Optimization method for ultralow frequency oscillation damping characteristic of one-pipe double-machine type pumped storage power station

Abstract

The invention belongs to the technical field of power system stability control, and particularly discloses an optimization method for ultralow frequency oscillation damping characteristics of a one-pipe double-machine type pumped storage power station. The method comprises the following steps: firstly, constructing a kinetic model of the one-pipe double-machine pumped storage power station; analyzing the stability of the model by using Hopf bifurcation, and determining critical parameters and dividing a stability domain through a Jacobian matrix eigenvalue; introducing a stability margin to quantify the stability, and analyzing a first influence of different working condition points on the oscillation frequency and the damping ratio under the same stability margin; obtaining a second influence of the parameter on the oscillation frequency and the damping ratio through sensitivity analysis; and constructing a three-dimensional curved surface of the oscillation frequency, the damping ratio and the control parameters based on the two influences, dividing an equal-frequency area and an equal-damping-ratio area on the three-dimensional curved surface under the stable allowance working condition, and identifying the optimal control parameters from the equal-frequency area and the equal-damping-ratio area. Optimized identification of the key parameters is realized, and support and guidance are provided for suppressing ultra-low frequency oscillation of the pumped storage power station and improving safe and stable operation of the system.

Description

Technical Field

[0001] This application belongs to the field of power system stability control technology, specifically relating to an optimization method for the ultra-low frequency oscillation damping characteristics of a single-pipe dual-machine pumped storage power station. Background Technology

[0002] In the context of building a new power system dominated by new energy sources, pumped storage power stations, as the most mature large-scale energy storage technology, are crucial for ensuring the safe and stable operation of the power grid. While the commonly used "one-pipe, two-unit" layout offers economic advantages, the strong hydraulic-mechanical coupling between units also presents stability challenges to the power station's operation. Furthermore, pumped storage power stations typically have long water intake systems, requiring surge tanks to reduce water hammer pressure. Inappropriate governor parameters and the water hammer effect are the main causes of ultra-low frequency oscillations in the system.

[0003] Most existing studies have failed to comprehensively and systematically investigate the impact of hydroelectric parameters on the stability of a single-pipe dual-machine system, lacking a method that can intuitively and globally guide the optimization of governor parameters to effectively suppress ultra-low frequency oscillations in pumped storage power stations. Therefore, there is an urgent need for a method that can comprehensively evaluate the damping characteristics of ultra-low frequency oscillations in pumped storage power stations and optimize parameters to suppress these oscillations. Summary of the Invention

[0004] In view of the shortcomings of the prior art, the purpose of this application is to provide an optimization method for the damping characteristics of ultra-low frequency oscillations in a single-pipe dual-machine pumped storage power station, aiming to solve the technical problem of how to suppress ultra-low frequency oscillations.

[0005] The first aspect of this application relates to a method for optimizing the damping characteristics of ultra-low frequency oscillations in a single-pipe dual-unit pumped storage power station, including: A nonlinear dynamic model of a single-pipe, dual-machine pumped storage power station with upstream series dual surge chambers is constructed. The stability of the equilibrium point of the nonlinear dynamic model is analyzed using Hopf bifurcation theory. Critical parameters are determined by the eigenvalues ​​of the Jacobian matrix, and the stability region is divided by the critical parameters. Based on the stability region, a stability margin is introduced to quantify stability. The first influence of different operating points on the oscillation frequency and damping ratio under the same stability margin is analyzed. The second influence of key parameters on the oscillation frequency and damping ratio is obtained through parameter sensitivity analysis. Based on the first and second effects, a three-dimensional surface is constructed for the oscillation frequency, damping ratio, and control parameters. On the three-dimensional surface, regions with equal frequency and equal damping ratio under stable margin conditions are divided, and the optimal combination of control parameters with frequency and damping ratio is identified from them.

[0006] Preferably, the stability region is obtained through the following steps: Define the equilibrium point of the nonlinear dynamic model; At the equilibrium point, the nonlinear dynamic model is linearized to obtain the Jacobian matrix; The stability of the characteristic equation of the Jacobian matrix is ​​determined by the Routh-Herwitz stability criterion, the critical parameter is found, and the stability region is divided by the critical parameter.

