Fractional order model of ultra-supercritical coal-fired unit coordinated control system and identification method

Abstract

The invention belongs to the technical field of power plant thermodynamic and control, and particularly relates to a fractional order model of an ultra-supercritical coal-fired unit coordination control system and an identification method. The fractional order model comprises a coal pulverizing system, a boiler steam-water system and a steam turbine power generation system; the modeling method comprises the following steps: S1, acquiring and storing data of an ultra-supercritical coal-fired unit coordinated control system DCS; s2, constructing a fractional order model of the coordination control system; and S3, fitting a to-be-solved function through acquired data, and identifying dynamic parameters of the fractional order model offline by adopting a segmented time-sharing adaptive particle swarm method. According to the method, fractional order modeling is carried out on the coordinated control system of the coal-fired unit, the dynamic parameters of the system are identified by adopting a segmented time-sharing adaptive particle swarm identification method, the optimal model parameters are obtained through iterative calculation, the precision of the unit coordinated control system model under the wide load is greatly improved, and the system performance is improved. And implementation of a control strategy based on a system model is facilitated.

Description

Technical Field

[0001] This invention belongs to the field of power plant thermal power and control technology, and specifically relates to a fractional-order model and identification method for the coordinated control system of ultra-supercritical coal-fired power units. Background Technology

[0002] To adapt to the rapid development of a new power system dominated by new energy sources, the flexible peak-shaving control requirements of coal-fired power units place more stringent demands on their rapid response to wide load conditions. However, the nonlinearity, strong coupling, and wide-range, high-load-rate operation requirements of the unit's coordinated control system severely restrict the unit's operational accuracy and controller optimization speed under safe and stable conditions. Therefore, establishing a more precise fractional-order coordinated control system model is crucial for improving the unit's load regulation capabilities, in order to enhance the safety, accuracy, and speed of wide-load operation.

[0003] Traditional particle swarm optimization (PSO) only identifies data from the entire unit, resulting in high model accuracy at intermediate loads but significant errors during low-load simulations. Most physical systems exhibit fractional-order phenomena, and integer-order calculus alone cannot fully describe their characteristics. Therefore, designing controllers based on integer-order models for the coordinated control system of coal-fired power units will inevitably result in a loss of accuracy. Summary of the Invention

[0004] This invention proposes a fractional-order model and identification method for the coordinated control system of ultra-supercritical coal-fired power units, which solves the problems of poor model adaptability and insufficient accuracy under strong coupling dynamics in existing technologies when the unit operates under wide load conditions.

[0005] The technical solution of this invention is implemented as follows: A fractional-order model and identification method for the coordinated control system of ultra-supercritical coal-fired power units, including the following steps: S1. Collect and save DCS data of the ultra-supercritical coal-fired power unit's coordinated control system. S2. Construct a fractional-order model of the coordinated control system; S3. By collecting DCS data from coal-fired power units and fitting the function to be determined, the dynamic parameters and order of the fractional-order model are identified offline using a piecewise time-sharing adaptive particle swarm optimization method.

[0006] Optionally, step S2 specifically includes the following: S21. Modeling of the pulverizing system: Construct fractional-order dynamic characteristic expressions for the pulverizing system based on its first-order inertial delay characteristics. ; in, Fuel quantity directive, kg / s; The amount of pulverized coal fed into the furnace, in kg / s; The inertial time of the coal mill is in seconds; The powder-making delay time is in seconds. The order of the derivative; The fractional differential expression for the variable; S22. Boiler steam-water system modeling: Based on the first law of thermodynamics, the lumped parameter method is used to treat the boiler steam-water system as a heated pipe of equal volume, and the mass conservation and energy conservation equations are established. ; ; in, , These are dynamic parameters; The density of the steam at the outlet of the steam-water separator is kg / m³. 3 ; Enthalpy of steam at the outlet of the steam-water separator, kJ / kg; The water supply flow rate is expressed in kg / s. The enthalpy of the feedwater is expressed in kJ / kg. The superheater outlet steam flow rate is kg / s; The enthalpy of the superheater outlet steam is expressed in kJ / kg. The average specific heat capacity of the heated section is kJ / (kg·K). The mass of the heated section metal is expressed in kg. The temperature of the heated section metal, in K; The heat absorbed by a unit of pulverized coal combustion working fluid, in kJ / kg; The order of the derivative; S23. Steam turbine power generation system modeling: Constructing the expression for the actual power generation of the steam turbine; ; in, For turbine gain; Main steam flow rate; The main steam enthalpy value; S24. Model Simplification: Simplify the expression in step S23 to obtain the fractional-order nonlinear model expression of the coordinated control system. Let... ; ; ; ; ; ; ; ; in, Let be the inertial constant of the coal mill; , , , These are the dynamic parameters to be identified; , , The order of the fraction to be identified.

