Synchronous generator excitation method based on mathematical modeling and gain scheduling

Abstract

The invention discloses a synchronous generator excitation method based on mathematical modeling and gain scheduling, and relates to the technical field of synchronous generator control, and the method comprises the steps: building a synchronous generator global dynamic mathematical model comprising the electromagnetic dynamic characteristics of a stator winding, a rotor winding and a damping winding through a modeling module; a discretization simulation platform is constructed in a Matlab / Simulink environment by utilizing a simulation module, model parameters are corrected, dynamic adjustment is realized through a gain scheduling excitation controller, an automatic voltage regulator (AVR) adopts PID (Proportion Integration Differentiation) control and comprises a voltage deviation integral separation strategy, and a power system stabilizer (PSS) dynamically adjusts parameters of a lead-lag compensator based on active power. According to the method, the deviation between a model and an actual system can be reduced by more than 30%, the electromechanical oscillation damping ratio within the rated power range of 10%-150% is increased by 25%-40%, the harmonic content of exciting current is reduced to be lower than 5%, the stability of an electric power system and the electric energy quality are remarkably improved, the engineering practicability is high, and the method is easy to transform and upgrade on an existing synchronous generator.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of synchronous generator control, in particular to a synchronous generator excitation method based on mathematical modeling and gain scheduling. BACKGROUND

[0002] In the power system, as the core equipment of power generation, the performance of the excitation system of the synchronous generator directly determines the stable operation level and power quality of the power system. There are two key problems in the traditional excitation system: 1. Insufficient modeling accuracy: The existing technology mostly uses low-order mathematical models to analyze the excitation system, which reduces the calculation complexity, but ignores the complex dynamic characteristics of the stator winding, rotor winding and damping winding, and cannot accurately reflect the actual operating state of the system. When the power system is disturbed by load fluctuations, short circuit faults and other disturbances, the deviation between the model and the actual system will cause the excitation regulation to lag, causing the generator terminal voltage to fluctuate greatly, and even seriously damaging the stability of the power grid.

[0003] 2. Control parameter fixation: The power system stabilizer PSS parameters in the traditional excitation controller are usually designed based on the rated operating point, such as 100% active power, using a fixed parameter control strategy. However, the operating conditions of the power system have strong dynamics, and the active power will fluctuate within a large range, such as 10%-150% of the rated power. The fixed parameter PSS cannot adapt to the nonlinear characteristics of different operating points, resulting in weakened electromechanical oscillation damping effect, unbalanced control signal strength, and reduced system transient stability and operating efficiency.

[0004] Therefore, there is an urgent need for an excitation system that combines high-precision modeling and dynamic parameter adjustment to solve the above technical problems. SUMMARY

[0005] The technical problem to be solved by the present application is to provide a synchronous generator excitation method based on mathematical modeling and gain scheduling, which overcomes the defects of insufficient modeling accuracy and inability to dynamically adapt control parameters in the prior art.

[0006] To solve the above technical problems, the technical solution adopted by the present application is: The synchronous generator excitation method based on mathematical modeling and gain scheduling includes a modeling module, a simulation module and a gain scheduling excitation controller, which work cooperatively; the modeling module establishes a full-domain dynamic mathematical model of the synchronous generator, which includes the electromagnetic dynamic characteristics of the stator winding, rotor winding and damping winding; the simulation module constructs a simulation platform for the mathematical model; the gain scheduling excitation controller includes an automatic voltage regulator AVR and a power system stabilizer PSS, which realizes dynamic parameter adjustment using a gain scheduling mechanism.

[0007] The global dynamic mathematical model of the synchronous generator described above comprises electromagnetic dynamic characteristics of the stator winding, the rotor winding and the damping winding, wherein the stator winding voltage equation is: ; wherein is a stator voltage vector, is a stator resistance, is a stator current vector, is a stator flux linkage vector; the rotor winding voltage equation is: ; wherein is a rotor excitation voltage, is a rotor resistance, is a rotor excitation current, is a rotor flux linkage; the damping winding voltage equation is: ; wherein is a damping winding resistance, is a damping winding current, is a damping winding flux linkage; Through the above equations, the electromagnetic coupling relationship of the synchronous generator under different operating states is described, and the representation accuracy of the model for the dynamic characteristics of the system is improved.

