A two-stage solution method, device and medium for multi-objective optimization scheduling of a cross-basin hydropower station group
Patent Information
- Application Number
- CN202611151516.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-31
- Publication Date
- 2026-10-30
AI Technical Summary
然而，本发明的发明人发现，当将此类降维方法直接用于多目标问题、并采用基于相对隶属度的模糊优选进行多目标评价时，存在一个此前未被认识到的技术问题：相对隶属度评价中各目标的上下限由当前离散状态下所有候选决策对应的目标值确定，不同状态下目标上下限不同，评价基准随状态漂移，导致即使每个状态下的决策均为该状态下的最优决策，最终得到的整体调度方案也未必最优，即存在多目标优选的局部性偏差；而若改用绝对隶属度、预设各目标的理论极值，则因动态规划求解过程中难以精准量化各时段叠加其余留期后的目标取值范围，在工程上缺乏可行性
[0081]第一，求解效率高。传统动态规划求解N座水库、每库M个离散状态的联合调度问题时，每个时段需遍历M^N量级的状态组合，计算量随水库数呈指数增长；本发明第一阶段以局部邻域动态搜索代替全空间遍历，并采用逐库单步寻优、交替流转的降维策略，使每轮迭代的计算量随水库数近似线性增长，可在工程可接受的时间内完成含数十座水库、数十年长系列径流的跨流域系统求解，显著降低计算资源消耗。
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Abstract
Description
Technical Field
[0001] This invention relates to the field of hydropower system optimization scheduling and operation technology, and in particular to a two-stage solution method, apparatus and computer-readable storage medium for multi-objective optimization scheduling of cross-basin hydropower station groups. Background Technology
[0002] Large-scale water conservancy projects typically undertake multiple tasks, such as flood control, power generation, navigation, ecological restoration, and water diversion. These different tasks often influence and constrain each other; therefore, the joint optimal scheduling of inter-basin reservoir groups is essentially a multi-objective optimization problem. With the advancement of cascade development in river basins, the scale of inter-basin hydropower station groups continues to expand, resulting in high system state dimension, numerous scheduling variables, and complex competitive relationships between objectives. This places high demands on the solution methods for multi-objective optimal scheduling models.
[0003] Existing methods for solving multi-objective optimization scheduling models for reservoirs mainly fall into two categories. The first category transforms the multi-objective problem into a single-objective problem through methods such as constraint methods, weighting methods, and membership function methods. This type of method faces difficulties in determining the upper and lower limits of the objectives and the weights of the objectives when dealing with multiple objectives. Especially in large-scale problems, it needs to be combined with dimensionality reduction strategies. Commonly used dimensionality reduction methods include discrete differential dynamic programming, successive approximation methods of dynamic programming, and stepwise optimization algorithms. These methods reduce the computational load through neighborhood search or decomposition per reservoir and per time period, and are effective in single-objective power generation scheduling problems. However, the inventors of this invention have discovered that when such dimensionality reduction methods are directly applied to multi-objective problems and multi-objective evaluation is performed using fuzzy optimization based on relative membership, there is a previously unrecognized technical problem: the upper and lower limits of each objective in relative membership evaluation are determined by the objective values corresponding to all candidate decisions in the current discrete state. The upper and lower limits of the objectives are different in different states, and the evaluation benchmark drifts with the state. This results in the overall scheduling scheme not being optimal even if the decision in each state is the optimal decision in that state, i.e., there is a local bias in multi-objective optimization. If absolute membership is used instead and the theoretical extreme values of each objective are preset, it is difficult to accurately quantify the range of objective values after superimposing the remaining time periods in each time period during the dynamic programming solution process, which lacks engineering feasibility.
[0004] The second category involves using multi-objective evolutionary algorithms, such as genetic algorithms based on non-dominated sorting and their parallelization improvements. Multi-objective evolutionary algorithms can directly generate a set of non-dominated solutions, but for large-scale cross-basin systems with a large number of hydropower stations, long scheduling periods, and complex constraints, evolutionary algorithms suffer from low solution efficiency, poor result stability, and difficulty in generating feasible solutions, making it difficult to meet the requirements of engineering applications for solution time and solution reliability.
[0005] Furthermore, although existing technologies have developed hybrid solution frameworks that combine dynamic programming methods with stepwise optimization methods, these frameworks are mainly geared towards single-objective power generation scheduling problems. The combination of these two types of algorithms is for computational efficiency considerations and has not recognized or resolved the local bias problem caused by the drift of the evaluation benchmark for multi-objective fuzzy optimization with state shift.
[0006] In summary, for the multi-objective optimization scheduling problem of complex large-scale cross-basin hydropower station groups, existing technologies lack a solution method that can overcome the curse of dimensionality, eliminate local biases in multi-objective optimization, and thus efficiently obtain high-quality scheduling schemes. Summary of the Invention
[0007] The technical problem to be solved by this invention is to provide a two-stage solution method for the multi-objective optimization scheduling of large-scale cross-basin hydropower station groups, which addresses the dimensionality curse problem and the local deviation problem caused by the drift of the multi-objective fuzzy optimization evaluation benchmark with state. This method obtains a higher quality multi-objective scheduling scheme with higher computational efficiency, coordinates multiple scheduling objectives such as power generation, flood control, water supply, and ecology, and uses the obtained scheduling scheme to control or guide the actual operation of the hydropower station group.
[0008] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:
[0009] A two-stage solution method for multi-objective optimization scheduling of cross-basin hydropower station groups includes the following steps:
[0010] Step S1, Data Acquisition: Acquire long-term historical runoff data or forecasted runoff data, inflow into the reservoir, initial and final water level boundary conditions during the scheduling period, reservoir water level-storage volume relationship curve, outflow-downstream water level relationship curve, unit output parameters, and grid load demand data for each hydropower station in the cross-basin hydropower station group, as inputs for scheduling calculations; the unit output parameters include maximum output limit, maximum power generation reference flow, comprehensive output coefficient, and head loss;
[0011] Step S2, Model Construction and Objective Transformation: Taking the maximum power generation, maximum minimum output, and minimum outflow damage as objective functions, and basin water balance, power station output limits, reservoir water level limits, reservoir water level-storage volume relationship, downstream water level-outflow relationship, maximum power generation flow limit, and hydropower station dynamic characteristics as constraints, a multi-objective optimization scheduling model for a cross-basin hydropower station group is constructed. The objective of minimizing minimum outflow damage is transformed into the minimum outflow constraint, and the objective of maximizing minimum output is transformed into the objective of minimizing the sum of squared damage values to the preset minimum output constraint. A multi-objective fuzzy optimization function based on relative membership degree is constructed as a multi-objective comprehensive evaluation standard.
