CN113343491A - Random scene analysis method considering time sequence autocorrelation and cross correlation - Google Patents
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Abstract
The invention relates to the field of random scene analysis methods, in particular to a random scene analysis method considering time sequence autocorrelation and cross correlation, and provides the following scheme, which comprises the following steps: sampling annual time sequence data of each uncertainty factor of a target area according to a probability model of each uncertainty factor to obtain an initial uncertainty factor time sequence, performing time sequence reconstruction on the initial uncertainty factor time sequence according to the autocorrelation of the initial uncertainty factor time sequence to generate an uncertainty factor random time sequence considering the time sequence autocorrelation, combining the uncertainty factor random time sequences to form a first random scene set considering the time sequence autocorrelation, and obtaining a second random scene set considering the time sequence autocorrelation and the cross correlation. The scene set generated by the invention can completely express the characteristics of historical data with less data volume, and provides data support for solving the problem of optimizing, planning and operating the power system containing renewable energy.
Description
Technical Field
The invention relates to the field of random scene analysis methods, in particular to a random scene analysis method considering time sequence autocorrelation and cross correlation.
Background
With the renewable energy grid connection, due to the access of uncertain energy including photovoltaic or wind power, the long-term planning, medium-term operation and short-term scheduling problems of the power system become uncertain optimization problems, and scene analysis is a mode for analyzing the uncertain problems of the power system by constructing a deterministic scene, and is an effective way for solving the problems of the optimized planning and operation of the power system containing the renewable energy.
At present, the research on scene analysis methods at home and abroad mainly obtains a scene capable of describing the uncertainty characteristics of an object by sampling according to the statistical characteristics of the object to be researched and adopting a certain method, wherein common sampling methods generally comprise a Monte Carlo sampling method, a Latin hypercube sampling method, a Gibbs sampling method and the like, and because random sampling can not reflect the self time sequence correlation of a long-time sequence and the cross correlation among multi-dimensional sequences, the initial random time sequence generally needs to be processed. Aiming at the processing of time sequence autocorrelation, mainly adopted modeling methods include a time sequence analysis method based on a Markov chain model, a time sequence analysis method based on an autoregressive moving average (ARMA) and the like, aiming at the processing of multidimensional sequence cross correlation, the mainly adopted method is a Copula function method, after an initial scene is generated by the existing scene analysis method, a large number of initial scenes generally need to be reduced, a small number of scenes capable of representing the characteristics of the initial scene are obtained, and the purpose of reducing the operation amount under the condition of ensuring the solution accuracy of an optimization model is achieved, and the currently common methods generally include two types: one is empirical subtraction, which is commonly known as a typical daily method, and the other is to combine and reduce an initial scene through a mathematical algorithm to obtain a typical scene, which commonly includes backward subtraction, forward subtraction, a scene tree construction method, a cluster analysis method, and the like.
At present, the research mainly carries out scene analysis on uncertainty factors from different angles, however, the research on the scene analysis which comprehensively considers the self time sequence correlation of each uncertainty factor and the cross correlation among the uncertainty factors is not deep enough, the calculation efficiency is low, and certain difficulty is brought to the optimized planning operation of the power system.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a random scene analysis method considering time sequence autocorrelation and cross-correlation.
In order to achieve the purpose, the invention adopts the following technical scheme:
a random scene analysis method considering time sequence autocorrelation and cross correlation comprises the following steps:
sampling annual time sequence data of all uncertainty factors of a target area according to the probability model of all uncertainty factors to obtain an initial uncertainty factor time sequence;
establishing a reference time sequence, and performing time sequence reconstruction on the initial uncertainty factor time sequence according to the autocorrelation of the initial uncertainty factor time sequence to generate an uncertainty factor random time sequence considering the time sequence autocorrelation;
combining uncertainty factor random time sequences to form a first random scene set considering time sequence autocorrelation;
and establishing a cross-correlation coefficient matrix according to the cross-correlation among the uncertainty factor time sequences, selecting at least one random scene with the minimum cross-correlation error between the cross-correlation and the reference time sequence from the first random scene set, and obtaining a second random scene set considering the time sequence self-correlation and the cross-correlation.
