A power grid coordinated cascade hydropower multi-objective optimization method and system

Abstract

This invention relates to the field of energy system control technology, and particularly to a multi-objective optimization method and system for cascade hydropower projects involving coordinated power plant and grid operation. The method includes: establishing a mathematical model based on the operating characteristics of the cascade hydropower stations and the receiving-end power grid; constructing a mixed-integer linear programming model with the optimization objectives of maximizing the total power generation of the cascade hydropower stations and minimizing the operating cost of the receiving-end power grid; determining the constraint system based on the linear and nonlinear constraints in the mixed-integer linear programming model, and linearizing the nonlinear constraints; using the EPO-AL algorithm to transform the mixed-integer linear programming model into a single-objective model, and solving to obtain the Pareto solution set; screening the global Pareto solution set; and using a compromise solution selection method to determine the optimal power generation plan from the global Pareto solution set. This invention effectively solves the problems of infeasible scheduling schemes and imbalanced optimization objectives in hydropower-thermal power hybrid systems caused by dynamic constraint propagation delays and dimensional explosion in nonlinear programming.

Description

Technical Field

[0001] This invention relates to the field of energy system control technology, and in particular to a multi-objective optimization method and system for coordinated power plant and grid cascade hydropower. Background Technology

[0002] In a hybrid energy system consisting of a cascade of hydropower stations and a receiving-end thermal power plant, the coordinated dispatch of hydropower and thermal power generation is a core element in improving energy utilization efficiency. The cascade hydropower stations form a hydraulic coupling chain through hydrological connections. There is a significant time delay in the transmission of water from upstream power stations to downstream power stations, while the receiving-end thermal power plants need to adjust their output in real time according to the grid load demand.

[0003] Existing dispatching technologies mainly rely on two types of methods: one is a hydropower independent optimization strategy based on a static hydraulic connection model, which simplifies cascade power stations into a series of reservoirs with fixed transmission delays and then simply superimposes them with thermal power plans; the other is a mixed integer programming algorithm with linear approximation, which approximates the dynamic characteristic curves of hydropower units piecewise by constants and solves the problem under a single objective function. However, existing technologies suffer from three systemic defects: First, ignoring the dynamic transmission characteristics of the water cycle leads to inaccurate dispatching. The static flow arrival time model cannot adapt to the significant differences in hydrological transmission speeds between flood and dry seasons, causing a misalignment between reservoir capacity control commands and measured water flow arrival times, leading to the risk of water wastage or power generation gaps. Second, the optimization objective design is unbalanced. When hydropower dispatching aims to maximize power generation, thermal power is forced to frequently start and stop for peak shaving, exacerbating fuel consumption. Conversely, aiming to minimize thermal power fuel consumption will suppress the hydropower absorption capacity, resulting in conflicting objectives and a decline in the grid's peak shaving capacity. Third, the solution to nonlinear constraints fails. Conventional linearization methods coarsely handle the complex non-convex characteristics of unit characteristic curves, producing infeasible solutions during periods of severe load fluctuations, causing the optimization model to collapse. The aforementioned defects together have resulted in the energy system operating in a sub-optimal state for a long time, characterized by "hydropower not daring to generate at full capacity and thermal power being difficult to reduce energy consumption."

[0004] The information disclosed in this background section is intended only to enhance the understanding of the general background of this disclosure and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0005] This invention provides a multi-objective optimization method and system for coordinated hydropower plant and grid operation, which can effectively solve the problems in the background technology.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A multi-objective optimization method for coordinated power plant and grid-connected cascade hydropower projects, the method comprising: A mathematical model is established based on the operating characteristics of cascade hydropower stations and the receiving-end power grid; Based on the mathematical model, a mixed-integer linear programming model is constructed with the optimization objectives of maximizing the total power generation of the cascade hydropower stations and minimizing the operating cost of the receiving-end power grid. The constraint system is determined based on the linear and nonlinear constraints in the mixed integer linear programming model, and the nonlinear constraints are linearized. The EPO-AL algorithm is used to transform the mixed-integer linear programming model into a single-objective model, and the Pareto solution set is obtained by solving the problem. The global Pareto solution set is filtered from the Pareto solution set using the Pareto filtering algorithm; The optimal power generation plan is determined from the global Pareto solution set using a TOPSIS-based compromise solution selection method.

[0007] Furthermore, the optimization objective includes: The goal of maximizing the total power generation of the cascade hydropower stations is to optimize the power station side. Minimizing the operating cost of the receiving-end power grid is taken as the optimization objective on the power grid side; The optimization objectives on the power plant side and the optimization objectives on the power grid side are jointly incorporated into the mixed-integer linear programming model.

[0008] Furthermore, the nonlinear constraints and linear constraints in the mixed-integer linear programming model include: The following constraints are defined as linear constraints: water balance constraint, initial and final reservoir capacity constraint, reservoir operation constraint, unit operation constraint, unit start-up and shutdown status constraint, unit start-up and shutdown duration and maximum number of start-up and shutdown constraints, unit power generation head constraint, and DC channel constraint. The upstream water level and reservoir capacity constraints, the tailrace water level and flow constraints, and the unit dynamic characteristic constraints are defined as the nonlinear constraints.

[0009] Further, linearization is performed, including: The reservoir capacity constraint at the upstream water level is linearized. The tailwater level-discharge constraint is linearized. The power output relationship of the hydropower unit corresponding to the power characteristic constraints of the unit is linearized. The linearization process employs triangular interpolation and linear interpolation.

[0010] Furthermore, the EPO-AL algorithm is used to transform it into a single-objective model, including: Construct an augmented Lagrangian function to update the main variables in the mixed-integer linear programming model; Based on the updated master variables, update the Lagrange multipliers and penalty parameters; An iterative solution process is performed based on the augmented Lagrange function, accompanied by adaptive updates of the penalty parameter; After completing the iterative solution, the Pareto solution set is obtained by changing the initial values ​​of the Lagrange multipliers.

[0011] Furthermore, the global Pareto solution set is filtered, including: Each solution in the Pareto solution set is compared with the remaining solutions, and solutions in the Pareto solution set that are dominated by the remaining solutions are removed. The undominated solutions in the Pareto solution set after the cleanup are retained to obtain the global Pareto solution.

[0012] Furthermore, a TOPSIS-based compromise solution selection method is adopted, including: The optimization objective corresponding to the global Pareto solution set is normalized, and the positive ideal solution and negative ideal solution are determined based on the normalization result. The proximity index is calculated based on the Euclidean distance between each of the power generation plans and the positive and negative ideal solutions. The power generation plan scheme with the highest proximity index is selected as the optimal power generation plan.

