Establishment method of high-water-head constant-speed pumped storage unit pump turbine frequency response analytical model during power generation

Abstract

At present, a time domain simulation model or a simplified model is usually adopted in the frequency response research of the pumped storage unit, or the calculation efficiency is low or the calculation precision is poor, so that the analysis requirement is difficult to meet. On the basis, the invention provides a method for establishing a frequency response analytical model of a water pump turbine of a high-water-head constant-speed pumped storage unit during power generation, and belongs to the technical field of frequency response of pumped storage units. The method comprises the steps that firstly, an internal parameter model is built according to a total characteristic curve of the pump turbine and the relation among unit torque, unit flow and unit rotating speed, and internal parameters comprise torque and guide vane opening; then, according to operation characteristics, a simplified equation is proposed, internal parameters in the internal parameter model are converted into external parameters, an external parameter model is constructed, and the external parameters comprise a water head and a load; according to the method, the problems that time domain simulation model parameters are difficult to obtain and calculation is complex can be avoided, and the frequency response characteristics of the unit can be accurately reflected.

Description

Technical Field

[0001] The invention belongs to the technical field of frequency response of pumped storage units, and designs a method for establishing a simplified analytical model of frequency response of a water pump turbine of a constant-speed pumped storage unit under power generation conditions. Background Art

[0002] With the rapid development of new power systems, the proportion of new energy installed capacity continues to grow, the demand for power system frequency regulation has increased dramatically, and frequency stability is facing new challenges. It is urgent to reasonably supplement and configure the system's frequency response resources. As a clean energy, pumped storage units have the advantages of high energy conversion rate, rapid start-up, flexible and reliable operation, and are important frequency response resources. They need to be considered in operation planning, planning and control for frequency stability analysis. Therefore, establishing a frequency response model that can accurately reflect the regulation characteristics of pumped storage resources is crucial for accurate and efficient system operation management analysis.

[0003] At present, the models used in the research on frequency adjustment of pumped storage units are mainly divided into two categories: time domain simulation model and simplified model. The time domain simulation model is accurate and complex, and can more accurately reflect the frequency response characteristics of the unit, so it has become the mainstream model and is widely used. However, due to its complex structure, the time domain simulation model has low computational efficiency. On the one hand, when faced with massive scenarios in planning and planning analysis, the calculation time is long and may not meet the work requirements; on the other hand, in the face of real-time control, the model cannot meet the requirements of calculation speed due to the long calculation time. Therefore, in some scenarios with high requirements for calculation speed, it is necessary to simplify the unit frequency response model and reduce the computational complexity to improve the computational efficiency. Some studies do not have high requirements for the accuracy of the frequency response capability of pumped storage units, so they directly use the static frequency response model of hydropower units to characterize the pumped storage units under power generation conditions, reducing the computational complexity. However, when the working point deviates greatly from the rated operating conditions, the simulation error of the above static analytical model becomes significant and cannot be ignored. Moreover, since the components of high-head pumped-storage units such as runners, guide vanes, and water guide mechanisms are quite different from those of conventional hydropower units, it is not appropriate to directly apply the above hydropower model to pumped-storage units. Therefore, in the construction of the dynamic model of the pumped-storage unit, it is necessary to consider its own dynamic frequency response characteristics and reduce the computational complexity.

[0004] In the current frequency response model of pumped storage units, the input-output relationship between the generator and load module, the governor module, the water diversion system and the servo system module generally does not change with the operating conditions, and there are mature analytical models that can be directly used; however, the pump-turbine module is quite different from the ordinary hydropower unit, and the model parameters change with the operating point, which makes it difficult for the existing pump-turbine static model to accurately reflect its frequency response characteristics, and the complex full-parameter analytical model involves Suter transformation and improved Suter transformation of the full characteristic curve of the pump-turbine, and the mathematical calculation is complex and the parameters are difficult to obtain. Therefore, it is necessary to select and establish a suitable and convenient dynamic analytical model of the pump-turbine frequency response. Summary of the invention

