CN113449471B - Wind power output simulation generation method for continuously improving MC (multi-channel) by utilizing AP (access point) clustering-skipping - Google Patents
Wind power output simulation generation method for continuously improving MC (multi-channel) by utilizing AP (access point) clustering-skipping Download PDFInfo
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Abstract
A wind power output simulation generation method utilizing AP clustering-skipping to continuously improve MC is characterized in that AP clustering is carried out on historical wind power output data, state transition matrixes of clustered wind power output are respectively established, and the state transition matrixes are converted into state skipping matrixes; forming a wind power output state skip sequence meeting the state skip characteristic based on the Markov chain; according to the wind power output state duration characteristic, fitting a wind power output state duration distribution histogram by adopting nuclear density estimation, and sampling to determine the duration of each state in a state skip sequence to obtain a wind power output state time sequence; the wind power output fluctuation quantity probability density distribution is fitted by adopting mixed Gaussian distribution, and the fluctuation components which accord with the mixed Gaussian distribution are superposed in the process of simulating and generating the wind power output so as to ensure the fluctuation characteristic of the wind power output; and generating a wind power output time sequence based on inter-class transfer matrix simulation. The method has the advantages of strong practicability, higher precision, better simulation effect and the like.
Description
Technical Field
The invention relates to the field of wind power output time sequence simulation generation in wind power grid-connected power system planning, in particular to a wind power output simulation generation method for continuously improving MC (media card) by utilizing AP (access point) clustering-skipping.
Background
In the prior art, wind power output time sequence simulation generation methods are mainly divided into a wind speed method and a wind power method according to different research objects.
The wind speed method firstly simulates and generates a wind speed time sequence, and then converts the wind speed time sequence into a wind power output time sequence through an energy conversion model. The wind speed method can avoid errors caused by the phenomenon of wind abandon in the operation process of a power grid, and an energy conversion model is complex and is easily influenced by the characteristics of a unit. The wind power method directly utilizes the historical measured data to establish a wind power output time series model without an energy conversion process, thereby avoiding errors in the process. The wind power method can better simulate and generate a wind power output time sequence, but the wind power output time sequence is easy to fall into a certain state and is difficult to jump when the time sequence is generated, and the problem of strong subjectivity exists in category division.
In conclusion, the wind power output simulation generation method for continuously improving MC by utilizing AP clustering-skipping is provided by comprehensively considering wind power output daily statistical characteristics, state transition characteristics, time domain characteristics and fluctuation characteristics.
Disclosure of Invention
The invention aims to provide a wind power output simulation generation method for continuously improving MC (multi-channel) by utilizing AP (access point) clustering-skipping, which has the advantages of strong practicability, higher precision and better simulation effect.
The technical scheme adopted for realizing the aim of the invention is that a wind power output simulation generation method for continuously improving MC by utilizing AP clustering-skipping is characterized by comprising the following steps: the method comprises the following steps of carrying out AP clustering on historical wind power output data, forming a wind power output state skip sequence under a certain clustering category, forming a wind power output state time sequence with the time sequence length of one day under a certain clustering category, sampling and superposing the wind power output fluctuation quantity on a primary wind power output time sequence formed under a certain clustering category, and generating a wind power output time sequence according to inter-category transfer probability matrix simulation, wherein the specific content is as follows:
1) AP clustering is carried out on historical wind power output data
An Affinity Propagation (AP) clustering algorithm is an unsupervised clustering algorithm based on "information transfer"; firstly, establishing a similarity matrix S of a sample set as formula (1), wherein elements S in the matrix are a,b Represents a sample x a And x b The similarity between the two is expressed by negative Euclidean distance and is expressed as formula (2); s a,a The reference degree of the clustering center is used as a judgment standard for judging whether the clustering center can be formed, a deviation parameter is set at the beginning, the deviation parameter directly influences the number of final clusters, and the larger the value of the deviation coefficient is, the more clusters are generated; constructing a vector capable of reflecting the characteristics of the corresponding solar wind power output according to the daily mean value and the daily minimum value of the actually measured historical wind power output at a set sampling interval in a unit time period, and carrying out AP clustering on the historical wind power output by using the vector in a day unit, wherein: the unit time period generally refers to month, season, year and years; the sampling interval is typically 1 minute, 5 minutes or 10 minutes;
S a,b ＝-||x a －x b || 2 (2)
in the formula: s is a similarity matrix of the sample set; s a,b Represents a sample x a And x b The similarity between them; s a,a The reference degree of the clustering center; x is the number of a And x b Are data sample points; a is 1,2, … …, n; b is 1,2, … …, n; n is the total number of samples used for AP clustering; | | x a -x b || 2 Denotes x a And x b The Euclidean distance between;
similarity of sample setsThe matrix S is used as input, and then the attraction r (x) of each sample point is calculated a ,x k ) Degree of affiliation a (x) a ,x k )；r(x a ,x k ) Denotes x k Whether a point is suitable as x a The cluster center of the points, i.e. x k For x a The degree of attraction of (c); a (x) a ,x k ) Represents x a Whether a point selects x or not k As its clustering center, i.e. x a For x k Degree of attribution of; r (x) a ,x k ) And a (x) a ,x k ) The larger the size, the more indicative of x k The more suitable as a clustering center; continuously updating the attraction degree matrix and the attribution degree matrix in the clustering process, and introducing a damping coefficient for avoiding oscillation in the iteration process until stable clustering centers and class attribution conditions are generated in the iteration process; thus, near the end of propagation, x a Is determined as x k (ii) a Wherein x is k Is represented by the formula (3):
x k ＝argmax{a(x a ,x k )+r(x a ,x k )} (3)
in the formula: argmax is the argument for finding the maximum function, i.e. x k To satisfy { a (x) } a ,x k )+r(x a ,x k ) Taking the value of the maximum value; a (x) a ,x k ) Is a sample point x a For sample point x k Degree of attribution of; r (x) a ,x k ) Is a sample point x k For sample point x a The degree of attraction of (c); x is the number of k And x a Are data sample points; k is 1,2, … …, n; a is 1,2, … …, n; n is the total number of samples used for AP clustering;
adopting a contour Coefficient (SC) as a clustering evaluation index; the larger the contour coefficient is, the better the clustering effect is; contour coefficient SC (x) k ) Defined by formulae (4) to (6):
in the formula: x is the number of k ，x a ，x b Is a data sample point; c (x) k ) Represents a sample point x k The cluster category to which it belongs; c (x) a ) Represents a sample point x a The cluster category to which it belongs; c (x) b ) Represents a sample point x b The cluster category to which it belongs; contour coefficient SC (x) k ) Has a value of [ -1,1 [)]Reflect x k Average distance I (x) between cluster center and sample in class when serving as cluster center k ) Whether it is significantly different from its average distance O (x) to the out-of-class sample k )；I(x k ) Representing the average distance between the clustering center and the samples in the class; d (x) k ,x a ) Represents a sample point x k And x a The distance between them; m represents the sum of sample point x k The number of data points belonging to the same category; o (x) k ) Representing the average distance between the cluster center and the sample outside the cluster; d (x) k ,x b ) Represents a sample point x k And x b The distance between them; g represents the sum of sample point x k The number of data points not belonging to the same category;
by carrying out AP clustering on historical wind power output data in units of days, the solar wind power output sequences with output levels similar to fluctuation characteristics can be classified into the same class;
