Design and multi-objective optimization method of low-voltage single-phase multi-winding transformer

Abstract

The invention provides a low-voltage single-phase multi-winding transformer design and multi-objective optimization method, and relates to the field of single-phase multi-winding transformer design, and the method comprises the steps: calculating the geometric dimension of an iron core according to a demand parameter set; setting an objective function and a constraint condition, and constructing an optimization model of the low-voltage single-phase multi-winding transformer according to the objective function, the constraint condition and the related parameter set; and solving the optimization model through an improved genetic algorithm to obtain an optimal design parameter set of the low-voltage single-phase multi-winding transformer. The optimization model of the low-voltage single-phase multi-winding transformer is solved through the improved genetic algorithm to obtain the optimal design parameter set, the loss and the cost of the transformer can be further reduced, the calculation process of the improved genetic algorithm is convenient, programming implementation is easy, other simulation software is not needed, and the method is suitable for large-scale popularization and application. The calculation process has little dependence on an empirical formula, and the calculation result is more accurate.

Description

Technical Field

[0001] The present invention relates to the field of single-phase multi-winding transformer design, and particularly to a design and multi-objective optimization method for a low-voltage single-phase multi-winding transformer. Background Art

[0002] In modern power systems, single-phase transformers are one of the commonly used electrical devices in the power system. It can change the voltage amplitude of alternating current through electromagnetic induction and can also protect the circuit through electrical isolation. Single-phase transformers are suitable for large-scale modern production due to their simple structure, which is conducive to improving product quality and efficiency. The primary and secondary side winding structures of low-voltage single-phase transformers are complex, and existing design methods cannot meet the transformer technical indicators in some special occasions. Traditional transformer design requires a large amount of manual calculation and testing, which is time-consuming, laborious and prone to errors. Summary of the Invention

[0003] In view of this, the purpose of the present invention is to provide a design and multi-objective optimization method for a low-voltage single-phase multi-winding transformer, which is used to solve the technical problems that existing design methods require a large amount of manual calculation and testing, are time-consuming, laborious and prone to errors.

[0004] The present invention provides a design and multi-objective optimization method for a low-voltage single-phase multi-winding transformer, including the steps of:

[0005] S1: Obtain the set of demand parameters of the low-voltage single-phase multi-winding transformer, and calculate the geometric dimensions of the iron core according to the set of demand parameters;

[0006] S2: Calculate the number of turns and wire diameter of the primary side winding, and the number of turns and wire diameter of the secondary side winding according to the set of demand parameters and the geometric dimensions of the iron core; calculate the total winding thickness through the number of turns and wire diameter. If the total winding thickness is greater than the iron core window coefficient threshold, reset the set of demand parameters and return to step S1 to increase the geometric dimensions of the iron core, otherwise enter step S3;

[0007] S3: Calculate the total copper loss and iron core loss of the winding according to the set of demand parameters, and calculate the temperature rise of the low-voltage single-phase multi-winding transformer according to the total copper loss and iron core loss of the winding; if the temperature rise is greater than the preset threshold, reset the set of demand parameters and return to step S1 to increase the geometric dimensions of the iron core, otherwise enter step S4;

[0008] S4: Calculate the total winding weight and total iron core weight according to the set of demand parameters, and use the geometric dimensions of the iron core, the number of turns and wire diameter of the primary side winding, the number of turns and wire diameter of the secondary side winding, the total copper loss of the winding, the iron core loss, the total winding weight and the total iron core weight as the relevant parameter set;

[0009] S5: Set the objective function and constraint conditions, and construct an optimization model for the low-voltage single-phase multi-winding transformer according to the objective function, constraint conditions, and relevant parameter sets.

[0010] S6: Solve the optimization model through an improved genetic algorithm to obtain the optimal design parameter set of the low-voltage single-phase multi-winding transformer.

[0011] Preferably:

[0012] The demand parameter set includes: the rated voltage U of the primary winding 1n , the rated voltages U of each independent winding in the secondary winding 2n , U 3n ,..., U jn , the rated currents I of each independent winding in the secondary winding 2n , I 3n ,..., I jn .

[0013] Preferably, in step S1:

[0014] The geometric dimensions of the iron core include: the width a of the center column of the iron core and the effective cross-sectional area A of the center column of the iron core c ;

[0015] The calculation formula for the width a of the center column of the iron core is:

[0016]

[0017] where, the unit of a is mm, K 0 is an empirical coefficient, b is the thickness of the center column of the iron core, and S n is the average value of the capacities of the primary winding and the secondary winding;

[0018] The calculation formula for the effective cross-sectional area A of the center column of the iron core c is:

[0019] A c = K c ab / 100

[0020] where, the unit of A c is cm 2 , and K c is the lamination factor of the iron core.

[0021] Preferably, in step S2:

[0022] The number of turns N per volt of voltage 0 is

[0023]

[0024] In the formula, N0 The unit of which is turns, f is the operating frequency of the transformer, B m is the maximum value of the magnetic flux density of the core center leg, A c is the effective cross-sectional area of the core center leg;

[0025] If there is no tap in the primary winding, the number of turns of the primary winding is:

[0026] N 1 = N 0 U 1n ;

[0027] If there is a tap in the primary winding, the number of turns of the primary winding is:

[0028] N 11 = N 0 U 11n , N 12 = N 0 U 12n ,..., N 1i = N 0 U 1in ;

[0029] where, i is the number of the independent winding, N 1i is the number of turns of the i-th independent winding in the primary winding, U 1in is the rated voltage of the i-th independent winding in the primary winding;

[0030] The wire diameter of the primary winding is calculated through the rated power and current of the primary winding;

