Ultra-supercritical unit flexible operation scheme based on improved error active disturbance rejection control and improved northern eagle optimizer

Abstract

The invention discloses an ultra-supercritical unit flexible operation scheme based on improved error active disturbance rejection control and an improved northern eagle optimizer. Firstly, a coordinated control system of an ultra-supercritical unit is used as a research object, and modeling and control difficulties of the coordinated control system are analyzed; then, a multi-working-condition transfer function matrix model of the unit is identified based on an improved northern eagle optimizer; and then, an improved error active disturbance rejection control strategy is designed. And finally, verifying the feasibility of the flexible operation scheme based on a simulation platform, and carrying out quantitative statistic analysis on the effectiveness of the control strategy by adopting a performance index. According to the invention, the reduced-order extended state observer is applied to the error active disturbance rejection controller, the complexity of the controller structure is reduced, the rapid load control performance of the system is effectively improved, and the flexible operation capability of the unit under the wide load working condition is improved.

Description

Technical Field

[0001] This invention relates to the fields of modeling and control technology for the flexible operation of thermal power generating units, and more specifically, to a flexible operation scheme for ultra-supercritical units based on improved error active disturbance rejection control and improved Northern Eagle optimizer. Background Technology

[0002] Against the backdrop of the continued rapid growth of new energy power, the power grid requires ultra-supercritical thermal power units to have a wider load regulation range and a higher load regulation rate to cope with frequent load changes and provide a guarantee for peak shaving and frequency regulation of the power system. Therefore, it is urgent to promote research on flexibility enhancement schemes for ultra-supercritical thermal power units to improve the safety and stability of the power system under high-proportion renewable energy grid integration, thereby accelerating the construction of a new type of power system.

[0003] Ultra-supercritical (USupercritical) units are widely used due to their high cycle thermal efficiency and low pollutant emissions. In engineering, units with working fluid temperatures and pressures exceeding 580℃ and 25MPa, respectively, are classified as USupercritical units. Practice has shown that USupercritical units achieve a cycle thermal efficiency of 46%, approximately 10% higher than subcritical units. USupercritical units track load commands externally and maintain energy balance and parameter stability in the boiler-turbine coupling system internally, making them the mainstay of my country's power generation in recent years. However, with the rapid growth of renewable energy grid-connected capacity, USupercritical units frequently participate in deep peak-shaving processes, exhibiting characteristics such as large inertia, large delay, strong nonlinearity, and strong coupling. This means that modeling and controlling the units will be extremely challenging during research. Therefore, this paper takes the coordinated control system of the USupercritical unit as the controlled object, designing an advanced intelligent model identification scheme and an improved error active disturbance rejection control strategy, which is of great significance for improving the flexible operation capability of USupercritical units.

[0004] The transfer function matrix model (JFMM) has a mature theoretical foundation. By transforming the dynamic characteristics of complex industrial systems into structured mathematical expressions, it achieves an efficient combination of theoretical analysis and engineering practice in thermal power plant control, especially suitable for multivariable control scenarios that require a balance between model accuracy, computational efficiency, and interpretability. Compared with state-space models, the elements of the JFMM have clear physical meanings, making it easier for engineers to understand system characteristics in conjunction with process technology, allowing them to configure the system without mastering state-space theory. Furthermore, when the model mismatch occurs at a certain operating point of the unit, only the transfer function of the corresponding channel needs to be re-identified, without the need for a full model reconstruction. In addition, the JFMM model has excellent control strategy adaptability. For example, it can provide the bandwidth design basis for extended state observers for active disturbance rejection control (ADRC) and can directly generate dynamic matrices for model predictive control (MMC), thereby supporting the rapid deployment of ADRC and MMC. In summary, this paper identifies multi-condition JFMM models based on on-site operating data of the unit using a modified Northern Eagle optimization algorithm. This model is not only simple in structure but also meets the modeling accuracy requirements, which is beneficial for further operation analysis and control system design, thus significantly enhancing its industrial applicability.

[0005] In recent years, Active Disturbance Rejection Control (ADRC) has gained widespread attention and application due to its simple structure, excellent control performance and anti-interference ability, and independence from precise mathematical models. By integrating internal and external disturbances, unmodeled dynamics, and parameter uncertainties into a total disturbance and expanding it into a new state for real-time estimation and compensation through an extended state observer (ESO), ADRC has not only achieved success in simulation experiments but has also been successfully applied in industrial control scenarios in thermal power plants. The proposed Linear Active Disturbance Rejection Controller (LADRC) and its bandwidth parameterized tuning method have solved the problem of complex nonlinear gains in the original ADRC. To improve the industrial competitiveness of ADRC technology, Error Active Disturbance Rejection Control (EADRC), which achieves a reasonable balance between control performance and industrial convenience, has been proposed and applied in industrial applications. EADRC inherits and develops the advantages of LADRC, determining state variables by analyzing tracking errors, which is more in line with common industrial scenarios and the requirements for improved tracking accuracy. Furthermore, applying a reduced-order extended state observer (RESO) to EADRC further reduces the complexity of the controller structure and effectively improves the response speed of the control system. Based on this, the core competitiveness of EADRC compared to traditional PID controllers is potentially enhanced, enabling efficient handling of industrial process control problems with strong nonlinearity. Addressing the difficulty in grasping the parameter tuning rules of controllers in complex multivariable systems, applying a simple, powerful, and accurate swarm intelligence algorithm to EADRC parameter optimization is undoubtedly a powerful combination. Therefore, designing a controller for the unit's coordinated control system using improved error active disturbance rejection control technology, combined with a modified Northern Eagle optimization algorithm, can effectively improve the system's rapid load control performance and enhance the flexible operation capability of ultra-supercritical units under wide load conditions. Summary of the Invention

[0006] This invention aims to provide a flexible operation scheme for ultra-supercritical units based on improved active disturbance rejection control (ADRC) and a modified Northern Eagle optimizer, thereby improving the control quality of the coordinated control system and enabling flexible operation of the unit under wide load conditions. This method fully considers the complex dynamic characteristics of the controlled object, model uncertainties, and disturbances caused by load changes and variations in coal quality or environment during actual unit operation. Based on the modified Northern Eagle optimization algorithm, the multi-condition transfer function matrix model of the unit is identified. Combining the advantages of improved ADRC technology, which can estimate and compensate for errors in real time, an advanced ADRC strategy is designed. Based on the designed improved ADRC, under the influence of load tracking commands and external disturbances, the models at each operating point of the unit's coordinated control system achieve fast and accurate load response.

