A water and electricity fine scheduling method based on nonlinear feature adaptive segmentation driving

Abstract

The application discloses a water and electricity fine scheduling method of nonlinear feature adaptive segmented driving, solves the problems of uneven nonlinear function linearization fitting error, poor robustness, and disconnection with scheduling modeling, etc. The water level-storage capacity and tail water level-discharge flow curve discrete data are acquired and sorted, and the segmented points are set as the to-be-optimized variables after the preset segmented number; the segmented linear fitting is completed through the L1 norm minimum absolute deviation, the deviation sum is taken as the linearization error index, and the optimal segmented point is obtained through the particle swarm optimization algorithm iteration optimization, so that the nonlinear function adaptive segmented linearization is completed; finally, the segmented linear function is embedded into the water and electricity scheduling MILP model. The application adopts a double-layer optimization framework, the algorithm is hierarchically integrated and has strong fitting robustness, the segmented points are adaptively distributed according to the function curvature, the solving efficiency is improved while the peak shaving accuracy is ensured, the application is suitable for multiple water and electricity scheduling scenes, a systematic solution is provided for the water and electricity fine scheduling, and the engineering practicability is obvious.

Description

Technical Field

[0001] This invention relates to the field of hydropower scheduling and optimization modeling technology, specifically to a nonlinear feature-adaptive segmented driving method for refined hydropower scheduling. Background Technology

[0002] In the optimal scheduling of reservoirs and hydropower stations, the water level-storage capacity relationship, the tailrace water level-discharge relationship, and the head loss function typically exhibit significant nonlinear characteristics. These nonlinear functions play a decisive role in key constraints such as water balance, net head calculation, and power output calculation, and are important factors affecting the accuracy of scheduling results. Due to the advantages of mixed integer linear programming (MILP) in solution efficiency and global optimality, MILP is currently widely used for hydropower scheduling optimization. However, MILP cannot directly handle nonlinear functions, and it is usually necessary to linearize the nonlinear relationships such as the water level-storage capacity curve and the tailrace water level-discharge curve.

[0003] In the prior art, patent CN121144876A proposes an automatic discretization method for hydropower nonlinear characteristic curves. The core of this patent is the automatic extraction of discrete points from the hydropower nonlinear curves, solving the problems of low efficiency and poor repeatability associated with manual selection of discrete points. However, this patented method still has the following drawbacks:

[0004] It only extracts discrete points without any subsequent piecewise linearization fitting process. It only uses the maximum distance point selection and distance threshold to extract discrete points that can represent the curve, without constructing a continuous piecewise linear function based on the discrete points, nor setting continuity constraints for the piecewise function. Therefore, the discrete points cannot be directly used as the basis for linearization for scheduling constraint modeling.

[0005] The criteria for selecting discrete points are out of sync with the needs of the scheduling project. Using "curve representation similarity" (minimum Minkowski distance) as the criterion for selecting discrete points, instead of minimizing the linear fitting error and optimizing the solution efficiency of the scheduling model required for hydropower scheduling, results in discrete points that, while able to reconstruct the curve shape, cannot meet the solution requirements of the MILP scheduling model.

[0006] The lack of integration with the scheduling model results in low practicality of discrete points. It only outputs a sequence of discrete points without designing an embedding method between discrete points / segmented points and the MILP scheduling model. Directly using the discrete points from this patent for scheduling modeling will lead to model failure or result deviation due to the lack of constraint handling.

[0007] The design does not consider the coordinated processing of multiple nonlinear functions. It does not address the need for coordinated linearization of various nonlinear functions such as water level-reservoir capacity and tailrace level-discharge flow in hydropower scheduling; it only applies to the extraction of discrete points from a single curve and cannot meet the multi-constraint linearization requirements of refined scheduling.

[0008] Patent CN106886839B proposes a combined optimal scheduling method for hydropower and thermal power units based on hybrid integer programming. The core of this patent is to decouple the nonlinear constraints of hydropower scheduling and then perform fixed piecewise linearization, which solves the problem of large errors in the traditional constant head assumption. However, it does not overcome the inherent limitation of uniform piecewise segmentation. The shortcomings of this patent are as follows: Without adaptive design of segmentation points, the fitting error distribution is uneven. The segmentation points are manually preset by n points to divide the n-1 sub-segments. It is impossible to adjust the position of the segmentation points according to the curvature change characteristics of nonlinear functions such as water level-reservoir capacity and tailwater level-discharge flow. As a result, there will still be problems such as insufficient segmentation and large error in areas with large curvature, and excessive segmentation and waste of computing resources in flat areas, thus limiting the overall accuracy of linearization.

