CN115859518A - Three-dimensional wound core transformer optimization design method based on improved gull optimization algorithm - Google Patents
Three-dimensional wound core transformer optimization design method based on improved gull optimization algorithm Download PDFInfo
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Abstract
The invention discloses an optimized design method of a three-dimensional wound core transformer based on an improved gull optimization algorithm. Firstly, according to a single-target optimization design mathematical model, establishing an optimization objective function taking the minimum electromagnetic manufacturing cost of the three-dimensional wound core transformer as an optimization target; and then processing constraint conditions required to be met by the transformer by adopting a penalty function to obtain an optimized design mathematical model of the three-dimensional wound core transformer, solving the optimized design mathematical model of the three-dimensional wound core transformer by adopting an improved gull optimization algorithm, outputting a current global optimal fitness value Gtest F as the electromagnetic manufacturing cost of the optimized transformer, and outputting a current global optimal gull individual position Gtest X as an optimized variable combination of the optimized transformer. The invention optimizes the three-dimensional wound core transformer by adopting the improved gull optimization algorithm, improves the optimization design efficiency and the design precision of the three-dimensional wound core transformer, effectively optimizes the design parameters of the three-dimensional wound core transformer and reduces the manufacturing cost.
Description
Technical Field
The invention relates to the field of optimization design of transformers, in particular to a three-dimensional wound core transformer optimization design method based on an improved gull optimization algorithm.
Background
The three-dimensional wound core transformer is an ideal energy-saving transformer, and compared with the traditional laminated core, the three-dimensional wound core has the advantages of three-phase balance, energy conservation, material conservation, low noise, small size and the like, and is highly fit with the green development direction of the transformer under the aim of 'double carbon'. In recent years, the system is widely applied to high-rise buildings, rail transit, new energy access and the like. In order to reduce the manufacturing cost of the three-dimensional wound core transformer, the design scheme of the transformer needs to be optimized.
Common solving methods for the transformer optimization design model include an evolutionary algorithm, a genetic algorithm, a particle swarm algorithm and the like. In the documents 'design and optimization of electromagnetic structures of reinforced liquid-cooled traction transformers [ J ]. Proc. Electrotechnics, 2021,36 (S2): 460-466', a genetic algorithm is adopted to optimally design high-speed rail vehicle-mounted traction transformers, so that the light weight design of the vehicle-mounted traction transformers is realized. The optimized design of amorphous alloy dry-type transformers based on IPSO [ J ] manufacturing automation, 2021,43 (01): 126-30 ] was optimized by using an improved particle swarm optimization algorithm. The multi-objective genetic algorithm is applied to the optimization design of the high-power high-frequency transformer in the literature Cao Xiaopeng, chengwu, ningguanfu, and the like, and the optimization design of the high-power high-frequency transformer is based on the multi-objective genetic algorithm [ J ], chinese Motor engineering reports, 2018,38 (5): 1348-1355. In conclusion, the performance index of the transformer can be improved by optimizing the design scheme of the transformer by adopting an intelligent optimization algorithm, but the algorithm has the defects of complex structure, poor stability and high time complexity.
Seagull Optimization Algorithm (SOA) is one of the representative algorithms of meta-heuristic algorithms, a complex Optimization design model is solved by simulating the migration and spiral attack behaviors of a Seagull group, and the Seagull Optimization Algorithm is successfully applied to challenging large-scale constraint Optimization problems such as unmanned aerial vehicle network spectrum allocation, load model parameter identification of a photovoltaic discovery system, renewable energy system design and the like.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to solve the technical problem of providing an optimized design method of a three-dimensional wound core transformer based on an improved gull optimization algorithm.