[0007] Preferred options also include: When the parameter crosses the critical parameter, the critical bifurcation category is determined by the rate of change of the real part of the eigenvalue in the characteristic equation of the Jacobian matrix. If the rate of change is greater than zero, it is determined to be a supercritical bifurcation; if the rate of change is less than zero, it is determined to be a subcritical bifurcation.

[0008] Preferably, the rate of change is specifically:

[0009]

[0010] in, Represents the rate of change of the real part; Indicates the critical parameter; Indicates parameters; Indicates taking the real part; This represents the eigenvalues ​​in the characteristic equation of the Jacobian matrix; The coefficients of the characteristic equation of the Jacobian matrix are represented.

[0011] Preferably, a stability margin is introduced based on the stability region to quantify stability, specifically as follows: Under the condition of small fluctuations in unit operation, a control model under frequency regulation mode is established with load disturbance as input and unit speed deviation as output. Define the stability margin index; A new control model is obtained by performing coordinate translation transformation on the control model based on the stability margin index. By applying the Routh-Hurwitz stability criterion to the new control model, the parameter conditions of the control model under the condition of ensuring the stability margin index are obtained.

[0012] Preferably, a new control model is obtained by performing a coordinate translation transformation on the control model based on the stability margin index; specifically: The control model is as follows:

[0013] in, These are the coefficients controlling the model; These are the eigenvalues ​​of the control model; The new control model obtained after coordinate translation of the control model is:

[0014] in, These are the coefficients of the new control model; These are the eigenvalues ​​of the new control model, satisfying... , This refers to the stability margin index.

[0015] Preferably, the coefficients of the new control model are as follows: ; ; ; ; ; ; ; ; ; ; .

[0016] Preferably, the nonlinear dynamic model integrates: the dynamic equations of the water diversion tunnel, the torque and flow equations of the water pump and turbine, the motion equation of the generator rotor, the governor equation, the pressure regulating chamber equation, and the pressure pipeline equation.

[0017] Preferably, the nonlinear dynamic model is as follows: ; ; ; ; ; ; ; ; ; ; in, This represents the relative value of the flow deviation in the water diversion tunnel. The inertial time constant of the water flow in the water diversion tunnel. This represents the relative deviation of the water level in surge tank 1. For the unit's working head, This refers to the head loss in the water diversion tunnel; The area time constant of pressure regulating chamber 1 This represents the relative value of the tailrace tunnel flow deviation. The relative speed of unit 1, The relative opening of the guide vanes of Unit 1. Let be the mechanical inertia time constant of Unit 1. The torque transfer coefficient of unit 1 to guide vane opening is given. The torque-to-speed transmission coefficient of unit 1. The torque-to-head transmission coefficient of Unit 1. The flow rate to head transfer coefficient of unit 1. The flow rate transfer coefficient of unit 1 to guide vane opening is given by [the relevant parameter]. The flow rate to speed transfer coefficient for unit 1. This is the generator load self-adjustment coefficient. This represents the relative deviation of the flow rate in pressure pipeline 1. This represents the relative value of the resistance torque of turbine 1. For the proportional gain of speed controller 1, The integral gain of speed controller 1; Let be the inertial time constant of the water flow in pressure pipe 1. This represents the initial value of water flow loss in the pressure pipeline. This represents the relative deviation of the water level in pressure chamber 2. The relative speed of unit 2, The relative opening of the two guide vanes of the unit. The mechanical inertia time constant of Unit 2, The torque transfer coefficient of unit 2 to guide vane opening is given. The torque transfer coefficient of unit 2 to guide vane opening is given. The torque-to-head transmission coefficient of Unit 2. The flow rate transfer coefficient of unit 2 to guide vane opening is given. The flow-to-speed transfer coefficient for unit 2. The flow rate to head transfer coefficient of Unit 2. This represents the relative value of the resistance torque of turbine 2. This represents the relative deviation of the flow rate in pressure pipeline 2. For the proportional gain of speed controller 2, The integral gain of the speed controller 2; The inertial time constant of the water flow in pressure pipe 2; The area time constant of pressure regulating chamber 2; is the inertial time constant of the tailrace tunnel flow rate.

[0018] In a second aspect, this application provides an electronic device, comprising: at least one memory for storing a program; and at least one processor for executing the program stored in the memory, wherein when the program stored in the memory is executed, the processor is configured to execute the method described in the first aspect or any possible implementation thereof.