[0007] Through the above technical solution, steps S21-S24 integrate fractional differential theory into the laws of thermodynamics. By introducing fractional differentials, the hysteresis of the pulverizing process in the coordinated control system, the strong coupling and nonlinearity of the boiler steam-water intermediate point pressure / enthalpy value with other variables are accurately described, and the expression of the fractional differential equation of the coordinated control system of ultra-supercritical coal-fired power units is constructed.

[0008] Optionally, in step S24, the fractional-order state-space standard form of the unit is: ; ; ; ; ; ; ; ; ; ; in, For fractional operators, U is the input variable, including , , X is a state variable, including , , Y is the output variable, including , , ; The fractional derivative order of the state variable, including , , A, B, C, and D are the coefficient matrices of the state equations.

[0009] Through the above technical solution, step S24 organizes the complex fractional differential equations into standard fractional nonlinear state-space expressions, integrates system dynamic information through state variables, simplifies complex nonlinear coupling relationships into matrix equations, provides clear mathematical tools for multivariable decoupling of the system, and facilitates controller design.

[0010] Optionally, step S3 specifically includes the following: S31. Divide the unit data into segments based on 10% of the rated power and calculate the static parameters for each segment; S32. Fit the function to be determined using a nonlinear regression method; S33. Establish a Matlab / Simulink model based on the state equation, and set the initial state of the state variables and input variables in segments as the minimum value of each segment. S34. The number of identification parameters is D in the particle swarm dimension. After assigning D random values ​​to the identification parameters, run 8 parameters at the same time and calculate the fitness function with state variables and output variables. S35. Individual particles in the swarm update their position and velocity by comparing the global optimum and the local optimum, and dynamically adjust the algorithm parameters according to the convergence situation to iteratively obtain the optimal solution.

[0011] Through the above technical solution, steps S31-S35 adopt a data-driven approach combined with a Simulink model method to process data in segments for wide-load operation of the unit. By fitting the substitution function through a large dataset, a method for identifying fitness values ​​based on the adaptive particle swarm algorithm for multi-segment collaborative time-sharing calculation is proposed. This achieves efficient and accurate identification of static parameters, dynamic parameters, fractional order, and substitution function in fractional nonlinear state equations across the entire operating range.

[0012] Optionally, step S31 specifically includes the following: After segmenting the unit's power generation capacity, the average value of the segmented static parameters is used as the approximate steady-state value to solve for the static parameters. The unit's static parameters are then calculated using the following formula: , , : ; ; ; The parameters marked with an asterisk (*) are approximate steady-state parameters.

[0013] Through the above technical solution, step S31 solves the static parameters of each segment in segments, avoiding the defect that a single parameter is difficult to adapt to the static characteristics within a wide load range. It solves the problem of large deviations in the model in low or high load areas, improves the model accuracy under wide loads, and is especially suitable for the precise control requirements of wide load scenarios under deep peak shaving of coal-fired units.

[0014] Optionally, step S32 specifically includes the following: The nonlinear regression method is used to find the function. , and The fitting results are as follows: ; ; .

[0015] Through the above technical solution, step S32 resolves the contradiction between the difficulty in solving the mechanism model and its accurate application by data fitting. While retaining the physical framework of the mechanism model, it accurately matches the actual operating characteristics of the unit, simplifies the variable relationships, and simplifies the system model by solving the substitution function in the expression of the coordinated control system through data-driven solution.

[0016] Optionally, step S34 specifically includes the following: defining the fitness function as the sum of squares of the relative errors of the variables, as shown in the following formula: ; The weights are set as follows: ; The formula for calculating the relative error between the state variable and the output variable is: ; vector Indicates the variable to be calculated. The difference between the output value of the j-th parameter and the approximate steady-state value. The relative error of the j-th parameter in segment q; In the above formula, At that time, Fitness value at any point in the simulation cycle; At this time, the simulation cycle ends. Fitness value; the fitness values ​​at two time points are multiplied by weight coefficients, and then a weighted sum is taken to obtain the final fitness value: .

