CN108876002B - Method for optimizing inventory of spare parts of wind generating set - Google Patents

Method for optimizing inventory of spare parts of wind generating set Download PDF

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CN108876002B
CN108876002B CN201810417122.9A CN201810417122A CN108876002B CN 108876002 B CN108876002 B CN 108876002B CN 201810417122 A CN201810417122 A CN 201810417122A CN 108876002 B CN108876002 B CN 108876002B
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陈棋
杨秦敏
傅凌焜
王旭东
廖元文
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Zhejiang Windey Co Ltd
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Abstract

The invention discloses a method for optimizing spare part inventory of parts of a wind generating set. It comprises the following steps: s1: carrying out mode influence analysis on the fault behavior of the wind generating set, and establishing a corresponding fault tree model; s2: finding out all minimum cut sets in the fault tree model according to the fault tree model of the wind generating set; s3: solving the occurrence probability of the top event in the fault tree model according to the structure functions of the minimum cut set and the fault tree model; s4: calculating fault duty ratios of different bottom events, and determining spare part shortage penalty losses corresponding to the different bottom events; s5: comprehensively considering the purchasing cost, the warehousing cost and the out-of-stock loss cost of the parts, and establishing a part inventory optimization model; s6: and calculating the optimal solution of the part inventory optimization model. The invention can reasonably evaluate the responsibility of different parts to system failure, establish an optimization model and solve the optimal replenishment strategy of different spare parts.

Description

Method for optimizing inventory of spare parts of wind generating set
Technical Field
The invention relates to the technical field of part inventory control and logistics management, in particular to a method for optimizing spare part inventory of parts of a wind generating set.
Background
The wind energy is a green, pollution-free and renewable new energy source, and has important significance for solving the environmental pollution and energy crisis. With the continuous progress of wind power generation technology, the global wind power industry develops rapidly. According to data statistics of the global wind energy council, by the end of 2016, the global wind power accumulated installed capacity reaches 486749MW, and the accumulated annual growth rate reaches 12.6%, wherein the installed capacity newly increased in the current year reaches 54600MW, and China still is a country running around the world. The total installed capacity of China reaches 23378MW, the market share accounts for 43% of the whole world, and the total capacity of the wind driven generator assembling machine in China exceeds the first of the United states to jump the world.
The wind energy resources in China are rich, the wind energy reserves which can be developed and utilized are about 10 hundred million, and the rich wind energy zones are mainly distributed in the northeast, the north China, the northwest and the southeast coastal areas. In recent years, the Chinese wind power industry rises rapidly, and wind power has become the third largest power source in China after coal power and water power.
However, if the environmental cost is not considered, the competitiveness of wind power generation is far less than that of conventional energy power generation from the viewpoints of unit power generation cost, wind power generation technology level, grid connection reliability and the like, and part of wind power enterprises need to be subsidized by national governments.
The unit wind power generation cost is high, and the unit wind power generation cost is still a main factor causing the insufficient competitiveness of wind power generation. The reason is that the wind field operation and maintenance cost accounts for a large proportion, the proportion of the operation and maintenance cost in unit electric quantity can reach 10% -30% of the whole power generation cost, and the operation and maintenance data of a certain wind field 2016 all year round are taken as an example, incomplete statistics is carried out, and the total economic loss value of the generated energy caused by faults is as high as 320 ten thousand yuan RMB. However, the existing wind farm in China at present does not adopt a scientific and effective strategy for managing parts and spare parts, but still follows a traditional empirical method, the management mode is extensive, and the effect is very little, so that the establishment of a scientific and reasonable spare part inventory control strategy is a powerful measure for reducing the unit wind power generation cost.
The main purpose of spare part inventory management of parts is to ensure the continuous and stable operation of large-scale production equipment and reduce the production pause loss caused by the damage or failure of the parts. Spare parts inventory management is different from the inventory management of semi-finished products and raw materials, and the number of spare parts is not dependent on the demand of customers, but is determined by equipment maintenance strategies, replenishment strategies and the like. By establishing an optimization model, the sum of expected values of purchase cost, warehousing cost and shutdown loss cost is taken as an objective function, and the optimal replenishment strategies corresponding to different parts, namely the optimal values of the stock levels of spare parts, can be obtained.
However, as the large-scale equipment of the wind generating set has a complex structure, the components have an intricate and complex dependency relationship, the factors causing system faults are various, and certain components also have substitutes corresponding to the components, the reasonable evaluation of the stock shortage loss cost of each component is a key step for establishing the spare part inventory optimization problem.