[0013] Furthermore, the linear constraint includes: Based on the water balance constraints, the correspondence between the reservoir capacity, interval flow, outflow, power generation flow and water abandonment flow in each time period is constrained; Based on the initial and final time period storage capacity constraints, constraints are imposed on the initial time period storage capacity and the final time period storage capacity. Based on the reservoir operation constraints, the upper and lower limits of the reservoir capacity, the upper and lower limits of the outflow, and the discharge flow are constrained; Based on the unit operation constraints and the unit start-up and shutdown state constraints, constraints are imposed on the unit output, unit power generation flow, and unit operation state; Based on the constraints of the unit start-up and shutdown duration and the maximum number of start-ups and shutdowns, constraints are imposed on the unit start-up operation and the unit shutdown operation. Based on the generator head constraint, the correspondence between the net head of power generation, the water level above the dam, the tailrace water level, and the head loss value is constrained. Based on the aforementioned DC channel constraints, the power allowed to pass through the DC transmission channel within a time period is constrained.

[0014] A multi-objective optimization system for cascade hydropower projects involving both power plants and the grid, the system comprising: The mathematical model building module establishes mathematical models based on the operational characteristics of cascade hydropower stations and the receiving-end power grid. The objective linear programming module, based on a mathematical model, constructs a mixed-integer linear programming model with the optimization objectives of maximizing the total power generation of the cascade hydropower stations and minimizing the operating cost of the receiving-end power grid. The constraint linear processing module determines the constraint system based on the linear and nonlinear constraints in the mixed-integer linear programming model, and performs linearization processing on the nonlinear constraints; The Pareto solution module uses the EPO-AL algorithm to transform the mixed-integer linear programming model into a single-objective model and solves it to obtain the Pareto solution set. The Pareto filtering module uses the Pareto filtering algorithm to filter the global Pareto solution set from the Pareto solution set. The compromise optimal selection module uses a TOPSIS-based compromise solution selection method to determine the optimal power generation plan from the global Pareto solution set.

[0015] Furthermore, the Pareto solver module includes: The main variable update unit constructs an augmented Lagrangian function to update the main variables in the mixed-integer linear programming model; The multiplier term setting unit updates the Lagrange multipliers and penalty parameters based on the updated master variables; The iterative solution unit performs an iterative solution process based on the augmented Lagrangian function, which adaptively updates the accompanying penalty parameter. The Pareto solution unit obtains the Pareto solution set by changing the initial values ​​of the Lagrange multipliers after completing the iterative solution.

[0016] The technical solution of this invention can achieve the following technical effects: By establishing a cascade reservoir capacity coupling model with dynamic flow time constraints, and combining the linearization compression technology of unit operating points with the augmented Lagrange hierarchical optimization algorithm with adaptive penalty coefficients, a dual-objective Pareto optimality is achieved to maximize hydropower generation and minimize thermal power fuel consumption under the premise of satisfying the dynamic transmission constraints of the hydraulic system. Furthermore, an engineerable power generation plan is generated based on the improved TOPSIS decision mechanism, thereby solving the problems of infeasible scheduling schemes and imbalance of optimization objectives caused by dynamic constraint transmission delays and nonlinear programming dimension explosion in hydro-thermal power hybrid systems.

[0017] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart illustrating a multi-objective optimization method for power plant-grid coordinated cascade hydropower. Figure 2 The Pareto front plot is obtained by solving the EPO-AL algorithm; Figure 3 The Pareto front plot after filtering global Pareto solutions using the Pareto filtering algorithm; Figure 4 This is a diagram of the DC power transmission and 3-node receiving-end power grid structure of a cascade hydropower station. Detailed Implementation

[0020] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0021] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0022] Example 1; like Figure 1 As shown, this application provides a multi-objective optimization method for cascade hydropower projects involving coordinated power plant and grid operations. The method includes: S10: Establish a mathematical model based on the operating characteristics of cascade hydropower stations and the receiving-end power grid; S20: Based on a mathematical model, a mixed-integer linear programming model is constructed with the optimization objectives of maximizing the total power generation of the cascade hydropower stations and minimizing the operating cost of the receiving-end power grid. S30: Determine the constraint system based on the linear and nonlinear constraints in the mixed-integer linear programming model, and linearize the nonlinear constraints; S40: The EPO-AL algorithm is used to transform the mixed-integer linear programming model into a single-objective model, and the Pareto solution set is obtained by solving the Pareto solution set. S50: Filter the global Pareto solution set from the Pareto solution set using the Pareto filtering algorithm; S60: The optimal power generation plan is determined from the global Pareto solution set using a compromise solution selection method based on TOPSIS.

[0023] Specifically, a mathematical model is first established based on the operational characteristics of the cascade hydropower stations and the receiving-end power grid. These operational characteristics include at least the hydraulic coupling relationship between the cascade hydropower stations, the time delay characteristics of upstream water flow to downstream, reservoir capacity variation characteristics, unit operating characteristics, and the receiving-end power grid's dispatching requirements for power output and operational economy. In this step, it is preferable to incorporate the water balance relationship of each level of the cascade hydropower station, initial and final reservoir capacity requirements, reservoir operating boundaries, unit operating status, unit start-up and shutdown constraints, unit head constraints, and DC transmission power limitations into the model foundation. This ensures that subsequent optimization results satisfy both the watershed hydraulic connectivity and the receiving-end power grid's requirements. The actual operational requirements of the power grid; after establishing the mathematical model, based on the mathematical model, a mixed-integer linear programming model is constructed with the optimization objectives of maximizing the total power generation of the cascade hydropower stations and minimizing the operating cost of the receiving-end power grid. Preferably, maximizing the total power generation of the cascade hydropower stations is taken as the optimization objective on the power station side, and minimizing the operating cost of the receiving-end power grid is taken as the optimization objective on the power grid side. Both optimization objectives are incorporated into the mixed-integer linear programming model, so that the model can simultaneously reflect the dual needs of power plants pursuing power generation efficiency and the power grid pursuing operational economy during the solution process. This avoids the problems of insufficient hydropower absorption or excessively high thermal power costs that occur when only a single objective is considered. Next, based on the linear and nonlinear constraints in the mixed-integer linear programming model, the constraint system is determined, and the nonlinear constraints are linearized. Specifically, the water balance constraint, initial and final reservoir capacity constraint, reservoir operation constraint, unit operation constraint, unit start-up and shutdown state constraint, unit start-up and shutdown duration and maximum number of start-ups and shutdowns constraint, unit power generation head constraint, and DC channel constraint are preferably defined as linear constraints. The upstream water level and reservoir capacity constraint, tailrace water level and flow rate constraint, and unit dynamic characteristic constraint are defined as nonlinear constraints. This is because the upstream water level and reservoir capacity relationship, tailrace water level and flow rate relationship, and unit dynamic characteristic relationship typically exhibit strong nonlinearity. Directly solving the problem would significantly increase the model's dimensionality, make the solution more difficult, and even lead to infeasibility. Therefore, it is preferable to use triangular interpolation and linear interpolation to linearize the nonlinear constraints. Specifically, the relationship between the upstream water level and reservoir capacity can be discretized into several segmented points, and the upstream water level corresponding to the change in reservoir capacity can be represented by interpolation. The relationship between the downstream water level and discharge can be discretized into several segmented points, and the downstream water level corresponding to the change in discharge can be represented by interpolation. At the same time, the dynamic characteristic relationship of the unit can be converted into a linear relationship that can be expressed by a finite number of operating points. This is to reduce the complexity of the model solution and improve the solvability and stability of the scheduling model without deviating from the original operating rules.After completing the constraint system construction and linearization, the EPO-AL algorithm is used to transform the mixed-integer linear programming model into a single-objective model and solve it to obtain the Pareto solution set. Preferably, an augmented Lagrangian function is first constructed to update the main variables, and then the Lagrange multipliers and penalty parameters are updated based on the updated main variables. An iterative solution process with adaptive updates of the penalty parameters is executed. After one iteration, the next iteration is continued based on the update results until the stopping condition is met. Then, multiple sets of Pareto solutions corresponding to different benefit trade-offs are obtained by changing the initial values ​​of the Lagrange multipliers. Since local Pareto solutions and global Pareto solutions may coexist in the Pareto solution set, it is preferable to further filter the global Pareto solution set from the Pareto solution set using a Pareto filtering algorithm. Specifically, each solution in the Pareto solution set is compared with the other solutions one by one, eliminating solutions dominated by other solutions and retaining the undominated solutions as the global Pareto solution set, thereby avoiding local optima from interfering with the final decision. After obtaining the global Pareto solution set, a TOPSIS-based folding algorithm is then used. The optimal power generation plan is determined from the global Pareto solution set. Preferably, the optimization objective corresponding to the global Pareto solution set is first normalized, and then the positive and negative ideal solutions are determined based on the normalization results. The distance between each power generation plan and the positive and negative ideal solutions is then calculated, and a proximity index is obtained for each plan. Finally, the power generation plan with the largest proximity index is selected as the optimal plan. For example, in a preferred application scenario, multiple cascade hydropower stations with upstream and downstream relationships in the Yalong River basin can be considered as power station-side objects, and the connected receiving-end power grid as the grid-side object. Within a given short-term scheduling period, the above model is established based on the reservoir capacity boundary of the cascade hydropower stations, unit operating conditions, upstream and downstream water flow transmission relationships, and the load demand of the receiving-end power grid. Then, bi-objective modeling, constraint classification and linearization, EPO-AL solution, Pareto filtering, and TOPSIS compromise solution selection are performed sequentially to obtain a short-term optimal power generation plan that balances the total power generation of the cascade and the operating cost of the receiving-end power grid.