[0005] In view of the problems existing in establishing the existing pump-turbine frequency response model, the present invention studies and establishes an analytical model that can conveniently and accurately describe the frequency response characteristics of the pump-turbine of a pumped-storage unit.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A method for establishing a simplified analytical model of a pump-turbine expressed by external parameters (such as head, power, etc.) based on the frequency response principle of a constant-speed pumped-storage unit under power generation conditions. To establish the model, it is first necessary to construct an internal parameter model based on the full characteristic curve of the pump-turbine and the relationship between unit torque, unit flow, and unit speed, where the internal parameters include torque and guide vane opening; then, based on the operating characteristics, a simplified equation is proposed to convert the difficult-to-obtain internal parameters in the model into external parameters that are easy to obtain, and the relevant part of the curve slope is omitted to construct an external parameter model. The external parameters include head, load, etc. Specifically, the following steps are included:

[0008] S1: Constructing an internal parameter analysis model

[0009] The present invention obtains an internal parameter analytical model through a full characteristic curve and a six-parameter model, and the specific process is as follows.

[0010] The relationship between the working parameters of a pump-turbine is complex, and a six-parameter model is usually used to describe the dynamic characteristics:

[0011]

[0012] Where: m t is the relative torque of the pump-turbine; q is the relative flow of the pump-turbine; y is the relative guide vane opening; ω is the relative speed of the pump-turbine; h is the relative water head of the pump-turbine.

[0013] Convert equation (1) into relative value and perform Taylor expansion, which is shortened to equation (2).

[0014]

[0015] Where: e y is the transfer coefficient of turbine torque to guide vane opening; e ω is the transfer coefficient of turbine torque to speed; e h is the transfer coefficient of turbine torque to water head; e qy is the transfer coefficient of turbine flow to guide vane opening; e qω is the transfer coefficient of turbine flow to speed; e qh is the transfer coefficient of turbine flow to water head; Δy is the change in relative guide vane opening; Δω is the change in relative speed of the pump turbine; Δh is the change in relative water head of the pump turbine. Considering that the research object of this invention is a constant-speed pumped storage unit, the speed does not change with the working conditions, so the two parameters related to the speed change rate can be ignored, and formula (2) is converted into

[0016]

[0017] To construct a dynamic analytical model of a pump-turbine, it is necessary to calculate the four parameters e in equation (3): y 、e h 、e qy 、e qh Start research.

[0018] The operating characteristic curve of a pump turbine is usually a set of full characteristic curves under different guide vane openings, such as Figure 1 As shown, the relationship between unit speed, unit torque and unit flow rate under different guide vane openings is described.

[0019] Unit speed n in the full characteristic curve of pump turbine 11 , unit flow Q 11 , Unit moment M 11 The definition is shown in formula (4).

[0020]

[0021] Where: n is the speed, in r / min; D is the diameter of the runner inlet, in m; H is the turbine working head, in m; Q is the flow rate, in m 3 / s; M is the moment, the unit is N·m; ρ is the water density, the unit is m 3 / s.

[0022] When the speed remains unchanged, perform differential calculation on equation (4):

[0023]

[0024] Arrangement available

[0025]

[0026] Also because

[0027]

[0028] Combining equations (6) and (7), we can obtain:

[0029]

[0030] The flow calculation formula is shown in formula (9):

[0031]

[0032] Where: C d With C Y is the pipe section coefficient; Y is the guide vane opening; g is the gravitational acceleration.

[0033] Taking the derivative, we get e qy :

[0034]

[0035] The calculation formula of water moment is shown in formula (11):

[0036] M=ρgQHr(11)

[0037] Where: r is the wheel radius.

[0038] The derivative is:

[0039]

[0040] Combining equations (8), (10), and (12), we can get the expressions of the four parameters in the pump-turbine model as follows:

[0041]

[0042] The internal parameter analytical model is shown in formula (13).

