WO2018107726A1 - 基于定子电流数据驱动的双馈风电机组桨叶不平衡检测方法 - Google Patents

基于定子电流数据驱动的双馈风电机组桨叶不平衡检测方法 Download PDF

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WO2018107726A1
WO2018107726A1 PCT/CN2017/091412 CN2017091412W WO2018107726A1 WO 2018107726 A1 WO2018107726 A1 WO 2018107726A1 CN 2017091412 W CN2017091412 W CN 2017091412W WO 2018107726 A1 WO2018107726 A1 WO 2018107726A1
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stator
speed
wind turbine
amplitude
doubly
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PCT/CN2017/091412
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叶杭冶
许国东
邱纪星
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浙江运达风电股份有限公司
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Priority to DK17881919.9T priority Critical patent/DK3557050T3/da
Priority to ES17881919T priority patent/ES2942286T3/es
Priority to EP17881919.9A priority patent/EP3557050B1/en
Publication of WO2018107726A1 publication Critical patent/WO2018107726A1/zh

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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01MTESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M1/00Testing static or dynamic balance of machines or structures
    • G01M1/14Determining imbalance
    • G01M1/16Determining imbalance by oscillating or rotating the body to be tested
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03DWIND MOTORS
    • F03D17/00Monitoring or testing of wind motors, e.g. diagnostics
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/34Testing dynamo-electric machines
    • G01R31/343Testing dynamo-electric machines in operation
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00Energy generation through renewable energy sources
    • Y02E10/70Wind energy
    • Y02E10/72Wind turbines with rotation axis in wind direction

