CN110969197A - Quantile prediction method for wind power generation based on instance migration - Google Patents

Quantile prediction method for wind power generation based on instance migration Download PDF

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CN110969197A
CN110969197A CN201911158049.9A CN201911158049A CN110969197A CN 110969197 A CN110969197 A CN 110969197A CN 201911158049 A CN201911158049 A CN 201911158049A CN 110969197 A CN110969197 A CN 110969197A
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顾洁
温洪林
蔡珑
金之俭
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Abstract

The invention discloses a quantile prediction method for wind power generation based on instance migration, which comprises the following steps of: collecting wind power generation data of other areas, and constructing a training set of a target problem by adopting an example migration method; constructing a quantile prediction model of wind power generation based on example migration; analyzing errors of the gradient lifting tree model based on the example migration; re-deriving the formula of the weights; deducing the most probable value of the parameter theta by adopting a maximum likelihood method; solving an optimal prediction function; solving the weight by adopting an iteration-based mode; according to the method, the transfer learning method is combined with the wind power generation probability prediction problem, the accuracy of wind power generation probability prediction under the condition of lacking historical data can be remarkably improved by utilizing information of other regions, a unique algorithm structure is designed aiming at the probability prediction, and a weight formula is deduced again by combining the characteristic of probability prediction of generalized load, so that the weight solving speed is improved, and the calculated amount is reduced.

Description

Quantile prediction method for wind power generation based on instance migration
Technical Field
The invention relates to the technical field of power electronics, in particular to a quantile prediction method for wind power generation based on instance migration.
Background
By the end of 2017, the wind power generation ratio in germany, irish, portugal, spain, sweden, and yerba mate has reached two digits. As an important component of the generalized load, wind power generation has a large fluctuation, and the point prediction cannot completely reflect the characteristics of wind power generation, so that it is necessary to deeply study the probability distribution of wind power generation by using probability prediction. Many decision making processes in the power system rely on this probability distribution, including determining unit output, wind energy trading, purchasing of reserve electrical energy, demand response, probabilistic power flow and economic dispatch of electrical energy;
with the rapid development of wind power generation, a large number of newly-built wind power plants are put into use, so that probability prediction needs to be made on the power generation capacity of the newly-built wind power plants. However, conventional wind power generation probability prediction algorithms all require a large amount of historical data to train the model. For a newly-built wind power plant, enough historical data cannot be obtained, and how to improve the accuracy of wind power generation probability prediction under the condition of lacking of the historical data is of great development significance.
Disclosure of Invention
Aiming at the problems, the invention provides a quantile prediction method of wind power generation based on example migration, which can improve the accuracy of wind power generation probability prediction by combining a migration learning method with a wind power generation probability prediction problem and by utilizing information of other regions, especially can obviously improve the accuracy of wind power generation probability prediction under the condition of lacking historical data, and improves the weight solving speed and reduces the calculated amount by designing a unique algorithm structure aiming at the probability prediction and deducing a weight formula again by combining the characteristic of probability prediction of generalized load.
The invention provides a quantile prediction method of wind power generation based on example migration, which comprises the following steps of:
the method comprises the following steps: collecting wind power generation data of other regions as data of a source problem, adopting a case migration method to assign a smaller weight to the data of the source problem, and forming a training set of a target problem together with a target problem data set of a region needing to be predicted;
step two: constructing a quantile prediction model of wind power generation based on example migration, and selecting the quantile prediction model based on the gradient lifting tree as a core prediction algorithm for fusion to obtain a gradient lifting tree model based on example migration;
step three: analyzing errors of the gradient lifting tree model based on the example migration, dividing the errors of the gradient lifting tree model based on the example migration into random errors and system errors, and ensuring that data of a target problem and data of a source problem meet a formula (1);
Figure BDA0002285331770000021
Figure BDA0002285331770000022
step four: can combine f and f(k)Modeling the differences between them as systematic errors, and using
Figure BDA0002285331770000023
Is shown, and
Figure BDA0002285331770000024
satisfying the formula (2), substituting the formula (2) into the formula (1) to obtain a formula (3);