[0009] The fitting lacks a robustness criterion and is sensitive to outlier data. The fitted value is calculated using an endpoint-weighted average method, without introducing an error metric to combat outliers. If there are observational data biases in actual engineering, it will directly lead to distortion of the linearization results, affecting the accuracy of subsequent scheduling model solutions.

[0010] Linearization is merely for constraint decoupling and does not aim to minimize the fitting error. The core objective of linearization in this patent is to decouple nonlinear constraints and simplify the solution of mixed integer programming (MILP). It does not take minimizing the overall linearization error as the optimization objective. The linearization result only satisfies the requirement of being solvable, rather than a high-precision solution.

[0011] The integration with the scheduling model is superficial, and the impact of linearization on scheduling performance is not considered. Only the conversion from nonlinear constraints to linear constraints is completed. No dedicated scheduling model embedding method is designed for the linearization results, nor is the actual impact of linearization accuracy on core scheduling objectives such as hydropower peak regulation and output calculation verified. Linearization and scheduling modeling are in a state of "disconnection".

[0012] Therefore, developing a refined hydropower scheduling method with high fitting accuracy, good solution efficiency, strong robustness, and better engineering applicability has become an urgent technical problem to be solved in this field. Summary of the Invention

[0013] To address the above problems, this invention provides a nonlinear characteristic adaptive segmented driving method for refined hydropower scheduling, comprising the following steps: Step 1: Obtain discrete sample data of the water level-reservoir capacity curve and the tailwater level-discharge flow curve. The data includes independent variables and corresponding dependent variables, and are sorted according to the size of the independent variables.

[0014] Step 2: Pre-determine the number of segments K within the domains of the water level-storage capacity function and the tailwater level-discharge flow function, and use the segment point locations as decision variables to be optimized.

[0015] Step 3: Based on the condition that the segmentation point positions are known in Step 2, construct a linear function in each segmentation interval, and use the minimum absolute deviation as the error metric to solve for the parameters of the corresponding piecewise linear function.

[0016] Step 4: Use the sum of the minimum absolute deviations of all segmented intervals as the overall linearization error evaluation index.

[0017] Step 5: Use the particle swarm optimization algorithm to search for the segment point positions. By iteratively updating the particle positions and velocities, minimize the overall linearization error to obtain the optimal combination of segment points.

[0018] Step 6: Output the optimal segmentation point position and the corresponding piecewise linear function parameters to complete the adaptive piecewise linearization of the nonlinear function.

[0019] Step 7: Embed the piecewise linear functions of the water level-reservoir capacity curve and the tailwater level-discharge flow curve into the hydropower dispatching model.

[0020] The mathematical model for the above steps is as follows: The definitions of the reservoir's nonlinear function and piecewise structure are as follows: Taking the tailwater level-discharge curve as an example, let the tailwater level-discharge function to be linearized be: ,in Let x be the discharge flow rate and y be the tailrace level. Given the number of segments (i.e., K segments, requiring K+1 segment points including the start and end points), let the tailrace level-discharge flow rate function be represented by discrete data as follows: (1) in: .

[0021] In the domain Construct a K-segment continuous piecewise function with the following breakpoints: (2) in and What remains constant is the internal segmentation points, which need to be optimized and determined. .

[0022] Inner layer optimization, given the known positions of the segmentation points, involves piecewise linear fitting based on the minimum absolute deviation: For a given set of segment points S, this invention constructs a continuous tailwater level-discharge flow rate piecewise linear function, where the k-th segment linear function is defined as: (3) In the formula: The discharge flow rate is the independent variable; This is the fitted value of the tailwater level; and Let be the slope and intercept of the linear function in the k-th segment, respectively. This represents the position of the k-th segment point.

[0023] Furthermore, since the K segments of linear functions are continuous functions, they satisfy the following constraints: (4) In the formula: K is the total number of segments.

[0024] For any tailwater level data point The approximation error is defined as: (5) In the formula: For the first The outflow value corresponding to each sample point; For the first Tailwater level values ​​corresponding to each sample point; For the first The fitting error for each sample point.

[0025] This invention uses the minimum absolute deviation (L1 norm) as a measure of the fitting error of the piecewise linear function of tailwater level-discharge flow rate: (6) In the formula: .

