CN108599147A - Combination section prediction technique based on normal state exponential smoothing and Density Estimator - Google Patents
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Abstract
The combination section prediction technique based on normal state exponential smoothing and Density Estimator that the invention discloses a kind of, the wind power interval prediction method is introduced into exponential smoothing in normal distribution estimation, when estimating the distribution of t+1 moment wind power prediction errors, the utilization weight of legacy data exponentially decays at any time so that result of calculation is more accurate；The thought of " mixing " and " sliding " is introduced into Density Estimator, when estimating the distribution of t+1 moment wind power prediction errors, the wind power prediction probability of error density function for the previous period at t+1 moment is estimated using different bandwidth, then the probability density function estimated by weighted array different bandwidth is come evaluated error of cancelling out each other；Forecast interval obtained by forecast interval and mixing sliding Density Estimator as obtained by entropy assessment rational weighted array normal state exponential smoothing estimation, generates final wind power prediction section so that two methods form complementation to a certain extent.
Description
Technical field
The present invention relates to wind power technical field, more particularly to based on normal state exponential smoothing with to mix sliding core close
Degree estimation combination wind power interval prediction method.
Background technology
With the finiteness of conventional energy resource and becoming increasingly conspicuous for environmental problem, with environmental protection and the renewable new energy for speciality
Source increasingly obtains the attention of national governments.Wind energy has obtained the extensive of countries in the world as a kind of regenerative resource of green
Using since the randomness of wind, unstability bring great challenge to power network safety operation.Accurately and effectively wind power
Prediction contributes to electric dispatching department to adjust operation plan in time, reduces the risk that wind-powered electricity generation is connected to the grid, reduces the spare of system
Capacity reduces the operating cost of electric system.
Wind power prediction can be divided into physical method and statistical method from prediction technique at present, and wherein physical method needs
Physical message around many wind turbines, applies complex.Statistical method only needs wind speed and power time series can be into
Row prediction, it is more convenient.Traditional most of wind power predictions are the result is that deterministic point prediction, can only obtain one definitely
Numerical value, the probability and fluctuation range be likely to occur to the numerical value can not all learn.The prediction probability of error is analyzed
To show that wind power section, interval prediction contribute to electric dispatching department in Electric Power Network Planning, risk analysis, reliability assessment
Etc. preferably utilize data information.
To predicting that the probability distribution of error is estimated usually there is two class of parameter and nonparametric method, common parametric method estimation
There are normal distribution, Beta distributions etc., parametric method estimation is simple and intuitive, but predicts error distribution form and parameter selection sometimes not
Accurately.Nonparametric method is not usually required to carry out a priori assumption to prediction error distribution, and every probability is determined by truthful data
Fixed, Density Estimator is a kind of common non-parametric estmation method, but the selection of bandwidth parameter is to the accuracy of Density Estimator
Have a significant impact.
Therefore, it is desirable to have, a kind of wind power interval prediction method can be directed to traditional parameters method and norm of nonparametric kernel density is estimated
The respective deficiency for counting wind power prediction probability of error density function, to solve problems of the prior art.
Invention content
The purpose of the present invention is to provide one kind combining wind power area with Density Estimator based on normal state exponential smoothing
Between prediction technique, combination section prediction technique includes the following steps：
Step 1：Determine wind power prediction error, i.e., between wind power actual measured value and wind power prediction value
Deviation；
Step 2：The first wind power prediction section at t+1 moment is calculated by normal state exponential smoothing, it is assumed that wind-powered electricity generation work(
Rate predicts error Normal Distribution, and the variance of all moment prediction errors before the t+1 moment, root are derived by exponential smoothing
T+1 moment wind power prediction errors quantile and on fiducial probability 1- α corresponding first is obtained according to Normal Distribution Theory
Quantile once, the wind power prediction value at t+1 moment add on first quantile and first time quantile as the first wind respectively
The upper and lower bound of electrical power forecast interval；
Step 3：The second wind power prediction section that kernel density estimation method calculates the t+1 moment is slided by mixing, is utilized
The probability density function of the wind power prediction error at n moment, close to probability before the mixing sliding Density Estimator t+1 moment
Degree function obtains wind power prediction error accumulation distribution function by integral, is obtained on corresponding second in fiducial probability 1- α
The wind power prediction value of quantile and second time quantile, t+1 moment adds quantile and second time quantile on second respectively
Upper and lower bound as the second wind power prediction section；
Step 4：By the first wind power prediction section covering measures, the second wind power prediction section covering measures and
The forecast interval bandwidth at each moment determines the first wind power prediction section and the second wind as evaluation index, by entropy assessment
The combining weights ω of electrical power forecast interval1And ω2；
Step 5：It is pre- according to step 4 determined combination weight pair the first wind power prediction section and the second wind power
Survey section is weighted combination and obtains the third wind power prediction section at final t+1 moment, is covered using forecast interval general
Rate (prediction interval coverage probability, PICP) and forecast interval average bandwidth
(prediction interval normalized average width, PINAW) evaluates third wind power prediction area
Between.
