Design method of a baffle air-cooled generator

Abstract

This application relates to a design method for a baffled air-cooled generator. The design method includes the following steps: Step S1, load an initial current I in the two-dimensional electromagnetic model of the baffled air-cooled generator, and determine a set TemA of m×n electromagnetic torques according to the first parameter; Step S2, determine m maximum currents Imax in the three-dimensional heat dissipation model of the baffled air-cooled generator, and determine a set TemB of electromagnetic torques according to the maximum value among the m maximum currents Imax, the set TemA of electromagnetic torques obtained in Step 1, the axial proportion η1 of the first lamination, and the axial proportion η2 of the second lamination; Step S3, adjust the value of Nz, determine the optimal value of Nz and the optimal electromagnetic torque, so as to form a set TemC of m×n optimal electromagnetic torques, and determine the global optimal solutions of Wz, Hex and Nz according to the set TemC of optimal electromagnetic torques.

Description

Technical Field

[0001] The present application relates to the technical field of generator stator design, and in particular to a design method for a baffled air-cooled generator. Background Art

[0002] Copper loss, iron loss, eddy current loss in the permanent magnets, and mechanical loss generated during motor operation cause the temperature of various motor components to rise. High temperatures not only degrade motor performance but also cause reliability issues. For example, high temperatures cause increased wire resistance and reduced permanent magnet remanence, significantly reducing the power and efficiency of permanent magnet motors. High temperatures also significantly reduce insulation life and cause irreversible demagnetization of permanent magnets. Therefore, optimized motor design and reliable cooling methods are necessary to effectively control motor temperature rise.

[0003] Currently, liquid cooling and air cooling are the most commonly used methods. Liquid cooling offers superior cooling performance, with a typical heat transfer coefficient 1-2 orders of magnitude higher than that of air cooling. However, liquid cooling faces a series of reliability and maintainability challenges, such as leakage, insulation, and water quality treatment, which hinder its widespread application. For applications with high reliability requirements and challenging maintenance, such as offshore wind power and aerospace, air cooling remains the most commonly used cooling technology. However, these applications often place significant demands on space and weight, leading to the desire for better cooling performance through air cooling, thereby further improving the motor's torque and power density within reliability constraints. Furthermore, enhanced air cooling also reduces the frequency of temperature fluctuations and peaks and valleys in non-stationary loads or operating conditions, improving the stability and controllability of the motor's operation.

[0004] Air cooling also has a place for motors in other application areas. For example, large steam turbine generators usually use water cooling, but many small and medium-sized steam turbine generators also use air cooling because air cooling has low supporting costs, low maintenance costs, and good safety performance.

[0005] In summary, while air cooling may not be as efficient as liquid cooling, its reliability, low cost, and maintenance-friendly features mean that it will continue to be widely adopted in future motor development. Improving the cooling effectiveness of air cooling would be crucial for the development of the motor industry and the entire industry. Summary of the Invention

[0006] The present application provides a design method for a baffled air-cooled generator, which achieves comprehensive optimization of the electromagnetic performance and cooling effect of the generator, effectively improves the torque density upper limit of the generator, and the optimization design process is efficient and accurate.

[0007] A design method for a baffled air-cooled generator, the design method comprising the following steps:

[0008] Step S1, load an initial current I in the two-dimensional electromagnetic model of the baffled air-cooled generator, and determine a set TemA of (m + 1)×(n + 1) electromagnetic torques according to the first parameters;

[0009] The first parameters include:

[0010] Wz, the dimension of the unilateral ventilation gap in the tooth width direction, set as a variable, with m + 1 values, including Wz = 0;

[0011] Hex, the radial dimension of the through hole of the laminated yoke, set as a variable, with n + 1 values, including Hex = 0;

[0012] Ws, the width of the stator slot, set as a fixed value;

[0013] Hs, the radial dimension of the stator slot, set as a fixed value;

[0014] Hy, the radial dimension of the yoke of the lamination, set as a fixed value;

[0015] Step S2, in the three-dimensional heat dissipation model of the baffled air-cooled generator, determine the maximum current Imax that can be loaded corresponding to each Wz when Nz is at the initial value and not higher than the maximum temperature limit of the generator according to the second parameters, where one set of Nz and Wz corresponds to one maximum current Imax, and a total of m maximum currents Imax are obtained, excluding Wz = 0;

[0016] Determine a set TemB of (m×n) electromagnetic torques of Nz at the initial value according to the m maximum currents Imax, the set TemA of electromagnetic torques determined in step S1, the axial proportion η1 of the first lamination, and the axial proportion η2 of the second lamination;

[0017] The second parameters include:

[0018] R, the resistance of the stator winding;

[0019] Lz, the dimension of the ventilation gap in the axial direction of the stator core, set as a fixed value;

[0020] Nz, the number of ventilation gaps in the axial direction of the stator core, set as a variable, and given an initial value;

[0021] Wz, the values of which are all the values except Wz = 0 in step S1;

[0022] Hex, set as a fixed value.

[0023] Step S3: Adjust the value of Nz. According to the method for determining each electromagnetic torque in the set TemB in step S2, determine the optimal value of Nz and the optimal electromagnetic torque for each (Wz, Hex) combination, so as to form a set TemC containing (m×n) optimal electromagnetic torques. Further determine the global optimal solution including Wz, Hex, and Nz according to the set TemC of the optimal electromagnetic torque.

[0024] Optionally, in step S1, the value range of Wz is: 0 ≤ Wz ≤ h, and the value of Wz gradually increases from zero to the axial height value h of the ventilation gap.

[0025] Optionally, the value range of Hex is: d ≤ Hex ≤ d + h, where d is the radial dimension d of the yoke of the second lamination, and h is the axial height of the ventilation gap.

[0026] Optionally, in step S1, the initial current I is estimated according to the maximum envelope size generated by the generator or an empirical value.

[0027] Optionally, in step S1, the width Ws of the stator slot, the radial dimension Hs of the stator slot, and the radial dimension Hy of the yoke of the lamination are determined one by one according to the width of the stator slot, the radial dimension of the stator slot, and the radial dimension of the yoke of the lamination of the radial ventilation type generator.

[0028] Optionally, in step S2, Hex is set to a fixed value and set to the non - zero minimum value.

[0029] Optionally, in step S2, the value of Lz is determined according to the height of the radial ventilation slot of the radial ventilation type generator.

