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

Abstract

In the current frequency response research of pumped storage unit, time domain simulation model or simplified model is usually adopted, or the calculation efficiency is low or the calculation precision is poor, and it is difficult to meet the analysis requirements. Based on this, the application provides a kind of establishment method of frequency response analytical model of high head constant speed pumped storage unit water pump turbine during power generation, which belongs to the technical field of frequency response of pumped storage unit. First, according to the full characteristic curve of the water pump turbine and the relationship between unit torque, unit flow and unit speed, the internal parameter model is constructed, wherein the internal parameters include torque and guide vane opening; then, according to the operation characteristics, the simplified equation is proposed, the internal parameters in the internal parameter model are converted into external parameters, and the external parameter model is constructed, wherein the external parameters include water head and load. The application can avoid the problems of difficult to obtain parameters and complex calculation of time domain simulation model, and can more accurately reflect the frequency response characteristics of the unit.

Description

Technical Field

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

[0002] With the rapid development of new power systems and the continuous increase in the proportion of new energy installed capacity, the demand for power system frequency regulation has surged, posing new challenges to frequency stability. There is an urgent need to rationally supplement and allocate the system's frequency response resources. Pumped storage units, as a clean energy source, possess advantages such as high energy conversion efficiency, rapid start-up, and flexible and reliable operation, making them important frequency response resources. They need to be considered in operation planning, scheduling, and control aspects oriented towards frequency stability analysis. Therefore, establishing a frequency response model that accurately reflects the regulation characteristics of pumped storage resources is crucial for accurate and efficient system operation management analysis.

[0003] Currently, the models used in pumped-storage units for frequency regulation research are mainly divided into two categories: time-domain simulation models and simplified models. Time-domain simulation models are precise and complex, and can accurately reflect the frequency response characteristics of the unit, thus becoming the mainstream model and widely used. However, due to their complex structure, time-domain simulation models have low computational efficiency. On the one hand, when facing massive scenarios in planning and program analysis, the computation time is long, which may not meet the work requirements; on the other hand, for real-time control, the model cannot meet the speed requirements due to its long computation time. Therefore, in some scenarios with high computational speed requirements, it is necessary to simplify the unit's frequency response model to reduce computational complexity and improve computational efficiency. Some studies do not have high requirements for the accuracy of the pumped-storage unit's frequency response capability, so they directly use the static frequency response model of hydropower units to characterize the pumped-storage unit under power generation conditions, reducing computational complexity. However, when the operating point deviates significantly from the rated operating condition, the simulation error of the above-mentioned static analytical model becomes significant and cannot be ignored. Furthermore, since the components of high-head pumped storage units, such as the runner, guide vanes, and guide vane mechanism, differ significantly from those of conventional hydroelectric units, directly applying the aforementioned hydroelectric model to pumped storage units is not appropriate. Therefore, the dynamic frequency response characteristics of pumped storage units need to be considered and computational complexity reduced when constructing their dynamic models.

[0004] In current pumped storage unit frequency response models, the input-output relationships between the generator and load modules, governor module, water intake system, and servo system modules generally do not change with operating conditions, and mature analytical models can be directly used. However, the pump-turbine module differs significantly from ordinary hydroelectric units, and its model parameters change with the operating point. This makes it difficult for existing static models of pump-turbines to accurately represent their frequency response characteristics. Complex full-parameter analytical models involve Suter transformations and improved Suter transformations of the pump-turbine's full characteristic curves, which are mathematically complex and difficult to obtain parameters. Therefore, it is necessary to select and establish a suitable and convenient dynamic analytical model for the frequency response of pump-turbines. Summary of the Invention

[0005] To address the problems existing in the establishment of frequency response models for pump-turbine units, this invention studies and establishes an analytical model that can conveniently and accurately describe the frequency response characteristics of pump-turbine units in pumped storage units.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for establishing a simplified analytical model of a pump-turbine turbine, expressed by external parameters (such as head and power), based on the frequency response principle of a constant-speed pumped-storage unit under power generation conditions. To establish the model, firstly, an internal parameter model is constructed based on the full characteristic curves of the pump-turbine and the relationships between unit torque, unit flow rate, and unit speed. Internal parameters include torque and guide vane opening. Then, based on operating characteristics, simplified equations are proposed to convert the difficult-to-obtain internal parameters into easily obtainable external parameters, omitting curve slopes to obtain relevant parts, thus constructing an external parameter model. External parameters include head and load. The specific steps include:

[0008] S1: Constructing an analytical model of internal parameters

[0009] This invention obtains an analytical model of internal parameters through full characteristic curves and a six-parameter model. The specific process is as follows.