Preferably, the step 1 includes the following contents：
1. choosing the wind power prediction value P of two weekspredWith the wind power actual measured value at moment of being corresponding to it
Pmeas；
2. taking PpredAnd PmeasDeviation as the wind power prediction error ε.
Preferably, the step 2 includes the following contents：
1. the wind power prediction error ε Normal Distribution is assumed, before the exponential smoothing derivation t+1 moment
The variance of the wind power prediction error at all momentExponential smoothing expression formula is formula (1)：
WhereinFor the wind power prediction square-error of t moment,It predicts for stability bandwidth, is obtained by successive ignition
Formula (2)：
Wherein 0 ＜ a ＜ 1,The profit of t+1 moment pervious wind power prediction square-error is obtained by formula (2)
Exponentially declined with weight, and weight summation is about 1；
2. according to the theory of normal distribution, wind power prediction error described in the t+1 moment is on fiducial probability 1- α are corresponding
QuantileWith lower quantileIt can be expressed as formula (3) and formula (4)：
Wherein z1-α/2It is obtained by standardized normal distribution table, since almost unbiased, μ are reduced to 0 to wind power prediction error；
3. the wind power prediction value P at t+1 momentpredIt adds respectivelyWithAs described
The upper and lower bound in one wind power prediction section is embodied as formula (5)：
Preferably, the step 3 includes the following contents：
1. carrying out different bandwidth h respectively to the wind power prediction error at n moment before the t+1 momentkCuclear density
Estimation, expression such as formula (6)：
2. using weight factor betakPassing through different bandwidth hkThe probability density letter of the wind power prediction error of estimation
Number fk,t+1(ε) is combined, expression such as formula (7)：
3. to fMSKD,t+1(ε) is integrated to obtain the cumulative distribution letter F (ξ) of the wind power prediction error, to F (ξ)
It negates to obtain its inverse functionIt is formula (8) to meet second wind power prediction section that fiducial probability is 1- α：
Preferably, the step 4 includes the following contents：
1. using first wind power prediction section and second wind power prediction section as evaluation object, entropy
The evaluation index of power method be first wind power prediction section and second wind power prediction section coverage rate and
Each moment forecast interval width is denoted as m, establishes evaluations matrix altogether
First wind power prediction section and second wind power prediction section covering measuresNtFor forecast sample number, k is Boolean quantity, if predicted target values tiIt is contained in the upper and lower of interval prediction
It limits, then k=1, otherwise k=0；
2. evaluations matrix A is standardizedThen first wind power prediction section and second wind
The entropy of electrical power forecast interval is：
Wherein,It is assumed that working as pijWhen=0, pijlnpij=0；
3. on the basis of entropy, the entropy in first wind power prediction section and second wind power prediction section
Quan Wei：
Preferably, the step 5 includes the following contents：
1. weights omega is pressed in first wind power prediction section and second wind power prediction section1And ω2Add
Power combination obtains third forecast interval：Wherein Third is predicted
Section is the power prediction section finally determined；
2. using third wind power described in forecast interval covering measures index and forecast interval average bandwidth metrics evaluation
Forecast interval, forecast interval average bandwidth WithThe respectively described third
The upper and lower bound in wind power prediction section.
