Large-scale hydroelectric generator stator winding confluence copper ring arrangement scheme solving algorithm
By employing a greedy algorithm and an improved DFS algorithm, the complexity of arranging the copper rings for the stator of a large hydroelectric generator was solved, enabling the automated generation of the copper ring paths, reducing design difficulty and cost, and improving production efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHINA THREE GORGES UNIV
- Filing Date
- 2025-12-11
- Publication Date
- 2026-04-28
AI Technical Summary
The stator busbar copper ring structure of large hydroelectric generators is complex, and manual design is difficult to meet the constraints and determine whether the design scheme is optimal, resulting in high design difficulty and increased cost, and there is a lack of automated generation methods.
By employing a greedy algorithm and an improved DFS algorithm, and taking the minimum total length of the copper ring as the objective function, and transforming the clamp constraints through quantitative mathematical formulas, an algorithm for solving the copper ring arrangement scheme of the stator winding of a large hydroelectric generator is designed to achieve the automatic generation of the copper ring path.
It has enabled the automated generation of copper ring solutions, significantly shortened the design cycle, reduced material costs, improved production efficiency and product quality, and laid the foundation for the design of fully automated production lines.
Smart Images
Figure CN121935455A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of intelligent algorithms, specifically to an algorithm for solving the arrangement scheme of the busbar copper rings in the stator winding of a large hydroelectric generator. Background Technology
[0002] The arrangement of the stator busbar copper ring structure in large hydroelectric generators is a crucial aspect of generator design. Each phase of the generator stator winding typically contains multiple parallel branches. After the stator bars of each branch are wound in the stator slots, the two ends of the stator bars of each parallel branch need to be connected to the corresponding outlet through a copper ring externally. However, the number of channel holes in the copper ring support clamp is limited, and the large number of parallel branches in each phase of the stator winding of large hydroelectric generators results in numerous and complex combination schemes for the busbar outlet and neutral point outlet.
[0003] Of all possible solutions, the vast majority fail to meet the clamp constraints. Furthermore, due to the numerous and complex constraints, it is difficult to determine whether a design can meet the overall constraints in the early stages of manually designing the generator busbar copper ring structure. This can easily lead to situations where the winding circuit design fails to meet the constraints in the later stages, or even if it does meet the constraints, it is difficult to determine whether the design is optimal or near-optimal. Consequently, the difficulty and time cost of manually designing and drawing a reasonable busbar scheme increase dramatically.
[0004] A well-designed copper ring busbar scheme can reduce the material cost of motors. Furthermore, with the increasing prevalence of automation, researching an automatic generation method for the copper ring structure arrangement of stator busbars in large hydroelectric generators can advance the design of fully automated production lines for motors, achieving automation and intelligence in the production process. This not only improves production efficiency and product quality but also reduces manual intervention and production costs. Therefore, combining computer technology and intelligent solution algorithms to study an automatic generation method for copper ring structure arrangement is of great significance for reducing the design difficulty and production cost of large hydroelectric generators, improving design efficiency, and promoting the automated and intelligent production of large hydroelectric generators.
[0005] The busbar copper ring structure layout scheme consists of four parts: the initial positions at both ends of each parallel branch, the positions of the six busbar outlets, the direction of copper ring rotation around the stator, and the arrangement of the copper ring channel holes.
[0006] Each parallel branch has two ends as the starting point of the copper ring. Therefore, the starting position of the copper ring is determined by the parameters of the generator itself. The generator stator is approximately cylindrical. The copper ring is selected at the starting point through a copper ring channel hole, and is wound through a clamp to the corresponding outlet. The copper ring channel hole cannot be changed midway. There are only two rotation directions: clockwise and counterclockwise. The overall copper ring busbar scheme must satisfy the clamp constraints. The rotation direction of the copper ring and the arrangement of the copper ring channel holes are extremely complex combinatorial optimization and integer programming problems. It is not difficult to prove that the copper ring structure arrangement problem of the stator busbar of a large hydroelectric generator is also an NP-complete problem. Its complexity increases exponentially with the increase of parallel branches per phase of the generator stator winding, but it is possible to verify whether a solution is feasible in polynomial time.
[0007] Current research on the structural arrangement of the stator busbar copper rings in large hydroelectric generators mainly focuses on simulation analysis of the stress and heat generation of the copper rings, with very few studies on intelligent algorithms for automatically generating busbar schemes. Although scholars in various fields have proposed effective solutions for other specific combinatorial optimization and integer programming problems, the models and solution methods for the optimization arrangement of the stator busbar copper rings in large hydroelectric generators still need further in-depth research. This project will, based on existing research, establish a mathematical model for the optimization arrangement of the stator busbar copper rings in large hydroelectric generators, and propose an efficient algorithm for automatically generating busbar schemes using a greedy algorithm and an improved DFS algorithm to adapt to different requirements. Based on the above methods, the optimization arrangement problem of the stator busbar copper rings in large hydroelectric generators can be effectively solved using computers. Summary of the Invention
[0008] This invention proposes an algorithm for solving the arrangement scheme of the busbar copper rings in the stator winding of a large hydroelectric generator. The method includes the following steps: S1. Clarify the NP-complete problem attributes of the stator busbar copper ring arrangement of large hydroelectric generators, sort out the five types of core constraints of the clamps, define key parameters such as the number of stator slots and the number of parallel branches per phase, establish quantitative standards such as slot coordinate system and binary representation of rotation direction, and calculate basic data such as the starting position of copper ring and ideal total length.
