A simulation method for hydraulic transients in pumped-storage power stations based on the finite volume method

Abstract

The present invention discloses a simulation method for hydraulic transients in a pumped storage power station based on the finite volume method, including: rewriting the unsteady flow equation of the pipeline into a classical water hammer equation; discretizing based on FVM to obtain the integral solution formula for each unit volume in the pressurized pipeline; adopting the solution format of the Riemann problem to obtain the flux calculation form at the boundary of each control volume; solving the flux according to the second-order Godunov solution format to obtain the second-order accurate flux calculation value at the boundary of each unit volume; merging the source terms through time integration to obtain the unit control equation; calculating the boundary by adopting the method of adding a virtual volume according to the Riemann invariant equation; processing the calculation results and conducting comparative verification. The present invention combines the control equation of the pump-turbine with the virtual volume, which can more conveniently handle the problems of complex calculation and low accuracy caused by the need for wave speed adjustment and simplified models in the MOC in the pipe network system of the pumped storage power station.

Description

Technical Field

[0001] The present invention belongs to the technical field of hydraulic numerical simulation calculation of hydropower stations, pumping stations and pumped - storage power stations, and particularly relates to a simulation method for hydraulic transients of a pumped - storage power station based on the finite volume method. Background Technique

[0002] At present, as an effective and indispensable energy - regulating structure in modern power systems, pumped - storage power stations have functions such as peak shaving, valley filling, and black start. They are of great significance for improving the power supply quality of the power grid, optimizing the power source structure, promoting the large - scale development of renewable energy sources such as nuclear power and wind power in China, and realizing the sustainable development of China's power industry. However, since the operation process of pumped - storage power stations involves the mutual blending of water - gas - mechanical three - phase media, and in order to meet the dynamic service requirements of the power system, they often have characteristics such as multi - purpose use of a single machine, rapid conversion of operating conditions, and frequent start - stop, which often lead to large hydraulic vibrations, resonances and other problems in the entire unit, thus endangering the operation of the power station and affecting the service life of the unit.

[0003] Currently, when solving the water hammer problem in a pressurized pipeline, the most commonly used method in one - dimensional water hammer solution calculation is the Method of Characteristics (MOC). However, in the pumped - storage pipe network system, there are generally many hydraulic components such as short pipes, branch pipes, and bifurcated pipes. In the MOC with a fixed grid length, the following two methods are generally adopted to solve the problem. One is to perform interpolation calculation in the calculation, but this method will lead to a decrease in calculation efficiency and accuracy; the other is to adjust the wave speed or grid length to achieve the numerical simulation process, or directly ignore the short pipes and simplify the pipe network model. Compared with the former, the calculation efficiency is increased, but adjusting the wave speed and simplifying the model bring new calculation errors.

[0004] Therefore, a new technical solution is needed to solve the above problems. Summary of the Invention

[0005] Object of the Invention: When simulating the transient hydraulic transients of the complex pipe network system of a pumped - storage power station, aiming at the calculation complexity and stability problems brought by adjusting the wave speed and simplifying the model in the traditional calculation format MOC in the pipe network system, a simulation method for hydraulic transients of a pumped - storage power station based on the finite volume method is provided. It can solve the calculation complexity and instability problems of MOC in the pumped - storage pipe network system, and can more accurately and stably solve the simulation calculation of hydraulic transients in the pumped - storage power station pipe network system, ensuring the safe and stable operation of the pumped - storage power station.

[0006] Technical Solution: To achieve the above object, the present invention provides a simulation method for hydraulic transients of a pumped - storage power station based on the finite volume method, including the following steps:

[0007] S1: Rewrite the unsteady flow equation of the pipeline, neglect the convection term, and write it as the classical water hammer equation;

[0008] S2: Based on the FVM (Finite Volume Method), discretize the water hammer equation obtained in step S1 to obtain the integral solution formula for each unit cell in the pressurized pipeline;

[0009] S3: Adopt the solution format of the Riemann problem to obtain the flux calculation form at the boundary of each control volume;

[0010] S4: According to the second-order Godunov solution format, solve the flux through the flux calculation form obtained in step S3 to obtain the second-order accurate flux calculation value at the boundary of each unit cell;

[0011] S5: According to the flux calculation value, merge the source terms through time integration;

[0012] S6: After obtaining the unit control equation, according to the Riemann invariant equation, calculate the boundary by adding a virtual body;

[0013] S7: Process the calculation results of step S6 and compare and verify them with the experimental results and the simulation results of MOC (Method of Characteristics).