[0017] Through the above technical solution, step S34 focuses on the accuracy of key parameters by setting weights, and optimizes the target identification in two time periods. The short time period captures the impact of parameters on the system's fast response characteristics, while the long time period strengthens the constraint on steady-state accuracy. This ensures both the speed and stability of the system, and realizes the dynamic unknown parameters in the fractional-order state-space expression. , , , , , And the fractional order to be identified is optimized collaboratively.

[0018] After adopting the above technical solution, the beneficial effects of the present invention are: This invention performs fractional-order modeling of the coordinated control system of an ultra-supercritical coal-fired power unit, obtaining a fractional-order model of the coordinated control system. The model is then identified using a piecewise time-sharing adaptive particle swarm optimization algorithm, and the optimal model parameters are obtained through iterative calculation. This enables dynamic description under wide load conditions, greatly improving the accuracy of the system model and facilitating the implementation of control strategies based on the system model.

[0019] The fractional order model in this invention introduces fractional order. It can more accurately describe the dynamic characteristics of the system, especially the nonlinear and time-varying characteristics exhibited under complex operating conditions. By introducing fractional calculus theory, the established unit coordinated control model has greater flexibility and adaptability. At the same time, combined with the piecewise time-sharing adaptive particle swarm optimization algorithm, the identification accuracy of the unit over a wide load range is improved, effectively enhancing the response speed and stability of the control system, and providing strong support for the optimized operation of the coal-fired unit coordinated control system.

[0020] This invention addresses the large inertia and hysteresis characteristics of coal-fired power plant pulverizing and boiler systems by employing fractional-order differentials to more accurately describe the dynamic time-varying characteristics of key parameters in the system, leveraging the historical dependence of variables and the continuity of their order. This significantly reduces the average relative error of system variables and improves the model's accuracy under wide-load operation. When applied to control systems, this model can effectively improve dynamic control accuracy, suppress fluctuations in key parameters, reduce energy and coal consumption in coal-fired power plants, enhance economic efficiency, extend equipment lifespan, and further improve the unit's flexible peak-shaving capabilities and operational safety. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 A schematic diagram of a coal-fired power unit coordinated control system provided in an embodiment of this application; Figure 2 A schematic diagram of the coal-fired power unit coordinated control system identification method provided in the embodiments of this application; Figure 3 A comparison chart of the average relative error of the system before and after using the time-segmented identification method; Figure 4 A comparison chart of the relative errors of different models for main steam pressure; Figure 5 A comparison chart of the relative errors of different models based on the enthalpy values ​​at the midpoint of the model; Figure 6 A comparison chart of the relative errors of different power generation models; Figure 7 Input variable step response plots for different system models; Figure 8 A comparison chart of main steam pressures for different models; Figure 9 A comparison chart of enthalpy values ​​at midpoints for different models; Figure 10 A comparison chart of the actual power generation of different models. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] This application discloses a fractional-order model and identification method for the coordinated control system of ultra-supercritical coal-fired power units, such as... Figures 1-10 .

[0025] Example I. Fractional-order model of coordinated control system for ultra-supercritical coal-fired power units Ultra-supercritical coal-fired power generation technology, characterized by low carbon emissions, high efficiency, and cleanliness, has become the mainstream of thermal power generation in recent years. This invention analyzes a 660MW ultra-supercritical coal-fired unit in Xinjiang, focusing on the coordinated control system. A fractional-order nonlinear state-space model is established to further explore its dynamic characteristics. The unit's boiler is a variable-pressure Π-type once-through boiler, and the turbine is a single-stage intermediate reheat indirect air-cooled unit. The boiler-turbine coordinated control system and the specific structure of the unit are as follows: Figure 1 As shown.

[0026] Figure 1In this unit, the boiler is a variable-pressure Π-type once-through boiler, and the turbine is a single-stage intermediate reheat indirect air-cooled unit. The boiler-turbine coordinated control system is the core device. Grid load commands are sent from the dispatch control center to the unit's remote control system. Under boiler-turbine coordinated control, the AGC command, after amplitude limiting, rate limiting, and increase / decrease interlocking functions, forms a load command. The boiler-turbine coordinated control system receives and processes this command to control the load changes of each unit. After receiving the processed load command, the boiler-turbine coordinated control system, in conjunction with sensors, transmits the steam-water separator outlet pressure p. m Temperature T m Main steam pressure p st Power generation N e Through control system optimization, boiler and turbine commands are sent to the corresponding basic control units to act on the coal feed u. B Air supply u V and water supply FW The flow valve simultaneously controls the opening degree u of the main steam valve. t .

