CN112682254B - Draught fan active power tracking method based on dynamic multi-model predictive controller - Google Patents
Draught fan active power tracking method based on dynamic multi-model predictive controller Download PDFInfo
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Abstract
The present disclosure provides a fan active power tracking method based on a dynamic multi-model predictive controller, the method includes: establishing each nonlinear model of the fan, and linearizing and discretizing each nonlinear model at each working condition point respectively to obtain a linear multi-working-condition multi-model of the fan; building a model predictive controller according to the linear multi-working-condition multi-model of the fan; updating and correcting parameters of the model in the model predictive controller according to the actual running state of the fan, and building a dynamic multi-model predictive controller; and verifying the effectiveness of the dynamic multi-model predictive controller on the active power tracking of the fan based on an actual experiment platform or high-fidelity simulation software. The method improves the defects of the traditional active power tracking strategy of the fan, and suppresses the fluctuation of the output power tracking of the fan based on the dynamic multi-model predictive controller, thereby improving the economic performance of the fan.
Description
Technical Field
The disclosure belongs to the technical field of active power tracking control of fans, and particularly relates to a fan active power tracking method based on a dynamic multi-model predictive controller.
Background
Because the energy output by the wind driven generator comes from the wind in the environment, the wind in the environment is difficult to be accurately predicted, and the conditions of turbulence and rapid change can occur, the output power of the fan is easy to fluctuate, the power of the fan is difficult to accurately control, the economic operation of the fan is influenced, the frequency of a power grid is also influenced, and great challenges are caused to the operation of the fan and the power grid.
Therefore, it is necessary to find effective means for improving the power tracking capability of the wind turbine, reducing the fluctuation of power, and improving the wind energy output quality. The existing technical means comprise a traditional PI control strategy, a gain scheduling PI control strategy, a traditional model prediction control strategy and the like. When the PI control strategy is mainly above the rated wind speed, the PI controller is used for adjusting the pitch angle to keep the rotating speed of the generator at the rated rotating speed, and the electromagnetic torque controller is matched with the rotating speed of the generator to realize power tracking of the rated power; the gain scheduling PI control strategy is used for solving the problem that the sensitivity of the output power of the generator to the pitch angle is different under different wind speeds, so that the PI controller is subjected to gain compensation and scheduling based on the sensitivity; according to the traditional model prediction control strategy, real-time optimization control can be carried out on the basis of a fan model to meet the output requirement of power, but the relation between the control accuracy and precision and the accuracy of the model is large, meanwhile, because the states of the fans are in a coupling relation, and the influence of input wind speed is large, the model is difficult to accurately establish, and if the difference of the model is larger than that of an actual model, the power of the fan cannot meet the control requirement.
Disclosure of Invention
The present disclosure is directed to solve at least one of the technical problems in the prior art, and provides a wind turbine active power tracking method based on a dynamic multi-model predictive controller.
In one aspect of the present disclosure, a wind turbine active power tracking method based on a dynamic multi-model predictive controller is provided, the method includes:
establishing each nonlinear model of the fan, and linearizing and discretizing each nonlinear model at each working condition point respectively to obtain a linear multi-working-condition multi-model of the fan;
building a model predictive controller according to the linear multi-working-condition multi-model of the fan;
updating and correcting parameters of the model in the model predictive controller according to the actual running state of the fan, and building a dynamic multi-model predictive controller;
and verifying the effectiveness of the dynamic multi-model predictive controller on the active power tracking of the fan based on an actual experiment platform or high-fidelity simulation software.
In some optional embodiments, the establishing each non-linear model of the wind turbine, and linearizing and discretizing each non-linear model at each operating point, respectively, to obtain a linear multi-operating-condition multi-model of the wind turbine includes:
establishing each nonlinear model of the fan based on a mechanism theory of the fan, wherein each nonlinear model of the fan comprises a nonlinear pneumatic model, a nonlinear transmission model, a nonlinear generator model and a nonlinear servo mechanism model;
establishing a plurality of small signal linear models by using Taylor expansion according to the dynamic characteristics of the fan under each wind condition, and establishing an expression among the small signal continuous states of the fan according to the small signal linear models;
discretizing the small-signal continuous state space expression to obtain a linear multi-working-condition multi-model of the fan.
