Method for determining model parameters for stability calculation of a hydraulic turbine and its governing control system

Abstract

The application discloses a method for determining model parameters for stable calculation of a hydraulic turbine and a regulating control system thereof, integrates a plurality of links such as specific checking items of PID parameters, a plurality of dynamic characteristic tests of an executing mechanism, and a transfer function model checking in a systematic manner, performs simulation verification under frequency disturbance, forms a closed-loop optimization process of "parameter test-model establishment-simulation verification-parameter correction", and significantly improves simulation precision of the hydraulic turbine and the regulating system thereof in stable calculation of a power system, so that more efficient and more flexible scheduling control can be realized, and stability and safety of operation of a hydropower station are improved.

Description

Technical Field

[0001] This invention belongs to the field of hydropower station automation control technology, and relates to a method for determining model parameters for stability calculation of a water turbine and its regulation and control system. Background Technology

[0002] As the core equipment for energy conversion in hydropower stations, the turbine's regulation and control system undertakes key tasks such as speed regulation, power control, and primary frequency regulation. Its dynamic performance directly determines the frequency stability, voltage quality, and power supply reliability of the power system. With the large-scale grid connection of new energy sources and increasingly complex power grid structures, the power system places higher demands on the response speed, anti-interference capability, and robustness of the turbine regulation system. Accurate system simulation analysis has become a core tool for power system planning and design, operation optimization, and fault diagnosis.

[0003] However, in existing technologies, determining the model parameters of hydro turbines and their regulating systems still faces significant bottlenecks: most parameters rely on industry empirical formulas for estimation, analogy with typical unit parameters, or simplified theoretical derivations, failing to fully consider the impact of factors such as the complex pipeline layout of the water diversion system, the nonlinear characteristics of the hydro turbine, the wear and aging of the regulating mechanism, and the coupling of power grid load fluctuations in actual engineering projects. Simultaneously, some key parameters (such as the water flow inertia time constant and the optimized value of the governor's PID gain) are difficult to obtain accurately through conventional experiments, leading to deviations between the simplified model and the actual system. This parameter uncertainty prevents simulation analysis from fully reproducing the dynamic response process of the actual system, resulting in deviations between simulation results and the actual operating state of the unit. This may mislead the formulation of power system stability control strategies and pose potential risks to the safe and stable operation of the power grid.

[0004] Therefore, it is urgent to break through the limitations of existing parameter determination methods, improve the accuracy and fit of model parameters, and provide reliable support for power system stability analysis. Developing a method that can accurately determine the model parameters of water turbines and their regulation and control systems is particularly important. Summary of the Invention

[0005] The purpose of this invention is to provide a method for determining model parameters for stability calculation of a water turbine and its regulation and control system, which solves the problem of low simulation accuracy of water turbine regulation system due to inaccurate model parameters in the prior art.

[0006] The technical solution adopted in this invention is a method for determining model parameters for stability calculation of a water turbine and its regulating control system, specifically including the following steps: Step 1: Establish the transfer function model of the turbine regulation system using the basic parameters of the hydropower station and hydroelectric generator units; The turbine regulation system includes a speed deviation detection component, a PID speed governor component, a dead zone function, a hydraulic servo system component, and a turbine component. Step 2: Verify the PID parameters of the PID speed controller by performing a frequency disturbance test. Step 3: Based on the verified PID parameters, verify the actuator model parameters that match them; Step 4: Using the validated model parameters, perform simulation verification of the turbine regulation system under frequency disturbances.

[0007] The invention is further characterized by: The basic parameters in step 1 include various parameters required for modeling the turbine, generator, and speed control system; The parameters of the water turbine include the head, the inertial time constant of the high-pressure water intake system, the regulating time constant of the water turbine, and the rated power of the water turbine; Generator parameters include rated voltage, rated frequency, rated capacity, synchronous reactance, and moment of inertia; Speed ​​control system parameters include gain parameters Time constant and dead zone width ; where the gain parameter Including proportional gain Integral gain Differential gain time constant Including the time constant of the speed measurement process Hydraulic system time constant Delay time of the implementing agency Water turbine inertial time constant .

[0008] The transfer function model of the turbine regulating system in step 1 is as follows: (1), In formula (1), Let be the transfer function for speed deviation detection. Here is the transfer function of the PID speed controller. For the transfer function of the hydraulic servo system component, Let be the transfer function of the turbine component. It is a complex frequency variable.

[0009] In the speed deviation detection stage, the speed deviation detection is represented by a delay element, and the transfer function is: (2), In formula (1), This is the time constant for the rotational speed measurement delay.

[0010] In the PID speed controller stage, based on the actual control structure of the system, a proportional-integral (PID) speed controller is adopted. Modeling can be done using a proportional-integral-derivative (PID) structure, with the transfer function being: (3); If we simplify it to a PI controller without the differential element: (4).

[0011] Add a nonlinear dead-zone function before the output of the PID speed controller to indicate that small deviations cannot drive the actuator. This is modeled using a saturation function. (5), In formula (5), This represents the output signal of the PID speed controller. This represents the output signal after saturation limiting. , These are the maximum and minimum opening limits of the system, respectively; In the hydraulic servo system, the hydraulic system is simplified to a first-order inertial element, and its transfer function is: (6), In formula (5), is the time constant of the hydraulic system.

[0012] The turbine stage employs a typical turbine inertial model, with the transfer function in the following form: (7), In formula (6), is the inertial time constant of the water turbine.

