CN110555566B - B-spline quantile regression-based photoelectric probability density prediction method - Google Patents

B-spline quantile regression-based photoelectric probability density prediction method Download PDF

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CN110555566B
CN110555566B CN201910852925.1A CN201910852925A CN110555566B CN 110555566 B CN110555566 B CN 110555566B CN 201910852925 A CN201910852925 A CN 201910852925A CN 110555566 B CN110555566 B CN 110555566B
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何耀耀
范慧玲
陈悦
张婉莹
王云
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Abstract

The invention discloses a B-spline quantile regression-based photoelectric probability density prediction method, which comprises the following steps of: 1, acquiring photoelectric data, carrying out normalization processing on the photoelectric data, and dividing historical photoelectric data into a training set and a test set; 2, constructing a B-spline quantile model, and calculating parameters of the B-spline quantile regression model by using training set data; and 3, substituting the test set data into the B-spline quantile model to obtain predicted values under different quantiles, and realizing photoelectric probability density prediction by using nuclear density estimation. The method can improve the prediction precision of the photovoltaic power generation and comprehensively measure the uncertainty of the prediction result, thereby providing a reliable basis for the safe and stable integration of the photovoltaic power generation into the power grid.

Description

B-spline quantile regression-based photoelectric probability density prediction method
Technical Field
The invention relates to the technical field of photoelectric power, in particular to a photoelectric probability density prediction method based on B-spline quantile regression.
Background
Due to the increasing environmental pollution and energy shortage, the application of renewable clean energy is widely concerned. Compared with traditional petroleum and coal resources which can cause air pollution and can not be regenerated, the global energy system is constantly changing, renewable energy becomes the preferred technology in the power market, and photovoltaic power generation is one of important renewable energy power generation methods. The photovoltaic power generation utilizes solar energy resources to generate power, and has the advantages of rich solar energy resources, less influence of solar energy on regions, cleanness and safety. However, photovoltaic power generation also has the defects of no power generation at night, less power generation amount in rainy days and the like, and because photovoltaic power generation has randomness and instability, a large number of photovoltaic power generation systems are merged into a power grid to operate, so that the quality of photovoltaic power generation and the safe and stable operation of a power system are influenced. Reliable and accurate photoelectric prediction can not only effectively assist decision making, but also play an important role in maintaining the stability of the power grid. Therefore, how to obtain a more reliable and accurate photoelectric prediction result still remains a key and difficult problem in the field of photovoltaic power generation prediction.
The photovoltaic power generation prediction method mainly comprises a direct method and an indirect method. The direct method is a statistical method for directly predicting the output power of the photovoltaic power generation system, wherein the researches of methods such as a time series method, an artificial neural network method, a support vector machine and the like are common. The indirect prediction method firstly predicts the solar radiation and then obtains the output power according to the model of the photovoltaic power generation system. At present, a plurality of photovoltaic power generation researchers research photovoltaic power generation prediction methods, and the prediction accuracy of photoelectric power is continuously improved, but the research for improving the photovoltaic power generation prediction accuracy still has a larger promotion space.
In addition, most of the traditional photovoltaic power generation prediction methods can only give a point prediction result or an interval prediction result of photovoltaic power generation, and the uncertainty of the photovoltaic power generation cannot be measured well. And the prediction of the photovoltaic power generation is usually influenced by factors such as weather and the like, and the photovoltaic power generation is not carried out at night, so that the reliability of the obtained point prediction result and the interval prediction result is low, and the photovoltaic power generation prediction method can be researched according to the old space.
Disclosure of Invention
The invention aims to overcome the defects of the existing prediction method, and provides a B-spline quantile regression-based photoelectric probability density prediction method so as to improve the prediction precision of photovoltaic power generation and comprehensively measure the uncertainty of a prediction result, thereby providing a reliable basis for the safe and stable incorporation of the photovoltaic power generation into a power grid.