[0026] The tailwater level-discharge curve is fitted by solving equation (7). To facilitate the solution, auxiliary variables can be introduced. This is equivalent to transforming into a linear programming problem: (7) Given that the locations of the segmentation points are known, the optimal objective value obtained by solving equation (7) is and will As the fitness value of the particle swarm optimization algorithm.

[0027] Construct an outer optimization model and search for the segmented point locations based on particle swarm optimization: For the problem of optimizing the location of segmentation points, this invention employs a particle swarm optimization algorithm. Each particle represents a set of candidate segmentation point locations, and iteratively evolves within the search space through velocity and position update rules. In each iteration, the particle fitness is calculated by solving for the corresponding minimum absolute deviation and a linear programming model, and the individual optimal solution and the global optimal solution of the swarm are updated.

[0028] The particle encoding method is as follows: Each particle Let represent a set of candidate segmentation point positions, and its search space constraint is given by equation (10).

[0029] (8) (9) In the formula: These represent the positions of the K-1 segment points of the p-th particle; and These represent the minimum and maximum values ​​of the downstream flow rate sample points, respectively.

[0030] The expressions for particle velocity and position update methods are as follows: (10) (11) In the formula: and Let represent the velocity and position of the p-th particle in the t-th iteration; Inertial weights; and For learning factors; and for Random numbers within the interval; This represents the historical best position of the p-th particle; It is the optimal position for the entire group.

[0031] The fitness assessment process is as follows: For each particle Construct a global minimum absolute deviation and linear programming model that includes all piecewise linear function parameters and continuity constraints, and solve for its optimal objective value. , which serves as the fitness value for the particle.

[0032] The objective function for particle swarm optimization is defined as: (12) The optimal segmentation point position is obtained by solving the above optimization problem. .

[0033] Constructing a hydropower dispatching model: To address the rapid fluctuations in intraday load during short-term power system operation, short-term hydropower dispatch often aims at peak shaving. This can be represented as maximizing peak-shaving and valley-filling capabilities by optimizing hydropower output, thereby improving the power grid's reliability and operational economy. The objective of short-term hydropower dispatch can be expressed as: (13) (14) In the formula: This represents the original load for time period t, in MW. This indicates the power output of a hydropower station during time period t, expressed in MW. This represents the remaining load for time period t, in MW.

[0034] Short-term hydropower dispatch must meet the following constraints: Water balance constraints: (15) (16) (17) In the formula: For the hydroelectric power station Storage capacity for a given period, in meters (m). 3 ; For the hydroelectric power station Interval flow rate during a given time period, in meters (m). 3 / s; For the hydroelectric power station Outbound flow rate for a given period, in meters (m). 3 / s; The upstream power station of the hydropower station is Outbound flow rate for a given period, in meters (m). 3 / s; For the hydroelectric power station Power generation flow rate during a given period, in meters (m³) 3 / s; For the hydroelectric power station Water discharge rate during a given period, in meters (m³) 3 / s.

[0035] Outbound flow constraints: (18) In the formula: and For the hydroelectric power station Lower and upper limits of outbound flow for a given period, in meters (m). 3 / s.

[0036] Storage capacity constraints: (19) In the formula: and For the hydroelectric power station Upper and lower limits of storage capacity for a given period, in meters (m). 3 .

[0037] Power generation flow constraints: (20) In the formula: and For the hydroelectric power station Lower and upper limits of power generation flow rate for a given period, in meters (m³) 3 / s.

[0038] Unit output limits: ;(twenty one) In the formula: and These are the lower and upper limits of the output of unit i, in MW; A value of 1 indicates that unit i is in operation during time period t, while a value of 0 indicates that unit i is in shutdown during time period t.

[0039] Water head constraints: ;(twenty two) ;(twenty three) ;(twenty four) In the formula: It is a hydroelectric power station Tailwater level for a given period, in meters (m). This represents the functional relationship between the tailrace level and the outflow from the hydropower station. It is a hydroelectric power station The net head of water during a given time period, measured in meters (m). It is a hydroelectric power station Head loss over a period of time, in meters (m).

[0040] The generator's power generation function is: (25) (26) In the formula: This represents the functional relationship between the output, power generation flow, and net head of the i-th unit of a hydropower station.