[0024] The technical solution of this invention establishes a cascade reservoir capacity coupling model with dynamic flow time constraints. Combining the linearization compression technology of unit operating points with the augmented Lagrange hierarchical optimization algorithm with adaptive penalty coefficient, it achieves a dual-objective Pareto optimality of maximizing hydropower generation and minimizing thermal power fuel consumption under the premise of satisfying the dynamic transmission constraints of the hydraulic system. Furthermore, it generates an engineering-executable power generation plan based on the improved TOPSIS decision mechanism, thereby solving the problems of infeasible scheduling schemes and imbalance of optimization objectives caused by dynamic constraint transmission delay and nonlinear programming dimension explosion in hydro-thermal power hybrid systems.

[0025] Furthermore, the optimization objectives include: Maximizing the total power generation of the cascade hydropower stations is taken as the optimization objective on the power station side. Minimizing the operating cost of the receiving-end power grid is taken as the optimization objective on the power grid side. The optimization objectives on both the power plant side and the power grid side are incorporated into the mixed-integer linear programming model.

[0026] As a preferred embodiment of the above embodiments, after the mathematical model is established, the approach of using only a single power generation revenue or a single operating cost as the basis for scheduling is no longer adopted. Instead, the maximum total power generation of the cascade hydropower stations is explicitly set as the power station-side optimization objective, and the minimum operating cost of the receiving-end power grid is explicitly set as the power grid-side optimization objective. Both the power station-side and power grid-side optimization objectives are jointly incorporated into the mixed-integer linear programming model, so that the mixed-integer linear programming model simultaneously reflects the pursuit of power generation efficiency by the cascade hydropower stations and the requirements of the receiving-end power grid for operational economy within the same scheduling framework. Preferably, the power station-side optimization objective is used to characterize the performance of each cascade hydropower station within the scheduling cycle. The overall power generation level formed by the unit output of the power station at different times is used to maximize the overall power generation efficiency of the cascade while meeting the requirements of reservoir capacity, flow, and unit operating conditions. The grid-side optimization objective is used to characterize the operating costs incurred by thermal power units in the receiving-end grid when they bear the remaining load during the corresponding dispatch cycle. This allows the receiving-end grid to reduce the operating expenses of thermal power units while accepting the cascade hydropower output. After the above two objectives are written into the mixed integer linear programming model, it can avoid the problems of traditional single-objective dispatching that only emphasize hydropower generation, leading to increased thermal power costs in the receiving-end grid, or only emphasize grid economy, compressing the space for cascade hydropower absorption. The coordinated balance of interests on both sides of the power plant and the grid is one of the preferred improvements of this application compared to existing scheduling methods. Furthermore, as a preferred implementation method, the expression of the power plant-side optimization objective and the grid-side optimization objective can be determined first based on the power generation demand of the cascade hydropower stations during the scheduling cycle and the power supply demand of the receiving-end grid during the same scheduling cycle. Then, these two are incorporated as parallel optimization contents into a mixed-integer linear programming model, ensuring that subsequent linear constraints, nonlinear constraints, linearization processing, and Pareto solutions all revolve around the dual objectives. This guarantees that the Pareto solution set obtained after subsequent solutions truly reflects the trade-off between the power plant-side optimization objective and the grid-side optimization objective. Relationship; as an example, in a preferred application scenario, multiple cascade hydropower stations with hydraulic connections between upstream and downstream can be regarded as power station-side objects, and the receiving-end power grid connected to the cascade hydropower stations can be regarded as the power grid-side objects. In the short-term dispatch cycle, on the one hand, the hydropower utilization level can be improved by increasing the total power generation of the cascade hydropower stations, and on the other hand, the economic burden on the thermal power side can be reduced by reducing the operating cost of the receiving-end power grid. These two objectives are simultaneously incorporated into a mixed integer linear programming model for unified solution, thereby obtaining an optimization basis that takes into account both the cascade power generation benefits and the power grid operation economy, providing support for the subsequent constraint system construction, linearization processing, and determination of the optimal power generation plan.

[0027] Furthermore, the nonlinear and linear constraints in mixed-integer linear programming models include: The constraints of water balance, initial and final reservoir capacity, reservoir operation, unit operation, unit start-up and shutdown status, unit start-up and shutdown duration and maximum number of start-ups and shutdowns, unit power generation head, and DC channel are defined as linear constraints. The constraints on reservoir capacity at the dam front, tailwater level and flow rate, and unit dynamic characteristics are defined as nonlinear constraints.