Further, the step of establishing the reference timing sequence includes: and dividing and processing the annual time sequence data of each uncertainty factor according to different seasons, and respectively selecting a one-day time sequence closest to the average daily variation time sequence of each seasonal uncertainty factor as a reference time sequence.
Further, the sampling method comprises a Latin hypercube sampling method.
Further, the method of combining uncertainty factor random timing includes a cartesian product method.
Further, the method also comprises analyzing the cross correlation between the uncertainty factor time sequences by using a Spearman rank correlation coefficient.
Further, the probability model of uncertainty factors includes:
f (v (t), a (t), b (t)), wherein f is a probability density function of each uncertainty factor, v (t) is the magnitude of each uncertainty factor value at time t, and a (t) and b (t) are scale parameters and shape parameters of each uncertainty factor at time t.
Further, the time sequence reconstruction criterion is to minimize the average absolute error of each reconstructed uncertainty factor fluctuation sequence and the reference fluctuation sequence.
Further, the cross-correlation error comprises:
A storage medium having stored thereon a computer program which, when executed, implements the above-described method.
The invention has the beneficial effects that:
the invention takes the autocorrelation and the cross correlation of a time sequence of regional uncertainty factors as research objects, provides a random scene analysis method considering the time sequence autocorrelation and the cross correlation, utilizes Latin hypercube sampling to initialize the random time sequence of each uncertainty factor, then utilizes a time sequence reconstruction method to improve the autocorrelation, utilizes Cartesian product combination, and finally utilizes a Spearman cross correlation coefficient matrix to select, finally obtains a random scene set considering the time sequence autocorrelation and the cross correlation, the generated scene set can completely express the characteristics of historical data with less data quantity, provides data support for solving the optimization planning operation problem of a power system containing renewable energy, and simultaneously, simulation results show that the wind speed and the illumination time sequence generated by the random scene analysis method considering the time sequence autocorrelation and the cross correlation can more reasonably reflect the change characteristics of wind and light, the selected random scene can better meet the actual situation.
Drawings
FIG. 1 is a flow chart of a method for stochastic scene analysis with consideration of timing auto-correlation and cross-correlation in an embodiment of the invention;
FIG. 2 is a time sequence of annual wind speeds in accordance with an embodiment of the present invention;
FIG. 3 is a time sequence of annual illumination in accordance with an embodiment of the present invention;
FIG. 4 is a typical daily time sequence for wind speed spring in accordance with an embodiment of the present invention;
FIG. 5 is a typical spring time sequence of illumination in accordance with an embodiment of the present invention;
FIG. 6 is a spring time sequence of random wind speed considering time sequence autocorrelation according to an embodiment of the present invention;
FIG. 7 is a diagram illustrating a random illumination spring time sequence with consideration of time sequence autocorrelation according to an embodiment of the present invention;
FIG. 8 is a stochastic scenario in which timing auto-correlation and cross-correlation are considered in an 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.
