CN106251027B - Electric load probability density Forecasting Methodology based on fuzzy support vector quantile estimate - Google Patents

Electric load probability density Forecasting Methodology based on fuzzy support vector quantile estimate Download PDF

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CN106251027B
CN106251027B CN201610682457.4A CN201610682457A CN106251027B CN 106251027 B CN106251027 B CN 106251027B CN 201610682457 A CN201610682457 A CN 201610682457A CN 106251027 B CN106251027 B CN 106251027B
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何耀耀
刘瑞
李海燕
王刚
郑丫丫
秦杨
严煜东
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Hefei University of Technology
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Abstract

The present invention relates to a kind of electric load probability density Forecasting Methodology based on fuzzy support vector quantile estimate, first, Collection and Forecast Day pervious Daily treatment cost data and average temperature data, and using historical data structure training set and test set.Then, the Lagrange multiplier and supporting vector subscript of fuzzy support vector quantile estimate model are obtained using training set, and fuzzy support vector quantile estimate prediction model is established according to obtained model parameter value, and test set substitution model is obtained into predicted value.Finally, using the predicted value under obtained different quantiles, and realize that the probability density of Daily treatment cost is predicted with Density Estimator.The present invention can be effectively reduced prediction error, improve load forecast precision, achieve good prediction effect, and adjust the more reliable foundations of offer such as electricity consumption plan, optimization generating set output for electric power system dispatching department.

Description

Electric load probability density Forecasting Methodology based on fuzzy support vector quantile estimate
Technical field
The invention belongs to the load forecast field that statistical method is combined with intelligence computation, relate generally to one kind and be based on The electric load probability density Forecasting Methodology of fuzzy support vector quantile estimate.
Background technology
Load Prediction In Power Systems are according to the historical data of electric load, economy, society, meteorology etc., explore power load Influence of the lotus historical data changing rule to future load, seeks the inner link between electric load and various correlative factors, So as to carry out the prediction of science to following electric load.Accurate Load Prediction In Power Systems are for electric power system dispatching, use Electricity, planning, formulate Transaction algorithm, arrange method of operation etc. to have great importance.This also requires electric system researcher to carry Go out more efficient way to improve precision of prediction.
In recent years, with the fast development of intelligent grid and the increase of uncertain factor, and the change of electric load It is subject to the more multifactor restriction such as system operating characteristics, social factor and natural conditions, therefore load prediction needs substantial amounts of number According to, and these data are it is difficult to ensure that accurately and reliably；Even if obtained data are accurate, but there is also uncertainty.For example, Temperature factor possible factor causes the change of load.Therefore, power system requirements more intelligentized methods improves power load The precision of lotus prediction.In addition, in order to improve the security of operation of power networks and economy, to improve power supply quality, electric system fortune Requirement of the row scheduling to load prediction precision is also higher and higher.
In recent years, traditional Load Prediction In Power Systems field simply considers historical load and influences load prediction Factor, and fail to handle uncertain influence factor.The shortcoming being primarily present has：
(1), it is many to influence the factor of load forecast, including date, meteorologic factor, temperature factor etc..These factors It is uncertain or fuzzy for how influencing load precision.And traditional Methods of electric load forecasting is not uncertain to these Factor is pre-processed.The historical data used when predicting is definite value, but these historical datas are formed with certain Accidentalia, ignore the uncertainty of historical data；
(2), traditional Methods of electric load forecasting only gives point prediction result or interval prediction as a result, can not be accurate The fluctuation of electric load is portrayed on ground, does not also provide the probability density distribution of obtained prediction result.
The content of the invention
The purpose of the present invention is to overcome above-mentioned the deficiencies in the prior art, propose that one kind is based on fuzzy support vector quantile The electric load probability density Forecasting Methodology of recurrence, to carry out Fuzzy processing to mean temperature factor, and greatly reduces The uncertainty of influence factor, so as to be effectively reduced prediction error, improves load forecast precision, and be electric system tune The more reliable foundations of offer such as the adjustment electricity consumption plan of degree department, optimization generating set output.
