CN115270607A - Optimization design method for nuclear power station dry-type transformer fused with expert experience - Google Patents

Optimization design method for nuclear power station dry-type transformer fused with expert experience Download PDF

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CN115270607A
CN115270607A CN202210788603.7A CN202210788603A CN115270607A CN 115270607 A CN115270607 A CN 115270607A CN 202210788603 A CN202210788603 A CN 202210788603A CN 115270607 A CN115270607 A CN 115270607A
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蔡定国
谢天舒
唐金权
禤冠星
谢玉徽
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Abstract

The invention discloses an expert experience fused dry type transformer optimization design method for a nuclear power station, which classifies and combs parameter variables designed for the dry type transformer for the nuclear power station, selects main decision variables and adopts an improved multi-target particle swarm algorithm to solve an optimal solution, wherein the improvement comprises the following steps: the improved algorithm has the advantages that the population updating mechanism fusing expert experience is adopted, the brand-new non-dominated solution set updating mechanism is adopted, the saturation counter mechanism is arranged, the individual is prevented from falling into local optimization, the improved algorithm has good convergence effect and stable calculation, the population diversity, the global search capability and the convergence speed are improved compared with the original algorithm, and the improved algorithm is very suitable for being applied to the multi-objective optimization design of the dry-type transformer for the nuclear power station and meets the dual requirements of optimization effect and rapid calculation.

Description

Optimization design method for nuclear power station dry-type transformer fused with expert experience
Technical Field
The invention relates to an optimization design method of a nuclear power station dry-type transformer fused with expert experience.
Background
Compared with an oil immersed transformer, the dry type transformer has the advantages of simple structure, convenience in maintenance, light weight, non-flammability, dust prevention, high safety and the like, is widely applied to the fields of chemical plants, high-speed rails, airports, high-rise buildings and the like, and has more outstanding superiority to small-space places and places with high fire-fighting requirements.
The 1E-grade dry transformer for the nuclear power station is one of the representatives of domestic nuclear-grade equipment, and is a kind of dry transformer with high difficulty and high requirement. When the nuclear power station normally operates and an accident occurs, the reliable operation of the nuclear power station can ensure the safe, reliable and economic operation of the nuclear power station, prevent radioactive substances from being released to the environment and ensure the safety of personnel and the public of the nuclear power station. The design of the dry type transformer for the nuclear power station needs to consider more design variables, the optimization design mainly relates to multiple aspects of basic parameters, cost, loss, service life identification, short circuit resistance, shock resistance and the like of the transformer, according to the design principle of the dry type transformer, the optimization design is a multi-objective, multi-variable, multi-constraint condition, discrete and non-linear optimization problem, on the premise of ensuring the product performance, the design parameters and the structure of the transformer are optimized through an intelligent optimization design algorithm to reduce the cost of main materials, improve the loss, temperature rise, impedance and the like of the transformer so as to strictly meet the service life identification, short circuit resistance and the like of the transformer, and shorten the design period of products, so that the design problem which needs to be solved urgently in the dry type transformer design industry is formed.
The dry-type transformer optimization design scheme comprises the following steps: the traditional manual design method and the intelligent optimization algorithm design method.
The traditional manual design method is based on a dry-type transformer design principle and manual design experience, design parameters in the dry-type transformer are sorted, and the design parameters are manually adjusted according to the relevance among the parameters and the manual design experience, so that a design scheme meeting design specifications and performance requirements is finally obtained.
The design method of the intelligent optimization algorithm aims at solving the problem of combinatorial optimization, such as Genetic Algorithm (GA), particle swarm algorithm (PSO), ant colony algorithm (AA), differential evolution algorithm (DE), neural network algorithm and the like.
The transformer is designed by adopting a traditional manual design method, the expected effect cannot be achieved frequently, the design period is long, the optimization efficiency is low, the production cost is high, and the optimal design scheme is difficult to obtain. The traditional manual design method also puts forward certain requirements on the design experience and professional degree of designers, and designers with slightly poor service levels are often difficult to design better design schemes.
In the existing intelligent optimization algorithm design method adopted in transformer design, most of the methods select a single optimization target, such as total material cost, and a method of performing weighted summation on multiple targets is also adopted, so that the designed scheme is limited and cannot meet the requirement of multi-target optimization in dry-type transformer optimization design. The transformer parameter optimization design relates to a complex engineering problem, and comprises a large number of variables and a plurality of constraint conditions, due to the increase of search complexity, the existing multi-objective optimization particle swarm optimization (MOPSO) has the problem that the existing MOPSO is easy to fall into local optimization, a global optimal design scheme is difficult to obtain, and the convergence and optimization performance of the algorithm in a high-dimensional problem need to be improved. In addition, some design schemes only aim at individual models or partial models of transformers, and the design requirements of designing and producing multiple varieties or full varieties of transformers in large-scale factories cannot be met.
The process of the multi-objective optimization particle swarm optimization algorithm can be simply summarized as follows:
initializing a particle position;
calculating a fitness value (generally an objective function value, i.e. an object of optimization);
initializing the historical optimal position of the particle as the optimal position, finding out a non-dominant solution and storing the non-dominant solution into a non-dominant solution set;
updating the particle position and velocity (population updating) according to a position and velocity formula;
recalculating the fitness;
updating the historical optimal position and the non-dominated solution set of the particle according to the fitness;
and (4) exiting after convergence or the maximum iteration times are reached, wherein the non-dominated solution set at the moment is the solved optimal solution.
Disclosure of Invention
The invention aims to provide an improved multi-objective optimization particle swarm optimization-based dry-type transformer optimization design method for a nuclear power station, aiming at the characteristics of large quantity of parameter variables, multiple constraints and multiple varieties in the multi-objective optimization problem of the design of the dry-type transformer for the nuclear power station, and solving the problems of poor convergence and optimization performance of the existing multi-objective optimization particle swarm optimization-based optimization design method.
