A maintenance task allocation method for hydropower plants considering time-dependent dynamics

Abstract

The present invention provides a method for allocating maintenance tasks for a hydropower plant that takes into account dynamic temporal dependencies. First, a maintenance preparation time model is proposed that takes into account uncertainties such as the travel time required for maintenance personnel to reach the maintenance site and the tool preparation time. Then, a maintenance process time model is proposed that takes into account the uncertainty of the maintenance time of a single working face, and the maintenance preparation time model and the maintenance process time model are converted into maintenance constraints for the maintenance task allocation model. Finally, under the maximum power generation power constraint allowed by the State Grid Dispatching Center, a maintenance task allocation model for a hydropower plant that takes into account dynamic temporal dependencies is established, taking into account maintenance constraints, hydraulic system operation constraints, and equipment post-maintenance commissioning constraints. This model can quickly, efficiently, and effectively allocate maintenance tasks for a hydropower plant, improve work efficiency, reduce labor costs, and ensure the quality and quantity of maintenance tasks are completed on time.

Description

Technical Field

[0001] The invention relates to the technical field of maintenance and dispatching of hydropower stations, and in particular to a method for allocating maintenance tasks of hydropower stations taking into account dynamic time dependency. Background Art

[0002] A hydroelectric power plant has multiple hydroelectric units. Every year, the operating personnel will arrange the A, B, C, and D maintenance of the units, the full maintenance, partial maintenance, and annual maintenance of the transmission lines and circuit breakers, and the maintenance period of each equipment based on factors such as historical and real-time water inflow conditions, the units' previous maintenance history, and the number of maintenance team members.

[0003] After the maintenance tasks are scheduled, the operations department first implements safety measures, followed by the maintenance department issuing invoices and carrying out the corresponding maintenance work. During this period, the production department faces challenges such as a large variety of equipment, rapid staff turnover, and heavy renovation tasks. This inevitably leads to many overlapping work schedules during the maintenance period. During this period, the maintenance department director generally conducts a manual assessment of the total workload, the expected completion time for each work area, the arrival time of maintenance personnel, and each person's expertise, based on the number of work areas that day, the number of personnel on duty, and past maintenance experience. This assessment then determines each person's work tasks and work order based on their experience.

[0004] However, arranging maintenance tasks based on experience will lead to negative effects such as low resource utilization, low staff efficiency, high time cost, some employees have to run back and forth on multiple work surfaces, and need to work overtime every day to complete the work on schedule; moreover, the maintenance task preparation time (including spare parts and tools preparation time, travel time from the office to the maintenance site) and the actual maintenance work time together lead to the maintenance time of a single work surface having a time dynamic dependence, which is specifically reflected in: ① The travel time from the office to the maintenance site, the spare parts and tool replenishment time are all uncertain, recorded as maintenance preparation time uncertainty; ② The maintenance time is uncertain due to the different majors of maintenance personnel, different work status on the day, and the time it takes to return to the office or warehouse to get tools because they forget to bring them, which is recorded as maintenance process time uncertainty. Summary of the Invention

[0005] In response to the problems in the above background technology, the present invention provides a method for allocating maintenance tasks of hydropower plants taking into account dynamic time dependence, which can quickly, efficiently and effectively allocate maintenance tasks of hydropower plants, improve work efficiency, reduce labor costs, ensure quality and quantity, and complete maintenance tasks on time.

[0006] In order to achieve the above-mentioned technical features, the purpose of the present invention is achieved as follows: a method for allocating maintenance tasks of a hydropower plant taking into account dynamic time dependencies, firstly, a maintenance preparation time model is proposed which takes into account the uncertainty factors of the movement time of maintenance personnel arriving at the maintenance site and the tool preparation time; then, a maintenance process time model is proposed which takes into account the uncertainty of the maintenance time of a single working face, and the maintenance preparation time model and the maintenance process time model are converted into maintenance constraints of a maintenance task allocation model; finally, under the constraint of the maximum power generation power allowed by the State Grid Dispatching Center, with minimizing the system's abandoned water power and minimizing the latest completion time of all maintenance tasks as the objective function, a maintenance task allocation model for a hydropower plant taking into account dynamic time dependencies is established, taking into account maintenance constraints, hydraulic system operation constraints, and equipment post-maintenance commissioning constraints.

