Water turbine unit equipment rotation method based on group representation theory and rotation voting algorithm

Abstract

The present application relates to a water turbine unit equipment rotation method based on group representation theory and rotation voting algorithm, comprising: establishing a permutation group having an isomorphic relationship with the unit equipment rotation logic; constructing a linear space and a base vector corresponding to the permutation group; determining the state and level of the unit equipment; determining the conjugate class of the permutation group and the corresponding matrix group element; determining the trigger condition of the unit equipment rotation; and calculating the new order of the main and standby equipment in a descending order k-rotation manner. The equipment rotation voting algorithm of the present application realizes the scientific and reasonable rotation and standby of the water turbine unit equipment, and the number of equipment used for rotation is not limited, improving the reliability of the water turbine unit operation, and solving the problems of algorithm complexity, program logic redundancy, poor readability, and difficult to find and troubleshoot logical errors in the design of the equipment rotation logic algorithm relying on experience and enumeration method.

Description

Technical Field

[0001] This invention belongs to the field of hydropower unit equipment control decision-making, specifically relating to a hydropower unit equipment rotation method based on group representation theory and rotation voting algorithm. Background Technology

[0002] Currently, the rotation method of multiple equipment is widely used in large hydro-generator units. However, the existing rotation voting mechanism has shortcomings. Its design method is mainly based on experience and lacks unified and complete theoretical guidance. The rotation logic is imperfect and needs further optimization and improvement. The characteristics of the commonly used rotation method are: (1) setting simple combinations of multiple equipment, resulting in a single equipment rotation method and failing to give full play to the advantages of multiple redundant equipment; (2) setting relatively complex rotation methods for multiple equipment, resulting in imperfect logic, poor program code readability, and difficulty in detecting hidden logical errors. The scientific and reasonable rotation method of equipment is one of the factors for its stable operation. Therefore, designing and adopting a more scientific and effective rotation algorithm is of great significance for the stable control of equipment and ensures the stable and safe operation of the unit.

[0003] In the industrial sector, the operation mode of rotating multiple pieces of equipment is quite common. However, the complexity of the rotation logic algorithm increases dramatically with the number of rotating devices, and a perfect and unified algorithm has yet to be found. For example, there are 6 ways to rotate 3 pieces of equipment, and a staggering 720 ways with 6 pieces! Existing rotation logic design methods are mainly based on empirical summaries and enumeration methods, which are only applicable to a specific number of devices, lacking systematicity and generality, and cannot be generalized. However, for complex rotation situations, without the guidance of a sound theoretical method, relying solely on experience and enumeration methods to complete the logic algorithm design is very difficult, and may face problems such as algorithm complexity, verbose program logic, poor readability, and difficulty in detecting and troubleshooting logical errors. In view of this, it is of great significance to conduct theoretical analysis and research on the rotation logic algorithm of multiple pieces of equipment and to formulate a rigorous, standardized, and widely applicable standard logic algorithm! Introducing group representation theory into the algorithm logic analysis will help solve this problem. By using the powerful algebraic tool of finite group representation theory, the essential characteristics of rotation logic can be perfectly characterized, and this problem can be explored and studied in depth.

[0004] Therefore, this invention conducts theoretical research on the rotation logic algorithm for multiple devices, and establishes a complete and standardized rotation logic algorithm with generalizable applications by leveraging the powerful algebraic tools of finite group representation theory. Summary of the Invention

[0005] The purpose of this invention is to address the aforementioned problems by providing a hydropower unit equipment rotation method based on group representation theory and a rotation voting algorithm. Based on finite group representation theory, a finite group representation-based equipment rotation voting algorithm is proposed to achieve the scientific and rational rotation and standby of hydropower unit equipment. Furthermore, it allows for unlimited rotation of equipment, improves the reliability of hydropower unit operation, and solves the problems of algorithm complexity, lengthy program logic, poor readability, and difficulty in detecting and troubleshooting logical errors inherent in equipment rotation logic algorithms that rely solely on experience and enumeration.

