Cascade pump station group multi-target collaborative optimization scheduling method and device

Abstract

The invention discloses a cascade pump station group multi-target collaborative optimization scheduling method and device, and belongs to the technical field of hydraulic engineering optimization scheduling. Firstly, pump station physical parameters, open channel hydraulic parameters and operation constraints are integrated, and model input data are constructed; then a double-layer optimization model is trained, the upper layer optimizes field range distribution according to the hydraulic coupling relation to minimize the total operation cost, and the lower layer optimizes the operation parameters of the single pump station in a collaborative mode and synchronously reduces the electric charge cost and the starting and stopping frequency of the pump set; then, an improved cuckoo search algorithm fusing Levy flight and a diffusion mechanism is adopted for solving, and dynamic balance of global exploration and local optimization is achieved; and finally, based on Pareto multi-target evaluation, screening and outputting an optimal operation scheme with economical efficiency and safety. According to the method, accurate optimization of cascade pump station group operation scheduling is realized, and the economic benefit and the operation reliability of the system are effectively improved.

Description

Technical Field

[0001] This invention relates to the field of water conservancy project optimization scheduling technology, and in particular to a multi-objective collaborative optimization scheduling method and device for a group of cascade pumping stations. Background Technology

[0002] With the continuous deepening of water resource development and utilization in my country, the energy consumption and cost control issues of cascade pumping station systems, as the core infrastructure of inter-basin and long-distance water transfer projects, are becoming increasingly prominent. Achieving the economical, safe, and efficient operation of pumping station groups has become a key technical challenge in the scheduling and management of water transfer projects.

[0003] In existing technologies, pump station operation optimization often focuses on a single economic objective: utilizing time-of-use pricing policies to concentrate water pumping during off-peak hours to reduce electricity costs. However, this strategy has significant limitations. On the one hand, simply pursuing minimal electricity costs easily leads to frequent start-ups and shutdowns of pump units, which not only exacerbates wear and tear on electrical and mechanical equipment and shortens equipment lifespan, but also causes drastic fluctuations in water levels and sudden changes in flow velocity within the channels. This hydraulic instability exacerbates erosion of the channel lining, posing a potential threat to the structural safety and long-term stable operation of the water conveyance system, making it difficult to simultaneously achieve both economic and safety objectives.

[0004] On the other hand, in a cascade pumping station system characterized by close hydraulic coupling, the operating status of the upstream pumping station directly affects the intake conditions of the downstream pumping station through the propagation of channel water flow. Existing optimization methods often treat the distribution of head among each pumping station separately from the optimization operation within a single pumping station, failing to establish a systematic hydraulic coupling model. This makes it difficult to accurately account for complex hydraulic constraints during the optimization process, such as channel head loss, the time lag effect of water level fluctuation propagation, and the water level connection requirements between upstream and downstream pumping stations. Consequently, the optimized scheme deviates from actual operating conditions, resulting in insufficient practicality and feasibility.

[0005] Furthermore, from a mathematical modeling perspective, the coordinated optimization scheduling of cascade pumping station groups is a typical high-dimensional, nonlinear, and multi-constraint complex optimization problem. Traditional mathematical programming or heuristic algorithms generally suffer from drawbacks such as slow convergence speed, sensitivity to initial values, and susceptibility to getting trapped in local optima when solving such problems, making it difficult to stably and efficiently obtain globally optimal or satisfactory solutions that meet engineering accuracy requirements.

[0006] In summary, existing technologies lack a collaborative optimization scheduling method for cascade pumping station groups that can comprehensively consider economic costs, equipment operation frequency, and system hydraulic safety, and can efficiently solve the problem at the global level. Summary of the Invention

[0007] The main objective of this invention is to provide a multi-objective collaborative optimization scheduling method and device for a cascade pumping station group. It aims to overcome the shortcomings of existing technologies, such as the difficulty in coordinating economy and safety, and the disconnect between optimization results and actual operating conditions, by constructing a two-layer optimization model that integrates hydraulic coupling relationships and an improved intelligent search algorithm. This achieves multi-objective global optimization of operating costs, equipment losses, and system safety, thereby improving the overall operating efficiency and stability of the pumping station group.

[0008] To achieve the above objectives, this invention provides a multi-objective collaborative optimization scheduling method for a cascade pumping station group. The method includes: S1, acquiring and integrating the physical parameters of the pumping station system, the hydraulic parameters of the open channel, and the operational constraint parameters to construct input data for an optimization model that includes pump group performance, channel dynamic characteristics, and scheduling boundary conditions; S2, training a two-layer optimization model using the input data; wherein the upper-layer model optimizes head allocation based on the hydraulic coupling relationship of the cascade pumping stations to minimize total operating costs, and the lower-layer model collaboratively optimizes the operating parameters of a single pumping station through multi-objective functions to minimize electricity costs and the number of pump group start-ups and shutdowns; S3, using an improved cuckoo search algorithm to collaboratively solve the two-layer optimization model, the algorithm integrating the Levy flight strategy and diffusion mechanism, iteratively balancing global exploration and local fine-grained search; S4, after iteration termination, selecting and outputting the optimal operating scheme that meets both economic and safety requirements based on Pareto multi-objective evaluation.

[0009] Furthermore, the step of acquiring and integrating the physical parameters of the pumping station system, the hydraulic parameters of the open channel, and the operational constraint parameters, and constructing the input data for an optimization model that includes pump set performance, channel dynamic characteristics, and scheduling boundary conditions includes: S11, establishing a multi-dimensional pump set performance database by collecting the efficiency curves, speed range, and impeller diameter parameters of the pump set to support the simulation of operational performance under different working conditions; S12, dynamically integrating the roughness, cross-sectional shape, and slope coefficient parameters of the channel into the hydraulic parameter system for real-time calculation of channel head loss and water level fluctuations.

[0010] Further, the step of training a two-layer optimization model using the input data, wherein the upper-layer model optimizes the head distribution based on the hydraulic coupling relationship of the cascade pumping stations to minimize the total operating cost, and the lower-layer model collaboratively optimizes the operating parameters of a single pumping station through multiple objective functions to minimize electricity costs and the number of pump start-ups and shutdowns, includes: S21, simulating the spatiotemporal changes of water flow using the Saint-Venant equation, and calculating the channel head loss using the Manning formula, as follows: ; ;in, For water level, For traffic, The cross-sectional area is... For hydraulic radius, This is the Manning coefficient.

[0011] Furthermore, the improved cuckoo search algorithm is used to collaboratively solve the bi-level optimization model. The algorithm integrates the Lévy flight strategy and the diffusion mechanism, and the step of iteratively and dynamically balancing between global exploration and local fine-grained search includes: S31, screening non-dominated solutions through Pareto dominance relation, as shown in the following formula: ; ;in, Total operating costs, This refers to the number of times the pump unit starts and stops. For the density of water, It is the acceleration due to gravity. For traffic, For Yang Cheng, For rotational speed, The duration is the length of the time period. For electricity prices.