[0013] The specific verification method for step 2 is as follows: Step 2-1: Inject frequency disturbance signals into the turbine regulating system using a small disturbance method; The amplitude of the small disturbance frequency signal is ±0.05Hz. In order to keep the system within the approximately linear region of the operating point, the amplitude of the small step signal of the small disturbance actuator is taken as 5% of the rated opening, and the amplitude of the large step signal is taken as 15% of the rated opening. Step 2-2: Simplify the transfer function model and set the initial test values ​​for the parameters to be identified, while collecting measured response data; Under the condition of small perturbation identification, the simplified transfer function to be identified is: (8), In formula (8), the parameter to be identified is , , , Time constant of rotational speed measurement process Actuator delay time parameters; Steps 2-3: Fit the transfer function using the least squares method to minimize the mean square error between the fitted output of the transfer function model and the measured response data; The fitting equation is: (9), In formula (9), , To fit the output, This refers to the actual measured response data output.

[0014] Step 2-4: If the mean square error obtained in step 2-3 is not greater than the set threshold, the verification is passed. If the mean square error is greater than the set threshold, return to step 2-2 to adjust the parameters to be identified, and then repeat step 2-3.

[0015] The method for simplifying the transfer function construction in step 2-2 is as follows: Under small disturbance identification conditions, with PID parameter verification as the objective, only the frequency measurement link, PID speed controller link, and actuator-dominated dynamic link directly related to PID parameter identification are retained; for dead zone and saturated nonlinear links, since their influence is weak under small disturbance conditions, they are linearized near the operating point or not identified in this step; for turbine links and other links with known parameters, initial parameters are used to fix them or they are equivalently incorporated into the controlled object. If the mean square error in steps 2-4 is greater than the set threshold, the parameters to be identified are iteratively corrected according to the deviation characteristics of the response curve. The basic principle for adjusting the parameters is: when the response speed is too slow, increase the proportional gain or integral gain first; when the oscillation or overshoot is too large, decrease the proportional gain first, adjust the derivative gain or measure the filter time constant; when the steady-state error is too large, adjust the integral gain first until the error meets the threshold requirement.

[0016] Step 3 specifically involves: performing simulation output tests and actual response tests on the actuator. The actual response tests include small step action characteristic tests, large step action characteristic tests, and fully open / fully closed action characteristic tests. Then, the simulation response curves from the simulation response tests are compared with the field response curves obtained from the different action characteristic tests. If the minimum mean square error is not greater than the set threshold, the verification is passed. If the minimum mean square error is less than the set threshold, the process returns to step 2 to readjust the model's gain parameters, time parameters, and dead zone width until the verification is passed.

[0017] The specific steps for simulation output testing are as follows: A model with dead zone and saturation characteristics of a first-order inertial element is adopted as the actuator for the guide vane and propeller blades, and its transfer function expression is as follows: (10) In formula (10), This is the gain coefficient. It is a time constant; If dead zone and saturation effect are considered, the output satisfy: (11), In formula (11), Input control signals; Dead zone width; Maximum saturation value; The small step action characteristic test is specifically performed as follows: a small-amplitude step signal within 5% of the rated opening is applied to the actuator to perform the small step action characteristic test, and the response time and final stable value are recorded; the measured response curve obtained from the small step test is compared with the simulated response curve, and the rise time deviation, settling time deviation, and steady-state value deviation are calculated; when all deviations do not exceed the preset allowable values, and the mean square error of the corresponding curve is not greater than the set threshold, the model is judged to be matched; otherwise, the actuator gain, time constant, or dead zone parameters are adjusted and re-verified. The large step action characteristic test is specifically conducted by applying a large-amplitude step signal of not less than 5% of the rated opening to test the maximum output change and response limit of the actuator; comparing the measured response obtained from the large step test with the simulated response, and calculating the maximum output deviation, response limit deviation, and time deviation to enter the saturation region; when the above deviations do not exceed the preset allowable values ​​and the mean square error is not greater than the set threshold, the saturation characteristic is determined to be matched; otherwise, the saturation upper limit, rate limit parameter, gain coefficient, or time constant is adjusted and re-verified. The full-open / full-close action characteristic test is as follows: when the actuator reaches the full-open or full-close state within a set time and the opening / closing time deviation is not greater than the set threshold, it is considered to pass; otherwise, the maximum displacement speed of the actuator, the hydraulic system time constant, the dead zone parameter or the opening limit value are adjusted and the test is repeated.

[0018] Step 4 is as follows: Step 4-1: In the simulation system, input the verified model parameters from Steps 2 and 3 into the complete turbine regulation system transfer model; Step 4-2: Simulate possible frequency fluctuations during system operation by using frequency up-frequency perturbation and frequency down-frequency perturbation; Step 4-3: Record the response curves of key parameters over time after the disturbance to characterize the dynamic response process and steady-state recovery of the system after the disturbance. Step 4-4: Compare the simulation output results obtained in Step 4-3 with the actual measured response data on site; If the minimum mean square error between the simulation results and the measured data is not greater than the set threshold, and the dynamic indicators all meet the set technical requirements, then the model can be used for subsequent stability calculation and analysis. If the minimum mean square error between the simulation results and the measured data is greater than the set threshold, return to steps 2-4 and adjust the PID speed controller parameters, actuator parameters, and frequency response model parameters in sequence until the simulation error meets the accuracy requirements, and then confirm the final model parameters.

[0019] Key parameters in step 4-3 include governor control variables, turbine power output, speed deviation, and guide vane opening. Dynamic indicators in step 4-4 include steady-state error, peak power deviation, peak occurrence time deviation, adjustment time, and maximum overshoot.