[0030] Optionally, in step S2, the initial value of Nz is determined according to the principle of equal flow area or equal heat dissipation area of the radial ventilation slot of the radial ventilation type generator.

[0031] Optionally, in step S2, the method for determining the set TemB of electromagnetic torques specifically includes:

[0032] At the initial value of Nz, for each (Wz, Hex) combination in the set TemA, after weighting according to the axial proportion η1 of the first lamination and the axial proportion η2 of the second lamination and adding them together, obtain a set TemA' of uncorrected electromagnetic torques corresponding to each non - zero (Wz, Hex);

[0033] According to the linear proportional relationship between the maximum current Imax and the initial current I, expand or shrink each electromagnetic torque in the set TemA' according to the same proportional relationship, so as to obtain each electromagnetic torque in the set TemB.

[0034] Optionally, in step S2, the method for adjusting the value of Nz includes:

[0035] Set Nz to increase round by round from the initial value. Determine whether the electromagnetic torque corresponding to each group (Wz, Hex) changes as Nz increases. If the increase in Nz in this round still causes the electromagnetic torque of a certain group (Wz, Hex) to continue to increase, then increase the Nz corresponding to this group (Wz, Hex) in the next round. Otherwise, do not increase Nz for this group (Wz, Hex) in subsequent rounds until the remaining group is an empty set, that is, the optimal Nz corresponding to each group (Wz, Hex) in the increasing direction of Nz is determined.

[0036] Optionally, set Nz to decrease round by round from the initial value. Determine whether the electromagnetic torque corresponding to each group (Wz, Hex) changes as Nz decreases. If the decrease in Nz in this round still causes the electromagnetic torque of a certain group (Wz, Hex) to continue to increase, then decrease the Nz corresponding to this group (Wz, Hex) in the next round. Otherwise, do not decrease Nz for this group (Wz, Hex) in subsequent rounds until the remaining group is an empty set, that is, the optimal Nz corresponding to each group (Wz, Hex) in the decreasing direction of Nz is determined.

[0037] The present application provides a design method for a baffled air-cooled generator. Among them, the design method includes establishing a two-dimensional electromagnetic model and a three-dimensional heat dissipation model, and obtaining the global optimal solutions of the key parameters Wz, Hex, and Nz of the generator by means of parameter scanning, correction, and adjustment of parameter sizes, realizing the comprehensive optimization of the electromagnetic performance and cooling effect of the generator, effectively improving the upper limit of the torque density of the generator, and the optimization design process is efficient and accurate. Description of the Drawings

[0038] Figure 1 is a half-sectional view of the generator shown in an exemplary embodiment of the present application;

[0039] Figure 2 is an axial view of the stator core of the generator shown in an exemplary embodiment of the present application;

[0040] Figure 3 is a schematic diagram of a lamination group of the stator core shown in an exemplary embodiment of the present application;

[0041] Figure 4 is Figure 3 a partial structural schematic diagram of the stator core shown in;

[0042] Figure 5 is Figure 3 a schematic diagram of the first lamination shown in;

[0043] Figure 6 is Figure 3Schematic diagram of the second lamination shown;

[0044] Figure 7 It is a schematic diagram showing that there is a ventilation gap formed between the stator winding and the tooth part of the lamination;

[0045] Figure 8 It is a schematic diagram of a stack of stator cores shown in another embodiment;

[0046] Figure 9 It is Figure 8 Schematic diagram of the first lamination shown in;

[0047] Figure 10 It is Figure 8 Schematic diagram of the second lamination shown in;

[0048] Figure 11 It is a flowchart of the design method of a baffled air-cooled generator;

[0049] Figure 12 It is a two-dimensional electromagnetic model diagram of a baffled air-cooled generator;

[0050] Figure 13 It is a three-dimensional heat dissipation model diagram of a baffled air-cooled generator;

[0051] Figure 14 It is a schematic diagram of a partial structure of the stator of a radially ventilated generator. Detailed implementation mode

[0052] Here, the exemplary embodiments will be described in detail, and the examples are shown in the drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present application. On the contrary, they are merely examples of devices and methods consistent with some aspects of the present application.

[0053] The terms used in this application are for the purpose of describing specific embodiments only and are not intended to limit this application. Unless otherwise defined, the technical or scientific terms used in this application shall have the ordinary meanings as understood by those of ordinary skill in the art to which this application pertains. The terms "first", "second" and similar words used in this application do not denote any order, quantity or importance, but are only used to distinguish different components. Similarly, words such as "a" or "an" do not denote a quantity limitation, but mean that there is at least one, and will be separately stated if only referring to "one". "Plurality" or "several" means two or more. Unless otherwise indicated, words such as "front", "rear", "lower" and / or "upper", "top", "bottom" are for convenience of description only and are not limited to a position or a spatial orientation. Words such as "comprising" or "including" mean that the elements or items appearing before "comprising" or "including" cover the elements or items listed after "comprising" or "including" and their equivalents, and do not exclude other elements or items. Words such as "connected" or "coupled" are not limited to physical or mechanical connections, and may include electrical connections, whether direct or indirect.

[0054] Please refer to Figure 1 , Figure 1 FIG. shows a half-sectional view of a partial structure of a baffled air-cooled generator 1 shown in an exemplary embodiment of this application.

[0055] An embodiment of this application provides a baffled air-cooled generator 1, including a generator stator 10 and a generator rotor 20. The generator rotor 20 is coaxially arranged with the generator stator 10, and the generator rotor 20 can rotate relative to the generator stator 10 to cause the generator stator 10 to generate current, thereby realizing power generation of the generator 1. The generator rotor 20 includes a rotor core 21 and a permanent magnet 22. The permanent magnet 22 is disposed on the side of the rotor core 21 facing the generator stator 10, and an air gap 30 is reserved between the permanent magnet 22 and the generator stator 10. The air gap 30 is an important part for realizing electromechanical energy conversion, and at the same time, it can also allow a cooling medium A, such as air, to enter the interior of the generator 1 to cool the generator stator 10 and the generator rotor 20. In one embodiment, the cooling medium A enters the air gap 30 from both axial ends of the generator 1, passes through the generator stator 10 and enters the cavity 10a inside the generator stator 10, and is discharged from two end plates 50 axially distributed on the generator 1, thereby circulatingly cooling the interior of the generator 1. A driving device and a heat exchange device, such as an air-water heat exchanger with a fan, may also be provided on the flow path of the cooling medium A to drive the circulating flow of the cooling medium A and dissipate the heat absorbed by the cooling medium A. It should be noted that the flow direction of the cooling medium A is not limited thereto.