Disclosure of Invention
The invention provides a spare part inventory optimization method for wind generating sets to solve the problems, which is based on a fault tree analysis method and reasonably evaluates responsibility proportion of different parts to system failure from two angles of system structure positions where the parts are located and historical fault rates of the parts, determines shutdown loss caused by shortage of each part, then establishes an optimization model, and solves the optimal inventory level of the different spare parts, namely an optimal replenishment strategy.
In order to solve the problems, the invention adopts the following technical scheme:
the invention discloses a method for optimizing spare part inventory of parts of a wind generating set, which comprises the following steps of:
s1: carrying out mode influence analysis on the fault behavior of the wind generating set, and establishing a corresponding fault tree model, wherein a top event in the fault tree model represents a system fault, and a bottom event in the fault tree model represents the damage of a certain replaceable part;
s2: finding out all minimum cut sets in the fault tree model according to the fault tree model of the wind generating set;
s3: solving the occurrence probability of the top event in the fault tree model according to the structure functions of the minimum cut set and the fault tree model;
s4: according to the occurrence probability of different bottom events in the fault tree model, the Bayesian posterior probability of the different bottom events is calculated by combining the logical structure relation of the different bottom events displayed by the fault tree model, the fault duty ratio of the different bottom events is further calculated, and finally, the part out-of-stock penalty loss corresponding to the different bottom events is determined by combining the total economic loss caused by the top event being in fault;
s5: comprehensively considering the purchasing cost, the warehousing cost and the out-of-stock loss cost of the parts, and establishing a part inventory optimization model;
s6: and calculating the optimal solution of the part inventory optimization model.
Preferably, the step S1 includes the steps of:
establishing a fault tree model, wherein in the fault tree model, capital letters represent all mutually independent fault reasons and represent specific replaceable parts damage, namely bottom events of the fault tree model; the middle event of the fault tree model is MjRepresenting a fault appearance or a previous level event; the top event of the fault tree model is T, which represents a system fault;
in the fault tree model of wind generating set, char i]Represents the ith bottom event, eiRepresenting the state variables corresponding to the ith base event, the values of the state variables can be determined by the following formula,
Figure GDA0003107277990000021
using vectors
Figure GDA0003107277990000022
Representing the combination of all state variables, the structural function of the fault tree model can then be written
Figure GDA0003107277990000023
State variable e of simultaneous top eventsTComprises the following steps:
Figure GDA0003107277990000024
preferably, the method for finding all the minimal cut sets in the fault tree model in step S2 includes the following steps: and simplifying the structural function of the fault tree model according to the Boolean power law, the Boolean absorption law and the Boolean distribution law, and solving all minimum cut sets in the fault tree model according to the simplified structural function.
Preferably, the step S3 includes the steps of:
the relationship between the probability of the top event and the structure function is:
Figure GDA0003107277990000031
because the minimal cut sets are not necessarily mutually exclusive, when solving the joint probability of the minimal cut sets with non-empty intersection, the union of all the minimal cut sets needs to be simplified into the union of a plurality of mutually exclusive sets by using a repulsion principle, and then a probability accumulation formula can be used, namely the non-intersection formula is used for solving, wherein the formula of the repulsion principle of the set is as follows:
Figure GDA0003107277990000032
wherein A isiThe minimum cut set of the fault tree model is Am, the mth cut set of the fault tree model is Am, and m is the number of the cut sets of the fault tree model; (As can be seen, as the fault tree is scaled up, the number of minimal cut sets increases, solving the probability of a top event based on the structure function in the form of the minimal cut sets creates a problem of combinatorial explosion, i.e., the number of additive terms in the probability expression grows exponentially.
According to an ITE rule, all the minimal cut sets of the fault tree model are taken as subtrees and converted into a binary decision diagram; combining the graph theory and an ITE rule to perform summation operation on the fault tree subtree; (in the ITE rule, it is specified that the left branch path of each intermediate node represents that the node occurs, the right branch path represents that the node does not occur, and the branch with the leaf node of "1" is the active branch).
Obtaining an uncrosslinked structure function through a depth-first search algorithm;
and mutually exclusive disjunctions formed by all the addition items in the uncrossed structural function, and obtaining the probability expression of the top event by combining the probability summation formula of the mutually exclusive set according to the uncrossed structural function.
