Calculation method of long-term limit performance response of wind turbine based on random importance sampling

Abstract

The present invention belongs to the technical field of wind turbine performance, and discloses a method for calculating the long-term extreme performance response of a wind turbine based on random importance sampling. First, the multi-source uncertainties and their joint probability density functions that need to be considered by the wind turbine are determined. The number of iterative calculation rounds and the total number of short-term performance simulations in each iteration are determined. Each uncertainty source is sampled, and a short-term performance simulation random model is run several times with each sample point as input to obtain extreme value samples of short-term performance response. The long-term extreme performance response is predicted, and the weight of each uncertainty source sample is calculated based on the probability of exceeding the long-term extreme performance response. The probability density function is fitted to the weighted uncertainty source sample through a Gaussian kernel function as the importance sampling function for the next round of iteration. When the convergence criterion is met, the predicted value of the last long-term extreme performance response is used as the result. The accuracy and stability of the calculation of the long-term extreme performance response of the wind turbine are improved.

Description

Technical Field

[0001] The invention belongs to the technical field of wind turbine performance, and in particular relates to a method for calculating the long-term limit performance response of a wind turbine based on random importance sampling. Background Art

[0002] According to the existing wind turbine (hereinafter referred to as "wind turbine") design standards (such as IEC 61400-1:2019), the long-term (for example, once in 50 years) extreme performance response needs to be considered in the wind turbine design process as a characteristic value for subsequent structural design. There are multi-source uncertainties in the wind turbine during its life cycle (such as the average wind speed and direction during service, turbulence intensity, material properties during manufacturing, structural strength, etc.), and due to the limitation of computing resources, it is difficult to directly perform long-term performance simulation on the wind turbine. Therefore, the existing long-term extreme performance response calculation process of the wind turbine is to perform a large number of sampling of multi-source uncertainties, perform a 10-minute short-term performance simulation, obtain the extreme value of the short-term performance response, and calculate the long-term extreme performance response by statistical extrapolation method based on the exceedance probability corresponding to the 50-year recurrence period. However, the existing long-term extreme performance response calculation method of the wind turbine has the following defects:

[0003] (1) The short-term performance response extreme value of the sample corresponding to the large probability density of the wind turbine multi-source uncertainty may not reach the maximum value. Therefore, the sampling efficiency of the existing wind turbine long-term limit performance response calculation method is difficult to achieve the optimal, resulting in the need for a large number of simulation samples for the calculation of the wind turbine long-term limit performance response, which takes up a lot of computing time and storage space resources.

[0004] (2) The wind turbine performance model itself has uncertainties due to turbulent wind and inaccurate model parameters. For example, at the same average wind speed, due to the presence of turbulent wind, the wind speed time series is uncertain, so the output short-term performance response extreme value is also a random variable. The existing wind turbine long-term extreme performance response calculation method cannot fully consider the model uncertainty, resulting in large fluctuations in the predicted long-term extreme performance response. Summary of the invention

[0005] The purpose of the present invention is to propose a method for calculating the long-term extreme performance response of a fan, aiming at the problem that the sampling efficiency is low and the model uncertainty and other factors in the process of calculating the long-term extreme performance response of the fan affect the speed and accuracy of the long-term extreme performance response calculation. By using a random importance sampling method, sample areas with larger extreme values ​​of the short-term performance response are identified while considering the model uncertainty, thereby improving the efficiency and accuracy of the prediction of the long-term extreme performance response of the fan.

[0006] In order to solve the above technical problems, the specific technical solution of the method for calculating the long-term limit performance response of a wind turbine based on random importance sampling of the present invention is as follows:

[0007] A method for calculating the long-term limit performance response of a wind turbine based on random importance sampling comprises the following steps:

[0008] S1: Based on the short-term simulation time t and the long-term service life T of the fan that needs to be considered;

[0009] S2: Identify the uncertainty sources that need to be considered X = [X 1 ,X 2 ,…,X d ], where d is the number of uncertainty sources that need to be considered, and the joint probability density function f(X) of the uncertainty sources is obtained based on test data, industrial standards, etc.;

[0010] S3: According to the actual available computing resources, determine the total number of short-term simulations N and the maximum number of iterations K that can be undertaken, thereby determining the total number of short-term simulations for each iteration satisfy

[0011]

[0012] S4: Setting the initial importance sampling function for uncertainty sources And set the iteration round

[0013] k = 1;

[0014] S5: Sampling function based on importance The uncertainty source is sampled by the acceptance-rejection algorithm or the Markov chain-Monte Carlo algorithm to obtain M (k) Sample points

[0015] Among them, M (k) For customized parameters;

[0016] S6: For each sample point, Short-term simulation, extract the maximum value from the short-term simulation performance response time series

[0017] S7: Find a Satisfaction The maximum l value (denoted as ), as the predicted value of the long-term extreme performance response;

[0018] S8: For each sample point, calculate a corresponding weight

[0019] S9: For sample points with weights Use Gaussian kernel function to fit its probability density distribution function As the next round of importance sampling function;

[0020] S10: Check whether the algorithm has converged by using the convergence criterion. If it has converged, use the value obtained in S7. As the final long-term extreme performance response prediction value, otherwise set k←k+1 and continue with steps S5-S9.