The present invention is based on normal state exponential smoothings to combine wind power interval prediction method with mixing sliding Density Estimator
It has the advantages that：
1. an exponential smoothing is introduced into normal distribution estimation, when estimating the distribution of t+1 moment wind power prediction errors,
The utilization weight of legacy data exponentially decays at any time so that result of calculation is more accurate；
2. the thought of " mixing " and " sliding " is introduced into Density Estimator, missed in estimation t+1 moment wind power predictions
When difference cloth, the wind power prediction probability of error density function for the previous period at t+1 moment is estimated using different bandwidth, then
The probability density function estimated by weighted array different bandwidth is come evaluated error of cancelling out each other；
3. forecast interval and mixing sliding core as obtained by entropy assessment rational weighted array normal state exponential smoothing estimation
Forecast interval obtained by density estimation, generates final wind power prediction section so that two methods are formed to a certain extent
It is complementary.
Description of the drawings
Fig. 1 is to combine wind power interval prediction method with mixing sliding Density Estimator based on normal state exponential smoothing
Flow chart.
Fig. 2 is actual prediction result schematic diagram of the wind power plant wind power in 80% level of confidence.
Fig. 3 is actual prediction result schematic diagram of the wind power plant wind power in 90% level of confidence.
Specific implementation mode
To keep the purpose, technical scheme and advantage that the present invention is implemented clearer, below in conjunction in the embodiment of the present invention
Attached drawing, technical solution in the embodiment of the present invention is further described in more detail.In the accompanying drawings, identical from beginning to end or class
As label indicate same or similar element or element with the same or similar functions.Described embodiment is the present invention
A part of the embodiment, instead of all the embodiments.The embodiments described below with reference to the accompanying drawings are exemplary, it is intended to use
It is of the invention in explaining, and be not considered as limiting the invention.Based on the embodiments of the present invention, ordinary skill people
The every other embodiment that member is obtained without creative efforts, shall fall within the protection scope of the present invention.
As shown in Figure 1, by taking the wind field of northwest as an example, temporal resolution 15min, fetch from collection in worksite to wind-powered electricity generation work(
Rate data, including actual power data and prediction power data are chosen 1500 groups of wherein representative data and are tested.
The method includes the steps of：
Step 1：The deviation between wind power actual measured value and wind power prediction value is taken, it is pre- to be defined as wind power
Survey error；
Step 101：Choose 600 groups of representative wind power prediction value PpredWith the wind-powered electricity generation work(at moment of being corresponding to it
Rate actual measured value Pmeas。
Step 102：Take PpredAnd PmeasDeviation as wind power prediction error ε.
Step 2：Calculate the wind power prediction section at each moment after the t+1 moment successively by normal state exponential smoothing
1, it is assumed that prediction error Normal Distribution, and more reasonably variance is derived by exponential smoothing, it is managed according to normal distribution
By obtaining t+1 moment wind power prediction errors in the corresponding upper quantiles of fiducial probability 1- α and lower quantile, the t+1 moment
Wind power prediction value adds the upper and lower bound of quantile and lower quantile as forecast interval 1 respectively.
Step 201：Assuming that wind power prediction error ε Normal Distribution, by exponential smoothing derive the t+1 moment with
The variance of preceding all moment prediction errorsExponential smoothing expression formula is：WhereinFor t moment
Squared prediction error,It predicts for stability bandwidth, is obtained by successive ignition：
Wherein 0 ＜ a ＜ 1,The utilization weight of all past squared prediction errors can be seen that exponentially by above formula
Decline, and weight summation is about 1.
Step 202：According to the theory of normal distribution, t+1 moment wind power prediction errors are corresponding in fiducial probability 1- α
Upper quantileWith lower quantileIt can be expressed as：
Wherein z1-α/2It can be obtained by standardized normal distribution table, since almost unbiased, μ can simply turn to 0 to wind power prediction error.
Step 203：The wind power prediction value P at t+1 momentpredIt adds respectivelyWithAs prediction
The upper and lower bound in section 1.It is embodied as：
Step 3：The wind power section 2 that kernel density estimation method calculates the t+1 moment is slided by mixing, is slided using mixing
The probability density function of the wind power prediction error at n moment before the Density Estimator t+1 moment is logical to probability density function
Integral is crossed to obtain predicting that error accumulation distribution function obtains its upper and lower quantile, the wind at t+1 moment at fiducial probability 1- α
Electrical power predicted value adds the upper and lower bound of quantile and lower quantile as forecast interval 2 respectively.
Step 301：Multiple and different bandwidth h are carried out respectively to the wind power prediction error at n moment before the t+1 momentk's
Density Estimator, expression are as follows：
Step 302：Use suitable weight coefficient βkBy notWith bandwidth hkEstimate
The prediction probability of error density function f of meterk,t+1(ε) is combined.