[0008] The simulation module described above constructs a simulation platform of the mathematical model under the Matlab / Simulink environment, adopts a discretization solving strategy, sets a discretization step T s ; the simulation module simulates the system response under different operating conditions in real time, provides a verification platform for excitation controller parameter optimization; at the same time, the model output is compared with the actual unit test data through simulation, the model parameters are continuously corrected, and the modeling accuracy is further improved.

[0009] The simulation module described above simulates the load mutation, short-circuit fault condition, and outputs the time-domain response curves of the generator terminal voltage, excitation current and speed deviation parameters, which are used for model verification and parameter optimization.

[0010] The automatic voltage regulator AVR described above adopts a classical linear PID controller, and the transfer function is: ; wherein is a proportional coefficient, is an integral coefficient, is a differential coefficient, is a Laplace complex variable; the AVR takes the deviation For input, output adjustment signal control excitation voltage, realize voltage fast stabilization.

[0011] The power system stabilizer PSS described above adopts a lead-lag compensator unit CU, whose transfer function is: ; Wherein , is the lead-lag time constant CU parameter; PSS with generator shaft speed deviation For input, output compensation signal to AVR, inhibit mechanical oscillation.

[0012] The gain scheduling mechanism described above includes: CU parameters , According to the active power output by the synchronous generator Dynamic adjustment, using a quadratic polynomial fitting to establish the mapping relationship between parameters and active power: ; Wherein , , Gain surface parameters.

[0013] The parameters described above , , Determined by two-stage tuning: The first stage: for multiple operating points, by solving the optimization problem: ; Determine the optimal parameters at each operating point, wherein is the voltage error, is the objective function, that is, the "error square and time multiplied by integral" at the i-th operating point, Integral of Time multiplied by SquaredError, used to quantify the pros and cons of system dynamic response; , Weighting coefficient; The second stage: the optimal , of each operating point is analyzed by least squares LS, and the quadratic polynomial coefficients , , are fitted to ensure smooth transition of parameters between different operating points.

[0014] The parameters described above , , In the first stage of tuning, the constraint condition of the optimization problem is: ; The weight coefficient satisfies .

[0015] The active power of the plurality of operating points covers 10%-150% of the rated power range of the synchronous generator, and the number of operating points is not less than 10.

[0016] The PSS dynamic gain adjustment process comprises: 1) active power collection: real-time collection of active power output by the synchronous generator , ensuring real-time parameter adjustment; 2) gain calculation: the lead-lag compensator parameters 、 of the PSS are calculated by using piecewise quadratic polynomial fitting according to the interval in which is located: When is less than 0.8 times the rated power, , ; When is greater than 1.2 times the rated power, , ; When is greater than 1.2 times the rated power, , ; 3) parameter update: the parameters are updated every 50ms 、 , and the update process adopts a smooth transition algorithm to avoid control signal fluctuations caused by parameter mutations.

[0017] The coefficients of the piecewise quadratic polynomial 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 are obtained by least square fitting of the optimal PSS parameters of 19 operating points.

[0018] The voltage deviation integral separation strategy is introduced in the PID control of the automatic voltage regulator AVR, and when the voltage deviation At rated voltage, only proportional and derivative regulation are activated. To avoid integral saturation; when Enable full PID control at rated voltage. .

[0019] The flux linkage calculation of the above-mentioned global dynamic mathematical model of the synchronous generator adopts the Park transformation, and the stator resistance... The value range is 0.01pu-0.02pu, rotor resistance. The value range is 0.005pu-0.01pu, damping winding resistance. The value range is 0.015pu-0.025pu.

[0020] The discretization step size mentioned above It can be adjusted according to the simulation accuracy requirements. When it is necessary to improve the simulation accuracy, Select 10μs-30μs; when it is necessary to balance simulation accuracy and computational efficiency, Select a time range of 30μs-100μs.

[0021] The parameters of the PID controller mentioned above , , It can be adjusted based on the rated power of the synchronous generator. In a synchronous generator with a rated power of 1000MW, The value range is 4.0-5.0. The value range is 14.0-15.0. The value range is 22.0-23.0.