[0012] Step S3, First Stage Solution: Based on the input data, an initial scheduling trajectory that meets the constraints is generated. A dynamic programming method is used to dynamically and recursively optimize the initial scheduling trajectory in the local neighborhood state space time by time. During the optimization process, each hydropower station is optimized sequentially according to the hydraulic topology. For each hydropower station, only a single-step optimization is performed, and the iteration is not until convergence is reached before moving on to the next hydropower station. After all hydropower stations have completed one round of optimization, the new scheduling scheme is compared with the previous scheduling scheme in a multi-objective comprehensive manner. The search neighborhood is reduced according to the variable step size strategy and the iteration continues until the convergence condition is met. The first stage scheduling trajectory is then output.
[0013] Step S4, Second Stage Solution: Using the scheduling trajectory of the first stage as the initial solution, a local search method is used to correct the trajectory: the scheduling period is discretized into several time periods for sliding optimization. Each time, only adjacent time periods are jointly optimized and the final water level of the optimized time period is fixed. The residual period benefit is not calculated. The multi-objective fuzzy optimization function value is directly calculated for the entire scheduling period as the optimization evaluation standard to eliminate the local deviation caused by the change of the relative membership evaluation benchmark with the discrete state in the first stage. During the optimization process, only the outflow of a single hydropower station is optimized step by step with a set search step size. Then, the next hydropower station is moved on. After all long-term regulating hydropower stations have completed one round of optimization within a time period, the next time period is entered. After the entire scheduling period is completed, the search step size is halved and the search continues. The convergence condition is that the overall scheduling process no longer changes. The final scheduling scheme is output.
[0014] Step S5, scheduling execution: Based on the final scheduling scheme, determine the outflow and output processes of each hydropower station in each time period, and control or guide the operation of the cross-basin hydropower station group accordingly.
[0015] Preferably, the objective function in step S2 includes:
[0016] Maximum power generation target:
[0017]
[0018] Minimum output maximum target:
[0019]
[0020] Minimum outbound flow rate disrupts minimum objective:
[0021]
[0022] in, To maximize power generation, To achieve the goal of maximizing output with minimum effort, To minimize outbound flow and disrupt the minimum objective, For time period The following number is The hydroelectric power station output, , Time periods The following number is The outflow and lower limit of the hydropower station. This represents the total number of time periods. The total number of hydropower stations, For time period The number of hours.
[0023] Preferably, the constraints in step S2 include:
[0024] Watershed water balance constraints:
[0025]
[0026] Power plant output limitations and constraints:
[0027]
[0028] Reservoir water level constraints:
[0029]
[0030] Reservoir water level-storage capacity constraint:
[0031]
[0032] Downstream water level - outflow constraint:
[0033]
[0034] Maximum power generation flow constraint:
[0035]
[0036] Dynamic characteristic constraints of hydropower stations:
[0037]
[0038] in, For time period First Hydropower Station The water storage capacity For hydroelectric power station During the period Inbound flow rate within the specified interval For hydroelectric power station No. Number of the directly upstream hydropower station, For hydroelectric power station The number of directly upstream hydropower stations, For time period hydroelectric power station Maximum output limit, , , Hydropower stations During the period Initial reservoir water level and its lower and upper limits, For hydroelectric power station The reservoir water level-storage volume relationship curve, For hydroelectric power station During the period The downstream water level, For hydroelectric power station The outflow-downstream water level relationship curve, , Hydropower stations During the period The power generation reference flow and the maximum power generation reference flow, For hydroelectric power station The overall output coefficient, For hydroelectric power station During the period Head loss.
[0039] Preferably, the target transformation in step S2 includes:
[0040] Minimum outflow rate disrupts minimum target Transform into constraints:
[0041]
[0042] Set a preset minimum output that is equal to or higher than the system limit. To achieve the maximum target with minimum output The objective is to minimize the sum of squares of the failure values of the preset minimum output constraint:
[0043]
[0044] in, For time period The total output of the system.
[0045] Preferably, the multi-objective fuzzy optimization function based on relative membership degree mentioned in step S2 is:
[0046]
[0047] Among them, relative membership degree
[0048]
[0049] , The first candidate solution The maximum and minimum values of target number 1. For the first Each candidate solution corresponds to the objective The function value, Assign weights to each objective. The target total number.
[0050] Preferably, the dynamic recursive process of the dynamic programming method in step S3 includes:
[0051] The recurrence relation for the objective function is:
[0052]
[0053] Objective function residual period equation:
[0054]
[0055] The recurrence relation for the penalty function is:
[0056]
[0057] Penalty function expression:
[0058]
[0059] in, For the first A discrete water storage state combination The optimal value of the objective function under the given conditions. The time period to be solved Number of the least optimal water storage state combination For time period initial state At the end of the period When the water storage state combination changes, the corresponding first The objective function value, For time period Last The optimal decision for the given water storage state combination is... The cumulative residual period of each objective function. For time period initial state At the end of the period The penalty function value corresponding to the transition of each water storage state combination includes negative outflow due to the state transition not satisfying water balance and violation of minimum outflow constraint. For time period Last Cumulative value of the residual period penalty function under each water storage state combination For time period The initial and final water storage state combination number is as follows: , When considering other factors The membership degree value for multi-objective fuzzy optimization of a decision. The total number of discrete state combinations. For time period Initial water storage state combination number The optimal decision-making number for the water storage capacity during the following time period. , This is the penalty coefficient.
[0060] Preferably, step S3 specifically includes:
[0061] (1) Taking the total power generation of the hydropower station group as the control target and the grid load as the guide for power output allocation, the time correlation constraints of unit ramping, output and fluctuation are processed through multivariate correlation search. The scheduling plan is gradually improved by adopting two modes: top-down and bottom-up. Through repeated corrections between upstream and downstream, a power generation plan that simultaneously meets the control targets of upstream and downstream reservoirs is obtained as the initial scheduling trajectory.
[0062] (2) Set the initial iteration round ;
[0063] (3) Calculate the initial calculation step size based on the current scheduling trajectory. Based on step size Determine the local neighborhood optimization range ;
[0064] (4) Regarding the current hydropower station Using the aforementioned dynamic programming method, to Perform a single optimization within the neighborhood of the current scheduled trajectory for the step size;
[0065] (5) When the hydroelectric power station After completing a single optimization, immediately move on to the next hydropower station, until all hydropower stations have been traversed;
[0066] (6) After all hydropower stations have completed one round of optimization, the new scheduling scheme is compared with the previous scheduling scheme in a multi-objective comprehensive comparison. If the new scheme is better and the preset convergence condition is not met, the new scheduling scheme is retained and the process proceeds to step (3) based on the new scheduling scheme; otherwise, the process proceeds to step (7).
[0067] (7) If the first If the convergence condition is not met in any round, the step size will be adjusted. Halve, Proceed to step (3), otherwise stop iterating and output the first stage scheduling trajectory.