[0019] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art: (1) This application realizes the optimized identification of key speed regulation parameters of a single-pipe dual-machine pumped storage power station, providing theoretical support and design guidance for suppressing ultra-low frequency oscillations of the single-pipe dual-machine pumped storage power station and improving the safe and stable operation of the power grid. (2) This application uses a nonlinear dynamic model of a single-pipe dual-machine pumped storage power station with upstream series double pressure regulating chambers to accurately characterize the water-mechanical-electric coupling effect of the power station and further analyze the ultra-low frequency oscillation characteristics of the system. (3) This application proposes a stability analysis framework based on the stability margin by introducing the concept of stability margin, and quantifies the oscillation characteristics of the system under different stability conditions; (4) This application transforms the stability margin requirement into a stability criterion by transforming the coordinate translation of the characteristic equation. Thus, all parameters that make the new characteristic equation satisfy the stability requirement also make the original characteristic equation satisfy the stability margin requirement. (5) This application constructs a three-dimensional distribution surface of the unit oscillation frequency and damping ratio as the governor parameters change, realizes the visualization of the key parameter optimization space, effectively identifies parameter combinations with both high frequency stability and sufficient damping, avoids harmful oscillations, and improves the dynamic quality and operational safety of the system. Attached Figure Description

[0020] Figure 1 This is a flowchart of the method for optimizing the damping characteristics of ultra-low frequency oscillations provided in the embodiments of this application.

[0021] Figure 2 This is a schematic diagram of system stability domain analysis provided in an embodiment of this application.

[0022] Figure 3 These are the system stability domains under the three stability margins provided in the embodiments of this application.

[0023] Figure 4 This refers to the time domain of the unit speed under the three stable margins provided in the embodiments of this application.

[0024] Figure 5 It is the frequency domain of the unit speed under the three stable margins provided in the embodiments of this application.

[0025] Figure 6The stability margin m=0.02 provided in this application embodiment is the group frequency and damping ratio.

[0026] Figure 7 The stability margin m=-0.02 provided in this application embodiment is the group frequency and damping ratio.

[0027] Figure 8 These are the frequency and damping ratio of the unit under different proportional gains and integral gains provided in the embodiments of this application.

[0028] Figure 9 These are the frequency and damping ratio of the unit under different water flow inertia time constants provided in the embodiments of this application.

[0029] Figure 10 These are the frequency and damping ratio of the unit under different mechanical inertia time constants provided in the embodiments of this application.

[0030] Figure 11 The embodiments of this application provide a three-dimensional distribution surface of frequency-proportional gain-integral gain and a three-dimensional distribution surface of damping ratio-proportional gain-integral gain within the full parameter space.

[0031] Figure 12 These are the frequency domain region diagram and the damping ratio region diagram of the fully stable margin provided in the embodiments of this application.

[0032] Figure 13 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0034] In this application, the terms "first" and "second," etc., are used to distinguish different objects, not to describe a specific order of objects. For example, "first stability margin" and "second stability margin," etc., are used to distinguish different stability margins, not to describe a specific order of stability margins.

[0035] In this application, the term "electrical connection" can refer to a direct circuit connection or a signal transmission via a communication protocol.

[0036] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0037] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple parameters means two or more parameters, multiple stability margins means two or more stability margins, etc.

[0038] First, the technical terms involved in the embodiments of this application will be introduced.

[0039] Hopf bifurcation is a bifurcation phenomenon in nonlinear dynamic systems, which manifests as periodic oscillations and instability as the system's stability changes with parameter variations.

[0040] The Jacobian matrix is ​​an important concept in multivariable calculus, describing the local behavior of functions in a multi-input multi-output system.

[0041] The Routh-Hurwitz stability criterion is a mathematical criterion used in control theory to determine the stability of linear time-invariant systems.

[0042] The embodiments of this application are described below with reference to the accompanying drawings.