Preferably, the step S4 includes the steps of:
according to a Bayes posterior probability formula:
Figure GDA0003107277990000033
and calculating the fault duty ratio of different bottom events by combining the minimum cut set obtained in the step S2 and the occurrence probability of the top event obtained in the step S3:
Figure GDA0003107277990000041
wherein, PjIndicates the fault duty ratio of the jth bottom event, char j]Represents the jth bottom event, Ω is the set of all bottom events, Pr { char [ j ]]T represents the probability of the top and jth bottom events occurring simultaneously, Pr { char [ i [ ]]T represents the probability of the top event and the ith bottom event occurring simultaneously, and Pr { T } represents the probability of the top event occurring;
total economic loss C caused after failure of the ultimate binding top eventtotalDetermining the part shortage penalty loss p corresponding to the jth bottom eventj，
Figure GDA0003107277990000042
Preferably, the step S5 includes the steps of:
selecting an (r, Q) replenishment strategy as a modeling basis, wherein the (r, Q) replenishment strategy is as follows: when the stock level of a certain part is lower than a threshold value r, ordering goods with the total number of Q from a part manufacturer at one time, wherein the random variable of the stock level is subjected to uniform distribution with the value range of { r +1, r + 2., (r + Q) };
assuming that the order delivery time is a constant L which does not change along with the time, the total demand of the parts during the replenishment period is D, the average value of the total demand is λ L, wherein λ is the demand rate of the parts in unit time, the demand of the parts during the replenishment period is essentially determined by the failure times of the parts, and the failure probability of the parts is the same each day, so that the process can be regarded as a Bernoulli test which repeats L times, the demand rate λ can be replaced by the failure rate, and the magnitude difference between the failure rate and the repetition times is very large, so that the total demand of the parts during the replenishment period is approximately regarded as a Poisson distribution with a parameter of λ L:
Figure GDA0003107277990000043
finally, establishing a part inventory optimization model as follows:
Figure GDA0003107277990000051
s.t.r＝0，1，2，...，N
Q＝0，1，2，...，N，
wherein C (r, Q) is an expectation value of the total cost in unit time, K is the purchase cost of the unit quantity of part goods, h is the warehousing cost of the unit goods in unit time, and p is the default penalty loss of the unit quantity of part goods in unit time; r and Q are decision variables in the optimization problem and are both non-negative integers.
Preferably, the step S6 includes the steps of:
extracting the following functions from the part inventory optimization model:
Figure GDA0003107277990000052
g (y) is a unimodal function with respect to y, and
Figure GDA0003107277990000053
the extreme point of g (y) is then the minimum point of the function, so that the following inequality can be obtained,
Figure GDA0003107277990000054
wherein, y*To solve for the initial value of the global optimal solution of the part inventory optimization model,
from the above inequality, y can be obtained*The analytical expression of (1):
Figure GDA0003107277990000055
and taking the obtained result as input, and finally obtaining the optimal (r, Q) replenishment strategy of the fan parts through the following iterative algorithm, wherein the iterative algorithm is as follows:
step1. according to y*Y is calculated by the analytical expression of*；
And step2, carrying out initial value assignment operation: q. q.smin＝y*，qmax＝y*；
And step3, carrying out assignment operation: r ═ qmin-1，Q＝qmax-qmin+1；
Step4. if min { g (r), g (r + Q +1) } is larger than or equal to c (r, Q), the program is jumped out, otherwise, the program jumps to Step 3;
step5, if g (r) is less than or equal to g (r + Q +1), carrying out assignment operation: q. q.smin＝qmin-1, otherwise performing an assignment operation: q. q.smax＝qmax+1；
Step6. jump to Step3.
The invention has the beneficial effects that: based on a fault tree analysis method, from two angles of the system structure position where the part is located and the historical fault rate of the part, the responsibility proportion of different parts to system failure is reasonably evaluated, the current market price level, the average generating power and the average generating time length are combined to determine the shutdown loss caused by the shortage of each part, then an optimization model is established, and the optimal stock level, namely the optimal replenishment strategy, of different spare parts is solved.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is an exemplary diagram of a fault tree model.
FIG. 3 is a diagram of a transformation process of a fault tree minimal cut set and a binary decision diagram.
FIG. 4 is a diagram of the final result of a binary decision diagram.
FIG. 5 is a case diagram of a fault tree model of a wind generating set.