[0068] Preferably, step S4 specifically includes:
[0069] (1) Start the second stage of optimization solution with the first stage scheduling trajectory as the initial solution;
[0070] (2) Set the iteration rounds Time period Set the number of groups for hydropower stations ;
[0071] (3) Set the initial search step size for each hydropower station and determine the time period. Does optimization calculation need to be performed? If so... , judge the first Rounds and Time Periods Have the final water levels of each reservoir changed? At the same time... and When, determine the first Rounds and Time Periods Check if the final water level of each reservoir has changed; if there is no change, proceed to step (8); otherwise, proceed to step (4).
[0072] (4) Set group number ;
[0073] (5) Fixed number Periods of each long-term regulating reservoir within the group initial water level With time period initial water level The search is performed within the neighborhood of the current solution for each hydropower station according to the current search step size, during the search period. , Find the optimal combination of outflow rates and solve for the corresponding water storage capacity. and When seeking the best option, the multi-objective fuzzy optimization function value calculated over the entire scheduling period is used as the evaluation criterion.
[0074] (6) Order ,like If yes, proceed to step (5); otherwise, proceed to step (7).
[0075] (7) Halve the search step size for each hydropower station. If the set minimum step size is not reached, proceed to step (4); otherwise, proceed to step (8).
[0076] (8) Order ,like If yes, proceed to step (3); otherwise, proceed to step (9).
[0077] (9) If the first If the overall scheduling process still changes after rounds of calculation, then let Proceed to step (2) if necessary, otherwise stop iterating and output the final scheduling scheme.
[0078] The present invention also provides a multi-objective optimization scheduling device for a cross-basin hydropower station group, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the two-stage solution method for multi-objective optimization scheduling of a cross-basin hydropower station group as described in any one of the claims.
[0079] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the steps of the two-stage solution method for multi-objective optimization scheduling of cross-basin hydropower station groups as described in any one of the claims.
[0080] The beneficial effects of this invention are:
[0081] First, it offers high solution efficiency. Traditional dynamic programming solutions for the joint scheduling problem of N reservoirs with M discrete states per reservoir require traversing M^N state combinations in each time period, with the computational load increasing exponentially with the number of reservoirs. In the first stage of this invention, a local neighborhood dynamic search replaces the full space traversal, and a dimensionality reduction strategy of single-step optimization and alternating flow is adopted, making the computational load of each iteration approximately linear with the number of reservoirs. This allows for the solution of a cross-basin system involving dozens of reservoirs and decades of long-term runoff within an acceptable engineering timeframe, significantly reducing computational resource consumption.
[0082] Second, the solution quality is high. This invention discovers and solves the local bias problem of evaluation benchmark drift with state shift when embedding dynamic programming in relative membership degree fuzzy optimization: the second stage fixes the water level at the end of the time period and eliminates the need for residual period benefit estimation, enabling multi-objective evaluation to be carried out under a unified benchmark throughout the scheduling period, thus providing a directional correction to the results of the first stage. The two stages function synergistically: the first stage provides a high-quality initial solution for the second stage, avoiding the convergence of local search methods to poor solutions due to weak optimization capabilities; the second stage eliminates the evaluation benchmark drift bias inherent in the first stage. Using only one stage cannot achieve the combined effect of the two stages.
[0083] Third, it has strong multi-objective coordination capabilities. By constraining the minimum outflow target and penalizing the minimum output target, the high-priority comprehensive utilization requirements of downstream water supply, ecology, and shipping are prioritized and satisfied in a constrained manner. At the same time, fuzzy optimization is used to achieve a quantitative trade-off between power generation and guaranteed output, thereby improving the scientific nature of multi-objective scheduling decisions for cross-basin hydropower station groups.
[0084] Fourth, the scheduling scheme is directly geared towards engineering applications. The input to the method is physical data such as measured or predicted runoff, water level, and unit parameters, and the output is the outflow and power output process of each hydropower station for each time period. It can be directly issued to the power station for execution or used to guide the scheduling operation, thereby improving the comprehensive benefits of joint scheduling of cross-basin reservoir groups.
[0085] Furthermore, the alternating optimization control strategy in the first stage, which avoids iterating a single hydropower station to complete convergence, overcomes the shortcomings of conventional successive approximation methods, which cause the priority optimization nodes to bear excessive responsibility for compensation and storage during the dry season, leading to an imbalance in the global water distribution. Attached Figure Description
[0086] Figure 1 This is a schematic diagram of the two-stage solution framework of the present invention;
[0087] Figure 2 This is a diagram of the two-stage target iteration process of Scheme 6 in this embodiment of the invention;
[0088] Figure 3 This is a diagram showing the water level process of some hydropower station reservoirs in an embodiment of the present invention;
[0089] Figure 4 This is a diagram illustrating the total output process of the system in an embodiment of the present invention;
[0090] Figure 5 This is a schematic diagram of the steps of the present invention. Detailed Implementation
[0091] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0092] This invention discloses a two-stage solution method for multi-objective optimal scheduling of cross-basin hydropower station groups, comprising the following steps:
[0093] Step S1, Data Acquisition: Acquire long-term historical or forecasted runoff data, inflow into the reservoir, initial and final water level boundary conditions during the scheduling period, reservoir water level-storage curve, outflow-downstream water level curve, unit output parameters, and grid load demand data for each hydropower station in the inter-basin hydropower station group. These data serve as inputs for scheduling calculations. All of the above data are measured or forecasted technical data reflecting the physical state of the hydropower system and form the physical basis for subsequent optimization calculations.
[0094] Step S2, Model Construction and Objective Transformation: Taking the maximum power generation, the maximum minimum output, and the minimum outflow damage as objective functions, and basin water balance, power station output limits, reservoir water level limits, reservoir water level-storage volume relationship, downstream water level-outflow relationship, maximum power generation flow limit, and hydropower station dynamic characteristics as constraints, a multi-objective optimization scheduling model for a cross-basin hydropower station group is constructed. The objective of minimizing minimum outflow damage is transformed into the minimum outflow constraint, and the objective of maximizing minimum output is transformed into the objective of minimizing the sum of squared damage values to the preset minimum output constraint. A multi-objective fuzzy optimization function based on relative membership degree is constructed as a multi-objective comprehensive evaluation standard.
[0095] Step S3, First Stage Solution: Based on the input data, an initial scheduling trajectory that meets the constraints is generated. A dynamic programming method is used to dynamically and recursively optimize the local neighborhood state space of the initial scheduling trajectory time by time. During the optimization process, each hydropower station is optimized sequentially according to the hydraulic topology. For each hydropower station, only a single step optimization is performed, and the iteration is not until convergence is reached before moving on to the next hydropower station. After all hydropower stations have completed one round of optimization, the new scheduling scheme is compared with the previous scheduling scheme in a multi-objective comprehensive manner. The search neighborhood is reduced according to the variable step size strategy and the iteration continues until the convergence condition is met, and the first stage scheduling trajectory is output.
