CN113685314B - Pitch control method, system and readable storage medium - Google Patents
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
- F03D—WIND MOTORS
- F03D7/00—Controlling wind motors
- F03D7/02—Controlling wind motors the wind motors having rotation axis substantially parallel to the air flow entering the rotor
- F03D7/022—Adjusting aerodynamic properties of the blades
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
- F03D—WIND MOTORS
- F03D7/00—Controlling wind motors
- F03D7/02—Controlling wind motors the wind motors having rotation axis substantially parallel to the air flow entering the rotor
- F03D7/0276—Controlling wind motors the wind motors having rotation axis substantially parallel to the air flow entering the rotor controlling rotor speed, e.g. variable speed
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
- F03D—WIND MOTORS
- F03D7/00—Controlling wind motors
- F03D7/02—Controlling wind motors the wind motors having rotation axis substantially parallel to the air flow entering the rotor
- F03D7/04—Automatic control; Regulation
- F03D7/042—Automatic control; Regulation by means of an electrical or electronic controller
- F03D7/043—Automatic control; Regulation by means of an electrical or electronic controller characterised by the type of control logic
- F03D7/045—Automatic control; Regulation by means of an electrical or electronic controller characterised by the type of control logic with model-based controls
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
- F05B—INDEXING SCHEME RELATING TO WIND, SPRING, WEIGHT, INERTIA OR LIKE MOTORS, TO MACHINES OR ENGINES FOR LIQUIDS COVERED BY SUBCLASSES F03B, F03D AND F03G
- F05B2270/00—Control
- F05B2270/30—Control parameters, e.g. input parameters
- F05B2270/328—Blade pitch angle
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- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E10/00—Energy generation through renewable energy sources
- Y02E10/70—Wind energy
- Y02E10/72—Wind turbines with rotation axis in wind direction
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Abstract
本申请提供一种风机的独立变桨控制方法、系统和可读存储介质。独立变桨控制方法包括确定目标函数和数据驱动模型,其中,目标函数的自变量包括降载控制目标,目标函数的因变量用于表示风机在变桨控制中的结构载荷大小,数据驱动模型的自变量包括风机的桨距角转速,数据驱动模型用于确定至少部分降载控制目标与桨距角转速的函数关系;根据目标函数和数据驱动模型,确定目标函数取值最小时对应的目标桨距角转速;根据目标桨距角转速,对风机进行变桨控制。降载效果好。
The present application provides an independent pitch control method, system and readable storage medium for a wind turbine. The independent pitch control method includes determining an objective function and a data-driven model, wherein the independent variable of the objective function includes the load reduction control objective, the dependent variable of the objective function is used to represent the structural load of the wind turbine in the pitch control, and the data-driven model is used. The independent variables include the pitch angle speed of the wind turbine, and the data-driven model is used to determine the functional relationship between at least part of the load reduction control target and the pitch angle speed; according to the objective function and the data-driven model, the target propeller corresponding to the minimum value of the objective function is determined Pitch angle speed; according to the target pitch angle speed, the fan is controlled by pitch angle. The load drop effect is good.
Description
技术领域technical field
本发明涉及风电领域,尤其涉及一种变桨控制方法、系统和可读存储介质。The present invention relates to the field of wind power, and in particular, to a pitch control method, system and readable storage medium.
背景技术Background technique
变桨距系统作为机组控制系统的核心部分之一,对风电机组安全、稳定、高效的运行具有重要的作用。一方面,变桨距控制器通过调节风机叶片的桨距角,改变对来流风速的阻力,进而控制风轮捕获的气动转矩和功率。另一方面,在风机转动过程中,由于水平垂直风剪切、塔影效应、风湍流、偏航失准等因素的影响,风机叶轮面上的气动载荷处于不平衡的状态。不平衡的气动载荷会使风机叶轮面产生部件结构载荷,从而导致风机振动。一些风机降载控制策略中,由风机的变桨距系统对每个风机叶片的桨距角进行独立调节,改变每个风机叶片承受的气动载荷,来减小风机叶片的周期性载荷和风机叶轮面的不对称载荷。As one of the core parts of the unit control system, the pitch system plays an important role in the safe, stable and efficient operation of the wind turbine. On the one hand, the pitch controller changes the resistance to the incoming wind speed by adjusting the pitch angle of the fan blades, thereby controlling the aerodynamic torque and power captured by the wind rotor. On the other hand, in the process of fan rotation, due to the influence of horizontal and vertical wind shear, tower shadow effect, wind turbulence, yaw misalignment and other factors, the aerodynamic load on the fan impeller surface is in an unbalanced state. Unbalanced aerodynamic loads can cause component structural loads on the fan impeller surface, resulting in fan vibration. In some fan load reduction control strategies, the pitch angle of each fan blade is independently adjusted by the fan pitch system, and the aerodynamic load on each fan blade is changed to reduce the periodic load of the fan blade and the fan impeller. Asymmetric loading of the face.
但随着风机的单机容量增大以及风机叶片的加长,这些风机降载控制策略对风机的降载效果降低。However, with the increase of the single capacity of the fan and the lengthening of the fan blades, the load reduction effect of these fan load reduction control strategies is reduced.
发明内容SUMMARY OF THE INVENTION
本申请提供一种变桨控制方法、系统和可读存储介质,降载效果较好。The present application provides a pitch control method, system and readable storage medium, which have better load reduction effect.
本申请提供一种变桨控制方法,所述变桨控制方法包括:The present application provides a pitch control method, and the pitch control method includes:
确定目标函数和数据驱动模型,其中,所述目标函数的自变量包括降载控制目标,所述目标函数的因变量用于表示风机在变桨控制中的结构载荷大小,所述数据驱动模型用于确定至少部分所述降载控制目标与桨距角转速的函数关系;Determine the objective function and the data-driven model, wherein the independent variable of the objective function includes a load reduction control objective, the dependent variable of the objective function is used to represent the size of the structural load of the wind turbine in the pitch control, and the data-driven model is used. for determining the functional relationship between at least part of the derating control target and the pitch angle rotational speed;
根据所述目标函数和所述数据驱动模型,确定所述目标函数取值最小时对应的目标桨距角转速;According to the objective function and the data-driven model, determine the target pitch angle rotation speed corresponding to the minimum value of the objective function;
根据所述目标桨距角转速,对所述风机进行变桨控制。According to the target pitch angle rotation speed, pitch control is performed on the wind turbine.