[0014] Further, step S1 is specifically as follows:

[0015] The control equation for unsteady flow in the pipeline is:

[0016]

[0017] Rewrite equations (1) - (2) into matrix form. Without considering the convection term, obtain the classical water hammer equation:

[0018]

[0019] In the formula:

[0020] In the formula: H is the piezometric head, m; V is the flow velocity, m / s; g is the acceleration due to gravity, m / s 2 ; a is the wave speed, m / s; D is the pipeline diameter, m; f is the constant friction coefficient of the pipeline; S 0 is the pipeline slope; x is the distance along the pipeline axis, m; t is the time, s.

[0021] Further, the integral solution formula for each unit cell in the pressurized pipeline in step S2 is:

[0022]

[0023] Where: i is the i-th control volume; F i+1 / 2 is the flux at the right boundary of the control volume; F i-1 / 2 is the flux at the left boundary of the control volume; Δt is the time step, s; Δx is the space step, m; the superscript n represents the t moment; the superscript n + 1 represents the t + Δt moment.

[0024] Furthermore, the calculation form of the flux at the boundary of each control volume in step S3 is:

[0025]

[0026] Here, in order to calculate the flux F on the right side of the control volume, the subscript i + 1 / 2 is used, and the values of the vector A and the variable U at the right boundary of the control volume are also used.

[0027] Furthermore, in step S4, in order to obtain a flux calculation result with second-order accuracy, the original data needs to be linearly reconstructed, and in order to avoid the generation of spurious oscillations, a corresponding slope limiter function is introduced, specifically:

[0028] A1: Data reconstruction

[0029]

[0030] Among them, Δi is calculated by the slope limiter function. For the MINMOD function

[0031]

[0032] A2: Time advancement

[0033]

[0034] A3: Problem solving

[0035]

[0036] Substitute the calculated (13) and (14) into equation (5) to obtain the flux calculation value with second-order accuracy at the boundary of each unit body.

[0037] Furthermore, step S5 is specifically:

[0038] Substitute the obtained flux calculation value with second-order accuracy into equation (4), perform time integration and source term solution. During the solution process, the explicit Runge-Kutta method is used, and a calculation format with second-order accuracy in time can be obtained.

[0039] Furthermore, the calculation process of the calculation format with second-order accuracy in time is:

[0040]

[0041] Furthermore, in step S6, the method of adding virtual bodies is adopted at the boundary. According to the solution method of the second-order Godunov format, when performing second-order solution for any unit cell i, the physical variable values of two unit cells on each side of unit cell i are required. Therefore, specific processing is needed for the unit cells at the boundary. To achieve the unity of grid calculation for all calculation regions within the pipeline, the processing method of adding virtual cells of -1, 0 and N + 1, N + 2 respectively on both sides of the boundary is adopted, and the added virtual bodies satisfy the following conditions:

[0042] U -1 = U 0 = U 1 / 2 (18)

[0043] U N+1 = U N+2 = U N+1 / 2 (19)

[0044] The physical variables of each virtual body respectively satisfy the Riemann invariant equation at the boundary. For the upstream and downstream reservoirs (H 1 / 2 = H u , H N+1 / 2 = H d ), the corresponding calculation equations can be obtained:

[0045]

[0046] Furthermore, the unit control equation in step S6 is the boundary control equation of the pump-turbine. Combining the boundary control equation of the pump-turbine with the virtual body, and the control equation of the pump-turbine can be obtained from the following several equations:

[0047] Full characteristic curve:

[0048] The full characteristic curve of the pump-turbine usually adopts the Suter transformation, but in the present invention, an improved Suter transformation is adopted, specifically as follows:

[0049]

[0050]

