Load distribution method for diversion cascade hydropower station based on multi-source coupling

Abstract

The application relates to the technical field of hydropower station optimal scheduling, and discloses a load distribution method for a water diversion series cascade hydropower station based on multi-source coupling, which aims to solve the problems of poor optimization effect and adaptability of the existing method, and mainly comprises the following steps: setting a target total power generation flow of the cascade hydropower station in a preset time period and a planned load of each power generation unit of the cascade hydropower station in the preset time period; calculating the unit power generation water head of each hydropower station according to the target total power generation flow; constructing a load distribution model for each power generation unit of the cascade hydropower station, taking the minimum total water consumption as the optimization target, and solving the optimal solution of the power generation flow of the power generation unit under the constraint condition of the objective function of the load distribution model; calculating the total power generation flow of the cascade hydropower station according to the solving result, and judging the deviation; and if the deviation does not satisfy the condition, the target total power generation flow is adjusted by using a dichotomy method, and then the calculation is re-performed. The application improves the optimization effect and adaptability.

Description

Technical Field

[0001] This invention relates to the field of hydropower station optimization scheduling technology, specifically to a load allocation method for a series-connected cascade hydropower station based on multi-source coupling. Background Technology

[0002] Traditional cascade hydropower stations are built along the main stream of a river, taking advantage of its drop and topographical conditions. Each station typically has a certain regulating capacity and flexible operation. In contrast, diversion-tandem cascade hydropower stations have a unique layout. A dam is built along the main stream to form a reservoir. The first-stage power station draws water from the reservoir to generate electricity. Two or more stations are then arranged along the diversion route, with hydraulic connections between each station via regulating reservoirs. The next-stage power station connects to the tailrace of the previous station for power generation, and the tailrace of the final station returns to the main stream. Diversion-tandem cascade hydropower stations not only feature large installed capacity, high operating head, and complex vibration zones, but also, compared to conventional dam-type cascade development, have a closer hydraulic-electric connection between upstream and downstream. The power generation process is generally controlled by the diversion flow of the first-stage power station, requiring real-time dynamic matching of the power generation flow of each station.

[0003] Traditional cascade hydropower stations typically treat each station as a discrete entity when allocating load, optimizing each station individually. This optimization method ignores the hydraulic connections between upstream and downstream stations and the hydraulic coupling between stations, achieving only local optimization with poor results. Furthermore, the open-loop control method used for one-time allocation is prone to instability when the actual inflow or reservoir capacity deviates from the prediction, resulting in poor adaptability. Summary of the Invention

[0004] This invention aims to address the problem of poor optimization effect and adaptability of existing water diversion series cascade power station scheduling schemes, and proposes a load allocation method for water diversion series cascade power stations based on multi-source coupling.

[0005] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0006] This invention provides a load distribution method for a series-connected hydropower station based on multi-source coupling, the method comprising:

[0007] Step 1: Set the target total power generation flow of the cascade power station in the preset time period, and the planned load of each power generation unit of the cascade power station in the preset time period;

[0008] Step 2: Obtain the initial reservoir capacity and inflow for the corresponding time period. Calculate the upstream average water level and downstream tailwater level of each power station based on the target total power generation flow, the initial reservoir capacity and inflow for the time period. Calculate the generating head of each power station based on the upstream average water level and downstream tailwater level.

[0009] Step 3: For each power generation unit of the cascade power station, perform the following steps respectively:

[0010] Step 31: Construct a load allocation model based on the corresponding generating head and planned load of the generating unit. The decision variable of the load allocation model is the generating flow of the corresponding generating unit, and the optimization object is the total water consumption of the cascade power station.

[0011] Step 32: Taking the minimum total water consumption as the optimization objective, solve for the optimal solution of the power generation flow of the power generation unit under the constraints of the objective function of the load allocation model;

[0012] Step 4: Based on the solution results of the load allocation model corresponding to each power generation unit, calculate the total power generation flow of the cascade power station, and determine whether the deviation between the calculated total power generation flow and the target total power generation flow is greater than the first deviation threshold. If so, allocate the load to the corresponding power generation unit according to the solution results; otherwise, adjust the target total power generation flow using the bisection method and then re-enter Step 1.

[0013] Furthermore, the objective function of the load sharing model is as follows:

[0014] ;

[0015] ;

[0016] ;

[0017] in, This indicates the total water consumption of the cascade hydropower stations. Indicates the first The power generation unit in the first Water consumption during a given time period This indicates the number of power generation units in a cascade power station. Indicates the number of time periods. Indicates the first The power generation unit in the first Power generation flow during the period Indicates the length of a time period. Indicates the first The power generation unit in the first Planned load for a time period Indicates the first The first power station The power generation unit in the first Average unit efficiency over a given period of time. Indicates the first The first power station The power generation unit in the first The generator head during the specified time period, Indicates the number of power stations.

[0018] Furthermore, the constraints include water balance constraints, load balance constraints, and upstream and downstream power generation flow matching constraints;

[0019] The water balance constraints are as follows:

[0020] ;

[0021] in, Indicates the first The power station in the first Storage capacity during different time periods Indicates the first The first power station The power generation unit in the first Inbound flow during a specific time period Indicates the first The first power station The power generation unit in the first Power generation flow during a given time period;

[0022] The load balancing constraints are as follows:

[0023] ;

[0024] in, Indicates the first The first power station The first power generation unit Taiwanese unit in Efforts during a specific time period Indicates the first The number of generating units in each power generation unit;

[0025] The matching constraints for the upper and lower level power generation flow are as follows:

[0026] .