[0043] Taking the regulating system of a single-pipe, dual-unit pumped storage power station with two upstream series surge tanks as an example, the basic parameters of the power station are: rated flow rate... Rated head m, head loss in water intake pipe m, head loss in the pressure pipe m, the inertial time constant of the water flow in the water pipe s, the inertial time constant of water flow in the pressure pipe s, generator set inertial time constant s, proportional gain and integral gain Integral gain Pressure regulating chamber area time constant The torque transfer coefficient of the generator unit to the guide vane opening. Unit torque to speed transmission coefficient The torque transfer coefficient of the generator unit to the head The transfer coefficient of unit flow rate to guide vane opening Unit flow rate to speed transfer coefficient Unit flow rate to head transfer coefficient Relative value of turbine resistance torque , Generator load self-adjustment coefficient Parameter optimization is performed on the pumped storage power station with upstream series-connected double surge tanks, such as... Figure 1 As shown, the specific steps include: (1) Construct a nonlinear dynamic model of a single-pipe dual-machine pumped storage power station with upstream series dual pressure regulating chambers.

[0044] (11) The nonlinear dynamic model integrates the dynamic equations of the water diversion tunnel, the torque and flow equations of the water pump and turbine, the motion equation of the generator rotor, the governor equation, the pressure regulating chamber equation, and the pressure pipeline equation.

[0045] The dynamic equations for the water diversion tunnel are as follows:

[0046] in, This represents the relative deviation of the water level in the upstream surge tank. The inertial time constant of the water flow in the water diversion tunnel. This represents the relative value of the flow deviation in the water diversion tunnel. For the head loss of the water diversion tunnel, The working head of the unit.

[0047] The equations for the torque and flow rate of a water pump turbine are as follows:

[0048]

[0049] in, This represents the relative value of the turbine's driving torque. This represents the relative deviation of the flow rate in the pressure pipeline. The relative speed of the unit, The relative opening of the guide vanes, This is a relative value of the water head. The torque-to-speed transmission coefficient is... The torque transfer coefficient to the guide vane opening is denoted as . The torque-to-head transfer coefficient is... The flow rate to speed transfer coefficient, The flow rate transfer coefficient to the guide vane opening is denoted as . denoted as the flow rate-to-head transfer coefficient.

[0050] The generator rotor motion equation is:

[0051] in, For time, The mechanical inertia time constant, is the relative value of the turbine resistance torque, and is the rate of change of the generator load torque with respect to speed.

[0052] The governor equation is:

[0053] For integral gain, This is the proportional gain.

[0054] The equation for the pressure regulating chamber is:

[0055] This refers to the cross-sectional area of ​​the pressure regulating chamber. The flow rate out of the pressure regulating chamber, For the water level in the surge tank, This refers to the flow rate flowing into the pressure regulating chamber.

[0056] The equation for a pressure pipeline is:

[0057] in, For the water level in the surge tank, The flow rate out of the pressure regulating chamber, The inertial time constant of the pressure pipeline flow rate. Head loss in pressure pipelines.

[0058] (12) The nonlinear dynamic model of a single-pipe dual-unit pumped storage power station is as follows: ; ; ; ; ; ; ; ; ; ; in, This represents the relative value of the flow deviation in the water diversion tunnel. The inertial time constant of the water flow in the water diversion tunnel. This represents the relative deviation of the water level in surge tank 1. For the unit's working head, This refers to the head loss in the water diversion tunnel; The area time constant of pressure regulating chamber 1 This represents the relative value of the tailrace tunnel flow deviation. The relative speed of unit 1, The relative opening of the guide vanes of Unit 1. Let be the mechanical inertia time constant of Unit 1. The torque transfer coefficient of unit 1 to guide vane opening is given. The torque-to-speed transmission coefficient of unit 1. The torque-to-head transmission coefficient of Unit 1. The flow rate to head transfer coefficient of unit 1. The flow rate transfer coefficient of unit 1 to guide vane opening is given by [the relevant parameter]. The flow rate to speed transfer coefficient for unit 1. This is the generator load self-adjustment coefficient. This represents the relative deviation of the flow rate in pressure pipeline 1. This represents the relative value of the resistance torque of turbine 1. For the proportional gain of speed controller 1, The integral gain of speed controller 1; Let be the inertial time constant of the water flow in pressure pipe 1. This represents the initial value of water flow loss in the pressure pipeline. This represents the relative deviation of the water level in pressure chamber 2. The relative speed of unit 2, The relative opening of the two guide vanes of the unit. The mechanical inertia time constant of Unit 2, The torque transfer coefficient of unit 2 to guide vane opening is given. The torque transfer coefficient of unit 2 to guide vane opening is given. The torque-to-head transmission coefficient of Unit 2. The flow rate transfer coefficient of unit 2 to guide vane opening is given. The flow-to-speed transfer coefficient for unit 2. The flow rate to head transfer coefficient of Unit 2. This represents the relative value of the resistance torque of turbine 2. This represents the relative deviation of the flow rate in pressure pipeline 2. For the proportional gain of speed controller 2, The integral gain of the speed controller 2; The inertial time constant of the water flow in pressure pipe 2; The area time constant of pressure regulating chamber 2; is the inertial time constant of the tailrace tunnel flow rate.

