CN117494605A - Linear model construction method of floating fan for linear analysis of load of transmission chain - Google Patents
Linear model construction method of floating fan for linear analysis of load of transmission chain Download PDFInfo
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Abstract
The invention discloses a linear model construction method of a floating fan for linear analysis of driving chain load, and belongs to the technical field of wind power generation. The method comprises the following steps: the main shaft of the transmission chain is equivalent to a flexible body, and a kinematic equation of the main shaft of the transmission chain is constructed; constructing a hub-fan blade system sub-model, a floating platform-tower cone model and a mooring system sub-model of the floating fan according to a kinematic equation of a main shaft of a transmission chain; according to each sub-model, constructing a nonlinear model of the floating fan; constructing a linear model of the floating fan according to the nonlinear model of the floating fan; and carrying out parameter identification on the linear model of the floating fan. According to the invention, the main shaft is considered as a flexible body, a kinematic equation considering axial tension, compression, bending and torsion deformation of the main shaft is constructed, and a linear model of the floating fan is constructed through a gain scheduling technology, so that the linear model construction of the floating fan for linear analysis of the load of a transmission chain is realized.
Description
Technical Field
The invention relates to the technical field of wind power generation, in particular to a linear model construction method of a floating fan for linear analysis of driving chain load.
Background
Because onshore, intertidal zones and offshore wind turbine sites are gradually saturated under the support of a decarburization policy, floating offshore wind power has become a necessary trend of wind power development. Compared with the offshore fixed pile fan electricity, the deep-open sea floating fan has the advantages of high ambient wind speed, small turbulence, difficult conflict with fishing ground and airlines, complete disassembly, easy migration and the like.
The floating foundation of the floating fan increases a plurality of degrees of freedom which are not easy to control, and under the combined excitation of external excitation such as wind, waves and the like, the floating platform and the multi-subsystem coupling body of the tower, the generator, the transmission shaft and the fan blades can generate motions such as rolling, pitching, bowing, swaying and heaving, so that the mechanical load of the unit is increased. In addition, due to the low damping of the front-to-rear first order vibration modes of the drive train, a small amount of excitation may result in a strong resonant response of the drive train. In wind power operation and maintenance statistics, the failure occurrence rate of a transmission chain and a gear box thereof is extremely high, so that the service life of a unit is reduced, and particularly in extreme environments, a deep-sea floating fan is easy to have a failure which is difficult to predict. Therefore, constructing a control-oriented drive train linear model is necessary to improve fan stabilizing power-load-reducing coordinated control capability.
Disclosure of Invention
The invention aims to provide a linear model construction method and a system for a floating fan for linear analysis of a transmission chain load, so as to realize linear model construction of the floating fan for linear analysis of the transmission chain load, and improve the coordination control capability of fan stable power and load reduction.
In order to achieve the above object, the present invention provides the following solutions:
the invention provides a linear model construction method of a floating fan for linear analysis of driving chain load, which comprises the following steps:
the main shaft of the transmission chain is equivalent to a flexible body, and a kinematic equation of the main shaft of the transmission chain is constructed;
constructing a hub-fan blade system sub-model, a floating platform-tower cone model and a mooring system sub-model of the floating fan according to a kinematic equation of a main shaft of a transmission chain;
constructing a nonlinear model of the floating fan according to the hub-fan blade system sub-model, the floating platform-tower cone model and the mooring system sub-model;
constructing a linear model of the floating fan according to the nonlinear model of the floating fan;
and carrying out parameter identification on the linear model of the floating fan.
Alternatively, the kinematic equation of the drive train spindle is:
wherein K is b The rigidity matrix of the main shaft of the transmission chain is C, the damping matrix of the main shaft of the transmission chain is M c For the mass matrix of the drive chain spindle,for the force vector acting on the main shaft of the drive chain, < >>For the torque vector acting on the main shaft of the drive chain, < >>Generalized coordinate direction of main shaft of transmission chainAmount of the components.
Optionally, the hub-fan blade system submodel is:
wherein F is 1 (x, u, v) represents aerodynamic force acting on the rotor axis direction of the floating fan, x is the state vector of the floating fan, u is the controlled quantity of the floating fan, v is the wind speed input vector, C t Is a aerodynamic coefficient, is a function of tip speed ratio lambda and pitch angle beta, ρ a Is the air density, R r Represents the wind sweeping radius of the fan blade,is the wind sweeping area of the fan blade, and is->Is an equivalent wind speed vector perpendicular to the wind sweeping surface and represents the corrected wind speed projected between the floating fan and the main shaft plane, T 1 (x, u, v) is the aerodynamic torque acting on the rotor, R (θ) represents the change matrix between world and body coordinates, +.>Is a direction distance vector which points from the gravity center of the floating fan to the action center point of various types of forces, N GR Is the transmission ratio of a gear box, T g Is generator torque>Is the z-axis unit vector in the principal axis coordinate system, R t Is a conversion matrix between the fan blade wind sweeping surface and the world coordinate system,/for>Is the force vector acting on the spindle, +.>Is the torque vector acting on the spindle.