The technical scheme for solving the technical problem is to provide a method for optimally designing a three-dimensional wound core transformer based on an improved gull optimization algorithm, which is characterized by comprising the following steps of:
minf(X)＝G Fe ×C Fe +G Cu ×C Cu (1)
in the formula (1), the optimization target f (X) is the electromagnetic manufacturing cost of the three-dimensional wound core transformer; x is an optimization variable; g Fe The weight of the three-dimensional wound core transformer core; c Fe Is the unit price of the silicon steel sheet; g Cu Is the winding weight; c Cu Is copper unit price;
step 2, obtaining constraint conditions required to be met by the transformer according to basic electrical parameters of the three-dimensional wound core transformer; and then, processing the constraint condition by adopting a penalty function to obtain an optimized objective function with a penalty function term, namely an optimized design mathematical model of the three-dimensional wound core transformer, as shown in the formula (3):
in formula (3), P (X) is a penalty function; q is the number of constraint conditions; a is i For the penalty factor, the larger a is, the greater the penalty degree of the constraint condition is; g i (X) is a constraint condition, and g is a constraint condition when the constraint condition is satisfied i (X) =0; p is a positive integer;
and 3, solving the optimized design mathematical model of the three-dimensional wound core transformer obtained in the step 2 by adopting an improved gull optimization algorithm, wherein the method specifically comprises the following steps:
step 3.1, initializing parameters of a gull optimization algorithm;
step 3.2, initializing the position of the individual gull by using Bernoulli chaotic mapping, and improving the ergodicity of the initial population;
step 3.3, initializing gull individual X with optimal population best The global optimal fitness value Gbest F and the global optimal gull individual position Gbest X;
step 3.4, initializing the current iteration times t;
step 3.5, starting to perform iterative updating, and simulating the population migration behavior of the gull individual carrying optimized variable information to realize global search of the effective range of the optimized variable;
step 3.6, the population individual simulates the self-adaptive spiral attack behavior to locally attack the optimal gull individual, so that local exploration on the optimal gull individual is realized;
3.7, after the gull individuals in the population are subjected to iterative updating, the optimization variables of each dimension of the gull individuals in the population are likely to cross the boundary; at this time, the optimization variables which are out of range should be processed: when the out-of-range optimization variable is larger than the upper bound Ub of the optimization variable, the out-of-range optimization variable is equal to the upper bound value; when the out-of-range optimization variable is smaller than the lower bound Lb of the optimization variable, the out-of-range optimization variable is equal to a lower bound value;
step 3.8, updating gull individual X with optimal population best Global optimal fitness value GbesF and global optimal gull individual position GbesX: calculating an objective function value fitness _ new (i) of each individual gull in the population after iterative updating, wherein i =1, \8230; then, sorting the population individuals in an ascending order according to the size of the objective function value fitness _ new (i), wherein fitness _ new (1) is the objective function value of the optimal gull individual in the updated population; the individual corresponding to the fitness _ new (1) is a gull individual X with the optimal current population best ；
Comparing the current global optimal fitness value Gbestf with the objective function value fitness _ new (1) of the optimal gull individual in the population after iterative update; when the fitness value Gbest of the current global optimum is better than Gbest (1), the fitness value Gbest of the current global optimum is equal to the fitness value Gbest of the current global optimum, and the individual position Gbest of the current global optimum gull is Gbest XSeagull individual X with optimal population at present best The location of the device; when the fixness _ new (1) is not superior to the current global optimal fitness value GestF, the global optimal fitness value GestF and the global optimal gull individual position GestX are kept unchanged;
step 3.9, checking whether the current iteration time T is less than the maximum iteration time T; if the current iteration time t is less than the maximum iteration time, returning to the step 3.5 to continue the iteration updating; and if the current iteration time t is equal to the maximum iteration time, outputting the current global optimal fitness value Gbesf as the electromagnetic manufacturing cost of the optimized transformer, and outputting the current global optimal gull individual position GbesX as the optimized variable combination of the optimized transformer.
Compared with the prior art, the invention has the beneficial effects that:
(1) The improved gull optimization algorithm is adopted to optimize the three-dimensional wound core transformer, the global search and local convergence capability of the algorithm are effectively improved, the optimization design efficiency and the design precision of the three-dimensional wound core transformer can be improved, the design parameters of the three-dimensional wound core transformer are effectively optimized, the manufacturing cost of the three-dimensional wound core transformer is reduced, and the economical efficiency of the three-dimensional wound core transformer is improved.
(2) The Bernoulli chaotic mapping is introduced in the population initialization stage, and the adoption of the Bernoulli chaotic mapping not only keeps the randomness of the initial population, but also enables the population to be more uniformly distributed in a solution space, and improves the convergence speed of the algorithm.
(3) According to the invention, the random walk model is introduced in the gull migration stage, and under the condition of not influencing the time complexity of the algorithm, the gull individual probabilistic selection of the migration model and the random walk model effectively avoids the individual population aggregation of the gull, and the global search capability of the gull optimization algorithm is improved.
(4) The invention introduces the self-adaptive thought in the spiral attack stage, so that the algorithm can self-adaptively adjust the attack radius, the larger exploration radius in the early stage of iteration and the smaller convergence radius in the later stage of iteration are met, and the local convergence capability of the seagull optimization algorithm is improved.
(5) According to the invention, the diversity of gull attack behaviors is increased by introducing a parabolic attack strategy in an attack stage, the diversity of the population at the later stage of the algorithm is improved, the algorithm is effectively prevented from falling into a local extreme value, and the optimizing capability of the gull optimization algorithm is improved.