[0010] The relationships between the operating parameters of a water pump turbine are complex, and a six-parameter model is typically used to describe its dynamic characteristics.

[0011]

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

[0013] Equation (1) is converted to a relative value and expanded using Taylor, and is simplified to Equation (2).

[0014]

[0015] In the formula: e y e is the transmission coefficient of turbine torque to guide vane opening. ω e is the torque-to-velocity transmission coefficient of the turbine; h e is the transmission coefficient of turbine torque to head; qy e is the transmission coefficient of turbine flow rate to guide vane opening. qω e is the transfer coefficient of flow rate to velocity in a water turbine. qh Δy is the transfer coefficient of the turbine flow rate to the 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 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 operating conditions, so the two parameters related to the rate of change of speed can be ignored, and equation (2) can be converted to

[0016]

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

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

[0019] The unit speed n in the full characteristic curve of a water pump turbine 11 Unit flow rate Q 11 Unit torque M 11 The definition is shown in equation (4).

[0020]

[0021] In the formula: n is the rotational speed, in r / min; D is the inlet diameter of the runner, in m; H is the turbine working head, in m; Q is the flow rate, in m³ / s. 3 / s; M is torque, in N·m; ρ is water density, in m³. 3 / s.

[0022] When the rotational speed remains constant, perform differential calculations on equation (4):

[0023]

[0024] Organizing can yield

[0025]

[0026] And because

[0027]

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

[0029]

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

[0031]

[0032] In the formula: C d With C Y y is the pipe section modulus; Y is the guide vane opening; g is the gravitational acceleration.

[0033] Differentiation yields e qy :

[0034]

[0035] The formula for calculating hydraulic torque is shown in equation (11):

[0036] M=ρgQHr(11)

[0037] In the formula: r is the radius of the wheel.

[0038] Differentiation yields:

[0039]

[0040] Combining equations (8), (10), and (12), the expressions for the four parameters in the pump-turbine model are:

[0041]

[0042] The internal parameter analysis model is shown in equation (13).

[0043] S2: Construction of the extrinsic parameter model

[0044] Compared to the simulation time-domain model, the proposed internal parameter model, while simplifying the model and enabling analytical analysis, still involves calculating the slope of the full characteristic curve and the internal parameters of the pump-turbine in its transfer function. This not only increases the computational workload but also presents difficulties in parameter acquisition. Therefore, this invention omits the part involving the calculation of the slope of the full characteristic curve in the internal parameter model and reduces the difficulty of model acquisition and the amount of data required by transforming the internal parameters of the pump-turbine into external parameters.

[0045] S2-1: Omitted part of curve slope calculation

[0046] Considering that pumped storage units mainly participate in frequency response operation in the stable operating range during power generation, and that the pump-turbine needs to meet the conditions shown in equation (14) when the turbine is operating stably:

[0047]

[0048] From equation (4) and the overall characteristic curve, it can be seen that the unit rotational speed gradually decreases with increasing head. Therefore, under high head conditions, the unit rotational speed n 11 The flow rate and torque characteristic curves of the water pump turbine are relatively small, and tend to be flat.

[0049] Combining equation (11), we can obtain:

[0050]

[0051] therefore

[0052]

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

[0054]

[0055] S2-2: Converting internal parameters to external parameters

[0056] To avoid generating suction vortices, the water flow in each channel of the pumped storage power station must maintain uniform velocity and flow rate. Meanwhile, analysis of the power characteristic curve of the pump-turbine reveals that the servo travel of the pump-turbine is approximately linear, and the pump-turbine typically operates in the linear region when participating in frequency regulation. Therefore, the simplified conditions for the dynamic analytical model of the pump-turbine can be set as follows: (1) the flow coefficient of the pump-turbine remains constant under power generation conditions; (2) the servo travel is approximately linear; (3) the efficiency of the pump-turbine remains approximately constant under power generation conditions.

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

[0058]

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

[0060] In the model described by Equation (17), the determination of the transmission parameters involves internal parameters such as flow rate and torque. In order to reduce the complexity of the determination, they can be converted into external parameters such as power and head, which are easier to determine, according to Equation (18), as shown in Equation (19).

