Cascade hydropower station short-term optimization scheduling method and application

Abstract

The invention discloses a cascade hydropower station short-term optimization scheduling method and application, and the method comprises the following steps: 1, constructing a cascade hydropower station scheduling model, and setting a target and a constraint condition; 2, initializing model parameters, and generating an initial scheduling scheme; step 3, based on a natural selection enhancement strategy, performing first optimization on the initial scheduling scheme by adopting a genetic algorithm to obtain a genetic optimization cascade hydropower station scheduling scheme; and 4, carrying out secondary optimization on the genetic optimization cascade hydropower station scheduling scheme by adopting an adaptive weight particle swarm algorithm to obtain an optimal scheduling scheme. According to the method, the generating capacity is effectively improved, the abandoned water amount is reduced, the stability of the scheduling scheme is remarkably improved, and an efficient and reliable intelligent optimization method is provided for short-term optimization scheduling of cascade hydropower stations.

Description

Technical Field

[0001] This application relates to the technical field of hydropower dispatching, and specifically provides a method for short-term optimal dispatching of cascade hydropower stations. Background Art

[0002] The short-term optimal dispatching of cascade hydropower stations is the core issue of the coordinated operation of water conservancy projects and power systems, and its goal is to balance multiple constraints such as power generation benefits, carbon emission control, and ecological flow guarantee. Traditional methods mostly use linear programming or dynamic programming, but in the face of complex non-linear and multi-objective coupling scenarios, there are defects such as the explosion of the solution space dimension and the lag of dynamic response. In recent years, intelligent optimization algorithms (such as genetic algorithm GA, particle swarm optimization PSO) have been introduced into this field due to their global search ability, but still face the following challenges:

[0003] Traditional intelligent optimization algorithms (such as standard PSO, GA) need a large number of iterations to approach the global optimal solution in the cascade hydropower station dispatching scenario. For the cascade dispatching method based on PSO, the number of iterations generally exceeds 500 times, and the convergence speed is significantly affected by the quality of the initial population, resulting in an increase in calculation time and difficulty in meeting the real-time requirements of short-term dispatching. Although the improved NSGA-II algorithm introduces crowding degree sorting, the scale of the non-dominated solution set expands due to multi-objective conflicts, further prolonging the iteration cycle. Summary of the Invention

[0004] According to one aspect of this application, a method for short-term optimal dispatching of cascade hydropower stations is provided to improve the short-term dispatching efficiency of cascade hydropower stations, reduce water waste, increase power generation, and ensure the stable operation of the power grid.

[0005] A method for short-term optimal dispatching of cascade hydropower stations in this application includes the following steps:

[0006] Step 1: Construct a cascade hydropower station dispatching model, and set goals and constraint conditions;

[0007] Step 2: Initialize the model parameters and generate an initial dispatching plan;

[0008] Step 3: Based on the natural selection enhancement strategy, use the genetic algorithm to perform the first optimization on the initial dispatching plan to obtain a genetically optimized cascade hydropower station dispatching plan;

[0009] Step 4: Perform secondary optimization on the genetically optimized cascade hydropower station dispatching plan using the adaptive weight particle swarm optimization algorithm to obtain the optimal dispatching plan.

[0010] Optionally, the goal of the cascade hydropower station dispatching model is to maximize the total power generation E of the cascade hydropower station total :

[0011]

[0012] where k k is the power generation efficiency of the k-th power station;

[0013] A k is the output coefficient of the k-th power station;

[0014] q k is the power generation flow rate of the k-th power station in period j, m 3 / s;

[0015] h k is the average head of the k-th power station, m;

[0016] t is the duration, s.

[0017] Optionally, the constraint conditions at least include a reservoir capacity constraint condition, a flow rate constraint condition, and a water volume-flow rate balance constraint condition.

[0018] Optionally, step 3 includes:

[0019] 3.1 Calculate the fitness value of each scheduling plan under the cascade hydropower station scheduling model using a genetic algorithm;

[0020] 3.2 Obtain a preliminary genetically optimized cascade hydropower station scheduling plan through several cycles of selection operations, crossover operations, and mutation operations based on the fitness value;

[0021] 3.3 Re-optimize the preliminary genetically optimized cascade hydropower station scheduling plan using a natural selection enhancement strategy;

[0022] 3.4 Update the scheduling plan population, and repeat steps 3.2 - 3.3 until the optimization termination condition is reached to obtain a genetically optimized cascade hydropower station scheduling plan.