[0007] The flexible operation scheme for ultra-supercritical units proposed in this invention, based on improved error active disturbance rejection control and improved Northern Eagle optimizer, consists of the following four steps:

[0008] S1: Analyze the dynamic characteristics, modeling, and control challenges of the boiler-turbine coupled system in an ultra-supercritical unit;

[0009] S2: Establish a smart model identification scheme for ultra-supercritical units based on the improved Northern Eagle optimization algorithm, and describe its principle and design steps;

[0010] S3: Establish the structure of an improved active disturbance rejection control strategy for the coordinated control system of ultra-supercritical units, and describe the principle and design steps of the improved active disturbance rejection control technology.

[0011] S4: Verify and analyze the feasibility of the proposed flexible operation scheme based on the simulation platform.

[0012] S1: With the rapid growth of renewable energy power grid connection capacity, ultra-supercritical units frequently participate in deep peak shaving processes, exhibiting characteristics such as large inertia, large delay, strong nonlinearity, and strong coupling. This means that modeling and controlling the units during research will be extremely challenging. From the perspective of thermal control in the power generation process, ultra-supercritical units should maintain a stable separator outlet temperature during load changes to prevent large fluctuations in main steam pressure. Simultaneously, the opening degree of the main steam valve, feedwater flow rate, and coal feed rate should avoid drastic changes to ensure valve lifespan and stabilize the fuel-water ratio regulation. The opening degree of the main steam valve directly determines the steam flow rate entering the turbine, thus affecting the unit's output power. The feedwater flow rate affects the separator outlet temperature and, consequently, the steam flow rate generated by the boiler. Maintaining a suitable feedwater flow rate is crucial for a stable steam supply, ensuring the safe and stable operation of the unit. The main steam pressure, as a key parameter for the energy balance of the boiler and turbine systems, is directly controlled by the coal feed rate. Therefore, after comprehensively considering the balance between accuracy and simplicity in the unit model, a simplified three-input, three-output model was established for the boiler-turbine coupling system of the ultra-supercritical unit. The three input variables are the main steam valve opening μ. T Water flow rate u W and coal feed flow rate u B The three output variables are the output power N. E Separator outlet temperature T I and main steam pressure P T Due to the lack of a steam drum for buffering, the unit's system variables are strongly coupled, and under deep peak-shaving requirements, the unit's dynamic characteristics change with varying operating conditions. Therefore, the operational flexibility of ultra-supercritical units under wide load conditions urgently needs to be improved.

[0013] Based on the analysis in S1, it is evident that the coordinated control system of ultra-supercritical units is difficult to model accurately due to its complex dynamic characteristics. Therefore, it is necessary to design an advanced intelligent model identification scheme to obtain a high-precision model. Step S2 can be further specified as follows:

[0014] S2.1: Selection of model structure;

[0015] For ultra-supercritical units requiring rapid response and high-precision control, a transfer function matrix model with sufficient accuracy is used to approximate the nonlinear characteristics of the unit. Based on detailed dynamic characteristic analysis, the transfer function model structure of each specific channel is determined, and equation (1) is selected as the model set to be identified. The three-input three-output model has a total of 45 parameters to be identified.

[0016]

[0017] Where k1 represents the transient response, K represents the process gain, T1 and T are time constants, and n is the order of the model.

[0018] S2.2: Improved Northern Eagle optimization algorithm;

[0019] Four enhancement measures were adopted for the original Northern Goshawk optimization algorithm: chaotic mapping, optimal value guidance, Cauchy mutation, and simulated annealing. Each Northern Goshawk represents a solution, which is actually the parameter matrix of the controller. The optimal position of the Northern Goshawk represents the optimal parameters of the three channel controllers. Tent chaotic mapping was added during the population initialization process to improve the diversity of the initial population, as shown in Equations (2) to (3).

[0020] X i (0) = X min +z i (X max -X min ), i = 1, 2, ..., N (2)

[0021]

[0022] Among them, X i (0) represents the initial position of the i-th Northern Goshawk, X max and X min These are the upper and lower bounds of the search range, respectively; N is the population size; and β is the chaos coefficient in the Tent map.

[0023] The algorithm is divided into two stages: prey identification and attack, and pursuit and escape.

[0024] S2.2.1: Prey identification and attack;

[0025] The algorithm performs a global search in this stage to determine the optimal region. It selects the Northern Goshawk with the highest current fitness to guide the population in updating its location. After extensive simulations, it was found that when… When the optimal value guidance strategy is applied, the effect is best. The improved formula for the first stage is as follows:

[0026] P i =X k ,i=1,2,...,N,k=1,2,...i-1,i+1,...,N (4)

[0027]

[0028]

[0029] Among them, P i It is the location of a random Northern Goshawk within the population. It is the new position of the i-th individual in the j-th dimension after the first phase update, and xbest is the current best position of the population. F i and F i new,P1 Both represent fitness function values ​​related to an individual's location. r is a random number between [0,1], and I is a random number between 1 and 2. Both r and I reflect the randomness of the algorithm during the global search process.

[0030] S2.2.2: Chase and escape;

[0031] The northern goshawk hunts prey within a radius of R, demonstrating the algorithm's local search capability. The position update in this stage incorporates a Cauchy mutation factor, denoted by α. Simultaneously, simulated annealing is integrated to enhance the algorithm's ability to escape local optima. The improved second-stage formula is as follows:

[0032]

[0033]

[0034] ΔF=F i new,P2 -F i (9)

[0035]

[0036] in, This represents the new position of the i-th individual after the second-stage update, where T is the maximum number of iterations and t is the current number of iterations. The improved Northern Eagle optimization algorithm, combining four enhancement measures, achieves higher search accuracy and faster convergence speed, and effectively avoids getting trapped in local optima.