[0027] Furthermore, the constraints also include water level constraints, generator flow rate constraints, and generator output constraints;

[0028] The water level constraints are as follows:

[0029] ;

[0030] In the formula, Indicates the first The power station in the first Water level during the period, Indicates the first The lower limit of the water level of each power station Indicates the first The upper limit of water level for each power station;

[0031] The power generation flow constraints of the unit are as follows:

[0032] , ;

[0033] in, Indicates the first The first power station The first power generation unit The generator set was at the Power generation flow during the period Indicates the first The first power station The first power generation unit The lower limit of the power generation flow of the generator set. Indicates the first The first power station The first power generation unit The maximum power generation flow of the generator set, Indicates the first The first power station The first power generation unit The generator set was at the The operational status indicator for a given time period;

[0034] The unit output constraints are as follows:

[0035] ;

[0036] in, Indicates the first The first power station The first power generation unit The generator set was at the Efforts during a specific time period Indicates the first The first power station The first power generation unit The lower limit of the output of the generator set, Indicates the first The first power station The first power generation unit The maximum output of the generator set.

[0037] Furthermore, the constraints also include ramp constraints and vibration zone constraints;

[0038] The ramping constraints are as follows:

[0039] ;

[0040] in, Indicates the first The first power station The first power generation unit The generator set was at the The climbing rate limit for a given time period;

[0041] The vibration zone is constrained as follows:

[0042] ;

[0043] in, Indicates the first The first power station The first power generation unit The generator set was at the The lower limit of output during a given time period. Indicates the first The first power station The first power generation unit The generator set was at the The maximum output limit for a given time period.

[0044] Furthermore, the average efficiency of the unit is calculated using the converted unit power generation characteristic curve, which is as follows:

[0045] ;

[0046] in, Indicates the first The first power station The generator set was at the Efforts during a specific time period Indicates the first The first power station Characteristic curve function of generator set, Indicates the first The first power station The generator set was at the Power generation flow during the period Indicates the first The first power station The generator set was at the The generating head of the unit during a given period.

[0047] Furthermore, the methods for converting the unit's power generation characteristic curves include:

[0048] The power generation flow of each power station's generator units is divided into... The flow rate intervals were defined, and the discrete values ​​corresponding to each flow rate interval were determined. The generating head of each power station's generator units was then divided into [various categories]. After determining the discrete values ​​corresponding to each head interval, the power generation characteristic curve of the unit is linearly transformed. The transformation formula is as follows:

[0049] ;

[0050] ;

[0051] ;

[0052] ;

[0053] ;

[0054] in, Indicates the first The power station in the first On the power characteristic curve of the generator set during the time period ( , The corresponding output, Indicates the first The power characteristic curve of the generator unit of the power station is the first Discrete values ​​corresponding to each flow interval; Indicates the first The power characteristic curve of the generator unit of the power station is the first Discrete values ​​corresponding to each head interval Indicates the first The generator units of the power station in the first On the dynamic characteristic curve of the time period ( , The corresponding weight value.

[0055] Furthermore, the calculation of the upstream average water level and downstream tailrace water level of each power station based on the target total power generation flow, initial reservoir capacity for the time period, and inflow includes:

[0056] The reservoir capacity at the end of the time period is calculated based on the target total power generation flow, the initial reservoir capacity for the time period, and the inflow. The average upstream water level of each power station within the preset time period is calculated based on the initial reservoir capacity and the end reservoir capacity for the time period, and based on the water level-reservoir capacity relationship curve.

[0057] Calculate the downstream tailwater level of each power station based on the tailwater level-discharge relationship curves.

[0058] Furthermore, the water level-reservoir capacity relationship curve is as follows:

[0059] , ;

[0060] ;

[0061] ;

[0062] ;

[0063] in, Indicates the first The corresponding reservoir of each power station is in the first Is the time period in the first Indicator variables for each storage capacity range, Indicates the number of storage capacity intervals. Indicates the first The corresponding reservoir of each power station is in the first The upper limit of the storage capacity for each storage range. Indicates the first The corresponding reservoir of each power station is in the first The storage capacity during this period is in the first Storage capacity value for a given storage capacity range Indicates the first The corresponding reservoir of each power station is in the first Storage capacity during different time periods Indicates the first The corresponding reservoir of each power station is in the first upstream water level during the period, Indicates the first The reservoir capacity corresponding to each power station is The corresponding upstream water level at that time;

[0064] The tailwater level-discharge relationship curve is as follows:

[0065] , ;

[0066] ;

[0067] ;

[0068] ;

[0069] in, Indicates the first The corresponding reservoir of each power station is in the first Is the time period in the first Indicator variables for each flow range, Indicates the number of flow intervals. Indicates the first The corresponding reservoir of each power station is in the first The upper limit of the traffic range, Indicates the first The corresponding reservoir of each power station is in the first Traffic volume during the period is in the first Flow values ​​for each flow range Indicates the first The corresponding reservoir of each power station is in the first Traffic during a specific time period Indicates the first The corresponding reservoir of each power station is in the first The tailwater level during the period, Indicates the first The flow rate of the reservoir corresponding to each power station is The corresponding tailwater level at that time.

[0070] Furthermore, the solution process for the load sharing model includes:

[0071] Step 321: Set the power generation flow rate of the power generation unit, and substitute the set power generation flow rate into the load distribution model to calculate the optimal output corresponding to the minimum total water consumption.

[0072] Step 322: Determine whether the deviation between the optimal output and the corresponding planned load is greater than the second deviation threshold. If so, adjust the power generation flow of the power generation unit based on the Brent search algorithm under the constraints, and then re-enter step 321. Otherwise, take the set power generation flow as the optimal solution for the corresponding power generation unit.