[0023] Optionally, the natural selection enhancement strategy is:

[0024] Retain the scheduling plans with high fitness values in the preliminary genetically optimized cascade hydropower station scheduling plan, sort the contemporary scheduling plan population according to the fitness values of these plans, and perform selection on the contemporary scheduling plan population based on the elite retention mechanism.

[0025] Optionally, the elite retention mechanism is: sort the contemporary scheduling plan population in descending order according to the fitness value, and cover the latter 50% of the inferior generation population with the former 50% of the high-quality population.

[0026] Optionally, the adaptive weight particle swarm optimization algorithm refers to replacing the inertia weight in the original particle swarm optimization algorithm with a dynamic adaptive weight w i as shown in the following formula:

[0027]

[0028] Among them, F i is the fitness value of particle i; F avg is the average fitness value of the population; w1 = 0.95, w2 = 0.6.

[0029] Optionally, step 4 further includes: introducing Gaussian perturbation in the adaptive weight particle swarm optimization algorithm.

[0030] On the other hand, the present application provides a visual digital twin scheduling platform for hydraulic scheduling based on the above short-term optimal scheduling method for cascade hydropower stations.

[0031] The beneficial effects that the present application can produce include: compared with traditional hydropower scheduling methods, the method of the present application has the advantages of fast convergence speed, high optimization accuracy, and adaptability to complex hydropower systems. NSE-GA improves the evolutionary quality of the genetic algorithm, making it more likely to converge under complex constraints, while AW-PSO enhances the global search ability by dynamically adjusting weights. Simulation experiments show that the method of the present application effectively improves the power generation, reduces the water abandonment volume, and significantly improves the stability of the scheduling scheme, providing an efficient and reliable intelligent optimization method for the short-term optimal scheduling of cascade hydropower stations. Description of the Drawings

[0032] Figure 1 is a schematic flow chart of the method of the present application;

[0033] Figure 2 is a simulation diagram of the power generation of a hydropower station under different iteration times of the method of the present application;

[0034] Figure 3 is a simulation diagram of the iteration efficiency of different optimization algorithms under the same total power generation;

[0035] Figure 4 is a comparison diagram of the historical and optimized power generation of Mamaya Hydropower Station for six consecutive weeks in the embodiment of the present application;

[0036] Figure 5 is a trend diagram of the change of two key efficiency indicators during the optimization process of Mamaya Hydropower Station in the embodiment of the present application;

[0037] Figure 6 is a bubble diagram of the average head, optimization improvement percentage and average flow of Mamaya Hydropower Station in the embodiment of the present application;

[0038] Figure 7 is an optimized effect diagram of the cascade scheduling of Mamaya Hydropower Station in the embodiment of the present application;

[0039] Figure 8 is an optimized analysis diagram of the water consumption rate of Mamaya Hydropower Station in the embodiment of the present application;

[0040] Figure 9 This is a radar chart for evaluating the optimization effect of Mamaya Hydropower Station in the embodiments of this application. Specific implementation manners

[0041] The following describes this application in detail with reference to the embodiments, but this application is not limited to these embodiments.

[0042] A method for short-term optimal scheduling of cascade hydropower stations in this application, the method includes the following steps:

[0043] Step 1, construct a mathematical model for the scheduling of cascade hydropower stations

[0044] Based on hydrological forecast data, the operating characteristics of cascade hydropower stations, and peak regulation requirements, establish a scheduling target model and optimize the model to enable the hydropower station group to achieve optimal operation in the short term and achieve goals such as efficient power generation, reduction of water abandonment, and meeting the grid scheduling requirements.

[0045] This application takes the total power generation E of the cascade hydropower stations total as the goal and establishes the following model:

[0046]

[0047] where k k is the power generation efficiency of the kth power station;

[0048] A k is the output coefficient of the kth power station;

[0049] q k is the power generation flow rate of the kth power station in period j, m 3 / s;

[0050] h k is the average head of the kth power station, m;

[0051] t is the duration, s.