In order to achieve the purpose, the invention adopts the technical scheme that:
the invention relates to a B-spline quantile regression-based photoelectric probability density prediction method which is characterized by comprising the following steps of:
step 1, collecting a photoelectric historical data set R ═ (R)1,r2,…,ri,…,rN) Wherein r isiI is more than or equal to 1 and less than or equal to N, wherein N is the total data number of the photoelectric historical data set R;
step 2, predicting the photoelectric power data of the K +1 th time point by using a rolling arrangement method according to the photoelectric power data of the previous K time points in the photoelectric historical data set R to obtain an n X (K +1) -dimensional matrix (X, Y), wherein X is (X ═ 1)1,x2,...,xk,...,xK) Is an input variable, xkIs the kth input variable, and
Figure BDA0002197391740000021
Figure BDA0002197391740000022
is the kth input variable xkThe j sample of (Y ═ Y)1,y2,...,yj,...,yn)TIs an output variable, yjIs the jth sample of the output variable Y, K is more than or equal to 1 and less than or equal to K, and j is more than or equal to 1 and less than or equal to n;
step 3, dividing the n X (K +1) dimensional matrix (X, Y) into a training set (X)train,Ytrain) And test set (X)test,Ytest)；
Step 4, K input variables X ═ X1,x2,...,xk,...,xK) Normalization processing is carried out to obtain normalized input variable Z ═ Z (Z)1,z2,...,zk,...,zK) Wherein z iskIs the kth normalized input variable; and is
Figure BDA0002197391740000023
Figure BDA0002197391740000024
Is the kth normalized input variable zkThe jth sample of (a);
step 5, utilizing a B spline method to normalize the kth normalized input variable zkProcessing to obtain the kth normalized input variable zkCorresponding F p-th-order B-spline basis matrixes
Figure BDA0002197391740000025
Wherein the content of the first and second substances,
Figure BDA0002197391740000026
is the k normalized input variable zkThe corresponding f-th-order B-spline basis matrix is obtained by the formula (1); f and p are the degree of freedom and the number of times of the B spline basis matrix respectively;
Figure BDA0002197391740000027
in the formula (1), the reaction mixture is,
Figure BDA0002197391740000028
is the k normalized input variable zkThe corresponding f 0 th-order B-spline basis matrix,
Figure BDA0002197391740000029
is the k normalized input variable zkThe corresponding f < th > p-1 th-order B-spline basis matrix,
Figure BDA00021973917400000210
is the k normalized input variable zkThe corresponding f +1 th p-1 th-order B spline basis matrix; u. offIs the f-th node, and ufE.g. U, U is a non-decreasing number of node vectors of F + p +2, and U0≤u1≤...≤uF+p+1，uf+pIs the f + p node;
defining a half-open interval [ u ]f,uf+1) Is the f-th node interval;
if the f-th node ufRepeated d times in the node vector U, and d>0, then it represents the f-th node ufIs a repetition node with repetition degree d, denoted as uf(d)；
If the f-th node ufIf the node vector U appears only once, the f-th node U is representedfA non-duplicate node;
recording the first p +1 nodes of the node vector U as left vertex U0(p + 1); recording the last p +1 nodes of the node vector U as right vertex UF+1(p +1), and the left vertex u0(p +1) and right vertex uF+1The values of (p +1) are the kth normalized input variable zkMinimum and maximum values of, and [ u ]0(p+1),uF+1(p+1)]＝[0,1]；
Dividing the left vertex U in the node vector U0(p +1) and right vertex uF+1F-p nodes outside the (p +1) are marked as internal nodes; when f node ufWhen the node is an internal node, u is determined according to the interval equal length principlefA value of (d);
step 6, constructing a B-spline quantile regression model shown as the formula (2), and normalizing the input variable Z in the training settrainAs the input of B-spline quantile model, the output variable Y in training settrainAs the output of the B-spline quantile model, the r-th quantile point tau is obtainedrRegression parameter vector of lower B-spline quantile regression model
Figure BDA0002197391740000031
Figure BDA0002197391740000032
In the formula (2)，QY(τr| Z) is the r-th quantile τ of the output variable Y under the normalized input variable ZrFraction of lower, τrDenotes the r-th quantile andrbelongs to the element (0,1), r is more than or equal to 1 and less than or equal to M, and M is the total number of quantile points;
Figure BDA0002197391740000033
is the r-th quantilerThe kth normalized input variable zkF-th B-spline basis matrix of
Figure BDA0002197391740000034
Corresponding parameter, and
Figure BDA0002197391740000035
θ(τr) Is the r-th quantilerThe following regression parameter vector is obtained by equation (3):
Figure BDA0002197391740000036
in the formula (3), the reaction mixture is,
Figure BDA0002197391740000037
is a check function and has:
Figure BDA0002197391740000038
in formula (4), v represents an intermediate variable and has:
Figure BDA0002197391740000039
in the formula (5), α (τ)r) Is the r-th quantilerA constant of;
step 7, the r-th quantile point taurRegression parameter vector θ (τ) ofr) Substituting into B-spline quantile regression model, and testing the normalized input variableZtestInputting the data into a B-spline quantile regression model to obtain a test set at an r-th quantile point taurPrediction of
Figure BDA0002197391740000041
Further obtaining the predicted value O of the test set under M quantites1,O2,…,Or,…,OMWherein
Figure BDA0002197391740000042
Is the output variable Y of the test settestInput variable Z of test set after normalizationtestAt the r-th quantile ofrLower quantile;
and 8, calculating a probability density prediction result of the photoelectric power of the test set by using a kernel density estimation function:
step 8.1, defining predicted values O under M quantiles1,O2,…,Or,…,OMAny point with the same distribution is O, and the kernel density estimation function is obtained by using the formula (6)
Figure BDA0002197391740000043
And as a prediction result of the photoelectric power of the test set:
Figure BDA0002197391740000044
in formula (6), the smoothing parameter h is the window width and has:
Figure BDA0002197391740000045
in the formula (7), the reaction mixture is,
Figure BDA0002197391740000046
is the predicted value O1,O2,…,Or,…,OMStandard deviation of (d);
in formula (6), K (. cndot.) is an Epanechnikov kernel function and has:
Figure BDA0002197391740000047
in the formula (8), η is a variable, and
Figure BDA0002197391740000048
compared with the prior art, the invention has the beneficial effects that:
1. the photoelectric data are combined with a B-spline regression method and a quantile regression method, a novel B-spline quantile regression photoelectric prediction model is constructed, model parameters can be obtained, and accurate prediction results are obtained. Meanwhile, the B-spline quantile regression method is combined with the kernel density method to obtain a probability density prediction graph of photoelectric data, so that uncertainty of prediction can be better measured, and more useful information can be provided for photoelectric workers.
2. In order to improve the prediction precision, the traditional quantile regression method and the B spline method are combined, and the B spline quantile regression photovoltaic power generation prediction model is constructed. The model adopts a B-spline method to process photovoltaic power generation data, so that data values are reduced, the prediction precision is improved, and a photoelectric worker can make scientific decisions conveniently.
3. According to the method, a quantile regression method is adopted, so that the predicted values of the photoelectric data under different quantiles can be obtained; the photovoltaic power generation predicted values under different quantiles are combined with Epanechnikov kernel density estimation, a probability density prediction graph of photovoltaic power generation data can be obtained, a point prediction result and an interval prediction result can be obtained, a complete probability density graph of photoelectric data at any time in the future can be obtained, uncertainty of photovoltaic power generation can be well quantified, and meanwhile, information support is provided for stable integration of photovoltaic power generation into a power grid.
Drawings
FIG. 1 is an overall flow chart of the method of the present invention.
Detailed Description
In this embodiment, a B-spline quantile regression-based photoelectric probability density prediction method, as shown in fig. 1, is performed according to the following steps:
step 1, collecting a photoelectric historical data set R ═ (R)1,r2,…,ri,…,rN) Wherein r isiThe photoelectric power data of the ith time point in the photoelectric historical data set R is represented by i which is more than or equal to 1 and less than or equal to N, and N is the total data number of the photoelectric historical data set R; this stage is mainly to obtain a normal photovoltaic power generation data set for prediction.
Step 2, according to the photoelectric power data of the first K time points in the photoelectric historical data set R, predicting the photoelectric power data of the (K +1) th time point by using the photoelectric power data of the first K time points through a rolling arrangement method to obtain an n X (K +1) dimensional matrix (X, Y), wherein X is (X is ═ X-1,x2,...,xk,...,xK) Is an input variable, xkIs the kth input variable, and
Figure BDA0002197391740000051
Figure BDA0002197391740000052
is the kth input variable xkThe j sample of (Y ═ Y)1,y2,...,yj,...,yn)TIs an output variable, yjIs the jth sample of the output variable Y, K is more than or equal to 1 and less than or equal to K, and j is more than or equal to 1 and less than or equal to n; this stage is to arrange the data into a matrix form that facilitates prediction.