[0037] S2.3: Model identification scheme;

[0038] The collected actual field operation data of the ultra-supercritical unit were subjected to zero initialization processing:

[0039]

[0040] Where L is the number of initial zeros, u(k) is the input data, and y(k) is the output data.

[0041] Before formal modeling, abnormal coarse values ​​caused by temporary failures of data acquisition equipment are intentionally removed, and then linear interpolation is performed on the blank data area. If the first (i-1) points of the dataset y(i) are normal values ​​and the i-th point satisfies formula (12), it can be regarded as a coarse value and linear interpolation is performed according to formula (13).

[0042]

[0043]

[0044] In the formula: m is the difference order, with a maximum value of (i-2); γ is the coarse coefficient, which is taken as 2i here; y(i - ) and y(i + ) represent the normal data before and after the coarse value y(i), respectively. This is the data after the coarse value has been updated.

[0045] The parameters to be identified in the model are used as decision variables, and the boundary of parameter optimization is used as a constraint. The improved Northern Eagle optimization algorithm is used to minimize the sum of squared errors between the model output and the actual output of the unit, as shown in Equation (14):

[0046]

[0047] Where: j = 1, 2, and 3 represent three outputs, ω j This represents the modeling error weight for each output. j (k) is the model output, y 0j (k) is the actual output of the unit after data preprocessing.

[0048] After establishing the multi-condition transfer function matrix model of the unit coordinated control system, the design steps of the improved error active disturbance rejection control technology are specified in S3:

[0049] S3.1: Design of a conventional active disturbance rejection controller (EADRC);

[0050] Consider the following second-order system:

[0051]

[0052] in, It is a lumped function containing unmodeled dynamics and unknown external disturbances; b≠0 is the uncertain input gain of the system; the estimated value of b is denoted as b0; the system of equation (15) can also be expressed as:

[0053]

[0054] at this time, This now also includes uncertainties related to the input gain. EADRC determines the state variables by analyzing the tracking error:

[0055]

[0056] To simplify the control law, By introducing error differential terms on both sides, we obtain a more simplified error-based model:

[0057]

[0058] Assume F is differentiable and Bounded, will Treat the total disturbance as an extended state and use the new state variable matrix. Let's design an extended state observer (ESO). Let z1, z2, and z3 be the estimates of x1, x2, and x3, respectively. Then, the ESO can be designed as follows:

[0059]

[0060] Where L = [l1, l2, l3] is the observer gain of the ESO, and (e-z1) is the observation error. After selecting an appropriate observer gain, the ESO can accurately estimate the system state in real time. The state feedback control law is chosen as follows:

[0061]

[0062] Where u0 is set to k0e, the derivative of the unknown reference signal has been included in the total disturbance term. The controller gain and observer gain are set using the pole placement method:

[0063]

[0064] Where, ω c and ω oThese are the controller bandwidth and the observer bandwidth, respectively. Compared to output-based linear active disturbance rejection controllers, EADRC avoids directly using the differential signal of the reference input in control law synthesis, further enhancing its industrial applicability.

[0065] S3.2: Design of an improved active disturbance rejection controller (IEADRC);

[0066] In fact, the tracking error *e* is a known quantity that can be directly read from the sensor without needing to be estimated. Therefore, the traditional ESO is reduced in order, resulting in the reduced-order extended state observer RESO, with the new state vector as follows:

[0067]

[0068] By defining new state variables ζ1 and ζ2, equation (22) can be transformed into:

[0069]

[0070] The new control law is shown in equation (24), and the controller gain and observer gain are selected based on the pole placement method as follows:

[0071]

[0072]

[0073] An improved automatic disturbance rejection controller (ARC) is designed for the output power, separator outlet temperature, and main steam pressure channel of the unit's boiler-turbine coordinated control system, respectively, and is denoted as IEADRC1, IEADRC2, and IEADRC3.

[0074] S3.3: Multi-objective optimization;

[0075] A modified Northern Eagle optimizer is used to tune the controller parameters, ω, of the three output channels in the coordinated control system. c1 b 01 ω o1 ω c2 b 02 ω o2 ω c3 b 03 and ω o3 To achieve flexible operation of ultra-supercritical units under a wide range of load conditions, the designed multi-objective optimization function comprehensively considers physical constraints, tracking process errors, control stability, economic costs of power generation, and carbon emissions during unit operation, as shown below:

[0076]

[0077] Where e and u are the tracking process error and control quantity, respectively, λ and w are adjustable weighting coefficients, and T a k represents the actual simulation time. c It is the standard coal conversion factor, k ce It is a discount factor. Q e Q u Q c and Q ce These represent tracking process error, control quantity stability, economic cost of power generation, and carbon emissions, respectively.

[0078] Based on the improved active disturbance rejection control structure obtained in step S3, an improved active disturbance rejection controller for the coordinated control system is established. In step S4, the feasibility of the proposed flexible operation scheme is verified and analyzed using a simulation platform. The specific process is as follows:

[0079] S4.1: Select actual field operation data of a 1000MW ultra-supercritical unit and establish the transfer function matrix model of the unit at four typical operating conditions within a wide load range;

[0080] S4.2: Based on the transfer function matrix model established in step S4.1, design an improved active disturbance rejection controller;

[0081] S4.3: Load tracking command N ESP Separator outlet temperature setpoint T ISP and main steam pressure setpoint P TSP Input the controlled object separately and perform tracking performance tests. Compare the control using EADRC, LADRC, and PID controllers to verify the effectiveness of the designed controller.

[0082] S4.4: Determine the set value of the external disturbance d and input it into the controlled object. Simulate the external disturbances experienced by the unit during actual operation, conduct anti-interference performance tests, observe the three output variables of the unit, and compare the control using EADRC, LADRC and PID controllers.