[0051] In the formula: WH and WM are the head characteristic function and the torque characteristic function respectively; y is the relative flow angle; z is the relative guide vane opening; h, q, ε, m are the dimensionless values of the head, flow rate, rotational speed and torque of the pump-turbine respectively; the subscript 11 represents the unit value, and the subscript r represents the rated value; c is a constant, generally taking 1.0 - 1.5, and in the present invention, c takes 1.2;

[0052] Equation of rotation:

[0053] Under the load rejection condition of the pump-turbine, the rotational speed balance equation is as follows

[0054]

[0055] where: ε and m are the dimensionless values of the rotational speed and torque of the pump-turbine respectively, the subscript 0 represents the value at the previous moment, and the subscript 00 represents the value at the moment before the previous moment; T a is the time inertia constant of the hydro-generator unit, and the calculation formula is:

[0056]

[0057] where: GD 2 is the flywheel torque of the unit, t·m 2 ; N r is the rated rotational speed of the pump; P r is the rated power of the pump, kw;

[0058] Head equation:

[0059] Denote the nodes at the inlet of the spiral case and the outlet of the draft tube as 1 and 2 respectively. Substitute them into the corresponding characteristic line equations, and according to the definition of the turbine head, the head balance equation of the turbine can be obtained as:

[0060] H = (C p -C m -(B p +B m )Q + C 2 |Q|Q)(27)

[0061]

[0062] where: A is the area of the penstock, m 2 ; the meanings of other symbols are the same as above;

[0063] By combining equations (22), (23), (25) and (27), the various parameters of the pump-turbine can be obtained;

[0064] Therefore, for the above boundary control equations of the pump-turbine, only the physical variable values of the virtual body of the pipeline at the spiral case and the draft tube need to be obtained, and combined with the Riemann invariant equation, the following can be obtained:

[0065]

[0066] where: and are the flow velocity and head of the last unit body of the penstock connected to the spiral case; V 1 n and is the flow velocity and head of the first unit of the penstock connected to the draft tube;

[0067] Substitute the obtained equations (29) - (30) into equation (27) to solve the head balance equation under virtual boundary conditions.

[0068] Based on the second-order Godunov solution scheme of the finite volume method, only the Courant number needs to be appropriately reduced during calculation, without wave speed adjustment, which simplifies the calculation process and has good calculation accuracy and efficiency. Therefore, studying the feasibility of the hydraulic transient simulation method for pumped storage power stations based on the finite volume method is of great significance for the stable and accurate calculation of complex pipe network systems involving multiple bifurcated pipes and multiple branch pipes in practical engineering. It can handle the problems that the calculation results of the MOC format for complex pipe network systems are not accurate enough and the calculation process is relatively complex, and can perform high-efficiency and high-precision hydraulic transient simulation calculations.

[0069] The calculation method proposed in the present invention for simulating the hydraulic transient of a pumped storage power station based on the finite volume method combines the control equation of the pump-turbine with a virtual body, which can more conveniently handle the problems of complex calculation and low accuracy caused by wave speed adjustment and simplified models required by the MOC in the pipe network system of the pumped storage power station.

[0070] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0071] (1) The FVM with the second-order Godunov format established in the present invention can accurately and efficiently realize the calculation and simulation of the hydraulic transient of a certain pumped storage power station, and the calculation results are closer to the measured values than those of the MOC.

[0072] (2) When Cr < 1, both the FVM of the second-order Godunov and the MOC will have a certain degree of numerical dissipation, but the FVM of the second-order Godunov can effectively suppress the numerical dissipation and the calculation is more stable.