[0009] S2. Taking the minimum total length of the copper rings as the objective function, the wire clamp constraint is transformed into a quantitative mathematical formula. An auxiliary function is used to determine whether the copper ring path meets the requirements. An RFA matrix is constructed to represent the compatibility of the two copper ring constraints. Key parameters such as the arrangable state of the copper rings and the remaining arrangable quantity after additional copper rings are arranged are calculated.
[0010] S3. Design a greedy algorithm and an improved DFS algorithm that combines the greedy algorithm. The greedy algorithm prioritizes arranging copper rings layer by layer with the least impact on other copper rings, which is suitable for small-scale motors. The improved DFS algorithm first obtains the approximate maximum copper ring capacity as a reference through the greedy algorithm to narrow the search range, and then accurately searches for the maximum capacity copper ring combination in each layer to adapt to large-scale motors, and iteratively optimizes the scheme.
[0011] S4. Based on the measured data of two large hydroelectric generators with different parameters, the algorithm was tested. The total length of the copper rings of the original scheme and the solution scheme was compared to verify that the algorithm satisfies the clamp constraint and the solution result is close to the ideal optimal value. The final copper ring arrangement scheme that takes into account both length optimization and solution efficiency was output.
[0012] In the preferred embodiment, the five core constraints of the wire clamp in step S1 include: the copper ring channel hole cannot be reused; each layer of the wire clamp and each bus outlet can carry a maximum number of copper rings; the copper ring cannot be replaced with a copper ring channel hole in another position midway; when the copper ring is wound using the outer row of copper ring channel holes, the inner row of copper ring channel holes of the first wire clamp used must be available and will occupy the inner row of copper ring channel holes of the first wire clamp used; when the copper ring is wound using the inner row of copper ring channel holes, the outer row of copper ring channel holes of the last wire clamp used must be available and will occupy the outer row of copper ring channel holes of the last wire clamp used.
[0013] In the preferred embodiment, the specific method for defining the number of stator slots in step S1 is as follows: when representing information such as the starting point, the ending point, and the copper ring path, position information will be used. Based on the specific characteristics of the problem, the solution establishes a slot coordinate system and defines the position using the stator slot number. Looking down at the generator stator, the slot number on the right side is defined as slot 1. Following industry practice, each slot is numbered clockwise from smallest to largest until the last slot.
[0014] In the preferred embodiment, the quantification standard of the rotation direction in step S1 is as follows: For a copper ring, the only selectable rotation directions are clockwise or counterclockwise. This paper uses binary to represent the rotation direction of the copper ring, where 0 represents counterclockwise rotation and 1 represents clockwise rotation. Considering that there are only two rotation directions for the copper ring, according to the definition of the superior and inferior arcs of a circle, the clockwise direction with the shorter winding distance is called the superior direction, and the clockwise direction with the longer winding distance is called the inferior direction. If the two are of equal length, then both clockwise directions are called the superior direction.
[0015] In a preferred embodiment, the quantification standard for the numbering of the copper ring channel holes in step S1 is specifically as follows: for wire clamps, there are a total of There are 10 copper ring channel holes, where row represents the total number of wire clamp layers and column represents the total number of wire clamp columns. The column closest to the stator is defined as the starting column, denoted as column 1. Column numbers increase progressively away from the stator. Starting from layer 1, the copper ring channel hole layers increase progressively upwards from the bottom of the wire clamp. Based on the definition of copper ring channel hole layers and columns, the p-th layer and q-th column copper ring channel hole are denoted as the p-th... One copper ring channel hole.
[0016] In the preferred embodiment, the formula for the objective function in step S2 is: ; Where mingap is the total length of the copper ring in the known shortest solution, and its initial value is... Where Z is the number of stator slots, This represents the number of parallel branches per phase. In this scheme, a copper ring must be used to connect the current to its corresponding outlet at any starting point. The formula is as follows: ; Among them, select_row i，j The algorithm calculates the number of wire interlayers where the j-th copper ring of phase i is located; if it is not arranged, the value is -1. The quantitative mathematical formula for the clamp constraint condition is as follows: ; ; Among them, out_capacity layer，i `select_column` represents the number of copper rings that can be led out from each bus outlet of each layer of the clamp, `capacity` represents the maximum copper ring capacity that can be led out from each bus outlet of each layer of the clamp, and `select_column` represents the number of copper rings that can be led out from each bus outlet of each layer of the clamp. n，p The algorithm calculates the number of columns in the line clamp of the p-th copper ring of n phases. If it is not arranged, the value is -1. `slect_column` q，r Similarly, select_row q，r With slect_row i，j Similarly, RFA arr,t,g When the starting bar of the winding is arr, and the t-th copper ring has already been arranged, the situation where the g-th copper ring can successfully charge using clockwise and counterclockwise rotation is represented in binary: 0b11 for both clockwise and counterclockwise rotation, 0b10 for only clockwise rotation, 0b01 for only counterclockwise rotation, and 0b00 for neither clockwise nor counterclockwise rotation.