[0007] The specific modeling process of the maintenance preparation time model is as follows:

[0008] For a hydropower plant, the maintenance department is divided into five departments: automation, power generation, measurement and control, protection, and machinery. Each department is further divided into equipment management teams. When the power plant issues a maintenance task r to the maintenance department g, each team will assign the task to the corresponding equipment management team s, where g = 1, 2, 3, 4, 5 respectively represent the automation, power generation, measurement and control, protection, and machinery departments; s = 1, 2, 3, ... respectively represent the sth equipment management team in a single department.

[0009] Assumptions It represents the preparation time for team s of maintenance department g to complete maintenance task r;

[0010] Using G g,s represents the g department s group, where G g,s When accepting r task, Need to consider before this G g,s Have you performed other tasks? Includes the following:

[0011]

[0012] Where, represents the maintenance preparation time of task r; represents the number of spare parts remaining after team s of department g completes task r1; M represents the maximum number of spare parts that team s of department g can carry; g,s,r represents the number of spare parts required by team s in department g to perform task r; represents the Dirac function, that is, when hour, when hour, vg,s represents the average walking speed of team s in department g; Represents the time it takes for maintenance personnel to prepare spare parts in the warehouse; p represents the warehouse location; Dis(r1,p,r) represents the shortest distance function between the maintenance personnel’s location at task r1, the location at warehouse p, and the location at task r, which is calculated here using the Dijkstra shortest path algorithm; Dis(r1,r) represents the shortest distance function between the location at task r1 and the location at task r, which is calculated here using the Dijkstra shortest path algorithm.

[0013] Maintenance preparation time is uncertain. Based on this, in order to characterize the uncertainty of the time it takes for a team to complete a task, β g,s Indicator to indicate actual completion time Completion time The ratio between

[0014] Different teams will have different β g,s , β g,s The calculation method includes the following steps:

[0015] Step 1: Create a historical database of the time that department g team s has completed a task over the years. Assume For a set of historical data, record N sets of data;

[0016] Step 2: Adoption Get the uncertainty index β of department g team s for many years g,s ;

[0017] Step 3: Obtain the probability distribution of the uncertainty parameters of the team maintenance time through a data-driven approach. Fit the historical maintenance time data of different teams separately to obtain the corresponding probability density distribution. The more historical data, the more accurate the probability distribution will be.

[0018] Step 4: Use the K-means clustering method to obtain the typical scenarios of maintenance time uncertainty for each team;

[0019] According to the fitted typical scenario, the maintenance preparation time is expressed as:

[0020] The specific modeling process of the maintenance process time model is as follows:

[0021] During the maintenance process, uncertainty in maintenance time comes from three sources: ① Forgetting certain maintenance tools means having to return to the warehouse or office to find them, which affects the maintenance process time; ② The difficulty of performing the same task varies in different on-site environments, resulting in different maintenance times; ③ Different teams and different professionals have different efficiency levels when handling the same maintenance task, making it difficult to accurately estimate the maintenance time for each maintenance task.

[0022] Based on this, the present invention assumes that the maintenance process time obeys a truncated normal distribution, and its probability density function is expressed as:

[0023]

[0024] Where, Indicates the maintenance process time; represent the mean and standard deviation of the paternal normal distribution, respectively; represents variance; a, b represent the lower and upper bounds of the truncation interval respectively; represents the probability density function; φ(·), Φ(·) represent the probability density function and cumulative distribution function of the parent normal distribution, respectively;

[0025] Then the cumulative distribution function of the maintenance process time is:

[0026]

[0027] Where, represents the cumulative distribution function;

[0028] The mean μ1 of the maintenance process time is:

[0029]

[0030] The standard deviation σ1 of the maintenance process time is:

[0031]

[0032] In the formula, α and β are intermediate variables;

[0033] For the maintenance process time, assuming but In the interval (a,b), we have:

[0034]

[0035] Therefore, the probability density function of the maintenance process time is derived as:

[0036]

[0037] According to formula (9), the maintenance process time for group s of maintenance department g to complete maintenance task r can be sampled.