[0022] The aforementioned CU operates at the rated power point of the synchronous generator, i.e. At rated power, parameters The value range is 0.50s-0.55s. The value range is 0.80s-0.85s.

[0023] The synchronous generator excitation method based on mathematical modeling and gain scheduling mentioned in this invention has the following beneficial effects: 1. Significantly improved modeling accuracy: By establishing a full-domain dynamic model that includes the stator, rotor, and damping windings, and combining Matlab / Simulink simulation verification and parameter correction, the deviation between the model and the actual system is reduced by more than 30%, providing a precise decision basis for excitation regulation; 2. Dynamic adaptability enhancement: Gain scheduling mechanism enables PSS parameters to be adjusted in real time with active power, within 10%-150% rated power range, mechanical and electrical oscillation damping ratio is improved by 25%-40%, control signal strength fluctuation amplitude is reduced by 20%, effectively improving system transient stability; 3. Power quality optimization: Optimized excitation regulation logic combined with high-precision modeling reduces excitation current harmonic content to below 5%, significantly reducing harmonic interference on the power grid, and improving power quality (such as voltage distortion rate) by 15%-25%; 4. Strong engineering practicability: Each module of the system is based on the mature Matlab / Simulink platform and industrial-grade hardware implementation, and the parameter tuning process can be completed through automatic algorithm without complex manual intervention, making it easy to upgrade on existing synchronous generators. BRIEF DESCRIPTION OF DRAWINGS

[0024] The present application will be further described below in conjunction with the drawings and examples: Figure 1 is the overall structure block diagram of the system of the present application; Figure 2 is a simulation schematic diagram of the global dynamic mathematical model of the synchronous generator of the present application; Figure 3 is a topology diagram of the gain scheduling mechanism of the present application. DETAILED DESCRIPTION

[0025] The technical solutions of the present application will be described in detail below in conjunction with the drawings and examples.

[0026] The synchronous generator excitation method based on mathematical modeling and gain scheduling includes a modeling module, a simulation module, and a gain scheduling excitation controller, which work cooperatively; the modeling module establishes a global dynamic mathematical model of the synchronous generator, which includes the electromagnetic dynamic characteristics of the stator winding, the rotor winding, and the damping winding; the simulation module constructs a simulation platform for the mathematical model; the gain scheduling excitation controller includes an automatic voltage regulator (AVR) and a power system stabilizer (PSS), which realizes dynamic parameter adjustment through a gain scheduling mechanism.

[0027] The above-mentioned global dynamic mathematical model of the synchronous generator includes the electromagnetic dynamic characteristics of the stator winding, the rotor winding, and the damping winding, wherein the stator winding voltage equation is: ; wherein is the stator voltage vector, is the stator resistance, is the stator current vector, is the stator flux linkage vector; The rotor winding voltage equation is: ; wherein is the rotor excitation voltage, is the rotor resistance, is the rotor excitation current, is the rotor flux linkage; damping winding voltage equation: ; wherein is the damping winding resistance, is the damping winding current, is the damping winding flux linkage; Through the above equations, the electromagnetic coupling relationship of the synchronous generator under different operating states is fully characterized, and the representation accuracy of the model for the dynamic characteristics of the system is improved.

[0028] The simulation module described above builds a simulation platform for the mathematical model under the Matlab / Simulink environment, adopts a discretization solving strategy, sets a discretization step T s , and the value range is 10 μs-100 μs; the simulation module can simulate the system response under different operating conditions such as load mutation and short-circuit fault in real time, provides a verification platform for excitation controller parameter optimization; at the same time, the model output is compared with the actual unit test data through simulation, and the model parameters are continuously corrected, further improving the modeling accuracy.

[0029] The simulation module described above can simulate the load mutation, short-circuit fault condition, output the time domain response curve of the generator terminal voltage, excitation current, and speed deviation parameters, and is used for model verification and parameter optimization.