[0056] InFigure 1 In the illustrated embodiment, the generator stator 10 is provided as an inner stator, and the generator stator 10 is located inside the generator rotor 20. In some other embodiments, the generator stator 10 may be provided as an outer stator, and the generator stator 10 surrounds the outside of the generator rotor 20.

[0057] Please refer to Figure 1 and Figure 2 , Figure 2 as shown in Figure 1 the axial view of the stator core 100 shown in

[0058] The generator stator 10 includes a stator core 100 and a plurality of stator windings 102. The stator core 100 has a hollow columnar structure and includes a cavity 10a located in the hollow part. The stator core 100 includes a yoke 100a and a plurality of stator teeth 100b. The yoke 100a is provided as a hollow column, and the hollow part is the cavity 10a. The plurality of stator teeth 100b are formed on the side of the yoke 100a facing the generator rotor 20 and are adjacent to the air gap 30. The plurality of stator teeth 100b extend radially along the stator core 100 and are arranged circumferentially along the stator core 100. The gap between two adjacent stator teeth 100b forms a stator slot 100c. A plurality of the stator slots 100c are formed. In one embodiment, a plurality of stator windings 102 are assembled in each of the stator slots 100c and are sleeved on the outside of each stator tooth 100b in a one-to-one correspondence.

[0059] As Figure 2 shown, the stator core 100 includes a plurality of lamination groups 200, and the specific number of the lamination groups 200 is not limited. The plurality of lamination groups 200 are arranged in a hollow columnar structure, and the lamination groups 200 are formed with stator teeth 100b and stator slots 100c on the side facing the generator rotor 20. It should be noted that Figure 2 the structure of the stator core 100 in Figure 2 is only schematic, and the number of stator teeth 100b in the actual generator 1 is much more than that shown in

[0060] Please refer to Figure 3 , Figure 3 as shown in the schematic diagram of one of the lamination groups 200 of the stator core 100.

[0061] The lamination stack 200 includes a plurality of laminations 201 stacked in the thickness direction, and the stacking direction of the plurality of laminations 201 is parallel to the axial direction of the stator core 100. It should be noted that for a rotating electrical machine, both the lamination stack 200 and the laminations 201 are in an arc structure. In the present application, for the sake of simplicity in drawing, both the lamination stack 200 and the laminations 201 are drawn as a straight-line structure.

[0062] The lamination stack 200 is provided with a ventilation gap 400. The stator winding 102 and at least one stator tooth 100b adjacent to the stator winding 102 form the ventilation gap 400 in the tooth width direction. The ventilation gap 400 is located outside the stator tooth 100b, and the gap between the stator tooth 100b and the stator winding 102 in the tooth width direction forms the ventilation gap 400. The ventilation gap 400 extends along the extending direction of the stator tooth 100b, that is, along the radial direction of the stator core 100. The stator core 100 includes a cooling air duct 300 (see Figure 1 ), the cooling air duct 300 communicates the ventilation gap 400 with the cavity 10a in the hollow part of the stator core 100, and the ventilation gap 400 is communicated with the air gap 30, so that the cooling medium A can flow between the air gap 30 and the cavity 10a. In one embodiment, when the cooling medium A enters the air gap 30, it can further flow along the ventilation gap 400 and the cooling air duct 300 to the cavity 10a in the hollow part of the stator core 100. During the flow of the cooling medium A, the cooling medium A exchanges heat with the stator tooth 100b and the stator winding 102, and the cooling of the stator core 100 can be realized.

[0063] Please refer to Figure 1 , the cooling air duct 300 includes a radial air duct 301 extending along the radial direction of the stator core 100 and an axial air duct 302 extending along the axial direction of the stator core 100. The radial air duct 301 is communicated with the axial air duct 302, and is communicated with the ventilation gap 400 and the cavity 10a in the hollow part of the stator core 100. Thus, the ventilation gap 400 and the cooling air duct 300 are communicated with each other to jointly form a cross-flow air duct of the generator stator.

[0064] Please refer to Figures 4 to 6 , Figure 4 is a schematic diagram of one of the lamination stacks 200. Figure 5 is Figure 4 a schematic diagram of the first lamination S1 in the lamination stack 200 shown in Figure 6 is Figure 4 a schematic diagram of the second lamination S2 in the lamination stack 200 shown in

[0065] The lamination 201 includes a yoke portion 201a and a tooth portion 201b connected to the yoke portion 201a. The tooth portion 201b is formed on a side of the yoke portion 201a facing the generator rotor 20, and the tooth portion 201b extends radially along the stator core 100. The tooth portions 201b of a plurality of laminations 201 are stacked to form the stator teeth 100b, and the yoke portions 201a of a plurality of laminations 201 are stacked to form the magnetic yoke 100a.

[0066] The lamination 201 may include a plurality of tooth portions 201b. The plurality of tooth portions 201b are arranged circumferentially along the stator core 100, and a gap between two adjacent tooth portions 201b forms a slot portion 201c. The slot portions 201c of a plurality of laminations 201 are stacked to form the stator slots 100c. The lamination 201 may be formed with a plurality of slot portions 201c. The plurality of slot portions 201c are arranged circumferentially along the stator core 100, and the slot portions 201c of a plurality of laminations 201 are stacked to form a plurality of stator slots 100c.

[0067] Figure 5 The dashed line in [reference] schematically shows the demarcation line between the yoke portion 201a and the tooth portion 201b of the first lamination S1. Figure 6 The dashed line in [reference] schematically shows the demarcation line between the yoke portion 201a and the tooth portion 201b of the second lamination S2. The tooth portions 201b of the laminations 201 in the lamination group 200 have the same dimension in the radial direction of the stator core 100. In the stacking direction, the ends of the tooth portions 201b of the laminations 201 are aligned (refer to Figure 4 ).

[0068] Please refer to Figure 4 and Figure 7 , Figure 7 which is a schematic view of the second lamination S2 forming ventilation gaps 400 on both sides in the tooth width direction.