[0021] Furthermore, S1 determines the exceedance probability P of the short-term performance response extreme value corresponding to the long-term limit performance response according to the following formula: T :

[0022]

[0023] Among them, r T is the number of years included in the long cycle to be considered, n t The number of short-term simulations in one year.

[0024] Furthermore, the S3 setting

[0025] Furthermore, the S4 It is defined as a uniform distribution function within the feasible range of uncertainty sources.

[0026] Further, the S5 takes Furthermore, the number of short-term simulations for each sample in S6 is Calculated by the following formula, when k≥2:

[0027]

[0028] When k = 1, according to M (1) and The number of short-term simulations is evenly distributed among the samples.

[0029] Furthermore, in S7 Calculated according to the following formula:

[0030]

[0031] Where 1(·) is an indicator function, which takes the value 1 when the expression in the brackets is true and takes the value 0 when the expression in the brackets is false; θ k Importance function parameters for construction.

[0032] Furthermore, the weight of S8 As shown below:

[0033]

[0034] in, Indicates that at the sample point At the point where the short-term performance response extreme value exceeds The probability of exceeding The ratio of the short-term performance response extreme value to the number of simulations at the sample point is approximately:

[0035]

[0036] Furthermore, the probability density distribution function of S9 is for:

[0037]

[0038] Among them, K d (·) is the Gaussian kernel function, θ k+1 is the bandwidth parameter of the kernel function.

[0039] Furthermore, the optimal kernel function bandwidth θ of S9 is k+1 The objective function R based on the integrated square error is minimized. The calculation of the objective function R is as follows:

[0040]

[0041] The method for calculating the long-term extreme performance response of a wind turbine based on random importance sampling of the present invention has the following advantages: (1) the present invention targets the multi-source uncertainty of the wind turbine, identifies the "important area" with larger extreme values ​​of the short-term performance response, concentrates more sample points in the area, and improves the calculation efficiency; (2) the uncertainty of the wind turbine performance model itself is taken into account, and the accuracy and stability of the calculation of the long-term extreme performance response of the wind turbine are improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a schematic flow chart of the method of the present invention;

[0043] Figure 2 It is a schematic diagram of the swing vibration and flapping bending moment of the fan blade root in the present invention;

[0044] Figure 3 It is a result schematic diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0045] In order to better understand the purpose, structure and function of the present invention, the long-term limit performance response calculation method of a wind turbine based on random importance sampling of the present invention is further described in detail below in conjunction with the accompanying drawings.

[0046] like Figure 1 As shown, the method for calculating the long-term limit performance response of a wind turbine generator based on random importance sampling of the present invention comprises the following steps:

[0047] S1: According to the short-term simulation time t and the long-term service life T of the wind turbine to be considered, the exceedance probability P of the long-term limit performance response corresponding to the short-term performance response extreme value is determined according to the following formula T :

[0048]

[0049] Among them, r T is the number of years included in the long cycle to be considered, n t The number of short-term simulations in one year.

[0050] S2: Identify the uncertainty sources that need to be considered X = [X 1 ,X 2 ,…,X d ], where d is the number of uncertainty sources that need to be considered, and the joint probability density function f(X) of the uncertainty sources is obtained based on test data, industrial standards, etc.

[0051] S3: According to the actual available computing resources, determine the total number of short-term simulations N and the maximum number of iterations K that can be undertaken, thereby determining the total number of short-term simulations for each iteration satisfy Typically, you can set

[0052] S4: Setting the initial importance sampling function for uncertainty sources And set the iteration number k = 1, typically, It can be defined as a uniform distribution function within the feasible range of uncertainty sources.

[0053] S5: Sampling function based on importance The uncertainty source is sampled by the acceptance-rejection algorithm or the Markov chain-Monte Carlo algorithm to obtain M (k) Sample points Among them, M (k) For custom parameters, generally

[0054] S6: For each sample point, Short-term simulation, extract the maximum value from the short-term simulation performance response time series The number of short-term simulations for each sample Calculated by the following formula (when k ≥ 2):

[0055]

[0056] When k = 1, according to M (1) and The number of short-term simulations is evenly distributed among the samples.