[0027] The grid load command is sent from the dispatch control center to the unit's remote control unit (RTU). Under the coordinated control mode (CCS), the automatic generation control system (AGC) commands are processed through amplitude limiting, rate limiting, and increase / decrease interlocking functions to form the load command. The coordinated control system receives the decomposed commands and performs load change control on each unit. The coordinated control unit (OTB) is the core of the coordinated control system and is usually simplified to a three-input, three-output control structure. The input variable is the coal combustion command. Water supply flow rate Main steam valve control The main output variable is steam pressure. Enthalpy at the outlet of the steam-water separator and generator power There are complex coupling relationships between input and output variables. The strong multivariate coupling and nonlinear characteristics of the coordination system place high demands on the model accuracy and stable operation of the unit. In order to improve the accuracy of the coordination system, this invention proposes a fractional-order nonlinear model for the unit's coordination control system.

[0028] The fractional-order model includes a pulverizing system, a boiler steam-water system, and a steam turbine power generation system. The pulverizing system is the process of grinding raw coal into pulverized coal through a coal mill and then conveying it into the furnace. The boiler steam-water system heats the feedwater to release steam through combustion in the boiler. The high-temperature steam expands in the steam turbine and does work, converting mechanical energy into electrical energy.

[0029] II. Fractional-order model and identification method of coordinated control system for ultra-supercritical coal-fired power units, including the following steps: (I) Modeling of the Pulverizing System: After receiving the coal feeding command, the pulverizing system of the coal-fired unit transports the raw coal to the coal mill for grinding by the coal feeder. After preheating with primary air, the pulverized coal is sent to the furnace for combustion. This process is mainly characterized by large delay and large inertia. Therefore, the dynamic characteristics of the pulverizing system are represented as follows: ; in, Fuel quantity directive, kg / s; The amount of pulverized coal fed into the furnace, in kg / s; The inertial time of the coal mill is in seconds; The powder-making delay time is in seconds. The order of the derivative; The fractional differential expression for the variable.

[0030] (II) Boiler steam-water system modeling: (1) The ultra-supercritical unit boiler is a once-through boiler. The boiler steam-water system includes water-cooled walls, steam-water separators, superheaters, economizers, spray desuperheaters, etc. In order to simplify the modeling process, the lumped parameter method is adopted to regard the above parts as a heating pipe of equal volume. Only the relationship between feedwater flow rate and superheater outlet steam flow rate is considered, and the mass and energy conservation equations are established: ; in, , These are dynamic parameters; The density of the steam at the outlet of the steam-water separator is kg / m³. 3 ; Enthalpy of steam at the outlet of the steam-water separator, kJ / kg; The water supply flow rate is expressed in kg / s. The enthalpy of the feedwater is expressed in kJ / kg. The superheater outlet steam flow rate is kg / s; The enthalpy of the superheater outlet steam is expressed in kJ / kg. The average specific heat capacity of the heated section is kJ / (kg·K). The mass of the heated section metal is expressed in kg. The temperature of the heated section metal, in K; The heat absorbed by a unit of pulverized coal combustion working fluid, in kJ / kg; The order of the derivative.

[0031] (2) The flow rate of the main steam is closely related to the pressure, density, and opening degree of the main steam valve. Since the density of the main steam is difficult to measure, measurable parameters such as pressure and enthalpy are used as substitutes, and the function to be determined is used. and Indicate their relationship: ; ; in, Main steam flow rate, kg / s; The main steam enthalpy, kJ / kg; Main steam valve opening, % Main steam pressure, MPa.

[0032] (3) The pressure loss caused by the superheater pipes can be expressed by differential pressure, which can be regarded as the steam pressure of the steam-water separator. The independent variable function: ; in, Main steam pressure, MPa.

[0033] (4) The mass and energy balance equation of the water spray desuperheater is: ; ; in, The superheater outlet steam flow rate is kg / s; The equivalent total flow rate of desuperheating water is expressed in kg / s. Main steam flow rate, kg / s; The enthalpy of the superheater outlet steam is expressed in kJ / kg. The enthalpy of the feedwater is expressed in kJ / kg. The value is the enthalpy of the main steam, kJ / kg.