[0030] The automatic voltage regulator AVR described above adopts a classical linear PID controller, and the transfer function is: ; wherein is the proportional coefficient, is the integral coefficient, is the differential coefficient, is the Laplace complex variable; the AVR takes the deviation of the generator terminal voltage from the reference value as the input, and outputs the regulation signal to control the excitation voltage, so as to realize the rapid and stable voltage.

[0031] The power system stabilizer PSS described above adopts a lead-lag compensator unit CU, and the transfer function is: ; wherein , are the lead-lag time constants of the CU parameters; the PSS takes the generator shaft speed deviation For input, output compensation signal to AVR, inhibit electromechanical oscillation.

[0032] The gain scheduling mechanism described above includes: CU parameters 、 According to the active power output by the synchronous generator Dynamic adjustment, using quadratic polynomial fitting to establish the mapping relationship between parameters and active power: ; Where 、 、 Gain surface parameters.

[0033] The parameters described above 、 、 Determined by two-stage tuning: First stage: for multiple operating points, by solving the optimization problem: ; Determine the optimal parameters at each operating point, where The voltage error, The objective function, i.e. the "integral of time multiplied by squared error" at the i-th operating point, is used to quantify the pros and cons of the system dynamic response; 、 Weighting coefficients; This function is a single-objective optimization function based on the ITSE criterion, and the core is to convert the dynamic changes of "voltage error" and "speed deviation" with time into a single quantitative index through integral operation. Among them: Integral term : square the voltage error and integrate it with time, time As a "dynamic weight" - in the early stage of disturbance Small, low sensitivity to error, in the later stage of disturbance Greater, more sensitive to error, can avoid the system being in a deviation state for a long time; Integral term : Similarly, quantify the cumulative impact of rotor speed deviation over time to ensure that the generator speed quickly returns to synchronous speed and avoid sustained electromechanical oscillation; Weighting coefficients 、 : through The value, such as 、 , priority to inhibit the speed deviation - the rotor speed fluctuations directly affect the grid frequency stability, is the core index of safe operation of power system, need to focus on control.

[0034] Parameter optimization: for each operating point, such as active power , 20% … 150% rated power, the optimization function is solved to obtain the optimal combination of , , AVR parameters and , PSS parameters under the current working conditions; Dynamic adaptation: to avoid the problem of traditional fixed parameter controller "trade-off" in different working conditions, such as parameter adaptation at rated power, but insufficient damping at low power, to ensure that the controller parameters at each operating point can minimize voltage error and speed deviation; Engineering landing: through the quantitative objective function, the abstract demand of "system stability" is converted into a calculable and optimized mathematical problem, which provides accurate parameter basis for subsequent gain scheduling mechanism, such as , Polynomial fitting.

[0035] The second stage: the least square LS analysis of the optimal , of each operating point is carried out, and the quadratic polynomial coefficients , , are fitted to ensure smooth transition of parameters between different operating points.

[0036] The above parameter , , tuning in the first stage, the constraint condition of optimization problem is: ; The weight coefficient satisfies .

[0037] The constraint is the upper and lower limit constraint of the parameter, that is, the value range of the optimization variable , , , , , to ensure that the optimized parameters meet the requirements of "engineering feasibility" and "system stability" — avoid parameter overshoot, equipment overload, or parameter lag, system instability.

[0038] PID controller parameters (Kp, Ki, Kd) , , ): upper limit 30, lower limit 0.

[0039] The proportional, integral, and derivative gains of the PID controller are all "regulation gains", which are non-negative. If , the voltage deviation will increase, the negative feedback will become positive feedback, and the system will diverge; if , the negative error will accumulate, and the steady-state deviation will increase; if , the speed fluctuation will be amplified, causing new oscillations. Therefore, the lower limit is set to 0 to ensure that the control logic is "negative feedback regulation", which is consistent with the basic principles of engineering.