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  • the invention belongs to the technical field of online fault diagnosis of a wind turbine, and relates to a method for detecting blade imbalance of a doubly-fed wind turbine based on stator current data driving.
  • the operating environment of wind turbines is usually harsh, and the blades are more unbalanced due to sand and icing. Especially in recent years, the increase of unit capacity and the promotion and application of low-speed units make the blades longer and longer.
  • the imbalance of the impeller, including the pneumatic imbalance, is easily transmitted to the transmission chain, causing the vibration of the whole machine to be intensified, and even causing an accident when it is serious.
  • the detection of wind turbine generator blade imbalance can be detected by video analysis, vibration detection, electrical information, etc.
  • most of these methods need to increase equipment, which is not only costly, but also has low reliability and poor adaptability.
  • various research institutes and wind turbine manufacturers have also conducted research on blade imbalance and published some patents. For example, "the stator current diagnosis method of doubly-fed wind turbine generator with impeller imbalance fault", the extraction of the characteristic components by the method requires secondary derivation to reconstruct the stator current and the quadratic FFT operation, and the processing process is complicated.
  • Another example is “a method for online fault diagnosis of blade unbalanced wind turbine generators", which processes electric power and needs to collect voltage and current quantities, and these methods are theoretically feasible, but The project has poor adaptability to wind farms in different regions, blades of different manufacturers, and different fan operating conditions.
  • the present invention provides a simple and easy to use, good accuracy and good applicability based on stator current data driven doubly-fed Wind turbine blade imbalance detection method.
  • a method for detecting blade imbalance of a doubly-fed wind turbine based on stator current data driving comprising the following steps:
  • stator phase current i A and the speed r during the constant speed operation are collected, and the amplitude Q (1) of the first frequency is calculated according to the methods in steps 1) and 2);
  • the rms value of the rotational speed is within a set reasonable range, and the reasonable range is between 0-15.
  • step 2) the method of calculating the impeller speed 1 octave f(1) according to the generator rotational speed is as follows:
  • Equation (1) r is the generator speed and b is the gearbox ratio.
  • step 3 the curve fitting is performed by the least squares method as follows:
  • a 0 , a 1 , ⁇ a n is the coefficient to be determined.
  • the invention obtains the reference value under the condition by fitting, and obtains the diagnosis conclusion by comparing with the reference value.
  • the noise interference is further eliminated, the effect is remarkable, and the detection rate is improved by the error compensation method.
  • Figure 1 is a flow chart of the present invention
  • Figure 2 is a flow chart of signal analysis
  • Figure 3 is the torque-speed curve of the unit in normal operation mode
  • Figure 4 is the A phase current and speed curve of the generator stator when the blade is balanced
  • Figure 5 is a comparison curve of A phase current FFT analysis of blade balance and unbalance
  • Figure 6 is a spectrum comparison curve after Hilbert processing when the blade is balanced and unbalanced
  • Figure 7 is the relationship between the characteristic amplitude and the phase current RMS value when the blade is balanced and unbalanced
  • Figure 8 is a comparison of diagnostic results for three blade states.
  • a method for detecting blade imbalance of a doubly-fed wind turbine based on stator current data is as follows:
  • T m is the wind turbine output torque and ⁇ m is the impeller speed. Is the initial phase.
  • T e is the generator electromagnetic torque
  • amplitude of the ⁇ T e unbalanced torque Is the initial phase
  • stator-side generator convention Under the grid voltage orientation, stator-side generator convention, rotor-side motor convention, coordinate transformation, the expression of electromagnetic torque in dq coordinates can be obtained, and then the stator d-axis current i sd can be obtained.
  • i sd is the d-axis current and ⁇ i sd is the amplitude of the oscillating component. Is the initial phase.
  • stator voltage equation and flux linkage in the dq axis system can be expressed as equations (7) and (8), respectively, and then (6), the stator q-axis current can be obtained.
  • the data collected in the data is subjected to Hilbert transform, and the amplitude envelope signal is processed by FFT.
  • the Hilbert transform is performed on the stator phase current i A to obtain the transformed signal i B , and the analytical signal Z(t) is further obtained, and the amplitude envelope A(t) is obtained for the analytical signal.
  • i B (t) is the Hilbert transform output value of i A (t).
  • A(t) is the envelope amplitude of i A .
  • a 0 , a 1 , ⁇ a n is the coefficient to be determined.
  • step 5 According to the stator current data collected in step 4), combined with the result of fitting in step 3), the corresponding reference amplitude Q_base(1) under the working condition is obtained.
  • the parameters involved in this embodiment can be obtained from the existing sensors of the wind power generator, without adding new equipment, and the monitoring cost is low;
  • the invention obtains the reference value under the condition by fitting, and obtains the diagnosis conclusion by comparing with the reference value.
  • the noise interference is further eliminated, the effect is remarkable, and the detection rate is improved by the error compensation method.
  • Figure 7 is the relationship between the characteristic amplitude and the stator A phase current when the blade balances and unbalances.
  • the solid line indicates the imbalance and the broken line indicates the balance, it is obvious that the output power increases with the stator side. The value also increases significantly.
  • the constant speed operation phase mentioned in the text refers to the rotation speed between 1700-1800 rpm, and the pitch does not move. If the pitch is generated during the period, the extraction of the fault information will become more difficult. Near rated power.
  • Fig. 8 shows the data under normal operation
  • the middle part shows the data when the single blade pitch angle deviation is artificially set by 2 degrees
  • the upper part shows the artificial setting of the single blade pitch angle deviation of 4 degrees. data.
  • the present invention judges the difference between Q(1) and Q_base(1) and offset, that is, when the difference is greater than zero, it can be determined that the blade imbalance exists, and the determination condition of the present invention is based on a large amount of experimental data. Is not limited to this instance.
  • the invention diagnoses the blade imbalance fault by the doubly-fed wind turbine speed and the stator phase current, and the required data can be collected by the existing data acquisition equipment of the wind power generator, and can be quickly obtained by running the test mode for a short time.
  • the effective data packet is simple and effective, and the diagnostic cost is low. It is an effective and reliable method for fault diagnosis of blade imbalance.