[0043] S2: Construction of external parameter model

[0044] Compared with the simulation time domain model, the proposed internal parameter model realizes model simplification and can be used for analytical analysis, but its transfer function still involves the slope of the full characteristic curve and the internal parameters of the pump turbine, which not only increases the calculation workload, but also has the problem of difficulty in parameter acquisition. Therefore, the present invention omits the part of the internal parameter model involving the calculation of the slope of the full characteristic curve, and on the other hand, reduces the difficulty of model acquisition and the amount of data required by converting the internal parameters of the pump turbine into external parameters.

[0045] S2-1: Omit the curve slope calculation part

[0046] Considering that the pumped storage unit under power generation conditions mainly participates in frequency response work in the stable working area, and the pump turbine is operating stably under turbine conditions, the conditions shown in formula (14) must be met:

[0047]

[0048] From formula (4) and the full characteristic curve, it can be seen that as the water head increases, the unit speed gradually decreases. Therefore, under high water head conditions, the unit speed n 11 The flow and torque characteristic curve of the pump-turbine tends to be flat.

[0049] Combining formula (11), we can get:

[0050]

[0051] therefore

[0052]

[0053] The part of the internal parameter analysis model involving the calculation of the slope of the full characteristic curve can be simplified

[0054]

[0055] S2-2: Conversion of internal parameters to external parameters

[0056] In order to avoid the generation of suction vortices, the water flow in each channel of the pumped storage power station must maintain uniform flow velocity and flow rate. At the same time, the analysis of the power characteristic curve of the pump-turbine shows that the relay stroke of the pump-turbine is approximately a straight line, and when participating in frequency regulation, the pump-turbine usually works in the linear region. Therefore, the simplified conditions of the dynamic analytical model of the pump-turbine can be set as follows: (1) The flow coefficient of the pump-turbine remains unchanged under power generation conditions; (2) The relay stroke is approximately a straight line; (3) The efficiency of the pump-turbine is approximately unchanged under power generation conditions.

[0057] Based on the above three simplified conditions, three operating equations of the pump turbine are proposed:

[0058]

[0059] Where, q is the relative flow rate; p is the relative power; m t is the relative torque; C d is the flow coefficient; C Y is the proportional coefficient; Y is the guide vane opening; g is the gravity acceleration; H is the water head; h is the relative water head; Y ris the rated guide vane opening; y is the relative guide vane opening; ρ is the water density; η is the efficiency; ω is the speed; ω r Indicates rated speed.

[0060] In the model described by formula (17), the transfer parameter calculation involves the internal parameters flow and torque. In order to reduce the complexity of the calculation, they can be converted into external parameters power and head that are easy to calculate according to formula (18), as shown in formula (19).

[0061]

[0062] Compared with the internal parameter model, the external parameter model of the pump-turbine is more convenient in practical applications. On the one hand, parameter selection is simpler, and there is no need to draw working characteristic curves to convert complex internal parameters into external parameters such as load and head. On the other hand, the transfer function form is simpler, which can effectively reduce the calculation complexity.

[0063] The beneficial effects of the present invention are:

[0064] Compared with the traditional model, the proposed model takes into account the impact of dynamic changes of the working point on the frequency response model, converts internal parameters that are difficult to obtain into external parameters, and omits the part of the model involving the calculation of the slope of the full characteristic curve. It can more accurately describe the frequency response characteristics of the constant-speed pumped-storage unit under the power generation condition, and avoids the problem that the parameters of the full-parameter model are difficult to obtain. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 is the flow and torque characteristic curve of the pump turbine; Figure 1 (a) is the flow characteristic curve of the pump turbine; Figure 1 (b) is the torque characteristic curve of the pump turbine;

[0066] Figure 2 This is the frequency response curve of the elastic water hammer model under high water head;

[0067] Figure 3 This is the frequency response curve of the approximate elastic water hammer model under high water head;

[0068] Figure 4 This is the frequency response curve of the rigid water hammer model under high water head. DETAILED DESCRIPTION

[0069] In view of the problems existing in establishing the existing pump-turbine frequency response model, the present invention studies and establishes an analytical model that can conveniently and accurately describe the frequency response characteristics of the pump-turbine of a pumped-storage unit.