[0040] Hardware limitations of the device: the execution unit of the synchronous generator excitation system, such as a thyristor rectifier, has a maximum output voltage / current limit, such as an excitation voltage upper limit of 1.5 times the rated excitation voltage. If , , is greater than 30, the control signal output by the PID, i.e., the excitation voltage regulation command, will exceed the hardware bearing range, causing thyristor overvoltage and overcurrent damage, or excitation winding overheating; System stability verification: through Matlab / Simulink simulation testing, when , , > 30, the system will have obvious overshoot (such as voltage overshoot > 20%) and oscillation decay time > 5s, which does not meet the standard of "voltage overshoot ≤ 15% and oscillation decay time ≤ 3s" in "Technical Requirements for Synchronous Motor Excitation System" (GB / T 7409.3-2015); Engineering experience accumulation: for 1000MW-1500MW synchronous generators, the traditional PID parameters are usually between 5-25, and the upper limit of 30 not only covers the traditional parameter range, but also reserves a regulation margin for high disturbance conditions such as three-phase short-circuit fault, taking into account safety and flexibility.

[0041] PSS lead-lag time constant , : upper limit 2s, lower limit 0.

[0042] If , the transfer function of the lead-lag compensator degenerates into a pure lag element, which cannot compensate for the phase lag of the system and loses the function of suppressing mechanical and electrical oscillations; if , the transfer function degenerates into a pure lead element, which will amplify high-frequency noise such as current harmonics, causing control signal fluctuations. Therefore, the lower limit is set to 0, and in actual optimization, 0 will be automatically avoided due to the minimization of the objective function, and usually , .

[0043] Electromechanical oscillation frequency matching: The frequency of electromechanical oscillation of power system is usually 0.1-2.5Hz, corresponding to a period of 0.4-10s, and the lead-lag time constant needs to be matched with the oscillation period - if 、 >2s, the phase compensation range of the compensator will deviate from the frequency range of electromechanical oscillation, and cannot effectively provide positive damping torque. For example, when the oscillation frequency is 1Hz and the period is 1s, 、 Taking 0.5-1.5s can achieve optimal phase compensation, and 2s is the effective upper limit verified by experience; Dynamic response speed requirement: if 、 >2s, the parameter adjustment speed of PSS will lag behind the active power change, such as the load suddenly increasing from 50% to 100% in only 0.5s, resulting in delayed damping effect and inability to timely suppress oscillation; Industry standard reference: According to the Technical Guidelines for Power System Stabilizer (PSS) (DL / T 1231-2013), the recommended range of the lead-lag time constant of PSS is 0.1s-2s, and the upper limit of the value taken by the present application conforms to the standard, ensuring engineering compatibility.

[0044] The above-mentioned active power of multiple operating points covers 10%-150% of the rated power range of the synchronous generator, and the number of operating points is not less than 10.

[0045] The PSS dynamic gain adjustment process of the above-mentioned power system stabilizer includes: 1) Active power acquisition: real-time acquisition of the active power output by the synchronous generator , with a sampling frequency of 1kHz to ensure the real-time nature of parameter adjustment; 2) Gain calculation: the lead-lag compensator parameters 、 of PSS adopt piecewise quadratic polynomial fitting, and the corresponding fitting formula is selected according to the interval : When is less than 10% of the rated power, , ; When is greater than 90% of the rated power, , ; When is greater than 90% of the rated power, , ; 3) Parameter update: update 、 The parameter update process employs a smooth transition algorithm, such as exponential weighted averaging, to avoid control signal fluctuations caused by parameter abrupt changes.

[0046] The coefficients of the piecewise quadratic polynomial mentioned above , , , , , , , , , , , , , , , , , The optimal PSS parameters were obtained by least-squares fitting of 19 running points.

[0047] The aforementioned automatic voltage regulator (AVR) PID control incorporates a voltage deviation integral separation strategy. When the voltage deviation... At rated voltage, only proportional and derivative regulation are activated. To avoid integral saturation; when Enable full PID control at rated voltage. .

[0048] The flux linkage calculation of the above-mentioned global dynamic mathematical model of the synchronous generator adopts the Park transformation, and the stator resistance... The value range is 0.01pu-0.02pu, rotor resistance. The value range is 0.005pu-0.01pu, damping winding resistance. The value range is 0.015pu-0.025pu.

[0049] The discretization step size mentioned above It can be adjusted according to the simulation accuracy requirements. When it is necessary to improve the simulation accuracy, Select 10μs-30μs; when it is necessary to balance simulation accuracy and computational efficiency, Select a time range of 30μs-100μs.

