CN111027732B - Method and system for generating multi-wind power plant output scene - Google Patents
Method and system for generating multi-wind power plant output scene Download PDFInfo
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Abstract
The invention provides a method and a system for generating a multi-wind power plant output scene, comprising the following steps: obtaining a multidimensional Gaussian distribution and cumulative state transition probability matrix based on output prediction error data of a plurality of wind power plants and a pre-constructed Gaussian hidden Markov model; determining a prediction error of each wind power plant at each moment in a preset period based on the multidimensional Gaussian distribution and the cumulative state transition probability matrix; and obtaining predicted output scenes of all wind power plants based on the predicted output values of the points of each wind power plant and the prediction errors of the wind power plants. According to the method, the correlation among the prediction errors of different wind power plants can be considered, modeling is conducted among the different wind power plants based on the method for generating the prediction output scenes of the plurality of wind power plants based on the Gaussian hidden Markov model, the generated prediction output scenes of the wind power plants can be considered, the correlation among the different wind power plants can be considered, and the obtained prediction output scenes are more scientific and reasonable and have high accuracy.
Description
Technical Field
The invention relates to the field of new energy power generation, in particular to a method and a system for generating a multi-wind power plant output scene.
Background
The traditional power system short-term optimization scheduling needs a point prediction result based on wind power output, and the point prediction output usually has larger error due to strong randomness and fluctuation of the wind power output, so that the accuracy of a scheduling plan is affected. In order to consider uncertainty of wind power output prediction errors, a random optimization scheduling method based on wind power predicted output scenes is provided at present, a series of wind power predicted output scenes are taken as input, and a scheduling plan under the condition of meeting expected meanings of all wind power output scenes is obtained through optimization solution. Therefore, the wind power predicted output scene is a key factor affecting the accuracy of a random optimization scheduling result, but the wind power predicted output scene is usually obtained by adding random prediction errors on the basis of the existing wind power point predicted output.
Because the wind power prediction system only provides point predicted output results under the general condition, the prediction errors of the output of different wind power stations are required to be modeled based on the point predicted output results, and the prediction output scenes of the wind power stations are obtained by randomly generating the prediction errors. However, when the power grid is connected to a plurality of wind power plants with similar distances, the optimal model needs to take predicted force scenes of all the wind power plants as input, and because the wind power plants are relatively close in distance, the wind power plants are generally affected by the same weather process, prediction errors of the wind power plants generally have strong correlation, but the influence of correlation factors is not fully considered when the predicted force scenes of the wind power plants are generated. Therefore, the correlation and actual deviation between the obtained predicted output scenes are larger, and the accuracy of the optimal scheduling result is affected.
Disclosure of Invention
In order to solve the problems that in the prior art, in a wind power plant prediction output scene generation method, the correlation of prediction errors among wind power plants is not considered, the obtained correlation and actual deviation among the prediction output scenes are larger, and the accuracy of an optimal scheduling result is influenced, the invention provides a multi-wind power plant output scene generation method and system, and firstly, a Gaussian hidden Markov model taking the correlation of the wind power plant prediction errors as a hidden state and taking the prediction errors as output is established; then training Gaussian hidden Markov model parameters based on a prediction error sample of the historical output of the wind farm; and finally, generating a plurality of wind power plant prediction output scenes meeting the prediction error correlation relation by a Monte Carlo simulation method.
The technical scheme provided by the invention is as follows: a method for generating a multi-wind power plant output scene comprises the following steps:
obtaining a multidimensional Gaussian distribution and cumulative state transition probability matrix based on output prediction error data of a plurality of wind power plants and a pre-constructed Gaussian hidden Markov model;
determining a prediction error of each wind power plant at each moment in a preset period based on the multidimensional Gaussian distribution and the cumulative state transition probability matrix;
And obtaining predicted output scenes of all wind power plants based on the predicted output values of the points of each wind power plant and the prediction errors of the wind power plants.
