Short-term optimal scheduling method for cascade hydropower based on multi-stage adaptive evolution mechanism

Abstract

The application discloses a cascade hydropower short-term optimization scheduling method based on a multi-stage adaptive evolution mechanism, aiming at solving the problems of insufficient adaptation of existing scheduling methods to new energy scenarios, poor optimization balance effect, and large time sequence fluctuation. The method first constructs a cascade hydropower short-term scheduling model with the minimum residual load fluctuation as the target and the uncertainty of wind and light output, then designs a target evaluation function with dynamic weights, and adaptively adjusts the evaluation focus according to the iteration progress. Then, the optimization search is completed in three stages, the candidate solution is obtained through initial global exploration, adaptive fine mining is adaptively carried out through deep optimization, and a multi-dimensional disturbance mechanism with a fixed cycle is used to jump out of the local optimum. In addition, strategies such as time period coordinated adjustment and historical information guided disturbance are also designed. Through the instance verification of the cascade system in the southwest basin, the method can balance the solution accuracy and efficiency in the wet, normal and dry seasons, adapt to the high penetration scenario of new energy, effectively reduce the scheduling time sequence fluctuation, and significantly improve the engineering implementability and robustness.

Description

Technical Field

[0001] This invention relates to the field of hydropower dispatching, specifically to a short-term optimal dispatching method for cascade hydropower based on a multi-stage adaptive evolution mechanism. Background Technology

[0002] With the increasing complexity of power system operation, cascade hydropower plays an increasingly prominent role in tasks such as grid peak shaving and load balancing. The short-term optimal scheduling problem of cascade hydropower typically requires rationally arranging the operating status of each power station at different times within a given scheduling period, taking into account water balance, reservoir capacity constraints, output boundaries, and upstream-downstream coupling relationships, in order to achieve system operation objectives. However, due to the generally strong nonlinearity and nonconvexity of cascade hydropower scheduling models, solving such problems in practice presents significant computational challenges.

[0003] In the prior art, patent CN109636043B proposes an adaptive optimization method and system for power generation scheduling in a cascade hydropower system. The core of this patent is to generate an initial population by serially encoding the water levels of each power station at different times as state variables; to update the individual positions using a sine and cosine algorithm evolution strategy; and to innovatively introduce three strategies: population position center mutation, neighborhood search, and simplex dynamic search, which respectively improve population diversity, global optimization ability, and algorithm convergence speed. The triggering of the simplex search is controlled by the dynamic search probability, and the optimal scheduling process is output after multiple iterations.

[0004] The patent with publication number CN111915163A proposes a high-efficiency and high-precision optimization scheduling method and system for the entire life cycle of a hydropower system. The core of this patent is to encode the reservoir capacity value of each power station at different times as a decision variable and randomly generate an initial population; to use a penalty function to calculate the fitness of individuals and update the historical best position of individuals and the global best position of the population; to select high-quality individuals to establish an external archive set, improve the traditional teaching and learning algorithm, and integrate the three steps of improved teaching strategy, improved learning strategy, and neighborhood exploration strategy to update the position of individuals in the population, and output the global optimal scheduling scheme through multiple rounds of iteration.

[0005] Both patents represent local improvements to a single intelligent optimization algorithm, focusing on "enhancing the algorithm's global optimization capability and avoiding local optima." While they have achieved good results in power generation dispatch scenarios, they exhibit significant common shortcomings in the practical engineering needs of short-term optimized dispatch of cascade hydropower, as detailed below:

[0006] All of these schemes take maximizing the total power generation of the cascade hydropower system as the sole optimization objective, focusing only on the power generation benefits of hydropower resources without considering core needs such as grid peak shaving and load balancing. At the same time, they do not take into account the uncertainty of the output of new energy sources such as wind power and photovoltaics, and are out of touch with the actual power system dispatch under the current "high penetration of new energy". The dispatch schemes cannot be directly adapted to the grid operation requirements.

[0007] Both are based on a single-stage search framework using a single improved algorithm. CN111915163A is a linear iteration of "teaching strategy - learning strategy - neighborhood exploration," while CN109636043B is a combined iteration of "sine and cosine evolution - mutation - neighborhood search - simplex search." Neither of them dynamically adjusts the search strategy and scale according to the evolutionary progress of the search process. In the early stages of the search, it is impossible to explore a large feasible region, and in the later stages, it is difficult to carry out fine-grained mining of high-quality solution regions. The balance between global optimization and local fine-grained optimization is not well achieved.

[0008] The core challenge of short-term scheduling of cascade hydropower is the strong coupling between output changes and water transfer in adjacent time periods. However, neither of the two patents mentioned above has designed a specific time-series coordination mechanism. They only use reservoir capacity / water level as a single decision / state variable and do not consider the correlation between hydraulic and electrical parameters in adjacent time periods. The fitness evaluation uses fixed rules and does not include the "stability of scheduling parameters in adjacent time periods" in the evaluation system, which can easily lead to large fluctuations in the scheduling results in time series and low feasibility in actual engineering.