[0020] The beneficial effects of this invention are: This invention systematically integrates multiple aspects such as specific verification items of PID parameters, testing of various dynamic characteristics of actuators, and verification of transfer function models. Simulation verification is performed under frequency disturbances, forming a closed-loop optimization process of "parameter testing - model establishment - simulation verification - parameter correction". This significantly improves the simulation accuracy of turbines and their regulating systems in power system stability calculations, helps to achieve more efficient and flexible scheduling control, and improves the stability and safety of hydropower station operation. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating the method for determining model parameters for stability calculation of a water turbine and its regulating control system according to the present invention. Figure 2 This is a comparison chart of the measured curve and the simulated curve of the PID output response under frequency disturbance conditions in Embodiment 1 of the present invention; Figure 3 This is a comparison chart of the measured curve and the simulated curve of the opening response of the actuator under a 5% step input in Embodiment 1 of the present invention; Figure 4 This is a comparison chart of the measured curve and the simulated curve of the output power of the transfer function model in Embodiment 1 of the present invention; Figure 5 This is a comparison chart of the measured curve and the PSASP simulation curve of the active power response of the unit under the frequency up-disturbance condition in Embodiment 1 of the present invention. Figure 6 This is a comparison chart of the measured curve and the PSASP simulation curve of the active power response of the unit under frequency disturbance conditions in Embodiment 1 of the present invention. Detailed Implementation

[0022] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0023] This invention comprehensively characterizes the dynamic characteristics of the actuator through a combination of small step, large step, and full-on / full-off tests; and ensures the accuracy of the model under real power grid disturbance conditions through comparative verification of frequency up-disturbance and down-disturbance.

[0024] This invention provides a method for determining model parameters for stability calculation of a water turbine and its regulating control system, specifically implemented according to the following steps: Step 1: Establish the transfer function model of the turbine regulation system using the basic parameters of the hydropower station and hydroelectric generator units; The basic parameters of hydropower stations and hydropower units include various parameters required for modeling turbines, generators and speed control systems. The basic parameter data collected based on actual equipment and construction requirements provide initial values ​​for testing each link of the turbine speed control system.

[0025] The parameters of a water turbine include head, inertial time constant of the high-pressure water intake system, regulating time constant of the water turbine, and rated power of the water turbine; the parameters of a generator include rated voltage, rated frequency, rated capacity, synchronous reactance, and moment of inertia. Speed ​​control system parameters are used to establish the transfer function model, including gain parameters. Time constant and dead zone width ; where the gain parameter Including proportional gain Integral gain Differential gain time constant Including the time constant of the speed measurement process Hydraulic system time constant Delay time of the implementing agency Water turbine inertial time constant .

[0026] The turbine regulating system includes a speed deviation detection stage, a PID governor stage, a dead-zone function, a hydraulic servo system stage, and the turbine stage. Therefore, the transfer function model of the turbine regulating system is: (1), In formula (1), Let be the transfer function for speed deviation detection. Here is the transfer function of the PID speed controller. For the transfer function of the hydraulic servo system component, Let be the transfer function of the turbine component. It is a complex frequency variable (Teplase variable).

[0027] The speed deviation detection is represented by a delay element, i.e., the transfer function of the speed deviation detection element is: (2), In formula (2), This is the time constant for the rotational speed measurement delay.

[0028] In the PID speed controller stage, based on the actual control structure of the system, a proportional-integral (PID) speed controller is adopted. Alternatively, a proportional-integral-derivative (PID) structure model can be used. The transfer function of a PID speed controller is: (3); If we simplify equation (3) to a PI controller without the differential element: (4).

[0029] Add a nonlinear dead-zone function before the output of the PID speed controller to indicate that small deviations cannot drive the actuator. This is modeled using a saturation function. (5), In formula (5), This represents the output signal of the PID speed controller. This represents the output signal after saturation limiting. , These are the maximum and minimum opening limits of the system, respectively. When the output of the PID speed controller is less than the dead zone width DB, the dead zone output is 0 and the actuator does not operate. When the output of the PID speed controller exceeds the dead zone width, the dead zone allows the signal to pass through. The dead zone will reduce the system's adjustment accuracy, but it can suppress high-frequency jitter and protect the actuator.

[0030] In the hydraulic servo system, the hydraulic system is simplified to a first-order inertial element, and its transfer function is: (6), In formula (6), is the time constant of the hydraulic system.

[0031] The turbine stage employs a typical turbine inertial model, with the transfer function being: (7), In formula (7), is the inertial time constant of the water turbine.

[0032] Step 2: Verify the basic parameters of the PID speed controller by performing a frequency disturbance test.

[0033] The specific verification method is as follows: Step 2-1: Inject frequency disturbance signals into the turbine regulating system using a small disturbance method; The amplitude of the small disturbance frequency signal is ±0.05Hz. In order to make the frequency disturbance signal in the near-linear region of the operating point, the amplitude of the small step signal of the small disturbance actuator is taken as 5% of the rated opening, and the amplitude of the large step signal is taken as 15% of the rated opening. In the frequency disturbance simulation verification, the amplitude of the upper and lower frequency disturbances can be selected as +0.1Hz and -0.1Hz, respectively.

[0034] Step 2-2: Simplify the transfer function model and set the initial test values ​​for the parameters to be identified, while collecting measured response data; Under the condition of small perturbation identification, the simplified transfer function to be identified is: (8), In formula (8), the parameters to be identified include , , , Time constant of rotational speed measurement process Actuator delay time parameters; The simplified method for constructing the transfer function is as follows: Under small disturbance identification conditions, with PID parameter verification as the objective, only the frequency measurement link, PID speed controller link, and actuator-dominated dynamic link directly related to PID parameter identification are retained; for nonlinear links such as dead zone and saturation, since their influence is weak under small disturbance conditions, they are linearized near the operating point or not included in this step of identification; for turbine links and other links with known parameters, initial parameters are used to fix them or they are equivalently incorporated into the controlled object.