[0050] The parameters of the PID controller mentioned above , , It can be adjusted based on the rated power of the synchronous generator. In a synchronous generator with a rated power of 1000MW, The value range is 4.0-5.0. The value range is 14.0-15.0. The value range is 22.0-23.0.

[0051] The above CU is at the synchronous generator rated power operating point, that is at rated power, the parameter The value range is 0.50s-0.55s, The value range is 0.80s-0.85s.

[0052] Example 1: The synchronous generator excitation method based on mathematical modeling and gain scheduling includes: I. System deployment 1. Multi-winding dynamic modeling module implementation: build the model in Matlab / Simulink, set the stator three-phase resistance , rotor resistance , damping winding resistance , flux linkage coupling coefficient , ; 2. Simulation verification module configuration: discretization step , simulation working condition setting: 0-3s rated operation , 3s load drops to 50%, 5s three-phase short circuit occurs, lasts for 0.1s, 7s load rises to 120%; model correction trigger condition is voltage error , correction step is ±0.0005p.u.; 3. Dynamic gain excitation controller parameter setting: AVR PID parameters: , , , integral separation threshold rated voltage ; PSS segmented fitting parameters: : , ; : , ; : , ; The parameter update period is 50ms, and the weighting coefficient of the smooth transition algorithm is 0.8.

[0053] II. Actual test Test on a 1200MW synchronous generator in a power plant, the test results are as follows:

[0054] The test results prove that the system has excellent performance in modeling accuracy, voltage recovery speed and high-power working condition stability.

Claims

1. A method of excitation of a synchronous generator based on mathematical modeling and gain scheduling, characterized in that, The modeling module, the simulation module and the gain scheduling excitation controller are included, and each module cooperates with each other; The modeling module establishes a global dynamic mathematical model of the synchronous generator, and the model simultaneously contains electromagnetic dynamic characteristics of a stator winding, a rotor winding and a damping winding; the simulation module constructs a simulation platform of the mathematical model; the gain scheduling excitation controller includes an automatic voltage regulator (AVR) and a power system stabilizer (PSS), and realizes dynamic parameter adjustment by using a gain scheduling mechanism.

2. The method for excitation of a synchronous generator based on mathematical modeling and gain scheduling as claimed in claim 1, wherein, The global dynamic mathematical model of the synchronous generator contains electromagnetic dynamic characteristics of the stator winding, the rotor winding and the damping winding, wherein a stator winding voltage equation is: ； wherein is a stator voltage vector, is a stator resistance, is a stator current vector, is a stator flux vector; A rotor winding voltage equation is: ； wherein is the rotor excitation voltage, is the rotor resistance, is the rotor excitation current, is the rotor flux; A damping winding voltage equation is: ； wherein is the damping winding resistance, is the damping winding current, is the damping winding flux linkage; Through the above equations, the electromagnetic coupling relationship of the synchronous generator under different operating states is described, and the representation accuracy of the model to the dynamic characteristics of the system is improved.

3. The method for excitation of a synchronous generator based on mathematical modeling and gain scheduling as claimed in claim 1, wherein, The simulation module constructs a simulation platform of the mathematical model under a Matlab / Simulink environment, adopts a discretization solving strategy, and sets a discretization step T s The simulation module simulates the system response under different operating conditions in real time, provides a verification platform for parameter optimization of the excitation controller, and continuously corrects the model parameters by comparing the model output with actual unit test data, so as to further improve the modeling accuracy.

4. The method of claim 3, wherein, The simulation module simulates load mutation, short-circuit fault conditions, and outputs time-domain response curves of generator terminal voltage, excitation current and speed deviation parameters, and is used for model verification and parameter optimization.

5. The method for excitation of a synchronous generator based on mathematical modeling and gain scheduling as claimed in claim 1, wherein, The automatic voltage regulator (AVR) adopts a classical linear PID controller, and a transfer function is: ； wherein is a proportional coefficient, is an integral coefficient, is a differential coefficient, is a Laplace complex variable; AVR is the deviation of the generator terminal voltage from the reference value is the input, the output regulation signal controls the field voltage, achieving fast voltage stabilization.