The purpose of the invention is realized by the following technical scheme: an expert experience fused dry-type transformer optimization design method for a nuclear power station comprises the following steps:
step 1) determining a plurality of (more than two) optimized performance indexes of a transformer design;
step 2), determining a main decision variable of the transformer design;
step 3) constructing a multi-target and multi-constraint optimization mathematical programming model of the transformer design;
step 4) solving an optimal solution by adopting a multi-target particle swarm algorithm;
step 5) calculating other design parameters according to a physical principle;
the method is characterized in that the improvement of the step 4) is as follows: solving an optimal solution by adopting an improved multi-target particle swarm algorithm, wherein the improvement on the multi-target particle swarm algorithm is mainly embodied as follows:
adopting a population updating mechanism fusing expert experience, wherein in the mechanism, the speed updating formula of the m-th dimension variable of the particle i is as follows:
vim(j+1)＝ω×vim(j)+r1×(pbest′im(j)-xim(j))+r2×(REP′hm(j)-xim(j)) (19)
wherein, the first and the second end of the pipe are connected with each other,
pbest′im(j)＝pbedstim(j)*(1-α) (20)
REP′hm(j)＝REPim(j)*(1-α) (21)
vim(j)、xim(j) Respectively representing the speed and the position of the m-dimensional variable of the individual i in the j iteration;
pbedstim(j) The mth dimension variable is the current historical optimal position of the individual i in the jth iteration;
REPhm(j) An m-dimensional variable for an h particle in the non-dominated solution set selected at the jth iteration;
omega is the inertial weight, r1、r2Is [0,1 ]]A random number within;
Figure BDA0003732714060000031
wherein f isi(X) representing an objective function of the performance index constructed by step 3) for measuring a deviation between a design value of the performance index i and a standard value, X representing a decision variable related to the performance index i in the set of design decision variables determined by step 2);
μithe value of (f) depends on the specific association relationship between each decision variable and the design performance index i determined according to expert experience, and if there is no association between a decision variable and the design performance index i in the particle, f is used for next generation updating of the decision variableiCoefficient of (X) μiTaking zero, if there is a correlation, mu according to the magnitude of the correlationiE {0,1}, such that the decision variable in the particle moves towards a direction that reduces the deviation of the design value associated with the optimized performance indicator from the standard value when updated in the next iteration.
The speed of the invention to individuals in the traditional particle swarm optimizationThe formula is adjusted, and when a next generation of decision variables in the individual i are updated by adopting a scheme of fusing expert experience into the updating of the speed and position of the individual, the current optimal position pbedst of the particle individual i is firstly updatedim(j) And the non-dominant solution REP in the iteration roundhm(j) The value of the mth dimension variable in the algorithm is subjected to fine adjustment, so that the individual is subjected to iterative update towards the correct direction as much as possible in the next iteration, and the iterative convergence efficiency of the algorithm is improved.
The improvement of the multi-target particle swarm algorithm is also embodied in that:
adopting a brand new non-dominated solution set (REP) updating mechanism, wherein the non-dominated solution set updating mode is as follows:
after each iteration, calculating the dominance condition among all particles in the population outside the current REP to obtain non-dominance particles in the population, and comparing the dominance relationship among the non-dominance particles in the population and the current REP member, wherein the REP is used for storing a non-dominance solution in the multi-objective optimization algorithm iteration process;
if the non-dominant particle is the same as one member in the current REP, abandoning the addition of the non-dominant particle into the REP;
otherwise, further judging the dominance relationship between the non-dominated particle and each REP member, if the particle dominates a certain REP member, marking the REP member as 'dominated', if the particle is dominated by the REP member, marking the particle as 'dominated';
finally, the unlabeled particles in the population and in the current REP are inserted into the new REP.
The above-mentioned non-dominated solution set updating mechanism, once it finds that some non-dominated particle is the same as or dominated by one member of the current REP, it will not be compared with the rest of the REP members, reducing the computation time, and at the same time, ensuring that there is no identical individual in the REP, so as to maintain the diversity of the non-dominated solution set.
And, when the number of members in its REP reaches the maximum, the following member deletion mechanism is adopted:
deleting its REP members based on the euclidean distance in the target space between each REP member and the most recently admitted member, with the greater the probability that members closer to the most recently admitted member are deleted.
The improvement of the multi-target particle swarm algorithm is further embodied in that:
a saturation counter mechanism is set, and the specific application mode is as follows:
and setting a saturation counter for controlling the iteration number for each particle, and randomly selecting an individual from the REP of the population to replace the particle if the solution represented by the particle cannot be superior to the solution represented by the particle per se according to a set scheme quality judgment standard in the future specified number of iterations of the particle.
By the mode of setting the saturation counter in the iteration process, the particles can be prevented from falling into local optimum, and meanwhile, the global search performance of the particles is improved.
The optimized performance indexes determined in the step 1) are as follows: no load loss Le(X), load loss Lb(X), a design life A (X), a short-circuit heat resistance temperature T (X), and a short-circuit dynamic stability force S (X).