本申请提供一种变桨控制系统,包括一个或多个处理器,用于实现如上任一项所述的变桨控制方法The present application provides a pitch control system, comprising one or more processors for implementing the pitch control method described in any one of the above
本申请提供一种可读存储介质,其上存储有程序,该程序被处理器执行时,实现如上任一项所述的变桨控制方法。The present application provides a readable storage medium on which a program is stored, and when the program is executed by a processor, implements the pitch control method described in any one of the above.
变桨控制方法确定目标函数和数据驱动模型,根据目标函数和数据驱动模型,确定结构载荷值最小时对应的目标桨距角转速,再基于目标桨距角转速对风机进行变桨控制。通过对桨距角转速进行控制,使得风机在变桨过程中,运行在使结构载荷最小时的桨距角转速,避免了桨距角转速恒定造成的变桨控制策略有效性下降的问题,提高了风机在变桨过程中的降载效果。The pitch control method determines the objective function and the data-driven model. According to the objective function and the data-driven model, the target pitch angle speed corresponding to the minimum structural load value is determined, and then the fan is pitched based on the target pitch angle speed. By controlling the pitch angle speed, the wind turbine can run at the pitch angle speed when the structural load is minimized during the pitching process, which avoids the problem of decreasing the effectiveness of the pitch control strategy caused by the constant pitch angle speed, and improves the The load reduction effect of the fan in the pitch process is obtained.
附图说明Description of drawings
图1是一种风机的结构示意图;Fig. 1 is a structural schematic diagram of a fan;
图2是图1中的风机的部分放大剖视图;Fig. 2 is a partial enlarged cross-sectional view of the fan in Fig. 1;
图3是图1中的风机在一种技术中的变桨控制流程示意图;Fig. 3 is a schematic diagram of a pitch control flow diagram of the fan in Fig. 1 in a technology;
图4a是一种工况下,风机的桨距角和叶根力矩的一个时间序列对比图;Figure 4a is a time series comparison diagram of the pitch angle and blade root moment of the fan under one working condition;
图4b是在与图4a相同的工况下,风机的桨距角和叶根力矩的另一个时间序列对比图;Fig. 4b is another time series comparison diagram of the pitch angle and blade root moment of the fan under the same working conditions as Fig. 4a;
图5是本申请的一个实施例提供的变桨控制方法的流程图;5 is a flowchart of a pitch control method provided by an embodiment of the present application;
图6是图5中的步骤S52的子流程图;Fig. 6 is the sub-flow chart of step S52 in Fig. 5;
图7是本申请一个实施例提供的变桨控制系统的模块框图。FIG. 7 is a block diagram of modules of a pitch control system provided by an embodiment of the present application.
具体实施方式Detailed ways
这里将详细地对示例性实施例进行说明,其示例表示在附图中。下面的描述涉及附图时,除非另有表示,不同附图中的相同数字表示相同或相似的要素。以下示例性实施例中所描述的实施例并不代表与本说明书一个或多个实施例相一致的所有实施例。相反,它们仅是与如所附权利要求书中所详述的、本说明书一个或多个实施例的一些方面相一致的装置和方法的例子。Exemplary embodiments will be described in detail herein, examples of which are illustrated in the accompanying drawings. Where the following description refers to the drawings, the same numerals in different drawings refer to the same or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments are not intended to represent all embodiments consistent with one or more embodiments of this specification. Rather, they are merely examples of apparatus and methods consistent with some aspects of one or more embodiments of this specification, as recited in the appended claims.
需要说明的是:在其他实施例中并不一定按照本说明书示出和描述的顺序来执行相应方法的步骤。在一些其他实施例中,其方法所包括的步骤可以比本说明书所描述的更多或更少。此外,本说明书中所描述的单个步骤,在其他实施例中可能被分解为多个步骤进行描述;而本说明书中所描述的多个步骤,在其他实施例中也可能被合并为单个步骤进行描述。It should be noted that: in other embodiments, the steps of the corresponding methods are not necessarily performed in the order shown and described in this specification. In some other embodiments, the method may include more or fewer steps than described in this specification. In addition, a single step described in this specification may be decomposed into multiple steps for description in other embodiments; and multiple steps described in this specification may also be combined into a single step in other embodiments. describe.
图1是一种风机100的结构示意图。参见图1,风机100为风力发电机,或称作风力涡轮机。风机100包括从支承系统14延伸的塔架11、安装在塔架11上的机舱12、和接至机舱12的转子13。转子13包括联接至机舱12的可旋转的毂131和联接至毂131并且从毂131向外延伸的至少一个叶片132。FIG. 1 is a schematic structural diagram of a
在一些实施例中,若转子13包括多个叶片132,叶片132围绕毂131间隔排布,以有利于转子13的旋转,从而使得动能能够从风能转化为可用机械能,并且随后转化为电能。In some embodiments, where
本实施例中,转子13包括三个叶片132。In this embodiment, the
其他一些实施例中,转子13可以包括多于或少于三个的叶片132。In other embodiments, the