[0017] In the preferred embodiment, the specific steps of the improved DFS algorithm in step S3 are as follows: S3.1 Given the number of stator slots Z of the motor and the number of parallel branches a per phase, the starting position data of the first group is denoted as... The terminal position of the j-th copper ring in phase i Total number of layers in the clamp (row); Total number of columns in the clamp (column); S3.2 Calculation based on FPA matrix calculation method The matrix is used to calculate the total length of the copper ring in the ideal solution. and starting point data for each group ; S3.3 Set layer=0, and randomly select a number less than Z to assign... And initialize all kinds of parameters; Where layer∈[0, row] represents the current number of online mezzanine layers, Z is the number of stator slots, and arr is the number of data groups for the selected winding starting point; S3.4 Let layer = layer + 1. If layer > row, then proceed to step S3.14; otherwise, proceed to step S3.5. S3.5 Calculate the approximate maximum number of copper rings that the current layer can accommodate using a greedy algorithm: greedy_number; S3.6 Let DFS_number=greedy_number, deep_floor=0, ∀k∈[0,2*6a*column), s∈[0,6a), let deep_slect k =0, deep_current s,k =0; Where DFS_number is the maximum number of copper rings that the current layer can accommodate, deep_floor is the depth order of the improved DFS algorithm, and deep_select is the maximum number of copper rings that the current layer can accommodate. k Assign the maximum number of copper ring combinations in history to the current layer, deep_current s,k To arrange copper rings in a certain layer of order s, deep_slect k and deep_current s,k This value is 1 when assigned, and 0 otherwise. S3.7∀k∈[0,2*6a*column), s∈[0,deep_floor), if deep_current s,k =1 and select_row i,j =layer, then record the parameters of the k-th type of copper ring dir i，j slect_column i，j slect_row i,j =layer, if deep_current s,k =0 and select_row i,j=layer, then initialize all parameters of the k-th type of copper ring, and calculate use regardless of any condition. k ; Among them, use k This indicates whether the k-th copper ring can be arranged given that there are already copper rings arranged in the current layer. The value is 1 if it can be arranged, and 0 otherwise. S3.8 Let u = -1; S3.9 Let u = u + 1. If u ≥ 2 * 6a * column, then proceed to step S3.12; otherwise, proceed to step S3.10. S3.10 If survive u +deep_floor+1≥DFS_number, then let DFS_number=survive u +deep_floor+1, execute step S3.11; if not satisfied, execute step S3.9. Among them, survival u Its initial value is 0, indicating the number of copper rings that can be arranged after the uth copper ring is added, given that there are already copper rings arranged in the current layer. S3.11 Let deep_current deep_floor,u =1, deep_floor=deep_floor+1, ∀k∈[0,2*6a*column), deep_slectk= use k =use_next u,k Proceed to step S3.8; Among them, use_next u,k Given that copper rings are already arranged in the current layer, this is the case where additional copper ring u is arranged, and the remaining k copper rings can be arranged. If they can be arranged, this value is 1, otherwise it is 0. S3.12 If deep_floor-1 < 0, then proceed to step S3.13. If not, then let deep_floor = deep_floor-1. There must exist k ∈ [0, 2*6a*column) such that deep_current deep_floor,k =1, let deep_current deep_floor,k =0, u=k, execute step S3.9; S3.13∀k∈[0,2*6a*column), if deep_slect k =1, then record the parameters of this copper ring dir i，j slect_column i，j slect_row i,j=The layer is added to the current layout scheme, and step S3.4 is executed; S3.14 Determine if select_row exists i,j =-1, if it does not exist, calculate the total length of the copper rings in the current calculation scheme, total_gap, and execute step S3.15; if it exists, execute step S3.16. S3.15 Determine whether mingap > total_gap. If it is satisfied, record all parameters of the current calculation scheme and record this scheme as the optimal scheme. S3.16 Determine whether the maximum number of iterations (total_number) specified by the algorithm has been reached. If it is, exit the operation and output the optimal solution. If it is not, execute step S3.3.
[0018] In the preferred embodiment, the formula for calculating the total length of the ideal copper ring in step S3.2 is: ; ; Among them, ideal arr The total length of the copper ring under ideal conditions when the winding start point data is selected as the arr group; st arr,i,j The starting position of the j-th copper ring in phase i when the winding start-point data is selected as the arr group; out i,j This is the location of the terminal point of the j-th copper ring in phase i.
[0019] In the preferred embodiment, the formula for calculating the total length of the copper rings in step S3.14 is as follows: ; ; Where Z is the number of stator slots; dir i,j , a 0-1 decision variable, represents the rotation direction of the j-th copper ring in phase i; gap i,j Let be the length of the j-th copper ring in phase i.
[0020] In the preferred embodiment, the survival in step S3.10 u The calculation formula is: ; Among them, use_next u,k Given that copper rings are already arranged in the current layer, this value represents the situation where copper ring number u is to be added, and the remaining copper rings number k can be arranged. If they can be arranged, this value is 1; otherwise, it is 0.
[0021] The parameters mentioned in the method of this invention are shown in Table 1.
[0022]
[0023]
[0024] Table 1 In this context, "%" represents the remainder, " / " represents the integer part, >> represents right shift, and << represents left shift.
[0025] Compared with the prior art, the beneficial effects of the present invention include: (1) The algorithm of this scheme solves the pain points of difficulty in judging feasibility in the early stage and the possibility of substandard schemes or failure to lock the optimal solution when manually designing bus copper ring schemes due to complex constraints. It realizes the automatic generation of bus schemes, greatly shortens the design cycle, and reduces the trial and error cost and professional threshold of manual design.
