A Simulation Method and Device for the Operation of Cascade Reversible Hydropower Stations Based on Segmented McCormick Relaxation

Abstract

A method and apparatus for simulating the operation of a cascade reversible hydropower station based on piecewise McCormick relaxation is disclosed. The method includes: constructing a simulation model of the reversible hydropower station operation based on the operating conditions of the station and aiming to maximize the total output of the station; linearizing the nonlinear part of the simulation model using piecewise McCormick relaxation and piecewise linearization to simplify it into a mixed-integer linear programming model; and iteratively relaxing the simulation model based on upstream runoff data and operating parameters to obtain the simulation results. This invention uses piecewise McCormick relaxation to transform the nonlinear problem into a linear problem, while employing an iterative relaxation algorithm to improve the solution accuracy. It does not require narrowing the feasible boundary of McCormick relaxation, has fewer iterations, and a faster convergence speed, thus improving the speed and stability of the solution while ensuring simulation accuracy.

Description

Technical Field

[0001] This invention relates to the field of electrical engineering, and in particular to a method and apparatus for simulating the operation of a cascade reversible hydropower station based on segmented McCormick relaxation. Background Technology

[0002] Reversible hydropower stations can perform both power generation and energy storage operations, possessing the ability to regulate grid load, store energy, and balance power supply and demand. Accurate and efficient hydropower station operation simulation is crucial for the economic operation and management of the station. Traditional operation simulation methods often require solving nonlinear and nonconvex optimization problems, making it difficult to guarantee finding the global optimum. Furthermore, the simulation process must consider various complex constraints, such as power output, head variations, flow limits, and reservoir capacity limitations. These factors increase the complexity and computational burden of the simulation. Therefore, existing hydropower station operation simulation methods not only have low solution accuracy but also poor solution speed and stability. Summary of the Invention

[0003] The purpose of this invention is to overcome the aforementioned defects and problems in the prior art and provide a method and apparatus for simulating the operation of a cascade reversible hydropower station based on piecewise McCormick relaxation. The method uses piecewise McCormick relaxation technology to transform nonlinear problems into linear problems, and at the same time uses an iterative relaxation solution algorithm to improve the solution accuracy. Compared with existing iterative solution methods, it does not require narrowing the feasible boundary of McCormick relaxation, has fewer iterations, and a faster convergence speed, thereby improving the solution speed and stability while ensuring simulation accuracy.

[0004] To achieve the above objectives, the technical solution of this invention is: a simulation method for the operation of a cascade reversible hydropower station based on segmented McCormick relaxation, comprising:

[0005] Based on the operation of reversible hydropower stations, and with the goal of maximizing the total output of reversible hydropower stations, a simulation model of reversible hydropower station operation is constructed.

[0006] Based on the piecewise McCormick relaxation method and piecewise linearization method, the nonlinear part of the reversible hydropower station operation simulation model is linearized to simplify it into a mixed integer linear programming model.

[0007] Based on the runoff data and operating parameters upstream of the reversible hydropower station, the simulation model of the reversible hydropower station is solved iteratively by relaxation, and the simulation results of the reversible hydropower station are obtained.

[0008] The piecewise McCormick relaxation formula for the output function of the cascade hydropower is as follows:

[0009] C=ρgη hydro ;

[0010]

[0011]

[0012] In the formula, C represents the unit output function coefficient; ρ represents the density of water; g represents the acceleration due to gravity; η hydro The conversion efficiency of cascade hydropower generation; This indicates the maximum flow rate during operation within the vibration zone; This represents the maximum generating flow rate of the cascade hydropower project. This indicates the minimum flow rate during operation within the vibration zone; H represents the minimum output force in the operating range of the vibration zone; max，i，x Indicates the maximum water head; This indicates the maximum flow rate in the operating section below the vibration zone; H represents the maximum output in the operating range below the vibration zone. min,i,x Indicates the minimum head; This indicates the minimum flow rate in the operating section within the vibration zone; This indicates the minimum output power in the operating range below the vibration zone; Indicates the unit's output; This indicates the lower bound of the first type of constraint in the operating range below the vibration zone; State variables indicating whether the unit is operating in the vibration zone or below; This indicates the lower bound of the first type of constraint on the operating interval within the vibration zone; State variables indicating whether the unit is allowed to operate within the vibration zone; This indicates the lower bound of the second type of constraint in the operating range below the vibration zone; This indicates the lower bound of the second type of constraint on the operating interval within the vibration zone; This indicates the upper bound of the first type of constraint in the operating section below the vibration zone; This indicates the upper bound of the first type of constraint on the operating interval within the vibration zone; This indicates the upper bound of the second type of constraint in the operating section below the vibration zone; This indicates the upper bound of the second type of constraint on the operating interval within the vibration zone; Indicates the head of the generator; Indicates the generator's power generation flow rate;