[0035] The measured response data can be real-time field data or historical waveform data, which can be used as a reference for parameter verification and model validation of this method; the response data includes the response sequences of the controlled variable and the control variable.

[0036] Steps 2-3: Fit the transfer function using the least squares method to ensure that the mean square error between the fitted output of the transfer function model and the measured response data is consistent. Minimum; where the fitted equation is: (9), In formula (9), , To fit the output, This refers to the actual measured response data output.

[0037] Step 2-4: If the mean square error obtained in step 2-3 If the mean square error is not greater than the set threshold, the verification is passed; otherwise, the verification is failed. If the value exceeds the set threshold, return to step 2-2 to adjust the parameter to be identified, and then repeat step 2-3. If the mean square error is greater than the set threshold, the parameters to be identified are iteratively corrected according to the deviation characteristics of the response curve. The basic principle for adjusting the parameters is: when the response speed is too slow, first increase the proportional gain or integral gain; when the oscillation or overshoot is too large, first decrease the proportional gain, adjust the derivative gain or measure the filter time constant; when the steady-state error is too large, first adjust the integral gain until the error meets the threshold requirement. Mean square error The set threshold is 5%.

[0038] Step 3: Based on the verified PID parameters, verify the actuator model parameters that match them.

[0039] The actuator is subjected to simulation output test and actual response test. The actual response test includes small step action characteristic test, large step action characteristic test and full open / full close action characteristic test. Then, the simulation response curve of the simulation response test is compared with the field response curve obtained from the different action characteristic tests. If the minimum mean square error is not greater than the set threshold (e.g., 5%), the verification is passed. If the minimum mean square error is less than the set threshold, return to step 2 to adjust the gain parameter, time parameter and dead zone width of the model until the verification is passed.

[0040] The specific steps for simulation output testing are as follows: A model with dead zone and saturation characteristics of a first-order inertial element is adopted as the actuator for the guide vane and propeller blades, and its transfer function expression is as follows: (10) In formula (10), This is the gain coefficient. is the time constant.

[0041] If dead zone and saturation effect are considered, the output satisfy: (11), In formula (11), Input control signals; Dead zone width; Maximum saturation value.

[0042] The small step action characteristic test is specifically performed as follows: a small step signal within 5% of the rated opening is applied to the actuator to perform the small step action characteristic test, and the response time and final stable value are recorded; the measured response curve obtained from the small step test is compared with the simulated response curve, and the rise time deviation, settling time deviation and steady-state value deviation are calculated; when all deviations do not exceed the preset allowable value, and the mean square error of the corresponding curve is not greater than the set threshold (such as 5%), the model is judged to be matched; otherwise, the actuator gain, time constant or dead zone parameter is adjusted and re-verified.

[0043] The large step action characteristic test is specifically performed by applying a large-amplitude step signal greater than 5% of the rated opening to test the maximum output change and response limit of the actuator; comparing the measured response obtained from the large step test with the simulated response, and calculating the maximum output deviation, response limit deviation, and time deviation to enter the saturation region; when the above deviations do not exceed the preset allowable value and the mean square error is not greater than the set threshold (e.g., 5%), the saturation characteristic is determined to be matched; otherwise, the saturation upper limit, rate limit parameter, gain coefficient, or time constant is adjusted and re-verified.

[0044] The full-open / full-close action characteristic test is as follows: when the actuator reaches the full-open or full-close state within a set time and the opening / closing time deviation is not greater than the set threshold, it is considered to pass; otherwise, the maximum displacement speed of the actuator, the hydraulic system time constant, the dead zone parameter or the opening limit value are adjusted and the test is repeated.

[0045] Step 4: Using the validated model parameters, perform simulation verification of the transmission function model of the turbine regulating system under frequency disturbance.

[0046] The specific steps are as follows: Step 4-1: In the simulation system, input the model parameters verified in Steps 2 and 3 into the complete transfer function model of the turbine regulation system.

[0047] Step 4-2: Simulate possible frequency fluctuations during system operation by using frequency up-frequency perturbation and frequency down-frequency perturbation; The frequencies for both up-frequency and down-frequency disturbances are set according to actual needs. For example, an up-frequency disturbance is a step increase of 0.1 Hz, and a down-frequency disturbance is a step decrease of 0.1 Hz.

[0048] Step 4-3: Record the response curves of key parameters over time after the disturbance to characterize the dynamic response process and steady-state recovery of the system after the disturbance. Key parameters include governor control variables, turbine power output, speed deviation, and guide vane opening.

[0049] Step 4-4: Compare the simulation output results obtained in Step 4-3 with the actual measured response data on site; If the minimum mean square error between the simulation results and the measured data is not greater than the set threshold (e.g., 5%), and the dynamic indicators all meet the set technical requirements, then the model can be used for subsequent stability calculation and analysis. If the minimum mean square error between the simulation results and the measured data is greater than the set threshold (e.g., 5%), return to steps 2-4 and adjust the PID governor parameters, actuator parameters, and other turbine-related parameters that affect the frequency disturbance in sequence until the simulation error meets the accuracy requirements and the final model parameters are confirmed. Dynamic indicators include steady-state error, peak power deviation, peak occurrence time deviation, settling time, and maximum overshoot.