[0083] S4.5: Perform robustness testing on the designed controller IEADRC; using the model at 39% load condition as the nominal model, select any two model parameters and subject them to ±10% perturbation relative to the nominal value; set the sample size for the Monte Carlo test to 200, and obtain the controlled variable output power N. E Analyze the cluster of response curves and observe their dispersion; statistically analyze the control performance indicators overshoot σ and settling time t. s The range of ITAE values ​​is calculated, along with their mean (Mean) and standard deviation (SD). Mean represents the average performance level of the nominal controller for the perturbation model, and SD represents the dispersion of the Monte Carlo test.

[0084] S4.6: Verify the superiority of the designed Northern Eagle optimizer; select a high-performance swarm intelligence optimization algorithm that has been proven in practice, set each algorithm with the same optimization conditions, and conduct controller parameter optimization tests. The parameter optimization results are taken as the optimal values ​​after multiple optimizations under the same conditions, and the unit's output variables are observed. Beneficial effects of this invention:

[0085] This invention, in line with the development trend of gradually increasing the capacity for renewable energy power consumption in my country's power production sector, designs an intelligent model identification scheme and an improved error self-disturbance rejection control strategy for the coordinated control system of ultra-supercritical units from the perspective of modeling and control, thereby improving the flexible operation capability of ultra-supercritical units under wide load conditions.

[0086] This invention simplifies the controlled object into a three-input, three-output system, which more accurately describes the dynamic characteristics of the boiler-turbine coupled system. The improved Northern Eagle optimization algorithm, combining four enhancement measures, achieves higher search accuracy and faster convergence speed, and effectively avoids getting trapped in local optima. Based on the improved Northern Eagle optimization algorithm, a high-precision multi-condition transfer function matrix model for ultra-supercritical units is identified, laying a solid foundation for further control strategy design.

[0087] The improved error active disturbance rejection control strategy of this invention fully considers the complex dynamic characteristics and control difficulties of the coordinated control system of ultra-supercritical units. It applies a reduced-order extended state observer to the high-performance error active disturbance rejection control technology, further reducing the complexity of the controller structure and effectively improving the rapid load regulation capability of the coordinated control system of ultra-supercritical units under deep peak shaving requirements. Attached Figure Description

[0088] Figure 1 This is a schematic diagram of the ultra-supercritical unit structure involved in this invention.

[0089] Figure 2 This is a simplified structural diagram of the coordinated control system for ultra-supercritical units involved in this invention.

[0090] Figure 3 This is a structural diagram of the improved error active disturbance rejection controller mentioned in this invention.

[0091] Figure 4 This is a block diagram of the improved error self-disturbance rejection control structure for flexible operation of ultra-supercritical units mentioned in this invention. Detailed Implementation

[0092] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0093] Please refer to the accompanying drawings in the instruction manual. Figure 1, Figure 1 This is a schematic diagram of the ultra-supercritical unit structure involved in this invention. The operation of the ultra-supercritical unit involves complex energy cascade utilization and conversion. First, fossil fuels are burned in a once-through boiler to produce high-temperature flue gas, whose chemical energy is converted into internal energy and transferred to the boiler feedwater through the furnace. Then, the feedwater from the high-pressure heater passes sequentially through the economizer, water-cooled walls, separator, and various superheaters, where it is heated to qualified ultra-supercritical steam under extremely high temperature and pressure. Subsequently, the steam passes through the main steam valve and enters the turbine system of each stage to expand and do work, driving the turbine blades to rotate. Its internal energy is converted into mechanical energy, which then drives the generator to generate electricity, and the mechanical energy is ultimately converted into electrical energy. In addition, the discharged steam, after condensation and deoxygenation, passes through the low-pressure heater and the high-pressure heater to become boiler circulating feedwater.

[0094] Please refer to the accompanying drawings in the instruction manual. Figure 2 , Figure 2 This is a simplified structural diagram of the coordinated control system for the ultra-supercritical unit involved in this invention. The controlled object is simplified into a three-input, three-output system, which more accurately describes the dynamic characteristics of the boiler-turbine coupled system. The three input variables are the main steam valve opening μ... T Water flow rate u W and coal feed flow rate u B The three output variables are the output power N. E Separator outlet temperature T I and main steam pressure P T .

[0095] Please refer to the accompanying drawings in the instruction manual. Figure 3 , Figure 3 This is a structural diagram of the improved active disturbance rejection controller mentioned in this invention. This controller can achieve real-time and accurate tracking and compensation of the estimated quantity, exhibiting good control performance and anti-interference performance.

[0096] Please refer to the accompanying drawings in the instruction manual. Figure 4 , Figure 4 This is a block diagram of the improved error active disturbance rejection control structure for flexible operation of ultra-supercritical units mentioned in this invention. An improved error active disturbance rejection controller is designed for the output power, separator outlet temperature, and main steam pressure channels of the unit's boiler-turbine coordinated control system, respectively, to achieve rapid load regulation while maintaining safe and stable operation of the unit. This example is based on a 1000MW ultra-supercritical unit in China, and the method steps include:

[0097] S1: Analyze the dynamic characteristics, modeling, and control challenges of the boiler-turbine coupled system in an ultra-supercritical unit;

[0098] S2: Establish a smart model identification scheme for ultra-supercritical units based on the improved Northern Eagle optimization algorithm, and describe its principle and design steps;

[0099] S3: Establish the structure of an improved active disturbance rejection control strategy for the coordinated control system of ultra-supercritical units, and describe the principle and design steps of the improved active disturbance rejection control technology.

[0100] S4: Verify and analyze the feasibility of the proposed flexible operation scheme based on the simulation platform.