A kind of the characteristics of electric load probability density Forecasting Methodology based on fuzzy support vector quantile estimate of the present invention It is to carry out as follows：
Step 1, gather and determine prediction day pervious Daily treatment cost data L ' and average temperature data W '=(w1′, w2′,…,wj′,…,w′N)；w′jFor the mean temperature in jth day；1≤j≤N, N are total number of days；
Step 2, be normalized the Daily treatment cost data L ', the Daily treatment cost number after being normalized According to L=(l1,l2,…,lj,…,lN)；ljFor Daily treatment cost after the normalization in jth day；
Step 3, to the average temperature data W ', Fuzzy processing is carried out using fuzzy theory, putting down after obscure Equal temperature data W=(w1,w2,…,wj,…,wN), wjFor jth day it is fuzzy after mean temperature；
Step 4, the Daily treatment cost value of first d days for choosing i-th dayIt is and fuzzy Mean temperature afterwardsAs the input vector of i-th day training sample, i.e.,Choose the Daily treatment cost of i-th dayAs the target output value of i-th day training sample, i.e.,So as to obtain training sample setI=1,2 ..., Ntrain, NtrainFor training sample This total number；
Step 5, the Daily treatment cost value of first d days for choosing kth dayAnd after obscuring Mean temperatureAs the input vector of kth day test sample, i.e.,Choose the Daily treatment cost of kth dayAs the target output value of kth day test sample, i.e.,So as to obtain test sample collectionK=1,2 ..., Ntest, NtestIt is total for test sample Number；
Step 6, the d dimension row vectors by i-th row inputIt is non-linear respectively as i-th of training input variable Component xiWith i-th of linear components ui, by the one-dimensional real output value of the i-th row in the training setIt is actual defeated as i-th Go out value yi, establishing the fuzzy support vector quantile estimate model as shown in formula (1) is：
In formula (1), T is transposition；wiRepresent the mean temperature factor after blurring in i-th day；τrRepresent r-th of quantile, and τr∈ (0,1), r=1,2 ..., Nτ；NτRepresent the number of quantile；Represent r-th of quantile τrUnder parameter vector, C is Punishment parameter,For r-th of quantile τrUnder coefficient vector, φ () represent nonlinear mapping function,Represent to examine Function；And have：Wherein, Represent r-th of quantile τr Under threshold value, and have：Wherein, αiWithRepresent i-th of optimal L agrange multiplier； K is the nuclear matrix in the input space, and is had：
K(xi,xv)=φ (xi)Tφ(xv)；v∈I；I is the subscript collection of obtained supporting vector
Step 7, according to the fuzzy support vector quantile estimate model, introduce slack variable structure Lagrange functions And solution formula (1) is carried out, obtain r-th of quantile τ as shown in formula (2)rUnder parameter vectorThreshold valueWith coefficient to Amount
In formula (2), α, α*For optimal L agrange multipliers vector, y={ yi|i∈I}；Design matrix is
Step 8, by r-th of quantile τrUnder parameter vectorThreshold valueAnd coefficient vectorSubstitute into fuzzy branch Hold vectorial quantile estimate prediction model；And the d for inputting row k in the test set ties up row vectorInputted as test K-th of non-linear component x of variablekWith k-th of linear components uk, so as to obtain r-th of quantile in test set using formula (3) τrUnder row k output valve
In formula (3), KkRepresent k-th of row vector of nuclear matrix K；
Step 9. realizes that the probability density of Daily treatment cost is predicted with Density Estimator：
Step 9.1, r-th of quantile τ for making kth dayrUnder prediction result be：So as to obtain Obtain the prediction result under all quantiles of kth dayAnd then obtain the survey of Daily treatment cost Try output valve
Step 9.2, obtain w-th of quantile τ of kth day using formula (4)wCorresponding probability density function values
In formula (4), zk,wRepresent w-th of quantile τ of kth daywUnder prediction result；Quantile number w=1,2 ..., Nτ；H is window width, K1(η) is Epanechnikov kernel functions, and is had：Wherein, | η≤1 |；
Step 9.2, utilize the rules of thumb calculating Epanechnikov kernel functions K shown in formula (5)1The optimal bandwidth of (η) h*：
h*=1.06sXNτ -1/5 (5)
In formula (5), sXFor the standard deviation of the test output valve of Daily treatment cost；
Step 9.3, according to Epanechnikov kernel functions K1(η) and the optimal bandwidth h*Ask for the general of Daily treatment cost Rate density prediction result.