Optionally, the floating platform-tower bobbin model is:
F 3,i (x,w)＝F 3t,i (x,w)+F 3h,i (x,w)；
wherein F is 2 (x) Is the resultant force of buoyancy and gravity applied to the floating platform, F 2,i (x) Is the buoyancy force exerted by a pontoon i immersed in water, F G Is the total gravity acting on the gravity center of the floating fan,is the y-axis unit vector in the world coordinate system, ρ w Is the density of liquid, A i Is the cross-sectional area of pontoon i i Is the submerged length of the pontoon i, m g The total mass of the floating fan is g is the gravity acceleration of the position where the fan is located;
T 2 (x) Is the total torque acted on the floating fan generated by the buoyancy on each pontoon, T 2,i (x) The buoyancy on the pontoon i generates a torque acting on the floating blower,the direction distance vector is a direction distance vector pointing to a buoyancy acting point of the pontoon i from the gravity center of the floating fan under the main body coordinate system;
F 3 (x, w) is the total resistance of each pontoon to fluid, F 3,i (x, w) is the resistance of pontoon i to fluid, F 3t,i (x, w) is the transverse resistance of pontoon i by fluid, F 3h,i (x, w) is the longitudinal resistance of pontoon i due to fluid influence, w is the wave input vector, C d,i Is the drag constant of pontoon i, C a,i Is the inertia constant of pontoon i, A t,i Is the side area of the pontoon i,is the velocity vector of the transverse water flow at the pontoon i, V i Volume of pontoon i>Is the velocity vector of the transverse water flow at pontoon i, < >>And->The cross-sectional areas of the bottom and the top of the pontoon immersed in water, w p,j And w p,n+j Representing the water pressure at the bottom and the top of the pontoon respectively, C dy,i And C ay,i Are all constant(s)>And->Respectively equivalent longitudinal velocity vector and acceleration vector of water flow, V h,i Is the reference volume of buoy i;
T 3 (x, w) is the total torque of the floating fan acted by the total resistance generated by the fluid influence of each pontoon, T 3,i (x, w) is the total torque that pontoon i produces by the fluid effect that the total resistance acts on the floating wind turbine.
Optionally, the mooring system submodel is:
wherein F is 4 (x) Is the mooring force of the floating fan, F 4,j (x) Is the mooring force generated by the j-th root mooring rope acting on the mooring point to the floating platform, T 4 (x) Is the moment generated by the mooring force of the floating fan,the gravity center of the floating fan points to the direction distance vector of the mooring point;
F t,j for horizontal tension of j-th mooring line acting on mooring point, mu j For the density of the j-th mooring line, L l,j For the length of the j-th mooring line L 0,j For the length of the jth mooring line falling on the seabed without wind and waves, L up,j For the height d of the jth mooring line raised or lowered above the seabed when the state is changed 4,j Is a directional distance vector from the gravity center of the floating fan to the j-th root system mooring action point, the unit vectors are x, y and z axes in the world coordinate system respectively.
Optionally, the nonlinear model of the floating fan is:
f T (x,u,v,w)＝(R(θ)I g R(θ) T )T(x,u,v,w)；
F(x,u,v,w)＝F 1 (x,u,v)+F 2 (x)+F 3 (x,w)+F 4 (x)；
wherein f (x, u, v, w) is a state function of a nonlinear model of the floating fan, generating a self-force function, a torque function and a shaft torque function respectively; p is the position vector of the floating fan, +.>A generalized position vector representing the principal axis, θ being the deflection vector, θ r Is the deflection angle of the main shaft, m ax 、m ay 、m az Virtual pneumatic masses along the x-axis, y-axis and z-axis directions of the world coordinate system respectively; j (J) r Is the moment of inertia of the low-speed shaft, T r For torque around the z-axis at low speed, J g For high-speed shaft moment of inertia, T g Is generator torque; f (F) 1 Is the integral aerodynamic force of the floating fan, F 2 For buoyancy, F 3 F is the resistance and inertial force due to the fluid 4 For mooring force, I g The floating fan inertia matrix is formed by taking F (x, u, v, w) as a resultant force born by a floating fan system, and taking T (x, u, v, w) as a resultant moment born by the floating fan system, wherein the superscript T represents transposition.
Optionally, the linear model of the floating fan is:
wherein P is e Representing the electromagnetic power of the generator, y is the output of a floating fan model, and the superscript T represents transposition, eta g Representing the mechanical efficiency of the generator, T e Which represents the electromagnetic torque and which is used to control the electromagnetic torque,represents average generator speed, ω g The generator speed.
Optionally, an algorithm for performing parameter identification on the linear model of the floating fan is as follows: and (5) optimizing and calculating hawk.
A linear model building system for a floating wind turbine for linear analysis of drive train load, the system being applied to the method described above, the system comprising:
the kinematic equation construction module is used for equivalent of the transmission chain main shaft as a flexible body to construct a kinematic equation of the transmission chain main shaft;
the sub-model construction module is used for constructing a hub-fan blade system sub-model, a floating platform-tower cone model and a mooring system sub-model of the floating fan according to a kinematic equation of a main shaft of the transmission chain;
the nonlinear model building module is used for building a nonlinear model of the floating fan according to the hub-fan blade system sub-model, the floating platform-tower drum model and the mooring system sub-model;
the linear model building module is used for building a linear model of the floating fan according to the nonlinear model of the floating fan;
and the parameter identification module is used for carrying out parameter identification on the linear model of the floating fan.