[0028] As a preferred embodiment of the above, when establishing the mixed-integer linear programming model, the constraints involved in the scheduling process are first systematically sorted out by combining the hydraulic connections of the cascade hydropower stations, reservoir capacity changes, unit operating status, and power acceptance requirements of the receiving-end power grid. Constraints that can be directly expressed as linear relationships and are easy to couple directly with the mixed-integer linear programming model are identified as linear constraints. Constraints that reflect the complex correspondence between water level, flow rate, and unit output and are difficult to express as linear relationships are identified as nonlinear constraints. Preferably, the linear constraints include water balance constraints, initial and final reservoir capacity constraints, reservoir operation constraints, unit operation constraints, unit start-up and shutdown state constraints, and unit start-up and shutdown duration constraints. The constraints include maximum start-up / shutdown frequency, unit head constraints, and DC transmission channel constraints. Nonlinear constraints preferably include upstream reservoir level and capacity constraints, tailrace water level and flow constraints, and unit dynamic characteristic constraints. This classification provides a clear modeling foundation for subsequent linearization and multi-objective solutions. Furthermore, as a preferred approach, to ensure that linear constraints fully reflect the operational boundaries of the cascade hydropower stations and the receiving-end power grid in the mixed-integer linear programming model, water balance constraints are used to define the conservation relationships between reservoir capacity and interval flow, outflow, power generation flow, and wastewater flow at each time period. Initial and final time period reservoir capacity constraints are used to define the reservoir capacity state at the start and end of the scheduling process. Reservoir operation constraints are used to define the upper and lower limits of reservoir capacity and outflow... The upper and lower limits of reservoir flow and the conditions for water discharge, the unit operation constraints and the unit start-up and shutdown state constraints are used to limit the unit output range, the unit power generation flow range and the unit operating state. The unit start-up and shutdown duration and maximum start-up and shutdown number constraints are used to avoid frequent switching of unit operating states. The unit power generation head constraints are used to limit the correspondence between the net power generation head and the water level at the dam, the tailrace water level and the head loss. The DC channel constraints are used to limit the power allowed to pass through the DC transmission channel within a time period. This ensures that the mixed integer linear programming model satisfies both the hydraulic and unit operation laws within the cascade hydropower station and the power absorption conditions of the receiving end power grid transmission channel. At the same time, the separate identification of nonlinear constraints is crucial for the solvability of the entire model. It plays an important role. Specifically, the reservoir capacity constraint at the front of the dam reflects the nonlinear correspondence between changes in reservoir capacity and changes in the water level at the front of the dam; the tailwater level and flow constraint reflects the nonlinear correspondence between changes in outflow and changes in tailwater level; and the unit dynamic characteristic constraint reflects the coupling relationship between head, power generation flow, and unit output. Since the above relationships are difficult to directly incorporate into a mixed integer linear programming model for stable solution, in this preferred embodiment, they are first clearly classified as nonlinear constraints. Then, interfaces are reserved for subsequent linearization processing using trigonometric interpolation and linear interpolation methods. This avoids the introduction of difficult-to-handle nonlinear components into the linear constraint system, thereby improving the solution stability and engineering applicability of the overall model.

[0029] Furthermore, linearization includes: Linearize the reservoir capacity constraint at the front of the dam; Linearize the tailrace level-discharge constraint; Linearize the power output relationship of the hydropower unit corresponding to the power characteristic constraints of the unit; The linearization process employs both triangular interpolation and linear interpolation.

[0030] As a preferred embodiment of the above, the process is carried out after classifying the linear and nonlinear constraints in the mixed-integer linear programming model. The focus is on addressing the nonlinear relationships in the constraints of upstream water level and reservoir capacity, tailrace water level and discharge rate, and unit dynamic characteristics that are difficult to directly incorporate into the mixed-integer linear programming model. Specifically, considering the nonlinear relationships between upstream water level and reservoir capacity, tailrace water level and discharge rate, and hydropower unit output and head / discharge rate, directly incorporating these nonlinear constraints into the mixed-integer linear programming model would easily lead to optimization difficulties. Therefore, a preferred approach is to use... Trigonometric interpolation and linear interpolation are used to linearize nonlinear constraints, reducing solution complexity and improving model solvability while maintaining the basic original operating rules. Furthermore, as a preferred approach, for the linearization of the reservoir capacity and water level constraints in front of the dam, multiple segmented points can be selected based on historical operating data or design characteristic curves of the power station, so that different reservoir capacity states correspond to corresponding reservoir capacities in front of the dam. Then, linear interpolation is used to describe the changing relationship between adjacent segmented points, thereby transforming the originally continuously changing reservoir capacity and water level relationship in front of the dam into a piecewise linear relationship that can be used by a mixed-integer linear programming model. For the linearization of tailrace level-discharge constraints, the same approach can be adopted. First, select multiple segmented points along the tailrace level-discharge relationship curve, and then characterize the transition relationship between adjacent segmented points using linear interpolation, so that the tailrace level-discharge relationship can participate in subsequent optimization solutions in a piecewise linear form. However, for the hydropower unit output relationship corresponding to the unit dynamic characteristic constraints, since this relationship involves the coupled changes between head, power generation flow, and unit output, it has stronger two-dimensional or even multi-dimensional nonlinearity than the previous two types of constraints. Therefore, triangular interpolation is preferred for processing. Specifically, it can be performed on the relationship between head and power generation flow. The operating space with a common flow rate is divided into several triangular regions. The operating conditions at the vertices of the triangular regions represent the power output variation of the units within those regions. By weighting the vertices of the selected triangular regions, a smooth transition between operating points is achieved. This transforms the power output relationship of the hydropower units corresponding to the power characteristic constraints into a linear expression suitable for solving a mixed-integer linear programming model. It can be seen that the key is not simply to discretize the curves, but to use linear interpolation and triangular interpolation to specifically process different types of nonlinear constraints according to their variable coupling characteristics, so as to balance model accuracy and solution efficiency.As an example, in a preferred application scenario, the upstream water level-reservoir capacity relationship curve and the tailrace water level-discharge relationship curve of a cascade hydropower station during the scheduling cycle can be discretized into multiple adjacent segments. The unit output conditions under different heads and power generation flows can be discretized into multiple triangular regions. In subsequent solutions, linear interpolation is used to express the upstream water level changes caused by reservoir capacity changes and the tailrace water level changes caused by downstream flow changes. Triangular interpolation is used to express the unit output changes caused by changes in both head and power generation flow. This unifies the upstream water level-reservoir capacity constraints, tailrace water level-discharge constraints, and unit dynamic characteristic constraints into a linear form that is easy to solve, and provides a stable model foundation for obtaining the Pareto solution set using the EPO-AL algorithm.

[0031] Furthermore, such as Figure 2 As shown, the EPO-AL algorithm is used to transform it into a single-objective model, including: Construct an augmented Lagrangian function to update the main variables in a mixed-integer linear programming model; Based on the updated master variables, update the Lagrange multipliers and penalty parameters; An iterative solution process based on the augmented Lagrange function is performed, which adaptively updates the adjoint penalty parameter. After completing the iterative solution, the Pareto solution set is obtained by changing the initial values ​​of the Lagrange multipliers.