The characteristics of electric load probability density Forecasting Methodology of the present invention, lies also in, the blurring in the step 3 Processing is to carry out according to the following procedure：
The membership function of medium temperature shown in the membership function of low temperature according to formula (6), formula (7) and formula (8) institute The high temperature membership function shown, by the mean temperature w ' in the jth dayjLow temperature data, medium temperature data or high-temperature data are divided into, Obtain the mean temperature w ' in jth dayjAffiliated fuzzy set；So that the average temperature data W==(w after being obscured1,w2,…, wj,…,wN)；
The membership function of the low temperature is：
The membership function of the medium temperature is：
The membership function of the high temperature is：
Meet e ＜ g ＜ f ＜ m ＜ n ＜ p in formula (6), formula (7) and formula (8).
Compared with the prior art, the present invention has the beneficial effect that：
1st, traditional support vector regression method and Quantile Regression are combined and introduce fuzzy membership by the present invention Degree function obtains fuzzy support vector Quantile Regression, and nonlinear problem can be solved using support vector regression method, And Quantile Regression estimates the condition quantile of response variable using the information that regression variable provides, obtain not With influence of the explanatory variable under quantile to response variable, and then explanatory variable can be described exactly model is changed to response variable The influence with condition distribution shape is enclosed, so two methods, which are combined, can obtain the complete probability distribution of future load, just In the science decision of policymaker.
2nd, present invention primarily contemplates the influence that mean temperature predicts Daily treatment cost, since mean temperature factor is fuzzy , so introduce fuzzy theory and Fuzzy processing is carried out to improve precision of prediction to mean temperature using membership function, and Give the probability density prediction result under different quantiles, it was demonstrated that the validity and accuracy of method.
3rd, the present invention not only significantly reduces prediction error, improves load forecast precision, and can be accurate Portray the fluctuation of electric load and give probability density prediction graph in ground.This is just used for the adjustment of electric power system dispatching department The more reliable foundations of offer such as electricity plan, optimization generating set output.
Brief description of the drawings
Fig. 1 is the method for the present invention overall flow figure；
Fig. 2 is the method for the present invention detail flowchart；
Fig. 3 is the method for the present invention probability density figure.
Embodiment
In implementation process, a kind of electric load probability density prediction side based on fuzzy support vector quantile estimate Method, the main influence for considering mean temperature to load forecast.Flow chart as shown in Figure 1, simultaneously carry out as follows：
Step 1, the factor of influence load forecast are more, draw mean temperature factor to power load by researching and analysing Lotus prediction result has a great influence；
Step 1.1, the present invention select the data of the global load prediction contest of EUNITE network tissues to be tested, The load data of time interval (per half an hour correspond to a load point) of the data including 1997-1998 daily 48 when small, And the average temperature data that 1997-1998 is daily.The data belong to partial data.And predict 31 days January in 1999 Per Daily treatment cost data；
Step 1.2, collection and definite prediction day pervious Daily treatment cost data L ' and average temperature data W '= (w′1,w′2,…,w′j,…,w′N)；w′jFor the mean temperature in jth day；1≤j≤N, N are total number of days；
Step 2, be to avoid occurring calculating saturated phenomenon in calculating process, and place is normalized to Daily treatment cost data Reason.
Daily treatment cost data L ' is normalized, the Daily treatment cost data L=(l after being normalized1, l2,…,lj,…,lN)；ljFor Daily treatment cost after the normalization in jth day, wherein, mean temperature factor is according to meteorological department Weather forecast determines that Daily treatment cost data are determined according to the data that Utilities Electric Co. provides；
Step 3, since mean temperature factor is uncertain or fuzzy in real life, so, using mould Paste theory establishes membership function and carries out Fuzzy processing to mean temperature factor.
To average temperature data W ', Fuzzy processing, the average temperature data W after being obscured are carried out using fuzzy theory =(w1,w2,…,wj,…,wN), wjFor jth day it is fuzzy after mean temperature；Wherein, Fuzzy processing be according to the following procedure into OK：
The membership function of medium temperature shown in the membership function of low temperature according to formula (6), formula (7) and formula (8) institute The high temperature membership function shown, by the mean temperature w ' in jth dayjLow temperature data, medium temperature data or high-temperature data are divided into, is obtained The mean temperature w ' in jth dayjAffiliated fuzzy set；So that the average temperature data W==(w after being obscured1,w2,…, wj,…,wN)；
The membership function of low temperature is：
The membership function of medium temperature is：
The membership function of high temperature is：
Meet the value of e ＜ g ＜ f ＜ m ＜ n ＜ p and these variables in formula (6), formula (7) and formula (8) as the case may be Determine.Wherein, e ∈ [- 10, -2], g ∈ [- 3,3], f ∈ [5,12], m ∈ [10,16] n ∈ [17,25], p ∈ [30,40].Root According to the data chosen herein, variable-value here is respectively：E=-5, g=0, f=10, m=15, n=20, p=35.