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  • Life Sciences & Earth Sciences (AREA)
  • Sustainable Development (AREA)
  • Sustainable Energy (AREA)
  • Chemical & Material Sciences (AREA)
  • Combustion & Propulsion (AREA)
  • Mechanical Engineering (AREA)
  • General Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
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  • Tests Of Circuit Breakers, Generators, And Electric Motors (AREA)

Abstract

一种基于定子电流数据驱动的双馈风电机组桨叶不平衡检测方法,在桨叶不平衡条件下,采集多组恒转速运行阶段的定子相电流i A和转速r信息,并进行希尔伯特变换,得到幅值包络信号,对包络信号进行FFT变换,提取叶轮1倍转频处幅值;利用最小二乘法拟合桨叶平衡时1倍转频处幅值与定子相电流的关系;机组运行中,采集恒转速运行阶段定子相电流i A和转速r,并计算出1倍频的幅值Q(1);根据采集的i A并结合拟合的曲线,计算出Q_base(1),若满足Q(1)>Q_base(1)+offset,则判断不平衡存在,且根据差值大小给出不平衡程度。该检测方法简单易行、准确性良好、适用性较好。

Description

基于定子电流数据驱动的双馈风电机组桨叶不平衡检测方法
本申请要求于2016年12月13日提交中国专利局、申请号为201611143926.1、发明名称为“基于定子电流数据驱动的双馈风电机组桨叶不平衡检测方法”的中国专利申请的优先权,其全部内容通过引用结合在本申请中。
技术领域
本发明属于风电机组的在线故障诊断技术领域,涉及一种基于定子电流数据驱动的双馈风电机组桨叶不平衡检测方法。
背景技术
风电机组的运行环境通常都比较恶劣,叶片更会因风沙、结冰等造成质量不平衡,特别是近年来机组容量的增大及低风速机组的推广应用,使得叶片越来越长。叶轮的不平衡,包括气动不平衡,易传递到传动链,造成整机的振动加剧,严重时甚至导致事故的发生。
考虑到不同叶片的差异性、故障机理的复杂性,难以建立较准确地诊断模型。采用传统类似固定阈值的判断方法,因阈值的确定依赖经验及少量试验,难以满足对不同风场、不同叶片的适应性。
目前风力发电机组桨叶不平衡的检测可通过视频分析、振动检测、电信息等手段,但是这些方法大都需要增加设备,不仅成本大,而且可靠性不高、适应性较差。近来各研究机构及风机制造商也对桨叶不平衡进行了相关研究,以及公布了一些专利。如“叶轮不平衡故障的双馈风力发电机定子电流诊断方法”,该方法对特征分量的提取需经二次求导重构定子电流和二次FFT运算,处理过程复杂。又如“一种双馈风力发电机叶片不平衡在线故障诊断方法”,是对电功率进行处理,需要采集电压和电流量,并且这些方法理论上可行,但 工程上面对不同地域的风场、不同厂家的叶片、不同的风机运行工况,适应性较差。
发明内容
为了克服已有双馈风力发电机组叶片不平衡检测方法在准确性、适应性方面的不足,本发明提供一种简单易行、准确性良好、适用性较好的基于定子电流数据驱动的双馈风电机组桨叶不平衡检测方法。
本发明解决其技术问题所采用的技术方案是:
一种基于定子电流数据驱动的双馈风电机组桨叶不平衡检测方法,所述检测方法包括如下步骤:
1)桨叶平衡条件下,采集多组机组恒转速运行阶段的定子相电流iA和转速r信息,并进行希尔伯特变换,得到幅值包络信号,要求数据采集期间未进行变桨动作;
2)对步骤1中的包络信号进行FFT变换,并根据发电机转速r计算叶轮1倍转频f(1);
3)根据步骤1)和2),得出叶轮1倍转频处的幅值大小,利用最小二乘法拟合出桨叶平衡时,1倍频处幅值与定子相电流的关系曲线;
4)机组运行中,采集恒转速运行期间定子相电流iA和转速r,并按照步骤1)和2)中方法计算出1倍频的幅值Q(1);
5)根据步骤4)中采集的电流,并结合步骤3)中拟合的曲线,计算出Q_base(1);
6)比较Q(1)和Q_base(1))及offset的关系,若其满足Q(1)>Q_base(1)+offset,则判断不平衡存在,且根据差值大小给出不平衡程度,其中offset为残差补偿。