[0096] Step S4, Second Stage Solution: Using the first stage scheduling trajectory as the initial solution, a local search method is used for trajectory correction: The scheduling period is discretized into several time periods for sliding optimization. Each time, joint optimization is performed only on adjacent time periods, and the final water level of the optimized time period is fixed. The residual period benefit is not calculated. The multi-objective fuzzy optimization function value calculated for the entire scheduling period is directly used as the optimization evaluation standard to eliminate the local deviation caused by the change of the relative membership evaluation benchmark with the discrete state in the first stage. During the optimization process, each time, only the outflow of a single hydropower station is optimized step by step with a set search step size, and then the process moves to the next hydropower station. After all long-term regulating hydropower stations have completed one round of optimization within a time period, the process moves to the next time period. After the entire scheduling period is completed, the search step size is halved and the search continues. The convergence condition is that the overall scheduling process no longer changes, and the final scheduling scheme is output.
[0097] Step S5, Scheduling Execution: Based on the final scheduling plan, determine the outflow and output processes of each hydropower station in each time period, and use this information to control or guide the operation of the cross-basin hydropower station group.
[0098] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0099] I. Multi-objective optimization scheduling model
[0100] (a) Objective Function
[0101] Maximum power generation target:
[0102]
[0103] in, To maximize power generation, For time period The following number is The hydroelectric power station output, This represents the total number of time periods. The total number of hydropower stations, For time period The number of hours.
[0104] Minimum output maximum target:
[0105]
[0106] in, The goal is to achieve the maximum output with the minimum effort.
[0107] Minimum outbound flow rate disrupts minimum objective:
[0108]
[0109] in, To minimize outbound flow and disrupt the minimum objective, , Time periods The following number is The outflow rate and lower limit of the hydropower station.
[0110] (ii) Constraints
[0111] Watershed water balance constraints:
[0112]
[0113] in, For time period First Hydropower Station The water storage capacity For hydroelectric power station During the period Inbound flow rate within the specified interval For hydroelectric power station No. Number of the directly upstream hydropower station, For hydroelectric power station The number of directly upstream hydropower stations. The hydraulic connections between different basins in a cross-basin system are established separately according to their respective topologies through this constraint.
[0114] Power plant output limitations and constraints:
[0115]
[0116] in, For time period hydroelectric power station Maximum output limit.
[0117] Reservoir water level constraints:
[0118]
[0119] in, , , Hydropower stations During the period Initial reservoir water level and its lower and upper limits.
[0120] Reservoir water level-storage capacity constraint:
[0121]
[0122] in, For hydroelectric power station The reservoir water level-storage volume relationship curve.
[0123] Downstream water level - outflow constraint:
[0124]
[0125] in, For hydroelectric power station During the period The downstream water level, For hydroelectric power station The curve showing the relationship between outflow and downstream water level.
[0126] Maximum power generation flow constraint:
[0127]
[0128] in, , Hydropower stations During the period The power generation flow rate and the maximum power generation flow rate.
[0129] Dynamic characteristic constraints of hydropower stations:
[0130]
[0131] in, For hydroelectric power station The overall output coefficient, For hydroelectric power station During the period The head loss is treated as a constant in this embodiment.
[0132] (III) Multi-objective problem handling
[0133] 1. Minimum outflow rate target constraint. Since the minimum outflow rate typically reflects the comprehensive utilization requirements of downstream water supply, ecology, and shipping, these requirements generally have high priority and need to be met first. Therefore, this invention sets the target... Transform it into constraint equation (11), retaining only the objective function. and :
[0134]
[0135] 2. Minimum output to maximum target conversion. Objective functions of the minimum-maximum type are unfavorable for solving: firstly, they do not satisfy the no-aftereffect condition of dynamic programming, making them unsolvable directly using dynamic programming algorithms; secondly, their objective function value is only related to the minimum output period, and scheduling decisions in other periods have no impact on the objective function, making it difficult to solve using successive approximation algorithms in the time dimension. Therefore, this invention transforms the objective function by setting a preset minimum output equal to or higher than the system limit. The minimum output maximum objective is replaced by minimizing the sum of squares of the failure values of this minimum output constraint:
[0136]
[0137] in, For time period The total output of the system.
[0138] 3. Fuzzy Optimization. A multi-objective fuzzy optimization method based on relative membership is used to process the multi-objective problem, and the original objective is further transformed into equation (13):
[0139]
[0140] Among them, relative membership degree
[0141]
[0142] , The first candidate solution The maximum and minimum values of target number 1. For the first Each candidate solution corresponds to the objective The function value, Assign weights to each objective. The target total number.
[0143] II. First Stage: Solving using Dynamic Programming Methods
[0144] To address the challenges of high state dimensionality, numerous scheduling variables, complex competitive relationships between objectives, and the curse of dimensionality inherent in traditional dynamic programming for multi-basin hydropower station systems, this invention employs a local optimization-oriented dynamic programming approach in its first phase. This method transforms the global state traversal of traditional dynamic programming into local dynamic optimization: firstly, an initial feasible trajectory satisfying spatiotemporal and boundary constraints is anchored based on prior information or heuristic rules; then, a local search neighborhood is defined around this baseline trajectory, and a refined search is performed within this reduced-dimensional local subspace using the recursive optimization logic of dynamic programming to obtain improved paths; the newly generated better paths are continuously fed back and replace the original baseline trajectory, triggering a new round of state reconstruction and optimization, iterating repeatedly until convergence conditions are met. This method replaces the full-space traversal with local neighborhood dynamic search, improving computational efficiency while providing a high-quality initial solution for the second-stage coordinated optimization.
[0145] For the multi-objective joint scheduling problem of this invention, the dynamic recursive process is as follows:
[0146] The recurrence relation for the objective function is:
[0147]
[0148] Objective function residual period equation:
[0149]
[0150] The recurrence relation for the penalty function is:
[0151]
[0152] Penalty function expression:
[0153]
[0154] in, For the first A discrete water storage state combination The optimal value of the objective function under the given conditions. The time period to be solved Number of the least optimal water storage state combination For time period initial state At the end of the period When the water storage state combination changes, the corresponding first The objective function value, For time period Last The optimal decision for the given water storage state combination is... The cumulative residual period of each objective function. For time period From the initial state to the end of the time period The penalty function value corresponding to the transition of each water storage state combination includes negative outflow due to the state transition not satisfying water balance and violation of minimum outflow constraint. For time period Last Cumulative value of the residual period penalty function under each water storage state combination For time period The initial and final water storage state combination number is as follows: , When considering other factors The membership degree value for multi-objective fuzzy optimization of a decision. The total number of discrete state combinations. For time period Initial water storage state combination number The optimal decision-making number for the water storage capacity during the following time period. , This is the penalty coefficient.