[0009] The perturbation / search strategies of the two patents are based on preset fixed rules and lack intelligent adaptive adjustment mechanisms. The neighborhood exploration strategy of CN111915163A only performs fixed-form perturbations based on the middle position of the search space, and the mutation and simplex search strategies of CN109636043B are triggered by fixed probabilities. Neither of them dynamically adjusts the intensity and method of perturbation by combining the algorithm's search history information. Furthermore, there is no collaborative perturbation design for adjacent time periods, and single-dimensional perturbations are difficult to effectively escape local optima in complex non-convex solution spaces.

[0010] Both patents use a fixed-weight fitness evaluation function, evaluating solely based on the objective function value and constraint violation penalties, without adjusting the evaluation focus according to the algorithm's iteration progress. In the early stages of the search, the emphasis should be on "the feasibility and global optimality of the solution," while in the later stages, the emphasis should be on "the refinement and temporal consistency of the solution." Fixed evaluation rules cannot adapt to this search pattern, resulting in insufficient guidance for the algorithm's evolutionary direction.

[0011] Therefore, developing a short-term optimal scheduling method for cascade hydropower with high solution speed, strong real-time performance, fast grid response capability, and better engineering adaptability has become an urgent technical problem to be solved in this field. Summary of the Invention

[0012] To address the above problems, this invention provides a short-term optimal scheduling method for cascade hydropower based on a multi-stage adaptive evolution mechanism, comprising the following steps: Construction of the short-term dispatch model for S1 cascade hydropower: The construction of a short-term optimal scheduling model for cascade hydropower is a complex optimization problem that requires the coordination of multiple factors, including renewable energy output scenarios and the hydropower connections between upstream and downstream cascades, aiming to achieve efficient utilization of hydropower resources in the short term. Its construction typically requires integrating data such as load curves, reservoir characteristics, and scheduling demands to maximize the system's peak-shaving capacity while ensuring the safety of both hydropower and power grid operations. Therefore, this invention aims to minimize the fluctuation of the remaining load of cascade hydropower, considering the impact of wind and solar uncertainties, and constructs the following objective function using a scenario-based approach: (1) (2) (3) In the formula: Indicates the system in the scenario Time period The remaining load; Representing a scene The probability of; Indicates the number of scenes; Indicates the number of time periods in the scheduling period; Indicates time period The system load; , They represent the scenes respectively. Time period Average output of wind and solar power; Indicates hydroelectric power station Time period The average output.

[0013] The short-term operational constraints of cascade hydropower are as follows: S1.1 Water Balance Constraint (4) (5) In the formula: Indicates hydroelectric power station During the period The final storage capacity; , , , They represent hydroelectric power stations During the period The interval flow, outflow, power generation flow, and wastewater discharge flow.

[0014] S1.2 Clean water head constraint (6) (7) (8) (9) In the formula: Indicates hydroelectric power station During the period The final water level; Indicates hydroelectric power station During the period The tailwater level; Indicates hydroelectric power station During the period Head loss; Indicates hydroelectric power station During the period The water purifier head; , , They represent hydroelectric power stations The water level-storage capacity relationship function, the tailwater level-discharge flow relationship function, and the head loss-power generation flow function.

[0015] S1.3 Hydropower Station Dynamic Characteristics Relationship (10) In the formula: Indicates hydroelectric power station The dynamic characteristic function relating average output, power generation flow rate, and net water head.

[0016] S1.4 Boundary Constraints (11) (12) (13) (14) (15) (16) In the formula: , They represent hydroelectric power stations Upper and lower limits of outbound flow; , They represent hydroelectric power stations Upper and lower limits of power generation flow rate; , They represent hydroelectric power stations Upper and lower limits of water level; , These represent the hydropower stations during the dispatch period. The initial and final water levels; , They represent hydroelectric power stations Upper and lower limits of output.

[0017] Construction of the S2 objective evaluation function: To effectively guide the optimization direction during the search process, this invention designs a target evaluation function for optimizing the search. This target evaluation function is used to uniformly evaluate candidate scheduling schemes and adaptively adjusts the evaluation focus according to different stages of the optimization search, thereby achieving a smooth transition from global exploration to local fine-tuning in the search process.

[0018] Cascade hydropower system during time period The remaining load of the system can be obtained after calculating the corresponding operating status. Based on this, the following evaluation function is constructed: (17) In the formula: and These are weighting coefficients, used to adjust the relative importance of different evaluation items in the objective function. The first term measures the overall operational level of the scheduling scheme throughout the entire scheduling cycle, while the second term reflects the fluctuation of the system's remaining load between adjacent time periods.

[0019] Weighting coefficient and They can be represented as: (18) (19) (20) In the formula: and These are the upper limits of the weighting coefficients; , This represents the maximum number of iterations and the current number of iterations; This is used to characterize the evolutionary progress of the search process from the initial exploration stage to the deep optimization stage. In the early stages of the search, Take the larger value Taking a smaller value strengthens the guiding role of the objective function in the overall performance, allowing the search process to explore a wide range of feasible solutions; as the search progresses, The weighting of the parameters gradually increases, making the target evaluation focus more on the coordination and stability between adjacent scheduling periods, thereby achieving fine-grained optimization of the scheduling scheme. It should be noted that the specific forms of the evaluation function and weighting coefficients can be set according to the actual operating characteristics of the cascade hydropower system and the scheduling requirements.