Referring to fig. 1 to 8, a stochastic scene analysis method considering temporal auto-correlation and cross-correlation, comprising the steps of:
the autocorrelation refers to the correlation degree between different time values in a time sequence;
the cross correlation refers to the correlation degree between different time sequences;
s1: acquiring annual time sequence data of uncertainty factors in a certain area, and preprocessing the data to form an uncertainty factor time sequence of typical days of each season in a real scene as a reference time sequence;
the annual time sequence data comprise annual historical data or planning data, the annual historical data mainly refer to wind speed, illumination and the like, and the historical data are generally used as original data;
the annual planning data mainly refers to loads, generally refers to planning data as original data, can also refer to historical data, and refers to acquired original data, specifically refers to an annual time sequence formed by 8760 data points by taking 1h as a unit;
the uncertainty factors comprise wind speed, illumination intensity or load and the like;
the typical day is the day closest to the average daily variation curve of each season uncertainty factor;
acquiring probability models of all uncertainty factors, sampling by using a Latin hypercube sampling method, and initializing random time sequences of all uncertainty factors;
the data preprocessing in step S1 includes the following steps, for example:
s1.1: let a local uncertainty factor, e.g. wind speed, light intensity and load, and annual historical or planning data value be xi(tn)(i＝1,2,…,k；tn＝t1,t2,…,tp) Where i represents the uncertainty factor type, tnAnd representing time, wherein the uncertainty factor matrix under the real scene is as follows:
s1.2: dividing the annual time sequence data of the uncertain factors in the real scene into four seasons of spring, summer, autumn and winter for processing, respectively selecting a day time sequence closest to the average daily variation time sequence of the uncertain factors in each season, namely a typical day, and forming an uncertain factor time sequence of the typical day in each season in the real scene as a reference time sequence, wherein in some embodiments, the specific process comprises the following steps:
1) calculating the average daily variation time sequence of each uncertainty factor in four seasons of spring, summer, autumn and winter under a real scene, and expressing the time sequence as follows:
in the formula (2), Li,s(t) represents the average daily variation time sequence of the ith uncertainty factor in the s season under a real scene; n is a radical ofsRepresents the total number of days of the s-th season;
2) selecting the time sequence L of the average daily variation of the uncertainty factors of each season by taking the time-to-time deviation and the minimum as the targetsi,s(t) timing of the closest day X'i,s,n(t), forming uncertainty factor time series of typical days of each season in a real scene as a reference time sequence, wherein the calculation method of the time-by-time deviation sum comprises the following steps:
in the formula (3), Li,s(t) represents the average daily variation time sequence of the ith uncertainty factor in the s season under a real scene; xi,s,n(t) represents the time sequence of the nth day of the s season of the ith uncertainty factor in the real scene;
the step S1 of obtaining the probability model of each uncertainty factor, sampling by utilizing a Latin hypercube sampling method, and initializing the random time sequence of each uncertainty factor comprises the following steps:
s1.3: obtaining a probability model of each uncertainty factor, wherein the probability model can be expressed as:
f＝f(v(t),a(t),b(t)) (4)
in the formula (4), f is a probability density function of each uncertainty factor, v (t) is the numerical value of each uncertainty factor at the time t, and a (t) and b (t) are a scale parameter and a shape parameter of each uncertainty factor at the time t;
each uncertain factor obeys a distribution, the general wind speed obeys weibull distribution, the illumination obeys beta distribution and the like, and the formula (4) is used for summarizing the distributions, and the distributions are sampled by using a Latin hypercube sampling method to form an initial sample;
wind speed is generally considered to follow the Weibull distribution, the probability density function of which can be represented by:
v(t)≥0；
wherein v (t) represents the actual wind speed at time t, a (t) and b (t) are respectively the scale parameter and the shape parameter at time t, σ (t) represents the standard deviation of the wind speed at time t,
representing the mean value of the wind speed at the moment t;
② generally, the illumination intensity is considered to obey the beta distribution, and the probability density function thereof can be represented by the following formula:
where g (t) represents the illumination intensity per unit value at time t, α (t) and β (t) represent shape parameters both of which are positive values at time t, and μ (t) and σ (t) represent the illumination intensity mean per unit value and standard deviation at time t.
S1.4: sampling by utilizing a Latin hypercube sampling method, initializing random time sequences of all uncertainty factors, and in some embodiments, comprising the following steps:
1) determining the number N of samples to be extracted;
2) equally dividing the interval (0, 1) into N sections;
3) randomly extracting a value in each of the N segments;
4) and mapping the extracted value by an inverse function to obtain a random sampling sample.