[0006] the term:

[0007] Group: a set and An operation on If the following conditions are met, then it is said that right Forming a group, or in other words It's a group, in short. It's a group:

[0008] i. Associative law;

[0009] ii. There is an identity element, that is, there is For any They all

[0010] ;

[0011] iii. Each element has an inverse element, that is, for any They all Make

[0012] ;

[0013] Conjugate: group Two elements , If in There exists a , making , It can be done When connected, it is called , Conjugate, denoted as .

[0014] Class: Group The set of all mutually conjugate elements in a given set is called a group. A class.

[0015] Isomorphism: If from group Join the group There exists a one-to-one full mapping above. Furthermore, this mapping itself preserves the multiplication rules of the group, that is, the group... The mapping of the product of two elements in a group is equal to the group. The product of two element mappings is called a group. with the group Isomorphism, denoted as .

[0016] Homomorphism: Suppose there exists a subgroup Join the group full mapping Furthermore, this mapping itself preserves the multiplication rules of the group, that is, the group... The mapping of the product of two elements in a group is equal to the group. The product of two element mappings is called a group. with the group Homomorphism, denoted as .

[0017] Symmetry group: Let It is Meta-set. Set arrive one-to-one correspondence Called A permutation on top. With express The set of all permutations above, and the permutation operations form a group. This is called a symmetric group on sets, and each of its subgroups is called a set. Permutation groups on.

[0018] Group representation: refers to a group To linear space linear transformation group on The homomorphic mapping relation. A group representation is a homomorphic mapping relation that exists between an abstract group and a linear transformation group of a linear space. The linear transformation group can be intuitively understood as a matrix group.

[0019] There is a group If there exists a from arrive 3D linear space linear transformation group on homomorphism Then it is called It is a group A linear representation of To represent space, The dimension of the representation is denoted as:

[0020]

[0021] For linear space If a specific set of basis vectors is selected, then each linear transformation can be represented by a matrix, and the group of linear transformations will also correspond to a matrix group.

[0022] Faithfully stating: If ,Right now If it is injective, then it means It is faithful.

[0023] k-rotation: a permutation If k different devices become Then it is called It is a k-cycle (cyclic) permutation, or simply k-cycle (cyclic), and is represented as... , where k represents the length of the rotating device sequence.

[0024] A transposition is a cycle of length 2. Any k-th order cycle can be written as the product of k-1 transpositions.

[0025] Permutation decomposition: Any element in a permutation group can be uniquely decomposed into a product of non-intersecting permutations.

[0026] That is, each Meta-substitution All of these can be written as the product of several unconnected cyclic permutations. For example...

[0027] Relationship between permutation structure and class: Permutations with the same permutation structure constitute a class of permutation group.

[0028] Relationship between rotation voting and group representation: Rotation voting refers to a group... Elements of the metaset The elements are rearranged in order. This arrangement corresponds to the priority of the switching equipment. The rearrangement of elements is a permutation relationship between elements. All permutations of elements and a The symmetric groups are isomorphic. Therefore, there is a one-to-one correspondence between the round-robin voting algorithm and the symmetric groups, allowing the symmetric groups to be applied to the round-robin voting algorithm.

[0029] The technical solution of this invention is a hydropower unit equipment rotation method based on group representation theory and rotation voting algorithm, comprising the following steps:

[0030] Step 1: Establish a permutation group that is isomorphic to the unit equipment rotation logic;

[0031] Step 2: Construct the linear space and basis vectors corresponding to the permutation group;

[0032] Step 3: Determine the triggering conditions for unit equipment rotation;

[0033] Step 4: Calculate the assigned scores of the unit equipment used for the switchover based on the attribute status of the unit equipment;

[0034] Step 5: Determine if the triggering conditions for unit equipment rotation are met. If the triggering conditions are met, then classify the equipment to be rotated according to the assigned scores of the unit equipment. m Each level m This indicates the number of equipment levels and decomposes the equipment rotation and replacement into... m For each k-cycle product, proceed to step 6; if the triggering condition is not met, repeat step 4.