[0073] The beneficial effects of this invention are as follows: The load allocation method for water diversion series cascade power stations based on multi-source coupling provided by this invention optimizes each power generation unit by minimizing the total water consumption of the cascade. It establishes hydraulic connections between power stations through dynamic water level coupling, achieving global optimization of water diversion series cascade power stations and improving load optimization effect. By dynamically verifying the deviation of total power generation through closed-loop feedback and using a bisection method for iterative adjustment, it ensures that the power generation flow of the power generation unit matches the total power generation flow, thereby improving the anti-interference and adaptability of load allocation. Attached Figure Description

[0074] Figure 1 A schematic flowchart illustrating a load allocation method for a series cascade hydropower station based on multi-source coupling, provided as an example.

[0075] Figure 2 A schematic diagram of three-dimensional interpolation calculation provided for an embodiment;

[0076] Figure 3 A schematic flowchart of another load allocation method for a series cascade hydropower station based on multi-source coupling provided for an embodiment;

[0077] Figure 4 A schematic diagram of the branch-bound + cutting plane method calculation provided for an embodiment;

[0078] Figure 5 A schematic diagram of the structure of the water diversion series cascade power station provided in the embodiment;

[0079] Figure 6 A typical load diagram of 96 points per day for each power generation unit is provided for the example.

[0080] Figure 7 A schematic diagram showing the daily output and power generation flow rate changes of power generation unit 1 provided in the embodiment;

[0081] Figure 8 A schematic diagram showing the daily output and power generation flow rate changes of power generation unit 2 provided in the embodiment;

[0082] Figure 9 A schematic diagram showing the daily output and power generation flow rate changes of power generation unit 3 provided in the embodiment;

[0083] Figure 10 This is a schematic diagram illustrating the output changes of each unit in the power generation unit 1 provided in the embodiment.

[0084] Figure 11 This is a schematic diagram illustrating the output changes of each unit in the power generation unit 2 provided in the embodiment.

[0085] Figure 12 This is a schematic diagram showing the output changes of each unit in the power generation unit 3 provided in the embodiment. Detailed Implementation

[0086] To enable those skilled in the art to better understand the present invention, the technical solutions in this embodiment will be clearly and completely described below with reference to the accompanying drawings.

[0087] In some of the processes described in the specification and accompanying drawings of this invention, multiple operations are included that appear in a specific order. However, it should be clearly understood that these operations may not be executed in the order they appear herein, or may be executed in parallel. The sequence numbers of the operations are merely used to distinguish different operations and do not themselves represent any execution order. Furthermore, these processes may include more or fewer operations, and these operations may be executed sequentially or in parallel.

[0088] The technical solution of the present invention is applicable to the technical solution of the embodiments of this application, which is applicable to a water diversion series cascade power station with multiple power generation units.

[0089] Currently, the load distribution scheme for water diversion series cascade power stations usually adopts a scheme that optimizes each power station individually. This approach ignores the hydraulic coupling between power stations, resulting in poor optimization effect. Furthermore, the open-loop control method of one-time allocation has poor adaptability.

[0090] Based on this, the technical solution of the present invention is proposed. In the present invention, firstly, the target total power generation flow of the cascade power station in a preset period and the planned load of each power generation unit of the cascade power station in the preset period are set; then, the initial reservoir capacity and inflow flow of the corresponding period are obtained, and the upstream average water level and downstream tailwater level of each power station are calculated based on the target total power generation flow, the initial reservoir capacity and inflow flow of the period, and the generating head of each power station is calculated based on the upstream average water level and the downstream tailwater level; then, for each power generation unit of the cascade power station, a load allocation model is constructed with the power generation flow of the power generation unit as the decision variable and the total water consumption of the cascade power station as the optimization object, with the minimum total water consumption as the optimization objective, and the optimal solution of the power generation flow of the power generation unit under the constraint of the objective function of the load allocation model is solved; finally, based on the solution results of the load allocation model corresponding to each power generation unit, the total power generation flow of the cascade power station is calculated, and it is determined whether the deviation between the calculated total power generation flow and the target total power generation flow is greater than a first deviation threshold. If so, the load is allocated to the corresponding power generation unit according to the solution results; otherwise, the target total power generation flow is adjusted by using the bisection method, and the load allocation model is reconstructed and solved.

[0091] Specifically, this invention decomposes the load allocation of a series-connected hydropower station under complex hydraulic-electric constraints into an outer-layer iteration and an inner-layer optimization. The outer-layer iteration calculates the generating head of each power station based on a set target total power generation flow, considering the hydraulic interference impact of flow changes in one generating unit on other generating units. Simultaneously, based on the solution results of the inner-layer optimization, a bisection method is used to adjust the total power generation flow of the cascade, ensuring that the unit power generation flow matches the total power generation flow. The inner-layer optimization transforms the goal of minimizing total water consumption into maximizing output, using the power generation flow of a single generating unit as the decision variable to construct a load allocation model, achieving optimal load allocation within the generating unit. This invention establishes hydraulic connections between power stations through dynamic water level coupling, achieving global optimization of the series-connected hydropower station and improving load optimization effectiveness. Furthermore, it improves the anti-interference and adaptability of load allocation by dynamically verifying the total power generation deviation through closed-loop feedback and using a bisection method for iterative adjustment.

[0092] The technical solutions in this embodiment will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0093] Figure 1 A load distribution method for a series-connected hydropower station based on multi-source coupling is shown. Please refer to [link / reference]. Figure 1 The method includes:

[0094] Step S1: Set the target total power generation flow of the cascade power station in a preset time period, and the planned load of each power generation unit of the cascade power station in the preset time period.

[0095] In practical applications, the target total power generation and planned load are set according to power generation demand.

