A Predictive Control Method for Gas Turbines Based on Parametric Adaptive Disturbance Immunity Controller

Abstract

This invention belongs to the field of information technology and discloses a predictive control method for gas turbines based on a parameter adaptive disturbance rejection controller. A mathematical model of the gas turbine is established based on the Rowen model, and its parameters are identified using data. Considering external disturbances during the gas turbine's variable operating conditions, an adaptive parameter active disturbance rejection controller is used to achieve fuel-speed control of the gas turbine. Furthermore, a model predictive control algorithm is used to track the power generation demand of the external grid, continuously optimizing the speed setpoint to improve the unit's peak-shaving capability. Verification using actual operating data from a domestic power plant shows that this method outperforms other algorithms in terms of speed, stability error, and resistance to external disturbances.

Description

Technical Field

[0001] This invention belongs to the field of information technology and relates to a predictive control method for gas turbines based on a parameter adaptive disturbance rejection controller. Background Art

[0002] Combined cycle (CCC) units are an important component of distributed energy systems, possessing advantages such as high thermal efficiency, low energy consumption, and minimal environmental pollution (Ge Zhihua, Ma Liqun, He Jie, & Zhao Shifei. (2020). Study on load characteristics of various operating modes of gas-steam combined cycle cogeneration units. Proceedings of the CSEE, 40(8), 10). Compared with conventional coal-fired power plants, CCC units can improve efficiency by more than 15%, which is of great significance for promoting industrial energy enterprises to achieve quality and efficiency improvement, cost reduction, carbon neutrality, and carbon peaking (Guo Lei, Song Wenzhe, Wang Xiangping, Yu Yang, & Wang Erxin. (2019). Optimization of operating performance of gas turbines using low-calorific-value fuels in IgCC. China Electric Power, 052(002), 14-19). As a crucial component of combined cycle gas turbines, gas turbines are complex nonlinear systems. When undertaking peak-shaving tasks for the power grid, the wide range of operating conditions poses a significant challenge to conventional PID controllers (Hou Guolian, Dai Xiaoyan, Gong Linjuan, Xu Haixin, Zhang Jianhua. (2020). Multi-objective predictive control of gas turbine system load tracking based on TS fuzzy model. China Electric Power, 53(11),9). Therefore, how to utilize model predictive control algorithms to achieve variable load control of gas turbines has always been a challenging task.

[0003] In recent years, many scholars have conducted research on gas turbine control based on model predictive control algorithms. For the V94.2 gas turbine installed in the Damavand combined cycle power plant, an adaptive model predictive control method with online parameter estimation is proposed (Ghorbani, H., Ghaffari, A., & Rahnama, M.. (2008). Constrained model predictive control implementation for a heavy-duty gas turbine powerplant. Wseas Transactions on Systems & Control, 3(6), 507-516). In addition, a linear model of the gas turbine is established using the traditional mathematical model and the Autoregressive Exogenous (ARX) identification method. The model predictive control algorithm is used to regulate and control the exhaust temperature and rotor speed of the GE9001E gas turbine through the compressor inlet guide vane position and fuel signal (Eslami, M., Shayesteh, MR, & Pourahmadi, M.. (2018). Optimal design of pid-based low-pass filter for gas turbine using intelligent method. IEEE Access, 15335-15345). For the control of gas turbine load shedding process, a nonlinear model predictive control algorithm is proposed to reduce nitrogen oxide emissions (Pires, TS, Cruz, ME, Colaco, MJ, & Alves, MAC. (2018). Application of nonlinear multivariable model predictive control to transient operation of a gas turbine and nox emissions reduction. Energy, 149 (APR. 15), 341-353). An asymptotic model predictive control strategy is also proposed for the speed control of gas turbines (Mu, J., & Rees, D.. (2004). Approximate model predictive control for gas turbine engines. American Control Conference, 2004. Proceedings of the 2004).Furthermore, an extended model predictive control method is proposed to improve the thermal efficiency and load frequency control performance of gas turbine power plants (Mohamed, Wang, JH, Khalil, & Limhabrash. (2016). Predictive control strategy of a gas turbine for improvement of combined cycle power plant dynamic performance and efficiency. SPRINGERPLUS). Although the above methods can effectively improve the operating performance of gas turbines in some aspects, they do not take into account disturbances from the external environment or actuators during gas turbine operation, particularly regarding variable load control.