The design decision variable set X defined in step 2) is specifically as follows:
X＝{XL，XH}
XL＝{Dcore，WNL，PNL，LPNL，WWL，ADL}
XH＝{PNH，SPNH，LPNH，WWH，ADH}
wherein, XLFor the main design parameters of the low-voltage part, including the core diameter DcoreWN, the number of turns of the low voltage coilLLow voltage envelope number PNLLow voltage number of turns of each encapsulated coil
Figure BDA0003732714060000051
Figure BDA0003732714060000052
Wherein lK＝PNLAndlow-voltage coil wire gauge WWLAir duct width AD between each packaging chamber of low voltageL；
XHFor the main design parameters of the high-voltage part, including the high-voltage envelope number PNHHigh pressure per number of packing stages
Figure BDA0003732714060000053
Number of high-voltage packaging layers
Figure BDA0003732714060000054
Figure BDA0003732714060000055
hq＝PNHWire gauge WW for high-voltage coilHAir duct width AD between high-pressure packaging chambersH。
The optimized mathematical programming model constructed in step 3) is as follows:
Figure BDA0003732714060000056
Figure BDA0003732714060000057
Figure BDA0003732714060000058
Figure BDA0003732714060000059
fA(X)＝(A-AS)/A，A≥AS (4)
fT(X)＝(TS-T)/TS，T≤TS (5)
Figure BDA0003732714060000061
Constraints：
Figure BDA0003732714060000062
Figure BDA0003732714060000063
Figure BDA0003732714060000064
Figure BDA0003732714060000065
Figure BDA0003732714060000066
Figure BDA0003732714060000067
Figure BDA0003732714060000068
Figure BDA0003732714060000069
Figure BDA00037327140600000610
Figure BDA00037327140600000611
WWL，WWH∈{WWi} (17)
ADL，ADH∈{ADi} (18)
wherein, the formula(1) 5 optimized performance objective functions designed for a transformer, each objective function
Figure BDA00037327140600000612
fA(X)，fT(X)，fs(X) is expressed by the following formulas (2) to (6), and is the no-load loss Le(X), load loss Lb(X), an expression of deviation of a design value from a standard value of a design life A (X), a short-circuit heat-resistant temperature T (X) and a short-circuit dynamic stability force S (X);
Le，LeSrespectively representing a no-load loss design value and a standard value;
Lb，Lb Srespectively representing a design value and a standard value of the design life;
A，ASrespectively representing a design value and a standard value of the design life;
T，TSrespectively designing a short circuit heat-resisting temperature value and a standard value;
Fa，
Figure BDA00037327140600000613
respectively representing a design value and a standard value of the axial force generated by the short circuit;
Fr，
Figure BDA00037327140600000614
respectively representing a design value and a standard value of the radial force generated by the short circuit;
equation (7) represents the no-load current I0Not exceeding the allowed standard value
Figure BDA0003732714060000071
Equation (8) represents the impedance voltage VrNot exceeding the allowed standard value
Figure BDA0003732714060000072
Equation (9) represents the core magnetic flux density BmNot exceeding the allowed standard range;
equation (10) represents the core diameter DcoreThe value is an integer;
equation (11) represents the number of low voltage coil turns WNLUpper and lower limits of value;
equation (12) represents the low voltage envelope number PNLTaking a value range and taking an integer;
the formula (13) shows that the sum of the turns of the low-voltage encapsulated coils is the total number of the low-voltage coils;
formula (14) is expressed as a high pressure envelope number value range and takes an integer;
the formula (15) represents the value range of the number of the sections of each high-voltage encapsulated coil, and the values are integers;
the formula (16) represents the value range of the number of layers of each high-voltage encapsulated coil, and integers are taken;
equation (17) indicates that the low voltage, high voltage coil wire gauge does not exceed the optional set of gauges { WW }iEquation (18) shows that the air channel width specification between the envelopes of the low-voltage and high-voltage coils does not exceed the optional die dimension set { ADi}。
In the optimized design method of the invention, the no-load loss LeLoad loss LbAnd a low pressure rise in temperature TLHigh pressure temperature rise THImpedance voltage VrThe equal performance constraints are constraint conditions which are considered preferentially in the design of the dry-type transformer, and in the iterative updating, the performance constraints are close to the set standard value or meet the set deviation range as much as possible.
According to expert experience, the adjusting scheme of the decision variables and the optimized design indexes comprises the following steps:
8) No load loss LeBelow its standard value
Figure BDA0003732714060000073
While reducing the diameter D of the iron corecoreOr reducing the number of coil turns;
9) No load loss LeHigher than its standard value
Figure BDA0003732714060000074
While increasing the core diameter Dcore；
10 ) loadLoss LbHigher than its standard value
Figure BDA0003732714060000075
When the wire gauge is enlarged;
11 ) load loss LbBelow its standard value
Figure BDA0003732714060000076
When the wire gauge is reduced;
12 ) impedance voltage VrHigher than its standard value
Figure BDA0003732714060000077
When, the following three cases are distinguished:
(1) when load loss LbHigher than its standard value
Figure BDA0003732714060000078
When the coil is wound, the wire gauge is increased in the height direction of the coil, so that the height of the coil is increased;
(2) when load loss LbBelow its standard value
Figure BDA0003732714060000079
When the coil is in use, the wire gauge is reduced along the height direction of the coil, and the height of the coil is reduced;
(3) when load loss LbAt its standard value
Figure BDA0003732714060000081
When the deviation is within the range, the number of coil layers is reduced, and the height of the coil is improved.
13 Impedance voltage V)rBelow its standard value
Figure BDA0003732714060000082
When, the following three cases are distinguished:
(1) when load loss LbHigher than its standard value
Figure BDA0003732714060000083
When the coil is wound, the wire gauge is reduced in the height direction of the coil, and the height of the coil is reduced;
(2) when load loss LbBelow its standard value
Figure BDA0003732714060000084
When the coil is wound, the wire gauge is increased in the height direction of the coil, so that the height of the coil is increased;
(3) when load loss LbAt its standard value
Figure BDA0003732714060000085
And when the deviation range is within the range, the number of coil layers is increased, and the height of the coil is reduced.
14 ) the temperature rise T is higher than its standard value TSWhen the heat dissipation area is increased, the wire gauge is increased, or the height of the coil is increased, and the number of the packages is increased.