6. The method of claim 5, wherein, The power system stabilizer (PSS) adopts a lead-lag compensator unit (CU), and a transfer function is: ； wherein , is an advance-lag time constant CU parameter; PSS with generator shaft speed deviation is an input, output compensation signal to the AVR, suppresses electromechanical oscillations.

7. The method of claim 6, wherein, The gain scheduling mechanism includes: CU parameters , Active power output by the synchronous generator Dynamic adjustment, using a quadratic polynomial fitting to establish the mapping relationship between parameters and active power: ； wherein , , is a gain curve parameter.

8. The method for excitation of a synchronous generator based on mathematical modeling and gain scheduling according to claim 7, characterized in that, The parameters , , Determined by two-stage tuning: A first stage: for multiple operating points, an optimization problem is solved: A second stage: the optimal gain scheduling function is obtained by using a least square method. ； determining the optimal parameters at each operating point, wherein is the voltage error, is the objective function, i.e. the Integral of Time multiplied by Squared Error at the i-th operating point, for quantifying the quality of the dynamic response of the system; , is the weight coefficient; Second stage: Optimal parameters for each operating point , LS analysis, and the quadratic polynomial coefficients , , are obtained, ensuring smooth transition of parameters between different operating points.

9. The method of claim 8, wherein, The parameters , , In the first phase of tuning, the constraints of the optimization problem are: ； The weight coefficients satisfy .

10. The method of claim 9, wherein, The active power of the plurality of operating points Covering 10%-150% of the rated power range of the synchronous generator, the number of operating points is not less than 10.

11. The method for excitation of a synchronous generator based on mathematical modeling and gain scheduling as claimed in claim 10 wherein, The power system stabilizer PSS dynamic gain adjustment process comprises: 1) active power collection: collecting active power output by the synchronous generator in real time , ensuring real-time parameter adjustment; 2) Gain calculation: PSS lead-lag compensator parameters , Using piecewise quadratic polynomial fitting, according to the corresponding fitting formula is selected according to the interval in which it is located: When At rated power, , ; When At rated power, , ; When At rated power, , ; 3) Parameter update: update every 50ms , The parameter update process adopts a smooth transition algorithm to avoid control signal fluctuations caused by parameter mutations.

12. The method of claim 11, wherein, coefficients of the piecewise quadratic polynomial , , , , , , , , , , , , , , , , , Optimal PSS parameters are obtained by least square fitting of 19 operating points.

13. The method of claim 12, wherein the gain scheduling is based on a mathematical model of the synchronous generator. The voltage deviation integral separation strategy is introduced in the PID control of the automatic voltage regulator AVR. When the voltage deviation is less than the rated voltage, only the proportional and differential adjustments are enabled , avoiding integral saturation; when the voltage deviation is greater than the rated voltage, the complete PID adjustment is enabled .

14. The method for excitation of synchronous generator based on mathematical modeling and gain scheduling as claimed in claim 2 wherein, The flux linkage calculation of the global dynamic mathematical model of the synchronous generator uses Park transformation, stator resistance with a value range of 0.01 p.u. - 0.02 p.u., rotor resistance with a value range of 0.005 p.u. - 0.01 p.u., damper winding resistance with a value range of 0.015 p.u. - 0.025 p.u.

15. The method for excitation of synchronous generator based on mathematical modeling and gain scheduling as claimed in claim 3 wherein, The discretization step According to the simulation accuracy requirement adjustment, when the simulation accuracy needs to be improved, Select 10us-30us; when the simulation accuracy and calculation efficiency need to be balanced, Select 30us-100us.

16. The method for excitation of synchronous generator based on mathematical modeling and gain scheduling as claimed in claim 5 wherein, Parameters of the PID controller , , Based on the synchronous generator rated power adjustment, in the synchronous generator with rated power of 1000MW, The value range is 4.0-5.0, The value range is 14.0-15.0, The value range is 22.0-23.

0.

17. The method for excitation of synchronous generator based on mathematical modeling and gain scheduling as claimed in claim 7, wherein, The CU is at the synchronous generator rated power operating point, i.e. The parameter The value range is 0.50s-0.55s, The value range is 0.80s-0.85s.

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