CN108599147B - Combined interval prediction method based on normal exponential smoothing method and kernel density estimation - Google Patents

Combined interval prediction method based on normal exponential smoothing method and kernel density estimation Download PDF

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CN108599147B
CN108599147B CN201810329787.4A CN201810329787A CN108599147B CN 108599147 B CN108599147 B CN 108599147B CN 201810329787 A CN201810329787 A CN 201810329787A CN 108599147 B CN108599147 B CN 108599147B
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wind power
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interval
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CN108599147A (en
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杨锡运
张艳峰
马雪
付果
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North China Electric Power University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
    • G06Q50/06—Electricity, gas or water supply
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

Abstract

The invention discloses a combined interval prediction method based on a normal exponential smoothing method and kernel density estimation, wherein the wind power interval prediction method introduces an exponential smoothing method into normal distribution estimation, and when wind power prediction error distribution at the moment of t +1 is estimated, the utilization weight of old data exponentially decays along with time, so that the calculation result is more accurate; introducing the ideas of 'mixing' and 'sliding' into kernel density estimation, adopting wind power prediction error probability density functions of different bandwidths for estimating a period of time before the t +1 moment when estimating the wind power prediction error distribution at the t +1 moment, and mutually offsetting estimation errors by weighting and combining the probability density functions estimated by different bandwidths; and generating a final wind power prediction interval by a prediction interval obtained by estimating a reasonable weighted combination normal exponential smoothing method by an entropy weight method and a prediction interval obtained by estimating a mixed sliding kernel density, so that the two methods form complementation to a certain extent.

Description

Combined interval prediction method based on normal exponential smoothing method and kernel density estimation
Technical Field
The invention relates to the technical field of wind power, in particular to a combined wind power interval prediction method based on a normal exponential smoothing method and mixed sliding nuclear density estimation.
Background
With the limitation of conventional energy and the increasing prominence of environmental problems, new energy with the characteristics of environmental protection and regeneration is more and more paid attention by governments of various countries. Wind energy has been widely used in various countries in the world as a green renewable energy source, and the randomness and instability of wind bring great challenges to the safe and stable operation of a power grid. Accurate and effective wind power prediction is helpful for a power dispatching department to adjust a dispatching plan in time, reduces the risk of merging wind power into a power grid, reduces the reserve capacity of a system, and reduces the operating cost of a power system.
At present, wind power prediction can be divided into a physical method and a statistical method from a prediction method, wherein the physical method needs physical information around a plurality of fans and is complex to apply. The statistical method can predict only by the wind speed and power time series, and is convenient. Most of traditional wind power prediction results are deterministic point predictions, only an exact numerical value is obtained, and the probability and fluctuation range of the numerical value which possibly occurs cannot be known. And analyzing the prediction error probability distribution to obtain a wind power interval, wherein the interval prediction is beneficial to a power dispatching department to better utilize data information in the aspects of power grid planning, risk analysis, reliability evaluation and the like.
The probability distribution of the prediction error is estimated by two types of parameter methods and nonparametric methods, the commonly used parameter methods are normal distribution, Beta distribution and the like, the parameter methods are simple and intuitive in estimation, and the prediction error distribution form and the parameter selection are sometimes inaccurate. The nonparametric method usually does not need a priori assumption on the prediction error distribution, the probability of each point is determined by real data, the kernel density estimation is a common nonparametric estimation method, but the selection of the bandwidth parameters has great influence on the accuracy of the kernel density estimation.
Therefore, a wind power interval prediction method is expected to be provided, which can solve the problems in the prior art by aiming at the respective defects of the traditional parameter method and the nonparametric kernel density estimation wind power prediction error probability density function.