[0070] In order to achieve the above object, the technical solution adopted by the present invention is:

[0071] A method for establishing a simplified analytical model of a pump-turbine expressed by external parameters (such as head, power, etc.) based on the frequency response principle of a constant-speed pumped-storage unit under power generation conditions. To establish the model, it is first necessary to construct an internal parameter model based on the full characteristic curve of the pump-turbine and the relationship between unit torque, unit flow, and unit speed, where the internal parameters include torque and guide vane opening; then, based on the operating characteristics, a simplified equation is proposed to convert the difficult-to-obtain internal parameters in the model into external parameters that are easy to obtain, and the relevant part of the curve slope is omitted to construct an external parameter model. The external parameters include head, load, etc. Specifically, the following steps are included:

[0072] S1: Constructing an internal parameter analysis model

[0073] The present invention obtains an internal parameter analytical model through a full characteristic curve and a six-parameter model, and the specific process is as follows.

[0074] The relationship between the working parameters of a pump-turbine is complex, and a six-parameter model is usually used to describe the dynamic characteristics:

[0075]

[0076] Where: m t is the relative torque of the pump-turbine; q is the relative flow of the pump-turbine; y is the relative guide vane opening; ω is the relative speed of the pump-turbine; h is the relative water head of the pump-turbine.

[0077] Convert equation (1) into relative value and perform Taylor expansion, which is shortened to equation (2).

[0078]

[0079] Where: e y is the transfer coefficient of turbine torque to guide vane opening; e ω is the transfer coefficient of turbine torque to speed; e h is the transfer coefficient of turbine torque to water head; e qy is the transfer coefficient of turbine flow to guide vane opening; e qω is the transfer coefficient of turbine flow to speed; e qh is the transfer coefficient of turbine flow to water head. Considering that the research object of this invention is a constant-speed pumped storage unit, the speed does not change with the working conditions, so the two parameters related to the speed change rate can be ignored, and formula (2) is converted into

[0080]

[0081] To construct a dynamic analytical model of a pump-turbine, it is necessary to calculate the four parameters e in equation (3): y、e h 、e qy 、e qh Start research.

[0082] The operating characteristic curve of a pump turbine is usually a set of full characteristic curves under different guide vane openings, such as Figure 1 As shown, the relationship between unit speed, unit torque and unit flow rate under different guide vane openings is described.

[0083] Unit speed n in the full characteristic curve of pump turbine 11 , unit flow Q 11 , Unit moment M 11 The definition is shown in formula (4).

[0084]

[0085] Where: n is the speed, in r / min; D is the diameter of the runner inlet, in m; H is the turbine working head, in m; Q is the flow rate, in m 3 / s; M is the moment, the unit is N·m; ρ is the water density, the unit is m 3 / s.

[0086] When the speed remains unchanged, perform differential calculation on equation (4):

[0087]

[0088] Arrangement available

[0089]

[0090] Also because

[0091]

[0092] Combining equations (6) and (7), we can obtain:

[0093]

[0094] The flow calculation formula is shown in formula (9):

[0095]

[0096] Where: C d is the flow coefficient; C Y is the proportional coefficient; Y is the guide vane opening; g is the gravitational acceleration.

[0097] Taking the derivative, we get e qy :

[0098]

[0099] The calculation formula of water moment is shown in formula (11):

[0100] M=ρgQHr(11)

[0101] Where: r is the wheel radius.

