CN105939026B - Wind power undulate quantity probability Distribution Model method for building up based on mixing Laplace distributions - Google Patents
Wind power undulate quantity probability Distribution Model method for building up based on mixing Laplace distributions Download PDFInfo
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Abstract
The invention discloses a kind of wind power undulate quantity probability Distribution Model method for building up based on mixing Laplace distributions, the wind power data and default time scale surveyed first according to wind power plant calculate wind power undulate quantity sequence, structure mixing Laplace distributed models, it is solved to obtain the parameter of mixing Laplace distributed models according to wind power undulate quantity sequence, so as to obtain wind power probability Distribution Model.Using the obtained wind power probability Distribution Model of the present invention, energy accurate description wind power swing characteristic in particular improves the accuracy that the heavy-tailed property of wind power swing distribution describes；For in the description problem of the different horizontal wind power swings of spatial and temporal scales, which can also reach satisfied precision.
Description
Technical Field
The invention belongs to the technical field of wind power fluctuation characteristic analysis, and particularly relates to a wind power fluctuation amount probability distribution model building method based on mixed Laplace distribution.
Background
With the rapid development of new energy power generation technology, the requirement of large-scale wind power integration is further increased, and the fluctuation and intermittence of wind power not only affect the quality of electric energy, increase the difficulty of power grid planning and dispatching, but also cause potential risks for the safe and stable operation of a power grid. Minute-scale fluctuation influences the control performance of the AGC of the power system; the small-scale fluctuation influences the day-to-day real-time scheduling of the power system; daily fluctuation influences arrangement of peak shaving modes of the power system; annual and monthly fluctuation influences the power and electric quantity balance of the power system, and the wind power fluctuation characteristics are accurately analyzed, so that the method is a basis for solving the problems and is also an important link for researching large-scale wind power grid-connected power generation. An effective and reliable model is established, and the method can be applied to wind power prediction evaluation and power generation plan correction and is also suitable for rotary standby estimation.
In the conventional method for describing the wind power fluctuation characteristic, there are usually three different directions. A method for establishing a wind power random series model by taking time as a dimension, namely a time series analysis method, is disclosed, for example, in the document: in Chen P, Pedersen T, Bak-Jensen B, et al ARIMA-based time series model of stored wind Power generation IEEE trans on Power Systems, Vol.25(2),2010, pp.667-676', a wind Power output sequence is regarded as a non-stationary sequence, and an autoregressive integral sliding average model based on wind Power fluctuation is established. One method is to assume that the wind power does not accord with a certain prior probability distribution, and model the probability characteristic of the wind power by adopting a non-parameter estimation method, such as in the document "Yang nan, Rut Home exhibition, Zhou Wu, etc., in the power grid technology, Vol.40(2),2016, pp.335-340", a non-parameter kernel density estimation method of a wind power probability model based on fuzzy sequence optimization is used for constructing a non-parameter estimation model of the wind power by taking a Gaussian function as a kernel function of the wind power probability density estimation. In the literature, "forest satellite, wenjingyu, aixiaokang, etc.. the probability distribution research of the wind power fluctuation characteristics, the chinese electro-mechanical engineering report, vol.32(1),2012, pp.38-46", the fluctuation condition of the wind farm power minute-level component is described by using the t distribution-scale distribution with the shift factor and the expansion coefficient.
Due to the strong randomness of the wind power change, the wind power fluctuation rules have large difference on different space-time scales, and the fluctuation characteristics of the wind power are difficult to accurately describe by a time sequence analysis method with a single space-time scale. However, the nonparametric estimation method is used for describing the fluctuation characteristic of the wind power, so that massive sample data is often needed, and the probability distribution of the wind power fluctuation is proved to be definite regularity through the existing data, so that the nonparametric estimation method is not an optimal scheme. The probability distribution of wind power fluctuation presents strong heavy tail characteristics, and the peak probability of the wind power fluctuation near the mean value is difficult to accurately reflect by aiming at a parameterized estimation method and a traditional distribution model.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a wind power fluctuation amount probability distribution model building method based on mixed Laplace distribution, provides a probability distribution model capable of accurately describing wind power fluctuation under different space-time scales, and effectively improves the fitting precision particularly on the description of the heavy tail characteristics of distribution.