FIG. 6 is a result diagram of a binary decision diagram of a wind turbine generator system.
Detailed Description
The technical scheme of the invention is further specifically described by the following embodiments and the accompanying drawings.
Example (b): the method for optimizing the stock of spare parts of the wind generating set in the embodiment is shown in fig. 1 and comprises the following steps:
s1: carrying out mode influence analysis on the fault behavior of the wind generating set, and establishing a corresponding fault tree model, wherein a top event in the fault tree model represents a system fault, and a bottom event in the fault tree model represents the damage of a certain replaceable part;
s2: performing qualitative analysis according to the fault tree model of the wind generating set, simplifying the structural function of the fault tree model and finding out all minimum cut sets in the fault tree model;
s3: carrying out quantitative analysis according to the minimum cut set and the structural function of the fault tree model, and solving the probability of occurrence of a top event in the fault tree model;
s4: according to the occurrence probability of different bottom events in the fault tree model, the Bayesian posterior probability of the different bottom events is calculated by combining the logical structure relation of the different bottom events displayed by the fault tree model, the fault duty ratio of the different bottom events is further calculated, and finally, the part out-of-stock penalty loss corresponding to the different bottom events is determined by combining the total economic loss caused by the top event being in fault;
s5: comprehensively considering the purchasing cost, the warehousing cost and the out-of-stock loss cost of the parts, and establishing a part inventory optimization model;
s6: and calculating the optimal solution of the part inventory optimization model.
Step S1 includes the following steps:
establishing a fault tree model, wherein in the fault tree model, capital letters represent all mutually independent fault reasons and represent specific replaceable parts damage, namely bottom events of the fault tree model; the middle event of the fault tree model is MjRepresenting a fault appearance or a previous level event; the top event of the fault tree model is T, which represents a system fault;
in the fault tree model of wind generating set, char i]Represents the ith bottom event, eiRepresenting the state variables corresponding to the ith base event, the values of the state variables can be determined by the following formula,
Figure GDA0003107277990000071
using vectors
Figure GDA0003107277990000072
Representing the combination of all state variables, the structural function of the fault tree model can then be written
Figure GDA0003107277990000073
State variable e of simultaneous top eventsTComprises the following steps:
Figure GDA0003107277990000074
the fault tree model can visually display all fault reasons causing system faults and can reflect complex logic relations among different fault reasons.
The method for finding all the minimal cut sets in the fault tree model in step S2 includes the following steps: and simplifying the structural function of the fault tree model according to the Boolean power law, the Boolean absorption law and the Boolean distribution law, and solving all minimum cut sets in the fault tree model according to the simplified structural function.
The Boolean power law is as follows: AA ═ a, a + a ═ a,
the boolean absorption law is as follows: a + AB is equal to A,
the boolean distribution law is as follows: a (B + C) ═ AB + AC.
Step S3 includes the following steps:
the relationship between the probability of the top event and the structure function is:
Figure GDA0003107277990000075
because the minimal cut sets are not necessarily mutually exclusive, when solving the joint probability of the minimal cut sets with non-empty intersection, the union of all the minimal cut sets needs to be simplified into the union of a plurality of mutually exclusive sets by using a repulsion principle, and then a probability accumulation formula can be used, namely the non-intersection formula is used for solving, wherein the formula of the repulsion principle of the set is as follows:
Figure GDA0003107277990000081
wherein A isiThe minimum cut set of the fault tree model is Am, the mth cut set of the fault tree model is Am, and m is the number of the cut sets of the fault tree model; (As can be seen, as the fault tree is scaled up, the number of minimal cut sets increases, solving the probability of a top event based on the structure function in the form of the minimal cut sets creates a problem of combinatorial explosion, i.e., the number of additive terms in the probability expression grows exponentially.
According to an ITE rule, all the minimal cut sets of the fault tree model are taken as subtrees and converted into a binary decision diagram; combining the graph theory and an ITE rule to perform summation operation on the fault tree subtree; (in the ITE rule, it is specified that the left branch path of each intermediate node represents that the node occurs, the right branch path represents that the node does not occur, and the branch with the leaf node of "1" is the active branch).
Obtaining an uncrosslinked structure function through a depth-first search algorithm; (it should be noted that in the process of searching for an effective branch, a pruning rule can be used to reduce the use of stacks and improve the search efficiency.