[0035] Step 6: Implement the steps obtained in Step 5 sequentially, starting with step 1- m k-rotations;

[0036] Step 7: Based on the results of Step 6, obtain the descending k-cycle product table;

[0037] Step 8: Obtain the sorted queue of primary and standby equipment based on the descending k-rotation product table, perform a switchover operation on the unit equipment, and complete the unit equipment rotation.

[0038] Further, in step 1, define for Metaset, where Indicates the first i Taiwanese unit equipment, collection arrive one-to-one correspondence Called On the substitution,

[0039]

[0040] by express The set consisting of all permutations, the permutation operation forms a group, i.e., a group. ,group Let be a symmetric group on a set, and each of its subgroups is called a set. On the permutation group, The permutation group on the fuzzy set is represented as .

[0041] Taking the rotation problem of three generating units as an example, the permutation group used for the rotation of three generating units... The three-dimensional representation is:

[0042] ,

[0043] ,

[0044]

[0045] ,

[0046] ,

[0047]

[0048] in This indicates a replacement group of 3 generating units. Matrix representation of the identity element; The matrix representation of group element (12); The matrix representation of the group element (2 3); The matrix representation of the group element (1 3); The matrix representation of the group element (1 2 3); The matrix representation of the group element (1 3 2).

[0049] With permutation group G Group elements in Corresponding operators The representation matrix is ​​a group operator. For basis vectors The effect of

[0050]

[0051]

[0052]

[0053] Interaction between two operators:

[0054]

[0055] Right now

[0056] .

[0057] Preferably, in step 4, the attribute status of the unit equipment includes whether the unit equipment is normal, whether the unit equipment is automatic, and whether the unit equipment is started.

[0058]

[0059] In the formula This indicates the priority assignment of the first attribute of the unit equipment. This indicates the priority assignment of the second attribute of the generator set equipment. This indicates the priority assignment of the third attribute of the generator set equipment;

[0060] The primary attribute of the unit equipment q The specific value of 1 is:

[0061]

[0062] Secondary attribute of unit equipment q The specific value of 2 is:

[0063]

[0064] The third attribute of the unit equipment q The specific values ​​for 3 are:

[0065]

[0066] The formula for calculating the score of the equipment status assignment is:

[0067]

[0068] In the formula, S represents the equipment status assignment score of the unit equipment.

[0069] Taking the rotation of main and standby hydraulic pumps as an example, the rotation voting and replacement group of the four hydraulic pumps in the unit governor hydraulic system. Isomorphic. The four hydraulic pumps are numbered 1, 2, 3, and 4, and their logical voting states are: primary, standby 1, standby 2, and standby 3, respectively represented as: , , and ,in Indicates the primary device. Indicates the first backup device. This indicates the second backup device. This represents the third backup device. The voting model for the rotation of four hydraulic pumps is abstracted as: maintaining... The sorting positions remain fixed, and the corresponding pump numbers are permuted. The group representation space corresponding to the rotating voting model of 4 hydraulic pumps is 4-dimensional, and the spatial basis vectors are taken as... These correspond to pumps 1, 2, 3, and 4 respectively, and the group representation adopts the aforementioned matrix faithful representation.

[0070] Displacement group There are 5 sets of matching numbers: [4], [3,1], [2, 2], [2,1,1], [1,1,1,1].

[0071] Displacement group The conjugate classes are divided into:

[0072] Type: Conjugate class is The corresponding matrix group element is:

[0073]

[0074] Type: Conjugate class is

[0075]

[0076] Type: Conjugate class is

[0077]

[0078] Type: Conjugate class is

[0079]

[0080] Type: Conjugate class is

[0081]

[0082] The unit equipment rotation problem is decomposed into permutation groups, and the permutation groups are classified into classes. Each permutation can be represented as a product of rotations, and there is a one-to-one correspondence between the rotation structure and the conjugate class.

[0083] right n Replacement group of Taiwanese unit equipment class Decompose it.

[0084]

[0085]

[0086] in express n The conjugate class corresponding to the equipment rotation problem of Taiwanese generator units. express j The number of order cycles; that is, the number of cycles in this class. A first-order cycle A second-order cycle, ... n-order cycles.