[0102] The derivative is:

[0103]

[0104] Combining equations (8), (10), and (12), we can get the expressions of the four parameters in the pump-turbine model as follows:

[0105]

[0106] The internal parameter analytical model is shown in formula (13).

[0107] S2: Construction of external parameter model

[0108] Compared with the simulation time domain model, the proposed internal parameter model realizes model simplification and can be used for analytical analysis, but its transfer function still involves the slope of the full characteristic curve and the internal parameters of the pump turbine, which not only increases the calculation workload, but also has the problem of difficulty in parameter acquisition. Therefore, the present invention omits the part of the internal parameter model involving the calculation of the slope of the full characteristic curve, and on the other hand, reduces the difficulty of model acquisition and the amount of data required by converting the internal parameters of the pump turbine into external parameters.

[0109] S2-1: Omit the curve slope calculation part

[0110] Considering that the pumped storage unit under power generation conditions mainly participates in frequency response work in the stable working area, and the pump turbine is operating stably under turbine conditions, the conditions shown in formula (14) must be met:

[0111]

[0112] From formula (4) and the full characteristic curve, it can be seen that as the water head increases, the unit speed gradually decreases. Therefore, under high water head conditions, the unit speed n 11 The flow and torque characteristic curve of the pump-turbine tends to be flat.

[0113] Combining formula (11), we can get:

[0114]

[0115] therefore

[0116]

[0117] The part of the internal parameter analysis model involving the calculation of the slope of the full characteristic curve can be simplified

[0118]

[0119] S2-2: Conversion of internal parameters to external parameters

[0120] In order to avoid the generation of suction vortices, the water flow in each channel of the pumped storage power station must maintain uniform flow velocity and flow rate. At the same time, the analysis of the power characteristic curve of the pump-turbine shows that the relay stroke of the pump-turbine is approximately a straight line, and when participating in frequency regulation, the pump-turbine usually works in the linear region. Therefore, the simplified conditions of the dynamic analytical model of the pump-turbine can be set as follows: (1) The flow coefficient of the pump-turbine remains unchanged under power generation conditions; (2) The relay stroke is approximately a straight line; (3) The efficiency of the pump-turbine is approximately unchanged under power generation conditions.

[0121] Based on the above three simplified conditions, three operating equations of the pump turbine are proposed:

[0122]

[0123] In the model described by formula (17), the transfer parameter calculation involves the internal parameters flow and torque. In order to reduce the complexity of the calculation, they can be converted into external parameters power and head that are easy to calculate according to formula (18), as shown in formula (19).

[0124]

[0125] Compared with the internal parameter model, the external parameter model of the pump-turbine is more convenient in practical applications. On the one hand, parameter selection is simpler, and there is no need to draw working characteristic curves to convert complex internal parameters into external parameters such as load and head. On the other hand, the transfer function form is simpler, which can effectively reduce the calculation complexity.

[0126] S3: Example verification

[0127] When analyzing the accuracy of the frequency response characteristics of the pumped storage unit described by the model, the quasi-steady state and the lowest point of the frequency are important research parameters. To study the degree of fit between the frequency response characteristics of the pumped storage unit described by the model and the actual situation, it is necessary to continuously sample the frequency response curve and calculate the difference between the studied model and the actual situation. Therefore, the present invention focuses on comparing the initial frequency drop rate, the lowest frequency point and arrival time, the quasi-steady state frequency and the mean square error of the frequency response curve of different models.

[0128] Since it is difficult to obtain the actual operating parameters of the pump-turbine and design the experimental environment, the present invention adopts a relatively accurate full-parameter model to represent the actual accurate data, adjusts the working conditions of the pump-turbine by changing the water head, and simulates the full-parameter model under different water heads and different water diversion system models, the ordinary hydropower unit model and the simplified design model of the present invention.

[0129] Under high water head, the simulation results of the full parameter model of the water diversion system model, the ordinary hydropower unit model and the design model of the present invention are described by three types of water hammer models respectively. Figure 2 to Figure 4 As shown in Tables 1 to 3.