[0057] S7: Find a Satisfaction The maximum l value (denoted as ), as the predicted value of the long-term extreme performance response, where Calculated according to the following formula:

[0058]

[0059] Where 1(·) is an indicator function, which takes the value 1 when the expression in the brackets is true and takes the value 0 when the expression in the brackets is false; θ κ Importance function parameters for construction.

[0060] S8: For each sample point, calculate a corresponding weight As shown below:

[0061]

[0062] in, Indicates that at the sample point At the point where the short-term performance response extreme value exceeds The probability of exceeding The ratio of the short-term performance response extreme value to the number of simulations at the sample point is approximately:

[0063]

[0064] S9: For sample points with weights Use Gaussian kernel function to fit its probability density distribution function As the next round of importance sampling function, that is,

[0065]

[0066] Among them, K d (·) is the Gaussian kernel function, θ k+1 is the bandwidth parameter of the kernel function. The optimal kernel function bandwidth θ k+1 The objective function T based on the integrated square error is minimized. The calculation of the objective function R is as follows:

[0067]

[0068] S10: Check whether the algorithm has converged by using the convergence criterion. If it has converged, use the value obtained in S7. As the final long-term extreme performance response prediction value, otherwise set k←k+1 and continue with steps S5-S9.

[0069] Example

[0070] The process of the present invention is applied to the 5MW reference model proposed by the American Renewable Energy Laboratory, thereby proving the effectiveness of the method of the present invention. The 5MW model has a blade length of 61.5m, a cut-in wind speed of 3m / s, a cut-out wind speed of 25m / s, a rated wind speed of 11.4m / s, a rated speed of 12.1rpm, a hub height of 90m, and an integrated variable speed and pitch control system. Under normal power generation conditions of the wind turbine, the method of the present invention predicts the long-term limit performance responses such as blade root swing and flapping moment. Figure 2 It is a schematic diagram of the swing and flapping bending moment of the fan blade root in the present invention.

[0071] In this embodiment, the 10-minute average wind speed V is considered as the uncertainty source, and the probability density function f of the 10-minute average wind speed is V (v) is as follows:

[0072]

[0073] Among them, f R (v) is the Rayleigh distribution probability density function. For the IIB type wind turbine designed according to IEC61400-1:2019 standard, the Rayleigh distribution parameter is 8.5 m / s. R (·) is the cumulative distribution function of the Rayleigh distribution, V in 、V out are the cut-in and cut-out wind speeds of the fan, which are 3 m / s and 25 m / s respectively in this embodiment.

[0074] The simulation model used in this embodiment comes from OpenFAST and TurbSim software developed by the American Renewable Energy Laboratory. After obtaining the sample v of the 10-minute average wind speed V by the sampling method, according to the IEC61400-1:2019 standard, the 10-minute turbulence intensity I is calculated by the following formula:

[0075]

[0076] Among them, I ref In this embodiment, 0.14 is taken. Given a set of 10-minute average wind speed and turbulence intensity, the TurbSim software will generate a set of random 10-minute three-dimensional wind speed sequences. The OpenFAST software calculates the short-term performance response of the wind turbine for 10 minutes based on the three-dimensional wind speed sequence. The maximum value of the short-term performance response is used as the output of the simulation model. Figure 3(a) and (b) show the scatter plots of the 10-minute extreme values ​​of the swing and flapping moments of the wind turbine blade root and the wind speed, respectively. It can be seen that the short-term extreme value of the swing bending moment is larger in the wind speed range of 12-19 m / s, while the short-term extreme value of the flapping bending moment is larger in the wind speed range of 11.7-16.3 m / s and 23.5-25 m / s. Therefore, when predicting the long-term extreme swing and flapping moments, more sample points should be arranged in the above ranges to achieve the optimal sampling and calculation efficiency.

[0077] In order to verify the effectiveness of the proposed method, the results obtained in this embodiment are compared with the existing long-term extreme performance response calculation method based on random importance sampling (the method flow refers to Pan Q, Byon E, Ko YM, et al. Adaptive importance sampling for extreme quantile estimation with stochastic black box computer models [J]. Naval Research Logistics (NRL), 2020, 67 (7): 524-547.). This embodiment calculates the short-term performance response extreme value exceedance probability P T =0.01 corresponding to the long-term limit performance response. In this embodiment, the total number of simulations N of the method proposed by the present invention and the method proposed by Pan et al. are limited to 3000 times, and the maximum number of iterations K is set to 10. When the change rate of the long-term limit performance response predicted for three consecutive rounds is less than 1%, it is considered to be converged. Both methods repeated the experiment 10 times, and compared the predicted mean and variance of the long-term limit performance response of the two. The results of the simulation by the Monte-Carlo method of Sandia Laboratory in the United States (refer to Barone MF, Paquette J A, Resor BR, et al. Decades of Wind Turbine Load Simulation [R]. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States), 2011.) are used as reference values ​​for comparison, and the results are shown in Table 1. The results show that the wind turbine long-term limit performance response prediction method proposed in the present invention is close to the results of the comparison method in predicting the blade root swing bending moment, and the standard deviation and average error rate in predicting the flapping bending moment are significantly lower than those of the method proposed by Pan et al., which reflects the stability and accuracy of the present method. In addition, Figure 3(c) and (d) in the figure show the distribution of 10-minute average wind speed samples collected by the two methods. The samples collected by the method proposed by Pan et al. still retain a lot of characteristics of the original wind speed probability density function, resulting in low calculation efficiency; while the method proposed by the present invention can more accurately arrange more sample points in the aforementioned important interval, thereby improving the sampling efficiency. The above results prove the effectiveness of the present invention.

