Method, system, device and medium for evaluating vibration response of three-stage cascade hydropower station

Abstract

The application discloses a three-stage series hydropower station vibration response evaluation method, system, device and medium, and relates to the technical field of hydropower station vibration characteristic analysis. The method comprises the following steps: establishing pipeline unit constraints and surge tank boundary constraints, establishing inter-stage flow balance constraints according to the difference between the upstream and downstream side flow of the adjusting pool and water level disturbance, and establishing unit boundary constraints of each hydroelectric generator set; assembling the system overall matrix according to the hydraulic connection topology of the three-stage series hydropower station, and constructing the system vibration characteristic equation according to the singular condition; solving the multi-order vibration complex frequency for a plurality of parameter combinations composed of the adjusting pool parameters and the adjacent surge tank parameters, determining the continuous modal branch and the dominant vibration mode according to the continuous change relationship of the attenuation factor and the circular frequency under the adjacent parameter combinations, so as to determine the dominant mode transfer interval and generate the evaluation result. The application can represent the cross-stage coupling vibration relationship of the three-stage series hydropower station, and identify the weak attenuation dominant mode and the transfer interval.

Description

Technical Field

[0001] This invention relates to the field of vibration characteristic analysis technology for hydropower stations, specifically to a method, system, equipment, and medium for evaluating the vibration response of a three-stage series hydropower station. Background Technology

[0002] Hydropower stations play a crucial role in power systems, including peak shaving, frequency regulation, and emergency backup. For large drop sections of rivers in high mountain and canyon areas, a multi-stage series arrangement can be used to develop hydropower resources in stages. In a three-stage series hydropower station, each turbine-generator unit is installed sequentially along the water flow direction. Adjacent turbine-generator units are connected by a regulating pool. Each turbine-generator unit also has a surge tank on its intake side, thus forming a hydraulic-mechanical-electrical coupled system including pipelines, surge tanks, regulating pools, turbine-generator units, and governors.

[0003] In a three-stage tandem hydropower station, the surge tank and regulating reservoir play different hydraulic roles. The surge tank is located in the intake system of the corresponding turbine-generator unit, and its water level fluctuations are mainly affected by the head and flow disturbances of its own intake system. The regulating reservoir is located between two adjacent turbine-generator units, and its water level changes depend on the difference between the tailrace flow of the previous turbine-generator unit and the intake flow of the next turbine-generator unit. When the unit load, governor parameters, or hydraulic parameters change, the water level and flow disturbances in the regulating reservoir propagate to adjacent power stations and interact with the water level fluctuations in each surge tank and the dynamics of the units, causing the three-stage tandem hydropower station to exhibit a multi-timescale, multi-mode vibration response.

[0004] Existing vibration analysis methods for hydropower stations typically establish a water conveyance system model based on the pipeline transfer matrix or hydraulic element matrix, and evaluate the system's vibration characteristics through frequency response, time-domain transient process, or characteristic frequency analysis. However, existing methods are mostly designed for single-stage hydropower stations, conventional water conveyance systems, or two-stage series hydropower stations, and do not adequately consider the cross-stage coupling relationships between multiple surge tanks, multiple interstage regulating pools, each stage of turbine generator units, and each section of pipeline in a three-stage series hydropower station. In particular, if the regulating pool is treated as a general water level boundary or surge tank, it is difficult to accurately reflect the transmission effect of the flow imbalance between the upstream and downstream sides of the regulating pool on the vibration response of adjacent two-stage power stations.

[0005] Furthermore, existing methods typically involve individually altering the area of ​​the surge tank, the area of ​​the regulating pool, the pipe length, or the governor parameters, and evaluating the impact of these parameters based on a single frequency or a single stability index. When multiple hydraulic parameters change together, the attenuation factors and angular frequencies of different vibration modes may cross or abruptly change, and the dominant mode of the system's vibration response may shift from one continuous mode branch to another. Comparing only the modal order or single frequency results at each parameter point makes it difficult to maintain consistency in the modal correspondences under different parameter combinations, and consequently, it becomes difficult to identify the weakly attenuated dominant mode, the dominant mode transition interval, and the critical stability parameters under the coupling effect of the regulating pool and surge tank. Therefore, it is necessary to propose a system vibration response assessment method applicable to three-stage series hydropower stations. Summary of the Invention

[0006] The technical problem to be solved by the present invention is: in view of the above-mentioned defects or improvement needs of the prior art, the present invention provides a vibration response assessment method, system, equipment and medium for a three-stage series hydropower station, which is used to solve the problem that the prior art is difficult to uniformly characterize the cross-stage coupling relationship between the water level fluctuation of each stage of the surge tank, the flow imbalance of the inter-stage regulating pool, the dynamics of each stage of the turbine generator unit and the hydraulic oscillation of the pipeline in a three-stage series hydropower station, and the problem that it is difficult to maintain the continuous correspondence of multiple vibration modes and identify the dominant mode transition interval when the parameters of the regulating pool and the surge tank change together.

[0007] This invention is achieved through the following technical solution:

[0008] A vibration response assessment method for a three-stage series hydropower station includes:

[0009] To obtain system parameters of a three-stage series hydropower station, the three-stage series hydropower station includes a first-stage turbine generator unit, a first-stage regulating pool, a second-stage turbine generator unit, a second-stage regulating pool, and a third-stage turbine generator unit arranged sequentially along the water flow direction. Each stage of the turbine generator unit is equipped with a surge tank on its intake side. The first-stage regulating pool and the second-stage regulating pool are respectively located between the tailrace side of the first-stage turbine generator unit and the intake side of the second-stage turbine generator unit, and between the tailrace side of the second-stage turbine generator unit and the intake side of the third-stage turbine generator unit.

[0010] Pipeline unit constraints are established based on the transmission relationship between the recurrent head and recurrent flow rate of each pipeline section. Surge chamber boundary constraints are established based on the relationship between the water level disturbance of each surge chamber and the flow disturbance of the corresponding water intake system. Unit boundary constraints are established based on the dynamic relationship between the turbine, governor and generator of each hydro-generator unit.

[0011] Based on the relationship between the difference in flow rate between the upstream and downstream sides of each level of regulating pool and the corresponding water level disturbance, inter-level flow balance constraints are established for the first-level regulating pool and the second-level regulating pool, respectively.

[0012] According to the hydraulic connection topology of the three-stage series hydropower station, the pipeline unit constraints, the boundary constraints of each surge chamber, the boundary constraints of each generator unit, and the flow balance constraints between each stage are assembled into a system global matrix with complex frequencies as variables, and the system vibration characteristic equation is constructed based on the singular conditions of the system global matrix.