[0061]

[0062] Compared to internal parameter models, external parameter models for pump-turbine systems are more convenient in practical applications. Firstly, parameter selection is simpler, eliminating the need to plot operating characteristic curves and transforming complex internal parameters into external parameters such as load and head. Secondly, the transfer function form is simpler, effectively reducing computational complexity.

[0063] The beneficial effects of this invention are as follows:

[0064] Compared with traditional models, the proposed model considers the impact of dynamic changes in the operating point on the frequency response model, converts difficult-to-obtain internal parameters into external parameters, and omits the part involving the calculation of the slope of the full characteristic curve in the model. It can more accurately describe the frequency response characteristics of the pumped storage unit under the power generation condition of constant speed, and avoids the problem of difficulty in obtaining parameters of the full parameter model. Attached Figure Description

[0065] Figure 1 The flow rate and torque characteristic curves of the water pump turbine; Figure 1 (a) is a flow characteristic curve of a water pump and a water turbine; Figure 1 (b) is a graph showing the torque characteristics of the water pump and turbine.

[0066] Figure 2 The frequency response curve of the elastic water hammer model under high water head is shown.

[0067] Figure 3 The frequency response curves of an approximate elastic water hammer model under high water head are shown.

[0068] Figure 4 The frequency response curves are for a rigid water hammer model under high water head conditions. Detailed Implementation

[0069] To address the problems existing in the establishment of frequency response models for pump-turbine units, this invention studies and establishes an analytical model that can conveniently and accurately describe the frequency response characteristics of pump-turbine units in pumped storage units.

[0070] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0071] A method for establishing a simplified analytical model of a pump-turbine turbine, expressed by external parameters (such as head and power), based on the frequency response principle of a constant-speed pumped-storage unit under power generation conditions. To establish the model, firstly, an internal parameter model is constructed based on the full characteristic curves of the pump-turbine and the relationships between unit torque, unit flow rate, and unit speed. Internal parameters include torque and guide vane opening. Then, based on operating characteristics, simplified equations are proposed to convert the difficult-to-obtain internal parameters into easily obtainable external parameters, omitting curve slopes to obtain relevant parts, thus constructing an external parameter model. External parameters include head and load. The specific steps include:

[0072] S1: Constructing an analytical model of internal parameters

[0073] This invention obtains an analytical model of internal parameters through full characteristic curves and a six-parameter model. The specific process is as follows.

[0074] The relationships between the operating parameters of a water pump turbine are complex, and a six-parameter model is typically used to describe its dynamic characteristics.

[0075]

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

[0077] Equation (1) is converted to a relative value and expanded using Taylor, and is simplified to Equation (2).

[0078]

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

[0080]

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

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

[0083] The unit speed n in the full characteristic curve of a water pump turbine 11 Unit flow rate Q 11 Unit torque M 11 The definition is shown in equation (4).

[0084]

[0085] In the formula: n is the rotational speed, in r / min; D is the inlet diameter of the runner, in m; H is the turbine working head, in m; Q is the flow rate, in m³ / s. 3 / s; M is torque, in N·m; ρ is water density, in m³. 3 / s.

[0086] When the rotational speed remains constant, perform differential calculations on equation (4):

[0087]

[0088] Organizing can yield

[0089]

[0090] And because

[0091]

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

[0093]

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

[0095]

[0096] In the formula: C d C is the flow coefficient; Y is the proportionality coefficient; Y is the guide vane opening; g is the gravitational acceleration.

[0097] Differentiation yields e qy :

[0098]

[0099] The formula for calculating hydraulic torque is shown in equation (11):

[0100] M=ρgQHr(11)

[0101] In the formula: r is the radius of the wheel.

[0102] Differentiation yields:

[0103]

[0104] Combining equations (8), (10), and (12), the expressions for the four parameters in the pump-turbine model are:

[0105]

[0106] The internal parameter analysis model is shown in equation (13).

[0107] S2: Construction of the extrinsic parameter model

[0108] Compared to the simulation time-domain model, the proposed internal parameter model, while simplifying the model and enabling analytical analysis, still involves calculating the slope of the full characteristic curve and the internal parameters of the pump-turbine in its transfer function. This not only increases the computational workload but also presents difficulties in parameter acquisition. Therefore, this invention omits the part involving the calculation of the slope of the full characteristic curve in the internal parameter model and reduces the difficulty of model acquisition and the amount of data required by transforming the internal parameters of the pump-turbine into external parameters.