[0041] Minimum start-up and shutdown time constraints: (27) (28) In the formula: It is a binary variable, and a value of 1 indicates that unit i is started during time period t; It is a binary variable, and a value of 1 indicates that unit i is shut down during time period t; and These represent the minimum start-up and shutdown times of the unit, in hours (h).

[0042] Initial and final water level constraints: (29) (30) In the formula: and This indicates the water level above the dam at the beginning and end of the hydropower station's scheduling period, in meters (m).

[0043] Embedding piecewise linear functions into the hydropower scheduling model: After the tailwater level-discharge flow curve and water level-storage capacity curve of the reservoir are piecewise linearized by the adaptive piecewise linearization method, the piecewise linear function is embedded into the scheduling model through expressions (31)-(35), and the model is transformed into a MILP model that can be solved by commercial solvers.

[0044] (31) (32) (33) (34) (35) In the formula This represents the k-th optimal segment point of the tailwater level. This represents the discharge flow value corresponding to the k-th optimal segment point of the tailwater level. This represents the weight variable for the k-th segment point in time period t. This represents a special ordered set of the second type.

[0045] Compared with the prior art, the beneficial effects of the present invention include: (1) The linearization fitting accuracy is significantly improved, and it better matches the true characteristics of the nonlinear function. By adaptively optimizing the segment points, the segment points are densely distributed in the region with large curvature of the nonlinear function and sparsely distributed in the region with gentle curvature, which completely solves the problem of uneven fitting error in the existing patent.

[0046] (2) The solution efficiency of the scheduling model is greatly improved, balancing accuracy and speed. After the piecewise linearization result of the new scheme is embedded into the MILP model, the solution efficiency is greatly improved compared with the direct solution of the original data, under the premise that the peak-shaving effect is basically consistent with the original nonlinear data (the difference in target value is close to 0). Compared with the uniform piecewise method, the solution time during the dry season is greatly shortened, and the solution time during the flood season is only slightly increased, achieving the optimal balance between "accuracy and efficiency" and solving the problem of existing patents that "either sacrifice accuracy for efficiency or sacrifice efficiency for accuracy".

[0047] (3) The model is significantly more robust to abnormal data and has greater applicability to engineering. Based on the minimum absolute deviation fitting criterion of L1 norm, the new scheme has strong anti-interference ability against common situations in engineering such as abnormal observation data and runoff forecast deviation. The linearization results and scheduling results will not be distorted due to local data deviation. Compared with the existing patent (without robust design), it is more suitable for the complex data environment of actual hydropower projects.

[0048] (4) The whole process is closed-loop design and is suitable for various hydropower dispatching scenarios. The new solution is not only applicable to short-term peak-shaving dispatching of a single hydropower station, but can also be extended to cascade hydropower stations, medium and long-term power generation dispatching and other scenarios. It can also flexibly adjust the number of segments and adapt and optimize according to the different requirements of the project for "precision" and "efficiency". Compared with the existing patents that are only applicable to a single scenario and a single requirement, it has stronger versatility and flexibility.

[0049] (5) Provide a systematic solution for refined hydropower scheduling. The new solution integrates intelligent optimization algorithms, robust fitting, and MILP models for the first time, solving the technical bottleneck of high precision and adaptive linearization of nonlinear functions in hydropower scheduling. It changes the approach of improving a single link in existing patents and provides a systematic solution from data processing to modeling and solving for refined scheduling of complex hydropower systems. It greatly improves the scientificity and accuracy of hydropower scheduling and has important engineering value for improving the grid peak-shaving capacity, power supply reliability, and operation economy. Attached Figure Description

[0050] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0051] Figure 1 This is a flowchart of the method of the present invention.

[0052] Figure 2 This is a graph showing the peak-shaving results obtained by recalculating the original data during the flood season.

[0053] Figure 3 This is a graph showing the peak-shaving results recalculated using the uniform segmentation method during the flood season.

[0054] Figure 4 This is a graph showing the peak-shaving results obtained by recalculating using an adaptive segmentation method during the flood season.

[0055] Figure 5 This is a graph showing the peak-shaving results obtained by recalculating the original data during the dry season.

[0056] Figure 6 This is a graph showing the peak-shaving results obtained by recalculating using the uniform segmentation method during the dry season.

[0057] Figure 7 This is a graph showing the peak-shaving results obtained by recalculating using an adaptive segmentation method during the dry season.