(6) Compared with the common transformer optimization design methods such as a particle swarm optimization algorithm, an evolutionary algorithm, a genetic algorithm and the like, the transformer optimization design method is simpler in structure and easy to realize. And the improved gull optimization algorithm is more suitable for solving the optimization design of the transformer, and the effect is better in the solution precision and the solution efficiency, so that the optimization effect of the transformer is optimized.
Drawings
Fig. 1 is a flowchart of an optimal design method of a three-dimensional wound core transformer according to the present invention;
FIG. 2 is a flow chart of an improved gull optimization algorithm of the present invention;
FIG. 3 shows the function F in example 1 of the present invention 1 (x) Comparing the simulation results of various algorithms;
FIG. 4 shows the function F in example 1 of the present invention 2 (x) Comparing the simulation results of various algorithms;
FIG. 5 shows the function F in example 1 of the present invention 3 (x) Comparing the simulation results of various algorithms;
FIG. 6 shows a function F in example 1 of the present invention 4 (x) Comparing the simulation results of various algorithms;
fig. 7 is a comparison graph of optimization results of various algorithms for optimization design of a transformer in embodiment 2 of the present invention.
Detailed Description
Specific examples of the present invention are given below. The specific examples are provided only for further elaboration of the invention and do not limit the scope of the claims.
The invention provides an optimized design method (method for short) of a three-dimensional wound core transformer based on an improved gull optimization algorithm, which is characterized by comprising the following steps of:
minf(X)＝G Fe ×C Fe +G Cu ×C Cu (1)
in the formula (1), the optimization target f (X) is the electromagnetic manufacturing cost of the three-dimensional wound core transformer; x is an optimization variable; g Fe The weight of the three-dimensional wound core transformer core; c Fe Is the unit price of the silicon steel sheet; g Cu Is the winding weight; c Cu Is copper unit price;
preferably, in the step 1, the mathematical model of the single-target optimization design is shown as a formula (2);
in the formula (2), f (X) is an optimization target; x is an optimization variable, X = [ X ] 1 ,…,x D ]D is the number of the optimized variables; g i (X) is a constraint condition, and q is the number of constraint conditions.
Preferably, in step 1, the optimized variable X with the minimum electromagnetic manufacturing cost for the three-dimensional wound core transformer is obtained according to the selection principle of the optimized variable X (that is, the optimized variables are independent from each other, the optimized variables should have direct influence on the values of the objective function and the constraint condition, and the number of the optimized variables should be reduced as much as possible), where the optimized variable X includes the number of low-voltage winding layers C, the diameter of the iron core R, and the number of low-voltage winding turns N 2 Specification S of low-voltage winding wire 2 And specification S of high-voltage winding wire 1 。
Step 2, obtaining constraint conditions required by the transformer according to basic electrical parameters of the three-dimensional wound core transformer; and then, processing the constraint condition by adopting a penalty function to obtain an optimized objective function with a penalty function term, namely an optimized design mathematical model of the three-dimensional wound core transformer, which is shown in the formula (3):
in the formula (3), P (X) is punishmentA penalty function; q is the number of constraint conditions; a is i For the penalty factor, the larger a is, the greater the penalty degree of the constraint condition is; g i (X) is a constraint condition, and g is a constraint condition when the constraint condition is satisfied i (X) =0; p is a positive integer;
preferably, in step 2, the basic electrical parameters include rated capacity, voltage class and coupling group.
Preferably, in step 2, the constraint conditions include performance criteria, process level constraints and material performance constraints;
the performance criteria include no-load loss P 0 No less than no-load loss standard value P 0N Load loss P k Less than or equal to the standard value P of load loss kN No-load current I 0 No-load current standard value I 0N Impedance voltage u kN ％∈[(1-k)u kN ％，(1+k)u kN ％]；
The process level constraint comprises that the width-thickness ratio of the flat wire BBA belongs to [ BBA ∈ ] min ,BBA max ]The number of the wire stacks Die is less than or equal to Die max The number of parallel wires is less than or equal to Bing max The sectional area S of the lead is formed as [ S ] min ,S max ]The diameter R of the iron core is a multiple of 5;
the material property constraints include oil temperature increase tau of the high-voltage winding u The allowable temperature rise tau of oil by high-voltage winding is less than or equal to uN Oil temperature rise tau of low-voltage winding l The allowable temperature rise tau of oil by low-voltage winding is less than or equal to lN Magnetic flux density B of iron core is formed as [ B ] min ,B max ]And the current density J of the lead is E [ J ] min ,J max ]。
Step 3, solving the optimized design mathematical model of the three-dimensional wound core transformer obtained in the step 2 by adopting an improved gull optimization algorithm (as shown in fig. 2), wherein the specific steps are as follows:
step 3.1, initializing parameters of a gull optimization algorithm;
preferably, in step 3.1, parameters of the gull optimization algorithm include a population size N (representing the number of groups of optimized variable combinations of the population in iteration), a population dimension D (representing the number of variables in a group of optimized variable combinations), a maximum iteration number T, an upper bound Ub of the optimized variables (a vector formed by maximum values of the optimized variables), a lower bound Lb of the optimized variables (a vector formed by minimum values of the optimized variables), a migration probability Pm, and a spiral attack probability Ps.