[0004] Active disturbance rejection controllers (ADRCs) are an extension of PID control technology. They can estimate and compensate for unmodeled dynamics and unknown external disturbances in the system as a "total disturbance". In recent years, this controller has been widely used in wind turbine control, boiler control, engine control, etc. Regarding the ADRC problem of gas turbines, a control method for the Titan 130 turbine engine based on ADRC is proposed (Jiang, JP, Zhang, Q., & Wang, LP. (2012). Research on modeling and simulation of active disturbance rejection controller for gas turbine. Applied Mechanics and Materials, 157-158, 507-510); a micro gas turbine ADRC speed controller is designed to achieve stable operation of the gas turbine (Xiao, Hongchang, Tong, Jiapeng, & Yu, Tao. (2009). Research on ADRC method of micro gas turbine generator system. Power System Protection and Control (13), 13-18+37). Combining active disturbance rejection controllers with model predictive control to achieve AGC control of gas turbines is a challenging task.

[0005] Gas turbines are an important component of combined cycle power units. Combined with waste heat boilers and steam turbines, gas turbines are gradually becoming a popular power generation technology. A structural diagram of a gas turbine is shown below. Figure 1As shown, a gas turbine includes a compressor, combustion chamber, turbine, generator, and regenerator. Currently, gas turbine control, in addition to reliability and fuel cost optimization, also requires improved load demand tracking to reduce power system frequency variations and increase power generation efficiency. However, during gas turbine operation, various disturbances from the external environment pose significant challenges to variable load control. Therefore, there is an urgent need for a gas turbine variable load predictive controller with disturbance rejection capabilities to achieve automatic power generation control of gas turbines in industrial scenarios.

[0006] Based on the above research, this invention proposes a predictive control algorithm based on an Adaptive Parameter Based Active Disturbance Rejection Controller (APADRC) to achieve variable load control of a gas turbine. To address disturbances present during the variable operating condition control of the gas turbine, APADRC is designed to implement fuel-speed control. Furthermore, in conjunction with peak-shaving commands issued by the external power grid, a model predictive control algorithm is used to continuously optimize the speed setpoint. Actual operating data from a domestic power plant verifies that the proposed model possesses advantages such as fast response time, small peak-shaving steady-state error, and strong resistance to external disturbances. Summary of the Invention

[0007] The stability of gas turbine control systems plays a crucial role in reducing environmental pollution and improving energy efficiency on the user side. This invention proposes a gas turbine predictive control algorithm based on a disturbance observer to address multi-condition gas turbine operation caused by load variations. A mathematical model of the gas turbine is established based on the Rowen model, and its parameters are identified using data. Considering external disturbances during the gas turbine's variable operating conditions, an adaptive parameter active disturbance rejection controller (APDC) is employed to achieve fuel-speed control. Furthermore, a model predictive control algorithm is used to track the power generation demand of the external grid, continuously optimizing the speed setpoint to improve the unit's peak-shaving capability. Verification using actual operating data from a domestic power plant demonstrates that this proposed method outperforms other algorithms in terms of speed, stability error, and resistance to external disturbances.

[0008] The technical solution of this invention:

[0009] A predictive control method for gas turbines based on a parameter adaptive disturbance rejection controller, comprising the following steps:

[0010] S1. Gas turbine modeling driven by mechanism and data synergy;

[0011] Combining the Rowen gas turbine model, the Rowen gas turbine model is identified using the ARX model; the fuel valve opening of the gas turbine is used as the input of the ARX model, and the fuel flow rate and speed are used as the output of the ARX model; the structure of the ARX model obtained through identification is as shown in equation (1):

[0012] A(q)y(t)=B(q)u(t)+e(t) (1)

[0013] Where y(t) is the output signal of the ARX model; u(t) is the input signal of the ARX model; and e(t) is white noise with a mean of 0 and a variance of σ. 2 A(q) and B(q) are polynomials in terms of the time-shift operator q, i.e., q -1 u(t) = u(t-1);

[0014] The ARX model is parameterized to obtain the parameterized ARX model as shown in equation (2):

[0015]

[0016] Where A(q,θ) and B(q,θ) are polynomial coefficients. θ is an adjustable parameter vector. n a ,n b The order of the ARX model;

[0017] The original input-output signal data form the regression vector. Parametric ARX models are subjected to linear regression.

[0018]

[0019]

[0020] Where l(t) is the residual output by the ARX model;

[0021] Estimate the order of the ARX model based on the AIC information criterion:

[0022] AIC = -2ln L + 2p (5)

[0023] Where L is the likelihood function of the ARX model; p = n a +n b +2 represents the number of parameters in the ARX model; p′ when AIC is minimized represents the result of the AIC criterion estimation.

