution representated by each particle, select iron core
The Maximum Area in section with its corresponding to silicon steel sheet stack thickness at different levels as optimization design scheme, according to the optimal case
The fabrication design conceptual scheme of transformer core is formulated, and enters according to fabrication design conceptual scheme the processing of line transformer.
It is an object of the invention to provide the cross section of transformer core design method based on particle group optimizing, by the PROBLEM DECOMPOSITION
To determine that every grade of sum of series particle cluster algorithm Optimization Solution unshakable in one's determination is folded based on transformer fe core diameter and series corresponding relation unshakable in one's determination
Two subproblems of thickness.Series unshakable in one's determination is determined by transformer fe core diameter and series corresponding relation, then by particle cluster algorithm
Calculate the optimal value of the folded thickness of silicon steel sheet.Make power transformer iron core section more reasonable in tectonic sieving by above method
While, it also ensure that core section is big as far as possible.Make that its utilization rate is higher, manufacturing cost is lower, reduce energy loss more
Many, practicality is stronger.
Brief description of the drawings
Fig. 1 is the mathematical modeling figure of the present invention；
The GUI that Fig. 2 is the present invention realizes surface chart；
Fig. 3 is the present invention using 100mm as diameter result of calculation figure；
Fig. 4 is the present invention using 150mm as diameter result of calculation figure；
Fig. 5 is the present invention using 200mm as diameter result of calculation figure.
Embodiment
Cross section of transformer core design method based on particle group optimizing, comprises the following steps：
As shown in figure 1, determining series unshakable in one's determination, the level unshakable in one's determination with series corresponding relation unshakable in one's determination according to transformer fe core diameter
Number relational expression is as follows：
As D ∈ (a1, a2) N=n can be obtained1；
As D ∈ (a2, a3) N=n can be obtained2；
As D ∈ (a3, a4) N=n can be obtained3；
As D ∈ (ai, ai+1) N=n can be obtainedi；
In the Series Relations formula unshakable in one's determination：
D--- inputs core-diameter；
ai--- the critical value of core-diameter span；
N--- outputs series unshakable in one's determination；
ni--- series numerical value unshakable in one's determination；
Step 2：The number of cross section of transformer core is set up according to the functional relation of area of core section and silicon steel sheet stack thickness
Learn model；
The functional relation of the area of core section and silicon steel sheet stack thickness is as follows：
The constraints of the area of core section and the functional relation of silicon steel sheet stack thickness is as follows：
ti＞ 0；
The functional relation and the area of core section and silicon steel sheet stack of the area of core section and silicon steel sheet stack thickness are thick
In the constraints of the functional relation of degree：
D--- core section diameters；
di--- the stack thickness of preceding i layers of silicon steel sheet；
bi--- the width of i-th layer of silicon steel sheet；
ti--- i-th layer of silicon steel sheet thickness；
S--- area of core sections；
Limit control is 0 outside the given diameter of iron core；
Step 3：MATLAB mathematical modeling softwares, the input transformer in MATLAB mathematical modeling softwares are stated are installed in PC
Specifications parameter；
Core section is drawn using particle swarm optimization algorithm according to following steps in the MATLAB mathematical modelings software
Long-pending maximum and the numerical value of silicon steel sheet stack thickness, and write in the MATLAB mathematical modelings software according to following steps
Software program principal function, and make gui interface as shown in Figure 2 in the MATLAB mathematical modelings software：
A. particle coding directly is carried out to folded thickness at different levels first：[t1, t2..., tn], wherein tnIt is n-th grade of silicon steel sheet
Folded thickness, tnFor real number；
B. the position of particle initial search point and its speed are typically randomly generated in allowed limits, each particle
Pbest coordinates be set to its current location, and calculate its corresponding individual extreme value, the individual extreme value is individual extreme point
Fitness value, and the optimal particle of whole neighborhood is exactly maximum in individual extreme value in the particle neighborhood, records this optimal example
The particle sequence number of son, and Pgd is set to the current location of the particle, to evaluate each particle, calculate the fitness value of particle：
If the individual extreme value current better than the particle, Pbest is set to the position of the particle, and more new individual extreme value；Such as
Fruit particle optimal in the individual extreme value of all particles in the neighborhood of the particle is better than current Pgd, then Pgd is set into this