Step 303：To fMSKD,t+1(ε) is integrated to obtain the cumulative distribution letter F (ξ) of prediction error, is negated to F (ξ)
To its inverse functionMeeting the forecast interval 2 that fiducial probability is 1- α is：
Step 4：Using forecast interval covering measures, the forecast interval bandwidth at each moment as evaluation index, pass through entropy weight
Method objectively determines the combining weights ω of forecast interval 1 and forecast interval 21And ω2。
Step 401：Using forecast interval 1 and forecast interval 2 as 2 evaluation objects, the evaluation index of entropy assessment is prediction
Section coverage rate (PICP) and each moment forecast interval width are denoted as m altogether.Establish evaluations matrix
Forecast interval covering measuresNtFor forecast sample number, k is Boolean quantity, if prediction target
Value tiIt is contained in the bound of interval prediction, then k=1, otherwise k=0.
Step 402：Evaluations matrix A is standardizedThen the entropy of forecast interval 1 and forecast interval 2 is：
Wherein,It is assumed that working as pijWhen=0, pijlnpij=0.
Step 403：On the basis of entropy, forecast interval 1 and 2 entropy weight of forecast interval are：
Step 5：According to step 4 determine weight to forecast interval 1 and forecast interval 2 be weighted combination obtain it is final
The forecast interval 3 at t+1 moment is evaluated using forecast interval covering measures (PICP) and forecast interval average bandwidth (PINAW)
Forecast interval 3.
Step 501：Forecast interval 1 and forecast interval 2 are pressed weights omega1And ω2Weighted array obtains forecast interval
Wherein,
Step 502：Carry out evaluation and foreca using forecast interval covering measures (PICP) and forecast interval average bandwidth (PINAW)
Section 3.
Forecast interval average bandwidth WithRespectively forecast interval 3
Upper and lower bound.
Evaluation result such as following table：
As shown in Figures 2 and 3, forecast interval coverage rate (PICP) has been more than desired value PINC, and forecast interval width is smaller, and
Increase with the increase of specified confidence level, situation is consistent with result in table in Fig. 2,3.
It is last it is to be noted that：The above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations.To the greatest extent
Present invention has been described in detail with reference to the aforementioned embodiments for pipe, it will be understood by those of ordinary skill in the art that：It is still
Can be with technical scheme described in the above embodiments is modified, or which part technical characteristic is equally replaced
It changes；And these modifications or replacements, the essence for various embodiments of the present invention technical solution that it does not separate the essence of the corresponding technical solution
God and range.
Claims (6)
1. a kind of combination section prediction technique based on normal state exponential smoothing and Density Estimator, which is characterized in that described group
Interval prediction method is closed to include the following steps：
Step 1：Determine wind power prediction error, i.e., it is inclined between wind power actual measured value and wind power prediction value
Difference；
Step 2：The first wind power prediction section at t+1 moment is calculated by normal state exponential smoothing, it is assumed that wind power is pre-
Error Normal Distribution is surveyed, the variance of all moment prediction errors before the t+1 moment is derived by exponential smoothing, according to just
State distribution theory obtains t+1 moment wind power prediction errors on fiducial probability 1- α corresponding first under quantile and first
Quantile, the wind power prediction value at t+1 moment add on first quantile and first time quantile as the first wind-powered electricity generation work(respectively
The upper and lower bound of rate forecast interval；
Step 3：The second wind power prediction section that kernel density estimation method calculates the t+1 moment is slided by mixing, utilizes mixing
The probability density function of the wind power prediction error at n moment before the sliding Density Estimator t+1 moment, to probability density letter
Number obtains wind power prediction error accumulation distribution function by integral, and point position on corresponding second is obtained in fiducial probability 1- α
Number and second time quantile, the wind power prediction value at t+1 moment add quantile and second time quantile conduct on second respectively
The upper and lower bound in the second wind power prediction section；
Step 4：By the first wind power prediction section covering measures, the second wind power prediction section covering measures and each
The forecast interval bandwidth at moment determines the first wind power prediction section and the second wind-powered electricity generation work(as evaluation index, by entropy assessment
The combining weights ω of rate forecast interval1And ω2；
Step 5：According to step 4 determined combination weight pair the first wind power prediction section and the second wind power prediction area
Between be weighted combination and obtain the third wind power prediction section at final t+1 moment, using forecast interval covering measures and
Forecast interval average bandwidth evaluates third wind power prediction section.