An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the method described above when executing the computer program.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the embodiment of the invention provides a linear model construction method and a system for a floating fan for linear analysis of a driving chain load, wherein the method comprises the following steps: the main shaft of the transmission chain is equivalent to a flexible body, and a kinematic equation of the main shaft of the transmission chain is constructed; constructing a hub-fan blade system sub-model, a floating platform-tower cone model and a mooring system sub-model of the floating fan according to a kinematic equation of a main shaft of a transmission chain; according to each sub-model, constructing a nonlinear model of the floating fan; constructing a linear model of the floating fan according to the nonlinear model of the floating fan; and carrying out parameter identification on the linear model of the floating fan. According to the invention, the main shaft is considered as a flexible body, a kinematic equation considering axial tension, compression, bending and torsion deformation of the main shaft is constructed, and a linear model of the floating fan is constructed through a gain scheduling technology, so that the linear model construction of the floating fan for linear analysis of the load of a transmission chain is realized.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for constructing a linear model of a floating fan for linear analysis of driving chain loads, which is provided by an embodiment of the invention;
FIG. 2 is a schematic diagram of a method for constructing a linear model of a floating fan for linear analysis of drive train loads according to an embodiment of the present invention;
FIG. 3 is a representation of a sub-model coupling relationship of a floating fan system provided by an embodiment of the present invention;
FIG. 4 is a schematic diagram of bending deformation of a spindle according to an embodiment of the present invention;
FIG. 5 shows a Γ of a spindle according to an embodiment of the present invention b Schematic diagram of a coordinate system;
FIG. 6 is a schematic diagram of 4 coordinate systems of a floating fan system model provided by an embodiment of the present invention;
FIG. 7 is a schematic illustration of wind generated forces and moments provided by an embodiment of the present invention;
FIG. 8 is a schematic representation of the buoyancy of a floating platform according to an embodiment of the present invention;
FIG. 9 is a schematic illustration of a single mooring line provided by an embodiment of the invention;
fig. 10 is a block diagram of an ladc disturbance rejection strategy provided by an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a linear model construction method and a system for a floating fan for linear analysis of a transmission chain load, so as to realize linear model construction of the floating fan for linear analysis of the transmission chain load, and improve the coordination control capability of fan stable power and load reduction.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
At present, the modeling mode of the existing floating wind turbine generator is divided into two major types, one type is a nonlinear model established based on a mechanism, and part of key components are introduced into a finite element flexible body model, so that the degree of freedom is more, the model order is high, the tracking precision is high, but the calculation amount is large, the calculation force consumption is high, and the method is not suitable for the design of a controller; the other model is a simplified model oriented to control, and in order to facilitate the design of the controller, the model has lower order, and the floating fan multi-degree-of-freedom motion and the transmission chain load cannot be well expressed, so that the performance of the controller is affected.
The embodiment of the invention provides a linear model construction method of a floating fan for linear analysis of a transmission chain load, which is shown in fig. 1 and comprises the following steps:
and 101, equivalent a main shaft of the transmission chain to be a flexible body, and constructing a kinematic equation of the main shaft of the transmission chain.
And 102, constructing a hub-fan blade system sub-model, a floating platform-tower cone model and a mooring system sub-model of the floating fan according to a kinematic equation of a main shaft of the transmission chain.
And 103, constructing a nonlinear model of the floating fan according to the hub-fan blade system sub-model, the floating platform-tower cone model and the mooring system sub-model.
And 104, constructing a linear model of the floating fan according to the nonlinear model of the floating fan.
And 105, carrying out parameter identification on the linear model of the floating fan.
As a specific implementation, as shown in fig. 2, implementation and application of the method provided by the embodiment of the present invention are specifically:
and 1, taking the load working conditions formed by control indexes such as wind, wave and current environment input and power generation power in the environment into consideration, and obtaining the environment variable of the floating fan system through force decomposition.
And 2, constructing a mechanism-based transmission chain refined nonlinear model considering the non-torque load.
And 3, performing simplified analysis modeling on other subsystems to construct a complete machine model of the floating fan.
And 4, establishing a full-working-condition linear floating fan model through a mechanism-data compound driving intelligent parameter identification algorithm.
And step 5, designing an intelligent control algorithm based on the model to realize the coordination control target of stabilizing power and inhibiting load.
The invention provides a control-oriented floating type fan transmission chain load linearization analysis system, which takes a semi-submerged floating type permanent magnet semi-direct drive wind driven generator as an example, and comprises the following components: the connection relationship of the mooring system submodel, the floating platform submodel, the tower submodel, the generator submodel, the transmission system submodel and the hub-fan blade submodel is shown in figure 3.
External excitation main bag of floating fanThe wind and sea waves are contained, the wind speed is decomposed into vectors in three directions of x, y and z axes in a world coordinate system, the sea waves are described from three dimensions of speed, acceleration and pressure, the speed and the acceleration are represented by n vectors, and the pressure is represented by n p The scalar representations.
v＝[v x [m/s] v y [m/s] v z [m/s]] T ；
Where v is the wind speed input vector; w is the wave input vector, where subscript v represents wave speed [ m/s ]]The subscript a represents the wave acceleration [ m/s ] 2 ]The subscript p represents the wave pressure [ Pa ]]N and n p Are all related to the structure of the floating platform.