Step 4, structure training set：Choose the Daily treatment cost value of first d days of i-th dayAnd the mean temperature after obscuringMake For the input vector of i-th day training sample, i.e.,Choose the Daily treatment cost of i-th dayAs i-th The target output value of its training sample, i.e.,So as to obtain training sample setI= 1,2,…,Ntrain, NtrainFor training sample total number；
Step 5, structure test set：Choose the Daily treatment cost value of first d days of kth dayAnd the mean temperature after obscuringAs The input vector of k days test samples, i.e.,Choose the Daily treatment cost of kth dayAs kth day test specimens This target output value, i.e.,So as to obtain test sample collectionK=1,2 ..., Ntest, NtestFor test sample total number；
Step 6, the d dimension row vectors by the input of the i-th rowRespectively as i-th of non-linear component of training input variable xiWith i-th of linear components ui, by the one-dimensional real output value of the i-th row in training setAs i-th of real output value yi, Establishing the fuzzy support vector quantile estimate model as shown in formula (1) is：
In formula (1), T is transposition；wiRepresent the mean temperature factor after blurring in i-th day；τrRepresent r-th of quantile, and τr∈ (0,1), r=1,2 ..., Nτ；NτRepresent the number of quantile；Represent r-th of quantile τrUnder parameter vector, C is Punishment parameter,For r-th of quantile τrUnder coefficient vector, φ（·）Represent nonlinear mapping function,Represent to examine Function；And have：Wherein, Represent r-th of quantile τr Under threshold value, and have：Wherein, αiWithRepresent that i-th of optimal L agrange multiplies Son；K is the nuclear matrix in the input space, and is had：
K(xi,xv)=φ (xi)Tφ(xv)；v∈I；I is the subscript collection of obtained supporting vector
Step 7, solve parameter value：According to fuzzy support vector quantile estimate model, slack variable structure is introduced Lagrange functions simultaneously carry out solution formula (1), obtain r-th of quantile τ as shown in formula (2)rUnder parameter vectorThreshold valueAnd coefficient vector
In formula (2), α, α*For optimal L agrange multipliers vector, y={ yi|i∈I}；Design matrix is
Step 8, substitute into obtained parameter value in model and solve test target output valve：
By r-th of quantile τrUnder parameter vectorThreshold valueAnd coefficient vectorSubstitute into fuzzy support vector and divide position Number regressive prediction model；And the d for inputting row k in test set ties up row vectorK-th as test input variable is non-thread Property component xkWith k-th of linear components uk, so as to obtain r-th of quantile τ in test set using formula (3)rUnder row k output Value
In formula (3), KkRepresent k-th of row vector of nuclear matrix K；
Step 9. carries out probability density prediction with Density Estimator to Daily treatment cost：Flow chart is as shown in Figure 2；
Test target output valve under step 9.1, the different quantiles of solution：Make r-th of quantile τ of kth dayrUnder it is pre- Surveying result is：So as to obtain the prediction result under all quantiles of kth dayAnd then obtain the test output valve of Daily treatment cost
Step 9.2, obtain probability density function values：W-th of quantile τ of kth day is obtained using formula (4)wCorresponding is general Rate density function values
In formula (4), zk,wRepresent w-th of quantile τ of kth daywUnder prediction result；Quantile number w=1,2 ..., Nτ；H is window width, K1(η) is Epanechnikov kernel functions, and is had：Wherein, | η≤1 |；
Step 9.2, solve optimal bandwidth：In the research of Density Estimator method, window width selection is probability density prediction One in function part Smoothing Problem it is extremely important the problem of.Calculated using the rules of thumb shown in formula (5) Epanechnikov kernel functions K1The optimal bandwidth h of (η)*：
h*=1.06sXNτ -1/5 (5)
In formula (5), sXFor the standard deviation of the test output valve of Daily treatment cost, then with 1.06 times of sample standard deviation this Standard, obtains optimal bandwidth.Rules of thumb namely by fixed standard, according to sample standard deviation, directly obtains optimal bandwidth.
