阅读说明：本技术 基于风能利用系数与多元多项式回归的风力机功率预测方法 (Wind turbine power prediction method based on wind energy utilization coefficient and multivariate polynomial regression ) 是由 黄佳颖 牛王强 杨华建 江佳腾 张炜婷 王晓彤 于 2021-09-07 设计创作，主要内容包括：本发明涉及一种基于风能利用系数与多元多项式回归的风力机功率预测方法,使用风能利用系数来选择影响风机输出功率的变量,通过多元多项式的方法来建模变量与风机输出功率的关系,以达到功率预测的目的。本方法采用风能利用系数来选择影响风机输出功率的变量,减少了专家分析影响因素的困难。本方法利用风机特性曲线对风机运行状态分段,使模型更具有物理意义。本方法采用多元多项式回归模型对风机输出功率进行预测,具有较高的准确率和较低的模型复杂度。(The invention relates to a wind turbine power prediction method based on wind energy utilization coefficient and multivariate polynomial regression. The method adopts the wind energy utilization coefficient to select the variable influencing the output power of the fan, thereby reducing the difficulty of analyzing the influencing factors by experts. The method segments the running state of the fan by utilizing the fan characteristic curve, so that the model has more physical significance. The method adopts a multivariate polynomial regression model to predict the output power of the fan, and has higher accuracy and lower model complexity.)

1. A wind turbine power prediction method based on wind energy utilization coefficient and multivariate polynomial regression is characterized by comprising the following steps:

s1, extracting the SCADA sampling data set D0 by taking wind speed, blade rotating speed, pitch angle and power as characteristics to form a data set D1;

s2, dividing a data set D1 into three stages of constant power, constant rotating speed and maximum power point tracking according to a fan characteristic curve, and dividing the three stages into a training set and a verification set according to a certain proportion;

s3, according to the theoretical foundation of the wind turbine, utilizing the wind energy coefficient C_pAs an intermediate variable of power modeling, respectively establishing a multivariate polynomial model for a constant power section data set D11-1, a constant rotating speed section data set D12-1 and a maximum power point tracking section data set D13-1;

s4, establishing the wind energy utilization coefficient C by the data sets D11-1, D12-1 and D13-1 in the step S3_pA polynomial model, which predicts the output power of the wind turbine on the validation data sets D11-2, D12-2 and D13-2;

the step S2 of segmenting the operation process of the fan comprises the following steps:

s201, taking the wind speed as a parting line, and parting the sampling data set D1 into three parts, namely D11, D12, D13, and D13, wherein the three parts are the wind speed which is greater than or equal to the rated wind speed, the wind speed which is greater than or equal to the rated rotating speed and less than the rated wind speed, and the wind speed which is less than the rated rotating speed and the wind speed represent the three states of the fan;

s202, dividing a data set D11 into two groups of data according to a certain proportion, and recording the two groups of data as D11-1 and D11-2; dividing a data set D12 into two groups of data according to a certain proportion, and marking the data as D12-1 and D12-2; dividing a data set D13 into two groups of data according to a certain proportion, and marking the data as D13-1 and D13-2; d11-1, D12-1 and D13-1 are used as training sets, namely modeling samples; d11-2, D12-2 and D13-2 as validation sets, i.e. prediction samples;

step S3 includes the following steps:

s301, establishing a multivariate polynomial model for the data set D11-1:

the wind energy utilization coefficient C is calculated by adopting a multivariate polynomial regression model_p(λ, θ) is expressed as an m1 order polynomial of tip speed ratio λ and pitch angle θ, as follows:

y＝∑a_ijx₁ ⁱx₂ ^j；

wherein y represents the wind energy utilization coefficient C_p，x₁Representing tip speed ratio λ, x₂Representing the pitch angle, a_ijDenotes the coefficient, where i, j is 0,1,2, …, m₁；i+j≤m₁(ii) a Finding order m1 and parameter a for minimizing cost function J by using least square method_ijSo that the precision of the polynomial model reaches the highest, and the cost function is as follows:

in the formula, N is the number of samples,and y_iRespectively the coefficient of wind energy utilization C_pPredicted and actual values of;