2) forming a wind power output state skip sequence under a certain cluster category
The historical wind power output data is expressed as (P) m ′ in ，P m ′ ax ) Evenly dividing the data into N data segments, wherein each data segment corresponds to one state, and the wind power output range corresponding to each state is (P) m ′ ax -P m ′ in ) N; wherein, P m ′ in Is the minimum value of historical wind power output, P m ′ ax The output is the maximum value of the historical wind power, and N is a state number; wind power generation output aiming at traditional Markov chainThe force sequence is easy to fall into a certain state and is difficult to jump, so that the generated wind power output time sequence possibly has the condition of overlong duration time in a certain state, and the improvement is carried out by adopting a state jump matrix to replace a state transition matrix;
when a state transition matrix is generated by a clustering reconstruction sequence, when the jump amplitude of the state number between two adjacent data is larger than 1/3 of the divided state number, the transition is considered to be not practical, the value of the state transition matrix is set to zero, and an improved state transition matrix is obtained;
secondly, setting all diagonal elements of the obtained state transition matrix to zero, calculating the proportion of each element in the sum of all elements of the row, and taking the proportion as a new probability value, wherein the obtained probability matrix is a state jump matrix; the state hopping matrix is of equations (7) - (8);
p ij ＝P(E t+1 ＝j|E t ＝i) (8)
in the formula: the matrix P is a state jump matrix; the row of the matrix P corresponds to the current output state of the wind power output, and the column corresponds to the output state at the next moment; n is the number of states; i and j are wind power output states; 1,2, … …, N; j ═ 1,2, … …, N; p is a radical of ij Representing the probability of the wind power output transferring from the state i to the state j; e t 、E t+1 The wind power output values at the t moment and the t +1 moment are in corresponding states; p (a | B) is a conditional probability function representing the probability of a occurring under the condition of B;
the corresponding accumulated state transition matrix is of formula (9):
the value of the element in Q is shown as formula (10):
in the formula: the matrix Q is an accumulated state jump matrix; q. q.s ul Jumping to the element of the u row and l column in the matrix Q for the accumulated state; p is a radical of uj The elements of the u-th row and the j-th column in the state jump matrix P; n is the number of states; 1,2, … …, N; 1,2, … …, N; j ═ 1,2, … …, N;
through the forming process of the accumulative state jump matrix Q, an accumulative state jump matrix under a certain cluster category, namely an intra-category accumulative state jump matrix, is obtained; then, sampling to form a state jump sequence under each cluster category according to the intra-category accumulated state jump matrix; under the cluster category, the state of the wind power output at the current moment is E t The state at the next time is E t+1 Generating random number xi following uniform distribution, if 0<ξ≤q Et,1 Then E is t+1 1 is ═ 1; if q is Et,l <ξ≤q Et,l+1 Then E is t+1 L +1, wherein q Et,1 E < th > representing intra-class accumulated state transition matrix Q t Row, column 1 elements; q. q.s Et,l E < th > representing intra-class accumulated state transition matrix Q t Row, column I elements; q. q.s Et,l+1 E < th > representing an intra-class accumulated state transition matrix Q t Row, column l + 1;
since the diagonal elements of the state-hopping matrix are zero, the diagonal elements in the corresponding intra-class accumulated state-hopping matrix are equal to the left elements, i.e., q i,i-1 Is equal to q ii So [ q ] i,i-1 ,q ii ]For an empty set, when a wind power output state sequence is generated by using a Markov chain method, xi does not fall to [ q ] i,i-1 ,q ii ]Within the range; wherein q is ii The elements in the ith row and ith column in the intra-class accumulated state jump matrix Q are represented by i, which is 1,2, … …, N; q. q of i,i-1 Jumping to the ith row and the (i-1) th column in the matrix Q for the accumulated state;
through the steps, a state skip sequence with different adjacent states when the wind power output is in a certain clustering category can be formed by sampling according to the intra-class accumulated state skip matrix in the clustering category;
3) forming a wind power output state time sequence with the time sequence length of one day under a certain cluster category
According to the method, the historical wind power output time sequence is traversed by a statistical method of recording the duration time T once from the first moment when the wind power output enters a certain state, and if the duration time is T, the times of occurrence of each duration time of the wind power output in the state are counted to obtain the distribution condition of the duration time in the state;
after a distribution histogram of the duration time of a certain state of the wind power output is obtained through statistics and drawing, a smooth curve is adopted to describe the histogram, so that the particularity existing in sampling the histogram can be avoided; when describing data distribution characteristics, Kernel Density Estimation (KDE) does not depend on the selection of a parameter Estimation model, and can effectively avoid the dependence of histogram Estimation on the group distance and the position of a histogram, so that the KDE is adopted to describe the distribution characteristics of the duration time of the wind power output state; KDE expression is formula (11):
in the formula:
a kernel density estimation function for the duration of the wind power output state; k (-) is a kernel function; h is the bandwidth; x is a radical of a fluorine atom 1 ,x 2 ,……,x W The data number is W, and the data number represents each duration value of the wind power output sequence in a certain state; x is the number of w The W-th sample value of the duration time of the wind power output state is 1,2, … … and W; w represents that W different durations of the wind power output sequence appear in a certain state;
in KDE, the selection of bandwidth determines the smoothness degree of a fitting curve, the larger the bandwidth is, the smoother the bandwidth is, but the poorer the fitting effect is; selecting a Gaussian function as a kernel function, and solving the bandwidth by adopting an empirical rule, wherein the formula is as follows (12):
h＝1.06σW -1/5 (12)
in the formula: h is the bandwidth; sigma is the normal distribution standard deviation of the duration time of the wind power output state; w represents that W different durations of the wind power output sequence appear in a certain state;
in order to obtain the state time sequence of the wind power output with the time sequence length of one day under a certain cluster category, after a random number set meeting the duration time of each state of a kernel density estimation function is generated, traversing the obtained wind power output state jump sequence under the cluster category, and repeatedly sampling: the current state is E t Then in state E t Is arbitrarily chosen as a value in the set of duration random numbers of (a) as state E t The time duration is repeated until the length of the generated time sequence meets the requirement;
4) sampling and superposing wind power output fluctuation quantity on a preliminary wind power output time sequence formed under a certain cluster category
After a wind power output state time sequence under a certain cluster category is formed, determining the initial wind power output at each moment; the current state of wind power output is E t Then the preliminary wind power output P 'at the moment can be randomly generated' t·cb Numerical value of (1), P' t·cb ∈(P Et.min ，P Et.max )，P Et.min 、P Et.max Are respectively in state E t The minimum value and the maximum value of the corresponding wind power output range;
the wind power output fluctuation refers to the difference of output values at adjacent moments, and the fluctuation characteristic is described by adopting a first-order differential fluctuation quantity, namely the output difference value in adjacent 2 unit times; the first-order difference fluctuation quantity expression of the wind power output is as shown in formula (13):
ΔP t ′＝P′ t+1 -P t ′ (13)
in the formula: t represents the wind power output moment; delta P t ' represents the fluctuation amount of wind power output at the moment t; p t 'and P' t+1 Respectively representing wind power output values at the time t and the time t + 1;
the probability density distribution fitting function of the first-order difference fluctuation quantity of the wind power output is as follows: normal distribution, t-location-scale distribution and logistic distribution; the wind power output fluctuation characteristic is depicted by using mixed Gaussian distribution with better fitting precision, the probability density function is the weight of a plurality of Gaussian probability density functions, when the data distribution is complex, the mixed Gaussian distribution function can overcome the defect of fitting precision of a single Gaussian distribution function, and the mathematical model expression is as formulas (14) - (15):