Step 3.2, initializing the position of the individual gull by using Bernoulli chaotic mapping, and improving the ergodicity of the initial population:
preferably, step 3.2 is in particular:
(3.2.1) generating a chaos sequence H = { H } through Bernoulli chaos mapping i I =1, \8230n }, where H i ＝{H i,d D =1, \ 8230a D }, D denotes dimension, H i The Bernoulli chaotic mapping formula is obtained according to the formula (4):
in the formula (4), lambda is a control parameter;
(3.2.2) mapping the chaotic sequence H into an effective range of an optimized variable to obtain an initial population X = { X = i I =1, \ 8230; N }; wherein, each seagull individual X in the population i ＝{X i,d D =1, \ 8230d }, wherein X i,d The following is obtained from equation (5):
X i,d ＝Lb d +H i,d ×(Ub d -Lb d ) (5)
in formula (5), X i,d The initialized value of the d-dimension optimization variable of the ith seagull individual in the initial population; ub d Optimizing the upper bound of the value range of the variable for the d-th dimension; lb d And optimizing the lower bound of the value range of the variable for the d-th dimension.
Step 3.3, initializing gull individual X with optimal population best (representing the variable combination in the population that minimizes the objective function value), global optimum fitness value GbestF (representing the minimum objective function value up to the t-th iteration), and global optimum gull individual position GbestX (representing the variable combination that minimizes the objective function value up to the t-th iteration):
preferably, step 3.3 is in particular: seagull individual X of initial population X i Substitution intoA transformer electromagnetic design process, and calculating a target function value fitness (i) of each individual gull in an initial population, wherein i =1, \8230, N; and then, sequencing the population individuals in an ascending order according to the size of the objective function value fitness (i), wherein fitess (1) is the objective function value of the optimal gull individual in the initial population, and the individual corresponding to fitness (1) is the optimal gull individual X in the initial population best The current global optimal fitness value Gbest F = fixness (1), and the current global optimal individual position Gbest X of the gull is the initial population optimal individual position of the gull X best The location of the same.
Step 3.4, initializing the current iteration times t;
step 3.5, starting to perform iterative updating, and simulating the population migration behavior of the gull individual carrying optimized variable information to realize global search of the effective range of the optimized variable;
preferably, step 3.5 is in particular:
(3.5.1) generating a random number M r ，M r Is of [0,1]A random number in between;
(3.5.2) when M is r When the migration probability Pm is less than or equal to 0.5 and less than or equal to 0.9, preferably Pm =0.7, the population individual performs migration behavior, and the migration behavior meets the following conditions:
first, collision avoidance: in order to avoid the repetition of the position of the individual gull in the migration process, an additional variable A is adopted to generate different positions, as shown in formula (6):
in the formula (6), C (t) is a new position after collision avoidance; a is an additional variable; x (t) is the current position of the gull individual; t is the current iteration number; fc is a fixed parameter of iterative update, and the value is 2; t is the maximum iteration number;
secondly, selecting the optimal migration direction: on the premise of ensuring no position repetition, the gull will approach to the direction of the current optimal gull individual, as shown in formula (7):
in the formula (7), M (t) is the moving direction of the gull individual; b is a Convergence factors for coordinating global and local search; x best The current best seagull individual position; r is d Is [0,1]]A random number in between;
finally, close to the optimal position: after the migration direction is determined, the individual gull takes the current non-repeating position as a starting point to migrate to the migration direction, as shown in formula (8):
D(t)＝|C(t)+M(t)| (8)
in the formula (8), D (t) is a new position of the individual gull after migration;
the gull individuals in the population migrate towards the optimal gull individual direction, so that the population diversity is reduced, the effective search range of the optimized variable of the transformer cannot be fully searched, and a random walk model is introduced for the purpose; when Mr is larger than the migration probability Pm, random walk behavior is carried out, and the new position D (t) of the individual gull after migration is shown as the formula (9):
D(t)＝X(t)+randn(1,D) (9)
in formula (9), randn generates random numbers between [0,1 ].
