CN105303250A - Wind power combination prediction method based on optimal weight coefficient - Google Patents

Abstract

The invention discloses a wind power combination prediction method based on the optimal weight coefficient. According to the method, four single prediction models of an ARIMA time sequence, a BP neural network, an RBF neural network and a support vector regression machine are integrated to form a combination prediction model so that the advantages of each single prediction model can be effectively integrated and the prediction risk can be reduced. The optimal weight coefficient in the combination prediction model is obtained with the minimum error sum of squares acting as the principle according to a combination prediction error information matrix so that performance of the combination prediction model is enhanced. The actually measured wind power prediction data indicate that the combination prediction model has high prediction precision, the optimal weight coefficient value can be quite conveniently and rapidly determined and prediction error can be reduced.

Description

A kind of wind power combination forecasting method based on optimum weight coefficient

Technical field

The invention belongs to wind power prediction technical field, be specifically related to a kind of wind power combination forecasting method based on optimum weight coefficient.

Background technology

Along with the fast development of wind-power electricity generation installed capacity, the ratio of wind-powered electricity generation in electrical network constantly increases.Because wind-powered electricity generation is a kind of intermittent, the undulatory property energy, the guarantee of large-scale wind power integration to the safety of electric system, stable operation and the quality of power supply brings severe challenge.Predict more accurately if can make the wind speed of wind energy turbine set and generated output, then effectively can alleviate the impact of wind-powered electricity generation fluctuation on whole electrical network.Dispatching of power netwoks department will be contributed to by wind power prediction and formulate the rational method of operation adjust operation plan exactly in time, thus ensure reliable, high-quality, the economical operation of electric system.Therefore carry out prediction to wind power to be of great significance.

Wind power forecasting method is classified according to the physical quantity of prediction, can be divided into indirect predictions method and direct forecast methods: the first prediction of wind speed of indirect predictions method, then obtains wind power according to the wind speed-power characteristic of Wind turbines or wind energy turbine set; Direct forecast methods adopts certain mathematical model directly to predict wind power.Wind power forecasting method conventional at present mainly comprises physical method and the large class of statistical method two.Physical method considers the information such as landform, level height and roughness, and utilize physical equation modeling and forecasting, the method needs numerical weather forecast data accurately and effectively, and without the need to a large amount of long-term observation data.Statistical method is then that desired data is single, amount is large, bad to abrupt information process by predicting the mathematical statistics analysis of forecasting object self historical data.Applying in statistical method more has persistence forecasting method, time series analysis method, artificial neural network method, support vector regression method, Kalman filtering method, spatial coherence method etc.These methods deeply expose along with wind power technology the defect being difficult to overcome, and as precision of prediction is poor, speed of convergence is slow, has the shortcomings such as limitation.

Summary of the invention

The object of the invention is to, a kind of wind power combination forecasting method based on optimum weight coefficient is provided, carry out comprehensively to these 4 kinds of individual event Forecasting Methodologies of ARIMA time series, BP neural network, RBF neural and support vector regression, minimum with error sum of squares is the optimum weight coefficient of principle determination combination forecasting, obtains combination forecasting.Effectively improve the precision of prediction of wind power, enhance the stability of wind-electricity integration, economy.

Based on a wind power combination forecasting method for optimum weight coefficient, comprise the following steps:

Step 1: gather continuous history wind power data, and the data gathered are normalized;

Four forecast model superpositions are obtained combination forecasting by step 2: set up wind power prediction model respectively to data acquisition ARIMA time series, BP neural network, RBF neural and support vector regression after normalized;

Step 3: the control information matrix E building combination forecasting:

E＝[(e _it) _4×n][(e _it) _4×n] ^T

Wherein, e _itrepresent the predicated error of i-th kind of forecast model in t: e _it=y (t)-y _i(t), t=1,2 ..., n, i=1,2 ..., 4; The wind power value that y (t) surveys for t, y _it () represents the predicted value of i-th kind of forecast model in t;

Step 4: make the weight coefficient of each model in combination forecasting be L=(l ₁, l ₂, l ₃, l ₄) _{4 × 1}, the expression formula of combination forecasting is as follows:

y ^*(t)＝l ₁y ₁(t)+l ₂y ₂(t)+l ₃y ₃(t)+l ₄y ₄(t)

Wherein, l ₁+ l ₂+ l ₃+ l ₄=1, y ₁, y ₂, y ₃, y ₄represent the predicted value of ARIMA time series, BP neural network, RBF neural and support vector regression wind power prediction model t respectively;

Step 5: the expression formula control information matrix of the combination forecasting in step 3 being substituted into combination forecasting, according to formula solve optimal weights coefficient;

Wherein, R=(1,1 ..., 1) _{4 × 1};

The computation process of optimum weight coefficient expression formula L to be asked in combination forecasting is as follows:

Combination forecasting in the predicated error of t is:

e _t＝y(t)-y ^*(t),t＝1,2,…,n

The error sum of squares expression formula being obtained combination forecasting by above formula is:

$S=\underset{t=1}{\overset{n}{\Σ}}{\left(e_t\right)}^2=\underset{t=1}{\overset{n}{\Σ}}{\left(\underset{i=1}{\overset{4}{\Σ}}{l}_i{e}_{it}\right)}^2=L^{T}EL$

With the minimum optimum weight coefficient asked for for principle in combination forecasting of the error sum of squares of combination forecasting, the quadratic programming problem solved shown in following formula can be converted to.

minS＝L ^TEL

$s.t.\left\{\begin{array}{c}{R}^{T}L=1\\ R={\left(1,1,\mathrm{...},\right)}_{4\×1}\end{array}\right.$

Introduce Lagrange multiplier λ *, can obtain L and λ * differentiate respectively:

$\frac{d[L^T\mathrm{EL}-2{\mathrm{\λ}}^{*}(R^{T}L-1)]}{\mathrm{dL}}=0\⇒\mathrm{EL}-{\mathrm{\λ}}^{*}R=0\⇒L={\mathrm{\λ}}^{*}{E}^{-1}R$

$\frac{d[L^T\mathrm{EL}-2{\mathrm{\λ}}^{*}(R^{T}L-1)]}{d{\mathrm{\λ}}^{*}}=0\⇒R^{T}L=1\⇒{R^T\mathrm{\λ}}^{*}{E}^{-1}R=1\⇒{\mathrm{\λ}}^{*}=\frac{1}{R^T{E}^{-1}R}$

By two formulas above, obtaining optimum weight coefficient expression formula to be asked in combination forecasting is:

$L=\frac{E^{-1}R}{R^T{E}^{-1}R}$

Step 6: optimal weights coefficient step 5 obtained substitutes in combination forecasting expression formula, obtains Optimal Combination Forecasting model, completes wind power prediction by data to be predicted input Optimal Combination Forecasting model.

Described ARIMA time series wind power prediction model is through first difference transformation, model parameter estimation and model and determines rank to determine the value of autoregressive process AR (p), moving average process MA (q).

Selected parameter is the ARIMA time series wind power prediction model of ARIMA (2, Isosorbide-5-Nitrae).

Described BP neural network wind power prediction model is according to root-mean-square error RMSE minimization principle, determines the node in hidden layer of BP neural network wind power prediction model;

Use the cluster centre number of K-means clustering method determination RBF neural wind power prediction model;

The input layer number of described BP neural network wind power prediction model and RBF neural wind power prediction model, the fillet weight between input layer and hidden layer and the fillet weight between hidden layer and output layer are obtained in model training automatically by the neural network model tool box of Matlab.

The hidden layer node quantity of described BP neural network wind power prediction model is 9;

The cluster centre number of described RBF neural wind power prediction model is set as 18;

The input node number of described BP neural network wind power prediction model and RBF neural wind power prediction model is 6.

Described support vector regression wind power prediction model selects RBF kernel function, and each learning parameter adopts particle cluster algorithm to carry out adaptive learning acquisition.

In described kernel function, the value of each parameter is respectively penalty coefficient C=8.572, insensitive loss coefficient ε=0.229, nuclear parameter σ=0.211.

Beneficial effect

The invention provides a kind of wind power combination forecasting method based on optimum weight coefficient, these 4 kinds of individual event Forecasting Methodologies of ARIMA time series, BP neural network, RBF neural and support vector regression are carried out comprehensively, adopt combination forecasting, can the advantage of comprehensive each Individual forecast model effectively, reduce forecasting risk.According to combined prediction control information matrix, with the minimum optimum weight coefficient obtained for principle in combination forecasting of error sum of squares, improve the performance of combination forecasting.Actual measurement wind power prediction data show: combination forecasting precision of prediction of the present invention is high, very conveniently can determine optimal weights coefficient value fast, reduces predicated error.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the method for the invention;

Fig. 2 is history wind power data and curves schematic diagram.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described further.

With the actual measurement wind power data instance of certain wind energy turbine set of China, the application of research combination forecasting method in wind power prediction.This wind energy turbine set has the aerogenerator 41 of rated power 750kW, suppose that all blower fans all have almost identical wind speed and direction, and the wake effect ignored between blower fan, use an equivalent aerogenerator to simulate the meritorious output of whole wind energy turbine set in example.Raw data measuring intervals of TIME is 1h, according to the needs of forecast model modeling, chooses 216 data of continuous 9d for modeling and forecasting, and wherein, front 192 data composition training sample set, rear 24 data are as test sample book collection.Prediction step gets 1, predicts with the rolling forecast method of continuous 6 steps.216 original wind power data as shown in Figure 2.