Has the advantages that:
1) The invention provides a population updating mechanism integrating expert experience, thereby improving the searching efficiency of the algorithm;
2) The method improves the traditional non-dominated solution set updating mode, reduces the calculated amount, improves the algorithm performance, and is beneficial to keeping the diversity of Pareto frontiers (namely non-dominated solution sets);
3) The invention adopts a mechanism of setting a saturation counter in the algorithm iteration process, and judges the quality of the particles by combining with the expert experience, thereby avoiding the particles from falling into local optimum and simultaneously improving the global search performance of the particles;
4) The invention provides a multi-objective and multi-constraint mathematical programming model for designing a dry type transformer, which is integrated with expert experience, aiming at the dry type transformer for a nuclear power station.
Drawings
FIG. 1 is a flow chart of the optimization design of a nuclear power station dry transformer incorporating expert experience;
fig. 2 is a sectional view of a dry type transformer for a substation;
FIG. 3 is a REP member insertion rule;
fig. 4 is a saturation counter mechanism.
Detailed Description
The invention will be described in further detail below with reference to specific embodiments and the attached drawings:
an optimization design method of a dry-type transformer for a nuclear power station, which is integrated with expert experience, is shown in fig. 1, and comprises the following steps:
step 1) determining multiple (more than two) optimized performance indexes of transformer design
The performance parameters of the dry-type transformer are used for measuring the magnitude of the useless work of the transformer in work. The transformer can not avoid various loss, temperature rise, noise and other useless work during operation. Aiming at the dry-type transformer for the nuclear power station, the arranged key performance indexes and standard values thereof are expressed as follows: loss of load
Figure BDA0003732714060000091
No load loss
Figure BDA0003732714060000092
No load current
Figure BDA0003732714060000093
Impedance voltage
Figure BDA0003732714060000094
Core temperature rise TC, low-voltage temperature rise
Figure BDA0003732714060000096
High pressure rise
Figure BDA0003732714060000097
And the like. Aiming at different factory requirements and industrial standards, the actual performance parameters of the designed transformer meet the standard requirements.
From the perspective of manufacturers and design enterprises of dry-type transformers, under the condition of meeting constraint conditions and performance indexes, a dry-type transformer with small weight, low cost and low energy consumption can be designed to the greatest extent.
For example, according to expert experience knowledge, the material cost and the total weight have a linear relationship, the material cost and the loss of the dry-type transformer have a mutually restricted contradiction relationship, and if the material cost is reduced, the total loss is increased. Synthesis ofConsider the invention with no-load loss Le(X), load loss LbAnd (X) and 5 core indexes of the design service life A (X), the short-circuit heat-resisting temperature T (X) and the short-circuit dynamic stability force S (X) are used as main optimization performance indexes of the transformer design. The correlation influence among the several core indexes is shown, wherein X is a design decision variable set. The more the 5 core indexes approach the design standard value, the easier the lower the cost value of the transformer material is obtained.
Step 2) fusing expert experience to determine main decision variables of transformer design
From the perspective of analyzing factors directly related to the optimized performance indexes, the factors related to the optimized performance indexes are determined by combining the design principle of the transformer:
no load loss Le(X) is related to the type of the silicon steel sheet used for the iron core, the total weight of the silicon steel sheet used, and the like;
load loss Lb(X) is related to high and low voltage turns, wire length, wire gauge, etc.;
the design life A (X) is related to the temperature rise of the transformer;
the short circuit heat resistance temperature T (X) is related to the short circuit resistance;
the short circuit dynamic stabilization force S (X) is related to the coil radial dimension, axial height dimension, number of turns, etc.
And further combing the design parameters of the transformer according to the determined related factors, selecting parameters which have important influence on the performance of the transformer, and defining a design decision variable set of the transformer according to the parameters. The design decision variable set X defined in the present invention is specifically as follows:
X＝{XL，XH}
XL＝{Dcore，WNL，PNL，LPNL，WWL，ADL}
XH＝{PNH，SPNH，LPNH，WWH，ADH}
wherein, XLThe main design parameters for the low voltage part (the transformer structure is shown in fig. 2), including the core diameter DcoreWN, the number of low voltage coil turnsLLow voltage envelope number PNLLow voltage number of turns of each packaging coil
Figure BDA0003732714060000101
Wherein lK＝PNLAnd low-voltage coil wire gauge WWLAir duct width AD between each packaging chamber of low voltageL；
XHFor the main design parameters of the high-voltage part, including the number of high-voltage envelopes PNHHigh pressure per packing segment
Figure BDA0003732714060000102
Number of high-voltage packaging layers
Figure BDA0003732714060000103
Figure BDA0003732714060000104
hq＝PNHWire gauge WW of high-voltage coilHAir duct width AD between high-pressure packaging chambersH。
Step 3) constructing a multi-target and multi-constraint optimization mathematical programming model of transformer design
The optimized mathematical programming model constructed in the invention is as follows:
Figure BDA0003732714060000105
Figure BDA0003732714060000106
Figure BDA0003732714060000107
fA(X)＝(A-AS)/A，A≥AS (4)
fT(X)＝(TS-T)/TS，T≤TS (5)
Figure BDA0003732714060000108
Constraints：
Figure BDA0003732714060000109
Figure BDA00037327140600001010
Figure BDA00037327140600001011
Figure BDA00037327140600001012
Figure BDA0003732714060000111
Figure BDA0003732714060000112
Figure BDA0003732714060000113
Figure BDA0003732714060000114
Figure BDA0003732714060000115
Figure BDA0003732714060000116
WWL，WWH∈{WWi} (17)
ADL，ADH∈{ADi} (18)
wherein, the formula (1) is 5 main optimization performance objective functions designed for the transformer, and each objective function
Figure BDA0003732714060000117
fA(X)，fT(X)，fs(X) is expressed by the following formulas (2) to (6), and is the no-load loss Le(X), load loss Lb(X), a design life A (X), a short-circuit heat resistant temperature T (X), and a deviation of a design value of a short-circuit dynamic stability force S (X) from a standard value. The specific expression and the numerical value of each optimized performance index can be calculated by an industry empirical formula, and are not described herein any more, the design numerical value of the optimized performance index is not allowed to exceed the standard value, and each standard value is determined according to the actual requirements of customers and an industry standard file. Le, leSRespectively representing a no-load loss design value and a standard value; l isb，Lb SRespectively representing a design value and a standard value of the design life; a, ASRespectively representing a design value and a standard value of the design life; t, TSRespectively designing a short circuit heat-resisting temperature value and a standard value; fa，
