Segmented McCormick relaxation-based cascade reversible hydropower station operation simulation method and device

Abstract

The invention discloses a cascade reversible hydropower station operation simulation method and device based on segmented McCormick relaxation, and the method comprises the steps: building a reversible hydropower station operation simulation model with the maximization of the total output of a reversible hydropower station as a target according to the operation condition of the reversible hydropower station; on the basis of a segmented McCormick relaxation method and a segmented linearization method, linearizing a nonlinear part in the reversible hydropower station operation simulation model so as to simplify the nonlinear part into a mixed integer linear programming model; and performing iterative relaxation solution on the reversible hydropower station operation simulation model according to the upstream runoff data and the operation parameters of the reversible hydropower station to obtain an operation simulation result of the reversible hydropower station. According to the method, a non-linear problem is converted into a linear problem by adopting a segmented McCormick relaxation method, meanwhile, the solving precision is improved by adopting an iterative relaxation solving algorithm, the feasible boundary of McCormick relaxation does not need to be reduced, the number of iterations is small, the convergence speed is high, and therefore the solving speed and stability are improved while the simulation precision is guaranteed.

Description

Technical Field

[0001] The invention relates to the field of electrical engineering, and in particular to a method and a device for simulating the operation of a cascade reversible hydropower station based on piecewise McCormick relaxation. Background Art

[0002] Reversible hydropower stations are capable of generating electricity and storing energy, and have the ability to regulate grid load, store energy, and balance electricity supply and demand. Accurate and efficient hydropower station operation simulation is crucial for the economic operation and management of power stations. In traditional operation simulation methods, it is often necessary to solve nonlinear and non-convex optimization problems, and it is difficult to ensure that the global optimal solution is found. In addition, a variety of complex constraints need to be considered during the simulation process, such as power generation output, head changes, flow restrictions, and reservoir capacity restrictions. These factors increase the complexity and computational burden of the simulation. Therefore, the 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 the present invention is to overcome the above-mentioned defects and problems existing in the prior art, and to provide a method and device for simulating the operation of a cascade reversible hydropower station based on piecewise McCormick relaxation. The piecewise McCormick relaxation technology is used to convert nonlinear problems into linear problems, and an iterative relaxation solution algorithm is used to improve the solution accuracy. Compared with the existing iterative solution method, there is no need to reduce the feasible boundary of McCormick relaxation, the number of iterations is small, and the convergence speed is fast, thereby improving the solution speed and stability while ensuring the simulation accuracy.

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

[0005] According to the operation status of the reversible hydropower station, with the goal of maximizing the total output of the reversible hydropower station, a reversible hydropower station operation simulation model 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] According to the runoff data and operation parameters upstream of the reversible hydropower station, the operation simulation model of the reversible hydropower station is solved by iterative relaxation to obtain the operation simulation results of the reversible hydropower station.

[0008] The piecewise McCormick relaxation formula for the cascade hydropower output function 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 of gravity; η hydro The conversion efficiency of cascade hydropower generation; Indicates the maximum flow rate in the operating range under the vibration zone; is the maximum power generation flow of cascade hydropower; Indicates the minimum flow rate in the operating range under the vibration zone; Indicates the minimum output of the operating range in the vibration zone; H max，i，x Indicates the maximum water head; Indicates the maximum flow rate in the operating range under the vibration zone; Indicates the maximum output in the operating range under the vibration zone; H min，i，x Indicates the minimum water head; Indicates the minimum flow rate in the operating range under the vibration zone; Indicates the minimum output in the operating range under the vibration zone; Indicates the unit output; It represents the lower bound of the first type constraint of the operating interval in the vibration zone; A state variable indicating whether the unit is operating in the lower vibration zone; It represents the lower bound of the first type constraint of the operating interval on the vibration zone; A state variable indicating whether the unit is allowed to operate in the vibration zone; It represents the lower bound of the second type constraint of the operating interval in the vibration zone; It represents the lower bound of the second type constraint of the operating interval on the vibration zone; It represents the upper bound of the first type constraint of the lower operating interval of the vibration zone; It represents the upper bound of the first type of constraint on the operating interval on the vibration zone; It represents the upper bound of the second type constraint of the lower operating interval of the vibration zone; It represents the upper bound of the second type of constraint on the operating interval on the vibration zone; Indicates the generating head; Indicates the power generation flow of the unit;

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

[0014]

[0015]

[0016] In the formula, Indicates the maximum power generation flow of the unit; Indicates the minimum power generation flow of the unit; Indicates the maximum pumping flow of the unit; Indicates the minimum pumping flow of the unit.