[0024]

[0025] Where N is the number of input-output signal data; This is the variance estimate of the error;

[0026] Combining formula (4), the sum of squares of the residuals is taken as the criterion function:

[0027]

[0028] Where Y is the output signal vector; For the overall regression vector;

[0029] J(θ) has a derivative of 0 with respect to θ, and ψ in equation (7) T If ψ is full rank, the least squares estimate is obtained;

[0030] θ LS =(ψ T ψ) -1 ψ T Y (8)

[0031] S2. Adaptive disturbance rejection control for gas turbine controller parameters;

[0032] The APADRC algorithm is used to control the speed of the gas turbine, so that the output value y ADRC (k) Tracking setpoint v0(k); The APADRC algorithm includes a differential tracker, a nonlinear state error feedback control law, an extended state observer, and a parameter adaptive regulator; where the expression of the differential tracker is shown in Equation (9) and Equation (10);

[0033] v1(k+1)=v1(k)+hv2(k) (9)

[0034] v2(k+1)=v2(k)+hfhan(k),|fhan(k)|≤r (10)

[0035] Where k is the current time; v1 is the target state; v2 is the derivative of the target state; r is the velocity factor; h is the integral step size; fhan is the calculated value of the fastest control synthesis function, as shown in equations (11) to (14);

[0036] a1(k)=v1(k)-v0(k)+h0v2(k) (11)

[0037] When, equation (12) calculates a2(k); |a1(k)|≤rh0 2 Equation (13) is used to calculate a2(k);

[0038]

[0039]

[0040]

[0041] Where a1 and a2 are intermediate calculation variables of the fastest control synthesis function; h0 is the filtering factor;

[0042] The extended state observer is based on the ARX model obtained by formula (2), measuring the system input u. ADRC (k) and system output y ADRC (k) Calculate the internal state information of the system and use the extended state z3 to estimate the internal uncertainty and external disturbance of the ARX model constructed based on formula (2), and its expression is shown in formula (15) to (17).

[0043] z1(k+1)=z1(k)+h(z2(k)-β1(z1(k)-y ADRC (k))) (15)

[0044]

[0045]

[0046] Where z1, z2 are state estimates; z3 is the extended state estimate; β1, β2, β3 are observer gains; fal(e, ε, δ) is the fal function filter;

[0047]

[0048] Where ε is a constant between 0 and 1; δ is a constant that affects the filtering effect;

[0049] The nonlinear state error feedback control law calculates the control quantity based on the state error between the differential tracker and the extended state observer, and then uses the extended state estimate z3 to compensate for the control quantity u. ADRC (k);

[0050]

[0051] Where α1, α2, and α3 are controller gains; b0 is a compensation factor that determines the strength of the disturbance estimate compensation for the z3 control quantity.

[0052] The parameter adaptive regulator uses gradient descent online to adjust the gains β1, β2, and β3 in the expanded state observer, while offline training error is used to adjust the relationship between the parameters. Five setpoints v0 are selected, and the gains β1, β2, and β3 of each observer are arranged and combined through grid search. The root mean square error E is calculated by traversing all parameters, and then a polynomial fitting method is used to construct the relationship between the root mean square error E and the observer gains β1 and β2. The parameters are adaptively adjusted using gradient descent with the root mean square error E as the objective function.

[0053]

[0054] Where η is the learning rate; the observer gain in the APADRC algorithm is adjusted, the error is calculated, and the parameters are adaptively adjusted online in a loop to minimize the performance index;

[0055] S3. Gas Turbine Model Variable Load Predictive Control

[0056] When the AGC load dispatch command of the gas turbine simulation model changes, the gas turbine is controlled by the Dynamic Matrix Control (DMC) algorithm to track its load demand, thereby reducing the frequency variation of the power system and improving the power generation efficiency. Under the condition of satisfying the system's control constraints and output constraints, the future state is calculated using the current state, past states, and DMC output. The optimal control quantity is solved through rolling optimization to minimize the deviation between the DMC output and the expected value.

[0057] At time k, with the control quantity remaining constant, the initial predicted output of the DMC over the next N time steps is obtained. The control quantity changes Δu DMC Under the condition of (k), the output value in the next N time steps is calculated according to equation (21).