[0026] (2) The algorithm of this scheme aims to minimize the total length of the copper ring, combining the advantages of the greedy algorithm and the improved DFS algorithm: the greedy algorithm can quickly obtain a high-quality scheme for small-scale motors, while the improved DFS algorithm can adapt to large-scale motors and accurately approximate the ideal optimal value. According to actual tests, the total length of the copper ring in the optimized scheme is significantly lower than that in the original scheme, and it satisfies all wire clamp constraints, effectively reducing the use of copper materials in the motor and reducing material costs.
[0027] (3) The algorithm of this scheme realizes the automatic solution of the bus copper ring arrangement scheme by computer, which provides core technical support for the design of fully automatic production line of large hydropower generator, reduces manual intervention in the production process, improves production efficiency and product quality stability, and lays a technical foundation for the transformation of the motor industry to intelligent manufacturing. Attached Figure Description
[0028] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0029] Figure 1 This is an overall flowchart of the method of the present invention.
[0030] Figure 2 This is a structural diagram of the generator stator clamp.
[0031] Figure 3 This is a diagram illustrating the calculation method for auxiliary functions.
[0032] Figure 4 For RFA arr,k,l Matrix calculation method diagram.
[0033] Figure 5 For copper rings, use is possible. k Calculation method diagram. Detailed Implementation
[0034] The algorithm for solving the stator winding busbar arrangement scheme of a large hydroelectric generator described in this invention is illustrated in the following flowchart: Figure 1 As shown, the specific steps are as follows: S1. Clarify the NP-complete problem attributes of the stator busbar copper ring arrangement of large hydroelectric generators, sort out the five types of core constraints of the clamps, define key parameters such as the number of stator slots and the number of parallel branches per phase, establish quantitative standards such as slot coordinate system, rotation direction, distance, and copper ring channel hole number, and calculate basic data such as the starting position of the copper ring and the ideal total length.
[0035] like Figure 2 The diagram shows a stator winding of a large hydroelectric generator, using 7 layers and 2 rows of clamps. After the stator bars are wound in the stator slots, copper rings are used to connect the ends of the stator bars before being introduced into the clamps. The copper rings are then channeled to their corresponding outlets. The copper rings are typically supported by multiple clamps arranged around the perimeter. Each clamp contains multiple layers and rows of copper ring channel holes, and the copper rings must pass through the same channel holes in each clamp. Because the distance between the copper ring channel holes must meet electrical safety requirements, when the copper ring is introduced from the bar into the clamp, it is first introduced to the same height as the selected copper ring channel hole, and then horizontally connected to the copper ring channel hole. Similarly, when the copper ring is led out of the clamp, it is first led horizontally out of the clamp area, and then connected to the outlet. The outlet arrangement is as follows: Figure 2 As shown, the three phases are horizontally parallel and in fixed positions. The parallel branch leads of each phase are symmetrically arranged and connected together by a special device. During the copper ring connection process, there must be no path collision.
[0036] By studying the operation process of the copper ring introducing the clamp and finally the current to the bus outlet, as well as the comprehensive electrical safety requirements, it can be seen that the constraints considered in this problem can be described as the following five requirements, collectively referred to as clamp constraints, and any feasible copper ring bus structure arrangement scheme should meet the following constraints.
[0037] (1) The copper ring channel hole cannot be reused.
[0038] (2) The number of copper rings that each layer of the clamp can carry at each bus outlet has a maximum value.
[0039] (3) The copper ring cannot be replaced with a copper ring channel hole in another position midway.
[0040] (4) When the copper ring is wound using the outer row of copper ring channel holes, the inner row of copper ring channel holes of the first clamp must be available and will occupy the inner row of copper ring channel holes of the first clamp used.
[0041] (5) When the copper ring is wound using the inner row of copper ring channel holes, the outer row of copper ring channel holes of the last clamp used must be available and will occupy the outer row of copper ring channel holes of the last clamp used.
[0042] The specific method for defining the number of stator slots in step S1 is as follows: When representing information such as the starting point, ending point, and copper ring path, position information will be used. Based on the specific characteristics of the problem, a slot coordinate system will be established, and the position will be defined by the stator slot number. Looking down at the generator stator, the slot number on the right side will be defined as slot 1. Following industry practice, each slot will be numbered clockwise from smallest to largest until the last slot.
[0043] The quantification standard for the rotation direction in step S1 is as follows: For a copper ring, the only selectable rotation directions are clockwise or counterclockwise. This paper uses binary to represent the rotation direction of the copper ring, where 0 represents counterclockwise rotation and 1 represents clockwise rotation. Considering that there are only two rotation directions for the copper ring, according to the definition of the superior and inferior arcs of a circle, the clockwise direction with the shorter winding distance is called the superior direction, and the clockwise direction with the longer winding distance is called the inferior direction. If the two are of equal length, then both clockwise directions are called the superior direction.
[0044] The quantification standard for the numbering of the copper ring channel holes in step S1 is as follows: For wire clamps, there are a total of There are 10 copper ring channel holes, where row represents the total number of wire clamp layers and column represents the total number of wire clamp columns. The column closest to the stator is defined as the starting column, denoted as column 1. Column numbers increase progressively away from the stator. Starting from layer 1, the copper ring channel hole layers increase progressively upwards from the bottom of the wire clamp. Based on the definition of copper ring channel hole layers and columns, the p-th layer and q-th column copper ring channel hole are denoted as the p-th... One copper ring channel hole.