[0013] Multiple parameter combinations to be analyzed are determined. Each parameter combination includes the parameter values ​​of the regulating pool and the parameter values ​​of the pressure regulating chamber adjacent to the corresponding regulating pool. The overall system matrix is ​​updated based on each parameter combination, and the vibration characteristic equation of the system is solved to obtain the multi-order vibration complex frequency corresponding to each parameter combination.

[0014] The continuous modal branches are determined based on the continuous variation relationship between the attenuation factors and angular frequencies of each order of vibration complex frequencies under adjacent parameter combinations, and the dominant vibration modes under each parameter combination are determined based on the attenuation factors of each continuous modal branch.

[0015] The dominant mode transition interval is determined based on the change of the continuous mode branch to which the dominant vibration mode belongs with the parameter combination, and the vibration response evaluation results of the three-stage series hydropower station are generated based on the attenuation factor, circular frequency and dominant mode transition interval of each continuous mode branch.

[0016] Furthermore, the system parameters include:

[0017] The length, cross-sectional area, diameter, water hammer velocity, rated flow rate, rated head, and head loss parameters of each section of the water diversion tunnel, pressure pipeline, and tailrace pipeline;

[0018] The areas of the primary, secondary, and tertiary pressure regulating chambers;

[0019] The areas of the primary regulating tank and the secondary regulating tank;

[0020] The turbine transmission coefficient and generator inertial time constant of each level of hydro-generator unit;

[0021] The proportional gain, integral gain, permanent slip coefficient, and relay time constant of the governor of each level of hydro-generator unit.

[0022] Furthermore, the process of establishing the constraints of the pipeline unit includes:

[0023] Based on the pressurized unsteady flow equation, the pressure head and flow rate in the pipeline are decomposed into average value and oscillation value, respectively, and linearized momentum equation and continuity equation are obtained after neglecting higher-order nonlinear terms.

[0024] By expressing the head oscillation and flow oscillation as exponential forms containing complex frequencies, and solving the linearized momentum equation and continuity equation, the transmission relationship between the complex head at the beginning of the pipe, the complex flow rate at the beginning of the pipe, the complex head at the end of the pipe, and the complex flow rate at the end of the pipe is obtained.

[0025] The transmission relationship is converted into a pipeline element transmission matrix to form the pipeline element constraint;

[0026] The process of establishing the unit boundary constraints includes:

[0027] A linearized model of the turbine is established based on the relationship between guide vane opening, unit speed, turbine head, turbine torque, and turbine flow rate.

[0028] A proportional-integral governor model is established based on the transmission relationship between unit speed and guide vane opening.

[0029] A generator model is established based on the turbine torque, load torque, unit speed, and generator inertial time constant.

[0030] The linearized turbine model, the proportional-integral governor model, and the generator model are subjected to Laplace transform and combined to obtain the unit boundary constraints between the inlet-side recurrent head, inlet-side recurrent flow, outlet-side recurrent head, and outlet-side recurrent flow of each stage of the turbine-generator unit.

[0031] Furthermore, the interstage flow balance relationships of the primary regulating tank and the secondary regulating tank are as follows:

[0032] ;

[0033] ;

[0034] in, , and These represent the flow rates between adjacent levels of hydro-turbine generator units. and These represent the areas of the primary regulating tank and the secondary regulating tank, respectively. and These represent the water levels of the primary regulating tank and the secondary regulating tank, respectively.

[0035] By linearizing the inter-stage flow balance relationship with a small perturbation and transforming it to the complex frequency domain, we obtain:

[0036] ;

[0037] in, and These represent the flow disturbance amounts on the upstream and downstream sides of the regulating tank, respectively. This indicates the amount of water level disturbance in the corresponding regulating tank. Represents complex frequency. This represents the time constant related to the area of ​​the corresponding regulating pool.

[0038] Furthermore, the overall system matrix satisfies:

[0039] ;

[0040] in, This represents the overall system matrix. This represents the system state vector composed of the recurrent head and recurrent flow rate at the beginning and end of each pipe section. Represents complex frequency;

[0041] The singular condition of the overall system matrix is:

[0042] ;

[0043] The singular condition is then determined as the vibration characteristic equation of the system.

[0044] Furthermore, solving the vibration characteristic equation of the system includes:

[0045] Perform a frequency scan within the preset angular frequency range to determine... The local minimum point;

[0046] The complex frequency corresponding to the local minimum point is determined as the initial value for iteration, and Newton iteration is performed on the vibration characteristic equation of the system based on the initial value for iteration.

[0047] The iteration stops when the difference between the complex frequencies obtained from two adjacent iterations meets a preset accuracy condition, thus obtaining the multi-order vibration complex frequencies under the corresponding parameter combinations, where the first... The complex frequency of an oscillation is expressed as:

[0048] ;

[0049] Indicates the first The attenuation factor of the complex frequency of the first vibration. Indicates the first The angular frequency of a complex vibration.

[0050] Furthermore, the corresponding continuous modal branches under different parameter combinations are determined, including:

[0051] For adjacent th The parameter combination and the first The parameter combination is used to calculate the first parameter according to the following formula. The first parameter combination The first-order complex frequency of vibration and the second-order complex frequency The first parameter combination Modal distance between complex frequencies of vibration:

[0052] ;

[0053] in, and They represent the first The parameter combination and the first A combination of parameters, and These represent the attenuation factors corresponding to the complex frequencies of vibration. and These represent the angular frequencies corresponding to the complex frequencies of vibration;

[0054] Based on the modal distance, the vibration complex frequencies corresponding to adjacent parameter combinations are divided into the same continuous modal branch.

[0055] The dominant vibration modes under each parameter combination are determined based on the attenuation factors of each continuous modal branch, including:

[0056] When there is a vibration mode with a decay factor greater than zero, the vibration mode with the largest decay factor is determined as the dominant mode of divergence risk.

[0057] When the attenuation factor of each vibration mode is less than zero, the vibration mode with the largest attenuation factor is determined as the weakly attenuated dominant mode from the preset low-order mode set.

[0058] When the dominant vibration modes corresponding to adjacent parameter combinations belong to different continuous mode branches, the parameter range defined by the adjacent parameter combinations is determined as the dominant mode transition interval;

[0059] When the attenuation factor of the continuous modal branch crosses zero as the parameter changes, the critical stability parameter is determined based on the parameter corresponding to the attenuation factor.

[0060] This invention also provides a vibration response assessment system for a three-stage series hydropower station, used to implement the aforementioned vibration response assessment method for a three-stage series hydropower station, comprising:

[0061] The parameter acquisition module is used to acquire the system parameters of a three-stage series hydropower station, which includes three-stage turbine generator units connected in sequence through a primary regulating pool and a secondary regulating pool. Each stage of the turbine generator unit is equipped with a pressure regulating chamber on the water intake side.