Step 9.3, according to Epanechnikov kernel functions K1(η) and optimal bandwidth h*The probability for asking for Daily treatment cost is close Spend prediction result.
Step 9.4, probability density curve figure are as shown in Figure 3：Fig. 3 give the 1st day, the 6th day, the 11st day, the 16th day, 21 days, the probability density distribution figure of the predicted value of the 26th day.It can be seen from the figure that predicted value is all appeared in larger probability At the mode of probability density prediction curve.

Claims (2)

  1. A kind of 1. electric load probability density Forecasting Methodology based on fuzzy support vector quantile estimate, it is characterized in that by as follows Step carries out：
    Step 1, gather and determine prediction day pervious Daily treatment cost data L ' and average temperature data W '=(w '1,w ′2,…,w′j,…,w′N)；w′jFor the mean temperature in jth day；1≤j≤N, N are total number of days；
    Step 2, be normalized the Daily treatment cost data L ', the Daily treatment cost data L after being normalized =(l1,l2,…,lj,…,lN)；ljFor Daily treatment cost after the normalization in jth day；
    Step 3, to the average temperature data W ', Fuzzy processing, the average temperature after being obscured are carried out using fuzzy theory Degrees of data W=(w1,w2,…,wj,…,wN), wjFor jth day it is fuzzy after mean temperature；
    Step 4, the Daily treatment cost value of first d days for choosing i-th dayAnd after obscuring Mean temperatureAs the input vector of i-th day training sample, i.e.,Choose the Daily treatment cost of i-th dayAs the target output value of i-th day training sample, i.e.,So as to obtain training sample setI=1,2 ..., Ntrain, NtrainFor training sample This total number；
    Step 5, the Daily treatment cost value of first d days for choosing kth dayIt is and flat after obscuring Equal temperatureAs the input vector of kth day test sample, i.e.,Choose the Daily treatment cost of kth dayAs the target output value of kth day test sample, i.e.,So as to obtain test sample collectionK=1,2 ..., Ntest, NtestIt is total for test sample Number；
    Step 6, the d dimension row vectors by i-th row inputRespectively as i-th of non-linear component of training input variable xiWith i-th of linear components ui, by the one-dimensional real output value of the i-th row in the training setAs i-th of real output value yi, establishing the fuzzy support vector quantile estimate model as shown in formula (1) is：
    <mrow> <munder> <mi>min</mi> <mrow> <msub> <mi>&amp;omega;</mi> <msub> <mi>&amp;tau;</mi> <mi>r</mi> </msub> </msub> <mo>,</mo> <msub> <mi>b</mi> <msub> <mi>&amp;tau;</mi> <mi>r</mi> </msub> </msub> </mrow> </munder> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>|</mo> <mo>|</mo> <msub> <mi>&amp;omega;</mi> <msub> <mi>&amp;tau;</mi> <mi>r</mi> </msub> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>+</mo> <mi>C</mi> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msup> <mi>N</mi> <mrow> <mi>t</mi> <mi>r</mi> <mi>a</mi> <mi>i</mi> <mi>n</mi> </mrow> </msup> </munderover> <msub> <mi>w</mi> <mi>i</mi> </msub> <msub> <mi>&amp;rho;</mi> <msub> <mi>&amp;tau;</mi> <mi>r</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>b</mi> <msub> <mi>&amp;tau;</mi> <mi>r</mi> </msub> </msub> <mo>-</mo> <msubsup> <mi>&amp;beta;</mi> <msub> <mi>&amp;tau;</mi> <mi>r</mi> </msub> <mi>T</mi> </msubsup> <msub> <mi>u</mi> <mi>i</mi> </msub> <mo>-</mo> <msubsup> <mi>&amp;omega;</mi> <msub> <mi>&amp;tau;</mi> <mi>r</mi> </msub> <mi>T</mi> </msubsup> <mi>&amp;phi;</mi> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    In formula (1), T is transposition；wiRepresent the mean temperature factor after blurring in i-th day；τrRepresent r-th of quantile, and τr∈ (0,1), r=1,2 ..., Nτ；NτRepresent the number of quantile；Represent r-th of quantile τrUnder parameter vector, C for punishment Parameter,For r-th of quantile τrUnder coefficient vector, φ () represent nonlinear mapping function,Represent to examine letter Number；And have：Wherein, Represent r-th of quantile τrUnder Threshold value, and have：Wherein, αiWithRepresent i-th of optimal L agrange multiplier；K For the nuclear matrix in the input space, and have：
    K(xi,xv)=φ (xi)Tφ(xv)；v∈I；I is the subscript collection of obtained supporting vector