2. the combination section prediction technique according to claim 1 based on normal state exponential smoothing and Density Estimator,
It is characterized in that：The step 1 includes the following contents：
1. choosing the wind power prediction value P of two weekspredWith the wind power actual measured value P at moment of being corresponding to itmeas；
2. taking PpredAnd PmeasDeviation as the wind power prediction error ε.
3. the combination section prediction technique according to claim 2 based on normal state exponential smoothing and Density Estimator,
It is characterized in that：The step 2 includes the following contents：
1. assuming the wind power prediction error ε Normal Distribution, own before deriving the t+1 moment by exponential smoothing
The variance of the wind power prediction error at momentExponential smoothing expression formula is formula (1)：
WhereinFor the wind power prediction square-error of t moment,It is predicted for stability bandwidth, formula is obtained by successive ignition
(2)：
Wherein 0 ＜ a ＜ 1,The exploitation right of t+1 moment pervious wind power prediction square-error is obtained by formula (2)
Weight exponentially declines, and weight summation is about 1；
2. according to the theory of normal distribution, wind power prediction error described in the t+1 moment divides position on fiducial probability 1- α are corresponding
NumberWith lower quantileIt can be expressed as formula (3) and formula (4)：
Wherein z1-α/2It is obtained by standardized normal distribution table, since almost unbiased, μ are reduced to 0 to wind power prediction error；
3. the wind power prediction value P at t+1 momentpredIt adds respectivelyWithAs first wind-powered electricity generation
The upper and lower bound in power prediction section is embodied as formula (5)：
4. the combination section prediction technique according to claim 3 based on normal state exponential smoothing and Density Estimator,
It is characterized in that：The step 3 includes the following contents：
1. carrying out different bandwidth h respectively to the wind power prediction error at n moment before the t+1 momentkDensity Estimator,
Expression such as formula (6)：
2. using weight factor betakPassing through different bandwidth hkThe probability density function of the wind power prediction error of estimation
fk,t+1(ε) is combined, expression such as formula (7)：
3. to fMSKD, t+1(ε) is integrated to obtain the cumulative distribution letter F (ξ) of the wind power prediction error, is negated to F (ξ)
Obtain its inverse functionIt is formula (8) to meet second wind power prediction section that fiducial probability is 1- α：
5. the combination section prediction technique according to claim 4 based on normal state exponential smoothing and Density Estimator,
It is characterized in that：The step 4 includes the following contents：
1. using first wind power prediction section and second wind power prediction section as evaluation object, entropy assessment
Evaluation index be the coverage rate in first wind power prediction section and second wind power prediction section and each
Moment forecast interval width is denoted as m, establishes evaluations matrix altogether
First wind power prediction section and second wind power prediction section covering measuresNtFor forecast sample number, k is Boolean quantity, if predicted target values tiIt is contained in the upper and lower of interval prediction
It limits, then k=1, otherwise k=0；
2. evaluations matrix A is standardizedThen first wind power prediction section and the second wind-powered electricity generation work(
The entropy of rate forecast interval is：
Wherein,It is assumed that working as pijWhen=0, pijln pij=0；
3. on the basis of entropy, the entropy weight in first wind power prediction section and second wind power prediction section
For：
6. the combination section prediction technique according to claim 5 based on normal state exponential smoothing and Density Estimator,
It is characterized in that：The step 5 includes the following contents：
1. weights omega is pressed in first wind power prediction section and second wind power prediction section1And ω2Set of weights
Conjunction obtains third forecast interval：WhereinThird forecast interval is
Finally determining power prediction section；
2. using third wind power prediction described in forecast interval covering measures index and forecast interval average bandwidth metrics evaluation
Section, forecast interval average bandwidth WithThe respectively described third wind-powered electricity generation
The upper and lower bound in power prediction section.
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| CN110850162A (en) * | 2019-11-22 | 2020-02-28 | 西南交通大学 | Frequency estimation method of three-phase power system based on error correlation entropy |
| CN113048043A (en) * | 2019-12-27 | 2021-06-29 | 北京国双科技有限公司 | Plunger pump parameter threshold setting method and device, electronic equipment and storage medium |
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