Step 3.6, the population individual simulates the self-adaptive spiral attack behavior to locally attack the optimal gull individual, so that local exploration on the optimal gull individual is realized;
preferably, step 3.6 is in particular:
(3.6.1) generating a random number Sr, wherein Sr is a random number belonging to the interval between [0,1 ];
(3.6.2) when Sr is less than or equal to the spiral attack probability Ps (in the present embodiment, 0.3 is less than or equal to Ps is less than or equal to 0.7, preferably Ps = 0.5), the individual gulls performs a spiral attack behavior:
in the formula (10), r is the spiral attack radius of the spiral attack behavior; u and v are coefficients for controlling the radius of the spiral attack, and both take the value of 1; theta is a random angle in the range of [0,2 pi ]; the algorithm can adaptively adjust the size of the spiral attack radius r by improving the coefficient v, and the method meets the requirements of a larger exploration range at the early stage of iteration and a smaller convergence range at the later stage of iteration; improved v is as shown in formula (11):
v＝1-2/(1+e -(t-(T/2))×10/t ) (11)
the optimization design of the transformer is a complex optimization design problem with multiple extreme values, the attack path of the spiral attack in the original gull optimization algorithm is too single, the algorithm is easy to fall into a local extreme value at the later stage, and a parabolic attack strategy is introduced in order to improve the capability of the gull optimization algorithm for jumping out of the local extreme value; when Sr is larger than spiral attack probability Ps, the individual gull carries out a parabolic attack strategy, as shown in formula (12):
in the formula (12), X (t + 1) is a new position of the gull individual after the gull individual is subjected to parabolic attack; x best Is the current optimal seagull individual; rand is [0,1]]A random number in between; x (t) is the current position of the gull individual; TF is a random number with a value of-1 or 1; p is a radical of n Is a parabolic control coefficient; t is the current iteration number; and T is the maximum iteration number.
Step 3.7, after the individual gulls in the population are subjected to iterative updating, the optimization variables of each dimension of the individual gulls in the population are likely to be out of range (namely, the effective search range of the optimization variables is exceeded); at this time, the optimization variables which are out of range should be processed: when the out-of-range optimization variable is larger than the upper bound Ub of the optimization variable, the out-of-range optimization variable is equal to the upper bound value; when the out-of-range optimization variable is smaller than the lower bound Lb of the optimization variable, the out-of-range optimization variable is equal to the lower bound value;
step 3.8, updating seagull individual X with optimal population best Global optimal fitness value GbesF and global optimal gull individual position GbesX: calculating an objective function value fitness _ new (i) of each individual gull in the population after iterative updating, wherein i =1, \8230; then according to the size of the objective function value fitness _ new (i)Sequencing the population individuals in an ascending order, wherein a fixness _ new (1) is an objective function value of the optimal gull individual in the updated population; the individual corresponding to the fitness _ new (1) is a gull individual X with the optimal current population best ；
Comparing the current global optimal fitness value Gbestf with the objective function value fitness _ new (1) of the optimal gull individual in the population after iterative update; when the fitness _ new (1) is better than the current global optimal fitness value Gtest F, the current global optimal fitness value Gtest F is equal to the fitness _ new (1), and the current global optimal gull individual position Gtest X is the current population optimal gull individual X best The location of the location; when the fixness _ new (1) is not superior to the current global optimal fitness value GestF, the global optimal fitness value GestF and the global optimal gull individual position GestX are kept unchanged;
step 3.9, checking whether the current iteration time T is less than the maximum iteration time T; if the current iteration time t is less than the maximum iteration time, returning to the step 3.5 to continue the iteration updating; and if the current iteration time t is equal to the maximum iteration time, outputting the current global optimal fitness value Gbesf as the electromagnetic manufacturing cost of the optimized transformer, and outputting the current global optimal gull individual position GbesX as the optimized variable combination of the optimized transformer.
Example 1
In this embodiment, 4 standard test functions are selected from the 23 standard test functions to test the optimization performance (i.e., global search capability and local search capability) of the improved gull optimization algorithm (ISOA), and a Whale Optimization Algorithm (WOA), a harris eagle optimization algorithm (HHO), a standard gull optimization algorithm (SOA) and an ISOA are selected to perform a comparison test. The standard test function information is shown in table 1 and the corresponding test results are shown in table 2.