in the formula: (x) is a Gaussian mixture distribution function; v ═ 1,2, … …, V; v is the number of single Gaussian distributions in the mixed Gaussian distribution; a is v Is the mixing coefficient; p is a radical of gs (x|b v ，c v ) A probability density function that is a v-th single gaussian distribution, where x represents a random number that follows the single gaussian distribution; b v And c v Respectively represent the mean and standard deviation of the v-th single gaussian distribution;
solving the distribution parameters corresponding to the Gaussian mixture distribution function by adopting an expectation-maximization (EM) algorithm, wherein the EM algorithm is divided into two steps: step 1, called the expectation (E), calculates the expectation of the likelihood function based on the parameters of the initial values or the previous iteration values; step 2 is a maximization (M) step, which maximizes the likelihood function and converts it into new parameter values that can be obtained, and the EM algorithm is a process of repeated iteration until the above two steps converge;
after a fluctuation amount random number set meeting the mixed Gaussian distribution function is generated, randomly extracting the fluctuation amount, and superposing the fluctuation amount on the formed initial wind power output value as shown in a formula (16); traversing the generated preliminary wind power output time sequence, and completing superposition of fluctuation components to form a wind power output time sequence with the time sequence length of one day under a certain cluster type;
P′ t·fd ＝P′ t·cb +ΔP t ′ (16)
in the formula: p' t·fd The wind power output value at the moment t of the wind power output time sequence under a certain clustering category is obtained; p' t·cb The preliminary wind power output value at the moment t of the wind power output time sequence under a certain cluster category is obtained; delta P t ' represents the fluctuation amount of wind power output at the moment t;
5) generating wind power output time sequence according to inter-class transition probability matrix simulation
Determining the time length of the wind power output time sequence generated by simulation according to the requirement of medium-long term optimization scheduling of the power system containing wind power generation, wherein the time length required by the medium-long term optimization scheduling is generally 2 days or more;
respectively counting the transfer times between the classes of the wind power output on two adjacent days, and calculating the corresponding transfer probability to obtain inter-class transfer probability matrixes, such as formulas (17) to (18), so as to obtain accumulated inter-class transfer probability matrixes, such as formulas (19) to (20);
p lj·rz ＝P(H e+1 ＝z|H e ＝r) (18)
in the formula: matrix P lj Is an inter-class transition probability matrix; matrix P lj The row of the corresponding cluster type of the wind power output of the current day, and the column of the corresponding cluster type of the wind power output of the next day; l is the number of categories generated by AP clustering; r and z are clustering categories to which the wind power output belongs; r is 1,2, … …, L; z is 1,2, … …, L; p is a radical of lj·rz Representing the probability that the cluster category to which the wind power output belongs is transferred from the category r to the category z; h e 、H e+1 The cluster type of the wind power output on the current day and the next day; p (a | B) is a conditional probability function representing the probability of a occurring under the condition of B;
in the formula: matrix Q lj Is an accumulative inter-class transition probability matrix; q. q.s lj·rg For accumulating inter-class transition probability matrix Q lj The elements of the r-th row and the g-th column; p is a radical of lj·rz As an inter-class transition probability matrix P lj The elements of the r-th row and the z-th column; l is the number of categories generated by AP clustering; r is 1,2, … …, L; z is 1,2, … …, L; g is 1,2, … …, L;
and sampling the cluster type to which the wind power output of the current day belongs according to the accumulated inter-class transition probability matrix to obtain the AP cluster type to which the wind power output of the next day belongs: the cluster type of the wind power output on the same day is H e The cluster type of the next-day wind power output is H e+1 Generating random number epsilon subject to uniform distribution if 0<ε≤q He,1 Then H is e+1 1 is ═ 1; if q is He,g <ε≤q He,g+1 Then H is e+1 G +1, wherein q He,1 Representing transition probability matrix Q between cumulative classes lj H of e Row, column 1 elements; q. q.s He,g Representing transition probability matrix Q between cumulative classes lj H of e Row, column g elements; q. q.s He,g+1 Representing transition probability matrix Q between cumulative classes lj H of e Row, column g +1 elements;
the method comprises the following steps of generating a wind power output time sequence within R days in a simulated mode at a set sampling interval, wherein R is a positive integer:
judging the AP clustering category to which the wind power output of the 1 st day belongs;
secondly, forming a wind power output simulation generation time sequence of the day 1 by executing the steps 2-4), and recording the time sequence as omega 1 ，Ω 1 ＝{P′ 1·fd(1) ,P′ 2·fd(1) ,……,P′ t·fd(1) In which Ω 1 Representing a wind power output simulation generation sequence of the 1 st day; wherein, P' t·fd(1) The simulation generation wind power output value of the tth moment of the 1 st day is shown, and t shows the wind power output moment;
thirdly, calculating to obtain a wind power output accumulation inter-class transition probability matrix in the step 5), and sampling to determine the AP cluster class to which the wind power output belongs on the day tau, wherein tau is 2,3, … … and R;
fourthly, repeating the steps 2) to 4) to obtain a wind power output simulation generation time sequence on the tau day, and recording the time sequence as omega τ ，Ω τ ＝{P′ 1·fd(τ) ,P′ 2·fd(τ) ,……,P′ t·fd(τ) In which Ω is τ Representing a wind power output simulation generation sequence on the tau day; p' t·fd(τ) Wherein, the simulation generation wind power output value at the tth moment on the Tth day is shown;
fifthly, repeatedly executing the third step and the fourth step until a wind power output time sequence of R days in total is generated and is recorded as omega, and omega is { omega } 1 ,……,Ω τ ,……,Ω R }。
The invention discloses a wind power output simulation generation method for continuously improving MC by utilizing AP clustering-skipping, which is characterized in that actually-measured wind power output data are classified by adopting AP clustering, the problem of poor modeling stability caused by artificial subjectivity is effectively solved, the skipping characteristic and the time sequence characteristic of a wind power output state are comprehensively considered, the problem of long duration time of a certain state in the simulation generation process is improved to a certain extent, a mixed Gaussian distribution is adopted to fit a wind power output fluctuation quantity probability density distribution histogram, the wind power output fluctuation characteristic can be better described, and the superiority of the method can be verified by comparing the probability characteristic, the autocorrelation characteristic and the statistical characteristic of a wind power output time sequence and a historical time sequence obtained by different simulation generation methods.
Drawings
FIG. 1 is a flow chart of wind power output time series simulation generation;
FIG. 2 is a wind power output AP cluster diagram in a certain area;
FIG. 3 is a wind power output state duration time fitting graph;
FIG. 4 is a schematic diagram of comparison of wind power output fluctuation amount fitted by normal distribution, Logistic distribution, t Location-scale distribution and mixed Gaussian distribution;
FIG. 5 is a schematic diagram showing comparison between a partial-length historical wind power output time series, a wind power output time series generated based on conventional Markov chain simulation, a wind power output time series generated based on continuous Markov chain simulation, and a wind power output time series generated by AP clustering-skip continuous improvement MC simulation;
FIG. 6 is a schematic diagram of a comparison of probability distributions of a historical wind power output time series, a wind power output time series generated based on conventional Markov chain simulation, a wind power output time series generated based on continuous Markov chain simulation, and a wind power output time series generated by utilizing AP clustering-skipping continuous improvement MC simulation;
FIG. 7 is a schematic diagram of the comparison of the autocorrelation coefficients of a historical wind power output time series, a wind power output time series generated based on conventional Markov chain simulation, a wind power output time series generated based on continuous Markov chain simulation, and a wind power output time series generated by utilizing AP clustering-skipping continuous improvement MC simulation.
Detailed Description
The invention will be further illustrated with reference to the accompanying figures 1-7 and examples.