[0034] (III) Steam Turbine Power Generation System Modeling: Ignoring working fluid mass loss, energy loss, and feedwater variations, the actual power generation of the steam turbine is simplified to the following formula: ; in, For turbine gain; Main steam flow rate; The main steam enthalpy value.

[0035] (iv) Simplification of nonlinear fractional differential equations for the coordinated control system of coal-fired power units: (1) Since the density of the steam at the outlet of the steam-water separator cannot be measured online, the partial derivative of the above equation is taken, and let... Simplifying the above formulas, we obtain the simplest nonlinear model for ultra-supercritical units: ; in, Let be the inertial constant of the coal mill; , , , These are the dynamic parameters to be identified; , , The order of the fraction to be identified.

[0036] (2) In order to further explore the nonlinear design of the controller, the above equation is rewritten in fractional state-space form, and the fuel command is taken. Water supply flow rate and the opening degree of the main steam valve For input variables, the main steam pressure Enthalpy at midpoint Steam turbine power The amount of pulverized coal entering the furnace is the output variable. Midpoint pressure and the enthalpy at the midpoint It is a state variable.

[0037] This state equation introduces fractional-order operators. Where α is limited to real numbers and t is the independent variable. The lower bound of this variable is defined as: ; Where α>0, the operator represents the independent variable. The α-order derivative, where α=0 represents the original signal and α<0 represents the -α-order integral.

[0038] The fractional-order state-space standard form of this unit is: ; in, ; ; ; ; ; ; ; ; in, For fractional operators, U is the input variable, including , , X is a state variable, including , , Y is the output variable, including , , ; The fractional derivative order of the state variable, including , , A, B, C, and D are the coefficient matrices of the state equations; The heat absorbed by a unit of pulverized coal combustion working fluid is expressed in kJ / kg.

[0039] III. Parameter identification of the fractional-order model of the coordinated control system of coal-fired power units includes static parameter identification, function to be determined, and dynamic parameter identification.

[0040] The unit selected monthly operating data of a 660MW ultra-supercritical coal-fired power unit with a sampling time of 5 minutes. It is necessary to identify its static parameters, dynamic parameters, fractional order, and unknown functions.

[0041] (1) Identification of static parameters and the function to be found The unit data is segmented according to 10% of the rated power. The average value of the calculated parameters for each segment is used as the dataset for solving the static parameters from the approximate steady-state values. The static parameters of the unit are then calculated as l, k0, and k1. The calculation formula is as follows: ; The parameters marked with an asterisk (*) are approximate steady-state parameters.

[0042] In the formula This refers to the above. In . It refers to In . It refers to In .

[0043] Will Defined as the ratio of the enthalpy of steam at the superheater outlet to the enthalpy of steam at the steam-water separator outlet, this value is determined by the proportion of heat absorbed by the flue gas by the water-cooled walls and the superheater, and is largely unaffected by unit load variations. Parameter Due to the influence of coal composition and boiler thermal efficiency, the static parameters exhibit a non-strict proportional relationship with load changes. Their values ​​are calculated using segmented datasets. Table 1 shows the statistical values ​​of static parameters under different operating conditions. Table 1. Segmented Data Table of Static Parameters for Coal-fired Units The function to be found is fitted using a nonlinear regression method. , and The fitting results are as follows: ; (2) Dynamic parameter identification The Adaptive Particle Swarm Optimization (APSO) algorithm is used to identify dynamic parameters. In the established Matlab / Simulink model, the initial state and input variables are set segment by segment, with each segment's initial state being the minimum value. The number of identification parameters is equal to the particle swarm dimension D. The APSO algorithm assigns D random values ​​to the identification parameters and simultaneously runs the algorithm on eight segments. The fitness function is calculated using the state and output variables. Individual particles update their position and velocity by comparing global and local optima, and the algorithm parameters are dynamically adjusted based on convergence to achieve faster and better convergence to the optimal solution. The specific identification approach is as follows: Figure 2 As shown.

[0044] Figure 2 The approach is a segmented, time-based adaptive particle swarm identification method to identify dynamic parameters. , , , , , In particle swarm optimization, a Simulink unit model is run simultaneously using eight static parameters, and... , The sum of fitness values ​​is calculated, and the minimum fitness value is obtained through adaptive iteration to obtain the optimal identification parameters.