[0101] S1: With the rapid growth of renewable energy power grid connection capacity, ultra-supercritical units frequently participate in deep peak shaving processes, exhibiting characteristics such as large inertia, large delay, strong nonlinearity, and strong coupling. This means that modeling and controlling the units during research will be extremely challenging. From the perspective of thermal control in the power generation process, ultra-supercritical units should maintain a stable separator outlet temperature during load changes to prevent large fluctuations in main steam pressure. Simultaneously, the opening degree of the main steam valve, feedwater flow rate, and coal feed rate should avoid drastic changes to ensure valve lifespan and stabilize the fuel-water ratio regulation. The opening degree of the main steam valve directly determines the steam flow rate entering the turbine, thus affecting the unit's output power. The feedwater flow rate affects the separator outlet temperature and, consequently, the steam flow rate generated by the boiler. Maintaining a suitable feedwater flow rate is crucial for a stable steam supply, ensuring the safe and stable operation of the unit. The main steam pressure, as a key parameter for the energy balance of the boiler and turbine systems, is directly controlled by the coal feed rate. Therefore, after comprehensively considering the balance between accuracy and simplicity in the unit model, a simplified three-input, three-output model was established for the boiler-turbine coupling system of the ultra-supercritical unit. The three input variables are the main steam valve opening μ. T Water flow rate u W and coal feed flow rate u B The three output variables are the output power N. E Separator outlet temperature T I and main steam pressure P T Due to the lack of a steam drum for buffering, the unit's system variables are strongly coupled, and under deep peak-shaving requirements, the unit's dynamic characteristics change with varying operating conditions. Therefore, the operational flexibility of ultra-supercritical units under wide load conditions urgently needs to be improved.

[0102] Based on the analysis in S1, it is evident that the coordinated control system of ultra-supercritical units is difficult to model accurately due to its complex dynamic characteristics. Therefore, it is necessary to design an advanced intelligent model identification scheme to obtain a high-precision model. Step S2 can be further specified as follows:

[0103] S2.1: Selection of model structure;

[0104] For ultra-supercritical units requiring rapid response and high-precision control, a transfer function matrix model with sufficient accuracy is used to approximate the nonlinear characteristics of the unit. Based on detailed dynamic characteristic analysis, the transfer function model structure of each specific channel is determined, and equation (1) is selected as the model set to be identified. The three-input three-output model has a total of 45 parameters to be identified.

[0105]

[0106] Where k1 represents the transient response, K represents the process gain, T1 and T are time constants, and n is the order of the model.

[0107] S2.2: Improved Northern Eagle optimization algorithm;

[0108] Four enhancement measures were adopted for the original Northern Goshawk optimization algorithm: chaotic mapping, optimal value guidance, Cauchy mutation, and simulated annealing. Each Northern Goshawk represents a solution, which is actually the parameter matrix of the controller. The optimal position of the Northern Goshawk represents the optimal parameters of the three channel controllers. Tent chaotic mapping was added during the population initialization process to improve the diversity of the initial population, as shown in Equations (2) to (3).

[0109] X i (0) = X min +z i (X max -X min ), i = 1, 2, ..., N (28)

[0110]

[0111] Among them, X i (0) represents the initial position of the i-th Northern Goshawk, X max and X min These are the upper and lower bounds of the search range, respectively; N is the population size; and β is the chaos coefficient in the Tent map.

[0112] The algorithm is divided into two stages: prey identification and attack, and pursuit and escape.

[0113] S2.2.1: Prey identification and attack;

[0114] The algorithm performs a global search in this stage to determine the optimal region. It selects the Northern Goshawk with the highest current fitness to guide the population in updating its location. After extensive simulations, it was found that when… When the optimal value guidance strategy is applied, the effect is best. The improved formula for the first stage is as follows:

[0115] P i =X k,i=1,2,...,N,k=1,2,...i-1,i+1,...,N (30)

[0116]

[0117]

[0118] Among them, P i It is the location of a random Northern Goshawk within the population. It is the new position of the i-th individual in the j-th dimension after the first phase update, and xbest is the current best position of the population. F i and F i new,P1 Both represent fitness function values ​​related to an individual's location. r is a random number between [0,1], and I is a random number between 1 and 2. Both r and I reflect the randomness of the algorithm during the global search process.

[0119] S2.2.2: Chase and escape;

[0120] The northern goshawk hunts prey within a radius of R, demonstrating the algorithm's local search capability. The position update in this stage incorporates a Cauchy mutation factor, denoted by α. Simultaneously, simulated annealing is integrated to enhance the algorithm's ability to escape local optima. The improved second-stage formula is as follows:

[0121]

[0122]

[0123] ΔF=F i new,P2 -F i (35)

[0124]

[0125] in, This represents the new position of the i-th individual after the second-stage update, where T is the maximum number of iterations and t is the current number of iterations. The improved Northern Eagle optimization algorithm, combining four enhancement measures, achieves higher search accuracy and faster convergence speed, and effectively avoids getting trapped in local optima.

[0126] S2.3: Model identification scheme;

[0127] The collected actual field operation data of the ultra-supercritical unit were subjected to zero initialization processing:

[0128]

[0129] Where L is the number of initial zeros, u(k) is the input data, and y(k) is the output data.

[0130] Before formal modeling, abnormal coarse values ​​caused by temporary failures of data acquisition equipment are intentionally removed, and then linear interpolation is performed on the blank data area. If the first (i-1) points of the dataset y(i) are normal values ​​and the i-th point satisfies formula (12), it can be regarded as a coarse value and linear interpolation is performed according to formula (13).

[0131]

[0132]

[0133] In the formula: m is the difference order, with a maximum value of (i-2); γ is the coarse coefficient, which is taken as 2i here; y(i - ) and y(i + ) represent the normal data before and after the coarse value y(i), respectively. This is the data after the coarse value has been updated.

[0134] The parameters to be identified in the model are used as decision variables, and the boundary of parameter optimization is used as a constraint. The improved Northern Eagle optimization algorithm is used to minimize the sum of squared errors between the model output and the actual output of the unit, as shown in Equation (14):

[0135]

[0136] Where: j = 1, 2, and 3 represent three outputs, ω j This represents the modeling error weight for each output. j (k) is the model output, y 0j (k) is the actual output of the unit after data preprocessing.