[0012] Furthermore, after the iteration terminates, the step of screening and outputting the optimal operating scheme that meets the requirements of economy and safety based on Pareto multi-objective evaluation includes: S41, generating new candidate solutions through the Lévy flight strategy, as shown in the following formula: ; ;in, For the new solution vector, This is the current solution vector. For step size parameters, Let Lévy distribution function be used. For gamma function, These are the distribution parameters.

[0013] Furthermore, the multi-objective collaborative optimization scheduling method for a cascade pumping station group according to the present invention also includes: S5, introducing a simulated annealing strategy, which accepts non-dominated solutions with probability during the iteration process, as shown in the following formula: ;in, A random number in the range [0,1]. and This is a random solution vector in the current population, used to enhance the algorithm's ability to escape local optima.

[0014] In another aspect, this invention provides a multi-objective collaborative optimization scheduling device for a cascade pumping station group. The device includes: a data integration module for acquiring and integrating the physical parameters, open channel hydraulic parameters, and operational constraint parameters of the pumping station system, and constructing input data for an optimization model that includes pump group performance, channel dynamic characteristics, and scheduling boundary conditions; a two-layer model construction module for training a two-layer optimization model using the input data; wherein the upper-layer model optimizes head allocation based on the hydraulic coupling relationship of the cascade pumping stations to minimize total operating costs, and the lower-layer model collaboratively optimizes the operating parameters of a single pumping station through multi-objective functions to minimize electricity costs and the number of pump group start-ups and shutdowns; an improved cuckoo search algorithm solution module for collaboratively solving the two-layer optimization model using an improved cuckoo search algorithm, which integrates the Levy flight strategy and diffusion mechanism, iteratively balancing global exploration and local fine-grained search; and a Pareto evaluation output module for selecting and outputting the optimal operating scheme that meets economic and safety requirements based on Pareto multi-objective evaluation after iteration termination.

[0015] Furthermore, the data integration module is also used for: By collecting pump set efficiency curves, speed ranges, and impeller diameter parameters, a multi-dimensional pump set performance database is established to support performance simulation under different operating conditions. The roughness, cross-sectional shape, and slope coefficient parameters of the channel are dynamically integrated into the hydraulic parameter system for real-time calculation of channel head loss and water level fluctuations.

[0016] Furthermore, the two-layer model construction module is also used to: simulate the spatiotemporal changes of water flow using the Saint-Venant equation, and calculate the channel head loss using the Manning formula, as follows: ; ;in, For water level, For traffic, The cross-sectional area is... For hydraulic radius, This is the Manning coefficient.

[0017] Furthermore, the improved cuckoo search algorithm solution module is also used to: filter non-dominated solutions using Pareto dominance relations, as shown in the following formula: ; ;in, Total operating costs, This refers to the number of times the pump unit starts and stops. For the density of water, It is the acceleration due to gravity. For traffic, For Yang Cheng, For rotational speed, The duration is the length of the time period. For electricity prices.

[0018] Furthermore, the Pareto evaluation output module is also used to generate new candidate solutions using the Lévy flight strategy, as shown in the following formula: ; ;in, For the new solution vector, This is the current solution vector. For step size parameters, Let Lévy distribution function be used. For gamma function, These are the distribution parameters.

[0019] Furthermore, the multi-objective collaborative optimization scheduling device for a cascade pumping station group according to the present invention further includes: a simulated annealing strategy module, used to introduce a simulated annealing strategy, which accepts non-dominated solutions with probability during the iteration process, as shown in the following formula: ;in, A random number in the range [0,1]. and This is a random solution vector in the current population, used to enhance the algorithm's ability to escape local optima.

[0020] Compared with the prior art, the technical solution provided by the present invention has at least the following beneficial effects: 1. Global collaborative optimization capability: By constructing a two-layer model that coordinates the upper-level field allocation and the lower-level single-station operation parameters, the minimization of the total system operating cost and the reduction of the electricity cost of a single pump station and the frequency of equipment start-up and shutdown are unified in the overall framework, realizing the effective coordination between economic goals and equipment operation safety, and overcoming the limitation of the single optimization goal of traditional methods.

[0021] 2. Accurate simulation of hydraulic dynamic characteristics: Based on the Saint-Venant equations and Manning formula, the spatiotemporal changes of open channel flow and head loss are dynamically calculated, accurately characterizing the hydraulic coupling relationship and water level fluctuation propagation effect between cascade pumping stations. This makes the optimization scheme more in line with actual hydraulic dynamics and engineering constraints, and significantly improves the feasibility and engineering applicability of the scheduling results.

[0022] 3. High-efficiency global search performance: The improved cuckoo search algorithm integrates the Levy flight strategy and diffusion mechanism, effectively balancing global exploration and local fine search during the iteration process. Combined with the Pareto multi-objective evaluation system, it significantly enhances the algorithm's ability to escape local optima, stably obtains global approximate optimal solutions that satisfy complex constraints, and improves the convergence speed and robustness of the optimization process.

[0023] This invention discloses a multi-objective collaborative optimization scheduling method and apparatus for a cascade pumping station group. By constructing a two-layer optimization architecture and an improved intelligent search algorithm, it effectively solves the core problems of traditional methods, such as the difficulty in coordinating economy and safety, and the disconnect between optimization results and actual hydraulic conditions. It achieves end-to-end optimization from data integration, model building, collaborative solving to scheme selection, significantly improving the economic efficiency of system operation and the safety and reliability of scheduling schemes, and enhancing the overall operational efficiency and engineering applicability of the pumping station group under complex hydraulic coupling conditions. Attached Figure Description

[0024] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 A flowchart of a multi-objective collaborative optimization scheduling method for a cascade pumping station group provided in an embodiment of the present invention; Figure 2 A flowchart illustrating the specific steps of a multi-objective collaborative optimization scheduling method for a cascade pumping station group, provided in an embodiment of the present invention; Figure 3 A flowchart illustrating the construction of an upper-level optimization model for a multi-objective collaborative optimization scheduling method for a cascade pumping station group, provided in an embodiment of the present invention; Figure 4 A flowchart illustrating the construction of a lower-level optimization model for a multi-objective collaborative optimization scheduling method for a cascade pumping station group, provided in an embodiment of the present invention; Figure 5 This is a schematic diagram of the structure of a multi-objective collaborative optimization scheduling device for a cascade pumping station group provided in an embodiment of the present invention. Detailed Implementation

[0025] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0026] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0027] The core idea of ​​this invention is to construct a two-layer model architecture that coordinates the upper-level field allocation with the lower-level single-station operating parameters, thereby unifying the minimization of total system operating costs with the reduction of single-station electricity costs and equipment start-up and shutdown frequency within the overall optimization framework. This achieves a deep synergy between economic objectives and equipment operational safety. Based on the Saint-Venant equations and Manning's formula, the spatiotemporal variations of open channel flow and head loss are dynamically calculated, accurately characterizing the hydraulic coupling relationship and water level fluctuation propagation effect between cascade pumping stations, ensuring the optimization scheme closely aligns with actual engineering constraints and hydraulic dynamic characteristics. An improved cuckoo search algorithm, incorporating the Levy flight strategy and diffusion mechanism, effectively balances global exploration and local fine-grained search during iteration. Combined with the Pareto multi-objective evaluation system, this significantly enhances the algorithm's ability to escape local optima, thus stably obtaining globally approximate optimal solutions that satisfy complex constraints. This achieves full-process optimization from data integration, model construction, collaborative solution to scheme decision-making, significantly improving the economic efficiency and scheduling safety and reliability of the system, providing technical support for the efficient and stable operation of cascade pumping station groups under complex hydraulic coupling conditions.