[0050] Example 1 This embodiment describes a method for determining the model parameters for stability calculations of the turbine and its regulating control system based on Unit 2 of the Huangjinxia Hydropower Station. The specific steps are as follows: Step 1: Establish the transfer function model of the turbine regulation system based on the basic parameters of the hydropower station and the hydropower unit, and provide initial test values; Step 2: Verify the basic parameters of the PID speed controller by performing a frequency disturbance test. Based on the PSASP platform, an 8-type speed governor digital control system model was developed. After completing the PID parameter testing, PID simulation verification was performed. The test conditions were: PID parameters were set to the opening mode. =10.0、 =10.0、 =0, adjustment rate bp=0.03, artificial dead zone =0.05; Test results are as follows Figure 2 As shown, the simulation and measured curves basically coincide, and the specific PID parameter verification results are shown in Table 1 below.

[0051] Table 1

[0052] Step 3: Based on the verified PID parameters, verify the actuator model parameters that match them.

[0053] Simulation output tests and actual response tests were conducted on the actuators. The actual response tests included small step action characteristic tests, large step action characteristic tests, and fully open / fully closed action characteristic tests. The small step motion characteristic test specifically involves: performing a 5% step simulation of the turbine actuator, and the simulation verification results are as follows: Figure 3 As shown, the two curves basically overlap, and the deviation between the simulation and the actual measurement is within the allowable deviation range. The simulation comparison results of the step disturbance of the turbine actuator are shown in Table 2.

[0054] Table 2

[0055] Step 4: Using the validated model parameters, perform simulation verification of the turbine regulation system under frequency disturbances; Comparison of actual waveform recordings and simulation curves, for example Figure 4As shown in the figure, the measured curve and the simulated curve of the generator power are in good agreement. Simulation verification was performed using PSASP under frequency disturbances. The system response test under frequency disturbances included upward frequency disturbance tests and downward frequency disturbance tests, and the results are shown in the figure. Figure 5 and 6 As shown in Table 3, the frequency upsampling test deviation is shown in Table 4.

[0056] Table 3

[0057] Table 4

[0058] In the single-machine infinite bus system of PSASP, the opening mode primary frequency regulation simulation verification was performed. The parameters of the generator and excitation system were adopted from the parameters of Huangjinxia Unit 2, and the parameters of the speed regulation system and transfer function model were adopted from the results of the above steps.

[0059] Example 2 This embodiment is based on the No. 1 hydro-generator unit of a certain engineering project. The method of the present invention is used to determine the parameters of the regulating system model and perform simulation verification. The specific steps are as follows: Step 1: Establish the transfer function model of the turbine regulation system based on the basic parameters of the hydropower station and the hydropower unit, and provide initial test values; Collect basic parameters of the turbine, generator, and regulating system, such as the governor. =6.0、 =8.0, dead zone width DB=0.04, etc., to establish the transfer function model of the regulation system, with the same structure as in Example 1.

[0060] Step 2: Verify the basic parameters of the PID speed controller by performing a frequency disturbance test. Set the test conditions as follows: =6.0、 =8.0、 =0, bp=0.025, the simulation curve and the measured curve are basically consistent, and the error is within the allowable range; the specific results of PID parameter verification are shown in Table 5 below.

[0061] Table 5

[0062] Step 3: Based on the verified PID parameters, verify the actuator model parameters that match them.

[0063] Simulation output tests and actual response tests were conducted on the actuators. The actual response tests included small step action characteristic tests, large step action characteristic tests, and fully open / fully closed action characteristic tests. The small step action characteristic test specifically involves: the actuator undergoing a 5% step response test, with simulation and measured response deviations of 0.03s rise time and 0.04s settling time, respectively, meeting the accuracy requirements; the specific comparison of the actuator's step response is shown in Table 6 below.

[0064] Table 6

[0065] Step 4: Use the PSASP platform to perform system simulation verification under frequency disturbances. The deviations between the simulation results and the measured data are all within a reasonable range. The simulation error of frequency upward disturbance is shown in Table 7 below, and the simulation error of frequency downward disturbance is shown in Table 8 below.

[0066] Table 3

[0067] Table 4

[0068] Simulation results show that the model parameters can meet the requirements of engineering simulation and verify the adaptability of the method to different units.

[0069] Example 3 The method for determining the model parameters for stability calculation of the water turbine and its regulating control system in this embodiment is implemented according to the following steps: Step 1: Establish the transfer function model of the turbine regulation system using the basic parameters of the hydropower station and hydroelectric generator units; The turbine regulation system includes a speed deviation detection component, a PID speed governor component, a dead zone function, a hydraulic servo system component, and a turbine component. Step 2: Verify the PID parameters of the PID speed controller by performing a frequency disturbance test. Step 3: Based on the verified PID parameters, verify the actuator model parameters that match them; Step 4: Using the validated model parameters, perform simulation verification of the turbine regulation system under frequency disturbances.

[0070] Example 4 The method for determining the model parameters for stability calculation of the water turbine and its regulating control system in this embodiment is implemented according to the following steps: Step 1: Establish the transfer function model of the turbine regulation system using the basic parameters of the hydropower station and hydroelectric generator units; Speed ​​control system parameters include gain parameters Time constant and dead zone width ; where the gain parameter Including proportional gain Integral gain Differential gain time constant Including the time constant of the speed measurement process Hydraulic system time constant Delay time of the implementing agency Water turbine inertial time constant .

[0071] The turbine regulation system includes a speed deviation detection stage, a PID speed governor stage, a dead zone function, a hydraulic servo system stage, and a turbine stage.