Preferably, the obtaining the multi-dimensional gaussian distribution and the cumulative state transition probability matrix based on the output prediction error data of the wind power plants and the pre-constructed gaussian hidden markov model includes:
based on the actual output values of the wind power plants and the predicted output values of the corresponding points, output prediction error data of each wind power plant are obtained;
determining a correlation state among the plurality of wind power plants according to the output prediction error data of each wind power plant;
setting the correlation state as a hidden state in the Gaussian hidden Markov model, and setting the number of the hidden states;
training a Gaussian hidden Markov model based on output prediction error data of each wind power plant and the number of hidden states, and iteratively calculating a state transition matrix of the Gaussian hidden Markov model, and a mean vector and a covariance matrix of Gaussian distribution corresponding to each hidden state through a forward-backward algorithm;
determining multidimensional Gaussian distribution based on mean vector and covariance matrix of Gaussian distribution corresponding to each hidden state;
Calculating an accumulated state transition probability based on the state transition matrix;
wherein the cumulative state transition probability matrix consists of cumulative state transition probabilities.
Preferably, the training the gaussian hidden markov model based on the output prediction error data of each wind farm and the number of the hidden states, and iteratively calculating a state transition matrix of the gaussian hidden markov model, and a mean vector and a covariance matrix of a gaussian distribution corresponding to each hidden state through a forward-backward algorithm, where the training comprises:
step 101, setting initial values for a state transition matrix, a mean value vector of Gaussian distribution, a covariance matrix of Gaussian distribution and a probability distribution vector of hidden states in a Gaussian hidden Markov model;
102, calculating forward probabilities of hidden states at initial moments in a training period, and sequentially calculating forward probabilities of hidden states at all other moments in the training period;
step 103, calculating backward probabilities of hidden states at the ending time in the training period, and sequentially calculating backward probabilities of hidden states at all other time points in the training period;
104, calculating the conditional probability of the hidden state at any moment based on an observation sequence formed by output prediction error data of a plurality of wind power plants, the forward probability of each hidden state and the backward probability of each hidden state;
Step 105, calculating joint conditional probabilities of hidden states at any moment and hidden states at the next moment at any moment based on an observation sequence formed by output prediction error data of a plurality of wind power plants, forward probabilities of hidden states and backward probabilities of the hidden states;
step 106, updating a state transition matrix, a mean vector of Gaussian distribution, a covariance matrix of Gaussian distribution and a probability distribution vector of hidden states in the Gaussian hidden Markov model based on the conditional probability and the joint conditional probability;
step 107, if the state transition matrix, the mean value vector of the gaussian distribution, the covariance matrix of the gaussian distribution and the probability distribution vector of the hidden state in the updated gaussian hidden markov model meet a preset convergence condition, the cycle is ended, the gaussian hidden markov model is set according to the current parameters, and otherwise, step 102 is executed.
Preferably, the forward probability is calculated as follows:
wherein: alpha t+1 (j) The method comprises the following steps Forward probability of the hidden state j at t+1; pi j : the hidden state of the wind power plant is theta j Probability of (2); b j (. Cndot.): probability distribution obeyed by an observation sequence with a hidden state of j; o (O) 1 : a historical observation sequence of the output of each wind power plant at the initial moment; n: the number of hidden states; alpha t (j) The method comprises the following steps the forward probability of the hidden state j at the time t; a, a ij : the hidden state at the moment t of the jth column of the ith row in the state transition matrix A is theta i The hidden state at time t+1 is converted to θ j Probability of (2); o (O) t+1 : a historical observation sequence of the output of each wind power plant at the time of t+1;
the probability of the hidden state at the initial moment of the wind power plant forms a probability distribution vector of the hidden state.
Preferably, the backward probability is calculated as follows:
wherein: beta t (j) The method comprises the following steps the backward probability of the hidden state j at the time t; a, a ji : the hidden state at the moment t of the jth row and the ith column in the state transition matrix A is theta j The hidden state at time t+1 is converted to θ i Probability of (2); b i (. Cndot.): probability distribution obeyed by an observation sequence with hidden state i; beta t+1 (i) The method comprises the following steps the backward probability that the hidden state is i at the time of t+1; o (O) t+1 : a historical observation sequence of the output of each wind power plant at the time of t+1; t: the termination time of the training period; n: number of hidden states.