图2是图1中的风机100的部分放大剖视图。参见图1和图2,机舱12包括转子轴122(也被称为主轴或低速轴)、齿轮箱123、高速轴124、联接件125和电机126。毂131通过转子轴122、齿轮箱123、高速轴124、和联接件125可旋转地联接至机舱12内的发电机126。叶片132带动毂131的旋转,驱动转子轴122旋转,转子轴122的旋转驱动齿轮箱123,齿轮箱123随后驱动高速轴124。高速轴124通过联接件125驱动发电机126发电。如此,实现从风能到机械能,再到电能的转换。FIG. 2 is a partially enlarged cross-sectional view of the
在一些实施例中,毂131包括变桨组件130。变桨组件130包括变桨驱动系统135、和操作性地联接至变桨驱动系统135的变桨控制器134。每个变桨驱动系统135都联接至相应的叶片132。变桨控制器134通过控制变桨驱动系统135,沿变桨轴线133改变相应的叶片132的桨距角或叶片桨距(即确定叶片132相对于风的方向17的透视(perspective)的角度),以控制风机100产生的荷载和动力。例如,在风机100工作时,变桨控制器134可以通过控制变桨驱动系统135,控制叶片132围绕桨距轴线133旋转,使得叶片132旋转至顺桨位置,从而有利于减小转子13的转速并且/或者有利于转子13的停转。又例如,在风机100工作时,变桨控制器134可以通过控制变桨驱动系统135,调节叶片132的桨距角,可以控制转子13的转速,进而控制发电机126的功率。具体的,变桨组件130包括联接至毂131且联接至相应的叶片132的至少一个变桨轴承136。变桨驱动系统135包括变桨驱动电机137、变桨驱动齿轮箱138、和变桨驱动小齿轮139。变桨驱动电机137联接至变桨驱动齿轮箱138,使得变桨驱动电机137向变桨驱动齿轮箱138施加机械力。变桨驱动齿轮箱138联接至变桨驱动小齿轮139,使得变桨驱动小齿轮139通过变桨驱动齿轮箱138旋转。变桨轴承136联接至变桨驱动小齿轮139,使得变桨驱动小齿轮139的旋转造成变桨轴承136旋转,进而带动叶片132围绕桨距轴线133旋转,以便改变叶片132的桨距角或叶片桨距。In some embodiments,
在一些实施例中,变桨控制器134可以是与多个变桨驱动系统135相关联的集中变桨控制器。每个变桨控制器134同时控制多个变桨驱动系统135,以对该多个变桨驱动系统135对应的叶片132的桨距角或叶片桨距进行控制。In some embodiments,
在其他一些实施例中,变桨控制器134包括分布式的多个独立变桨控制器。每个变桨控制器134控制与之对应的一个变桨驱动系统135,以对该变桨驱动系统135对应的叶片132的桨距角或叶片桨距进行控制。In some other embodiments,
在一些实施例中,机舱12包括主控制器121。变桨控制器134与主控制器121通信连接。变桨控制器134从主控制器121接收一个或多个控制信号,和/或将表示叶片132的运行信息的信号发送给变桨控制器134,来对叶片132的桨距角或叶片桨距进行控制。In some embodiments, the
图3是图1中的风机100在一种技术中的变桨控制流程示意图。FIG. 3 is a schematic diagram of a pitch control process of the
参见图3,变桨控制器134包括集中变桨控制器1341和独立变桨控制器1342。集中变桨控制器1341根据转子13的当前转速w和基于预测风速得到的参考转速wref,得到三个叶片132理论上需要达到的桨距角βc,用于控制风机100捕获的气动转矩和功率;独立变桨控制器1342根据传感器感测到的三个叶片132的当前转矩M1、M2、M3,得到三个叶片132理论上需要达到的桨距角β1、β2、β3,用于对风机100进行降载控制。变桨控制器134根据桨距角βc、β1、β2、β3,通过控制变桨驱动系统135,对叶片132进行变桨控制,在控制风机100捕获的气动转矩和功率时,对风机100进行降载控制。Referring to FIG. 3 , the
在图3中,风机100的变桨控制原理是:变桨控制器134根据每个叶片132理论上需要达到的桨距角,通过控制变桨驱动系统135,使叶片132以恒定的桨距角转速转动至对应的角度位置。但随着风机技术发展,风机100的单机容量增大,叶片132加长,风机100的体积增大,叶片132在转动过程中的惯量会增大。基于桨距角转速恒定的变桨控制技术,存在降载控制效果下降的问题。具体而言,一方面,可能无法准确控制叶片132的桨距角。比如若将叶片132的桨距角转速设置过大时,在叶片132转动至理论上需要到达的桨距角位置后,很可能会因为惯量过大而不能及时制动,从而导致叶片132实际转动至的桨距角位置与理论上需要到达的桨距角位置存在偏差,使得风机100的降载控制效果降低;另一方面,降载控制的时效性降低。比如叶片132的桨距角转速较小时,驱动叶片132转动的转矩较小,叶片132从停止状态转换为转动状态的时间较长,导致降载控制的时效性降低,降载控制效果降低。由此可见,为了提高风机100的降载控制效果,有必要基于桨距角转速可变的变桨控制策略对风机100进行变桨控制。比如在变桨控制的前期,控制叶片132以较大的桨距角转速进行变桨,提高降载控制的时效性;在变桨控制的后期,控制叶片132以较小的桨距角转速进行变桨,降低因惯量导致的桨距角偏差。In FIG. 3 , the pitch control principle of the
进一步的,本申请的发明人发现,在同一工况下(指风机100的运行环境相同,例如所在位置的风速、风向等相同),不同的桨距角转速设定,会影响叶片132的叶根力矩大小。结合参见在同一运行工况下的风电机组动态特性图4a和图4b,图4a是叶片132转速设定为[-3.5,3.5]deg/s时,风机100的桨距角和叶根力矩的一个时间序列对比图。图4b是叶片132转速设定为[-5,5]deg/s时,风机100的桨距角和叶根力矩的一个时间序列对比图。在图4a和图4b中,曲线132_1A、132_1A、132_1A分别表示三个叶片132的桨距角随时间的变化特性,基于曲线132_1A、132_1A、132_1A可以确定不同时间段的桨距角转速。曲线132_1B、132_1B、132_1B与曲线132_1A、132_1A、132_1A一一对应,分别表示三个叶片132的叶根力矩随时间的变化特性。从图4a和图4b可以看出,在不同的桨距角转速设定下,影响了风机100的变桨角度的位置,进一步导致三个叶片132的叶根力矩不同。不同的叶根力矩,会导致风机100的叶轮面载荷力矩不平衡,而叶轮面载荷力矩不平衡会加剧风机100的振动,使风机100的结构载荷增大;反之,若叶轮面载荷力矩平衡,风机100的振动较小,风机100的结构载荷较小。Further, the inventor of the present application found that under the same working condition (meaning that the operating environment of the
综上所述,基于桨距角转速可变的变桨控制策略对风机100进行变桨控制时,需要考虑桨距角转速对结构载荷的影响。为达到较好的降载控制效果,需要选择结构载荷最小时对应的桨距角转速。基于以上描述,本申请提出了一种变桨控制方法,其基本思路是:在变桨控制的一个控制周期内,预测该控制周期之后未来一段时间(又称为该控制周期对应的预测周期)内的风速信息,并基于预测的风速信息,确定预测周期内的桨距角转速,从而根据预测的桨距角转速,在预测周期内对风机进行变桨控制。其中,预测的桨距角转速满足如下条件:可以使风机100在预测周期内的结构载荷最小。To sum up, when pitch control is performed on the
图5是本申请的一个实施例提供的变桨控制方法的流程图。变桨控制方法可应用于图1中的风机100,比如应用于风机100的主控制器121。变桨控制方法包括步骤S51至步骤S53。FIG. 5 is a flowchart of a pitch control method provided by an embodiment of the present application. The pitch control method can be applied to the
步骤S51,确定目标函数和数据驱动模型,其中,目标函数的自变量包括降载控制目标,目标函数的因变量用于表示风机在变桨控制中的结构载荷大小,数据驱动模型用于确定至少部分降载控制目标与桨距角转速的函数关系。Step S51, determine the objective function and the data-driven model, wherein the independent variable of the objective function includes the load reduction control objective, the dependent variable of the objective function is used to represent the size of the structural load of the wind turbine in the pitch control, and the data-driven model is used to determine at least The functional relationship between the partial derating control objective and the pitch angle speed.
