Extreme Loads Calculate and Security Analysis of Wind Turbine Variable Pitch Drive Control
DENG Ying， JIANG Yujie，ZHOU Feng，LEI Hang，TIAN De 1. Wind Energy Research Centre Of North China Electric Power University, 2. National Key Laboratory For New Energy Power System, Beijing 102206, China Variable pitch drive load, Extrapolation method, Limit load, Safety analysis.
Key Abstract: word:
Wind turbine pitch control can adjust the output power and the load of wind turbine, the control goals is achieved by variable pitch drive device. Variable pitch device endures load in the operation process, and the loadbearing capacity influences the safe operation of wind turbine. Variable pitch drive device as an important part of the wind turbine, the unit reliability depends on its performance. In this paper, according to the wind turbine operation control requirements, combine different working conditions, using GL-bladed software carry out variable pitch drive device load calculation to estimate the variable pith drive device maximum load during the wind turbine 20 years running, and take it as the benchmark threshold of safety design， in addition, make a reasonable assessment of the degree of confidence of this calculation. According to IEC61400-1: 2005 infer extreme loads of 50 years ,take this as the reference threshold of the safety design , but take this threshold as a design rating of the variable pitch drive device, greatly improve the security, so as the cost .This paper puts forward a kind of variable pitch drive model to infer pitch drive device load and to calculate confidence based on statistical methods, calculated wind turbine variable pitch drive device safety margin based on the safety standards, This method will be verified in simulation experiment of 3.0 MW direct drive wind turbine design.
Text 0. Introduction As an important part of wind turbine, variable pitch drive load bearing ability affects the safety of the wind turbine. Take an emergency feathering operation as example , if the driving torque of the variable pitch drive unit is insufficient to complete the feathering operation, emergency feathering operation cannot be fully finished, easily lead to major security accident，such as speeding coaster, collapse etc. At the same time, there is not a unified standard load calculation of variable pitch drive at home and abroad did. According the above, in this article, first infer DLC 1.1 (IEC61400-1 design situations) 50 years extreme loads using the load extrapolation method and as the unit's security domain. Then three extreme wind situations of DLC 1.3, 1.4, 1.5 will be simulated, the maximum loads sample of different wind speeds bins achieved ,and thus the sample expectations value confidence analysis and the confidence interval determined. Finally, the extreme loads and the upper limit of the confidence interval are selected to analysis their security and economy, thereby determining the rational design load of variable pitch drive. 1. Variable pitch drive device safety threshold determination 1.1 Extreme load extrapolation method IEC61400-1: 2005 standard requires the use of dynamic simulation of structural dynamics model to calculate the load of the wind turbine, the limit load extrapolation method based on statistical principles, the probability of the
maximum load Fext greater than a given the load in observation time T is reformulated as[2,3]:
Prob（Fext ? F| V,T） ? 1? （Fmax （F| V,T））?
E n|V,T?
(1)
Where Fmax is short-term probability distribution function of local maximum load, E (n | V, T) is expectation number of a local maximum within the observation time, V is average wind speed and T is observation time. The statistic is determined by the average wind speed V and the observation time T, consider all running wind situations, long-term probability of exceedance is the integration within the entire operating wind speed, namely:
Prob（F =P （ ext ? F | V, T） e F, T）
1.2. Extrapolation Method Extreme Loads Calculate Based on statistical extrapolation method calculate the limit loads of DLC 1.1 in accordance with the provisions of IEC61400-1E3.Take 3.0MW direct drive wind turbine design load calculation as an example, the unit technical parameters shown in Table1:
=?
Vout
Vin
Prob（Fext ? F | V, T）P(V)dV
(2)
Where P(V) is the probability density function of the wind speed at hub height, the acceptable probability of exceedance is the ratio of characteristic loads return period T and time interval Tr, Fk is characteristic loads which can be evaluated by the following formula:
Pe（Fk, T） ? T / Tr
(3)
The response of Prob(Fext ≧ F ∣ V,T) is determined by the computer simulation, extreme loads can be obtained through following methods: Select Retrieve extreme value principle is to ensure that these extremes are independent for each other; The number of extreme values must be sufficient to determine the probability distribution type (Gumbel, Weibull, etc.), and a reliable wake distribution estimation must be provided; Turbulent wind situations which cause the greatest load must be included in the simulation. The characteristic load can be estimated by the following steps mentioned in reference [2]:
Table 1： 3.0MW direct drive wind turbine technology parameters According to the extrapolation method calculation steps mentioned in reference [2],DLC 1.1 extreme loads in 50 years can be achieved, the results are shown in Fig1：
Fig1 Maximum and Minimum Mz, distance along blade=0m(kNm)
1.3 Determine safety threshold In order to estimate the wind turbine pitch driving apparatus maximum load during the 20-year run, in this article take extrapolation extreme load in 50 years as benchmark threshold for safety design. 2. Pitch driving apparatus load calculation DLC 1.3 embodies the requirements for ultimate loading resulting from extreme turbulence conditions. DLC 1.4 and 1.5 specify transient cases that have been selected as potentially critical events in the life of a wind turbine [1]. DLC 1.3 is divided into 12 wind segments and 12 wind seeds were established correspondingly, and using GL-bladed software simulate the maximum load calculation; the Maximum on -8 ° ,0 ° , +8 ° three directions of each winds segment were selected; the maximum load sample of DLC 1.3constitute of the maximum load each wind segments, as shown in table 2: 25138.9 64684.7 -59318.8 41276.4 63033.4 67593.6 61697.7 60454.4 54266.4 52641.4 74410.9 54459
confidence interval. Let θ is a total unknown parameters, if there is a random interval [θ1,θ2] for а given0<а<1, if it satisfies P{θ1≦θ≦θ2}=1-а, then the interval [θ1,θ2] is called θ’s confidence interval, which confidence level IS 1-а; thereby θ1 and θ2 are two statistics which determined by the sample of the overall Mz: Mz1, Mz2 ... Mzn.