[0017] The tailwater height-total discharge flow curve, the maximum discharge flow-upper reservoir water level curve, and the water level-storage capacity curve are linearized; the linearization formula of 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 kth point on the water level-reservoir capacity curve; y k 、z k is an auxiliary variable.

[0027] The iterative relaxation solution of the reversible hydropower station operation simulation model is performed to obtain the reversible hydropower station operation simulation result, including:

[0028] After solving the reversible hydropower station operation simulation model and obtaining the first solution result, the McCormick relaxation model is rewritten into a relaxation iteration model according to the values ​​of the variables in the solution result;

[0029] The reversible hydropower station operation simulation model is iteratively relaxed and solved by means of the relaxation iterative model until the convergence condition is met, and the reversible hydropower station operation simulation result is obtained.

[0030] The relaxed iterative model is:

[0031]

[0032] In the formula, represents the value of the power generation head variable solved for the n+1th time, represents the value of the power generation head variable obtained by the nth solution; represents the value of the pumping head variable solved for the n+1th time, Represents the value of the pumping head variable obtained by the nth solution.

[0033] The relaxed iterative model is obtained by the following method:

[0034] Rewrite the reversible unit output function into the following inequality form:

[0035]

[0036] After obtaining the first solution result through the McCormick relaxation model, the water head height obtained is used to calculate the output function of the reversible unit. and After linearization, the relaxed iterative model is obtained as follows:

[0037]

[0038] The feasible domain of the linearized relaxed iterative model is:

[0039]

[0040]

[0041] Rewrite the McCormick relaxation model into the following relaxation iterative model:

[0042]

[0043] The convergence condition is:

[0044]

[0045] Where ε represents the set allowable error.

[0046] A cascade reversible hydropower station operation simulation device based on segmented McCormick relaxation, which is applied to the above-mentioned method, and comprises:

[0047] An operation simulation model building module is used to build an operation simulation model of a reversible hydropower station according to the operation status of the reversible hydropower station and to maximize the total output of the reversible hydropower station;

[0048] Model linearization module, 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 to simplify it into a mixed integer linear programming model;

[0049] The model solving module is used to perform iterative relaxation solving on the reversible hydropower station operation simulation model according to the runoff data and operation parameters upstream of the reversible hydropower station, so as to obtain the reversible hydropower station operation simulation results.

[0050] A cascade reversible hydropower station operation simulation device based on piecewise McCormick relaxation, comprising 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 used to execute the method according to the instructions in the computer program code.

[0053] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method described above is implemented.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] In the operation simulation method and device of a cascade reversible hydropower station based on piecewise McCormick relaxation of the present invention, piecewise McCormick relaxation technology is used to convert nonlinear problems into linear problems, and the original nonlinear function is approximated by introducing additional variables and constraints, so that the problem can be solved in the form of linear programming or mixed integer linear programming, and an iterative relaxation solution algorithm is used to improve the solution accuracy. Compared with the existing iterative solution method, it does not need to reduce the feasible boundary of McCormick relaxation, the number of iterations is small, and the convergence speed is fast, thereby improving the speed and stability of the solution while ensuring the simulation accuracy. The present invention uses advanced mathematical methods to improve simulation technology, which can better optimize the operation strategy of the reversible hydropower station, improve energy utilization, and reduce operating costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a flow chart of the operation simulation method of the cascade reversible hydropower station based on segmented McCormick relaxation of the present invention.

[0057] Figure 2 It is a structural block diagram of the cascade reversible hydropower station operation simulation device based on segmented McCormick relaxation of the present invention.