In some optional embodiments, each non-linear model of the wind turbine is as follows:
for the pneumatic system of the fan:
according to aerodynamic theory, the capture of aerodynamic torque by a fan rotor can be expressed as the following relation (1):
where ρ is the air density, R is the rotor radius, v is the average wind speed of the wind flowing through the rotor, C P (λ, β) is the aerodynamic power coefficient, β is the actual pitch angle, λ is the tip speed ratio, which can be expressed as ω r R/v，ω r Is the rotor speed, C P The following relation (2) can be written using empirical formulas:
wherein λ is * Introducing an intermediate variable for fitting the wind energy utilization coefficient for simplifying the expression of the formula (2);
for the drive train of the fan:
assuming that a high-speed shaft and a low-speed shaft of the fan are flexible shafts, establishing a double-mass model of the transmission system, and obtaining a dynamic equation of the transmission system as the following relational expression (3):
wherein, J r And J g The rotational inertia of the rotor and the generator, N is the gear ratio of the gear box, K s For the stiffness of the intermediate shaft, B s Damping coefficient of intermediate shaft, T g For generator electromagnetic torque, T s For intermediate shaft torque, ω g The rotating speed of the generator is shown, and phi is the torsion angle of the rotating shaft;
for the servomechanism of the fan:
the pitch system is a nonlinear servo mechanism, and can be equivalent to a second-order system with a limiting and a speed-limiting link, and the following relation (4) is provided:
wherein beta is * Is the pitch angle reference, typically the output of the pitch controller; omega n The natural angular frequency of the pitch actuator is shown, and xi is the damping coefficient of the pitch actuator;
for a generator of a wind turbine:
neglecting the non-important converter model, regarding the generator as a torque source, the generator can be equivalent to a first-order inertia link, and the dynamic equation can be expressed as the following relation (5):
wherein, T * Is an electromagnetic torque reference value, typically the output of an electromagnetic torque controller; tau is g Is the first-order inertia time constant of the electromagnetic torque, eta is the generator efficiency, P g Outputting power for the generator.
In some optional embodiments, the nonlinear dynamical equation in the wind turbine is linearized with a small signal at the operating point by using taylor expansion, and a small signal linear model is obtained, which is expressed by the following relation (6):
and establishing a small signal continuous state space expression of the fan according to the relational expression (6), wherein the small signal continuous state space expression is represented by the following relational expression (7):
wherein the content of the first and second substances,
u＝[δT * ,δβ * ,δv] T ，y＝[δP g ] T ；
C＝[0 0 0 0 η 1]D＝[0 0 0]；
discretizing the small-signal continuous state space expression according to the following relation (8):
wherein the content of the first and second substances,
in some optional embodiments, constructing a model predictive controller according to the linear multi-condition multi-model of the wind turbine includes:
the model predictive controller is built by taking the electromagnetic torque and the pitch angle of the generator as control quantities, and comprises the following steps:
a1) determining a state variable, a control variable, an output variable and a disturbance quantity of a system according to the linear multi-working-condition multi-model, and completing the compiling of a model library program;
b1) determining parameters of a prediction controller, wherein the parameters comprise a prediction time domain, a control time domain and sampling time;
c1) determining an optimized performance index and each index weight according to the control target, and determining constraint conditions of each variable according to the range and the property of each variable;
d1) at the current moment, under the control of a future control time domain, the system state variable and the output variable of each time of the future prediction time domain are determined according to the model base;
e1) according to the system state variable and the output variable of each time of the future prediction time domain predicted in the step d1), solving the controller output with the best performance index optimization under the constraint condition by using an optimization solver;
f1) and repeating the prediction and optimization solution of the steps d1) and e1) in each step to realize the rolling optimization of the whole control process, and building the model prediction controller.