[0028] The following description, with reference to the accompanying drawings, describes a multi-objective collaborative optimization scheduling method and apparatus for a cascade pumping station group according to an embodiment of the present invention.

[0029] Example 1 This embodiment provides a multi-objective collaborative optimization scheduling method for a group of cascade pumping stations. For example... Figure 1 As shown, the method includes the following steps: S1: Obtain and integrate the physical parameters, open channel hydraulic parameters, and operational constraint parameters of the pumping station system to construct the input data for an optimization model that includes pump set performance, channel dynamic characteristics, and scheduling boundary conditions.

[0030] Specifically, this step is the foundation of the entire optimization scheduling method, and its data quality directly affects the modeling accuracy and solution effect of the upper-level head allocation model and the lower-level single pump station operation optimization model.

[0031] Specifically, S1 constructs a multi-dimensional parameter database through systematic data acquisition and structured processing. Specifically, the sub-steps are responsible for collecting the physical parameters of the pump set, including design flow rate, head, efficiency curve, speed range, pump type structure, and impeller diameter. These parameters are used to establish the performance mapping relationship of the pump set under different operating conditions. Then, it focuses on the hydraulic parameters of the open channel, such as channel bottom elevation, channel longitudinal slope, slope coefficient, roughness coefficient, and cross-sectional shape, to construct an unsteady flow model that simulates the dynamic changes of water flow in time and space. It is also responsible for integrating operational constraint parameters, including time-of-use electricity pricing policies, scheduling cycle division, daily water demand of pumping stations at all levels, inlet and outlet water level limits, and reservoir capacity-water level relationship curves, providing external boundary conditions for the optimization model.

[0032] Specifically, the pump set efficiency curve is usually based on A ternary relation is represented as follows, in which For traffic ( ), Head (m) Efficiency (%). Open channel roughness. Using Manning's formula, its value range is generally within... The exact amount depends on the channel materials and surface condition. Within operational constraints, the electricity price... Input variables for different time periods, scheduling period Daily water demand is typically divided by hour. by Units.

[0033] Furthermore, this step is widely applied to long-distance water transfer projects, such as the South-to-North Water Transfer Project (Eastern Route). By integrating the operational data of pump station groups and open channel systems, it provides an accurate input basis for subsequent two-layer optimization models. This step ensures that the model can accurately reflect pump group performance, channel hydraulic response, and scheduling boundary conditions, thereby improving the engineering applicability and system stability of the optimization results.

[0034] Specifically, S1 significantly improves the model's input accuracy and constraint completeness through structured data integration, providing reliable data support for improving the collaborative optimization of the Cuckoo Search algorithm, and is a key prerequisite for achieving multi-objective optimization that balances economy and safety.

[0035] Furthermore, S1 includes: S11 establishes a multi-dimensional pump set performance database by collecting pump set efficiency curves, speed ranges, and impeller diameter parameters to support performance simulation under different operating conditions.

[0036] Specifically, this step involves collecting and standardizing core parameters of the pump set, such as design flow rate, head, efficiency curve, speed range, and impeller diameter. The efficiency curve is typically represented as discrete points or a fitted function, describing the efficiency variation of the pump set under different flow rate and head combinations. Its typical input format is... - - 3D dataset, units are respectively , And percentage (%). The speed range is defined as the minimum and maximum speed of the pump unit within the safe operating range, usually expressed as... and The unit is The impeller diameter, as one of the geometric parameters of a pump unit, directly affects its flow rate and head characteristics, and is typically measured in terms of... It indicates that the unit is .

[0037] Furthermore, this step employs structured data acquisition and modeling methods to normalize the pump set's operating efficiency, power, and other performance indicators under different speeds and flow rates, and establishes parameter mapping relationships to form a queryable database structure. This database supports rapid retrieval of key performance parameters such as pump set operating efficiency and power at any operating point (such as a specific flow rate and head combination), providing real-time and accurate input data for subsequent multi-objective optimization models.

[0038] Specifically, this step is widely used in cascade pumping station systems in long-distance water transfer projects, such as the South-to-North Water Transfer Project (Eastern Route). By establishing a high-precision pump set performance database, the system can simulate the operating status of pump sets during different scheduling periods, evaluate their energy consumption and start-up / shutdown frequency, thereby providing a data foundation for upper-level head allocation and lower-level single-station optimization.

[0039] Specifically, by integrating and modeling multi-dimensional parameters, the accuracy and efficiency of pump station operation simulation were significantly improved, providing reliable data support for the subsequent collaborative optimization of the cuckoo search algorithm. This is a key prerequisite for achieving the dual objectives of economic efficiency and safety optimization.

[0040] S12 dynamically integrates the channel roughness, cross-sectional shape, and slope coefficient parameters into the hydraulic parameter system for real-time calculation of channel head loss and water level fluctuations.

[0041] Specifically, dynamically integrating parameters such as channel roughness, cross-sectional shape, and slope coefficient into the hydraulic parameter system is one of the key technical steps for achieving coordinated and optimized scheduling of cascade pumping station groups. This step provides a foundation for real-time calculation of channel head loss and water level fluctuations by constructing an open channel hydraulic calculation model, thereby improving the hydraulic rationality and system stability of the pumping station scheduling scheme.

[0042] Specifically, this step first involves modeling the channel head loss based on Manning's formula. Manning's formula is... ,in For channel traffic ( ), Cross-sectional area ( ), hydraulic radius ( ), This represents the Manning roughness coefficient. This formula reflects the nonlinear relationship between channel roughness, cross-sectional geometry, and flow conditions. In practical applications, the channel's cross-sectional shape (e.g., trapezoidal, rectangular, or U-shaped) determines... and The calculation method is as follows, while the slope coefficient is used to determine the geometric parameters of the cross-section, such as the slope ratio of a trapezoidal channel. This affects the dynamic changes in cross-sectional area and hydraulic radius. By integrating these parameters into the hydraulic model in real time, the system can dynamically calculate head loss based on the current flow rate and water level, providing accurate hydraulic feedback for pump station head allocation.

[0043] Furthermore, roughness The typical value range is: The specific values ​​depend on the channel lining material (such as concrete, soil, or masonry). Cross-sectional shape parameters include the bottom width. Slope ratio , water depth Its combination form determines and The expression for, for example, the area of ​​a trapezoidal cross-section. hydraulic radius These parameters need to be initialized based on channel design drawings or on-site measurement data, and dynamically updated according to water level changes during operation.