And mutually exclusive disjunctions formed by all the addition items in the uncrossed structural function, and obtaining the probability expression of the top event by combining the probability summation formula of the mutually exclusive set according to the uncrossed structural function.
The main purpose of the step is to convert the fault tree model into a corresponding binary decision diagram based on the minimum cut set according to the fragrance decomposition theorem and the IF-THEN-ELSE rule. And then, carrying out binary decision diagram operation according to a graph theory, and obtaining an uncrosslinked form of a structural function by utilizing a depth-first search algorithm for calculating the top event fault probability. The binary decision diagram method can be used for quickly and effectively calculating the failure probability of the top event, and the problem of combined explosion caused by the repulsion principle is solved.
For example: fig. 2 shows an exemplary diagram of a fault tree model, in which there are 5 bottom events, A, B, C, D, E respectively, and 5 state variables e1，e2，...，e5Correspondingly, the structure function of the fault tree model is as follows:
Figure GDA0003107277990000082
the 4 minimal cut sets of the fault tree are obtained according to the structure function as follows:
{e1，e2}，{e3，e4}，{e1，e4，e5}，{e2，e3，e5}。
according to the ITE rule, all the minimal cut sets of the fault tree model are taken as subtrees and converted into a binary decision diagram, as shown in FIG. 3, wherein MCS refers to the minimal cut sets which are already obtained;
the sum operation is performed on the fault tree subtrees by combining the graph theory and the ITE rule, the obtained result is shown in FIG. 4, and the uncrossed structure function obtained by the depth-first search algorithm is as follows:
Figure GDA0003107277990000091
according to an uncrossed structure function, combining a probability summation formula of a mutual exclusion set to obtain a probability expression formula of a top event:
Figure GDA0003107277990000092
step S4 includes the following steps:
according to a Bayes posterior probability formula:
Figure GDA0003107277990000093
and calculating the fault liability ratio of different bottom events (replaceable parts) by combining the minimum cut set obtained in the step S2 and the occurrence probability of the top event obtained in the step S3:
Figure GDA0003107277990000094
wherein, PjIndicates the fault duty ratio of the jth bottom event, char j]Represents the jth bottom event, Ω is the set of all bottom events, Pr { char [ j ]]T represents the probability of the top and jth bottom events occurring simultaneously, Pr { char [ i [ ]]Table of, TShowing the probability of the top event and the ith bottom event occurring simultaneously, and Pr { T } showing the probability of the top event occurring;
total economic loss C caused after failure of the ultimate binding top eventtotalDetermining the part shortage penalty loss p corresponding to the jth bottom eventj，
Figure GDA0003107277990000095
The main purpose of the step is to calculate the accident responsibility proportion of different parts, namely to evaluate the responsibility of different parts after the fan is stopped (or the subsystem is in fault). By the index, the stock shortage penalty cost of different parts in a complex system can be quantitatively evaluated.
Step S5 includes the following steps:
selecting an (r, Q) replenishment strategy as a modeling basis, wherein the (r, Q) replenishment strategy is as follows: when the stock level of a certain part is lower than a threshold value r, ordering goods with the total number of Q from a part manufacturer at one time, wherein the random variable of the stock level is subjected to uniform distribution with the value range of { r +1, r + 2., (r + Q) };
assuming that the order delivery time is a constant L which does not change along with the time, the total demand of the parts during the replenishment period is D, the average value of the total demand is λ L, wherein λ is the demand rate of the parts in unit time, the demand of the parts during the replenishment period is essentially determined by the failure times of the parts, and the failure probability of the parts is the same each day, so that the process can be regarded as a Bernoulli test which repeats L times, the demand rate λ can be replaced by the failure rate, and the magnitude difference between the failure rate and the repetition times is very large, so that the total demand of the parts during the replenishment period is approximately regarded as a Poisson distribution with a parameter of λ L:
Figure GDA0003107277990000101
finally, establishing a part inventory optimization model as follows:
Figure GDA0003107277990000102
s.t.r＝0，1，2，...，N
Q＝0，1，2，...，N，
wherein C (r, Q) is an expectation value of the total cost in unit time, K is the purchase cost of the unit quantity of part goods, h is the warehousing cost of the unit goods in unit time, and p is the default penalty loss of the unit quantity of part goods in unit time; r and Q are decision variables in the optimization problem and are both non-negative integers.