进一步,所述步骤1)中,所述的恒转速运行阶段,转速方均根值在设定的合理范围内,所述合理范围为0-15之间。
再进一步,在步骤2)中,根据发电机转速计算叶轮转速1倍频f(1)的方法如下:
Figure PCTCN2017091412-appb-000001
式(1)中,r为发电机转速,b为齿轮箱速比。
更进一步,在步骤3)中,采用最小二乘法进行曲线拟合,方法如下:
Figure PCTCN2017091412-appb-000002
式中
Figure PCTCN2017091412-appb-000003
为待求函数,
Figure PCTCN2017091412-appb-000004
为某一函数类,a0,a1,···an为待求系数。
Figure PCTCN2017091412-appb-000005
式中,P表示求得的数据与实际数据满足误差的平方和的最小值。
本发明的有益效果主要表现在:
1)本发明涉及的信息的提取无需增加新的设备,硬件成本较低;
2)因故障特征量本身很小,且不同工况下亦有不同。本发明通过拟合的方式,得出该条件下基准值,通过与基准值的比较得出诊断结论。进一步排除了噪声的干扰,效果显著,且通过误差补偿的方式,提高了检测率。
附图说明
为了更清楚地说明本发明实施例中的技术方案,下面将对实施例描述中所需要使用的附图作简要介绍,显而易见地,下面描述中的附图仅仅是本发明的一些实施例,对于本领域的普通技术人员来讲,在不付出创造性劳动的前提下,还可以根据这些附图获得其他的附图。
图1为本发明流程图;
图2为信号分析流程图;
图3为机组正常运行模式下的转矩-转速曲线;
图4为桨叶平衡时发电机定子A相电流和转速曲线;
图5为桨叶平衡与不平衡时A相电流FFT分析对比曲线;
图6为桨叶平衡与不平衡时Hilbert处理后频谱对比曲线;
图7为桨叶平衡与不平衡时特征幅值与相电流有效值关系;
图8为三种桨叶状态下,诊断结果的对比图。
具体实施方式
下面结合附图对本发明作进一步描述。
参照图1-图8,一种基于定子电流数据驱动的双馈风电机组桨叶不平衡检测方法,该方法步骤如下:
1)风电机组运行于恒转速附近,且叶片平衡时采集定子相电流iA和发电机转速r。在叶片不平衡时,会在定子电流中有呈现,如以质量不平衡为例进行介绍。假设某一叶片在距轮毂R处增加了一质量块m,此时的气动转矩可表示成:
Figure PCTCN2017091412-appb-000006
式中Tm为风力机输出转矩,ωm为叶轮转速,
Figure PCTCN2017091412-appb-000007
为初始相位。
1.1)对(4)式,结合转子运动方程,可以得到电磁转矩中也含有振荡分量。
Figure PCTCN2017091412-appb-000008
式中Te为发电机电磁转矩,ΔTe不平衡转矩的幅值,
Figure PCTCN2017091412-appb-000009
为初始相位。
1.2)在电网电压定向下,定子侧发电机惯例、转子侧电动机惯例,进行坐标变换,可以得到dq坐标下电磁转矩的表达式,进而可求得定子d轴电流isd
Figure PCTCN2017091412-appb-000010
式中,isd为d轴电流,Δisd为震荡分量幅值,
Figure PCTCN2017091412-appb-000011
为初始相位。
1.3)在1.2)的条件下,dq轴系下定子电压方程和磁链可分别表示为式(7)和(8),再有(6)式,可求出定子q轴电流。
Figure PCTCN2017091412-appb-000012
Figure PCTCN2017091412-appb-000013
Figure PCTCN2017091412-appb-000014
1.4)由定子dq轴电流,根据坐标变换即可求出abc坐标系下的值iA
Figure PCTCN2017091412-appb-000015
从式(10)中,可以看到不平衡时会在定子电流中产生f1±fm次的谐波分量。
中采集的数据进行Hilbert变换,对幅值包络信号FFT处理。
对定子相电流iA做Hilbert变换,得到变换之后的信号iB,进一步得到解析信号Z(t),对解析信号求幅值包络A(t)
Figure PCTCN2017091412-appb-000016
式中iB(t)是iA(t)的希尔伯特变换输出值。
Z(t)=iA(t)+jiB(t)           (12)
式中Z(t)为解析函数。
Figure PCTCN2017091412-appb-000017
式中A(t)为iA的包络幅值。
2)对步骤1中的包络信号进行FFT变换,并根据发电机转速r计算叶轮1倍转频f(1);方法如下:
Figure PCTCN2017091412-appb-000018