[0044] Specifically, this step is widely used in the scheduling systems of cascade pumping stations in long-distance water transfer projects, especially in the eastern route of the South-to-North Water Transfer Project, where fluctuations in channel water levels have a significant impact on pumping station operating efficiency and equipment lifespan. By integrating hydraulic parameters into the optimization model in real time, the system can accurately assess the pumping station's head demand and head loss during different scheduling periods, thereby avoiding pump overload or idling caused by sudden changes in water level.

[0045] Specifically, by accurately modeling the hydraulic characteristics of the channels, the physical consistency and dynamic response capability of the pump station scheduling model are significantly improved. Combined with the global optimization capability of the improved cuckoo search algorithm, the system can achieve coordinated optimization of head distribution and pump group operation while meeting the constraints of total water lifting volume and motor power, thereby reducing operating energy consumption and water level fluctuations, and enhancing the operational safety and economy of the entire water conveyance system.

[0046] S2, using the input data to train a two-layer optimization model; wherein, the upper-layer model optimizes the head allocation based on the hydraulic coupling relationship of the cascade pumping stations to minimize the total operating cost, and the lower-layer model optimizes the operating parameters of a single pumping station through multi-objective functions to minimize the electricity cost and the number of pump start-ups and shutdowns.

[0047] Specifically, this step involves establishing a two-layer optimization model. Its core lies in achieving multi-objective optimization of the cascade pumping station system's economy and operational stability through the collaborative solution of the upper and lower layers. At the technical implementation level, the upper-layer model uses head distribution as the decision variable and, based on the hydraulic coupling relationship between the cascade pumping stations, constructs an optimization function with the objective of minimizing total operating costs. Specifically, the upper-layer model dynamically calculates the head loss caused by changes in water flow using an unsteady flow model and combines this with the Saint-Venant equation to simulate the spatiotemporal changes in water flow. The formula is: ; Based on this, the relationship between head and head loss is established: ; in, For the head of the k-th pumping station, $H_{out}$ represents the water levels in the inlet and outlet pools, respectively. This represents the head loss in the channel. The head loss is calculated using Manning's formula: ; The upper-level model also needs to satisfy head constraints, water level constraints, and water balance constraints, such as: ; ; ; The lower-level model optimizes the operating parameters of a single pumping station, simultaneously minimizing electricity costs and the number of pump start-ups and shutdowns through multiple objective functions. The objective functions are as follows: ; ; in, Characterizing electricity costs, This represents the number of start-stop cycles. The lower-level model also needs to satisfy operational constraints such as motor power, speed, and flow rate, for example: ; ; ; Specifically, this two-layer model is applicable to long-distance water transfer projects such as the eastern route of the South-to-North Water Transfer Project. It uses a SCADA system to collect real-time pump station operation data and combines time-of-use electricity pricing strategies with pump efficiency characteristics to achieve intelligent decision-making for operation scheduling. The technical value of this step lies in effectively reducing the total system operating cost through the coordinated optimization of head allocation and individual station operating parameters. Simultaneously, it reduces equipment wear and hydraulic fluctuation risks caused by frequent pump start-ups and shutdowns, thereby improving the economy and stability of the scheduling scheme.

[0048] Furthermore, S2 includes: S21, the spatiotemporal variation of water flow is simulated using the Saint-Venant equation, and the channel head loss is calculated using the Manning formula, as follows: ; ; in, For water level, For traffic, The cross-sectional area is... For hydraulic radius, This is the Manning coefficient.

[0049] Specifically, this step plays a fundamental role in the hydraulic simulation of the cascade pumping station system, providing accurate hydraulic response data for subsequent optimization models.

[0050] Furthermore, Saint-Venant's equations are used to describe the dynamic changes of open channel flow under unsteady flow conditions, and their basic form is:

[0051] in, Indicates spatial location and time Water level (m) at the location. This represents the flow rate (m³ / s) at the same location and time. The equation reflects the principle of mass conservation, which states that at any given time and spatial location, the rate of change of water level is inversely proportional to the rate of change of flow rate. In practical applications, this equation is typically solved numerically using the finite difference method or the finite volume method to obtain the water level and flow rate distributions of the entire water conveyance system under different operating conditions.

[0052] Furthermore, Manning's formula is used to calculate head loss in channels, and its expression is: ; in, Flow rate (m³ / s) The cross-sectional area of ​​the water passage is (m²). The hydraulic radius is (m). is the Manning roughness coefficient, which typically ranges from 0.01 to 0.06, with the specific value depending on the channel material and surface roughness. This formula is based on an empirical hydraulic model and is widely used in the simulation of unsteady flow in open channels, effectively reflecting the energy loss of water flow in the channel.

[0053] Specifically, this step is typically deployed in the hydraulic simulation systems of long-distance water transfer projects, such as the Eastern Route of the South-to-North Water Transfer Project. By combining the Saint-Venant equation and the Manning formula, the system can dynamically predict water level changes and head losses between pumping stations, providing real-time and accurate hydraulic response data for head allocation. This technique significantly improves the model's adaptability to complex hydraulic conditions, laying the physical foundation for the coordinated and optimized scheduling of cascade pumping stations.

[0054] Specifically, this step, through high-precision hydraulic simulation, effectively solves the problem of neglecting the dynamic response of channels in traditional methods, improving the physical rationality of the optimization model and the feasibility of the operation scheme. Simultaneously, the calculation results can serve as input constraints for the upper-level optimization model, ensuring that the head distribution scheme meets the requirements of hydraulic balance and energy loss control in actual operation, thereby improving the system's operating efficiency and stability.

[0055] S3 employs an improved cuckoo search algorithm to collaboratively solve the bi-layer optimization model. The algorithm integrates the Levy flight strategy and diffusion mechanism, achieving iterative dynamic balance between global exploration and local fine-grained search.

[0056] Specifically, in step S3, this invention employs an improved cuckoo search algorithm to collaboratively solve the constructed two-layer optimization model. Its core lies in integrating the Lévy flight strategy and the diffusion mechanism to achieve a dynamic balance between global exploration and local fine-grained search, thereby effectively preventing the algorithm from getting trapped in local optima and improving convergence accuracy and solution efficiency. This algorithm has significant advantages in complex multi-objective optimization problems of cascade pumping station systems.

[0057] Specifically, the improved cuckoo search algorithm first generates new candidate solutions using the Lévy flight strategy. Lévy flight is a random walk mechanism based on a heavy-tailed distribution, where the step size follows a Lévy distribution. ,in The value is usually taken from between, Let gamma be the function. This strategy allows the algorithm to make long jumps in the solution space, thereby enhancing global search capabilities. The generation of new solutions follows the formula: ; in, Indicates the first The middle generation The solution vector for each bird's nest. This is the step size control parameter, used to adjust the size of the search step. Through this mechanism, the algorithm can flexibly switch between different head distributions and pump unit operation combinations, avoiding getting trapped in local optima.