[0052] The target optimization includes: improving the overall power generation efficiency of the hydropower station group to maximize the power generation power per unit of water volume; reducing the water abandonment rate, that is, making full use of the incoming water for power generation as much as possible to reduce unnecessary water resource waste; ensuring that the water level of the reservoir is within a reasonable range to ensure operation safety and avoid risks brought by extreme water levels at the same time; smoothing the output change, reducing the frequent start and stop of units, improving the equipment life, and ensuring the stable operation of the power grid.

[0053] Some series of constraint conditions need to be considered during the optimization process:

[0054] ① Storage capacity constraint condition: The water storage volume of the reservoir needs to be within a safe range to ensure that the water storage volume of the reservoir is reasonable in different time periods and conforms to the actual basin hydrological conditions.

[0055] V min,k ≤V k (j) ≤ V max,k

[0056] where V k (j) is the water volume of the k-th reservoir at time j; V min,k is the minimum allowable water volume of the k-th reservoir; V max,k is the maximum allowable water volume of the k-th reservoir.

[0057] ② Discharge flow constraint: The power generation flow is limited by the unit capacity to ensure that the output of the unit is within the allowable range, neither overloaded nor operating in an ineffective state.

[0058] q min,k ≤ q k (j) ≤ q max,k

[0059] where q k (j) is the average inflow and outflow discharge of the k-th reservoir at time j, i.e., the power generation flow; q min,k is the minimum allowable discharge of the k-th reservoir; q max,k is the maximum allowable discharge of the k-th reservoir.

[0060] ③ Water volume - flow balance constraint: The relationship between the water volume of the reservoir changing with time ensures that the water level of the reservoir is within the allowable range, which can not only ensure the power generation efficiency of the unit but also not affect the flood control safety.

[0061] V k (j + 1) = V k (j) + (I k (j) - q k (j)) · t

[0062] where V k (j + 1) is the water volume of the k-th reservoir at time j + 1; I k (j) is the average inflow of the k-th reservoir at time j.

[0063] In addition, the following constraint relationships are also involved:

[0064] Head - storage relationship, used to convert the water level measurement value into storage V(H) for water volume balance calculation: V(H) = aH 2 + bH + c, where a, b, and c are fitting coefficients obtained by regression of hydrological data; H is the current water level, i.e., the head.

[0065] Calculation of the water discharge S k (j), when the reservoir is full, the excess water is discharged through the flood discharge channel and not included in the power generation benefit: Sk V(j) = max(V k (j) + (I k (j) - q k (j))t - V max，k , 0).

[0066] Multi - level power station coupling constraint. The inflow of the downstream power station V2 includes the water abandonment volume S1 and the power generation flow q1 of the upstream power station, reflecting the hydraulic connection of cascade power stations: V2(j + 1) = V2(j) + [I2(j) - q2(j) + S1(j) + q1(j)]t.

[0067] Step 2: Collect and organize the hydrological parameters of the power station group and the basic parameters of the cascade hydropower stations, set the initial conditions of the optimization algorithm, and randomly generate an initial scheduling plan.

[0068] The hydrological parameters include key information such as upstream water inflow, downstream water discharge, and initial reservoir water level;

[0069] The basic parameters of the cascade hydropower stations include the number of units, minimum and maximum output, conversion efficiency, etc. of each hydropower station;

[0070] The initial conditions of the optimization algorithm include parameters such as population size, maximum number of iterations, and convergence accuracy.

[0071] Step 3: Use the genetic algorithm based on natural selection enhancement strategy (NSE - GA) to optimize the plan.

[0072] 3.1 Calculate the fitness value of each scheduling plan respectively with power generation efficiency, water abandonment rate, and water level safety as indicators;

[0073] 3.2 Perform genetic operations on the initial scheduling plan: Select the individuals participating in reproduction through the selection mechanism to form an intermediate population.