TABLE 1
TABLE 2
| Function(s) | SOA | WOA | HHO | ISOA |
| F 1 | 5.088E-01 | 4.057E-43 | 4.177E-66 | 0 |
| F 2 | 3.325E-04 | 3.745E-32 | 1.636E-35 | 0 |
| F 3 | 5.187E+00 | 0 | 0 | 0 |
| F 4 | 7.097E-01 | 0 | 0 | 0 |
In the selected standard test function, F 1 (x)、F 2 (x) For a unimodal test function, the global search capability of the algorithm is tested, and as can be seen from fig. 3 and 4, the global search capability of the ISOA is the first of the four algorithms. F 3 (x)、F 4 (x) For the multi-peak test function, the local convergence capability of the test algorithm, as can be seen from table 2, the optimal values of ISOA, HHO, and WOA are found, but as can be seen from fig. 5 and 6, the convergence speed of ISOA is faster. In conclusion, the comprehensive optimization performance of the ISOA has great advantages.
Example 2
In this embodiment, an S11-MRL-200/10 three-dimensional wound core transformer is taken as an example to perform the example optimization design, and the basic technical parameters of the three-dimensional wound core transformer are shown in table 3.
TABLE 3
| Product type | S11-MRL-200/10 | Load loss | ≤ |
| Voltage ratio | |||
| 10±5％/0.4kV | No load loss | ≤340W | |
| Connecting group | Dyn11 | Short circuit impedance | 4％ |
| Rated frequency | 50Hz | Temperature rise of winding to oil | ≤23℃ |
And solving the three-dimensional wound core transformer optimization design mathematical model by adopting a cyclic traversal method, WOA, HHO, SOA and ISOA. The cyclic traversal method selects an optimal design scheme by traversing all combinations and comparing the values of the objective function, and the scheme obtained by the cyclic traversal method can be used as an optimal solution, but the optimization time is too long due to the traversal of all combinations, and the efficiency is low. And meanwhile, WOA, HHO and SOA are used as comparison algorithms to analyze the optimization performance of the ISOA in the optimization design of the transformer. The WOA, HHO, SOA and ISOA optimization fitness curve is shown in fig. 7, and the convergence curve in fig. 7 shows that the ISOA has the highest convergence accuracy and the fastest convergence speed, which indicates that the ISOA is more adept in solving the transformer optimization problem. The transformer design before and after optimization is shown in table 4.
TABLE 4
As can be seen from table 4, the solution after the ISOA optimization is consistent with the optimization precision of the loop traversal method, and the optimization time is improved by 270 times, and compared with the manual design solution, the optimized design solution reduces the electromagnetic manufacturing cost by 3.09% on the premise of meeting the performance constraint standard, improves the economy of the three-dimensional wound core transformer, and proves the effectiveness of the ISOA in the transformer optimization.
Nothing in this specification is said to apply to the prior art.
Claims (10)
1. A three-dimensional wound core transformer optimization design method based on an improved gull optimization algorithm is characterized by comprising the following steps:
step 1, establishing an optimization objective function minf (X) taking the minimum electromagnetic manufacturing cost of the three-dimensional wound core transformer as an optimization objective according to a single-objective optimization design mathematical model:
minf(X)＝G Fe ×C Fe +G Cu ×C Cu (1)
in the formula (1), the optimization target f (X) is the electromagnetic manufacturing cost of the three-dimensional wound core transformer; x is an optimization variable; g Fe The weight of the three-dimensional wound core transformer core; c Fe Is the unit price of the silicon steel sheet; g Cu Is the winding weight; c Cu Is copper unit price;
step 2, obtaining constraint conditions required to be met by the transformer according to basic electrical parameters of the three-dimensional wound core transformer; and then, processing the constraint condition by adopting a penalty function to obtain an optimized objective function with a penalty function term, namely an optimized design mathematical model of the three-dimensional wound core transformer, as shown in the formula (3):
in formula (3), P (X) is a penalty function; q is the number of constraint conditions; a is i For the penalty factor, the larger a is, the greater the penalty degree of the constraint condition is; g i (X) is a constraint condition, and g is a constraint condition when the constraint condition is satisfied i (X) =0; p is a positive integer;
step 3, solving the optimized design mathematical model of the three-dimensional wound core transformer obtained in the step 2 by adopting an improved gull optimization algorithm, wherein the method comprises the following specific steps:
step 3.1, initializing parameters of a gull optimization algorithm;
step 3.2, initializing the position of the individual gull by using Bernoulli chaotic mapping, and improving the ergodicity of the initial population;
step 3.3, initializing seagull individual X with optimal population best The global optimal fitness value GbesF and the global optimal seagull individual position GbesX;
step 3.4, initializing the current iteration times t;
step 3.5, starting to perform iterative updating, and realizing global search of the effective range of the optimized variable by simulating the migration behavior of the individual seagull group carrying the optimized variable information;
step 3.6, the population individual simulates the self-adaptive spiral attack behavior to locally attack the optimal gull individual, so that local exploration on the optimal gull individual is realized;
