A method for optimizing non-uniform arrangement of flat wire winding

Abstract

A non-uniform arrangement optimization method for flat wire windings, belonging to the field of motor design, is disclosed. This method addresses the challenge of synergistically optimizing the non-uniform arrangement of variable cross-section flat wire windings in stator slots while ensuring fabrication feasibility. The goal is to balance slot fill factor, copper usage, DC losses, and high-frequency AC losses, thereby reducing total winding losses and improving motor efficiency. The method involves discretizing the stator slot cross-section into a grid and constructing a binary model to describe the winding distribution. Under manufacturing constraints such as slot fill factor, dimensions, and insulation, an initial scheme satisfying reduction constraints is generated. With the optimization objective of minimizing the sum of DC losses and AC losses considering a non-uniform magnetic field, a genetic algorithm is used for iterative optimization. During the iteration process, geometric continuity and slot fill factor constraints ensure the manufacturability of the results. Finally, the method quickly finds the non-uniform arrangement scheme of variable cross-section flat wire windings with the lowest total losses. This invention reduces total winding losses and improves motor operating efficiency.

Description

Technical Field

[0001] This invention relates to the field of motor design, and more specifically to an optimization method for non-uniform arrangement of flat wire windings. Background Technology

[0002] With the continuous improvement of motor power density, variable cross-section flat wire windings have been widely used in new energy vehicles and aerospace electric drive fields due to their high slot fill factor and low DC loss characteristics. However, in actual operation, traditional constant cross-section variable cross-section flat wire windings in stator slots are severely affected by the skin effect and proximity effect under high-frequency conditions. Because the magnetic field in the slot exhibits a highly uneven, stepped distribution along the slot depth, this magnetic field gradient induces higher AC losses in conductors near the slot opening, deteriorating the overall performance of the motor. Furthermore, the uniform winding size and fixed cross-sectional area result in non-uniform conductor distribution between the slot bottom and slot opening, increasing the heat dissipation pressure on the cooling system and the difficulty of thermal design, thus limiting further increases in motor power density.

[0003] Current loss optimization methods mostly employ uniform arrangement, slot-bottom side winding offset arrangement, and slot-bottom side winding lamination refinement. While these methods can reduce the total winding loss, uniform arrangement is difficult to adapt to non-uniform magnetic field characteristics in practical applications, while lamination cutting or winding offset increases manufacturing difficulty. Furthermore, none of these methods can satisfy the synergistic optimization of slot fill factor, copper usage, DC loss, and high-frequency AC loss within the limited stator slot space. Therefore, how to construct a fast and feasible optimization method for non-uniform arrangement of variable cross-section flat wire windings, achieving optimal non-uniform matching of the cross-sectional area and arrangement of variable cross-section flat wire windings within the slots while meeting manufacturing feasibility constraints, has become an urgent need for improving motor power density. Summary of the Invention

[0004] To address the challenge of optimizing the non-uniform arrangement of variable cross-section flat wire windings in stator slots while ensuring fabrication feasibility, thereby balancing slot fill factor, copper usage, DC losses, and high-frequency AC losses to reduce total winding losses and improve motor efficiency, this invention provides a method for optimizing the non-uniform arrangement of flat wire windings, comprising:

[0005] S1: Establish a two-dimensional mesh array of the stator slot cross section. Based on the stator slot geometric parameters, the variable range of flat wire thickness and the subdivision step size, construct a binary discrete model to describe the winding distribution properties, and determine the effective number of mesh cells in each layer along the slot width direction.

[0006] S2: Based on the binary discrete model, an initial winding arrangement is constructed. Combining the slot fill factor, the thickness and width of the flat wire, the maximum feasible current density and insulation thickness constraints, an initial population that meets the processing feasibility is generated. Each individual is a matrix unit, and the conductor units of each layer of conductors meet the reduction constraint of continuous distribution from the stator tooth to the slot centerline side.

[0007] S3: For the initial population, evaluate the fitness of each of the matrix units, where the fitness is the sum of the DC loss and AC loss of the matrix unit; wherein the AC loss is calculated based on the magnetic flux density interpolation corresponding to the slot depth direction of each layer of grid.

[0008] S4: Based on the fitness, perform genetic algorithm evolution iteration, generate a new generation of population through elite retention, row crossover and layer thickness width mutation operators, and coordinately restrict the geometric continuity of conductors and slot fill rate threshold during the iteration process to eliminate invalid units.

[0009] S5: After the evolutionary iteration is completed, the non-uniform arrangement of variable cross-section flat wire windings with the minimum total loss is output from the new generation population, and is converted into the processing parameters of variable cross-section flat wire windings accordingly.