The invention discloses a wind power output simulation generation method for continuously improving MC (multi-core) by utilizing AP (access point) clustering-skipping, which is characterized by comprising the following steps of: the method comprises the following steps of carrying out AP clustering on historical wind power output data, forming a wind power output state skip sequence under a certain clustering category, forming a wind power output state time sequence with the time sequence length of one day under a certain clustering category, sampling and superposing the fluctuation amount of the wind power output on a preliminary wind power output time sequence formed under a certain clustering category, and simulating to generate a wind power output time sequence according to an inter-category transfer probability matrix, wherein the specific contents are as follows:
1) AP clustering is carried out on historical wind power output data
An Affinity Propagation (AP) clustering algorithm is an unsupervised clustering algorithm based on "information transfer"; firstly, establishing a similarity matrix S of a sample set as formula (1), wherein elements S in the matrix are a,b Represents a sample x a And x b The similarity between the two is expressed by negative Euclidean distance and is expressed as formula (2); s a,a The reference degree of the cluster center is used as the criterion for judging whether the cluster center can be formed, and the reference degree is set as the bias initiallyThe number of final clusters is directly influenced by the directional parameters, and the larger the value of the deviation coefficient is, the more clusters are generated; and constructing a vector capable of reflecting the characteristics of the corresponding solar wind power output by using the daily mean value and the daily minimum value difference of the actually measured historical wind power output of a set sampling interval in a unit time period, and performing AP clustering on the historical wind power output by using days as a unit by using the vector, wherein: the unit time period generally refers to month, season, year and years; the sampling interval is typically 1 minute, 5 minutes or 10 minutes;
S a,b ＝-||x a －x b || 2 (2)
in the formula: s is a similarity matrix of the sample set; s a,b Represents a sample x a And x b The similarity between them; s a,a The reference degree of the clustering center; x is the number of a And x b Are data sample points; a is 1,2, … …, n; b is 1,2, … …, n; n is the total number of samples used for AP clustering; | x a -x b || 2 Represents x a And x b The Euclidean distance therebetween;
taking the similarity matrix S of the sample set as input, and then calculating the attraction r (x) of each sample point a ,x k ) Degree of affiliation a (x) a ,x k )；r(x a ,x k ) Represents x k Whether a point is suitable as x a The cluster center of the points, i.e. x k For x a The degree of attraction of (c); a (x) a ,x k ) Denotes x a Whether a point selects x or not k As its clustering center, i.e. x a For x k Degree of attribution of; r (x) a ,x k ) And a (x) a ,x k ) The larger, indicates x k The more suitable as a clustering center; continuously updating the attraction degree matrix and the attribution degree matrix in the clustering process, and introducing a damping coefficient for avoiding oscillation in the iteration process until stable clustering centers and class attribution conditions are generated in the iteration process; thus, near the end of propagation, x a Cluster center ofIs determined as x k (ii) a Wherein x is k Is represented by the formula (3):
x k ＝argmax{a(x a ,x k )+r(x a ,x k )} (3)
in the formula: argmax is the argument for finding the maximum function, i.e. x k To satisfy { a (x) } a ,x k )+r(x a ,x k ) Taking the value of the maximum value; a (x) a ,x k ) Is a sample point x a For sample point x k Degree of attribution of; r (x) a ,x k ) Is a sample point x k For sample point x a The degree of attraction of (c); x is the number of k And x a Are data sample points; k is 1,2, … …, n; a is 1,2, … …, n; n is the total number of samples used for AP clustering;
adopting a contour Coefficient (SC) as a clustering evaluation index; the larger the contour coefficient is, the better the clustering effect is; contour coefficient SC (x) k ) Defined by formulae (4) to (6):
in the formula: x is the number of k ，x a ，x b Are data sample points; c (x) k ) Represents a sample point x k The cluster category to which it belongs; c (x) a ) Represents a sample point x a The cluster category to which it belongs; c (x) b ) Represents a sample point x b The cluster category to which it belongs; contour coefficient SC (x) k ) Has a value of [ -1,1 [)]Reflect x k Average distance I (x) between cluster center and sample in class when serving as cluster center k ) Whether it is significantly different from its average distance O (x) to the out-of-class sample k )；I(x k ) To representAverage distance between the cluster center and the intra-class sample; d (x) k ,x a ) Represents a sample point x k And x a The distance between them; m represents the sum of sample point x k The number of data points belonging to the same category; o (x) k ) Representing the average distance between the cluster center and the sample outside the cluster; d (x) k ,x b ) Represents a sample point x k And x b The distance between them; g represents the sum of sample point x k The number of data points not belonging to the same category;
by carrying out AP clustering on historical wind power output data in units of days, the solar wind power output sequences with output levels similar to fluctuation characteristics can be classified into the same class;
2) forming a wind power output state skip sequence under a certain cluster category
The historical wind power output data is expressed as (P' min ，P′ max ) The wind power output range is divided into N data segments uniformly, each data segment corresponds to one state, and the wind power output range corresponding to each state is (P' max -P′ min ) N; wherein, P' min Is the minimum value of historical wind power output, P' max The output is the maximum value of the historical wind power, and N is a state number; aiming at the situation that the wind power output sequence is easy to fall into a certain state and is difficult to jump in the traditional Markov chain, so that the generated wind power output time sequence possibly has overlong duration in a certain state, the method adopts a state jump matrix to replace a state transition matrix for improvement;
when a state transition matrix is generated by a clustering reconstruction sequence, when the jump amplitude of the state number between two adjacent data is larger than 1/3 of the divided state number, the transition is considered to be not practical, the value of the state transition matrix is set to zero, and an improved state transition matrix is obtained;
secondly, setting all diagonal elements of the obtained state transition matrix to zero, calculating the proportion of each element in the sum of all elements of the row, and taking the proportion as a new probability value, wherein the obtained probability matrix is a state jump matrix; the state hopping matrix is of equations (7) - (8);
p ij ＝P(E t+1 ＝j|E t ＝i) (8)
in the formula: the matrix P is a state jump matrix; the row of the matrix P corresponds to the current output state of the wind power output, and the column corresponds to the output state at the next moment; n is the number of states; i and j are wind power output states; 1,2, … …, N; j ═ 1,2, … …, N; p is a radical of ij Representing the probability of the wind power output transferring from the state i to the state j; e t 、E t+1 The wind power output values at the t moment and the t +1 moment are in corresponding states; p (a | B) is a conditional probability function representing the probability of a occurring under the condition of B;
the corresponding accumulated state transition matrix is of formula (9):
the value of the element in Q is represented by formula (10):
in the formula: the matrix Q is an accumulated state skipping matrix; q. q of ul Jumping to the element of the u row and l column in the matrix Q for the accumulated state; p is a radical of uj The elements of the u-th row and the j-th column in the state jump matrix P; n is the number of states; 1,2, … …, N; 1,2, … …, N; j-1, 2, … …, N;
through the forming process of the accumulative state jump matrix Q, an accumulative state jump matrix under a certain cluster category, namely an intra-category accumulative state jump matrix, is obtained; then, sampling to form a state jump sequence under each cluster category according to the intra-category accumulated state jump matrix; under the cluster category, the state of the current wind power output moment is E t The state at the next time is E t+1 Generating random number xi obeying uniform distribution, if 0<ξ≤q Et,1 Then E is t+1 1 is ═ 1; if q is Et,l <ξ≤q Et,l+1 Then E is t+1 L +1, wherein q Et,1 E < th > representing an intra-class accumulated state transition matrix Q t Row, column 1 elements; q. q.s Et,l E < th > representing intra-class accumulated state transition matrix Q t Row, column I elements; q. q of Et,l+1 E < th > representing intra-class accumulated state transition matrix Q t Row, column l + 1;
since the diagonal elements of the state-hopping matrix are zero, the diagonal elements in the corresponding intra-class accumulated state-hopping matrix are equal to the left elements, i.e., q i,i-1 Is equal to q ii So [ q ] i,i-1 ,q ii ]For an empty set, when a wind power output state sequence is generated by using a Markov chain method, xi does not fall to [ q ] i,i-1 ,q ii ]Within the range; wherein q is ii The elements of the ith row and the ith column in the intra-class accumulated state jump matrix Q are represented by i, which is 1,2, … …, N; q. q.s i,i-1 Jumping to the ith row and the (i-1) th column elements in the matrix Q for the accumulated state;
through the steps, a state skip sequence with different adjacent states when the wind power output is in a certain clustering category can be formed by sampling according to the intra-class accumulated state skip matrix in the clustering category;
3) forming a wind power output state time sequence with the time sequence length of one day under a certain cluster category
According to the method, the historical wind power output time sequence is traversed by a statistical method of recording the duration time T once if the duration time of the historical wind power output time sequence is T from the first moment when the wind power output enters a certain state, the times of occurrence of each duration time of the wind power output in the state are counted, and the distribution condition of the duration time in the state is obtained;