In some optional embodiments, constructing a model predictive controller according to the linear multi-condition multi-model of the wind turbine includes:
model parameter A obtained by off-line calculation under different working conditions d ,B d C, forming an off-line parameter library, specifically comprising determining a prediction time domain N p And control time domain N c Determining objective functions and constraints of predictive control, e.g.The following relational expressions (9) to (13):
s.t.0≤β 0 +δβ≤β max ； (10)
|δβ|≤Δβ max (11)
T g，min ≤T g，0 +δT g ≤T g，max (12)
|δT g |≤ΔT g,max (13)
wherein min appearing in the subscript represents the minimum value allowed by the parameter, max represents the maximum value allowed by the parameter, Δ represents the change rate of the parameter, and 0 appearing in the subscript represents the steady-state value of the parameter under the working condition;
the specific process of the operation control calculation of the model predictive controller is as follows:
a2) at the moment k, according to the working condition and the running state of the fan, taking corresponding parameters from the model parameter library to the model prediction controller for the following calculation;
b2) calculating x (k +1), x (k +2), …, x (k + N) according to the discrete linear state space expression p ) Model predicted values for states, and model predicted values for y (k +1), y (k +2), …, y (k + N) outputs;
c2) solving the target optimization problem with the constraints according to the model prediction value by using an optimization solver fmincon in Matlab to obtain u (k), u (k +1), … and u (k + N) c ) An optimized output of the controller;
d2) and using u (k) as the output value of the current controller, and returning to the step a2) to realize rolling optimization when calculating the output value of the next step, thereby ensuring that the output of each step of the controller is the value optimized according to the target.
In some optional embodiments, the updating and correcting parameters of a model in the model predictive controller according to the actual operating state of the wind turbine, and building a dynamic multi-model predictive controller include:
a3) calculating and storing the actual parameter value of the model at each moment in real time;
b3) when the norm of the model parameter value recorded in a certain working condition is continuously kept in a range for a plurality of times, replacing the corresponding parameter in the original model library by using the central value model parameter value in the range;
c3) and when a certain parameter of the model recorded under a certain working condition is continuously kept in a range for a plurality of times, replacing the corresponding parameter in the original model library by the mean value of the range.
In some optional embodiments, the updating and correcting parameters of a model in the model predictive controller according to the actual operating state of the wind turbine, and building a dynamic multi-model predictive controller include:
a4) calculating the actual parameter value of the model at the current moment each time the wind speed acquisition is completed, and recording the actual parameter value and the wind speed together to form a model parameter correction library;
b4) when the model prediction controller extracts parameters from the model parameter library, firstly extracting N in total from the current time to the previous time from the model parameter correction library according to the wind speed at the current time j Next real-time value, i.e. N j Vectors P (1), P (2), …, P (N) j ) If N is recorded j+1 The next value, the P (1) value is discarded and the next N is used j Values are covered forward;
c4) if
If | | P (i) is less than or equal to epsilon, the central value of P (i) is used as a correction value to replace the parameter of the corresponding working condition in the model parameter library;
d4) recording and processing the values p (i, j) of each model parameter for the wind speed at the current moment as in steps b4) and c4), and if a certain parameter meets the condition of being kept in a range for a plurality of times, using N j The mean of the values replaces the corresponding parameters in the original model library.
In another aspect of the present disclosure, an electronic device is provided, including:
one or more processors;
a storage unit for storing one or more programs which, when executed by the one or more processors, enable the one or more processors to implement the method according to the preceding description.
In another aspect of the disclosure, a computer-readable storage medium is provided, on which a computer program is stored, which, when being executed by a processor, is adapted to carry out the method according to the above.
The fan active power tracking method based on the dynamic multi-model predictive controller improves the defects of the traditional fan active power tracking strategy, and restrains the fluctuation of the fan output power during tracking based on the dynamic multi-model predictive controller. In addition, the problem that a single model or multiple models of a traditional model predictive controller cannot be corrected in real time with an actual model is also solved, so that the power tracking of the generator is more stable, and the economic performance of the fan is improved.