[0010] Furthermore, in S1, the binary discrete model is defined by a Boolean matrix, where a logic value "1" represents a conductor unit region and a logic value "0" represents a non-conductive region, and the mesh subdivision step size is set according to the minimum processing accuracy and thickness variation range of the flat wire.

[0011] Furthermore, in S2, the reduction constraint refers to the following: in each layer of conductor grid cells, conductor grid cells are continuously distributed on the starting side, and non-conductive grid cells are continuously distributed on the slot centerline side. By changing the number of cells with a logic value of "1" in each layer, the winding cross section and the slot centerline side are adaptively matched.

[0012] Furthermore, in S3, the evaluation of the fitness of each of the matrix units is achieved by the following formula:

[0013]

[0014] in, Total loss per unit length The DC loss per unit length of the r-th layer is... The AC loss per unit length of the nth layer;

[0015] DC loss per unit length in the r-th layer The calculation is as follows:

[0016]

[0017] Where m is the total number of layers, and I is the effective value of the conductor current. t is the resistivity of the conductor. r w represents the number of units with a logical value of "1" in the r-th layer. unit为 h is the width of the grid cell. unit The height of the grid cell;

[0018] AC loss per unit length in the r-th layer The calculation is as follows:

[0019]

[0020] in, is the average magnetic induction intensity of the r-th layer determined by the layered linear interpolation method along the groove depth direction; w is the electric angular frequency of the motor.

[0021] Furthermore, in S4, the slot fill rate threshold is set between 0.5 and 0.8; for substandard individuals generated during iteration, matrix unit reconstruction is performed to ensure the processing feasibility of the optimized population.

[0022] The beneficial effects of this invention are:

[0023] 1. This invention takes into account the synergistic optimization between winding slot fill factor, copper consumption, DC loss and high-frequency AC loss. The method of this invention can quickly and accurately calculate the non-uniform arrangement of variable cross-section flat wire windings, providing guidance for the efficient arrangement of variable cross-section flat wire windings.

[0024] 2. By applying constraints such as reduction constraints, slot fill factor, flat wire cross-sectional dimensions, maximum feasible current density, and insulation thickness constraints, this invention ensures that the generated layout scheme is practically feasible and has good engineering practice value and manufacturability. Attached Figure Description

[0025] Figure 1 This is a flowchart of the invention;

[0026] Figure 2 This is a schematic diagram of the groove cross-section mesh discretization of the present invention;

[0027] Figure 3 This is a cloud diagram showing the arrangement of the variable cross-section flat wire windings of the present invention;

[0028] Figure 4 This is a convergence curve of winding loss in this invention. Detailed Implementation

[0029] The technical solution of the present invention will be further described below with reference to embodiments, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention. In the following embodiments, process equipment or devices not specifically specified are all conventional equipment or devices in the art. Unless specifically specified, the technical means used in the embodiments of the present invention are all conventional means well known to those skilled in the art.

[0030] Example 1, combined with Figure 1 This embodiment describes a method for optimizing the non-uniform arrangement of flat wire windings, comprising:

[0031] S1: Establish a two-dimensional mesh array of the stator slot cross section. Based on the stator slot geometric parameters, the variable range of flat wire thickness and the subdivision step size, construct a binary discrete model to describe the winding distribution properties, and determine the effective number of mesh cells in each layer along the slot width direction.

[0032] S2: Based on the binary discrete model, an initial winding arrangement is constructed. Combining the slot fill factor, the thickness and width of the flat wire, the maximum feasible current density and insulation thickness constraints, an initial population that meets the processing feasibility is generated. Each individual is a matrix unit, and the conductor units of each layer of conductors meet the reduction constraint of continuous distribution from the stator tooth to the slot centerline side.

[0033] S3: For the initial population, evaluate the fitness of each of the matrix units, where the fitness is the sum of the DC loss and AC loss of the matrix unit; wherein the AC loss is calculated based on the magnetic flux density interpolation corresponding to the slot depth direction of each layer of grid.

[0034] S4: Based on the fitness, perform genetic algorithm evolution iteration, generate a new generation of population through elite retention, row crossover and layer thickness width mutation operators, and coordinately restrict the geometric continuity of conductors and slot fill rate threshold during the iteration process to eliminate invalid units.

[0035] S5: After the evolutionary iteration is completed, the non-uniform arrangement of variable cross-section flat wire windings with the minimum total loss is output from the new generation population, and is converted into the processing parameters of variable cross-section flat wire windings accordingly.

[0036] Furthermore, in S1, the binary discrete model is defined by a Boolean matrix, where a logic value "1" represents a conductor unit region and a logic value "0" represents a non-conductive region, and the mesh subdivision step size is set according to the minimum processing accuracy and thickness variation range of the flat wire.