Preferably, the conditional probability of the hidden state at any moment is calculated according to the following formula:
wherein: gamma ray t (j) The method comprises the following steps Conditional probability of the hidden state j at t; alpha t (j) The method comprises the following steps the forward probability of the hidden state j at the time t; beta t (j) The method comprises the following steps the backward probability of the hidden state j at the time t; alpha t (i) The method comprises the following steps the forward probability of the hidden state i at the time t; beta t (i) The method comprises the following steps the backward probability of the hidden state i at the t moment; n: number of hidden states.
Preferably, the joint conditional probability is calculated as follows:
wherein: zeta type toy t (i, j): joint conditional probability of hidden state j at time t; alpha t (j) The method comprises the following steps the forward probability of the hidden state j at the time t; a, a ij : the hidden state at the moment t of the jth column of the ith row in the state transition matrix A is theta i The hidden state at time t+1 is converted to θ j Probability of (2); b j (. Cndot.): probability distribution obeyed by an observation sequence with a hidden state of j; o (O) t+1 : time t+1A historical observation sequence of the output of each wind power plant; beta t+1 (j) The method comprises the following steps Backward probability of the hidden state j at the time of t+1; alpha t (r): the forward probability that the hidden state is r is at the t moment; a, a rs : the hidden state at the time t of the ith row and the ith column in the state transition matrix A is theta r The hidden state at time t+1 is converted to θ s Probability of (2); b s (. Cndot.): probability distribution obeyed by an observation sequence with the hidden state s; beta t+1 (s): backward probability that the hidden state is s at t+1; n: number of hidden states.
Preferably, the updating of the state transition matrix, the mean vector of the gaussian distribution, the covariance matrix of the gaussian distribution and the probability distribution vector of the hidden state in the gaussian hidden markov model based on the conditional probability and the joint conditional probability is performed according to the following formula:
π j ＝γ 1 (j),j＝1,2,...,N
Wherein: pi j : the relevant state of the wind power plant is theta j Probability of (2); gamma ray 1 (j) The method comprises the following steps Conditional probability of the hidden state j at the initial moment; n: the number of hidden states;
wherein: a, a ij : the hidden state at the moment t of the jth column of the ith row in the state transition matrix A is theta i The hidden state at time t+1 is converted to θ j Probability of (2); zeta type toy t (i, j): joint conditional probability of hidden state j at time t; gamma ray t (j) The method comprises the following steps Conditional probability of the hidden state j at t;
wherein: mu (mu) j : a mean vector of Gaussian distribution with hidden state j; o (O) t : a historical observation sequence of the output of each wind power plant at the time t;
wherein: sigma and method for producing the same j : the hidden state is a covariance matrix of the gaussian distribution of j.
Preferably, the cumulative state transition probability is calculated as follows:
wherein: c ij : the accumulated state transition probability of the ith row and the jth column in the accumulated state transition probability matrix C; a, a ik : the hidden state at the moment t of the kth column of the ith row in the state transition matrix A is theta i The hidden state at time t+1 is converted to θ k Is a probability of (2).
Preferably, the multidimensional gaussian distribution is calculated according to the following formula:
b j (O)＝N(μ j ,Σ j ),1≤j≤N
wherein: b j (. Cndot.): a plurality of wind power plants are distributed in a multi-dimensional Gaussian mode with a hidden state j; o: a historical observation sequence formed by output data of each wind power plant;
the mean vector is +. >
Covariance matrix +.>
Is a multi-dimensional gaussian distribution of (c).
Preferably, the determining the prediction error of each wind farm at each moment in the preset period based on the multidimensional gaussian distribution and the cumulative state transition probability matrix includes:
determining the correlation states of the plurality of wind power plants at each moment in a preset period based on the cumulative state transition probability matrix;
based on the correlation states of the wind power plants at each moment and the corresponding multidimensional Gaussian distribution, the prediction error of each wind power plant at the moment is generated through random sampling.