Drawings
FIG. 1 is a flowchart illustrating a method for tracking active power of a wind turbine based on a dynamic multi-model predictive controller according to an embodiment of the present disclosure;
FIG. 2 is a simulated wind velocity plot of another embodiment of the present disclosure;
FIG. 3 is a simulated power comparison graph of another embodiment of the present disclosure.
Detailed Description
For a better understanding of the technical aspects of the present disclosure, reference is made to the following detailed description taken in conjunction with the accompanying drawings.
As shown in fig. 1, a wind turbine active power tracking method S100 based on a dynamic multi-model predictive controller includes:
s110, establishing each nonlinear model of the fan, and linearizing and discretizing each nonlinear model at each working condition point to obtain a linear multi-working-condition multi-model of the fan;
s120, building a model predictive controller according to the linear multi-working-condition multi-model of the fan;
s130, updating and correcting parameters of a model in the model prediction controller according to the actual running state of the fan, and building a dynamic multi-model prediction controller;
and S140, verifying the effectiveness of the dynamic multi-model predictive controller on the active power tracking of the fan based on an actual experiment platform or high-fidelity simulation software.
The active power tracking method of the fan based on the dynamic multi-model predictive controller improves the defects of the traditional active power tracking strategy of the fan, and restrains the fluctuation of the output power of the fan during tracking based on the dynamic multi-model predictive controller. In addition, the problem that a single model or multiple models of a traditional model predictive controller cannot be corrected in real time with an actual model is also solved, so that the power tracking of the generator is more stable, and the economic performance of the fan is improved.
In some optional embodiments, step S110 specifically includes:
and establishing each nonlinear model of the fan based on a mechanism theory of the fan, wherein each nonlinear model of the fan comprises a nonlinear pneumatic model, a nonlinear transmission model, a nonlinear generator model and a nonlinear servo mechanism model.
And establishing a plurality of small signal linear models by using Taylor expansion according to the dynamic characteristics of the fan under each wind condition, and establishing an expression among the small signal continuous states of the fan according to the small signal linear models.
Discretizing the small-signal continuous state space expression to obtain a linear multi-working-condition multi-model of the fan.
In some optional embodiments, each non-linear model of the wind turbine is as follows:
for the pneumatic system of the fan:
according to the aerodynamic theory, the aerodynamic torque captured by the rotor of the wind turbine can be expressed as the following relation (1):
where ρ is the air density and R is the rotor halfDiameter, v is the average wind speed of the wind flowing through the rotor, C P (λ, β) is the aerodynamic power coefficient, β is the actual pitch angle, λ is the tip speed ratio, which can be expressed as ω r R/v，ω r Is the rotor speed, C P The following relation (2) can be written using empirical formulas:
wherein λ is * To fit intermediate variables of the wind energy utilization coefficient, the expression of equation (2) is introduced for simplicity.
For the drive train of the fan:
assuming that a high-speed shaft and a low-speed shaft of the fan are flexible shafts, establishing a double-mass model of the transmission system, and obtaining a dynamic equation of the transmission system as the following relational expression (3):
wherein, J r And J g Rotor and generator moment of inertia, N gear ratio of gear box, K s For the stiffness of the intermediate shaft, B s For mid-shaft damping coefficient, T g For generator electromagnetic torque, T s For intermediate shaft torque, ω g The rotating speed of the generator is shown, and phi is the torsional angle of the rotating shaft;
for the servomechanism of the fan:
the pitch system is a nonlinear servo mechanism, and can be equivalent to a second-order system with a limiting and a speed limiting link, and is represented by the following relation (4):
wherein, beta * Is the pitch angle reference, typically the output of the pitch controller; omega n The natural angular frequency of the pitch actuator is shown, and xi is the damping coefficient of the pitch actuator;
for a generator of a wind turbine:
neglecting the non-important converter model, regarding the generator as a torque source, the generator can be equivalent to a first-order inertia link, and the dynamic equation can be expressed as the following relation (5):
wherein, T * Is an electromagnetic torque reference value, typically the output of an electromagnetic torque controller; tau is g Is the first-order inertia time constant of the electromagnetic torque, eta is the generator efficiency, P g Outputting power for the generator.