[0058]

[0059] Where a is the step response vector of the model; the first step controls the increment Δu DMC (k);

[0060] a = [a1, a2, ..., a N ] (twenty two)

[0061] At time k, with the control variable remaining constant, the initial predicted output of the DMC output over the next P time steps is obtained. Given that the control quantity changes over M time points, the control increment is Δu. DMC (k),Δu DMC (k+1),…,Δu DMC (k+M-1), calculate the output value of the model at the next P times according to equation (23). Where P is the prediction time domain and M is the control time domain, and M ≤ P ≤ N;

[0062]

[0063] Where A is the P×M dynamic matrix, constructed from the model's step response vector a; the first M steps of control increment ΔU DMC ;

[0064] Solving the optimization problem, the optimal control quantity is applied to the ARX model constructed based on formula (2), making the DMC output close to the desired value and satisfying the condition that the control quantity changes little; at time k, the performance index is obtained according to the expectation and constraint conditions:

[0065]

[0066] Where Q = diag(q1,q2,…,q) P R = diag(r1, r2, ..., r) is the output error weighting matrix; M () represents the control increment weighting matrix;

[0067] To minimize the performance index J, take ΔU for J. DMC Taking the derivative of and setting it to zero, we get:

[0068]

[0069] For the optimal control quantity ΔU DMC Only the first control increment Δu is taken. DMC (k) Calculate the model's predicted output for future time periods. and u DMC (k)=u DMC (k-1)+Δu DMC (k) Input into the actual model to obtain y(k+1), where c is an M-dimensional column vector c T =[1 0 …0] 1×M ;

[0070] DMC output The error between the actual model output y(k+1) and the actual model output is used to weight and correct the future prediction model output;

[0071]

[0072]

[0073] Where H = [h1, h2, ..., h N ] T The error correction vector is N-dimensional; the initial prediction output at time k+1. pass Obtained by shifting:

[0074]

[0075] Where S is the shift matrix, we get Then, calculations are performed at time k+1, and the optimal value is solved by rolling optimization, gradually approaching the expected value;

[0076] S4 performance indicators verify the effectiveness of this invention.

[0077] Combined with the power plant peak shaving dispatch instructions, the root mean square error (RMSE), mean absolute percentage error (MAPE), and mean absolute error (MAE) were selected to verify the effectiveness of the proposed method in gas turbine power generation and gas turbine speed tracking control. The expressions are shown in equations (29) to (31).

[0078]

[0079]

[0080]

[0081] Where n is the number of calculations; pred i For predicted values; real i This is the actual value.

[0082] This invention relates to a predictive control method for gas turbines based on a parameter-adaptive disturbance rejection controller. This method addresses the issue of controllers adaptively adjusting parameters during gas turbine load shedding, reducing power system frequency variations and improving power generation efficiency. Actual operating data from a domestic power plant validates the advantages of the proposed model, including fast response, small peak-shaving steady-state error, and strong resistance to external disturbances. Attached Figure Description

[0083] Figure 1 This is a structural diagram of a gas turbine.

[0084] Figure 2 This is a diagram of the predictive control architecture for a gas turbine based on APADRC.

[0085] Figure 3(a) shows the APADRC parameter optimization process based on gradient descent.

[0086] Figure 3(b) shows the speed tracking control of the gas turbine load shedding APADRC.

[0087] Figure 4 shows the effect of gas turbine AGC control in scenarios with noise and disturbance.

[0088] Figure 4(a) is a comparison diagram of outer loop control.

[0089] Figure 4(b) is a comparison diagram of inner loop control.

[0090] Figure 4(c) shows the observed noise of the gas turbine power generation.

[0091] Figure 4(d) shows the fuel valve opening disturbance.

[0092] Figure 4(e) is a comparison of the dynamic response of the opening.

[0093] Figure 4(f) is a comparison of the dynamic response of combustion amount. Detailed Implementation

[0094] This invention proposes a model predictive control method based on a parameter-adaptive active disturbance rejection controller (APADRC), which consists of three parts: a data-driven gas turbine system model, an APADRC, and a model predictive controller. The data-driven gas turbine system model is identified using an asymptotic identification method. APADRC enables adaptive control of the gas turbine's fuel and speed, and the model predictive control algorithm achieves variable load operation of the gas turbine based on scheduling instructions.

