An in-plant economic operation optimization method and system for cascade hydropower stations

Abstract

The present application relates to the technical field of hydroelectric power generation, and discloses a method and system for optimizing economic operation of cascade hydropower stations, comprising the following steps: establishing a hydraulics relationship model of the cascade hydropower stations and a dynamics characteristic model of the cascade hydropower stations according to the hydropower topological relationship of each hydropower station in a river basin; determining a target function of the cascade hydropower stations in the river basin by using a water-determined power or power-determined water operation mode according to the hydraulics relationship model and the dynamics characteristic model of the cascade hydropower stations in the river basin; and optimizing and solving the target function of the cascade hydropower stations in the river basin determined by the water-determined power operation mode or the target function of the cascade hydropower stations in the river basin determined by the power-determined water operation mode to obtain a target function value of the cascade hydropower stations in the river basin, i.e. the optimal economic operation efficiency of the cascade hydropower stations in the river basin. The present application has the characteristics of high model precision and good optimization effect, and can optimally distribute the loads of the units of each hydropower station in the cascade hydropower stations.

Description

Technical Field

[0001] This invention relates to the field of hydropower technology, specifically to a method and system for optimizing the economic operation of a cascade hydropower station. Background Technology

[0002] Economic operation of a hydropower plant refers to the active power that each generating unit should provide under certain external requirements for water or electricity, while satisfying all internal physical constraints and maximizing the overall power generation efficiency of the plant. Economic operation ensures that the generating units operate at high efficiency, thereby generating more electricity with limited water or generating the same amount of electricity with minimal water, thus improving the economic benefits of the hydropower plant. A river basin cascade hydropower station comprises multiple hydropower stations with complex hydraulic and electrical connections. Therefore, the economic operation of a river basin cascade hydropower station is more complex than that of a single hydropower station, exhibiting higher nonlinearity and coupling, and making the problem more difficult to solve.

[0003] Currently, mathematical models for the economic operation of cascade hydropower plants in river basins mainly consider conventional hydraulic equations and the head-active power relationship curve of the entire plant. The result of model optimization is the active power of the entire plant. Its limitation is that the head-active power characteristic curve of the entire plant cannot reflect the efficiency characteristics of each unit under all operating conditions. The active power of the entire plant is usually distributed to each unit using a simple strategy (such as the averaging method), which reduces the accuracy of the optimization results and leads to low economic benefits of cascade hydropower plant operation. Summary of the Invention

[0004] To address the aforementioned shortcomings in existing technologies, this invention provides a method and system for optimizing the economic operation of cascade hydropower stations. By providing an economic operation model and optimization system for cascade hydropower stations in a river basin, this invention solves the problems of low precision in current economic operation models for cascade hydropower stations, lack of consideration for the efficiency characteristics of units under all operating conditions, and low overall economic benefits for all cascade hydropower stations in a river basin due to simple load allocation methods.

[0005] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0006] A method for optimizing the economic operation of a cascade hydropower station includes the following steps:

[0007] S1. Based on the hydraulic topology of each hydropower station in the basin, establish a hydraulic relationship model of the cascade hydropower stations in the basin;

[0008] S2. Based on the active power and head of the generating units of each hydropower station in the basin, establish a dynamic characteristic model of the cascade hydropower stations in the basin.

[0009] S3. Based on the hydraulic relationship model of the cascade hydropower stations in the basin established in step S1 and the dynamic characteristic model of the cascade hydropower stations in the basin established in step S2, determine the objective function of the cascade hydropower stations in the basin by adopting the operation mode of determining power generation by water or determining water generation by power.

[0010] Among them, the maximum power generation of the hydropower station is determined based on the planned curve of water inflow and reservoir water level.

[0011] The minimum water consumption of a hydropower station is determined based on the load planning curve, using electricity-driven water consumption as the basis.

[0012] The objective function of the cascade hydropower stations in the basin is to maximize the power generation or minimize the water consumption of all hydropower stations in the basin.

[0013] S4. Optimize and solve the objective function of the cascade hydropower stations in the basin, which is determined by the operation mode of water-based power generation or by the operation mode of electricity-based water generation, to obtain the objective function value of the cascade hydropower stations in the basin, that is, to obtain the optimal economic operating efficiency of the cascade hydropower stations in the basin.

[0014] An in-plant economic operation optimization system for cascade hydropower stations includes:

[0015] The system objective function value determination unit is used to determine the active power or flow rate of the units required for the objective function calculation of the cascade hydropower stations in the basin. When the operation mode of water-based power generation is adopted, the flow rate of the units is calculated based on the active power of the units. When the operation mode of electricity-based water generation is adopted, the active power of the units is calculated based on the flow rate of the units.

[0016] The system initial state determination unit is used to obtain the reservoir capacity and active power of the generating units in the initial period based on the measured signals of the hydropower station monitoring system, obtain the water level of the reservoir based on the reservoir capacity, and calculate the flow rate and head of the generating units.

[0017] The system operation mode optimization unit is used to determine the flow rate and active power of the unit calculated by the system objective function value, so as to optimize and solve the objective function of the cascade hydropower station in the basin determined by the water-determined power operation mode or the objective function of the cascade hydropower station in the basin determined by the power-determined water operation mode, and obtain the objective function value of the cascade hydropower station in the basin, that is, to obtain the optimal economic operating efficiency of the cascade hydropower station in the basin.

[0018] The present invention has the following beneficial effects:

[0019] 1. This invention optimizes the initial parameters of a BP neural network using a particle swarm optimization method, thereby constructing a refined efficiency model for a hydroelectric turbine, which is used to predict the efficiency of units in a hydroelectric power station, thus improving the prediction accuracy;

[0020] 2. The established hydraulic relationship model, dynamic characteristic model, and objective function of the cascade hydropower stations in the basin, along with the operation mode of determining power generation based on water availability or power generation based on water availability, form part of the economic operation model within the cascade hydropower stations. Specifically, the hydraulic relationship model reflects the hydraulic relationships between hydraulic structures, the dynamic characteristic model reflects the characteristics of the generating units, the objective function evaluates the economic efficiency of the active power allocation results of the generating units, and the objective function is optimized to obtain the objective function value of the cascade hydropower stations in the basin, thus achieving the optimal economic operating efficiency of the cascade hydropower stations.