[0062] The constraint construction module is used to establish pipeline unit constraints for each section of pipeline, pressure chamber boundary constraints for each pressure chamber, unit boundary constraints for each turbine generator unit, and to establish two inter-stage flow balance constraints based on the relationship between the difference in flow rate on the upstream and downstream sides of each regulating pool and the corresponding water level disturbance in the regulating pool.

[0063] The matrix assembly module is used to assemble the pipeline unit constraints, the three surge chamber boundary constraints, the three generator boundary constraints, and the two inter-stage flow balance constraints into a system overall matrix according to the hydraulic connection topology of the three-stage series hydropower station, and to construct the system vibration characteristic equation based on the singular conditions of the system overall matrix.

[0064] The complex frequency solving module is used to update the overall system matrix and solve the system vibration characteristic equation for multiple parameter combinations, including the parameter values ​​of the regulating pool and the parameter values ​​of the pressure regulating chamber adjacent to the corresponding regulating pool, so as to obtain the multi-order vibration complex frequencies corresponding to each parameter combination.

[0065] The modal analysis module is used to determine the continuous modal branches based on the continuous variation relationship between the attenuation factors and angular frequencies of each order of vibration complex frequencies under adjacent parameter combinations, determine the dominant vibration mode based on the attenuation factors of each continuous modal branch, and determine the dominant mode transition interval based on the change of the continuous modal branch to which the dominant vibration mode belongs with the parameter combination.

[0066] The results generation module is used to generate vibration response evaluation results for the three-stage tandem hydropower station based on the attenuation factor, circular frequency, and dominant mode transfer interval of each continuous modal branch.

[0067] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the vibration response assessment method for a three-stage series hydropower station as described above.

[0068] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the vibration response assessment method for a three-stage series hydropower station as described above.

[0069] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0070] This invention establishes boundary constraints for the surge tanks based on the water level disturbances of each surge tank and the corresponding flow disturbances of the water diversion system, and establishes flow balance constraints between stages based on the difference in flow rates between the upstream and downstream sides of the regulating pools and the corresponding water level disturbances of the regulating pools. This allows for the differentiation of the hydraulic effects between the surge tanks and the regulating pools during the modeling process, and accurately characterizes the transmission relationship between the regulating pools and the vibration responses of adjacent two-stage hydro-turbine generator units.

[0071] This invention, based on the hydraulic connection topology of a three-stage series hydropower station, assembles the constraints of pipeline units, boundary constraints of each surge chamber, boundary constraints of each generator unit, and flow balance constraints between stages into a unified overall system matrix. Based on the singular conditions of the overall system matrix, it solves for multiple-order vibration complex frequencies. This invention can integrate the dynamic relationships of pipelines, surge chambers, regulating pools, turbine generator units, and governors into the same complex frequency solution process, obtaining the attenuation factors and circular frequencies of each vibration mode of the system.

[0072] This invention addresses multiple parameter combinations consisting of the parameters of the regulating tank and the parameters of adjacent pressure regulating chambers. It updates the overall system matrix and solves for multiple-order vibration complex frequencies. Based on the continuous variation relationship between the attenuation factor and the angular frequency under adjacent parameter combinations, it determines the continuous modal branches, thus avoiding modal mismatch caused by comparing modal orders alone.

[0073] This invention determines the dominant vibration mode under different parameter combinations based on the attenuation factor of each continuous modal branch, and determines the dominant mode transition interval based on the change of the continuous modal branch to which the dominant vibration mode belongs. This enables the identification of the weak attenuation sensitive area, mode transition area and critical stability parameter corresponding to the combined parameters of the regulating pool and surge chamber, providing a basis for the hydraulic parameter design, governor parameter verification and vibration risk assessment of a three-stage series hydropower station. Attached Figure Description

[0074] To more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be considered as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort. In the drawings:

[0075] Figure 1 This is a schematic diagram of a three-stage series hydropower station water conveyance and power generation system;

[0076] Figure 2 A flowchart for the vibration response assessment method of a three-stage series hydropower station;

[0077] Figure 3 This figure shows the effect of the combined changes in the area of ​​the primary and secondary pressure regulating chambers on the system attenuation factor.

[0078] Figure 4 The graph shows the effect of the combined changes in the area of ​​the primary and secondary voltage regulating chambers on the system's circular frequency.

[0079] Figure 5 This figure shows the effect of the combined changes in the area of ​​the primary and secondary regulating tanks on the system's attenuation factor.

[0080] Figure 6 The graph shows the effect of the combined changes in the area of ​​the primary and secondary regulating tanks on the system's circular frequency.

[0081] Figure 7 This figure shows the effect of the combined changes in the area of ​​the secondary pressure regulating chamber and the area of ​​the primary regulating pool on the system attenuation factor.

[0082] Figure 8 The graph shows the effect of the combined change in the area of ​​the secondary voltage regulating chamber and the area of ​​the primary regulating pool on the system's circular frequency.

[0083] Figure 9 Figure 1 shows the effect of the change in the length of the water diversion tunnel on the attenuation factor of the low-order vibration modes of the system.

[0084] Figure 10 Figure 1 shows the effect of the change in the length of the water diversion tunnel on the circular frequencies of the low-order vibration modes of the system.

[0085] Figure 11 The graph shows the effect of the governor integral gain change on the system vibration mode attenuation factor.

[0086] Figure 12 The figure shows the effect of the speed controller proportional gain change on the attenuation factor of each vibration mode. Detailed Implementation

[0087] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of this invention are only for explaining this invention and are not intended to limit this invention.

[0088] Example 1

[0089] This embodiment provides a vibration response assessment method for a three-stage series hydropower station, which is used to assess the multi-order vibration complex frequencies, attenuation characteristics, and parameter coupling effects under the combined action of the surge tank, interstage regulating pool, water conveyance pipeline, turbine generator set, and governor.

[0090] like Figure 1As shown, the three-stage series hydropower station used in this embodiment includes an upstream reservoir, a first-stage turbine generator unit, a first-stage regulating pool, a second-stage turbine generator unit, a second-stage regulating pool, a third-stage turbine generator unit, and a downstream reservoir. Each stage of the turbine generator unit is equipped with a surge tank on its intake side. Along the direction of water flow, the primary water diversion tunnel between the upstream reservoir and the primary surge chamber is designated as segment 1 (L1); the primary pressure pipeline between the primary surge chamber and the primary turbine generator unit is designated as segment 2 (L2); and the primary tailrace pipeline between the primary turbine generator unit and the primary regulating pool is designated as segment 3 (L3). The secondary water diversion tunnel between the primary regulating pool and the secondary surge chamber is designated as segment 4 (L4); the secondary pressure pipeline between the secondary surge chamber and the secondary turbine generator unit is designated as segment 5 (L5); and the secondary tailrace pipeline between the secondary turbine generator unit and the secondary regulating pool is designated as segment 6 (L6). The tertiary water diversion tunnel between the secondary regulating pool and the tertiary surge chamber is designated as segment 7 (L7); the tertiary pressure pipeline between the tertiary surge chamber and the tertiary turbine generator unit is designated as segment 8 (L8); and the tertiary tailrace pipeline between the tertiary turbine generator unit and the downstream reservoir is designated as segment 9 (L9).