[0095] Content 1: Gas Turbine Modeling Based on Mechanism and Data Collaboration

[0096] To verify the effectiveness of the proposed method, the Rowen gas turbine model was identified using the ARX model in conjunction with the Rowen gas turbine model. The fuel valve opening of the gas turbine was used as the input of the ARX model, and the fuel flow rate and speed were used as the outputs of the ARX model. The structure of the ARX model obtained through identification is shown in equation (1):

[0097] A(q)y(t)=B(q)u(t)+e(t) (1)

[0098] Where y(t) is the output signal of the model; u(t) is the input signal of the model; and e(t) is white noise with a mean of 0 and a variance of σ. 2 A(q) and B(q) are polynomials in terms of the time-shift operator q, i.e., q -1 u(t) = u(t-1);

[0099] The ARX model is parameterized to obtain the parameterized ARX model as shown in equation (2):

[0100]

[0101] Where A(q,θ) and B(q,θ) are polynomial coefficients. θ is an adjustable parameter vector. n a ,n b The order of the ARX model;

[0102] The original input-output signal data form the regression vector. Parametric ARX models are subjected to linear regression.

[0103]

[0104]

[0105] in, The residuals output by the ARX model;

[0106] Estimate the order of the ARX model based on the AIC information criterion:

[0107] AIC = -2ln L + 2p (5)

[0108] Where L is the likelihood function of the ARX model; p = n a +n b +2 represents the number of parameters in the ARX model; p′ when AIC is minimized represents the result of the AIC criterion estimation.

[0109]

[0110] Where N is the number of input-output signal data; This is the variance estimate of the error;

[0111] Combining formula (4), the sum of squares of the residuals is taken as the criterion function:

[0112]

[0113] Where Y is the output signal vector; For the overall regression vector;

[0114] J(θ) has a derivative of 0 with respect to θ, and ψ in equation (7) T If ψ is full rank, the least squares estimate is obtained;

[0115] θ LS =(ψ T ψ) -1 ψ T Y (8)

[0116] Content 2: Adaptive Disturbance Immunity Control for Gas Turbine Controller Parameters

[0117] Considering the input disturbances and observation noise in the variable load control process of gas turbines, an APADRC algorithm is proposed to realize the gas turbine speed control. This method consists of four parts: a differential tracker, a nonlinear state error feedback control law, an extended state observer, and a parameter adaptive regulator. The differential tracker is a transient process that arranges an inertial element to extract the differential signal, making the output value y... ADRC (k) The fast and overshoot-free tracking setpoint v0(k) is expressed as shown in equations (1) and (2);

[0118] v1(k+1)=v1(k)+hv2(k) (9)

[0119] v2(k+1)=v2(k)+hfhan(k),|fhan(k)|≤r (10)

[0120] Where k is the current time; v1 is the target state; v2 is the derivative of the target state; r is the velocity factor; h is the integral step size; fhan is the calculated value of the fastest control synthesis function, as shown in equations (11) to (14);

[0121] a1(k)=v1(k)-v0(k)+h0v2(k) (11)

[0122] When, equation (12) calculates a2(k); |a1(k)|≤rh0 2 Equation (13) is used to calculate a2(k);

[0123]

[0124]

[0125]

[0126] Where a1 and a2 are intermediate calculation variables of the fastest control synthesis function; h0 is the filtering factor;

[0127] The extended state observer is based on the ARX model obtained by formula (2), measuring the system input u. ADRC (k) and system output y ADRC (k) Calculate the internal state information of the system and use the extended state z3 to estimate the internal uncertainty and external disturbance of the ARX model constructed based on formula (2), and its expression is shown in formula (15) to (17).

[0128] z1(k+1)=z1(k)+h(z2(k)-β1(z1(k)-y ADRC (k))) (15)

[0129]

[0130]

[0131] Where z1, z2 are state estimates; z3 is the extended state estimate; β1, β2, β3 are observer gains; fal(e, ε, δ) is the fal function filter;

[0132]

[0133] Where ε is a constant between 0 and 1; δ is a constant that affects the filtering effect;

[0134] The nonlinear state error feedback control law calculates the control quantity based on the state error between the differential tracker and the extended state observer, and then uses the extended state estimate z3 to compensate for the control quantity u. ADRC (k);

[0135]

[0136] Where α1, α2, and α3 are controller gains; b0 is a compensation factor that determines the strength of the disturbance estimate compensation for the z3 control quantity.

[0137] The parameter adaptive regulator uses gradient descent online to adjust the gains β1, β2, and β3 in the expanded state observer, while offline training error is used to adjust the relationship between the parameters. Five setpoints v0 are selected, and the gains β1, β2, and β3 of each observer are arranged and combined through grid search. The root mean square error E is calculated by traversing all parameters, and then a polynomial fitting method is used to construct the relationship between the root mean square error E and the observer gains β1 and β2. The parameters are adaptively adjusted using gradient descent with the root mean square error E as the objective function.