[0038] The maintenance model constraint conditions of the maintenance constraint are as follows:

[0039] When the maintenance sequence is a variable to be determined, the maintenance sequence and maintenance preparation time need to be reflected in the form of constraints. Maintenance process time the connections between them;

[0040] ① Maintenance constraints:

[0041]

[0042]

[0043] Where S g,s,r,r2 Indicates the maintenance order. If the maintenance order of department g team s is: task r first and then r2, then S g,s,r,r2 =1, otherwise S g,s,r,r2 =0;S g,s,r1,r Indicates the maintenance order. If the maintenance order of department g team s is: task r1 first and then r, then S g,s,r1,r =1, otherwise S g,s,r1,r =0;S g,s,p,r Indicates the maintenance order. If the maintenance order of department g team s is: task p first and then r, then S g,s,p,r =1, otherwise S g,s,p,r =0; Z b represents the set of all teams in department g; Z g It represents the combination of automation, power generation, measurement and control, protection, and machinery; Z a , Z d and Z e They correspond to the task nodes, starting nodes and virtual ending nodes in the set, and the virtual ending node indicates the end of the maintenance sequence of all maintenance groups; if the team s of the maintenance department g starts from the warehouse p, then ξ g,s,p =1;h r Indicates the start time of maintenance; f p The departure time from warehouse p is set as time 0; f r 、f r1 Indicates the maintenance completion time of task r and task r1; y r,t Indicates whether component r can be put into operation at time t, 1 indicates that it is put into operation; r, r1, and r2 are the maintenance task numbers, and the order is: r1, r, r2; M is a large number; t represents time; χ represents the latest completion time of the task in a day;

[0044] In constraint (16), the maintenance preparation time Maintenance process time It is still a variable. According to the maintenance preparation time model, the maintenance preparation time The constraints are expressed as:

[0045]

[0046] Constraints (20) and (22) mean that if S g,s,r1,r =1, then The calculation formula is (1); otherwise, Constraint (23) is the same as constraint (2); constraint (24) can be used to achieve the Logical judgment; Constraint (25) represents the number of spare parts initially brought by team s of department g; T represents the time interval;

[0047] ② Equipment commissioning constraints:

[0048] The maintenance task decision model for a hydropower plant needs to further consider the order in which equipment is put into operation after maintenance is completed. Based on this, the following constraints are used to represent this operation problem:

[0049]

[0050] Where Z n and Z l Respectively represent the connection points of the hydropower plant units and the high-voltage line set; n and l represent the nth unit connection point and the lth line; o(l) and p(l) represent the first and last nodes of line l; j i,t 、j i,t-1 Represents the actual operating status of device i at time t and t-1 respectively; j l,t Indicates the actual operating status of device l at time t; j o(l),t ,j p(l),t Respectively represent the actual operating status of the beginning and end of line l at time t; y n,t ,y l,t Respectively represent the operational status of equipment n and equipment l;

[0051] Where, the constraint on the right is nonlinear, and the nonlinear term is linearized into the following constraint condition:

[0052]

[0053] Where y l,t ,j o(l),t 、j p(l),t If one of them is 0, then j l,t is equal to 0, which means that line l cannot be put into operation at time t;

[0054] ③System operation constraints:

[0055] 1) Power balance constraints:

[0056]

[0057] Where A G ,A Line They represent the incidence matrix respectively; represents the power flow of line l at hour t; represents the dispatching demand of the national power dispatching center for the power plant at the i-th contact unit in time period t; represents the power output of the i-th hydroelectric generating unit in the hydroelectric power plant during period t; represents the power generated by the unit at the i-th node abandoning water at time t; θ i,t represents the voltage phase angle of node i at hour t; θ j,t represents the voltage phase angle of node j at hour t; X ij represents the reactance of line (i, j);

[0058] 2) Phase angle upper and lower limit constraints:

[0059] θ i,t,min ≤θ i,t ≤θ i,t,max (34)

[0060] θ i,t,min ,θ i,t,max They represent the minimum and maximum voltage phase angles of node i at the tth moment respectively;

[0061] 3) Upper and lower limits of hydroelectric generator power

[0062]

[0063] Where, They represent the minimum output power and maximum output power of hydropower unit i at time t respectively;

[0064] 4) Hydroelectric generator climbing constraints:

[0065]

[0066] Where, They represent the upward or downward ramp rate of hydropower unit i at time t respectively; represents the power output of the i-th hydroelectric generator unit in the hydroelectric power plant during the period t-1;

[0067] 5) Reservoir water constraints:

[0068]

[0069] Where V t Hrepresents the reservoir storage capacity at time t, q t represents the reservoir inflow at time t, Q t It represents the power generation flow utilized by the hydropower unit at time t, and Δt is the time interval;

[0070] 6) Reservoir capacity constraints:

[0071]

[0072] Where V t H represents the water storage capacity of the reservoir at time t, and They represent the maximum and minimum values ​​of the reservoir capacity respectively.