[0020] Global search during the initial exploration phase of S3: The main objective of this stage is to fully explore the scheduling variables within their feasible region, while satisfying the constraints of the scheduling model, to obtain a diverse and representative set of candidate solutions. This reduces the optimization process's dependence on the initial solution and lays a solid foundation for the subsequent deep optimization stage. The specific process is as follows: S3.1 Candidate Solution Generation Method in the Initial Exploration Phase Let the first The scheduling solution for the next iteration is: (twenty one) In the formula, Indicates the time period of the cascade system The water level vector.

[0021] Introducing a perturbation to generate candidate solutions, the update method of which can be expressed as: (twenty two) In the formula, The perturbation vector has its components randomly generated within a preset step size to enhance search diversity. To ensure the feasibility of the scheduling scheme, candidate solutions must satisfy various operational constraints, which are corrected using the following method: (twenty three) In the formula, and These represent the time periods of the cascade system. Upper and lower limits constraints on water level vectors.

[0022] S3.2 Evaluate candidate solutions using an evaluation function. The generated candidate solutions are evaluated using the designed objective evaluation function. When a candidate solution is better than the current solution in terms of objective function value or maintains scheduling coordination within a certain tolerance range, the candidate solution is accepted as a new evolutionary individual, thereby guiding the search direction to gradually move towards the region of high-quality solutions.

[0023] In the initial exploration phase, the evaluation function prioritizes evaluation terms that emphasize overall performance, thus preventing the search from prematurely focusing on local details and enhancing the algorithm's global awareness of the solution space structure. Simultaneously, through multiple iterative processes of random perturbation and evaluation filtering, the scheduled solutions are explored in a leapfrog manner over a wider range, providing a diverse and potentially superior initial solution foundation for the subsequent deep optimization phase.

[0024] Adaptive fine-grained search in the S4 deep optimization phase: After completing the global search in the initial exploration phase, the scheduled solution has been guided to a feasible solution region with high potential merit values. At this point, continuing to employ a large-scale random perturbation strategy can easily lead to a decrease in search efficiency. Therefore, this invention further introduces an adaptive fine-grained search mechanism in the deep optimization phase. By reducing the search scale and enhancing search directionality, it achieves high-precision mining of high-quality solution regions. The specific process is as follows: S4.1 Candidate Solution Generation Method in the Deep Optimization Stage With the current optimal scheduling scheme Centered on the decision variables within the scheduling period, a local perturbation search is performed. The first... The candidate solution at the next iteration is represented as follows: (twenty four) In the formula, It is a zero-mean random perturbation vector, whose components are generated within the standardized interval; This is an adaptive step size factor used to control search accuracy. Dynamic adjustments are made based on the improvements observed during the search process: when candidate solutions effectively improve the evaluation function value in consecutive iterations, the value is appropriately increased. To accelerate convergence; when the search stalls or the objective function fluctuates significantly, the value is gradually reduced. To enhance the stability of the local search, the adjustment method can be expressed as follows: (25) In the formula, , This is the adjustment coefficient; , These are the upper and lower limits of the step size, respectively.

[0025] S4.2 Evaluate candidate solutions using evaluation functions. As the search process enters the deep optimization phase, the weights of evaluation terms reflecting temporal coordination in the objective evaluation function gradually increase, shifting the search focus from global feasibility to fine-grained coordination optimization. Through this adaptive weight adjustment mechanism, the search process can automatically adjust its optimization priorities according to the evolutionary stage, thereby continuously improving scheduling quality while ensuring solution stability. Furthermore, if significant improvement is not achieved after several consecutive iterations in this stage, it is determined that the current search may have approached a local optimum. In this case, the step size can be reduced and the perturbation range limited to avoid ineffective oscillations in the search process.

[0026] Adaptive Evolution Mechanism of S5 Multidimensional Perturbation Stage The multidimensional perturbation stage aims to address the problem of getting stuck in local optima during the optimization search process due to continuous iterations without improvement. This stage is interspersed throughout the optimization process at a fixed period. This invention designs multiple cooperative perturbation strategies, which are adaptively selected and executed based on the current search state.

[0027] S5.1 Establishing a Collaborative Adjustment Mechanism The search process in this stage of the invention not only focuses on local improvements within a single scheduling period, but also introduces a collaborative adjustment mechanism for adjacent scheduling periods. By applying relevant perturbations to the decision variables of adjacent periods, its joint update form can be expressed as: (26) This collaborative update method helps reduce drastic fluctuations in scheduling schemes between adjacent time periods, and improves the coordination and feasibility of the operation of cascade hydropower systems.

[0028] S5.2 Guided by Historical Information Once enough historical evaluation data has been accumulated during the optimization process, a targeted perturbation based on historical volatility analysis is triggered with a certain probability. Let the most recent... The historical set of the evaluation values ​​of the candidate solutions is ,but: (27) (28) In the formula, This represents the average variation of the candidate solution's evaluation value; The standard deviation of historical records; To prevent extremely small positive numbers with a denominator of zero; and These represent the lower and upper limits of the volatility factor, respectively. This formula ensures that the algorithm applies a strong perturbation when the search trajectory oscillates violently, while applying a mild perturbation when volatility is low to perform a fine search near the stable region.