[0138]

[0139] Where η is the learning rate; the observer gain in the APADRC algorithm is adjusted, the error is calculated, and the parameters are adaptively adjusted online in a loop to minimize the performance index;

[0140] Content 3: Predictive Control of Variable Load in Gas Turbine Models

[0141] When the AGC load dispatch command of the gas turbine simulation model changes, the gas turbine is controlled by the Dynamic Matrix Control (DMC) algorithm to track its load demand, thereby reducing the frequency variation of the power system and improving the power generation efficiency. Under the condition of satisfying the system's control constraints and output constraints, the future state is calculated using the current state, past states, and DMC output. The optimal control quantity is solved through rolling optimization to minimize the deviation between the DMC output and the expected value.

[0142] At time k, with the control quantity remaining constant, the initial predicted output of the DMC over the next N time steps is obtained. The control quantity changes Δu DMC Under the condition of (k), the output value in the next N time steps is calculated according to equation (21).

[0143]

[0144] Where a is the step response vector of the model; the first step controls the increment Δu DMC (k);

[0145] a = [a1, a2, ..., a N ] (twenty two)

[0146] At time k, with the control variable remaining constant, the initial predicted output of the DMC output over the next P time steps is obtained. Given that the control quantity changes over M time points, the control increment is Δu. DMC (k),Δu DMC (k+1),…,Δu DMC (k+M-1), calculate the output value of the model at the next P times according to equation (23). Where P is the prediction time domain and M is the control time domain, and M ≤ P ≤ N;

[0147]

[0148] Where A is the P×M dynamic matrix, constructed from the model's step response vector a; the first M steps of control increment ΔU DMC ;

[0149] Solving the optimization problem, the optimal control quantity is applied to the ARX model constructed based on formula (2), making the DMC output close to the desired value and satisfying the condition that the control quantity changes little; at time k, the performance index is obtained according to the expectation and constraint conditions:

[0150]

[0151] Where Q = diag(q1,q2,…,q) P R = diag(r1, r2, ..., r) is the output error weighting matrix; M () represents the control increment weighting matrix;

[0152] To minimize the performance index J, take ΔU for J. DMC Taking the derivative of and setting it to zero, we get:

[0153]

[0154] For the optimal control quantity ΔU DMC Only the first control increment Δu is taken. DMC (k) Calculate the model's predicted output for future time periods. and u DMC (k)=u DMC (k-1)+Δu DMC (k) Input into the actual model to obtain y(k+1), where c is an M-dimensional column vector c T =[1 0 … 0] 1×M ;

[0155] DMC output The error between the actual model output y(k+1) and the actual model output is used to weight and correct the future prediction model output;

[0156]

[0157]

[0158] Where H = [h1, h2, ..., h N ] T The error correction vector is N-dimensional; the initial prediction output at time k+1. pass Obtained by shifting:

[0159]

[0160] Where S is the shift matrix, we get Then, calculations are performed at time k+1, and the optimal value is solved by rolling optimization, gradually approaching the expected value;

[0161] Content 4: Performance indicators verify the effectiveness of the invention

[0162] Combined with the power plant peak shaving dispatch instructions, the root mean square error (RMSE), mean absolute percentage error (MAPE), and mean absolute error (MAE) were selected to verify the effectiveness of the proposed method in gas turbine power generation and gas turbine speed tracking control. The expressions are shown in equations (29) to (31).

[0163]

[0164]

[0165]

[0166] Where n is the number of calculations; pred i For predicted values; real i This is the actual value.

[0167] The model was identified using actual operating data from a domestic power plant, and verified in two scenarios that the proposed model has advantages such as fast performance, small peak-shaving steady-state error, and strong resistance to external interference.

[0168] Scenario 1: Gas turbine load shedding operation scenario

[0169] The gas turbine control model based on a dual closed loop is divided into gas turbine power generation control and gas turbine speed control. Combining the gas turbine load variation values, a model predictive control algorithm is used to dynamically optimize the gas turbine speed setpoint. Given that the gas turbine fuel opening and the observer parameters of the speed controller are affected by changes in operating conditions, a parameter-adaptive gas turbine load shedding controller is proposed. In offline scenarios, the observer gain parameters β1, β2, and β3 are obtained using a grid search, and their root mean square error distribution is obtained using a surface fitting algorithm. If the speed setpoint changes, an appropriate surface model is selected, and the observer parameters corresponding to the local minimum are solved using the gradient descent method and provided to the active disturbance rejection controller, as shown in Figure 3.