[0073] The maintenance task decision objective function is specifically:

[0074] The optimization goal of the maintenance task decision model is to minimize the system water abandonment power and minimize the latest completion time of all maintenance tasks. Therefore, the overall objective function of the maintenance task decision problem is:

[0075]

[0076] Where ω1 and ω2 represent the weights of the abandoned water power and the latest completion time of the maintenance task, respectively; Ψ represents the overall objective function.

[0077] The objective function and constraints of comprehensive maintenance task decision-making, as well as the mathematical programming problem, are solved using Gurobi10.0.3 on the Matlab platform.

[0078] The present invention has the following beneficial effects:

[0079] 1. A method for allocating maintenance tasks for a hydropower plant taking into account dynamic time dependence of the present invention can quickly, efficiently and effectively allocate maintenance tasks for a hydropower plant, thereby improving work efficiency, reducing labor costs, and ensuring quality and quantity and completing maintenance tasks on time.

[0080] 2. The computational complexity of the maintenance task decision model of the present invention is related to the number of maintenance process time uncertainty scenarios. Therefore, the present invention uses the K-means clustering method to process the uncertainty of the maintenance process time to obtain typical scenarios of the maintenance process time. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 It is a diagram of the maintenance arrangement process of the present invention.

[0082] Figure 2 This is the data flow diagram of the maintenance task decision model of the present invention. DETAILED DESCRIPTION

[0083] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0084] Example 1:

[0085] See also Figure 1-2 A maintenance task allocation method for a hydropower plant considering dynamic temporal dependencies is proposed. First, a maintenance preparation time model is proposed that takes into account the uncertainties of the travel time of maintenance personnel arriving at the maintenance site and the tool preparation time. Then, a maintenance process time model is proposed that takes into account the uncertainty of the maintenance time of a single working face, and the maintenance preparation time model and the maintenance process time model are converted into maintenance constraints for the maintenance task allocation model. Finally, under the constraint of the maximum power generation power allowed by the State Grid Dispatching Center, with minimizing the system's abandoned water power and minimizing the latest completion time of all maintenance tasks as the objective function, a maintenance task allocation model for a hydropower plant considering dynamic temporal dependencies is established, taking into account maintenance constraints, hydraulic system operation constraints, and equipment post-maintenance commissioning constraints.

[0086] Example 2:

[0087] 1. The specific modeling process of the maintenance preparation time model is as follows:

[0088] For a hydropower plant, the maintenance department is divided into five departments: automatic, power generation, measurement and control, protection, and machinery. Each department is further divided into more detailed equipment management teams. When the power plant issues a maintenance task r to the maintenance department g, each team will assign the task to the corresponding equipment management team s, where g = 1, 2, 3, 4, 5 respectively represent the automatic, power generation, measurement and control, protection, and machinery departments; s = 1, 2, 3, ... respectively represent the sth equipment management team in a single department. This invention assumes that It represents the preparation time for the maintenance department g's s team to complete the maintenance task r; g,s Indicates g department s group.

[0089] Among them, it should be noted that G g,s When accepting r task, Need to consider before this G g,s Have you performed other tasks? Includes the following:

[0090]

[0091] Where, represents the maintenance preparation time of task r; represents the number of spare parts remaining after team s of department g completes task r1; M represents the maximum number of spare parts that team s of department g can carry; g,s,rrepresents the number of spare parts required by team s in department g to perform task r; represents the Dirac function, that is, when hour, when hour, v g,s represents the average walking speed of team s in department g; Represents the time it takes for maintenance personnel to prepare spare parts in the warehouse; p represents the warehouse location; Dis(r1,p,r) represents the shortest distance function between the maintenance personnel’s location at task r1, the location at warehouse p, and the location at task r, which is calculated here using the Dijkstra shortest path algorithm; Dis(r1,r) represents the shortest distance function between the location at task r1 and the location at task r, which is calculated here using the Dijkstra shortest path algorithm.

[0092] It should be noted that the above analysis shows that the maintenance preparation time is uncertain. Based on this, in order to characterize the uncertainty of the team's task completion time, the present invention proposes β g,s Indicator to indicate actual completion time Completion time The ratio between

[0093] Generally speaking, different teams will have different β g,s , β g,s The calculation method includes the following steps:

[0094] Step 1: Create a historical database of the time that department g team s has completed a task over the years. Assume For a set of historical data, record N sets of data;

[0095] Step 2: Adoption Get the uncertainty index β of department g team s for many years g,s ;

[0096] Step 3: Obtain the probability distribution of the uncertainty parameters of the team maintenance time through a data-driven approach. Fit the historical maintenance time data of different teams separately to obtain the corresponding probability density distribution. The more historical data, the more accurate the probability distribution will be.