[0029] S5.3 Dynamic Tolerance Acceptance Criterion The perturbated candidate solutions are evaluated using a tolerance acceptance criterion, allowing the objective value to temporarily degrade within a certain tolerance range. A dynamic tolerance coefficient is defined. Its size and problem dimensions and scheduling cycle Proportional: (29) In the formula, This is the tolerance base coefficient. and This is the normalization constant. If the new solution generated after the perturbation... Acceptance will be granted if the following conditions are met: (30) This criterion allows for the evaluation value of new solutions. To some extent, it is inferior to the current best evaluation value. In high-dimensional and complex problems, it gives the search process greater freedom of exploration and enables global collaborative evolution.

[0030] Compared with the prior art, the beneficial effects of the present invention include: (1) The optimization target is highly compatible with the actual needs of the power system and is suitable for the dispatching scenario with high penetration of new energy. Abandoning the single goal of maximizing power generation, the core goal is to minimize the fluctuation of remaining load, which directly meets the core needs of grid peak shaving and load balancing. By incorporating the uncertainty of wind and solar power output through the scenario method, the shortcomings of existing patents that do not consider new energy are made up for, and the dispatching scheme is more in line with the actual operation of the power system under the current high penetration of new energy.

[0031] (2) The multi-stage collaborative evolution mechanism achieves a dynamic balance between global exploration and local fine-tuning optimization, significantly improving the quality of the solution. The dynamic collaborative design of the three stages of initial exploration, deep optimization, and multi-dimensional perturbation breaks through the limitations of the single-stage search in existing patents. It obtains diverse high-quality candidate solutions through global exploration and improves the accuracy of the solution through local fine-tuning. At the same time, the dedicated multi-dimensional perturbation stage effectively avoids the algorithm from getting trapped in local optima. The final scheduling scheme obtained is significantly better than the improved algorithm of existing patents in terms of excellence.

[0032] (3) Strengthen the characterization of the time-series coupling characteristics of cascade hydropower, significantly reduce the time-series fluctuation of scheduling results, and improve the actual feasibility. By using the time-series coordination evaluation item of the objective evaluation function and the collaborative adjustment mechanism of adjacent time periods in the multi-dimensional disturbance stage, the problem of insufficient characterization of hydraulic / electric coupling relationship between time periods of cascade hydropower in existing patents is specifically solved. It effectively suppresses the drastic fluctuation of scheduling parameters in adjacent time periods, makes the scheduling scheme more in line with the actual execution requirements of the project, and greatly improves the operability.

[0033] (4) An adaptive evaluation and perturbation system enhances the robustness and intelligence of global optimization. The objective evaluation function with dynamic weight adjustment can automatically switch the optimization focus according to the iteration progress, thus providing scientific guidance for the search direction. The adaptive multi-dimensional perturbation strategy combined with search history information can dynamically adjust the perturbation intensity and method according to the algorithm's running state. Combined with the dynamic tolerance acceptance criterion, the algorithm has stronger global exploration capabilities and stability in complex non-convex solution spaces, and its robustness is significantly better than the fixed rule search / perturbation method of existing patents.

[0034] (5) The special design for short-term scheduling balances solution accuracy and computational efficiency to meet the real-time requirements of the project. Special designs such as adaptive step size adjustment, nonlinear constraint nonlinearization-free processing, and fast constraint correction of candidate solutions not only avoid the accuracy loss of existing patent linearization processing, but also significantly reduce computational complexity; while ensuring the accuracy of the scheduling scheme, the solution speed is significantly improved, achieving a dual balance between accuracy and efficiency, and fully meeting the engineering requirements of real-time and speed for short-term scheduling of cascade hydropower. Attached Figure Description

[0035] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0036] Figure 1 This is a general framework diagram of a short-term optimal scheduling method for cascade hydropower based on a multi-stage adaptive evolution mechanism.

[0037] Figure 2 This is a diagram showing the peak-shaving results obtained by solving the short-term scheduling model of cascade hydropower using a multi-stage adaptive evolution method during the high-water season.

[0038] Figure 3 This is a diagram showing the peak-shaving results obtained by solving the short-term scheduling model of cascade hydropower using the mixed integer linear programming method during the high-water season.

[0039] Figure 4 This is a diagram showing the peak-shaving results obtained by solving the short-term scheduling model of cascade hydropower using an improved stepwise optimization algorithm during the high-water season.

[0040] Figure 5 This is a graph showing the peak-shaving results obtained by using a genetic algorithm to solve the short-term scheduling model of cascade hydropower during the high-water season.

[0041] Figure 6 This is a diagram showing the peak-shaving results obtained by solving the short-term scheduling model of cascade hydropower using a multi-stage adaptive evolution method during the normal water period.

[0042] Figure 7 This is a diagram showing the peak-shaving results obtained by solving the short-term scheduling model of cascade hydropower using the mixed integer linear programming method during the normal water period.

[0043] Figure 8 This is a peak-shaving result diagram obtained by solving the short-term scheduling model of cascade hydropower using an improved stepwise optimization algorithm during the normal water period.

[0044] Figure 9 This is a diagram showing the peak-shaving results obtained by using a genetic algorithm to solve the short-term scheduling model of cascade hydropower during the normal water period.

[0045] Figure 10 This is a diagram showing the peak-shaving results obtained by solving the short-term scheduling model of cascade hydropower using a multi-stage adaptive evolution method during the dry season.