[0074] 3.3 Perform crossover operations on some strategies of the plan obtained in step 3.2 to explore new possibilities;

[0075] 3.4 Randomly adjust some parameters of certain plans obtained in step 3.3 to increase population diversity and prevent falling into local optimal solutions.

[0076] 3.5 Combine the natural selection enhancement strategy, select excellent plans and retain the plans with high fitness values, and eliminate the plans with low fitness values:

[0077] Retain the plans with high fitness values in the preliminary genetic optimization of the cascade hydropower station scheduling plan, sort the contemporary scheduling plan population based on the fitness values of the retained plans, and perform selection on the contemporary scheduling plan population based on the elite retention mechanism.

[0078] The elite retention mechanism is as follows: Sort the contemporary scheduling plan population in descending order according to the fitness value, and use the top 50% of the high-quality population to cover the bottom 50% of the inferior population.

[0079] Through this step, the evolution ability of excellent individuals can be enhanced, individuals with high fitness can be preferentially retained, and the convergence speed of the algorithm can be accelerated; moreover, multiple optimization objectives can be comprehensively considered, rather than only focusing on the power generation, improving the overall rationality of the plan; at the same time, through the elite retention mechanism, it can be ensured that the current optimal scheduling plan will not be destroyed by genetic operations, thus improving the stability of the algorithm.

[0080] 3.6 Update the scheduling plan population, and repeat the operations in 3.2 - 3.5 above until the optimization termination condition is reached.

[0081] Step 4: Further optimize the above plan by using the Adaptive Weight Particle Swarm Optimization (AW-PSO) algorithm.

[0082] Adjust the weight in the particle swarm algorithm to a dynamic adaptive weight:

[0083] The particle velocity iteration formula of the standard Particle Swarm Optimization (PSO) algorithm is:

[0084] v new = w·v old + c1r1(P best - q)+ c2r2(G best - q)

[0085] In the formula, v new is the updated particle velocity; w is the inertia weight; v old is the particle velocity before update; P best is the historical best position of the particle; G best is the historical best position of the group; c1, c2 are acceleration factors; r1, r2 are random numbers between 0 and 1, and q is the current position of the particle.

[0086] Among them, the inertia weight w is a fixed value, but as the number of iterations increases, the solution details of the problem will also change, and the fixed value will bring defects to solving the problem. Therefore, this application introduces a dynamic adaptive weight w i , as shown in the following formula:

[0087]

[0088] Among them, F i is the fitness value of particle i; F avg is the average fitness value of the population; w1 = 0.95, w2 = 0.6.

[0089] Dynamic adaptive weight representation: When the particle performance is lower than the average, the weight increases linearly according to the deviation degree to strengthen the global search; when the particle performance is higher than the average, the maximum weight is maintained to avoid premature convergence.

[0090] By dynamically adjusting the weight parameters, the exploration and exploitation capabilities of different individuals can be automatically adjusted during the search process, ensuring that both the global optimal solution can be found and the search efficiency can be improved.

[0091] 4.1 Initialize the particle swarm

[0092] Based on the optimization scheme in step 3, generate multiple different scheduling schemes as particle individuals.

[0093] 4.2 Calculate the fitness value of each particle and record the current optimal scheduling scheme;

[0094] 4.3 Update the velocity and position of the particles

[0095] Adjust the movement trajectory of the particles according to the quality of the current solution to make it gradually approach the optimal solution, that is, the optimal scheduling.

[0096] 4.4 Randomly introduce Gaussian perturbations to the parameters of some particles to improve the global search ability by introducing random mutations;

[0097] 4.5 Repeat steps 4.3 - 4.4 until the termination condition is met.

[0098] The termination condition can be any one of the following: reaching the maximum number of iterations, the optimization result converges, or the scheduling requirements are met;

[0099] The optimization result converges means that when the improvement amplitude of the optimization scheme is less than a certain set threshold after continuous multiple iterations, it is considered that the optimal solution has been reached.

[0100] The scheduling requirements are met means that a certain scheduling scheme has met all the operation constraints and the optimization goal has reached the expectation.

[0101] Step 5: Select the optimal scheme obtained during the optimization process as the final scheduling scheme for the short-term scheduling of cascade hydropower stations, and output the results for actual operation.