[0021] 3. Compared with traditional methods, the present invention has the advantages of high model accuracy and good optimization effect. Moreover, by utilizing the modules of the system proposed in this invention, the load of each unit of the cascade hydropower station can be optimally allocated, thereby maximizing the economic operation benefits of the cascade hydropower station in the basin. Attached Figure Description

[0022] Figure 1 This is a flowchart illustrating an optimization method for the economic operation of a cascade hydropower station proposed in this invention.

[0023] Figure 2 This is a schematic diagram of the hydraulic topology of the cascade hydropower station group in the experimental watershed in the embodiment.

[0024] Figure 3 This is a turbine efficiency model for hydropower station S1 in the embodiment;

[0025] Figure 4 This is a schematic diagram comparing the error of the turbine efficiency model of hydropower station S1 obtained by the method proposed in this invention and the traditional method in the embodiment.

[0026] Figure 5 This is a schematic diagram comparing the daily active power variation curves of the two generating units of hydropower station S1 obtained by the method of the present invention and the conventional method.

[0027] Figure 6 This is a schematic diagram comparing the daily active power variation curves of the two generating units of hydropower station S2 obtained by the method of the present invention and the conventional method.

[0028] Figure 7 This is a schematic diagram comparing the daily water level changes of reservoir R1 obtained by the method of this invention and the traditional method. Detailed Implementation

[0029] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0030] like Figure 1 As shown, a method for optimizing the economic operation of a cascade hydropower station includes the following steps S1-S4:

[0031] S1. Based on the hydraulic topology of each hydropower station in the basin, establish a hydraulic relationship model of the cascade hydropower stations in the basin.

[0032] In this embodiment, the hydraulic relationship model of the cascade hydropower stations in the basin reflects the hydraulic relationship between the hydraulic structures.

[0033] Specifically, step S1 includes S11-S16:

[0034] S11. Based on the fact that the change in reservoir capacity within a set time period equals the difference between the inflow and outflow volumes of water within that time period, the reservoir capacity for the current period is obtained. Simultaneously, the thin-plate spline method is used to fit historical data on the reservoir capacity and water level to construct a mathematical model of the reservoir capacity and water level. When the reservoir capacity for the current period is input, the water level for the current period is obtained, i.e.:

[0035]

[0036] in, This represents the reservoir capacity R1 during time period t. This represents the reservoir capacity R1 during time period t-1, where in indicates inflow and out indicates outflow. This represents the inflow rate of reservoir R1 during time period t. Δt represents the outflow from reservoir R1 during time period t, where Δt represents the set time interval. This represents the water level of reservoir R1 during time period t. This function represents the fitted relationship between the reservoir's capacity and water level.

[0037] In this embodiment, reservoir R1 is the upstream reservoir.

[0038] S12. Based on the minimum and maximum water levels of the reservoir, construct a water level constraint model for the reservoir, namely:

[0039]

[0040] in, This indicates the minimum water level of reservoir R1. This indicates the highest water level of reservoir R1.

[0041] S13. Based on the fact that the current flow rate of the hydropower station is equal to the sum of the total flow rate of all generating units and the amount of water discharged during the current period, the current flow rate of the hydropower station is obtained. Simultaneously, the thin-plate spline method is used to fit the historical data of the hydropower station's flow rate and water level, constructing a mathematical model of the hydropower station's flow rate and water level. When the current flow rate of the hydropower station is input, the current water level of the hydropower station is obtained, i.e.:

[0042]

[0043] in, This represents the flow rate of hydropower station S1 during time period t. This indicates the number of generating units in hydropower station S1, where i represents the corresponding generating unit. Let 'a' represent the flow rate of the i-th generating unit of hydropower station S1 during time period t, and 'a' represent the water discharge. This represents the amount of water discharged by hydropower station S1 during time period t. This represents the water level of hydropower station S1 during time period t. This represents the fitting relationship between the flow rate and water level of a hydropower station.

[0044] S14. Based on the lowest and highest tailwater levels of the hydropower station, construct a water level constraint model for the hydropower station, namely:

[0045]

[0046] in, This indicates the lowest tailwater level of hydroelectric power station S1. This indicates the highest tailwater level of hydroelectric power station S1.

[0047] S15. Based on the spatial direction of water flow, the water level of the upstream hydropower station is not lower than the water level of the downstream reservoir. Simultaneously, within the interval, the inflow to the downstream reservoir equals the sum of the flow from the upstream hydropower station and the inflow within the interval. Construct a model relating the water level and flow between the upstream hydropower station and the downstream reservoir, namely:

[0048]

[0049] in, This represents the water level of the upstream hydropower station S1 during time period t. This represents the water level of downstream reservoir R2 during time period t. Let li represent the inflow to downstream reservoir R2 during time period t, and li represent the inflow within the interval. This represents the inflow between the upstream hydropower station and the downstream reservoir during time period t.

[0050] S16. Based on the mathematical models of reservoir capacity and water level, reservoir water level limitation model, hydropower station flow rate and water level, hydropower station water level limitation model, and the relationship model of water level and flow rate between upstream hydropower station and downstream reservoir, establish a hydraulic relationship model for cascade hydropower stations in the basin.

[0051] S2. Based on the active power and head of the generating units of each hydropower station in the basin, establish a dynamic characteristic model of the cascade hydropower stations in the basin.

[0052] In this embodiment, the established dynamic characteristic model of the cascade hydropower station in the basin reflects the characteristics of the units within the hydropower station.

[0053] Specifically, step S2 includes S21-S26:

[0054] S21. Based on the principle that the sum of the active power of all generating units in a hydropower station equals the load carried by the hydropower station, construct a power balance equation model for the hydropower station, namely:

[0055]

[0056] in, L1 represents the active power of the i-th generating unit of hydropower station S1 during time period t, and L1 represents the load. This represents the load carried by the hydropower station during time period t.

[0057] S22. Based on the minimum and maximum active power allowed for each generating unit in the hydropower station, construct a power constraint model for the generating units in the hydropower station, namely:

[0058]

[0059] in, This represents the minimum allowed active power of the i-th generating unit in hydropower station S1. This represents the maximum allowed active power of the i-th generating unit in hydropower station S1.

[0060] S23. Construct a head calculation model for the generating units in a hydropower station, namely:

[0061]

[0062] in, K represents the head of the i-th generating unit in hydropower station S1. f This represents the head loss coefficient of a hydroelectric power station.