a suitable value of m1 is the order corresponding to the minimum root mean square error RMSE for the model prediction, and is given by:

in the formula, N is the number of verification samples; y is_iFor verifying the wind energy utilization coefficient C of the sample_pAn actual value;is polynomial model C_pPredicting a value;

s302, establishing a multivariate polynomial model for the data set D12-1:

because the fan is in the stage of constant rotating speed, the rotating speed is considered to be constant as the rated rotating speed, and the tip speed ratio of the fan in the state is represented by lambda':

wherein the rotational speed n_NTaking the rated rotating speed of the motor to be measured,

the wind energy utilization coefficient C is obtained by adopting a multivariate polynomial regression model_p(λ, θ) is expressed as an m2 order polynomial of tip speed ratio λ' and pitch angle θ, and the optimal order m2 and parameter a are also found by least squares_ijA suitable value of m2 is the order corresponding to the minimum RMSE predicted by the model;

s303, establishing a multivariate polynomial model for the data set D13-1:

considering that the change of the pitch angle of the fan is extremely small due to the pitch control technology in low wind speed, the wind energy utilization coefficient C is established for the data set_pRegarding the unary polynomial model of the tip speed ratio lambda, the optimal order m3 and parameter a of the polynomial are found through least square fitting_ijA suitable value of m3 is the order corresponding to the minimum RMSE predicted by the model;

step S4 includes the following steps:

s401, establishing a wind energy utilization coefficient C by using the data set D11-1 in the step S301_pAnd (3) a polynomial model, wherein the fan output power prediction is carried out in a verification data set D11-2, and the specific calculation formula is as follows:

wherein the content of the first and second substances,coefficient of wind energy utilization C_pThe predicted value of (2);

s402, establishing the wind energy by using the data set D12-1 in the step S302Using coefficient C_pA polynomial model, wherein the fan output power prediction is carried out on a verification data set D12-2, and a specific calculation formula is the same as that in the step S401;

s403, establishing a wind energy utilization coefficient C by using the data set D13-1 in the step S303_pAnd (4) performing fan output power prediction on the verification data set D13-2 by using a polynomial model, wherein a specific calculation formula is the same as that in the step S401.

Technical Field

The invention belongs to the field of new energy, and particularly relates to a wind turbine power prediction method based on a wind energy utilization coefficient and multivariate polynomial regression.

Background

The reduction of fossil fuel reserves and the steady rise in energy demand have created new challenges for the world. Wind energy is a renewable energy source and also a clean energy source, and wind power generation is a main use mode of wind energy. The power curve is a direct reflection of the utilization efficiency of the wind turbine generator on the input wind energy and the overall generation performance of the wind turbine generator, and reflects the output power level of the wind turbine at different wind speeds measured by the height of the hub. The modeling and monitoring of the power curve of the wind turbine can timely find the abnormal operation and early failure of the wind turbine, improve the availability of the wind turbine and reduce the maintenance cost of the wind turbine. Generally, the wind power prediction method uses a fan power curve model provided by a manufacturer. However, the curve does not take into account the specific installation position of the wind turbine and the wear condition after operation, and the difference between the theoretical wind power data and the actual data can cause additional errors. Power curve modeling uses a number of different techniques: a "bin" method, a parametric function, a logistic regression model, etc. given in the IEC61400-12 standard. However, the conventional wind speed-power curve only shows the relationship between power and wind speed, and does not consider other influencing factors, such as wind direction, rotor speed and pitch angle, and has certain limitations.

At present, multivariable regression models for predicting the output power of a fan mainly comprise an artificial neural network model, a Gaussian process model and the like. The input characteristics of the multivariate model are mainly obtained by analyzing the operating characteristics of the wind turbines by experts, but factors influencing the power of the wind turbines are different in different wind power plant environments. In addition, the training process of the artificial neural network model usually takes a lot of time, and has certain limitations on the transparency and the interpretability of the model.

Disclosure of Invention

The invention aims to predict the output power of a fan by adopting a wind energy utilization coefficient and a multivariate polynomial regression based on SCADA data of the fan.