[0058] Figure 3It is a structural block diagram of the cascade reversible hydropower station operation simulation device based on segmented McCormick relaxation of the present invention. DETAILED DESCRIPTION

[0059] The present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0060] See also Figure 1 , a cascade reversible hydropower station operation simulation method based on piecewise McCormick relaxation, including:

[0061] S1. According to the operation status of the reversible hydropower station, considering the constraints such as output, head, flow and reservoir capacity, and taking the maximization of the total output of the reversible hydropower station as the goal, a reversible hydropower station operation simulation model is constructed;

[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. According to the runoff data and operation parameters upstream of the reversible hydropower station, the operation simulation model of the reversible hydropower station is iteratively relaxed and solved to obtain the operation simulation results of the reversible hydropower station.

[0064] In order to improve the accuracy of simulation and the efficiency of solution, the present invention adopts the piecewise McCormick relaxation technology to convert nonlinear problems into linear problems. This method approximates the original nonlinear function by introducing additional variables and constraints, so that the problem can be solved in the form of linear programming or mixed integer linear programming. At the same time, an iterative relaxation solution algorithm is used to improve the solution accuracy. Compared with the existing iterative solution method, it does not need to reduce the feasible boundary of McCormick relaxation, the number of iterations is small, and the convergence speed is fast, thereby improving the speed and stability of solution while ensuring the simulation accuracy. By carefully considering all aspects of the operation of the hydropower station and using mathematical methods to improve the simulation technology, the operation strategy of the hydropower station can be better optimized, the energy utilization efficiency can be improved, and the operation cost can be reduced.

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

[0066]

[0067]

[0068] In the formula, Indicates total output; Indicates the unit output; Indicates the total power generation flow; Indicates the power generation flow of the unit; Indicates total increase in reserve; Indicates that the unit is on standby; Indicates total downgrade reserve; Indicates that the unit is downgraded to standby; ρ indicates the density of water; g indicates the acceleration of gravity; η hydro It indicates the conversion efficiency of power generation of cascade power stations; Indicates the generating head; Indicates the maximum output of the operating range in the vibration zone; H i，t Indicates the water level of the upper reservoir; Indicates tailwater height; It represents the head loss; Indicates the discharge flow; f HQ It represents the tailwater height-total discharge flow curve. The subscripts i, x, and t represent the power station, unit and time number.

[0069] The operating constraint formula of cascade power station units is as follows:

[0070]

[0071] In the formula, Indicates the minimum output in the operating range under the vibration zone; Indicates the minimum output of the operating range in the vibration zone; Indicates the maximum output in the operating range under the vibration zone; Indicates the maximum output of the operating range in the vibration zone; A state variable indicating whether the unit is operating in the lower vibration zone; A state variable indicating whether the unit is operating in the vibration zone; Indicates the maximum downstream flow rate; Indicates the maximum power generation flow; f QH Represents the maximum discharge flow-upper reservoir water level curve; H min，i，x Indicates the minimum water head; H max，i，x Indicates the maximum water head.

[0072] The operating model formula of the reversible power station is as follows:

[0073]

[0074] In the formula, Represents the total output of the reversible power station, Represents the power generation of the reversible unit, represents the pumping power of the reversible unit, represents the total flow of the reversible power station, represents the power generation flow of the reversible unit, Indicates the pumping flow rate of the reversible unit, Indicates that the reversible power station is always adjusted to standby. Indicates that the generator set is put on standby. Indicates that the pumping unit is on standby. Indicates that the reversible power station is always down-regulated for standby. Indicates that the generator set is downgraded to standby. Indicates that the pumping unit is lowered to standby, η gen It represents the energy conversion efficiency of power generation. represents the generating head, η pump represents the pumping energy conversion efficiency, Indicates the pumping head, Indicates the maximum power output. Indicates the maximum pumping power, H i，t represents the water level of the upstream reservoir, H i+1，t represents the water level of the downstream reservoir, Indicates head loss.

