CN114091720A - Multi-target coal blending method based on decision maker preference - Google Patents

Multi-target coal blending method based on decision maker preference Download PDF

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CN114091720A
CN114091720A CN202111153910.XA CN202111153910A CN114091720A CN 114091720 A CN114091720 A CN 114091720A CN 202111153910 A CN202111153910 A CN 202111153910A CN 114091720 A CN114091720 A CN 114091720A
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preference
coal
individual
population
quality characteristic
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李�一
施文
杨枫
张泉水
程婷婷
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Shanghai Shidongkou First Power Plant of Huaneng Power International Inc
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Abstract

The invention relates to a multi-target coal blending method based on decision maker preference, which comprises the following steps: constructing a decision variable and a plurality of objective functions for representing a coal blending scheme, and obtaining an optimal coal blending scheme through an NSGA-II algorithm according to the decision variable and the objective functions; wherein, the NSGA-II algorithm comprises the following steps: 1) taking the decision variable as an individual to perform population initialization; 2) selecting, crossing and mutating the population; 3) combining the parent population and the child population; 4) carrying out preference angle non-dominated layering on the population; 5) calculating individual aggregation distances of the individuals, and reserving the individual with the largest individual aggregation distance in each non-dominant layer; 6) and (3) judging whether the population evolution algebra is larger than the maximum iteration number, if so, ending, selecting individuals meeting the preference angle judgment condition from the population as a preference solution set, and otherwise, executing the step 2). Compared with the prior art, the method has high efficiency and strong pertinence.

Description

Multi-target coal blending method based on decision maker preference
Technical Field
The invention relates to the technical field of coal blending of power plants, in particular to a multi-target coal blending method based on decision maker preference.
Background
The dynamic coal blending technology is a clean coal technology which accords with the national conditions of China, and can effectively relieve the pressure on the coal blending work of a power plant caused by the problems of complexity and changeability of coal types, large coal quality difference and the like of the coal in China, so the coal blending technology has wide application prospect in China.
In order to ensure the flexibility and scientificity of the power coal blending technology, theoretical research on the aspect of power coal blending is developed at home. Due to the fact that the classical single-target coal blending model has the problem of considering one plane and cannot adapt to the actual coal blending problem, the current multi-target coal blending method becomes a research hotspot. Although the multi-target coal blending combustion theoretical method makes a certain progress, the multi-target optimization algorithm always has the problems of high calculation complexity, multiple optimization results and the like, so that a decision maker cannot select the most appropriate coal blending scheme, and the high efficiency and the actual value are lacked.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a multi-target coal blending method based on the preference of a decision maker, which has high efficiency and strong pertinence.
The purpose of the invention can be realized by the following technical scheme:
a multi-target coal blending method based on decision maker preference comprises the following steps:
constructing decision variables and a plurality of objective functions for representing a coal blending scheme, wherein the coal blending scheme comprises the steps of selecting single coal types and blending proportion;
obtaining an optimal coal blending scheme through an NSGA-II algorithm according to the decision variables and a plurality of objective functions;
wherein, the NSGA-II algorithm comprises the following steps:
1) taking the decision variable as an individual to perform population initialization;
2) selecting, crossing and mutating the population;
3) combining the parent population and the child population;
4) carrying out preference angle non-dominated layering on the population;
5) calculating individual aggregation distances of the individuals, and reserving the individual with the largest individual aggregation distance in each non-dominant layer;
6) judging whether population evolution algebra is larger than the maximum iteration times, if so, ending, selecting individuals meeting preference angle judgment conditions from the population as a preference solution set, acquiring an optimal coal blending scheme according to the preference solution set, and otherwise, executing the step 2);
the preference information is fused into the NSGA-II algorithm, so that a preference solution set appears in a preference area, the workload of screening the optimal solution is greatly reduced, and the practicability and pertinence of the algorithm are improved.
Further, the calculation formula of the individual focusing distance is as follows:
Figure BDA0003288056580000021
wherein C (X) is the individual aggregation distance of the individual X, p is a preference point, epsilon is a sparse value, theta is an individual angle, and the calculation formula is as follows;
Figure BDA0003288056580000022
where θ (A, B) is the angle between individual A and individual B, M is the number of objective functions,
Figure BDA0003288056580000023
and
Figure BDA0003288056580000024
respectively the maximum and minimum, x, of the mth objective function in the populationmAnd ymActual values of the mth objective function, p, for the individual A and the individual B, respectivelymIs the preference point of the mth objective function.