The technical solution for realizing the purpose of the invention is as follows:

a wind power prediction method based on wind energy utilization coefficient and multivariate polynomial regression comprises the following steps:

step 1, extracting characteristics of a SCADA sampling data set D0 by taking wind speed, blade rotating speed, pitch angle and power as characteristics to form a data set D1.

And 2, dividing the operation process of the wind driven generator into three stages of constant power, constant rotating speed and maximum power point tracking according to the fan characteristic curve. The wind speed is taken as a parting line, the sampling data set D1 is divided into three parts, namely D11, namely the wind speed is greater than or equal to the rated wind speed, D12, namely the wind speed is greater than or equal to the rated rotating speed and is less than the rated wind speed, and D13, namely the wind speed is less than the rated rotating speed and represents three states of the fan. Dividing a data set D11 into two groups of data according to a certain proportion, and marking the data as D11-1 and D11-2; dividing a data set D12 into two groups of data according to a certain proportion, and marking the data as D12-1 and D12-2; the data set D13 was divided into two groups of data in certain proportions, denoted D13-1 and D13-2. D11-1, D12-1 and D13-1 are used as training sets, namely modeling samples; d11-2, D12-2 and D13-2 were used as validation sets, i.e., prediction samples.

Step 3, according to the theoretical foundation of the fan, utilizing the wind energy coefficient C_pAs an intermediate variable for power modeling. The blades of the fan have aerodynamic shapes, so that the wind wheel rotates around the axis of the wind wheel, and wind energy can be converted into mechanical energy. The pneumatic equation is calculated as follows:

in the formula, P_wIs available air kinetic energy; ρ is the air density; r is the blade radius; v is the wind speed. Ideally, the power extracted from wind energy by a wind generator can be expressed as:

in the formula, C_p(λ, θ) is the wind energy utilization coefficient; λ is the tip speed ratio, which is the ratio of the tip linear velocity to the wind speed; θ is the pitch angle; ω is the blade angular velocity. C_p(λ, θ) is a non-linear function of the tip speed ratio λ and the pitch angle θ, expressed as:

in the formula, C₁-C₉The power parameter is determined by the type of the wind driven generator. The actual wind energy utilization coefficient C can be calculated by using the actual output power P and the wind speed v_p：

Step 4, respectively establishing a multivariate polynomial model for the constant power section data set D11-1, the constant rotating speed section data set D12-1 and the maximum power point tracking section data set D13-1:

data set D11-1:

the wind energy utilization coefficient C is calculated by adopting a multivariate polynomial regression model_p(λ, θ) is expressed as an m1 order polynomial of tip speed ratio λ and pitch angle θ, as follows:

y＝∑a_ijx₁ ⁱx₂ ^j；

wherein y represents the wind energy utilization coefficient C_p，x₁Representing tip speed ratio λ, x₂Representing the pitch angle, a_ijDenotes the coefficient, where i, j is 0,1,2, …, m₁；i+j≤m₁. Finding order m1 and parameter a for minimizing cost function J by using least square method_ijThe accuracy of the polynomial model is maximized. The cost function is:

in the formula, N is the number of samples,and y_iRespectively the coefficient of wind energy utilization C_pThe predicted value and the actual value of (c).

A suitable value of m1 is the order corresponding to the minimum root mean square error RMSE for the model prediction, and is given by:

in the formula, N is the number of verification samples; y is_iFor verifying the wind energy utilization coefficient C of the sample_pAn actual value;is polynomial model C_pAnd (5) predicting the value.

Data set D12-1:

because the fan is in the stage of constant rotating speed, the rotating speed is considered to be constant as the rated rotating speed, and the tip speed ratio of the fan in the state is represented by lambda':

wherein the rotational speed n_NAnd taking a rated rotating speed.

The wind energy utilization coefficient C is obtained by adopting a multivariate polynomial regression model_p(λ, θ) is expressed as an m2 order polynomial of tip speed ratio λ' and pitch angle θ, and the optimal order m2 and parameter a are also found by least squares_ijA suitable value of m2 is the order corresponding to the minimum RMSE predicted by the model.