The position of particle, records the sequence number of the particle, and updates Pgd functional value, more new particle；
Particle cluster algorithm is according to following particle relational expression come the speed of more new particle and position：
Vi=Vi+c1×rand×(Pid-Xi)+c2×rand×(Pgd-Xi)；
Xi=Xi+Vi；
In the particle relational expression：
Vi--- i-th of particle present speed；
Xi--- i-th of particle current location；
C1, c2--- Studying factors, also referred to as aceleration pulse；
Uniform random number in the range of rand--- [0,1]；
Pid--- particle individual extreme value；
Pgd--- the maximum individual extreme value of particle neighborhood；
C. introduce penalty O and carry out the situation that treatment conditions exceed prescribed limit, when folded thick sums at different levels are advised beyond unshakable in one's determination
During lattice, mono- larger penalty value of penalty term O is given；Penalty relational expression is as follows：
WhenWhen,
In the penalty relational expression：
D--- core section diameters；
ti--- the silicon steel sheet stack thickness of i-stage；
D. optimization object function is set up, the characteristics of being minimized according to particle swarm optimization algorithm and the constraints are built
Vertical object function relational expression：
In the object function relational expression：
Y------ object functions；
S------ area of core sections；
O------ penalties；
Step 4：Emulated in the MATLAB mathematical modelings software, simulation result is analyzed, from receipts
Hold back in speed and convergence process that these aspects are contrasted to the average value and variance of the solution representated by each particle, select iron core
The Maximum Area in section with its corresponding to silicon steel sheet stack thickness at different levels as optimization design scheme, according to the optimal case
The fabrication design conceptual scheme of transformer core is formulated, and enters according to fabrication design conceptual scheme the processing of line transformer.
As Fig. 2 (emulation gui interface is carried out by diameter of 100mm) show the transformer designed on the basis of the present invention
Corn section design gui interface, inputs the rule of the transformer of MATLAB mathematical modeling software emulations on gui interface described in user
Lattice parameter, MATLAB mathematical modeling software emulations go out the series of core section and the optimization area of core section, and can obtain
To the thickness of every one-level, the core model figure and particle fitness curve map after emulation are also show in Fig. 2, respectively with 100mm,
150mm, 200mm are the optimization area that core section diameter obtains silicon steel sheet stack thickness at different levels and area of core section, such as following table institute
Show：
The corresponding core model figure that MATLAB mathematical modeling software emulations go out is with particle fitness curve map respectively as schemed
3rd, shown in Fig. 4 and Fig. 5, user's putting down to the solution representated by each particle from convergence rate and convergence process according to simulation result
These aspects of average and variance are contrasted, and the Maximum Area and the silicon at different levels corresponding to it of core section are selected by comparing
Steel disc folds thickness as optimization design scheme, and the fabrication design conceptual scheme of transformer core is formulated according to the optimal case, and
Enter the processing of line transformer according to fabrication design conceptual scheme.
Claims (1)
1. the cross section of transformer core design method based on particle group optimizing, it is characterised in that comprise the following steps：
Step 1：Series unshakable in one's determination, the Series Relations formula unshakable in one's determination are determined with series corresponding relation unshakable in one's determination according to transformer fe core diameter
It is as follows：
As D ∈ (a1, a2) N=n can be obtained1；
As D ∈ (a2, a3) N=n can be obtained2；
As D ∈ (a3, a4) N=n can be obtained3；
As D ∈ (ai, ai+1) N=n can be obtainedi；
In the Series Relations formula unshakable in one's determination：
D--- inputs core-diameter；
ai--- the critical value of core-diameter span；
N--- outputs series unshakable in one's determination；
ni--- series numerical value unshakable in one's determination；
Step 2：The mathematical modulo of cross section of transformer core is set up according to the functional relation of area of core section and silicon steel sheet stack thickness
Type；
The functional relation of the area of core section and silicon steel sheet stack thickness is as follows：
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The functional relation and the area of core section and silicon steel sheet stack thickness of the area of core section and silicon steel sheet stack thickness
In the constraints of functional relation：
D--- core section diameters；
di--- the stack thickness of preceding i layers of silicon steel sheet；
bi--- the width of i-th layer of silicon steel sheet；
ti--- i-th layer of silicon steel sheet thickness；
S--- area of core sections；
Limit control is 0 outside the given diameter of iron core；