[0063] S24. Based on the maximum and minimum allowable head for each generating unit in the hydropower station, construct a head constraint model for the generating units in the hydropower station, namely:

[0064]

[0065] in, This represents the minimum allowable head for the i-th generating unit in hydropower station S1. This represents the maximum allowable head for the i-th generating unit in hydropower station S1.

[0066] S25. Using the head and active power of the generating units in the hydropower station as raw data, and the efficiency of the generating units in the hydropower station as labeled data, the raw data with labeled data is input into a BP neural network for training. At the same time, the initial parameters of the BP neural network are optimized by the particle swarm optimization method during training to construct a refined efficiency model of the turbine, which is used to predict the efficiency of the generating units in the hydropower station.

[0067] In this embodiment, the initial parameters of the BP neural network are optimized using the particle swarm optimization method, thereby constructing a refined efficiency model for the turbine and improving the prediction accuracy of the refined efficiency model.

[0068] Specifically, step S25 includes S251-S259:

[0069] S251. Settings include population size N, inertia weight w, first learning rate c1 and second learning rate c2, and maximum number of iterations T. max The initial parameters.

[0070] S252. Based on the set initial parameters, randomly generate the positions of the first N particles within the feasible region.

[0071] S253. The positions of the first N particles are used as the initial weights and thresholds of the BP neural network. The head and active power of the generator units in the hydropower station are used as the raw data, and the efficiency of the generator units in the hydropower station is used as the label data. The raw data with label data is input into the BP neural network for training to obtain N trained BP neural networks. The objective function of the N trained BP neural networks is used to calculate the current fitness of each particle in the first generation.

[0072] In this embodiment, the objective function of the BP neural network refers to the prediction error of the BP neural network.

[0073] S254. Take the current fitness of each particle in the first generation as the historical best value of the individual particle, and record the position and velocity of the historical best value of the individual particle. At the same time, take the best value of the current fitness of each particle in the first generation as the historical best value of the population, record the position and fitness of the population at the time of the historical best value, and increment the iteration number by 1.

[0074] S255. Determine whether the N trained BP neural networks have reached the maximum number of iterations or the prediction accuracy meets the set requirements. If so, stop the iteration and output the trained optimal BP neural network as the refined efficiency model of the turbine, which is used to predict the efficiency of the units in the hydropower station. Otherwise, proceed to step S256.

[0075] S256. Based on the recorded position and velocity of the individual particle's historical best value, and the recorded position and fitness of the population at the time of the population's historical best value, calculate the position of the current particle using the particle's velocity and position update formula.

[0076] S257. Using the position of the current particle as the initial weights and threshold of the BP neural network, train the BP neural network to obtain N trained BP neural networks. At the same time, use the objective function of the N trained BP neural networks to calculate the fitness of each current particle.

[0077] S258. Determine whether the fitness of each particle in the current era is better than the historical best value of the particle. If so, take the fitness of the particle in the current era as the historical best value of the particle. Otherwise, keep the historical best value of the particle unchanged.

[0078] At the same time, the optimal value of the fitness of each particle in the current generation is taken as the optimal value of the current generation population. It is then determined whether the optimal value of the current generation population is better than the historical optimal value of the population. If so, the optimal value of the current generation population is taken as the historical optimal value of the population; otherwise, the historical optimal value of the population is kept unchanged.

[0079] S259. Increment the iteration count by 1 and return to step S255.

[0080] S26. Based on the power balance equation model of the hydropower station, the power limitation model of the generator unit in the hydropower station, the head calculation model of the generator unit in the hydropower station, the head limitation model of the generator unit in the hydropower station, and the refined efficiency model of the turbine, establish the dynamic characteristic model of the cascade hydropower station in the basin.

[0081] S3. Based on the hydraulic relationship model of the cascade hydropower stations in the basin established in step S1 and the dynamic characteristic model of the cascade hydropower stations in the basin established in step S2, determine the objective function of the cascade hydropower stations in the basin by adopting the operation mode of determining power generation by water or determining water generation by power.

[0082] Among them, the maximum power generation of the hydropower station is determined based on the planned curve of water inflow and reservoir water level; the minimum water consumption of the hydropower station is determined based on the planned curve of load; the objective function of the cascade hydropower station in the basin is to maximize the power generation or minimize the water consumption of all hydropower stations in the basin.

[0083] In this embodiment, the purpose of determining the objective function of the cascade hydropower stations in the basin using different operating modes is to evaluate the economic efficiency of the active power allocation results of all units in the hydropower station.

[0084] Specifically, step S3 includes S31-S33:

[0085] S31. Solve the hydraulic relationship model of the cascade hydropower stations in the basin established in step S1 and the dynamic characteristic model of the cascade hydropower stations in the basin established in step S2 to obtain the active power and flow rate of all hydropower station units.

[0086] S32. Based on the active power and flow rate of all hydropower station units obtained in step S31, determine the objective function of the cascade hydropower stations in the basin using the water-determined power generation operation mode, i.e.:

[0087]

[0088] Where F1 represents the objective function of the cascade hydropower stations in the basin, determined by the water-dependent power generation operation mode; max represents taking the maximum value; and m represents the total number of cascade hydropower stations in the basin. S represents the j-th hydroelectric power station. j The number of generating units, where T represents the number of time periods to be optimized. S represents the j-th hydropower station in time period t. j The active power of the i-th generating unit S represents the j-th hydropower station in time period t. j The flow rate of the i-th unit.

[0089] S33. Based on the active power and flow rate of all hydropower station units obtained in step S31, determine the objective function of the cascade hydropower stations in the basin using the power-determined water supply operation mode, i.e.:

[0090]

[0091] Where F2 represents the objective function of the cascade hydropower stations in the basin, determined by the operation mode of electricity-driven water supply.

[0092] In this embodiment, the hydraulic relationship model of the cascade hydropower stations in the basin, the dynamic characteristic model of the cascade hydropower stations in the basin, and the objective function of the cascade hydropower stations in the basin, which are determined by the operation mode of water-based power generation or power-based water generation, are part of the economic operation model of the cascade hydropower stations in the basin. The hydraulic relationship model of the cascade hydropower stations in the basin is used to reflect the hydraulic relationship between hydraulic structures, the dynamic characteristic model of the cascade hydropower stations in the basin is used to reflect the characteristics of the units in the hydropower station, and the objective function of the cascade hydropower stations in the basin is used to evaluate the economy of the active power allocation results of the units.