[0031] The number of turns of the secondary winding is:

[0032] N 2 = (1.05 ~ 1.10) × N 0 U 2n , N 3 = (1.05 ~ 1.10) × N 0 U 3n ,..., N j = (1.05 ~ 1.10) × N 0 U jn ;

[0033] where, j is the total number of independent windings, N j is the number of turns of the j-th independent winding in the secondary winding, U jn is the rated voltage of the j-th independent winding in the secondary winding;

[0034] The wire diameter of the secondary winding is calculated through the rated power and current of the secondary winding;

[0035] Multiply the number of winding layers of each winding in the primary winding by the corresponding wire diameter to obtain the thickness of the primary winding; multiply the number of winding layers of each winding in the secondary winding by the corresponding wire diameter to obtain the thickness of the secondary winding; add the thickness of the primary winding and the thickness of the secondary winding to obtain the total thickness of the winding.

[0036] Preferably, in step S3:

[0037] The total copper loss P Cu The calculation formula is:

[0038] P Cu = P 1 + P 2 + P 3 + L + P j

[0039] Among them, the unit of P Cu is W, P 1 is the power of the primary winding, P 2 to P j are the powers of each independent winding in the secondary winding;

[0040] The core loss P Fe The calculation formula is:

[0041] P Fe = P kg V Fe ρ Fe × 10 -3

[0042] Among them, the unit of P Fe is W, V Fe is the volume of the core material, ρ Fe is the density of the core material, P kg is the core loss per kilogram of mass;

[0043] The calculation formula for the temperature rise ΔT is:

[0044]

[0045] Among them, the unit of ΔT is °C, A t is the surface area of the low-voltage single-phase multi-winding transformer.

[0046] Preferably, in step S4:

[0047] The total weight G of the winding Cu The calculation formula is:

[0048]

[0049] Among them, G CuThe unit of is kg, i is the number of the independent winding, j is the total number of the independent windings, N i is the number of turns of the i-th independent winding, A i is the cross-sectional area of the i-th independent winding, ρ Cu is the density of the winding material;

[0050] The total weight G of the iron core Fe The calculation formula is:

[0051] G Fe = V Fe ρ Fe × 10 -3

[0052] Among them, G Fe The unit of is kg, V Fe is the volume of the iron core material, ρ Fe is the density of the iron core material.

[0053] Preferably, in step S5:

[0054] The expression of the optimization model of the low-voltage single-phase multi-winding transformer is:

[0055]

[0056] Among them, f(x) is the objective function, A is the unit electricity price, B is the operation time of the transformer, C is the unit price of the iron core material, D is the unit price of the winding material, g t (x) is the constraint condition, m is the total number of constraint conditions, P Fe is the iron core loss, P Cu is the total copper loss of the winding, G Fe is the total weight of the iron core, G Cu is the total weight of the winding;

[0057] The set of optimization variables of the optimization model includes: the geometric dimensions of the iron core, the number of turns of the primary winding, the wire diameter of the primary winding, the number of turns of the secondary winding, and the wire diameter of the secondary winding.

[0058] Preferably, step S6 is specifically:

[0059] S61: Set the population size, the maximum number of iterations, the crossover probability, and the mutation probability, and define the range of each optimization variable;

[0060] S62: Generate an initial population through the initialization function, and the initial population includes multiple individuals;

[0061] S63: Each individual includes multiple optimization variables, and the objective function value of each individual is obtained by calculating through the objective function;

[0062] S64: Perform non-dominated sorting on each objective function value to obtain the Pareto front;

[0063] S65: If the number of iterations reaches the maximum number of iterations, go to step S67; otherwise, go to step S66;

[0064] S66: Pair individuals pairwise to form multiple parent individuals. Pair the parent individuals pairwise to generate offspring individuals through the crossover probability, and mutate each offspring individual through the mutation probability to obtain a new population, and return to step S63;

[0065] S67: Output the final Pareto front, obtain the optimal set of optimization variables through the final Pareto front, and use the optimal set of optimization variables as the optimal design parameter set of the low-voltage single-phase multi-winding transformer.

[0066] A storage medium stores instructions and data for implementing the design and multi-objective optimization method of the low-voltage single-phase multi-winding transformer.

[0067] A design and multi-objective optimization device for a low-voltage single-phase multi-winding transformer includes: a processor and a storage medium; the processor loads and executes the instructions and data in the storage medium for implementing the design and multi-objective optimization method of the low-voltage single-phase multi-winding transformer.

[0068] The present invention has the following beneficial effects:

[0069] During the process of designing the low-voltage single-phase multi-winding transformer, important parameters such as the number of turns of the primary and secondary windings of the low-voltage single-phase transformer, transformer losses, and temperature rise are calculated. Especially for multi-winding transformers, the influence of complex structures such as independent windings and in-tapped windings on the transformer performance is considered, which can effectively improve the design efficiency and operating performance of the single-phase transformer; on the basis of the basic genetic algorithm, non-dominated sorting is added to obtain an improved genetic algorithm. The optimal design parameter set is obtained by solving the optimization model of the low-voltage single-phase multi-winding transformer through the improved genetic algorithm, which can further reduce the losses and costs of the transformer. Moreover, the calculation process of the improved genetic algorithm is convenient and easy to program and implement, without the need to rely on other simulation software, and the calculation process has less dependence on empirical formulas, and the calculation results are more accurate. Description of the Drawings

[0070] Figure 1 It is a flowchart of the method of the embodiment of the present invention;

[0071] Figure 2 It is a schematic diagram of the structure and dimensions of the iron core of the embodiment of the present invention;