Further, the step 4) comprises:
performing layered sequencing on the populations according to the preference dominance relationship, and dividing the individuals meeting the dominance relationship into the same layer;
wherein the preference dominance relationship includes:
for any two individuals a and B in the population, determining that individual a dominates individual B if and only if one of two conditions is met;
the two conditions are:
individual a Pareto dominates individual B;
the individual A and the individual B are not Pareto, and theta (B, N) -theta (A, N) is larger than or equal to delta, wherein delta is a preference angle range, and N is a reference point.
Further, the preference angle determination condition is as follows:
θ(x,N)＜δ
wherein x is an individual.
Further, the calculation formula of the reference point is as follows:
Figure BDA0003288056580000031
wherein N is a reference point, βiPreference weight, f, for the ith objective functioni(x) And fi(p) the values of the ith objective function, f, corresponding to the individual x and the preference point p, respectivelyi maxAnd fi minRespectively the maximum value and the minimum value of the ith objective function in the population;
and the individual corresponding to the reference point is the individual with the optimal preference.
Further, the objective function comprises a coal price economy objective function and a coal quality deviation type objective function.
Further, the coal price economy objective function FeThe expression of (a) is:
Figure BDA0003288056580000032
wherein n is the total number of mixed single coal types, and XiSelecting the blending proportion of the single coal for the ith kind, PiThe price of the selected individual coal of the ith category,Paand alpha is an economic adjustment coefficient for market reference minimum coal price.
Further, the coal quality characteristic parameters of the single coal are divided into strong preference coal quality characteristic parameters and weak preference coal quality characteristic parameters;
the coal quality deviation type objective function FpThe expression of (a) is:
Figure BDA0003288056580000033
wherein, S [ g ]i(x)]And V [ g ]i(x)]Respectively a strong preference coal quality deviation function and a weak preference coal quality deviation function, R and T are respectively the number of strong preference coal quality characteristic parameters and weak preference coal quality characteristic parameters, RiAnd tjAnd deviation adjusting coefficients of the ith strong preference coal quality characteristic parameter and the jth weak preference coal quality characteristic parameter are respectively obtained.
Further, the expression of the strong preference coal quality deviation function is as follows:
Figure BDA0003288056580000034
wherein, giFor the predicted value of the ith strongly preferred coal quality characteristic parameter, Yimin、YimaxAnd YipRespectively defining minimum value, maximum value and optimal value of the ith strong preference coal quality characteristic parameter, wherein Q is a set value;
the expression of the weak preference coal quality deviation function is as follows:
Figure BDA0003288056580000041
wherein, gjFor the predicted value, y, of the jth weakly preferred coal quality characteristic parameterjmin、yjmaxAnd ujRespectively, a defined minimum value, a maximum value and a limit tolerance value of the jth weak preference coal quality characteristic parameter.
Further, for each individual, the calculation process of the predicted value of the coal quality characteristic parameter comprises the following steps:
and according to the coal quality characteristic parameters and the mixing proportion of various selected single coals in the individual, obtaining the predicted value of the individual coal quality characteristic parameters through weighted average.
Compared with the prior art, the invention has the following beneficial effects:
the multi-target coal blending method constructs decision variables and a plurality of target functions representing a coal blending scheme, and obtains an optimal coal blending scheme through an NSGA-II algorithm according to the decision variables and the target functions, the currently common multi-target algorithm usually obtains a large number of calculation results, and the workload of screening optimal solutions is increased.