[0032] As a preferred embodiment of the above, this is performed after the construction of the mixed-integer linear programming model and the linearization of nonlinear constraints. It is particularly useful for addressing the conflict between maximizing the total power generation of cascade hydropower stations and minimizing the operating cost of the receiving-end power grid. Traditional single-weighted processing can easily lead to an undesirable solution set distribution and the substitution of local optima for global optima. Therefore, in this embodiment, the algorithm is first initialized for the established multi-objective optimization problem. Preferably, initial values ​​are selected for the initial decision variables, the initial values ​​of the Lagrange multipliers, the initial values ​​of the penalty parameters, the growth coefficient of the penalty parameters, and the upper limit of the penalty parameters to ensure the success of subsequent iterative solutions. The stability and convergence efficiency are assessed. After initialization, an augmented Lagrangian function is constructed to update the main variables in the mixed-integer linear programming model. The augmented Lagrangian function integrates the objective and constraint information from the original bi-objective optimization problem into the same solution framework, ensuring that the update process of the main variables reflects not only the power generation demand of the cascade hydropower stations but also the operational economic requirements of the receiving-end power grid. This allows the single-objective model to retain the trade-offs in the original bi-objective problem. After obtaining the updated main variables, the Lagrange multipliers and penalty parameters are updated based on the main variables. The Lagrange multipliers are used to... To reflect the degree of constraint satisfaction, the penalty parameter is used to adjust the impact of constraint violation on the objective function. Through the coordinated update of both, the solution process can gradually approach a feasible solution that simultaneously satisfies the objective and constraint requirements. Furthermore, based on the augmented Lagrangian function, an iterative solution process with adaptive updates of the penalty parameter is performed. Preferably, in each iteration, the main variable update is completed first, followed by the Lagrange multiplier and penalty parameter update. The decision to continue iteration is based on the changes in the results of two adjacent iterations. When the change of the augmented Lagrangian function in two adjacent iterations tends to stabilize, the current solution result can be considered as a stable solution. If a Pareto optimal solution is found corresponding to the current parameter settings, the next iteration continues. After completing the above iterative solution, the initial values ​​of the Lagrange multipliers are changed, and the solution process of the single-objective model is repeated to obtain multiple solution results that reflect the balance of interests between different power plants and the grid, thus forming a Pareto solution set. The advantage of the above processing method is that it does not only output a single optimal point, but outputs a set of candidate solutions that can be screened and compromised for subsequent processing. This provides a basis for using the Pareto filtering algorithm to screen global Pareto solutions and using the TOPSIS-based compromise solution selection method to determine the optimal power generation plan.As an example, in a preferred application scenario, a mixed-integer linear programming model can be established for multiple cascade hydropower stations with upstream and downstream hydraulic connections and connected receiving-end power grids. After handling linear and nonlinear constraints, the EPO-AL algorithm is initiated by setting a set of initial Lagrange multipliers and penalty parameters. First, a candidate solution that balances the power generation benefits of the cascade hydropower stations and the operational economy of the receiving-end power grid is obtained. Then, by adjusting the initial values ​​of the Lagrange multipliers, the solution is repeated to obtain multiple candidate solutions under different trade-offs, ultimately forming a Pareto solution set.

[0033] Furthermore, such as Figure 3 As shown, filtering the global Pareto solution set includes: Each solution in the Pareto solution set is compared with the other solutions, and solutions in the Pareto solution set that are dominated by the other solutions are removed. The undominated solutions in the cleared Pareto solution set are retained to obtain the global Pareto solution.

[0034] As a preferred embodiment, this step is performed after solving the mixed-integer linear programming model using the EPO-AL algorithm and obtaining the Pareto solution set. The purpose of this step is to further distinguish between local Pareto optimal solutions and global Pareto optimal solutions. The solutions generated by the EPO-AL algorithm are usually Pareto solutions, but non-Pareto solutions may occur in some cases. Furthermore, a global Pareto solution is always a local Pareto solution, but a local Pareto solution is not necessarily a global Pareto solution. Therefore, it is necessary to further filter the Pareto solution set using the Pareto filtering algorithm and use the filtered global solutions as candidate solutions for the final output of the scheduling model to improve the reliability and engineering usability of subsequent compromise solution selection. Preferably, the filtering process is performed point-by-point. The method involves comparison and point-by-point elimination. Specifically, each solution in the Pareto set is sequentially taken as the current solution to be judged. Then, the current solution to be judged is compared one by one with the remaining solutions in the Pareto set. If the comparison results show that the current solution to be judged is not better than another solution in all optimization objectives, and is worse than another solution in at least one optimization objective, then the current solution to be judged is considered to be dominated by another solution, and is removed from the Pareto set. If the current solution to be judged is not dominated by any solution after comparison with the remaining solutions, then the current solution to be judged is retained, and the same process is continued for the next solution until the comparison and selection of all solutions in the Pareto set is completed. Finally, the undominated solutions in the cleared Pareto set are retained to obtain the global Pareto solution. Further... Preferably, and for ease of implementation by those skilled in the art, the Pareto filtering algorithm can first use all solutions in the Pareto solution set as the input set, and then complete the filtering by sequentially selecting the solution to be judged and the comparison solution. After each comparison between the solution to be judged and the other solutions, if it is determined that the solution to be judged is dominated, then the solution to be judged is no longer retained as a candidate optimal solution; if it is determined that the solution to be judged is not dominated, then the solution to be judged is retained and the next solution to be judged is examined. This avoids bringing locally optimal but not globally optimal solutions into the subsequent decision-making process. This preferred method does not lie in simply performing comparison operations, but in adding a global filtering process after the Pareto solution set output by the EPO-AL algorithm, thereby filtering out solutions that may exist in the original candidate solution set. Non-global Pareto solutions are further eliminated, allowing subsequent TOPSIS-based compromise solution selection to be based on higher-quality candidate solutions. For example, in a preferred application scenario, multiple candidate power generation plans obtained through the EPO-AL algorithm can be used as input to the Pareto solution set. For any one of these power generation plans, it is compared with the other power generation plans in turn on the two optimization objectives of total power generation of cascade hydropower stations and operating cost of the receiving-end power grid. If there is another power generation plan that can reduce the operating cost of the receiving-end power grid without reducing the total power generation of cascade hydropower stations, or increase the total power generation of cascade hydropower stations without increasing the operating cost of the receiving-end power grid, then the current power generation plan can be considered dominant and eliminated.After all power generation plans have undergone the above comparison, the remaining unused power generation plans constitute the global Pareto solution, thus providing a more reliable candidate basis for subsequently selecting the optimal compromise power generation plan suitable for a specific environment.

[0035] Furthermore, a compromise solution selection method based on TOPSIS is adopted, including: The optimization objective corresponding to the global Pareto solution set is normalized, and the positive ideal solution and negative ideal solution are determined based on the normalization result. The proximity index is calculated based on the Euclidean distance between each power generation plan and the positive and negative ideal solutions; The power generation plan with the highest proximity index is selected as the optimal power generation plan.