Step 3：MATLAB mathematical modeling softwares, the input transformer in the MATLAB mathematical modelings software are installed in PC
Specifications parameter；
Area of core section is drawn using particle swarm optimization algorithm according to following steps in the MATLAB mathematical modelings software
The numerical value of maximum and silicon steel sheet stack thickness, and write software according to following steps in the MATLAB mathematical modelings software
Program principal function：
A. particle coding directly is carried out to folded thickness at different levels first：[t1, t2..., tn], wherein tnBe n-th grade silicon steel sheet stack it is thick
Degree, tnFor real number；
B. the position of particle initial search point and its speed are typically randomly generated in allowed limits, each particle
Pbest coordinates are set to its current location, and calculate its corresponding individual extreme value, and the individual extreme value is individual extreme point
Fitness value, and the optimal particle of whole neighborhood is exactly maximum in individual extreme value in the particle neighborhood, records this optimal example
Particle sequence number, and Pgd is set to the current location of the particle, to evaluate each particle, calculates the fitness value of particle：Such as
Pbest, then be set to the position of the particle, and more new individual extreme value by the fruit individual extreme value current better than the particle；If
Particle optimal in the individual extreme value of all particles is better than current Pgd in the neighborhood of the particle, then Pgd is set into the grain
The position of son, records the sequence number of the particle, and update Pgd functional value, more new particle；
Particle cluster algorithm is according to following particle relational expression come the speed of more new particle and position：
Vi=Vi+c1×rand×(Pid-Xi)+c2×rand×(Pgd-Xi)；
Xi=Xi+Vi；
In the particle relational expression：
Vi--- i-th of particle present speed；
Xi--- i-th of particle current location；
C1, c2--- Studying factors, also referred to as aceleration pulse；
Uniform random number in the range of rand--- [0,1]；
Pid--- particle individual extreme value；
Pgd--- the maximum individual extreme value of particle neighborhood；
C. introduce penalty O and carry out the situation that treatment conditions exceed prescribed limit, when folded thick sums at different levels exceed specification unshakable in one's determination,
Mono- larger penalty value of penalty term O is given, penalty relational expression is as follows：
WhenWhen,
In the penalty relational expression：
D--- core section diameters；
ti--- the silicon steel sheet stack thickness of i-stage；
D. optimization object function is set up, the characteristics of being minimized according to particle swarm optimization algorithm and the constraints set up mesh
Scalar functions relational expression：
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<mi>L</mi>
<mo>+</mo>
<msqrt>
<mrow>
<msup>
<mi>D</mi>
<mn>2</mn>
</msup>
<mo>-</mo>
<mn>4</mn>
<msup>
<mrow>
<mo>(</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>t</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>&times;</mo>
<msub>
<mi>t</mi>
<mi>n</mi>
</msub>
<mo>&rsqb;</mo>
</mrow>
</mfrac>
<mo>+</mo>
<mi>O</mi>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>;</mo>
</mrow>
In the object function relational expression：
Y------ object functions；
S------ area of core sections；
O------ penalties；
Step 4：Emulated in the MATLAB mathematical modelings software, simulation result is analyzed, from convergence speed
To the average value and variance of the solution representated by each particle, these aspects are contrasted in degree and convergence process, select core section
Maximum Area with the silicon steel sheet stack thickness at different levels corresponding to it as optimization design scheme, formulated according to the optimal case
The fabrication design conceptual scheme of transformer core, and enter according to fabrication design conceptual scheme the processing of line transformer.
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| CN102208274A (en) * | 2011-01-05 | 2011-10-05 | 蒋雪峰 | Optimization design method for cross section of iron core column of power transformer |
| CN102737277A (en) * | 2012-04-11 | 2012-10-17 | 湖南工业大学 | Multi-objective optimization design method for passive filter in multiisland particle swarm optimization (PSO)-based mixed type filter |
| CN103336855A (en) * | 2013-05-24 | 2013-10-02 | 浙江工业大学 | Two-dimensional irregular layout method based on multi-subpopulation particle swarm optimization |
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| CN102208274A (en) * | 2011-01-05 | 2011-10-05 | 蒋雪峰 | Optimization design method for cross section of iron core column of power transformer |
| CN102737277A (en) * | 2012-04-11 | 2012-10-17 | 湖南工业大学 | Multi-objective optimization design method for passive filter in multiisland particle swarm optimization (PSO)-based mixed type filter |
| CN103336855A (en) * | 2013-05-24 | 2013-10-02 | 浙江工业大学 | Two-dimensional irregular layout method based on multi-subpopulation particle swarm optimization |
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