In order to achieve the purpose, the method for establishing the wind power fluctuation amount probability distribution model based on the mixed Laplace distribution comprises the following steps:
s1: calculating a wind power fluctuation quantity sequence P [ P ] according to wind power data measured in a wind power plant and a preset time scale delta t1，p2，p3,···,pM]TWherein M represents the dimension of the wind power fluctuation quantity sequence;
s2: constructing a mixed Laplace distribution model:
wherein,α＝{α1,α2,···,αNdenotes a set of weight parameters, αiIs the weight of the ith Laplace distribution, andμ＝{μ1,μ2,···,μNdenotes the mean parameter set, μiRepresents the variation of the sequence of the fluctuation amount of the wind power in the ith Laplace distribution, and delta is { delta ═ delta }1,δ2,···,δNDenotes the variance parameter set, δiRepresenting the mean value of the sequence of fluctuation quantity of the wind power in the ith Laplace distribution; n is the number of Laplace distributions, and N is more than 1; f. ofi(p|μi,δi) A probability density function representing the ith single M-dimensional Laplace distribution;
s3: according to the wind power fluctuation quantity sequence P ═ P1，p2，p3,···,pM]TAnd (5) solving the mixed Laplace distribution model obtained in the step (S2) to obtain a weight parameter set α, a mean parameter set mu and a variance parameter set delta, so as to obtain a probability distribution model of the wind power fluctuation quantity.
The invention relates to a method for establishing a wind power fluctuation amount probability distribution model based on hybrid Laplace distribution. The wind power probability distribution model obtained by the method can accurately describe the wind power fluctuation characteristics, and particularly improves the precision of the heavy tail characteristic description of the wind power fluctuation distribution; aiming at the description problems of wind power fluctuation at different time scale levels and different space scale levels, the model can also reach satisfactory precision, and provides reliable basic reference for problems such as peak regulation margin evaluation of a power system, wind power prediction evaluation, power generation plan correction, probability load flow calculation, power electric quantity balance analysis and the like.
Drawings
FIG. 1 is a flow chart of a wind power fluctuation amount probability distribution model building method based on mixed Laplace distribution according to the invention;
FIG. 2 is a flow chart of the solution of the hybrid Laplace distribution model;
FIG. 3 is a wind power fluctuation probability distribution diagram of the present invention and the comparative model in the present embodiment;
FIG. 4 is a probability distribution diagram of the wind power fluctuation amount of the present invention and the comparison model at different time scales in the present embodiment;
FIG. 5 is a wind power fluctuation probability distribution diagram of the present invention and the comparative model at different spatial scales in the present embodiment.
Detailed Description
The following description of the embodiments of the present invention is provided in order to better understand the present invention for those skilled in the art with reference to the accompanying drawings. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.
Examples
FIG. 1 is a flow chart of a wind power fluctuation amount probability distribution model building method based on mixed Laplace distribution. As shown in fig. 1, the method for establishing a probability distribution model of wind power fluctuation amount based on hybrid Laplace distribution according to the present invention includes the following steps:
s101: calculating the fluctuation amount of the wind power:
calculating a wind power fluctuation sequence according to wind power data actually measured by a wind power plant and a preset time scale delta tColumn P ═ P1,p2,p3,···,pM]TAnd M represents the dimension of the wind power fluctuation quantity sequence.