Since λ characterizes the parts demand rate per unit time, the numerator of the first term of the objective function is the acquisition cost per unit time. The second term of the objective function reflects the storage cost expectation value, and when the inventory level y is larger than the total demand i, part of the parts need to be stored. The third term of the objective function reflects the expected value of the stock shortage penalty loss, which occurs because the stock level is not enough to meet the total demand during replenishment. Finally, the objective function reflects the expected total cost per unit time corresponding to a unit number of parts, through the action of the denominator.
In the actual logistics management of the wind farm, due to the fact that corresponding discounts exist when a large number of orders are ordered, the wind farm usually adopts a batch type goods feeding strategy, and an (r, Q) replenishment strategy is selected as a basis of modeling. During actual procurement, the time of shipment of the goods is substantially constant, so the order delivery time is considered herein to be a constant L that does not vary with time. During restocking, the parts still need to be used and replaced.
Step S6 includes the following steps:
extracting the following functions from the part inventory optimization model:
Figure GDA0003107277990000111
g (y) is a unimodal function with respect to yAnd is and
Figure GDA0003107277990000112
the extreme point of g (y) is then the minimum point of the function, so that the following inequality can be obtained,
Figure GDA0003107277990000113
wherein, y*To solve for the initial value of the global optimal solution of the part inventory optimization model,
from the above inequality, y can be obtained*The analytical expression of (1):
Figure GDA0003107277990000114
and taking the obtained result as input, and finally obtaining the optimal (r, Q) replenishment strategy of the fan parts through the following iterative algorithm, wherein the iterative algorithm is as follows:
step1. according to y*Y is calculated by the analytical expression of*；
And step2, carrying out initial value assignment operation: q. q.smin＝y*，qmax＝y*；
And step3, carrying out assignment operation: r ═ qmin-1，Q＝qmax-qmin+1；
Step4. if min { g (r), g (r + Q +1) } is larger than or equal to c (r, Q), the program is jumped out, otherwise, the program jumps to Step 3;
step5, if g (r) is less than or equal to g (r + Q +1), carrying out assignment operation: q. q.smin＝qmin-1, otherwise performing an assignment operation:
qmax＝qmax+1；
step6. jump to Step3.
Examples are: in the following, taking a foundation and tower support subsystem of a large-scale wind generating set with a certain amount of rated power and 2MW produced by a certain wind power generation corporation as an example, the optimal storage level and the optimal replenishment strategy of replaceable parts in the system are analyzed in detail.
According to the existing literature and relevant operation and maintenance manuals, a fault tree model of the foundation and tower system of the wind generating set is built, as shown in fig. 5, and explanatory descriptions of corresponding events are shown in a table I and a table II.
Figure GDA0003107277990000115
Figure GDA0003107277990000121
Table-fault tree bottom event fault probability statistics
Reference number Intermediate events
G01 Foundation tower failure
G02 Yaw drive failure
G03 Weather unit failure
G04 Yaw motor power supply loop fault
Table two fault tree intermediate events
According to the principle described in step S2, the 5 minimal cut sets of the fault tree can be obtained as:
{A}，{B}，{C}，{D，E}，{F}，
the minimal cut sets are converted into corresponding binary decision diagrams according to the method described in step S3, and finally simplified by graph theory method to obtain the result, as shown in fig. 6,
through depth-first search, the uncrosslinked form of the original structure function can be obtained from the binary tree
Figure GDA0003107277990000122
Correspondingly, the expression for obtaining the probability of the top event is as follows:
Pr{TE}＝x1+(1-x1)x2+(1-x1)(1-x2)x3+(1-x1)(1-x2)(1-x3)x4x5
+(1-x1)(1-x2)(1-x3)x4(1-x5)x6+(1-x1)(1-x2)(1-x3)(1-x4)x6，
in order to calculate the shortage penalty losses of different parts, the actual power consumption cost of wind power and the average single-day power generation time length need to be referred to, and the economic loss caused by the failure of the foundation and the tower system is determined. And then according to the formula given in the step S4, calculating the duty ratio of different parts by combining the minimum cut set and the top event probability, and finally decoupling the total loss of the shutdown of the fan and refining the total loss of the shutdown of the fan to the default penalty loss of the different parts.
Research shows that the loss of the power generation amount per day caused by the fault of the supporting system is converted into economic benefit, and the cost is about 18095 yuan. The statistical probability of the historical faults of each bottom event in the table is substituted into a formula, the probability of the top event can be estimated to be 0.037957, and the duty ratio corresponding to each part in the fault tree is calculated, as shown in table three.