3.7, after the gull individuals in the population are subjected to iterative updating, the optimization variables of each dimension of the gull individuals in the population are likely to cross the boundary; at this time, the optimization variables which are out of range should be processed: when the out-of-range optimization variable is larger than the upper bound Ub of the optimization variable, the out-of-range optimization variable is equal to the upper bound value; when the out-of-range optimization variable is smaller than the lower bound Lb of the optimization variable, the out-of-range optimization variable is equal to the lower bound value;
step 3.8, updating gull individual X with optimal population best Global optimal fitness value GbesF and global optimal gull individual position GbesX: calculating a target function value fitness _ new (i) of each individual gull in the population after iterative update, wherein i =1, \8230N; then, sorting the population individuals in an ascending order according to the size of an objective function value fitness _ new (i), wherein fitness _ new (1) is the objective function value of the optimal gull individual in the updated population; the individual corresponding to the fitness _ new (1) is a gull individual X with the optimal current population best ；
Comparing the current global optimal fitness value Gbestf with the objective function value fitness _ new (1) of the optimal gull individual in the population after iterative update; when the fitness _ new (1) is better than the current global optimal fitness value Gtest F, the current global optimal fitness value Gtest F is equal to the fitness _ new (1), and the current global optimal gull individual position Gtest X is the current population optimal gull individual X best The location of the location; when the fitness _ new (1) is not better than the current global optimum fitness value GWhen bestF is carried out, the global optimal fitness value Gtest F and the global optimal gull individual position Gtest X are kept unchanged;
step 3.9, checking whether the current iteration time T is less than the maximum iteration time T; if the current iteration time t is less than the maximum iteration time, returning to the step 3.5 to continue the iteration updating; and if the current iteration time t is equal to the maximum iteration time, outputting the current global optimal fitness value Gbesf as the electromagnetic manufacturing cost of the optimized transformer, and outputting the current global optimal gull individual position GbesX as the optimized variable combination of the optimized transformer.
2. The method for optimally designing the three-dimensional wound core transformer based on the improved gull optimization algorithm of claim 1, wherein in the step 1, a single-target optimal design mathematical model is shown as a formula (2);
in the formula (2), f (X) is an optimization target; x is an optimization variable, X = [ X ] 1 ,…,x D ]D is the number of the optimized variables; g i (X) is a constraint condition, and q is the number of constraint conditions.
3. The method for optimally designing the three-dimensional wound core transformer based on the improved gull optimization algorithm of claim 1, wherein in the step 1, the optimized variables X including the number of low-voltage winding layers C, the diameter of the core R and the number of low-voltage winding turns N are obtained according to the selection principle of the optimized variables X 2 Specification S of low-voltage winding wire 2 And specification S of high-voltage winding wire 1 。
4. The method of claim 1, wherein in step 2, the basic electrical parameters include rated capacity, voltage class and connection group.
5. The method for optimally designing the three-dimensional wound core transformer based on the improved gull optimization algorithm of claim 1, wherein in the step 2, the constraint conditions comprise a performance standard, a process level constraint and a material performance constraint;
the performance criteria include no-load loss P 0 No less than no-load loss standard value P 0N Load loss P k Less than or equal to the standard value P of load loss kN No-load current I 0 No-load current standard value I 0N Impedance voltage u kN ％∈[(1-k)u kN ％，(1+k)u kN ％]；
The process level constraint comprises that the width-thickness ratio of the flat wire BBA is E [ BBA ∈ [) min ,BBA max ]The number of the wire stacks Die is less than or equal to Die max The number of parallel wires is less than or equal to Bing max The sectional area S of the lead is formed as [ S ] min ,S max ]The diameter R of the iron core is a multiple of 5;
the material property constraints include oil temperature increase tau of the high-voltage winding u The allowable temperature rise tau of oil by high-voltage winding is less than or equal to uN Oil temperature rise tau of low-voltage winding l The allowable temperature rise tau of oil by low-voltage winding is less than or equal to lN And magnetic flux density B of iron core is B min ,B max ]The current density J of the conductor is equal to [ J ∈ ] min ,J max ]。
6. The method for optimally designing the three-dimensional wound core transformer based on the improved gull optimization algorithm according to claim 1, wherein in step 3.1, parameters of the gull optimization algorithm include a population size N, a population dimension D, a maximum iteration number T, an upper bound Ub of an optimized variable, a lower bound Lb of the optimized variable, a migration probability Pm, and a spiral attack probability Ps.