[0045] S2. Taking the minimum total length of the copper rings as the objective function, the wire clamp constraint is transformed into a quantitative mathematical formula. An auxiliary function is used to determine whether the copper ring path meets the requirements. An RFA matrix is constructed to represent the compatibility of the two copper ring constraints. Key parameters such as the arrangable state of the copper rings and the remaining arrangable quantity after additional copper rings are arranged are calculated.
[0046] The formula for the objective function mentioned in step S2 is: ; Where mingap is the total length of the copper ring in the known shortest solution, and its initial value is... Where Z is the number of stator slots, This represents the number of parallel branches per phase. In this scheme, a copper ring must be used to connect the current to its corresponding outlet at any starting point. The formula is as follows: ; Among them, select_row i，j The algorithm calculates the number of wire interlayers where the j-th copper ring of phase i is located; if it is not arranged, the value is -1. The quantitative mathematical formula for the clamp constraint condition is as follows: ; ; Among them, out_capacity layer，i `select_column` represents the number of copper rings that can be led out from each bus outlet of each layer of the clamp, `capacity` represents the maximum copper ring capacity that can be led out from each bus outlet of each layer of the clamp, and `select_column` represents the number of copper rings that can be led out from each bus outlet of each layer of the clamp. n，p The algorithm calculates the number of columns in the line clamp of the p-th copper ring of n phases. If it is not arranged, the value is -1. `slect_column` q，r Similarly, select_row q，r With slect_row i，j Similarly, RFA arr,t,g When the starting bar of the winding is arr, and the t-th copper ring has already been arranged, the situation where the g-th copper ring can successfully charge using clockwise and counterclockwise rotation is represented in binary: 0b11 for both clockwise and counterclockwise rotation, 0b10 for only clockwise rotation, 0b01 for only counterclockwise rotation, and 0b00 for neither clockwise nor counterclockwise rotation.
[0047] via RFA arr,k,l The matrix indicates whether the two copper rings satisfy the clamp constraint relationship. However, directly calculating this by selecting the start and end points of the two copper rings and the copper ring channel holes is quite complex. To simplify the calculation, an auxiliary function is first created to perform some preliminary calculations before RFA is performed. arr,k,l Matrix calculation, define the auxiliary function as pointjudgment(starr,i,j,outi,j,diri,j,p), the calculation method of the auxiliary function is as follows. Figure 3 As shown, RFA arr,k,l Matrix calculation methods are as follows Figure 4 As shown.
[0048] As mentioned above, 6a copper rings are needed to complete the busbar connection. Each copper ring has multiple possible configurations, such as rotation direction and copper ring channel hole. Therefore, in the entire clamp, a single copper ring has 2*row*column possible configurations. Since the method used in this paper arranges the copper rings layer by layer using the copper ring channel hole, after determining that no copper ring can be arranged in the current layer, we move to the next layer. Therefore, the configuration options caused by the number of layers can be eliminated. Since the number of layers is determined, the configuration options for a single copper ring are reduced to 2*column. This allows for the initial decoupling of the complex spatial relationship between the copper rings coupled together by the clamp, significantly reducing complexity and computational load.
[0049] Summarize the various forms of 6a copper rings, denoted as k types of copper rings, and use... k Calculation method as follows Figure 5As shown. use_next u,k Calculation method and use k Similarly, assuming only that copper ring u is added, the rest of the calculations are the same.
[0050] S3. Design a greedy algorithm and an improved DFS algorithm that combines the greedy algorithm. The greedy algorithm prioritizes arranging copper rings layer by layer with the least impact on other copper rings, which is suitable for small-scale motors. The improved DFS algorithm first obtains the approximate maximum copper ring capacity as a reference through the greedy algorithm to narrow the search range, and then accurately searches for the maximum capacity copper ring combination in each layer to adapt to large-scale motors, and iteratively optimizes the scheme.
[0051] The specific steps of the improved DFS algorithm in step S3 are as follows: S3.1 Given the number of stator slots Z of the motor and the number of parallel branches a per phase, the starting position data of the first group is denoted as... The terminal position of the j-th copper ring in phase i Total number of layers in the clamp (row); Total number of columns in the clamp (column); S3.2 Calculation based on FPA matrix calculation method The matrix is used to calculate the total length of the copper ring in the ideal solution. and starting point data for each group ; S3.3 Set layer=0, and randomly select a number less than Z to assign... And initialize all kinds of parameters; Where layer∈[0, row] represents the current number of online mezzanine layers, Z is the number of stator slots, and arr is the number of data groups for the selected winding starting point; S3.4 Let layer = layer + 1. If layer > row, then proceed to step S3.14; otherwise, proceed to step S3.5. S3.5 Calculate the approximate maximum number of copper rings that the current layer can accommodate using a greedy algorithm: greedy_number; S3.6 Let DFS_number=greedy_number, deep_floor=0, ∀k∈[0,2*6a*column), s∈[0,6a), let deep_slect k =0, deep_current s,k =0; Where DFS_number is the maximum number of copper rings that the current layer can accommodate, deep_floor is the depth order of the improved DFS algorithm, and deep_select is the maximum number of copper rings