Preferably, the determining the correlation states of the plurality of wind farms at each moment in the preset period based on the cumulative state transition probability matrix includes:
randomly generating a positive integer based on the number of hidden states to serve as a correlation state of a plurality of wind power plants at initial moments in a preset period;
and obtaining the correlation states of the plurality of wind farms at the rest time in a preset period based on the iterative computation of the correlation states of the plurality of wind farms at the initial time and the cumulative state transition probability matrix.
Preferably, the obtaining the correlation states of the plurality of wind farms in the rest time in the preset period based on the iterative computation of the correlation states of the plurality of wind farms in the initial time and the cumulative state transition probability matrix includes:
Step 201, taking the initial time as a known time;
step 202, generating random numbers in the interval [0,1 ];
step 203, comparing the random number with all elements of a row corresponding to a known time in the cumulative state transition probability matrix, and determining that the correlation states of a plurality of wind power plants at the next time are values corresponding to a previous column in two adjacent columns of the row corresponding to the known time when the size of the random number is between two adjacent columns of elements of the row corresponding to the known time;
step 204, when the next time is the ending time of the preset period, the cycle is ended, and the correlation states of the plurality of wind power plants corresponding to all the times in the preset period are output; otherwise, step 202 is performed with the next time as a known time.
Preferably, the predicted force scenes of all wind farms are as shown in the following formula:
wherein: theta (theta) k : k group of M wind farmsPredicting an output scene;
m wind farms at t T Predicting a vector composed of forces at a point of time; epsilon M (t T )：t T Prediction errors of M wind power plants at moment; />
M. wind farm at t T Predicting output at moment; m: the number of wind farms; t: and predicting a period.
Preferably, the predicting output value based on the point of each wind farm and the predicting error of the wind farm obtain the predicted output scenes of all the wind farms, further includes:
And circularly generating the predicted output scenes of all the wind power plants with the preset quantity based on the predicted output scenes of all the wind power plants.
Preferably, the generating, based on the predicted power scenes of all wind farms, a preset number of predicted power scenes of all wind farms in a circulating manner includes:
when the number of the predicted output scenes of all the wind power plants is equal to the preset number, obtaining the predicted output scenes of all the wind power plants with the preset number;
when the number of the predicted power scenes of all the wind power plants is smaller than the preset number, continuously determining the prediction error of each wind power plant at each moment in a preset period based on the multidimensional Gaussian distribution and the cumulative state transition probability matrix, and generating the predicted power of the scenes based on the point predicted power value of each wind power plant and the prediction error of the wind power plant until the predicted power scenes of all the wind power plants with the preset number are obtained;
wherein the predicted output scenes of all the wind power plants with the preset quantity are { Θ } 1 ,Θ 2 ,...,Θ K }；
Wherein: theta (theta) K : predicting the force of the K group of M wind power plants; k: the preset predicted output group number.
Based on the same inventive concept, the invention also provides a system for generating the multi-wind power plant output scene, which comprises:
The processing module is used for obtaining multidimensional Gaussian distribution and accumulated state transition probability matrixes based on output prediction error data of a plurality of wind power plants and a pre-constructed Gaussian hidden Markov model;
the prediction error module is used for determining the prediction error of each wind power plant at each moment in a preset period based on the multidimensional Gaussian distribution and the cumulative state transition probability matrix;
and the generating scene module is used for predicting the force value and the prediction error of the wind power plant based on the points of each wind power plant to obtain the predicted force scenes of all the wind power plants.
Preferably, the processing module includes:
the power output prediction error data generation sub-module is used for obtaining power output prediction error data of each wind power plant based on actual power output values of the plurality of wind power plants and the corresponding points;
the correlation state submodule is used for determining the correlation state among the plurality of wind power plants according to the output prediction error data of each wind power plant;
the setting submodule is used for setting the correlation state as a hidden state in the Gaussian hidden Markov model and setting the number of the hidden states;
the iteration sub-module is used for training the Gaussian hidden Markov model based on the output prediction error data of each wind power plant and the number of the hidden states, and iteratively calculating a state transition matrix of the Gaussian hidden Markov model, and a mean vector and a covariance matrix of Gaussian distribution corresponding to each hidden state through a forward-backward algorithm;
The multidimensional Gaussian distribution submodule is used for determining multidimensional Gaussian distribution based on mean vectors and covariance matrixes of Gaussian distribution corresponding to each hidden state;
an accumulated state transition probability sub-module for calculating an accumulated state transition probability based on the state transition matrix;
wherein the cumulative state transition probability matrix consists of cumulative state transition probabilities.