[0013] The piecewise McCormick relaxation formula for the output function of the reversible unit is as follows:

[0014]

[0015]

[0016] In the formula, This indicates the unit's maximum power generation flow rate; Indicates the minimum power generation flow of the unit; This indicates the unit's maximum pumping flow rate; This indicates the minimum pumping flow rate of the unit.

[0017] The tailrace height-total discharge curve, the maximum discharge-upper reservoir water level curve, and the water level-storage capacity curve were linearized. The linearization formula for the water level-storage capacity curve is as follows:

[0018] H k =f HV (V k ),k∈1~n;

[0019]

[0020] y 1 ≤z 1 ;

[0021] y n ≤z n-1 ;

[0022] y k ≤z k-1 +z k k∈2~n-1;

[0023] y k ≥0, k∈1~n;

[0024] z k ∈{0,1},k∈1~n-1;

[0025]

[0026] In the formula, (V k H k ) represents the k-th point on the water level-reservoir capacity curve; y k z k It is an auxiliary variable.

[0027] The iterative relaxation solution of the reversible hydropower station operation simulation model yields the following simulation results:

[0028] After obtaining the first solution result from the simulation model of the reversible hydropower station, the McCormick relaxation model is rewritten into a relaxation iterative model based on the values ​​of the variables in the solution result.

[0029] The simulation model of reversible hydropower station operation is iteratively relaxed and solved using a relaxation iterative model until the convergence condition is met, thus obtaining the simulation results of reversible hydropower station operation.

[0030] The relaxation iteration model is as follows:

[0031]

[0032] In the formula, This represents the value of the hydroelectric head variable obtained in the (n+1)th solution. This represents the value of the hydroelectric head variable obtained in the nth solution; This represents the value of the pumping head variable obtained in the (n+1)th solution. This represents the value of the pumping head variable obtained from the nth solution.

[0033] The relaxation iterative model is obtained through the following method:

[0034] The output function of the reversible unit can be rewritten in the following inequality form:

[0035]

[0036] After obtaining the first solution using the McCormick relaxation model, the obtained head height was used to apply the output function of the reversible unit. and After linearization, the relaxation iterative model is obtained as follows:

[0037]

[0038] The feasible region of the linearized relaxation iterative model is:

[0039]

[0040]

[0041] The McCormick relaxation model is rewritten as the following relaxation iterative model:

[0042]

[0043] The convergence condition is:

[0044]

[0045] In the formula, ε represents the set allowable error.

[0046] A simulation device for the operation of a cascade reversible hydropower station based on segmented McCormick relaxation, wherein the device is applied to the method described above, and the device comprises:

[0047] The simulation model building module is used to build a simulation model of the operation of a reversible hydropower station based on the operation of the reversible hydropower station and with the goal of maximizing the total output of the reversible hydropower station.

[0048] The model linearization module is used to linearize the nonlinear part of the reversible hydropower station operation simulation model based on the piecewise McCormick relaxation method and piecewise linearization method, so as to simplify it into a mixed integer linear programming model.

[0049] The model solving module is used to iteratively relax and solve the reversible hydropower station operation simulation model based on the runoff data and operating parameters upstream of the reversible hydropower station, and obtain the operation simulation results of the reversible hydropower station.

[0050] A simulation device for the operation of a cascade reversible hydropower station based on piecewise McCormick relaxation includes a memory and a processor;

[0051] The memory is used to store computer program code and transmit the computer program code to the processor;

[0052] The processor is configured to execute the method described above according to instructions in the computer program code.

[0053] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described above.