[0109] S2-1: Omitted part of curve slope calculation

[0110] Considering that pumped storage units mainly participate in frequency response operation in the stable operating range during power generation, and that the pump-turbine needs to meet the conditions shown in equation (14) when the turbine is operating stably:

[0111]

[0112] From equation (4) and the overall characteristic curve, it can be seen that the unit rotational speed gradually decreases with increasing head. Therefore, under high head conditions, the unit rotational speed n 11 The flow rate and torque characteristic curves of the water pump turbine are relatively small, and tend to be flat.

[0113] Combining equation (11), we can obtain:

[0114]

[0115] therefore

[0116]

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

[0118]

[0119] S2-2: Converting internal parameters to external parameters

[0120] To avoid generating suction vortices, the water flow in each channel of the pumped storage power station must maintain uniform velocity and flow rate. Meanwhile, analysis of the power characteristic curve of the pump-turbine reveals that the servo travel of the pump-turbine is approximately linear, and the pump-turbine typically operates in the linear region when participating in frequency regulation. Therefore, the simplified conditions for the dynamic analytical model of the pump-turbine can be set as follows: (1) the flow coefficient of the pump-turbine remains constant under power generation conditions; (2) the servo travel is approximately linear; (3) the efficiency of the pump-turbine remains approximately constant under power generation conditions.

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

[0122]

[0123] In the model described by Equation (17), the determination of the transmission parameters involves internal parameters such as flow rate and torque. In order to reduce the complexity of the determination, they can be converted into external parameters such as power and head, which are easier to determine, according to Equation (18), as shown in Equation (19).

[0124]

[0125] Compared to internal parameter models, external parameter models for pump-turbine systems are more convenient in practical applications. Firstly, parameter selection is simpler, eliminating the need to plot operating characteristic curves and transforming complex internal parameters into external parameters such as load and head. Secondly, the transfer function form is simpler, effectively reducing computational complexity.

[0126] S3: Case Verification

[0127] When analyzing the accuracy of the model in describing the frequency response characteristics of pumped storage units, the quasi-steady-state frequency and the minimum frequency are important research parameters. To study the degree of agreement between the model's description of the pumped storage unit's frequency response characteristics and the actual situation, it is necessary to continuously sample the frequency response curve and calculate the differences between the model and the actual situation. Therefore, this invention focuses on comparing the initial frequency decay rate, the minimum frequency point and its arrival time, the quasi-steady-state frequency, and the mean square error of the frequency response curve for different models.

[0128] Since it is difficult to obtain the actual operating parameters of the pump-turbine and design the experimental environment, this invention uses a more accurate full-parameter model to represent the actual accurate data. By changing the water head to adjust the operating conditions of the pump-turbine, simulations are performed on the full-parameter model, the ordinary hydropower unit model, and the simplified model designed in this invention under different water heads and different water intake system models.

[0129] Simulation results for the full-parameter model of the water diversion system, the ordinary hydropower unit model, and the design model of this invention, respectively, using three types of water hammer models, are as follows: Figures 2-4 As shown in Tables 1 to 3.

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

[0131]

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

[0133]

[0134]

[0135] Table 3 Simulation results and errors using 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 this invention describes the lowest frequency point of the unit more accurately.

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

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

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

[0142] (3) The design model of this invention describes the time when the unit reaches the lowest point with higher accuracy.

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

[0144] (4) The design model of this invention describes the initial frequency drop rate of the unit with higher accuracy.

[0145] Under high head conditions, the error range of the model of this invention is 0.30% to 0.86%, while the error range of the turbine model is 3.05% to 11.10%. Therefore, the model of this 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 has a higher degree of consistency with the actual situation.

[0147] Therefore, it can be concluded that the design model of this invention is more accurate and reasonable in describing the frequency response characteristics of water pump turbines under high head conditions.