[0093] S4. Optimize and solve the objective function of the cascade hydropower stations in the basin, which is determined by the operation mode of water-based power generation or by the operation mode of electricity-based water generation, to obtain the objective function value of the cascade hydropower stations in the basin, that is, to obtain the optimal economic operating efficiency of the cascade hydropower stations in the basin.

[0094] An in-plant economic operation optimization system for cascade hydropower stations includes:

[0095] The system objective function value determination unit is used to determine the active power or flow rate of the units required for the objective function calculation of the cascade hydropower stations in the basin. When the operation mode of water-based power generation is adopted, the flow rate of the units is calculated based on the active power of the units. When the operation mode of electricity-based water generation is adopted, the active power of the units is calculated based on the flow rate of the units.

[0096] The system initial state determination unit is used to obtain the reservoir capacity and active power of the generating units for the initial period based on the measured signals of the hydropower station monitoring system, obtain the water level of the reservoir based on the reservoir capacity, and calculate the flow rate and head of the generating units.

[0097] The system operation mode optimization unit is used to determine the flow rate and active power of the unit calculated by the system objective function value, so as to optimize and solve the objective function of the cascade hydropower station in the basin determined by the water-determined power operation mode or the objective function of the cascade hydropower station in the basin determined by the power-determined water operation mode, and obtain the objective function value of the cascade hydropower station in the basin, that is, to obtain the optimal economic operating efficiency of the cascade hydropower station in the basin.

[0098] In this embodiment, the system objective function value determination unit, the system initial state determination unit, and the system operation mode optimization unit are used to calculate and optimize various variables in the process of optimizing the economic operation of the cascade hydropower station.

[0099] Specifically, the system objective function value determination unit includes a module for estimating unit active power from unit flow rate, a module for estimating unit flow rate from unit active power, and a penalty module.

[0100] The module for deriving active power from unit flow rate is used to calculate the active power and efficiency of the unit using an iterative method, given the unit's flow rate and head. The specific process is as follows:

[0101] In the efficiency interval [0, η] max The efficiency η of the i-th unit is randomly generated within the range. i , where η max This indicates the unit's maximum efficiency.

[0102] Based on the efficiency η of the i-th unit i Calculate the active power of the i-th unit, i.e.:

[0103] Pi =γQ i H i η i

[0104] Among them, P i Let Q represent the active power of the i-th generating unit, γ represent a constant, and Q represent the active power of the i-th generating unit. i H represents the flow rate of the i-th unit. i Let represent the head of the i-th generator unit.

[0105] In this embodiment, γ is 9.81.

[0106] The head H of the i-th unit i With the active power P of the i-th unit i By inputting the refined efficiency model of the water turbine, the actual efficiency under the head and active power conditions of the i-th unit is obtained.

[0107] Determine the efficiency η of the generated i-th unit. i The actual efficiency under the head and active power of the i-th unit If the relative error reaches the first preset value, then stop the iteration and output the efficiency η of the i-th unit. i With the active power P of the i-th unit i Otherwise, let η i ′ Let α represent the efficiency of the regenerated i-th unit. The active power of the i-th unit is recalculated and the next iteration is performed, where α represents a constant value.

[0108] In this embodiment, α is 0.5.

[0109] The active power of the generating unit is used to derive the unit's flow rate module. Given the active power of the generating unit and the water level of the reservoir, the module uses an iterative method to calculate the unit's flow rate and head. The specific process is as follows:

[0110] Assume the head H of the i-th unit i Equal to the rated head H of the i-th unit i ′ Then the head H of the i-th unit will be... i With the active power P of the i-th unit i Input the refined efficiency model of the water turbine to obtain the efficiency η of the i-th unit. i .

[0111] Based on the efficiency η of the i-th unit i Calculate the flow rate of the i-th unit, i.e.:

[0112]

[0113] The total flow of all units in the hydropower station is obtained by summing the flow rates of all units.

[0114] Based on the total flow of all units of the hydropower station, the water level of the hydropower station is calculated using the dynamic characteristic model of the cascade hydropower stations in the basin.

[0115] Calculate the actual head of the i-th unit using the head calculation model of the generating units in a hydropower station.

[0116] Determine the actual head of the i-th unit With the head H of the i-th unit i If the relative error reaches the second preset value, then stop the iteration and output the efficiency η of the i-th unit. i The flow rate Q of the i-th unit i Otherwise, let H″ i Let β represent the head of the i-th unit in the next iteration. The efficiency of the i-th unit is calculated again and the next iteration is performed, where β represents a constant value.

[0117] In this embodiment, β is 0.5.

[0118] The penalty module is used to determine whether the system state of the cascade hydropower stations in the basin satisfies the inequality conditions in the hydraulic relationship model and dynamic characteristic model of the cascade hydropower stations in the basin. If so, the objective function value is calculated based on the objective function of the cascade hydropower stations in the basin. Otherwise, the objective function value of the cascade hydropower stations in the basin is set to a set value. The system state is the water level of the hydropower station, the active power of the generator unit and the head.

[0119] In this embodiment, the module for deriving active power from unit flow rate, the module for deriving unit flow rate from active power, and the penalty module are used for accurate calculation of the objective function to accurately evaluate the performance of candidate solutions.

[0120] Specifically, the system initial state determination unit is used to obtain the reservoir capacity and active power of the generating units for the initial time period based on the measured signals from the hydropower station monitoring system, obtain the reservoir water level based on the reservoir capacity, and calculate the flow rate and head of the generating units. The specific process is as follows:

[0121] The reservoir capacity and active power of the generating units are obtained from the measured signals of the hydropower station monitoring system during the initial period.

[0122] The reservoir capacity for the initial period is input into the mathematical model of reservoir capacity and water level to obtain the reservoir water level for the initial period.

[0123] The initial water level of the reservoir and the active power of the generator unit are input into the generator unit active power derivation module to obtain the generator unit flow rate and head.

[0124] In this embodiment, the system initial state determination unit is used to determine the initial state of the system, thereby providing boundary conditions for optimizing the economic operation of the hydropower station in subsequent time periods.

[0125] Specifically, the system operation mode optimization unit is used to determine the flow rate and active power of the units calculated by the unit based on the system objective function value. This allows for the optimization and solution of the objective function of the cascade hydropower stations in the basin, determined by either a water-based power generation or an electricity-based water generation operation mode, to obtain the objective function value of the cascade hydropower stations in the basin. In other words, it yields the optimal economic operating efficiency of the cascade hydropower stations in the basin. The specific process is as follows:

[0126] Step 1: Determine the flow rate and head of the unit computer group using the initial state of the system, and use the flow rate or active power of the unit as the optimization variable, while recording the current time period as 0.