[0058] Furthermore, to enhance the algorithm's local search capability and solution diversity, this invention introduces a diffusion mechanism. This mechanism is applied to the current optimal solution. A Gaussian perturbation is applied to the vicinity to generate new solutions with diversity, the formula of which is:

[0059] in, Denotes a random matrix that follows a Gaussian distribution. The parameter represents the perturbation intensity. This strategy facilitates a finer search near the Pareto front, improving the accuracy and stability of multi-objective optimization.

[0060] Specifically, the iteration termination condition of the algorithm is usually set to reaching the maximum number of iterations. Or the fitness value changes less than a preset threshold. Probability of discovery Used to control the elimination of inferior solutions and the generation of new solutions, its value ranges from [0,1], and is usually set to to This balances population diversity and convergence speed.

[0061] Specifically, this step plays the role of the core solution engine in the entire technical solution. Through intelligent optimization algorithms, it coordinates the upper-level head allocation with the lower-level pump group operation strategy, which significantly improves the coordination ability between economy and safety of the cascade pump station system and provides efficient and reliable scheduling decision support for complex hydraulic systems.

[0062] Furthermore, S3 includes: S31, non-dominated solutions are selected using the Pareto dominance relation, as shown in the following formula: ; ; in, Total operating costs, This refers to the number of times the pump unit starts and stops. For the density of water, It is the acceleration due to gravity. For traffic, For Yang Cheng, For rotational speed, The duration is the length of the time period. For electricity prices.

[0063] Specifically, this step is based on multi-objective optimization theory, aiming to identify from the current population a set of solutions that are not dominated by other solutions in multiple optimization objectives, thereby gradually approaching the Pareto optimal front. In this invention, the optimization objectives include minimizing total operating electricity costs and minimizing the number of pump start-ups and shutdowns, respectively, as shown by the formulas... and express.

[0064] Specifically, this step first calculates the objective function value for all candidate solutions to obtain their fitness values ​​for both objectives. Then, the Pareto dominance relation is used to compare the solutions: if the solution... Superior to the solution in at least one objective And is not inferior to in other objectives Then it is called Dominate By traversing the entire population, solutions not dominated by any other solution are selected to form a non-dominated solution set. Furthermore, crowding distance is used to sort the non-dominated solutions to maintain population diversity and prevent the algorithm from getting stuck in local optima during convergence.

[0065] Furthermore, determining Pareto dominance depends on the accuracy of the objective function and the strictness of the constraints. For example, calculating the electricity cost objective requires considering pump efficiency. ,flow Yangcheng Length of time period and electricity price The target number of start-stop cycles depends on the operating status of the pump unit in adjacent time periods. The difference is calculated. In practical applications, this step is embedded in the iterative optimization process of the improved cuckoo search algorithm to update the elite solution set, ensuring that the population evolves towards the Pareto front, thereby achieving synergistic optimization of economy and stability in cascade pumping station systems. This method effectively improves the convergence speed and solution quality of multi-objective optimization, providing a scientific basis for scheduling decisions in complex hydraulic systems.

[0066] S4. After the iteration terminates, the optimal operating scheme that meets the requirements of economy and safety is selected and output based on Pareto multi-objective evaluation.

[0067] Specifically, after the iteration terminates, this step, based on the Pareto multi-objective evaluation mechanism, filters and ranks all candidate operating schemes in the population, ultimately outputting the optimal operating scheme that simultaneously satisfies the requirements of economy and safety. This step is the key decision-making link in the entire optimization scheduling method, and its technical implementation relies on the concept of Pareto Optimality in multi-objective optimization theory. Through non-dominated sorting and crowding calculation, it achieves efficient solution set screening for high-dimensional, nonlinear, and multi-constraint optimization problems.

[0068] Specifically, this step first performs a multi-objective fitness evaluation on the population solution set obtained by jointly solving the upper-level head distribution model and the lower-level single-pump station operation optimization model. Specifically, each solution vector... Head distribution values ​​for K pump stations and the operating speed of pump set J during the T time periods. Its fitness function consists of two objectives: one is the total operating electricity cost. Secondly, the number of pump start-ups and shutdowns. These two objectives correspond to the following formulas:

[0069]

[0070] in, This indicates the electricity cost for operating a single pumping station. This represents the cumulative change in the number of pump start-ups and shutdowns. Using Pareto dominance, the system performs a non-dominated sort of the solution set, dividing it into multiple leading edge layers and prioritizing solutions with stronger dominance. Simultaneously, crowding distance calculation is introduced to assess the distribution density of solutions in the target space, preventing the solution set from becoming too concentrated and thus improving the diversity and uniformity of solution distribution.

[0071] Furthermore, the number of levels in non-dominated sorting is typically no more than 5 to ensure the interpretability and practicality of the solution set; the weighting coefficients for crowding calculation can be adjusted according to the relative importance of the objective function, for example, when emphasizing economy, they can be appropriately reduced. The weights are determined by the number of solutions. Furthermore, the elite solution set size can be set to 50-100 during the screening process to balance computational efficiency with solution coverage.

[0072] Specifically, in practical applications, this step is mainly used in long-distance water transfer systems such as the South-to-North Water Diversion Project (Eastern Route) to make final decisions on the operation plan of cascade pumping stations. By comprehensively considering electricity costs and equipment start-up and shutdown frequency, the operation and maintenance costs of pumping stations can be effectively reduced, the service life of equipment can be extended, and the hydraulic risks caused by channel water level fluctuations can be mitigated.

[0073] Specifically, this step enables solution set selection and decision support for multi-objective optimization problems, ensuring that the output solution achieves an optimal balance between economy and safety. Compared to traditional single-objective optimization methods, this method can provide multiple Pareto optimal solutions for dispatchers to choose from, enhancing the flexibility and robustness of the dispatching scheme and significantly improving the operating efficiency and stability of the cascade pumping station system.

[0074] Furthermore, S4 includes: S41, a new candidate solution is generated using the Lévy flight strategy, as shown in the following formula: ; ; in, For the new solution vector, This is the current solution vector. For step size parameters, Let Lévy distribution function be used. For gamma function, These are the distribution parameters.

[0075] Specifically, in the improved cooperative optimization scheduling method of the Cuckoo Search algorithm, generating new candidate solutions through the Lévy Flight strategy is a key step in enhancing the algorithm's global search capability and convergence performance. This strategy is based on the random walk mechanism of Lévy Flight, whose step size follows the Lévy Distribution. It can organically combine long-distance jumps in the solution space with local fine-grained search, thereby effectively avoiding the algorithm from getting trapped in local optima and improving optimization efficiency.

[0076] In its implementation, the step size update formula for Levy's flight is: ; in, Indicates the first The middle generation The solution vector for each bird's nest. For its in the The new position of the era; This is the step size control parameter, used to adjust the scale of the search step. It is usually set according to the size of the search space of the problem, and the value range is [0.1, 1.0]. It is the Lévy distribution function, and its mathematical expression is: ; in, This is a distribution parameter, typically taking values ​​within... Between these, the tail characteristics used to control the step size distribution, This refers to the gamma function. In practical applications... It is usually set to 1.5 to strike a balance between exploration and development.