[0097] Step 4: Use the K-means clustering method to obtain the typical scenarios of maintenance time uncertainty for each team;

[0098] Therefore, according to the fitted typical scenario, the maintenance preparation time is expressed as:

[0099] 2. The specific modeling process of the maintenance process time model is as follows:

[0100] During the maintenance process, uncertainty in maintenance time comes from three sources: ① Forgetting certain maintenance tools means having to return to the warehouse or office to find them, which affects the maintenance process time; ② The difficulty of performing the same task varies in different on-site environments, resulting in different maintenance times; ③ Different teams and different professionals have different efficiency levels when handling the same maintenance task, making it difficult to accurately estimate the maintenance time for each maintenance task.

[0101] It is important to note that the uncertainty in the time it takes for a team to complete a maintenance task can affect the total completion time of the task, which in turn can affect the power delivery time of the unit or line, resulting in significant economic losses for the hydropower plant. Therefore, finding an appropriate model to describe the time uncertainty of different teams completing a maintenance task is crucial.

[0102] Therefore, the present invention assumes that the maintenance process time obeys the truncated normal distribution, and its probability density function is expressed as:

[0103]

[0104] Where, Indicates the maintenance process time; represent the mean and standard deviation of the paternal normal distribution, respectively; represents variance; a, b represent the lower and upper bounds of the truncation interval respectively; represents the probability density function; φ(·), Φ(·) represent the probability density function and cumulative distribution function of the parent normal distribution, respectively;

[0105] Then the cumulative distribution function of the maintenance process time is:

[0106]

[0107] Where, represents the cumulative distribution function;

[0108] The mean μ1 of the maintenance process time is:

[0109]

[0110] The standard deviation σ1 of the maintenance process time is:

[0111]

[0112] Where α and β are intermediate variables.

[0113] For the maintenance process time, assuming but In the interval (a,b), we have:

[0114]

[0115] Therefore, the probability density function of the maintenance process time can be derived as:

[0116]

[0117] According to formula (9), the maintenance process time for group s of maintenance department g to complete maintenance task r can be sampled.

[0118] However, the computational complexity of the maintenance task decision model is related to the number of maintenance process time uncertainty scenarios. Therefore, the present invention adopts the K-means clustering method to deal with the uncertainty of the maintenance process time to obtain typical scenarios of the maintenance process time.

[0119] 3. Maintenance model constraints The specific maintenance model constraints are:

[0120] The above maintenance preparation time model and maintenance process time model are used to calculate the total maintenance time under the condition that the maintenance sequence is known. When the maintenance sequence is a variable to be determined, the maintenance sequence and maintenance preparation time need to be reflected in the form of constraints. Maintenance process time the connections between them;

[0121] ① Maintenance constraints:

[0122]

[0123]

[0124] Where S g,s,r,r2 Indicates the maintenance order. If the maintenance order of department g team s is: task r first and then r2, then S g,s,r,r2 =1, otherwise S g,s,r,r2 =0;S g,s,r1,r Indicates the maintenance order. If the maintenance order of department g team s is: task r1 first and then r, then S g,s,r1,r =1, otherwise S g,s,r1,r =0;S g,s,p,r Indicates the maintenance order. If the maintenance order of department g team s is: task p first and then r, then S g,s,p,r =1, otherwise S g,s,p,r =0; Z b represents the set of all teams in department g; Z g It represents the combination of automation, power generation, measurement and control, protection, and machinery; Z a , Z d and Z e They correspond to the task nodes, start nodes and virtual end nodes in the set, and the virtual end node indicates the end of the maintenance sequence of all maintenance groups; Figure 1As shown; if the team s of the maintenance department g starts from warehouse p, then ξ g,s,p =1;h r Indicates the start time of maintenance; f p The departure time from warehouse p is set as time 0; f r 、f r1 Indicates the maintenance completion time of task r and task r1; y r,t Indicates whether component r can be put into operation at time t, 1 indicates that it is put into operation; r, r1, and r2 are the maintenance task numbers, and the order is: r1, r, r2; M is a large number; t represents time; χ represents the latest completion time of the task in a day.