[0069] The width dimension of the tooth portion 201b of the first lamination S1 is smaller than that of the tooth portion 201b of the second lamination S2. The tooth portion 201b of the first lamination S1 and the tooth portion 201b of the second lamination S2 are aligned along the center line of the tooth width. The tooth portion 201b of the first lamination S1 and the tooth portion 201b of the second lamination S2 are staggered on both sides in the tooth width direction, so that ventilation gaps 400 are left between the stator winding 102 and the lamination 201 on both sides in the tooth width direction. Specifically, the stator winding 102 includes a first winding portion 102' and a second winding portion 102" located on different sides of the tooth portion 201b of the first lamination S1 and the second lamination S2 in the tooth width direction. The first winding portion 102' contacts the tooth portion 201b of the first lamination S1 and forms a ventilation gap 400 with the tooth portion 201b of the second lamination S2. The second winding portion 102" contacts the tooth portion 201b of the first lamination S1 and forms a ventilation gap 400 with the tooth portion 201b of the second lamination S2, so that ventilation gaps 400 are formed between the stator winding 102 and the lamination 201 on both sides in the tooth width direction. Among them, other laminations may be provided between the first lamination S1 and the second lamination S2, or the first lamination S1 and the second lamination S2 are in direct contact.

[0070] Please refer to Figure 4 , Figure 5 and Figure 6 , along the radial direction of the stator core 100, the dimension of the yoke portion 201a of the second lamination S2 is smaller than that of the yoke portion 201a of the first lamination S1. Among them, the yoke portion 201a of the first lamination S1 is provided with an opening 500 penetrating along the thickness direction. In the orthographic projection along the stacking direction, the projection area of the opening 500 is located outside the projection area of the yoke portion 201a of the second lamination S2, so that the opening 500 forms the axial air duct 302 (refer to Figure 1 and Figure 4 ).

[0071] The radial air duct 301 includes a winding-side radial section 301a and a cavity-side radial section 301b radially distributed on both sides of the axial air duct 302 and interconnected. The winding-side radial section 301a connects the ventilation gap 400 with the axial air duct 302, and the cavity-side radial section 301b connects the axial air duct 302 with the cavity 10a in the hollow portion of the stator core 100. In this embodiment, the winding-side radial section 301a is disposed on a side of the axial air duct 302 near the ventilation gap 400 to achieve communication between the ventilation gap 400 and the axial air duct 302. The cavity-side radial section 301b is disposed on a side of the axial air duct 302 near the cavity 10a to achieve communication between the axial air duct 302 and the cavity 10a. This achieves communication between the ventilation gap 400 and the cooling air duct 300, allowing the cooling medium A to flow from the air gap 30 through the deflection air duct of the stator core 100 to the cavity 10a.

[0072] The yoke 201a of the first laminate S1 is provided with a slot connecting hole 600, which connects the opening 500 with its own slot 201c. The slot connecting hole 600 forms the winding side radial section 301a on one side of the yoke 201a of the second laminate S2.

[0073] Please refer to Figures 8 to 10 , Figure 8 FIG. 2 is a schematic diagram of another embodiment of a lamination stack 200 . Figure 9 for Figure 8 Schematic diagram of the first laminate S1 in FIG. Figure 10 for Figure 8 Schematic diagram of the second laminate S2.

[0074] and Figures 4 to 6 The difference of the illustrated embodiment is that the width of the teeth of the first laminate S1 is greater than the width of the teeth of the second laminate S2, and in order to ensure the connectivity of the deflection air duct, a groove 700 needs to be provided on the first laminate S1.

[0075] The teeth 201b of the first lamination S1 and the teeth 201b of the second lamination S2 are aligned along the centerline of the tooth width. The teeth 201b of the first lamination S1 and the teeth 201b of the second lamination S2 are staggered on either side of the tooth width, leaving a ventilation gap 400 between the stator winding 102 and the laminations 201 along the tooth width. This is not described in detail here. The yoke 201a of the first lamination S1 is provided with a communicating opening 500 and a slot communication hole 600.

[0076] Please refer to Figures 11 to 13 , Figure 11 Flowchart of a design method for a baffled air-cooled generator stator 10 . Figure 12 This is a two-dimensional electromagnetic model diagram of a baffled air-cooled generator.Figure 13 It is a three-dimensional heat dissipation model of a baffled air-cooled generator.

[0077] This application provides a design method for a baffled air-cooled generator. The design method is an electromagnetic / heat dissipation comprehensive optimization design method proposed based on simulation data. By using a modeling and analysis design method, it realizes the comprehensive optimization of the electromagnetic performance and cooling effect of the generator, effectively improves the upper limit of the torque density of the generator, and the optimization design process is efficient and accurate. The design method includes step S1, step S2, and step S3.

[0078] Step S1: Load the initial current I in the two-dimensional electromagnetic model (refer to Figure 12 ) of the baffled air-cooled generator, and determine a set TemA containing (m + 1)×(n + 1) electromagnetic torques according to the first parameter. The two-dimensional electromagnetic model can be a finite element two-dimensional electromagnetic model. For example, a finite element two-dimensional electromagnetic model and the initial current I can be established in ANSYS, but it is not limited to this. The two-dimensional electromagnetic model can also be established by analytical methods, magnetic circuit methods, etc. It should be noted that the axial length needs to be set in the two-dimensional electromagnetic model, and it is specifically set to the axial length of the actual baffled air-cooled generator.

[0079] The first parameter includes: the dimension Wz of the unilateral ventilation gap in the tooth width direction, the radial dimension Hex of the through hole in the yoke of the lamination, the width Ws of the stator slot, the radial dimension Hs of the stator slot, and the radial dimension Hy of the yoke of the lamination. Among them, Wz is Figure 7 the dimension of the unilateral ventilation gap 400 in the tooth width direction shown in Figure 5 , Wz is set as a variable and has m + 1 values, including Wz = 0, and the remaining m values are non-zero values; Hex is

[0080] the sum of the radial dimensions of the opening 500 and the slot communicating hole 600 shown in

[0081]

[0082] , Hex is set as a variable and has n + 1 values, including Hex = 0, and the remaining n values are non-zero values; Ws, Hs, and Hy are all set as fixed values. Among them, Wz = 0 and Hex = 0 describe the situation where there are no ventilation gaps 400, openings 500, and slot communicating holes 600 in the lamination.

[0080] In step S1, after setting the first parameter, (m + 1)*(n + 1) electromagnetic simulations are run in the two-dimensional electromagnetic model, and m*n kinds of baffled air duct structures can be combined. The m*n kinds of baffled air ducts correspond to m*n combinations when the values of Wz and Hex are both non-zero terms.