在一些实施例中,降载控制目标指风机100的结构载荷的影响因素。以风机100的塔架11顶部前后方向的受力值为例,塔架11顶部的前后方向受力值会影响风机100的结构载荷,塔架11顶部的前后方向受力值的变化,会影响风机100的结构载荷大小。通过控制风机100的塔架11顶部的前后方向受力值,可以控制风机100的结构载荷。因此塔架11顶部的前后方向受力值可以称为降载控制目标。在本实施例中,降载控制目标包括但不限于变桨控制过程中风机100的桨距角速度变化率、塔架11顶部的前后方向受力值以及叶片132的叶根力矩均值与各叶片132的叶根力矩差异。In some embodiments, the load reduction control target refers to the influence factor of the structural load of the
以下以本申请的降载控制目标仅包括桨距角速度变化率、塔架11顶部的前后方向受力值以及叶片132的叶根力矩均值与各叶片132的叶根力矩差异为例,对目标函数进行说明。The following is an example of the load reduction control target of the present application including only the pitch angular velocity change rate, the force value of the front and rear directions of the top of the
在一些实施例中,目标函数的表达式可以表达为表达式(1):In some embodiments, the expression of the objective function can be expressed as expression (1):
其中,J表示目标函数值。J取值越大,表示风机100在一个控制周期之后未来一段时间内(预测周期)的结构载荷越大;反之,表示风机100在一个控制周期之后未来一段时间内(预测周期)的结构载荷越小。t0表示预测周期的起始时间点,n表示预测周期的预测步长;Δt表示每一个预测步长的时长;表示三个转子叶片1、2、3在预测周期内的叶根力矩均值;Mi表示第i个转子叶片在预测周期的第z个预测步长内的叶根力矩,其中,z的取值为1、2……、n;表示叶片132的叶根力矩均值与各叶片132的叶根力矩差异;Ffore-aft表示预测周期的第z个预测步长Δt内的塔架11顶部的前后方向受力值;表示第i个转子叶片在预测周期的第z个预测步长Δt内的桨距角速度变化率;通过上述相关描述可知,Ffore-aft、分别表示降载控制目标;w1(vwind)、w2(vwind)、w3(vwind)分别表示对应降载控制目标的权重值。其中,(Ffore-aft)2、也可以为绝对值的形式,比如用于保证降载控制目标的取值为正数。Among them, J represents the objective function value. The larger the value of J is, the greater the structural load of the
在一些实施例中,考虑到风电机组PLC控制器在执行过程不支持积分算法,表达式(1)也可以表达为表达式(2)中的离散形式:In some embodiments, considering that the PLC controller of the wind turbine does not support the integral algorithm in the execution process, the expression (1) can also be expressed as a discrete form in the expression (2):
其中,k表示第k个控制周期,j表示第k个控制周期内的第j个预测步长。Among them, k represents the kth control cycle, and j represents the jth prediction step size in the kth control cycle.
在一些实施例中,数据驱动模型可以是基于克里金(Kriging)插值法和风机100的运行数据建立的。风机100的运行数据可以是风机100的仿真数据,包括风机100在不同工况下多个采样时间点的桨距角转速、风速、风向、桨距角、叶片132的叶根力矩、塔架11顶部的前后方向受力值等数据。数据驱动模型以风机状态作为输出,以与风机状态相关的自变量参数作为输入。风机状态包括但不限于叶片132的叶根力矩Mi、塔架11顶部的前后方向受力值Ffore-aft。与风机状态相关的自变量参数包括浆距角转速。不同的风机状态,对应不同的数据驱动模型。以降载控制目标为例,数据驱动模型可以确定第i个叶片132的叶根力矩Mi和桨距角转速的函数关系,基于该函数关系,进而可以确定降载控制目标与桨距角转速的函数关系;再以降载控制目标Ffore-aft为例,基于数据驱动模型,便可直接确定降载控制目标Ffore-aft与桨距角转速的函数关系。将根据数据驱动模型确定的降载控制目标与桨距角转速的函数关系代入到上述表达式(1)或(2)中,便可建立目标函数值与桨距角转速的函数关系。In some embodiments, the data-driven model may be built based on Kriging interpolation and operating data of the
在一些实施例中,基于克里金方插值法建立的数据驱动模型可以表达为表达式(3):In some embodiments, the data-driven model established based on the kriging interpolation method can be expressed as expression (3):
根据克里金方法原理,表达式(3)中各参数含义如下:According to the principle of kriging method, the meaning of each parameter in expression (3) is as follows:
Y(x)表示风机状态;x表示与风机状态相关的自变量参数向量;表示对Y(x)全局近似的回归模型;fp(x)为回归模型的基函数;c=[c1,c2,…,cp]T,为回归模型的回归系数向量;m表示与风机状态相关的自变量参数的个数;Z(x)表示回归模型近似Y(x)的系统偏差函数,其均值为0,其协方差矩阵可以表达为表达式(4):Y(x) represents the fan state; x represents the independent variable parameter vector related to the fan state; Represents a regression model that approximates Y(x) globally; f p (x) is the basis function of the regression model; c=[c 1 , c 2 ,..., c p ] T , is the regression coefficient vector of the regression model; m represents The number of independent variable parameters related to the fan state; Z(x) represents the regression model Approximate the systematic deviation function of Y(x), its mean is 0, and its covariance matrix can be expressed as expression (4):
其中,表示Z(x)的方差,是以θ为超参数的相关函数,表示试验点x和x′之间的空间相关关系。在本实施例中,R(xp,xp′,θp)为一维相关函数,具体采用高斯函数,表示为表达式(5):in, represents the variance of Z(x), is a correlation function with θ as a hyperparameter, which represents the spatial correlation between the test points x and x′. In this embodiment, R(x p , x p ′, θ p ) is a one-dimensional correlation function, specifically a Gaussian function, which is expressed as Expression (5):