θ1 =θ1 (Mz1 ,Mz 2 ,L,Mz n )
θ2 =θ2 (Mz1 ,Mz 2 ,L,Mz n )
(?1 ? ? 2 )
(4)
Where1-а is Confidence, а is significant level and [θ1, θ2] is confidence interval. 2.3 Determine the confidence interval of expectations value It is necessary to determine the maximum load value sample space, sample mean, sample variance and confidence level before determine the desired load value.Through the 2.1 chapters calculation sample space can determined, as shown in Table 4： DLC1.3 DLC1.3 DLC1.3 DLC1.3 DLC1.4 DLC1.5 DLC1.5 DLC1.5 DLC1.5 25138.9 52641.4 60454.4 67593.6 44099.4 9860.42 44922.2 57402.9 38557 41276.4 64684.7 74410.9 54266.4 68388 21775.2 49009.3 45613.5 35759.1 61697.7 63033.4 -59318.8 54459 52717.5 36047.7 49659.3 48136.4 32874.5
Table 2 Maximum load sample of DLC 1.3 ECD and EWS model were established corresponding to DLC 1.4 and 1.5, and simulation calculate were taking on GL-bladed. The maximum load value calculation results as shown in Table 3: DLC1.4 DLC1.5 DLC1.5 DLC1.5 DLC1.5 44099.4 9860.42 44922.2 57402.9 38557 68388 21775.2 49009.3 45613.5 35759.1 52717.5 36047.7 49659.3 48136.4 32874.5
Table 4 Maximum load sample space Sample mean and sample variance can be determined by the formula (8) and (9):
Mz = 1 n ? Mzi n i=1
（ 8）
Table 3 Maximum load sample of DLC 1.4 and DLC 1.5 2.2 Confidence The concept of confidence was introduced to the security analyzing process of pitch driving apparatus; thereby determining the expectation value of pitch driving apparatus design load through the distribution of the
?2 ?
1? n ? ? Mzi ? Mz n? ? i ?1
?
?
2
? ? ? ?
（9）
Where n is the number of sample space, n = 27; Mi is the sample values. Take sample values into the formula (8) and (9), sample mean and sample variance can be achieved:
Mz ?? 4.8659e ? 004 , ? 2 ? 2.3188e ? 008 .
The confidence level is always selected according to actual needs, it is advisable confidence level is а=0.025,0.05,0.01, in this paper а=0.05 is selected, then the confidence can be determined : 1-а=0.95. Now we can determine the confidence interval of expectation value ( μ ). As we know the overall can be expressed as follow:
Mz~N(Mz,σ2 )
Suppose:
Mz ~ N ( ? ,
EMz ? ?
?2
n
)
DMz ?
?2
n
Then the random variable:
Z? Mz ? ?
?2
~ N (0,1)
n
and thus realize the simulation of wind turbine operation. It analysis the load distribution of pitch driving apparatus based on a large number of experimental sample data, Then draw a proper values of the maximum load at a reliable confidence. This maximum load, not the extreme loads, but the load situation that consider the probability that satisfying certain conditions throughout the operation life. Taking economic benefits into account, the costs should be as low as possible under the premise of meet certain reliability requirements, so as to obtain the optimal integrated benefits. Therefore in the design of pitch driving apparatus load, the extreme loads can be used as the reference for judging system failure state and take the maximum load that meet a certain confidence as reference for pitch driving apparatus load design.
Let’s suppose:
P{ Mz ? ?
?2
? z? }? 1 ??
2
Reference [1]IEC.IEC61400-1 third edition 2005-08
Wind Turbine-Part 1: Design requirement, International Electro technical Commission[S], IEC, 2005. [2] Deng Ying, Xie Ting, LEI Hang, He Wei, TIAN De. wind turbine design extreme load extrapolation method comparative study IEC61400-1: 2005 version and the 1999 version of the extreme loads [J] wind energy,01, pp.64-71, (2013) [3] Wang Qingbo, Zhao Wei, Zeng Qingzhong. Statistical extrapolation method of the wind turbine load analysis [J] Dongfang Electrical Machinery, pp.33-37 (2012) [4] Deng Ying. wind turbine design and technology [M] Beijing: Chemical Industry Press, 2011,7 [5] Sheng Zhou, Xie Shiqian, Pan Chengyi. Probability theory and mathematical statistics [M] Beijing: Higher Education Press, 2009,8
n
Then confidence interval of μ can be obtained:
[ Mz ?
?
n
z? 2 , Mz ?
?
n
z? 2 ]
Look-up the table we can get that
z? ? z0.025 ? 1.96 .
2
Take Sample mean and sample variance into the confidence interval expression, and confidence interval can be obtained: [4.2915e +004 5.4403e +004].
2. Conclusion The extrapolation method is based on the principles of statistics, extreme loads for long-term operation has been deduced from the short-term operation load situations. However the extreme loads on this method are rarely occurs throughout the operation life cycle.Confidence load calculation method is dependent on wind turbine design situations,