[0072] The transfer function model of the turbine regulating system in step 1 is as follows: (1), In formula (1), Let be the transfer function for speed deviation detection. Here is the transfer function of the PID speed controller. For the transfer function of the hydraulic servo system component, Let be the transfer function of the turbine component. It is a complex frequency variable.

[0073] In the speed deviation detection stage, the speed deviation detection is represented by a delay element, and the transfer function is: (2), In formula (1), This is the time constant for the rotational speed measurement delay.

[0074] In the PID speed controller stage, based on the actual control structure of the system, a proportional-integral (PID) speed controller is adopted. Modeling can be done using a proportional-integral-derivative (PID) structure, with the transfer function being: (3); If we simplify it to a PI controller without the differential element: (4).

[0075] Add a nonlinear dead-zone function before the output of the PID speed controller to indicate that small deviations cannot drive the actuator. This is modeled using a saturation function. (5), In formula (5), This represents the output signal of the PID speed controller. This represents the output signal after saturation limiting. , These are the maximum and minimum opening limits of the system, respectively; In the hydraulic servo system, the hydraulic system is simplified to a first-order inertial element, and its transfer function is: (6), In formula (5), is the time constant of the hydraulic system.

[0076] The turbine stage employs a typical turbine inertial model, with the transfer function in the following form: (7), In formula (6), is the inertial time constant of the water turbine.

[0077] Step 2: Verify the PID parameters of the PID speed controller by performing a frequency disturbance test.

[0078] Step 3: Based on the verified PID parameters, verify the actuator model parameters that match them.

[0079] Step 4: Using the validated model parameters, perform simulation verification of the turbine regulation system under frequency disturbances.

[0080] Example 5 The method for determining the model parameters for stability calculation of the water turbine and its regulating control system in this embodiment is implemented according to the following steps: Step 1: Establish the transfer function model of the turbine regulation system using the basic parameters of the hydropower station and hydroelectric generator units; Speed ​​control system parameters include gain parameters Time constant and dead zone width ; where the gain parameter Including proportional gain Integral gain Differential gain time constant Including the time constant of the speed measurement process Hydraulic system time constant Delay time of the implementing agency Water turbine inertial time constant .

[0081] The turbine regulation system includes a speed deviation detection stage, a PID speed governor stage, a dead zone function, a hydraulic servo system stage, and a turbine stage.

[0082] The transfer function model of the turbine regulating system in step 1 is as follows: (1), In formula (1), Let be the transfer function for speed deviation detection. Here is the transfer function of the PID speed controller. For the transfer function of the hydraulic servo system component, Let be the transfer function of the turbine component. It is a complex frequency variable.

[0083] Step 2: Verify the PID parameters of the PID speed controller by performing a frequency disturbance test.

[0084] The specific verification method is as follows: Step 2-1: Inject frequency disturbance signals into the turbine regulating system using a small disturbance method; The amplitude of the small disturbance frequency signal is ±0.05Hz. In order to keep the system within the approximately linear region of the operating point, the amplitude of the small step signal of the small disturbance actuator is taken as 5% of the rated opening, and the amplitude of the large step signal is taken as 15% of the rated opening. Step 2-2: Simplify the transfer function model and set the initial test values ​​for the parameters to be identified, while collecting measured response data; Under the condition of small perturbation identification, the simplified transfer function to be identified is: (8), In formula (8), the parameter to be identified is , , , Time constant of rotational speed measurement process Actuator delay time parameters; Steps 2-3: Fit the transfer function using the least squares method to minimize the mean square error between the fitted output of the transfer function model and the measured response data; The fitting equation is: (9), In formula (9), , To fit the output, This refers to the actual measured response data output.

[0085] Step 2-4: If the mean square error obtained in step 2-3 is not greater than the set threshold, the verification is passed. If the mean square error is greater than the set threshold, return to step 2-2 to adjust the parameters to be identified, and then repeat step 2-3.

[0086] Step 3: Based on the verified PID parameters, verify the actuator model parameters that match them.

[0087] Step 4: Using the validated model parameters, perform simulation verification of the turbine regulation system under frequency disturbances.

[0088] Example 6 The method for determining the model parameters for stability calculation of the water turbine and its regulating control system in this embodiment is implemented according to the following steps: Step 1: Establish the transfer function model of the turbine regulation system using the basic parameters of the hydropower station and hydroelectric generator units; Speed ​​control system parameters include gain parameters Time constant and dead zone width ; where the gain parameter Including proportional gain Integral gain Differential gain time constant Including the time constant of the speed measurement process Hydraulic system time constant Delay time of the implementing agency Water turbine inertial time constant .

[0089] The turbine regulation system includes a speed deviation detection stage, a PID speed governor stage, a dead zone function, a hydraulic servo system stage, and a turbine stage.

[0090] The transfer function model of the turbine regulating system in step 1 is as follows: (1), In formula (1), Let be the transfer function for speed deviation detection. Here is the transfer function of the PID speed controller. For the transfer function of the hydraulic servo system component, Let be the transfer function of the turbine component. It is a complex frequency variable.

[0091] Step 2: Verify the PID parameters of the PID speed controller by performing a frequency disturbance test.

[0092] Step 3: Based on the verified PID parameters, verify the actuator model parameters that match them.

[0093] Specifically, the following steps are performed: simulated output tests and actual response tests are conducted on the actuator. The actual response tests include small step action characteristic tests, large step action characteristic tests, and fully open / fully closed action characteristic tests. Then, the simulated response curves from the simulated response tests are compared with the field response curves obtained from the different action characteristic tests. If the minimum mean square error is not greater than the set threshold, the verification is passed. If the minimum mean square error is less than the set threshold, the process returns to step 2 to readjust the model's gain parameters, time parameters, and dead zone width until the verification is passed.