可以理解的是,针对不同的风机状态,表达式(3)中的x和Y(x)是不相同的,即不同风机状态对应的数据驱动模型不同。比如风机状态为叶片132的叶根力矩时,Y(x)表示叶根力矩的取值,x表示与叶根力矩相关的自变量参数向量,m表示与叶根力矩相关的自变量参数个数;又比如风机状态为塔架11顶部的前后方向受力值时,Y(x)表示塔架11前后受力值的取值,x表示与塔架11顶部的前后方向受力值相关的自变量参数向量,m表示与塔架11顶部的前后方向受力值相关的自变量参数个数。通过对风机100的运行数据进行回归分析,可以分别确定各风机状态对应的数据驱动模型的回归系数向量c,进而确定各风机状态对应的数据驱动模型。此处分别以风机状态为叶片132的叶根力矩和塔架11顶部的前后方向受力值为例,对数据驱动模型进行说明。It can be understood that, for different fan states, x and Y(x) in expression (3) are different, that is, the data-driven models corresponding to different fan states are different. For example, when the fan state is the blade root moment of the
在一些实施例中,风机状态为叶片132的叶根力矩时,与叶根力矩相关的自变量参数向量其中,Vwind表示风机100所在环境的风速;θwind表示风机100所在环境的风向;σwind表示风剪切系数;θazimuth表示叶片132在转动过程中的方位角,用于描述塔影效应;βi表示第i个叶片132的桨距角;表示第i个叶片132的桨距角转速;ωr表示第i个叶片132的转子13的转速。第i个叶片132的叶根力矩可以表达为表达式(6):In some embodiments, when the fan state is the blade root moment of the
表达式(6)中,Mi表示风机100的其中第i个叶片132的叶根力矩,表示与第i个叶片132的叶根力矩对应的自变量参数。In the expression (6), M i represents the blade root moment of the i-
同理,风机状态为塔架11顶部的前后方向受力值时,与塔架11顶部的前后方向受力值相关的自变量参数向量其中,Vwind表示风速;θwind表示风向;σwind表示风剪切系数;θazimuth表示叶片132在转动过程中的方位角,用于描述塔影效应;β1,β2,β3分别表示三个叶片132的桨距角;分别表示三个叶片132的桨距角转速。塔架11顶部的前后方向受力值可以表达为表达式(7):In the same way, when the fan state is the force value of the front and rear directions of the top of the
表达式(7)中,Ffore-aft表示塔架11顶部的前后方向受力值。In the expression (7), F fore-aft represents the force value in the front-rear direction of the top of the
在表达式(6)和(7)中,风速Vwind、风向θwind、风剪切系数σwind表示预测来流风信息,为在变桨控制的任一控制周期内,通过激光雷达等预测的未来一段时间内(即预测周期)的风速Vwind、风向θwind、风剪切系数σwind。可以将预测来流风信息直接代入到上述表达式(6)或(7),同时,将其他的参数通过桨距角转速来表示,以建立降载控制目标和桨距角转速的函数关系。以桨距角β和转子13的转速ωr为例:In expressions (6) and (7), the wind speed V wind , the wind direction θ wind , and the wind shear coefficient σ wind represent the predicted incoming wind information, which are predicted by lidar or the like in any control period of the pitch control. Wind speed V wind , wind direction θ wind , and wind shear coefficient σ wind in a future period of time (ie, forecast period). The predicted incoming wind information can be directly substituted into the above expression (6) or (7), and at the same time, the other parameters are passed through the pitch angle speed. to represent to establish the derating control target and the pitch angle speed functional relationship. Take the pitch angle β and the rotational speed ω r of the
在一个实施例中,通过桨距角转速来表示桨距角β的表达式可以表达为表达式(8):In one embodiment, the rotational speed through the pitch angle The expression to express the pitch angle β can be expressed as expression (8):
其中,t表示时间。where t represents time.
在一个实施例中,通过桨距角转速来表示转子13的转速ωr的表达式可以基于如下方法确定:In one embodiment, the rotational speed through the pitch angle The expression to express the rotational speed ω r of the
根据风机相关知识可知,风机100的功率计算公式可以表达为表达式(9):According to the relevant knowledge of the fan, the power calculation formula of the
进一步的,λ又可表达为表达式(10):Further, λ can be expressed as expression (10):
其中,λ表示参考叶尖速比;ρ为空气密度;R为转子13的半径,CP(λ,β)是风能捕获系数。进一步的,CP(λ,β)又可以表达为表达式(11):Among them, λ represents the reference tip speed ratio; ρ is the air density; R is the radius of the
进一步的,λi又可以基于表达式(12)确定:Further, λ i can be determined based on expression (12):
在一些实施例中,表达式(11)和表达式(12)中的a1为0.5176,a2为116,a3为0.4,a4为5,a5为21,a6为0.0068,b1为0.08,b2为0.035。In some embodiments, a 1 in Expression (11) and Expression (12) is 0.5176, a 2 is 116, a 3 is 0.4, a 4 is 5, a 5 is 21, a 6 is 0.0068, and b 1 is 0.08 and b2 is 0.035.