[0125] In constraint (16), the maintenance preparation time Maintenance process time It is still a variable. According to the maintenance preparation time model, the maintenance preparation time The constraints are expressed as:

[0126]

[0127]

[0128] Constraints (20) and (22) mean that if S g,s,r1,r =1, then The calculation formula is (1); otherwise, Constraint (23) is the same as constraint (2); constraint (24) can be used to achieve the logical judgment; constraint (25) represents the number of spare parts initially brought by team s of department g; T represents the time interval.

[0129] ② Equipment commissioning constraints:

[0130] The maintenance task decision model for a hydropower plant needs to further consider the order in which equipment is put into operation after maintenance is completed. Based on this, the following constraints are used to represent this operation problem:

[0131]

[0132] Where Z n and Z l Respectively represent the connection points of the hydropower plant units and the high-voltage line set; n and l represent the nth unit connection point and the lth line; o(l) and p(l) represent the first and last nodes of line l; j i,t 、j i,t-1 Represents the actual operating status of device i at time t and t-1 respectively; j l,t Indicates the actual operating status of device l at time t; j o(l),t ,j p(l),tRespectively represent the actual operating status of the beginning and end of line l at time t; y n,t ,y l,t Respectively represent the operational status of equipment n and equipment l;

[0133] In the formula, the constraint on the right is nonlinear. The present invention linearizes the nonlinear term into the following constraint condition:

[0134]

[0135] Where y l,t ,j o(l),t 、j p(l),t If one of them is 0, then j l,t is equal to 0, which means that line l cannot be put into operation at time t;

[0136] ③System operation constraints:

[0137] 1) Power balance constraints:

[0138]

[0139] Where A G ,A Line They represent the incidence matrix respectively; represents the power flow of line l at hour t; represents the dispatching demand of the national power dispatching center for the power plant at the i-th contact unit in time period t; represents the power output of the i-th hydroelectric generating unit in the hydroelectric power plant during period t; represents the power generated by the unit at the i-th node abandoning water at time t; θ i,t represents the voltage phase angle of node i at hour t; θ j,t represents the voltage phase angle of node j at hour t; X ij represents the reactance of line (i, j);

[0140] 2) Phase angle upper and lower limit constraints:

[0141] θ i,t,min ≤θ i,t ≤θ i,t,max (34)

[0142] θ i,t,min ,θ i,t,max They represent the minimum and maximum voltage phase angles at node i at the tth moment respectively.

[0143] 3) Upper and lower limits of hydroelectric generator power

[0144]

[0145] Where, They represent the minimum output power and maximum output power of hydropower unit i at time t respectively;

[0146] 4) Hydroelectric generator climbing constraints:

[0147]

[0148] Where, They represent the upward or downward climbing rate of hydropower unit i at time t respectively. represents the power output of the i-th hydroelectric generator unit in the hydroelectric power plant during the period t-1;

[0149] 5) Reservoir water constraints:

[0150]

[0151] Where V t H represents the reservoir storage capacity at time t, q t represents the reservoir inflow at time t, Q t It represents the power generation flow utilized by the hydropower unit at time t, and Δt is the time interval;

[0152] 6) Reservoir capacity constraints:

[0153]

[0154] Where V t H represents the water storage capacity of the reservoir at time t, and They represent the maximum and minimum values ​​of the reservoir capacity respectively.

[0155] 4. The specific objective function of maintenance task decision is:

[0156] The optimization goal of the maintenance task decision model is to minimize the system water abandonment power and minimize the latest completion time of all maintenance tasks. Therefore, the overall objective function of the maintenance task decision problem is:

[0157]

[0158] Where ω1 and ω2 represent the weights of the abandoned water power and the latest completion time of the maintenance task, respectively; Ψ represents the overall objective function.

[0159] Based on the above objective functions and constraints, all mathematical programming problems of the present invention were solved using Gurobi 10.0.3 on the Matlab 2018a platform.

[0160] The invention provides a method for allocating maintenance tasks for a hydropower plant taking into account time dynamic dependency. Compared with traditional task allocation methods, the method can not only improve allocation efficiency, but also improve maintenance efficiency and increase the income of the hydropower plant.