Data set D13-1:

considering that the change of the pitch angle of the fan is extremely small due to the pitch control technology in low wind speed, the wind energy utilization coefficient C is established for the data set_pFinding the majority of the tip speed ratio lambda related univariate polynomial model by least squares fittingOptimal order m3 and parameter a of the term_ijA suitable value of m3 is the order corresponding to the minimum RMSE predicted by the model.

Step 5, establishing a wind energy utilization coefficient C by utilizing the data sets D11-1, D12-1 and D13-1 in the step 4_pAnd a polynomial model, performing the prediction of the output power of the fan on the verification data sets D11-2, D12-2 and D13-2, wherein the power expression is as follows:

in the formula (I), the compound is shown in the specification,coefficient of wind energy utilization C_pThe predicted value of (2).

Drawings

FIG. 1 is a schematic view of a wind speed-power curve of a wind turbine according to the present invention in an operating state.

FIG. 2 is a schematic view of a wind speed-rotational speed curve of a fan according to the present invention in an operating state.

FIG. 3 is a schematic diagram of a rotational speed-power curve of a fan according to the present invention in an operating state.

FIG. 4 is a diagram showing the variation of the root mean square error of the constant power section with the polynomial order.

FIG. 5 is a diagram showing the variation of the root mean square error of the constant rotation speed section with the polynomial order.

Fig. 6 is a schematic diagram showing the relationship between the root mean square error of the maximum power point tracking section and the polynomial order change.

FIG. 7 is a schematic diagram of a multivariate polynomial regression modeling process according to the present invention.

FIG. 8 is a graphical illustration of predicted time-power curves on SCADA validation data in accordance with the present invention.

FIG. 9 is a schematic illustration of predicted wind speed-power scatter on SCADA validation data in accordance with the present invention.

Detailed Description

The method for predicting the output power of the fan based on the multivariate polynomial regression and the maximum information coefficient comprises the following steps of:

s1, collecting SCADAThe sample data set D0 extracts wind speed, blade speed, pitch angle and power as features, and forms a data set, denoted as D1. For a wind power generator as an example, the rated power is 2MW, the SCADA sampling time is 60s, and the records D0 are 5915. The rated wind speed of the fan is 14m/s, the rated rotational speed is 8.5m/s, the rated rotational speed is 15.1rpm, the diameter of the blade is 105m, and the air density is 1.25kg/m³. The 5915 records D0 are extracted with wind speed, blade speed, pitch angle and power as characteristic variables to form a data set D1.

And S2, dividing the running state of the wind driven generator into three stages of constant power AB, constant rotating speed BC and maximum power point tracking CD according to the fan characteristic curve, as shown in figures 1-3. FIG. 1 is a wind speed-power curve. FIG. 2 is a wind speed-rotational speed curve. Fig. 3 is a speed-power curve. The data set D1 was divided into three parts with wind speed as the dividing line. 2675 data sets D11 in the constant power stage, namely the wind speed is greater than or equal to the rated wind speed; 2481 data sets D12 in the constant rotating speed stage, namely the wind speed is greater than or equal to the rated rotating speed and is less than the rated wind speed; 759 data sets D13 in the maximum power point tracking stage, namely the wind speed is less than the rated speed, which represents three states of the wind turbine. Dividing the data set D11 into 2275 pieces for D11-1 and 400 pieces for D11-2; d12 is divided into 2131 pieces of D12-1 and 350 pieces of D12-2; d13 was divided into 609D 13-1 and 150D 13-2. The data sets D11-1, D12-1 and D13-1 are used as training sets; d11-2, D12-2 and D13-2 were used as verification sets.

S3, respectively establishing a multivariate polynomial model for the constant power section data set D11-1, the constant rotating speed section data set D12-1 and the maximum power point tracking section data set D13-1:

a constant power section:

training a multivariate polynomial regression model on dataset D11-1 will predict the quantityAn m1 order polynomial expressed as a tip speed ratio λ and a pitch angle θ, as follows:

y＝∑a_ijx₁ ⁱx₂ ^j；

wherein y represents the wind energy utilization coefficient C_p，x₁Representing tip speed ratio λ, x₂Representing the pitch angle, a_ijDenotes the coefficient, where i, j is 0,1,2, …, m₁；i+j≤m₁. Finding order m1 and parameter a for minimizing cost function J by using least square method_ijThe accuracy of the polynomial model is maximized. The cost function is:

in the formula, N is the number of samples,and y_iRespectively the coefficient of wind energy utilization C_pThe predicted value and the actual value of (c).