Figure BDA0002285331770000025
Figure BDA0002285331770000031
Figure BDA0002285331770000032
step five: assume a random variable δ(k)+ε(k)And
Figure BDA0002285331770000033
are independent and obey a laplacian distribution and then, under the assumption, re-derive the formula of weights for any one possible prediction function fθ(theta is a parameter), fθThe likelihood calculation formula for being a correct prediction function is shown in equation (4);
Figure BDA0002285331770000034
step six: deducing the most probable value of the parameter theta by adopting a maximum likelihood method
Figure BDA0002285331770000035
Step seven: solving the optimal prediction function fθFirst, the loss function shown in equation (5) is solved, and then the weight w is guaranteed(target)And w(k)Satisfies the formulas (6) and (7), and then the weight of the source problem is normalized to (0, 1)]Interval, ensuring that the weight after all source problems are normalized meets the formula (8);
Figure BDA0002285331770000036
Figure BDA0002285331770000037
Figure BDA0002285331770000038
Figure BDA0002285331770000039
step seven: according to normalizationThe weight of the source problem after conversion is used to find the weight w of the target problem by using the formula (9)(target)；
Figure BDA0002285331770000041
Step eight: weight solving, adopting an iteration-based mode to solve the weight, firstly selecting w(target)Then all w are combined(k)Initialized to 1, and then the operation is repeated to update w(k)According to the updated w(k)Retraining the gradient lifting tree model based on example migration, and then calculating
Figure BDA0002285331770000042
Then, w is calculated according to the formula (9)(k)Up to all w(k)Convergence, based finally on the convergence result w(k)Completing the training w of the model with the tau being 0.01-0.99(k)
The further improvement lies in that: the gradient lifting tree model based on example migration in the second step comprises two parts, one part trains a traditional point prediction model with tau being 0.5 by using an iterative weighting algorithm, and the other part directly applies the weight obtained by solving in the former part to the training of the rest models.
The further improvement lies in that: f in the formula (1) of the step three represents an input variable
Figure BDA0002285331770000043
And output variables
Figure BDA0002285331770000044
True mapping relationship between, input variables
Figure BDA0002285331770000045
And output variables
Figure BDA0002285331770000046
The real mapping relationship between the two is represented by f(k)And (4) showing.
The further improvement lies in that: the above-mentionedStep five random variable delta(k)+ε(k)And
Figure BDA0002285331770000047
the error distribution range of (2) is shown in equation (10):
Figure BDA0002285331770000048
Figure BDA0002285331770000049
wherein the content of the first and second substances,
Figure BDA00022853317700000410
and
Figure BDA00022853317700000411
respectively represents epsilon(target)And delta(k)+ε(k)The scale parameter of (2).
The further improvement lies in that: the most probable value of the parameter theta in the sixth step
Figure BDA00022853317700000412
The calculation formula of (c) is shown in formula (11).
Figure BDA0002285331770000051
The invention has the beneficial effects that: according to the method, the migration learning method is combined with the wind power generation probability prediction problem, the accuracy of wind power generation probability prediction can be improved by utilizing information of other regions, particularly the accuracy of wind power generation probability prediction under the condition of lacking historical data can be obviously improved, a unique algorithm structure is designed aiming at the probability prediction, and a weight formula is deduced again by combining the characteristic of probability prediction of generalized load, so that the weight solving speed is improved, and the calculated amount is reduced.
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FIG. 1 is a diagram illustrating the reliability comparison of the two models according to the embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. 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.
Example one
The embodiment provides a quantile prediction method for wind power generation based on example migration, which comprises the following steps:
the method comprises the following steps: collecting wind power generation data of other regions as data of a source problem, adopting a case migration method to assign a smaller weight to the data of the source problem, and forming a training set of a target problem together with a target problem data set of a region needing to be predicted;
step two: constructing a quantile prediction model of wind power generation based on example migration, and selecting the quantile prediction model based on the gradient lifting tree as a core prediction algorithm for fusion to obtain a gradient lifting tree model based on example migration, wherein the gradient lifting tree model based on example migration comprises two parts, one part uses an iterative weighting algorithm to train a traditional point prediction model with tau being 0.5, and the other part directly applies the weight obtained by solving in the former part to the training of the other models;
step three: analyzing errors of the gradient lifting tree model based on the example migration, dividing the errors of the gradient lifting tree model based on the example migration into random errors and system errors, and ensuring that data of a target problem and data of a source problem meet a formula (1);
Figure BDA0002285331770000061