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

[0076]

[0077] In the formula, Indicates the minimum power output, Indicates the maximum power generation output; represents the minimum pumping power; Indicates the maximum pumping power; State variables representing the unit operating in power generation conditions; State variables indicating that the unit is operating in pumping conditions; Indicates the minimum generating head; represents the maximum generating head, Indicates the minimum pumping head, Indicates the maximum pumping head.

[0078] The operation model and constraint formula of the reservoir are as follows:

[0079]

[0080] V min ≤V i，t ≤V max ;

[0081]

[0082] In the formula, f HV represents the water level-reservoir capacity curve, Represents the average storage capacity of the reservoir during the period, V i，t represents the initial reservoir capacity of the time period, V i，t+1 represents the reservoir capacity at the end of the period, V minRepresents the minimum storage capacity, V max represents the maximum storage capacity, It indicates the total discharge of the reservoir to the lower reservoir; Δt indicates the length of the time period. Represents natural runoff.

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

[0084]

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

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

[0087] C=ρgη hydro ;

[0088]

[0089] In the formula, C represents the unit output function coefficient, Indicates the maximum flow rate of the operating interval on the vibration zone. Indicates the maximum flow rate in the operating range under the vibration zone. Indicates the minimum flow rate in the operating range under the vibration zone. Indicates the minimum flow rate of the operating interval in the vibration zone. represents the lower bound of the first type of constraint in the operating range under the vibration zone, represents the lower bound of the second type of constraint in the operating range under the vibration zone, represents the upper bound of the first type of constraint in the lower operating range of the vibration zone, represents the upper bound of the second type of constraint in the lower operating range of the vibration zone, It represents the lower bound of the first type of constraint on the operating interval in the vibration zone, It represents the lower bound of the second type of constraint on the operating interval in the vibration zone. It represents the upper bound of the first type of constraint on the operating interval in the vibration zone. It represents the upper bound of the second type constraint of the operating interval on the vibration zone.

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

[0091]

[0092] In the formula, Indicates the maximum power generation flow of the unit, Indicates the minimum power generation flow of the unit, Indicates the maximum pumping flow of the unit. Indicates the minimum pumping flow of the unit.

[0093] Further, in step S2, the linearization formula of tailwater height-total discharge flow curve, maximum discharge flow=upper reservoir water level curve and water level-storage capacity curve is as follows (taking 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 kth point on the water level-reservoir capacity curve; y k 、z k 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 by calling gurobipy solver in Python. First, the non-decision variables in the model are defined according to the actual data, including natural runoff, water flow time lag, output, head, head, upper and lower limits of flow, energy conversion efficiency, etc., and then the objective function and constraints of the model are input into the solver, and the solution parameters are defined, including the number of iterations, tolerance error, etc., and finally the model solution results are output to obtain the operation simulation results of the cascade reversible hydropower station.

[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 solving the reversible hydropower station operation simulation model and obtaining the first solution result, the McCormick relaxation model is rewritten into a relaxation iteration model according to the values ​​of the variables in the solution result;

[0106] The reversible hydropower station operation simulation model is iteratively relaxed and solved by means of the relaxation iterative model until the convergence condition is met, and the reversible hydropower station operation simulation result is obtained.

[0107] The relaxed iterative model is:

[0108]

[0109]

[0110] In the formula, represents the value of the power generation head variable solved for the n+1th time, represents the value of the power generation head variable obtained by the nth solution; represents the value of the pumping head variable solved for the n+1th time, Represents the value of the pumping head variable obtained by the nth solution.

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

[0112]

[0113] In order to establish the relaxation iteration model, after obtaining the first solution result through the McCormick relaxation model, the water head height obtained by the solution is used to calculate the output function of the reversible unit in and Linearization is performed, and we get:

[0114]

[0115] It can be proved from the properties of bilinear functions that the feasible domain of the linearized relaxed iterative model is smaller than the feasible domain of the original problem, which is a strict and tight constraint, namely:

[0116]

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

[0118]

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

[0120] The convergence conditions of the iterative solution are as follows:

[0121]

[0122] Where ε represents the set allowable error.

[0123] A new relaxed iterative model is established based on the results of the previous solution, and the model is iteratively relaxed and solved until the convergence conditions are met.