In the prior art, the first-order difference Δ P ═ P (t + Δ t) -P (t) of the wind power data is usually adopted as the wind power fluctuation amount, and the wind power output change rate P may also be usedv＝[P(t+Δt)-P(t)]/PNAs the fluctuation amount of the wind power, wherein P (t + Δ t) and P (t) respectively represent the wind power at the time t + Δ t and the time t, and PNIndicating the rated installed capacity. Because the wind speed directly influences the wind power output, although the non-stationarity of the wind power fluctuation is weakened after the first-order difference, if the time span of the time scale delta t is selected to be large, the wind power can generate large fluctuation or the presented regularity is poor in delta t. Therefore, in order to accurately reflect the natural fluctuation condition of the wind power and weaken the coupling of the mean value and the variance of the fluctuation sequence and the heteroscedasticity of the sequence, the wind power output is subjected to natural logarithm conversion first and then to first-order difference in the embodiment to describe the wind power fluctuation amount, namely the wind power fluctuation amount p of the moment ttThe calculation formula of (2) is as follows:
pt＝lnP(t+Δt)-lnP(t)
obviously, when the length of the wind power data sequence measured by the wind power plant is L, M is L- Δ t.
S102: constructing a mixed Laplace distribution model:
the Laplace distribution model is widely applied to speech signal processing and is a two-parameter probability model. The mathematical expression for a single Laplace distribution density function can be written as:
where exp denotes an exponential function.
Researches prove that the wind power fluctuation rule cannot be accurately described by single distribution. Therefore, the present inventionAnd finally, deriving a finite element mixed Laplace distribution model on the basis of the single Laplace distribution. Assuming that the wind power fluctuation quantity sequence P is [ P ═ P1，p2，p3,···,pM]TObeying the weighted distribution of the N Laplace distributions, the mathematical expression is as follows:
wherein f (P | α, mu, B) represents the distribution probability density function of the mixed Laplace distribution model, α ═ α1,α2,···,αNDenotes a set of weight parameters, andαiis the weight of the ith Laplace distribution, i is 1,2, …, N; mu-mu ═ mu1,μ2,···,μNDenotes a mean parameter set, B ═ B1,B2,···,BNDenotes the covariance matrix parameter set; n is the number of Laplace distribution, N is more than 1, generally, the complexity and the model precision of the model are comprehensively considered, and the value range of N is more than or equal to 2 and less than or equal to 5; f. ofi(P|μi,Bi) The probability density function of a single M-dimensional Laplace distribution is expressed as follows:
μiis fi(P|μi,Bi) Corresponding wind power fluctuation quantity mean value sequence mui＝[μi,1,μi,2,···μi,M]T；BiIs fi(P|μi,Bi) After natural logarithm difference processing, the vector P can be considered to be independent from each other, so that:
in order to simplify the calculation, the invention assumes that the M-dimensional wind power fluctuation quantity sequences have the same mean value and variance, and can obtain:
μi＝[μi,1,μi,2,···μi,M]T＝[μi,μi,···μi]T＝μiE
it can be seen that mu ═ mu at this time1,μ2,···,μNDenotes the mean parameter set, μiRepresents the variation of the sequence of the fluctuation amount of the wind power in the ith Laplace distribution, and delta is { delta ═ delta }1,δ2,···,δNDenotes the variance parameter set, δiAnd (4) representing the mean value of the sequence of fluctuation amounts of the wind power in the ith Laplace distribution.
Thus, the mean vector and covariance matrix can be expressed as a product of a constant and a unity matrix, and the probability density function of a single M-dimensional Laplace distribution can be expressed as:
wherein p represents the amount of wind power fluctuation.
The hybrid Laplace distribution model can be expressed as:
as can be seen, Θ ═ αi,μi,δiI.e. a parameter set of the finite element hybrid Laplace, i.e. Θ ═ α1,α2,···,αN；μ1,μ2,···,μN；δ1,δ2,···,δN}
S103: solving a mixed Laplace distribution model:
and solving the mixed Laplace distribution model obtained in the step S102 to obtain a weight parameter set α, a mean parameter set mu and a variance parameter set delta, so as to obtain a wind power probability distribution model.
In this embodiment, a hybrid Laplace distribution model is solved by using a maximum expectation algorithm for hybrid Laplace distribution. FIG. 2 is a flow chart of the solution of the hybrid Laplace distribution model. As shown in fig. 2, the solving process of the hybrid Laplace distribution model includes the following steps:
s201: let the number of solving times d equal to 1.
S202: initializing parameters:
initializing a set of weight parametersMean parameter setSum variance parameter setTypically a random assignment. Let the iteration number t equal to 1.