[0096] Step S2: Obtain the initial reservoir capacity and inflow for the corresponding time period. Calculate the upstream average water level and downstream tailwater level of each power station based on the target total power generation flow, the initial reservoir capacity and inflow for the time period. Calculate the generating head of each power station based on the upstream average water level and downstream tailwater level.

[0097] In this embodiment, the calculation method for the upstream average water level and the downstream tailwater water level includes:

[0098] The reservoir capacity at the end of the time period is calculated based on the target total power generation flow, the initial reservoir capacity for the time period, and the inflow. The average upstream water level of each power station within the preset time period is calculated based on the initial and final reservoir capacities for the time period and the water level-capacity relationship curve. The downstream tailwater water level of each power station is calculated based on the tailwater level-flow relationship curve of each power station.

[0099] When calculating the reservoir capacity at the end of a time period, since the reservoir capacity change = (inflow - power generation flow) × time period length, the target total power generation flow, the initial reservoir capacity of the time period, the inflow flow, and the time period length can be input into this formula to calculate the reservoir capacity at the end of the time period.

[0100] When calculating the upstream average water level, based on the water level-reservoir capacity relationship curve, the initial water level and the final water level of the time period are obtained by querying or interpolating the initial reservoir capacity and the final reservoir capacity of the time period, respectively. The average water level of the upstream can be obtained by averaging the two.

[0101] In this embodiment, the water level-reservoir capacity relationship curve is as follows:

[0102] , ;

[0103] ;

[0104] ;

[0105] ;

[0106] in, Indicates the first The corresponding reservoir of each power station is in the first Is the time period in the first Indicator variables for each storage capacity range, When, it indicates that it is in the first position. One storage capacity range, When, it indicates that it is not in the first position. One storage capacity range, Indicates the number of storage capacity intervals. Indicates the first The corresponding reservoir of each power station is in the first The upper limit of the storage capacity for each storage range. Indicates the first The reservoir of the power station is in the first The storage capacity during this period is in the first Storage capacity value for a given storage capacity range Indicates the first The corresponding reservoir of each power station is in the first Storage capacity during different time periods Indicates the first The corresponding reservoir of each power station is in the first upstream water level during the period, Indicates the first The reservoir capacity corresponding to each power station is The corresponding upstream water level at that time.

[0107] In this embodiment, the tailwater level-discharge relationship curve is as follows:

[0108] , ;

[0109] ;

[0110] ;

[0111] ;

[0112] in, Indicates the first The corresponding reservoir of each power station is in the first Is the time period in the first Indicator variables for each flow range, Indicates the number of flow intervals. Indicates the first The corresponding reservoir of each power station is in the first The upper limit of the traffic range, Indicates the first The corresponding reservoir of each power station is in the first Traffic volume during the period is in the first Flow values ​​for each flow range Indicates the first The corresponding reservoir of each power station is in the first Traffic during a specific time period Indicates the first The corresponding reservoir of each power station is in the first The tailwater level during the period, Indicates the first The flow rate of the reservoir corresponding to each power station is The corresponding tailwater level at that time.

[0113] When calculating the downstream tailrace water level, the target total power generation flow is used as the tailrace flow based on the tailrace water level-flow relationship curve, and the downstream tailrace water level is obtained by querying or interpolation.

[0114] When calculating the generator head of the computer unit, the generator head can be obtained by subtracting the downstream tailwater level from the upstream average water level and then deducting the head loss.

[0115] Step S3: For each power generation unit of the cascade power station, execute steps S31 to S32 respectively.

[0116] Step S31: Construct a load allocation model based on the corresponding generator head and planned load. The decision variable of the load allocation model is the power generation flow of the corresponding generator unit, and the optimization object is the total water consumption of the cascade power station.

[0117] In this embodiment, a load allocation model is constructed based on a Mixed Integer Quadratic Programming (MIQP) model, and the objective function of the load allocation model is as follows:

[0118] ;

[0119] ;

[0120] ;

[0121] in, This indicates the total water consumption of the cascade hydropower stations. Indicates the first The power generation unit in the first Water consumption during a given time period This indicates the number of power generation units in a cascade power station. Indicates the number of time periods. Indicates the first The power generation unit in the first Power generation flow during the period Indicates the length of a time period. Indicates the first The power generation unit in the first Planned load for a time period Indicates the first The first power station The power generation unit in the first Average unit efficiency over a given period of time. Indicates the first The first power station The power generation unit in the first The generator head during the specified time period, Indicates the number of power stations.

[0122] The constraints of the load distribution model include water balance constraints, load balance constraints, matching constraints of upstream and downstream power generation flow, water level constraints, unit power generation flow constraints, unit output constraints, ramping constraints, and vibration zone constraints.

[0123] The water balance constraints are as follows:

[0124] ;

[0125] in, Indicates the first The power station in the first Storage capacity during different time periods Indicates the first The first power station The power generation unit in the first Inbound flow during a specific time period Indicates the first The first power station The power generation unit in the first Power generation flow during a given period.

[0126] The load balancing constraints are as follows:

[0127] ;

[0128] in, Indicates the first The first power station The first power generation unit Taiwanese unit in Efforts during a specific time period Indicates the first The number of generating units in each power generation unit.

[0129] The matching constraints for the upper and lower level power generation flow are as follows:

[0130] .

[0131] The water level constraints are as follows:

[0132] ;

[0133] In the formula, Indicates the first The power station in the first Water level during the period, Indicates the first The lower limit of the water level of each power station Indicates the first The upper limit of water level for each power station.