[0054] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0055] This invention discloses a method and apparatus for simulating the operation of a cascade reversible hydropower station based on piecewise McCormick relaxation. The piecewise McCormick relaxation technique transforms a nonlinear problem into a linear one. By introducing additional variables and constraints to approximate the original nonlinear function, the problem can be solved using linear programming or mixed-integer linear programming. Simultaneously, an iterative relaxation algorithm improves the solution accuracy. Compared to existing iterative methods, it does not require narrowing the feasible boundary of McCormick relaxation, has fewer iterations, and faster convergence, thus improving the speed and stability of the solution while maintaining simulation accuracy. This invention utilizes advanced mathematical methods to improve simulation technology, enabling better optimization of the operation strategy of reversible hydropower stations, improving energy utilization, and reducing operating costs. Attached Figure Description

[0056] Figure 1 This is a flowchart of the operation simulation method for a cascade reversible hydropower station based on segmented McCormick relaxation, as described in this invention.

[0057] Figure 2 This is a structural block diagram of the cascade reversible hydropower station operation simulation device based on segmented McCormick relaxation, as described in this invention.

[0058] Figure 3This is a structural block diagram of the cascade reversible hydropower station operation simulation device based on segmented McCormick relaxation, as described in this invention. Detailed Implementation

[0059] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0060] See Figure 1 A simulation method for the operation of a cascade reversible hydropower station based on piecewise McCormick relaxation includes:

[0061] S1. Based on the operation of the reversible hydropower station, considering constraints such as output, head, flow rate and reservoir capacity, construct a simulation model of the operation of the reversible hydropower station with the goal of maximizing the total output of the reversible hydropower station.

[0062] S2. Based on the piecewise McCormick relaxation method and piecewise linearization method, the nonlinear part of the reversible hydropower station operation simulation model is linearized to simplify it into a mixed integer linear programming model.

[0063] S3. Based on the runoff data and operating parameters upstream of the reversible hydropower station, the reversible hydropower station operation simulation model is iteratively relaxed to obtain the operation simulation results of the reversible hydropower station.

[0064] To improve the accuracy and efficiency of simulation, this invention employs a piecewise McCormick relaxation technique to transform nonlinear problems into linear ones. This method approximates the original nonlinear function by introducing additional variables and constraints, allowing the problem to be solved in the form of linear programming or mixed-integer linear programming. Simultaneously, an iterative relaxation algorithm is used to improve solution accuracy. Compared to existing iterative methods, it does not require narrowing the feasible boundary of McCormick relaxation, has fewer iterations, and converges faster, thus improving both simulation accuracy and solution speed and stability. By carefully considering various aspects of hydropower station operation and utilizing mathematical methods to improve simulation technology, the operating strategy of hydropower stations can be better optimized, energy utilization efficiency improved, and operating costs reduced.

[0065] Furthermore, in step S1, the formula for the cascade hydropower station model is as follows:

[0066]

[0067]

[0068] In the formula, Indicates total output; Indicates the unit's output; Indicates total power generation flow; Indicates the generator's power generation flow rate; This indicates a total increase in reserve requirements; This indicates that the generator unit has been moved to standby mode. This indicates a total reduction in reserve requirements; This indicates that the unit has been downgraded to standby mode; ρ represents the density of water; g represents the acceleration due to gravity; η hydro This indicates the conversion efficiency of power generation in a cascade hydropower station. Indicates the head of the generator; H represents the maximum output force in the operating range of the vibration zone; i，t Indicates the water level of the upper reservoir; Indicates the tailrace height; Indicates head loss; Indicates the outflow rate; f HQ This represents the tailrace height-total discharge flow curve, with subscripts i, x, and t indicating the power plant, unit, and time period.

[0069] The operating constraint formulas for cascade power plant units are as follows:

[0070]

[0071] In the formula, This indicates the minimum output power in the operating range below the vibration zone; This indicates the minimum output force during the operating range of the vibration zone; This indicates the maximum output power in the operating section below the vibration zone; This indicates the maximum output force in the operating range of the vibration zone; State variables indicating whether the unit is operating in the vibration zone or below; State variables indicating whether the unit is operating within the vibration zone during the operating range; Indicates the maximum discharge flow rate; f represents the maximum power generation flow rate; QH This represents the maximum discharge flow rate versus the upper reservoir water level curve; H min，i，x H represents the minimum head; max，i，x This indicates the maximum water head.