[0087] Medium The number of permutation group elements in the is:

[0088]

[0089] Compared with the prior art, the beneficial effects of the present invention include:

[0090] 1) Based on the theory of finite group representation, this invention proposes a device rotation voting algorithm based on finite group representation, which realizes the scientific and reasonable rotation and standby of hydropower unit equipment, and the number of equipment used for rotation is unlimited, which improves the reliability of hydropower unit operation and can effectively prevent the phenomenon of hydropower production being affected by equipment failure.

[0091] 2) The method of the present invention adopts a hierarchical k-rotation approach, which realizes the hierarchical relationship between hydropower unit equipment with different priorities. This is beneficial to setting the priority relationship between different equipment according to the attributes of the unit equipment, and improving the scientific rationality of equipment switching.

[0092] 3) This invention classifies the unit equipment according to the assigned scores of the unit equipment calculated in real time. Corresponding to the unit equipment level, the equipment rotation replacement is decomposed into a product of multiple k-rotations. The number of decomposed k-rotations varies with the real-time status of the unit equipment, which can always ensure that the equipment in good condition is at the forefront of the main and standby equipment for replacement, and is given priority for unit equipment replacement, thereby improving the reliability of unit operation.

[0093] 4) The equipment rotation method of the present invention has low computational complexity, is easy to implement and execute on a computer, and solves the problems of algorithm complexity, lengthy program logic, poor readability, and difficulty in finding and troubleshooting logical errors faced by equipment rotation logic algorithm design that relies purely on experience and enumeration.

[0094] 5) The computer program for the equipment rotation method of the present invention has no restrictions on the computer compilation and running environment, is easy to copy and deploy, and is conducive to its promotion and use in hydropower stations. Attached Figure Description

[0095] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0096] Figure 1 This is a flowchart illustrating the oil pump rotation algorithm of the speed governor hydraulic system according to an embodiment of the present invention.

[0097] Figure 2 This is a user interface diagram of the hydropower unit equipment rotation decision system according to an embodiment of the present invention. Detailed Implementation

[0098] In this embodiment, the unit equipment is the hydraulic oil pump of the governor hydraulic system, that is, the main and backup hydraulic oil pumps of the hydropower unit are rotated and voted on.

[0099] like Figure 1 and Figure 2 As shown, the hydropower unit equipment rotation method based on group representation theory and rotation voting algorithm includes:

[0100] Step 1: Establish a permutation group that is isomorphic to the hydraulic pump switching logic;

[0101] Step 2: Construct the linear space and basis vectors corresponding to the permutation group;

[0102] Step 3: Determine the triggering conditions for unit equipment rotation;

[0103] Step 4: Calculate the assigned scores of the unit equipment used for the switchover based on the attribute status of the unit equipment;

[0104] The properties and status of the hydraulic pump include whether the hydraulic pump is normal, whether the hydraulic pump is automatic, and whether the hydraulic pump is started.

[0105]

[0106] In the formula This indicates the priority assignment of the first attribute of the hydraulic pump. This indicates the priority assignment of the second attribute of the hydraulic pump. This indicates the priority assignment of the third attribute of the hydraulic pump;

[0107] The primary attribute of a hydraulic pump q The specific value of 1 is:

[0108]

[0109] Secondary property of hydraulic pump q The specific value of 2 is:

[0110]

[0111] The third property of the hydraulic pump q The specific values ​​for 3 are:

[0112]

[0113] The formula for calculating the score of the equipment status assignment is:

[0114]

[0115] In the formula, S represents the equipment status assignment score of the hydraulic oil pump;

[0116] In the embodiments, The value is 100; The value is 10; The value of is 1.

[0117] Step 5: Determine if the triggering conditions for unit equipment rotation are met. If the triggering conditions are met, then classify the equipment to be rotated according to the assigned scores of the unit equipment. m Each level mThis indicates the number of equipment levels and decomposes the equipment rotation and replacement into... m For each k-cycle product, proceed to step 6; if the triggering condition is not met, repeat step 4.