Disclosure of Invention
The invention aims to provide a combined wind power interval prediction method based on a normal exponential smoothing method and kernel density estimation, which comprises the following steps:
the method comprises the following steps: determining a wind power prediction error, namely a deviation between an actual wind power measured value and a wind power predicted value;
step two: calculating a first wind power prediction interval at the time of t +1 by a normal exponential smoothing method, assuming that wind power prediction errors obey normal distribution, deriving variances of the prediction errors at all times before the time of t +1 by the exponential smoothing method, obtaining a first upper quantile and a first lower quantile corresponding to the wind power prediction errors at the time of t +1 at a confidence probability of 1-alpha according to a normal distribution theory, and adding the first upper quantile and the first lower quantile to a wind power prediction value at the time of t +1 as an upper limit and a lower limit of the first wind power prediction interval respectively;
step three: calculating a second wind power prediction interval at the t +1 moment by a mixed sliding kernel density estimation method, estimating a probability density function of wind power prediction errors at n moments before the t +1 moment by using the mixed sliding kernel density, obtaining a wind power prediction error cumulative distribution function by integrating the probability density function, obtaining a corresponding second upper quantile and a second lower quantile at a confidence probability 1-alpha, and adding the second upper quantile and the second lower quantile to a wind power prediction value at the t +1 moment as an upper limit and a lower limit of the second wind power prediction interval respectively;
step four: determining the combined weight omega of the first wind power prediction interval and the second wind power prediction interval by an entropy weight method by taking the coverage probability of the first wind power prediction interval, the coverage probability of the second wind power prediction interval and the bandwidth of the prediction interval at each moment as evaluation indexes1And ω2；
Step five: and performing weighted combination on the first wind power prediction interval and the second wind power prediction interval according to the combination weight determined in the fourth step to obtain a third wind power prediction interval at the final t +1 moment, and evaluating the third wind power prediction interval by using a Prediction Interval Coverage Probability (PICP) and a prediction interval average bandwidth (PINAW).
Preferably, the first step comprises the following steps:
firstly, selecting a wind power predicted value P of two-cycle timepredAnd the actual measured value P of the wind power at the corresponding momentmeas；
② taking PpredAnd PmeasAs the wind power prediction error.
Preferably, the second step comprises the following steps:
firstly, assuming that the wind power prediction error obeys normal distribution, and deriving the variance of the wind power prediction error at all moments before t +1 moment by an exponential smoothing method
Figure BDA0001627625180000031
The exponential smoothing expression is formula (1):
Figure BDA0001627625180000032
wherein
Figure BDA0001627625180000033
For the square of the wind power prediction error at time t,
Figure BDA0001627625180000034
for the fluctuation rate prediction, the formula (2) is obtained through multiple iterations:
Figure BDA0001627625180000035
wherein a is more than 0 and less than 1,
Figure BDA0001627625180000036
the utilization weight of the square of the wind power prediction error before the t +1 moment is obtained by the formula (2) and decreases exponentially, and the total weight is about 1;
secondly, according to the theory of normal distribution, the wind power prediction error at the moment of t +1 is in an upper quantile corresponding to the confidence probability 1-alpha
Figure BDA0001627625180000037
And lower quantile
Figure BDA0001627625180000038
Can be expressed as formula (3) and formula (4), respectively:
Figure BDA0001627625180000039
Figure BDA00016276251800000310
wherein z is1-α/2The method is obtained by a standard normal distribution table, and mu is simplified to 0 because the wind power prediction error is almost unbiased;
③ the predicted value P of the wind power at the moment t +1predAre respectively provided with
Figure BDA00016276251800000311
And
Figure BDA00016276251800000312
the upper limit and the lower limit of the first wind power prediction interval are specifically expressed as a formula (5):
Figure BDA00016276251800000313
preferably, the third step includes the following steps:
respectively carrying out different bandwidths h on the wind power prediction errors at n moments before the t +1 momentkThe specific expression is as shown in formula (6):
Figure BDA00016276251800000314
② using weight coefficient betakWill pass through different bandwidths hkEstimated probability density function f of the wind power prediction errork,t+1() And combining, wherein the specific expression is as formula (7):