[0102] This application is based on a hybrid intelligent optimization strategy (abbreviated as NSE-GA-AW-PSO) that combines the natural selection enhanced genetic algorithm (NSE-GA) and the adaptive weight particle swarm optimization (AW-PSO), and has the advantages of fast convergence speed, high optimization accuracy, and adaptability to complex hydropower systems. NSE-GA improves the evolutionary quality of the genetic algorithm, enhances the population diversity, ensures the wide distribution of the multi-objective solution set, makes it easier to converge under complex constraints, while AW-PSO improves the global search ability by dynamically adjusting the weight and avoids premature convergence.

[0103] This application also proposes a digital twin visualization management and scheduling platform based on the above method.

[0104] First, a digital twin visualization scheduling management platform built based on Vue.js and Three.js:

[0105] Vue.js is a popular front-end framework designed with the ideas of data-driven and componentization, which is easy to get started and integrate.

[0106] Three.js is a general Web 3D engine encapsulated based on native WebGL, and it can be found in various fields such as small games, product displays, Internet of Things, digital twins, smart city parks, machinery, architecture, panoramic house viewing, GIS, etc.

[0107] Through the combination of Vue.js and Three.js, a lightweight componentized design of the management platform can be implemented. Using this method for 3D scene design is a conventional method for building platforms in this field.

[0108] Secondly, drive digital twin interaction through real-time data:

[0109] Real-time access to SCADA system, meteorological API and hydrological sensor data through the WebSocket protocol, driving the dynamic update of water level, flow rate, and unit status in the 3D model, realizing the linkage between the data center and the 3D scene. For example, the change in reservoir water level is real-time mapped to the water surface elevation through Shader programming, with an error accuracy ≤ 0.1 meters.

[0110] At the same time, users can trigger the online calculation of the NSE-GA-AW-PSO algorithm by dragging the time axis or adjusting the power generation flow rate parameters, and dynamically display the power generation, carbon emissions, and ecological flow changes of different scenarios in the 3D scene. The preview process supports pausing, playback, and multi-scenario comparison, improving decision-making transparency. This makes the platform have an interactive scheduling preview function.

[0111] Select the data of a week from January 29th to February 4th, 2023 of Guangzhao - Mamaya Hydropower Station as the research objects of the first and second-level hydropower stations for short-term optimal scheduling of cascade hydropower stations, with the maximization of total power generation as the optimization goal, and conduct simulation experiments using the optimal scheduling method of this application.

[0112] 1. Compare the program operation parameters of the standard PSO algorithm (hereinafter referred to as the PSO algorithm), the AW-PSO algorithm, and the NSE-GA-AW-PSO algorithm. The results are shown in Table 1 and Figure 2 as follows:

[0113] Table 1

[0114] Parameter PSO AW-PSO NSE-GA-AW-PSO <![CDATA[Maximum weight w1]]> 0.9 0.95 0.95 <![CDATA[Minimum weight w2]]> 0.4 0.6 0.6 <![CDATA[Cross probability b c > - - 0.95 Convergence algebra 200 35-55 15-28

[0115] Note: In the standard PSO algorithm for conventional references, the number of particle swarms is relatively large (30 - 50 or more), so the number of iterative convergence generations generally exceeds 500 times. In the experiment of this application, due to the reduction of the optimization scheduling scale, only 14 dimensions were optimized (2 hydropower stations, and the tail water volume of each station for 7 time periods), so only 20 examples were used for optimization. Therefore, in this experiment, the number of iterative convergence generations of the standard PSO algorithm is less than the publicly reported data.

[0116] Meanwhile, comparing the number of iterations of different types of PSO-related algorithms for the same total power generation scheduling optimization of hydropower stations, the results are as Figure 3 shown, where GA-AW-PSO refers to the adaptive weight particle swarm optimization algorithm based on genetic operations, NSE-GA-PSO refers to the genetic particle swarm algorithm enhanced by natural selection, and NSE-AW-PSO refers to the adaptive particle swarm optimization algorithm enhanced by natural selection.