[0081] In step S1, the initial current I can be estimated according to the maximum envelope size or empirical value of the generator, and the initial current I can be corrected in step S2.

[0082] In one embodiment, the maximum value of the Wz value can be set to the axial height value h of the ventilation gap 400, that is, 0 ≤ Wz ≤ h. The non-zero value of Hex can be selected between the radial dimension d of the yoke of the lamination and the sum of the radial dimension d of the yoke of the lamination and the axial height value h of the ventilation gap 400, that is, d < Hex < d + h. Among them, h can be selected according to empirical values.

[0083] Please refer to Table 1. Table 1 is the set TemA of (m + 1) × (n + 1) electromagnetic torques determined in step S1. The values of Wz are 0 mm, 1.3 mm, 2.6 mm, 3.9 mm, 4.55 mm, 5.2 mm respectively. The value of Wz can gradually increase from small, but is not limited to this. The values of Hex are 0 mm, 40 mm, 42.6 mm, 45.2 mm, 47.8 mm and 50.4 mm respectively. Table 1 is the set TemA of 6 × 6 electromagnetic torques, and the unit of each electromagnetic torque is MN〃m.

[0084] Table 1

[0085]

[0086] Please refer to Figure 14 , Figure 14 which is a schematic diagram of a partial structure of the stator 10' of a radially ventilated generator.

[0087] The stator 10' of the radially ventilated generator includes an iron core 11', a winding 12' and a radial ventilation groove 13'.

[0088] In one embodiment, in step S1, the width Ws of the stator slot, the radial dimension Hs of the stator slot, and the radial dimension Hy of the yoke of the lamination can be determined one by one according to the width of the stator slot, the radial dimension of the stator slot, and the radial dimension of the yoke of the lamination of the stator of the radially ventilated generator. For example, Ws, Hs, and Hy can take the preferred values corresponding to the three in the stator of the radially ventilated generator. The value of Ws is equal to the width of the stator slot of the radially ventilated generator, the value of Hs is equal to the radial dimension of the stator slot of the radially ventilated generator, and the value of Hy is equal to the radial dimension of the yoke of the lamination of the stator of the radially ventilated generator. That is to say, before designing the baffle air-cooled generator, the stator of the radially ventilated generator can be optimized, and the optimal structural dimension parameters can be used as the initial parameters of the baffle air-cooled generator stator.

[0089] The steps for optimizing the stator of the radially ventilated generator include the following steps S01 to S06.

[0090] Step S01, determine the temperature limits, which at least include the stator winding temperature Tw and may also include the permanent magnet temperature Tm. Both the stator winding temperature Tw and the permanent magnet temperature Tm at least depend on the insulation class and the permanent magnet grade. For example, for class F insulation, the long-term operating temperature is 155°C. When the N52H grade permanent magnet is applied to an outer-rotor permanent magnet wind generator, a typical critical temperature for irreversible demagnetization under short-circuit conditions is 70°C.

[0091] Step S02, define the axial proportion of the radial ventilation groove 13’ as η3, and give the initial value of η3 according to experience. Typically, for example, the initial value of η3 is 0.1.

[0092] Step S03, perform a scanning optimization on the structural dimensions of the two-dimensional electromagnetic model of the generator stator with the radial ventilation groove 13’ to determine the optimal structural dimension set and the corresponding optimal electromagnetic torque. The optimal dimension set includes parameters such as tooth width, slot width, and slot depth. Typically, the optimization aims to maximize the electromagnetic torque, or multi-objective optimization can also be adopted with objectives such as electromagnetic torque, efficiency, and effective material cost.

[0093] The stator winding temperature Tw and the permanent magnet temperature Tm are respectively assumed to be a value lower than the limit (for determining the material physical property parameters during electromagnetic calculation). For example, according to the above example of temperature limits, assume the stator winding temperature Tw = 140°C and the permanent magnet temperature Tm = 65°C. The temperature here refers to the average temperature used to determine the stator winding resistance, the remanence, and the coercivity of the permanent magnet. Considering that there are temperature gradients in both the stator winding and the permanent magnet (especially in the axial direction), it is necessary to ensure that the highest temperature corresponding to the average temperature still does not exceed the limit.

[0094] In step S03, two methods can be used to approximately consider the influence of the radial ventilation groove 13’ and calculate the electromagnetic torque. The first method is to calculate the electromagnetic torque Te through the two-dimensional electromagnetic model, and then weight it according to η3, that is, Te×λ(1 - η3), where λ is the stator core stacking factor, and the typical value range of λ is 0.95 - 0.99. The second method is to correct the relative magnetic permeability μr of the ferromagnetic material in the two-dimensional electromagnetic model, and then use the corrected relative magnetic permeability for electromagnetic performance calculation. The expression of the corrected μr’ is as follows:

[0095] μ r =λ(1 - η3)μ r +(1 - λ + λη3)μ0

[0096] where μ0 is the vacuum magnetic permeability.

[0097] The second of the above two methods is preferred because the first method cannot consider the edge effect generated by the radial ventilation groove.

[0098] In step S03, η3 is a hypothetical value selected based on experience.

[0099] In step S04, keep the values in the optimal dimension set unchanged and scan η3. For example, the value range of η3 is 0.05 - 0.2, and multiple electromagnetic torques Te corresponding to η3 are obtained.

[0100] In step S05, for the scanned η3 above, establish multiple three - dimensional heat dissipation models and analyze them. Here, it is assumed that the axial dimension of each radial ventilation duct 13’ is a fixed value h3 (h3 is determined according to experience and should be taken as small as possible. Typically, h3 = 5mm, usually limited by the processing and assembly process, structural strength, and flow resistance for the minimum ventilation dimension). Thus, one η3 corresponds to a fixed number n3 of radial ventilation ducts 13’ (n3 calculated according to η3 and h3 may be a decimal, and then it is rounded). And it is assumed that they are evenly distributed axially. The corresponding multiple winding temperatures Tw and multiple permanent magnet temperatures Tm can be calculated. When performing heat dissipation calculations, usually consider the most severe environmental conditions, such as high - temperature and low - wind - speed environments. The above three - dimensional heat dissipation model is typically a CFD model, or it can also be a three - dimensional heat dissipation model established by the thermal network method, etc.