after a distribution histogram of the duration time of a certain state of the wind power output is obtained through statistics and drawing, a smooth curve is adopted to describe the histogram, so that the particularity existing in sampling the histogram can be avoided; when describing data distribution characteristics, Kernel Density Estimation (KDE) does not depend on selection of a parameter Estimation model, and dependence of histogram Estimation on a histogram group distance and a histogram position can be effectively avoided, so that the KDE is adopted to describe wind power output state duration distribution characteristics; the KDE expression is formula (11):
in the formula:
a kernel density estimation function for the duration of the wind power output state; k (-) is a kernel function; h is the bandwidth; x is the number of 1 ,x 2 ,……,x W The data number is W; x is the number of w The W-th sample value of the duration time of the wind power output state is 1,2, … … and W; w represents that W different durations of the wind power output sequence appear in a certain state;
in KDE, the selection of the bandwidth determines the smoothness degree of a fitting curve, the larger the bandwidth is, the smoother the bandwidth is, but the poorer the fitting effect is; selecting a Gaussian function as a kernel function, and solving the bandwidth by adopting an empirical rule, wherein the formula is as follows (12):
h＝1.06σW -1/5 (12)
in the formula: h is the bandwidth; sigma is the normal distribution standard deviation of the duration time of the wind power output state; w represents that W different durations of the wind power output sequence appear in a certain state;
in order to obtain the state time sequence of the wind power output with the time sequence length of one day under a certain clustering category, after a random number set meeting the duration time of each state of a kernel density estimation function is generated, traversing the obtained wind power output state jump sequence under the clustering category, and performing repeated sampling: the current state is E t Then in state E t Is arbitrarily chosen as a value in the set of duration random numbers of (a) as state E t The time duration is repeated until the length of the generated time sequence meets the requirement;
4) sampling and superposing wind power output fluctuation quantities on a preliminary wind power output time sequence formed under a certain cluster category
After a wind power output state time sequence under a certain cluster category is formed, determining the initial wind power output at each moment; the current state of wind power output is E t Then the preliminary wind power output P 'at the moment can be randomly generated' t·cb Numerical value of (1), P' t·cb ∈(P Et.min ，P Et.max )，P Et.min 、P Et.max Are respectively in state E t The minimum value and the maximum value of the corresponding wind power output range;
the wind power output fluctuation is that the output values at adjacent moments are different, and the fluctuation characteristic is described by adopting a first-order difference fluctuation quantity, namely the output difference value in adjacent 2 unit times; the first-order difference fluctuation quantity expression of the wind power output is as shown in formula (13):
ΔP t ′＝P′ t+1 -P t ′ (13)
in the formula: t represents the wind power output moment; delta P t ' represents the fluctuation amount of wind power output at the moment t; p t 'and P' t+1 Respectively representing wind power output values at the time t and the time t + 1;
the probability density distribution fitting function of the first-order difference fluctuation quantity of the wind power output is as follows: normal distribution, t-location-scale distribution and logistic distribution; the wind power output fluctuation characteristic is characterized by mixed Gaussian distribution with better fitting precision, the probability density function is the weighting of a plurality of Gaussian probability density functions, when the data distribution is complex, the mixed Gaussian distribution function can solve the problem of the insufficient fitting precision of a single Gaussian distribution function, and the mathematical model expression is as the following formulas (14) - (15):
in the formula: (x) is a Gaussian mixture distribution function; v ═ 1,2, … …, V; v is the single Gaussian distribution in the mixed Gaussian distributionCounting; a is a v Is the mixing coefficient; p is a radical of gs (x|b v ，c v ) A probability density function that is a v-th single gaussian distribution, where x represents a random number that follows the single gaussian distribution; b v And c v Respectively represent the mean and standard deviation of the v-th single gaussian distribution;
solving distribution parameters corresponding to the Gaussian mixture distribution function by adopting an expectation-maximization (EM) algorithm, wherein the EM algorithm comprises two steps: step 1, called the expectation (E), calculates the expectation of the likelihood function based on the parameters of the initial values or the previous iteration values; step 2 is a maximization (M) step, which maximizes the likelihood function and converts it into new parameter values that can be obtained, and the EM algorithm is a process of repeated iteration until the above two steps converge;
after a fluctuation amount random number set meeting the mixed Gaussian distribution function is generated, randomly extracting the fluctuation amount, and superposing the fluctuation amount on the formed initial wind power output value, as shown in a formula (16); traversing the generated preliminary wind power output time sequence, and completing superposition of fluctuation components to form a wind power output time sequence with the time sequence length of one day under a certain cluster type;
P′ t·fd ＝P′ t·cb +ΔP t ′ (16)
in the formula: p' t·fd The wind power output value at the moment t of the wind power output time sequence under a certain clustering category is obtained; p' t·cb The preliminary wind power output value at the moment t of the wind power output time sequence under a certain clustering category is obtained; delta P t ' represents the fluctuation amount of wind power output at the moment t;
5) generating wind power output time sequence according to inter-class transition probability matrix simulation
Determining the time length of the wind power output time sequence generated by simulation according to the requirement of medium-long term optimization scheduling of the power system containing wind power generation, wherein the time length required by the medium-long term optimization scheduling is generally 2 days or more;
respectively counting the transfer times between the classes of the wind power output on two adjacent days, and calculating the corresponding transfer probability to obtain inter-class transfer probability matrixes, such as formulas (17) to (18), so as to obtain accumulated inter-class transfer probability matrixes, such as formulas (19) to (20);
p lj·rz ＝P(H e+1 ＝z|H e ＝r) (18)
in the formula: matrix P lj Is an inter-class transition probability matrix; matrix P lj The row of the corresponding cluster type of the current day wind power output, and the column of the corresponding cluster type of the next day wind power output; l is the number of categories generated by AP clustering; r and z are clustering categories to which the wind power output belongs; r is 1,2, … …, L; z is 1,2, … …, L; p is a radical of lj·rz Representing the probability that the cluster category to which the wind power output belongs is transferred from the category r to the category z; h e 、H e+1 The cluster type of the wind power output on the current day and the next day; p (a | B) is a conditional probability function representing the probability of a occurring under the condition of B;
in the formula: matrix Q lj Is an accumulative inter-class transition probability matrix; q. q.s lj·rg For accumulating inter-class transition probability matrices Q lj The elements of the r-th row and the g-th column; p is a radical of formula lj·rz As an inter-class transition probability matrix P lj The elements of the r-th row and the z-th column; l is the number of categories generated by AP clustering; r is 1,2, … …, L; z-1, 2, … …, L; g is 1,2, … …, L;
and sampling the cluster type to which the wind power output of the current day belongs according to the accumulated inter-class transition probability matrix to obtain the AP cluster type to which the wind power output of the next day belongs: the cluster type of the wind power output on the same day is H e The cluster category to which the next-day wind power output belongs is H e+1 Generating random number epsilon subject to uniform distribution if 0<ε≤q He,1 Then, thenH e+1 1 is ═ 1; if q is He,g <ε≤q He,g+1 Then H is e+1 G +1, wherein q He,1 Representing cumulative inter-class transition probability matrix Q lj H of e Row, column 1 elements; q. q.s He,g Representing transition probability matrix Q between cumulative classes lj H of e Row, column g elements; q. q.s He,g+1 Representing transition probability matrix Q between cumulative classes lj H of e Row, column g +1 elements;
the method comprises the following steps of generating a wind power output time sequence within R days in a simulated mode at a set sampling interval, wherein R is a positive integer:
judging the AP clustering category to which the wind power output of the 1 st day belongs;
secondly, forming a wind power output simulation generation time sequence of the day 1 by executing the steps 2-4), and recording the time sequence as omega 1 ，Ω 1 ＝{P′ 1·fd(1) ,P′ 2·fd(1) ,……,P′ t·fd(1) In which Ω is 1 Representing a wind power output simulation generation sequence of the 1 st day; wherein, P' t·fd(1) The simulation generation wind power output value of the 1 st day at the t moment is shown, and t shows the wind power output moment;
thirdly, calculating to obtain a wind power output accumulated inter-class transfer probability matrix in the step 5), and sampling to determine the AP cluster class to which the wind power output belongs on the day tau, wherein tau is 2,3, … … and R;
fourthly, repeating the steps 2) to 4) to obtain a wind power output simulation generation time sequence on the tau day, and recording the time sequence as omega τ ，Ω τ ＝{P′ 1·fd(τ) ,P′ 2·fd(τ) ,……,P′ t·fd(τ) In which Ω is τ Representing a wind power output simulation generation sequence on the tau day; p' t·fd(τ) Wherein, the simulation generation wind power output value at the tth moment on the Tth day is shown;
fifthly, repeatedly executing the third step and the fourth step until a wind power output time sequence of R days in total is generated and is recorded as omega, and omega is { omega } 1 ,……,Ω τ ,……,Ω R }。
Specific examples are as follows: the invention provides a wind power output simulation generation method for continuously improving MC by utilizing AP clustering-skipping, which comprises the following steps:
analyzing the wind power output data of the whole year from 2018, month 1 and year 2019, month 9 and month 30 of a wind power plant in a certain area as a sample, wherein the total installed capacity is 1904MW, the data sampling time interval is 1min, and the wind power output time sequence from 2019, month 1 to year 2019, month 10 and day 31 is generated by performing normalization processing on the basis of the total installed capacity.