[0059] (2) The stability of the equilibrium point of the nonlinear dynamic model is analyzed by using the Hopf bifurcation theory, the critical parameters are determined by the eigenvalues ​​of the Jacobian matrix, and the stability region is divided by the critical parameters.

[0060] (21) Define the equilibrium point of the nonlinear dynamic model; when the model reaches the equilibrium point, it satisfies:

[0061] in, For the state variable vector, To control the parameters, This represents the vector of state variables when the equilibrium point is reached. (22) At the equilibrium point, the nonlinear dynamic model is linearized to obtain the Jacobian matrix, and the characteristic equation of the Jacobian matrix is:

[0062] in, Represents the Jacobian matrix. It is the identity matrix. Representation matrix The determinant of the Jacobian matrix. Expanding the characteristic equation of the Jacobian matrix yields:

[0063] in, The coefficients of the characteristic equation of the Jacobian matrix are obtained by simplifying the determinant. get; These are the eigenvalues ​​of the characteristic equation of the Jacobian matrix; (23) The stability of the characteristic equation of the Jacobian matrix is ​​judged by the Routh-Herwitz stability criterion, the critical parameter is found, and the stability region is divided by the critical parameter; When the stability critical point is reached The following conditions must be met:

[0064]

[0065]

[0066] in, Describe a Hurwitz determinant that satisfies:

[0067] These are the coefficients of the characteristic equation.

[0068] Continuously changing parameters When satisfied ,correspond These are the critical parameters. The stability region of the system is determined based on the set of all critical parameters, specifically as follows: Figure 2 As shown in the figure For proportional gain, For integral gain, For amplitude, For time.

[0069] (24) When the parameter crosses the critical parameter, the critical bifurcation category is determined by the rate of change of the real part of the eigenvalues ​​in the characteristic equation of the Jacobian matrix; if the rate of change is greater than zero, it is determined to be a supercritical bifurcation, that is, in A limiting cycle is generated within a sufficiently small neighborhood; if the rate of change is less than zero, it is determined to be a subcritical bifurcation, i.e., in... A limit cycle is generated within a sufficiently small neighborhood.

[0070] The rate of change is specifically:

[0071]

[0072] in, Represents the rate of change of the real part; Indicates the critical parameter; Indicates parameters; Indicates taking the real part; Denotes the eigenvalues ​​in the characteristic equation of the Jacobian matrix; represents the coefficients of the characteristic equation of the Jacobian matrix.

[0073] (3) Based on the stability domain, a stability margin is introduced to quantify stability, and the first influence of different operating points on the oscillation frequency and damping ratio under the same stability margin is analyzed; and the second influence of key parameters on the oscillation frequency and damping ratio is obtained through parameter sensitivity analysis.

[0074] (31) Under the condition of small fluctuation in unit operation, with load disturbance as input and unit speed deviation as output, a control model under frequency regulation mode is established, and a 10th-order nonlinear differential equation model is obtained:

[0075] in, These are the coefficients controlling the model; These are the eigenvalues ​​of the control model, specifically the imaginary part of the eigenvalues. Characterizing the natural oscillation frequency of the system, the real part Damping characteristics characterizing oscillation modes.

[0076] (32) Define the stability margin index; define the stability margin as... ,have:

[0077] The angular frequency corresponding to this oscillation mode is:

[0078] For pi, the corresponding damping ratio is:

[0079] (33) Based on the stability margin index, the control model is transformed by coordinate translation to obtain a new control model.

[0080] The new control model obtained after coordinate translation of the control model is:

[0081] in, These are the eigenvalues ​​of the new control model, satisfying... .