Step 3, dividing the n X (K +1) dimensional matrix (X, Y) into training sets (X)train,Ytrain) And test set (X)test,Ytest) And is and
Figure BDA0002197391740000053
wherein the training set data is used to train the parameters of the model and the test set is used for prediction and validation.
Step 4, respectively setting K input variables X ═ X1,x2,...,xk,...,xK) Normalization processing is carried out to obtain normalized input variable Z ═ Z (Z)1,z2,...,zk,...,zK) Wherein z iskIs the kth normalized input variable; and is
Figure BDA0002197391740000054
Figure BDA0002197391740000055
Is the kth normalized input variable zkThe jth sample of (a);
step 5, utilizing a B spline method to normalize the kth normalized input variable zkProcessing to obtain the kth normalized input variable zkCorresponding F p-th-order B-spline basis matrixes
Figure BDA0002197391740000056
Wherein the content of the first and second substances,
Figure BDA0002197391740000057
is the k normalized input variable zkThe corresponding f-th-order B-spline basis matrix is obtained by the formula (1); f and p are the degree of freedom and the number of times of the B spline basis matrix respectively;
Figure BDA0002197391740000061
in the formula (1), the reaction mixture is,
Figure BDA0002197391740000062
is the k normalized input variable zkThe corresponding f 0 th-order B-spline basis matrix,
Figure BDA0002197391740000063
is the k normalized input variable zkThe corresponding f < th > p-1 th-order B-spline basis matrix,
Figure BDA0002197391740000064
is the k normalized input variable zkThe corresponding f +1 th p-1 th-order B spline basis matrix; u. offIs the (f) th node and,and u isfE.g. U, U is a non-decreasing number of node vectors of F + p +2, and U0≤u1≤...≤uF+p+1，uf+pIs the f + p node;
defining a half-open interval [ u ]f,uf+1) Is the f-th node interval;
if the f-th node ufRepeated d times in the node vector U, and d>0, then it represents the f-th node ufIs a repetition node with repetition degree d, denoted as uf(d)；
If the f-th node ufIf the node vector U appears only once, the f-th node U is representedfA non-duplicate node;
the first p +1 nodes of the node vector U are designated as left vertices U0(p + 1); the last p +1 nodes of the node vector U are recorded as the right vertex UF+1(p +1), and the left vertex u0(p +1) and right vertex uF+1The values of (p +1) are the kth normalized input variable zkMinimum and maximum values of (d), i.e. the interval [ u ]0(p+1),uF+1(p+1)]＝[0,1]。
Dividing left vertex U in node vector U0(p +1) and right vertex uF+1F-p nodes outside the (p +1) are marked as internal nodes; when f node ufWhen the node is an internal node, u is determined according to the interval equal length principlefA value of (d);
this stage is the kth normalized input variable zkCorresponding f-th p-th B-spline basis matrix
Figure BDA0002197391740000066
The method of (3).
Step 6, constructing a B-spline quantile regression model shown as the formula (2), and normalizing the input variable Z in the training settrainAs the input of B-spline quantile model, the output variable Y in training settrainAs the output of the B-spline quantile model, the r-th quantile point tau is obtainedrRegression parameter vector of lower B-spline quantile regression model
Figure BDA0002197391740000065
Figure BDA0002197391740000071
In the formula (2), QY(τr| Z) is the r-th quantile τ of the output variable Y under the normalized input variable ZrFraction of lower, τrDenotes the r-th quantile andrbelongs to the element (0,1), r is more than or equal to 1 and less than or equal to M, and M is the total number of quantile points;
Figure BDA0002197391740000072
is the r-th quantilerThe kth normalized input variable zkF-th B-spline basis matrix of
Figure BDA0002197391740000073
Corresponding parameter, and
Figure BDA0002197391740000074
θ(τr) Is the r-th quantilerThe following regression parameter vector is obtained by equation (3):
Figure BDA0002197391740000075
in the formula (3), the reaction mixture is,
Figure BDA0002197391740000076
is a check function and has:
Figure BDA0002197391740000077
in formula (4), v represents an intermediate variable and has:
Figure BDA0002197391740000078
formula (A), (B) and5) in, α (τ)r) Is the r-th quantilerA constant of;
in the stage, parameters of a B-spline quantile regression model are calculated by using training set data.