[0077] Furthermore, in the optimized scheduling of cascade pumping stations, this step is used to update the combined solution vector of the upper-level head allocation and the lower-level pump group operating parameters, including the head of each level of pumping station. Operating speed of each pump unit at different times By employing the Lévy flight strategy, the algorithm can explore a wider solution space while satisfying complex constraints (such as upper and lower limits of head, water level limits, water balance, etc.), thereby improving the robustness and adaptability of the optimization model.

[0078] Specifically, this strategy, combined with the subsequent diffusion mechanism, further enhances population diversity, ensuring that the Pareto front can be effectively approximated during multi-objective optimization processes (such as minimizing operating electricity costs and the number of pump start-ups and shutdowns). Therefore, this step has significant technical value in improving optimization accuracy, accelerating convergence speed, and enhancing algorithm stability, and is one of the core technical means to achieve collaborative optimization scheduling of cascade pump station groups.

[0079] This invention discloses a multi-objective collaborative optimization scheduling method for a cascade pumping station group. By constructing a two-layer optimization model and an improved intelligent search algorithm, it effectively solves the core problems of traditional methods, such as the difficulty in balancing economy and safety, and the disconnect between optimization results and actual hydraulic conditions. This method achieves end-to-end optimization from data integration, model construction, collaborative solution to scheme selection, significantly improving the economic efficiency of system operation and the safety and reliability of scheduling schemes, and enhancing the overall operational efficiency and engineering applicability of the pumping station group under complex hydraulic coupling conditions.

[0080] Example 2 To achieve the above invention, embodiments of the present invention also provide specific steps of a multi-objective collaborative optimization scheduling method for a cascade pumping station group, such as... Figure 2 As shown, it includes: S101 acquires and integrates the basic data required for the optimization of pump station system operation, providing data support for model construction.

[0081] S102. Establish an upper-level head distribution optimization model. Based on the hydraulic coupling relationship of the system, optimize the head distribution of each pump station to minimize the total operating cost of the cascade pump station system.

[0082] S103. Establish a lower-level single pump station operation optimization model, taking into account both the goals of minimizing electricity costs and minimizing the number of pump start-ups and shutdowns. By reasonably arranging the number of pump start-ups and shutdowns, the system's electricity cost is ensured to be at its lowest.

[0083] S104 is an optimization model built upon S102 and S103. It employs an improved cuckoo search algorithm to adapt to the decision variables and constraints of the water conveyance system and perform collaborative solution.

[0084] S105, after the iteration terminates, outputs the running scheme obtained from S4, which has the best fitness in the population.

[0085] Specifically, S101 includes the following steps: S1011: Collect and organize the physical parameters of the pump set, including but not limited to key performance parameters such as design flow rate, head, efficiency curve, and speed range, as well as basic equipment information such as pump type structure and impeller diameter, and establish a physical parameter database that reflects the operating performance of the pump set under different working conditions.

[0086] S1012: Collect and organize hydraulic parameters of open channels, including but not limited to hydraulic elements such as channel bottom elevation, channel longitudinal slope, side slope coefficient, roughness coefficient, and cross-sectional shape, and construct a basic parameter system for open channel flow simulation and hydraulic loss calculation.

[0087] S1013: Collect and organize operational constraint parameters, mainly including the electricity price division and price level of each time period in the time-of-use electricity pricing policy, the time period division of the dispatch cycle and the daily water demand of each level of pumping station, the water level limit of the inlet and outlet pools, the reservoir capacity-water level relationship curve, etc., to provide external boundary and operating condition inputs for the optimization model.

[0088] Specifically, S102 includes the following steps: S1021: Establish an unsteady flow model to dynamically calculate the head loss caused by changes in water flow.

[0089] S1022: Based on the hydraulic coupling characteristics of the cascade pumping station system, establish the head distribution values ​​for each pumping station. It serves as the core decision variable to coordinate the operating conditions of each pumping station within the system.

[0090] S1023: Based on the principle of minimizing the total system operating cost, an optimization function is established with the objective of minimizing the total power consumption cost of the cascade pumping stations, where K is the total number of pumping stations and T is the number of time periods within the scheduling cycle. It is the power (kW) of the kth pump station in time period t. It is the pumping flow rate (m³ / s) of the k-th pumping station in time period t. 3 / s), The electricity price (yuan / kWh) for time period t is given by the following formula: .

[0091] S1024: Based on the hydraulic dynamic response characteristics of the water conveyance system of the South-to-North Water Diversion East Route Project, system, hydraulic and operational constraints are introduced.

[0092] Specifically, S1021 includes the following steps: S10211: Simulates the temporal and spatial variations of water flow using the Saint-Venant equation, where h(x,t) is the water level (m) and Q(x,t) is the flow rate (m³). 3 / s), the formula is as follows: .

[0093] S10212: Calculate the channel head loss, where Q is the flow rate (m³ / s). 3 / s), A is the cross-sectional area of ​​the channel (m²) 2 R is the hydraulic radius (m), and n is the Manning coefficient, which reflects the channel roughness. The formula is as follows: .

[0094] S10213: Calculate the head, where It is the head (m) of the k-th pump station. and These are the water levels (m) in the pump station's inlet and outlet pools, respectively. The head loss (m) is given by the following formula: .

[0095] Specifically, S1024 includes the following steps: S10241: Head constraint for cascade pumping stations. The head (m) of the kth pump station; and These are the water levels of the outlet pool of the final pumping station and the inlet pool of the first pumping station, respectively. The head loss (m) between the k-th pumping station and the (k+1)-th pumping station is given by the following formula: .

[0096] S10242: Head constraint for a single pumping station. , Let be the minimum and maximum head of the k-th pumping station, respectively, and the formula is as follows: .

[0097] S10243: Water level constraint on the inlet and outlet sides. , These are the water levels (m) on the inlet and outlet sides of the k-th pumping station, respectively. , These are the minimum and maximum water levels (m) on the inlet side of the k-th pumping station, respectively. , Let be the minimum and maximum water levels (m) at the outlet side of the k-th pumping station, respectively, as shown in the following formula: ; .

[0098] S10244: Water balance constraint. Let m be the water volume (m) of the reservoir at the previous time n+1. 3 ); Let m be the water volume (m³) of the reservoir at the current time n. 3 ); The inflow volume of the pool during this period (m³) 3 ); The outflow of water from the pool during this period (m³) 3 The formula is as follows: .

[0099] Specifically, S103 includes the following steps: S1031: Define the model decision variables: the number of pump units in operation for each time period t within the scheduling cycle. and the operating speed of each pump unit As a core decision variable, it represents the real-time operating status of the pumping station.

[0100] S1032: Define the multi-objective function of the model and establish a dual-objective optimization function that takes into account both economy and stability.

[0101] S1033: To achieve the two objectives in S302, the following constraints are required during the operation of the pumping station: total water lifting capacity, output power of the motor, rated speed of the pump set, and design flow rate of a single pump.