[0072] Figure 3 It is a result diagram of the improved genetic algorithm of the embodiment of the present invention;

[0073] Figure 4 Structural diagram of the device according to an embodiment of the present invention;

[0074] The implementation, functional features and advantages of the present invention will be further described with reference to the embodiments and the accompanying drawings. Specific embodiments

[0075] It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0076] Referring to Figure 1 , the present invention provides a design and multi-objective optimization method for a low-voltage single-phase multi-winding transformer, including the steps of:

[0077] S1: Obtain the set of required parameters of the low-voltage single-phase multi-winding transformer, and calculate the geometric dimensions of the iron core according to the set of required parameters;

[0078] As an embodiment, the specific values of each required parameter are given by the product requirements;

[0079] The set of required parameters includes: the rated voltage U of the primary winding 1n , the rated voltages U of each independent winding in the secondary winding 2n , U 3n ,..., U jn , and the rated currents I of each independent winding in the secondary winding 2n , I 3n ,..., I jn .

[0080] Specifically, the output apparent power S of the single-phase transformer 2n is the algebraic sum of the output apparent powers of each independent winding in the secondary side

[0081] S 2n =U 2n I 2n +U 3n I 3n +L+U jn I jn

[0082] In the formula, the unit of S 2n is VA, and j-1 is the number of independent windings in the secondary side.

[0083] The input apparent power S of the single-phase transformer 1n is

[0084] S 1n =S 2n / η n

[0085] In the formula, the unit of S 1n is VA, and ηn is the rated efficiency of a single-phase transformer.

[0086] The rated capacity S of a single-phase transformer n is the average value of the capacities of the primary and secondary windings, i.e., S n =(S 1n +S 2n ) / 2.

[0087] In an embodiment of the present invention, a single-phase transformer with a rated capacity of 1625 VA is selected for illustration. The rated input and output parameters of this transformer are shown in Table 1. The taps on the primary side winding are derated according to the voltage level, and the secondary side winding is composed of 4 independent tapless windings.

[0088] The specific steps for the design and optimization of this single-phase transformer are as follows:

[0089] In the embodiment, the output apparent power S of the single-phase transformer 2n is the algebraic sum of the output apparent powers of the secondary side windings

[0090] S 2n =U 2n I 2n +U 3n I 3n +U 4n I 4n +U 5n I 5n =1625 (VA)

[0091] In the embodiment, the input apparent power S of the single-phase transformer 1n is

[0092]

[0093] Table 1 Rated input and output parameters of the transformer

[0094]

[0095]

[0096] Rated capacity S n is the average value of the capacities of the primary and secondary windings, i.e.,

[0097] As an embodiment:

[0098] In step S1:

[0099] The geometric dimensions of the iron core include: the width a of the center column of the iron core and the effective cross-sectional area A of the center column of the iron core c ;

[0100] Low-voltage single-phase transformers generally use EI-shaped silicon steel sheets as the iron core. The calculation formula for the width a of the center column of the iron core is as follows:

[0101]

[0102] where the unit of a is mm, and K 0 is an empirical coefficient (the value range is 58 - 64), b is the thickness of the center column of the iron core, and S n is the average value of the capacities of the primary winding and the secondary winding;

[0103] The effective cross-sectional area A c of the center column of the iron core is calculated as follows:

[0104] A c = K c ab / 100

[0105] where the unit of A c is cm 2 , and K c is the lamination factor of the iron core.

[0106] Specifically, K c is the lamination factor of the iron core that takes into account the reduction of the iron core area caused by the insulation space between the iron core laminations (the value range is 0.90 - 0.97). According to the width a of the center column of the iron core and the effective cross-sectional area A c of the center column of the iron core, select the iron core model, and then obtain other geometric dimensions of the iron core, such as the window height, thickness, etc.

[0107] In the embodiment of the present invention, after multiple iterative operations, the single-phase transformer selects an EI-171 type iron core, and its center column width a and thickness b are respectively

[0108] a = 57 (mm), b = 85.5 (mm)

[0109] According to the width a of the center column of the iron core and the effective cross-sectional area A c , select the iron core model EI-171, and the structure and dimensions of the iron core are as Figure 2 shown.

[0110] S2: Calculate and obtain the number of turns and wire diameter of the primary winding, and the number of turns and wire diameter of the secondary winding according to the demand parameter set and the geometric dimensions of the iron core; calculate the total thickness of the winding through the number of turns and wire diameter. If the total thickness of the winding is greater than the iron core window coefficient threshold, reset the demand parameter set and return to step S1 to increase the geometric dimensions of the iron core, otherwise enter step S3;

[0111] As an embodiment

[0112] In step S2:

[0113] The number of turns of winding N corresponding to each volt of voltage 0 is

[0114]

[0115] In the formula, N 0 has the unit of turn, f is the operating frequency of the transformer, B m is the maximum value of the magnetic flux density of the center leg of the iron core, A c is the effective cross-sectional area of the center leg of the iron core;

[0116] If there is no tap in the primary winding, the number of turns of the primary winding is:

[0117] N 1 = N 0 U 1n ;

[0118] If there is a tap in the primary winding, and the input voltages from large to small are U 11n > U 12n >... > U 1in , and the number of taps is (i - 1), then the wire diameters of each tap winding remain unchanged and the number of turns is distributed in direct proportion to the voltage. Then the number of turns of the primary winding is:

[0119] N 11 = N 0 U 11n , N 12 = N 0 U 12n ,..., N 1i = N 0 U 1in ;

[0120] Among them, i is the number of the independent winding, N 1i is the number of turns of the i-th independent winding in the primary winding, and U 1in is the rated voltage of the i-th independent winding in the primary winding;