Adopt percentage ratio error (RPE), mean absolute error (MAE) and mean absolute percentage error (MAPE) as the evaluation index of combination forecasting prediction effect.The expression formula of each evaluation index is as follows.

e _RPE＝|F(t)-A(t)|/[F(t)]×100

$e_{MAE}=\frac{1}{n}\underset{t=1}{\overset{n}{\Σ}}|F\left(t\right)-A\left(t\right)|$

$e_{MAPE}=\frac{1}{n}\underset{t=1}{\overset{n}{\Σ}}|F\left(t\right)-A\left(t\right)|/\[F\left(t\right)\]\×100$

In formula, F (t) is actual measurement wind power; A (t) is prediction wind power; N is prediction verification msg number; T is the sequence numbering of future position.

Based on a wind power combination forecasting method for optimum weight coefficient, as shown in Figure 1, comprise the following steps:

Step 1: use [0,1] interval method for normalizing to be normalized front 192 wind power data, normalization formula is:

${\hat{x}}_i=\frac{x_i-x_{min}}{x_{\max }-x_{\min }},i=1,2,...,192$

In formula, x _ifor the wind power value before normalization; x _maxit is the maximal value in 192 wind power values; x _minit is the minimum value in 192 wind power values.

Step 2: first difference transformation is carried out to the original wind power sequence after normalized, after first order difference, the coefficient of autocorrelation of wind power sequence can decay to zero faster, to (p, q)=(0,1,2,3,4) various order combinations carry out matching and inspection according to low order successively to the order of high-order, and consider stationarity and reversibility condition, final Confirming model is ARIMA (2, Isosorbide-5-Nitrae).The input variable number of BP neural network and RBF neural model is defined as 6.According to RMSE minimization principle, by test of many times, determine that the node in hidden layer of BP neural network model is 9.The cluster centre number using K-means clustering method determination RBF neural model is 18.For support vector regression model, select the good RBF kernel function of universality, each learning parameter adopts particle cluster algorithm to carry out adaptive learning, and the parameter obtaining kernel function is penalty coefficient C=8.572, insensitive loss coefficient ε=0.229, nuclear parameter σ=0.211.The wind power prediction of 4 kinds of wind power prediction model the results are shown in Table 1.

The wind power prediction result of table 14 kind of wind power prediction model

Step 3: the control information matrix E by the data construct combination forecasting in table 1:

E＝[(e _it) _4×n][(e _it) _4×n] ^T

Wherein, e _itrepresent the predicated error of i-th kind of forecast model in t: e _it=y (t)-y _i(t), t=1,2 ..., n, i=1,2 ..., 4; The wind power value that y (t) surveys for t, y _it () represents the predicted value of i-th kind of forecast model in t;

$E=\left[\begin{array}{cccc}456.598& 213.786& 92.607& 132.258\\ 213.786& 230.401& 142.956& 135.128\\ 92.607& 142.956& 210.931& 157.491\\ 132.258& 135.128& 157.491& 176.761\end{array}\right]$

Step 4: according to formula calculate the optimum weight coefficient vector L of combination forecasting:

L＝[0.0631,0.2067,0.2056,0.5246]

Step 5: obtain electric power combination forecasting, expression is:

y ^*＝0.0631y ₁+0.2067y ₂+0.2056y ₃+0.5246y ₄

In formula: y ₁, y ₂, y ₃and y ₄represent predicting the outcome of ARIMA time series, BP neural network, RBF neural and support vector regression Single model respectively.

According to combination forecasting, calculate wind power combined prediction result as shown in table 2.The mean absolute error that 4 kinds of wind power prediction model and combination forecasting predict the outcome and mean absolute percentage error are in table 3, and the distribution situation of the percentage ratio error that predicts the outcome is shown in Table 4.

The wind power prediction result of table 2 combination forecasting

Predicting the outcome and MAE and the MAPE index predicted the outcome of combination forecasting of table 34 kind of wind power prediction model

Predicting the outcome and the distribution situation of the RPE that predicts the outcome of combination forecasting of table 44 kind of wind power prediction model

The data of analytical table 3 are known, the mean absolute error that combination forecasting obtains is 1.969MW, reduces 1.682MW, 0.592MW, 0.527MW and 0.256MW respectively than the result of ARIMA time series, BP neural network, RBF neural and support vector regression; Combination forecasting method obtain 15.882% mean absolute percentage error be also minimum in 4 kinds of wind power prediction model, reduce 11.995%, 4.259%, 3.830% and 1.331% than the result of ARIMA time series, BP neural network, RBF neural and support vector regression respectively.The above results shows, combination forecasting, on the basis predicted the outcome of comprehensive each single wind power prediction model, effectively can improve the accuracy of wind power prediction, reduces predicated error.