[0073] (3) When dealing with the hydraulic transient problem of a pumped storage power station, the MOC needs to adjust the wave speed or directly ignore the short pipe to meet the Courant number condition, thus generating calculation errors; the FVM of the second-order Godunov only appropriately reduces the Courant number condition, without wave speed adjustment, simplifies the calculation process, and has high calculation efficiency and accuracy. Description of the Drawings

[0074] Figure 1 is the implementation flowchart of the present invention;

[0075] Figure 2 is the FVM grid diagram of the pressure pipeline of the present invention;

[0076] Figure 3It is the layout diagram of a certain pumped-storage power station;

[0077] Figure 4 It is the calculation result diagram of FVM and MOC under different Courant numbers in Embodiment 1;

[0078] Figure 5 It is the calculation result diagram of FVM and MOC under different grid numbers in Embodiment 1;

[0079] Figure 6 It is the calculation result diagram of wave velocity and head at the spiral case under the same load rejection test for FVM and MOC. Specific implementation manner

[0080] The present invention will be further clarified below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, various equivalent modifications of the present invention by those skilled in the art all fall within the scope defined by the appended claims of this application.

[0081] The present invention provides a simulation method for hydraulic transients of a pumped-storage power station based on the finite volume method. Refer to Figure 1 , which includes the following steps:

[0082] S1: Rewrite the unsteady flow equation of the pipeline, neglect the convective term, and write it as the classical water hammer equation:

[0083] The control equation for unsteady flow in the pipeline is:

[0084]

[0085] Rewrite equations (1) to (2) into matrix form. Without considering the convective term, the classical water hammer equation is obtained:

[0086]

[0087] In the formula:

[0088] In the formula: H is the piezometric head, m; V is the flow velocity, m / s; g is the acceleration due to gravity, m / s 2 ; a is the wave velocity, m / s; D is the pipeline diameter, m; f is the constant friction coefficient of the pipeline; S 0 is the pipeline slope; x is the distance along the pipeline axis, m; t is the time, s.

[0089] S2: Based on FVM, refer to Figure 2 , discretize the water hammer equation obtained in step S1 to obtain the integral solution formula for each unit in the pressurized pipeline:

[0090] The integral solution formula for each unit in the pressurized pipeline is:

[0091]

[0092] where: i is the i-th control volume; F i+1 / 2 is the flux at the right boundary of the control volume; F i-1 / 2 is the flux at the left boundary of the control volume; Δt is the time step, s; Δx is the space step, m; the superscript n represents the time t; the superscript n+1 represents the time t+Δt.

[0093] S3: Adopt the solution format of the Riemann problem to obtain the flux calculation form at the boundaries of each control volume:

[0094] The flux calculation form at the boundaries of each control volume is:

[0095]

[0096] S4: According to the second-order Godunov solution format, perform flux solution through the flux calculation form obtained in step S3 to obtain the second-order accurate flux calculation values at the boundaries of each unit cell:

[0097] In order to obtain the second-order accurate flux calculation result, it is necessary to perform linear reconstruction on the original data, and in order to avoid the generation of spurious oscillations, introduce the corresponding slope limiter function, specifically:

[0098] A1: Data recombination

[0099]

[0100] where, Δi is calculated by the slope limiter function. For the MINMOD function

[0101]

[0102] A2: Time advancement

[0103]

[0104] A3: Problem solution

[0105]

[0106] Substitute the calculated (13) and (14) into Equation (5) to obtain the second-order accurate flux calculation values at the boundaries of each unit cell.

[0107] S5: According to the flux calculation values, merge the source terms through time integration to obtain the unit control equation:

[0108] For the calculated flux value with second-order accuracy obtained, substitute it into Equation (4), perform time integration and source term solution. During the solution process, use the explicit Runge-Kutta method, then a calculation format with second-order accuracy in time can be obtained. The specific calculation process is as follows:

[0109]

[0110] S6: According to the Riemann invariant equation, use the method of adding virtual bodies to calculate the boundary:

[0111] At the boundary, the method of adding virtual bodies is adopted. According to the solution method of the second-order Godunov format, when performing second-order solution for any unit cell i, the physical variable values of two unit cells on each side of unit cell i are required. Therefore, specific processing is needed for the unit cells at the boundary. To achieve the unity of grid calculation for all calculation regions inside the pipeline, the processing method of adding virtual cells of -1, 0 and N + 1, N + 2 respectively on both sides of the boundary is adopted, and the added virtual bodies satisfy the following conditions:

[0112] U -1 = U 0 = U 1 / 2 (18)

[0113] U N+1 = U N+2 = U N+1 / 2 (19)