[0121] The wire diameter of the primary winding is calculated through the rated power and current of the primary winding;

[0122] The number of turns of the secondary winding is:

[0123] N 2 = (1.05 - 1.10) × N 0 U 2n , N 3 = (1.05 - 1.10) × N 0 U 3n ,..., N j = (1.05 - 1.10) × N 0 Ujn ;

[0124] Among them, j is the total number of independent windings, N j is the number of turns of the j-th independent winding in the secondary winding, and U jn is the rated voltage of the j-th independent winding in the secondary winding;

[0125] Specifically, for the secondary winding:

[0126] 1) If there is only one winding with a tap inside, the number of taps is (i - 1), and the wire diameter remains unchanged within the same winding;

[0127] 2) If there are (j - 1) groups of independent windings and each independent winding has no tap, the output power of each winding is U 2n I 2n , U 3n I 3n ,..., U jn I jn , and the wire diameters of each independent winding are distributed in direct proportion to the current, and the number of turns are distributed in direct proportion to the voltage;

[0128] 3) If there are (j - 1) groups of independent windings and each independent winding has no tap, the output power of each winding is U 2n I 2n , U 3n I 3n ,..., U jn I jn , and the wire diameters of each winding are distributed in direct proportion to the current, and the number of turns are distributed in direct proportion to the voltage. For the winding with a tap, the tap position is distributed in direct proportion to the voltage;

[0129] The wire diameter of the secondary winding is calculated through the rated power and current of the secondary winding;

[0130] Multiply the number of winding layers of each winding in the primary winding by the corresponding wire diameter to obtain the thickness of the primary winding; multiply the number of winding layers of each winding in the secondary winding by the corresponding wire diameter to obtain the thickness of the secondary winding; add the thickness of the primary winding and the thickness of the secondary winding to obtain the total thickness of the winding.

[0131] Specifically, according to the rated power and current of each winding, combined with the set current density, calculate the cross-sectional area of the wire. The single-phase transformer is a naturally cooled dry-type transformer, and the allowable current density is generally 3 - 5 A / mm 2 . Select a suitable round wire specification according to the calculated cross-sectional area of the wire and the wire diameter. Considering the skin effect of alternating current, ensure that the wire diameter does not exceed 2 times the skin depth during design, otherwise multi-strand wires should be wound in parallel or flat copper foil should be used.

[0132] After determining the number of turns and winding wire diameter of each winding of the single-phase transformer, design the winding arrangement method, consider the insulation between winding layers, the insulation between windings, and the electrostatic shielding layers on the primary and secondary sides, etc., and calculate the number of winding layers and thickness of each winding, as well as the total thickness of the transformer winding.

[0133] The resistances of the primary and secondary windings of the single-phase transformer are

[0134] R 1 = MLT(N 1 )×ρ 1 (Ω)

[0135] R 2 = MLT(N 2 )×ρ 2 (Ω), R 3 = MLT(N 3 )×ρ 3 (Ω), L, R j = MLT(N j )×ρ j (Ω)

[0136] Wherein, MLT(N i )(i = 1, 2, 3, …, j) is the average length of each winding, and ρ i is the winding resistivity of each winding at 75°C.

[0137] In the embodiments of the present invention, the number of turns N 0 corresponding to each volt of voltage is

[0138]

[0139] In the embodiment, for the primary winding: there are taps in the winding, the tap output capacity is derated, the wire diameters of each tap winding are kept consistent, the number of turns corresponding to 415V input is 382, the number of turns corresponding to the 400V tap is 368, the number of turns corresponding to the 380V tap is 350, and the number of turns corresponding to the 360V tap is 331;

[0140] For the secondary winding: there are 4 groups of independent windings 121V, 220V, 110V, and 24V. Each independent winding does not contain taps, the output powers of each independent winding are 605VA, 440VA, 220VA, and 360VA respectively, the wire diameters of each independent winding are proportional to the current, and the number of turns of each independent winding are 115, 208, 104, and 23 respectively.

[0141] According to the rated power and current of each winding, combined with the set current density, calculate the cross-sectional area of the wire. The single-phase transformer is a naturally cooled dry-type transformer, and the allowable current density is generally 3 - 5 A / mm2. Select a suitable round wire specification according to the calculated cross-sectional area and diameter of the wire. Considering the skin effect of alternating current, ensure that the wire diameter does not exceed 2 times the skin depth during design, otherwise multi-strand wires should be wound in parallel or flat copper foils should be used.

[0142] The primary side winding selects QZ-2 / 130 Φ1.3 enameled wire (wire diameter 1.3 mm), the 220V winding on the secondary side selects QZ-2 / 130 Φ0.8 enameled wire (wire diameter 0.8 mm), the 120V winding selects QZ-2 / 130 Φ1.3 enameled wire (wire diameter 1.3 mm), the 110V winding selects QZ-2 / 130 Φ0.8 enameled wire (wire diameter 0.8 mm), and the 24V winding selects QZ-2 / 130 Φ2.24 enameled wire (wire diameter 2.24 mm).

[0143] After determining the number of turns and winding diameter of each winding of the single-phase transformer, design the winding arrangement method. Consider the interlayer insulation of the winding, the insulation between windings, and the electrostatic shielding layers on the primary and secondary sides, etc. Calculate the number of winding layers and thickness of each winding, as well as the total thickness of the transformer winding. The calculated total thickness of the winding must be less than the core window factor threshold, otherwise return to step 2, select a core with a larger center post, and recalculate the number of winding turns, arrangement, and thickness.