[0155] In its implementation, this invention, based on the dynamic programming framework and following the upstream and downstream flow direction of the hydraulic topology, decouples the global multidimensional reservoir scheduling decision into a dimensionality-reduced optimization process executed sequentially by reservoir. Addressing the technical shortcomings of conventional successive approximation methods, where priority optimization nodes are prone to overburdening themselves with dry season compensation and storage tasks, leading to an imbalance in global reservoir water distribution, this invention constructs a cross-node alternating iterative optimization control strategy: when sequentially optimizing each cascade power station within the basin, it avoids iterating to complete convergence at a single node, controlling each power station to perform only one single-step optimization based on the defined neighborhood of the current state solution, and immediately proceeding to the next level power station after calculation.
[0156] The specific solution steps for the first stage are as follows:
[0157] (1) Taking the total power generation of the hydropower station group as the control target and the grid load as the guide for power output allocation, the time-related constraints such as unit ramping, output, and fluctuation are processed through multivariate correlation search. Then, the scheduling plan is gradually improved by adopting two modes: top-down and bottom-up. Through repeated corrections between upstream and downstream, a power generation plan that simultaneously meets the control targets of upstream and downstream reservoirs is obtained. Based on the above method, the output of each hydropower station in each time period is gradually adjusted to meet the scheduling requirements of the control target and the initial scheduling trajectory is obtained.
[0158] (2) Set the initial iteration round ;
[0159] (3) Calculate the initial calculation step size based on the current scheduling trajectory. Based on step size Determine the local neighborhood optimization range ;
[0160] (4) Regarding the current hydropower station Using dynamic programming methods, Perform a single optimization within the neighborhood of the current scheduled trajectory for the step size;
[0161] (5) When the hydroelectric power station After completing a single optimization, immediately move on to the next hydropower station, until all hydropower stations have been traversed;
[0162] (6) After all hydropower stations have completed one round of optimization, the new scheduling scheme is compared with the previous scheduling scheme in a multi-objective comprehensive comparison. If the new scheme is better and the preset convergence condition is not met, the new scheduling scheme is retained and the process proceeds to step (3) based on the new scheduling scheme; otherwise, the process proceeds to step (7).
[0163] (7) If the first If the convergence condition is not met in any round, the step size will be adjusted. Halve, Proceed to step (3), otherwise stop iterating and output the first stage scheduling trajectory.
[0164] III. Second Stage: Solving with Local Search Methods
[0165] While the first-stage dynamic programming approach is highly efficient in solving multi-objective scheduling problems across watersheds, its multi-objective collaborative optimization mechanism suffers from inherent locality bias. Specifically, when using relative membership for multi-objective fuzzy decision-making, the upper and lower limits of each objective are determined by the objective values corresponding to all discrete decisions in the current state. These upper and lower limits differ across states, causing the evaluation benchmark to drift with the state. Even if the decision in each state is optimal, the final scheduling scheme may not be optimal. Furthermore, if absolute membership is used instead of relative membership, i.e., pre-setting the theoretical extreme values of each objective, the dynamic programming solution struggles to accurately quantify the range of objective values after superimposing other retention periods in each time period, rendering the solution impractical in engineering.
[0166] To overcome the local bias in the first-stage solution, this invention introduces a trajectory correction mechanism based on local search theory in the second stage to decouple the high-dimensional characteristics of the cross-basin reservoir group in time and reconstruct them with an adaptive step size: the entire scheduling cycle is discretized into several time periods, and sliding optimization is performed on each time period; joint optimization is performed only on two adjacent time periods at a time, and the water level at the end of the solution period is fixed, so there is no need to introduce the residual period benefit, and the objective function is directly calculated on the entire scheduling period. Multi-objective evaluation is carried out under a unified benchmark throughout the scheduling period, which fundamentally eliminates the problem of evaluation benchmark drift with state. Also for dimensionality considerations, a dimensionality reduction strategy is still adopted when solving each two-time period sub-problem, that is, only the outflow of a single power station is optimized step by step with a set search step size before moving on to the next power station. After all long-term regulating power stations have completed one round of optimization within a time period, the next time period is moved on; each calculation does not need to iterate to convergence on the power station and time period sub-problems, and the convergence condition is that the final overall scheduling process no longer changes; after the search with the set step size converges, the step size is halved multiple times for further search.
[0167] The specific solution steps for the second stage are as follows:
[0168] (1) Using the scheduling trajectory obtained from the first stage of dynamic programming optimization as the initial solution, start the second stage of local search optimization;
[0169] (2) Set the iteration rounds Time period Set the number of groups for hydropower stations ;
[0170] (3) Set the initial search step size for each hydropower station and determine the time period. Does optimization calculation need to be performed? If so... , judge the first Rounds and Time Periods Have the final water levels of each reservoir changed? At the same time... and When, determine the first Rounds and Time Periods Check if the final water level of each reservoir has changed; if there is no change, proceed to step (8); otherwise, proceed to step (4). This skip criterion avoids repeated calculations of the already stable period and further reduces the amount of calculation.
[0171] (4) Set group number ;
[0172] (5) Fixed number Periods of each long-term regulating reservoir within the group initial water level With time period initial water level The search is performed within the neighborhood of the current solution for each hydropower station according to the current search step size, during the search period. , Find the optimal combination of outflow rates and solve for the corresponding water storage capacity. and When seeking the best option, the multi-objective fuzzy optimization function value of formula (13) is directly used as the evaluation standard during the entire scheduling period.
[0173] (6) Order ,like If yes, proceed to step (5); otherwise, proceed to step (7).
[0174] (7) Halve the search step size for each hydropower station. If the set minimum step size is not reached, proceed to step (4); otherwise, proceed to step (8).
[0175] (8) Order ,like If yes, proceed to step (3); otherwise, proceed to step (9).
[0176] (9) If the first If the overall scheduling process still changes after rounds of calculation, then let Proceed to step (2) if necessary, otherwise stop iterating and output the final scheduling scheme.
[0177] Based on the final scheduling plan, the outflow and output processes of each hydropower station at each time period are determined and issued to each hydropower station for execution or to guide scheduling operations.
[0178] IV. Examples
[0179] This embodiment takes the inter-basin reservoir group scheduling problem consisting of the Jinsha River (partial), Yalong River, Wujiang River, and the Three Gorges-Gezhouba basin as the background, with a total of 27 hydropower stations, including 13 hydropower stations with seasonal regulation or above performance. The structure and installed capacity of the power stations are as follows. Figure 1 As shown (diagram of watershed structure). Scheduling calculations were performed using a long-term historical runoff data series from 1959 to 2012, totaling 54 years, with the scheduling period being monthly.
[0180] Through trial calculations and analysis, the target for the minimum power output of the system in each time period was set at 42,000 MW. Various weight combinations of the maximum power generation target and the minimum power output penalty target were solved separately, and the calculated annual average power generation, minimum power output penalty value, and minimum power output are shown in Table 1.