[0078] Table 1 Comparison of calculation results of implementation cases (10 test results)

[0079]

Claims

1. A method for calculating the long-term limit performance response of a wind turbine based on random importance sampling, characterized in that: The steps include: S1: Based on the short-term simulation time t and the long-term service life T of the fan that needs to be considered; S2: Identify the uncertainty sources X = [X1, X2, …, X d ], where d is the number of uncertainty sources that need to be considered, and the joint probability density function f(X) of the uncertainty sources is obtained based on test data and industrial standards; S3: According to the actual available computing resources, determine the total number of short-term simulations N and the maximum number of iterations K that can be undertaken, thereby determining the total number of short-term simulations for each iteration satisfy S4: Setting the initial importance sampling function for uncertainty sources And set the iteration round k = 1; S5: Sampling function based on importance The uncertainty source is sampled by the acceptance-rejection algorithm or the Markov chain-Monte Carlo algorithm to obtain M (k) Sample points Among them, M (k) For customized parameters; S6: For each sample point, Short-term simulation, extract the maximum value from the short-term simulation performance response time series The number of short-term simulations performed for each sample in S6 Calculated by the following formula, when k≥2: When k = 1, according to M (1) and The number of short-term simulations is evenly distributed at each sample; where, Indicates that at the sample point At the point where the short-term performance response extreme value exceeds probability; Indicates that at the sample point At the point where the short-term performance response extreme value exceeds probability; S7: Find a Satisfaction The maximum l value is denoted by , as the predicted value of the long-term extreme performance response; where P T is the probability of exceeding the extreme value of the short-term performance response corresponding to the long-term extreme performance response; The S7 Calculated according to the following formula: Where 1(·) is an indicator function, which takes the value 1 when the expression in the brackets is true and takes the value 0 when the expression in the brackets is false; θ κ are the constructed importance function parameters; S8: For each sample point, calculate a corresponding weight The weight of the S8 As shown below: in, Indicates that at the sample point At the point where the short-term performance response extreme value exceeds The probability of exceeding The ratio of the short-term performance response extreme value to the number of simulations at the sample point is approximately: S9: For sample points with weights Use Gaussian kernel function to fit its probability density distribution function As the next round of importance sampling function; where θ k+1 is the bandwidth parameter of the kernel function; S10: Check whether the algorithm has converged by using the convergence criterion. If it has converged, use the value obtained in S7. As the final long-term extreme performance response prediction value, otherwise set k←k+1 and continue with steps S5-S9.

2. The method for calculating the long-term limit performance response of a wind turbine generator based on random importance sampling according to claim 1, characterized in that: S1 determines the exceedance probability P of the short-term performance response extreme value corresponding to the long-term limit performance response according to the following formula T : Among them, r T is the number of years included in the long cycle to be considered, n t The number of short-term simulations in one year.

3. The method for calculating the long-term limit performance response of a wind turbine generator based on random importance sampling according to claim 1, characterized in that: The S3 settings 4. The method for calculating the long-term limit performance response of a wind turbine generator based on random importance sampling according to claim 1, characterized in that: The S4 It is defined as a uniform distribution function within the feasible range of uncertainty sources.

5. The method for calculating the long-term limit performance response of a wind turbine generator based on random importance sampling according to claim 1, characterized in that: The S5 takes 6. The method for calculating the long-term limit performance response of a wind turbine generator based on random importance sampling according to claim 1, characterized in that: The probability density distribution function of S9 for: Among them, K d (·) is the Gaussian kernel function, θ k+1 is the bandwidth parameter of the kernel function.

7. The method for calculating the long-term limit performance response of a wind turbine generator based on random importance sampling according to claim 1, characterized in that: The optimal kernel function bandwidth θ of S9 k+1 The objective function R based on the integrated square error is minimized. The calculation of the objective function R is as follows:

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