[0114] The physical variables of each virtual body respectively satisfy the Riemann invariant equation at the boundary. For the upstream and downstream reservoirs (H 1 / 2 = H u , H N+1 / 2 = H d ), the corresponding calculation equations can be obtained:

[0115]

[0116] Combine the boundary control equation of the pump-turbine with the virtual body. The control equation of the pump-turbine can be obtained from the following several equations:

[0117] Full characteristic curve:

[0118] The full characteristic curve of the pump-turbine usually adopts the Suter transformation, but in the present invention, an improved Suter transformation is adopted, specifically as follows:

[0119]

[0120]

[0121] Where: WH and WM are the head characteristic function and the torque characteristic function respectively; y is the relative flow angle; z is the relative guide vane opening; h, q, ε, and m are the dimensionless values of the head, flow rate, rotational speed, and torque of the pump-turbine respectively; the subscript 11 represents the unit value, and the subscript r represents the rated value; c is a constant, generally taking a value of 1.0 to 1.5, and in the present invention, c takes 1.2;

[0122] Equation of rotation:

[0123] Under the load rejection condition of the pump-turbine, the rotational speed balance equation is as follows

[0124]

[0125] Where: ε and m are the dimensionless values of the rotational speed and torque of the pump-turbine respectively, the subscript 0 represents the value at the previous moment, and the subscript 00 represents the value at the moment before the previous moment; T a is the time inertia constant of the hydro-turbine unit, and the calculation formula is:

[0126]

[0127] Where: GD 2 is the flywheel torque of the unit, t·m 2 ; N r is the rated rotational speed of the pump; P r is the rated power of the pump, kw;

[0128] Head equation:

[0129] The nodes at the inlet of the spiral case and the outlet of the draft tube are denoted as 1 and 2 respectively. Substituting them into the corresponding characteristic line equations, the head balance equation of the hydro-turbine can be obtained according to the definition of the hydro-turbine head:

[0130] H=(C p -C m -(B p +B m )Q+C 2 |Q|Q)(27)

[0131]

[0132] Where: A is the area of the penstock, m 2 ; the meanings of other symbols are the same as above;

[0133] By simultaneously solving equations (22), (23), (25), and (27), the various parameters of the pump-turbine can be obtained;

[0134] Therefore, for the above boundary control equations of the pump-turbine, only the physical variable values of the virtual body of the pipeline at the spiral case and the draft tube need to be obtained, and combined with the Riemann invariant equation, the following can be obtained:

[0135]

[0136] In the formula: and are the flow velocity and water head of the last unit of the penstock connected to the scroll case; V 1 n and are the flow velocity and water head of the first unit of the penstock connected to the draft tube;

[0137] By substituting the obtained formulas (29) - (30) into formula (27), the water head balance equation under the virtual boundary conditions can be solved.

[0138] S7: Process the calculation results of step S6, and compare and verify them with the experimental results and the MOC simulation results.

[0139] Based on the above solution, in order to verify and analyze the simulation method of hydraulic transients in a pumped - storage power station based on the finite - volume method of the present invention, the following Examples 1 and 2 are carried out:

[0140] Example 1 selects a simple pipeline system to verify the accuracy of the second - order Godunov scheme based on FVM in the present invention. In Example 1, the upstream is a reservoir and the downstream is a simple pipeline with a valve. The pipeline is 500 m long, the calculation area has 10 units, the wave velocity is 1000 m / s, the upstream reservoir water level is 10 m, the initial flow velocity is 0.1 m / s, and the gravitational acceleration is 9.8 m / s 2 , the total calculation time is taken as 10 s, the downstream valve is set to close instantaneously, and there is no friction in the pipeline.

[0141] Example 2 selects the pipeline layout of hydraulic transients in a certain pumped - storage power station and the experimental results to verify the applicability of the calculation model of the present invention. Example 2: The upstream water intake system of a certain pumped - storage power station adopts the layout of "one penstock for two turbines", and the downstream tail - water system adopts the layout of "one penstock for one turbine". Its specific layout is as Figure 3 shown, and the parameters of each pipeline are shown in Table 1. Given that the rated head of the unit is 105.8 m, the rated flow rate is 148.8 m 3 / s, the rated speed is 200 r / min, the rated power is 139000 kw, and the moment of inertia is 10920 t·m 2 ; in the calculation condition, the upper reservoir water level is 412.4 m, the lower reservoir water level is 290.97 m, the initial guide - vane opening is 73.8%, the guide - vane closing is in two stages. The first - stage closing time is 3.62 s, the second - stage is 32.53 s, and the turning opening is 60%.