[0072] The operating model formula for a reversible power plant is as follows:

[0073]

[0074] In the formula, This represents the total output of the reversible power plant. This indicates the generating capacity of the reversible generator unit. This indicates the pumping power of the reversible unit. This represents the total flow rate of the reversible power plant. This indicates the power generation flow rate of the reversible generator unit. This indicates the pumping flow rate of the reversible unit. This indicates that the total reserve of reversible power plants has been increased. This indicates that the generator set has been moved to standby mode. This indicates that the water pumping unit has been moved to standby mode. This indicates a reduction in the total reserve of reversible power plants. This indicates that the generator set has been downgraded to standby mode. This indicates that the pumping unit has been downgraded to standby mode, η gen Indicates the energy conversion efficiency of power generation. Indicates the hydroelectric head, η pump Indicates the pumping energy conversion efficiency. Indicates the pumping head. Indicates the maximum power generation output. H represents the maximum pumping power. i，t H represents the water level of the upstream reservoir. i+1，t Indicates the water level of the downstream reservoir. This indicates head loss.

[0075] The operating constraints of a reversible power plant are as follows:

[0076]

[0077] In the formula, Indicates the minimum power output. Indicates maximum power generation output; Indicates the minimum pumping power; Indicates the maximum pumping power; This represents the state variable of the generating unit when it is operating in power generation mode; This represents the state variable of the unit when it is operating in pumping mode; Indicates the minimum head required for power generation; Indicates the maximum head for power generation. Indicates the minimum pumping head. This indicates the maximum pumping head.

[0078] The reservoir's operation model and constraint formulas are as follows:

[0079]

[0080] V min ≤V i，t ≤V max ;

[0081]

[0082] In the formula, f HV This represents the water level-reservoir capacity curve. V represents the average reservoir capacity over a given period. i，t V represents the initial reservoir capacity at the beginning of the time period. i，t+1 V represents the reservoir capacity at the end of the time period. minV represents the minimum storage capacity. max Indicates the maximum storage capacity. Δt represents the total discharge from this level of reservoir to the next level reservoir; Δt represents the length of the time period. Indicates natural runoff.

[0083] The objective function of the reversible hydropower station operation simulation model is:

[0084]

[0085] In the formula, T represents the total time period; N represents the total number of power stations.

[0086] Furthermore, in step S2, the piecewise McCormick relaxation formula for the cascade hydropower output function is as follows:

[0087] C=ρgη hydro ;

[0088]

[0089] In the formula, C represents the unit output function coefficient. This indicates the maximum flow rate in the operating range within the vibration zone. This indicates the maximum flow rate in the operating section below the vibration zone. This indicates the minimum flow rate in the operating section within the vibration zone. This indicates the minimum flow rate during operation within the vibration zone. This indicates the lower bound of the first type of constraint in the operating range below the vibration zone. This indicates the lower bound of the second type of constraint in the operating range below the vibration zone. This indicates the upper bound of the first type of constraint in the operating range below the vibration zone. This indicates the upper bound of the second type of constraint in the operating range below the vibration zone. This represents the lower bound of the first type of constraint on the operating interval within the vibration zone. This indicates the lower bound of the second type of constraint on the operating interval within the vibration zone. This indicates the upper bound of the first type of constraint on the operating interval within the vibration zone. This indicates the upper bound of the second type of constraint on the operating interval within the vibration zone.

[0090] The piecewise McCormick relaxation formula for the output function of the reversible unit is as follows:

[0091]

[0092] In the formula, This indicates the maximum power generation flow of the unit. This indicates the minimum power generation flow of the unit. This indicates the unit's maximum pumping flow rate. This indicates the minimum pumping flow rate of the unit.

[0093] Furthermore, in step S2, the linearization formulas for the tailrace height-total discharge curve, the maximum discharge = upper reservoir water level curve, and the water level-storage capacity curve are as follows (taking the water level-storage capacity curve as an example):

[0094] H k =f HV (V k ),k∈1~n;

[0095]

[0096] y 1 ≤z 1 ;

[0097] y n ≤z n-1 ;

[0098] y k ≤z k-1 +z k k∈2~n-1;

[0099] y k ≥0, k∈1~n;

[0100] z k ∈{0,1},k∈1~n-1;

[0101]

[0102] In the formula, (V k H k ) represents the k-th point on the water level-reservoir capacity curve; y k z k It is an auxiliary variable.