[0127] Step 2: Determine whether the economic operation of the cascade hydropower stations in the last time period has been optimized. If so, output the optimal solution for each time period; otherwise, proceed to Step 3. The optimal solution is the optimal active power or optimal flow rate of each unit.

[0128] Step 3: Randomly generate an initial population. Within the feasible region of the given optimization variables, a certain size initial population is randomly generated. Each individual in the population contains all the information of the candidate solutions, namely the active power or flow of each unit.

[0129] Step 4: Determine the objective function based on the operation mode of the cascade hydropower stations in the basin, and determine the unit based on all the information of the candidate solutions contained in each individual in the population and the system objective function value. Calculate the fitness of each individual in the population, i.e., the objective function value.

[0130] Step 5: Record the information of the individual with the highest fitness in the population, including its corresponding optimal solution and objective function value.

[0131] Step 6: Check if the maximum number of iterations has been reached. If so, stop the calculation, output the optimal solution and proceed to Step 11; otherwise, proceed to Step 7.

[0132] Step 7: Generate a new population based on the evolutionary mechanism of the gravity search method and the previous generation population.

[0133] Step 8: Calculate the fitness of the new population. Use the system objective function value to determine the fitness of each individual in the new population, that is, the optimal active power or optimal flow of each unit in the current period.

[0134] Step 9: Update the information of the individual with the highest fitness in the population at the current moment. If the best individual in the new population is better than the best individual in the previous generation in terms of fitness, then the best individual in the new population is taken as the historical best individual; otherwise, the historical best individual remains unchanged.

[0135] Step 10: Increment the iteration count by 1 and return to Step 6.

[0136] Step 11: Calculate the initial state of the cascade hydropower stations in the basin for the next time period. Calculate the initial state of the cascade hydropower stations in the basin for the next time period using the output optimal solution, the hydraulic relationship model and dynamic characteristic model of the cascade hydropower stations in the basin, and increment the current time period number by 1 and proceed to Step 2 for iteration.

[0137] In this embodiment, the system operation mode optimization unit is used to determine the optimal mode of economic operation within the cascade hydropower station, that is, to achieve the optimal allocation of active power of each unit of each hydropower station, thereby making up for the shortcomings of traditional load allocation methods in terms of economic operation within the hydropower station.

[0138] In this embodiment, a cascade hydropower station group in an experimental river basin is used as the implementation object of the proposed method and system for optimizing the economic operation of cascade hydropower stations, thereby verifying the effectiveness of the proposed method and system. Specifically, as follows... Figure 2 As shown, Figure 2 This is a schematic diagram of the hydraulic topology of the cascade hydropower station group in the experimental watershed. Figure 2 The experimental basin includes two hydroelectric power stations, denoted as S1 and S2, where S1 is the upstream power station of S2. Hydroelectric power station S1 is equipped with two generating units with a rated capacity of 8MW, and hydroelectric power station S2 is equipped with two generating units with a rated capacity of 2MW. There is an upstream reservoir upstream of hydroelectric power station S1, denoted as R1. The water level of the upstream reservoir at time t is expressed as... There is a downstream reservoir, denoted as R2, upstream of hydropower station S2. The water level of the downstream reservoir at time t is expressed as... The water level at hydropower station S1, i.e., the downstream tailwater level, is expressed as follows: The water level of hydropower station S2 is expressed as follows: Furthermore, the main parameters of the generating units of each hydropower station in the cascade hydropower station group in this basin are shown in Table 1, and the detailed parameters of the hydraulic structure constraints of the cascade hydropower station group in this basin are shown in Table 2.

[0139] Table 1. Main parameters of the generating units of each hydropower station in the cascade hydropower station group of the basin.

[0140]

[0141] Table 2. Detailed parameter table of hydraulic structure constraints for a cascade hydropower station group.

[0142]

[0143]

[0144] like Figure 3 As shown, Figure 3 For the turbine efficiency model of hydropower station S1, Figure 3 The horizontal axis represents the generator head, the vertical axis represents the generator active power, and the vertical axis represents the efficiency. Figure 3 The curved surface is generated from the turbine efficiency model of hydropower station S1, obtained by the in-plant economic operation optimization method of a cascade hydropower station proposed in this invention. Points near the curved surface are sample points of the turbine efficiency characteristics relating the unit's head, active power, and efficiency. It can be seen that most of the turbine efficiency characteristic sample points are located on the curved surface generated by the turbine efficiency model of hydropower station S1 obtained by the method proposed in this invention. In addition, the turbine efficiency model of hydropower station S2 can also be obtained by the method proposed in this invention.

[0145] like Figure 4 As shown, Figure 4 This is a schematic diagram comparing the errors of the turbine efficiency model of hydropower station S1 obtained by the method of the present invention and the traditional method; Figure 4 The horizontal axis represents the number of samples, and the vertical axis represents the absolute error of the samples. The solid line represents the traditional method, and the dashed line represents the method of this invention. The traditional method directly uses samples of the turbine's efficiency characteristics, namely the turbine's head and active power, to train a BP neural network without using particle swarm optimization to optimize the initial weights and thresholds of the network. The method of this invention, however, uses particle swarm optimization to optimize the initial weights and thresholds of the network. Figure 4 It can be observed that the absolute error of the turbine efficiency model obtained by the method of the present invention is smaller than that of the traditional method on most samples, indicating that the method of the present invention is superior to the traditional method in fitting the turbine efficiency characteristics.

[0146] Therefore, when using Figure 2 When the cascade hydropower stations shown operate using a power-determined water supply mode, the objective function of the cascade hydropower stations in the basin is to minimize the sum of the flow rates of all units of all hydropower stations within a certain time period of the entire basin, that is: Based on the main parameters of the generating units of each hydropower station in the cascade hydropower station group given in Tables 1 and 2, the detailed parameters of the hydraulic structure constraints of the cascade hydropower station group, and the hydraulic relationship model and dynamic characteristic model of the cascade hydropower station in the basin established by the method of this invention, under the given total load conditions of hydropower station S1 and hydropower station S2, the load allocation of a total of 4 generating units of hydropower station S1 and hydropower station S2 is optimized using the system operation mode optimization unit proposed in this invention, and the daily active power variation curve of each generating unit and the daily water level variation curve of the reservoir are obtained.