Figure BDA0003732714060000118
Respectively representing a design value and a standard value of the axial force generated by the short circuit; fr，
Figure BDA0003732714060000119
Respectively representing a design value and a standard value of the short circuit generating radial force. Equation (7) represents the no-load current I0Not exceeding the allowed standard value
Figure BDA00037327140600001110
Equation (8) represents the impedance voltage VrNot exceeding the allowed standard value
Figure BDA00037327140600001111
Equation (9) represents the core magnetic flux density BmNot exceeding the allowed standard range; equation (10) represents the core diameter DcoreThe value is an integer; equation (11) represents the number of low voltage coil turns WNLUpper and lower limits of value; equation (12) represents the low voltage envelope number PNLTaking a value range and taking an integer; the formula (13) shows that the sum of the turns of the low-voltage encapsulated coils is the total number of the low-voltage coils; the formula (14) is expressed as a high-pressure encapsulation number value range, and an integer is taken; the formula (15) represents the value range of the number of the sections of each high-voltage encapsulated coil, and the values are integers; the formula (16) represents the value range of the number of layers of each high-voltage encapsulated coil, and integers are taken; equation (17) indicates that the low voltage, high voltage coil wire gauge does not exceed the optional wire gauge set { WW }iEquation (18) shows that the air channel width specification between the envelopes of the low-voltage and high-voltage coils does not exceed the optional die dimension set { ADi}。
Step 4) adopting an improved multi-target particle swarm algorithm to solve the optimal solution
In order to improve the performance of a traditional particle swarm algorithm in the process of solving optimization problems with high dimensional variables (more design variables need to be considered in the design of a dry type transformer for a nuclear power plant) and complex constraint relations, such as the parameter optimization design of a similar dry type transformer, an updating mechanism for changing the speed of each individual by the individual following the track of a single leader in the traditional particle swarm algorithm is changed, and the invention integrates expert experience into the traditional individual speed position updating mechanism, thereby solving the problems that the traditional particle swarm algorithm is easy to fall into local optimization and the searching efficiency is low. The invention carries out the following improvement on the traditional particle swarm algorithm, and the improvement is mainly embodied in the following three aspects:
(1) Population updating mechanism adopting fusion expert experience
The dry type transformer for the nuclear power station has a plurality of constraints in the design process, and the constraints are key factors influencing the iterative updating direction of particles. According to expert design experience, no-load loss LeLoad loss LbAnd a low pressure rise TLHigh pressure temperature rise THImpedance voltage VrThe constraint of equal performance is in the dry typeThe constraints to be considered preferentially in the design of the transformer should be made as close as possible to their set standard values or meet the set deviation range in the iterative update.
In the multi-target particle swarm algorithm, the position updating direction of individuals in a swarm needs to comprehensively consider the current speed and the historical optimal position of the individuals and follow a leader selected from a non-dominated solution set of the swarm. The conventional individual velocity update formula is as follows:
vid(j+1)＝ω×vid(j)+r1×(pbedstia(j)-xid(j))+r2×(REPhd(j)-xid(j)) (18)
wherein the particles are
Figure BDA0003732714060000121
vid(j)、xid(j) Respectively representing the speed and the position of a d-dimensional variable of an individual i in a j-th iteration;
pbedstid(j) The d-dimension variable of the current historical optimal position of the individual i at the j iteration is determined in the following way: assuming that the position of the particle in the first iteration is the optimal position, in the later iteration process, if the new position can dominate the current optimal position, setting the position at the moment as the optimal position, if the current position is dominated by the historical optimal position, keeping the historical optimal position, and if the current position is not dominated by each other, randomly selecting one of the two as the current individual optimal position;
REPhd(j) The d-dimensional variable of the h-th particle in the non-dominant solution set selected for the j-th iteration is determined in the following manner: the range of the solutions of the five objective functions forms a solution space, the solution space is equally divided into a plurality of grids in the target solution space, all REP solutions exist in each divided grid, and h is a particle randomly selected from the grids with the minimum density in all grids;
omega is the inertial weight, r1、r2Is [0,1 ]]Random number within.
With the speed, the location update is naturally also clear.
In order to improve the efficiency of iterative convergence of the algorithm, the speed updating mode is adjusted, and the individual is updated in an iterative way towards the correct direction as much as possible in the iteration by adopting a scheme of fusing expert experience into the updating of the speed and the position of the individual. The new particle velocity update is shown in equation (19).
Specifically, the no-load loss L is calculated according to the decision variable valuee(X), load loss Lb(X), deviation between design value and standard value of design life A (X), short-circuit heat-resisting temperature T (X) and short-circuit dynamic stability force S (X)
Figure BDA0003732714060000131
fA(X)，fT(X)，fS(X), optimal location for particle history pbedstim(j) And non-dominant solution REPhm(j) The position is fine-tuned as shown in equations (20-22), where μiThe value of (c) depends on the correlation between each specific decision variable and the design performance index.
vim(j+1)＝ω×vim(j)+r1×(pbest′im(j)-xim(j))+r2×(REP′hm(j)-xim(j)) (19)
Wherein the content of the first and second substances,
pbest′im(j)＝pbedstim(j)*(1-α) (20)
REP′hm(j)＝REPim(j)*(1-α) (21)
Figure BDA0003732714060000132
for example, when the empty load loss LeLess than its standard value
Figure BDA0003732714060000133
According to the expert design experience, the diameter D of the iron core in the decision variable can be reducedcoreThe manner in which the components are adjusted. If xim(j) Represents the individual i m-dimension variables at the j-th iteration (here the table)Diameter of iron corecore) For individual i, the variable core diameter D is determinedcoreWhen next generation updating is carried out, the optimal position pbedst of the particle individual i is firstly carried outim(j) And the non-dominant solution REP in the iteration roundhm(j) The value of the m-dimension variable in (b) is finely adjusted according to the diameter D of the iron corecoreIn relation to no-load loss, set μ2，μ3，μ4All values are 0, mu1E {0,1}, and is used to update the particle velocity so that the particle is updated toward the core diameter D at the next iterationcoreDecreasing direction of motion.