Drawings
FIG. 1 is a flow chart of the NSGA-II algorithm;
FIG. 2 is a schematic diagram of Pareto optimal boundaries;
fig. 3 is a preference solution set distribution diagram.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
A multi-target coal blending method based on decision maker preference comprises the following steps:
constructing decision variables and a plurality of objective functions for representing a coal blending scheme, wherein the coal blending scheme comprises the steps of selecting single coal types and blending proportion;
obtaining an optimal coal blending scheme through an NSGA-II algorithm according to the decision variables and a plurality of objective functions, and carrying out coal blending and burning work of the coal-fired power plant according to the optimal coal blending scheme;
as shown in fig. 1, the NSGA-II algorithm includes:
1) taking the decision variable as an individual to perform population initialization;
2) selecting, crossing and mutating the population;
3) combining the parent population and the child population;
4) carrying out preference angle non-dominated layering on the population;
5) calculating individual aggregation distances of the individuals, and reserving the individual with the largest individual aggregation distance in each non-dominant layer;
6) judging whether population evolution algebra is larger than the maximum iteration times, if so, ending, selecting individuals meeting preference angle judgment conditions from the population as a preference solution set, acquiring an optimal coal blending scheme according to the preference solution set, and otherwise, executing the step 2);
the preference information is fused into the NSGA-II algorithm, so that a preference solution set appears in a preference area, the workload of screening the optimal solution is greatly reduced, and the practicability and pertinence of the algorithm are improved.
The individual gather distance is calculated as:
Figure BDA0003288056580000051
wherein C (X) is the individual aggregation distance of the individual X, p is a preference point, epsilon is a sparse value, theta is an individual angle, and the calculation formula is as follows;
Figure BDA0003288056580000052
where θ (A, B) is the angle between individual A and individual B, M is the number of objective functions,
Figure BDA0003288056580000053
and
Figure BDA0003288056580000054
respectively the maximum and minimum, x, of the mth objective function in the populationmAnd ymActual values of the mth objective function, p, for the individual A and the individual B, respectivelymIs the preference point of the mth objective function.
The step 4) comprises the following steps:
performing layered sequencing on the populations according to the preference dominance relationship, and dividing the individuals meeting the dominance relationship into the same layer;
wherein the preference dominance relationship comprises:
for any two individuals a and B in the population, determining that individual a dominates individual B if and only if one of two conditions is met;
the two conditions are:
individual a Pareto dominates individual B;
the individual A and the individual B are not Pareto, and theta (B, N) -theta (A, N) is larger than or equal to delta, wherein delta is a preference angle range, and N is a reference point.
Individual a Pareto dominates individual B as defined below:
for minimizing multi-objective problems, n objective components fiA vector f (x) = (f) consisting of (i ═ 1,.. n)1(X),f2(X),...,fn(X)), arbitrarily given two XU,XVIf and only if, for
Figure BDA0003288056580000061
All have fi(XU)≤fi(XV) Then XUDominating XVSimply stated, for the non-dominated ordering of two objective functions, when (x)1≤x2and y1≤y2)and(x1＜x2or y1＜y2) Then f (x)1,y1) Pareto dominate f (x)2,y2)。
The preference angle judgment condition is as follows:
θ(x,N)＜δ (3)
wherein x is an individual.
The calculation formula of the reference point is as follows:
Figure BDA0003288056580000062
wherein N is a reference point, βiPreference weight, f, for the ith objective functioni(x) And fi(p) the values of the ith objective function, f, corresponding to the individual x and the preference point p, respectivelyi maxAnd fi minRespectively the maximum value and the minimum value of the ith objective function in the population;
and the individual corresponding to the reference point is the individual with the optimal preference.
The objective function comprises a coal price economy objective function and a coal quality deviation type objective function.
Coal cost economy objective function FeThe expression of (a) is:
Figure BDA0003288056580000063
wherein n is the total number of mixed single coal types, and XiSelecting the blending proportion of the single coal for the ith kind, PiPrice of selected coal of ith category, PaAnd alpha is an economic adjustment coefficient for market reference minimum coal price.
The coal quality characteristic parameters of the single coal are divided into strong preference coal quality characteristic parameters and weak preference coal quality characteristic parameters;
coal quality deviation type objective function FpThe expression of (a) is:
Figure BDA0003288056580000071
wherein, S [ g ]i(x)]And V [ g ]i(x)]Respectively a strong preference coal quality deviation function and a weak preference coal quality deviation function, R and T are respectively the number of strong preference coal quality characteristic parameters and weak preference coal quality characteristic parameters, RiAnd tjAnd deviation adjusting coefficients of the ith strong preference coal quality characteristic parameter and the jth weak preference coal quality characteristic parameter are respectively obtained.