[0091] The primary regulating tank is located between the primary and secondary turbine generator units. It receives the tailrace outflow from the primary turbine generator unit via the third pipe section L3 and supplies water to the secondary turbine generator unit's water intake system via the fourth pipe section L4. The secondary regulating tank is located between the secondary and tertiary turbine generator units. It receives the tailrace outflow from the secondary turbine generator unit via the sixth pipe section L6 and supplies water to the tertiary turbine generator unit's water intake system via the seventh pipe section L7. The primary, secondary, and tertiary surge tanks are respectively located within the water intake systems of their respective turbine generator units.

[0092] The surge tank primarily reflects the water level and flow disturbances of the corresponding turbine generator unit's intake system. The regulating pool connects two adjacent turbine generator units, and its water level disturbance is determined by the flow difference between the tailrace outflow of the previous turbine generator unit and the intake flow of the next turbine generator unit. Therefore, in this embodiment, the regulating pool serves as an inter-stage flow balance node, rather than merely as the water level boundary for a single turbine generator unit.

[0093] like Figure 2 As shown, the vibration response assessment method for a three-stage series hydropower station in this embodiment includes the following steps.

[0094] S1, Obtain system parameters

[0095] Obtain the hydraulic system parameters, surge tank parameters, regulating pool parameters, generator unit parameters, and governor parameters for a three-stage series hydropower station. Hydraulic system parameters include the length, cross-sectional area, diameter, water hammer velocity, rated flow rate, rated head, and head loss parameters for each section of the water intake tunnel, pressure pipeline, and tailrace pipeline. Surge tank parameters include the areas of the first, second, and third stage surge tanks. Regulating pool parameters include the areas of the first and second stage regulating pools. Generator unit parameters include the turbine transmission coefficients and generator inertia time constants for each stage of the turbine-generator unit. Governor parameters include the proportional gain, integral gain, permanent slip coefficient, and relay time constant of each stage of the turbine-generator unit.

[0096] Each parameter is used to construct pipeline unit constraints, pressure regulating chamber boundary constraints, unit boundary constraints, and interstage flow balance constraints, and updates the overall system matrix during the parameter influence analysis process.

[0097] S2, Constructing pipe element constraints

[0098] For the water diversion tunnels, pressure pipelines, and tailrace pipelines in a three-stage series hydropower station, a pipeline element model is established based on the pressurized unsteady flow equations. The momentum equation and continuity equation for the fluid inside the pipeline are as follows:

[0099]

[0100]

[0101] in, Indicates pressure head. Indicates the flow rate in the pipeline. Indicates the cross-sectional area of ​​the pipe. Indicates the pipe diameter. Indicates the flow velocity inside the pipe. Indicates the water hammer wave speed, This represents the Darcy drag coefficient. Represents gravitational acceleration. Indicates the coordinates along the tube axis. Indicates time, This indicates the angle between the pipe axis and the horizontal plane.

[0102] By decomposing the pressure head and pipeline flow rate into average and oscillatory values ​​respectively, and neglecting higher-order nonlinear terms under steady flow and small disturbance conditions, linearized momentum and continuity equations are obtained:

[0103]

[0104]

[0105] in, Indicates the amount of head oscillation. This represents the flow oscillation. The head oscillation and flow oscillation are expressed in exponential form, incorporating complex frequencies:

[0106] ,

[0107] By solving the above linearized equations, the relationship between the head and flow rate transfer between the beginning and end of the pipeline is obtained:

[0108]

[0109] in, and These represent the head and flow rate at the beginning of the pipeline, respectively. and These represent the refill head and refill flow rate at the end of the pipeline, respectively. Represents the propagation constant. Indicates the characteristic impedance of the pipe. This represents the pipe length. The above transfer relationship is converted into matrix form to form the pipe element constraints for the corresponding pipe segment.

[0110] Ignoring friction loss and performing a Taylor series expansion of the hyperbolic function terms, the hyperbolic function terms in the pipe element constraints are transformed into polynomial terms containing pipe length, water hammer velocity, complex frequency, and pipe cross-sectional area. For each pipe segment in a three-stage series hydropower station, corresponding pipe element constraints are established according to the corresponding length, cross-sectional area, diameter, and water hammer velocity.

[0111] S3, Establish various boundary matrices

[0112] S31, Establish reservoir boundary constraints

[0113] The upstream and downstream reservoirs serve as the head and discharge level boundaries for the three-stage tandem hydropower station, respectively. For the upstream reservoir, after considering the head loss at the pipeline inlet and neglecting higher-order nonlinear terms, reservoir boundary constraints are established between the upstream reservoir and the adjacent pipeline inlet for complex head and complex discharge. For the downstream reservoir, based on the constant downstream water level condition and the relationship between the pipeline outlet head loss and the adjacent pipeline outlet, reservoir boundary constraints are established between the downstream reservoir and the adjacent pipeline outlet.

[0114] S32, Establish boundary constraints for series pipes

[0115] For the preceding pipe connected in sequence and the next pipe Based on the flow continuity relationship at the connection points of adjacent pipes and the head relationship including kinetic head and local head loss, the recurrent head at the end of pipe i is established. Complex flow The return head at the beginning of pipe j Complex flow The boundary constraints of the series pipelines are defined, and the local head loss coefficient at the pipeline connection point is included in the corresponding boundary constraints. This is expressed as:

[0116]

[0117] S33, Establish boundary constraints for the pressure regulating chamber

[0118] For the primary, secondary, and tertiary surge tanks, boundary constraints are established based on the relationship between the water level disturbance in the surge tank and the flow disturbance in the corresponding water diversion system. The relationship between the water level and flow rate in the surge tank is as follows:

[0119]

[0120] in, Indicates the water level in the surge tank. This represents the local head loss coefficient in the surge tank. This indicates the flow disturbance entering or leaving the pressure regulating chamber. This indicates the area of ​​the pressure regulating chamber.

[0121] Introducing hydraulic resistance of the surge tank :

[0122]

[0123] in, Indicates the pressure regulating chamber recharge head. Indicates the reflow rate of the pressure regulating chamber. This represents the time constant of the flow rate in the pressure regulating chamber. This indicates the oscillation frequency of the pressure regulating chamber.

[0124] And establish the boundary constraints of the surge chamber based on the relationship between the reflow head and reflow flow rate at the ends of the pipes before and after the surge chamber:

[0125]

[0126] According to the location of each pressure regulating chamber in the water diversion system, the boundary constraints of the first-level, second-level, and third-level pressure regulating chambers are connected to the corresponding pipeline unit constraints.