[0101] It should be noted that the cooling medium flow rate Q in the three - dimensional heat dissipation model can be determined according to the pressure - flow characteristic curve of the selected cooling medium driving device (such as a fan), and the cooling cycle pressure drop P depends on Q. Or approximately, according to PQ = cooling device power × efficiency, assuming that the value on the right - hand side of the equation remains unchanged for a selected cooling device, Q and the corresponding P can be iteratively obtained.

[0102] In step S06, the actual winding temperature Tw and permanent magnet temperature Tm are calculated through the heat dissipation model. At this time, there must be a difference from the assumed value of Tw = 140°C in the electromagnetic model. Adjust the copper loss part in the heat dissipation model until Tw = 140°C, and based on copper loss = I 2 R, reverse - deduce the required current I. Then, correct the electromagnetic torque according to the current I to obtain the electromagnetic torque Te at this current. To ensure the rapidity of the calculation, it can be simply assumed that the electromagnetic torque Te is proportional to the current value, so there is no need to iterate with the electromagnetic model. Based on the above calculation results, determine the optimal value of the electromagnetic torque and its corresponding structure dimension set as the initial parameters for the design of the cross - flow air - cooled generator.

[0103] Step S2 includes step S21 and step S22.

[0104] In step S21, in the three - dimensional heat dissipation model of the cross - flow air - cooled generator (refer to Figure 13) Among them, when determining Nz as the initial value according to the second parameter, the maximum current Imax that can be loaded corresponding to each Wz and not higher than the maximum temperature limit of the generator is determined. Among them, a group (Nz, Wz) corresponds to a maximum current Imax, and a total of m maximum currents Imax are obtained. Among them, except for Wz = 0, and Hex is set as a fixed value. That is to say, running m simulations in the three-dimensional heat dissipation model can obtain m maximum currents Imax. The second parameter includes Wz, Hex, the axial dimension Lz of the ventilation gap, the number Nz of ventilation gaps in the axial direction, and the resistance R of the stator winding. Among them, Wz ≠ 0, and its value is the remaining values except Wz = 0 in step S1; Lz is set as a fixed value and Lz ≠ 0; Nz is set as a variable, Nz ≠ 0, and an initial value is given to Nz. The setting of Nz describes that the laminated core is divided into a first laminated core and a second laminated core. Among them, the first laminated core corresponds to non-zero values of Wz and Hex. That is, the first laminated core is provided with a ventilation gap 400, an opening 500, and a slot connecting hole 600. The second laminated core corresponds to zero values of Wz and Hex. That is, the second laminated core is not provided with a ventilation gap 400, an opening 500, and a slot connecting hole 600. In this step, the heat source loaded in the three-dimensional heat dissipation model is determined by the initial current I in step 1 and the resistance R of the stator winding.

[0105] The stator winding is the armature winding of a rotor-type permanent magnet wind generator. The resistance R of the stator winding can be determined according to parameters such as the size and number of turns of the stator winding and the winding temperature. The temperature value of the stator winding should be less than or equal to the maximum temperature limit of the generator. Therefore, the maximum temperature limit of the generator can be determined according to the temperature value of the stator winding.

[0106] In step S22, according to the m maximum currents Imax, the set TemA of electromagnetic torques obtained in step 1, the axial proportion η1 of the first laminated core, and the axial proportion η2 of the second laminated core, determine the set TemB of (m × n) electromagnetic torques protected under the initial value of Nz. According to Nz, the axial proportion η1 of the first laminated core and the axial proportion η2 of the second laminated core can be determined.

[0107] Specifically, under the condition that Nz takes the initial value, after weighting and adding according to the axial proportion η1 of the first laminated core and the axial proportion η2 of the second laminated core, an uncorrected electromagnetic torque TemA' under multiple non-zero (Wz, Hex) number pairs is obtained.

[0108] According to the linear proportional relationship between the m maximum currents Imax determined in step S21 and the initial current I, each electromagnetic torque in the electromagnetic torque set TemA' is enlarged or reduced according to the proportional relationship between the corresponding maximum current Imax and the initial current I, so as to obtain the electromagnetic torque set TemB corresponding to each non-zero (Wz, Hex) array and corrected by temperature.

[0109] It should be noted that for different Nz values, the maximum current Imax is different, and the linear proportional relationship between each maximum current Imax and the initial current I may be different. That is to say, for a part of the electromagnetic torques in the electromagnetic torque set TemB, the proportional relationship may be enlarged or reduced, and the specific proportional values for enlargement or reduction are also different.

[0110] In one embodiment, the initial value of Nz can be set according to experience. For example, the initial value of Nz can be determined according to the principle of equal flow area of the radial ventilation slots of the stator of a radially ventilated generator, or according to the principle of equal heat dissipation area.

[0111] In step S22, after weighting and adding according to the axial proportion η1 of the first lamination and the axial proportion η2 of the second lamination, the uncorrected-by-temperature electromagnetic torque TemA' under each (Wz, Hex) pair is obtained, specifically including:

[0112] According to Nz, the axial proportion η1 of the first lamination and the axial proportion η2 of the second lamination can be determined, and thus the axial proportion η1 of the first lamination and the axial proportion η2 of the second lamination under the initial value of Nz can be determined.

[0113] Find the corresponding electromagnetic torques Tem1 and Tem2 in the set Tem A, then the electromagnetic torques Ta in TemA' can be determined, Ta = Tem1 * η1 + Tem2 * η2. Wherein, Tem1 is the electromagnetic torque corresponding to the non-zero (Wz, Hex) in the electromagnetic torque set TemA, Tem2 is the electromagnetic torque corresponding to (0, 0) in the electromagnetic torque set TemA, and the electromagnetic torques in the electromagnetic torque set TemA' are obtained by weighting through the proportion relationship of η1 and η2. Among them, the non-zero (Wz, Hex) value corresponds to the first lamination, and (0, 0) corresponds to the second lamination. η1 + η2 = 1. For example, in one embodiment, η1 = 0.3, η2 = 0.7; for the first lamination (Wz, Hex) = (2.6 mm, 40 mm), and for the second lamination (Wz, Hex) = (0, 0), then the electromagnetic torque corresponding to (Wz, Hex) = (2.6 mm, 40 mm) in TemA' = 7.555 * 0.7 + 6.672 * 0.3 = 7.290. In this way, the electromagnetic torques in the set TemA' can be determined in sequence. Table 2 shows the electromagnetic torques in the set TemA'.