[0103] The operation model of the cascade reversible hydropower station, after piecewise McCormick relaxation and linearization, is a mixed-integer linear programming model, which can be solved using the gurobipy solver in Python. First, non-decision variables in the model are defined based on actual data, including natural runoff, flow time lag, output, head, pump head, upper and lower limits of flow, and energy conversion efficiency. Then, the objective function and constraints of the model are input into the solver, and solution parameters are defined, including the number of iterations and tolerance error. Finally, the model solution results are output, yielding the simulation results of the cascade reversible hydropower station operation.

[0104] Furthermore, in step S3, the reversible hydropower station operation simulation model is iteratively relaxed to obtain the reversible hydropower station operation simulation results, including:

[0105] After obtaining the first solution result from the simulation model of the reversible hydropower station, the McCormick relaxation model is rewritten into a relaxation iterative model based on the values ​​of the variables in the solution result.

[0106] The simulation model of reversible hydropower station operation is iteratively relaxed and solved using a relaxation iterative model until the convergence condition is met, thus obtaining the simulation results of reversible hydropower station operation.

[0107] The relaxation iteration model is as follows:

[0108]

[0109]

[0110] In the formula, This represents the value of the hydroelectric head variable obtained in the (n+1)th solution. This represents the value of the hydroelectric head variable obtained in the nth solution; This represents the value of the pumping head variable obtained in the (n+1)th solution. This represents the value of the pumping head variable obtained from the nth solution.

[0111] Considering the operating characteristics and objective function properties of cascade reversible hydropower stations, namely, the tendency to generate more electricity and consume less electricity, the output function of the reversible unit in step S1 can be rewritten in the following inequality form:

[0112]

[0113] To establish a relaxation iterative model, after obtaining the first solution using the McCormick relaxation model, the obtained head height was used to apply the output function of the reversible unit. and After linearization, we get:

[0114]

[0115] It can be proven from the properties of bilinear functions that the feasible region of the linearized relaxed iterative model is smaller than the feasible region of the original problem, which is a strictly tight constraint, i.e.:

[0116]

[0117] Therefore, in the relaxation iterative model, the McCormick relaxation model is rewritten as follows:

[0118]

[0119] From the above derivation, it can be concluded that the objective function of the relaxation iterative model is strictly smaller than the objective function of the original problem, and they are equal when the iteration converges. This model has good convergence properties and can guarantee the optimality of the solution.

[0120] The convergence conditions for iterative solutions are as follows:

[0121]

[0122] In the formula, ε represents the set allowable error.

[0123] A new relaxation iterative model is established based on the results of the previous solution. The model is then iteratively relaxed and solved until the convergence condition is met.

[0124] A simplified simulation was used for the case study. The data is shown in the table below:

[0125] Table 1 Data for Upstream and Downstream Conventional Hydropower Stations

[0126]

[0127]

[0128] The model is built according to the steps in S1, linearized according to the steps in S2, and solved according to the steps in S3. The results are shown in the table below:

[0129] Table 2 Simulation Results

[0130]

[0131]

[0132] The comparison of the bilinear constraint error of the output function between the first and final solution results in step S3 is shown in the table below:

[0133] Table 3 Comparison of Solution Errors

[0134] Upstream power plant output Downstream power plant output Reversible output Reversible pumping first 7.9047 8.6262 58.6530 46.5843 Final result 5.3452e-07 8.0015e-07 2.7636e-07 1.8523e-07

[0135] As can be seen, after iterative solution, the bilinear constraint error of the model's output function is significantly reduced.

[0136] See Figure 2 A simulation device for the operation of a cascade reversible hydropower station based on segmented McCormick relaxation is disclosed. This device is applied to the aforementioned simulation method for the operation of a cascade reversible hydropower station based on segmented McCormick relaxation. The device comprises:

[0137] The simulation model building module is used to build a simulation model of the operation of a reversible hydropower station based on the operation of the reversible hydropower station and with the goal of maximizing the total output of the reversible hydropower station.

[0138] The model linearization module is used to linearize the nonlinear part of the reversible hydropower station operation simulation model based on the piecewise McCormick relaxation method and piecewise linearization method, so as to simplify it into a mixed integer linear programming model.