Figure BDA0001627625180000041
③ to fMSKD,t+1() Integrating to obtain cumulative distribution function F (xi) of wind power prediction error, and negating F (xi) to obtain its inverse function
Figure BDA0001627625180000042
The second wind power prediction interval satisfying the confidence probability of 1-alpha is a formula (8):
Figure BDA0001627625180000043
preferably, the fourth step includes the following steps:
taking the first wind power prediction interval and the second wind power prediction interval as evaluation objects, recording the evaluation indexes of an entropy weight method as the coverage rate of the first wind power prediction interval and the second wind power prediction interval and the width of the prediction interval at each moment as m, and establishing an evaluation matrix
Figure BDA0001627625180000044
Coverage probability of the first wind power prediction interval and the second wind power prediction interval
Figure BDA0001627625180000045
NtFor predicting the number of samples, k is a Boolean quantity, if a target value t is predictediIf the k is equal to 1, otherwise, k is equal to 0;
② standardizing the evaluation matrix A to obtain
Figure BDA0001627625180000046
The entropy of the first wind power prediction interval and the second wind power prediction interval is as follows:
Figure BDA0001627625180000047
wherein the content of the first and second substances,
Figure BDA0001627625180000048
let when p beijWhen equal to 0, pijlnpij＝0；
On the basis of entropy, the entropy weights of the first wind power prediction interval and the second wind power prediction interval are as follows:
Figure BDA0001627625180000049
preferably, the step five comprises the following steps:
firstly, the first wind power prediction interval and the second wind power prediction interval are weighted according to the weight omega1And ω2And obtaining a third prediction interval by weighted combination:
Figure BDA0001627625180000051
wherein
Figure BDA0001627625180000052
Figure BDA0001627625180000053
The third prediction interval is the finally determined power prediction interval;
evaluating the third wind power prediction interval by using a prediction interval coverage probability index and a prediction interval average bandwidth index, wherein the prediction interval average bandwidth index
Figure BDA0001627625180000054
Figure BDA0001627625180000055
And
Figure BDA0001627625180000056
and the upper limit and the lower limit of the third wind power prediction interval are respectively.
The wind power interval prediction method based on the combination of the normal exponential smoothing method and the mixed sliding kernel density estimation has the following beneficial effects:
1. an exponential smoothing method is introduced into normal distribution estimation, and when wind power prediction error distribution at the moment of t +1 is estimated, the utilization weight of old data exponentially decays along with time, so that the calculation result is more accurate;
2. introducing the ideas of 'mixing' and 'sliding' into kernel density estimation, adopting wind power prediction error probability density functions of different bandwidths for estimating a period of time before the t +1 moment when estimating the wind power prediction error distribution at the t +1 moment, and mutually offsetting estimation errors by weighting and combining the probability density functions estimated by different bandwidths;
3. and generating a final wind power prediction interval by a prediction interval obtained by estimating a reasonable weighted combination normal exponential smoothing method by an entropy weight method and a prediction interval obtained by estimating a mixed sliding kernel density, so that the two methods form complementation to a certain extent.
Drawings
FIG. 1 is a flow chart of a wind power interval prediction method based on a combination of a normal exponential smoothing method and a mixed slip kernel density estimation.
FIG. 2 is a schematic diagram of an actual prediction result of wind power of a wind farm at an 80% confidence level.
FIG. 3 is a schematic diagram of an actual prediction result of wind power of a wind farm at a 90% confidence level.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiments of the present invention. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are only some, but not all embodiments of the invention. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, taking a certain northwest wind farm as an example, the time resolution is 15min, wind power data collected from the site, including actual power data and predicted power data, are taken, and 1500 representative groups of data are selected for experiments. The method comprises the following steps:
step 1: taking the deviation between the actual wind power measured value and the predicted wind power value, and defining the deviation as a wind power prediction error;
step 101: selecting 600 groups of representative wind power predicted values PpredAnd the actual measured value P of the wind power at the corresponding momentmeas。
Step 102: get PpredAnd PmeasThe deviation of (a) is taken as a wind power prediction error.