[0147] like Figure 5 As shown, Figure 5 This is a schematic diagram comparing the daily active power variation curves of the two generating units of hydropower station S1 obtained by the method of this invention and the conventional method; from Figure 5 As can be seen from the above, the traditional method distributes the total load of the power plant to the two generating units according to the principle of average distribution. However, the active power of the two generating units optimized by the method of this invention is not the same in each hour, but the total active power of the two methods is the same in each hour.

[0148] like Figure 6 As shown, Figure 6 This is a schematic diagram comparing the daily active power variation curves of the two generating units of hydropower station S2 obtained by the method of this invention and the conventional method; from Figure 6 As can be seen from the above, the traditional method distributes the total load of the power plant to the two generating units according to the principle of average distribution. However, the active power of the two generating units optimized by the method of this invention is not the same in each hour, but the total active power of the two methods is the same in each hour.

[0149] like Figure 7 As shown, Figure 7 This is a schematic diagram comparing the daily water level changes of reservoir R1 obtained by the method of this invention and the conventional method; from Figure 7 As can be seen, under the condition of the same total active power, the load allocation result of the two power stations with a total of four generating units obtained by the method of the present invention can consume less reservoir capacity or flow, making the operation of the cascade power stations in the basin more economical.

[0150] In summary, based on Figures 5-7 The comparative results show that the method of this invention can establish the hydraulic relationship model and dynamic characteristic model of the cascade hydropower station in the basin, and determine the objective function of the cascade hydropower station in the basin by adopting the operation mode of water-determined power generation or power-determined water generation. By solving the objective function, it can overcome the limitations of traditional methods that lack consideration of the efficiency characteristics of the turbine under all operating conditions and the simple determination of the load distribution strategy. It can be applied to any nonlinear system with complex hydraulic and electric coupling relationship and has high calculation accuracy.

[0151] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

[0152] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for optimizing the economic operation of a cascade hydropower station, characterized in that, Includes the following steps: S1. Based on the hydraulic topology of each hydropower station in the basin, establish a hydraulic relationship model of the cascade hydropower stations in the basin; S2. Based on the active power and head of the generating units of each hydropower station in the basin, establish a dynamic characteristic model of the cascade hydropower stations in the basin, specifically including: S21. Based on the principle that the sum of the active power of all generating units in a hydropower station equals the load carried by the hydropower station, construct a power balance equation model for the hydropower station, namely: in, Indicates hydroelectric power station The number of generating units, Indicates the first Periodic hydroelectric power station The The active power of the generator unit. Indicates load, Indicates the first The load carried by the hydropower station during a given period; S22. Based on the minimum and maximum active power allowed for each generating unit in the hydropower station, construct a power constraint model for the generating units in the hydropower station, namely: in, Indicates hydroelectric power station The Middle The minimum active power allowed for the generator set. Indicates hydroelectric power station The Middle The maximum allowable active power of the generator unit; S23. Construct a head calculation model for the generating units in a hydropower station, namely: in, Indicates hydroelectric power station The Middle The head of the Taiwanese generator unit, Indicates the first Periodic Reservoir water level, Indicates the first Periodic hydroelectric power station water level, This represents the head loss coefficient of a hydroelectric power station. Indicates the first Periodic hydroelectric power station The The flow rate of the unit; S24. Based on the maximum and minimum allowable head for each generating unit in the hydropower station, construct a head constraint model for the generating units in the hydropower station, namely: in, Indicates hydroelectric power station The Middle The minimum allowable head for the turbine unit. Indicates hydroelectric power station The Middle The maximum allowable head for the turbine unit; S25. The head and active power of the generator units in the hydropower station are used as raw data, and the efficiency of the generator units in the hydropower station is used as label data. The raw data with label data is input into the BP neural network for training. At the same time, the particle swarm optimization method is used to optimize the initial parameters of the BP neural network during training to build a refined efficiency model of the turbine, which is used to predict the efficiency of the generator units in the hydropower station. S26. Based on the power balance equation model of the hydropower station, the power limitation model of the generator unit in the hydropower station, the head calculation model of the generator unit in the hydropower station, the head limitation model of the generator unit in the hydropower station, and the refined efficiency model of the turbine, establish the dynamic characteristic model of the cascade hydropower station in the basin. S3. Based on the hydraulic relationship model of the cascade hydropower stations in the basin established in step S1 and the dynamic characteristic model of the cascade hydropower stations in the basin established in step S2, determine the objective function of the cascade hydropower stations in the basin by adopting the operation mode of determining power generation by water or determining water generation by power. Among them, the maximum power generation of the hydropower station is determined based on the planned curve of water inflow and reservoir water level. The minimum water consumption of a hydropower station is determined based on the load planning curve, using electricity-driven water consumption as the basis. The objective function of the cascade hydropower stations in the basin is to maximize the power generation or minimize the water consumption of all hydropower stations in the basin. S4. Optimize and solve the objective function of the cascade hydropower stations in the basin, which is determined by the operation mode of water-based power generation or by the operation mode of electricity-based water generation, to obtain the objective function value of the cascade hydropower stations in the basin, that is, to obtain the optimal economic operating efficiency of the cascade hydropower stations in the basin.