根据表达式(9)至表达式(12),可以确定由桨距角转速来表示的转子13转速ωr的表达式。According to Expressions (9) to (12), it is possible to determine the rotational speed by the pitch angle to express the expression of the
在一些实施例中,由于风机100的运行数据是仿真得到的,因此需要针对风机100建立风机模型,并基于风机模型对数据驱动模型中各参数的取值范围进行约束。其中一个实施例中,桨距角转速转子13的转速ωr、以及风机100的有效功率输出的约束条件如下:In some embodiments, since the operation data of the
ωr_cut≤ωr≤ωr_rate ω r_cut ≤ω r ≤ω r_rate
95%·Pref≤Pg≤105%·Pref 95%·P ref ≤P g ≤105%·P ref
其中,表示风机100的最小桨距角转速;表示风机100的最大桨距角转速;in, Indicates the minimum pitch angle speed of the
ωr_cut表示转子13的切入转速;ωr_rate表示转子13的额定转速;ω r_cut represents the cut-in rotational speed of the
Pref表示风机100的有效功率参考值。P ref represents the effective power reference value of the
需要说明的是,表达式(1)和(2)中,由于桨距角速度变化率可以直接表达为前后两个预测步长的桨距角转速之差,因此,针对降载控制目标可以无需建立对应的数据驱动模型来确定降载控制目标和桨距角转速的函数关系。It should be noted that in expressions (1) and (2), since the rate of change of the pitch angular velocity can be directly expressed as the pitch angular rotation speed of the two prediction steps before and after The difference, therefore, for the shedding control objective It is possible to determine load shedding control targets without establishing a corresponding data-driven model as a function of the pitch angle speed.
在一些实施例中,考虑到风机100所在环境的风况处于不断变化的过程中,在不同的工况下,一方面,上述表达式(1)和表达式(2)中的降载控制目标的权重可能会不一样。比如,在风速10m/s时,预测周期内的桨距角速度变化率的权重w3(vwind)可能为0.2,但在风速18m/s时,预测周期内的桨距角速度变化率的权重w3(vwind)可能需要调整到0.5。另一方面,在不同的风况下,每个控制周期获取的预测来流风信息可能不同,为使目标函数和数据驱动模型具有自适应性,提高预测准确性,在本申请一些实施例中,对于任一控制周期,根据该控制周期对应的预测来流风信息,确定对应该控制周期的目标函数中的多个降载控制目标分别对应的权重值,同时,数据驱动模型用于根据多个控制周期中每个控制周期对应的预测来流风信息,分别确定相应控制周期的至少部分降载控制目标与桨距角转速的函数关系。In some embodiments, considering that the wind condition of the environment where the
进一步的,每个控制周期的预测来流风信息可以包括相应控制周期之后多个预测步长内的预测来流风信息。对于任一控制周期来说,可以根据该控制周期之后任一预测步长内的预测来流风信息,确定该控制周期的与该预测步长对应的至少部分降载控制目标与桨距角转速的函数关系,以及该控制周期的与该预测步长对应的目标函数的各降载控制目标的权重值。基于此,上述表达式(6)又可以表达为表达式(15):Further, the predicted incoming wind information for each control period may include the predicted incoming wind information within a plurality of prediction steps after the corresponding control period. For any control period, the relationship between at least part of the derating control target and the pitch angle speed corresponding to the predicted step of the control period can be determined according to the predicted flow wind information in any predicted step after the control period. function relationship, and the weight value of each load-shedding control objective of the objective function corresponding to the prediction step size of the control period. Based on this, the above expression (6) can be expressed as expression (15):
其中,Mi(k+j)表示第i个叶片132在第k个控制周期的第j个预测步长的叶根力矩。Wherein, M i (k+j) represents the blade root moment of the i-
同理,上述表达式(7)又可以表达为表达式(16):Similarly, the above expression (7) can be expressed as the expression (16):
其中,表示塔架11在第k个控制周期的第j个预测步长的前后受力值。in, Represents the force value of the
继续参见图5,在确定目标函数和数据驱动模型后,可以执行步骤S52。Continuing to refer to FIG. 5 , after determining the objective function and the data-driven model, step S52 may be performed.
步骤S52,根据目标函数和数据驱动模型,确定目标函数取值最小时对应的目标桨距角转速。Step S52, according to the objective function and the data-driven model, determine the target pitch angle rotation speed corresponding to the minimum value of the objective function.
通过上述相关描述可知,数据驱动模型主要用于根据每个控制周期的预测来流风信息,确定各控制周期的至少部分降载控制目标与桨距角转速的函数关系,进而可以根据目标函数和每个控制周期确定的至少部分降载控制目标与桨距角转速的函数关系,分别确定对应的目标桨距角转速。结合参考图6,图6是图5中的步骤S52的子流程图,包括步骤S61和步骤S62。It can be seen from the above related descriptions that the data-driven model is mainly used to determine the functional relationship between at least part of the load reduction control target and the pitch angle speed of each control cycle based on the prediction of each control cycle to flow wind information. The functional relationship between at least part of the load reduction control target determined in each control cycle and the pitch angle rotational speed is determined, and the corresponding target pitch angle rotational speed is respectively determined. Referring to FIG. 6 in conjunction, FIG. 6 is a sub-flow chart of step S52 in FIG. 5 , including step S61 and step S62.
步骤S61,对于任一控制周期,根据目标函数和该控制周期确定的至少部分降载控制目标与桨距角转速的函数关系,确定待求解目标函数,其中,待求解目标函数的自变量包括桨距角转速,待求解目标函数的因变量用于表示风机在变桨控制中的结构载荷大小。Step S61, for any control period, determine the objective function to be solved according to the objective function and the functional relationship between at least part of the load reduction control target and the pitch angle rotational speed determined by the control period, wherein the independent variable of the objective function to be solved includes the propeller. The pitch angle speed, the dependent variable of the objective function to be solved is used to represent the structural load of the wind turbine in the pitch control.
在一些实施例中,根据上述相关描述可知,可以将该控制周期确定的至少部分降载控制目标与桨距角转速的函数关系代入到目标函数中,得到该控制周期的待求解目标函数。In some embodiments, according to the above related descriptions, the functional relationship between at least part of the load reduction control target determined in the control period and the pitch angle speed can be substituted into the objective function to obtain the objective function to be solved for the control period.
进一步的,对于包括多个预测步长的一个控制周期来说,可以根据目标函数和该控制周期之后任一预测步长对应的至少部分降载控制目标与桨距角转速的函数关系,确定该控制周期的与该预测步长对应的待求解目标函数。即分别将每个预测步长对应的至少部分降载控制目标与桨距角转速的函数关系代入到目标函数中,以得到与该预测步长对应的待求解目标函数。Further, for a control cycle including a plurality of prediction steps, the target function can be determined according to the functional relationship between the objective function and any prediction step after the control cycle corresponding to at least part of the derating control target and the pitch angle speed. The objective function to be solved corresponding to the prediction step size of the control period. That is, the functional relationship between at least part of the load reduction control target corresponding to each prediction step and the pitch angular rotation speed is substituted into the objective function, so as to obtain the objective function to be solved corresponding to the prediction step.