[0117] It can be seen from the above results that in the typical cascade scheduling case, the average number of iterations of the NSE-GA-AW-PSO algorithm is reduced from more than 200 times of the standard PSO algorithm to more than 20 times. After improvement, the number of iterations is reduced by more than 80%, and the standard deviation of the fitness value is reduced by 42%, indicating enhanced stability.

[0118] 2. The results of the simulation operation of the key indicators of the hydropower station after scheduling optimization using the method of this application are shown in Table 2:

[0119] Table 2

[0120] Index Before optimization After optimization Change situation Total power generation (10,000 kWh) 389.4 422.5 +8.5％ <![CDATA[Waste water volume (10,000 m 3 )]]> 76.3 53.2 -30.3％ Number of times of reservoir capacity constraint violation 5.8 0.6 -89.7％

[0121] It can be seen that if scheduling optimization is carried out using the method of this application, the total power generation will increase significantly, the water abandonment volume will be greatly reduced, and the power generation efficiency will be significantly improved.

[0122] 3. Selecting six consecutive weeks of data from the end of winter to the beginning of spring in 2023 (from the end of January to the middle of March) to optimize the scheduling of the Mamyag Hydropower Station using the method of this application, the results of the simulation operation are shown in Table 3 and Table 4:

[0123] Table 3

[0124]

[0125] Table 4

[0126] Week number Operation mode Wasted water rate (%) <![CDATA[Average water consumption rate (m 3 / kWh)]]> Efficiency improvement (%) Contribution of upstream inflow (%) 5 Base load 7.3 10.45 6.8 62.1 6 Base load 6.9 10.38 7.2 63.5 7 Base load - medium peak 6.5 10.21 7.5 64.7 8 Base load - medium peak 6.2 10.15 7.7 65.3 9 Medium peak 7.0 10.30 6.6 63.8 10 Medium peak 5.8 10.05 8.1 66.0

[0127] The research results show that after optimization, the power generation efficiency of Mamaya Hydropower Station has increased by 8.9% (average value), reaching a maximum of 9.8%, which is significantly better than the typical improvement level (3% - 8%) of the PSO algorithm reported in the literature. It can be observed that there is an obvious correlation between hydraulic parameters and power generation efficiency: as the average head increases from 15.3 meters to 16.1 meters, the power generation efficiency generally shows an upward trend, reaching a peak of 9.8% in the 10th week. This indicates that in this case, even a head difference of 0.8 meters can have a significant impact on efficiency. At the same time, the increase in average flow rate (from 512.7 m 3 / s to 548.3 m 3 / s) is positively correlated with the efficiency improvement, which reveals that the method of this application can effectively utilize the increased flow resources. During the research period, the operation mode of Mamaya Hydropower Station showed a trend of transitioning from pure base load operation to mid-peak operation. The following conclusions can be drawn:

[0128] ① The water consumption rate corresponding to the mid-peak operation mode (weeks 9 - 10) is significantly lower than that in the base load period (weeks 5 - 6), with an average decrease of 0.24 m 3 / kWh, indicating the optimization potential of the load adjustment strategy.

[0129] ② With the change of the operation mode, the water rejection rate generally shows a downward trend, from 7.3% to 5.8%, indicating that the method of this application has an optimization effect in water resource utilization.

[0130] ③ The water energy utilization rate shows a steady increase, from 92.4% to 94.1%, fully reflecting the value of the optimized dispatching method of this application.

[0131] Moreover, the data shows that the contribution of the upstream Guangzhao Power Station to the water inflow of Mamaya increases week by week (from 62.1% to 66.0%), indicating that the method of this application effectively coordinates the operation of cascade power stations. The upstream contribution rate is positively correlated with the efficiency improvement (correlation coefficient r = 0.94), emphasizing the importance of cascade coordination for the optimization effect. The simulation results show that: through the optimized dispatching method of this application, Mamaya Hydropower Station can continuously achieve an 8% - 10% increase in power generation efficiency without additional equipment investment, with significant economic benefits and practical value.

[0132] Figure 4 It shows the comparison of the historical and optimized power generation of Mamaya Hydropower Station for six consecutive weeks. The chart shows that the power generation efficiency improvement during the entire optimization process is stable between 7% - 10%, especially reaching a maximum improvement rate of 9.8% in the 10th week. From the power generation data, the historical power generation shows a weekly increasing trend, while the optimized dispatching method of this application can continuously maintain a high improvement rate, indicating good adaptability of the algorithm.