2. The method for optimizing the economic operation of a cascade hydropower station according to claim 1, characterized in that, Step S1 specifically includes: S11. Based on the fact that the change in reservoir capacity within a set time period equals the difference between the inflow and outflow volumes of water within that time period, the reservoir capacity for the current period is obtained. Simultaneously, the thin-plate spline method is used to fit historical data on the reservoir capacity and water level to construct a mathematical model of the reservoir capacity and water level. When the reservoir capacity for the current period is input, the water level for the current period is obtained, i.e.: in, Indicates the first Periodic Reservoir Storage capacity, Indicates the first Periodic Reservoir Storage capacity, Indicates entry into the warehouse. Indicates outbound shipment. Indicates the first Periodic Reservoir Inbound traffic, Indicates the first Periodic Reservoir Outbound flow Indicates the set time interval. Indicates the first Periodic Reservoir water level, A function representing the fitted relationship between the reservoir's capacity and water level; S12. Based on the minimum and maximum water levels of the reservoir, construct a water level constraint model for the reservoir, namely: in, Reservoir The lowest water level, Reservoir The highest water level; S13. Based on the fact that the current flow rate of the hydropower station is equal to the sum of the total flow rate of all generating units and the amount of water discharged during the current period, the current flow rate of the hydropower station is obtained. Simultaneously, the thin-plate spline method is used to fit the historical data of the hydropower station's flow rate and water level, constructing a mathematical model of the hydropower station's flow rate and water level. When the current flow rate of the hydropower station is input, the current water level of the hydropower station is obtained, i.e.: in, Indicates the first Periodic hydroelectric power station Traffic, Indicates hydroelectric power station The number of generating units, Indicates the corresponding unit. Indicates the first Periodic hydroelectric power station The The flow rate of the Taiwanese unit This indicates the abandonment of water. Indicates the first Periodic hydroelectric power station The amount of water discarded, Indicates the first Periodic hydroelectric power station water level, A function representing the fitted relationship between the flow rate and water level of a hydropower station; S14. Based on the lowest and highest tailwater levels of the hydropower station, construct a water level constraint model for the hydropower station, namely: in, Indicates hydroelectric power station The lowest tailwater level, Indicates hydroelectric power station The highest tailwater level; S15. Based on the spatial direction of water flow, the water level of the upstream hydropower station is not lower than the water level of the downstream reservoir. Simultaneously, within the interval, the inflow to the downstream reservoir equals the sum of the flow from the upstream hydropower station and the inflow within the interval. Construct a model relating the water level and flow between the upstream hydropower station and the downstream reservoir, namely: in, Indicates the first upstream hydropower station during the period water level, Indicates the first downstream reservoirs during the period water level, Indicates the first downstream reservoirs during the period Inbound traffic, Indicates interval inflow. Indicates the first The inflow between the upstream hydropower station and the downstream reservoir during a given period; S16. Based on the mathematical models of reservoir capacity and water level, reservoir water level limitation model, hydropower station flow rate and water level, hydropower station water level limitation model, and the relationship model of water level and flow rate between upstream hydropower station and downstream reservoir, establish a hydraulic relationship model for cascade hydropower stations in the basin.

3. The method for optimizing the economic operation of a cascade hydropower station according to claim 2, characterized in that, Step S25 specifically includes: S251, Settings including population size Inertia weight First learning rate With the second learning rate and the maximum number of iterations The initial parameters; S252. Randomly generate the initial generation within the feasible region based on the set initial parameters. The position of each particle; S253, the first generation The positions of individual particles are used as the initial weights and thresholds of the BP neural network. Simultaneously, the head and active power of the generating units in the hydropower station are used as raw data, and the efficiency of the generating units is used as labeled data. The raw data with these labeled values ​​are then input into the BP neural network for training, resulting in... A trained BP neural network, using The objective function of a trained BP neural network is used to calculate the current fitness of each particle in the first generation. S254. Take the current fitness of each particle in the first generation as the historical best value of the individual particle, and record the position and velocity of the historical best value of the individual particle. At the same time, take the best value of the current fitness of each particle in the first generation as the historical best value of the population, record the position and fitness of the population at the historical best value, and increment the iteration number by 1. S255, Judgment If the trained BP neural network has reached the maximum number of iterations or the prediction accuracy meets the set requirements, then stop the iteration and output the trained optimal BP neural network as a refined efficiency model for water turbines, which is used to predict the efficiency of units in hydropower stations; otherwise, proceed to step S256. S256. Based on the recorded position and velocity of the individual particle's historical best value and the recorded position and fitness of the population at the time of the population's historical best value, calculate the position of the current particle using the particle's velocity and position update formula. S257. Using the positions of the current particles as the initial weights and thresholds of the BP neural network, train the BP neural network to obtain... A trained BP neural network, simultaneously utilizing The objective function of a trained BP neural network is used to calculate the fitness of each particle in the current generation. S258. Determine whether the fitness of each particle in the current era is better than the historical best value of the particle. If so, take the fitness of the particle in the current era as the historical best value of the particle. Otherwise, keep the historical best value of the particle unchanged. At the same time, the best value of fitness of each particle in the current generation is taken as the best value of the current generation population. It is determined whether the best value of the current generation population is better than the best value in the history of the population. If so, the best value of the current generation population is taken as the best value in the history of the population. Otherwise, the best value in the history of the population is kept unchanged. S259. Increment the iteration count by 1 and return to step S255.

4. The method for optimizing the economic operation of a cascade hydropower station according to claim 3, characterized in that, Step S3 specifically includes: S31. Solve the hydraulic relationship model of the cascade hydropower stations in the basin established in step S1 and the dynamic characteristic model of the cascade hydropower stations in the basin established in step S2 to obtain the active power and flow rate of all hydropower station units. S32. Based on the active power and flow rate of all hydropower station units obtained in step S31, determine the objective function of the cascade hydropower stations in the basin using the water-determined power generation operation mode, i.e.: in, Let represent the objective function of the cascade hydropower stations in the river basin, determined by the operation mode of water-based power generation. This indicates taking the maximum value. This indicates the total number of cascade hydropower stations in the river basin. Indicates the first Hydropower station The number of generating units, This indicates the number of time periods for optimization. Indicates the first Time period Hydropower station The The active power of the generator unit. Indicates the first Time period Hydropower station The The flow rate of the unit; S33. Based on the active power and flow rate of all hydropower station units obtained in step S31, determine the objective function of the cascade hydropower stations in the basin using the power-determined water supply operation mode, i.e.: in, This represents the objective function of a cascade hydropower station in a river basin, determined by the operation mode of "electricity-driven water supply".

5. A system for optimizing the economic operation of a cascade hydropower station, characterized in that, Applied to the method as described in any one of claims 1-4, comprising: The system objective function value determination unit is used to determine the active power or flow rate of the units required for the objective function calculation of the cascade hydropower stations in the basin. When the operation mode of water-based power generation is adopted, the active power of the units is calculated based on the flow rate of the units. When the operation mode of electricity-based water generation is adopted, the flow rate of the units is calculated based on the active power of the units. The system initial state determination unit is used to obtain the reservoir capacity and active power of the generating units in the initial period based on the measured signals of the hydropower station monitoring system, obtain the water level of the reservoir based on the reservoir capacity, and calculate the flow rate and head of the generating units. The system operation mode optimization unit is used to determine the flow rate and active power of the unit calculated by the system objective function value, so as to optimize and solve the objective function of the cascade hydropower station in the basin determined by the water-determined power operation mode or the objective function of the cascade hydropower station in the basin determined by the power-determined water operation mode, and obtain the objective function value of the cascade hydropower station in the basin, that is, to obtain the optimal economic operating efficiency of the cascade hydropower station in the basin.