In some optional embodiments, the nonlinear dynamical equation in the wind turbine is linearized with a small signal at the operating point by using taylor expansion, and a small signal linear model is obtained, which is expressed by the following relation (6):
and establishing a small signal continuous state space expression of the fan according to the relational expression (6), wherein the small signal continuous state space expression is represented by the following relational expression (7):
wherein the content of the first and second substances,
u＝[δT * ,δβ * ,δv] T ，y＝[δP g ] T ；
C＝[0 0 0 0 η 1]D＝[0 0 0]；
discretizing the small-signal continuous state space expression according to the following relation (8):
wherein, the first and the second end of the pipe are connected with each other,
in some optional embodiments, constructing a model predictive controller according to the linear multi-condition multi-model of the wind turbine includes:
the model predictive controller is built by taking the electromagnetic torque and the pitch angle of the generator as control quantities, and comprises the following steps:
a1) determining a state variable, a control variable, an output variable and a disturbance quantity of a system according to the linear multi-working-condition multi-model, and completing the compiling of a model library program;
b1) determining parameters of a prediction controller, wherein the parameters comprise a prediction time domain, a control time domain and sampling time;
c1) determining an optimized performance index and each index weight according to the control target, and determining constraint conditions of each variable according to the range and the property of each variable;
d1) at the current moment, under the control of a future control time domain, the system state variable and the output variable of each time of the future prediction time domain are determined according to the model base;
e1) according to the system state variable and the output variable of each time of the future prediction time domain predicted in the step d1), solving the controller output with the best performance index optimization under the constraint condition by using an optimization solver;
f1) and repeating the prediction and optimization solution of the steps d1) and e1) in each step to realize the rolling optimization of the whole control process, and building the model prediction controller.
In some optional embodiments, said building a model predictive controller according to said linear multi-regime multi-model of said wind turbine comprises:
model parameter A obtained by off-line calculation under different working conditions d ,B d C, forming an off-line parameter library, specifically including determining a prediction time domain N p And control time domain N c Determining an objective function and a constraint condition of the predictive control according to the following relations (9) to (13):
s.t.0≤β 0 +δβ≤β max ； (10)
|δβ|≤Δβ max (11)
T g，min ≤T g，0 +δT g ≤T g，max (12)
|δT g |≤ΔT g,max (13)
wherein min appearing in the subscript represents the minimum value allowed by the parameter, max represents the maximum value allowed by the parameter, Δ represents the change rate of the parameter, and 0 appearing in the subscript represents the steady-state value of the parameter under the working condition;
the specific process of the operation control calculation of the model predictive controller is as follows:
a2) at the moment k, according to the working condition and the running state of the fan, taking corresponding parameters from the model parameter library to the model prediction controller for the following calculation;
b2) calculating x (k +1), x (k +2), …, x (k + N) according to the discrete linear state space expression p ) Model predicted values for states, and model predicted values for y (k +1), y (k +2), …, y (k + N) outputs;
c2) solving the target optimization problem with the constraints according to the model prediction value by using an optimization solver fmincon in Matlab to obtain u (k), u (k +1), … and u (k + N) c ) An optimized output of the controller;
d2) and using u (k) as the output value of the current controller, and returning to the step a2) to realize rolling optimization when calculating the output value of the next step, thereby ensuring that the output of each step of the controller is the value optimized according to the target.