[0144] In the embodiment of the present invention, the total thickness of the winding is 0.36, which is less than the set core window factor threshold of 0.4, indicating that the selected EI-171 core fully meets the requirements.

[0145] S3: Calculate the total copper loss and core loss of the winding according to the set of demand parameters, and calculate the temperature rise of the low-voltage single-phase multi-winding transformer based on the total copper loss and core loss of the winding; if the temperature rise is greater than the preset threshold, reset the set of demand parameters and return to step S1 to increase the geometric size of the core, otherwise enter step S4;

[0146] As an embodiment

[0147] In step S3:

[0148] The total copper loss P Cu The calculation formula is:

[0149] P Cu = P 1 + P 2 + P 3 + L + P j

[0150] Among them, the unit of P Cu is W, P1 is the power of the primary winding, P 2 to P j are the powers of the independent windings in the secondary winding;

[0151] Specifically:

[0152]

[0153] The core loss P Fe has the following calculation formula:

[0154] P Fe = P kg V Fe ρ Fe × 10 -3

[0155] where P Fe is in W, V Fe is the volume of the core material, ρ Fe is the density of the core material, and P kg is the core loss per kilogram of mass;

[0156] Specifically, the core loss per kilogram of mass is:

[0157] The calculation formula for the temperature rise ΔT is:

[0158]

[0159] where the unit of ΔT is °C, and A t is the surface area of the low-voltage single-phase multi-winding transformer.

[0160] In the embodiments of the present invention:

[0161]

[0162] The total copper loss of the windings of the single-phase transformer is

[0163] P Cu = P 1 + P 2 + P 3 + P 4 + P 5 = 64.47 (W)

[0164] The core loss per kilogram of mass is

[0165]

[0166] The volume of the core material of the single-phase transformer is

[0167] V Fe=(6c × 5c - 2 × 3c × c)K c b = 24c 2 K c b = 1.07(cm 3 )

[0168] The core loss of the transformer is

[0169] P Fe = P kg V Fe ρ Fe × 10 -3 = 8.14(W)

[0170] The temperature rise ΔT of the transformer is

[0171]

[0172] Therefore, the temperature rise of the single - phase transformer is within the threshold of 75°C.

[0173] S4: Calculate and obtain the total winding weight and the total core weight according to the set of required parameters, and use the geometric dimensions of the core, the number of turns and wire diameter of the primary - side winding, the number of turns and wire diameter of the secondary - side winding, the total copper loss of the winding, the core loss, the total winding weight and the total core weight as the set of relevant parameters;

[0174] As an embodiment

[0175] In step S4:

[0176] The formula for calculating the total winding weight G Cu is:

[0177]

[0178] where G Cu is in kg, i is the number of the independent winding, j is the total number of independent windings, N i is the number of turns of the i - th independent winding, A i is the cross - sectional area of the i - th independent winding, ρ Cu is the density of the winding material;

[0179] The formula for calculating the total core weight G Fe is:

[0180] G Fe = V Fe ρ Fe × 10 -3

[0181] where G Fe is in kg, V Fe is the volume of the core material, ρ Fe is the density of the core material.

[0182] Specifically, the volume of the iron core material of the single-phase transformer is: V Fe =(6c×5c - 2×3c×c)K c b = 24c 2 K c b(cm 3 )

[0183] where c is the window width of the EI-shaped iron core.

[0184] In the embodiment of the present invention:

[0185] The weight of the iron core is

[0186] G Fe = V Fe ρ Fe ×10 -3 = 8.13(kg)

[0187] The weight of the winding is

[0188]

[0189] S5: Set the objective function and constraint conditions, and construct an optimization model for the low-voltage single-phase multi-winding transformer according to the objective function, constraint conditions, and relevant parameter sets;

[0190] As an embodiment:

[0191] In step S5:

[0192] The expression of the optimization model of the low-voltage single-phase multi-winding transformer is:

[0193]

[0194] where f(x) is the objective function, A is the unit electricity price, B is the operation time of the transformer, C is the unit price of the iron core material, D is the unit price of the winding material, g t (x) is the constraint condition, m is the total number of constraint conditions, P Fe is the iron core loss, P Cu is the total copper loss of the winding, G Fe is the total weight of the iron core, G Cu is the total weight of the winding;

[0195] The optimization variable set of the optimization model includes: the geometric dimensions of the iron core, the number of turns of the primary winding, the wire diameter of the primary winding, the number of turns of the secondary winding, and the wire diameter of the secondary winding.

[0196] In the embodiment of the present invention, the optimization model (objective function and constraint conditions) is

[0197]

[0198] Wherein, P Fe,max , P Cu,max and T max are respectively the allowable maximum iron loss, copper loss and temperature rise, and k u is the winding window coefficient. Parameter setting: A = 0.6 (yuan / kWh), B = 1000 (h), C = 7 (yuan / kg), D = 60 (yuan / kg), P Fe,max = 20 (W), P Cu,max = 60 (W), T max = 75 ().

[0199] It should be noted that the variables for transformer design optimization are discrete variables with a certain interval.

[0200] The value range of the core center column is

[0201]

[0202] The value range of the saturation magnetic flux density is

[0203] 1.155 (T) < B m < 1.410 (T)

[0204] The value range of the number of turns of the primary winding is

[0205] 255 < N1 < 510 (turns)

[0206] The value range of the wire diameter of the primary winding is

[0207] 1.2 (mm) < d1 < 1.6 (mm)

[0208] The value range of the wire diameter of the secondary winding is

[0209] 1.3 (mm) < d21 < 1.8 (mm)

[0210] 0.8 (mm) < d22 < 1.2 (mm)

[0211] 0.8 (mm) < d23 < 1.2 (mm)

[0212] 2 (mm) < d24 < 7 (mm)

[0213] The winding window coefficient is

[0214] 0.35 ≤ k u ≤ 0.45

[0215] S6: Solve the optimization model through the improved genetic algorithm to obtain the optimal design parameter set of the low-voltage single-phase multi-winding transformer.