Claims

1. A method for allocating maintenance tasks in a hydropower plant taking into account time dynamic dependencies, characterized in that: First, a maintenance preparation time model is proposed that takes into account the uncertainties of the travel time of maintenance personnel arriving at the maintenance site and the tool preparation time. Then, a maintenance process time model is proposed that takes into account the uncertainty of the maintenance time of a single working face. The maintenance preparation time model and the maintenance process time model are converted into maintenance constraints for the maintenance task allocation model. Finally, under the maximum power generation constraint allowed by the State Grid Dispatching Center, with minimizing the system's abandoned water power and minimizing the latest completion time of all maintenance tasks as the objective function, a maintenance task allocation model for a hydropower plant is established that takes into account maintenance constraints, hydraulic system operation constraints, and equipment post-maintenance commissioning constraints, taking into account time dynamic dependencies. The specific modeling process of the maintenance preparation time model is as follows: For hydropower plants, the maintenance department is divided into five departments: automation, power generation, measurement and control, protection, and machinery. Each department is further divided into more detailed equipment management teams. When the power plant issues a maintenance task, r Go to the maintenance department g After that, each team will assign the task to the corresponding equipment management team s ,in, g =1,2,3,4,5 represent the automation, power generation, measurement and control, protection, and mechanical departments respectively; s =1,2,3,…represent the first s a facility management team; Assumptions Indicates maintenance department g of s Group completion r Preparation time for maintenance tasks; use express g department s Group, among them, accept r When the task Need to consider before this Have you performed other tasks? Includes the following: （1） （2） Where, Indicates a task r Maintenance preparation time; Indicates department g Team s In execution r 1. The number of spare parts remaining after the task; Indicates department g Team s The maximum number of spare parts that can be carried; Indicates department g Team s In execution r the number of spare parts required for the mission; represents the Dirac function, that is, when hour, ;when hour, ; Indicates department g Team s Average walking speed; Indicates the time maintenance personnel spend preparing spare parts in the warehouse; p Indicates the warehouse location; Indicates that maintenance personnel are on task r 1. Location, warehouse p Position, mission r The shortest distance function of the position is calculated using Dijkstra's shortest path algorithm. Indicates a task r 1. Position and mission r The shortest distance function of the position is calculated using Dijkstra's shortest path algorithm. Maintenance preparation time is uncertain. Based on this, in order to characterize the uncertainty of the team's task completion time, we propose Indicator to indicate actual completion time Completion time The ratio between Different teams will have different , The calculation method includes the following steps: Step 1: Create a department g team s A historical database of time spent completing a task over the years, assuming As a set of historical data, record N Group data; Step 2: Adoption Get Department g team s Multi-year uncertainty indicators ; Step 3: Obtain the probability distribution of the uncertainty parameters of the team maintenance time through a data-driven approach. Fit the historical maintenance time data of different teams separately to obtain the corresponding probability density distribution. The more historical data, the more accurate the probability distribution will be. Step 4: Use the K-means clustering method to obtain the typical scenarios of maintenance time uncertainty for each team; According to the fitted typical scenario, the maintenance preparation time is expressed as: ; The specific modeling process of the maintenance process time model is as follows: During the maintenance process, the uncertainty of maintenance time comes from three aspects: ① not bringing certain maintenance tools, and needing to return to the warehouse or office to find tools, which affects the maintenance process time; ② in different on-site environments, the difficulty of performing the same task varies, resulting in different maintenance times; ③ different work teams s Different professionals have different efficiencies when handling the same maintenance task; therefore, it is difficult to accurately assess the maintenance time for each maintenance task; Based on this, assuming that the maintenance process time obeys the truncated normal distribution, its probability density function is expressed as: （3） Where, Indicates the maintenance process time; represent the mean and standard deviation of the paternal normal distribution, respectively; represents variance; Respectively represent the lower and upper bounds of the truncation interval; represents the probability density function; represent the probability density function and cumulative distribution function of the parent normal distribution respectively; Then the cumulative distribution function of the maintenance process time is: （4） Where, represents the cumulative distribution function; Mean maintenance process time for: （5） Standard deviation of maintenance process time for: （6） （7） Where, is an intermediate variable; For the maintenance process time, assuming ,but In the interval ( a , b ), there are: （8） Therefore, the probability density function of the maintenance process time is derived as: （9） According to formula (9), we can sample the maintenance department g of s Group completion r Maintenance process time of the maintenance task; The maintenance model constraint conditions of the maintenance constraint are as follows: When the maintenance sequence is a variable to be determined, the maintenance sequence and maintenance preparation time need to be reflected in the form of constraints. , Maintenance process time the connections between them; ① Maintenance constraints: （12） （13） （14） （15） （16） （17） （18） （19） Where, Indicates the maintenance order, if the department g team s The maintenance order is: first task back ,but ,otherwise ; Indicates the maintenance order, if the department g team s The maintenance order is: first task back ,but ,otherwise ; Indicates the maintenance order, if the department g team s The maintenance order is: first task p back ,but ,otherwise ; Indicates department g All teams are gathered; It represents the collection of automation, power generation, measurement and control, protection, and machinery; 、 and They correspond to the task nodes, start nodes and virtual end nodes respectively. The virtual end node indicates the end of the maintenance sequence of all maintenance groups. If the maintenance department g Team s from p The warehouse starts to depart, then ; Indicates the start time of maintenance; From the warehouse p The departure time is set as 0 o'clock; 、 Indicates a task r and tasks r 1. The maintenance completion time; Display components r exist t Whether it can be put into operation at any time, Indicates that it is put into operation; 、 、 All are maintenance task numbers, and the order is: 、 、 ; M For large numbers; t Indicates time; Indicates the latest completion time of a task in a day; In constraint (16), the maintenance preparation time , Maintenance process time It is still a variable. According to the maintenance preparation time model, the maintenance preparation time The constraints are expressed as: （20） （21） （22） （23） （24） （25） The meaning of constraints (20) and (22) is: if ,but The calculation formula is (1); otherwise, ; Constraint (23) is the same as constraint (2); constraint (24) can be used to achieve (2) Logical judgment of; constraint (25) represents the department g Team s The number of spare parts initially brought; T Indicates a time interval.