Step 7, the r-th quantile point taurRegression parameter vector θ (τ) ofr) Substituting into B-spline quantile regression model, and testing the normalized input variable ZtestInputting the data into a B-spline quantile regression model to obtain a test set at an r-th quantile point taurPrediction of
Figure BDA0002197391740000079
Further obtaining the predicted value O of the test set under M quantites1,O2,…,Or,…,OMWherein
Figure BDA00021973917400000710
Is the output variable Y of the test settestInput variable Z of test set after normalizationtestAt the r-th quantile ofrLower quantile;
in the stage, input variables of the test set are input into a B spline model, and the predicted values of the test set under M quantiles are calculated.
And 8, calculating a probability density prediction result of the photoelectric power of the test set by using a kernel density estimation function:
step 8.1, defining predicted values O under M quantiles1,O2,…,Or,…,OMAny point with the same distribution is O, and the kernel density estimation function is obtained by using the formula (6)
Figure BDA00021973917400000711
And as a prediction result of the photoelectric power of the test set:
Figure BDA0002197391740000081
in formula (6), the smoothing parameter h is the window width and has:
Figure BDA0002197391740000082
in the formula (7), the reaction mixture is,
Figure BDA0002197391740000083
is the predicted value O1,O2,…,Or,…,OMStandard deviation of (d);
in formula (6), K (. cndot.) is an Epanechnikov kernel function and has:
Figure BDA0002197391740000084
in the formula (8), η is a variable, and
Figure BDA0002197391740000085
in the stage, the probability density prediction result of the test set is obtained by combining the prediction values under the M quantiles of the test set with the nuclear density method, namely, a complete photovoltaic power generation probability density curve graph under the future target can be obtained, and the effectiveness of the method can be verified through the probability density prediction result of the test set.

Claims (1)

1. A photoelectric probability density prediction method based on B-spline quantile regression is characterized by comprising the following steps:
step 1, collecting a photoelectric historical data set R ═ (R)1,r2,…,ri,…,rN) Wherein r isiI is more than or equal to 1 and less than or equal to N, wherein N is the total data number of the photoelectric historical data set R;
step 2, predicting the photoelectric power data of the K +1 th time point by using a rolling arrangement method according to the photoelectric power data of the previous K time points in the photoelectric historical data set R to obtain an n X (K +1) -dimensional matrix (X, Y), wherein X is (X ═ 1)1,x2,...,xk,...,xK) Is thatInput variable, xkIs the kth input variable, and
Figure FDA0002829892840000011
Figure FDA0002829892840000012
is the kth input variable xkThe j sample of (Y ═ Y)1,y2,...,yj,...,yn)TIs an output variable, yjIs the jth sample of the output variable Y, K is more than or equal to 1 and less than or equal to K, and j is more than or equal to 1 and less than or equal to n;
step 3, dividing the n X (K +1) dimensional matrix (X, Y) into a training set (X)train,Ytrain) And test set (X)test,Ytest)；
Step 4, K input variables X ═ X1,x2,...,xk,...,xK) Normalization processing is carried out to obtain normalized input variable Z ═ Z (Z)1,z2,...,zk,...,zK) Wherein z iskIs the kth normalized input variable; and is
Figure FDA0002829892840000013
Figure FDA0002829892840000014
Is the kth normalized input variable zkThe jth sample of (a);
step 5, utilizing a B spline method to normalize the kth normalized input variable zkProcessing to obtain the kth normalized input variable zkCorresponding F p-th-order B-spline basis matrixes
Figure FDA0002829892840000015
Wherein the content of the first and second substances,
Figure FDA0002829892840000016
is the k normalized input variable zkThe corresponding f th B-th spline base matrix is represented by the formula (1)Obtaining; f and p are the degree of freedom and the number of times of the B spline basis matrix respectively;
Figure FDA0002829892840000017
in the formula (1), the reaction mixture is,
Figure FDA0002829892840000018
is the k normalized input variable zkThe corresponding f 0 th-order B-spline basis matrix,