[0130] Table 1 Simulation results and errors of elastic water hammer model under high water head

[0131]

[0132] Table 2 Simulation results and errors of the approximate elastic water hammer model under high water head

[0133]

[0134]

[0135] Table 3 Simulation results and errors of the rigid water hammer model under high water head

[0136]

[0137] Comparing the frequency response simulation results, we can see that:

[0138] (1) The design model of the present invention has higher accuracy in describing the lowest frequency point of the unit.

[0139] When the elastic water hammer model is adopted, the frequency minimum point deviation of the design model of the present invention is only 0.0362Hz, accounting for 7.43% of the maximum drop frequency, and the frequency minimum point deviation of the turbine model is 0.1469Hz, accounting for 33.49% of the maximum drop frequency; when the approximate elastic water hammer model is adopted, the frequency minimum point deviation of the design model of the present invention is only 0.0333Hz, accounting for 7.55% of the maximum drop frequency, and the frequency minimum point deviation of the turbine model is 0.1572Hz, accounting for 35.65% of the maximum drop frequency; when the rigid water hammer model is adopted, the frequency minimum point deviation of the design model of the present invention is only 0.0309Hz, accounting for 7.11% of the maximum drop frequency, and the frequency minimum point deviation of the turbine model is 0.1249Hz, accounting for 28.76% of the maximum drop frequency. Therefore, under high water head, the frequency minimum point in the frequency response process of the design model of the present invention is closer to the actual situation.

[0140] (2) The quasi-steady-state frequency values ​​of the turbine model and the design model of the present invention are very close to the simulation model.

[0141] The quasi-steady-state frequency errors of the three models are all less than 10 -4 Hz.

[0142] (3) The design model of the present invention has higher accuracy in describing the time when the unit reaches the lowest point.

[0143] Under high head conditions, the error range of the model of the present invention is less than 2.20%, while the error range of the turbine model is 16.85% to 17.98%, so the model of the present invention is more accurate.

[0144] (4) The design model of the present invention has higher accuracy in describing the initial frequency drop rate of the unit.

[0145] Under high water head conditions, the error range of the model of the present invention is 0.30% to 0.86%, while the error range of the turbine model is 3.05% to 11.10%, so the model of the present invention is more accurate.

[0146] (5) The mean square error of the frequency response curve of the design model of the present invention is smaller and more consistent with the actual situation.

[0147] It can be concluded that under high water head conditions, it is more accurate and reasonable to use the design model of the present invention to describe the frequency response characteristics of the pump-turbine.

[0148] The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A method for establishing an analytical model of the frequency response of a pump-turbine of a high-head constant-speed pumped-storage unit during power generation, characterized in that: The establishment method first constructs an internal parameter model based on the relationship between the full characteristic curve of the pump-turbine and the unit torque, unit flow, and unit speed, wherein the internal parameters include torque and guide vane opening; Then, according to the operation characteristics, simplified equations are proposed to convert the internal parameters in the internal parameter model into external parameters and construct the external parameter model, in which the external parameters include head and load.