[0036] As a preferred embodiment of the above, the global Pareto solution obtained by the Pareto filtering algorithm is usually not a single solution, but a series of optimal candidate solutions representing different power plant-grid balance relationships. Therefore, it is necessary to further select a power generation plan scheme more suitable for a specific scheduling environment as the final result within the global Pareto solution set. Preferably, the optimization objectives corresponding to the global Pareto solution set are first normalized. The role of normalization is to eliminate the impact of differences in dimensions, orders of magnitude, and value ranges between different optimization objectives on the evaluation results, so that the maximum total power generation of the cascade hydropower stations and the minimum operating cost of the receiving-end grid can be compared on the same evaluation basis. After the normalization is completed, the positive ideal solution and the negative ideal solution are determined according to the normalization result. The positive ideal solution is used to characterize the reference direction when all optimization objectives tend to a better state, and the negative ideal solution is used to characterize the reference direction when all optimization objectives tend to a worse state. Thus, a unified evaluation benchmark is established between each power generation plan scheme and the ideal reference. Further, as a preferred embodiment, after determining the positive ideal solution and the negative ideal solution, the following steps are taken: After solving the problem, the proximity index is calculated based on the Euclidean distance between each power generation plan and the positive and negative ideal solutions. The smaller the distance to the positive ideal solution, the closer the corresponding power generation plan is to the optimal direction in a comprehensive sense; the larger the distance to the negative ideal solution, the further the corresponding power generation plan is from the poor direction in a comprehensive sense. Based on this, a unified proximity evaluation result can be formed for each power generation plan, and the power generation plan with the largest proximity index is finally selected as the optimal power generation plan. As an example, in an optimal application scenario, multiple power generation plans retained after Pareto filtering can be used as a set of candidate plans. The performance of each candidate plan on the two optimization objectives of total power generation of cascade hydropower stations and operating cost of the receiving-end power grid is used as the evaluation basis. First, the two optimization objectives are normalized, and then the positive and negative ideal solutions are determined separately. Then, the Euclidean distance of each candidate plan relative to the positive and negative ideal solutions is calculated, and the proximity index of each candidate plan is obtained accordingly. Finally, the candidate plan with the largest proximity index is determined as the optimal power generation plan.

[0037] Furthermore, linear constraints include: Based on water balance constraints, the correspondence between reservoir capacity, interval flow, outflow, power generation flow and water abandonment flow in different time periods is constrained; Based on the initial and final storage capacity constraints, constraints are imposed on the initial and final storage capacity. Based on reservoir operation constraints, the upper and lower limits of reservoir capacity, the upper and lower limits of outflow, and the discharge flow are constrained; Based on unit operation constraints and unit start-up and shutdown state constraints, constraints are imposed on unit output, unit power generation flow and unit operating status; Constraints are imposed on unit start-up and shutdown operations based on constraints on unit start-up and shutdown duration and maximum number of start-up and shutdown operations. Based on the head constraint of the generating unit, the correspondence between the net head of power generation, the water level above the dam, the tailrace water level, and the head loss value is constrained; Based on DC channel constraints, the power allowed to pass through the DC transmission channel within a time period is constrained.

[0038] As a preferred embodiment of the above, after the mixed-integer linear programming model has completed the objective construction and the classification of linear and nonlinear constraints, it is further refined. This set of linear constraints is not a simple list of several independent conditions, but rather a constraint system collaboratively established around four levels during the short-term scheduling of cascade hydropower stations: water conservation, reservoir capacity controllability, unit operability, and grid acceptance. Specifically, it is preferable to first constrain the correspondence between reservoir capacity, inter-regional flow, outflow, power generation flow, and water abandonment flow at each time period based on water balance constraints, so as to ensure that the water entering each time period... The water volume changes in the reservoir, the storage reservoir, and the outflow reservoir satisfy a conservation relationship. The reservoir discharge consists of both power generation discharge and water discharge discharge. Furthermore, the linear constraint model simultaneously considers the impact of the water flow time lag between cascade hydropower stations on the downstream transmission of upstream water. Therefore, this constraint is preferred as the fundamental constraint of the entire linear constraint system to ensure that subsequent reservoir capacity and output arrangements are based on the actual water transmission relationship. On this basis, further constraints are imposed on the initial and final reservoir capacity to ensure that the reservoir capacity states at the start and end points of short-term scheduling meet predetermined boundaries. To avoid compromising the operating conditions of subsequent cycles by pursuing only the optimization results of the current cycle, further constraints are imposed on the upper and lower limits of reservoir capacity, outflow, and water discharge based on reservoir operation constraints. This ensures that the reservoir remains within the allowable operating range throughout the entire scheduling cycle, preventing both capacity overruns and unreasonable discharge and water discharge arrangements. Simultaneously, constraints are imposed on unit output, power generation flow, and unit operating status based on unit operation constraints and unit start-up and shutdown status constraints. This ensures that the unit output level is consistent with the corresponding power generation flow, and that the unit's operating status is correlated with its corresponding output. To further improve the executability of the scheduling results, constraints are also imposed on the unit start-up and shutdown operations based on the duration of unit start-up and shutdown and the maximum number of start-up and shutdown operations. This is to avoid unit wear and operational instability caused by frequent start-ups and shutdowns in a short period of time. In addition, based on the unit's power generation head constraint, the correspondence between the net power generation head, the dam water level, the tailrace water level, and the head loss value is constrained to ensure that the unit's power generation capacity is consistent with the actual hydraulic conditions. Among these, the net power generation head, the dam water level, the tailrace water level, and the head loss value together determine the effective power generation conditions of the unit in each time period.Finally, based on DC channel constraints, the allowable power transmission through the DC transmission channel within a given time period is constrained to ensure that the power output of the cascade hydropower stations matches the transmission capacity of the receiving-end power grid. This avoids a scheduling outcome where power generation is possible but transmission is not. These constraints collectively constitute the linear constraint model within the mixed-integer linear programming model. By coordinating these linear constraints according to scheduling logic, the model not only satisfies the water volume and unit operation requirements within a single power station but also considers the hydraulic connections between cascades and the channel acceptance conditions of the receiving-end power grid. This provides a stable and reliable constraint foundation for subsequent linearization of nonlinear constraints, multi-objective solutions, and selection of the optimal power generation plan. As a result, For example, in a preferred application scenario, a short-term scheduling model can be established for multiple cascade hydropower stations with hydraulic connections between upstream and downstream areas. First, water balance constraints and initial and final reservoir capacity constraints are used to determine the range of reservoir capacity evolution for each time period. Then, combined with reservoir operation constraints, unit operation constraints, unit start-up and shutdown status constraints, and constraints on unit start-up and shutdown duration and maximum number of start-ups and shutdowns, the operable status and output range of each unit in each time period are determined. Simultaneously, unit head constraints ensure that power generation conditions are consistent with hydraulic conditions, and DC channel constraints ensure that the transmitted power does not exceed the transmission channel capacity. This forms a complete linear constraint system supporting the solution of the multi-objective optimization method for cascade hydropower with plant-grid coordination.