Step 2: sequentially calculating the wind power prediction interval 1 at each moment after the t +1 moment by a normal exponential smoothing method, assuming that the prediction error obeys normal distribution, deriving more reasonable variance by the exponential smoothing method, obtaining an upper quantile and a lower quantile corresponding to the wind power prediction error at the t +1 moment at a confidence probability 1-alpha according to a normal distribution theory, and respectively adding the quantile and the lower quantile to the wind power prediction value at the t +1 moment to serve as the upper limit and the lower limit of the prediction interval 1.
Step 201: assuming that the wind power prediction error obeys normal distribution, deriving the variance of the prediction errors at all moments before t +1 moment by an exponential smoothing method
Figure BDA0001627625180000061
The exponential smoothing expression is:
Figure BDA0001627625180000062
wherein
Figure BDA0001627625180000063
For the square of the prediction error at time t,
Figure BDA0001627625180000064
for fluctuation rate prediction, the following results are obtained through multiple iterations:
Figure BDA0001627625180000065
wherein a is more than 0 and less than 1,
Figure BDA0001627625180000066
from the above equation, it can be seen that the utilization weights of all past prediction error squares decrease exponentially, and the sum of the weights is about 1.
Step 202: according to the theory of normal distribution, the wind power prediction error at the moment of t +1 is divided into upper quantiles corresponding to the confidence probability 1-alpha
Figure BDA0001627625180000071
And lower quantile
Figure BDA0001627625180000072
Can be respectively expressed as:
Figure BDA0001627625180000073
Figure BDA0001627625180000074
wherein z is1-α/2It can be derived from a standard normal distribution table, since the wind power prediction error is almost unbiased, μ can be simplified to 0.
Step 203: wind power predicted value P at t +1 momentpredAre respectively provided with
Figure BDA0001627625180000075
And
Figure BDA0001627625180000076
as the upper and lower limits of prediction interval 1. The concrete expression is as follows:
Figure BDA0001627625180000077
and step 3: calculating a wind power interval 2 at the t +1 moment by a hybrid sliding kernel density estimation method, estimating a probability density function of wind power prediction errors at n moments before the t +1 moment by using the hybrid sliding kernel density, obtaining a prediction error cumulative distribution function by integrating the probability density function, obtaining an upper quantile and a lower quantile under a confidence probability of 1-alpha, and respectively adding the quantile and the lower quantile to a wind power predicted value at the t +1 moment to serve as an upper limit and a lower limit of the prediction interval 2.
Step 301: respectively carrying out a plurality of different bandwidths h on the wind power prediction errors at n moments before the t +1 momentkThe specific expression of the kernel density estimation is as follows:
Figure BDA0001627625180000078
step 302: using a suitable weighting factor betakHandle passing through
Figure BDA0001627625180000079
Same bandwidth hkEstimated prediction error probability density function fk,t+1() And (4) combining.
Step 303: to fMSKD,t+1() Integrating to obtain cumulative distribution function F (xi) of prediction error, and negating F (xi) to obtain its inverse function
Figure BDA00016276251800000710
The prediction interval 2 satisfying the confidence probability of 1- α is:
Figure BDA00016276251800000711
and 4, step 4: the combination weight ω of the prediction section 1 and the prediction section 2 is objectively determined by the entropy weight method using the prediction section coverage probability and the prediction section bandwidth at each time as evaluation indexes1And ω2。
Step 401: the prediction interval 1 and the prediction interval 2 are set as 2 evaluation targets, and the evaluation indexes of the entropy weight method are Prediction Interval Coverage (PICP) and prediction interval width at each time, which are collectively expressed as m. Establishing an evaluation matrix
Figure BDA0001627625180000081
Predicting interval coverage probability
Figure BDA0001627625180000082
NtFor predicting the number of samples, k is a Boolean quantity, if a target value t is predictediAnd if the k is equal to 1, and if the k is not equal to 0, the upper limit and the lower limit of the interval prediction are included.