[0148] The above-described embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A method for establishing an analytical model of the frequency response of a pump-turbine in a high-head, constant-speed pumped-storage unit during power generation, characterized in that... The aforementioned method first constructs an internal parameter model based on the full characteristic curve of the water pump turbine and the relationship between unit torque, unit flow rate, and unit speed. The internal parameters include torque and guide vane opening. Then, based on the operating characteristics, simplified equations are proposed to convert the internal parameters in the internal parameter model into external parameters, and an external parameter model is constructed, in which the external parameters include head and load. Includes the following steps: S1: Construct an analytical model of internal parameters using the full characteristic curves and the six-parameter model, as follows: The dynamic characteristics of the pump-turbine are described using a six-parameter model: (1) ； Where: m t ω is the relative torque of the pump-turbine; q is the relative flow rate of the pump-turbine; y is the relative guide vane opening; ω is the relative speed of the pump-turbine; h is the relative head of the pump-turbine. Equation (1) can be transformed into: (2) ； In the formula: e y e is the transmission coefficient of turbine torque to guide vane opening. h e is the transmission coefficient of turbine torque to head; qy e is the transfer coefficient of turbine flow rate to guide vane opening. qh Δy is the transfer coefficient of water head from the turbine flow rate; Δω is the change in relative guide vane opening; Δω is the change in relative speed between the pump and turbine; Δh is the change in relative head between the pump and turbine. The expressions for the four parameters in the pump-turbine model are: (3) ； The internal parameter analytical model is shown in equation (3); Where, n 11 This represents the unit speed and Q value in the full characteristic curve of a water pump turbine. 11 This represents the unit flow rate, M in the full characteristic curve of the water pump and turbine. 11 The unit torque in the full characteristic curve of the pump-turbine is represented by: q, relative flow rate, h, relative head, m, relative torque, n, rotational speed (r / min), and D, runner inlet diameter (m). r Q is the rated flow rate, and Q is the flow rate in cubic meters per second (m³). 3 / s;H r H is the rated head of the turbine, and H is the operating head of the turbine, both in meters (m). r The rated torque is ρ; the density of water is m³. 3 / s; S2: Constructing the extrinsic parameter model S2-1: Omitted part of the calculation of the slope of the full characteristic curve of the water pump and turbine. Considering that the pumped storage unit participates in frequency response operation in the stable operating range under power generation conditions, and that the pump turbine needs to meet the conditions shown in equation (4) when the turbine is operating stably: (4) ； From equation (4) and the overall characteristic curve, it can be seen that under high head conditions, the unit rotational speed n 11 The flow rate and torque characteristic curve of the water pump turbine tends to be flatter when the flow rate is relatively small. Combining the hydraulic moment calculation formula, we can obtain: (5) ； therefore (6) ； The part of the internal parameter analytical model involving the calculation of the slope of the full characteristic curve is simplified: (7) ； S2-2: Converting internal parameters to external parameters Simplification conditions are set for the dynamic analytical model of the pump-turbine: (1) the flow coefficient of the pump-turbine remains constant under power generation conditions; (2) the stroke of the servo motor is approximately linear; (3) the efficiency of the pump-turbine remains approximately constant under power generation conditions. Based on the simplification conditions, the operating equation of the pump-turbine is proposed: (8) ； Where q is the relative flow rate; p is the relative power; m t C represents the relative torque; d C is the flow coefficient; Y y is the proportionality coefficient; Y is the guide vane opening; g is the gravitational acceleration; H is the head; h is the relative head; Y r ρ represents the rated guide vane opening; y represents the relative guide vane opening; ρ is the water density; η represents the efficiency; ω represents the rotational speed; ω r Indicates the rated speed; The transfer parameters in equation (7) involve internal parameters such as flow rate and torque. According to formula (8), the transfer parameters obtained in equation (7) are transformed into external parameters such as power and head, as shown in equation (9). (9)。 2. The method for establishing an analytical model of the frequency response of a high-head, constant-speed pumped-storage unit's pump-turbine during power generation, as described in claim 1, is characterized in that... The process of constructing the expressions for the four parameters in the pump-turbine model in S1 is as follows: The unit speed n in the full characteristic curve of a water pump turbine 11 Unit flow rate Q 11 Unit torque M 11 The definition is shown in equation (10); (10) ； In the formula: n is the rotational speed, in r / min; D is the inlet diameter of the runner, in m; H is the operating head of the turbine, in m; Q represents flow rate, measured in meters (m). 3 / s; M is torque, in N·m; ρ is water density, in m³. 3 / s; When the rotational speed remains constant, equation (10) can be processed to obtain: (11) ； And because (12) ； Combining equations (11) and (12), we can obtain: (13) ； The flow rate calculation formula is shown in equation (9): (14) ； In the formula: C d C is the flow coefficient; Y Y is the proportionality coefficient; Y is the guide vane opening; g is the gravitational acceleration. Differentiation yields e qy : (15) ； The formula for calculating hydraulic torque is shown in equation (16): (16)； In the formula: r is the radius of the wheel; Differentiation yields: (17) ； Combining equations (13), (15), and (17), we can obtain the expressions for the four parameters in the pump-turbine model as shown in equation (2).

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