S203: calculating the posterior probability:
for wind power fluctuation sequence P ═ P1,p2,p3,···pM]TEach fluctuation amount p injJ 1,2, …, M, which is calculated according to bayes' theorem, the posterior probability of which is generated by the kth Laplace distribution in the tth iterationThe calculation formula is as follows:
wherein k is 1,2, …, N, pit-1(x) Is the probability of occurrence of the event x obtained according to the mixed Laplace distribution model obtained from the t-1 th iteration.Represents pjIn a manner thatIs the probability in a single M-dimensional Laplace distribution of the parameter. It is clear that,representing the weight parameter α obtained at the t-1 st iterationkMean value μkSum variance δk。
S204: calculating parameters of each Laplace distribution:
p is determined according to step S203jPosterior probability η generated from kth Laplace distributionk t(pj) Only the parameter of the kth Laplace distribution needs to be solved.
Establishing a wind power fluctuation vector P ═ P1,p2,p3,···,pm]TMaximum likelihood function of (2):
wherein, Θ is a parameter set of the mixed Laplace distribution model;
introducing a variable phi (theta) and assuming that a parameter set is obtained after a certain iterationIt is always necessary to find out a new thetaThus, it is possible to obtain:
wherein:and for a particular pj，Is a constant; order to
Therefore, when Φ (Θ) > 0 is continuously increased, H (Θ) is continuously increased, and it is only necessary to obtain Θ at which Φ (Θ) has the maximum value.
Calculating mu for phi (theta)k、δkThe derivative of (c) can be:
where sgn (. cndot.) represents a sign function.
Order toThe following can be obtained:
from the lagrange operator method, we can get:
in summary, the posterior probability obtained in step S202The parameter calculation formula for calculating the kth Laplace distribution in the t iteration is as follows:
s205: judging whether theta is greater than or equal tot-Θt-1| < epsilon, wherein thetat、Θt-1And respectively representing parameter sets obtained by the t-th iteration and the t-1 th iteration, namely vectors formed by all parameters in the weight parameter set, the mean parameter set and the variance parameter set together, wherein epsilon represents a preset error threshold value. If not, the process proceeds to step S206, otherwise, the process proceeds to step S207.
S206: let t be t +1, return to step S203.
S207: obtaining parameters of the hybrid Laplace distribution model for solving:
and taking the mixed Laplace distribution model parameters obtained by the t-th iteration as the parameters of the mixed Laplace distribution model.
S208: and judging whether D is less than D, wherein D represents the preset total solving times, D is more than or equal to 1, if so, entering step S209, otherwise, entering step S210.
S209: and d +1, the process returns to step S202.
S210: calculating parameters of a final mixed Laplace distribution model:
since the parameter initial values are randomly set in the solving process, in order to avoid iteration local convergence, in this embodiment, D sets of different parameter initial values are set, D times of solving are performed, corresponding parameters of the mixed Laplace distribution model obtained by D times of solving are averaged, and the average value is used as a parameter of the final mixed Laplace distribution model.
Namely, it isα thereini(d)、μi(d) And deltai(d) And respectively representing parameters obtained by the d-th solving.
In summary, the hybrid Laplace distribution model is constructed, the parameters of the hybrid Laplace distribution model are obtained through actually measuring wind power data, the wind power probability distribution model is obtained, the wind power probability distribution curve can be drawn according to the model, and therefore the wind power fluctuation characteristics of the wind power plant are displayed.
In order to illustrate the effectiveness of the wind power probability distribution Model obtained by the invention on the wind power fluctuation characteristics, four wind power probability distribution models are adopted for index comparison, and the four comparison models are a normal distribution Model, a logistic distribution Model, a GMM (Gaussian Mixture Model) Model and a t Location-Scale Model. The adopted indexes are heavy tail index psi (X), mean absolute error MAE, residual standard deviation RSD and goodness of fit R2And (4) four indexes. The wind power data is measured power data of a certain wind power plant cluster in Sichuan province at 10min level, and each wind power plant is 47520 pieces of sampling data. In this embodiment, the number N of Laplace in the hybrid Laplace distribution model is set to 2. Table 1 is a table comparing the indexes of the present invention with four comparative models.