[0134] The power generation flow constraints of the unit are as follows:

[0135] , ;

[0136] in, Indicates the first The first power station The first power generation unit The generator set was at the Power generation flow during the period Indicates the first The first power station The first power generation unit The lower limit of the power generation flow of the generator set. Indicates the first The first power station The first power generation unit The maximum power generation flow of the generator set, Indicates the first The first power station The first power generation unit The generator set was at the The operational status indicator for a given time period.

[0137] The unit output constraints are as follows:

[0138] ;

[0139] in, Indicates the first The first power station The first power generation unit The generator set was at the Efforts during a specific time period Indicates the first The first power station The first power generation unit The lower limit of the output of the generator set, Indicates the first The first power station The first power generation unit The maximum output of the generator set.

[0140] The ramping constraints are as follows:

[0141] ;

[0142] in, Indicates the first The first power station The first power generation unit The generator set was at the The climbing rate limit for a given time period.

[0143] The vibration zone is constrained as follows:

[0144] ;

[0145] in, Indicates the first The first power station The first power generation unit The generator set was at the The lower limit of output during a given time period. Indicates the first The first power station The first power generation unit The generator set was at the The maximum output limit for a given time period.

[0146] In the objective function of the load sharing model, the average efficiency of the unit satisfies the unit's power generation characteristic curve, which is calculated from the unit's power generation characteristic curve as follows:

[0147] ;

[0148] in, Indicates the first The first power station The generator set was at the Efforts during a specific time period Indicates the first The first power station Characteristic curve function of generator set, Indicates the first The first power station The generator set was at the Power generation flow during the period Indicates the first The first power station The generator set was at the The generating head of the unit during a given period.

[0149] This embodiment addresses the linearization of complex constraint problems by employing piecewise linearization or introducing 0-1 variables to transform the nonlinear function corresponding to the unit's power generation characteristic curve into a linear function.

[0150] Specifically, this embodiment utilizes a three-dimensional curve linearization process to linearize the generator characteristic curves of the units. Specifically, the power generation flow of each power station's generator units can be divided into... The flow rate intervals were defined, and the discrete values ​​corresponding to each flow rate interval were determined. The generating head of each power station's generator units was then divided into [various categories]. After determining the discrete values ​​corresponding to each head interval, the power generation characteristic curve of the unit is linearly transformed. The transformation formula is as follows:

[0151] ;

[0152] ;

[0153] ;

[0154] ;

[0155] ;

[0156] in, Indicates the first The power station in the first On the power characteristic curve of the generator set during the time period ( , The corresponding output; Indicates the first The power characteristic curve of the generator unit of the power station is the first Discrete values ​​corresponding to each flow interval; Indicates the first The power characteristic curve of the generator unit of the power station is the first Discrete values ​​corresponding to each head interval Indicates the first The generator units of the power station in the first On the dynamic characteristic curve of the time period ( , The corresponding weight value.

[0157] Please see Figure 2 In this embodiment, the power generation flow rate and power generation head are divided into multiple intervals, and then a system is constructed as follows: Figure 2 Several triangular regions are shown, and then three-dimensional interpolation calculations are performed using the above formula to ensure that the calculation result falls within only one triangular region. This yields the weight value of the vertex of the triangle and calculates the output value. Then, based on the obtained output value, the average unit efficiency is calculated (output = average unit efficiency × unit head × power generation flow). Figure 2 In the diagram, the horizontal axis represents the first... The discrete values ​​of the generating head corresponding to each head interval on the power characteristic curve of the generator units of each power station, where, Indicates the first The power characteristic curve of the generator unit of the power station is the first The discrete values ​​of the power generation head corresponding to the head interval are represented by the vertical axis. The discrete values ​​of the power generation flow corresponding to each flow range on the power characteristic curve of the generator units of a power station, where, Indicates the first The power characteristic curve of the generator unit of the power station is the first The discrete values ​​of power generation flow corresponding to each flow interval.

[0158] Step S32: Taking the minimum total water consumption as the optimization objective, solve for the optimal solution of the power generation flow of the power generation unit under the constraints of the objective function of the load allocation model.

[0159] In this embodiment, the solution process of the load sharing model includes:

[0160] Step S321: Set the power generation flow rate of the power generation unit, and substitute the set power generation flow rate into the load distribution model to calculate the optimal output corresponding to the minimum total water consumption.

[0161] Step S322: Determine whether the deviation between the optimal output and the corresponding planned load is greater than the second deviation threshold. If so, adjust the power generation flow of the power generation unit based on the Brent search algorithm under the constraints, and then re-enter step S321. Otherwise, take the set power generation flow as the optimal solution for the corresponding power generation unit.

[0162] Specifically, a multi-level recursive optimization method is established for the aforementioned objective function and constraints, using power generation flow as the decision variable. The power generation flow of each power generation unit serves as the decision variable for the inner-level optimization calculation. During the inner-level optimization process, for the load allocation model corresponding to each power generation unit, the Gurobi solver is invoked for parallel computation, employing a collaborative optimization strategy combining the branch-and-bound method and the cutting plane method to solve the model. Please refer to [link to relevant documentation]. Figure 3 To accelerate computational efficiency, this embodiment establishes a parallel computing architecture with multiple nodes. Each power generation unit corresponds to a sub-problem and is allocated independent memory space. Data races are avoided using Gurobi's Model.copy() method. Please refer to [link to relevant documentation]. Figure 4 Branch and bound methods decompose the feasible solution space step by step, using relaxed linear programming to obtain upper and lower bounds, and then selecting branches to further search until the optimal solution is found or the stopping condition is met. Cutting plane methods are a way to accelerate integer programming solutions; they reduce the feasible solution space by continuously adding cutting planes.