[0094] The specific steps for simulation output testing are as follows: A model with dead zone and saturation characteristics of a first-order inertial element is adopted as the actuator for the guide vane and propeller blades, and its transfer function expression is as follows: (10) In formula (10), This is the gain coefficient. is the time constant.

[0095] If dead zone and saturation effect are considered, the output satisfy: (11), In formula (11), Input control signals; Dead zone width; Maximum saturation value; The small step action characteristic test is specifically performed as follows: a small-amplitude step signal within 5% of the rated opening is applied to the actuator to perform the small step action characteristic test, and the response time and final stable value are recorded; the measured response curve obtained from the small step test is compared with the simulated response curve, and the rise time deviation, settling time deviation, and steady-state value deviation are calculated; when all deviations do not exceed the preset allowable values, and the mean square error of the corresponding curve is not greater than the set threshold, the model is judged to be matched; otherwise, the actuator gain, time constant, or dead zone parameters are adjusted and re-verified. The large step action characteristic test is specifically conducted by applying a large-amplitude step signal of not less than 5% of the rated opening to test the maximum output change and response limit of the actuator; comparing the measured response obtained from the large step test with the simulated response, and calculating the maximum output deviation, response limit deviation, and time deviation to enter the saturation region; when the above deviations do not exceed the preset allowable values ​​and the mean square error is not greater than the set threshold, the saturation characteristic is determined to be matched; otherwise, the saturation upper limit, rate limit parameter, gain coefficient, or time constant is adjusted and re-verified. The full-open / full-close action characteristic test is as follows: when the actuator reaches the full-open or full-close state within a set time and the opening / closing time deviation is not greater than the set threshold, it is considered to pass; otherwise, the maximum displacement speed of the actuator, the hydraulic system time constant, the dead zone parameter or the opening limit value are adjusted and the test is repeated.

[0096] Step 4: Using the validated model parameters, perform simulation verification of the turbine regulation system under frequency disturbances.

Claims

1. A method for determining model parameters for stability calculation of a water turbine and its regulating control system, characterized in that, The specific steps are as follows: Step 1: Establish the transfer function model of the turbine regulation system using the basic parameters of the hydropower station and hydroelectric generator units; The turbine regulation system includes a speed deviation detection component, a PID speed governor component, a dead zone function, a hydraulic servo system component, and a turbine component. Step 2: Verify the PID parameters of the PID speed controller by performing a frequency disturbance test. Step 3: Based on the verified PID parameters, verify the actuator model parameters that match them; Step 4: Using the validated model parameters, perform simulation verification of the turbine regulation system under frequency disturbances.

2. The method for determining the model parameters for stability calculation of a water turbine and its regulating control system according to claim 1, characterized in that, The basic parameters in step 1 include various parameters required for modeling the turbine, generator, and speed control system. The parameters of the water turbine include the head, the inertial time constant of the high-pressure water intake system, the regulating time constant of the water turbine, and the rated power of the water turbine; Generator parameters include rated voltage, rated frequency, rated capacity, synchronous reactance, and moment of inertia; Speed ​​control system parameters include gain parameters Time constant and dead zone width ; where the gain parameter Including proportional gain Integral gain Differential gain time constant Including the time constant of the speed measurement process Hydraulic system time constant Delay time of the implementing agency Water turbine inertial time constant .

3. The method for determining the model parameters for stability calculation of a water turbine and its regulating control system according to claim 1, characterized in that, The transfer function model of the turbine regulating system in step 1 is as follows: （1）， In formula (1), Let be the transfer function for speed deviation detection. Here is the transfer function of the PID speed controller. For the transfer function of the hydraulic servo system component, Let be the transfer function of the turbine component. It is a complex frequency variable.

4. The method for determining the model parameters for stability calculation of a water turbine and its regulating control system according to claim 3, characterized in that, In the speed deviation detection stage, the speed deviation detection is represented by a delay stage, and the transfer function is: （2）， In formula (1), The time constant for the rotational speed measurement delay; In the PID speed controller stage, based on the actual control structure of the system, a proportional-integral (PID) speed controller is adopted. Modeling can be done using a proportional-integral-derivative (PID) structure, with the transfer function being: （3）； If we simplify it to a PI controller without the differential element: （4）； Add a nonlinear dead-zone function before the PID controller output to indicate that small deviations cannot drive the actuator. This is modeled using a saturation function. （5）， In formula (5), This represents the output signal of the PID speed controller. This represents the output signal after saturation limiting. , These are the maximum and minimum opening limits of the system, respectively; In the hydraulic servo system, the hydraulic system is simplified to a first-order inertial element, and its transfer function is: （6）， In formula (5), The time constant of the hydraulic system; The turbine stage employs a typical turbine inertial model, with the transfer function in the following form: （7）， In formula (6), is the inertial time constant of the water turbine.

5. The method for determining the model parameters for stability calculation of a water turbine and its regulating control system according to claim 1, characterized in that, The specific verification method for step 2 is as follows: Step 2-1: Inject frequency disturbance signals into the turbine regulating system using a small disturbance method; The amplitude of the small disturbance frequency signal is ±0.05Hz. In order to keep the system within the approximately linear region of the operating point, the amplitude of the small step signal of the small disturbance actuator is taken as 5% of the rated opening, and the amplitude of the large step signal is taken as 15% of the rated opening. Step 2-2: Simplify the transfer function model and set the initial test values ​​for the parameters to be identified, while collecting measured response data; Under the condition of small perturbation identification, the simplified transfer function to be identified is: （8）， In formula (8), the parameter to be identified is , , , Time constant of rotational speed measurement process Actuator delay time parameters; Steps 2-3: Fit the transfer function using the least squares method to minimize the mean square error between the fitted output of the transfer function model and the measured response data; The fitting equation is: （9）， In formula (9), , To fit the output, This refers to the actual measured response data output. Step 2-4: If the mean square error obtained in step 2-3 is not greater than the set threshold, the verification is passed. If the mean square error is greater than the set threshold, return to step 2-2 to adjust the parameters to be identified, and then repeat step 2-3.