Further, modeling is performed on a main shaft of a transmission chain of the floating fan, and considering that the main shaft belongs to a linear small deformation structure, and deformation comprises tension, compression, bending and torsion. And according to the material and the geometric shape of the main shaft, the tensile rigidity, the bending rigidity and the torsional rigidity of the main shaft in all directions are calculated. As shown in fig. 4, in practice, the bending deformation ψ of the main shaft is small, the change of the cross section is small, the error epsilon caused by the change of the cross section is small, and the error epsilon is reduced along with the reduction of the bending deformation ψ. It is therefore assumed that the cross-sectional slice is rigid and always perpendicular to the neutral axis of deformation, i.e. only the free deformation of the out-of-plane principal axis is considered.
Defining a coordinate system Γ of the principal axis b As shown in fig. 5, Γ b The origin of the coordinate system is located at the mass center of the main shaft, the z-axis is parallel to the neutral axis of the main shaft which is not deformed, and the x-y plane is perpendicular to the z-axis.
The stiffness matrix defining the principal axis is:
wherein,for the tensile and compressive stiffness along the z-axis +.>For the tensile and compressive stiffness along the z-axis +.>For the tensile and compressive stiffness along the z-axis +.>For cross tension and compression rigidity->For bending stiffness around the x-axis->For bending stiffness around the y-axis +.>For torsional rigidity about the z-axis +.>Is the cross bending stiffness.
Defining a quality matrix as:
wherein m is c Is the mass per unit length of the material,for the moment of inertia density about the x-axis +.>For a moment of inertia density about the y-axis,for the moment of inertia density around the z-axis +.>Is the product of the moment of inertia and the density. Defining a damping matrix as:
C＝αM c +σK b ；
where α is the mass matrix coefficient and σ is the stiffness matrix coefficient. The kinematic equation for the spindle is:
wherein,for the force vector acting on the spindle, +.>For the torque vector acting on the spindle, +.>Is a generalized coordinate vector of a principal axis, and
wherein,is a pulling force acting on the spindle along the x-axis, < >>Is the pulling force acting on the spindle along the y-axis, < >>Is a pulling force acting on the spindle along the z-axis, < >>Is applied to the spindle around xBending moment of shaft>Is a bending moment acting on the main shaft around the y axis,is the torque for twisting the main shaft epsilon z Is tensile and compressive strain along the z-axis, κ x Is the curvature of bending around the x-axis, κ y Is the curvature of the curve around the y-axis, κ z Is the twist angle about the z-axis.
Further, a floating fan combined coordinate system is constructed, a system state is determined, and a system state space relation is expressed. To facilitate the analytical calculations, four coordinate systems are constructed as shown in fig. 5.Γ -shaped structure 0 Is a world coordinate system, and is used as a reference coordinate system of a system model and comprises three unit vectors which are orthogonal in pairsAnd->Wherein (1)>The vertical direction is opposite to the gravity direction,parallel to the horizontal plane. Γ -shaped structure b Is a main body coordinate system, the origin of which coincides with the mass center of the fan, < >>Parallel to the tower centre line, vertically upwards, < >>Parallel to the wind direction, add>And->Two by two. Γ -shaped structure n Is the cabin coordinate system with origin at cabin centroid +.>Parallel to the high-speed axis>And->Two by two. Γ -shaped structure s Is a principal axis coordinate system with origin coincident with principal axis centroid, < >>Parallel to the tangential direction of the end point of the main shaft deformation central shaft hub, < + >>And->Two by two. When the floating fan is not affected by wind and wave disturbance, the main body coordinate system and the cabin coordinate system are parallel to the world coordinate system, as shown in fig. 6.
From the above analysis of the load of the main shaft, it is found that the load of the main shaft in the non-torque direction is derived from the main motion of the main body of roll, pitch, yaw and roll, pitch and heave of the fan in the power generation process, so that the deflection angle θ= [ θ ] of the main body coordinate system and the world coordinate system x θ y θ z ] T [rad]First order time derivative of body displacement vector of floating fanAs a state quantity, where θ x ,θ y ,θ z Respectively represent Γ b Wherein the three axes of x, y and z are equal to Γ 0 Deflection angles of three axes of x, y and z can be defined by the methodChemical matrix
In addition, consider the deformation of the flexible body of drive chain, combine the traditional control state quantity of fan: low speed shaft rotational speed omega r [rad]High speed shaft rotational speed omega g [rad]Also comprises a position vector p of the floating fan system 3×1 And its first derivative, deflection vector θ 3×1 And the first derivative thereof, the generalized position vector of the principal axis and the first derivative thereof, thereby obtaining 26 state vectors of the floating fan system as follows:
the controlled quantity is as follows:
wherein beta is the pitch angle, T e Is electromagnetic torque, and gamma is yaw angle.
Thus, a kinematic equation (i.e., a nonlinear model) of the floating fan can be established:
wherein f F ，f T ，f Q Generating self force, torque and shaft torque respectively;
f T (x,u,v,w)＝(R(θ)I g R(θ) T )T(x,u,v,w)；
F(x,u,v,w)＝F 1 +F 2 +F 3 +F 4 ；
wherein m is ax 、m ay 、m az Virtual aerodynamic masses, J, along the x-, y-, and z-axes of the world coordinate system, respectively r Is the moment of inertia of the low-speed shaft, J g For high-speed shaft moment of inertia, T g For generator torque, F 1 Is the integral aerodynamic force of the floating fan, F 2 For buoyancy, F 3 F is the resistance and inertial force due to the fluid 4 Is mooring force.