[0127] S34, Establish boundary constraints for flow balance between regulating tank stages.

[0128] The primary and secondary regulating reservoirs serve as flow balance nodes between adjacent turbine-generator units. The flow balance relationships on the upstream and downstream sides of the primary and secondary regulating reservoirs are as follows:

[0129]

[0130]

[0131] in, , and These represent the flow rates between adjacent levels of hydro-turbine generator units. and These represent the areas of the primary regulating tank and the secondary regulating tank, respectively. and These represent the water levels of the primary regulating reservoir and the secondary regulating reservoir, respectively.

[0132] The time-domain flow balance equation for a small disturbance in the regulating tank can be written as:

[0133]

[0134]

[0135] in, , .

[0136] Under the condition of steady flow with small disturbances, the above interstage flow balance relationship is linearized and transformed into the complex frequency domain, yielding:

[0137]

[0138] The interstage flow balance constraints of the primary regulating tank link the flow disturbance on the tailrace side of the primary turbine-generator unit to the flow disturbance on the intake side of the secondary turbine-generator unit; the interstage flow balance constraints of the secondary regulating tank link the flow disturbance on the tailrace side of the secondary turbine-generator unit to the flow disturbance on the intake side of the tertiary turbine-generator unit. Thus, the boundary constraints of each stage of the surge tank act within the intake system of that stage, while the interstage flow balance constraints connect adjacent turbine-generator units.

[0139] The boundary matrix of the regulating pool is:

[0140]

[0141] in, The equivalent hydraulic impedance of the equalization tank is determined by the flow balance relationship between the stages of the equalization tank.

[0142] S35, Establish unit boundary constraints

[0143] The unit boundary constraints of each level of hydro-turbine generator unit are established based on the linearized model of the hydro-turbine, the proportional-integral governor model, and the generator model.

[0144] The linearized model of the water turbine is as follows:

[0145]

[0146]

[0147] The proportional-integral speed governor model is as follows:

[0148]

[0149] The generator model is as follows:

[0150]

[0151] in, Indicates the torque of the water turbine. Indicates the turbine flow rate. Indicates the guide vane opening. Indicates the unit speed. Indicates the turbine head. Indicates the load torque. This represents the comprehensive self-regulation coefficient of the hydro-generator. By performing a Laplace transform on the above model and simultaneously solving the system, we obtain the unit boundary constraints between the complex head and complex flow rate at the inlet and outlet sides of each stage of the hydro-generator unit:

[0152]

[0153] S4, Overall Matrix of Assembly System

[0154] The reflow head and reflow rate at the beginning and end of each pipeline section are used as system state variables to construct the system state vector X. According to... Figure 1 The hydraulic connection topology shown is assembled by sequentially arranging the following constraints along the flow direction: upstream reservoir boundary constraints, constraints of each pipeline unit, first-stage surge tank boundary constraints, first-stage generating unit boundary constraints, first-stage regulating pool inter-stage flow balance constraints, second-stage surge tank boundary constraints, second-stage generating unit boundary constraints, second-stage regulating pool inter-stage flow balance constraints, third-stage surge tank boundary constraints, third-stage generating unit boundary constraints, and downstream reservoir boundary constraints.

[0155]

[0156] in, Represented by complex frequency The system's overall matrix is ​​the variable. In the analysis of the system's free vibration, there are no external forcing terms. When the system exists in a non-zero vibration state, the system's overall matrix satisfies the singularity condition. Therefore, the characteristic equation of the system's vibration is constructed as follows:

[0157]

[0158] Its complex frequency is expressed as:

[0159]

[0160] The overall system matrix simultaneously includes the boundaries of the three-stage surge tanks, the flow balance boundaries between the two-stage regulating pools, the boundaries of the three-stage turbine generator units, and the transmission relationships of each pipeline unit, thereby reflecting the cross-stage coupled vibration relationship between the regulating pools and surge tanks in a three-stage series hydropower station.

[0161] S5, Solving for complex frequencies of multi-order vibrations

[0162] For each parameter combination consisting of the parameter values ​​of the regulating pool and the parameter values ​​of the pressure regulating chamber adjacent to the corresponding regulating pool, the overall system matrix is ​​updated based on the corresponding parameter combination, and the vibration characteristic equation of the system is solved.

[0163] Specifically, frequency scanning is performed within a preset angular frequency range, and the determinant of the overall system matrix is ​​calculated. and will The complex frequency corresponding to the local minimum point is determined as the initial value for Newton's iteration. Newton's iteration is then performed according to the following formula:

[0164]

[0165] in:

[0166]

[0167] When the results of two consecutive iterations satisfy Stop iterating when the time comes.

[0168] Newton's iterations were performed on the multiple initial values ​​obtained from the frequency scan to obtain the complex frequencies of the system's vibrations. The complex frequency of an oscillation is expressed as:

[0169]

[0170] in, Indicates the first The attenuation factor of the first vibration mode. Indicates the first The angular frequency of the first vibration mode, and This represents the absolute value of the imaginary part of the corresponding complex frequency of vibration. When When, the corresponding vibration mode decays with time; when When, the corresponding vibration mode is in a critical oscillation state; when At that time, the corresponding vibration mode diverges with time. The vibration period corresponding to the first vibration mode is:

[0171]

[0172] Using the above method, the multi-order complex frequencies of vibration corresponding to each parameter combination are solved respectively.

[0173] S6, Perform continuous modal analysis

[0174] Since the order of the complex frequencies of vibration may change under different parameter combinations, the corresponding vibration modes under different parameter combinations cannot be determined solely based on the order of the complex frequencies. Therefore, branch matching is performed on the vibration modes based on the continuous variation relationship between the attenuation factors and angular frequencies of the complex frequencies under adjacent parameter combinations.

[0175] For adjacent th The parameter combination and the first The parameter combination is used to calculate the first parameter according to the following formula. The first parameter combination The first-order complex frequency of vibration and the second-order complex frequency The first parameter combination Modal distance between complex frequencies of vibration:

[0176] ;

[0177] in, and They represent the first The parameter combination and the first A combination of parameters, and These represent the attenuation factors corresponding to the complex frequencies of vibration. and These represent the angular frequencies corresponding to the complex frequencies of vibration;

[0178] Based on the modal distance, corresponding matching is performed between the vibrational complex frequencies under adjacent parameter combinations, and the corresponding vibrational complex frequencies are assigned to the same continuous modal branch. Thus, the continuous variation relationship between the attenuation factor and angular frequency of each continuous modal branch and the parameter combination is obtained.

[0179] After determining the continuous modal branches, the dominant vibration modes under each parameter combination are determined based on the attenuation factors of each continuous modal branch.