6. The method for determining the model parameters for stability calculation of a water turbine and its regulating control system according to claim 5, characterized in that, The method for simplifying the transfer function construction in step 2-2 is as follows: Under small disturbance identification conditions, with PID parameter verification as the objective, only the frequency measurement link, PID speed controller link, and actuator-dominated dynamic link directly related to PID parameter identification are retained; for dead zone and saturated nonlinear links, since their influence is weak under small disturbance conditions, they are linearized near the operating point or not identified in this step; for turbine links and other links with known parameters, initial parameters are used to fix them or they are equivalently incorporated into the controlled object. If the mean square error in steps 2-4 is greater than the set threshold, the parameters to be identified are iteratively corrected according to the deviation characteristics of the response curve. The basic principle for adjusting the parameters is: when the response speed is too slow, increase the proportional gain or integral gain first; when the oscillation or overshoot is too large, decrease the proportional gain first, adjust the derivative gain or measure the filter time constant; when the steady-state error is too large, adjust the integral gain first until the error meets the threshold requirement.

7. The method for determining model parameters for stability calculation of a water turbine and its regulating control system according to claim 1, characterized in that, Step 3 specifically involves: performing simulation output tests and actual response tests on the actuator, including small step action characteristic tests, large step action characteristic tests, and fully open / fully closed action characteristic tests; then comparing the simulation response curves from the simulation response tests with the field response curves obtained from the different action characteristic tests. If the minimum mean square error is not greater than a set threshold, the verification is passed; if the minimum mean square error is less than the set threshold, the process returns to step 2 to readjust the model's gain parameters, time parameters, and dead zone width until the verification is passed.

8. The method for determining model parameters for stability calculation of a water turbine and its regulating control system according to claim 7, characterized in that, The specific steps for the simulation output test are as follows: A model with dead zone and saturation characteristics of a first-order inertial element is adopted as the actuator for the guide vane and propeller blades, and its transfer function expression is as follows: （10）， In formula (10), This is the gain coefficient. It is a time constant; If dead zone and saturation effect are considered, the output satisfy: （11）， In formula (11), Input control signals; Dead zone width; Maximum saturation value; The small step action characteristic test is specifically performed as follows: a small-amplitude step signal within 5% of the rated opening is applied to the actuator to perform the small step action characteristic test, and the response time and final stable value are recorded; the measured response curve obtained from the small step test is compared with the simulated response curve, and the rise time deviation, settling time deviation, and steady-state value deviation are calculated; when all deviations do not exceed the preset allowable values, and the mean square error of the corresponding curve is not greater than the set threshold, the model is judged to be matched; otherwise, the actuator gain, time constant, or dead zone parameters are adjusted and re-verified. The large step action characteristic test is specifically conducted by applying a large-amplitude step signal of not less than 5% of the rated opening to test the maximum output change and response limit of the actuator; comparing the measured response obtained from the large step test with the simulated response, and calculating the maximum output deviation, response limit deviation, and time deviation to enter the saturation region; when the above deviations do not exceed the preset allowable values ​​and the mean square error is not greater than the set threshold, the saturation characteristic is determined to be matched; otherwise, the saturation upper limit, rate limit parameter, gain coefficient, or time constant is adjusted and re-verified. The full-open / full-close action characteristic test is as follows: when the actuator reaches the full-open or full-close state within a set time and the opening / closing time deviation is not greater than the set threshold, it is considered to pass; otherwise, the maximum displacement speed of the actuator, the hydraulic system time constant, the dead zone parameter or the opening limit value are adjusted and the test is repeated.

9. The method for determining the model parameters for stability calculation of a water turbine and its regulating control system according to claim 1, characterized in that, Step 4 specifically involves: Step 4-1: In the simulation system, input the verified model parameters from Steps 2 and 3 into the complete turbine regulation system transfer model; Step 4-2: Simulate possible frequency fluctuations during system operation by using frequency up-frequency perturbation and frequency down-frequency perturbation; Step 4-3: Record the response curves of key parameters over time after the disturbance to characterize the dynamic response process and steady-state recovery of the system after the disturbance. Step 4-4: Compare the simulation output results obtained in Step 4-3 with the actual measured response data on site; If the minimum mean square error between the simulation results and the measured data is not greater than the set threshold, and the dynamic indicators all meet the set technical requirements, then the model can be used for subsequent stability calculation and analysis. If the minimum mean square error between the simulation results and the measured data is greater than the set threshold, return to steps 2-4 and adjust the PID speed controller parameters, actuator parameters, and frequency response model parameters in sequence until the simulation error meets the accuracy requirements, and then confirm the final model parameters.

10. The method for determining model parameters for stability calculation of a water turbine and its regulating control system according to claim 9, characterized in that, The key parameters in step 4-3 include governor control variables, turbine power output, speed deviation, and guide vane opening. The dynamic indicators in step 4-4 include steady-state error, peak power deviation, peak occurrence time deviation, adjustment time, and maximum overshoot.

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