Using Residual Sum of Squares (RSS), Root Mean Square Error (RMSE), coefficient R-square, Mean Error epsilon mean Error of sum standard deviation epsilon std As an evaluation index of the effect of the simulation generation method. RSS, RMSE, ε mean And ε std The smaller the R-square is, the closer the R-square is to 1, which shows that the more consistent the statistical property, the probability distribution property and the autocorrelation property of the time sequence generated by simulation and the historical measured sequence are, the better the simulation generation effect is.
The measured wind power output data of a certain area in one year is constructed into a vector capable of reflecting the characteristics of the wind power output corresponding to each day according to the daily mean value and the daily minimum difference of the measured wind power output data, the vector is utilized to perform AP clustering on the historical wind power output in units of days, the data sampling time interval is 1min, the historical measured wind power output data can be clustered into 5 classes through an AP clustering algorithm, and the clustering effect is shown in figure 2.
And respectively fitting the duration time distribution histogram of each state of the wind power output by utilizing an inverse Gaussian function, a t-location scale function and kernel density estimation, taking the duration time of the state 4 in the wind power output of the category 2 as an example, as shown in FIG. 3 (the probability that the state duration time is more than 50min is extremely small, so that only the state duration time is drawn in the portion of less than 50min in FIG. 3). And comparing the fitting curves with the wind power output state duration distribution histogram, and finding out that the fitting effect of the kernel density estimation is better and the wind power output state duration histogram can be better approximated.
The mixed gaussian distribution function is solved by using the EM algorithm to obtain the estimated values of each parameter, as shown in table 1.
TABLE 1 estimation of three-component Gaussian mixture distribution parameters
The wind power output fluctuation amount probability density distribution histogram is fitted by utilizing normal distribution, Logistic distribution, t Location-scale distribution and mixed Gaussian distribution, as shown in fig. 4.
As can be seen from FIG. 4, the fluctuation amount of the wind power output is concentrated at the low value end, the per unit value of the maximum fluctuation amount is less than 0.05, the probability density distribution has the characteristic of thick tail, and the whole has symmetry. The evaluation index results of the wind power output fluctuation amount probability density distribution fitting functions are shown in table 2.
TABLE 2 wind power output fluctuation quantity probability density distribution fitting function evaluation index comparison
In the distribution, 3 indexes of the mixed Gaussian distribution model are optimal, wherein RSS and RMSE of the mixed Gaussian distribution are respectively reduced by 98% and 86% compared with normal distribution, R-square is improved by 33% compared with normal distribution, and the fitting effect of the mixed Gaussian distribution on the fluctuation amount probability density distribution histogram is best.
The statistical inter-class transition probability matrix of the wind power output of the wind power plant in a certain area from 2018, 10 months and 1 days to 2019, 9 months and 30 days is as follows:
FIG. 5 compares the historical sequence with the time sequences generated by the wind power output simulation generation method, the continuous Markov chain method and the traditional Markov chain method using AP clustering-skipping continuous improvement MC. The method for simulating and generating the wind power output by continuously improving the MC through the AP clustering-skipping better solves the problem that the wind power output sequence in the traditional Markov chain method has overlong duration time in a low-output section, and the method for simulating and generating the wind power output by continuously improving the MC through the AP clustering-skipping considers the time domain characteristic of the wind power output and solves the problem that the generated time sequence fluctuates too frequently in a certain state to a certain extent.
Fig. 6 compares Probability Distribution Function (PDF) of the wind power output time series generated by different methods with the historical time series. As can be seen from fig. 6, the probability density distribution of the wind power output shows the characteristics of high probability density of the low-output part and low probability density of the high-output part, and the probability density distribution of the wind power output time sequence generated by the wind power output simulation generation method of the AP clustering-skipping continuous improvement MC is closer to the probability density distribution corresponding to the historical sequence, and further shows the superiority of the wind power output simulation generation method of the MC continuous improvement by the AP clustering-skipping from the aspect of the probability density distribution.
Autocorrelation calculation is performed on time sequences generated by the wind power output simulation generation method, the continuous Markov chain method and the traditional Markov chain method which utilize the AP clustering-skipping continuous improvement MC, and the result is shown in FIG. 7. The abscissa represents the lag time, and the ordinate represents the Auto Correlation Function (ACF) corresponding to different lag times, and the lag time is calculated to be 200min at intervals of 1 min. It can be seen from fig. 7 that, when the lag time is less than 50min, the autocorrelation coefficients of the wind power output time series generated by the three methods are relatively close to the historical sequence, but as the lag time increases, the autocorrelation coefficients of the wind power output time series obtained by the wind power output simulation generation method of continuously improving MC by AP clustering-skipping are closer to the historical sequence, i.e., it is verified that the wind power output simulation generation method of continuously improving MC by AP clustering-skipping can better retain the autocorrelation of the original wind power output time series.
TABLE 3 comparison of probability distribution characteristics and autocorrelation of sequences obtained by different simulation generation methods
Table 3 shows that the probability density distribution values of different model sequences and RSS, RMSE and R-square of autocorrelation function values are quantitatively compared, and the three indexes of the method are superior to those of a continuous Markov chain method and a traditional Markov chain method. Wherein, the RSS and RMSE of the probability density distribution value are respectively reduced by 64.3 percent and 94.2 percent compared with the sequences generated by the continuous Markov chain method in a simulation way, and the R-square is improved by 0.9 percent compared with the continuous Markov chain sequences; the RSS and RMSE of the autocorrelation function value are respectively reduced by 77.9% and 53.5% compared with the sequence generated by the continuous Markov chain method, and the R-square is improved by 0.3% compared with the continuous Markov chain sequence, namely the probability density distribution characteristic and the autocorrelation characteristic of the wind power output time sequence obtained by the method are more approximate to those of the historical wind power output time sequence, and the simulation effect is better.
TABLE 4 statistical index comparisons of sequences obtained by different simulation Generation methods
To verify the superiority and inferiority of the time series obtained by each simulation generation method in the statistical properties, table 4 lists the average error (epsilon) between the sequence generated by each method and the historical wind power output time series mean ) And standard deviation error (. epsilon.) std ). It can be seen that epsilon of wind power output time sequence generated by simulation by using the method mean Index and epsilon std The indexes are respectively reduced by 76.8% and 53.1% compared with a continuous Markov chain, so that the wind power output simulation generation method for continuously improving MC by utilizing AP clustering-skipping has obvious superiority in simulation generation precision.
While the present invention has been described in detail and with reference to specific embodiments thereof, it will be apparent to one skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope thereof as defined in the appended claims.