[0181] Table 1 Summary of results for various weight combinations
[0182] Scheme Number Electricity generation weight Output destroys weight Average annual power generation (100 million kWh) Minimum output penalty Minimum output (MW)
[0183] Option 1 1.0 0.0 5029.6 -1.29E10 21734 Option 2 0.9 0.1 5029.1 -1.29E10 21734 Option 3 0.8 0.2 5029.0 -1.28E10 21734 Option 4 0.7 0.3 5029.0 -1.27E10 22244 Option 5 0.6 0.4 5028.8 -1.03E10 23763 Option 6 0.5 0.5 5011.6 -780169 41663 Option 7 0.4 0.6 4997.2 -37526 41921 Option 8 0.3 0.7 4990.4 -17469 41970 Option 9 0.2 0.8 4985.9 -4609 41974 Option 10 0.1 0.9 4981.3 -3787 41960 Option 11 0.0 1.0 4654.9 0 42000
[0184] It is evident that in weighted configurations where the power generation weight is below 0.5, the calculated minimum output is consistently below 24,000 MW, significantly lower than the reasonable range. Conversely, in weighted configurations where the power generation weight is above 0.5, the calculated minimum output is consistently above 41,000 MW. This phenomenon arises because: when the power generation weight is larger, the dispatching method that maximizes power generation from the initial solution is usually accompanied by a rapid decrease in minimum output, ultimately converging into a region where minimum output disruption is significant, making it difficult to achieve a substantial reduction in minimum output disruption by sacrificing power generation. Conversely, when the minimum output disruption target weight is larger, the solution restricts dispatching methods that sacrifice minimum output for increased power generation, resulting in higher power generation at higher minimum output. When the minimum output weight is 1, power generation drops sharply.
[0185] For the schemes in Table 1, a fuzzy optimization method based on relative membership is further used to optimize the schemes. Table 2 shows the weights of various power generation quantities when all schemes participate in the optimization. Minimum output destruction weight The optimal result under the combination. Except for the two cases that are actually single-objective problems (one with a weight of 0), the largest membership degree in all other cases is Scheme 6, that is, the weight combination (0.5, 0.5) (due to numerical precision issues, some larger membership degree values are displayed as 1, and there are slight differences in reality).
[0186] Table 2 Optimal Results of All Schemes
[0187] serial number We Wp Option 1 Option 2 Option 3 Option 4 Option 5 Option 6 Option 7 Option 8 Option 9 Option 10 Option 11 1 0.0 1.0 0.00 0.00 0.00 0.00 0.06 1.00 1.00 1.00 1.00 1.00 1.00 2 0.1 0.9 0.01 0.01 0.01 0.01 0.08 1.00 1.00 1.00 1.00 1.00 0.99 3 0.2 0.8 0.06 0.06 0.06 0.06 0.14 1.00 1.00 1.00 1.00 1.00 0.94 4 0.3 0.7 0.16 0.15 0.16 0.16 0.26 1.00 1.00 1.00 1.00 1.00 0.84 5 0.4 0.6 0.31 0.31 0.31 0.31 0.43 1.00 1.00 1.00 1.00 0.99 0.69 6 0.5 0.5 0.50 0.50 0.50 0.51 0.62 1.00 1.00 0.99 0.99 0.99 0.50 7 0.6 0.4 0.69 0.69 0.69 0.70 0.78 1.00 0.99 0.99 0.99 0.99 0.31 8 0.7 0.3 0.84 0.84 0.85 0.85 0.90 1.00 0.99 0.99 0.99 0.98 0.16 9 0.8 0.2 0.94 0.94 0.94 0.94 0.96 1.00 0.99 0.99 0.98 0.98 0.06 10 0.9 0.1 0.99 0.99 0.99 0.99 0.99 1.00 0.99 0.99 0.98 0.98 0.01 11 1.0 0.0 1.00 1.00 1.00 1.00 1.00 1.00 0.99 0.99 0.98 0.98 0.00
[0188] Since the results of schemes 1-5 and scheme 11 are significantly inconsistent with scheduling practices, these schemes were eliminated, and the remaining five schemes were further optimized. The results are shown in Table 3. At this point, except for a single-objective case with a weight of 0, scheme 7 (weight combination 0.4, 0.6) was selected when the power generation target weight was small; and scheme 6 (weight combination 0.5, 0.5) was selected when the power generation target weight was large. It can be seen that regardless of whether schemes were eliminated, the final optimization results were concentrated in schemes 6 and 7, i.e., schemes where the two target weights are close and the power generation target weight is no greater than the target weight corresponding to the minimum output. This has strong reference value for cross-basin multi-objective optimization decision-making.
[0189] Table 3. Optimal Results of Some Schemes
[0190] serial number We Wp Option 6 Option 7 Option 8 Option 9 Option 10 1 0.0 1.0 0.00 1.00 1.00 1.00 1.00 2 0.1 0.9 0.01 0.99 0.99 0.99 0.99 3 0.2 0.8 0.06 0.98 0.97 0.96 0.94 4 0.3 0.7 0.16 0.96 0.92 0.88 0.84 5 0.4 0.6 0.31 0.91 0.82 0.76 0.69 6 0.5 0.5 0.50 0.84 0.68 0.59 0.50 7 0.6 0.4 0.69 0.75 0.51 0.39 0.31 8 0.7 0.3 0.84 0.66 0.35 0.22 0.16 9 0.8 0.2 0.94 0.60 0.24 0.11 0.06 10 0.9 0.1 0.99 0.56 0.17 0.05 0.01 11 1.0 0.0 1.00 0.55 0.16 0.03 0.00
[0191] Figure 2This describes the iterative process of solving Scheme 6 (weight combination (0.5, 0.5)) in the first and second stages, where one iteration refers to all power stations completing one round of solution within the entire scheduling period. It can be seen that in the initial stage of the first stage, both objectives change towards a better direction, stabilizing and converging after multiple updates to the neighborhood width. After entering the second stage with the solution obtained in the first stage as the initial solution, the two objectives undergo drastic changes in the initial stage, showing a similar better direction again after approximately 10 iterations and finally converging. This process shows that using only the first-stage dynamic programming method results in a deviation from the result of using a unified evaluation throughout the entire scheduling period due to the different evaluation criteria for multiple objectives under different states. Conversely, directly using the second stage without the first stage, due to the weaker optimization ability of local search methods compared to dynamic programming methods, easily converges to a poor solution. Therefore, the two stages in the two-stage solution framework are mutually complementary and indispensable, verifying the necessity and effectiveness of the two-stage collaborative mechanism of this invention.