[0137] After establishing the multi-condition transfer function matrix model of the unit coordinated control system, the design steps of the improved error active disturbance rejection control technology are specified in S3:

[0138] S3.1: Design of a conventional active disturbance rejection controller (EADRC);

[0139] Consider the following second-order system:

[0140]

[0141] in, It is a lumped function containing unmodeled dynamics and unknown external disturbances; b≠0 is the uncertain input gain of the system; the estimated value of b is denoted as b0; the system of equation (15) can also be expressed as:

[0142]

[0143] at this time, This now also includes uncertainties related to the input gain. EADRC determines the state variables by analyzing the tracking error:

[0144]

[0145] To simplify the control law, By introducing error differential terms on both sides, we obtain a more simplified error-based model:

[0146]

[0147] Assume F is differentiable and Bounded, will Treat the total disturbance as an extended state and use the new state variable matrix. Let's design an extended state observer (ESO). Let z1, z2, and z3 be the estimates of x1, x2, and x3, respectively. Then, the ESO can be designed as follows:

[0148]

[0149] Where L = [l1, l2, l3] is the observer gain of the ESO, and (e-z1) is the observation error. After selecting an appropriate observer gain, the ESO can accurately estimate the system state in real time. The state feedback control law is chosen as follows:

[0150]

[0151] Where u0 is set to k0e, the derivative of the unknown reference signal has been included in the total disturbance term. The controller gain and observer gain are set using the pole placement method:

[0152]

[0153] Where, ω c and ω o These are the controller bandwidth and the observer bandwidth, respectively. Compared to output-based linear active disturbance rejection controllers, EADRC avoids directly using the differential signal of the reference input in control law synthesis, further enhancing its industrial applicability.

[0154] S3.2: Design of an improved active disturbance rejection controller (IEADRC);

[0155] In fact, the tracking error *e* is a known quantity that can be directly read from the sensor without needing to be estimated. Therefore, the traditional ESO is reduced in order, resulting in the reduced-order extended state observer RESO, with the new state vector as follows:

[0156]

[0157] By defining new state variables ζ1 and ζ2, equation (22) can be transformed into:

[0158]

[0159] The new control law is shown in equation (24), and the controller gain and observer gain are selected based on the pole placement method as follows:

[0160]

[0161]

[0162] An improved automatic disturbance rejection controller (ARC) is designed for the output power, separator outlet temperature, and main steam pressure channel of the unit's boiler-turbine coordinated control system, respectively, and is denoted as IEADRC1, IEADRC2, and IEADRC3.

[0163] S3.3: Multi-objective optimization;

[0164] A modified Northern Eagle optimizer is used to tune the controller parameters, ω, of the three output channels in the coordinated control system. c1 b 01 ω o1 ω c2 b 02 ω o2 ω c3 b 03 and ω o3 To achieve flexible operation of ultra-supercritical units under a wide range of load conditions, the designed multi-objective optimization function comprehensively considers physical constraints, tracking process errors, control stability, economic costs of power generation, and carbon emissions during unit operation, as shown below:

[0165]

[0166] Where e and u are the tracking process error and control quantity, respectively, λ and w are adjustable weighting coefficients, and T a k represents the actual simulation time. c It is the standard coal conversion factor, k ce It is a discount factor. Q e Q u Q c and Q ce These represent tracking process error, control quantity stability, economic cost of power generation, and carbon emissions, respectively.

[0167] Based on the improved active disturbance rejection control structure obtained in step S3, an improved active disturbance rejection controller for the coordinated control system is established. In step S4, the feasibility of the proposed flexible operation scheme is verified and analyzed using a simulation platform. The specific process is as follows:

[0168] S4.1: Select actual field operation data of a 1000MW ultra-supercritical unit and establish the transfer function matrix model of the unit at four typical operating conditions within a wide load range;

[0169] S4.2: Based on the transfer function matrix model established in step S4.1, design an improved active disturbance rejection controller;

[0170] S4.3: Load tracking command N ESP Separator outlet temperature setpoint T ISP and main steam pressure setpoint P TSP Input the controlled object separately and perform tracking performance tests. Compare the control using EADRC, LADRC, and PID controllers to verify the effectiveness of the designed controller.

[0171] S4.4: Determine the set value of the external disturbance d and input it into the controlled object. Simulate the external disturbances experienced by the unit during actual operation, conduct anti-interference performance tests, observe the three output variables of the unit, and compare the control using EADRC, LADRC and PID controllers.

[0172] S4.5: Perform robustness testing on the designed controller IEADRC; using the model at 39% load condition as the nominal model, select any two model parameters and subject them to ±10% perturbation relative to the nominal value; set the sample size for the Monte Carlo test to 200, and obtain the controlled variable output power N. E Analyze the cluster of response curves and observe their dispersion; statistically analyze the control performance indicators overshoot σ and settling time t. s The range of ITAE values ​​is calculated, along with their mean (Mean) and standard deviation (SD). Mean represents the average performance level of the nominal controller for the perturbation model, and SD represents the dispersion of the Monte Carlo test.

[0173] S4.6: Verify the superiority of the designed Northern Eagle optimizer; select a high-performance swarm intelligence optimization algorithm that has been verified in practice, set each algorithm to have the same optimization conditions, conduct controller parameter optimization tests, take the optimal value after multiple optimizations under the same conditions, and observe the unit's output variables.

[0174] S4.7: Actual output power N of the computer group E and load tracking command N ESPTo assess the degree of fit and further quantify control performance, statistical analysis was conducted on control performance indicators such as overshoot σ and settling time t. s Steady-state error e s IAE value, ITAE value, and fitness function value;

[0175]

[0176]

[0177] Statistical results show that the proposed flexible operation scheme for ultra-supercritical units based on improved error active disturbance rejection control and improved Northern Eagle optimizer exhibits excellent rapid load regulation performance in this example, effectively improving the flexible operation capability of ultra-supercritical units under wide load conditions.

Claims

1. A flexible operation scheme for ultra-supercritical units based on improved error active disturbance rejection control and improved Northern Eagle optimizer is characterized by: Includes the following steps: S1: Analyze the dynamic characteristics, modeling, and control challenges of the boiler-turbine coupled system in an ultra-supercritical unit; S2: Establish a smart model identification scheme for ultra-supercritical units based on the improved Northern Eagle optimization algorithm, and describe its principle and design steps; S3: Establish the structure of an improved active disturbance rejection control strategy for the coordinated control system of ultra-supercritical units, and describe the principle and design steps of the improved active disturbance rejection control technology. S4: Verify and analyze the feasibility of the proposed flexible operation scheme based on the simulation platform.