| Model (model) | MAE | RSD | R2 | ψ |
| Normal distribution model | 3.1793×10-3 | 9.3728×10-3 | 0.73963 | 1.7320 |
| logistic distribution model | 1.8137×10-3 | 6.7692×10-3 | 0.86092 | 2.6544 |
| GMM model | 1.2561×10-3 | 5.2273×10-3 | 0.91387 | 3.7683 |
| t Location-Scale model | 1.0637×10-3 | 4.5494×10-3 | 0.93452 | 4.3506 |
| Mixed Laplace distribution model | 8.4161×10-4 | 3.0110×10-3 | 0.97157 | 5.5092 |
TABLE 1
As can be seen from Table 1, the MAE and RSD of the hybrid Laplace distribution model are minimal, R2The method is closer to 1, which shows that the hybrid Laplace distribution model can more accurately reflect the fluctuation law of the wind power, and the hybrid Laplace distribution model has obvious advantages in heavy tail characteristic description as can be seen from psi indexes of various distributions.
And setting the time scale delta t as 10min, and drawing the wind power fluctuation amount probability distribution map of the invention and the four comparison models. FIG. 3 is a wind power fluctuation probability distribution diagram of the present invention and the comparative model in the present embodiment. As shown in fig. 3, on a time Scale of 10min, when the wind power fluctuation is large, the GMM distribution model and the t Location-Scale model can better fit the wind power fluctuation, but when the wind power fluctuation is small or stable, the two models are not well described. The hybrid Laplace distribution model can be closer to a probability histogram of the fluctuation quantity of the wind power, and particularly has advantages over other comparison models under the condition that the fluctuation quantity of the wind power is not large.
The fluctuation amount of the wind power is closely related to the selected time scale, and the fluctuation characteristics of the wind power corresponding to different time scales are far away. In actual power grid operation, the fluctuation characteristics of wind power at the second(s) level and the minute (min) level generally provide bases for primary high frequency and secondary high frequency, and the fluctuation characteristics of the hour (h) level and the day (d) level provide references for wind power scheduling and reasonable wind power consumption, and are also evaluation indexes for wind power prediction. Therefore, in order to verify the effectiveness of the hybrid Laplace distribution model on the wind power fluctuation characteristics under different space-time scales, the hybrid Laplace distribution model is constructed on the actually measured power data under different space-time scales.
FIG. 4 is a wind power fluctuation probability distribution diagram of the present invention and the comparative model at different time scales in the present embodiment. As shown in fig. 4, the mixed Laplace distribution model of the invention has higher accuracy on different time scales than other models, and can accurately reflect the heavy tail characteristics of distribution, so that the mixed Laplace distribution model is suitable for the wind power fluctuation rule description of different time scales.
FIG. 5 is a wind power fluctuation probability distribution diagram of the present invention and the comparative model at different spatial scales in the present embodiment. As shown in fig. 5, the hybrid Laplace distribution model can also be accurately fitted for wind power fluctuation distribution of different spatial scales.
In conclusion, the wind power fluctuation amount probability distribution model based on the mixed Laplace distribution can accurately describe the wind power fluctuation rule under different space-time scales.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.