3)对包络信号A(t)进行FFT变换得到频谱信号,从中提取叶轮转速的1 倍频幅值;利用最小二乘法拟合出桨叶平衡时,1倍频处特征幅值与定子相电流的关系:
Figure PCTCN2017091412-appb-000019
式中
Figure PCTCN2017091412-appb-000020
为待求函数,
Figure PCTCN2017091412-appb-000021
为某一函数类,a0,a1,···an为待求系数。
Figure PCTCN2017091412-appb-000022
式中,P表示求得的数据与实际数据满足误差的平方和的最小值;
4)风机运行时,采集定子侧相电流和转速信息,按照步骤1)和2)中方法求出叶轮转速1倍频处特征幅值Q(1);
5)根据步骤4)中采集的定子电流数据,结合步骤3)中拟合的结果,求出该工况下对应的基准幅值Q_base(1)。
6)比较Q(1)和Q_base(1)的关系,若满足Q(1)>Q_base(1)+offset,则判断桨叶不平衡存在。
本实施例涉及的参数均可从风力发电机的现有传感器中获取,无需增加新设备,监测成本低;
因故障特征量本身很小,且不同工况下亦有不同。本发明通过拟合的方式,得出该条件下基准值,通过与基准值的比较得出诊断结论。进一步排除了噪声的干扰,效果显著,且通过误差补偿的方式,提高了检测率。
以某三桨叶的1.5MW双馈风力发电机组为研究对象,机组运行于恒转速阶段时,即转速为1750rpm附近,运行区域如图3中所示,采集双馈机组恒转速运行附近的转速和定子相电流并进行信号分析,电流和转速时域波形如图4所示。图5是叶片平衡与不平衡时电流的频域图,可以明显看到在频率f=50±0.275Hz处两者的区别,叶片不平衡时该处幅值偏大。为了进一步消除噪声、使特征量的提取更加准确,进行Hilbert变换,对幅值包络FFT分析, 频谱如图6所示。图7是桨叶平衡与不平衡时特征幅值与定子A相电流的关系曲线,其中实线表示不平衡时,虚线表示平衡时,很明显看到随着定子侧输出功率的增加,特征幅值也明显的增大。
需要说明的是,文中提到的恒转速运行阶段是指转速在1700-1800rpm之间,且变桨未动作,若期间发生变桨,则故障信息的提取将变得更加困难,此时机组输出接近额定功率。
现分别对下面三种情况进行试验:叶片平衡时、人为设置某一叶片桨距角偏差2度、人为设置某一叶片桨距角偏差4度。分别在上述三种情况下,机组运行于恒转速阶段时,采集定子相电流和发电机转速进行分析,需多采集平衡情况下的数据。
对上述三种实验情况进行检测分析,每种实验情况采集8组数据,共24组数据,用本发明方法对24组数据进行分析,比较Q(1)和Q_base(1)及offset的大小,图8为三种实验情况的效果统计图,横坐标为数据组数,纵坐标为Q(1)与Q_base(1)和offset的差值。
图8中最下面部分表示正常运行情况下的数据,中间部分表示人为设置单片桨叶桨距角偏差2度时的数据,上面部分表示人为设置单片桨叶桨距角偏差4度时的数据。从图中可以看出,桨叶平衡时,其值小于或接近于零,不平衡时,其值大于零;且不平衡度越大时,其值也越大。于是,统计分析测试点的纵坐标位置即可得出对叶轮平衡性的判断结论。针对不同的叶片,根据其结构和气动设计的差异,以及考虑到最小二乘法中残差的影响,应从理论分析和实测数据出发来选取合适的offset。
从大量的实验数据中,得出正常情况时,Q(1)与Q_base(1)和offset的差值小于零,桨叶不平衡时其差值大于零。因此本发明以判断Q(1)与Q_base(1)及offset的差值为判断依据,即当其差值大于零时,可以判定桨叶不平衡存在,本发明的判定条件是基于大量实验数据的,并不局限于该实例.
本发明通过双馈风力发电机转速和定子相电流对桨叶不平衡故障进行诊断,所需数据可通过风力发电机组现有的数据采集设备采集,通过运行短时间运行于检测模式,可快速得到有效数据包,简单有效,诊断成本低,是一种有效可靠的桨叶不平衡故障诊断方法。
最后需要说明的是,以上实施例仅用以说明本发明的技术方案而非限制,本领域技术人员应当理解,可以在形式上和细节上对本发明做出改变,而不偏离发明权利要求书所限定的范围。
还需要说明的是,本文中所公开的实例描述的各参数,仅是为了更好的描述本发明,专业人员可以意识到,通过修改本发明的参数值可达到同样的诊断效果,但是这种实现不应认为超出本发明的范围。
对所公开的实施例的上述说明,使本领域专业技术人员能够实现或使用本发明。本文中所定义的一般原理可以在不脱离本发明的精神或范围的情况下,在其它实施例中实现。因此,本发明将不会被限制于本文所示的这些实施例,而是要符合与本文所公开的原理和新颖特点相一致的最宽的范围。