[0192] Figure 3 , Figure 4 The data presents the reservoir water level processes and total system output processes for some hydropower stations under Schemes 1, 6, and 11. Lianghekou, located at the uppermost reaches of the Yalong River, tends to increase the drawdown depth during the dry season to raise downstream water levels under Schemes 1 and 6, which consider power generation factors. However, under Scheme 11, the drawdown depth is relatively small. Wudongde, due to its limited regulation capacity, exhibits similar water level processes under all three schemes, sometimes emptying its system during pre-flood periods to increase power generation or compensate for system output. Hongjiadu has the strongest regulation capacity among the stations, showing the greatest differences in water level processes across schemes. Under Scheme 11, it almost annually increases the drawdown during the dry season to regulate downstream inflow. The Three Gorges Dam, a long-term regulating station located at the lowest reaches of the system, almost annually emptys its system under Scheme 11 to increase dry season output. The differences in performance of each station under different schemes reflect the differences in dispatching methods resulting from their different locations within the basin, installed capacity, and regulation capabilities. In terms of total system output, the minimum output of Scheme 6 and Scheme 11 can be maintained at a high level every year, while Scheme 1 has frequent lower output before the flood season, which reflects the requirement of power generation target for high water head power generation.
[0193] V. Comparative Examples
[0194] To further verify the technical effectiveness of the two-stage solution method of this invention compared with existing methods, the following comparative method was used to solve the problem under the same computing environment (CPU 11th Gen Intel(R) Core(TM) i5-1135G7 @ 2.40GHz (2.42 GHz), onboard RAM 16.0 GB (15.8 GB available), 64-bit operating system, x64-based processor) for 27 hydropower stations and 54-year long-series runoff examples as in the embodiment:
[0195] Comparison Method 1: Solve the problem using only the dynamic programming method of the first stage, that is, only execute step S3 of this invention and not step S4;
[0196] Comparison Method 2: Solve the problem using the local search method of the second stage alone, that is, do not execute step S3 of this invention, and directly execute step S4 with the initial scheduling trajectory generated by the heuristic rules as the initial solution.
[0197] The calculation results of each method under the weight combination (0.5, 0.5) are shown in Table 4.
[0198] Table 4 Comparison of calculation results between the method of the present invention and the comparative method
[0199] Solution method Average annual power generation (100 million kWh) Minimum output (MW) Calculation time (min) Is it stable and convergent? The two-stage method of the present invention 5011.6 41663 31.8 yes Comparison Method 1 (First Stage Only) 4979.8 41523 8.0 yes Comparison Method Two (Second Stage Only) 4922.5 37517 22.1 yes
[0200] As shown in Table 4, compared with Comparative Method 1 (first stage only), the method of this invention introduces a second-stage evaluation correction mechanism based on the overall objective function, which corrects the local optimization results caused by the relative membership evaluation in the first stage, and verifies the effectiveness of the correction mechanism. Compared with Comparative Method 2, the method of this invention avoids the problem of premature convergence to poor solutions due to poor initial solution quality and weak optimization ability in local searches. The above results are consistent with... Figure 2 The two-stage iterative process shown corroborates each other, indicating that the two stages in the two-stage framework of this invention are functionally complementary and indispensable, and their overall technical effect exceeds the simple summation of the individual effects of each stage.
[0201] The above embodiments and comparative results show that the method of the present invention can stably converge on a large-scale inter-basin system containing 27 hydropower stations and a long series of runoff over 54 years, and obtain a high-quality dispatching scheme that balances power generation and ensures output, providing technical support for realizing the comprehensive benefits of joint dispatching of inter-basin reservoir groups.
[0202] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A two-stage solution method for multi-objective optimal scheduling of cross-basin hydropower station groups, characterized in that, Includes the following steps: Step S1, Data Acquisition: Acquire long-term historical runoff data or forecasted runoff data, inflow into the reservoir, initial and final water level boundary conditions during the scheduling period, reservoir water level-storage volume relationship curve, outflow-downstream water level relationship curve, unit output parameters, and grid load demand data for each hydropower station in the cross-basin hydropower station group, as inputs for scheduling calculations; the unit output parameters include maximum output limit, maximum power generation reference flow, comprehensive output coefficient, and head loss; Step S2, Model Construction and Objective Transformation: Taking the maximum power generation, maximum minimum output, and minimum outflow damage as objective functions, and basin water balance, power station output limits, reservoir water level limits, reservoir water level-storage volume relationship, downstream water level-outflow relationship, maximum power generation flow limit, and hydropower station dynamic characteristics as constraints, a multi-objective optimization scheduling model for a cross-basin hydropower station group is constructed. The objective of minimizing minimum outflow damage is transformed into the minimum outflow constraint, and the objective of maximizing minimum output is transformed into the objective of minimizing the sum of squared damage values to the preset minimum output constraint. A multi-objective fuzzy optimization function based on relative membership degree is constructed as a multi-objective comprehensive evaluation standard. Step S3, first stage solution: Based on the input data, generate an initial scheduling trajectory that meets the constraints, and use a dynamic programming method to dynamically and recursively optimize in the local neighborhood state space of the initial scheduling trajectory time by time. During the optimization process, each hydropower station is optimized in sequence according to the hydraulic topology, and only a single step optimization is performed for each hydropower station without iterating until convergence before moving on to the next hydropower station. After all hydropower stations have completed one round of optimization, the new scheduling scheme is compared with the previous scheduling scheme in a multi-objective comprehensive manner. The search neighborhood is reduced by a variable step size strategy and the iteration continues until the convergence condition is met, and the first stage scheduling trajectory is output. Step S4, Second Stage Solution: Using the scheduling trajectory of the first stage as the initial solution, a local search method is used to correct the trajectory: the scheduling period is discretized into several time periods for sliding optimization. Each time, only adjacent time periods are jointly optimized and the final water level of the optimized time period is fixed. The residual period benefit is not calculated. The multi-objective fuzzy optimization function value is directly calculated for the entire scheduling period as the optimization evaluation standard to eliminate the local deviation caused by the change of the relative membership evaluation benchmark with the discrete state in the first stage. During the optimization process, only the outflow of a single hydropower station is optimized step by step with a set search step size. Then, the next hydropower station is moved on. After all long-term regulating hydropower stations have completed one round of optimization within a time period, the next time period is entered. After the entire scheduling period is completed, the search step size is halved and the search continues. The convergence condition is that the overall scheduling process no longer changes. The final scheduling scheme is output. Step S5, scheduling execution: Based on the final scheduling scheme, determine the outflow and output processes of each hydropower station in each time period, and control or guide the operation of the cross-basin hydropower station group accordingly.