[0133] Figure 5Shows the changing trends of two key efficiency indicators during the optimization process of Mama Cliff Hydropower Station. The green line represents the water energy utilization rate, showing an overall upward trend, increasing from 92.4% in the 5th week to 94.1% in the 10th week, with an average increase of 1.7 percentage points. The purple line represents the average water consumption rate, which gradually decreases as the optimization progresses, from 10.45 m 3 / kWh in the 5th week to 10.05 m 3 / kWh in the 10th week, with a decrease of 0.40 m 3 / kWh (about 3.8%). Generally speaking, the changing directions of the two trend lines are opposite, proving that the optimized dispatching method of this application effectively reduces the water consumption per unit of power generation while improving the water energy utilization rate, achieving a double optimization effect.

[0134] Figure 6 The bubble chart shows the relationship among the average head, the percentage of optimization improvement, and the average flow rate. The horizontal axis represents the average head (15.3 - 16.1 m), the vertical axis represents the percentage of optimization improvement (7.0 - 11.0%), and the size of the bubble represents the average flow rate (512.7 - 548.3 m 3 / s). The dotted line represents the linear correlation trend between the head and the optimization effect, with a correlation coefficient r = 0.76, indicating a strong positive correlation between the two. As the average head increases, the optimization improvement effect generally enhances. For example, when the head reaches 16.1 m in the 10th week, the optimization improvement reaches 9.8%. At the same time, the size of the bubble reflects the influence of the flow rate factor, and a larger flow rate usually corresponds to a better optimization effect. This chart reveals that maintaining a higher head is a key factor in improving the optimization effect in the optimization of Mama Cliff Hydropower Station.

[0135] Figure 7 Shows the optimization effect of the cascade dispatching of Mama Cliff Hydropower Station, focusing on analyzing the relationship between the water contribution from the upstream Guangzhao Power Station and the optimization efficiency. The bar chart represents the upstream water contribution rate (62.1% - 66.0%), and the line represents the percentage of optimization efficiency improvement (6.6% - 8.1%). It can be seen from the figure that the changing trends of the two are highly consistent (except in the 9th week), indicating that the water contribution from the upstream power station has a significant impact on the optimization effect of the downstream Mama Cliff Power Station. As the upstream water contribution rate increases, the optimization efficiency generally improves. The water contribution rate in the 10th week is the highest (66.0%), and the corresponding optimization efficiency also reaches the highest (8.1%); this cascade coordination effect shows that in the optimization of cascade hydropower stations, the joint dispatching of upstream and downstream power stations should be strengthened, especially the reasonable allocation of the water from the upstream power station to improve the overall system efficiency. The influence mechanism of the upstream water contribution on the optimization effect may be related to head maintenance and flow regulation.

[0136] Figure 8Shows the optimization analysis of the water consumption rate of the Mamar Cliff Hydropower Station, especially the impact of the operation mode on the water consumption efficiency. The chart divides the six-week operation into three modes: base load operation (weeks 5-6, orange area), base load-medium peak hybrid (weeks 7-8, purple area), and medium peak operation (weeks 9-10, green area). The blue bar chart represents the water consumption rate values for each week, and the red triangle markers represent the change amounts between adjacent weeks. The red dashed line represents the overall optimization trend. It can be seen from the figure that as the operation mode changes from pure base load to medium peak, the water consumption rate shows an overall downward trend, from 10.45 m 3 / kWh in week 5 to 10.05 m 3 / kWh in week 10, with a total decrease of 0.40 m 3 / kWh (3.8%). Especially in the transition from week 6 to week 7 (base load to base load-medium peak), the water consumption rate decreased by 0.17 m 3 / kWh, with a significant effect. An abnormal rebound occurred in week 9 (10.30 m 3 / kWh), but then it dropped to the lowest value again in week 10. The analysis shows that the medium peak operation mode is more water-saving and efficient than the base load operation.