[0142] Table 1: Calculation parameters of each pipeline in a certain pumped - storage power station for FVM and MOC

[0143]

[0144] Examples 1 and 2 were programmed and calculated by the method of the present invention, and the calculation results of the second-order Godunov format based on the finite volume method were compared with the MOC calculation. The calculation results under different Courant numbers are as Figure 4 shown, and the calculation results under different grid numbers are as Figure 5 shown. The calculation time is shown in Table 2; the calculation results of the wave velocity and the head at the spiral case under the same load rejection test of FVM and MOC are as Figure 6 shown.

[0145] As Figure 4 shown, where Fig. (a) is the calculation result of MOC and Fig. (b) is the calculation result of FVM. It can be seen that when Cr = 1.0, the calculation results of the two methods are exactly the same as the exact solution. However, when Cr < 1.0, the numerical dissipation of the second-order Godunov format of FVM is much smaller than that of MOC.

[0146] As Figure 5 shown, when Cr = 0.5, the calculation accuracy of the MOC format with 512 grids is basically the same as that of the FVM format with 64 grids. However, as can be seen from Table 2, the CPU calculation time of the MOC format with 512 grids is about 3 times that of the FVM calculation time with 64 grids.

[0147] Table 2: Calculation time of FVM and MOC with different grid numbers in Example 1

[0148]

[0149] As Figure 6 shown, where (a) is the calculated value of the rotational speed and (b) is the calculated value at the spiral case. It can be seen that when MOC and FVM are used to calculate the load rejection of the pumped-storage power station model, the calculation results are basically in agreement with the experimental values. However, the calculation results of FVM are closer to the experimental values. And when the rotational speed changes rapidly, both will produce a certain amount of numerical fluctuations, but the calculation results of FVM are relatively more stable.

[0150] Therefore, it can be seen that the simulation method of the hydraulic transients of the pumped-storage power station based on the finite volume method can effectively solve the problems of wave velocity adjustment in complex pipe networks, poor accuracy and low efficiency caused by simplified models of MOC, and can simulate the hydraulic transient phenomenon in the load rejection experiment of a certain pumped-storage power station more efficiently and accurately.