步骤S62,基于智能优化求解算法,对待求解目标函数进行求解,以确定对应的目标桨距角转速。Step S62, based on the intelligent optimization solution algorithm, the objective function to be solved is solved to determine the corresponding target pitch angle rotation speed.
对于包括多个预测步长的一个控制周期来说,可以基于智能优化求解算法,对该控制周期的与各预测步长对应的待求解目标函数进行求解,以确定对应的目标桨距角转速。在一些实施例中,可以使M个粒子在空间进行搜索,以确定该控制周期的与多个预测步长对应的目标桨距角转速序列。具体而言,可以在该控制周期迭代N次,每次迭代针对该控制周期对应的所有预测步长,即每迭代一次,分别确定该控制周期的与各预测步长对应的一个桨距角转速。比如假如一个控制周期对应10个预测步长,风机100包括3个叶片132,每迭代一次,便可确定10×3个桨距角转速,该10×3个桨距角转速分别与该10个预测步长对应,为当次迭代中使表达式(2)所示的目标函数取值最小的最优点。For a control cycle including multiple prediction steps, the objective function to be solved corresponding to each prediction step of the control cycle can be solved based on an intelligent optimization solution algorithm to determine the corresponding target pitch angle speed. In some embodiments, M particles may be searched in space to determine a target pitch angle rotation speed sequence corresponding to a plurality of predicted step sizes for the control period. Specifically, it is possible to iterate N times in the control cycle, and for each iteration, for all prediction steps corresponding to the control cycle, that is, each iteration, determine a pitch angle rotation speed corresponding to each prediction step in the control cycle. . For example, if one control cycle corresponds to 10 prediction steps, and the
此处假设在第k个控制周期第i次迭代,第l个粒子表示的第j个预测步长对应的三个叶片132的桨距角转速可以表达为表达式(17):It is assumed here that in the i-th iteration of the k-th control cycle, the pitch angular rotation speeds of the three
其中,l=1,2,…,M,i=1,2,…,N,i_1、i_2、i_3用于区分三个叶片132。Wherein, l=1,2,...,M, i=1,2,...,N, i_1, i_2, i_3 are used to distinguish the three
则在第k个控制周期第i次迭代,第l个粒子表示的所有预测步长对应的三个叶片132的桨距角转速可以表达为表达式(18):Then in the i-th iteration of the k-th control cycle, the pitch angular rotation speeds of the three
其中,n表示预测步长的数量。where n represents the number of prediction steps.
在寻找目标函数取值最小时对应的目标桨距角转速时,第l个粒子可以根据表达式(19)和表达式(20)定义参数空间中的轨迹:When looking for the target pitch angle rotation speed corresponding to the minimum value of the objective function, the lth particle can define the trajectory in the parameter space according to expressions (19) and (20):
表示第i+1次迭代桨距角转速相对于第i次迭代的桨距角转速的变化率; Represents the i+1th iteration pitch angle speed The pitch angle speed relative to the ith iteration rate of change;
表示第i+1次的桨距角转速; Indicates the i+1th pitch angle speed;
为第i次迭代中使表达式(2)所示的目标函数取值最小时所对应的局部最优点; is the local optimum point corresponding to the minimum value of the objective function shown in expression (2) in the ith iteration;
为所有1至i次迭代中使表达式(2)所示的目标函数取值最小时所对应的全局最优点。 is the global optimal point corresponding to the minimum value of the objective function shown in expression (2) in all 1 to i iterations.
c1和c2是学习因子;c 1 and c 2 are learning factors;
r1和r2为均匀分布与[0,1]之间的两个随机数;r 1 and r 2 are two random numbers between uniform distribution and [0,1];
ω为惯性权重,表示对的速度变化率的继承。ω is the inertia weight, representing the pair The rate of change of velocity is inherited.
基于如上计算,可以最终确定在第k个控制周期,经过N次迭代后,使目标函数中的目标函数取值最小时所对应的各个预测步长的桨距角转速,并将该桨距角转速作为目标桨距角转速。此处假设目标桨距角转速为则可以表达为表达式(20):Based on the above calculation, the pitch angle rotation speed of each prediction step corresponding to the minimum value of the objective function in the objective function can be finally determined after N iterations in the kth control cycle, and the pitch angle The rotational speed is taken as the target pitch angle rotational speed. Here, it is assumed that the target pitch angle speed is but can be expressed as expression (20):
其中,表示第k个控制周期第1个预测步长对应的桨距角转速;in, represents the pitch angle speed corresponding to the first prediction step of the kth control cycle;
类似的,表示第k个控制周期第2个预测步长对应的桨距角转速;akin, represents the pitch angle speed corresponding to the second prediction step of the kth control cycle;
类似的,表示第k个控制周期第n个预测步长对应的桨距角转速。akin, Indicates the pitch angle speed corresponding to the nth prediction step of the kth control cycle.
基于粒子群算法来对待求解目标函数求解,求解速度快,收敛性更好。Based on the particle swarm algorithm to solve the objective function, the solution speed is fast and the convergence is better.
继续参见图5,在确定目标桨距角转速,可继续执行步骤S53。Continue to refer to FIG. 5 , after determining the target pitch angle rotation speed, step S53 may be continued.
步骤S53,根据目标桨距角转速,对风机100进行变桨控制。Step S53, performing pitch control on the
在一些实施例中,对于任一控制周期,根据在该控制周期内确定的目标桨距角转速在该控制周期之后下一个控制周期内对风机100进行变桨控制。从而使得在下一个控制周期对风机100进行变桨控制时,桨距角转速使结构载荷最小。In some embodiments, for any control period, according to the target pitch angle speed determined in the control period The pitch control of the
进一步的,在一些实施例中,控制周期、预测周期和预测步长的关系可是这样的:比如假设每秒为一个控制周期,每个控制周期对应的预测周期为相应控制周期之后10秒的时段,在预测周期内,每1秒为一个预测步长。Further, in some embodiments, the relationship between the control period, the prediction period and the prediction step size may be as follows: for example, assuming that every second is a control period, the prediction period corresponding to each control period is a period of 10 seconds after the corresponding control period. , in the prediction period, every 1 second is a prediction step.