[0216] As an embodiment, the optimization model of the single-phase transformer needs to be converted into a fitness function in the genetic algorithm, generate an initial population of M individuals, calculate the fitness of each individual in the population and sort them from largest to smallest, select the individuals in the top 1 / 4 of the population and use them to replace the individuals in the bottom 1 / 4 of the population, and finally use it as a sub-population for crossover and mutation operations. Perform single-point crossover operations on the individuals in the population with a crossover rate that adaptively changes based on the similarity degree of the population fitness values, perform basic mutation operations on the individuals in the population with a mutation rate that adaptively changes based on the similarity degree of the population fitness values, and iterate the population after selection, crossover, and mutation as a new generation of population until the iteration terminates to obtain the optimal design parameters.

[0217] Step S6 is specifically as follows:

[0218] S61: Set the population size, maximum number of iterations, crossover probability, and mutation probability, and define the range of each optimization variable;

[0219] S62: Generate an initial population through an initialization function, and the initial population includes multiple individuals;

[0220] S63: Each individual includes multiple optimization variables, and the objective function value of each individual is obtained through the objective function;

[0221] S64: Perform non-dominated sorting on the objective function values to obtain the Pareto front;

[0222] Specifically, the cost is x, the loss is y, and the objective function value z = 0.2y + 0.8x. For the objective function value z, it is composed of x and y. In non-dominated sorting, compare p[0], q[0] of the cost x and p[1], q[1] of the loss y in each individual. In fact, it is comparing their superiority and inferiority in the objective function value z.

[0223] The process of non-dominated sorting is as follows:

[0224] Define variables to store the non-dominated sorting array. Since the population size is 100 and the number of individuals is 100, the following S, n, and rank have 100 elements.

[0225] Array S: Store the list of other individuals dominated by each individual, and it is a two-dimensional list.

[0226] n: Store the number of times each individual is dominated (initially 0).

[0227] rank: Store the ranking of each individual. When the number of times this individual is dominated is less (here it means the cost x is smaller and the loss y is smaller), the ranking is more forward, that is, it is superior to other individuals. That is, when the number of times this individual is dominated is 0, the ranking is 0, and so on.

[0228] front: Stores the front of each layer, initially empty, front = [[]]. According to the obtained rank, the individuals ranked 0 are placed in the first layer until the 100th layer is finally updated. front[0] represents the Pareto optimal front, front[1] represents the sub-optimal front, and so on, which can be used as the index of the front.

[0229] Further, given the objective

[0230] P = [[x 0 , y 0 , [x 1 , y 1 , [x 2 , y 2 , …… [x 99 , y 99

[0231] Perform non-dominated sorting on x and y. If x 0 > x 1 , y 0 ≤ y 1 , individual 1 dominates individual 0 (p dominates q), add individual 0 to the list of individuals dominated by individual 1 (add q to the list of individuals dominated by p) to get

[0232] S = [ [], [0], [], …… [] ]

[0233] If individual 0 is dominated by individual 1 (q is dominated by p), then increment the count

[0234] n = [1, 0, 0, …… 0]

[0235] If x 0 > x 2 , y 0 > y 2 , then individual 2 dominates individual 0, and after updating the array, we get

[0236] S = [ [], [0], [0], …… [] ]

[0237] n = [2, 0, 0, …… 0]

[0238] If x 1 > x 2 , y 1 > y 2 , individual 2 dominates individual 1, and after continuing to update the array, we get

[0239] S = [ [], [0], [0, 1], …… [] ]

[0240] n = [2, 1, 0, …… 0]

[0241] ​And so on, continue to update the array. Finally, process the number of dominated individuals, and find the individuals with zero dominated number. If the dominated number of individual k is zero, that is, n[k]=0, then rank[k]=0, and front = [[k]] to find the first front. Each front is a set of non-dominated individuals until 100 fronts are found. The overall realization of the non-dominated sorting of the population individuals lays the foundation for the subsequent selection operation of multi-objective optimization.

[0242] S65: If the number of iterations reaches the maximum number of iterations, enter step S67; otherwise, enter step S66.

[0243] S66: Pair individuals in pairs to form multiple parent individuals. Pair the parent individuals in pairs to generate offspring individuals through the crossover probability, and mutate each offspring individual through the mutation probability to obtain a new population, and return to step S63.

[0244] S67: Output the final Pareto front, obtain the optimal set of optimization variables through the final Pareto front, and use the optimal set of optimization variables as the optimal design parameter set of the low-voltage single-phase multi-winding transformer.

[0245] In the embodiment of the present invention, the objective function of the single-phase transformer needs to be transformed into the fitness function in the genetic algorithm. Generate an initial population of 1000 individuals, calculate the fitness of each individual in the population and sort them from largest to smallest. Select the first 250 individuals in the population and use them to replace the last 250 individuals in the population. Finally, use them as the sub-population for crossover and mutation operations. Perform single-point crossover operations on the individuals in the population with a crossover rate that adaptively changes based on the similarity degree of the population fitness values, and perform basic mutation operations on the individuals in the population with a mutation rate that adaptively changes based on the similarity degree of the population fitness values. Iterate the population after selection, crossover, and mutation as the new generation population until the iteration terminates to obtain the optimal design parameter set. The result graph of the improved genetic algorithm is as Figure 3 shown, the abscissa is the number of iterations, the ordinate is the total objective parameter, and the objective function value is the sum of the total loss with a set weight of 0.2 and the total cost with a set weight of 0.8.