[0114] Table 2

[0115]

[0116] After obtaining the set TemA', each electromagnetic torque in the set TemA' is enlarged or reduced according to the proportional relationship between the maximum current Imax corresponding to each and the initial current I, so as to obtain a set TemB of temperature-corrected electromagnetic torques corresponding to each (Wz, Hex) array.

[0117] In one embodiment, in step S2, Hex is set to a fixed value and a non-zero minimum value is set. For example, Hex = 40 mm. In the three-dimensional heat dissipation model analysis, the influence of Hex on the results is small. Therefore, setting Hex to a fixed value in the three-dimensional heat dissipation model can reduce the computational amount of each round of iteration from m * n to m. Moreover, the dimensional change during the process of changing the flow direction of the cooling gas is small, the fluid simulation accuracy is relatively high, and the convergence is good. However, it should be noted that the number of electromagnetic torques in the set TemB of electromagnetic torques is (m × n).

[0118] In one embodiment, in step S2, the value of Lz can be determined according to the height of the radial ventilation slots of the stator of the radial ventilation type generator. For example, the value of Lz can be equal to the height of the radial ventilation slot 13' of the stator of the radial ventilation type generator.

[0119] In one embodiment, in step S2, the value of Nz can be determined according to the principle of equal flow area or equal heat dissipation area of the radial ventilation slots 13' in the stator of the radial ventilation type generator. On the premise that the value of Lz is a fixed value, Nz can be calculated according to the principle of equal flow area or equal heat dissipation area. For example, define the flow area of the ventilation gap 400 as FA and the heat dissipation area as HA. Specifically, the flow area of each ventilation gap 400 refers to the average value of the cross-sectional areas at both ends of the ventilation gap 400, and the heat dissipation area of each ventilation gap 400 refers to the four contact surfaces between the cooling medium A and the ventilation gap 400, including three contact surfaces with the stator core 100 and one contact surface with the stator winding 102. The corresponding concepts of FA and HA are also applicable to Figure 14 the radial ventilation slots of the stator of the radial ventilation type generator shown in, the difference is only that the flow area of each radial ventilation slot is the average value of the cross-sectional areas at both ends of the tooth part of the ventilation slot, and the four contact surfaces are two contact surfaces with the stator core and two contact surfaces with the winding.

[0120] Equal flow area means: the number of radial ventilation slots × the flow cross-sectional area (tooth part) of the radial ventilation slot = the number of ventilation gaps × the cross-sectional area of the ventilation gap.

[0121] Equal heat dissipation area means: the number of radial ventilation slots × the total contact area of the tooth part of the radial ventilation slot with the stator core and the stator winding = the number of ventilation gaps × the total contact area of the tooth part of the baffle ventilation slot with the stator core and the stator winding.

[0122] Step S3: Adjust the value of Nz. According to the determination method of each electromagnetic torque in the electromagnetic torque set TemB in step S2, determine the optimal value of Nz and the optimal electromagnetic torque under each (Wz, Hex) combination, so as to obtain a set TemC containing (m×n) optimal electromagnetic torques. Further determine the global optimal solution including Wz, Hex, and Nz according to the set TemC of the optimal electromagnetic torque.

[0123] Before step S3, Nz is a given initial value. Under the condition that Nz is the initial value, there are deviations in the values of the electromagnetic torques in the electromagnetic torque set TemB, which are not the optimal values. The purpose of adjusting the size of Nz is to find the optimal Nz corresponding to each non-zero (Wz, Hex) value and the optimal electromagnetic torque corresponding to the optimal Nz, so as to determine the global optimal solution of Wz, Hex, and Nz. In step S3, adjust the size of Nz. The adjustment method can first gradually increase from the initial value and then gradually decrease from the initial value. Or, first gradually decrease from the initial value and then gradually increase from the initial value, and the order is not limited.

[0124] Adjusting the value of Nz is equivalent to adjusting the axial proportion η1 of the first stack and the axial proportion η2 of the second stack. Correspondingly, each electromagnetic torque in TemA’ changes, and m maximum currents Imax change. Therefore, each electromagnetic torque in the electromagnetic torque set TemB changes, and thus re-determine a set TemC containing (m×n) optimal electromagnetic torques. Each electromagnetic torque in the set TemC of the optimal electromagnetic torque is the electromagnetic torque that satisfies the maximum temperature limit of the generator and has the largest value.

[0125] In one embodiment, the method for adjusting Nz specifically includes:

[0126] Set Nz to increase round by round from the initial value. According to each Nz, determine whether the electromagnetic torque corresponding to each (Wz, Hex) changes as Nz increases. If the increase of Nz in this round still causes the electromagnetic torque corresponding to a certain group (Wz, Hex) to continue to increase, then increase the Nz corresponding to this group (Wz, Hex) in the next round. Otherwise, no longer increase Nz for this group (Wz, Hex) in the subsequent rounds until the remaining group is an empty set, that is, the electromagnetic torques corresponding to all (Wz, Hex) no longer increase, that is, determine the optimal Nz corresponding to each group (Wz, Hex) in the increasing direction of Nz.

[0127] In this step, if increasing Nz still causes the electromagnetic torques corresponding to several (Wz, Hex) to continue to increase, it means that the electromagnetic torque corresponding to this group (Wz, Hex) is not yet optimal. Until the increase of Nz makes the electromagnetic torque corresponding to this group (Wz, Hex) unchanged or decreased, the optimal value of Nz can be determined. Among them, each group (Wz, Hex) corresponds to an optimal Nz.

[0128] In step S3, the method for adjusting Nz may further include:

[0129] Set Nz to decrease round by round from the initial value, and determine whether the electromagnetic torque corresponding to each (Wz, Hex) changes as Nz decreases. If the decrease of Nz in this round still causes the electromagnetic torque of a certain group (Wz, Hex) to continue to increase, then in the next round, still decrease Nz corresponding to this group (Wz, Hex). Otherwise, in subsequent rounds, no longer decrease Nz for this group (Wz, Hex) until the remaining group is an empty set, that is, the electromagnetic torque corresponding to all (Wz, Hex) no longer increases, that is, the optimal Nz corresponding to each group (Wz, Hex) in the decreasing direction of Nz is determined.