Further, other subsystem models are constructed based on the floating fan kinematic expression and the main shaft flexible model.
(1) Hub-fan blade system submodel
Characterizing interactions between wind and wind turbine by constructing a hub-blade system sub-model, converting wind forces on the blades into aerodynamic forces F acting in the direction of the rotor shaft z a And aerodynamic torque T acting on the rotor a As shown in fig. 7.
The aerodynamic forces of the three fan blades are concentrated at the center point of the hub, so that the hub is used as an aerodynamic force center. Then, aerodynamic force can be expressed as:
wherein C is t Is a aerodynamic coefficient, is a function of Tip Speed Ratio λ (TSR) and pitch angle β, ρ a Is the air density of the air, and the air is compressed,is the wind sweeping area of the fan blade, and is->Is an equivalent wind speed vector perpendicular to the wind sweeping surface and represents the corrected wind speed projected between the floating fan and the main shaft plane.
In order to express the corrected wind speed, a conversion matrix between the fan blade wind sweeping surface and a world coordinate system is constructed:
R t ＝R(θ tilt )R(γ)R(θ)；
wherein R (θ) tilt ) Indicating theta due to spindle twist tilt The resulting coordinate deflection, R (γ), represents the coordinate deflection due to the yaw angle γ. Further, the equivalent wind speed calculation expression is as follows:
wherein,representing the relative input wind speed after taking into account disturbances>Wherein->Representing the vector directed from the center of gravity of the fan to the aerodynamic center. Tip speed ratio can be expressed in simplified terms:
considering that the rotor acceleration or deceleration is the control amount using the generator torque as the control amount in the control system, and the rotational inertia of the low-speed shaft rotor is much larger than the generator, the low-speed shaft torque is made approximately equal to the generator torque T g Ratio to gearbox N GR Is a product of (a) and (b). The total aerodynamic torque can thus be expressed as:
thus, the pneumatic power P can be obtained a ：
Wherein C is p Is a power coefficient.
Further, the rotation motion equation of the low-speed shaft and the high-speed shaft can be obtained:
wherein J is r And J g The moments of inertia of the low-speed shaft and the high-speed shaft, respectively. Two-dimensional vector f Q (x, u, v, w) can also be determined byAnd->Is expressed by the expression of (2).
(2) Floating platform-tower bobbin model
According to the euclidean principle, the buoyancy force of an object is equal to the gravity force of boiled water, and the resultant force of the buoyancy force and the gravity force of a floating platform can be expressed as:
wherein,representing the total gravity acting on the centre of gravity of the floating fan, +.>Representing the buoyancy of a certain submerged pontoon unit, dividing the pontoon unit into i buoyancy equivalent pontoons, m according to the different cross-sectional areas of all pontoons of the floating platform g Is the total mass of the floating fan, g is the gravity acceleration of the position of the fan, ρ w Is the density of liquid, A i And l i Representing the cross-sectional area of pontoon i and the pontoon length immersed in water, i.e. draft, respectively, and assuming buoyancy is acting +.>At the geometric center of the cross section.
As shown in FIG. 8, for a fully submerged pontoon, its draft is constant i,0 However, for a partially submerged top buoy, which is elliptical in its waterline cross section (waterplane plane) due to displacement and tilting of the floating platform, the modified buoy draft should be expressed as:
wherein l i,0 Represents the draft of the pontoon i under the windless and wave-less working condition,the constant vector (only influenced by the structure of the floating fan and not changed with the state of the floating fan) which points from the gravity center of the floating fan to the action point of the floating force under the world coordinate system is expressed.
The buoyancy acting on each pontoon generates a torque acting on the floating blower, which can be expressed as:
wherein,in order to direct the vector of the floating forces 'points of action from the floating wind turbine's center of gravity in the body coordinate system, the vector is made constant for a fully submerged buoy, and for a partially submerged top buoy the vector is expressed as:
in addition, the gravity of the floating fan system acts on the center of gravity of the floating fan, so that no torque is generated to deflect the floating fan.
Further, the effects of drag and inertial pontoon movement due to fluid effects are contemplated in the present invention. The total resistance and torque are:
the lateral force can be expressed as:
wherein C is d,i Is the resistance constant of the pontoon i, C a,i Is the inertia constant of the pontoon i, A t,i For the side area of pontoon i, V i For the volume of the pontoon i,and->Velocity vectors of the transverse water flow respectivelyAnd an acceleration vector;
wherein,representing the corrected seawater flow rate, k representing the number of actual pontoons, and the floating platform in this example comprises 4 actual pontoons.
For pontoons, there is also a resistance in the lifting direction and inertial forces, which can be described as:
wherein C is dy,i And C ay,i Are all constant and are used for the preparation of the high-voltage power supply,and->The cross-sectional areas of the bottom and the top of the pontoon immersed in water, w p,j And w p,n+j Representing the water pressure at the bottom and the top of the pontoon respectively, V h,i As a reference volume of the pontoon,and->Is equivalent to the longitudinal velocity vector and the acceleration vector of the water flow. Thus, the total resistance and inertia force of the single pontoon and the torque thereof can be obtained:
F 3,i (x,w)＝F 3t,i (x,w)+F 3h,i (x,w)；
(3) Mooring system sub-model
The mooring system of the floating fan mainly comprises a plurality of mooring ropes, the top of the mooring system is connected with the floating platform, and the bottom of the mooring system is anchored on the seabed through anchors. These mooring lines provide a restoring and stabilizing reaction force when the floating platform is displaced and deflected by wind and wave disturbances. Thus, the mooring force of the floating wind turbine and the moment generated thereby can be expressed as:
/>
wherein F is 4,j The j-th mooring line acts on the mooring force generated by the mooring point to the floating platform,representing a directional vector from the center of gravity of the floating wind turbine to the mooring point.