[0058] Figure 8 It is a tailwater level discharge flow function diagram obtained by adaptive piecewise linearization and uniform piecewise division. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0060] Example 1 like Figure 1 As shown, this invention provides a nonlinear characteristic adaptive segmented driving method for refined hydropower scheduling, comprising the following steps: Step 1: Obtain discrete sample data of the water level-reservoir capacity curve and the tailwater level-discharge flow curve. The data includes independent variables and corresponding dependent variables, and are sorted according to the size of the independent variables.

[0061] Step 2: Pre-determine the number of segments K within the domains of the water level-storage capacity function and the tailwater level-discharge flow function, and use the segment point locations as decision variables to be optimized.

[0062] Step 3: Based on the condition that the segmentation point positions are known in Step 2, construct a linear function in each segmentation interval, and use the minimum absolute deviation as the error metric to solve for the parameters of the corresponding piecewise linear function.

[0063] Step 4: Use the sum of the minimum absolute deviations of all segmented intervals as the overall linearization error evaluation index.

[0064] Step 5: Use the particle swarm optimization algorithm to search for the segment point positions. By iteratively updating the particle positions and velocities, minimize the overall linearization error to obtain the optimal combination of segment points.

[0065] Step 6: Output the optimal segmentation point position and the corresponding piecewise linear function parameters to complete the adaptive piecewise linearization of the nonlinear function.

[0066] Step 7: Embed the piecewise linear functions of the water level-reservoir capacity curve and the tailwater level-discharge flow curve into the hydropower dispatching model.

[0067] The definitions of the reservoir's nonlinear function and piecewise structure are as follows: Taking the tailwater level-discharge curve as an example, let the tailwater level-discharge function to be linearized be: ,in Let x be the discharge flow rate and y be the tailrace level. Given the number of segments (i.e., K segments, requiring K+1 segment points including the start and end points), let the tailrace level-discharge flow rate function be represented by discrete data as follows: (1) in: .

[0068] In the domain Construct a K-segment continuous piecewise function with the following breakpoints: (2) in and What remains constant is the internal segmentation points, which need to be optimized and determined. .

[0069] Inner layer optimization, given the known positions of the segmentation points, involves piecewise linear fitting based on the minimum absolute deviation: For a given set of segment points S, this invention constructs a continuous tailwater level-discharge flow rate piecewise linear function, where the k-th segment linear function is defined as: (3) In the formula: The discharge flow rate is the independent variable; This is the fitted value of the tailwater level; and Let be the slope and intercept of the linear function in the k-th segment, respectively. This represents the position of the k-th segment point.

[0070] Furthermore, since the K segments of linear functions are continuous functions, they satisfy the following constraints: (4) In the formula: K is the total number of segments.

[0071] For any tailwater level data point The approximation error is defined as: (5) In the formula: For the first The outflow value corresponding to each sample point; For the first Tailwater level values ​​corresponding to each sample point; For the first The fitting error for each sample point.

[0072] This invention uses the minimum absolute deviation (L1 norm) as a measure of the fitting error of the piecewise linear function of tailwater level-discharge flow rate: (6) In the formula: .

[0073] The tailwater level-discharge curve is fitted by solving equation (7). To facilitate the solution, auxiliary variables can be introduced. This is equivalent to transforming into a linear programming problem: (7) Given that the locations of the segmentation points are known, the optimal objective value obtained by solving equation (7) is and will As the fitness value of the particle swarm optimization algorithm.

[0074] Construct an outer optimization model and search for the segmented point locations based on particle swarm optimization: For the problem of optimizing the location of segmentation points, this invention employs a particle swarm optimization algorithm. Each particle represents a set of candidate segmentation point locations, and iteratively evolves within the search space through velocity and position update rules. In each iteration, the particle fitness is calculated by solving for the corresponding minimum absolute deviation and a linear programming model, and the individual optimal solution and the global optimal solution of the swarm are updated.

[0075] The particle encoding method is as follows: Each particle Let represent a set of candidate segmentation point positions, and its search space constraint is given by equation (10).

[0076] (8) (9) In the formula: These represent the positions of the K-1 segment points of the p-th particle; and These represent the minimum and maximum values ​​of the downstream flow rate sample points, respectively.

[0077] The expressions for particle velocity and position update methods are as follows: (10) (11) In the formula: and Let represent the velocity and position of the p-th particle in the t-th iteration; Inertial weights; and For learning factors; and for Random numbers within the interval; This represents the historical best position of the p-th particle; It is the optimal position for the entire group.