Similar adjustment schemes commonly used according to expert experience are (including but not limited to):
1) No load loss LeBelow its standard value
Figure BDA0003732714060000141
While reducing the diameter D of the iron corecoreOr reducing the number of coil turns;
2) No load loss LeHigher than its standard value
Figure BDA0003732714060000142
While, the diameter D of the iron core is increasedcore；
3) Load loss LbHigher than its standard value
Figure BDA0003732714060000143
When the wire gauge is increased;
4) Load loss LbBelow its standard value
Figure BDA0003732714060000144
When the wire gauge is reduced;
5) Impedance voltage VrHigher than its standard value
Figure BDA0003732714060000145
When, the following three cases are distinguished:
(1) when load loss LbHigher than its standard value
Figure BDA0003732714060000146
When the coil is wound, the wire gauge is increased in the height direction of the coil, so that the height of the coil is increased;
(2) when load loss LbBelow its standard value
Figure BDA0003732714060000147
When the coil is in use, the wire gauge is reduced along the height direction of the coil, and the height of the coil is reduced;
(3) when load loss LbAt its standard value
Figure BDA0003732714060000148
When the deviation is within the range, the number of coil layers is reduced, and the height of the coil is improved.
6) Impedance voltage VrBelow its standard value
Figure BDA0003732714060000149
When, divide into the following three kinds:
(1) when load loss LbHigher than its standard value
Figure BDA00037327140600001410
When the coil is wound, the wire gauge is reduced in the height direction of the coil, and the height of the coil is reduced;
(2) when load loss LbBelow its standard value
Figure BDA00037327140600001411
When the coil is in use, the wire gauge is increased in the height direction of the coil, so that the height of the coil is increased;
(3) when load loss LbAt its standard value
Figure BDA00037327140600001412
And when the deviation range is within, the number of coil layers is increased, and the height of the coil is reduced.
7) Temperature rise T higher than its standard value TSWhen the coil is used, the wire gauge is increased, or the height of the coil is increased, and the number of the packages is increased to increase the heat dissipation area.
(2) Adopts a brand-new non-dominated solution set updating mechanism
In multi-objective optimization algorithms involving Pareto frontiers (i.e. non-dominant solution sets), each algorithm sets a Repository (REP) for storing non-dominant solutions during the iteration of the algorithm. In the iterative process of the algorithm, the conventional MOPSO algorithm needs to determine the dominance of the member in each REP every time a new member needs to be added to the REP, and the found new non-dominance solution is added to the REP, that is, the capacity of the REP gradually increases, which results in a large amount of computation consumption. Also under this mechanism, the same solutions and particles in the population will be added to the limited space of REP, which will cause REP to saturate quickly.
A REP member may represent a feasible transformer design, and REP may also affect the efficiency of iterative optimization of subsequent algorithms. In a completely new non-dominated solution set update method, the dominance of all members within the REP is not checked every time a new member is admitted. It only compares the dominating relations between non-dominating particles in the population (outside the REP) and REP members, as shown in fig. 3, if the non-dominating particles are the same as one member in the current REP, then it abandons the non-dominating particles to be added to the REP; otherwise, the dominance relationship between the non-dominated particle and each REP member is further determined, if the particle dominates a certain REP member, the REP member is marked as "dominated", and if the particle is dominated by the REP member, the particle is marked as "dominated". Finally, the unlabeled particles in the population and in the current REP are inserted into the new REP. The above updating approach, in addition to reducing the computation time, also ensures that no identical individuals are present in REP to preserve the diversity of Pareto fronts (i.e. non-dominated solution sets).
When the number of members in REP reaches a maximum, some individuals that delete REP are required. The traditional MOPSO algorithm compares the density of non-dominant solutions in the grid of the target space mapping, and the individuals in the grid with high density have a high probability of being deleted. In the new mechanism, each REP member is deleted based on its euclidean distance in the target space between it and the most recently admitted member, with the greater probability that members closer to the most recently admitted member are deleted. Its euclidean distance can be expressed as:
Figure BDA0003732714060000151
wherein (x)1，x2，…，xi) Represents a certain member of the original REP, (y)1，y2，…，yi) Indicating a certain particle that was recently admitted into the REP.
(3) Mechanism for setting saturation counter to avoid individual falling into local optimum
In a traditional particle swarm algorithm, each iteration selects a new leader individual and replaces the previous leader, and particles in a swarm can follow the track of the leader to change the speed of the particles to update the search direction. This mechanism is not conducive to maintaining population diversity and tends to trap particles into local optimality, especially when dealing with high dimensional multi-constraint problems such as transformer design.
In order to avoid the individual falling into the local optimum, a saturation counter is set for each particle (if the total number of iterations of the population is set to 100, the limit value of the saturation counter is generally set to be about 5-10 times, which is 5% -10% of the total number). The saturation counter is used to randomly select an individual from the REP of the population to replace a particle when the particle cannot represent a solution better than the current solution represented by itself according to the criterion of the determined solution quality during the specified number of iterations (i.e. the number set by the saturation counter) in the future, as shown in fig. 4.
For the criterion of the quality of the scheme, due to the complexity of the transformer parameter optimization problem, if only performance indexes such as single cost, loss or temperature rise are relied on to judge the quality of the particles in the iteration process in the algorithm iteration process, potential optimal particles may be missed. Expert experience is combined to set a judgment criterion for the quality of the solution represented by the particles.