[0045] The fitness function is defined as the sum of squares of the relative errors of the variables, as shown in the following formula: ; Weights set to ; The formula for calculating the relative error between the state variable and the output variable is: ; Where, vector Indicates the variable to be calculated; The difference between the output value of the j-th parameter and the approximate steady-state value; Let be the relative error of the j-th parameter in segment q. At that time, Fitness value at any point in the simulation cycle; At this time, the simulation cycle ends. Fitness value; the fitness values ​​at two time points are multiplied by weight coefficients, and then a weighted sum is taken to obtain the final fitness value: .

[0046] Fractional state equations can be divided into three cases according to their order: The state equations are of integer order; fractional order in the same variable. Non-same degree fractional order Three scenarios were identified, and the identification results were represented by the fitness value fv. The parameter identification results are shown in Table 2. Table 2 Dynamic parameter identification results IV. Model Validation 1. Steady-state characteristic analysis Steady-state error is the degree of deviation between the system's output in a simulated steady-state state and the actual operating output of the unit. In this invention, the coal-fired unit operates with identified static and dynamic parameters. After the operation stabilizes, the steady-state relative error is calculated to evaluate the system's steady-state error.

[0047] (1) Comparison of piecewise time-sharing steady-state errors of integer order The parameter identification fitness function designed in this invention embodies the idea of ​​piecewise time-sharing synthesis. Taking integer order as an example, let's compare the steady-state error of the data before and after the time segment: After identification using the adaptive particle swarm optimization algorithm with the same parameters, the system parameters are as follows: , , , , , The fitness function here is the sum of squares of the relative errors of each variable. The dynamic parameters of the system after segmented and time-division identification are shown in Table 1 above. The steady-state error is calculated after stable operation.

[0048] Using approximate steady-state parameters from eight time periods as baseline data, the three output variables are: main steam pressure. Enthalpy value at the outlet of the steam-water separator and output power The average relative error of the output variables is calculated as shown in the table below. The results show that the steady-state error of the system before and after time-segmentation is smaller than that before the improvement. Running the 8-power segmented parameters, the steady-state error of the output variables in each segment (solid diamond line) is generally smaller than the steady-state error before time-segmentation (dashed square line), as detailed below. Figure 3 As shown, the fitness function can improve the accuracy of the unit model by considering the time-sharing and segmented cumulative error.

[0049] Table 3 Comparison of Average Relative Errors (2) Comparison of steady-state errors of different models Using the identification results of integer order, fractional order with the same degree, and fractional order with different degrees, the relative error of each segment of the output variable is compared during steady-state operation of the above three models, specifically as follows: Figures 4-6 As shown.

[0050] Analysis of the relative error of the output variable shows that the time-segmented and segmented relative error covers the unit's 20%Pe~100%Pe load range relatively small and evenly. This identification method improves the model accuracy for coal-fired unit operation under wide load ranges. Comparing the steady-state error of the output variable of different models, the results show that the errors of the fractional-order and integer-order models of the same order are basically the same. The output error of the non-fractional-order model under 20%Pe~100%Pe loads is smaller than the former two, especially at low load operation, where the relative error is less than 1%. The output variable N e The steady-state error is very ideal. It is evident that the time-sharing and segmented identification approach and the non-same-element fractional-order model proposed in this invention have significant advantages in model accuracy under wide-load steady-state operation of coal-fired power units.

[0051] 2. Dynamic characteristic analysis (1) Open-loop verification analysis To further analyze the dynamic characteristics of the unit under different models, the steady-state power generation of the unit was selected. Analyze input variables , , The dynamic curve under a +10% step disturbance is compared with the characteristic curves of integer order, fractional order of the same degree, and fractional order of different degrees under the open-loop step response, as shown in the figure. Figure 7 As shown.

[0052] Fuel command +10% step response: When the coal feed command increases, the unit will experience a delay within minutes. The actual unit delay time depends on the time spent on coal feeding and grinding. The delay time of the established model is determined by the identified dynamic parameters. The constraint range of this parameter is determined by the actual unit. During time-sharing particle swarm identification, to improve rapid response (i.e., to reduce the difference between 1 / 10 of the cycle and T), this parameter will be identified as the minimum value of the constraint range. As the coal feed rate increases, the amount of steam generated increases, and the pressure at the intermediate point... Increased steam pressure inside the boiler leads to increased main steam pressure, thus increasing the turbine's power generation capacity. Increase. Enthalpy at the midpoint. The increase is due to the influence of temperature and pressure at the outlet of the steam-water separator.