that the current layer can accommodate. k Assign the maximum number of copper ring combinations in history to the current layer, deep_current s,kTo arrange copper rings in a certain layer of order s, deep_slect k and deep_current s,k This value is 1 when assigned, and 0 otherwise. S3.7∀k∈[0,2*6a*column), s∈[0,deep_floor), if deep_current s,k =1 and select_row i,j =layer, then record the parameters of the k-th type of copper ring dir i，j slect_column i，j slect_row i,j =layer, if deep_current s,k =0 and select_row i,j =layer, then initialize all parameters of the k-th type of copper ring, and calculate use regardless of any condition. k ; Among them, use k This indicates whether the k-th copper ring can be arranged given that there are already copper rings arranged in the current layer. The value is 1 if it can be arranged, and 0 otherwise. S3.8 Let u = -1; S3.9 Let u = u + 1. If u ≥ 2 * 6a * column, then proceed to step S3.12; otherwise, proceed to step S3.10. S3.10 If survive u +deep_floor+1≥DFS_number, then let DFS_number=survive u +deep_floor+1, execute step S3.11; if not satisfied, execute step S3.9. Among them, survival u Its initial value is 0, indicating the number of copper rings that can be arranged after the uth copper ring is added, given that there are already copper rings arranged in the current layer. S3.11 Let deep_current deep_floor,u =1, deep_floor=deep_floor+1, ∀k∈[0,2*6a*column), deep_slectk= use k =use_next u,k Proceed to step S3.8; Among them, use_next u,k Given that copper rings are already arranged in the current layer, this is the case where additional copper ring u is arranged, and the remaining k copper rings can be arranged. If they can be arranged, this value is 1, otherwise it is 0. S3.12 If deep_floor-1 < 0, then proceed to step S3.13. If not, then let deep_floor = deep_floor-1. There must exist k ∈ [0, 2*6a*column) such that deep_current deep_floor,k =1, let deep_current deep_floor,k =0, u=k, execute step S3.9; S3.13∀k∈[0,2*6a*column), if deep_slect k =1, then record the parameters of this copper ring dir i，j slect_column i，j slect_row i,j =The layer is added to the current layout scheme, and step S3.4 is executed; S3.14 Determine if select_row exists i,j =-1, if it does not exist, calculate the total length of the copper rings in the current calculation scheme, total_gap, and execute step S3.15; if it exists, execute step S3.16. S3.15 Determine whether mingap > total_gap. If it is satisfied, record all parameters of the current calculation scheme and record this scheme as the optimal scheme. S3.16 Determine whether the maximum number of iterations (total_number) specified by the algorithm has been reached. If it is, exit the operation and output the optimal solution. If it is not, execute step S3.3.
[0052] The formula for calculating the total length of the ideal copper ring in step S3.2 is as follows: ; ; Among them, ideal arr The total length of the copper ring under ideal conditions when the winding start point data is selected as the arr group; st arr,i,j The starting position of the j-th copper ring in phase i when the winding start-point data is selected as the arr group; out i,j This is the location of the terminal point of the j-th copper ring in phase i.
[0053] The formula for calculating the total length of the copper rings in step S3.14 is as follows: ; ; Where Z is the number of stator slots; diri,j , a 0-1 decision variable, represents the rotation direction of the j-th copper ring in phase i; gap i,j Let be the length of the j-th copper ring in phase i.
[0054] The survival in step S3.10 u The calculation formula is: ; Among them, use_next u,k Given that copper rings are already arranged in the current layer, this value represents the situation where copper ring number u is to be added, and the remaining copper rings number k can be arranged. If they can be arranged, this value is 1; otherwise, it is 0.
[0055] S4. Based on the measured data of two large hydroelectric generators with different parameters, the algorithm was tested. The total length of the copper rings of the original scheme and the solution scheme was compared to verify that the algorithm satisfies the clamp constraint and the solution result is close to the ideal optimal value. The final copper ring arrangement scheme that takes into account both length optimization and solution efficiency was output.
[0056] All algorithms and tests were implemented using Dev-C++ programming, and the experimental platform was a computer configured with Windows 11, an AMD Ryzen 57500F 6-Core Processor (3.70GHz), and 32.00 GB of RAM. The algorithm testing experiments were carried out using stator winding data from two large hydroelectric generators. The original winding scheme was obtained from the collection and processing of data from a real power plant, and its original specific parameters are shown in Tables 2 and 3.
[0057]
[0058] Table 2
[0059] Table 3 The parameters optimized by the method of this invention are shown in Tables 4 and 5. For two large hydroelectric generators, the DFS algorithm combined with the greedy algorithm proposed in this paper can solve the problem better than the original winding scheme, and it can be seen that the solution is extremely close to the optimal solution.
[0060]
[0061] Table 4
[0062] Table 5 The performance of the algorithm of this invention is shown in Table 6. As can be seen, for large hydroelectric generators with different parameters, different algorithms can meet different requirements in terms of solution time and solution quality.
[0063]
[0064] Table 6 In summary, a mathematical model and description of the clamp constraints for the task of optimizing the stator busbar arrangement of large hydroelectric generators were established, providing quantifiable constraints for solving this task. An algorithm suitable for optimizing the stator busbar arrangement of large hydroelectric generators was implemented. The effectiveness of the algorithm in solving the problem of optimizing the stator busbar arrangement of large hydroelectric generators was verified using actual data from two three-phase motor windings, yielding satisfactory results.