In some optional embodiments, the updating and correcting parameters of a model in the model predictive controller according to the actual operating state of the wind turbine, and building a dynamic multi-model predictive controller include:
a3) calculating and storing the actual parameter value of the model at each moment in real time;
b3) when the norm of the model parameter value recorded in a certain working condition is continuously kept in a range for a plurality of times, replacing the corresponding parameter in the original model library by using the central value model parameter value in the range;
c3) and when a certain parameter of the model recorded under a certain working condition is continuously kept in a range for a plurality of times, replacing the corresponding parameter in the original model library by the mean value of the range.
In some optional embodiments, the updating and correcting parameters of a model in the model predictive controller according to the actual operating state of the wind turbine, and building a dynamic multi-model predictive controller include:
a4) calculating the actual parameter value of the model at the current moment each time the wind speed acquisition is completed, and recording the actual parameter value and the wind speed together to form a model parameter correction library;
b4) when the model prediction controller extracts parameters from the model parameter library, firstly extracting N in total from the current time to the previous time from the model parameter correction library according to the wind speed at the current time j Next real-time value, i.e. N j Vectors P (1), P (2), …, P (N) j ) If N is recorded j+1 The next value, the P (1) value is discarded and the next N is used j Values are forward covered;
c4) if
If | | P (i) is less than or equal to epsilon, the central value of P (i) is used as a correction value to replace the parameter of the corresponding working condition in the model parameter library;
d4) for the wind speed at the current moment, recording and processing the values p (i, j) of each model parameter as in steps b4) and c4), and if a certain parameter meets the condition of being kept in a range for a plurality of times, using N j The mean of the values replaces the corresponding parameters in the original model library.
In some optional embodiments, step S140 may verify the effectiveness of the method provided by the present disclosure by using a FAST as a high fidelity wind turbine load simulation platform, using IEC turbulent wind with an average wind speed of 12m/S as an input, and comparing the power tracking effects of the conventional control method and the dynamic multi-model predictive controller.
Specifically, the present disclosure uses FAST for validation instructions based on field fan actual operation testing or validation using high fidelity fan simulation FAST.
The simulation input wind is IEC turbulent wind with the average wind speed of 20m/s, the simulation time is 150s, the sampling time is 0.01s, and the first 50s are removed for analysis due to the starting disturbance of the fan during starting. And compiling a program according to the first three steps, and building a dynamic multi-model predictive controller and a traditional controller for simulation comparison and verification. The simulation result is shown in fig. 2-3, fig. 2 is a simulation input wind, fig. 3 is a comparison graph of a traditional prediction control strategy, a dynamic multi-model prediction control strategy of the disclosure and an output power of a generator under a traditional PI controller, wherein the maximum absolute error of the output power of a generator controlled by the PI controller is 48.2358kW, the standard deviation is 19.1950kW, the maximum absolute error of the output power of the generator controlled by the traditional prediction controller is 14.3228kW, and the standard deviation is 5.3024kW, the maximum absolute error of the output power of the generator controlled by the dynamic multi-model prediction controller of the disclosure is 6.5659kW, and the standard deviation is 2.3849kW, and it can be seen that the method of the disclosure can effectively suppress the tracking error and fluctuation of the output power of the generator under variable working conditions of the fan.
Therefore, compared with the traditional PI control and the traditional predictive control, the dynamic multi-model-based predictive control designed by the method can track the active power more stably, and the economic performance of the fan is improved.
In another aspect of the present disclosure, an electronic device is provided, including:
one or more processors;
a storage unit for storing one or more programs which, when executed by the one or more processors, enable the one or more processors to carry out a method according to the preceding description.
In another aspect of the disclosure, a computer-readable storage medium is provided, on which a computer program is stored, which computer program, when being executed by a processor, is adapted to carry out the method according to the preamble.
The computer readable medium may be included in the apparatuses, devices, and systems of the present disclosure, or may exist separately.
The computer readable storage medium may be any tangible medium that can contain or store a program, and may be an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, more specific examples of which include, but are not limited to: an electrical connection having one or more wires, a portable computer diskette, a hard disk, an optical fiber, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof.