[0046] Figure 11 This is a diagram showing the peak-shaving results obtained by solving the short-term scheduling model of cascade hydropower using the mixed integer linear programming method during the dry season.

[0047] Figure 12 This is a diagram showing the peak-shaving results obtained by solving the short-term scheduling model of cascade hydropower using an improved stepwise optimization algorithm during the dry season.

[0048] Figure 13 This is a graph showing the peak-shaving results obtained by using a genetic algorithm to solve the short-term scheduling model of cascade hydropower during the dry season. Detailed Implementation

[0049] 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.

[0050] Example 1 This invention provides a short-term optimal scheduling method for cascade hydropower based on a multi-stage adaptive evolution mechanism, comprising the following steps: Construction of the short-term dispatch model for S1 cascade hydropower: The construction of a short-term optimal scheduling model for cascade hydropower is a complex optimization problem that requires the coordination of multiple factors, including renewable energy output scenarios and the hydropower connections between upstream and downstream cascades, aiming to achieve efficient utilization of hydropower resources in the short term. Its construction typically requires integrating data such as load curves, reservoir characteristics, and scheduling demands to maximize the system's peak-shaving capacity while ensuring the safety of both hydropower and power grid operations. Therefore, this invention aims to minimize the fluctuation of the remaining load of cascade hydropower, considering the impact of wind and solar uncertainties, and constructs the following objective function using a scenario-based approach: (1) (2) (3) In the formula: Indicates the system in the scenario Time period The remaining load; Representing a scene The probability of; Indicates the number of scenes; Indicates the number of time periods in the scheduling period; Indicates time period The system load; , They represent the scenes respectively. Time period Average output of wind and solar power; Indicates hydroelectric power station Time period The average output.

[0051] The short-term operational constraints of cascade hydropower are as follows: S1.1 Water Balance Constraint (4) (5) In the formula: Indicates hydroelectric power station During the period The final storage capacity; , , , They represent hydroelectric power stations During the period The interval flow, outflow, power generation flow, and wastewater discharge flow.

[0052] S1.2 Clean water head constraint (6) (7) (8) (9) In the formula: Indicates hydroelectric power station During the period The final water level; Indicates hydroelectric power station During the period The tailwater level; Indicates hydroelectric power station During the period Head loss; Indicates hydroelectric power station During the period The water purifier head; , , They represent hydroelectric power stations The water level-storage capacity relationship function, the tailwater level-discharge flow relationship function, and the head loss-power generation flow function.

[0053] S1.3 Hydropower Station Dynamic Characteristics Relationship (10) In the formula: Indicates hydroelectric power station The dynamic characteristic function relating average output, power generation flow rate, and net water head.

[0054] S1.4 Boundary Constraints (11) (12) (13) (14) (15) (16) In the formula: , They represent hydroelectric power stations Upper and lower limits of outbound flow; , They represent hydroelectric power stations Upper and lower limits of power generation flow rate; , They represent hydroelectric power stations Upper and lower limits of water level; , These represent the hydropower stations during the dispatch period. The initial and final water levels; , They represent hydroelectric power stations Upper and lower limits of output.

[0055] Construction of the S2 objective evaluation function: To effectively guide the optimization direction during the search process, this invention designs a target evaluation function for optimizing the search. This target evaluation function is used to uniformly evaluate candidate scheduling schemes and adaptively adjusts the evaluation focus according to different stages of the optimization search, thereby achieving a smooth transition from global exploration to local fine-tuning in the search process.

[0056] Cascade hydropower system during time period The remaining load of the system can be obtained after calculating the corresponding operating status. Based on this, the following evaluation function is constructed: (17) In the formula: and These are weighting coefficients, used to adjust the relative importance of different evaluation items in the objective function. The first term measures the overall operational level of the scheduling scheme throughout the entire scheduling cycle, while the second term reflects the fluctuation of the system's remaining load between adjacent time periods.

[0057] Weighting coefficient and They can be represented as: (18) (19) (20) In the formula: and These are the upper limits of the weighting coefficients; , This represents the maximum number of iterations and the current number of iterations; This is used to characterize the evolutionary progress of the search process from the initial exploration stage to the deep optimization stage. In the early stages of the search, Take the larger value Taking a smaller value strengthens the guiding role of the objective function in the overall performance, allowing the search process to explore a wide range of feasible solutions; as the search progresses, The weighting of the parameters gradually increases, making the target evaluation focus more on the coordination and stability between adjacent scheduling periods, thereby achieving fine-grained optimization of the scheduling scheme. It should be noted that the specific forms of the evaluation function and weighting coefficients can be set according to the actual operating characteristics of the cascade hydropower system and the scheduling requirements.

[0058] Global search during the initial exploration phase of S3: The main objective of this stage is to fully explore the scheduling variables within their feasible region, while satisfying the constraints of the scheduling model, to obtain a diverse and representative set of candidate solutions. This reduces the optimization process's dependence on the initial solution and lays a solid foundation for the subsequent deep optimization stage. The specific process is as follows: S3.1 Candidate Solution Generation Method in the Initial Exploration Phase Let the first The scheduling solution for the next iteration is: (twenty one) In the formula, Indicates the time period of the cascade system The water level vector.