[0118] Step 6: Implement the steps obtained in Step 5 sequentially, starting with step 1- m k-rotations;

[0119] Step 7: Based on the results of Step 6, obtain the descending k-cycle product table;

[0120] Step 8: Obtain the sorted queue of primary and standby equipment based on the descending k-rotation product table, perform a switchover operation on the unit equipment, and complete the unit equipment rotation.

[0121] Voting by rotating 6 hydraulic pumps and Taking the conjugate class as an example, the descending k-cycle product table includes a 3-cycle permutation, a 2-cycle permutation, and a 1-cycle permutation, namely (abc)(ef)(g).

[0122] The initial master / slave information for the hydraulic pump is as follows:

[0123]

[0124] in u 1 indicates the main pump. u 2 indicates the first standby pump. u 3 indicates the second standby pump. u 4 indicates the third standby pump. u 5 indicates the fourth standby pump. u 6 indicates the fifth standby pump; array Used to store master-slave sorting; array Store the pump serial numbers corresponding to the primary and backup order; e i , i = 1,2,…6 represents the pump serial number i .

[0125] The first cyclic permutation of the descending k-cycle product table is

[0126]

[0127] The second cyclic permutation is

[0128]

[0129] The third cyclic permutation is

[0130]

[0131] The implementation process of the descending k-round product table specifically includes:

[0132] (1) First cyclic permutation update operation

[0133]

[0134] The example specifies that the multiplication order is right multiplication, that is, first... ,back , then multiply .

[0135] In the formula , i = 1,2,3 represents the Yang diagram number 1,2,3 The composition of layer permutation group elements is the product; , i = 1,2,3 j = 1,2,3 represents the first Yang diagram. Layer The corresponding rotating group element of the column.

[0136]

[0137]

[0138]

[0139] In the formula, For the first Position Position rotation.

[0140] For example

[0141]

[0142]

[0143] The corresponding operator is

[0144]

[0145] through After the action is taken, the primary and backup information is updated to...

[0146]

[0147] array Updated to

[0148]

[0149] In the formula, This indicates an assignment operation.

[0150] for It can be decomposed into the product of commutative group elements.

[0151] For example

[0152]

[0153] All transformations can be decomposed into Multiplying the basic transformation group elements eliminates the need to define and write out a large number of transformation matrices separately.

[0154] The corresponding operator is

[0155]

[0156] Right now

[0157]

[0158] Therefore

[0159]

[0160] Therefore, the array sorted by primary and secondary elements after the first loop replacement update. Updated to

[0161] (1)

[0162] The first cyclic permutation is

[0163] (2)

[0164] After the first cyclic permutation, find the current position of the original second cyclic permutation and sort them from left to right with increasing numbers.

[0165] (3)

[0166] Similarly, find the current position information of the original third cyclic permutation.

[0167] (4)

[0168] (2) Second cyclic permutation update operation

[0169] The primary and backup information after the first cyclic permutation has been obtained as Equation (1), the first cyclic permutation is Equation (2), the second cyclic permutation is Equation (3), and the third cyclic permutation is Equation (4).

[0170] Similarly to step (1),

[0171]

[0172]

[0173]

[0174] Right now

[0175]

[0176] The corresponding operator is

[0177]

[0178] Therefore, the array sorted by primary and secondary elements after the second loop replacement update Updated to

[0179]

[0180]

[0181] (3) The third cyclic permutation update operation

[0182] Similar to step (1) or step (2), after performing the third cyclic permutation, the array sorted by master and slave is... Updated to

[0183]

[0184]

[0185]

[0186] At this point, the sorting and updating operation of the main and standby hydraulic pumps is complete, the descending k-cycle product table is updated, and a new sorting queue of the main and standby hydraulic pumps is obtained, as shown in Table 1.

[0187] Table 1. Updated Ranking of Main and Backup Oil Pumps for Unit Equipment Replacement

[0188]

[0189] In the embodiments, a hydropower unit equipment rotation decision system was constructed based on the method of the present invention, such as... Figure 2 As shown, it includes a module for calculating equipment assignment scores, a module for setting equipment rotation trigger conditions, a module for setting equipment failover criteria, and a module for sorting and updating primary and backup equipment.