2. The flexible operation scheme for ultra-supercritical units based on improved error active disturbance rejection control and improved Northern Eagle optimizer as described in claim 1, characterized in that: The specific difficulties in analyzing, modeling, and controlling the dynamic characteristics of the boiler-turbine coupled system of the ultra-supercritical unit described in step S1 are as follows: S1: With the rapid growth of renewable energy power grid connection capacity, ultra-supercritical units frequently participate in deep peak shaving processes, exhibiting characteristics such as large inertia, large delay, strong nonlinearity, and strong coupling. This means that modeling and controlling the units during research will be extremely challenging. From the perspective of thermal control in the power generation process, ultra-supercritical units should maintain a stable separator outlet temperature during load changes to prevent large fluctuations in main steam pressure. Simultaneously, the opening degree of the main steam valve, feedwater flow rate, and coal feed rate should avoid drastic changes to ensure valve lifespan and stabilize the fuel-water ratio regulation. The opening degree of the main steam valve directly determines the steam flow rate entering the turbine, thus affecting the unit's output power. The feedwater flow rate affects the separator outlet temperature and, consequently, the steam flow rate generated by the boiler. Maintaining a suitable feedwater flow rate is crucial for a stable steam supply, ensuring the safe and stable operation of the unit. The main steam pressure, as a key parameter for the energy balance of the boiler and turbine systems, is directly controlled by the coal feed rate. Therefore, after comprehensively considering the balance between accuracy and simplicity in the unit model, a simplified three-input, three-output model was established for the boiler-turbine coupling system of the ultra-supercritical unit. The three input variables are the main steam valve opening μ. T Water flow rate u W and coal feed flow rate u B The three output variables are the output power N. E Separator outlet temperature T I and main steam pressure P T Due to the lack of a steam drum for buffering, the unit's system variables are strongly coupled, and under deep peak-shaving requirements, the unit's dynamic characteristics change with varying operating conditions. Therefore, the operational flexibility of ultra-supercritical units under wide load conditions urgently needs to be improved.

3. The flexible operation scheme for ultra-supercritical units based on improved error active disturbance rejection control and improved Northern Eagle optimizer as described in claim 1, characterized in that: A smart model identification scheme for ultra-supercritical units based on the improved Northern Eagle optimization algorithm is established, and its principle and design steps are described. Step S2 is the specific implementation step of the smart model identification scheme for the boiler-turbine coupled system, including: S2.1: Selection of model structure; For ultra-supercritical units requiring rapid response and high-precision control, a transfer function matrix model with sufficient accuracy is used to approximate the nonlinear characteristics of the unit. Based on detailed dynamic characteristic analysis, the transfer function model structure of each specific channel is determined, and equation (1) is selected as the model set to be identified. The three-input three-output model has a total of 45 parameters to be identified. Where k1 represents the transient response, K represents the process gain, T1 and T are time constants, and n is the order of the model. S2.2: Improved Northern Eagle Optimization Algorithm; Four enhancement measures were adopted for the original Northern Goshawk optimization algorithm: chaotic mapping, optimal value guidance, Cauchy mutation, and simulated annealing. Each Northern Goshawk represents a solution, which is actually the parameter matrix of the controller. The optimal position of the Northern Goshawk represents the optimal parameters of the three channel controllers. Tent chaotic mapping was added during the population initialization process to improve the diversity of the initial population, as shown in Equations (2) to (3). X i (0)=X min +z i (X max -X min ),i=1,2,...,N (2) Among them, X i (0) represents the initial position of the i-th Northern Goshawk, X max and X min These are the upper and lower bounds of the search range, respectively; N is the population size; and β is the chaos coefficient in the Tent map. The algorithm is divided into two stages: prey identification and attack, and pursuit and escape. S2.2.1: Prey identification and attack; The algorithm performs a global search in this stage to determine the optimal region. It selects the Northern Goshawk with the highest current fitness to guide the population in updating its location. After extensive simulations, it was found that when… When the optimal value guidance strategy is applied, the effect is best. The improved formula for the first stage is as follows: P i =X k ,i=1,2,...,N,k=1,2,...i-1,i+1,...,N (4) Among them, P i It is the location of a random Northern Goshawk within the population. It is the new position of the i-th individual in the j-th dimension after the first phase update, and xbest is the current best position of the population. F i and F i new,P1 Both represent fitness function values ​​related to an individual's location. r is a random number between [0,1], and I is a random number between 1 and 2. Both r and I reflect the randomness of the algorithm during the global search process. S2.2.2: Chase and escape; The northern goshawk hunts prey within a radius of R, demonstrating the algorithm's local search capability. The position update in this stage incorporates a Cauchy mutation factor, denoted by α. Simultaneously, simulated annealing is integrated to enhance the algorithm's ability to escape local optima. The improved second-stage formula is as follows: ΔF=F i new,P2 -F i (9) in, This represents the new position of the i-th individual after the second-stage update, where T is the maximum number of iterations and t is the current number of iterations. The improved Northern Eagle optimization algorithm, combining four enhancement measures, achieves higher search accuracy and faster convergence speed, and effectively avoids getting trapped in local optima. S2.3: Model identification scheme; The collected actual field operation data of the ultra-supercritical unit were subjected to zero initialization processing: Where L is the number of initial zeros, u(k) is the input data, and y(k) is the output data. Before formal modeling, abnormal coarse values ​​caused by temporary failures of data acquisition equipment are intentionally removed, and then linear interpolation is performed on the blank data area. If the first (i-1) points of the dataset y(i) are normal values ​​and the i-th point satisfies formula (12), it can be regarded as a coarse value and linear interpolation is performed according to formula (13). In the formula: m is the difference order, with a maximum value of (i-2); γ is the coarse coefficient, which is taken as 2i here; y(i - ) and y(i + ) represent the normal data before and after the coarse value y(i), respectively. This is the data after the coarse value has been updated. The parameters to be identified in the model are used as decision variables, and the boundary of parameter optimization is used as a constraint. The improved Northern Eagle optimization algorithm is used to minimize the sum of squared errors between the model output and the actual output of the unit, as shown in Equation (14): Where: j = 1, 2, and 3 represent three outputs, ω j This represents the modeling error weight for each output. j (k) is the model output, y 0j (k) is the actual output of the unit after data preprocessing.