Wherein the mooring force of a single mooring line can be expressed as:
wherein F is t,j For mooring ofHorizontal tension of point, mu j For mooring cable density, L l,j For mooring line length, L 0,j For the length of the mooring line falling on the seabed without wind and waves, L up,j To the height at which the mooring line rises or falls on the seabed when the state is changed. As shown in fig. 9, the broken line represents the state of the mooring line when the wind and wave are absent, and the solid line represents the state of the mooring line when the mooring point is lifted.
Further, based on the nonlinear model, through a multi-gain scheduling technology, through standard model output data analysis, a description of a linear time-invariant system (LinerTime Invariant, LTI) of a plurality of floating fans at a set of steady-state operating points is established by utilizing an intelligent parameter identification method. Specifically, the unified expression of the linear time-invariant systems is as follows:
wherein,represents partial differentiation, delta represents increment, P e For the power generation of the generator, < > for>And->The average generator speed and the average electromagnetic torque at a certain operating point are respectively. Scheduling variables are obtained based on refined standard model data, and the LTI model at each steady-state operating point is parameterized. Thereby, it is easy to openThe load was analyzed by the above-described variable LTI model set.
Based on the operation data of the IEA 15MW fan under the multiple conditions of turbulent wind, stepped wind and the like, a hawk optimization Algorithm (AO) is introduced to correct partial differential parameter items in the variable parameter LTI model. Thus, the cost function of the optimization problem can be described as:
s.t.0≤|δK i |≤0.1*K i ；
wherein e p (t) represents the electromagnetic power P of the model generator e Error from standard data, K i For partial differential parameter term to be optimized and for correction term delta K i Setting an allowable optimization range, wherein partial differential parameter terms are as follows:
AO is a group-based meta heuristic optimization algorithm, and has the advantages of easiness in implementation, high convergence speed, high stability of an optimization result and the like. Firstly, initializing partial differential parameter item X= [ delta K ] by using partial differential result of working point 1 δK 2 … δK 6 ] T Further, the optimal parameters of the partial differential correction term are obtained through iteration through the following four methods, and are expressed as:
X * ＝[K 1 +δK 1 K 2 +δK 2 … K 6 +δK 6 ] T 。
AO is a group-based meta heuristic optimization algorithm, has the advantages of easy realization, high convergence speed, high stability of an optimization result and the like, and mainly obtains the optimal parameters of a model through the following four steps:
1) Extended search
In the extended search phase, the best hunting area is selected to mainly simulate the area where the hawk identifies the prey in the high air, and can be expressed as follows:
wherein T is the current iteration number, T is the iteration number, X 1 (t+1) is the solution of the next iteration of time, X, obtained by an extended search best (t) is the optimal solution obtained in the previous t iterations, X M (t) is the average of the solutions of the previous t iterations, and rand is a random number between 0 and 1.
2) Contracted search
In the second phase, the simulated hawk swirls over the target prey and then attacks the target. X is X 2 (t+1)＝X best (t)×Levy(D)+X R (t)+(y-x)*rand；
Wherein X is 2 (t+1) is the solution for the next iteration of time from the systolic search, levy (D) is the Levy flight distribution function, X R (t) is a random solution in the range of 1-N in the ith iteration.
3) Global mining
Further, the process of lowering the eagle low altitude and slowly attacking was simulated. Within the constraints, an optimal solution is sought.
Wherein X is 3 (t + 1) is the solution for the next iteration of time from global mining,and ζ is an adjustable parameter, default to 0.1, LB represents the lower bound for a given problem and UB represents the upper bound for a given problem.
4) Local mining
Furthermore, when the eagle approaches the target, the target is attacked according to the random movement of the target. Can be expressed as:
X 4 (t+1)＝QF×X best (t)-(G 1 ×X(t)×rand)-G 2 ×Levy(D)+rand×G 1 ；
wherein X is 4 (t+1) is the next time iteration solution from partial mining, QF represents the equilibrium search quality function, G 1 Representing the movement of AO, G 2 Represents the slope of the motion of AO, X (t) is the solution at the current time.
In order to achieve the aim of power stabilization-load suppression of the floating fan under the rated working condition, a linear active disturbance rejection controller (LinerActive Disturbance Rejection Control, LADRC) shown in figure 10 is designed, and a small pitch angle compensation signal is generated for pitching motion of the fan and the like and is overlapped on a pitch rotation speed control loop to generate virtual pneumatic damping, so that the damping force of a unit is increased, and the load of a transmission chain is reduced. Internal and external disturbances such as model errors and the cross influence of the load suppression control signal and the rotating speed control loop are taken as total system disturbances, and estimated and compensated by a linear expansion state observer (Liner Extended State Observer, LESO). Thus, the coordinated control target of stabilizing the power suppression load is achieved.