[0037] Specifically, S1 transforms the continuous physical space of the stator slot cross-section into a discretized digital model composed of grid cells, and uses a Boolean matrix (1 represents a conductor, 0 represents a non-conductor) to accurately characterize the distribution of winding materials. Its core purpose is to provide a quantifiable, computable mathematical model foundation that strictly adheres to manufacturing precision for subsequent automatic optimization algorithms, thereby transforming the complex physical arrangement problem into a mathematical problem that can be searched and processed by a computer.

[0038] Furthermore, in S2, the reduction constraint refers to the following: in each layer of conductor grid cells, conductor grid cells are continuously distributed on the starting side, and non-conductive grid cells are continuously distributed on the slot centerline side. By changing the number of cells with a logic value of "1" in each layer, the winding cross section and the slot centerline side are adaptively matched.

[0039] Specifically, S2 embeds key physical manufacturing rules into the abstract optimization space by mandating in the mathematical model that the effective units (value "1") of each conductor layer must be continuously and closely arranged from the stator tooth side to the slot centerline side. Its fundamental purpose is to ensure that every arrangement scheme generated by the algorithm corresponds geometrically to a complete, continuous, and uninterrupted solid flat wire, avoiding the problem of mathematically optimal results that are physically unmanufacturable, thus fundamentally guaranteeing the engineering feasibility and manufacturability of the optimization results.

[0040] Furthermore, in S3, the evaluation of the fitness of each of the matrix units is achieved by the following formula:

[0041]

[0042] in, Total loss per unit length The DC loss per unit length of the r-th layer is... The AC loss per unit length of the nth layer;

[0043] DC loss per unit length in the r-th layer The calculation is as follows:

[0044]

[0045] Where m is the total number of layers, and I is the effective value of the conductor current. t is the resistivity of the conductor. r w represents the number of units with a logical value of "1" in the r-th layer. unit为 h is the width of the grid cell. unit The height of the grid cell;

[0046] AC loss per unit length in the r-th layer The calculation is as follows:

[0047]

[0048] in, is the average magnetic induction intensity of the r-th layer determined by the layered linear interpolation method along the groove depth direction; w is the electric angular frequency of the motor.

[0049] Specifically, the AC loss calculation described in S3 takes into account the eddy current loss of the conductive unit under high-frequency operating conditions, and the magnetic induction intensity at different positions in the groove depth direction is determined by the layered linear interpolation method.

[0050] Furthermore, in S4, the slot fill rate threshold is set between 0.5 and 0.8; for substandard individuals generated during iteration, matrix unit reconstruction is performed to ensure the processing feasibility of the optimized population.

[0051] Example 2, in a specific embodiment of the present invention, takes a hydromagnetic synchronous drive motor with open trapezoidal stator slots as an example to illustrate the optimization method for non-uniform arrangement of variable cross-section flat wire windings. The key geometric and electrical parameters of the motor windings and stator slots used in this embodiment are shown in Table 1.

[0052] Table 1 Winding and Stator Slot Parameters

[0053]

[0054] The implementation process of this embodiment follows the core steps of the method of the present invention, as follows:

[0055] S1. First, based on the stator slot geometric parameters (slot top width, slot bottom width, slot depth) in Table 1 and the preset mesh partitioning step size (element width 0.3 / 0.4 / 0.5 mm, element height 0.1 mm), the stator slot cross-section is discretized into a two-dimensional mesh array. Based on this mesh, a binary discrete model represented by a Boolean matrix is ​​constructed, where logic "1" represents a conductor element and logic "0" represents a non-conductive element (such as insulation or voids within the slot), and the effective number of elements in each mesh layer along the slot width direction is determined.

[0056] S2, based on the discrete model established in S1, and combined with process constraints such as slot fill factor, variable range of flat wire thickness and width, maximum allowable current density, and insulation thickness, an initial winding arrangement population that satisfies the "reduction constraint" is generated. For example... Figure 2 As shown, each individual (i.e., an arrangement scheme) is represented as a matrix unit, where the conductor units (with a value of 1) of each layer are continuously distributed from the stator tooth side to the slot centerline side, ensuring physical manufacturability.

[0057] S3. For each matrix unit (i.e. each arrangement scheme) in the initial population, calculate its fitness value, which is defined as the total loss per unit length of winding under that arrangement scheme. The total loss is the sum of DC loss and AC loss.