7. The optimized design method of the three-dimensional wound core transformer based on the improved gull optimization algorithm according to claim 1, wherein the step 3.2 is specifically as follows:
(3.2.1) generating a chaos sequence H = { H } through Bernoulli chaos mapping i I =1, \8230n }, where H i ＝{H i,d D =1, \8230AD }, D represents dimension H i The Bernoulli chaotic mapping formula is obtained according to the formula (4):
in the formula (4), lambda is a control parameter;
(3.2.2) mapping the chaotic sequence H into an effective range of an optimized variable to obtain an initial population X = { X = i I =1, \ 8230; N }; wherein, each seagull individual X in the population i ＝{X i,d D =1, \ 8230d }, wherein X i,d The following is obtained from equation (5):
X i,d ＝Lb d +H i,d ×(Ub d -Lb d ) (5)
in the formula (5), X i,d The initialized value of the d-dimension optimization variable of the ith seagull individual in the initial population; ub d Optimizing the upper bound of the value range of the variable for the d-th dimension; lb d And optimizing the lower bound of the value range of the variable for the d-th dimension.
8. The optimized design method of the three-dimensional wound core transformer based on the improved gull optimization algorithm according to claim 1, wherein the step 3.3 is specifically as follows: seagull individual X of initial population X i Substituting into the electromagnetic design process of the transformer, and calculating the objective function value fitness (i) of each individual gull in the initial population, wherein i =1, \8230, N; and then, sequencing the population individuals in an ascending order according to the size of the objective function value fitness (i), wherein fitess (1) is the objective function value of the optimal gull individual in the initial population, and the individual corresponding to fitness (1) is the optimal gull individual X in the initial population best The current global optimal fitness value Gbestff = fixness (1), and the current global optimal individual position Gbestx is the initial population optimal individual position of seagull X best The location of the same.
9. The optimized design method of the three-dimensional wound core transformer based on the improved gull optimization algorithm of claim 1, wherein the step 3.5 is specifically:
(3.5.1) generating a random number M r ，M r Is of [0,1]A random number in between;
(3.5.2) when M is r When the migration probability Pm is less than or equal to, the population individual carries out migration behavior, and the migration behavior meets the following conditions:
first, collision avoidance: in order to avoid the repetition of the position of the individual gull during the migration process, an additional variable A is adopted to generate different positions, as shown in formula (6):
in the formula (6), C (t) is a new position after collision avoidance; a is an additional variable; x (t) is the current position of the individual gull; t is the current iteration number; fc is a fixed parameter of iterative update; t is the maximum iteration number;
secondly, selecting the optimal migration direction: on the premise of ensuring that no position repetition exists, the gull can be closed to the direction of the current optimal gull individual, as shown in formula (7):
in the formula (7), M (t) is the moving direction of the individual gull; b a Convergence factors for coordinating global and local search; x best The individual is the current optimal seagull; r is d Is [0,1]]A random number in between;
finally, close to the optimal position: after the optimal migration direction is determined, the individual gull takes the current unrepeated position as a starting point to migrate to the optimal migration direction, as shown in formula (8):
D(t)＝|C(t)+M(t)|| (8)
in the formula (8), D (t) is a new position of the individual gull after migration;
when Mr is larger than the migration probability Pm, random walk behavior is carried out, and the new position D (t) of the individual gull after migration is shown as the formula (9):
D(t)＝X(t)+randn(1,D) (9)
in formula (9), randn generates random numbers between [0,1 ].
10. The optimized design method of the three-dimensional wound core transformer based on the improved gull optimization algorithm according to claim 1, wherein the step 3.6 is specifically as follows:
(3.6.1) generating a random number Sr, wherein Sr is a random number belonging to the interval between [0,1 ];
(3.6.2) when Sr is less than or equal to the spiral attack probability Ps, the gull individual performs a spiral attack behavior:
in the formula (10), r is the spiral attack radius of the spiral attack behavior; u and v are coefficients for controlling the radius of the spiral attack, and both take the value of 1; theta is a random angle in the range of [0,2 pi ]; the algorithm can adaptively adjust the size of the radius r of the spiral attack by improving the coefficient v, and the larger exploration range in the early stage of iteration and the smaller convergence range in the later stage of iteration are met; improved v is as shown in formula (11):
v＝1-2/(1+e -(t-(T/2))×10/t ) (11)
when Sr is larger than spiral attack probability Ps, the individual gull carries out a parabolic attack strategy, as shown in formula (12):
in the formula (12), X (t + 1) is a new position of the gull individual after the gull individual is subjected to parabola attack; x best The individual is the current optimal seagull; rand is [0,1]]A random number in between; x (t) is the current position of the gull individual; TF is a random number with a value of-1 or 1; p is a radical of n Is a parabolic control coefficient; t is the current iteration number; and T is the maximum iteration number.
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