The embodiment of the invention also provides a linear model construction system of the floating fan for linear analysis of the load of the transmission chain, which is applied to the method, and comprises the following steps:
and the kinematic equation construction module is used for equivalent of the transmission chain main shaft as a flexible body and constructing a kinematic equation of the transmission chain main shaft.
The sub-model construction module is used for constructing a hub-fan blade system sub-model, a floating platform-tower cone model and a mooring system sub-model of the floating fan according to a kinematic equation of a main shaft of the transmission chain.
The nonlinear model building module is used for building a nonlinear model of the floating fan according to the hub-fan blade system sub-model, the floating platform-tower drum model and the mooring system sub-model.
And the linear model construction module is used for constructing a linear model of the floating fan according to the nonlinear model of the floating fan.
And the parameter identification module is used for carrying out parameter identification on the linear model of the floating fan.
The embodiment of the invention also provides electronic equipment, which comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the processor realizes the method when executing the computer program.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
a rigid-flexible coupling nonlinear model oriented to control is constructed, a transmission chain component is considered as a flexible body, a kinematic equation which considers that a main shaft comprises axial tension and compression, bending and torsion deformation is constructed, and a linearization model is constructed and the load of the transmission chain is accurately analyzed through a gain scheduling technology.
Based on a linear model for the load analysis of the transmission chain, an LADRC control strategy is constructed, a virtual pneumatic damping concept is introduced, and the load is superposed in the control quantity beta to inhibit the small pitch angle, so that the damping force of the floating fan is increased, the load of the transmission chain is reduced, finally, the coordination control target of stabilizing power and inhibiting the load is realized, the fluctuation of the power generation power during the rated working condition operation of the floating fan is greatly reduced, the load of the transmission chain of the unit is reduced, and the safe operation capacity of the unit is improved.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (10)
1. A method for constructing a linear model of a floating fan for linear analysis of drive train load, the method comprising the steps of:
the main shaft of the transmission chain is equivalent to a flexible body, and a kinematic equation of the main shaft of the transmission chain is constructed;
constructing a hub-fan blade system sub-model, a floating platform-tower cone model and a mooring system sub-model of the floating fan according to a kinematic equation of a main shaft of a transmission chain;
constructing a nonlinear model of the floating fan according to the hub-fan blade system sub-model, the floating platform-tower cone model and the mooring system sub-model;
constructing a linear model of the floating fan according to the nonlinear model of the floating fan;
and carrying out parameter identification on the linear model of the floating fan.
2. The method for constructing a linear model of a floating fan for linear analysis of drive train loads according to claim 1, wherein the kinematic equation of the drive train main shaft is:
wherein K is b The rigidity matrix of the main shaft of the transmission chain is C, the damping matrix of the main shaft of the transmission chain is M c For the mass matrix of the drive chain spindle,for the force vector acting on the main shaft of the drive chain, < >>For the torque vector acting on the main shaft of the drive chain, < >>Is the generalized coordinate vector of the main shaft of the transmission chain.
3. The method of constructing a linear model of a floating wind turbine for linear analysis of drive train loads according to claim 1, wherein the hub-and-blade system sub-model characterizes interactions between wind and the floating wind turbine, converting forces of wind acting on blades of the floating wind turbine into aerodynamic forces acting on rotor shaft of the floating wind turbine and aerodynamic torque acting on the rotor;
the hub-fan blade system submodel is as follows:
wherein F is 1 (x, u, v) represents aerodynamic force acting on the rotor axis direction of the floating fan, x is the state vector of the floating fan, u is the controlled quantity of the floating fan, v is the wind speed input vector, C t Is a aerodynamic coefficient, is a function of tip speed ratio lambda and pitch angle beta, ρ a Is the air density of the air, and the air is compressed,is the wind sweeping area of the fan blade, R r Represents the wind sweeping radius of the fan blade->Is an equivalent wind speed vector perpendicular to the wind sweeping surface and represents the corrected wind speed projected between the floating fan and the main shaft plane, T 1 (x, u, v) is the aerodynamic torque acting on the rotor, R (θ) represents the change matrix between world and body coordinates, +.>Is a direction distance vector which points from the gravity center of the floating fan to the action center point of various types of forces, N GR Is the transmission ratio of a gear box, T g Is generator torque>Is the principal axis coordinateZ-axis unit vector in the system, R t Is a conversion matrix between the fan blade wind sweeping surface and the world coordinate system,/for>Is the force vector acting on the spindle, +.>Is the torque vector acting on the spindle.