Compared with the prior art, the invention has the beneficial effects that:
according to the technical scheme, a multidimensional Gaussian distribution and cumulative state transition probability matrix is obtained based on output prediction error data of a plurality of wind power plants and a pre-constructed Gaussian hidden Markov model; determining a prediction error of each wind power plant at each moment in a preset period based on the multidimensional Gaussian distribution and the cumulative state transition probability matrix; the method can be used for considering the correlation among the prediction errors of different wind power plants, and improves the accuracy of the generated wind power prediction force scene.
According to the technical scheme provided by the invention, the method for generating the predicted output scenes of the wind power plants based on the Gaussian hidden Markov model is used for modeling different wind power plants, the generated predicted output scenes of the wind power plants can account for the correlation among different wind power plants, and the obtained predicted output scenes are more scientific and reasonable.
The technical scheme provided by the invention is not limited by the number of the wind power plants, and can simultaneously predict the generation of the output scene of a plurality of wind power plants.
According to the technical scheme provided by the invention, the generated predicted output scene well reflects the correlation of the prediction errors among the wind power plants.
Drawings
FIG. 1 is a flow chart of a method for generating a multi-wind farm output scenario according to the present invention;
FIG. 2 is a schematic diagram of a hidden Markov model according to the present invention;
FIG. 3 is a schematic diagram of a set effect of predicted output scenarios of two wind farms according to an embodiment of the present invention;
fig. 4 is a schematic diagram of a cross-correlation coefficient result of a predicted force scene of two wind farms according to an embodiment of the present invention.
Detailed Description
For a better understanding of the present invention, reference is made to the following description, drawings and examples.
Under the framework of a random optimization scheduling method, a power grid scheduling center takes a series of wind power predicted output scenes as input, and obtains a scheduling plan under the condition of meeting the expected meaning of all wind power output scenes through optimization solution. Because wind power output has strong randomness and volatility, a wind power predicted output scene is usually obtained by adding random prediction errors on the basis of point predicted output. At present, when a predicted output scene is generated for a plurality of wind power plants, correlation factors among the wind power plants are not fully considered, the accuracy of the generated predicted output scene is affected, and finally, the obtained scheduling plan error is larger.
In the existing wind power plant predicted output scene generation method, the correlation of the prediction errors among wind power plants is not considered, and the prediction errors of the output of the wind power plants are obtained through independent sampling, so that the correlation and actual deviation among the obtained predicted output scenes are larger, and the accuracy of the optimal scheduling result is affected. Aiming at the defects, the invention provides a method for generating a plurality of wind power plant prediction output scenes based on a Gaussian hidden Markov model (Gaussian Hidden Markov Model, GHMM), which can be used for considering the correlation among prediction errors of different wind power plants, and the generated wind power prediction output scenes can be used for considering the correlation among different wind power plants, so that the obtained prediction output scenes are more scientific and reasonable, and the scheduling method generated by the wind power prediction output scenes is higher in accuracy.
Example 1:
FIG. 1 is a flowchart of a method for generating a plurality of predicted output scenarios of a plurality of wind farms according to the present invention, as shown in FIG. 1, including:
s1, obtaining multidimensional Gaussian distribution and accumulated state transition probability matrixes based on output prediction error data of a plurality of wind power plants and a pre-constructed Gaussian hidden Markov model;
S2, determining a prediction error of each wind power plant at each moment in a preset period based on the multidimensional Gaussian distribution and the cumulative state transition probability matrix;
s3, predicting force values and prediction errors of the wind power plants based on points of the wind power plants to obtain predicted force scenes of all the wind power plants.