    Step 7, according to the fuzzy support vector quantile estimate model, introduce slack variable structure Lagrange functions and go forward side by side Row solution formula (1), obtains r-th of quantile τ as shown in formula (2)rUnder parameter vectorThreshold valueAnd coefficient vector
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;omega;</mi> <msub> <mi>&amp;tau;</mi> <mi>r</mi> </msub> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msup> <mi>N</mi> <mrow> <mi>t</mi> <mi>r</mi> <mi>a</mi> <mi>i</mi> <mi>n</mi> </mrow> </msup> </munderover> <mrow> <mo>(</mo> <msub> <mi>&amp;alpha;</mi> <mi>i</mi> </msub> <mo>-</mo> <msubsup> <mi>&amp;alpha;</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mo>)</mo> </mrow> <mi>&amp;phi;</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>b</mi> <msub> <mi>&amp;tau;</mi> <mi>r</mi> </msub> </msub> <mo>,</mo> <msub> <mi>&amp;beta;</mi> <msub> <mi>&amp;tau;</mi> <mi>r</mi> </msub> </msub> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msup> <mi>U</mi> <mi>T</mi> </msup> <mi>U</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msup> <mi>U</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>y</mi> <mo>-</mo> <mi>K</mi> <mo>(</mo> <mrow> <mi>&amp;alpha;</mi> <mo>-</mo> <msup> <mi>&amp;alpha;</mi> <mo>*</mo> </msup> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    In formula (2), α, α*For optimal L agrange multipliers vector, y={ yi|i∈I}；Design matrix is
    Step 8, by r-th of quantile τrUnder parameter vectorThreshold valueAnd coefficient vectorSubstitute into it is fuzzy support to Measure quantile estimate prediction model；And the d for inputting row k in the test set ties up row vectorAs test input variable K-th of non-linear component xkWith k-th of linear components uk, so as to obtain r-th of quantile τ in test set using formula (3)rUnder Row k output valve
    <mrow> <msub> <mi>Q</mi> <msub> <mi>y</mi> <mi>k</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;tau;</mi> <mi>r</mi> </msub> <mo>|</mo> <msub> <mi>u</mi> <mi>k</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>b</mi> <msub> <mi>&amp;tau;</mi> <mi>r</mi> </msub> </msub> <mo>+</mo> <msubsup> <mi>&amp;beta;</mi> <msub> <mi>&amp;tau;</mi> <mi>r</mi> </msub> <mi>T</mi> </msubsup> <msub> <mi>u</mi> <mi>k</mi> </msub> <mo>+</mo> <msub> <mi>K</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;alpha;</mi> <mo>-</mo> <msup> <mi>&amp;alpha;</mi> <mo>*</mo> </msup> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    In formula (3), KkRepresent k-th of row vector of nuclear matrix K；
    Step 9. realizes that the probability density of Daily treatment cost is predicted with Density Estimator：
    Step 9.1, r-th of quantile τ for making kth dayrUnder prediction result be：So as to obtain kth Prediction result under its all quantileAnd then the test for obtaining Daily treatment cost is defeated Go out value
    Step 9.2, obtain w-th of quantile τ of kth day using formula (4)wCorresponding probability density function values
    <mrow> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mi>h</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>w</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>N</mi> <mi>&amp;tau;</mi> </msub> <mi>h</mi> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>r</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>&amp;tau;</mi> </msub> </munderover> <msub> <mi>K</mi> <mn>1</mn> </msub> <mfrac> <mrow> <msub> <mi>z</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>w</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> </mrow> <mi>h</mi> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    In formula (4), zk,wRepresent w-th of quantile τ of kth daywUnder prediction result；Quantile number w=1,2 ..., Nτ；H is Window width, K1(η) is Epanechnikov kernel functions, and is had：Wherein, | η≤1 |；
    Step 9.3, utilize the rules of thumb calculating Epanechnikov kernel functions K shown in formula (5)1The optimal bandwidth h of (η)*：
    h*=1.06sXNτ -1/5 (5)
    In formula (5), sXFor the standard deviation of the test output valve of Daily treatment cost；
    Step 9.4, according to Epanechnikov kernel functions K1(η) and the optimal bandwidth h*The probability for asking for Daily treatment cost is close Spend prediction result.