基于上述假设,可以明显看到,第一个控制周期(例如:第1秒),会确定第一预测周期(例如:第2秒至第11秒)内每个预测步长的目标桨距角转速,即会分别确定第2秒、第3秒、……、第11秒的目标桨距角转速;Based on the above assumptions, it can be clearly seen that the first control period (for example: the first second) will determine the target pitch angle of each prediction step in the first prediction period (for example: the second to the 11th second). speed, the target pitch angle speed at the 2nd, 3rd, ... and 11th seconds will be determined respectively;
同理,第二个控制周期(第2秒),会确定第二预测周期(第3秒至第12秒)内每个预测步长的目标桨距角转速,即会分别确定第3秒、第4秒、……、第12秒的目标桨距角转速。Similarly, in the second control cycle (second second), the target pitch angle speed of each prediction step in the second prediction cycle (second to 12th second) will be determined, that is, the third second, The target pitch angle rotation speed at the 4th second, ..., the 12th second.
根据上述举例可以看出,在第一个控制周期(第1秒),只需输出第一预测周期内第一预测步长(第2秒)的目标桨距角转速即可,用于在第二个控制周期(第2秒)对风机100进行变桨控制;等风机100运行到第3秒,此时,第二个控制周期已经基于最新的预测来流风信息,输出了针对第3秒的目标桨距角转速,此时可以基于第二个控制周期(第2秒)输出的第一预测周期内(第3秒)的目标桨距角转速对风机100进行变桨控制即可。即对于任一控制周期,可以根据该控制周期的与第一个预测步长对应的目标桨距角转速,即表达式20第一列的目标桨距角转速在该控制周期之后下一个控制周期内对风机100进行变桨控制。如此,可以在变桨过程中,进一步降低风机100的结构载荷。According to the above example, it can be seen that in the first control period (the 1st second), it is only necessary to output the target pitch angle speed of the first prediction step (the 2nd second) in the first prediction period, which is used in the first prediction period. Two control cycles (the second second) to control the pitch of the
基于以上描述可知,本申请的一些实施例中,变桨控制方法确定目标函数和数据驱动模型,根据目标函数和数据驱动模型,确定目标函数值最小时对应的目标桨距角转速,再基于目标桨距角转速对风机100进行变桨控制。通过对桨距角转速进行控制,使得风机100在变桨过程中,运行在使结构载荷最小时的桨距角转速,避免了桨距角转速恒定造成的变桨控制策略有效性下降的问题,提高了风机100在变桨过程中的降载效果。Based on the above description, in some embodiments of the present application, the pitch control method determines an objective function and a data-driven model, and according to the objective function and the data-driven model, determines the target pitch angle rotation speed corresponding to the minimum value of the objective function, and then based on the target The pitch angle rotational speed controls the pitch of the
图7是本申请一个实施例提供的变桨控制系统800的模块框图。FIG. 7 is a module block diagram of a
变桨控制系统800包括一个或多个处理器801,用于实现如上描述的变桨控制方法。在一些实施例中,变桨控制系统800可以包括可读存储介质809,可读存储介质809可以存储有可被处理器801调用的程序,可以包括非易失性存储介质。The
在一些实施例中,变桨控制系统800可以包括内存808和接口807。In some embodiments,
在一些实施例中,变桨控制系统800还可以根据实际应用包括其他硬件。In some embodiments, the
本申请实施例的可读存储介质809,其上存储有程序,该程序被处理器801执行时,用于实现如上描述的变桨控制方法。The
本申请可采用在一个或多个其中包含有程序代码的可读存储介质809(包括但不限于磁盘存储器、CD-ROM、光学存储器等)上实施的计算机程序产品的形式。可读存储介质809包括永久性和非永久性、可移动和非可移动媒体,可以由任何方法或技术来实现信息存储。信息可以是计算机可读指令、数据结构、程序的模块或其他数据。可读存储介质809的例子包括但不限于:相变内存(PRAM)、静态随机存取存储器(SRAM)、动态随机存取存储器(DRAM)、其他类型的随机存取存储器(RAM)、只读存储器(ROM)、电可擦除可编程只读存储器(EEPROM)、快闪记忆体或其他内存技术、只读光盘只读存储器(CD-ROM)、数字多功能光盘(DVD)或其他光学存储、磁盒式磁带,磁带磁磁盘存储或其他磁性存储设备或任何其他非传输介质,可用于存储可以被计算设备访问的信息。The present application may take the form of a computer program product embodied on one or more readable storage media 809 (including but not limited to disk storage, CD-ROM, optical storage, etc.) having program code embodied therein.
以上所述仅为本说明书的较佳实施例而已,并不用以限制本说明书,凡在本说明书的精神和原则之内,所做的任何修改、等同替换、改进等,均应包含在本说明书保护的范围之内。The above descriptions are only preferred embodiments of this specification, and are not intended to limit this specification. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of this specification shall be included in this specification. within the scope of protection.
以上所述仅为本说明书的较佳实施例而已,并不用以限制本说明书,凡在本说明书的精神和原则之内,所做的任何修改、等同替换、改进等,均应包含在本说明书保护的范围之内。The above descriptions are only preferred embodiments of this specification, and are not intended to limit this specification. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of this specification shall be included in this specification. within the scope of protection.
还需要说明的是,术语“包括”、“包含”或者其任何其他变体意在涵盖非排他性的包含,从而使得包括一系列要素的过程、方法、商品或者设备不仅包括那些要素,而且还包括没有明确列出的其他要素,或者是还包括为这种过程、方法、商品或者设备所固有的要素。在没有更多限制的情况下,由语句“包括一个……”限定的要素,并不排除在包括所述要素的过程、方法、商品或者设备中还存在另外的相同要素。It should also be noted that the terms "comprising", "comprising" or any other variation thereof are intended to encompass a non-exclusive inclusion such that a process, method, article or device comprising a series of elements includes not only those elements, but also Other elements not expressly listed, or which are inherent to such a process, method, article of manufacture, or apparatus are also included. Without further limitation, an element qualified by the phrase "comprising a..." does not preclude the presence of additional identical elements in the process, method, article of manufacture, or device that includes the element.
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