Claims (1)
1. A wind power output simulation generation method for continuously improving MC by utilizing AP clustering-skipping is characterized by comprising the following steps: the method comprises the following steps of carrying out AP clustering on historical wind power output data, forming a wind power output state skip sequence under a certain clustering category, forming a wind power output state time sequence with the time sequence length of one day under a certain clustering category, sampling and superposing the wind power output fluctuation quantity on a primary wind power output time sequence formed under a certain clustering category, and generating a wind power output time sequence according to inter-category transfer probability matrix simulation, wherein the specific content is as follows:
1) AP clustering is carried out on historical wind power output data
An Affinity Propagation (AP) clustering algorithm is an unsupervised clustering algorithm based on "information transfer"; firstly, establishing a similarity matrix S of a sample set as formula (1), wherein elements S in the matrix are a,b Represents a sample x a And x b The similarity between the two is expressed by negative Euclidean distance and is expressed as formula (2); s a,a The reference degree of the clustering center is used as a judgment standard for judging whether the clustering center can be formed, a deviation parameter is set at the beginning, the deviation parameter directly influences the number of final clusters, and the larger the value of the deviation coefficient is, the more clusters are generated; constructing a vector capable of reflecting the characteristics of the corresponding solar wind power output according to the daily mean value and the daily minimum value of the actually measured historical wind power output at a set sampling interval in a unit time period, and carrying out AP clustering on the historical wind power output by using the vector in a day unit, wherein: the unit time period generally refers to month, season, year and years; the sampling interval is typically 1 minute, 5 minutes or 10 minutes;
S a,b ＝-||x a －x b || 2 (2)
in the formula: s is a similarity matrix of the sample set; s a,b Represents a sample x a And x b The similarity between them; s. the a,a The reference degree of the clustering center; x is the number of a And x b Are data sample points; a is 1,2, … …, n; b is 1,2, … …, n; n is for AP aggregationTotal number of samples of class; | x a -x b || 2 Represents x a And x b The Euclidean distance between;
taking the similarity matrix S of the sample set as input, and then calculating the attraction r (x) of each sample point a ,x k ) Degree of affiliation a (x) a ,x k )；r(x a ,x k ) Denotes x k Whether a point is suitable as x a The cluster center of the points, i.e. x k For x a The degree of attraction of (c); a (x) a ,x k ) Denotes x a Whether a point selects x or not k As its clustering center, i.e. x a For x k Degree of attribution of; r (x) a ,x k ) And a (x) a ,x k ) The larger, indicates x k The more suitable as a clustering center; continuously updating the attraction degree matrix and the attribution degree matrix in the clustering process, and introducing a damping coefficient for avoiding oscillation in the iteration process until stable clustering centers and class attribution conditions are generated in the iteration process; thus, near the end of propagation, x a Is determined as x k (ii) a Wherein x is k Is represented by the formula (3):
x k ＝argmax{a(x a ,x k )+r(x a ,x k )} (3)
in the formula: argmax is the argument for finding the maximum function value, i.e. x k To satisfy { a (x) } a ,x k )+r(x a ,x k ) Taking the value of the maximum value; a (x) a ,x k ) Is a sample point x a For sample point x k Degree of attribution of; r (x) a ,x k ) Is a sample point x k For sample point x a The degree of attraction of (c); x is the number of k And x a Are data sample points; k is 1,2, … …, n; a is 1,2, … …, n; n is the total number of samples used for AP clustering;
adopting a contour Coefficient (Silhouette Coefficient, SC) as a clustering evaluation index; the larger the contour coefficient is, the better the clustering effect is; contour coefficient SC (x) k ) Defined by formulae (4) to (6):
in the formula: x is the number of k ，x a ，x b Is a data sample point; c (x) k ) Represents a sample point x k The cluster category to which it belongs; c (x) a ) Represents a sample point x a The cluster category to which it belongs; c (x) b ) Represents a sample point x b The cluster category to which it belongs; contour coefficient SC (x) k ) Has a value of [ -1,1 [)]Reflect x k Average distance I (x) between cluster center and sample in class when serving as cluster center k ) Whether it is significantly different from its average distance O (x) to the out-of-class sample k )；I(x k ) Representing the average distance between the cluster center and the samples in the class; d (x) k ,x a ) Represents a sample point x k And x a The distance between them; m represents the sum of sample point x k The number of data points belonging to the same category; o (x) k ) Representing the average distance between the cluster center and the sample outside the cluster; d (x) k ,x b ) Represents a sample point x k And x b The distance between them; g represents the sum of sample point x k The number of data points not belonging to the same category;
by carrying out AP clustering on historical wind power output data in units of days, the solar wind power output sequences with output levels similar to fluctuation characteristics can be classified into the same class;
2) forming a wind power output state skip sequence under a certain cluster category
The historical wind power output data is expressed as (P' min ，P′ max ) The wind power output range is divided into N data segments uniformly, each data segment corresponds to one state, and the wind power output range corresponding to each state is (P' max -P′ min ) N; wherein,P′ min is the minimum value of historical wind power output, P' max The output is the maximum value of the historical wind power, and N is a state number; aiming at the situation that the wind power output sequence is easy to fall into a certain state and is difficult to jump in the traditional Markov chain, so that the generated wind power output time sequence possibly has overlong duration in a certain state, the method adopts a state jump matrix to replace a state transition matrix for improvement;
when a state transition matrix is generated by a clustering reconstruction sequence, when the jump amplitude of the state number between two adjacent data is larger than 1/3 of the divided state number, the transition is considered to be not practical, the value of the state transition matrix is set to zero, and an improved state transition matrix is obtained;
secondly, setting all diagonal elements of the obtained state transition matrix to zero, calculating the proportion of each element in the sum of all elements of the row, and taking the proportion as a new probability value, wherein the obtained probability matrix is a state jump matrix; the state hopping matrix is of equations (7) - (8);
p ij ＝P(E t+1 ＝j|E t ＝i) (8)
in the formula: the matrix P is a state jump matrix; the row of the matrix P corresponds to the current output state of the wind power output, and the column corresponds to the output state at the next moment; n is the number of states; i and j are wind power output states; 1,2, … …, N; j ═ 1,2, … …, N; p is a radical of ij Representing the probability of the wind power output transferring from the state i to the state j; e t 、E t+1 The wind power output values at the t moment and the t +1 moment are in corresponding states; p (A | B) is a conditional probability function and represents the probability of A appearing under the condition of B;
the corresponding accumulated state transition matrix is of formula (9):
the value of the element in Q is represented by formula (10):
in the formula: the matrix Q is an accumulated state jump matrix; q. q.s ul Jumping to the element of the u row and l column in the matrix Q for the accumulated state; p is a radical of uj The elements of the u-th row and the j-th column in the state jump matrix P; n is the number of states; u-1, 2, … …, N; 1,2, … …, N; j ═ 1,2, … …, N;
through the forming process of the accumulative state jump matrix Q, an accumulative state jump matrix under a certain cluster category, namely an intra-category accumulative state jump matrix, is obtained; then, sampling to form a state jump sequence under each cluster category according to the intra-category accumulated state jump matrix; under the cluster category, the state of the wind power output at the current moment is E t The state at the next time is E t+1 Generating random number xi following uniform distribution, if 0<ξ≤q Et,1 Then E is t+1 1 is ═ 1; if q is Et,l <ξ≤q Et,l+1 Then E is t+1 L +1, wherein q Et,1 E < th > representing intra-class accumulated state transition matrix Q t Row, column 1 elements; q. q.s Et,l E < th > representing intra-class accumulated state transition matrix Q t Row, column I elements; q. q.s Et,l+1 E < th > representing intra-class accumulated state transition matrix Q t Row, column l + 1;
since the diagonal elements of the state-hopping matrix are zero, the diagonal elements in the corresponding intra-class accumulated state-hopping matrix are equal to the left elements, i.e., q i,i-1 Is equal to q ii Therefore [ q ] i,i-1 ,q ii ]For an empty set, when a wind power output state sequence is generated by using a Markov chain method, xi does not fall to [ q ] i,i-1 ,q ii ]Within the range; wherein q is ii The elements of the ith row and the ith column in the intra-class accumulated state jump matrix Q are represented by i, which is 1,2, … …, N; q. q.s i,i-1 Jumping to the ith row and the (i-1) th column elements in the matrix Q for the accumulated state;
through the steps, a state skip sequence with different adjacent states when the wind power output is in a certain clustering category can be formed by sampling according to the intra-class accumulated state skip matrix in the clustering category;
3) forming a wind power output state time sequence with the time sequence length of one day under a certain cluster category
According to the method, the historical wind power output time sequence is traversed by a statistical method of recording the duration time T once from the first moment when the wind power output enters a certain state, and if the duration time is T, the times of occurrence of each duration time of the wind power output in the state are counted to obtain the distribution condition of the duration time in the state;