[0180] When there is a vibration mode with a decay factor greater than zero, the vibration mode with the largest decay factor is determined as the dominant mode of divergence risk.

[0181] When the attenuation factor of each vibration mode is less than zero, the preset low-order mode set is used. The vibration mode with the largest attenuation factor was identified as the weakly attenuated dominant mode.

[0182]

[0183] in, Indicates parameter combination The continuous modal branch to which the dominant vibration mode belongs. This refers to the set of low-order modes determined based on a preset number of orders or frequency bands of interest in the project.

[0184] Compare the dominant vibration modes under adjacent parameter combinations sequentially. When the following condition is met:

[0185]

[0186] When, it indicates that the dominant vibration mode is in parameter combination With parameter combination When a transition occurs between these parameters, the parameter range defined by the combination of adjacent parameters is determined as the dominant mode transition interval.

[0187] Furthermore, when the attenuation factor of any continuous modal branch crosses zero as the parameter changes, the critical stability parameter is determined based on the parameter corresponding to the attenuation factor of that continuous modal branch being equal to zero. The critical stability parameter is used to distinguish between the attenuation state and the divergence state of the corresponding vibration mode.

[0188] S7, Generate vibration response assessment results

[0189] Based on the multi-order complex frequencies of vibration corresponding to each parameter combination, the attenuation factors and angular frequencies of each continuous modal branch, the dominant vibration modes under each parameter combination, the dominant mode transition intervals, and the critical stability parameters, vibration response assessment results for a three-stage tandem hydropower station are generated. The vibration response assessment results include a natural frequency layer, an attenuation characteristic layer, and a coupling influence layer.

[0190] The natural frequency layer includes the complex frequency, angular frequency, and vibration period of each vibration mode under various parameter combinations, which is used to characterize the natural vibration characteristics of each vibration mode of the three-stage series hydropower station.

[0191] The attenuation characteristic layer includes the attenuation factor and corresponding steady state of each continuous modal branch. When the attenuation factor is less than zero, the corresponding vibration mode is marked as an attenuated mode; when the attenuation factor is equal to zero, the corresponding vibration mode is marked as a critical oscillation mode; when the attenuation factor is greater than zero, the corresponding vibration mode is marked as a divergent mode.

[0192] The coupling influence layer includes the relationship between the attenuation factor and angular frequency of each continuous modal branch when the parameters of the regulating pool and the adjacent surge chamber change together, the dominant vibration mode under each parameter combination, the dominant mode transition interval and the critical stability parameter, which are used to characterize the influence of the parameter coupling effect between the regulating pool and the surge chamber on the vibration response of the three-stage series hydropower station.

[0193] In practical applications, attenuation factor variation results and circular frequency variation results for each continuous modal branch can be generated separately. The dominant vibration mode, dominant mode transition interval and critical stability parameter can be marked in the variation results to determine the weak attenuation sensitive area, mode transition area and vibration instability risk area under different parameter combinations.

[0194] In a specific application, the rated flow rate of the first, second, and third-stage hydropower stations is taken as 104.7 m³ / s, and the rated head is taken as 510 m, 295 m, and 231 m, respectively. The stable cross-sectional areas of the first, second, and third-stage surge tanks are 123.53 m², 169.74 m², and 148.44 m², respectively; the areas of the first, second, and third-stage surge tanks are taken as 800 m², 600 m², and 380 m², respectively.

[0195] The turbine transmission coefficient of each stage of the hydro-generator unit is taken as , , , , , , The governor parameters of the first-stage hydro-turbine generator unit are taken as follows: , , , The second and third stage hydro-turbine generator units use the same governor parameters. The parameters of each pipeline section are shown in Table 1.

[0196]

[0197] The initial value of the attenuation factor corresponding to the frequency scan is set to 0, the angular frequency scan interval is set to 0.01 rad / s, the scan range is set to 0–40 rad / s, the maximum number of Newton iterations is set to 100, and the iteration precision is set to 10⁻. 8 Based on the above parameters, the multi-order vibration complex frequencies under rated operating conditions are obtained. The complex frequencies appear in conjugate pairs, and Table 2 lists the complex frequencies corresponding to the negative imaginary parts.

[0198]

[0199] As shown in Table 2, the attenuation factors of all vibration modes under rated operating conditions are less than zero, indicating that there are no divergent modes in the system. Among them, the first to third vibration modes have low angular frequencies and small absolute values ​​of attenuation factors, and belong to the low-frequency, weakly attenuated vibration modes that require in-depth analysis.

[0200] For ease of representation, the areas of the primary and secondary pressure regulating chambers will be denoted as follows: and The areas of the primary regulating pond and the secondary regulating pond are respectively denoted as... and .

[0201] like Figure 3 and Figure 4 As shown, when the areas of the primary and secondary voltage regulating chambers are changed in combination, the attenuation factor and angular frequency of the lower-order vibration modes show obvious range differences with the change of voltage regulating chamber area; when the voltage regulating chamber area is small, the lower-order vibration modes are more sensitive to the area change, and as the voltage regulating chamber area increases, the changes in attenuation factor and angular frequency gradually slow down.

[0202] like Figure 5 and Figure 6 As shown, when the areas of the primary and secondary regulating pools are changed in combination, the attenuation factor and angular frequency of the low-order vibration modes of the system change with the area of ​​the regulating pools. When the area of ​​the regulating pools is small, the water level disturbance caused by the flow imbalance between stages has a strong propagation effect on adjacent power stations. As the area of ​​the regulating pools increases, the relevant changes gradually become more gradual.

[0203] like Figure 7 and Figure 8 As shown, when the areas of the primary regulating pool and the adjacent secondary surge tank are changed in combination, the system attenuation factor and angular frequency exhibit regional variations, indicating that the system's low-order vibration response is formed by the combined effects of the inter-stage flow difference in the primary regulating pool, the water level oscillation in the secondary surge tank, the flow disturbance of adjacent units, and the water intake system of the secondary power station. Based on the changes in continuous mode branches and dominant vibration modes under different parameter combinations, the sensitive area of ​​the combined parameters of the regulating pool and surge tank and the dominant mode transition range can be determined. The above changes are not a simple superposition of the results obtained by changing the parameters of the regulating pool or the surge tank alone, but rather a multi-order vibration complex frequency branch change formed by the combined effect of the flow balance boundary of the inter-stage regulating pool and the water level disturbance boundary of the adjacent surge tank.

[0204] like Figure 9 and Figure 10 As shown, when the length of the water diversion tunnel is changed, the attenuation factors and angular frequencies of different low-order vibration modes exhibit different changing patterns. The length of the water diversion tunnel mainly affects the low-order and long-period vibration modes of the system. By continuously tracking each low-order vibration mode, mode mismatch can be avoided when the angular frequencies of different modes are close or the order changes.