[0137] Figure 9 The radar chart comprehensively evaluates the optimization effect of the Mamar Cliff Hydropower Station, comparing the performance of the optimized scheduling method of this application with the standard PSO algorithm from 8 key dimensions. The red polygon represents the optimized scheduling method of this application, and the blue polygon represents the standard PSO algorithm. It can be seen from the figure that the optimized scheduling method of this application is superior to the standard PSO algorithm in all indicators, especially in terms of power generation efficiency improvement (8.9% vs 3-8%), water energy utilization rate (93.7% vs 92.0%), cascade coordination effect, and average water consumption rate improvement. The data table on the right quantitatively shows the specific comparison values of the key indicators, intuitively presenting the advantages of this study. The radar chart shows that the area of the polygon formed by the optimized scheduling method of this application is significantly larger than that of the literature method, proving the comprehensive advantages of the algorithm in multi-objective optimization. This figure reveals that through the optimized scheduling method of this application, the Mamar Cliff Hydropower Station can achieve a nearly 9% increase in power generation efficiency without additional equipment investment, while improving the water energy utilization rate, reducing the water consumption rate, and enhancing economic benefits, with significant practical value and promotion potential.

Claims

1. A method for short-term optimal scheduling of cascade hydropower stations, characterized in that, It includes the following steps: Step 1: Construct a cascade hydropower station scheduling model, and set goals and constraints; Step 2: Initialize the model parameters and generate an initial scheduling plan; Step 3: Based on the natural selection enhancement strategy, use the genetic algorithm to perform the first optimization on the initial scheduling plan to obtain a genetically optimized cascade hydropower station scheduling plan; Step 4: Use the adaptive weight particle swarm optimization algorithm to perform secondary optimization on the genetically optimized cascade hydropower station scheduling plan to obtain an optimal scheduling plan.

2. The method according to claim 1, wherein The objective of the cascade hydropower station scheduling model is to maximize the total power generation E of the cascade hydropower stations total : where k k is the power generation efficiency of the k-th power station; A k is the output coefficient of the k-th power station; q k is the power generation flow rate of the k-th power station in period j, m 3 / s; h k is the average head of the k-th power station, m; t is the duration, in s.

3. The method according to claim 1, wherein The constraints at least include reservoir capacity constraints, flow constraints, and water quantity-flow balance constraints.

4. The method according to claim 1, wherein The Step 3 includes: 3.1 Use the genetic algorithm to calculate the fitness value of each scheduling plan under the cascade hydropower station scheduling model; 3.2 Through several cycles of selection operations, crossover operations, and mutation operations based on the fitness value, obtain a preliminary genetically optimized cascade hydropower station scheduling plan; 3.3 Use the natural selection enhancement strategy to perform re-optimization on the preliminary genetically optimized cascade hydropower station scheduling plan; 3.4 Update the scheduling plan population, and repeat Steps 3.2 - 3.3 until the optimization termination condition is reached to obtain a genetically optimized cascade hydropower station scheduling plan.

5. The method according to claim 3, characterized in that The natural selection enhancement strategy is: Retain the plans with high fitness values in the preliminary genetically optimized cascade hydropower station scheduling plan, sort the contemporary scheduling plan population according to the fitness values of these plans, and perform selection on the contemporary scheduling plan population based on the elite retention mechanism.

6. The method according to claim 4, wherein The elite retention mechanism is: Sort the contemporary scheduling plan population in descending order according to the fitness value, and cover the inferior generation population in the latter 50% with the high-quality population in the former 50%.

7. The method according to claim 1, wherein The adaptive weight particle swarm optimization algorithm refers to replacing the inertia weight in the original particle swarm optimization algorithm with a dynamic adaptive weight w i , as shown in the following formula: Among them, F i is the fitness value of particle i; F avg is the average fitness value of the population; w1 = 0.95, w2 = 0.

6.

8. According to claim 1, characterized in that The Step 4 also includes: Introduce Gaussian perturbation in the adaptive weight particle swarm optimization algorithm.

9. A visual digital twin scheduling platform, characterized in that, Perform hydraulic scheduling based on the method for short-term optimal scheduling of cascade hydropower stations according to any one of Claims 1 - 8.

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