[0058] S4. Based on the fitness value calculated in S3, perform iterative optimization using a genetic algorithm. In each generation, an elite retention strategy is adopted, and operators such as row crossover, layer thickness, and width mutation are used to generate a new population. During the iteration process, strict reduction constraints and geometric continuity constraints are applied, and the slot fill factor is limited to a feasible range of 0.5 to 0.8 to eliminate invalid individuals that do not meet the manufacturing process requirements.

[0059] S5: After iterative optimization in S4, the algorithm converges, and the individual with the minimum total loss is selected as the optimal solution from the final population. The non-uniform arrangement parameters of the variable cross-section flat wire winding corresponding to this optimal solution are shown in Table 2. This can directly guide the processing and manufacturing of flat wire windings. The curve showing the decrease in total loss with the number of iterations during the optimization process is shown in Table 2. Figure 4 As shown, the final optimal layout cloud diagram is as follows: Figure 3 As shown, this visually demonstrates the non-uniform distribution of conductors within the groove.

[0060] Table 2. Optimal winding layout parameters (optimal solution)

[0061]

[0062] Through optimization in this embodiment, a non-uniform arrangement scheme for variable cross-section flat wire windings, as shown in Table 2, was obtained. Compared with traditional constant cross-section or uniform arrangement methods, this method reduces AC losses by using thinner and wider conductors near the slot opening and thicker and narrower conductors near the slot bottom to ensure conductive area and low DC resistance. This effectively reduces the total winding loss while meeting all process constraints, verifying the effectiveness and engineering applicability of the method in improving motor efficiency.

Claims

1. A method for optimizing the non-uniform arrangement of flat wire windings, characterized in that, include: S1: Establish a two-dimensional mesh array of the stator slot cross section. Based on the stator slot geometric parameters, the variable range of flat wire thickness and the subdivision step size, construct a binary discrete model to describe the winding distribution properties, and determine the effective number of mesh cells in each layer along the slot width direction. S2: Based on the binary discrete model, an initial winding arrangement is constructed. Combining the slot fill factor, the thickness and width of the flat wire, the maximum feasible current density and insulation thickness constraints, an initial population that meets the processing feasibility is generated. Each individual is a matrix unit, and the conductor units of each layer of conductors meet the reduction constraint of continuous distribution from the stator tooth to the slot centerline side. S3: For the initial population, evaluate the fitness of each of the matrix units, where the fitness is the sum of the DC loss and AC loss of the matrix unit; wherein the AC loss is calculated based on the magnetic flux density interpolation corresponding to the slot depth direction of each layer of grid. S4: Based on the fitness, perform genetic algorithm evolution iteration, generate a new generation of population through elite retention, row crossover and layer thickness width mutation operators, and coordinately restrict the geometric continuity of conductors and slot fill rate threshold during the iteration process to eliminate invalid units. S5: After the evolutionary iteration is completed, the non-uniform arrangement of variable cross-section flat wire windings with the minimum total loss is output from the new generation population, and is converted into the processing parameters of variable cross-section flat wire windings accordingly.

2. The method for optimizing the non-uniform arrangement of flat wire windings according to claim 1, characterized in that, In S1, the binary discrete model is defined by a Boolean matrix, where a logic value "1" represents a conductor unit region and a logic value "0" represents a non-conductive region. The mesh division step size is set according to the minimum processing accuracy and thickness variation range of the flat wire.

3. The method for optimizing the non-uniform arrangement of flat wire windings according to claim 1, characterized in that, In S2, the reduction constraint means that in each layer of conductor grid cells, conductor grid cells are continuously distributed on the starting side and non-conductive grid cells are continuously distributed on the slot centerline side. The adaptive matching between the winding cross section and the slot centerline side is achieved by changing the number of cells with a logic value of "1" in each layer.

4. The method for optimizing the non-uniform arrangement of flat wire windings according to claim 1, characterized in that, In S3, the fitness of each of the matrix elements is evaluated using the following formula: in, Total loss per unit length The DC loss per unit length of the r-th layer is... The AC loss per unit length of the nth layer; DC loss per unit length in the r-th layer The calculation is as follows: Where m is the total number of layers, and I is the effective value of the conductor current. t is the resistivity of the conductor. r w represents the number of units with a logical value of "1" in the r-th layer. unit为 h is the width of the grid cell. unit The height of the grid cell; AC loss per unit length in the r-th layer The calculation is as follows: in, is the average magnetic induction intensity of the r-th layer determined by the layered linear interpolation method along the groove depth direction; w is the electric angular frequency of the motor.

5. The method for optimizing the non-uniform arrangement of flat wire windings according to claim 1, characterized in that, In S4, the slot fill rate threshold is set between 0.5 and 0.8; for substandard individuals generated during iteration, matrix unit reconstruction is performed to ensure the processing feasibility of the optimized population.

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