[0130] In this step, when Nz decreases round by round from the initial value, if the decrease of Nz still causes the electromagnetic torque corresponding to a certain group (Wz, Hex) to continue to increase, it means that the electromagnetic torque corresponding to this group (Wz, Hex) is not yet optimal. Until the decrease of Nz makes the electromagnetic torque corresponding to all groups (Wz, Hex) unchanged or decreased, the optimal value of Nz is determined. Among them, each group (Wz, Hex) corresponds to an optimal Nz.

[0131] When the sequential scan of Nz from large to small or from small to large is completed, the set TemC containing (m×n) optimal electromagnetic torques can be determined. From the set TemC, the global optimal solution including Wz, Hex, and Nz can be determined. The Wz, Hex, and Nz including the global optimal solution can be used as the design data of the flow deflecting air duct of the generator stator.

[0132] The above are only the preferred embodiments of the present application and are not intended to limit the present application. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present application shall be included within the scope of protection of the present application.

Claims

1. A design method for a baffled air-cooled generator, characterized in that, The design method includes the following steps: Step S1: Load an initial current I into the two-dimensional electromagnetic model of the baffled air-cooled generator, and determine a set TemA of (m + 1)×(n + 1) electromagnetic torques according to the first parameters. The first parameters include: Wz: The dimension of the unilateral ventilation gap in the tooth width direction, set as a variable with m + 1 values, including Wz = 0. Hex: The radial dimension of the through holes in the laminated yoke, set as a variable with n + 1 values, including Hex = 0. Ws: The width of the stator slots, set as a fixed value. Hs: The radial dimension of the stator slots, set as a fixed value. Hy: The radial dimension of the laminated yoke, set as a fixed value. Step S2: In the three-dimensional heat dissipation model of the baffled air-cooled generator, determine the maximum current Imax that can be loaded corresponding to each Wz when Nz is at the initial value and does not exceed the maximum temperature limit of the generator according to the second parameters. Among them, one set of Nz and Wz corresponds to one maximum current Imax, and a total of m maximum currents Imax are obtained, excluding Wz = 0. Determine a set TemB of (m×n) electromagnetic torques at the initial value of Nz according to the m maximum currents Imax, the set TemA of electromagnetic torques determined in step S1, the axial proportion η1 of the first lamination, and the axial proportion η2 of the second lamination. The second parameters include: R: The resistance of the stator winding. Lz: The dimension of the ventilation gap in the axial direction of the stator core, set as a fixed value. Nz: The number of ventilation gaps in the axial direction of the stator core, set as a variable and given an initial value. Wz: Its values are all the values in step S1 except Wz = 0. Hex: Set as a fixed value. Step S3: Adjust the value of Nz. According to the method for determining each electromagnetic torque in the set TemB in step S2, determine the optimal value of Nz and the optimal electromagnetic torque for each combination of (Wz, Hex), so as to determine a set TemC of (m×n) optimal electromagnetic torques, and further determine the global optimal solution including Wz, Hex, and Nz according to the set TemC of optimal electromagnetic torques.

2. The design method of the baffled air-cooled generator according to claim 1, characterized in that In step S1, the value range of Wz is: 0 ≤ Wz ≤ h, and the value of Wz gradually increases from zero to the height value h of the ventilation gap in the axial direction; and / or The value range of Hex is: d ≤ Hex ≤ d + h, where d is the radial dimension d of the yoke of the second lamination, and h is the height of the ventilation gap in the axial direction.

3. The design method of the baffle air-cooled generator according to claim 1, characterized in that In step S1, the initial current I is estimated according to the maximum envelope size of the generator or an empirical value.

4. The design method of the baffled air-cooled generator according to claim 1, characterized in that In step S1, the width Ws of the stator slots, the radial dimension Hs of the stator slots, and the radial dimension Hy of the laminated yoke are determined one by one according to the width of the stator slots, the radial dimension of the stator slots, and the radial dimension of the laminated yoke of the radial ventilation generator.

5. The design method of the baffle air-cooled generator according to claim 1, characterized in that, In step S2, Hex is set as a fixed value and set as the non-zero minimum value.

6. The design method of the baffled air-cooled generator according to claim 1, characterized in that In step S2, the value of Lz is determined according to the height of the radial ventilation slots of the radially ventilated generator.

7. The design method of the baffled air-cooled generator according to claim 1, characterized in that In step S2, the initial value of Nz is determined according to the principle of equal flow area or equal heat dissipation area of the radial ventilation slots of the radially ventilated generator.

8. The design method of the baffle air-cooled generator according to claim 1, characterized in that, In step S2, the method for determining the set TemB of electromagnetic torques specifically includes: At the initial value of Nz, for each (Wz, Hex) combination in the set TemA, after weighting according to the axial proportion η1 of the first lamination and the axial proportion η2 of the second lamination and adding them together, a set TemA' of uncorrected electromagnetic torques corresponding to each non-zero (Wz, Hex) is obtained. According to the linear proportional relationship between the maximum current Imax and the initial current I, each electromagnetic torque in the set TemA' is enlarged or reduced by the same proportional relationship, so as to obtain each electromagnetic torque in the set TemB.

9. The design method of the baffled air-cooled generator according to claim 1, characterized in that, In step S2, the method for adjusting the value of Nz includes: It is set that Nz increases round by round from the initial value. According to each Nz, it is determined whether the electromagnetic torque corresponding to each group (Wz, Hex) changes as Nz increases. If the increase of Nz in this round still makes the electromagnetic torque of a certain group (Wz, Hex) continue to increase, then in the next round, Nz corresponding to this group (Wz, Hex) is still increased. Otherwise, in the subsequent rounds, Nz of this group (Wz, Hex) is no longer increased until the remaining group is an empty set, that is, the optimal Nz corresponding to each group (Wz, Hex) in the increasing direction of Nz is determined.

10. The design method of the baffled air-cooled generator according to claim 9, characterized in that, It is set that Nz decreases round by round from the initial value. According to each Nz, it is determined whether the electromagnetic torque corresponding to each group (Wz, Hex) changes as Nz decreases. If the decrease of Nz in this round still makes the electromagnetic torque of a certain group (Wz, Hex) continue to increase, then in the next round, Nz corresponding to this group (Wz, Hex) is still decreased. Otherwise, in the subsequent rounds, Nz of this group (Wz, Hex) is no longer decreased until the remaining group is an empty set, that is, the optimal Nz corresponding to each group (Wz, Hex) in the decreasing direction of Nz is determined.

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