Further, the root mean square error RMSE formula is as follows:

in the formula, N is the number of verification samples; y is_iFor verifying the wind energy utilization coefficient C of the sample_pAn actual value;is polynomial model C_pAnd (5) predicting the value. The training procedure RMSE varies with order m1 as shown in fig. 4. When the polynomial order m1 changes from 1 to 2, the RMSE of the model decreases rapidly with little change. When m1 is 2, the RMSE of training sample D11-1 is 0.0037, and that of validation sample D11-2 is 0.0022, at which time the model is optimal, determining the appropriate m1 value to be 2. Established wind energy utilization coefficient C_pThe model is as follows:

wherein y represents the wind energy utilization coefficient C_pPredicted value of (a), x₁Representing tip speed ratio λ, x₂Representing the pitch angle theta.

A constant rotating speed section:

because the fan is in the stage of constant rotating speed, the rotating speed is considered to be constant as the rated rotating speed, and the tip speed ratio lambda' in the state is as follows:

wherein the rotational speed n_NAnd taking a rated rotating speed.

Coefficient of wind energy utilization C_p(λ, θ) is expressed as an m2 order polynomial of tip speed ratio λ' and pitch angle θ, and the optimal order m2 and parameter a are also found by least squares_ij. A suitable value of m2 is the order corresponding to the minimum RMSE predicted by the model. The RMSE during training varies with order m2 as shown in fig. 5. The RMSE of the training sample D12-1 and the test sample D12-2 increased and then decreased as the polynomial order increased, and when the polynomial order was greater than 5, the model was overfit. Therefore, when the order m2 is 5, the model works best, the RMSE of the training samples is 0.0215, and the RMSE of the validation samples is 0.0344. Established wind energy utilization coefficient C_pThe model is as follows:

wherein y represents the wind energy utilization coefficient C_pPrediction value, x₁Representing tip speed ratio λ', x₂Representing the pitch angle theta.

Maximum power point tracking section:

considering that the change of the pitch angle of the wind turbine is extremely small due to the pitch control technology at low wind speed, the wind energy utilization coefficient C is established on the data set D13-1_pRegarding the unary polynomial model of the tip speed ratio lambda, the optimal order m3 and parameter a of the polynomial are found through least square fitting_ijA suitable value of m3 is the order corresponding to the minimum RMSE predicted by the model. The RMSE during training varies with order m3 as shown in fig. 6. When the polynomial order m3 is 3, verify the sample D13RMSE of-2 was lowest, 0.0107. Established wind energy utilization coefficient C_pThe model is as follows:

y＝2.9798-0.9899x+0.1091x²-0.37·10^-2x³；

wherein y represents the wind energy utilization coefficient C_pPredicted value, x, represents tip speed ratio λ.

S4, utilizing the wind energy utilization coefficient C established by the S3_pAnd a polynomial model, performing the prediction of the output power of the fan on the verification data sets D11-2, D12-2 and D13-2, wherein the power expression is as follows:

in the formula (I), the compound is shown in the specification,to predict the power value. The specific steps for establishing the multivariate polynomial regression model are shown in fig. 7. The results are shown in FIGS. 8 and 9. FIG. 8 is a predicted time-power plot on a test set, with the solid line representing actual SCADA data and the dashed line representing predicted values. FIG. 9 is a predicted wind speed-power scatter plot on the test set with circles representing true data values and a plus sign representing predicted values. The predicted results show that wind speed and power are in a "banded" relationship. As can be seen from both figures, the model can predict most power values.

The mean absolute percentage error MAPE of the predicted value of the validation data was 6.29%, and the formula is as follows:

where N is the verification lump number, y_iIs to verify the actual output power of the sample,is the model power prediction value.

The invention has the following advantages:

1) the invention adopts the wind energy utilization coefficient to select the variable influencing the output power of the fan, thereby reducing the difficulty of analyzing the influencing factors by experts.

2) The method has higher accuracy and lower model complexity in the aspect of fan output power prediction.