2. A method for allocating maintenance tasks of a hydropower plant taking into account time dynamic dependency according to claim 1, characterized in that: Also includes: ② Equipment commissioning constraints: The maintenance task decision model for a hydropower plant needs to further consider the order in which equipment is put into operation after maintenance is completed. Based on this, the following constraints are used to represent this operation problem: （26） （27） （28） Where, and They represent the unit connections and high-voltage line collections of the hydroelectric power plant respectively; n and l Indicates the n Unit connection point and line l; 、 Indicates line l The first and last nodes of 、 Respectively 、 t -1 moment device The actual operating status of express The actual operating status of device 1 at the moment; Respectively represent the beginning and end of line l t The actual operating status at the moment; Respectively represent devices n and equipment l operational status; Where, the constraint on the right is nonlinear, and the nonlinear term is linearized into the following constraint condition: （29） （30） （31） Where, , 、 If one of them is 0, then Equal to 0, that is, the line l exist t Unable to be put into operation at any time; ③System operation constraints: 1) Power balance constraints: （32） （33） Where, They represent the incidence matrix respectively; Indicates line l In the t the tide of the hour; Indicates the i The contact unit is t The dispatching demand of the National Electric Power Dispatching Center for power plants during the time period; express t The hydropower plant i Power output of each hydroelectric generating unit; Indicates the i The units of nodes are t The power generated by discarding water at all times; Representation node i In the t Voltage phase angle in hours; Representation node j In the t Voltage phase angle in hours; Indicates line ( i , j )’s reactance; 2) Phase angle upper and lower limit constraints: （34） Represents nodes respectively i The minimum and maximum values ​​of the voltage phase angle at the tth moment; 3) Upper and lower limits of hydroelectric generator power: （35） Where, 、 Respectively represent hydropower units i exist t The minimum output power and maximum output power at the moment; 4) Hydroelectric generator climbing constraints: （36） Where, 、 Respectively represent hydropower units i exist t The upward or downward climbing rate at a moment; express t- Hydropower plant in period 1 i Power output of each hydroelectric generating unit; 5) Reservoir water constraints: （37） Where, express t Reservoir water storage capacity at any given moment, q t express t Reservoir water flow at any moment, Q t express t The power generation flow used by the hydropower unit at each moment, is the time interval; 6) Reservoir capacity constraints: （38） Where, express t The water storage capacity of the reservoir at the time, and They represent the maximum and minimum values ​​of the reservoir capacity respectively.

3. A method for allocating maintenance tasks of a hydropower plant taking into account time dynamic dependency according to claim 2, characterized in that: The maintenance task decision objective function is specifically: The optimization goal of the maintenance task decision model is to minimize the system water abandonment power and minimize the latest completion time of all maintenance tasks. Therefore, the overall objective function of the maintenance task decision problem is: （39） Where, and They represent the weights of the abandoned water power and the latest completion time of the maintenance task respectively; represents the overall objective function.

4. A method for allocating maintenance tasks of a hydropower plant taking into account time dynamic dependency according to claim 3, characterized in that: The objective function and constraints of comprehensive maintenance task decision-making, as well as the mathematical programming problem, are solved using Gurobi10.0.3 on the Matlab platform.

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