[0163] Please see Figure 4 The model solution using the combined optimization strategy of branch and bound method and cutting plane method includes the following steps:

[0164] (1) Initialize the relaxation problem: relax the original integer programming problem into a linear programming problem (LP), that is, ignore the integer constraints, solve the linear programming problem, and obtain the relaxed solution and its objective value, which serve as the lower bound (for the maximization problem) or upper bound (for the minimization problem) of the current problem.

[0165] (2) Determine if the relaxed solution is an integer: Check if all variables in the relaxed solution satisfy the integer constraint. If so, the solution is a feasible solution to the original problem and proceed to the next step. If not, further processing is required and the solution should proceed to the branch or cut plane step.

[0166] (3) Update the global optimal solution: If the current relaxed solution is an integer solution and is better than the previously found integer solution, then update the global optimal solution.

[0167] (4) Determine if the termination condition is met: The termination condition may include: all nodes have been processed, the upper and lower bounds have converged (the current optimal solution is close enough to the relaxation bound), or the time or number of iterations has reached the limit. If the condition is met, output the current optimal solution; if the condition is not met, continue with the subsequent steps.

[0168] (5) Selecting a branch variable: Select a variable from the current non-integer solutions to branch (e.g., select the variable with the largest fractional part); common branching strategies include: maximum violation scale, pseudo cost branch, etc.

[0169] (6) Generate child nodes: For the selected branch variable, generate two subproblems and divide the current feasible domain into two disjoint subsets.

[0170] (7) Solve the LP relaxation of the child nodes: Solve the corresponding LP relaxation problem for each child node. If the subproblem has no feasible solution, then prune (discard).

[0171] (8) Determine whether to prune: Pruning conditions include: the subproblem has no feasible solution, or the target value of the relaxed solution of the subproblem is not as good as the current optimal solution; if the pruning conditions are met, discard the node (prune); if not, keep the node and may add cut planes.

[0172] (9) Generate a cutting plane and resolve: If the relaxation solution of the current node is not an integer solution, but does not meet the pruning condition, a cutting plane can be generated. The cutting plane is a linear constraint that can cut off the current non-integer solution, but does not cut off any integer feasible solution. After adding the cutting plane, resolve the LP relaxation and repeat the judgment process.

[0173] Please see Figure 3During the memory optimization calculation process, for each node, the initial power generation flow of the power generation unit is first obtained by back-interpolation based on the corresponding planned load. Then, based on the corresponding load allocation model, the optimal output (i.e., maximum output) of the power generation unit under the set power generation flow is solved, and it is determined whether the deviation between the optimal output and the corresponding planned load is greater than the second deviation threshold. If so, the power generation flow is adjusted by using the Brent search algorithm and then the calculation is repeated in step S321 until the deviation between the optimal output and the corresponding planned load is less than or equal to the second deviation. The second deviation threshold can be set according to the actual situation.

[0174] When solving for optimal output based on the load distribution model, the Gurobi solver, under the premise of satisfying the unit's power generation characteristic curve and constraints, seeks the unit's average efficiency that minimizes water consumption (at which point the output is maximized), and uses the formula Output = Unit Average Efficiency × Unit Head × Power Generation Flow to obtain the optimal output.

[0175] Step S4: Based on the solution results of the load allocation model corresponding to each power generation unit, calculate the total power generation flow of the cascade power station, and determine whether the deviation between the calculated total power generation flow and the target total power generation flow is greater than the first deviation threshold. If so, allocate the load to the corresponding power generation unit according to the solution results; otherwise, adjust the target total power generation flow using the bisection method and re-enter step S1.

[0176] Please see Figure 3 In the outer layer iterative calculation process, after obtaining the power generation flow of each power generation unit through step S3, the summation calculation is performed to obtain the total power generation flow. Then, it is determined whether the deviation between the calculated total power generation flow and the target total power generation flow is greater than the first deviation threshold. If so, the target total power generation flow is adjusted by the bisection method and then the process enters step S1 to iterate again until the deviation between the calculated total power generation flow and the target total power generation flow is less than or equal to the first deviation threshold. The first deviation threshold can be set according to the actual situation.

[0177] Figure 5 A schematic diagram of a series-connected hydroelectric power station is shown. Please refer to [link / reference]. Figure 5 This cascade hydropower station draws water from an upstream reservoir via diversion tunnels, and consists of two interconnected power stations, A and B, arranged like beads on a string. Power stations A and B are each connected by three tunnels, forming two cascade hydropower stations with three tunnels at each stage. Each tunnel corresponds to a power generation unit: Unit 1, Unit 2, and Unit 3. Within each stage, each tunnel connects to four generator sets, meaning each power generation unit contains eight generator sets, for a total of 24 generator sets. A regulating reservoir upstream of power station B facilitates the hydraulic connection between the upstream and downstream cascade power stations.

[0178] The maximum output of each generating unit at power stations A and B is 50MW, with a total maximum output of 400MW. The maximum power generation flow rate for each station within each tunnel is 100 kW. The maximum power generation flow of each station in the cascade is 300. These two power plants have wide power transmission areas, and the grid combination and power receiving ratio at the receiving end may vary. For ease of modeling and analysis, this example assumes that each power generation unit corresponds to one power transmission grid, and the receiving end issues separate power generation plans for each power generation unit, without interference between them. Please refer to [link to relevant documentation]. Figure 6 Based on the typical load planning curve issued by the power grid, and using a 15-minute calculation period, the daily planned load of 96 points for three power generation units is issued respectively. Based on the short-term load allocation model of cascade power stations and related constraints, a multi-level recursive optimization algorithm is used to solve the daily time-period output of each power generation unit of the cascade hydropower station.