Claims (3)
1. A wind power fluctuation amount probability distribution model building method based on mixed Laplace distribution is characterized by comprising the following steps:
s1: calculating a wind power fluctuation quantity sequence P [ P ] according to wind power data measured in a wind power plant and a preset time scale delta t1,p2,p3,…,pM]TWherein M represents the dimension of the wind power fluctuation quantity sequence;
s2: constructing a mixed Laplace distribution model:
<mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>P</mi> <mo>|</mo> <mi>&alpha;</mi> <mo>,</mo> <mi>&mu;</mi> <mo>,</mo> <mi>&delta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>&alpha;</mi> <mi>i</mi> </msub> <msub> <mi>f</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>p</mi> <mo>|</mo> <msub> <mi>&mu;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&delta;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow>
wherein α ═ { α ═ c1,α2,…,αNDenotes a set of weight parameters, αiIs the weight of the ith Laplace distribution, andμ＝{μ1,μ2,…,μNdenotes the mean parameter set, μiRepresenting the sequence variance of the fluctuation quantity of the wind power in the ith Laplace distribution; δ ═ δ1,δ2,…,δNDenotes the variance parameter set, δiRepresenting the mean value of the sequence of fluctuation quantity of the wind power in the ith Laplace distribution; n is the number of Laplace distributions, and N is more than 1; f. ofi(p|μi,δi) A probability density function representing the ith single Laplace distribution;
s3: according to the wind power fluctuation quantity sequence P ═ P1,p2,p3,…,pM]TSolving the mixed Laplace distribution model obtained in the step S2 to obtain a weight parameter set α, a mean parameter set mu and a variance parameter set delta, so as to obtain a probability distribution model of the wind power fluctuation quantity, wherein the solving method of the mixed Laplace distribution model comprises the following steps:
s3.1: making the solving times d equal to 1;
s3.2: initializing a set of weight parametersMean parameter setSum variance parameter setMaking the iteration number t equal to 1;
s3.3: for wind power fluctuation sequence P ═ P1,p2,p3,…pM]TEach fluctuation amount p injCalculating the posterior probability generated by the kth Laplace distribution in the t iterationThe calculation formula is as follows:
<mrow> <msubsup> <mi>&eta;</mi> <mi>k</mi> <mi>t</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>&alpha;</mi> <mi>k</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>|</mo> <msubsup> <mi>&mu;</mi> <mi>k</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>&delta;</mi> <mi>k</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> </mrow> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msubsup> <mi>&alpha;</mi> <mi>i</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>|</mo> <msubsup> <mi>&mu;</mi> <mi>i</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>&delta;</mi> <mi>i</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>
wherein k is 1,2, …, N;
s3.4: respectively calculating parameters of each Laplace distribution:
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>&mu;</mi> <mi>k</mi> <mi>t</mi> </msubsup> <mo>=</mo> <mfrac> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msubsup> <mi>&eta;</mi> <mi>k</mi> <mi>t</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>p</mi> <mi>j</mi> </msub> </mrow> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msubsup> <mi>&eta;</mi> <mi>k</mi> <mi>t</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>&alpha;</mi> <mi>k</mi> <mi>t</mi> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mi>M</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msubsup> <mi>&eta;</mi> <mi>k</mi> <mi>t</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>&delta;</mi> <mi>k</mi> <mi>t</mi> </msubsup> <mo>=</mo> <msqrt> <mn>2</mn> </msqrt> <mfrac> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msubsup> <mi>&eta;</mi> <mi>k</mi> <mi>t</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>|</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>-</mo> <msubsup> <mi>&mu;</mi> <mi>k</mi> <mi>t</mi> </msubsup> <mo>|</mo> </mrow> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msubsup> <mi>&eta;</mi> <mi>k</mi> <mi>t</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced>
s3.5: if it is not|Θt-Θt-1| < epsilon, wherein thetat、Θt-1Respectively representing parameter set vectors obtained by the t-th iteration and the t-1-th iteration, wherein epsilon represents a preset error threshold value to obtain parameters of the hybrid Laplace distribution model solved at this time, otherwise, making t equal to t +1, and returning to the step S3.3;
s3.6: and if D is less than D, making D equal to D +1, returning to the step S3.2, otherwise, averaging the parameters of the mixed Laplace distribution model obtained by the D times of solution, and taking the average value as the parameters of the final mixed Laplace distribution model.
2. The method for establishing the wind power fluctuation amount probability distribution model according to claim 1, wherein the wind power fluctuation amount in step S1 is calculated by:
pt＝lnP(t+Δt)-lnP(t)
wherein p istAnd the wind power fluctuation quantity at the moment t is represented, and P (t + delta t) and P (t) respectively represent the wind power at the moment t + delta t and the moment t.
3. The method for establishing the wind power fluctuation amount probability distribution model according to claim 1, wherein the value range of the number N of Laplace distributions in the step S2 is 2-5.
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