Claims
1. An algorithm for solving the arrangement scheme of the busbar copper rings in the stator winding of a large hydroelectric generator, characterized in that, Includes the following steps: S1. Clarify the NP-complete problem attributes of the stator busbar copper ring arrangement of large hydroelectric generator, sort out the five types of core constraints of the clamp, define key parameters such as the number of stator slots and the number of parallel branches per phase, establish quantitative standards such as slot coordinate system, rotation direction, distance, and copper ring channel hole number, and calculate basic data such as the starting position of copper ring and ideal total length. S2. Taking the minimum total length of the copper ring as the objective function, the wire clamp constraint is transformed into a quantitative mathematical formula. The auxiliary function is used to determine whether the copper ring path meets the requirements. An RFA matrix is constructed to represent the compatibility of the two copper ring constraints. Key parameters such as the copper ring arrangement state and the remaining arrangement quantity after additional copper rings are arranged are calculated. S3. Design a greedy algorithm and an improved DFS algorithm that combines the greedy algorithm. The greedy algorithm prioritizes the copper rings that have the least impact on other copper rings and arranges them layer by layer to adapt to small-scale motors. The improved DFS algorithm first obtains the approximate maximum copper ring capacity as a reference through the greedy algorithm to narrow the search range, and then accurately searches for the maximum copper ring combination in each layer to adapt to large-scale motors. The algorithm iteratively optimizes the solution. S4. Based on the measured data of two large hydroelectric generators with different parameters, the algorithm was tested. The total length of the copper rings of the original scheme and the solution scheme was compared to verify that the algorithm satisfies the clamp constraint and the solution result is close to the ideal optimal value. The final copper ring arrangement scheme that takes into account both length optimization and solution efficiency was output.
2. The algorithm for solving the stator winding busbar arrangement scheme of a large hydroelectric generator according to claim 1, characterized in that, In step S1, the five core constraints of the wire clamp include: the copper ring channel hole cannot be reused; each layer of the wire clamp and each bus outlet can carry a maximum number of copper rings; the copper ring cannot be replaced with a copper ring channel hole in another position midway; when the copper ring is wound using the outer row of copper ring channel holes, the inner row of copper ring channel holes of the first wire clamp used must be available and will occupy the inner row of copper ring channel holes of the first wire clamp used; when the copper ring is wound using the inner row of copper ring channel holes, the outer row of copper ring channel holes of the last wire clamp used must be available and will occupy the outer row of copper ring channel holes of the last wire clamp used.
3. The algorithm for solving the stator winding busbar arrangement scheme of a large hydroelectric generator according to claim 1, characterized in that, The specific method for defining the number of stator slots in step S1 is as follows: When representing information such as the starting point, ending point, and copper ring path, position information will be used. Based on the specific characteristics of the problem, a slot coordinate system will be established, and the position will be defined by the stator slot number. Looking down at the generator stator, the slot number on the right side will be defined as slot 1. Following industry practice, each slot will be numbered clockwise from smallest to largest until the last slot.
4. The algorithm for solving the stator winding busbar arrangement scheme of a large hydroelectric generator according to claim 1, characterized in that, The quantification standard for the rotation direction in step S1 is as follows: For a copper ring, the only selectable rotation directions are clockwise or counterclockwise. This paper uses binary to represent the rotation direction of the copper ring, where 0 represents counterclockwise rotation and 1 represents clockwise rotation. Considering that there are only two rotation directions for the copper ring, according to the definition of the superior and inferior arcs of a circle, the clockwise direction with the shorter winding distance is called the superior direction, and the clockwise direction with the longer winding distance is called the inferior direction. If the two are of equal length, then both clockwise directions are called the superior direction.
5. The algorithm for solving the arrangement scheme of the stator winding busbar copper rings of a large hydroelectric generator according to claim 1, characterized in that, The quantification standard for the numbering of the copper ring channel holes in step S1 is as follows: For wire clamps, there are a total of There are 10 copper ring channel holes, where row represents the total number of wire clamp layers and column represents the total number of wire clamp columns. The column closest to the stator is defined as the starting column, denoted as column 1. Column numbers increase progressively away from the stator. Starting from layer 1, the copper ring channel hole layers increase progressively upwards from the bottom of the wire clamp. Based on the definition of copper ring channel hole layers and columns, the p-th layer and q-th column copper ring channel hole are denoted as the p-th... One copper ring channel hole.
6. The algorithm for solving the stator winding busbar arrangement scheme of a large hydroelectric generator according to claim 1, characterized in that, The formula for the objective function in step S2 is: ； Where mingap is the total length of the copper ring in the known shortest solution, and its initial value is... Where Z is the number of stator slots, This represents the number of parallel branches per phase. In this scheme, a copper ring must be used to connect the current to its corresponding outlet at any starting point. The formula is as follows: ； Among them, select_row i，j The algorithm calculates the number of wire interlayers where the j-th copper ring of phase i is located; if it is not arranged, the value is -1. The quantitative mathematical formula for the clamp constraint condition is as follows: ； ； Among them, out_capacity layer，i `select_column` represents the number of copper rings that can be led out from each bus outlet of each layer of the clamp, `capacity` represents the maximum copper ring capacity that can be led out from each bus outlet of each layer of the clamp, and `select_column` represents the number of copper rings that can be led out from each bus outlet of each layer of the clamp. n，p The algorithm calculates the number of columns in the line clamp of the p-th copper ring of n phases. If it is not arranged, the value is -1. `slect_column` q，r Similarly, select_row q，r With slect_row i，j Similarly, RFA arr,t,g When the starting bar of the winding is arr, and the t-th copper ring has already been arranged, the situation where the g-th copper ring can successfully charge using clockwise and counterclockwise rotation is represented in binary: 0b11 for both clockwise and counterclockwise rotation, 0b10 for only clockwise rotation, 0b01 for only counterclockwise rotation, and 0b00 for neither clockwise nor counterclockwise rotation.