Claims

1. A simulation method for hydraulic transients in pumped storage power stations based on the finite volume method, characterized in that, it includes the following steps: S1: Rewrite the unsteady flow equation of the pipeline, neglect the convection term, and write it as the classical water hammer equation; S2: Based on FVM, discretize the water hammer equation obtained in step S1 to obtain the integral solution formula for each unit volume in the pressurized pipeline; S3: Adopt the solution format of the Riemann problem to obtain the flux calculation form at the boundaries of each control volume; S4: According to the second-order Godunov solution format, solve the flux through the flux calculation form obtained in step S3 to obtain the second-order accurate flux calculation value at the boundaries of each unit volume; S5: According to the flux calculation value, merge the source terms through time integration; S6: After obtaining the unit control equation, according to the Riemann invariant equation, calculate the boundary between the reservoir and the unit by adding a virtual volume; S7: Process the calculation results of step S6 for comparison and verification; The flux calculation form at the boundaries of each control volume in step S3 is: where, g is the acceleration due to gravity; a is the wave speed; Step S4 is specifically: A1: Data reorganization where, Δx is the spatial step; the superscript n represents the t moment; Δi is calculated by the slope limiter function, for the MINMOD function A2: Time advancement where, Δt is the time step; A3: Problem solving Substitute the calculated (13) and (14) into equation (5) to obtain the second-order accurate flux calculation value at the boundaries of each unit volume; In step S6, the boundary control equation of the pump-turbine is combined with the virtual volume, and the control equation of the pump-turbine is obtained from the following several equations: Full characteristic curve: The full characteristic curve of the pump-turbine is subjected to an improved Suter transformation, specifically as follows: In the formula: WH and WM are the head characteristic function and the torque characteristic function respectively; y is the relative flow angle; z is the relative guide vane opening; h, q, ε, m are the dimensionless values of the head, flow rate, rotational speed and torque of the pump-turbine respectively; the subscript 11 represents the unit value, and the subscript r represents the rated value; c is a constant; Rotation equation: Under the load rejection condition of the pump-turbine, the rotational speed balance equation is as follows Where: ε and m are the dimensionless values of the rotational speed and torque of the pump-turbine, respectively. The subscript 0 represents the value at the previous moment, and the subscript 00 represents the value at the moment before the previous one; T a is the time inertia constant of the hydro turbine unit, and the calculation formula is: Where: GD 2 is the flywheel moment of the unit; N r is the rated speed of the water pump; P r is the rated power of the water pump; Head equation: Denote the nodes at the inlet of the spiral case and the outlet of the draft tube as 1 and 2 respectively, substitute them into the corresponding characteristic line equation, and then according to the definition of the turbine head, the head balance equation of the turbine can be obtained as: H = (C p - C m - (B p + B m ) Q + C 2 |Q| Q) (27) Where: A is the area of the penstock, m 2 ; The meanings of other symbols are the same as above; By combining equations (22), (23), (25) and (27), the various parameters of the pump-turbine can be obtained; Therefore, for the above boundary control equation of the pump-turbine, only the physical variable values of the virtual volume of the pipeline at the spiral case and the draft tube need to be obtained, and combined with the Riemann invariant equation, the following can be obtained: In the formula: and are the flow velocity and head of the last unit of the penstock connected to the scroll case; V 1 n and are the flow velocity and head of the first unit of the penstock connected to the draft tube; Substitute the obtained equations (29) to (30) into equation (27) to solve the head balance equation under the virtual boundary conditions.

2. The simulation method for hydraulic transients in pumped storage power stations based on the finite volume method according to claim 1, characterized in that, Step S1 is specifically: The control equation of unsteady flow in the pipeline is: Rewrite equations (1)-(2) into matrix form. Without considering the convective terms, the classical water hammer equation can be obtained: Wherein: Where: H is the piezometric head; V is the flow velocity; g is the acceleration due to gravity; a is the wave velocity; D is the pipe diameter; f is the constant friction factor of the pipe; S 0 is the pipe slope; x is the distance along the pipe axis; t is the time.

3. A simulation method for hydraulic transients in a pumped storage power station based on the finite volume method according to claim 2, wherein, the integral solution formula for each unit cell in the pressurized pipeline in step S2 is: where: i is the i-th control volume; F i+1 / 2 is the flux at the right boundary of the control volume; F i-1 / 2 is the flux at the left boundary of the control volume; Δt is the time step; Δx is the space step; the superscript n represents the t moment; the superscript n+1 represents the t+Δt moment.

4. A simulation method for hydraulic transients in a pumped storage power station based on the finite volume method according to claim 3, wherein, step S5 is specifically: Substitute the calculated value of the flux with second-order accuracy into equation (4), perform time integration and source term solution. During the solution process, use the explicit Runge-Kutta method, and a calculation format with second-order accuracy in time can be obtained.

5. A simulation method for hydraulic transients in a pumped storage power station based on the finite volume method according to claim 4, wherein, the calculation process of the calculation format with second-order accuracy in time is:

6. A simulation method for hydraulic transients in a pumped storage power station based on the finite volume method according to claim 1, wherein, in step S6, a processing method of adding virtual cells of -1, 0 and N+1, N+2 on both sides of the boundary is adopted, and the added virtual bodies meet the following conditions: U -1 = U 0 = U 1 / 2 (18) U N+1 = U N+2 = U N+1 / 2 (19) The physical variables of each virtual body respectively satisfy the Riemann invariant equations at the boundaries. For the upstream and downstream reservoirs, H 1 / 2 = H u , H N+1 / 2 = H d , and the corresponding calculation equations are obtained:

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