The expression of the strong preference coal quality deviation function is as follows:
Figure BDA0003288056580000072
wherein, giFor the predicted value of the ith strongly preferred coal quality characteristic parameter, Yimin、YimaxAnd YipRespectively defining minimum value, maximum value and optimal value of the ith strong preference coal quality characteristic parameter, wherein Q is a set value;
the expression of the weak preference coal quality deviation function is as follows:
Figure BDA0003288056580000073
wherein, gjFor the predicted value, y, of the jth weakly preferred coal quality characteristic parameterjmin、yjmaxAnd ujRespectively, a defined minimum value, a maximum value and a limit tolerance value of the jth weak preference coal quality characteristic parameter.
For each individual, the calculation process of the predicted value of the coal quality characteristic parameter comprises the following steps:
and according to the coal quality characteristic parameters and the mixing proportion of various selected single coals in the individual, obtaining the predicted value of the individual coal quality characteristic parameters through weighted average.
In this embodiment, a certain coal-fired power plant boiler is used for power coal blending research, 8 kinds of single coals in a coal storage database are stored, real number coding is adopted to construct decision variables, three kinds of single coals are selected for blending, and the coal blending method is composed of a single coal sequence number and a single coal proportion, and the concrete form is as follows:
{d1,d2,d3,l1％,l2％,l3％}
8 kinds of single coals in the coal storage database are coded, and the actual value range is as follows:
min{1,1,1,15,15,15}
max{8,8,8,70,70,70}
in the step 2), the genetic selection operator adopts a championship selection method, and individuals with high fitness value are preferentially selected; the crossover operator adopts a group crossover method, each group of the first three bits and the last three bits is crossed in the group, and the mutation operator adopts a near number mutation method and performs mutation by using random numbers near the original individuals. During the genetic operation, the blending ratio of the three mixed coals is always kept to be 100 percent.
The strongly preferred coal quality characteristic parameter includes calorific value (Q)ad) Volatile matter (V)ad) And sulfur component (S)ad) The weak preference coal quality characteristic parameter comprises ash content (A)ad) And moisture (M)ad) The design coal quality and the limit tolerance condition of the power plant boiler are shown in table 1:
TABLE 1 design parameter table for coal type and quality
Figure BDA0003288056580000081
The coal quality characteristic parameters of 8 kinds of single coal are shown in the table 2:
TABLE 28 list of coal quality characteristic parameters of single coal
Figure BDA0003288056580000082
The calculation formula of the annual energy production of the coal-fired power plant is as follows:
Figure BDA0003288056580000083
wherein E isaIs annual energy production, and has a unit of 108kW·h，WsThe unit is 10 for the power on the internet8kW.h, eta is the power consumption rate of the power plant, and the unit is percent;
the calculation formula of the annual coal consumption of the coal-fired power plant is as follows:
Figure BDA0003288056580000091
wherein: hmFor annual coal consumption, 104t，gaFor supplying power, g/kW.h, QsThe calorific value is preferred for coal blending, the unit is MJ/kg,4.1816 is conversion coefficient of calorie and Joule, and the unit is 7000kcal/kg is heat productivity of standard coal, and the unit is 105As a unit conversion factor, the calorific value Q is biased by the coal blendingsThe annual energy production of the power plant EaAnd annual coal consumption HmIn connection, the annual coal control quantity index is classified into a coal quality deviation index, and the complexity of the optimization index is reduced.
The coal-fired power plant needs to generate the most electricity by using a specific coal consumption amount, which puts higher requirements on coal blending and burning work of the power plant, and in 2020, the state requires the annual coal consumption amount H of the power plantmControlling the power generation amount to 233.67 ten thousand t, comparing the power generation amount data of the power plant in recent years, and calculating the annual power generation amount E of the power plantaAt least 62.789 hundred million kW.h, the power consumption eta of the power plant is 5.5 percent, and the standard coal consumption g of power supplyaAt 290 g/kWh, the preferential calorific value Q of the mixed coal can be calculated through the formula (9) and the formula (10)s21.56MJ/kg, taking the historical minimum coal blending price of 688 Yuan/t as the coal blending preference coal price, namely the coal blending preference coal price in the formula (5)
Figure BDA0003288056580000092
As shown in fig. 2, in the last iteration, individuals in each layer of non-dominated layers gather to form an original optimal solution set, where the original optimal solution set is a Pareto optimal boundary, in step (6), a preference solution is selected from the original optimal solution set to form a preference solution set, and the bias heating value of the coal blending preference, the coal blending preference coal price, and the optimal values of the other coal quality characteristic parameters are substituted into an objective function to obtain the coordinate of a bias point p in a solution space, where the coordinate of the bias point p in this embodiment is (1.9,1.6), and the origin is selected by the bias point.