[0082] These are the coefficients of the new control model: ; ; ; ; ; ; ; ; ; ; .

[0083] (34) Apply the Routh-Hurwitz stability criterion to the new control model to obtain the parameter conditions of the control model under the condition of ensuring the stability margin index. For example... Figure 3 The figure shows the system stability regions when the stability margins are 0.02, 0, and -0.02, respectively. The Case axis represents the sequence number of the stability margin. Figure 4 The figure shows the time domain of the unit speed when the stability margins are 0.02, 0, and -0.02. For amplitude, For time. Figure 5 The figure shows the frequency domain of the unit speed when the stability margins are 0.02, 0, and -0.02. For amplitude, For frequency, This is the proportional gain. Figure 6 It is a stable margin Timing frequency and damping ratio. Figure 7 It is a stable margin Timing frequency and damping ratio.

[0084] (35) And the second influence of key parameters on the oscillation frequency and damping ratio is obtained through parameter sensitivity analysis. Figure 8 The frequency and damping ratio of the generator unit under different proportional gain and integral gain, among which For frequency, For proportional gain, For integral gain, The damping ratio is denoted as . Figure 9 These are the frequency and damping ratio of the unit under different water flow inertia time constants, where For frequency, For the damping ratio, It is the inertial time constant of the water flow. Figure 10 These are the frequency and damping ratio of the unit under different mechanical inertia time constants, where For frequency, For the damping ratio, It is the mechanical inertia time constant.

[0085] (4) Construct a three-dimensional surface for the oscillation frequency, damping ratio, and control parameters based on the first and second effects, such as... Figure 11 As shown, where For frequency, For the damping ratio, For proportional gain, This is the integral gain.

[0086] Regions with equal frequency and equal damping ratio under stable margin conditions are divided on the three-dimensional curved surface, such as... Figure 12 As shown, where For frequency, For the damping ratio, For proportional gain, This is the integral gain. Then, the optimal combination of control parameters for frequency and damping ratio is identified from this.

[0087] Based on the methods in the above embodiments, this application provides an electronic device, such as... Figure 13As shown, the electronic device may include a processor, a communications interface, a memory, and a communication bus, wherein the processor, communications interface, and memory communicate with each other via the communication bus. The processor can invoke logical instructions stored in the memory to execute the methods described in the above embodiments.

[0088] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application.

[0089] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0090] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0091] It is understood that the processor in the embodiments of this application can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0092] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0093] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0094] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0095] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. An optimization method for the ultra-low frequency oscillation damping characteristics of a single-pipe dual-unit pumped storage power station, characterized in that, include: A nonlinear dynamic model of a single-pipe, dual-machine pumped storage power station with upstream series dual surge chambers is constructed. The stability of the equilibrium point of the nonlinear dynamic model is analyzed using Hopf bifurcation theory. Critical parameters are determined by the eigenvalues ​​of the Jacobian matrix, and the stability region is divided by the critical parameters. Based on the stability region, a stability margin is introduced to quantify stability. The first influence of different operating points on the oscillation frequency and damping ratio under the same stability margin is analyzed. The second influence of key parameters on the oscillation frequency and damping ratio is obtained through parameter sensitivity analysis. Based on the first and second effects, a three-dimensional surface is constructed for the oscillation frequency, damping ratio, and control parameters. On the three-dimensional surface, regions with equal frequency and equal damping ratio under stable margin conditions are divided, and the optimal combination of control parameters with frequency and damping ratio is identified from them.

2. The optimization method according to claim 1, characterized in that, The stability region is obtained through the following steps: Define the equilibrium point of the nonlinear dynamic model; At the equilibrium point, the nonlinear dynamic model is linearized to obtain the Jacobian matrix; The stability of the characteristic equation of the Jacobian matrix is ​​determined by the Routh-Herwitz stability criterion, the critical parameter is found, and the stability region is divided by the critical parameter.

3. The optimization method according to claim 2, characterized in that, Also includes: When the parameter crosses the critical parameter, the critical bifurcation category is determined by the rate of change of the real part of the eigenvalue in the characteristic equation of the Jacobian matrix. If the rate of change is greater than zero, it is determined to be a supercritical bifurcation; if the rate of change is less than zero, it is determined to be a subcritical bifurcation.