Claims

1. A hydropower unit equipment rotation method based on group representation theory and rotation voting algorithm, characterized in that, The hydropower unit equipment rotation method classifies the unit equipment to be replaced according to the equipment attribute status. Corresponding to the unit equipment level, the equipment rotation replacement is decomposed into a product of multiple k-rotations. The k-rotations are implemented in stages to obtain a descending k-rotation product table, and then a sorted queue of unit equipment to be replaced is obtained. The hydropower unit equipment rotation method includes the following steps: Step 1: Establish a permutation group that is isomorphic to the unit equipment rotation logic; definition for Meta-set, n This indicates the number of devices used for rotation operations, where Indicates the first i Taiwanese unit equipment, collection arrive one-to-one correspondence Called On the substitution, ； by express The set consisting of all permutations, the permutation operation forms a group, i.e., a group. ,group It is a symmetric group on the set. n Subgroups of the symmetric group of the element are n Meta-substitution group, The permutation group of elements is represented as ; If from the group Join the group There exists a one-to-one full mapping above. Furthermore, this mapping itself preserves the multiplication rules of the group, that is, the group... The mapping of the product of two elements in a group is equal to the group. The product of two element mappings is called a group. with the group Isomorphism, denoted as ; Step 2: Construct the linear space and basis vectors corresponding to the permutation group; Step 3: Determine the triggering conditions for unit equipment rotation; Step 4: Calculate the assigned scores of the unit equipment used for the switchover based on the attribute status of the unit equipment; The attribute status of the unit equipment includes the first attribute of the unit equipment, namely whether the unit equipment is normal; the second attribute of the unit equipment, namely whether the unit equipment is automatic; and the third attribute of the unit equipment, namely whether the unit equipment is started. The priority relationship of unit equipment based on equipment attributes is as follows: ； In the formula This indicates the priority assignment of the first attribute of the unit equipment. This indicates the priority assignment of the second attribute of the generator set equipment. This indicates the priority assignment of the third attribute of the generator set equipment; The primary attribute of the unit equipment q The specific value of 1 is: ； Secondary attribute of unit equipment q The specific value of 2 is: ； The third attribute of the unit equipment q The specific values ​​for 3 are: ； Step 5: Determine if the triggering conditions for unit equipment rotation are met. If the triggering conditions are met, then classify the equipment to be rotated according to the assigned scores of the unit equipment. m Each level m This indicates the number of equipment levels and decomposes the equipment rotation and replacement into... m For each k-cycle product, proceed to step 6; if the triggering condition is not met, repeat step 4. Step 6: Implement the steps obtained in Step 5 sequentially, starting with step 1- m k-rotations; Step 7: Based on the results of Step 6, obtain the descending k-cycle product table; Step 8: Obtain the sorted queue of primary and standby equipment based on the descending k-rotation product table, perform a switchover operation on the unit equipment, and complete the unit equipment rotation.

2. The hydropower unit equipment rotation method according to claim 1, characterized in that, The formula for calculating the score of the equipment status assignment is: ； In the formula, S represents the equipment status assignment score of the unit equipment.

3. The hydropower unit equipment rotation method according to claim 2, characterized in that, Taking the main and standby oil pump rotation of the hydraulic system of a hydropower unit governor as an example, the triggering condition for oil pump rotation is: according to n Changes in the status assignment of the pressure pump trigger a rotation process. n Indicates the number of devices used for rotation operations; If used for rotation operations n If the attribute status of the pressure pump remains unchanged, the rotation operation will not be triggered, and the original master / standby order will be maintained.

4. The hydropower unit equipment rotation method according to claim 3, characterized in that, The equipment rotation permutation decomposition decomposes the unit equipment rotation problem into permutation groups and classifies the permutation groups; each permutation can be represented as a product of rotations, and there is a one-to-one correspondence between the rotation structure and the conjugate class. right n Replacement group of Taiwanese unit equipment class Decompose it. ； ； in express n The conjugate class corresponding to the equipment rotation problem of Taiwanese generator units. express j The number of order cycles; Medium The number of permutation group elements in the is: 。

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