[0059] Introducing a perturbation to generate candidate solutions, the update method of which can be expressed as: (twenty two) In the formula, The perturbation vector has its components randomly generated within a preset step size to enhance search diversity. To ensure the feasibility of the scheduling scheme, candidate solutions must satisfy various operational constraints, which are corrected using the following method: (twenty three) In the formula, and These represent the time periods of the cascade system. Upper and lower limits constraints on water level vectors.

[0060] S3.2 Evaluate candidate solutions using an evaluation function. The generated candidate solutions are evaluated using the designed objective evaluation function. When a candidate solution is better than the current solution in terms of objective function value or maintains scheduling coordination within a certain tolerance range, the candidate solution is accepted as a new evolutionary individual, thereby guiding the search direction to gradually move towards the region of high-quality solutions.

[0061] In the initial exploration phase, the evaluation function prioritizes evaluation terms that emphasize overall performance, thus preventing the search from prematurely focusing on local details and enhancing the algorithm's global awareness of the solution space structure. Simultaneously, through multiple iterative processes of random perturbation and evaluation filtering, the scheduled solutions are explored in a leapfrog manner over a wider range, providing a diverse and potentially superior initial solution foundation for the subsequent deep optimization phase.

[0062] Adaptive fine-grained search in the S4 deep optimization phase: After completing the global search in the initial exploration phase, the scheduled solution has been guided to a feasible solution region with high potential merit values. At this point, continuing to employ a large-scale random perturbation strategy can easily lead to a decrease in search efficiency. Therefore, this invention further introduces an adaptive fine-grained search mechanism in the deep optimization phase. By reducing the search scale and enhancing search directionality, it achieves high-precision mining of high-quality solution regions. The specific process is as follows: S4.1 Candidate Solution Generation Method in the Deep Optimization Stage With the current optimal scheduling scheme Centered on the decision variables within the scheduling period, a local perturbation search is performed. The first... The candidate solution at the next iteration is represented as follows: (twenty four) In the formula, It is a zero-mean random perturbation vector, whose components are generated within the standardized interval; This is an adaptive step size factor used to control search accuracy. Dynamic adjustments are made based on the improvements observed during the search process: when candidate solutions effectively improve the evaluation function value in consecutive iterations, the value is appropriately increased. To accelerate convergence; when the search stalls or the objective function fluctuates significantly, the value is gradually reduced. To enhance the stability of the local search, the adjustment method can be expressed as follows: (25) In the formula, , This is the adjustment coefficient; , These are the upper and lower limits of the step size, respectively.

[0063] S4.2 Evaluate candidate solutions using evaluation functions. As the search process enters the deep optimization phase, the weights of evaluation terms reflecting temporal coordination in the objective evaluation function gradually increase, shifting the search focus from global feasibility to fine-grained coordination optimization. Through this adaptive weight adjustment mechanism, the search process can automatically adjust its optimization priorities according to the evolutionary stage, thereby continuously improving scheduling quality while ensuring solution stability. Furthermore, if significant improvement is not achieved after several consecutive iterations in this stage, it is determined that the current search may have approached a local optimum. In this case, the step size can be reduced and the perturbation range limited to avoid ineffective oscillations in the search process.

[0064] Adaptive Evolution Mechanism of S5 Multidimensional Perturbation Stage The multidimensional perturbation stage aims to address the problem of getting stuck in local optima during the optimization search process due to continuous iterations without improvement. This stage is interspersed throughout the optimization process at a fixed period. This invention designs multiple cooperative perturbation strategies, which are adaptively selected and executed based on the current search state.

[0065] S5.1 Establishing a Collaborative Adjustment Mechanism The search process in this stage of the invention not only focuses on local improvements within a single scheduling period, but also introduces a collaborative adjustment mechanism for adjacent scheduling periods. By applying relevant perturbations to the decision variables of adjacent periods, its joint update form can be expressed as: (26) This collaborative update method helps reduce drastic fluctuations in scheduling schemes between adjacent time periods, and improves the coordination and feasibility of the operation of cascade hydropower systems.

[0066] S5.2 Guided by Historical Information Once enough historical evaluation data has been accumulated during the optimization process, a targeted perturbation based on historical volatility analysis is triggered with a certain probability. Let the most recent... The historical set of the evaluation values ​​of the candidate solutions is ,but: (27) (28) In the formula, This represents the average variation of the candidate solution's evaluation value; The standard deviation of historical records; To prevent extremely small positive numbers with a denominator of zero; and These represent the lower and upper limits of the volatility factor, respectively. This formula ensures that the algorithm applies a strong perturbation when the search trajectory oscillates violently, while applying a mild perturbation when volatility is low to perform a fine search near the stable region.

[0067] S5.3 Dynamic Tolerance Acceptance Criterion The perturbated candidate solutions are evaluated using a tolerance acceptance criterion, allowing the objective value to temporarily degrade within a certain tolerance range. A dynamic tolerance coefficient is defined. Its size and problem dimensions and scheduling cycle Proportional: (29) In the formula, This is the tolerance base coefficient. and This is the normalization constant. If the new solution generated after the perturbation... Acceptance will be granted if the following conditions are met: (30) This criterion allows for the evaluation value of new solutions. To some extent, it is inferior to the current best evaluation value. In high-dimensional and complex problems, it gives the search process greater freedom of exploration and enables global collaborative evolution.