Figure BDA0002285331770000062
wherein f represents an input variable
Figure BDA0002285331770000063
And output variables
Figure BDA0002285331770000064
True mapping relationship between, input variables
Figure BDA0002285331770000065
And output variables
Figure BDA0002285331770000066
The real mapping relationship between the two is represented by f(k)Represents;
step four: can combine f and f(k)Modeling the differences between them as systematic errors, and using
Figure BDA0002285331770000067
Is shown, and
Figure BDA0002285331770000068
satisfying the formula (2), substituting the formula (2) into the formula (1) to obtain a formula (3);
Figure BDA0002285331770000069
Figure BDA00022853317700000610
Figure BDA00022853317700000611
step five: assume a random variable δ(k)+ε(k)And
Figure BDA0002285331770000071
are independent and obey a laplacian distribution, and then under the assumption, re-derive weightsHeavy formula, for any one possible prediction function fθ(theta is a parameter), fθThe likelihood calculation formula for being a correct prediction function is shown in equation (4);
Figure BDA0002285331770000072
random variable delta(k)+ε(k)And
Figure BDA0002285331770000073
the error distribution range of (2) is shown in equation (10):
Figure BDA0002285331770000074
Figure BDA0002285331770000075
wherein the content of the first and second substances,
Figure BDA0002285331770000076
and
Figure BDA0002285331770000077
respectively represents epsilon(target)And delta(k)+ε(k)A scale parameter of (d);
step six: deducing the most probable value of the parameter theta by adopting a maximum likelihood method
Figure BDA0002285331770000078
Most probable value of the parameter θ
Figure BDA0002285331770000079
The calculation formula (2) is shown in formula (11);
Figure BDA00022853317700000710
step seven: solving the optimal prediction function fθFirst, solve the equation (5)Loss function shown, then weight w is guaranteed(target)And w(k)Satisfies the formulas (6) and (7), and then the weight of the source problem is normalized to (0, 1)]Interval, ensuring that the weight after all source problems are normalized meets the formula (8);
Figure BDA0002285331770000081
Figure BDA0002285331770000082
Figure BDA0002285331770000083
Figure BDA0002285331770000084
most probable value of the parameter θ
Figure BDA0002285331770000085
The calculation formula (2) is shown in formula (11);
Figure BDA0002285331770000086
step seven: the weight w of the target problem is solved by using the formula (9) according to the weight of the source problem after normalization(target)；
Figure BDA0002285331770000087
Step eight: weight solving, adopting an iteration-based mode to solve the weight, firstly selecting w(target)Then all w are combined(k)Initialized to 1, and then the operation is repeated to update w(k)According to the updated w(k)Retraining the gradient lifting tree model based on example migration, and then calculating
Figure BDA0002285331770000088
Then, w is calculated according to the formula (9)(k)Up to all w(k)Convergence, based finally on the convergence result w(k)Completing the training w of the model with the tau being 0.01-0.99(k)。
In this embodiment, a model is constructed by using data of a wind power generation prediction problem in the global load prediction competition in 2014, the wind power generation prediction competition is aimed at predicting wind power generation conditions (normalized power generation amount) of 10 australian regions of a wind farm, and the 10 regions can be sequentially named as zones 1 to 10. The input variables given in the data set are wind speed vectors at 10m altitude and wind speed vectors at 100m altitude. The output of the target is the probability distribution condition of wind power generation in the corresponding time period, namely, the predicted wind power generation quantiles are given to each quantile point in 0.01-0.99.
To facilitate comparison with predicted results of other algorithms in the GEFCom2014 game, the present embodiment constructs predicted tasks in a manner of the game, where the GEFCom2014 game includes 15 predicted tasks, where the first 3 tasks are unscored trial predicted tasks and the last 12 tasks are scored predicted tasks. To simulate the real-world prediction process, all prediction tasks present a pattern of rolling predictions. The time period of the training set data for each scored predicted task and the time period during which wind power generation needs to be predicted are shown in table 1:
TABLE 1
Figure BDA0002285331770000091
In the embodiment, three GBDT-based models are introduced as reference models; the first is a Double-layer gradient boosting tree model (DL-GBDT); the DL-GBDT model obtains the first achievement in the GEFCom2014 wind power generation prediction competition; in the DL-GBDT model, a first layer is used for fitting a wind power generation median, and a second layer establishes a quantile regression model for each quantile; the second layer selects the local area load prediction result given by the first layer as an input variable, and introduces the prediction results given by the prediction models of other areas in the first layer as the input variable; the other two reference models based on the GBDT are the same single-layer GBDT model, and the training data used by the two reference models are different; the first single-layer GBDT model selects only the data set of the target problem as training data, and the second single-layer GBDT model selects the data sets of the target problem and the source problem (namely, the wind power generation data of all regions) as training data; the two GBDT-based reference models are represented using GBDT1 and GBDT2, respectively.