The computer readable storage medium may also include a propagated data signal with computer readable program code embodied therein, for example, in a non-transitory form, such as in a carrier wave or in a carrier wave, wherein the carrier wave is any suitable carrier wave or carrier wave for carrying the program code.
It will be understood that the above embodiments are merely exemplary embodiments employed to illustrate the principles of the present disclosure, and the present disclosure is not limited thereto. It will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the disclosure, and these are to be considered as the scope of the disclosure.
Claims (5)
1. A wind turbine active power tracking method based on a dynamic multi-model predictive controller is characterized by comprising the following steps:
establishing each nonlinear model of the fan, and linearizing and discretizing each nonlinear model at each working condition point respectively to obtain a linear multi-working-condition multi-model of the fan;
building a model predictive controller according to the linear multi-working-condition multi-model of the fan;
updating and correcting parameters of a model in the model prediction controller according to the actual running state of the fan, and building a dynamic multi-model prediction controller;
verifying the effectiveness of the dynamic multi-model predictive controller on active power tracking of the fan based on an actual experiment platform or high-fidelity simulation software;
the establishing of each nonlinear model of the fan, and the linearization and discretization of each nonlinear model at each working condition point respectively to obtain the linear multi-working-condition multi-model of the fan comprises the following steps:
establishing each nonlinear model of the fan based on a mechanism theory of the fan, wherein each nonlinear model of the fan comprises a nonlinear pneumatic model, a nonlinear transmission model, a nonlinear generator model and a nonlinear servo mechanism model;
establishing a plurality of small signal linear models by using Taylor expansion according to the dynamic characteristics of the fan under each wind condition, and establishing an expression among the small signal continuous states of the fan according to the small signal linear models;
discretizing the small-signal continuous state space expression to obtain a linear multi-working-condition multi-model of the fan;
the non-linear models of the fan are as follows:
for the pneumatic system of the fan:
according to aerodynamic forceTheory, the rotor of the fan captures the aerodynamic torque T r Expressed by the following relational expression (1):
where ρ is the air density, R is the rotor radius, v is the average wind speed of the wind flowing through the rotor, C P (λ, β) is the aerodynamic power coefficient, β is the actual pitch angle, λ is the tip speed ratio, denoted ω r R/v，ω r Is the rotor speed, C P The following relation (2) is written using an empirical formula:
wherein λ is * Introducing an intermediate variable for fitting the wind energy utilization coefficient for simplifying the expression of the formula (2);
for the drive train of the fan:
assuming that a high-speed shaft and a low-speed shaft of the fan are flexible shafts, establishing a double-mass model of the transmission system, and obtaining a dynamic equation of the transmission system as the following relational expression (3):
wherein, J r And J g The rotational inertia of the rotor and the generator, N is the gear ratio of the gear box, K s For the stiffness of the intermediate shaft, B s For mid-shaft damping coefficient, T g For generator electromagnetic torque, T s For intermediate shaft torque, ω g The rotating speed of the generator is shown, and phi is the torsional angle of the rotating shaft;
for the servomechanism of the fan:
the variable pitch system is a nonlinear servo mechanism, and is equivalent to a second-order system with a limiting and speed limiting link, and the second-order system is represented by the following relation (4):
wherein, beta * Is the pitch angle reference, typically the output of the pitch controller; omega n The natural angular frequency of the pitch actuator is shown, and xi is the damping coefficient of the pitch actuator;
for a generator of a wind turbine:
neglecting a non-important converter model, regarding the generator as a torque source, and equivalently forming a first-order inertia link, wherein a dynamic equation is expressed as the following relational expression (5):
wherein, T * Is an electromagnetic torque reference value, typically the output of an electromagnetic torque controller; tau. g Is the first-order inertia time constant of the electromagnetic torque, eta is the generator efficiency, P g Outputting power for the generator;
carrying out small signal linearization on a nonlinear dynamic equation in the fan at a working condition point by using Taylor expansion to obtain a small signal linear model, wherein the small signal linear model is represented by the following relational expression (6):