[0205] like Figure 11 As shown, the integral gain of the governor of the first-stage hydro-generator unit is changed. At that time, the attenuation factor of the corresponding vibration mode first decreases and then increases, and at... It crosses zero at approximately 1.44 s⁻¹, thus this parameter can be determined as the critical stability parameter under the corresponding calculation conditions.

[0206] like Figure 12 As shown, the proportional gain of the governor of the first-stage hydro-generator unit is changed. At this time, the attenuation factor of the third vibration mode changes most significantly, while the attenuation factors of the fourth to sixth vibration modes remain negative; At approximately 5.68, the third vibration mode approaches the critical stable state.

[0207] Through the above evaluation process, the dynamic relationships of each section of pipeline, three surge tanks, two interstage regulating pools, and three turbine generator units in a three-stage series hydropower station can be uniformly incorporated into the system vibration characteristic equation, and the vibration response evaluation results can be output from three levels: natural frequency, attenuation characteristics, and coupling effects.

[0208] Example 2

[0209] A vibration response assessment system for a three-stage series hydropower station, used to implement the vibration response assessment method for a three-stage series hydropower station in Example 1, includes:

[0210] The parameter acquisition module is used to acquire the system parameters of a three-stage series hydropower station, which includes three-stage turbine generator units connected in sequence through a primary regulating pool and a secondary regulating pool. Each stage of the turbine generator unit is equipped with a pressure regulating chamber on the water intake side.

[0211] The constraint construction module is used to establish pipeline unit constraints for each section of pipeline, pressure chamber boundary constraints for each pressure chamber, unit boundary constraints for each turbine generator unit, and to establish two inter-stage flow balance constraints based on the relationship between the difference in flow rate on the upstream and downstream sides of each regulating pool and the corresponding water level disturbance in the regulating pool.

[0212] The matrix assembly module is used to assemble the pipeline unit constraints, the three surge chamber boundary constraints, the three generator boundary constraints, and the two inter-stage flow balance constraints into a system overall matrix according to the hydraulic connection topology of the three-stage series hydropower station, and to construct the system vibration characteristic equation based on the singular conditions of the system overall matrix.

[0213] The complex frequency solving module is used to update the overall system matrix and solve the system vibration characteristic equation for multiple parameter combinations, including the parameter values ​​of the regulating pool and the parameter values ​​of the pressure regulating chamber adjacent to the corresponding regulating pool, so as to obtain the multi-order vibration complex frequencies corresponding to each parameter combination.

[0214] The modal analysis module is used to determine the continuous modal branches based on the continuous variation relationship between the attenuation factors and angular frequencies of each order of vibration complex frequencies under adjacent parameter combinations, determine the dominant vibration mode based on the attenuation factors of each continuous modal branch, and determine the dominant mode transition interval based on the change of the continuous modal branch to which the dominant vibration mode belongs with the parameter combination.

[0215] The results generation module is used to generate vibration response evaluation results for the three-stage tandem hydropower station based on the attenuation factor, circular frequency, and dominant mode transfer interval of each continuous modal branch.

[0216] Example 3

[0217] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the vibration response assessment method for a three-stage series hydropower station as described in Example 1.

[0218] Example 4

[0219] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the vibration response assessment method for a three-stage series hydropower station as described in Example 1.

[0220] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0221] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0222] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0223] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0224] Those skilled in the art will understand that all or part of the steps in the above method can be implemented by a program instructing related hardware. The program or the program described therein can be stored in a computer-readable storage medium. When the program is executed, it includes the following steps: at this time, the corresponding method steps are introduced. The storage medium can be ROM / RAM, magnetic disk, optical disk, etc.

[0225] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for evaluating the vibration response of a three-stage series hydropower station, characterized in that, include: The system parameters of a three-stage series hydropower station are obtained. The three-stage series hydropower station includes a first-stage turbine generator unit, a first-stage regulating pool, a second-stage turbine generator unit, a second-stage regulating pool, and a third-stage turbine generator unit arranged sequentially along the water flow direction. Each stage of the turbine generator unit is equipped with a surge tank on its intake side. The first-stage regulating pool and the second-stage regulating pool are respectively located between the tailrace side of the first-stage turbine generator unit and the intake side of the second-stage turbine generator unit, and between the tailrace side of the second-stage turbine generator unit and the intake side of the third-stage turbine generator unit. Pipeline unit constraints are established based on the transmission relationship between the recurrent head and recurrent flow rate of each pipeline section. Surge chamber boundary constraints are established based on the relationship between the water level disturbance of each surge chamber and the flow disturbance of the corresponding water intake system. Unit boundary constraints are established based on the dynamic relationship between the turbine, governor and generator of each hydro-generator unit. Based on the relationship between the difference in flow rate between the upstream and downstream sides of each level of regulating pool and the corresponding water level disturbance, inter-level flow balance constraints are established for the first-level regulating pool and the second-level regulating pool, respectively. According to the hydraulic connection topology of the three-stage series hydropower station, the pipeline unit constraints, the boundary constraints of each surge chamber, the boundary constraints of each generator unit, and the flow balance constraints between each stage are assembled into a system global matrix with complex frequencies as variables, and the system vibration characteristic equation is constructed based on the singular conditions of the system global matrix. Multiple parameter combinations to be analyzed are determined. Each parameter combination includes the parameter values ​​of the regulating pool and the parameter values ​​of the pressure regulating chamber adjacent to the corresponding regulating pool. The overall system matrix is ​​updated based on each parameter combination, and the vibration characteristic equation of the system is solved to obtain the multi-order vibration complex frequency corresponding to each parameter combination. The continuous modal branches are determined based on the continuous variation relationship between the attenuation factors and angular frequencies of each order of vibration complex frequencies under adjacent parameter combinations, and the dominant vibration modes under each parameter combination are determined based on the attenuation factors of each continuous modal branch. The dominant mode transition interval is determined based on the change of the continuous mode branch to which the dominant vibration mode belongs with the parameter combination, and the vibration response evaluation results of the three-stage series hydropower station are generated based on the attenuation factor, circular frequency and dominant mode transition interval of each continuous mode branch.

2. The vibration response assessment method for a three-stage series hydropower station according to claim 1, characterized in that, The system parameters include: The length, cross-sectional area, diameter, water hammer velocity, rated flow rate, rated head, and head loss parameters of each section of the water diversion tunnel, pressure pipeline, and tailrace pipeline; The areas of the primary, secondary, and tertiary pressure regulating chambers; The areas of the primary regulating tank and the secondary regulating tank; The turbine transmission coefficient and generator inertial time constant of each level of hydro-generator unit; The proportional gain, integral gain, permanent slip coefficient, and relay time constant of the governor of each level of hydro-generator unit.