[0039] Example 2; Based on the same inventive concept as the multi-objective optimization method for plant-grid coordinated cascade hydropower in the foregoing embodiments, the present invention also provides a multi-objective optimization system for plant-grid coordinated cascade hydropower, the system comprising: The mathematical model building module establishes mathematical models based on the operational characteristics of cascade hydropower stations and the receiving-end power grid. The objective linear programming module, based on a mathematical model, constructs a mixed-integer linear programming model with the optimization objectives of maximizing the total power generation of the cascade hydropower stations and minimizing the operating cost of the receiving-end power grid. The constraint linear processing module determines the constraint system based on the linear and nonlinear constraints in the mixed-integer linear programming model, and performs linearization processing on the nonlinear constraints; The Pareto solution module uses the EPO-AL algorithm to transform the mixed-integer linear programming model into a single-objective model and solves it to obtain the Pareto solution set. The Pareto filtering module uses the Pareto filtering algorithm to filter the global Pareto solution set from the Pareto solution set. The compromise optimal selection module uses a TOPSIS-based compromise solution selection method to determine the optimal power generation plan from the global Pareto solution set.

[0040] The adjustment system described above in this invention can effectively realize a multi-objective optimization method for cascade hydropower with plant-grid coordination, and the technical effects it can achieve are as described in the above embodiments, and will not be repeated here.

[0041] Furthermore, the Pareto solver module includes: The main variable update unit constructs an augmented Lagrangian function to update the main variables in the mixed-integer linear programming model; The multiplier term setting unit updates the Lagrange multipliers and penalty parameters based on the updated master variables; The iterative solution unit performs an iterative solution process based on the augmented Lagrangian function, which adaptively updates the accompanying penalty parameter. The Pareto solution unit obtains the Pareto solution set by changing the initial values ​​of the Lagrange multipliers after completing the iterative solution.

[0042] Similarly, the above-mentioned optimization schemes for the system can also achieve the optimization effects corresponding to the methods in Embodiment 1, which will not be repeated here.

[0043] Example 3; Hydropower stations in the Yalong River basin were selected as application examples, with the Jinxi, Jindong, and Guandi cascade hydropower stations as the research subjects. The Jinxi Hydropower Station, with its 305-meter-high concrete double-curvature arch dam, is the highest dam of its type in the world. The station primarily generates electricity, but also serves as a reservoir for energy storage, flood control, and sediment retention. The Jindong Hydropower Station is the second cascade hydropower station in the five-stage development project from Kala to Jiangkou on the Yalong River, and is China's largest and most technologically complex diversion-type hydropower station. The downstream Guandi Hydropower Station is one of the main power sources for the Yalong River hydropower base. Specific parameters for each power station are shown in Table 1. Due to the large inflow of water in the basin during the flood season, cascade hydropower stations usually operate at full capacity to bear the basic load of the power grid in order to ensure the flood control safety of the power stations during the flood season. It is difficult to respond to the peak-shaving demand of the power grid. Therefore, this paper only conducts relevant research on hydropower participation in power grid peak-shaving under the condition of no water abandonment during the non-flood season.

[0044] like Figure 4 As shown, the receiving-end power grid is a 3-node system, with the DC transmission channel from the new energy base connected to node 1, and a scheduling cycle of 24 hours. A representative scenario was selected in March 2021 to validate the proposed model, and historical actual load data was used for the power grid load.

[0045] First, a short-term multi-objective function for plant-grid coordination of cascade hydropower stations under complex constraints is established, including: The optimization objective is to maximize the total power generation of the cascade hydropower stations and minimize the operating cost of the receiving-end power grid.

[0046] The goal of the power plant is to maximize the cascade power generation, that is: ; Where: E is the total power generation of the cascade hydropower stations during the scheduling period; T is the total number of scheduling periods, which is taken as 1 hour in this embodiment; I is the total number of cascade hydropower stations participating in the scheduling. Let i be the number of generating units in power station i. Let n be the output of unit n in power plant i during time period t.

[0047] The goal on the grid side is to minimize operating costs. ; In the formula: F represents the operating cost of thermal power plants; The output of the i-th thermal power unit in time period t; , , is the corresponding thermal power operating cost coefficient; N is the total number of thermal power units on the grid side.

[0048] When addressing conflicting multi-objective optimization functions, the EPO-AL algorithm is employed to transform the multi-objective problem into a single-objective problem, simplifying model complexity, including: For the established multi-objective optimization problem: ; ; In the formula, This is the opposite of the total power generation of the cascade hydropower stations. It is the cost of thermal power in the receiving-end power grid; It is by and A matrix constructed by combination.

[0049] Perform algorithm initialization and select initial decision variables. Initial values ​​of Lagrange multipliers Initial value of penalty parameter Penalty parameter growth coefficient Penalty parameter upper limit This ensures the stability and convergence efficiency of the algorithm iteration.

[0050] After determining the initial parameters, the solution is iteratively performed. First, an augmented Lagrangian function is constructed to update the main variables. : ; ; In the formula, The Lagrange multipliers from the previous iteration; This is the penalty parameter from the previous iteration.

[0051] Then, based on the update results of the main variables, the priorities of the bi-objective optimization are balanced, and the Lagrange multipliers and penalty parameters are updated: ; ; Calculate the difference of the augmented Lagrangian function between two consecutive iterations. ,like Then the iteration stops, current If a Pareto optimal solution is found, the iteration continues; otherwise, iteration continues.

[0052] Therefore, the original multi-objective optimization problem is transformed into solving a single-objective optimization problem: ; Change the initial values ​​of the Lagrange multipliers Solving the single-objective optimization problem yields a Pareto curve, i.e., the Pareto front.

[0053] Since the solutions generated by the EPO-AL algorithm are usually Pareto solutions, but some non-Pareto solutions may also appear in certain situations, and a global Pareto solution is always a local Pareto solution, but a local Pareto solution may not always be a global Pareto solution, it is necessary to use a Pareto filtering algorithm to distinguish between local and global Pareto optimal solutions and output the global solution as the final optimal solution of the scheduling model.

[0054] The principle of the Pareto filtering algorithm is as follows: A point on the Pareto front is compared with other points; if the point is dominated by other points, it is eliminated. Domination is defined as: for different points within a given feasible region... and if If the condition is met (for any s-th objective), then point is considered to be true. Selected The specific steps for control are as follows: Step 1: Initialization, setting: i←0, j←0, k←1; Input all points: k=1,2,......,K Step 2: Set: i←i+1, j←0; remove non-global Pareto points, let j←j+1, if Then skip to the beginning of step two. If and Then point Not a global Pareto point. Skip to step three. If Then point It is a global Pareto point. k←k+1. Jump to step 3, otherwise jump to the beginning of step 2.

[0055] Step 3: If If the result is positive, proceed to step 1; otherwise, the algorithm terminates.

[0056] The global Pareto solution obtained by the Pareto filtering algorithm is a series of different optimal solutions. Therefore, a compromise solution selection method based on TOPSIS is needed to select the optimal solution suitable for the specific environment, including: ; ; ; ; ; ; ; In the formula: and These are the k-th optimal solutions for the first objective and the second objective, respectively. and The target after normalization; and These are the i-th optimal ideal solution and the worst ideal solution, respectively; and These are the positive and negative combined distances for the k-th solution, respectively. Let be the overall score of the k-th solution. Therefore, the solution with the highest overall score can be chosen as a compromise solution.