The data of further analytical table 4 are known, and in 24 future positions, these 3 kinds of methods of BP neural network, RBF neural and support vector regression respectively have the percentage ratio error of 20,20 and 21 points to be less than 30%, and prediction stability is roughly the same.The prediction less stable of ARIMA model, the percentage ratio error of whole 24 points is all greater than 5%, and has the result of 6 future positions to be greater than 30%.Combination forecasting is compared with other 4 kinds of single forecast models, the prediction that percentage ratio error is less than 5% is counted at most, more than the result of ARIMA time series, BP neural network, RBF neural and support vector regression 9,4,7 and 6 respectively, and have the percentage ratio error of the future position of 87.5% to be less than 30%.Therefore, compare compared with other single wind power prediction model, the prediction stability of combination forecasting is better.

Above-mentioned comparative analysis shows, combination forecasting method is compared with individual event Forecasting Methodology, and forecasting accuracy is better, and it is more stable to predict the outcome, and the mean absolute percentage error of wind power prediction is 15.882%, can meet the needs at Practical Project scene.In addition, the Prediction sum squares of Optimal Combination Forecasting method is not more than the minimum value of Prediction sum squares in each individual event Forecasting Methodology of participating in combined prediction.Therefore, combination forecasting method has good practicality in wind power prediction.

The present invention is illustrated according to the preferred embodiment, but above-described embodiment does not limit the present invention in any form, the technical scheme that the form that all employings are equal to replacement or equivalent transformation obtains, and all drops within protection scope of the present invention.

Claims (7)

1., based on a wind power combination forecasting method for optimum weight coefficient, it is characterized in that, comprise the following steps:

Step 1: gather continuous history wind power data, and the data gathered are normalized;

Four forecast model superpositions are obtained combination forecasting by step 2: set up wind power prediction model respectively to data acquisition ARIMA time series, BP neural network, RBF neural and support vector regression after normalized;

Step 3: the control information matrix E building combination forecasting:

E＝[(e _it) _4×n][(e _it) _4×n] ^T

Wherein, e _itrepresent the predicated error of i-th kind of forecast model in t: e _it=y (t)-y _i(t), t=1,2 ..., n, i=1,2 ..., 4; The wind power value that y (t) surveys for t, y _it () represents the predicted value of i-th kind of forecast model in t;

Step 4: make the weight coefficient of each model in combination forecasting be L=(l ₁, l ₂, l ₃, l ₄) _{4 × 1}, the expression formula of combination forecasting is as follows:

y ^*(t)＝l ₁y ₁(t)+l ₂y ₂(t)+l ₃y ₃(t)+l ₄y ₄(t)

Wherein, l ₁+ l ₂+ l ₃+ l ₄=1, y ₁, y ₂, y ₃, y ₄represent the predicted value of ARIMA time series, BP neural network, RBF neural and support vector regression wind power prediction model t respectively;

Step 5: the expression formula control information matrix of the combination forecasting in step 3 being substituted into combination forecasting, according to formula solve optimal weights coefficient;

Wherein, R=(1,1 ..., 1) _{4 × 1};

Step 6: optimal weights coefficient step 5 obtained substitutes in combination forecasting expression formula, obtains Optimal Combination Forecasting model, completes wind power prediction by data to be predicted input Optimal Combination Forecasting model.

2. method according to claim 1, it is characterized in that, described ARIMA time series wind power prediction model is through first difference transformation, model parameter estimation and model and determines rank to determine the value of autoregressive process AR (p), moving average process MA (q).

3. method according to claim 2, is characterized in that, selected parameter is the ARIMA time series wind power prediction model of ARIMA (2, Isosorbide-5-Nitrae).

4. method according to claim 1, is characterized in that, described BP neural network wind power prediction model is according to root-mean-square error RMSE minimization principle, determines the node in hidden layer of BP neural network wind power prediction model;

Use the cluster centre number of K-means clustering method determination RBF neural wind power prediction model;

The input layer number of described BP neural network wind power prediction model and RBF neural wind power prediction model, the fillet weight between input layer and hidden layer and the fillet weight between hidden layer and output layer are obtained in model training automatically by the neural network model tool box of Matlab.

5. method according to claim 4, is characterized in that, the hidden layer node quantity of described BP neural network wind power prediction model is 9;

The cluster centre number of described RBF neural wind power prediction model is set as 18;

The input node number of described BP neural network wind power prediction model and RBF neural wind power prediction model is 6.

6. method according to claim 1, is characterized in that, described support vector regression wind power prediction model selects RBF kernel function, and each learning parameter adopts particle cluster algorithm to carry out adaptive learning acquisition.

7. method according to claim 6, is characterized in that, in described kernel function, the value of each parameter is respectively penalty coefficient C=8.572, insensitive loss coefficient ε=0.229, nuclear parameter σ=0.211.