[0078] The fitness assessment process is as follows: For each particle Construct a global minimum absolute deviation and linear programming model that includes all piecewise linear function parameters and continuity constraints, and solve for its optimal objective value. , which serves as the fitness value for the particle.

[0079] The objective function for particle swarm optimization is defined as: (12) The optimal segmentation point position is obtained by solving the above optimization problem. .

[0080] Constructing a hydropower dispatching model: To address the rapid fluctuations in intraday load during short-term power system operation, short-term hydropower dispatch often aims at peak shaving. This can be represented as maximizing peak-shaving and valley-filling capabilities by optimizing hydropower output, thereby improving the power grid's reliability and operational economy. The objective of short-term hydropower dispatch can be expressed as: (13) (14) In the formula: This represents the original load for time period t, in MW. This indicates the power output of a hydropower station during time period t, expressed in MW. This represents the remaining load for time period t, in MW.

[0081] Short-term hydropower dispatch must meet the following constraints: Water balance constraints: (15) (16) (17) In the formula: For the hydroelectric power station Storage capacity for a given period, in meters (m). 3 ; For the hydroelectric power station Interval flow rate during a given time period, in meters (m). 3 / s; For the hydroelectric power station Outbound flow rate for a given period, in meters (m). 3 / s; The upstream power station of the hydropower station is Outbound flow rate for a given period, in meters (m). 3 / s; For the hydroelectric power station Power generation flow rate during a given period, in meters (m³) 3 / s; For the hydroelectric power station Water discharge rate during a given period, in meters (m³) 3 / s.

[0082] Outbound flow constraints: (18) In the formula: and For the hydroelectric power station Lower and upper limits of outbound flow for a given period, in meters (m). 3 / s.

[0083] Storage capacity constraints: (19) In the formula: and For the hydroelectric power station Upper and lower limits of storage capacity for a given period, in meters (m). 3 .

[0084] Power generation flow constraints: (20) In the formula: and For the hydroelectric power station Lower and upper limits of power generation flow rate for a given period, in meters (m³) 3 / s.

[0085] Unit output limits: ;(twenty one) In the formula: and These are the lower and upper limits of the output of unit i, in MW; A value of 1 indicates that unit i is in operation during time period t, while a value of 0 indicates that unit i is in shutdown during time period t.

[0086] Water head constraints: ;(twenty two) ;(twenty three) ;(twenty four) In the formula: It is a hydroelectric power station Tailwater level for a given period, in meters (m). This represents the functional relationship between the tailrace level and the outflow from the hydropower station. It is a hydroelectric power station The net head of water during a given time period, measured in meters (m). It is a hydroelectric power station Head loss over a period of time, in meters (m).

[0087] The generator's power generation function is: (25) (26) In the formula: This represents the functional relationship between the output, power generation flow, and net head of the i-th unit of a hydropower station.

[0088] Minimum start-up and shutdown time constraints: (27) (28) In the formula: It is a binary variable, and a value of 1 indicates that unit i is started during time period t; It is a binary variable, and a value of 1 indicates that unit i is shut down during time period t; and These represent the minimum start-up and shutdown times of the unit, in hours (h).

[0089] Initial and final water level constraints: (29) (30) In the formula: and This indicates the water level above the dam at the beginning and end of the hydropower station's scheduling period, in meters (m).

[0090] Embedding piecewise linear functions into the hydropower scheduling model: After the tailwater level-discharge flow curve and water level-storage capacity curve of the reservoir are piecewise linearized by the adaptive piecewise linearization method, the piecewise linear function is embedded into the scheduling model through expressions (31)-(35), and the model is transformed into a MILP model that can be solved by commercial solvers.

[0091] (31) (32) (33) (34) (35) In the formula This represents the k-th optimal segment point of the tailwater level. This represents the discharge flow value corresponding to the k-th optimal segment point of the tailwater level. This represents the weight variable for the k-th segment point in time period t. This represents a special ordered set of the second type.

[0092] Example 2 Based on the method described in Example 1, a WDD hydropower station in the lower reaches of a river basin in a southwestern province of my country was selected as an engineering case to verify the proposed method. The WDD is an annual regulating hydropower station with an installed capacity of 10200MW, a normal high water level of 975 meters, and a dead water level of 945 meters. Due to its large installed capacity and strong regulating performance, the WDD has undertaken an important task of peak shaving for the power grid since its commissioning; therefore, the case study focuses on the WDD. Three methods—raw data processing, uniform segmentation, and adaptive segmentation—were used to handle the nonlinear characteristics of the reservoir. A hydropower dispatching model was constructed using Python and solved using Gurobi.