[0053] Step response of +10% feedwater flow: Increasing the feedwater flow causes the water level inside the steam-water separator to rise, increasing the steam flow and the pressure at the steam-water separator outlet. Slightly increase, main steam pressure A slight increase in feedwater will decrease the enthalpy of the steam, and thus the enthalpy at the steam-water separator outlet. It will decrease slightly, and the steam turbine power generation capacity will be reduced. It will increase due to a slight increase in the main steam pressure.

[0054] Step response of main steam valve +10%: When the main steam valve is opened, the main steam pressure will increase rapidly, the enthalpy at the midpoint will suddenly decrease due to the release of stored heat, and then return to a stable state. The power generation of the steam turbine will increase rapidly, but the coal feed rate and water feed rate will remain unchanged and gradually return to their initial values.

[0055] In summary, the open-loop dynamic response of the three unit coordinated control system models is consistent with the actual unit operation trend, indicating that the established models have the correct physical structure.

[0056] The coordinated control model studied in this invention uses a fractional-order model to more accurately describe the dynamic characteristics of the system in terms of dynamic open-loop characteristics. The fractional-order model has advantages while simplifying the model.

[0057] (2) Comparison of dynamic operating errors Typical daily data with a wide operating range of unit power generation, including both stable and fluctuating sections, is selected, as shown in the figure below. The operating curves of the integer-order, fractional-order, and fractional-order coordinated control systems are compared with the actual operating curves of the unit, and the root mean square error (RMSE) is calculated. ; In the formula, m is the number of data points, and y i For model simulation data, y data This is the actual operating data of the unit.

[0058] Table 4. Root Mean Square Error Data of Output Variables for Different Models From the above Figures 4-10 Analyzing Tables 3 and 4, it can be seen that, from the perspective of unit power generation... Main steam pressure and the enthalpy at the midpoint The simulation results analysis of three models—integer order, fractional order with the same degree, and fractional order with different degrees—shows that the root mean square error of the fractional order model with different degrees is the smallest.

[0059] In summary, the non-fractional order coordinated control system model proposed in this invention improves both steady-state and dynamic characteristics over a wide load operating range. Compared to the integer order model, the output variable p of the model proposed in this invention... st The average steady-state relative error decreased from 3.08% to 0.94%, h m The average steady-state relative error decreased from 2.5% to 1.37%, N e The average steady-state relative error decreased from 2.51% to 0.53%; the output variable p st The dynamic root mean square error decreased from 82.3 MPa to 33.9 MPa.m The dynamic root mean square error decreased from 1.35 kJ / kg to 0.97 kJ / kg, N e The dynamic root mean square error of operation decreased from 21.78 MW to 16.91 MW.

[0060] Fractional order models can better fit different types of generator units by changing their order, and have high modeling universality. The order of the fractional order of the response variable determines the speed of the variable's response to dynamics.

[0061] This invention establishes a fractional-order model of a coal-fired power unit coordinated control system, identifies dynamic parameters and fractional-order orders by combining data-driven methods, and compares the static and dynamic errors of integer-order, same-order fractional-order, and non-same-order fractional-order coordinated control system models.

[0062] This invention takes the coordinated control system of a 660MW ultra-supercritical coal-fired power unit as the research object, proposes a piecewise time-sharing objective function identification method, establishes a fractional-order nonlinear model, and improves the steady-state and dynamic accuracy of the model under wide load conditions. Results show that the fractional-order coordinated control system model has significant advantages in both static / dynamic accuracy and dynamic characteristics during wide load operation of the unit, meeting the precise control requirements of wide load scenarios under deep peak shaving of coal-fired power units.

[0063] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the technical solution of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for constructing and identifying a fractional-order model of a coordinated control system for ultra-supercritical coal-fired power units, characterized in that, Includes the following steps: S1. Collect and save DCS data of the ultra-supercritical coal-fired power unit's coordinated control system. S2. Construct a fractional-order model of the coordinated control system; S3. By collecting DCS data from coal-fired power units and fitting the function to be determined, the dynamic parameters and order of the fractional-order model are identified offline using a piecewise time-sharing adaptive particle swarm optimization method.