[0139] The model solving module is used to iteratively relax and solve the reversible hydropower station operation simulation model based on the runoff data and operating parameters upstream of the reversible hydropower station, and obtain the operation simulation results of the reversible hydropower station.

[0140] See Figure 3 The present invention also provides a simulation device for the operation of a cascade reversible hydropower station based on segmented McCormick relaxation, including a memory and a processor;

[0141] The memory is used to store computer program code and transmit the computer program code to the processor;

[0142] The processor is configured to execute, according to instructions in the computer program code, a method for simulating the operation of a cascade reversible hydropower station based on segmented McCormick relaxation as described in any one of claims 1 to 7.

[0143] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-described method for simulating the operation of a cascade reversible hydropower station based on piecewise McCormick relaxation.

[0144] Generally, the computer instructions for implementing the method of the present invention can be carried on any combination of one or more computer-readable storage media. Non-transitory computer-readable storage media can include any computer-readable medium except for the signal itself, which is temporarily propagating.

[0145] Computer-readable storage media can be, for example, but not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatuses, or any combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EKROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this invention, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0146] Computer program code for performing the operations of this invention can be written in one or more programming languages ​​or a combination thereof. These programming languages ​​include object-oriented programming languages—such as Java, Smalltalk, and C++—as well as conventional procedural programming languages—such as the "C" language or similar programming languages. In particular, Python, suitable for neural network computation, and platform frameworks such as TensorFlow and PyTorch can be used. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer or to an external computer (e.g., via the Internet using an Internet service provider) through any type of network, including a local area network (LAN) or a wide area network (WAN).

[0147] For details regarding the aforementioned equipment and non-transitory computer-readable storage media, please refer to the specific description of a cascade reversible hydropower station operation simulation method based on piecewise McCormick relaxation and its beneficial effects, which will not be repeated here.

[0148] Although embodiments of the present invention have been shown and described above, it should be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A simulation method for the operation of a cascade reversible hydropower station based on piecewise McCormick relaxation, characterized in that, include: Based on the operation of reversible hydropower stations, and with the goal of maximizing the total output of reversible hydropower stations, a simulation model of reversible hydropower station operation is constructed. Based on the piecewise McCormick relaxation method and piecewise linearization method, the nonlinear part of the reversible hydropower station operation simulation model is linearized to simplify it into a mixed integer linear programming model. Based on the runoff data and operating parameters upstream of the reversible hydropower station, after obtaining the first solution result from the reversible hydropower station operation simulation model, the McCormick relaxation model is rewritten into a relaxation iterative model based on the values ​​of the variables in the solution result. The reversible hydropower station operation simulation model is iteratively relaxed and solved through the relaxation iterative model until the convergence condition is met, and the operation simulation result of the reversible hydropower station is obtained. The relaxation iteration model is as follows: ； ； ； ； In the formula, Indicates the first The value of the hydroelectric head variable is solved in this step. Indicates the first The values ​​of the hydroelectric head variable obtained from this solution; Indicates the first The value of the pumping head variable is solved in this step. Indicates the first The value of the pumping head variable obtained from the second solution; This indicates the generating capacity of the reversible generator unit; Indicates the energy conversion efficiency of power generation; This indicates the unit's maximum power generation flow rate; This indicates the power generation flow rate of the reversible generator unit; Indicates the minimum power generation flow of the unit; Indicates the pumping power of the reversible unit; Indicates the pumping energy conversion efficiency; This indicates the unit's maximum pumping flow rate; Indicates the pumping flow rate of the reversible unit; This indicates the minimum pumping flow rate of the unit.