Figure GDA0003107277990000123
Duty ratio of tree-bottom event with table three faults
Finally, the economic loss caused by the top event fault and the responsibility proportion of different bottom events are comprehensively considered, and the economic loss and the responsibility proportion of different bottom events are calculated according to a formula
Figure GDA0003107277990000131
The out-of-stock penalty loss p per unit quantity of parts per unit time is calculated as shown in table four. By combining the failure rates of different parts and the logical relations of different parts shown in fig. 5, the effectiveness of the duty ratio given by table three can be analyzed: although the failure rate of the bottom events D and E is relatively large, the final calculated duty ratio is not the maximum due to the special logical relationship ("and").
Figure GDA0003107277990000132
Parameters for table four spare part inventory optimization model
Meanwhile, the parameters used in the part inventory optimization model, including the part demand rate λ and the order delivery time L in unit time, the acquisition cost K of the parts in unit quantity, and the warehousing cost h of the parts in unit quantity in unit time, are listed in table four.
According to the optimization algorithm introduced in step S5, through programmed calculation, the optimal replenishment threshold r and the corresponding optimal replenishment quantity Q of the parts corresponding to different bottom events can be obtained, as shown in table five.
Details of the components Replenishment threshold r Replenishment quantity Q
Yaw brake
1 31
Yaw motor 0 12
Yaw brake disc 0 7
Mechanical anemometer 0 29
Mechanical anemoscope 0 27
Yaw loop contactor 0 3
Optimal replenishment strategy for spare parts of different wind generating set parts
And the optimal replenishment strategies of different fan parts can be obtained by integrating the optimal replenishment threshold and the single replenishment quantity. For example, the yaw brake has a higher number of single restocks due to higher penalty costs for out-of-stock, longer lead times for orders, and lower storage costs. Meanwhile, in order to avoid the situation of out-of-stock in the order delivery period, the replenishment threshold value of the part is larger than zero, and the part is immediately kept replaceable by spare parts.

Claims (3)

1. A method for optimizing inventory of spare parts of a wind generating set is characterized by comprising the following steps:
step S1: carrying out mode influence analysis on the fault behavior of the wind generating set, and establishing a corresponding fault tree model, wherein a top event in the fault tree model represents a system fault, and a bottom event in the fault tree model represents the damage of a certain replaceable part;
establishing a fault tree model, wherein in the fault tree model, capital letters represent all mutually independent fault reasons and represent specific replaceable parts damage, namely bottom events of the fault tree model; the middle event of the fault tree model is MjRepresenting a fault appearance or a previous level event; the top event of the fault tree model is T, which represents a system fault;
in the fault tree model of wind generating set, char i]Represents the ith bottom event, eiRepresenting the state variables corresponding to the ith base event, the values of the state variables can be determined by the following formula,
Figure FDA0003107277980000011
using vectors
Figure FDA0003107277980000012
Representing the combination of all state variables, the structural function of the fault tree model can then be written
Figure FDA0003107277980000013
Meanwhile, the state variable eT of the top event is as follows:
Figure FDA0003107277980000014
step S2: finding out all minimum cut sets in the fault tree model according to the fault tree model of the wind generating set;
step S3: according to the structure function of the minimum cut set and the fault tree model, solving the occurrence probability of the top event in the fault tree model:
the relationship between the probability of the top event and the structure function is:
Figure FDA0003107277980000015
because the minimal cut sets are not necessarily mutually exclusive, when solving the joint probability of the minimal cut sets with non-empty intersection, the union of all the minimal cut sets needs to be simplified into the union of a plurality of mutually exclusive sets by using a repulsion principle, and then a probability accumulation formula can be used, namely the non-intersection formula is used for solving, wherein the formula of the repulsion principle of the set is as follows:
Figure FDA0003107277980000016
wherein A isiIs a minimal cut set of fault tree models, AmM is the mth cut set of the fault tree model, and m is the number of the cut sets of the fault tree model;
according to an ITE rule, all the minimal cut sets of the fault tree model are taken as subtrees and converted into a binary decision diagram;
combining the graph theory and an ITE rule to perform summation operation on the fault tree subtree;
obtaining an uncrosslinked structure function through a depth-first search algorithm;