Step 402: normalizing the evaluation matrix A to
Figure BDA0001627625180000083
The entropy of prediction interval 1 and prediction interval 2 is then:
Figure BDA0001627625180000084
wherein the content of the first and second substances,
Figure BDA0001627625180000085
let when p beijWhen equal to 0, pijlnpij＝0。
Step 403: on the basis of entropy, entropy weights of the prediction interval 1 and the prediction interval 2 are as follows:
Figure BDA0001627625180000086
Figure BDA0001627625180000087
and 5: and (4) performing weighted combination on the prediction interval 1 and the prediction interval 2 according to the weight determined in the step (4) to obtain a final prediction interval 3 at the time of t +1, and evaluating the prediction interval 3 by using a Prediction Interval Coverage Probability (PICP) and a prediction interval average bandwidth (PINAW).
Step 501: the prediction interval 1 and the prediction interval 2 are weighted by the weight omega1And ω2Weighted combination to obtain prediction interval
Figure BDA0001627625180000088
Wherein the content of the first and second substances,
Figure BDA0001627625180000089
step 502: prediction interval 3 was evaluated using Prediction Interval Coverage Probability (PICP) and prediction interval average bandwidth (PINAW).
Predicting interval average bandwidth
Figure BDA0001627625180000091
Figure BDA0001627625180000092
And
Figure BDA0001627625180000093
the upper and lower limits of prediction interval 3 are respectively.
The evaluation results are shown in the following table:
Figure BDA0001627625180000094
as shown in fig. 2 and 3, the Prediction Interval Coverage (PICP) exceeds the target value PINC, the prediction interval width is small, and increases with increasing nominal confidence level, and the cases in fig. 2 and 3 match the results in the table.
Finally, it should be pointed out that: the above examples are only for illustrating the technical solutions of the present invention, and are not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (4)

1. A combined interval prediction method based on a normal exponential smoothing method and kernel density estimation is characterized by comprising the following steps:
the method comprises the following steps: determining a wind power prediction error, namely a deviation between an actual wind power measured value and a wind power predicted value;
selectingTaking a predicted value P of the wind power in two weekspredAnd the actual measured value P of the wind power at the corresponding momentmeas；
② taking PpredAnd PmeasThe deviation of (a) is taken as the wind power prediction error;
step two: calculating a first wind power prediction interval at the time of t +1 by a normal exponential smoothing method, assuming that wind power prediction errors obey normal distribution, deriving variances of the prediction errors at all times before the time of t +1 by the exponential smoothing method, obtaining a first upper quantile and a first lower quantile corresponding to the wind power prediction errors at the time of t +1 at a confidence probability of 1-alpha according to a normal distribution theory, and adding the first upper quantile and the first lower quantile to a wind power prediction value at the time of t +1 as an upper limit and a lower limit of the first wind power prediction interval respectively;
firstly, assuming that the wind power prediction error obeys normal distribution, and deriving the variance of the wind power prediction error at all moments before t +1 moment by an exponential smoothing method
Figure FDA0002561820830000011
The exponential smoothing expression is formula (1):
Figure FDA0002561820830000012
wherein
Figure FDA0002561820830000013
For the square of the wind power prediction error at time t,
Figure FDA0002561820830000014
for the fluctuation rate prediction, the formula (2) is obtained through multiple iterations:
Figure FDA0002561820830000015
wherein a is more than 0 and less than 1,
Figure FDA0002561820830000016
the utilization weight of the square of the wind power prediction error before the t +1 moment is obtained by the formula (2) and decreases exponentially, and the total weight is about 1;
secondly, according to the theory of normal distribution, the wind power prediction error at the moment of t +1 is in an upper quantile corresponding to the confidence probability 1-alpha
Figure FDA0002561820830000017
And lower quantile
Figure FDA0002561820830000018
Can be expressed as formula (3) and formula (4), respectively:
Figure FDA0002561820830000019
Figure FDA00025618208300000110
wherein z is1-α/2The method is obtained by a standard normal distribution table, and mu is simplified to 0 because the wind power prediction error is almost unbiased;
③ the predicted value P of the wind power at the moment t +1predAre respectively provided with