[0068] Example 2 Based on the short-term optimal scheduling method for cascade hydropower based on a multi-stage adaptive evolution mechanism described in Example 1, a downstream cascade system in a river basin in Southwest my country is selected as a research example to verify the proposed method. The total installed capacity of this cascade system is 6770MW, and Table 1 shows the basic information of each power station in the upstream and downstream order of the cascade. To verify the effectiveness of the proposed method, four algorithms were designed to solve and compare the constructed short-term scheduling model for cascade hydropower, including: the multi-stage adaptive evolution method, the mixed integer linear programming method, an improved algorithm combining the stepwise optimization algorithm and the successive approximation dynamic programming method (hereinafter referred to as the stepwise optimization algorithm), and the genetic algorithm. In addition, to handle the nonlinear constraints of the model in the mixed integer linear programming framework, this paper uses a special sequence set method to piecewise linearize the relevant nonlinear function relationships. Typical days during the high-water season, normal-water season, and low-water season were selected for simulation calculations. The reservoir's initial and final storage capacity, interval runoff, and upper and lower limits of output in the model input are all actual parameters of the power stations. The program is implemented using Python 3.10, and the code runs on a Windows 11 operating system with an Intel Core i9-14900K 3.20 GHz processor and 64GB of RAM.

[0069] Table 1 Basic Data Information Table for Hydropower Stations

[0070] Figures 2-5The results of peak shaving using different methods to solve the short-term optimal scheduling model of cascade hydropower during the high-water season are presented. Table 2 shows the target values ​​and solution times obtained by different methods. It can be observed that in the high-water scenario, the proposed multi-stage adaptive evolution algorithm exhibits significant comprehensive advantages in solving the short-term scheduling problem of cascade hydropower. First, from the optimization results, the target value obtained by this algorithm is significantly lower than that of mixed-integer linear programming, the improved stepwise optimization algorithm, and the traditional genetic algorithm. This indicates its outstanding ability to search for high-quality solutions and its ability to more effectively coordinate hydropower and renewable energy output. Regarding computational efficiency, the solution time of this method is 79.40 seconds, slightly higher than that of the genetic algorithm, but far lower than that of mixed-integer linear programming, and on the same order of magnitude as the 86.13 seconds of the improved stepwise optimization algorithm, demonstrating its practical performance in obtaining high-quality solutions within a limited time.

[0071] Table 2. Comparative Analysis of Calculation Results Using Different Methods During the High-Water Season

[0072] Figures 6-9 The results of peak shaving during the normal water season using different methods to solve the short-term optimal scheduling model of cascade hydropower are presented. Table 3 shows the target values ​​and solution times obtained by different methods. Under the normal water season scenario, the proposed multi-stage adaptive evolution algorithm continues to demonstrate excellent overall performance. Comparison shows that the algorithm obtains the optimal objective function value, significantly lower than the mixed-integer linear programming method, and far lower than the improved stepwise optimization algorithm and the traditional genetic algorithm. This indicates that it can still effectively coordinate the hydropower output process under normal water conditions. In terms of computational efficiency, this method can complete the solution in only 71.95 seconds, significantly faster than the other comparative algorithms, indicating that it has better convergence speed and solution efficiency while maintaining optimization accuracy.

[0073] Table 3. Comparative Analysis of Calculation Results Using Different Methods During the Normal Water Period

[0074] Figures 10-13 The results of peak shaving using different methods to solve the short-term optimal scheduling model of cascade hydropower during the dry season are shown. Table 4 shows the target values ​​and solution times obtained by different methods. Under the dry season scenario, the proposed multi-stage adaptive evolution algorithm still exhibits good overall performance and stability. This algorithm still outperforms several other comparative algorithms in terms of the objective function value. Regarding computation time, the proposed method takes 58.57 seconds, slightly longer than the 41.97 seconds of mixed integer linear programming, but significantly shorter than the 67.35 seconds of the improved stepwise optimization algorithm, and comparable to the genetic algorithm, demonstrating its acceptable solution efficiency during the dry season.

[0075] Table 4. Comparison and Analysis of Calculation Results Using Different Methods During the Dry Season

[0076] The above results show that the short-term optimal scheduling method for cascade hydropower based on a multi-stage adaptive evolution mechanism proposed in this invention can maintain a good balance between solution quality and computation speed under different hydrological conditions, verifying its applicability and robustness under different inflow scenarios.

[0077] 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 short-term optimal scheduling method for cascade hydropower based on a multi-stage adaptive evolution mechanism, characterized in that, Includes the following steps: S1. Construct a short-term dispatch model for cascade hydropower, with the goal of minimizing the fluctuation of the remaining load of cascade hydropower. The model incorporates the uncertainty of wind and solar power output using a scenario-based approach and sets water balance, net head, hydropower station dynamic characteristics, and boundary constraints. S2. Construct a target evaluation function with dynamic weights. The evaluation function includes an overall operational level evaluation item and an evaluation item for the fluctuation of remaining load in adjacent time periods. The weight coefficients are adaptively adjusted with the iteration progress. S3. Global search: Under the premise of satisfying the constraints of the scheduling model, the scheduling variables are fully explored within their feasible domain to obtain a diverse and representative set of candidate solutions; S4. Adaptive fine search in the deep optimization stage: high-precision mining of high-quality solution regions by narrowing the search scale and enhancing the search directionality; S5. Design a coordinated perturbation strategy, adaptively select the execution based on the current search state, and output the optimal scheduling scheme after iterative optimization.