[0124] The example analysis is carried out with simulated simplified data. The data is shown in the following table:

[0125] Table 1 Data of upstream and downstream conventional hydropower stations

[0126]

[0127]

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

[0129] Table 2 Simulation results

[0130]

[0131]

[0132] Among them, the comparison of the bilinear constraint error of the output function between the first solution result in step S3 and the final solution result is shown in the following table:

[0133] Table 3 Solution error comparison table

[0134] Upstream power station output Downstream power station 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] It can be seen that after iterative solution, the bilinear constraint error of the model's output function is significantly reduced.

[0136] See also Figure 2 , a cascade reversible hydropower station operation simulation device based on piecewise McCormick relaxation, the device is applied to the above-mentioned cascade reversible hydropower station operation simulation method based on piecewise McCormick relaxation, the device comprises:

[0137] An operation simulation model building module is used to build an operation simulation model of a reversible hydropower station according to the operation status of the reversible hydropower station and to maximize the total output of the reversible hydropower station;

[0138] Model linearization module, 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 to simplify it into a mixed integer linear programming model;

[0139] The model solving module is used to perform iterative relaxation solving on the reversible hydropower station operation simulation model according to the runoff data and operation parameters upstream of the reversible hydropower station, so as to obtain the reversible hydropower station operation simulation results.

[0140] See also Figure 3 , the present invention also provides a cascade reversible hydropower station operation simulation device based on segmented McCormick relaxation, comprising 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 used to execute the operation simulation method of cascade reversible hydropower station based on piecewise McCormick relaxation as described in any one of claims 1 to 7 according to the instructions in the computer program code.

[0143] The present invention also provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the method for simulating the operation of a cascade reversible hydropower station based on segmented McCormick relaxation is implemented.

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

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

[0146] Computer program code for performing the operation of the present invention can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, C++, and conventional procedural programming languages ​​such as "C" or similar programming languages, in particular, Python suitable for neural network computing and platform frameworks based on TensorFlow, PyTorch, etc. can be used. The program code can be executed entirely on the user's computer, partially on the user's computer, as an independent software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer can be connected to the user's computer or to an external computer (for example, using an Internet service provider to connect via the Internet) through any type of network, including a local area network (LAN) or a wide area network (WAN).

[0147] The above-mentioned device and non-temporary computer-readable storage medium can be found in the detailed description of a cascade reversible hydropower station operation simulation method based on segmented McCormick relaxation and its beneficial effects, which will not be repeated here.

[0148] Although the 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 limitations on the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A cascade reversible hydropower station operation simulation method based on piecewise McCormick relaxation, characterized in that: include: According to the operation status of the reversible hydropower station, with the goal of maximizing the total output of the reversible hydropower station, a reversible hydropower station operation simulation model 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. According to the runoff data and operation parameters upstream of the reversible hydropower station, the operation simulation model of the reversible hydropower station is solved by iterative relaxation to obtain the operation simulation results of the reversible hydropower station.

2. The operation simulation method of a cascade reversible hydropower station based on piecewise McCormick relaxation according to claim 1 is characterized in that: The piecewise McCormick relaxation formula for the cascade hydropower output function is as follows: C=ρgn hydro ; In the formula, C represents the unit output function coefficient; ρ represents the density of water; g represents the acceleration of gravity; η hydro The conversion efficiency of cascade hydropower generation; Indicates the maximum flow rate in the operating range under the vibration zone; is the maximum power generation flow of cascade hydropower; Indicates the minimum flow rate in the operating range under the vibration zone; Indicates the minimum output of the operating range in the vibration zone; H max，i，x Indicates the maximum water head; Indicates the maximum flow rate in the operating range under the vibration zone; Indicates the maximum output in the operating range under the vibration zone; H min，i，x Indicates the minimum water head; Indicates the minimum flow rate in the operating range under the vibration zone; Indicates the minimum output in the operating range under the vibration zone; Indicates the unit output; It represents the lower bound of the first type constraint of the operating interval in the vibration zone; A state variable indicating whether the unit is operating in the lower vibration zone; It represents the lower bound of the first type constraint of the operating interval on the vibration zone; A state variable indicating whether the unit is allowed to operate in the vibration zone; It represents the lower bound of the second type constraint of the operating interval in the vibration zone; It represents the lower bound of the second type constraint of the operating interval on the vibration zone; It represents the upper bound of the first type constraint of the lower operating interval of the vibration zone; It represents the upper bound of the first type of constraint on the operating interval on the vibration zone; It represents the upper bound of the second type constraint of the lower operating interval of the vibration zone; It represents the upper bound of the second type of constraint on the operating interval on the vibration zone; Indicates the generating head; Indicates the power generation flow of the unit; The piecewise McCormick relaxation formula for the reversible unit output function is as follows: In the formula, Indicates the maximum power generation flow of the unit; Indicates the minimum power generation flow of the unit; Indicates the maximum pumping flow of the unit; Indicates the minimum pumping flow of the unit.