4. The method for constructing a linear model of a floating wind turbine for linear analysis of drive train load according to claim 3, wherein the floating platform-tower model is:
F 3,i (x,w)＝F 3t,i (x,w)+F 3h,i (x,w)；
wherein F is 2 (x) Is the resultant force of buoyancy and gravity applied to the floating platform, F 2,i (x) Is the buoyancy force exerted by a pontoon i immersed in water, F G Is the total gravity acting on the gravity center of the floating fan,is the unit vector of the y-axis in the world coordinate system, ρ w Is the density of liquid, A i Is the cross-sectional area of pontoon i i Is the submerged length of the pontoon i, m g The total mass of the floating fan is g is the gravity acceleration of the position where the fan is located;
T 2 (x) Is the total torque acted on the floating fan generated by the buoyancy on each pontoon, T 2,i (x) The buoyancy on the pontoon i generates a torque acting on the floating blower,the direction distance vector is a direction distance vector pointing to a buoyancy acting point of the pontoon i from the gravity center of the floating fan under the main body coordinate system;
F 3 (x, w) is the total resistance of each pontoon to fluid, F 3,i (x, w) is pontoon i currentResistance produced by body influence, F 3t,i (x, w) is the transverse resistance of pontoon i by fluid, F 3h,i (x, w) is the longitudinal resistance of pontoon i due to fluid influence, w is the wave input vector, C d,i Is the drag constant of pontoon i, C a,i Is the inertia constant of pontoon i, A t,i Is the side area of the pontoon i,is the velocity vector of the transverse water flow at the pontoon i, V i Volume of pontoon i>Is the velocity vector of the transverse water flow at pontoon i, < >>And->The cross-sectional areas of the bottom and the top of the pontoon immersed in water, w p,j And w p,n+j Representing the water pressure at the bottom and the top of the pontoon respectively, C dy,i And C ay,i Are all constant(s)>And->Respectively equivalent longitudinal velocity vector and acceleration vector of water flow, V h,i Is the reference volume of buoy i;
T 3 (x, w) is the total torque of the floating fan acted by the total resistance generated by the fluid influence of each pontoon, T 3,i (x, w) is the total torque that pontoon i produces by the fluid effect that the total resistance acts on the floating wind turbine.
5. The method for linear model construction of a floating wind turbine for linear analysis of drive train loads according to claim 4, wherein the mooring system sub-model is:
wherein F is 4 (x) Is the mooring force of the floating fan, F 4,j (x) Is the mooring force generated by the j-th root mooring rope acting on the mooring point to the floating platform, T 4 (x) Is the moment generated by the mooring force of the floating fan,the gravity center of the floating fan points to the direction distance vector of the mooring point;
F t,j for horizontal tension of j-th mooring line acting on mooring point, mu j For the density of the j-th mooring line, L l,j For the length of the j-th mooring line L 0,j For the length of the jth mooring line falling on the seabed without wind and waves, L up,j For the height d of the jth mooring line raised or lowered above the seabed when the state is changed 4,j Is a directional distance vector from the gravity center of the floating fan to the j-th root system mooring action point, the unit vectors are x, y and z axes in the world coordinate system respectively.
6. The method for constructing the linear model of the floating fan for linear analysis of the load of the transmission chain according to claim 5, wherein the nonlinear model of the floating fan is:
f T (x,u,v,w)＝(R(θ)I g R(θ) T )T(x,u,v,w)；
F(x,u,v,w)＝F 1 (x,u,v)+F 2 (x)+F 3 (x,w)+F 4 (x)；
wherein f (x, u, v, w) is a state function of a nonlinear model of the floating fan, generating a self-force function, a torque function and a shaft torque function respectively; p is the position vector of the floating fan, +.>A generalized position vector representing the principal axis, θ being the deflection vector, θ r Is the deflection angle of the main shaft, m ax 、m ay 、m az Virtual aerodynamic masses along the x-axis, y-axis, and z-axis of the world coordinate system, respectivelyAn amount of; j (J) r Is the moment of inertia of the low-speed shaft, J g For high-speed shaft moment of inertia, T g Is generator torque; f (F) 1 Is the integral aerodynamic force of the floating fan, F 2 For buoyancy, F 3 F is the resistance and inertial force due to the fluid 4 For mooring force, I g Is a floating fan inertia matrix, F (x, u, v, w) is the resultant force born by the floating fan system, T (x, u, v, w) is the resultant moment born by the floating fan system, and the superscript T represents transposition and P a For pneumatic power, ++>Torque, ω, acting on spindle torsion about z-axis r Is the low speed shaft rotational speed.
7. The method for constructing a linear model of a floating wind turbine for linear analysis of drive train load according to claim 6, wherein the linear model of the floating wind turbine is:
wherein P is e Representing the electromagnetic power of the generator, y is the output of the floating fan system, and the superscript T represents transposition, eta g Representing the mechanical efficiency of the generator, T e Which represents the electromagnetic torque and which is used to control the electromagnetic torque,represents the average generator speed, omega at the operating point g Indicating the rotational speed of the generator>Indicating the operating point average generator speed.
8. The method for constructing a linear model of a floating fan for linear analysis of driving chain load according to claim 1, wherein the algorithm for performing parameter identification on the linear model of the floating fan is as follows: hawk optimization algorithm.
9. A linear model building system for a floating wind turbine for linear analysis of drive train load, the system being applied to the method of any one of claims 1-8, the system comprising:
the kinematic equation construction module is used for equivalent of the transmission chain main shaft as a flexible body to construct a kinematic equation of the transmission chain main shaft;
the sub-model construction module is used for constructing a hub-fan blade system sub-model, a floating platform-tower cone model and a mooring system sub-model of the floating fan according to a kinematic equation of a main shaft of the transmission chain;
the nonlinear model building module is used for building a nonlinear model of the floating fan according to the hub-fan blade system sub-model, the floating platform-tower drum model and the mooring system sub-model;
the linear model building module is used for building a linear model of the floating fan according to the nonlinear model of the floating fan;
and the parameter identification module is used for carrying out parameter identification on the linear model of the floating fan.
10. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the method of any one of claims 1 to 8 when the computer program is executed.
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