2. The method for simulating the operation of a cascade reversible hydropower station based on piecewise McCormick relaxation as described in claim 1, characterized in that, The piecewise McCormick relaxation formula for the output function of the cascade hydropower is as follows: ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； In the formula, Indicates the unit output function coefficient; Indicates the density of water; Represents gravitational acceleration; The conversion efficiency of cascade hydropower generation; This indicates the maximum flow rate during operation within the vibration zone; This represents the maximum generating flow rate of the cascade hydropower project. This indicates the minimum flow rate during operation within the vibration zone; This indicates the minimum output force during the operating range of the vibration zone; Indicates the maximum water head; This indicates the maximum flow rate in the operating section below the vibration zone; This indicates the maximum output power in the operating section below the vibration zone; Indicates the minimum head; This indicates the minimum flow rate in the operating section within the vibration zone; This indicates the minimum output power in the operating range below the vibration zone; Indicates the unit's output; This indicates the lower bound of the first type of constraint in the operating range below the vibration zone; State variables indicating whether the unit is operating in the vibration zone or below; This indicates the lower bound of the first type of constraint on the operating interval within the vibration zone; State variables indicating whether the unit is allowed to operate within the vibration zone; This indicates the lower bound of the second type of constraint in the operating range below the vibration zone; This indicates the lower bound of the second type of constraint on the operating interval within the vibration zone; This indicates the upper bound of the first type of constraint in the operating section below the vibration zone; This indicates the upper bound of the first type of constraint on the operating interval within the vibration zone; This indicates the upper bound of the second type of constraint in the operating section below the vibration zone; This indicates the upper bound of the second type of constraint on the operating interval within the vibration zone; Indicates the head of the generator; Indicates the generator's power generation flow rate; The piecewise McCormick relaxation formula for the output function of the reversible unit is as follows: ； ； ； ； ； ； ； ； ； ； ； ； ； ； In the formula, This indicates the unit's maximum power generation flow rate; Indicates the minimum power generation flow of the unit; This indicates the unit's maximum pumping flow rate; This indicates the unit's minimum pumping flow rate; This indicates the generating capacity of the reversible generator unit; Indicates the energy conversion efficiency of power generation; This indicates the power generation flow rate of the reversible generator unit; Indicates the head of the generator; Indicates the pumping power of the reversible unit; Indicates the pumping flow rate of the reversible unit; Indicates the pumping head; Indicates the pumping energy conversion efficiency; Indicates maximum power generation output; Indicates the minimum head required for power generation; Indicates the minimum power output; Indicates the maximum head for power generation; Indicates the maximum pumping power; Indicates the minimum pumping head; Indicates the minimum pumping power; This indicates the maximum pumping head.

3. The method for simulating the operation of a cascade reversible hydropower station based on piecewise McCormick relaxation as described in claim 1, characterized in that, The tailrace height-total discharge curve, the maximum discharge-upper reservoir water level curve, and the water level-storage capacity curve were linearized. The linearization formula for the water level-storage capacity curve is as follows: ； ； ； ； ； ； ； ； ； ； In the formula, The first point on the water level-reservoir capacity curve One point; , It is an auxiliary variable.

4. The method for simulating the operation of a cascade reversible hydropower station based on piecewise McCormick relaxation as described in claim 1, characterized in that, The relaxation iterative model is obtained through the following method: The output function of the reversible unit can be rewritten in the following inequality form: ； ； After obtaining the first solution using the McCormick relaxation model, the obtained head height was used to apply the output function of the reversible unit. and After linearization, the relaxation iterative model is obtained as follows: ； ； ； ； The feasible region of the linearized relaxation iterative model is: ； ； The McCormick relaxation model is rewritten as the following relaxation iterative model: ； ； ； 。 5. The method for simulating the operation of a cascade reversible hydropower station based on piecewise McCormick relaxation as described in claim 1, characterized in that, The convergence condition is: ； ； In the formula, This indicates the set allowable error.

6. A simulation device for the operation of a cascade reversible hydropower station based on segmented McCormick relaxation, characterized in that, The device is used in the method according to any one of claims 1-5, the device comprising: The simulation model building module is used to build a simulation model of the operation of a reversible hydropower station based on the operation of the reversible hydropower station and with the goal of maximizing the total output of the reversible hydropower station. The model linearization module is used to linearize the nonlinear part of the reversible hydropower station operation simulation model based on the piecewise McCormick relaxation method and piecewise linearization method, so as to simplify it into a mixed integer linear programming model. The model solving module is used to iteratively relax and solve the reversible hydropower station operation simulation model based on the runoff data and operating parameters upstream of the reversible hydropower station, and obtain the operation simulation results of the reversible hydropower station.

7. A simulation device for the operation of a cascade reversible hydropower station based on segmented McCormick relaxation, characterized in that, Including memory and processor; The memory is used to store computer program code and transmit the computer program code to the processor; The processor is configured to execute the method as described in any one of claims 1 to 5 according to instructions in the computer program code.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method as described in any one of claims 1 to 5.

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