[0057] Although this application has been described in conjunction with specific features and embodiments, it is obvious that various modifications and combinations can be made thereto without departing from the spirit and scope of this application. Accordingly, this specification and drawings are merely exemplary illustrations of the application as defined herein, and are to be considered as covering any and all modifications, variations, combinations, or equivalents within the scope of this application. Clearly, those skilled in the art can make various alterations and modifications to this application without departing from its scope. Thus, if such modifications and modifications fall within the scope of this application and its equivalents, this application intends to include such modifications and modifications.

Claims

1. A multi-objective optimization method for coordinated power plant and grid-based cascade hydropower projects, characterized in that, The method includes: A mathematical model is established based on the operating characteristics of cascade hydropower stations and the receiving-end power grid; Based on the mathematical model, a mixed-integer linear programming model is constructed with the optimization objectives of maximizing the total power generation of the cascade hydropower stations and minimizing the operating cost of the receiving-end power grid. The constraint system is determined based on the linear and nonlinear constraints in the mixed integer linear programming model, and the nonlinear constraints are linearized. The EPO-AL algorithm is used to transform the mixed-integer linear programming model into a single-objective model, and the Pareto solution set is obtained by solving the problem. The global Pareto solution set is filtered from the Pareto solution set using the Pareto filtering algorithm; The optimal power generation plan is determined from the global Pareto solution set using a TOPSIS-based compromise solution selection method.

2. The multi-objective optimization method for cascade hydropower with plant-grid coordination as described in claim 1, characterized in that, The optimization objectives include: The goal of maximizing the total power generation of the cascade hydropower stations is to optimize the power station side. Minimizing the operating cost of the receiving-end power grid is taken as the optimization objective on the power grid side; The optimization objectives on the power plant side and the optimization objectives on the power grid side are jointly incorporated into the mixed-integer linear programming model.

3. The multi-objective optimization method for cascade hydropower with plant-grid coordination according to claim 1, characterized in that, The nonlinear and linear constraints in the mixed-integer linear programming model include: The following constraints are defined as linear constraints: water balance constraint, initial and final reservoir capacity constraint, reservoir operation constraint, unit operation constraint, unit start-up and shutdown status constraint, unit start-up and shutdown duration and maximum number of start-up and shutdown constraints, unit power generation head constraint, and DC channel constraint. The upstream water level and reservoir capacity constraints, the tailrace water level and flow constraints, and the unit dynamic characteristic constraints are defined as the nonlinear constraints.

4. The multi-objective optimization method for cascade hydropower with plant-grid coordination according to claim 3, characterized in that, Linearization processing includes: The reservoir capacity constraint at the upstream water level is linearized. The tailwater level-discharge constraint is linearized. The power output relationship of the hydropower unit corresponding to the power characteristic constraints of the unit is linearized. The linearization process employs triangular interpolation and linear interpolation.

5. The multi-objective optimization method for cascade hydropower with plant-grid coordination according to claim 1, characterized in that, The EPO-AL algorithm is used to transform the model into a single-objective model, including: Construct an augmented Lagrangian function to update the main variables in the mixed-integer linear programming model; Based on the updated master variables, update the Lagrange multipliers and penalty parameters; An iterative solution process is performed based on the augmented Lagrange function, accompanied by adaptive updates of the penalty parameter; After completing the iterative solution, the Pareto solution set is obtained by changing the initial values ​​of the Lagrange multipliers.

6. The multi-objective optimization method for plant-grid coordinated cascade hydropower as described in claim 5, characterized in that, Filter the global Pareto solution set, including: Each solution in the Pareto solution set is compared with the remaining solutions, and solutions in the Pareto solution set that are dominated by the remaining solutions are removed. The undominated solutions in the Pareto solution set after the cleanup are retained to obtain the global Pareto solution.

7. The multi-objective optimization method for plant-grid coordinated cascade hydropower as described in claim 1, characterized in that, A compromise solution selection method based on TOPSIS is adopted, including: The optimization objective corresponding to the global Pareto solution set is normalized, and the positive ideal solution and negative ideal solution are determined based on the normalization result. The proximity index is calculated based on the Euclidean distance between each of the power generation plans and the positive and negative ideal solutions. The power generation plan scheme with the highest proximity index is selected as the optimal power generation plan.

8. The multi-objective optimization method for cascade hydropower with plant-grid coordination according to claim 3, characterized in that, The linear constraints include: Based on the water balance constraints, the correspondence between the reservoir capacity, interval flow, outflow, power generation flow and water abandonment flow in each time period is constrained; Based on the initial and final time period storage capacity constraints, constraints are imposed on the initial time period storage capacity and the final time period storage capacity. Based on the reservoir operation constraints, the upper and lower limits of the reservoir capacity, the upper and lower limits of the outflow, and the discharge flow are constrained; Based on the unit operation constraints and the unit start-up and shutdown state constraints, constraints are imposed on the unit output, unit power generation flow, and unit operation state; Based on the constraints of the unit start-up and shutdown duration and the maximum number of start-ups and shutdowns, constraints are imposed on the unit start-up operation and the unit shutdown operation. Based on the generator head constraint, the correspondence between the net head of power generation, the water level above the dam, the tailrace water level, and the head loss value is constrained. Based on the aforementioned DC channel constraints, the power allowed to pass through the DC transmission channel within a time period is constrained.

9. A multi-objective optimization system for cascade hydropower projects with coordinated power plant and grid operation, characterized in that, The system includes: The mathematical model building module establishes mathematical models based on the operational characteristics of cascade hydropower stations and the receiving-end power grid. The objective linear programming module, based on a mathematical model, constructs a mixed-integer linear programming model with the optimization objectives of maximizing the total power generation of the cascade hydropower stations and minimizing the operating cost of the receiving-end power grid. The constraint linear processing module determines the constraint system based on the linear and nonlinear constraints in the mixed-integer linear programming model, and performs linearization processing on the nonlinear constraints; The Pareto solution module uses the EPO-AL algorithm to transform the mixed-integer linear programming model into a single-objective model and solves it to obtain the Pareto solution set. The Pareto filtering module uses the Pareto filtering algorithm to filter the global Pareto solution set from the Pareto solution set. The compromise optimal selection module uses a TOPSIS-based compromise solution selection method to determine the optimal power generation plan from the global Pareto solution set.

10. The multi-objective optimization system for plant-grid coordinated cascade hydropower as described in claim 9, characterized in that, The Pareto solver module includes: The main variable update unit constructs an augmented Lagrangian function to update the main variables in the mixed-integer linear programming model; The multiplier term setting unit updates the Lagrange multipliers and penalty parameters based on the updated master variables; The iterative solution unit performs an iterative solution process based on the augmented Lagrangian function, which adaptively updates the accompanying penalty parameter. The Pareto solution unit obtains the Pareto solution set by changing the initial values ​​of the Lagrange multipliers after completing the iterative solution.

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