6. The cascade hydropower station in-plant economic operation optimization system according to claim 5, characterized in that, The system objective function value determination unit includes a module for deriving active power from unit flow rate, a module for deriving unit flow rate from active power, and a penalty module; The module for deriving active power from unit flow rate is used to calculate the active power and efficiency of the unit using an iterative method, given the unit's flow rate and head. The specific process is as follows: Within the efficiency range Randomly generated within the first generation Taiwan unit efficiency ,in This indicates the unit's maximum efficiency; According to the Taiwan unit efficiency Calculate the first The active power of the generator set, namely: in, Indicates the first The active power of the generator unit. Represents a constant. Indicates the first The flow rate of the Taiwanese unit Indicates the first The head of the Taiwanese generator unit; The first The head of the Taiwanese unit With the Active power of the Taiwanese generator set Input the refined efficiency model of the water turbine to obtain the efficiency results during operation at the [number]th [time period]. The actual efficiency of the generator unit under head and active power ; Determine the generated first Taiwan unit efficiency With running in the The actual efficiency of the generator unit under head and active power If the relative error reaches the first preset value, then stop the iteration and output the first value. Taiwan unit efficiency With the Active power of the Taiwanese generator set Otherwise, let , Indicates the regenerated first The efficiency of the unit was calculated again. The active power of the generator set is then used for the next iteration, among which... Indicates a constant value; The active power of the generating unit is used to derive the unit's flow rate module. Given the active power of the generating unit and the water level of the reservoir, the module uses an iterative method to calculate the unit's flow rate and head. The specific process is as follows: Assume the first The head of the Taiwanese unit equal to the Rated head of the Taiwanese unit Then the first The head of the Taiwanese unit With the Active power of the Taiwanese generator set Input the refined efficiency model of the water turbine, and obtain the first... Taiwan unit efficiency ; According to the Taiwan unit efficiency Calculate the first The flow rate of the unit, i.e.: ； The total flow rate of all units in the hydropower station is obtained by summing the flow rates of all units. Based on the total flow of all units of the hydropower station, the water level of the hydropower station is calculated using the hydraulic relationship model of the cascade hydropower stations in the basin. Calculate the head of the generating units in a hydropower station using a head calculation model. Actual head of the Taiwanese unit ; Judge the first Actual head of the Taiwanese unit With the The head of the Taiwanese unit If the relative error reaches the second preset value, then stop the iteration and output the first value. Taiwan unit efficiency With the Taiwan unit flow rate Otherwise, let , Indicates the number of iterations in the next iteration. The head of the turbine unit is calculated again. The efficiency of the machine group will be improved and the next iteration will be carried out. Indicates a constant value; The penalty module is used to determine whether the system state of the cascade hydropower stations in the basin satisfies the inequality conditions in the hydraulic relationship model and dynamic characteristic model of the cascade hydropower stations in the basin. If so, the objective function value is calculated based on the objective function of the cascade hydropower stations in the basin. Otherwise, the objective function value of the cascade hydropower stations in the basin is set to a predetermined value. The system status includes the water level of the hydropower station, the active power of the generating units, and the water head.

7. The cascade hydropower station in-plant economic operation optimization system according to claim 6, characterized in that, The system initial state determination unit is used to obtain the reservoir capacity and active power of the generating units for the initial time period based on the measured signals from the hydropower station monitoring system, determine the reservoir water level based on the reservoir capacity, and calculate the unit flow rate and head. The specific process is as follows: The reservoir capacity and active power of the generating units for the initial period are obtained from the measured signals of the hydropower station monitoring system. The reservoir capacity for the initial period is input into the mathematical model of reservoir capacity and water level to obtain the reservoir water level for the initial period. The initial water level of the reservoir and the active power of the generator unit are input into the generator unit active power derivation module to obtain the generator unit flow rate and head.

8. The cascade hydropower station in-plant economic operation optimization system according to claim 7, characterized in that, The system operation mode optimization unit is used to determine the flow rate and active power of the units calculated by the unit based on the system objective function value. This allows for the optimization and solution of the objective function of the cascade hydropower stations in the basin, determined by either a water-driven or electricity-driven operation mode, to obtain the objective function value of the cascade hydropower stations, thus achieving the optimal economic operating efficiency of the cascade hydropower stations. The specific process is as follows: Step 1: Determine the flow rate and head of the unit computer group using the initial state of the system, and use the flow rate or active power of the unit as the optimization variable, while recording the current time period as 0; Step 2: Determine whether the economic operation of the cascade hydropower stations in the last time period has been optimized. If so, output the optimal solution for each time period; otherwise, proceed to Step 3. The optimal solution is the optimal active power or optimal flow rate of each unit; Step 3: Randomly generate an initial population. Within the feasible region of the given optimization variables, a certain size initial population is randomly generated. Each individual in the population contains all the information of the candidate solutions, namely the active power or flow of each unit. Step 4: Determine the objective function based on the operation mode of the cascade hydropower stations in the basin, and determine the unit based on all the information of the candidate solutions contained in each individual in the population and the system objective function value. Calculate the fitness of each individual in the population, i.e., the objective function value. Step 5: Record the information of the individual with the highest fitness in the population, including its corresponding optimal solution and objective function value; Step 6: Check if the maximum number of iterations has been reached. If so, stop the calculation, output the optimal solution and proceed to Step 11; otherwise, proceed to Step 7. Step 7: Generate a new population based on the evolutionary mechanism of the gravity search method and the previous generation population; Step 8: Calculate the fitness of the new population. Use the system objective function value to determine the fitness of each individual in the new population, that is, the optimal active power or optimal flow of each unit in the current period. Step 9: Update the information of the individual with the highest fitness in the population at the current moment. If the best individual in the new population is better than the best individual in the previous generation in terms of fitness, then the best individual in the new population is taken as the historical best individual; otherwise, the historical best individual remains unchanged. Step 10: Increment the iteration count by 1 and return to Step 6; Step 11: Calculate the initial state of the cascade hydropower stations in the basin for the next time period. Calculate the initial state of the cascade hydropower stations in the basin for the next time period using the output optimal solution, the hydraulic relationship model and dynamic characteristic model of the cascade hydropower stations in the basin, and increment the current time period number by 1 and proceed to Step 2 for iteration.

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