Figure FDA0002829892840000019
is the k normalized input variable zkThe corresponding f < th > p-1 th-order B-spline basis matrix,
Figure FDA00028298928400000110
is the k normalized input variable zkThe corresponding f +1 th p-1 th-order B spline basis matrix; u. offIs the f-th node, and ufE.g. U, U is a non-decreasing number of node vectors of F + p +2, and U0≤u1≤...≤uF+p+1，uf+pIs the f + p node;
defining a half-open interval [ u ]f,uf+1) Is the f-th node interval;
if the f-th node ufRepeated d times in the node vector U, and d>0, then it represents the f-th node ufIs a repetition node with repetition degree d, denoted as uf(d)；
If the f-th node ufIf the node vector U appears only once, the f-th node U is representedfA non-duplicate node;
recording the first p +1 nodes of the node vector U as left vertex U0(p + 1); recording the last p +1 nodes of the node vector U as right vertex UF+1(p +1), and left vertex u0(p +1) and right vertex uF+1The values of (p +1) are the kth normalized input variable zkMinimum and maximum values of, and [ u ]0(p+1),uF+1(p+1)]＝[0,1]；
Dividing the left vertex U in the node vector U0(p +1) and right vertex uF+1F-p nodes outside the (p +1) are marked as internal nodes; when f node ufWhen the node is an internal node, u is determined according to the interval equal length principlefA value of (d);
step 6, constructing a B-spline quantile regression model shown as the formula (2), and normalizing the input variable Z in the training settrainAs the input of the B-spline quantile regression model, the output variable Y in the training settrainAs the output of the B-spline quantile regression model, to obtain the r-th quantile point taurRegression parameter vector of lower B-spline quantile regression model
Figure FDA0002829892840000021
Figure FDA0002829892840000022
In the formula (2), QY(τr| Z) is the r-th quantile τ of the output variable Y under the normalized input variable ZrFraction of lower, τrDenotes the r-th quantile andrbelongs to the element (0,1), r is more than or equal to 1 and less than or equal to M, and M is the total number of quantile points;
Figure FDA0002829892840000023
is the r-th quantilerThe kth normalized input variable zkF-th B-spline basis matrix of
Figure FDA0002829892840000024
Corresponding parameter, and
Figure FDA0002829892840000025
θ(τr) Is the r-th quantilerThe following regression parameter vector is obtained by equation (3):
Figure FDA0002829892840000026
in the formula (3), the reaction mixture is,
Figure FDA0002829892840000027
is a check function and has:
Figure FDA0002829892840000028
in formula (4), v represents an intermediate variable and has:
Figure FDA0002829892840000029
in the formula (5), α (τ)r) Is the r-th quantilerA constant of;
step 7, dividing the r th quantile point taurRegression parameter vector θ (τ) ofr) Substituting into B-spline quantile regression model, and testing the normalized input variable ZtestInputting the data into a B-spline quantile regression model to obtain a test set at an r-th quantile point taurPrediction of
Figure FDA0002829892840000031
Further obtaining the predicted value O of the test set under M quantites1,O2,…,Or,…,OMWherein
Figure FDA0002829892840000032
Is the output variable Y of the test settestInput variable Z of test set after normalizationtestAt the r-th quantile ofrLower quantile;
and 8, calculating a probability density prediction result of the photoelectric power of the test set by using a kernel density estimation function:
step 8.1, defining predicted values O under M quantiles1,O2,…,Or,…,OMAny point with the same distribution is O, and the kernel density estimation function is obtained by using the formula (6)
Figure FDA0002829892840000033
And as a prediction result of the photoelectric power of the test set:
Figure FDA0002829892840000034
in formula (6), the smoothing parameter h is the window width and has:
Figure FDA0002829892840000035
in the formula (7), the reaction mixture is,
Figure FDA0002829892840000036
is the predicted value O1,O2,…,Or,…,OMStandard deviation of (d);
in formula (6), K (. cndot.) is an Epanechnikov kernel function and has:
Figure FDA0002829892840000037
in the formula (8), η is a variable, and
Figure FDA0002829892840000038
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