Figure FDA0002561820830000021
And
Figure FDA0002561820830000022
the upper limit and the lower limit of the first wind power prediction interval are specifically expressed as a formula (5):
Figure FDA0002561820830000023
step three: calculating a second wind power prediction interval at the t +1 moment by a mixed sliding kernel density estimation method, estimating a probability density function of wind power prediction errors at n moments before the t +1 moment by using the mixed sliding kernel density, obtaining a wind power prediction error cumulative distribution function by integrating the probability density function, obtaining a corresponding second upper quantile and a second lower quantile at a confidence probability 1-alpha, and adding the second upper quantile and the second lower quantile to a wind power prediction value at the t +1 moment as an upper limit and a lower limit of the second wind power prediction interval respectively;
step four: determining the combined weight omega of the first wind power prediction interval and the second wind power prediction interval by an entropy weight method by taking the coverage probability of the first wind power prediction interval, the coverage probability of the second wind power prediction interval and the bandwidth of the prediction interval at each moment as evaluation indexes1And ω2；
Step five: and carrying out weighted combination on the first wind power prediction interval and the second wind power prediction interval according to the combination weight determined in the fourth step to obtain a third wind power prediction interval at the final t +1 moment, and evaluating the third wind power prediction interval by using the coverage probability of the prediction interval and the average bandwidth of the prediction interval.
2. The combined interval prediction method based on normal exponential smoothing and kernel density estimation according to claim 1, characterized in that: the third step comprises the following steps:
respectively carrying out different bandwidths h on the wind power prediction errors at n moments before the t +1 momentkThe specific expression is as shown in formula (6):
Figure FDA0002561820830000024
② using weight coefficient betakWill pass through different bandwidths hkEstimated probability density function f of the wind power prediction errork,t+1() And combining, wherein the specific expression is as formula (7):
Figure FDA0002561820830000031
③ to fMSKDt+1() Integrating to obtain cumulative distribution function F (xi) of wind power prediction error, and negating F (xi) to obtain its inverse function
Figure FDA0002561820830000032
The second wind power prediction interval satisfying the confidence probability of 1-alpha is a formula (8):
Figure FDA0002561820830000033
3. the combined interval prediction method based on normal exponential smoothing and kernel density estimation according to claim 2, characterized in that: the fourth step comprises the following steps:
taking the first wind power prediction interval and the second wind power prediction interval as evaluation objects, recording the evaluation indexes of an entropy weight method as the coverage rate of the first wind power prediction interval and the second wind power prediction interval and the width of the prediction interval at each moment as m, and establishing an evaluation matrix
Figure FDA0002561820830000034
Coverage probability of the first wind power prediction interval and the second wind power prediction interval
Figure FDA0002561820830000035
NtFor predicting the number of samples, k is a Boolean quantity, if a target value t is predictediIf the k is equal to 1, otherwise, k is equal to 0;
② standardizing the evaluation matrix A to obtain
Figure FDA0002561820830000036
The entropy of the first wind power prediction interval and the second wind power prediction interval is as follows:
Figure FDA0002561820830000037
wherein the content of the first and second substances,
Figure FDA0002561820830000038
let when p beijWhen equal to 0, pijlnpij＝0；
On the basis of entropy, the entropy weights of the first wind power prediction interval and the second wind power prediction interval are as follows:
Figure FDA0002561820830000041
4. the combined interval prediction method based on normal exponential smoothing and kernel density estimation according to claim 3, characterized in that: the fifth step comprises the following steps:
the first wind power prediction interval and the second wind power prediction interval are weighted according to the weight omega1And ω2And obtaining a third prediction interval by weighted combination:
Figure FDA0002561820830000042
wherein
Figure FDA0002561820830000043
The third prediction interval is the finally determined power prediction interval.
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