mutually exclusive disjunctions formed by all the addition items in the uncrossed structural function, and obtaining a probability expression of the top event by combining a probability summation formula of the mutually exclusive set according to the uncrossed structural function;
step S4: according to a Bayes posterior probability formula:
Figure FDA0003107277980000021
and calculating the fault duty ratio of different bottom events by combining the minimum cut set obtained in the step S2 and the occurrence probability of the top event obtained in the step S3:
Figure FDA0003107277980000022
wherein, PjIndicates the fault duty ratio of the jth bottom event, char j]Represents the jth bottom event, Ω is the set of all bottom events, Pr { char [ j ]]T represents the probability of the top and jth bottom events occurring simultaneously, Pr { char [ i [ ]]T represents the probability of the top event and the ith bottom event occurring simultaneously, and Pr { T } represents the probability of the top event occurring;
total economic loss C caused after failure of the ultimate binding top eventtotalDetermining the part shortage penalty loss p corresponding to the jth bottom eventj，
Figure FDA0003107277980000023
Step S5: taking an (r, Q) replenishment strategy as a modeling basis, integrating the part purchase cost, the storage cost and the stock shortage loss cost, assuming that the order delivery time is a constant L which does not change along with time, and the total demand of the parts during replenishment is D, the average value of the total demand is lambda L, wherein lambda is the part demand rate in unit time, and during replenishment, the demand of the parts is determined by the fault times of the parts,
Figure FDA0003107277980000025
the probability of the fault of the part every day is the same, the process is a Bernoulli test which is repeated for L times, the demand rate lambda is replaced by the fault rate, and the total demand of the part during the replenishment period follows Poisson distribution with the parameter lambda L:
Figure FDA0003107277980000024
establishing a part inventory optimization model;
Figure FDA0003107277980000031
s.t.r＝0，1，2，...，N
Q＝0，1，2，...，N
wherein r is a stock level threshold, Q is a replenishment quantity, L is an order delivery time, D is a part demand quantity during replenishment, lambda is a part demand rate in unit time, C (r, Q) is an expected value of total cost in unit time, K is a purchase cost of a unit quantity of part goods, h is a warehousing cost of the unit goods in unit time, and p is an out-of-stock penalty loss of the unit quantity of parts in unit time; r and Q are decision variables in the optimization problem and are both non-negative integers; the (r, Q) replenishment strategy is: when the stock level of a certain part is lower than a threshold value r, ordering goods with the total number of Q from a part manufacturer at one time, wherein the stock level is subjected to uniform distribution with the value range of { r +1, r + 2., (r + Q) };
step S6: and calculating the optimal solution of the part inventory optimization model.
2. The method for optimizing inventory of spare parts for parts of a wind turbine generator system as claimed in claim 1, wherein the step S2 of finding all the minimal cut sets in the fault tree model comprises the steps of: and simplifying the structural function of the fault tree model according to the Boolean power law, the Boolean absorption law and the Boolean distribution law, and solving all minimum cut sets in the fault tree model according to the simplified structural function.
3. The method for optimizing inventory of spare parts for parts of a wind turbine generator system according to claim 1 or 2, wherein the step S6 comprises the steps of:
extracting the following functions from the part inventory optimization model:
Figure FDA0003107277980000032
g (y) is a unimodal function with respect to y, and
Figure FDA0003107277980000033
thus, the extreme point of G (y) is the minimum point of G (y), the following inequality is obtained,
Figure FDA0003107277980000034
wherein, y*To solve for the initial value of the global optimal solution of the part inventory optimization model,
from the above inequality, y can be obtained*The analytical expression of (1):
Figure FDA0003107277980000041
wherein, p is the loss of the goods shortage punishment of the parts in unit quantity in unit time, and h is the warehousing cost of the unit goods in unit time;
will obtain the result y*And finally, obtaining an optimal (r, Q) replenishment strategy of the fan parts by using the following iterative algorithm as input, wherein the iterative algorithm is as follows:
step1, according to y*Y is calculated by the analytical expression of*；
And Step2, performing initial value assignment operation: q. q.smin＝y*，qmax＝y*；
Step3, carrying out assignment operation: r ═ qmin-1，Q＝qmax-qmin+1；
Step4, if min { g (r), g (r + Q +1) } is larger than or equal to c (r, Q), jumping out of the program, otherwise jumping to Step 3;
step5, if g (r) is less than or equal to g (r + Q +1), carrying out assignment operation: q. q.smin＝qmin-1, otherwise performing an assignment operation: q. q.smax＝qmax+1；
Step6, jump to Step3.
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