[0246] In the embodiment of the present invention, the optimal design parameter set is shown in Table 2, and the objective function value, cost, and loss are shown in Table 3.

[0247] Table 2 Optimal design parameter set

[0248]

[0249]

[0250] Table 3 Objective function value, cost, and loss

[0251]

[0252] As can be seen from Table 2, the single-phase transformer before optimization fully meets the required electrical parameters. After optimization using the genetic algorithm, since the price of copper is much higher than that of silicon steel, the algorithm mainly optimizes the weight of the copper wire, and the cost can be reduced after optimization. Compared with the traditional method, the low-voltage single-phase multi-winding transformer designed in the present invention can be applied to various complex winding structures. The design process comprehensively considers the influences of structure, cost, loss and temperature rise, and can optimize the design results according to different design objectives, which has reference value for the auxiliary design of engineering transformers.

[0253] Please refer to Figure 4 , Figure 4 which is a schematic diagram of the operation of the hardware device in the embodiment of the present invention. The hardware device specifically includes: a device 401 for designing and multi-objective optimizing a low-voltage single-phase multi-winding transformer, a processor 402, and a storage medium 403.

[0254] A device 401 for designing and multi-objective optimizing a low-voltage single-phase multi-winding transformer: The device 401 for designing and multi-objective optimizing a low-voltage single-phase multi-winding transformer implements the method for designing and multi-objective optimizing the low-voltage single-phase multi-winding transformer.

[0255] Processor 402: The processor 402 loads and executes the instructions and data in the storage medium 403 to implement the method for designing and multi-objective optimizing the low-voltage single-phase multi-winding transformer.

[0256] Storage medium 403: The storage medium 403 stores instructions and data; the storage medium 403 is used to implement the method for designing and multi-objective optimizing the low-voltage single-phase multi-winding transformer.

[0257] It should be noted that in this article, the terms "include", "comprise" or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article or system including a series of elements not only includes those elements, but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or system. Without further limitation, an element defined by the statement "including one..." does not exclude the existence of additional identical elements in the process, method, article or system including that element.

[0258] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments. In the unit claims listing several devices, several of these devices may be embodied by the same hardware item. The use of the words first, second, and third, etc. does not indicate any order and these words may be interpreted as identifiers.

[0259] The above are only the preferred embodiments of the present invention, and do not limit the patent scope of the present invention accordingly. Any equivalent structure or equivalent process transformation made by using the content of the specification and drawings of the present invention, or directly or indirectly applied in other related technical fields, shall be similarly included in the patent protection scope of the present invention.

Claims

1. A design and multi-objective optimization method for a low voltage single-phase multi-winding transformer, characterized in that: Includes steps: S1: Obtain a set of required parameters of a low-voltage single-phase multi-winding transformer, and calculate the geometric dimensions of the core according to the set of required parameters; S2: Calculate the number of turns and wire diameter of the primary winding and the number of turns and wire diameter of the secondary winding according to the required parameter set and the geometric size of the core; calculate the total thickness of the winding by the number of turns and wire diameter. If the total thickness of the winding is greater than the core window coefficient threshold, reset the required parameter set and return to step S1 to increase the geometric size of the core, otherwise proceed to step S3; S3: Calculate the total copper loss and core loss of the winding according to the required parameter set, and calculate the temperature rise of the low-voltage single-phase multi-winding transformer according to the total copper loss and core loss of the winding; if the temperature rise is greater than the preset threshold, reset the required parameter set and return to step S1 to increase the geometric size of the core, otherwise enter step S4; S4: Calculate the total weight of the winding and the total weight of the core according to the required parameter set, and take the geometric size of the core, the number of turns and wire diameter of the primary winding, the number of turns and wire diameter of the secondary winding, the total copper loss of the winding, the core loss, the total weight of the winding and the total weight of the core as the relevant parameter set; S5: setting the objective function and constraint conditions, and constructing an optimization model of a low-voltage single-phase multi-winding transformer according to the objective function, constraint conditions and related parameter sets; S6: The optimization model is solved by an improved genetic algorithm to obtain the optimal design parameter set of the low-voltage single-phase multi-winding transformer.

2. The design and multi-objective optimization method of a low voltage single-phase multi-winding transformer according to claim 1 is characterized in that: The required parameter set includes: the rated voltage U of the primary winding 1n , the rated voltage U of each independent winding in the secondary winding 2n , U 3n , ..., U jn , the rated current of each independent winding in the secondary winding is I 2n ,I 3n ,...,I jn .

3. The design and multi-objective optimization method of a low voltage single-phase multi-winding transformer according to claim 2 is characterized in that: In step S1: The geometric dimensions of the core include: the width a of the core center column and the effective cross-sectional area A of the core center column c ; The calculation formula for the width a of the core center column is: Among them, a is in mm, K0 is the empirical coefficient, b is the thickness of the core center column, S n is the average value of the capacity of the primary winding and the secondary winding; The effective cross-sectional area A of the core center column c The calculation formula is: <h2 style=";text-align:left;direction:ltr">A<h2 style=";text-align:left;direction:ltr"> c <h2 style=";text-align:left;direction:ltr"> =K<h2 style=";text-align:left;direction:ltr"> c <h2 style=";text-align:left;direction:ltr"> ab / 100 Among them, A c The unit is cm 2 , K c is the core lamination coefficient.