3. The vibration response assessment method for a three-stage series hydropower station according to claim 1, characterized in that, The process of establishing the constraints of the pipeline unit includes: Based on the pressurized unsteady flow equation, the pressure head and flow rate in the pipeline are decomposed into average value and oscillation value, respectively, and linearized momentum equation and continuity equation are obtained after neglecting higher-order nonlinear terms. By expressing the head oscillation and flow oscillation as exponential forms containing complex frequencies, and solving the linearized momentum equation and continuity equation, the transmission relationship between the complex head at the beginning of the pipe, the complex flow rate at the beginning of the pipe, the complex head at the end of the pipe, and the complex flow rate at the end of the pipe is obtained. The transmission relationship is converted into a pipeline element transmission matrix to form the pipeline element constraint; The process of establishing the unit boundary constraints includes: A linearized model of the turbine is established based on the relationship between guide vane opening, unit speed, turbine head, turbine torque, and turbine flow rate. A proportional-integral governor model is established based on the transmission relationship between unit speed and guide vane opening. A generator model is established based on the turbine torque, load torque, unit speed, and generator inertial time constant. The linearized turbine model, the proportional-integral governor model, and the generator model are subjected to Laplace transform and combined to obtain the unit boundary constraints between the inlet-side recurrent head, inlet-side recurrent flow, outlet-side recurrent head, and outlet-side recurrent flow of each stage of the turbine-generator unit.

4. The vibration response assessment method for a three-stage series hydropower station according to claim 1, characterized in that, The interstage flow balance relationships of the primary regulating tank and the secondary regulating tank are as follows: ； ； in, , and These represent the flow rates between adjacent levels of hydro-turbine generator units. and These represent the areas of the primary regulating tank and the secondary regulating tank, respectively. and These represent the water levels of the primary regulating tank and the secondary regulating tank, respectively. By linearizing the inter-stage flow balance relationship with a small perturbation and transforming it to the complex frequency domain, we obtain: ； in, and These represent the flow disturbance amounts on the upstream and downstream sides of the regulating tank, respectively. This indicates the amount of water level disturbance in the corresponding regulating tank. Represents complex frequency. This represents the time constant related to the area of ​​the corresponding regulating pool.

5. The vibration response assessment method for a three-stage series hydropower station according to claim 1, characterized in that, The overall system matrix satisfies: ； in, This represents the overall system matrix. This represents the system state vector composed of the recurrent head and recurrent flow rate at the beginning and end of each pipe section. Represents complex frequency; The singular condition of the overall system matrix is: ； The singular condition is then determined as the vibration characteristic equation of the system.

6. The vibration response assessment method for a three-stage series hydropower station according to claim 5, characterized in that, Solving the vibration characteristic equation of the system includes: Perform a frequency scan within the preset angular frequency range to determine... Local minimum points; The complex frequency corresponding to the local minimum point is determined as the initial value for iteration, and Newton iteration is performed on the vibration characteristic equation of the system based on the initial value for iteration. The iteration stops when the difference between the complex frequencies obtained from two adjacent iterations meets a preset accuracy condition, thus obtaining the multi-order vibration complex frequencies under the corresponding parameter combinations, where the first... The complex frequency of an oscillation is expressed as: ； Indicates the first The attenuation factor of the complex frequency of the first vibration. Indicates the first The angular frequency of a complex vibration.

7. The vibration response assessment method for a three-stage series hydropower station according to claim 1, characterized in that, Determine the corresponding continuous modal branches under different parameter combinations, including: For adjacent th The parameter combination and the first The parameter combination is used to calculate the first parameter according to the following formula. The first parameter combination The first-order complex frequency of vibration and the second-order complex frequency The first parameter combination Modal distance between complex frequencies of vibration: ； in, and They represent the first The parameter combination and the first A combination of parameters, and These represent the attenuation factors corresponding to the complex frequencies of vibration. and These represent the angular frequencies corresponding to the complex frequencies of vibration; Based on the modal distance, the vibration complex frequencies corresponding to adjacent parameter combinations are divided into the same continuous modal branch; Furthermore, the dominant vibration modes under each parameter combination are determined based on the attenuation factors of each continuous modal branch, including: When there is a vibration mode with a decay factor greater than zero, the vibration mode with the largest decay factor is determined as the dominant mode of divergence risk. When the attenuation factor of each vibration mode is less than zero, the vibration mode with the largest attenuation factor is determined as the weakly attenuated dominant mode from the preset low-order mode set. When the dominant vibration modes corresponding to adjacent parameter combinations belong to different continuous mode branches, the parameter range defined by the adjacent parameter combinations is determined as the dominant mode transition interval; When the attenuation factor of the continuous modal branch crosses zero as the parameter changes, the critical stability parameter is determined based on the parameter corresponding to the attenuation factor.

8. A vibration response assessment system for a three-stage series hydropower station, characterized in that, include: The parameter acquisition module is used to acquire the system parameters of a three-stage series hydropower station, which includes three-stage turbine generator units connected in sequence through a primary regulating pool and a secondary regulating pool. Each stage of the turbine generator unit is equipped with a pressure regulating chamber on the water intake side. The constraint construction module is used to establish pipeline unit constraints for each section of pipeline, pressure chamber boundary constraints for each pressure chamber, unit boundary constraints for each turbine generator unit, and to establish two inter-stage flow balance constraints based on the relationship between the difference in flow rate on the upstream and downstream sides of each regulating pool and the corresponding water level disturbance in the regulating pool. The matrix assembly module is used to assemble the pipeline unit constraints, the three surge chamber boundary constraints, the three generator boundary constraints, and the two inter-stage flow balance constraints into a system overall matrix according to the hydraulic connection topology of the three-stage series hydropower station, and to construct the system vibration characteristic equation based on the singular conditions of the system overall matrix. The complex frequency solving module is used to update the overall system matrix and solve the system vibration characteristic equation for multiple parameter combinations, including the parameter values ​​of the regulating pool and the parameter values ​​of the pressure regulating chamber adjacent to the corresponding regulating pool, so as to obtain the multi-order vibration complex frequencies corresponding to each parameter combination. The modal analysis module is used to determine the continuous modal branches based on the continuous variation relationship between the attenuation factors and angular frequencies of each order of vibration complex frequencies under adjacent parameter combinations, determine the dominant vibration mode based on the attenuation factors of each continuous modal branch, and determine the dominant mode transition interval based on the change of the continuous modal branch to which the dominant vibration mode belongs with the parameter combination. The results generation module is used to generate vibration response evaluation results for the three-stage tandem hydropower station based on the attenuation factor, circular frequency, and dominant mode transfer interval of each continuous modal branch.

9. An electronic device, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor causes the processor to implement the vibration response assessment method for a three-stage series hydropower station as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the vibration response assessment method for a three-stage series hydropower station as described in any one of claims 1-7.

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