[0170] When the gas turbine load changes, the speed tracking effects of APADRC and ADRC are shown in Table 1 and Figure 3. The method proposed in this invention can adaptively and quickly track the settings with small deviations, while the ADRC controller based on fixed parameters has a better tracking effect under certain operating conditions, but a poor effect when shedding load. This verifies that the tracking effect of the method proposed in this invention is better than that of the ADRC controller based on fixed parameters.

[0171] Table 1 Statistical Analysis of Tracking Error in Gas Turbine AGC Control

[0172]

[0173] Scenario 2: Gas turbine load shedding operation scenario with disturbances and noise

[0174] To verify the robustness of the proposed method, the controller proposed in this paper is compared and analyzed by combining observation noise with different distributions and disturbance signal types with different intensities, using DMC+ADRC and DMC+PI type controller domains.

[0175] Table 2 Statistical Analysis of Gas Turbine AGC Control Tracking Error under Noise and Disturbance Scenarios

[0176]

[0177]

[0178] The effects of DMC+APADRC, DMC+ADRC, and DMC+PI type controllers on gas turbines under disturbance and noise are shown in Table 2 and Figure 4. The DMC+PI type controller is affected by external factors, resulting in low control accuracy. The DMC+ADRC type controller performs well in tracking power generation but poorly in tracking speed, leading to decreased accuracy. In contrast, the controller proposed in this paper has a certain degree of reliability in controlling power generation and speed, indicating that the robustness and tracking performance of the proposed method are significantly better than the comparative methods.