[0093] Tables 1 and 2 show the target values ​​and solution times obtained from solving the three hydropower dispatch optimization models during the flood season and dry season, respectively. It can be found that during the flood season, the peak-shaving effect obtained by using adaptive piecewise processing of the reservoir nonlinear function is the same as that obtained by using uniform piecewise processing, although the solution time is 8.57% slower. However, compared with solving using the original data, the solution time is 41.23% faster. During the dry season, the peak-shaving effect obtained by using adaptive piecewise linearization to process the reservoir's nonlinear function was the same as that obtained by using the uniform piecewise linearization method, with a solution time that was 32.79% faster and 41.04% faster than using the original data. These results indicate that the target value obtained by using the adaptive piecewise linearization method to process the reservoir's nonlinear characteristics is not significantly different from that obtained using the original data, but the computational efficiency is improved by more than 41.04%. Furthermore, compared with the uniform piecewise linearization method, it achieves a balance between solution accuracy and solution time.

[0094] Table 1. Comparative Analysis of Calculation Results of Three Methods During the Flood Season

[0095] Table 2. Comparative Analysis of Calculation Results of Three Methods During the Dry Season

[0096] Figure 8 The diagram shows a comparison between the tailrace level-discharge curve and the original curve, using adaptive piecewise linearization and uniform piecewise linearization as examples. The diagram shows that the adaptive piecewise linearization method fits the original nonlinear curve better and better reproduces the nonlinear characteristics; while the curve after uniform piecewise linearization shows a discharge flow rate between 0 and 10000 m³ / h. 3 At a rate of / s, the deviation from the original nonlinear curve is significant, and the nonlinear characteristics of the tailrace discharge curve cannot be accurately reproduced within this range. This indicates that the adaptive piecewise linearization method provides higher accuracy in handling the nonlinear characteristics of the reservoir.

[0097] Figures 2-7This paper demonstrates how, based on water level and flow information from the optimized original model, three methods—original data, fixed piecewise linearization, and adaptive piecewise linearization—were used to calculate the actual power output using a water-determined power generation method, thus obtaining peak-shaving results for the flood and dry seasons. Specifically, the scheduling results obtained by solving the scheduling model using the original nonlinear function were used as the actual data. This actual data was then substituted into models using the three methods to process the nonlinearity, recalculating the power output of the hydropower station for each period during the flood and dry seasons, ultimately yielding six peak-shaving effect diagrams. Comparison of these six diagrams reveals that the result obtained using the adaptive piecewise linearization method is closer to the result obtained using the original data. The result obtained using the uniform piecewise linearization method differs significantly from the result obtained using the original data, indicating that the adaptive piecewise linearization method better restores the original nonlinear function.

[0098] The embodiments described above are merely illustrative of implementation methods of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A nonlinear characteristic adaptive segmented driving method for refined hydropower scheduling, characterized in that, Includes the following steps: S1. Obtain discrete sample data of the water level-reservoir capacity curve and the tailwater level-discharge flow curve, including independent variables and corresponding dependent variables, and sort them; S2. Pre-determine the number of segments within the domains of the water level-storage capacity function and the tailwater level-discharge flow function, and use the segment point locations as decision variables to be optimized; S3. Construct a linear function within each segmented interval, and use the minimum absolute deviation as the error metric to solve for the parameters of each segmented linear function; S4. Use the sum of the minimum absolute deviations of all segmented intervals as the overall linearization error evaluation index; S5. The particle swarm optimization algorithm is used to search for the position of the segment points. By iteratively updating the particle position and velocity, the overall linearization error is minimized to obtain the optimal combination of segment points. S6. Output the optimal segmentation point position and the corresponding piecewise linear function parameters to complete the adaptive piecewise linearization of the nonlinear function; S7. Embed the piecewise linear functions of the water level-reservoir capacity curve and the tailwater level-discharge flow curve into the hydropower dispatching model, and transform the model into a mixed integer linear programming model that can be solved by a commercial solver.

2. The nonlinear characteristic adaptive segmented driving method for refined hydropower scheduling according to claim 1, characterized in that, The step S3, which uses the minimum absolute deviation as the error metric, specifically employs the L1 norm as the error metric for piecewise linear fitting of the nonlinear function. By introducing auxiliary variables, the problem of finding the minimum absolute deviation is equivalently transformed into a linear programming problem, and the optimal parameters of the piecewise linear function are obtained by solving the problem.