  2. 2. electric load probability density Forecasting Methodology according to claim 1, it is characterized in that, it is fuzzy in the step 3 Change processing is to carry out according to the following procedure：
    Shown in the membership function and formula (8) of medium temperature shown in the membership function of low temperature according to formula (6), formula (7) High temperature membership function, by the mean temperature w ' in the jth dayjLow temperature data, medium temperature data or high-temperature data are divided into, is obtained The mean temperature w ' in jth dayjAffiliated fuzzy set；So that the average temperature data W==(w after being obscured1,w2,…, wj,…,wN)；
    The membership function of the low temperature is：
    <mrow> <msub> <mi>w</mi> <mi>j</mi> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mn>0</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>w</mi> <mi>j</mi> <mo>&amp;prime;</mo> </msubsup> <mo>&gt;</mo> <mi>f</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mi>f</mi> <mo>-</mo> <msubsup> <mi>w</mi> <mi>j</mi> <mo>&amp;prime;</mo> </msubsup> </mrow> <mrow> <mi>f</mi> <mo>-</mo> <mi>e</mi> </mrow> </mfrac> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>e</mi> <mo>&amp;le;</mo> <msubsup> <mi>w</mi> <mi>j</mi> <mo>&amp;prime;</mo> </msubsup> <mo>&lt;</mo> <mi>f</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>1</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>w</mi> <mi>j</mi> <mo>&amp;prime;</mo> </msubsup> <mo>&lt;</mo> <mi>e</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
    The membership function of the medium temperature is：
    The membership function of the high temperature is：
    <mrow> <msub> <mi>w</mi> <mi>j</mi> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mn>0</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>w</mi> <mi>j</mi> <mo>&amp;prime;</mo> </msubsup> <mo>&lt;</mo> <mi>n</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <msubsup> <mi>w</mi> <mi>j</mi> <mo>&amp;prime;</mo> </msubsup> <mo>-</mo> <mi>n</mi> </mrow> <mrow> <mi>p</mi> <mo>-</mo> <mi>n</mi> </mrow> </mfrac> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>n</mi> <mo>&amp;le;</mo> <msubsup> <mi>w</mi> <mi>j</mi> <mo>&amp;prime;</mo> </msubsup> <mo>&amp;le;</mo> <mi>p</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>1</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>w</mi> <mi>j</mi> <mo>&amp;prime;</mo> </msubsup> <mo>&gt;</mo> <mi>p</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
    Meet e ＜ g ＜ f ＜ m ＜ n ＜ p, and e ∈ [- 10, -2], g ∈ [- 3,3] in formula (6), formula (7) and formula (8), f ∈ [5, 12], m ∈ [10,16], n ∈ [17,25], p ∈ [30,40].
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102270279A (en) * 2011-07-27 2011-12-07 华北电力大学 Short-term power load predicting method
CN104217258A (en) * 2014-09-15 2014-12-17 国家电网公司 Method for power load condition density prediction
CN104217105A (en) * 2014-08-21 2014-12-17 国家电网公司 Energy demand condition density prediction method
CN104239968A (en) * 2014-09-02 2014-12-24 浙江大学 Short-term load predicting method based on quick fuzzy rough set

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102270279A (en) * 2011-07-27 2011-12-07 华北电力大学 Short-term power load predicting method
CN104217105A (en) * 2014-08-21 2014-12-17 国家电网公司 Energy demand condition density prediction method
CN104239968A (en) * 2014-09-02 2014-12-24 浙江大学 Short-term load predicting method based on quick fuzzy rough set
CN104217258A (en) * 2014-09-15 2014-12-17 国家电网公司 Method for power load condition density prediction

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
一种模糊模型的混合建模方法及在短期负荷预测中的应用;谢宏等;《中国电机工程学报》;20050430;第25卷(第8期);第17-22页 *
基于支持向量分位数回归多期VaR测度;许启发等;《***工程学报》;20140430;第29卷(第2期);第202-214页 *
核密度估计逐点最优窗宽选择的改进;黎运发;《统计与决策》;20111231(第14期);第28-32页 *

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