The input variables provided in the data set are wind speed vectors for 10 meters high and 100 meters high per hour for each region. Based on the wind speed vector, variables such as Wind Speed (WS), Wind Energy (WE), and Wind Direction (WD) can be derived. If u, v are used to represent the two components of the wind velocity vector, the wind velocity, wind energy, and wind direction can be calculated using the following equations:
Figure BDA0002285331770000101
WD＝180/π×arctan(u，v)
WE＝0.5×ws3
by using the characteristic engineering, more input variables are further derived based on the wind speed, the wind energy and the wind direction, various combination modes of the input variables are checked by using cross validation, and then the combination of the input variables selected by the DL-GBDT model is considered to be very effective, so that the model provided by the embodiment also selects the same input variable combination, adds the input variable of 'hour' on the basis, and then obtains the data shown in table 2:
TABLE 2
Figure BDA0002285331770000111
Selecting wind power generation quantile prediction scores as indexes for evaluating and measuring the probability prediction effectiveness, wherein the wind power generation quantile prediction scores are defined as the average of Pinball error functions at all target quantiles, and the calculation formula is as follows;
Figure BDA0002285331770000112
two sets of hyper-parameters are then determined for τ: selecting one set of hyper-parameters when the tau is within the interval of 0.16-0.84, and selecting another set of hyper-parameters under other conditions, wherein the parameter values are shown in table 3:
TABLE 3
Figure BDA0002285331770000121
In the embodiment, the hyper-parameter w in the IBT-GBDT model(target)The values of (a) are shown in table 4:
TABLE 4
Figure BDA0002285331770000122
And selecting the prediction problem of the Zone7 in the task 4 as a target problem, wherein the wind power generation historical data of the Zone7 form a basic training set, and correspondingly selecting the wind power generation historical data of other areas as an auxiliary training set. The results of the cross-validation show that the hyperparameter w(target)The optimal value of (3) is 50, so 50 is selected as the weight of the Zone7 training data, the weights of other areas are initialized to 1, then a quantile regression model is trained according to the solved weight, and the convergence process of the weight is shown in table 5:
TABLE 5
Figure BDA0002285331770000131
The results according to table 5 show that after approximately 7 iterations the weights converge and that in addition the weight of Zone8 takes a value of 1, which indicates that Zone8 has the highest correlation with Zone 7.
Example two
According to the embodiment shown in fig. 1, the reliability of the probabilistic prediction model is verified, the average deviation between the experimental proportion and the target proportion is used as an index for measuring the reliability, and the indication variables are defined firstMeasurement of
Figure BDA0002285331770000132
Then using dτDenotes the average deviation at the quantile point tau,
Figure BDA0002285331770000133
the expression is as follows
Figure BDA0002285331770000134
Wherein, ytRepresenting the actual value of the wind power generation at time t,
Figure BDA0002285331770000135
representing the probabilistic predictions at the quantile τ for wind power generation at time t.
Indicating variable
Figure BDA0002285331770000141
Is used to detect whether the actual value falls within
Figure BDA0002285331770000142
In this interval; obtained by taking multiple measurements based on law of large numbers
Figure BDA0002285331770000143
The true probability p that the actual value falls into the prediction interval can be estimated by averagingτ：
Figure BDA0002285331770000144
Based on pτCan define dτ，dτThe expression of (a) is:
dτ＝τ-pτ
as can be seen from the formula, dτThe actual effect of (d) is to measure the difference between the true probability of falling into the prediction interval with probability τ and τ, for the IBT-GBDT model and other reference models, when τ takes different valuesτOff from tauAs shown in FIG. 1:
as can be seen from FIG. 1, for all GBDT-based models, d is when the target quantile is less than 0.5τHas a small value, d is 0.5 when the target quantile pointτThe value of (A) is large. The phenomenon shows that the prediction interval given by the model is narrow, in addition, a basic GBDT model obtained by training based on all data in the model is the model with the worst performance, the main reason of the phenomenon is negative migration, and the other model with the worse performance is the GBDT model obtained by training only by a target problem data set;
when the value of the target quantile is in the interval of [0.8,0.95], the performance of two basic models based on GBDT is obviously poorer, because in the marginal area of probability distribution, the distribution of a training set is sparse, and the complex model is easy to be over-fitted; however, the IBT-GBDT model does not have the problem, because the IBT-GBDT model has more training data, the complex model can be selected, the model can be kept to be sufficiently trained, and the over-fitting phenomenon can be inhibited.