2. The fractional-order model construction and identification method for the coordinated control system of ultra-supercritical coal-fired power units according to claim 1, characterized in that, Step S2 specifically includes the following: S21. Modeling of the pulverizing system: Construct fractional-order dynamic characteristic expressions for the pulverizing system based on its first-order inertial delay characteristics. ； in, Fuel quantity directive, kg / s; The amount of pulverized coal fed into the furnace, in kg / s; The inertial time of the coal mill is in seconds; The powder-making delay time is in seconds. The order of the derivative; The fractional differential expression for the variable; S22. Boiler steam-water system modeling: Based on the first law of thermodynamics, the lumped parameter method is used to treat the boiler steam-water system as a heated pipe of equal volume, and the mass conservation and energy conservation equations are established. ； ； in, , These are dynamic parameters; The density of the steam at the outlet of the steam-water separator is kg / m³. 3 ; Enthalpy of steam at the outlet of the steam-water separator, kJ / kg; The water supply flow rate is expressed in kg / s. The enthalpy of the feedwater is expressed in kJ / kg. The superheater outlet steam flow rate is kg / s; The enthalpy of the superheater outlet steam is expressed in kJ / kg. The average specific heat capacity of the heated section is kJ / (kg·K). The mass of the heated section metal is expressed in kg. The temperature of the heated section metal, in K; The heat absorbed by a unit of pulverized coal combustion working fluid, in kJ / kg; The order of the derivative; S23. Steam turbine power generation system modeling: Constructing the expression for the actual power generation of the steam turbine; ； in, For turbine gain; Main steam flow rate; The main steam enthalpy value; S24. Model Simplification: Simplify the expression in step S23 to obtain the fractional-order nonlinear model expression of the coordinated control system. Let... ; ； ； ； ； ； ； ； in, Let be the inertial constant of the coal mill; , , , These are the dynamic parameters to be identified; , , The order of the fraction to be identified.

3. The fractional-order model construction and identification method for the coordinated control system of ultra-supercritical coal-fired power units according to claim 2, characterized in that, In step S24, the fractional-order state-space standard form of the unit is: ； ； ； ； ； ； ； ； ； ； in, For fractional operators, U is the input variable, including , , X is a state variable, including , , Y is the output variable, including , , ; The fractional derivative order of the state variable, including , , A, B, C, and D are the coefficient matrices of the state equations.

4. The fractional-order model construction and identification method for the coordinated control system of ultra-supercritical coal-fired power units according to claim 1, characterized in that, Step S3 specifically includes the following: S31. Divide the unit data into segments based on 10% of the rated power and calculate the static parameters for each segment; S32. Fit the function to be determined using a nonlinear regression method; S33. Establish a Matlab / Simulink model based on the state equation, and set the initial state of the state variables and input variables in segments as the minimum value of each segment. S34. The number of identification parameters is D in the particle swarm dimension. After assigning D random values ​​to the identification parameters, run 8 parameters at the same time and calculate the fitness function with state variables and output variables. S35. Individual particles in the swarm update their position and velocity by comparing the global optimum and the local optimum, and dynamically adjust the algorithm parameters according to the convergence situation to iteratively obtain the optimal solution.

5. The fractional-order model construction and identification method for the coordinated control system of ultra-supercritical coal-fired power units according to claim 4, characterized in that, Step S31 specifically includes the following: After segmenting the unit's power generation capacity, the average value of the segmented static parameters is used as the approximate steady-state value to solve for the static parameters. The unit's static parameters are then calculated using the following formula: , , : ； ； ； The parameters marked with an asterisk (*) are approximate steady-state parameters.

6. The fractional-order model construction and identification method for the coordinated control system of ultra-supercritical coal-fired power units according to claim 4, characterized in that, Step S32 specifically includes the following: The nonlinear regression method is used to find the function. , and The fitting results are as follows: ； ； 。 7. The fractional-order model construction and identification method for the coordinated control system of ultra-supercritical coal-fired power units according to claim 4, characterized in that, Step S34 specifically includes the following: Define the fitness function as the sum of squares of the relative errors of the variables, as shown in the following formula: ； The weights are set as follows: ; The formula for calculating the relative error between the state variable and the output variable is: ； vector Indicates the variable to be calculated. The difference between the output value of the j-th parameter and the approximate steady-state value. The relative error of the j-th parameter in segment q; In the above formula, At that time, Fitness value at any point in the simulation cycle; At this time, the simulation cycle ends. Fitness value; the fitness values ​​at two time points are multiplied by weight coefficients, and then a weighted sum is taken to obtain the final fitness value: 。

Images