S2: considering autocorrelation inside each uncertainty factor time sequence, performing time sequence reconstruction on the initial random scene set, and further generating each uncertainty factor random time sequence considering the time sequence autocorrelation, in some embodiments, the method includes the following steps:
s2.1: performing first-order difference calculation on the uncertainty factor time sequence (namely, transverse vector) of each season typical day in the real scene in the step S1 to serve as a reference fluctuation sequence of each season uncertainty factor;
s2.2: reconstructing the order of the column vectors in the random time sequence of each initial uncertainty factor generated by Latin hypercube sampling in the step S2, wherein the time sequence reconstruction criterion is to minimize the average absolute error of each reconstructed uncertainty factor fluctuation sequence and the reference fluctuation sequence, and the calculation method comprises the following steps:
in the formula (5), EMAEIs the mean absolute error; ei,s(t) and E* i,s(t) a wave sequence and a reference wave sequence of the ith uncertainty factor in the s-th season, respectively;
thus, random timings can be generated that take into account uncertainty factors of timing autocorrelation.
S3: combining the uncertainty factor random time sequences by using a Cartesian product method to form a random scene set considering the time sequence autocorrelation, wherein in some embodiments, the method comprises the following steps:
s3.1: because the time sequence values of all uncertainty factors are mutually independent, the thought based on the Cartesian product combines random time sequences of all uncertainty factors to form a random scene set considering the time sequence autocorrelation.
S4: analyzing the cross correlation among the time sequences of all uncertainty factors by using a Spearman rank correlation coefficient, establishing a cross correlation coefficient matrix, selecting N random scenes with the minimum error between the cross correlation and the target cross correlation from the random scene sets, and finally obtaining the random scene set considering the time sequence auto-correlation and the cross correlation, wherein in some embodiments, the method comprises the following steps:
s4.1: spearman rank correlation coefficients are introduced to characterize the temporal cross-correlation, describing the correlation between time-series of different uncertainty factors, and the Spearman rank correlation coefficient between the time-series X, Y of two uncertainty factors can be expressed as:
in the formula (6), diIs the difference of the rank of two random variables;
s4.2: calculating a cross-correlation coefficient matrix of the reference time sequence obtained in step S1 and a cross-correlation coefficient matrix of the random scene set obtained in step S3, wherein the cross-correlation coefficient matrix among the k uncertainty factor time series can be represented as:
s4.3: selecting N random scenes with the optimal cross-correlation from the random scene set obtained in step S4, and finally forming a random scene set considering the time sequence auto-correlation and the cross-correlation, wherein the selection principle is to select N random scenes that minimize the cross-correlation error between each uncertainty factor and the reference time sequence obtained in step S1, and the cross-correlation error can be expressed as:
in the formula (8), Eh,sThe cross correlation error of the h-th random scene and the reference scene in the s-th season is obtained; rhoh,sIs the cross-correlation coefficient matrix, rho, of the h-th random scene in the s-th seasonref,sThe cross-correlation coefficient matrix of the reference timing obtained in step S1.
Taking the actual annual wind speed and illumination intensity time sequence of a certain area as an example, the random scene analysis method considering the time sequence autocorrelation and the cross correlation is applied to construct a new energy typical scene set;
fig. 2 and 3 show wind speed and light intensity data from 1/2015 to 31/2015 in 12/2015 in the area, and considering that both the wind speed and the light intensity have periodicity related to seasons, samples of the wind speed and the light intensity data are first divided into spring, summer, autumn and winter to be considered, and the present embodiment is described by taking spring as an example;
through data preprocessing, fig. 4 and 5 can be obtained, which are respectively the typical day time sequences of wind speed and illumination in spring in the specific embodiment of the present invention, and then fig. 6 and 7 can be obtained through latin hypercube sampling and time sequence reconstruction, which are respectively the random wind speed and illumination spring time sequences considering time sequence autocorrelation in the specific embodiment of the present invention;
finally, 5 groups of random scenes with optimal cross-correlation are selected by combining through a Cartesian product method and optimizing the cross-correlation, and a graph 8 can be obtained, namely, the random scene set considering the time sequence self-correlation and the cross-correlation in the embodiment.