According to the method, the migration learning method is combined with the wind power generation probability prediction problem, the accuracy of wind power generation probability prediction can be improved by utilizing information of other regions, particularly the accuracy of wind power generation probability prediction under the condition of lacking historical data can be obviously improved, a unique algorithm structure is designed aiming at the probability prediction, and a weight formula is deduced again by combining the characteristic of probability prediction of generalized load, so that the weight solving speed is improved, and the calculated amount is reduced.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (5)

1. A quantile prediction method of wind power generation based on instance migration is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: collecting wind power generation data of other regions as data of a source problem, adopting a case migration method to assign a smaller weight to the data of the source problem, and forming a training set of a target problem together with a target problem data set of a region needing to be predicted;
step two: constructing a quantile prediction model of wind power generation based on example migration, and selecting the quantile prediction model based on the gradient lifting tree as a core prediction algorithm for fusion to obtain a gradient lifting tree model based on example migration;
step three: analyzing errors of the gradient lifting tree model based on the example migration, dividing the errors of the gradient lifting tree model based on the example migration into random errors and system errors, and ensuring that data of a target problem and data of a source problem meet a formula (1);
Figure FDA0002285331760000011
step four: can combine f and f(k)Modeling the differences between them as systematic errors, and using
Figure FDA0002285331760000012
Is shown, and
Figure FDA0002285331760000013
satisfying the formula (2), substituting the formula (2) into the formula (1) to obtain a formula (3);
Figure FDA0002285331760000014
Figure FDA0002285331760000015
step five: assume a random variable δ(k)+ε(k)And
Figure FDA0002285331760000016
are independent and obey a laplacian distribution and then, under the assumption, re-derive the formula of weights for any one possible prediction function fθ(theta is a parameter), fθThe likelihood calculation formula for being a correct prediction function is shown in equation (4);
Figure FDA0002285331760000021
step six: deducing the most probable value of the parameter theta by adopting a maximum likelihood method
Figure FDA0002285331760000022
Step seven: solving the optimal prediction function fθFirst, the loss function shown in equation (5) is solved, and then the weight w is guaranteed(target)And w(k)Satisfies the formulas (6) and (7), and then the weight of the source problem is normalized to (0, 1)]Interval, ensuring that the weight after all source problems are normalized meets the formula (8);
Figure FDA0002285331760000023
Figure FDA0002285331760000024
Figure FDA0002285331760000025
Figure FDA0002285331760000026
step seven: solving the target problem by using the formula (9) according to the weight of the source problem after normalizationWeight w of(target)；
Figure FDA0002285331760000027
Step eight: weight solving, adopting an iteration-based mode to solve the weight, firstly selecting w(target)Then all w are combined(k)Initialized to 1, and then the operation is repeated to update w(k)According to the updated w(k)Retraining the gradient lifting tree model based on example migration, and then calculating
Figure FDA0002285331760000031
Then, w is calculated according to the formula (9)(k)Up to all w(k)Convergence, based finally on the convergence result w(k)Completing the training w of the model with the tau being 0.01-0.99(k)。
2. The method for quantile prediction of wind power generation based on instance migration according to claim 1, wherein the method comprises the following steps: the gradient lifting tree model based on example migration in the second step comprises two parts, one part trains a traditional point prediction model with tau being 0.5 by using an iterative weighting algorithm, and the other part directly applies the weight obtained by solving in the former part to the training of the rest models.
3. The method for quantile prediction of wind power generation based on instance migration according to claim 1, wherein the method comprises the following steps: f in the formula (1) of the step three represents an input variable
Figure FDA0002285331760000032
And output variables
Figure FDA0002285331760000033
True mapping relationship between, input variables
Figure FDA0002285331760000034
And output variables
Figure FDA0002285331760000035
The real mapping relationship between the two is represented by f(k)And (4) showing.
4. The method for quantile prediction of wind power generation based on instance migration according to claim 1, wherein the method comprises the following steps: the random variable delta in the step five(k)+ε(k)And
Figure FDA0002285331760000036
the error distribution range of (2) is shown in equation (10):
Figure FDA0002285331760000037
wherein the content of the first and second substances,
Figure FDA0002285331760000038
and
Figure FDA0002285331760000039
respectively represents epsilon(target)And delta(k)+ε(k)The scale parameter of (2).
5. The method for quantile prediction of wind power generation based on instance migration according to claim 1, wherein the method comprises the following steps: the most probable value of the parameter theta in the sixth step
Figure FDA00022853317600000310
The calculation formula of (c) is shown in formula (11).
Figure FDA0002285331760000041
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