4. The optimization method according to claim 3, characterized in that, The rate of change is specifically: in, Represents the rate of change of the real part; Indicates the critical parameter; Indicates parameters; Indicates taking the real part; This represents the eigenvalues ​​in the characteristic equation of the Jacobian matrix; The coefficients of the characteristic equation of the Jacobian matrix are represented.

5. The optimization method according to claim 1, characterized in that, Based on the aforementioned stability region, a stability margin is introduced to quantify stability, specifically as follows: Under the condition of small fluctuations in unit operation, a control model under frequency regulation mode is established with load disturbance as input and unit speed deviation as output. Define the stability margin index; A new control model is obtained by performing coordinate translation transformation on the control model based on the stability margin index. By applying the Routh-Hurwitz stability criterion to the new control model, the parameter conditions of the control model under the condition of ensuring the stability margin index are obtained.

6. The optimization method according to claim 5, characterized in that, A new control model is obtained by performing a coordinate translation transformation on the control model based on the stability margin index; specifically: The control model is as follows: in, These are the coefficients controlling the model; These are the eigenvalues ​​of the control model; The new control model obtained after coordinate translation of the control model is: in, These are the coefficients of the new control model; These are the eigenvalues ​​of the new control model, satisfying... , This refers to the stability margin index.

7. The optimization method according to claim 6, characterized in that, The coefficients of the new control model are as follows: ； ； ； ； ； ； ； ； ； ； 。 8. The optimization method according to claim 1, characterized in that, The nonlinear dynamic model integrates the following equations: dynamic equations for water diversion tunnels, torque and flow equations for water pumps and turbines, motion equations for generator rotors, equations for governors, equations for pressure regulating chambers, and equations for pressure pipelines.

9. The optimization method according to claim 1 or 8, characterized in that, The nonlinear dynamic model is specifically as follows: ； ； ； ； ； ； ； ； ； ； in, This represents the relative value of the flow deviation in the water diversion tunnel. The inertial time constant of the water flow in the water diversion tunnel. This represents the relative deviation of the water level in surge tank 1. For the unit's working head, This refers to the head loss in the water diversion tunnel; The area time constant of pressure regulating chamber 1 This represents the relative value of the tailrace tunnel flow deviation. The relative speed of unit 1, The relative opening of the guide vanes of Unit 1. Let be the mechanical inertia time constant of Unit 1. The torque transfer coefficient of unit 1 to guide vane opening is given. The torque-to-speed transmission coefficient of unit 1. The torque-to-head transmission coefficient of Unit 1. The flow rate to head transfer coefficient of unit 1. The flow rate transfer coefficient of unit 1 to guide vane opening is given by [the relevant parameter]. The flow rate to speed transfer coefficient for unit 1. This is the generator load self-adjustment coefficient. This represents the relative deviation of the flow rate in pressure pipeline 1. This represents the relative value of the resistance torque of turbine 1. For the proportional gain of speed controller 1, The integral gain of speed controller 1; Let be the inertial time constant of the water flow in pressure pipe 1. This represents the initial value of water flow loss in the pressure pipeline. This represents the relative deviation of the water level in pressure chamber 2. The relative speed of unit 2, The relative opening of the two guide vanes of the unit. The mechanical inertia time constant of Unit 2, The torque transfer coefficient of unit 2 to guide vane opening is given. The torque transfer coefficient of unit 2 to guide vane opening is given. The torque-to-head transmission coefficient of Unit 2. The flow rate transfer coefficient of unit 2 to guide vane opening is given. The flow-to-speed transfer coefficient for unit 2. The flow rate to head transfer coefficient of Unit 2. This represents the relative value of the resistance torque of turbine 2. This represents the relative deviation of the flow rate in pressure pipeline 2. For the proportional gain of speed controller 2, The integral gain of the speed controller 2; The inertial time constant of the water flow in pressure pipe 2; The area time constant of pressure regulating chamber 2; is the inertial time constant of the tailrace tunnel flow rate.

10. An electronic device, characterized in that, Includes memory and one or more processors; The memory is coupled to the one or more processors, and the memory is used to store computer program code, the computer program code including computer instructions; The one or more processors invoke the computer instructions to cause the electronic device to perform the method as described in any one of claims 1-9.

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