By the mode of setting the saturation counter in the iteration process, the particles can be prevented from falling into local optimum, and meanwhile, the global search performance of the particles is improved.
Step 5) calculating other design parameters according to physical principles
According to the optimized mathematical programming model in the step 3), solving the combination optimization problem by using an improved multi-objective particle swarm algorithm to obtain an optimal decision variable combination (non-dominated solution set), and then calculating other variable parameter values by using a dry-type transformer design principle to obtain a set of optimized dry-type transformer design scheme for the nuclear power station.
The method is improved in the aspects of population iterative evolution mode, non-dominated solution set updating and the like, the improved algorithm has good convergence effect and stable calculation, is improved in population diversity, global search capability and convergence speed compared with the original algorithm, is very suitable for being applied to the multi-objective optimization design of the dry-type transformer for the nuclear power station, and meets the dual requirements of optimization effect and rapid calculation.

Claims (8)

1. An expert experience fused dry-type transformer optimization design method for a nuclear power station comprises the following steps:
step 1) determining a plurality of optimized performance indexes of transformer design;
step 2), determining a main decision variable of the transformer design;
step 3) constructing a multi-target and multi-constraint optimization mathematical programming model of the transformer design;
step 4) solving an optimal solution by adopting a multi-target particle swarm algorithm;
step 5) calculating other design parameters according to a physical principle;
the method is characterized in that the improvement of the step 4) is as follows: solving an optimal solution by adopting an improved multi-target particle swarm algorithm, wherein the improvement on the multi-target particle swarm algorithm is mainly embodied as follows:
adopting a population updating mechanism fusing expert experience, wherein in the mechanism, the speed updating formula of the m-dimension variable of the particle i is as follows:
vim(j+1)＝ω×vim(j)+r1×(pbest′im(j)-xim(j))+r2×(REP′hm(j)-xim(j)) (19)
wherein, the first and the second end of the pipe are connected with each other,
pbest′im(j)＝pbedstim(j)*(1-α) (20)
REP′hm(j)＝REPim(j)*(1-α) (21)
vim(j)、xim(j) Respectively representing the speed and the position of the m-dimension variable of the individual i in the j iteration;
pbedstim(j) The mth dimension variable is the current historical optimal position of the individual i in the jth iteration;
REPhm(j) An m-dimensional variable for an h particle in the non-dominated solution set selected at the jth iteration;
omega is the inertial weight, r1、r2Is [0,1 ]]A random number within;
Figure FDA0003732714050000011
wherein f isi(X) representing an objective function of the performance index constructed by step 3) for measuring a deviation between a design value of the performance index i and a standard value, X representing a decision variable related to the performance index i in the set of design decision variables determined by step 2);
μithe value of f depends on the correlation between each decision variable and the design performance index i determined according to expert experience, if there is no correlation between a decision variable and the design performance index i in the particle, f is used for next generation updating of the decision variableiCoefficient of (X) [ mu ]iTaking zero, if there is a correlation, mu according to the magnitude of the correlationiE {0,1}, such that the decision variable in the particle moves towards a direction that reduces the deviation of the design value associated with the optimized performance indicator from the standard value when updated in the next iteration.
2. The dry-type transformer optimization design method for nuclear power plant as recited in claim 1,
the improvement of the multi-target particle swarm algorithm is also embodied in that:
adopting a brand new non-dominated solution set updating mechanism, wherein the non-dominated solution set updating mode is as follows:
after each iteration, calculating the dominance condition among all particles in the population outside the current REP to obtain non-dominance particles in the population, and comparing the dominance relationship among the non-dominance particles in the population and the current REP member, wherein the REP is used for storing a non-dominance solution in the multi-objective optimization algorithm iteration process;
if the non-dominant particle is the same as one member of the current REP, abandoning the addition of the non-dominant particle into the REP;
otherwise, further judging the dominance relationship between the non-dominated particle and each REP member, if the particle dominates a certain REP member, marking the REP member as 'dominated', if the particle is dominated by the REP member, marking the particle as 'dominated';
finally, inserting the unlabeled particles in the population and in the current REP into the new REP;
and, when the number of members in its REP reaches the maximum, the following member deletion mechanism is adopted:
deleting its REP members based on the euclidean distance in the target space between each REP member and the most recently admitted member, with the greater the probability that members closer to the most recently admitted member are deleted.
3. The dry-type transformer optimization design method for nuclear power plant as recited in claim 2,
the improvement of the multi-target particle swarm algorithm is further embodied in that:
a saturation counter mechanism is set, and the specific application mode is as follows:
and setting a saturation counter for controlling the iteration number for each particle, and randomly selecting an individual from the REP of the population to replace the particle if the solution represented by the particle cannot be superior to the solution represented by the particle per se according to a set scheme quality judgment standard in the future specified number of iterations of the particle.
4. The dry-type transformer optimization design method for nuclear power plant as recited in claim 3,
the optimized performance indexes determined in the step 1) are as follows: no load loss Le(X), load loss Lb(X), a design life A (X), a short-circuit heat resistance temperature T (X), and a short-circuit dynamic stability force S (X).