Claims (4)

  1. 一种基于定子电流数据驱动的双馈风电机组桨叶不平衡检测方法,其特征在于:所述检测方法包括如下步骤:
    1)桨叶平衡条件下,采集多组机组恒转速运行阶段的定子相电流iA和转速r信息,并进行希尔伯特变换,得到幅值包络信号,要求数据采集期间未进行变桨动作;
    2)对步骤1中的包络信号进行FFT变换,并根据发电机转速r计算叶轮1倍转频f(1);
    3)根据步骤1)和2)的计算,得出叶轮1倍转频处的幅值大小,利用最小二乘法拟合出桨叶平衡时,1倍频处幅值与定子相电流的关系曲线;
    4)机组运行中,采集恒转速运行期间定子相电流iA和转速r,并按照步骤1)和2)中方法计算出1倍频的幅值Q(1);
    5)根据步骤4)中采集的电流,并结合步骤3)中拟合的曲线,计算出Q_base(1);
    6)比较Q(1)和Q_base(1)及offset的关系,若其满足Q(1)>Q_base(1)+offset,则判断不平衡存在,且根据差值大小给出不平衡程度,其中offset为残差补偿。
  2. 如权利要求1所述的一种基于定子电流数据驱动的双馈风电机组桨叶不平衡检测方法,其特征在于:所述步骤1)中,所述的恒转速运行阶段,转速方均根值在设定的合理范围内。
  3. 如权利要求1或2所述的一种基于定子电流数据驱动的双馈风电机组桨叶不平衡检测方法,其特征在于:在步骤2)中,根据发电机转速计算叶轮转速1倍频f(1)的方法如下:
    Figure PCTCN2017091412-appb-100001
    式(1)中,r为发电机转速,b为齿轮箱速比。
  4. 如权利要求1或2所述的一种基于定子电流数据驱动的双馈风电机组桨叶不平衡检测方法,其特征在于:在步骤3)中,采用最小二乘法进行曲线拟合,方法如下:
    Figure PCTCN2017091412-appb-100002
    式中
    Figure PCTCN2017091412-appb-100003
    为待求函数,
    Figure PCTCN2017091412-appb-100004
    为某一函数类,a0,a1,···an为待求系数;
    Figure PCTCN2017091412-appb-100005
    式中,P表示求得的数据与实际数据满足误差的平方和的最小值。
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