[0179] 1) Analysis of the calculation process

[0180] The calculation process is as follows:

[0181] (1) Set the target total power generation flow of the cascade power stations in the preset time period to 150 The upstream and downstream water levels are calculated using a piecewise linear interpolation method.

[0182] (2) Using 0 respectively 50 and 100 The three power generation flows and their corresponding outputs form a quadratic curve (a quadratic function between power generation flow and power generation unit output).

[0183] (3) Set the initial power generation flow of each power generation unit based on the power generation flow obtained by back interpolation of the planned load of the three power generation units;

[0184] (4) The optimal power output combination of the three power generation units is calculated in parallel using the branch-and-bound method and the cutting plane method to obtain the optimal power output of the three power generation units;

[0185] (5) Determine whether the optimal output of each power generation unit is consistent with the planned load. If not, reconstruct the quadratic curve according to the search range and return to step 3 until the convergence condition is met.

[0186] (6) Determine whether the power generation flow of the three power generation units is consistent with the target total power generation flow. If not, adjust the target total power generation flow and return to step (2) until the convergence condition is met. After the convergence condition is met, perform the calculation for the next time period.

[0187] According to the calculation process, the total calculation time of the inner layer optimization in each time period is about 0.12s to 0.15s (of which the number of Brent searches is between 4 and 6), and the outer layer iterative calculation is about 8 to 12 times before the convergence condition is met.

[0188] 2) Analysis of Calculation Results

[0189] Please see Figures 7 to 12 Based on the daily load distribution calculation results at 96 points, the deviation between the output of each power generation unit in the cascade and the load plan was less than 0.1MW in each time period. The power generation flow of each power generation unit was strictly matched between the upstream and downstream stations, the total power generation flow of the cascade was matched, the water level of the regulating reservoir remained basically stable, and the output of each unit within the power generation unit was within the high-efficiency operating range. Taking 17:00 as an example, the output of power generation units 1 and 2 underwent significant adjustments compared to the previous time period, and the power generation flow within the units increased significantly. Power generation unit 3, with its load unchanged, saw a 0.6% increase in power generation flow. The calculation results show that the multi-level recursive optimization solution method can achieve precise and coordinated control of the power generation flow, unit output, and load plan of each power generation unit.

[0190] In summary, the load allocation method for water diversion series cascade power stations based on multi-source coupling provided in this embodiment optimizes the total water consumption of each power generation unit by minimizing the total water consumption of the cascade. It establishes hydraulic connections between power stations through dynamic water level coupling, achieving global optimization of the water diversion series cascade power stations and improving load optimization performance. Furthermore, it uses closed-loop feedback to dynamically verify the deviation of total power generation and employs a bisection method for iterative adjustment to ensure that the power generation flow of each power generation unit matches the total power generation flow, thereby improving the anti-interference and adaptability of load allocation.

Claims

1. A load distribution method for a multi-source coupled series-connected cascade hydropower station, characterized in that, The method includes: Step 1: Set the target total power generation flow of the cascade power station in the preset time period, and the planned load of each power generation unit of the cascade power station in the preset time period; Step 2: Obtain the initial reservoir capacity and inflow for the corresponding time period. Calculate the upstream average water level and downstream tailwater level of each power station based on the target total power generation flow, the initial reservoir capacity and inflow for the time period. Calculate the generating head of each power station based on the upstream average water level and downstream tailwater level. Step 3: For each power generation unit of the cascade power station, perform the following steps respectively: Step 31: Construct a load allocation model based on the corresponding generating head and planned load of the generating unit. The decision variable of the load allocation model is the generating flow of the corresponding generating unit, and the optimization object is the total water consumption of the cascade power station. The objective function of the load allocation model is as follows: ； ； ； in, This indicates the total water consumption of the cascade hydropower stations. Indicates the first The power generation unit in the first Water consumption during a given time period This indicates the number of power generation units in a cascade power station. Indicates the number of time periods. Indicates the first The power generation unit in the first Power generation flow during the period Indicates the length of a time period. Indicates the first The power generation unit in the first Planned load for a time period Indicates the first The first power station The power generation unit in the first Average unit efficiency over a given period of time. Indicates the first The first power station The power generation unit in the first The generator head during the specified time period, Indicates the number of power stations; Step 32: Taking the minimum total water consumption as the optimization objective, solve for the optimal solution of the power generation flow of the power generation unit under the constraints of the objective function of the load allocation model; Step 4: Based on the solution results of the load allocation model corresponding to each power generation unit, calculate the total power generation flow of the cascade power station, and determine whether the deviation between the calculated total power generation flow and the target total power generation flow is greater than the first deviation threshold. If so, allocate the load to the corresponding power generation unit according to the solution results; otherwise, adjust the target total power generation flow using the bisection method and then re-enter Step 1.

2. The load allocation method for a multi-source coupled series-cascade hydropower station based on water diversion as described in claim 1, characterized in that, The constraints include water balance constraints, load balance constraints, and upstream and downstream power generation flow matching constraints. The water balance constraints are as follows: ； in, Indicates the first The power station in the first Storage capacity during a given time period Indicates the first The first power station The power generation unit in the first Inbound flow during a specific time period Indicates the first The first power station The power generation unit in the first Power generation flow during a given time period; The load balancing constraints are as follows: ； in, Indicates the first The first power station The first power generation unit Taiwanese unit in Efforts during a specific time period Indicates the first The number of generating units in each power generation unit; The matching constraints for the upper and lower level power generation flow are as follows: 。 3. The load allocation method for a multi-source coupled series-cascade hydropower station based on water diversion as described in claim 2, characterized in that, The constraints also include water level constraints, generator flow rate constraints, and generator output constraints. The water level constraints are as follows: ； In the formula, Indicates the first The power station in the first Water level during the period, Indicates the first The lower limit of the water level of each power station Indicates the first The upper limit of water level for each power station; The power generation flow constraints of the unit are as follows: ， ； in, Indicates the first The first power station The first power generation unit The generator set was at the Power generation flow during the period Indicates the first The first power station The first power generation unit The lower limit of the power generation flow of the generator set. Indicates the first The first power station The first power generation unit The maximum power generation flow of the generator set, Indicates the first The first power station The first power generation unit The generator set was at the The operational status indicator for a given time period; The unit output constraints are as follows: ； in, Indicates the first The first power station The first power generation unit The generator set was at the Efforts during a specific time period Indicates the first The first power station The first power generation unit The lower limit of the output of the generator set, Indicates the first The first power station The first power generation unit The maximum output of the generator set.