5. The method for optimally designing a dry-type transformer for a nuclear power plant as recited in claim 4,
the design decision variable set X defined in step 2) is specifically as follows:
X＝{XL，XH}
XL＝{Dcore，WNL，PNL，LPNL，WWL，ADL}
XH＝{PNH，SPNH，LPNH，WWH，ADH}
wherein, XLFor the main design parameters of the low-voltage part, including the core diameter DcoreWN, the number of turns of the low voltage coilLLow voltage envelope number PNLLow voltage number of turns of each packaging coil
Figure FDA0003732714050000031
Figure FDA0003732714050000032
Wherein lK＝PNLAnd low-voltage coil wire gauge WWLAir duct width AD between each packaging chamber of low voltageL；
XHFor the main design parameters of the high-voltage part, including the number of high-voltage envelopes PNHHigh pressure per packing segment
Figure FDA0003732714050000033
High voltage number of encapsulating layers
Figure FDA0003732714050000034
Figure FDA0003732714050000035
Wire gauge WW for high-voltage coilHAir duct width AD between high-pressure packaging chambersH。
6. The dry-type transformer optimization design method for nuclear power plant as recited in claim 5,
the optimized mathematical programming model constructed in step 3) is as follows:
Figure FDA00037327140500000313
Figure FDA0003732714050000036
Figure FDA0003732714050000037
fA(X)＝(A-AS)/A，A≥AS (4)
fT(X)＝(TS-T)/TS，T≤TS (5)
Figure FDA0003732714050000038
Constraints：
Figure FDA0003732714050000039
Figure FDA00037327140500000310
Figure FDA00037327140500000311
Figure FDA00037327140500000312
Figure FDA0003732714050000041
Figure FDA0003732714050000042
Figure FDA0003732714050000043
Figure FDA0003732714050000044
Figure FDA0003732714050000045
Figure FDA0003732714050000046
WWL，WWH∈{WWi} (17)
ADL，ADH∈{ADi} (18)
wherein, the formula(1) 5 optimized performance objective functions designed for a transformer, each objective function
Figure FDA00037327140500000412
fA(X)，fT(X)，fs(X) is expressed by the following formulas (2) to (6), and is the no-load loss Le(X), load loss Lb(X), an expression of deviation of a design value of a design life A (X), a short-circuit heat-resistant temperature T (X) and a short-circuit dynamic stability force S (X) from a standard value;
Le，LeSrespectively representing a no-load loss design value and a standard value;
Lb，Lb Srespectively representing a design value and a standard value of the design life;
A，ASrespectively representing a design value and a standard value of the design life;
T，TSrespectively designing a short circuit heat-resisting temperature value and a standard value;
Fa，
Figure FDA0003732714050000048
respectively representing a design value and a standard value of the axial force generated by the short circuit;
Fr，
Figure FDA0003732714050000049
respectively representing a design value and a standard value of the radial force generated by the short circuit;
equation (7) represents the no-load current I0Not exceeding the allowed standard value
Figure FDA00037327140500000410
Equation (8) represents the impedance voltage VrNot exceeding the allowed standard value
Figure FDA00037327140500000411
Equation (9) represents the core magnetic flux density BmNot exceeding the allowed standard range;
equation (10) represents the core diameter DcoreThe value is an integer;
equation (11) represents the number of low voltage coil turns WNLUpper and lower limits of value;
equation (12) represents the low voltage envelope number PNLTaking a value range and taking an integer;
formula (13) shows that the sum of the number of turns of each low-voltage encapsulated coil is the total number of turns of the low-voltage coil;
formula (14) is expressed as a high pressure envelope number value range and takes an integer;
the formula (15) represents the value range of the number of the sections of each high-voltage encapsulated coil, and the values are integers;
the formula (16) represents the value range of the number of layers of each high-voltage encapsulated coil, and integers are taken;
equation (17) indicates that the low voltage, high voltage coil wire gauge does not exceed the optional set of gauges { WW }iEquation (18) shows that the air channel width specification between the envelopes of the low-voltage and high-voltage coils does not exceed the optional die dimension set { ADi}。
7. The dry-type transformer optimization design method for nuclear power plant as recited in claim 6,
no load loss LeLoad loss LbAnd a low pressure rise in temperature TLHigh pressure temperature rise THImpedance voltage VrAre constraints that are considered preferentially in dry-type transformer design, and in iterative updating, these performance constraints should be made as close as possible to their set standard values or meet set deviation ranges.
8. The dry-type transformer optimization design method for nuclear power plant as recited in claim 6 or 7,
the adjusting scheme of the decision variables and the optimized design indexes comprises the following steps:
1) No load loss LeBelow its standard value
Figure FDA0003732714050000051
While reducing the core diameterDcoreOr reducing the number of coil turns;
2) No load loss LeHigher than its standard value
Figure FDA0003732714050000052
While, the diameter D of the iron core is increasedcore；
3) Load loss LbHigher than its standard value
Figure FDA0003732714050000053
When the wire gauge is increased;
4) Load loss LbBelow its standard value
Figure FDA0003732714050000054
When the wire gauge is reduced;
5) Impedance voltage VrHigher than its standard value
Figure FDA0003732714050000055
When, the following three cases are distinguished:
(1) when load loss LbHigher than its standard value
Figure FDA0003732714050000056
When the coil is in use, the wire gauge is increased in the height direction of the coil, so that the height of the coil is increased;
(2) when load loss LbBelow its standard value
Figure FDA0003732714050000057
When the coil is in use, the wire gauge is reduced along the height direction of the coil, and the height of the coil is reduced;
(3) when load loss LbAt its standard value
Figure FDA0003732714050000058
When the deviation range is within, reduce the coil number of piles, improve coil height.
6) Impedance voltage VrBelow its standard value
Figure FDA0003732714050000059
When, the following three cases are distinguished:
(1) when load loss LbHigher than its standard value
Figure FDA00037327140500000510
When the coil is in use, the wire gauge is reduced along the height direction of the coil, and the height of the coil is reduced;
(2) when load loss LbBelow its standard value
Figure FDA0003732714050000061
When the coil is in use, the wire gauge is increased in the height direction of the coil, so that the height of the coil is increased;
(3) when load loss LbAt its standard value
Figure FDA0003732714050000062
And when the deviation range is within, the number of coil layers is increased, and the height of the coil is reduced.
7) Temperature rise T higher than its standard value TSWhen the heat dissipation area is increased, the wire gauge is increased, or the height of the coil is increased, and the number of the packages is increased.
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