2. The method for establishing a frequency response analytical model of a pump-turbine of a high-head constant-speed pumped-storage unit during power generation according to claim 1, characterized in that: The following steps are involved: S1: Construct an internal parameter analysis model through the full characteristic curve and six-parameter model, as follows: The working parameters of the pump turbine are described by a six-parameter model: Where: m t is the relative torque of the pump-turbine; q is the relative flow of the pump-turbine; y is the relative guide vane opening; ω is the relative speed of the pump-turbine; h is the relative water head of the pump-turbine; Convert equation (1) to: Where: e y is the transfer coefficient of turbine torque to guide vane opening; e h is the transfer coefficient of turbine torque to water head; e qy is the transfer coefficient of turbine flow to guide vane opening; e qh is the transfer coefficient of turbine flow to water head; Δy is the change in relative guide vane opening; Δω is the change in relative speed of the pump-turbine; Δh is the change in relative water head of the pump-turbine; Then the expressions of the four parameters in the pump-turbine model are: Then the internal parameter analytical model is shown in formula (3); Among them, n 11 Indicates the unit speed, Q in the full characteristic curve of the pump turbine 11 Indicates the unit flow rate, M in the full characteristic curve of the pump turbine 11 It represents the unit torque in the full characteristic curve of the pump turbine; q is the relative flow rate; h is the relative head; m is the relative torque; n is the speed, in r / min; D is the diameter of the impeller inlet, in m; Q r is the rated flow rate, Q is the flow rate, the unit is m 3 / s;H r is the rated water head of the turbine, H is the working water head of the turbine, the unit is m; M r is the rated moment; ρ is the water density, in m 3 / s; S2: Building an external parameter model S2-1: Omit the calculation part of the slope of the full characteristic curve of the pump turbine Considering that the pumped storage unit under power generation conditions mainly participates in frequency response work in the stable working area, and the pump turbine is operating stably under turbine conditions, the conditions shown in formula (4) must be met: From formula (4) and the full characteristic curve, it can be seen that under high head conditions, the unit speed n 11 Small, the flow and torque characteristic curve of the pump turbine tends to be flat; Combined with the water torque calculation formula, we can get: therefore Simplify the part of the internal parameter analysis model involving the calculation of the slope of the full characteristic curve: S2-2: Conversion of internal parameters to external parameters The simplified conditions of the dynamic analytical model of the pump-turbine are set, and based on the simplified conditions, the operating equation of the pump-turbine is proposed: Where, q is the relative flow rate; p is the relative power; m t is the relative torque; C d is the flow coefficient; C Y is the proportional coefficient; Y is the guide vane opening; g is the gravity acceleration; H is the water head; h is the relative water head; Y r is the rated guide vane opening; y is the relative guide vane opening; ρ is the water density; η is the efficiency; ω is the speed; ω r Indicates rated speed; The transfer parameters in formula (7) involve the internal parameters flow and torque. According to formula (8), the transfer parameters in formula (7) are converted into the external parameters power and head, as shown in formula (9); 3. The method for establishing a frequency response analytical model of a pump-turbine of a high-head constant-speed pumped-storage unit during power generation according to claim 2, characterized in that: In S1, the construction process of the expressions of the four parameters in the pump-turbine model is as follows: Unit speed n in the full characteristic curve of pump turbine 11 , unit flow Q 11 , Unit moment M 11 The definition is as shown in formula (10); Where: n is the rotation speed, unit is r / min; D is the diameter of the runner inlet, unit is m; H is the working water head of the turbine, unit is m; Q is the flow rate, in m 3 / s; M is the moment, the unit is N·m; ρ is the water density, the unit is m 3 / s; When the speed remains unchanged, the equation (10) can be processed to obtain: Also because Combining equations (11) and (12), we can obtain: The flow calculation formula is shown in formula (9): Where: C d is the flow coefficient; C Y is the proportional coefficient; Y is the guide vane opening; g is the gravitational acceleration; Taking the derivative, we get e qy : The calculation formula of water moment is shown in formula (16): M=ρgQHr(16) Where: r is the wheel radius; The derivative is: Combining equations (13), (15), and (17), we can obtain the expressions of the four parameters in the pump-turbine model as shown in equation (2).

4. The method for establishing a frequency response analytical model of a pump-turbine of a high-head constant-speed pumped-storage unit during power generation according to claim 2, characterized in that: In the above-mentioned S2-2, the simplified conditions of the dynamic analytical model of the pump-turbine are set as follows: (1) the flow coefficient of the pump-turbine remains unchanged under the power generation condition; (2) the relay stroke is approximately a straight line; (3) the efficiency of the pump-turbine remains approximately unchanged under the power generation condition.

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