The method specifically comprises the following steps:
step 101. Gaussian hidden Markov model modeling considering the correlation of prediction errors
The invention adopts a Gaussian hidden Markov model to model the correlation of a plurality of wind power stations. The Gaussian hidden Markov model is a double random process consisting of a hidden state sequence and an observation sequence; the hidden state sequences are described by a hidden Markov chain, each hidden state corresponds to a group of observation sequences, and finally a hidden state sequence and an observation sequence are formed.
The Gaussian hidden Markov model is shown in FIG. 2, { Q 1 ,Q 2 ,...,Q t The hidden state sequence at each time is not observable; { O 1 ,O 2 ,...,O t -an observation sequence; the horizontal arrows in the figure represent transitions between hidden states at two adjacent times, and the vertical arrows represent outputs from the hidden states to observed quantities.
The hidden states and observables are assumed to have markov properties in the gaussian hidden markov model, namely:
The first equation shows that the state at any instant depends only on the state at the previous instant, and the second equation shows that the observed quantity at any instant depends only on the state at the current instant.
The invention adopts a Gaussian hidden Markov model, and the mathematical model is described as follows:
1) Assuming that the possible value of the hidden state variable is θ 1 ,θ 2 ,...,θ N N is the number of hidden states, and the range of the hidden states under the moment t is Q t ∈{θ 1 ,θ 2 ,...,θ N -a }; suppose that the observed quantity contains M elements, namely O t Is an M-dimensional column vector.
2) The probability distribution vector of the hidden state at the initial moment is pi= [ pi ] 1 ,π 2 ,...,π N ] T Wherein
π j ＝P(Q 1 ＝θ j ),1≤j≤N
Representing t 1 The hidden state at the moment is theta j Probability of time.
3) Describing state variables with discrete markov chains, state transition matrix a= (a) ij ) N×N An N x N matrix, wherein the elements of row i and j are:
a ij ＝P(Q t+1 ＝θ j |Q t ＝θ i ),1≤i,j≤N
a ij indicating that the state at time t is theta i State transition to θ at time t+1 j Is a probability of (2).
4) Observation probability b= { B j (O), j=1, 2,..
b j (O)＝N(μ j ,Σ j ),1≤j≤N
b j (x) Represents the probability distribution obeyed by the observation variable O when the state was j.
In this example it is assumed that the observed variable follows an M-dimensional Gaussian distribution, where μ j Mean vector, Σ, representing gaussian distribution corresponding to state j j For the covariance matrix of the gaussian distribution corresponding to state j, mu= { mu 1 ,μ 2 ,...,μ N Sum Σ= { Σ 1 ,Σ 2 ,...,Σ N And the sum of the mean vectors and covariance matrixes of the gaussian distribution corresponding to all N hidden states is represented.
The invention adopts a Gaussian hidden Markov model to model the correlation of a plurality of wind power stations, and the specific modeling method comprises the following steps:
taking the correlation state of the output prediction errors of a plurality of wind power plants as the hidden state of a Gaussian hidden Markov model, corresponding to one discrete hidden state at each moment, setting the number of the hidden states as N, and setting the value of the hidden states as a positive integer between 1 and N, namely theta 1 ＝1,θ 2 ＝2,...,θ N ＝N；
And taking the prediction error of the normalized output of each wind power plant as the observed quantity of the Gaussian hidden Markov model, namely taking the observed quantity as a vector formed by the prediction errors of the output of all wind power plants at the current moment.
At this time, the established gaussian hidden markov model can be represented by a plurality of tuples λ= (a, μ, Σ, pi).
Step 102, gaussian hidden Markov model parameter estimation
Based on time 1, 2..a, a historical observation sequence o= { O of T wind farm output prediction error 1 ,O 2 ,...,O T The parameters λ= (a, μ, Σ, pi) of the gaussian hidden markov model established in step 101 are estimated. The parameters of the gaussian hidden markov model are estimated using a forward-backward algorithm (Baum Welch algorithm) with the aim of maximizing the probability P (o|λ) given the observation sequence O.