2. The two-stage solution method for multi-objective optimal scheduling of cross-basin hydropower station groups according to claim 1, characterized in that, The objective function mentioned in step S2 includes: Maximum power generation target: ； Minimum output maximum target: ； Minimum outbound flow rate disrupts minimum objective: ； in, To maximize power generation, To achieve the goal of maximizing output with minimum effort, To minimize outbound flow and disrupt the minimum objective, For time period The following number is The hydroelectric power station output, , Time periods The following number is The outflow and lower limit of the hydropower station. This represents the total number of time periods. The total number of hydropower stations, For time period The number of hours.
3. The two-stage solution method for multi-objective optimal scheduling of cross-basin hydropower station groups according to claim 2, characterized in that, The constraints mentioned in step S2 include: Watershed water balance constraints: ； Power plant output limitations and constraints: ； Reservoir water level constraints: ； Reservoir water level-storage capacity constraint: ； Downstream water level - outflow constraint: ； Maximum power generation flow constraint: ； Dynamic characteristic constraints of hydropower stations: ； in, For time period Chushui Hydropower Station Water storage capacity For hydroelectric power station During the period Inbound flow rate within the specified interval For hydroelectric power station No. Number of the directly upstream hydropower station, For hydroelectric power station The number of directly upstream hydropower stations, For time period hydroelectric power station Maximum output limit, , , Hydropower stations During the period Initial reservoir water level and its lower and upper limits, For hydroelectric power station The reservoir water level-storage volume relationship curve, For hydroelectric power station During the period The downstream water level, For hydroelectric power station The outflow-downstream water level relationship curve, , Hydropower stations During the period The power generation reference flow and the maximum power generation reference flow, For hydroelectric power station The overall output coefficient, For hydroelectric power station During the period Head loss.
4. The two-stage solution method for multi-objective optimal scheduling of cross-basin hydropower station groups according to claim 2, characterized in that, The target transformation mentioned in step S2 includes: Minimum outflow rate disrupts minimum target Transform into constraints: ； Set a preset minimum output that is equal to or higher than the system limit. To achieve the maximum target with minimum output The objective is to minimize the sum of squares of the failure values of the preset minimum output constraint: ； in, For time period The total output of the system.
5. The two-stage solution method for multi-objective optimal scheduling of cross-basin hydropower station groups according to claim 4, characterized in that, The multi-objective fuzzy optimization function based on relative membership degree mentioned in step S2 is: ； Among them, relative membership degree ； , The first candidate solution The maximum and minimum values of target number 1. For the first Each candidate solution corresponds to the objective The function value, Assign weights to each objective. The target total number.
6. The two-stage solution method for multi-objective optimal scheduling of cross-basin hydropower station groups according to claim 5, characterized in that, The dynamic recursion process of the dynamic programming method described in step S3 includes: The recurrence relation for the objective function is: ； Objective function residual period equation: ； The recurrence relation for the penalty function is: ； Penalty function expression: ； in, For the first A discrete water storage state combination The optimal value of the objective function under the given conditions. The time period to be solved Number of the least optimal water storage state combination For time period initial state At the end of the period When the water storage state combination changes, the corresponding first The objective function value, For time period Last The optimal decision under the given water storage state combination is the... The cumulative residual period of each objective function. For time period initial state At the end of the period The penalty function value corresponding to the transition of each water storage state combination includes negative outflow due to the state transition not satisfying water balance and violation of minimum outflow constraint. For time period Last Cumulative value of the residual period penalty function under each water storage state combination For time period The initial and final water storage state combination number is as follows: , When considering other factors The membership degree value for multi-objective fuzzy optimization of a decision. The total number of discrete state combinations. For time period Initial water storage state combination number The optimal decision-making number for the water storage capacity during the following time period. , This is the penalty coefficient.
7. The two-stage solution method for multi-objective optimal scheduling of cross-basin hydropower station groups according to claim 6, characterized in that, Step S3 specifically includes: (1) Taking the total power generation of the hydropower station group as the control target and the grid load as the guide for power output allocation, the time correlation constraints of unit ramping, output and fluctuation are processed through multivariate correlation search. The scheduling plan is gradually improved by adopting two modes: top-down and bottom-up. Through repeated corrections between upstream and downstream, a power generation plan that simultaneously meets the control targets of upstream and downstream reservoirs is obtained as the initial scheduling trajectory. (2) Set the initial iteration round ; (3) Calculate the initial calculation step size based on the current scheduling trajectory. Based on step size Determine the local neighborhood optimization range ; (4) Regarding the current hydropower station Using the aforementioned dynamic programming method, to Perform a single optimization within the neighborhood of the current scheduled trajectory for the step size; (5) When the hydroelectric power station After completing a single optimization, immediately move on to the next hydropower station, until all hydropower stations have been traversed; (6) After all hydropower stations have completed one round of optimization, the new scheduling scheme is compared with the previous scheduling scheme in a multi-objective comprehensive comparison. If the new scheme is better and the preset convergence condition is not met, the new scheduling scheme is retained and the process proceeds to step (3) based on the new scheduling scheme; otherwise, the process proceeds to step (7). (7) If the first If the convergence condition is not met in any round, the step size will be adjusted. Halve, Proceed to step (3), otherwise stop iterating and output the first stage scheduling trajectory.
8. The two-stage solution method for multi-objective optimal scheduling of cross-basin hydropower station groups according to claim 7, characterized in that, Step S4 specifically includes: (1) Start the second stage of optimization solution with the first stage scheduling trajectory as the initial solution; (2) Set the iteration rounds Time period Set the number of groups for hydropower stations ; (3) Set the initial search step size for each hydropower station and determine the time period. Does optimization calculation need to be performed? If so... , judge the first Rounds and Time Periods Have the final water levels of each reservoir changed? At the same time... and When, determine the first Rounds and Time Periods Check if the final water level of each reservoir has changed; if there is no change, proceed to step (8); otherwise, proceed to step (4). (4) Set group number ; (5) Fixed number Periods of each long-term regulating reservoir within the group initial water level With time period initial water level The search is performed within the neighborhood of the current solution for each hydropower station according to the current search step size, during the search period. , Find the optimal combination of outflow rates and solve for the corresponding water storage capacity. and When seeking the best option, the multi-objective fuzzy optimization function value calculated over the entire scheduling period is used as the evaluation criterion. (6) Order ,like If yes, proceed to step (5); otherwise, proceed to step (7). (7) Halve the search step size for each hydropower station. If the set minimum step size is not reached, proceed to step (4); otherwise, proceed to step (8). (8) Order ,like If yes, proceed to step (3); otherwise, proceed to step (9). (9) If the first If the overall scheduling process still changes after rounds of calculation, then let Proceed to step (2) if necessary, otherwise stop iterating and output the final scheduling scheme.
9. A multi-objective optimization scheduling device for a cross-basin hydropower station group, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the two-stage solution method for multi-objective optimization scheduling of cross-basin hydropower station groups as described in any one of claims 1 to 8.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the two-stage solution method for multi-objective optimal scheduling of cross-basin hydropower station groups as described in any one of claims 1 to 8.