4. The design and multi-objective optimization method of a low voltage single-phase multi-winding transformer according to claim 2 is characterized in that: In step S2: The number of winding turns N0 corresponding to each volt of voltage is In the formula, N0 is in turns, f is the transformer operating frequency, B m A is the maximum value of the magnetic flux density of the core center column. c is the effective cross-sectional area of ​​the core center column; If there is no tap in the primary winding, the number of turns of the primary winding is: N1=N0U 1n ; If there is a tap in the primary winding, the number of turns of the primary winding is: N 11 =N0U 11n ,N 12 =N0U 12n ,...,N 1i =N0U 1in ; Where i is the number of the independent winding, N 1i is the number of turns of the ith independent winding in the primary winding, U 1in is the rated voltage of the ith independent winding in the primary winding; The wire diameter of the primary winding is calculated by the rated power and current of the primary winding; The number of turns of the secondary winding is: <h2 style=";text-align:left;direction:ltr">N2 = (1.05 x 1.10) x N0U<h2 style=";text-align:left;direction:ltr"> 2n <h2 style=";text-align:left;direction:ltr"> N3 = (1.05 x 1.10) x N0U<h2 style=";text-align:left;direction:ltr"> 3n <h2 style=";text-align:left;direction:ltr"> ,...,N<h2 style=";text-align:left;direction:ltr"> j <h2 style=";text-align:left;direction:ltr"> (1.05-1.10)×N0U<h2 style=";text-align:left;direction:ltr"> jn <h2 style=";text-align:left;direction:ltr"> ; Where j is the total number of independent windings, N j is the number of turns of the jth independent winding in the secondary winding, U jn is the rated voltage of the jth independent winding in the secondary winding; The wire diameter of the secondary winding is calculated by the rated power and current of the secondary winding; The thickness of the primary winding is obtained by multiplying the number of winding layers of each winding in the primary winding by the corresponding wire diameter; the thickness of the secondary winding is obtained by multiplying the number of winding layers of each winding in the secondary winding by the corresponding wire diameter; the thickness of the primary winding is added to the thickness of the secondary winding to obtain the total thickness of the winding.

5. The design and multi-objective optimization method of a low voltage single-phase multi-winding transformer according to claim 2, characterized in that: In step S3: Total winding copper loss P Cu The calculation formula is: P Cu =P1+P2+P3+L+P j Among them, P Cu The unit is W, P1 is the power of the primary winding, P2 to P j is the power of each independent winding in the secondary winding; Core loss P Fe The calculation formula is: P.S Fe JP kg V Fe ρ Fe ×1 -3 Among them, P Fe The unit is W, V Fe is the volume of the core material, ρ Fe is the density of the core material, P kg is the core loss per kilogram mass; The calculation formula for temperature rise ΔT is: The unit of ΔT is ℃, A t is the surface area of ​​a low voltage single-phase multi-winding transformer.

6. The design and multi-objective optimization method of a low voltage single-phase multi-winding transformer according to claim 2, characterized in that: In step S4: Total winding weight G Cu The calculation formula is: Among them, G Cu The unit is kg, i is the number of the independent winding, j is the total number of independent windings, N i is the number of turns of the ith independent winding, A i is the cross-sectional area of ​​the ith independent winding, ρ Cu is the density of the winding material; Total weight of core G Fe The calculation formula is: G Fe =V Fe r Fe ×10 -3 Among them, G Fe The unit is kg, V Fe is the volume of the core material, ρ Fe is the density of the core material.

7. The design and multi-objective optimization method of a low voltage single-phase multi-winding transformer according to claim 2, characterized in that: In step S5: The expression of the optimization model of low-voltage single-phase multi-winding transformer is: Among them, f(x) is the objective function, A is the unit electricity price, B is the transformer operation time, C is the core material unit price, D is the winding material unit price, g t (x) is the constraint condition, m is the total number of constraints, P Fe is the core loss, P Cu is the total copper loss of the winding, G Fe is the total weight of the core, G Cu is the total weight of the winding; The optimization variable set of the optimization model includes: the geometric size of the core, the number of turns of the primary winding, the wire diameter of the primary winding, the number of turns of the secondary winding and the wire diameter of the secondary winding.

8. The design and multi-objective optimization method of a low voltage single-phase multi-winding transformer according to claim 7, characterized in that: Step S6 is specifically as follows: S61: Set the population size, maximum number of iterations, crossover probability and mutation probability, and define the range of each optimization variable; S62: Generate an initial population through an initialization function, where the initial population includes a plurality of individuals; S63: Each individual includes a plurality of optimization variables, and an objective function value of each individual is obtained by objective function calculation; S64: Perform non-dominated sorting on each objective function value to obtain the Pareto frontier; S65: If the number of iterations reaches the maximum number of iterations, proceed to step S67, otherwise proceed to step S66; S66: Individuals are paired in pairs to form multiple parent individuals. Parent individuals are paired in pairs to generate offspring individuals through crossover probability. Each offspring individual is mutated through mutation probability to obtain a new population, and the process returns to step S63; S67: Output the final Pareto frontier, obtain the optimal set of optimization variables through the final Pareto frontier, and use the optimal set of optimization variables as the optimal design parameter set of the low-voltage single-phase multi-winding transformer.

9. A storage medium, characterized in that: The storage medium stores instructions and data for implementing the design and multi-objective optimization method of the low-voltage single-phase multi-winding transformer as described in any one of claims 1 to 8.

10. A design and multi-objective optimization device for a low voltage single-phase multi-winding transformer, characterized in that: include: Processor and storage medium; the processor loads and executes instructions and data in the storage medium to implement the design and multi-objective optimization method of the low-voltage single-phase multi-winding transformer as described in any one of claims 1 to 8.

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