Claims

1. A predictive control method for gas turbines based on a parameter adaptive disturbance rejection controller, characterized in that, The specific steps are as follows: S1. Gas turbine modeling driven by mechanism and data synergy; Combining the Rowen gas turbine model, the Rowen gas turbine model is identified using the ARX model; the fuel valve opening of the gas turbine is used as the input of the ARX model, and the fuel flow rate and speed are used as the output of the ARX model; the structure of the ARX model obtained through identification is as shown in equation (1): A(q)y(t)=B(q)u(t)+e(t) (1) Where y(t) is the output signal of the ARX model; u(t) is the input signal of the ARX model; and e(t) is white noise with a mean of 0 and a variance of σ. 2 A(q) and B(q) are polynomials in terms of the time-shift operator q, i.e., q -1 u(t) = u(t-1); The ARX model is parameterized to obtain the parameterized ARX model as shown in equation (2): Where A(q,θ) and B(q,θ) are polynomial coefficients. θ is an adjustable parameter vector. n a ,n b The order of the ARX model; The original input-output signal data form the regression vector. Parametric ARX models are subjected to linear regression. Where l(t) is the residual output by the ARX model; Estimate the order of the ARX model based on the AIC information criterion: AIC = -2lnL + 2p (5) Where L is the likelihood function of the ARX model; p = n a +n b +2 represents the number of parameters in the ARX model; p′ when AIC is minimized represents the result of the AIC criterion estimation. Where N is the number of input-output signal data; This is the variance estimate of the error; Combining formula (4), the sum of squares of the residuals is taken as the criterion function: Where Y is the output signal vector; For the overall regression vector; J(θ) has a derivative of 0 with respect to θ, and ψ in equation (7) T If ψ is full rank, the least squares estimate is obtained; i LS =(ψ T (ψ) -1 ψ T Y (8) S2. Adaptive disturbance rejection control for gas turbine controller parameters; The APADRC algorithm is used to control the speed of the gas turbine, so that the output value y ADRC (k) Tracking setpoint v0(k); The APADRC algorithm includes a differential tracker, a nonlinear state error feedback control law, an extended state observer, and a parameter adaptive regulator; where the expression of the differential tracker is shown in Equation (9) and Equation (10); v1(k+1)=v1(k)+hv2(k) (9) v2(k+1)=v2(k)+hfhan(k),|fhan(k)|≤r (10) Where k is the current time; v1 is the target state; v2 is the derivative of the target state; r is the velocity factor; h is the integral step size; fhan is the calculated value of the fastest control synthesis function, as shown in equations (11) to (14); a1(k)=v1(k)-v0(k)+h0v2(k) (11) When, equation (12) calculates a2(k); |a1(k)|≤rh0 2 Equation (13) is used to calculate a2(k); Where a1 and a2 are intermediate calculation variables of the fastest control synthesis function; h0 is the filtering factor; The extended state observer is based on the ARX model obtained by formula (2), measuring the system input u. ADRC (k) and system output y ADRC (k) Calculate the internal state information of the system and use the extended state z3 to estimate the internal uncertainty and external disturbance of the ARX model constructed based on formula (2), and its expression is shown in formula (15) to (17). z1(k+1)=z1(k)+h(z2(k)-β1(z1(k)-y ADRC (k))) (15) Where z1, z2 are state estimates; z3 is the extended state estimate; β1, β2, β3 are observer gains; fal(e, ε, δ) is the fal function filter; Where ε is a constant between 0 and 1; δ is a constant that affects the filtering effect; The nonlinear state error feedback control law calculates the control quantity based on the state error between the differential tracker and the extended state observer, and then uses the extended state estimate z3 to compensate for the control quantity u. ADRC (k); Where α1, α2, and α3 are controller gains; b0 is a compensation factor that determines the strength of the disturbance estimate compensation for the z3 control quantity. The parameter adaptive regulator uses gradient descent online to adjust the gains β1, β2, and β3 in the expanded state observer, while offline training error is used to adjust the relationship between the parameters. Five setpoints v0 are selected, and the gains β1, β2, and β3 of each observer are arranged and combined through grid search. The root mean square error E is calculated by traversing all parameters, and then a polynomial fitting method is used to construct the relationship between the root mean square error E and the observer gains β1 and β2. The parameters are adaptively adjusted using gradient descent with the root mean square error E as the objective function. Where η is the learning rate; the observer gain in the APADRC algorithm is adjusted, the error is calculated, and the parameters are adaptively adjusted online in a loop to minimize the performance index; S3. Gas Turbine Model Variable Load Predictive Control When the AGC load dispatch command of the gas turbine simulation model changes, the gas turbine is controlled by the Dynamic Matrix Control (DMC) algorithm to track its load demand, thereby reducing the frequency variation of the power system and improving the power generation efficiency. Under the condition of satisfying the system's control constraints and output constraints, the future state is calculated using the current state, past states, and DMC output. The optimal control quantity is solved through rolling optimization to minimize the deviation between the DMC output and the expected value. At time k, with the control quantity remaining constant, the initial predicted output of the DMC over the next N time steps is obtained. The control quantity changes Δu DMC Under the condition of (k), the output value in the next N time steps is calculated according to equation (21). Where a is the step response vector of the model; the first step controls the increment Δu DMC (k); a=[a1,a2,…,a N (22) At time k, with the control variable remaining constant, the initial predicted output of the DMC output over the next P time steps is obtained. Given that the control quantity changes over M time points, the control increment is Δu. DMC (k),Δu DMC (k+1),…,Δu DMC (k+M-1), calculate the output value of the model at the next P times according to equation (23). Where P is the prediction time domain and M is the control time domain, and M ≤ P ≤ N; Where A is the P×M dynamic matrix, constructed from the model's step response vector a; the first M steps of control increment ΔU DMC ; Solving the optimization problem, the optimal control quantity is applied to the ARX model constructed based on formula (2), making the DMC output close to the desired value and satisfying the condition that the control quantity changes little; at time k, the performance index is obtained according to the expectation and constraint conditions: Where Q = diag(q1,q2,…,q) P R = diag(r1, r2, ..., r) is the output error weighting matrix; M () represents the control increment weighting matrix; To minimize the performance index J, take ΔU for J. DMC Taking the derivative of and setting it to zero, we get: For the optimal control quantity ΔU DMC Only the first control increment Δu is taken. DMC (k) Calculate the model's predicted output for future time periods. and u DMC (k)=u DMC (k-1)+Δu DMC (k) Input into the actual model to obtain y(k+1), where c is an M-dimensional column vector c T =[1 0…0] 1×M ; DMC output The error between the actual model output y(k+1) and the actual model output is used to weight and correct the future prediction model output; Where H = [h1, h2, ..., h N ] T The error correction vector is N-dimensional; the initial prediction output at time k+1. pass Obtained by shifting: Where S is the shift matrix, we get Then, calculations are performed at time k+1, and the optimal value is solved by rolling optimization, gradually approaching the expected value; S4 performance indicators verify the effectiveness of this invention. Combined with the power plant peak shaving dispatch instructions, the root mean square error (RMSE), mean absolute percentage error (MAPE), and mean absolute error (MAE) were selected to verify the effectiveness of the proposed method in gas turbine power generation and gas turbine speed tracking control. The expressions are shown in equations (29) to (31). Where n is the number of calculations; pred i For predicted values; real i This is the actual value.

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