and establishing a small signal continuous state space expression of the fan according to the relational expression (6), wherein the small signal continuous state space expression is represented by the following relational expression (7):
wherein the content of the first and second substances,
u＝[δT * ,δβ * ,δv] T ，y＝[δP g ] T ；
C＝[0 0 0 0 η 1]D＝[0 0 0]；
discretizing the small-signal continuous state space expression according to the following relation (8):
wherein the content of the first and second substances,
the method for building a model predictive controller according to the linear multi-working-condition multi-model of the fan comprises the following steps:
model parameter A obtained by off-line calculation under different working conditions d ,B d C, forming an off-line parameter library, specifically including determining a prediction time domain N p And control time domain N c An objective function and a constraint condition of the predictive control are determined as the following relations (9) to (13):
s.t.0≤β 0 +δβ≤β max ； (10)
|δβ|≤Δβ max (11)
T g，min ≤T g，0 +δT g ≤T g，max (12)
|δT g |≤ΔT g,max (13)
wherein min appearing in the subscript represents the minimum value allowed by the parameter, max represents the maximum value allowed by the parameter, Δ represents the change rate of the parameter, and 0 appearing in the subscript represents the steady-state value of the parameter under the working condition;
the specific process of the operation control calculation of the model predictive controller is as follows:
a2) at the moment k, according to the working condition and the running state of the fan, taking corresponding parameters from the model parameter library to the model prediction controller for the following calculation;
b2) calculating x (k +1), x (k +2), …, x (k + N) according to the discrete linear state space expression p ) Model predicted values for states, and model predicted values for y (k +1), y (k +2), …, y (k + N) outputs;
c2) solving the target optimization problem with the constraints according to the model prediction value by using an optimization solver fmincon in Matlab to obtain u (k), u (k +1), … and u (k + N) c ) An optimized output of the controller;
d2) and using u (k) as the output value of the current controller, and returning to the step a2) to realize rolling optimization when calculating the output value of the next step, thereby ensuring that the output of each step of the controller is the value optimized according to the target.
2. The method according to claim 1, wherein the updating and correcting parameters of the model in the model predictive controller according to the actual operating state of the wind turbine to build a dynamic multi-model predictive controller comprises:
a3) calculating and storing the actual parameter value of the model at each moment in real time;
b3) when the norm of the model parameter value recorded in a certain working condition is continuously kept in a range for a plurality of times, replacing the corresponding parameter in the original model library by using the central value model parameter value in the range;
c3) and when a certain parameter of the model recorded under a certain working condition is continuously kept in a range for a plurality of times, replacing the corresponding parameter in the original model library by the mean value of the range.
3. The method according to claim 1 or 2, wherein the updating and correcting parameters of the model in the model predictive controller according to the actual operating state of the wind turbine to build a dynamic multi-model predictive controller comprises:
a4) calculating the actual parameter value of the model at the current moment each time the wind speed acquisition is completed, and recording the actual parameter value and the wind speed together to form a model parameter correction library;
b4) when the model prediction controller extracts parameters from the model parameter library, firstly extracting N in total from the current time to the previous time from the model parameter correction library according to the wind speed at the current time j Next real-time value, i.e. N j Vectors P (1), P (2), …, P (N) j ) If N is recorded j+1 The next value, the P (1) value is discarded and the next N is used j Values are forward covered;
c4) if
Replacing the parameters of the corresponding working conditions in the model parameter library by the central value of P (i) as a correction value;
d4) recording and processing the values p (i, j) of each model parameter for the wind speed at the current moment as in steps b4) and c4), and if a certain parameter meets the condition of being kept in a range for a plurality of times, using N j The mean of the values replaces the corresponding parameters in the original model library.
4. An electronic device, comprising:
one or more processors;
a storage unit for storing one or more programs which, when executed by the one or more processors, enable the one or more processors to carry out the method according to any one of claims 1 to 3.
5. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, is able to carry out a method according to any one of claims 1 to 3.
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