2. The method for short-term optimal scheduling of cascade hydropower based on a multi-stage adaptive evolution mechanism according to claim 1, characterized in that, The objective function constructed by the scenario method in step S1 is as follows: ； ； ； In the formula: Indicates the system in the scenario Time period The remaining load; Representing a scene The probability of; Indicates the number of scenes; Indicates the number of time periods in the scheduling period; Indicates time period The system load; , They represent the scenes respectively. Time period Average output of wind and solar power; Indicates hydroelectric power station Time period The average output.

3. The method for short-term optimal scheduling of cascade hydropower based on a multi-stage adaptive evolution mechanism according to claim 1, characterized in that, The expression for the objective evaluation function mentioned in step S2 is: ； In the formula: It is a cascade hydropower system in time period The remaining load of the system can be obtained by calculating the corresponding operating status; and These are weighting coefficients, used to adjust the relative importance of different evaluation items in the objective function; The first item measures the overall operational level of the scheduling scheme throughout the entire scheduling cycle. The second item reflects the fluctuation of the system's remaining load between adjacent time periods.

4. The short-term optimal scheduling method for cascade hydropower based on a multi-stage adaptive evolution mechanism according to claim 3, characterized in that, The and The expression is: ； ； ； In the formula: and These are the upper limits of the weighting coefficients; , This represents the maximum number of iterations and the current number of iterations; Used to characterize the evolutionary progress of the search process from the initial exploration stage to the deep optimization stage; In the early stages of the search, Take the larger value By taking a smaller value, the guiding role of the objective function on the overall performance is strengthened, allowing the search process to explore a wide range of feasible solutions. As the search progresses... The weight of the target is gradually increased, so that the evaluation of the target pays more attention to the coordination and stability between adjacent scheduling periods, thereby achieving fine optimization of the scheduling scheme.

5. The short-term optimal scheduling method for cascade hydropower based on a multi-stage adaptive evolution mechanism according to claim 1, characterized in that, The global search in step S3 includes: using the water level vectors of each time period of the cascade system as the scheduling solution, introducing a random disturbance vector with a preset step size to generate candidate solutions, and after constraining the upper and lower limits of water level on the candidate solutions, evaluating and screening the candidate solutions using the objective evaluation function of step S2.

6. The method for short-term optimal scheduling of cascade hydropower based on a multi-stage adaptive evolution mechanism according to claim 1, characterized in that, The adaptive fine search in the deep optimization stage of step S4 includes: taking the current optimal scheduling scheme as the center, introducing a zero-mean random perturbation vector and an adaptive step size factor to generate candidate solutions.

7. The method for short-term optimal scheduling of cascade hydropower based on a multi-stage adaptive evolution mechanism according to claim 6, characterized in that, The adaptive step size factor Dynamic adjustments will be made based on improvements made during the search process. When candidate solutions can effectively improve the evaluation function value in continuous iterations, appropriately increase... To accelerate the convergence speed; When the search stalls or the objective function fluctuates significantly, gradually reduce... To enhance the stability of the local search, the adjustment method can be expressed as follows: ； In the formula, , This is the adjustment coefficient; , These are the upper and lower limits of the step size, respectively.

8. The method for short-term optimal scheduling of cascade hydropower based on a multi-stage adaptive evolution mechanism according to claim 1, characterized in that, The specific perturbation strategy in step S5 involves introducing a collaborative adjustment mechanism for adjacent time periods, applying relevant perturbations to the decision variables of adjacent scheduling time periods for joint updates, thereby reducing the inter-time fluctuations of the scheduling scheme.

9. The method for short-term optimal scheduling of cascade hydropower based on a multi-stage adaptive evolution mechanism according to claim 1, characterized in that, The coordinated perturbation strategy in step S5 also includes directional perturbation based on historical information. A fluctuation factor is constructed by calculating the average change amplitude and standard deviation of the evaluation values ​​of the most recent candidate solutions, and the perturbation intensity is adaptively adjusted according to the magnitude of the fluctuation factor.

10. The method for short-term optimal scheduling of cascade hydropower based on a multi-stage adaptive evolution mechanism according to claim 1, characterized in that, After the perturbation strategy in step S5 is executed, the candidate solutions after perturbation are evaluated using the dynamic tolerance acceptance criterion. The dynamic tolerance coefficient is proportional to the problem dimension and scheduling cycle, allowing the evaluation value of the candidate solution to temporarily degrade within the tolerance range.

11. The method for short-term optimal scheduling of cascade hydropower based on a multi-stage adaptive evolution mechanism according to claim 1, characterized in that, The iterative optimization in step S5 specifically involves reducing the search scale and limiting the perturbation range when no significant improvement is achieved in several consecutive iterations during the deep optimization phase; when the iteration meets the multidimensional perturbation triggering condition, switching to the multidimensional perturbation phase, and continuing the iteration until the maximum number of iterations is reached.

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