[0102] Specifically, S1032 includes the following steps: S10321: Minimum target for electricity consumption for water lifting from a single pumping station, aiming to fully utilize time-of-use pricing to reduce operating costs, as shown in the following formula: .

[0103] S10322: The goal is to minimize the number of pump start-ups and shutdowns. This is achieved by reducing start-up and shutdown operations to decrease equipment mechanical wear and the risk of channel hydraulic scouring, thereby improving operational reliability. The formula is as follows: .

[0104] Specifically, S1033 includes the following steps: S10331: Total Water Diversion Constraint. Ensure that the total water diversion volume within the scheduling cycle meets the planned requirements, of which... Let the operating flow rate (m³) of the j-th pump unit during time period t be... 3 / s); N t This represents the number of pump units operating within time period t. The duration is in hours (h). The formula for the total water demand is as follows: .

[0105] S10332: Motor output power constraint. Ensure that the operating efficiency of each pump unit does not exceed the rated capacity of its matching motor. Let be the shaft power (kW) of the j-th pump unit during time period t; The rated maximum output power (kW) of the motor equipped with this pump set is given by the following formula: .

[0106] S10333: Pump unit rated speed constraint. This restricts the operating speed of each pump unit within the permissible range, where... Let be the operating speed (r / min) of the j-th pump unit during time period t; , These are the minimum and maximum allowable operating speeds of the pump unit, respectively, as shown in the following formula: .

[0107] S10334: Single pump design flow constraint. This prevents a single pump from operating beyond its design flow rate, ensuring equipment safety. The upper limit of the design flow rate of the j-th pump unit (m³) 3 / s), the formula is as follows: .

[0108] Specifically, S104 includes the following steps: S1041: Initialize the bird flock, randomly generate N bird nests, and the location vector of each bird nest is shown in the following formula, where... For the k-th level pumping station, Let be the rotational speed of the j-th pump unit during time period t.

[0109] .

[0110] S1042: The upper-level model (such as...) Figure 2 The head distribution scheme (as shown) is input into the lower-level single-pump station operation optimization model (such as...). Figure 3 The solution is obtained by solving the upper-level scheme (as shown in the figure). Each upper-level scheme will generate a set of lower-level pump station operation schemes to ensure that the multi-objective optimization requirements of each pump station are met.

[0111] S1043: Determine whether the conditions for termination, such as reaching the maximum number of iterations or the fitness value converging to a preset value, are met. If the conditions are met, terminate the iteration; otherwise, return to S402 to continue iterative optimization.

[0112] Specifically, S1042 includes the following steps: S10421: The Cuckoo Search algorithm primarily generates new candidate scheduling schemes through Lévy flight. Lévy flight is a special stochastic search mode whose step size follows the Lévy distribution. By using a small number of longer jump step sizes and a large number of shorter step sizes, the algorithm can perform a fine search near the current solution while also having a certain probability of escaping the local optimum. This indicates the new position of the new solution i in the (t+1)th generation. It is the solution vector of the i-th bird's nest in the t-th generation. It is the step size control parameter; It is the Lévy distribution. The value is usually between (1, 3). It is the gamma function. The generation of new candidate scheduling schemes follows the formula as follows: ; .

[0113] S10422: To address the issue of traditional cuckoo search algorithms potentially missing some high-quality solutions, a diffusion mechanism is used to enhance the algorithm's global exploration capability. This is achieved by applying Gaussian perturbations near the current optimal solution, generating diverse new candidate solutions. For new candidate scheduling schemes generated through the diffusion strategy, This represents generating a random matrix that follows a Gaussian distribution, where B is the current global optimal position. These are random numbers that follow a normal distribution, and the formula is as follows: .

[0114] S10423: Perform multi-objective fitness evaluation on the generated candidate solutions, calculating the total operating cost and the number of pump start-ups and shutdowns. Pareto dominance is used for solution selection: if a new solution is superior to the original solution in at least one objective and not inferior in others, then the new solution is said to dominate the original solution. Based on non-dominated ranking and crowding calculation, an elite solution set is maintained to ensure the population evolves towards the Pareto front.

[0115] S10424: Population update and inferior solution elimination mechanism, based on a preset discovery probability. The nest with the worst fitness is eliminated, and a new solution is generated randomly to maintain population diversity, where r is a random number in the range [0,1]. The formula is as follows: .

[0116] This invention discloses a multi-objective collaborative optimization scheduling method for a cascade pumping station group. By constructing a two-layer model for collaborative optimization of upper-level head allocation and lower-level individual station operation, combined with an improved intelligent search algorithm, it effectively solves the core problems of traditional methods, such as the difficulty in balancing economy and safety, and the disconnect between optimization results and actual hydraulic conditions. It achieves end-to-end optimization from data integration, model construction, collaborative solution to scheme decision-making, significantly improving the economic efficiency and scheduling safety and reliability of the system, and providing reliable technical support for the efficient and stable operation of cascade pumping station groups under complex hydraulic coupling conditions.

[0117] Example 3 This invention also provides a multi-objective collaborative optimization scheduling device 10 for a cascade pumping station group, such as... Figure 5 As shown, the device includes: The data integration module 100 is used to acquire and integrate the physical parameters, open channel hydraulic parameters and operational constraint parameters of the pumping station system, and to construct the input data of an optimization model that includes pump set performance, channel dynamic characteristics and scheduling boundary conditions.

[0118] Specifically, by collecting the efficiency curves, speed ranges, and impeller diameter parameters of the pump sets, a multi-dimensional pump set performance database is established to support the simulation of operating performance under different working conditions; the roughness, cross-sectional shape, and slope coefficient parameters of the channel are dynamically integrated into the hydraulic parameter system for real-time calculation of channel head loss and water level fluctuations.

[0119] The two-layer model construction module 200 is used to train a two-layer optimization model using the input data. The upper-layer model optimizes the head allocation based on the hydraulic coupling relationship of the cascade pumping stations to minimize the total operating cost, while the lower-layer model optimizes the operating parameters of a single pumping station through multi-objective functions to minimize electricity costs and the number of pump start-ups and shutdowns.

[0120] Specifically, the spatiotemporal variations of water flow are simulated using the Saint-Venant equation, and the channel head loss is calculated using the Manning formula, as follows: ; ;in, For water level, For traffic, The cross-sectional area is... For hydraulic radius, This is the Manning coefficient.

[0121] The improved cuckoo search algorithm solution module 300 is used to collaboratively solve the bi-layer optimization model using the improved cuckoo search algorithm. The algorithm integrates the Levy flight strategy and diffusion mechanism, and iteratively and dynamically balances the global exploration and local fine search.

[0122] Specifically, non-dominated solutions are screened using the Pareto dominance relation, as shown in the following formula: ; ;in, Total operating costs, This refers to the number of times the pump unit starts and stops. For the density of water, It is the acceleration due to gravity. For traffic, For Yang Cheng, For rotational speed, The duration is the length of the time period. For electricity prices.

[0123] The Pareto evaluation output module 400 is used to screen and output the optimal operating scheme that meets the requirements of economy and safety based on Pareto multi-objective evaluation after the iteration terminates.