In order to prove the reasonability of the random scene analysis method considering the time sequence autocorrelation and the cross correlation, the method provided by the invention, a Monte Carlo random scene generation method and a Monte Carlo + Kmeans clustering random scene generation and reduction method are respectively adopted for comparison and analysis;
the typical time sequence of spring of wind speed and illumination is used as a comparison reference, and error pairs of three scene analysis methods are obtained, wherein the error pairs are shown in a table 1:
TABLE 1 error comparison of three scene analysis methods
It can be seen that the wind speed and the illumination time sequence generated by the random scene analysis method considering the time sequence autocorrelation and the cross correlation are greatly reduced in average time sequence autocorrelation error compared with other two methods, so that the method provided by the invention can more reasonably reflect the change characteristics of wind and light; meanwhile, compared with the other two methods, the average cross correlation error of the final random scene set selected by the method provided by the invention is greatly reduced, so that the random scene generated by the method provided by the invention can better accord with the actual situation and has practical application value.
The present invention also proposes a storage medium having stored thereon a computer program which, when executed, implements the above-described method.
The invention takes the autocorrelation and the cross correlation of a time sequence of regional uncertainty factors as research objects, provides a random scene analysis method considering the time sequence autocorrelation and the cross correlation, utilizes Latin hypercube sampling to initialize the random time sequence of each uncertainty factor, then utilizes a time sequence reconstruction method to improve the autocorrelation, utilizes Cartesian product combination, and finally utilizes a Spearman cross correlation coefficient matrix to select, finally obtains a random scene set considering the time sequence autocorrelation and the cross correlation, the generated scene set can completely express the characteristics of historical data with less data quantity, provides data support for solving the optimization planning operation problem of a power system containing renewable energy, and simultaneously, simulation results show that the wind speed and the illumination time sequence generated by the random scene analysis method considering the time sequence autocorrelation and the cross correlation can more reasonably reflect the change characteristics of wind and light, the selected random scene can better meet the actual situation.
In the description of the present invention, it is to be understood that the terms "first", "second" and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implying any number of technical features indicated.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.
Claims (9)
1. A random scene analysis method is characterized by comprising the following steps:
sampling annual time sequence data of all uncertainty factors of a target area according to the probability model of all uncertainty factors to obtain an initial uncertainty factor time sequence;
establishing a reference time sequence, and performing time sequence reconstruction on the initial uncertainty factor time sequence according to the autocorrelation of the initial uncertainty factor time sequence to generate an uncertainty factor random time sequence considering the time sequence autocorrelation;
combining uncertainty factor random time sequences to form a first random scene set considering time sequence autocorrelation;
and establishing a cross-correlation coefficient matrix according to the cross-correlation among the uncertainty factor time sequences, selecting at least one random scene with the minimum cross-correlation error between the cross-correlation and the reference time sequence from the first random scene set, and obtaining a second random scene set considering the time sequence self-correlation and the cross-correlation.
2. The method of claim 1, wherein the step of establishing the reference timing sequence comprises: and dividing and processing the annual time sequence data of each uncertainty factor according to different seasons, and respectively selecting a one-day time sequence closest to the average daily variation time sequence of each seasonal uncertainty factor as a reference time sequence.
3. A method for stochastic scene analysis according to claim 1, wherein the sampling comprises latin hypercube sampling.
4. A stochastic scene analysis method according to claim 1, wherein the method of combining uncertainty factor stochastic timing comprises cartesian product method.
5. A stochastic scene analysis method as claimed in claim 1, further comprising using Spearman rank correlation to analyse cross-correlation between uncertainty factor sequences.
6. The stochastic scene analysis method of claim 1, wherein the probabilistic model of uncertainty factors comprises:
f (v (t), a (t), b (t)), wherein f is a probability density function of each uncertainty factor, v (t) is the magnitude of each uncertainty factor value at time t, and a (t) and b (t) are scale parameters and shape parameters of each uncertainty factor at time t.
7. The stochastic scene analysis method of claim 1, wherein the time sequence reconstruction criterion is to minimize an average absolute error between each reconstructed uncertainty factor fluctuation sequence and a reference fluctuation sequence.
8. A stochastic scene analysis method according to claim 2, wherein the cross-correlation error comprises:
9. A storage medium having stored thereon a computer program which, when executed, implements the method of any one of claims 1 to 8.
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