3. The operation simulation method of a cascade reversible hydropower station based on piecewise McCormick relaxation according to claim 1 is characterized in that: The tailwater height-total discharge flow curve, the maximum discharge flow-upper reservoir water level curve, and the water level-storage capacity curve are linearized; the linearization formula of the water level-storage capacity curve is as follows: H k =f HV (V k ),k∈1~n; and 1 ≤z 1 ; and n ≤z n-1 ; y k ≤z k-1 +z k ,k∈2~n-1; and k ≥0,k∈1~n; z k ∈{0,1},k∈1~n-1; In the formula, (V k , H K ) represents the kth point on the water level-reservoir capacity curve; y k 、z k is an auxiliary variable.

4. The operation simulation method of a cascade reversible hydropower station based on piecewise McCormick relaxation according to claim 1 is characterized in that: The iterative relaxation solution of the reversible hydropower station operation simulation model is performed to obtain the reversible hydropower station operation simulation result, including: After solving the reversible hydropower station operation simulation model and obtaining the first solution result, the McCormick relaxation model is rewritten into a relaxation iteration model according to the values ​​of the variables in the solution result; The reversible hydropower station operation simulation model is iteratively relaxed and solved by means of the relaxation iterative model until the convergence condition is met, and the reversible hydropower station operation simulation result is obtained.

5. The operation simulation method of cascade reversible hydropower station based on piecewise McCormick relaxation according to claim 4 is characterized in that: The relaxed iterative model is: In the formula, represents the value of the power generation head variable solved for the n+1th time, represents the value of the power generation head variable obtained by the nth solution; represents the value of the pumping head variable solved for the n+1th time, Represents the value of the pumping head variable obtained by the nth solution.

6. The operation simulation method of cascade reversible hydropower station based on piecewise McCormick relaxation according to claim 5 is characterized in that: The relaxed iterative model is obtained by the following method: Rewrite the reversible unit output function into the following inequality form: After obtaining the first solution result through the McCormick relaxation model, the water head height obtained is used to calculate the output function of the reversible unit. and After linearization, the relaxed iterative model is obtained as follows: The feasible domain of the linearized relaxed iterative model is: Rewrite the McCormick relaxation model into the following relaxation iterative model:

7. The operation simulation method of cascade reversible hydropower station based on piecewise McCormick relaxation according to claim 4 is characterized in that: The convergence condition is: Where ε represents the set allowable error.

8. A cascade reversible hydropower station operation simulation device based on segmented McCormick relaxation, characterized in that: The device is applied to the method described in any one of claims 1 to 7, and the device comprises: An operation simulation model building module is used to build an operation simulation model of a reversible hydropower station according to the operation status of the reversible hydropower station and to maximize the total output of the reversible hydropower station; Model linearization module, 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 to simplify it into a mixed integer linear programming model; The model solving module is used to perform iterative relaxation solving on the reversible hydropower station operation simulation model according to the runoff data and operation parameters upstream of the reversible hydropower station, so as to obtain the reversible hydropower station operation simulation results.

9. A cascade reversible hydropower station operation simulation device 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 according to any one of claims 1 to 7 according to instructions in the computer program code.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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