3. The nonlinear characteristic adaptive segmented driving method for refined hydropower scheduling according to claim 1, characterized in that, The execution process of the particle swarm optimization algorithm in step S5 is as follows: each candidate segment point position is encoded as a particle, and the search space of the particles is limited to the domain range of the nonlinear function. The velocity and position of the particles are iteratively updated according to the inertia weight, learning factor, and random number update rules. The overall linearization error evaluation index is used as the particle fitness value. After each iteration, the individual optimal solution of the particle and the global optimal solution of the population are updated until the iteration termination condition is met.

4. The nonlinear characteristic adaptive segmented driving method for refined hydropower scheduling according to claim 1, characterized in that, The linear function constructed in step S3 is a continuous function. The linear functions of adjacent segmented intervals satisfy the function value continuity constraint at the segmentation point, so that the piecewise linear function can completely represent the changing trend of the original nonlinear function.

5. The nonlinear characteristic adaptive segmented driving method for refined hydropower scheduling according to claim 1, characterized in that, Step S7, which involves embedding the piecewise linear function into the hydropower scheduling model, specifically employs a second type of special ordered set combined with segmentation point weight variables. By assigning weights, the optimal segmentation point and its corresponding linear function parameters are embedded into the core constraints of the hydropower scheduling model, such as net head and reservoir capacity. This achieves deep integration of the linearization result with the scheduling model. The expression is: ； ； ； ； ； In the formula This represents the k-th optimal segment point of the tailwater level. This represents the discharge flow value corresponding to the k-th optimal segment point of the tailwater level. This represents the weight variable for the k-th segment point in time period t. This represents a special ordered set of the second type.

6. The nonlinear characteristic adaptive segmented driving method for refined hydropower scheduling according to claim 1, characterized in that, The hydropower dispatch model in step S7 takes power system peak shaving as its core objective. It maximizes peak shaving and valley filling capacity by optimizing the output process of hydropower stations. The objective function is to minimize the fluctuation of the remaining load in each time period, which can be expressed as: ； ； In the formula: This represents the original load for time period t, in MW. This indicates the power output of a hydropower station during time period t, expressed in MW. This represents the remaining load for time period t, in MW.

7. The nonlinear characteristic adaptive segmented driving method for refined hydropower scheduling according to claim 6, characterized in that, The objective function simultaneously incorporates multiple engineering constraints, including water balance, outflow, reservoir capacity, power generation flow, unit output limits, minimum start-up and shutdown times, and initial and final water levels.

8. The nonlinear characteristic adaptive segmented driving method for refined hydropower scheduling according to claim 7, characterized in that, The expression for the water balance constraint is: ； ； ； In the formula: For the hydroelectric power station Storage capacity for a given period, in meters (m). 3 ; For the hydroelectric power station Interval flow rate during a given time period, in meters (m). 3 / s; For the hydroelectric power station Outbound flow rate for a given period, in meters (m). 3 / s; The upstream power station of the hydropower station is Outbound flow rate for a given period, in meters (m). 3 / s; For the hydroelectric power station Power generation flow rate during a given period, in meters (m³) 3 / s; For the hydroelectric power station Water discharge rate during a given period, in meters (m³) 3 / s.

9. The nonlinear characteristic adaptive segmented driving method for refined hydropower scheduling according to claim 1, characterized in that, The number of segments mentioned in step S2 is a parameter that can be flexibly adjusted. It can be set according to the different requirements of hydropower projects for scheduling accuracy and solution efficiency, so that the method can be adapted to various hydropower scheduling scenarios such as short-term peak shaving of a single hydropower station, scheduling of cascade hydropower stations, and medium- and long-term power generation scheduling.

10. The nonlinear characteristic adaptive segmented driving method for refined hydropower scheduling according to claim 1, characterized in that, A two-layer optimization architecture, consisting of an inner layer of linear fitting and an outer layer of particle swarm optimization, is adopted to achieve adaptive linearization of nonlinear functions. The inner layer solves the piecewise linear function parameters with the minimum absolute deviation and outputs the overall linearization error. The outer layer uses this error as the fitness value of particle swarm optimization to achieve iterative optimization of the piecewise point positions. The two-layer architecture iterates together until convergence, achieving synchronous optimal solution of the piecewise point positions and linear function parameters.

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