[0124] Specifically, new candidate solutions are generated using the Lévy flight strategy, as shown in the following formula: ; ;in, For the new solution vector, This is the current solution vector. For step size parameters, Let Lévy distribution function be used. For gamma function, These are the distribution parameters.

[0125] Specifically, a multi-objective collaborative optimization scheduling device for a cascade pumping station group according to an embodiment of the present invention further includes: a simulated annealing strategy module, used to introduce a simulated annealing strategy, which accepts non-dominated solutions with probability during the iteration process, as shown in the following formula: ;in, A random number in the range [0,1]. and This is a random solution vector in the current population, used to enhance the algorithm's ability to escape local optima.

[0126] This invention discloses a multi-objective collaborative optimization scheduling device for a cascade pumping station group. By constructing a system architecture that integrates data integration, two-layer model building, intelligent algorithm solving, and multi-objective evaluation, it effectively solves the technical challenge of coordinating economic objectives with operational safety in traditional scheduling devices. The device achieves fully automated processing from parameter acquisition, model training, collaborative solving to scheme decision-making, significantly improving the economic benefits and system safety stability of the cascade pumping station group. It provides efficient hardware support and decision-making assurance for the optimized scheduling of pumping station groups under complex hydraulic coupling conditions.

[0127] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0128] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0129] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

Claims

1. A multi-objective collaborative optimization scheduling method for a group of cascade pumping stations, characterized in that, include: S1: Obtain and integrate the physical parameters, open channel hydraulic parameters, and operational constraint parameters of the pumping station system to construct the input data for an optimization model that includes pump set performance, channel dynamic characteristics, and scheduling boundary conditions. S2, using the input data to train a two-layer optimization model; wherein, the upper-layer model optimizes the head allocation based on the hydraulic coupling relationship of the cascade pumping stations to minimize the total operating cost, and the lower-layer model optimizes the operating parameters of a single pumping station through multi-objective functions to minimize the electricity cost and the number of pump start-ups and shutdowns. S3 employs an improved cuckoo search algorithm to collaboratively solve the bi-layer optimization model. The algorithm integrates the Levy flight strategy and diffusion mechanism, achieving iterative dynamic balance between global exploration and local fine-grained search. S4. After the iteration terminates, the optimal operating scheme that meets the requirements of economy and safety is selected and output based on Pareto multi-objective evaluation.

2. The method as described in claim 1, characterized in that, S1 includes: S11 establishes a multi-dimensional pump set performance database by collecting pump set efficiency curves, speed ranges, and impeller diameter parameters to support performance simulation under different operating conditions. S12 dynamically integrates the channel roughness, cross-sectional shape, and slope coefficient parameters into the hydraulic parameter system for real-time calculation of channel head loss and water level fluctuations.

3. The method as described in claim 1, characterized in that, S2 includes: S21, the spatiotemporal variation of water flow is simulated using the Saint-Venant equation, and the channel head loss is calculated using the Manning formula, as follows: ； ； in, For water level, For traffic, The cross-sectional area is... For hydraulic radius, This is the Manning coefficient.

4. The method as described in claim 1, characterized in that, S3 includes: S31, non-dominated solutions are selected using the Pareto dominance relation, as shown in the following formula: ； ； in, Total operating costs, This refers to the number of times the pump unit starts and stops. For the density of water, It is the acceleration due to gravity. For traffic, For Yang Cheng, For rotational speed, The duration is the length of the time period. For electricity prices.

5. The method as described in claim 1, characterized in that, S4 includes: S41, a new candidate solution is generated using the Lévy flight strategy, as shown in the following formula: ； ； in, For the new solution vector, This is the current solution vector. For step size parameters, Let Lévy distribution function be used. For gamma function, These are the distribution parameters.

6. The method as described in claim 1, characterized in that, include: S5 introduces a simulated annealing strategy, which accepts non-dominated solutions with probability during the iteration process, as shown in the following formula: ； in, A random number in the range [0,1]. and This is a random solution vector in the current population, used to enhance the algorithm's ability to escape local optima.

7. A multi-objective collaborative optimization scheduling device for a cascade pumping station group, characterized in that, include: The data integration module is used to acquire and integrate the physical parameters, open channel hydraulic parameters, and operational constraint parameters of the pumping station system, and to construct the input data for an optimization model that includes pump set performance, channel dynamic characteristics, and scheduling boundary conditions. A two-layer model construction module is used to train a two-layer optimization model using the input data. The upper-layer model optimizes the head allocation based on the hydraulic coupling relationship of the cascade pumping stations to minimize the total operating cost, while the lower-layer model optimizes the operating parameters of a single pumping station through multi-objective functions to minimize electricity costs and the number of pump start-ups and shutdowns. An improved cuckoo search algorithm solution module is used to collaboratively solve a two-layer optimization model using the improved cuckoo search algorithm. The algorithm integrates the Levy flight strategy and diffusion mechanism, and iteratively and dynamically balances global exploration and local fine search. The Pareto evaluation output module is used to select and output the optimal operating scheme that meets the requirements of economy and safety based on Pareto multi-objective evaluation after the iteration terminates.

8. The apparatus as claimed in claim 7, characterized in that, The data integration module is also used for: By collecting the efficiency curves, speed ranges, and impeller diameter parameters of the pump sets, a multi-dimensional pump set performance database is established to support the simulation of operating performance under different working conditions. The roughness, cross-sectional shape, and slope coefficient parameters of the channel are dynamically integrated into the hydraulic parameter system for real-time calculation of channel head loss and water level fluctuations.

9. The apparatus as claimed in claim 7, characterized in that, The two-layer model construction module is also used for: The spatiotemporal variations of water flow are simulated using the Saint-Venant equation, and the channel head loss is calculated using the Manning formula, as follows: ； ； in, For water level, For traffic, The cross-sectional area is... For hydraulic radius, This is the Manning coefficient.

10. The apparatus as claimed in claim 7, characterized in that, The improved cuckoo search algorithm solution module is also used for: The non-dominated solutions are selected using the Pareto dominance relation, as shown in the following formula: ； ； in, Total operating costs, This refers to the number of times the pump unit starts and stops. For the density of water, It is the acceleration due to gravity. For traffic, For Yang Cheng, For rotational speed, The duration is the length of the time period. For electricity prices.

11. The apparatus as claimed in claim 7, characterized in that, The Pareto evaluation output module is also used for: New candidate solutions are generated using the Lévy flight strategy, as shown in the following formula: ； ； in, For the new solution vector, This is the current solution vector. For step size parameters, Let Lévy distribution function be used. For gamma function, These are the distribution parameters.

12. The apparatus as claimed in claim 7, characterized in that, Also includes: The simulated annealing strategy module is used to introduce a simulated annealing strategy, which accepts non-dominated solutions with probability during the iteration process, as shown in the following formula: ； in, A random number in the range [0,1]. and This is a random solution vector in the current population, used to enhance the algorithm's ability to escape local optima.

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