after a distribution histogram of the duration time of a certain state of the wind power output is obtained through statistics and drawing, a smooth curve is adopted to describe the histogram, so that the particularity existing in sampling the histogram can be avoided; when describing data distribution characteristics, Kernel Density Estimation (KDE) does not depend on selection of a parameter Estimation model, and dependence of histogram Estimation on a histogram group distance and a histogram position can be effectively avoided, so that the KDE is adopted to describe wind power output state duration distribution characteristics; the KDE expression is formula (11):
in the formula:
a kernel density estimation function for the duration of the wind power output state; k (-) is a kernel function; h is the bandwidth; x is the number of 1 ,x 2 ,……,x W The data number is W; x is the number of w The W-th sample value of the duration time of the wind power output state is 1,2, … … and W; w represents that W different durations of the wind power output sequence appear in a certain state;
in KDE, the selection of the bandwidth determines the smoothness degree of a fitting curve, the larger the bandwidth is, the smoother the bandwidth is, but the poorer the fitting effect is; selecting a Gaussian function as a kernel function, and solving the bandwidth by adopting an empirical rule, wherein the empirical rule is as follows:
h＝1.06σW -1/5 (12)
in the formula: h is the bandwidth; sigma is the normal distribution standard deviation of the duration time of the wind power output state; w represents that W different durations of the wind power output sequence appear in a certain state;
in order to obtain the state time sequence of the wind power output with the time sequence length of one day under a certain clustering category, after a random number set meeting the duration time of each state of a kernel density estimation function is generated, traversing the obtained wind power output state jump sequence under the clustering category, and performing repeated sampling: the current state is E t Then in state E t Is arbitrarily chosen as a value in the set of duration random numbers of (a) as state E t The time duration is repeated until the length of the generated time sequence meets the requirement;
4) sampling and superposing wind power output fluctuation quantity on a preliminary wind power output time sequence formed under a certain cluster category
After a wind power output state time sequence under a certain cluster category is formed, determining the initial wind power output at each moment; the current state of wind power output is E t Then, the preliminary wind power output P 'at the moment can be randomly generated' t·cb Numerical value of (1), P' t·cb ∈(P Et.min ，P Et.max )，P Et.min 、P Et.max Are respectively in the state E t The minimum value and the maximum value of the corresponding wind power output range;
the wind power output fluctuation refers to the difference of output values at adjacent moments, and the fluctuation characteristic is described by adopting a first-order differential fluctuation quantity, namely the output difference value in adjacent 2 unit times; the first-order difference fluctuation quantity expression of the wind power output is as shown in formula (13):
ΔP′ t ＝P′ t+1 -P′ t (13)
in the formula: t represents wind power outputEngraving; delta P' t Representing the fluctuation quantity of the wind power output at the time t; p' t And P' t+1 Respectively representing wind power output values at the time t and the time t + 1;
the probability density distribution fitting function of the first-order difference fluctuation quantity of the wind power output is as follows: normal distribution, t-location-scale distribution and logistic distribution; the wind power output fluctuation characteristic is characterized by mixed Gaussian distribution with better fitting precision, the probability density function is the weighting of a plurality of Gaussian probability density functions, when the data distribution is complex, the mixed Gaussian distribution function can solve the problem of the insufficient fitting precision of a single Gaussian distribution function, and the mathematical model expression is as the following formulas (14) - (15):
in the formula: (x) is a Gaussian mixture distribution function; v ═ 1,2, … …, V; v is the number of single Gaussian distributions in the mixed Gaussian distribution; a is v Is the mixing coefficient; p is a radical of gs (x|b v ，c v ) A probability density function which is a v-th single gaussian distribution, wherein x represents a random number obeying the single gaussian distribution; b v And c v Respectively represent the mean and standard deviation of the v-th single gaussian distribution;
solving the distribution parameters corresponding to the Gaussian mixture distribution function by adopting an expectation-maximization (EM) algorithm, wherein the EM algorithm is divided into two steps: step 1, called the expectation (E), calculates the expectation of the likelihood function based on the parameters of the initial values or the previous iteration values; step 2 is a maximization (M) step, which maximizes the likelihood function and converts it into new parameter values that can be obtained, and the EM algorithm is a process of repeated iteration until the above two steps converge;
after a fluctuation amount random number set meeting the mixed Gaussian distribution function is generated, randomly extracting the fluctuation amount, and superposing the fluctuation amount on the formed initial wind power output value, as shown in a formula (16); traversing the generated preliminary wind power output time sequence, and completing superposition of fluctuation components to form a wind power output time sequence with the time sequence length of one day under a certain cluster type;
P′ t·fd ＝P′ t·cb +ΔP′ t (16)
in the formula: p' t·fd The wind power output value at the moment t of the wind power output time sequence under a certain clustering category is obtained; p' t·cb The preliminary wind power output value at the moment t of the wind power output time sequence under a certain clustering category is obtained; delta P' t Representing the fluctuation quantity of the wind power output at the t moment;
5) generating wind power output time sequence according to inter-class transition probability matrix simulation
Determining the time length of the wind power output time sequence generated by simulation according to the requirement of medium-long term optimization scheduling of the power system containing wind power generation, wherein the time length required by the medium-long term optimization scheduling is generally 2 days or more;
respectively counting the transfer times between the categories of the wind power output on two adjacent days, and calculating the corresponding transfer probability to obtain inter-category transfer probability matrixes as formulas (17) to (18), so as to obtain accumulated inter-category transfer probability matrixes as formulas (19) to (20);
p lj·rz ＝P(H e+1 ＝z|H e ＝r) (18)
in the formula: matrix P lj Is an inter-class transition probability matrix; matrix P lj The row of the corresponding cluster type of the wind power output of the current day, and the column of the corresponding cluster type of the wind power output of the next day; l is the number of categories generated by AP clustering; r and z are clustering categories to which the wind power output belongs; r is 1,2, … …, L; z-1, 2, … …, L; p is a radical of lj·rz Representing the probability that the cluster category to which the wind power output belongs is transferred from the category r to the category z; h e 、H e+1 The cluster type of the wind power output on the current day and the next day; p (A | B) is a conditional summaryA rate function representing the probability of occurrence of a under the condition of B;
in the formula: matrix Q lj Is an accumulative inter-class transition probability matrix; q. q.s lj·rg For accumulating inter-class transition probability matrices Q lj The elements of the r-th row and the g-th column; p is a radical of lj·rz As an inter-class transition probability matrix P lj The elements of the middle r row and the z column; l is the number of categories generated by AP clustering; r is 1,2, … …, L; z-1, 2, … …, L; g is 1,2, … …, L;
and sampling the cluster type to which the wind power output of the current day belongs according to the accumulated inter-class transition probability matrix to obtain the AP cluster type to which the wind power output of the next day belongs: the cluster type of the wind power output on the same day is H e The cluster category to which the next-day wind power output belongs is H e+1 Generating random number epsilon subject to uniform distribution if 0<ε≤q He,1 Then H is e+1 1 is ═ 1; if q is He,g <ε≤q He,g+1 Then H is e+1 G +1, wherein q He,1 Representing transition probability matrix Q between cumulative classes lj H of e Row, column 1 elements; q. q.s He,g Representing transition probability matrix Q between cumulative classes lj H of e Row, column g elements; q. q of He,g+1 Representing cumulative inter-class transition probability matrix Q lj H of e Row, column g +1 elements;
the method comprises the following steps of generating a wind power output time sequence within R days in a simulated mode at a set sampling interval, wherein R is a positive integer:
judging the AP clustering category to which the wind power output of the 1 st day belongs;
secondly, forming a wind power output simulation generation time sequence of the day 1 by executing the steps 2-4), and recording the time sequence as omega 1 ，Ω 1 ＝{P′ 1·fd(1) ,P′ 2·fd(1) ,……,P′ t·fd(1) In which Ω is 1 Representing a wind power output simulation generation sequence of the 1 st day; wherein, P' t·fd(1) The simulation generation wind power output value of the tth moment of the 1 st day is shown, and t shows the wind power output moment;
thirdly, calculating to obtain a wind power output accumulated inter-class transfer probability matrix in the step 5), and sampling to determine the AP cluster class to which the wind power output belongs on the day tau, wherein tau is 2,3, … … and R;
fourthly, repeating the steps 2) to 4) to obtain a wind power output simulation generation time sequence on the tau day, and recording the time sequence as omega τ ，Ω τ ＝{P′ 1·fd(τ) ,P′ 2·fd(τ) ,……,P′ t·fd(τ) In which Ω is τ Representing a wind power output simulation generation sequence on the tau day; p' t·fd(τ) Wherein, the simulation generation wind power output value at the tth moment on the Tth day is shown;
fifthly, repeatedly executing the third step and the fourth step until a wind power output time sequence of R days in total is generated and is recorded as omega, and omega is { omega } 1 ,……,Ω τ ,……,Ω R }。
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