7. The algorithm for solving the stator winding busbar arrangement scheme of a large hydroelectric generator according to claim 1, characterized in that, The specific steps of the improved DFS algorithm in step S3 are as follows: S3.1 Given the number of stator slots Z of the motor and the number of parallel branches a per phase, the starting position data of the first group is denoted as... The terminal position of the j-th copper ring in phase i Total number of layers in the clamp (row); Total number of columns in the clamp (column); S3.2 Calculation based on FPA matrix calculation method The matrix is used to calculate the total length of the copper ring in the ideal solution. and starting point data for each group ; S3.3 Set layer=0, and randomly select a number less than Z to assign... And initialize all kinds of parameters; Where layer∈[0, row] represents the current number of online mezzanine layers, Z is the number of stator slots, and arr is the number of data groups for the selected winding starting point; S3.4 Let layer = layer + 1. If layer > row, then proceed to step S3.14; otherwise, proceed to step S3.
5. S3.5 Calculate the approximate maximum number of copper rings that the current layer can accommodate using a greedy algorithm: greedy_number; S3.6 Let DFS_number = greedy_number, deep_floor = 0, for all k ∈ [0, 2 * 6a * column), s ∈ [0, 6a), let deep_slect k = 0, deep_current s,k = 0; Where DFS_number is the maximum number of copper rings that the current layer can accommodate, deep_floor is the depth order of the improved DFS algorithm, and deep_select is the maximum number of copper rings that the current layer can accommodate. k Assign the maximum number of copper ring combinations in history to the current layer, deep_current s,k To arrange copper rings in a certain layer of order s, deep_slect k and deep_current s,k This value is 1 when assigned, and 0 otherwise. S3.7∀k∈[0,2*6a*column), s∈[0,deep_floor), if deep_current s,k =1 and select_row i,j =layer, then record the parameters of the k-th type of copper ring dir i，j slect_column i，j slect_row i,j =layer, if deep_current s,k =0 and select_row i,j =layer, then initialize all parameters of the k-th type of copper ring, and calculate use regardless of any condition. k ; Among them, use k This indicates whether the k-th copper ring can be arranged given that there are already copper rings arranged in the current layer. The value is 1 if it can be arranged, and 0 otherwise. S3.8 Let u = -1; S3.9 Let u = u + 1. If u ≥ 2 * 6a * column, then proceed to step S3.12; otherwise, proceed to step S3.
10. S3.10 If survive u +deep_floor+1≥DFS_number, then let DFS_number=survive u +deep_floor+1, execute step S3.11; if not satisfied, execute step S3.
9. Among them, survival u Its initial value is 0, indicating the number of copper rings that can be arranged after the uth copper ring is added, given that there are already copper rings arranged in the current layer. S3.11 Let deep_current deep_floor,u =1, deep_floor=deep_floor+1, ∀k∈[0,2*6a*column), deep_slectk= use k =use_next u,k Proceed to step S3.8; Among them, use_next u,k Given that copper rings are already arranged in the current layer, this is the case where additional copper ring u is arranged, and the remaining k copper rings can be arranged. If they can be arranged, this value is 1, otherwise it is 0. S3.12 If deep_floor-1 < 0, then proceed to step S3.
13. If not, then let deep_floor = deep_floor-1. There must exist k ∈ [0, 2*6a*column) such that deep_current deep_floor,k =1, let deep_current deep_floor,k =0, u=k, execute step S3.9; S3.13∀k∈[0,2*6a*column), if deep_slect k =1, then record the parameters of this copper ring dir i，j slect_column i，j slect_row i,j =The layer is added to the current layout scheme, and step S3.4 is executed; S3.14 Determine if select_row exists i,j =-1, if it does not exist, calculate the total length of the copper rings in the current calculation scheme, total_gap, and execute step S3.15; if it exists, execute step S3.
16. S3.15 Determine whether mingap > total_gap. If it is satisfied, record all parameters of the current calculation scheme and record this scheme as the optimal scheme. S3.16 Determine whether the maximum number of iterations (total_number) specified by the algorithm has been reached. If it is, exit the operation and output the optimal solution. If it is not, execute step S3.
3.
8. The algorithm for solving the stator winding busbar arrangement scheme of a large hydroelectric generator according to claim 7, characterized in that, The formula for calculating the total length of the ideal copper ring in step S3.2 is as follows: ; ； Among them, ideal arr The total length of the copper ring under ideal conditions when the winding start point data is selected as the arr group; st arr,i,j The starting position of the j-th copper ring in phase i when the winding start-point data is selected as the arr group; out i,j This is the location of the terminal point of the j-th copper ring in phase i.
9. The algorithm for solving the stator winding busbar arrangement scheme of a large hydroelectric generator according to claim 7, characterized in that, The formula for calculating the total length of the copper rings in step S3.14 is as follows: ; ; Where Z is the number of stator slots; dir i,j , a 0-1 decision variable, represents the rotation direction of the j-th copper ring in phase i; gap i,j Let be the length of the j-th copper ring in phase i.
10. The algorithm for solving the arrangement scheme of the stator winding busbar copper rings of a large hydroelectric generator according to claim 7, characterized in that, The survival in step S3.10 u The calculation formula is: ； Among them, use_next u,k Given that copper rings are already arranged in the current layer, this value represents the situation where copper ring number u is to be added, and the remaining copper rings number k can be arranged. If they can be arranged, this value is 1; otherwise, it is 0.