The value of the dispersion epsilon in equation (1) is set to 0.12, the angle range of preference in equation (3) is 12, and the market reference minimum coal price P in equation (5)aAt 770 m/t, the economic adjustment coefficient α is 15, r in equation (8)iAnd tjRespectively 50 and 30, the maximum iteration number is 100, the crowd scale is set to 100, the preference solution set obtained after simulation calculation is shown in fig. 3, as can be seen from fig. 3, the number of the original optimal solution sets obtained by using a common multi-objective algorithm is large, which is not beneficial for a decision maker to make decisionsAnd selecting, namely, the solution set can be selected by improving the algorithm and adding preference information to obtain partial solutions which are interested by a decision maker, repeated results can be removed in the optimizing process, and the practicability, the efficiency and the flexibility of the algorithm are further improved. In order to make the algorithm more universal, a decision maker can set parameters according to actual conditions, different decision makers have different preferences, different solution set distributions can be obtained, and the decision maker is helped to select preference solutions better and faster.
The actual coal blending schedules for the individuals in the preference solution set are shown in table 3:
TABLE 3 actual coal blending schedule corresponding to individuals in preference solution set
Figure BDA0003288056580000101
As shown in Table 3, the coal blending coal price is close to the lowest coal price referred by the market, certain economical efficiency is guaranteed, the calorific value of the blended coal exceeds the preferential calorific value of the blended coal, the quantity of coal blending results is moderate, the decision maker can conveniently select the coal blending results, the multi-target coal blending method preferred by the decision maker can comprehensively consider various preferential information indexes, and meanwhile, a solution set meeting requirements is obtained. A decision maker can adjust various parameters according to the real-time condition of the power plant and select the best coal blending scheme, so that various complex coal blending conditions can be quickly and flexibly dealt with.
The invention provides a multi-target coal blending method based on decision maker preference, which comprises the steps of constructing a decision variable and a plurality of target functions for representing a coal blending scheme, and obtaining an optimal coal blending scheme through an NSGA-II algorithm according to the decision variable and the target functions.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims (10)

1. A multi-target coal blending method based on decision maker preference is characterized by comprising the following steps:
constructing decision variables and a plurality of objective functions for representing a coal blending scheme, wherein the coal blending scheme comprises the steps of selecting single coal types and blending proportion;
obtaining an optimal coal blending scheme through an NSGA-II algorithm according to the decision variables and a plurality of objective functions;
wherein, the NSGA-II algorithm comprises the following steps:
1) taking the decision variable as an individual to perform population initialization;
2) selecting, crossing and mutating the population;
3) combining the parent population and the child population;
4) carrying out preference angle non-dominated layering on the population;
5) calculating individual aggregation distances of the individuals, and reserving the individual with the largest individual aggregation distance in each non-dominant layer;
6) and (3) judging whether the population evolution algebra is larger than the maximum iteration number, if so, ending, selecting individuals meeting preference angle judgment conditions from the population as a preference solution set, acquiring an optimal coal blending scheme according to the preference solution set, and otherwise, executing the step 2).
2. The multi-objective coal blending method based on decision maker preference according to claim 1, wherein the calculation formula of the individual aggregation distance is as follows:
Figure FDA0003288056570000011
wherein C (X) is the individual aggregation distance of the individual X, p is a preference point, epsilon is a sparse value, theta is an individual angle, and the calculation formula is as follows;
Figure FDA0003288056570000012
where θ (A, B) is the angle between individual A and individual B, M is the number of objective functions,
Figure FDA0003288056570000013
and
Figure FDA0003288056570000014
respectively the maximum and minimum, x, of the mth objective function in the populationmAnd ymActual values of the mth objective function, p, for the individual A and the individual B, respectivelymIs the preference point of the mth objective function.