4. The load allocation method for a multi-source coupled series-cascade hydropower station based on water diversion as described in claim 3, characterized in that, The constraints also include ramp constraints and vibration zone constraints; The ramping constraints are as follows: ； in, Indicates the first The first power station The first power generation unit The generator set was at the The climbing rate limit for a given time period; The vibration zone is constrained as follows: ； in, Indicates the first The first power station The first power generation unit The generator set was at the The lower limit of output during a given time period. Indicates the first The first power station The first power generation unit The generator set was at the The maximum output limit for a given time period.

5. The load allocation method for a multi-source coupled series-connected hydropower station according to claim 1, characterized in that, The average efficiency of the unit is calculated using the converted unit power generation characteristic curve, which is shown below: ； in, Indicates the first The first power station The generator set was at the Efforts during a specific time period Indicates the first The first power station Characteristic curve function of generator set, Indicates the first The first power station The generator set was at the Power generation flow during the period Indicates the first The first power station The generator set was at the The generating head of the unit during a given period.

6. The load allocation method for a multi-source coupling-based series-cascade hydropower station as described in claim 5, characterized in that, Methods for converting the generator set's power generation characteristic curves include: The power generation flow of each power station's generator units is divided into... The flow rate intervals were defined, and the discrete values ​​corresponding to each flow rate interval were determined. The generating head of each power station's generator units was then divided into [various categories]. After determining the discrete values ​​corresponding to each head interval, the power generation characteristic curve of the unit is linearly transformed. The transformation formula is as follows: ； ； ； ； ； in, Indicates the first The power station in the first On the power characteristic curve of the generator set during the time period ( , The corresponding output, Indicates the first The power characteristic curve of the generator unit of the power station is the first Discrete values ​​corresponding to each flow interval; Indicates the first The power characteristic curve of the generator unit of the power station is the first Discrete values ​​corresponding to each head interval Indicates the first The generator units of the power station in the first On the dynamic characteristic curve of the time period ( , The corresponding weight value.

7. The load allocation method for a multi-source coupled series-cascade hydropower station based on water diversion as described in claim 1, characterized in that, The calculation of the upstream average water level and downstream tailrace water level of each power station based on the target total power generation flow, initial reservoir capacity for the time period, and inflow flow includes: The reservoir capacity at the end of the time period is calculated based on the target total power generation flow, the initial reservoir capacity for the time period, and the inflow. The average upstream water level of each power station within the preset time period is calculated based on the initial reservoir capacity and the end reservoir capacity for the time period, and based on the water level-reservoir capacity relationship curve. Calculate the downstream tailwater level of each power station based on the tailwater level-discharge relationship curves.

8. The load allocation method for a multi-source coupling-based series-cascade hydropower station as described in claim 7, characterized in that, The water level-reservoir capacity relationship curve is as follows: ， ； ； ； ； in, Indicates the first The corresponding reservoir of each power station is in the first Is the time period in the first Indicator variables for each storage capacity range, Indicates the number of storage capacity intervals. Indicates the first The corresponding reservoir of each power station is in the first The upper limit of the storage capacity for each storage range. Indicates the first The corresponding reservoir of each power station is in the first The storage capacity during this period is in the first Storage capacity value for a given storage capacity range Indicates the first The corresponding reservoir of the power station is in the first Storage capacity during a given time period Indicates the first The corresponding reservoir of each power station is in the first upstream water level during the period, Indicates the first The reservoir capacity corresponding to each power station is The corresponding upstream water level at that time; The tailwater level-discharge relationship curve is as follows: ， ； ； ； ； in, Indicates the first The corresponding reservoir of each power station is in the first Is the time period in the first Indicator variables for each flow range, Indicates the number of flow intervals. Indicates the first The corresponding reservoir of each power station is in the first The upper limit of the traffic range, Indicates the first The corresponding reservoir of each power station is in the first Traffic volume during the period is in the first Flow values ​​for each flow range Indicates the first The corresponding reservoir of each power station is in the first Traffic during a specific time period Indicates the first The corresponding reservoir of each power station is in the first The tailwater level during the period, Indicates the first The flow rate of the reservoir corresponding to each power station is The corresponding tailwater level at that time.

9. The load allocation method for a multi-source coupled series-cascade hydropower station based on water diversion as described in claim 1, characterized in that, The solution process for the load allocation model includes: Step 321: Set the power generation flow rate of the power generation unit, and substitute the set power generation flow rate into the load distribution model to calculate the optimal output corresponding to the minimum total water consumption. Step 322: Determine whether the deviation between the optimal output and the corresponding planned load is greater than the second deviation threshold. If so, adjust the power generation flow of the power generation unit based on the Brent search algorithm under the constraints, and then re-enter step 321. Otherwise, take the set power generation flow as the optimal solution for the corresponding power generation unit.

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