4. The flexible operation scheme for ultra-supercritical units based on improved error active disturbance rejection control and improved Northern Eagle optimizer as described in claim 1, characterized in that: An improved active disturbance rejection control (ADRC) strategy for coordinated control systems of ultra-supercritical units is established, and the principle and design steps of the improved ADRC technology are described, including: S3.1: Design of a conventional active disturbance rejection controller (EADRC); Consider the following second-order system: in, It is a lumped function containing unmodeled dynamics and unknown external disturbances; b≠0 is the uncertain input gain of the system; the estimated value of b is denoted as b0; the system of equation (15) can also be expressed as: at this time, This now also includes uncertainties related to the input gain. EADRC determines the state variables by analyzing the tracking error: To simplify the control law, By introducing error differential terms on both sides, we obtain a more simplified error-based model: Assume F is differentiable and Bounded, will Treat the total disturbance as an extended state and use the new state variable matrix. Let's design an extended state observer (ESO). Let z1, z2, and z3 be the estimates of x1, x2, and x3, respectively. Then, the ESO can be designed as follows: Where L = [l1, l2, l3] is the observer gain of the ESO, and (e-z1) is the observation error. After selecting an appropriate observer gain, the ESO can accurately estimate the system state in real time. The state feedback control law is chosen as follows: Where u0 is set to k0e, the derivative of the unknown reference signal has been included in the total disturbance term. The controller gain and observer gain are set using the pole placement method: Where, ω c and ω o These are the controller bandwidth and the observer bandwidth, respectively. Compared to output-based linear active disturbance rejection controllers, EADRC avoids directly using the differential signal of the reference input in control law synthesis, further enhancing its industrial applicability. S3.2: Design of an improved active disturbance rejection controller (IEADRC); In fact, the tracking error *e* is a known quantity that can be directly read from the sensor without needing to be estimated. Therefore, the traditional ESO is reduced in order, resulting in the reduced-order extended state observer RESO, with the new state vector as follows: By defining new state variables ζ1 and ζ2, equation (22) can be transformed into: The new control law is shown in equation (24), and the controller gain and observer gain are selected based on the pole placement method as follows: An improved automatic disturbance rejection controller (ARC) is designed for the output power, separator outlet temperature, and main steam pressure channel of the unit's boiler-turbine coordinated control system, respectively, and is denoted as IEADRC1, IEADRC2, and IEADRC3. S3.3: Multi-objective optimization; A modified Northern Eagle optimizer is used to tune the controller parameters, ω, of the three output channels in the coordinated control system. c1 b 01 ω o1 ω c2 b 02 ω o2 ω c3 b 03 and ω o3 To achieve flexible operation of ultra-supercritical units under a wide range of load conditions, the designed multi-objective optimization function comprehensively considers physical constraints, tracking process errors, control stability, economic costs of power generation, and carbon emissions during unit operation, as shown below: Q min =λ1Q e +λ2Q u +λ3Q c +λ4Q ce Where e and u are the tracking process error and control quantity, respectively, λ and w are adjustable weighting coefficients, and T a k represents the actual simulation time. c It is the standard coal conversion factor, k ce It is a discount factor. Q e Q u Q c and Q ce These represent tracking process error, control quantity stability, economic cost of power generation, and carbon emissions, respectively.

5. The flexible operation scheme for ultra-supercritical units based on improved error active disturbance rejection control and improved Northern Eagle optimizer as described in claim 1, characterized in that: Based on the intelligent model identification scheme based on the improved Northern Eagle optimizer designed in step S2 and the improved error active disturbance rejection control technology designed in step S3, the feasibility of the proposed flexible operation scheme is verified and analyzed in step S4 using a simulation platform, specifically including: S4.1: Select actual field operation data of a 1000MW ultra-supercritical unit and establish the transfer function matrix model of the unit at four typical operating conditions within a wide load range; S4.2: Based on the transfer function matrix model established in step S4.1, design an improved active disturbance rejection controller; S4.3: The load tracking command N... ESP Separator outlet temperature setpoint T ISP and main steam pressure setpoint P TSP Input the controlled object separately and perform tracking performance tests. Compare the control using EADRC, LADRC, and PID controllers to verify the effectiveness of the designed controller. S4.4: Determine the set value of the external disturbance d and input it into the controlled object. Simulate the external disturbances experienced by the unit during actual operation, conduct anti-interference performance tests, observe the three output variables of the unit, and compare the control using EADRC, LADRC and PID controllers. S4.5: Perform robustness testing on the designed controller IEADRC; using the model at 39% load condition as the nominal model, select any two model parameters and subject them to ±10% perturbation relative to the nominal value; set the sample size for the Monte Carlo test to 200, and obtain the controlled variable output power N. E Analyze the cluster of response curves and observe their dispersion; statistically analyze the control performance indicators overshoot σ and settling time t. s The range of ITAE values ​​is calculated, along with their mean (Mean) and standard deviation (SD). Mean represents the average performance level of the nominal controller for the perturbation model, and SD represents the dispersion of the Monte Carlo test. S4.6: Verify the superiority of the designed Northern Eagle optimizer; select a high-performance swarm intelligence optimization algorithm that has been verified in practice, set each algorithm to have the same optimization conditions, conduct controller parameter optimization tests, take the optimal value after multiple optimizations under the same conditions, and observe the unit's output variables. S4.7: Actual output power N of the computer group E and load tracking command N ESP To assess the degree of fit and further quantify control performance, statistical analysis was conducted on control performance indicators such as overshoot σ and settling time t. s Steady-state error e s IAE value, ITAE value, and fitness function value;

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