3. The multi-objective coal blending method based on decision maker preference as claimed in claim 2, wherein the step 4) comprises:
performing layered sequencing on the populations according to the preference dominance relationship, and dividing the individuals meeting the dominance relationship into the same layer;
wherein the preference dominance relationship includes:
for any two individuals a and B in the population, determining that individual a dominates individual B if and only if one of two conditions is met;
the two conditions are:
individual a Pareto dominates individual B;
the individual A and the individual B are not Pareto, and theta (B, N) -theta (A, N) is larger than or equal to delta, wherein delta is a preference angle range, and N is a reference point.
4. The multi-target coal blending method based on the preference of the decision maker as claimed in claim 3, wherein the preference angle judgment condition is as follows:
θ(x，N)＜δ
wherein x is an individual.
5. The multi-objective coal blending method based on decision maker preference according to claim 3, wherein the calculation formula of the reference point is as follows:
Figure FDA0003288056570000021
wherein N is a reference point, βiPreference weight, f, for the ith objective functioni(x) And fi(p) the values of the ith objective function corresponding to the individual x and the preference point p, respectively,
Figure FDA0003288056570000022
and
Figure FDA0003288056570000023
respectively the maximum value and the minimum value of the ith objective function in the population;
and the individual corresponding to the reference point is the individual with the optimal preference.
6. The multi-objective coal blending method based on decision maker preference according to claim 1, wherein the objective function comprises a coal price economy objective function and a coal quality deviation type objective function.
7. The multi-objective coal blending method based on decision maker preference as claimed in claim 6, wherein the coal price economic objective function FeThe expression of (a) is:
Figure FDA0003288056570000024
whereinN is the total number of single coal types to be mixed, XiSelecting the blending proportion of the single coal for the ith kind, PiPrice of selected coal of ith category, PaAnd alpha is an economic adjustment coefficient for market reference minimum coal price.
8. The multi-target coal blending method based on decision maker preference according to claim 7, wherein the coal quality characteristic parameters of the single coal are divided into strong preference coal quality characteristic parameters and weak preference coal quality characteristic parameters;
the coal quality deviation type objective function FpThe expression of (a) is:
Figure FDA0003288056570000031
wherein, S [ g ]i(x)]And V [ g ]i(x)]Respectively a strong preference coal quality deviation function and a weak preference coal quality deviation function, R and T are respectively the number of strong preference coal quality characteristic parameters and weak preference coal quality characteristic parameters, RiAnd tjAnd deviation adjusting coefficients of the ith strong preference coal quality characteristic parameter and the jth weak preference coal quality characteristic parameter are respectively obtained.
9. The multi-target coal blending method based on decision maker preference according to claim 8, wherein the expression of the strong preference coal quality deviation function is as follows:
Figure FDA0003288056570000032
wherein, giFor the predicted value of the ith strongly preferred coal quality characteristic parameter, Yimin、YimaxAnd YipRespectively defining minimum value, maximum value and optimal value of the ith strong preference coal quality characteristic parameter, wherein Q is a set value;
the expression of the weak preference coal quality deviation function is as follows:
Figure FDA0003288056570000033
wherein, gjFor the predicted value, y, of the jth weakly preferred coal quality characteristic parameterjmin、yjmaxAnd ujRespectively, a defined minimum value, a maximum value and a limit tolerance value of the jth weak preference coal quality characteristic parameter.
10. The multi-objective coal blending method based on decision maker preference according to claim 9, wherein the calculation process of the predicted value of the coal quality characteristic parameter for each individual comprises:
and according to the coal quality characteristic parameters and the mixing proportion of various selected single coals in the individual, obtaining the predicted value of the individual coal quality characteristic parameters through weighted average.
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Publication number Priority date Publication date Assignee Title
CN115310353A (en) * 2022-07-26 2022-11-08 明珠电气股份有限公司 Power transformer design method based on rapid multi-objective optimization

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115310353A (en) * 2022-07-26 2022-11-08 明珠电气股份有限公司 Power transformer design method based on rapid multi-objective optimization
CN115310353B (en) * 2022-07-26 2024-02-20 明珠电气股份有限公司 Power transformer design method based on rapid multi-objective optimization

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