The basic flow of the Baum Welch algorithm is as follows:
1) Randomly initializing all parameters lambda= (a, μ, Σ, pi);
2) The forward probability of each hidden state at time 1 is calculated:
α 1 (j)＝π j b j (O 1 ),j＝1,2,...,N
recursively calculating the forward probability of time 2,..:
3) Backward probability of each hidden state at the initial time T:
β T (j)＝1,j＝1,2,...,N
recursively calculating the backward probability at time T-1, T-2..1:
4) The conditional probability of the state at time t is calculated at a given model parameter λ= (a, μ, Σ, pi) and observation sequence O:
5) Calculating joint conditional probabilities of states at given model parameters λ= (a, μ, Σ, pi) and observation sequence O, times t and t+1:
6) Updating model parameters λ= (a, μ, Σ, pi):
π j ＝γ 1 (j),j＝1,2,...,N
7) Judging whether the parameters before and after updating are converged, and if the parameters are not converged, repeating the steps 2) to 7); if so, the algorithm ends.
The parameters lambda= (a, mu, Σ, pi) of the gaussian hidden markov model can be obtained by the above Baum Welch algorithm.
Step 103, calculating the cumulative state transition probability matrix of the Gaussian hidden Markov model
The state transition matrix of the Gaussian hidden Markov model describes probability transition characteristics of different states, and when a predicted force scene of a plurality of wind power fields is randomly generated by adopting a Monte Carlo simulation mode, the state transition matrix needs to be based on an accumulated state transition probability matrix.
State transition matrix a= (a) by gaussian hidden markov model ij ) N×N Calculate its corresponding cumulative state transition probability matrix c= (C) ij ) N×(N+1) 。
The elements of the cumulative state transition matrix are calculated as follows:
c ij the element of the ith row and the jth column in the C represents that the correlation state is theta at the current moment i At the next moment at theta 1 ,...,θ j The sum of the probabilities of the states.
Step 201, generating a predicted output scene of a plurality of wind power plants based on Monte Carlo simulation
Assume that the range of the period corresponding to the predicted output scene of the wind power plant to be generated is { t } 1 ,t 2 ,...,t T The predicted forces at the points of all wind farms in this period are:
wherein M is the number of wind farms,
and a vector representing the predicted force composition of the points of the M wind power plants at the time t.
Assuming that the number of the predicted output scenes of the wind power plant to be generated is K, the scene generation steps are as follows:
1) Training a model through a Baum Welch algorithm based on wind farm historical prediction error data to obtain hidden Markov model parameters lambda= (A, mu, sigma and pi);
2) Assuming that the kth random scene is currently generated, at initial t 1 Randomly generating a positive integer q between 1 and N at a time 1 Then t 1 Correlation state Q between M wind farms at time 1 ＝q 1 Based on multidimensional Gaussian distribution
Generating a random vector [ epsilon ] 1 (t 1 ),ε 2 (t 1 ),...,ε M (t 1 )]Let it be t 1 Prediction errors of M wind power plants at moment;
3) Let the current time be t l L is more than or equal to 1 and less than or equal to T, and the correlation state Q l ＝q l Based on [0,1 ]]Evenly distributed, generating intervals [0,1 ]]Inside random number x l Will be associated with the qth in the cumulative state transition probability matrix C l All elements of a row are compared, when x l When the size of (c) is between the y-th and y+1-th column elements of the row, then t can be determined l+1 Time dependency state Q l+1 ＝y；
4) Based on multidimensional Gaussian distribution
Generating a random vector [ epsilon ] 1 (t l+1 ),ε 2 (t l+1 ),...,ε M (t l+1 )]Let it be t l+1 Prediction errors of M wind power plants at moment;
5) Judgment of t l+1 Whether or not the moment is the last moment t T If not, repeating steps 3) to 5), if so, obtaining a time t 1 ,t 2 ,...,t T Next, the kth predicted output scene of the M wind farms:
6) Judging whether K is equal to K, if not, repeating the steps 2) to 5), and if so, obtaining a time t 1 ,t 2 ,...,t T K predicted output scene sets { Θ ] of M wind power plants 1 ,Θ 2 ,...,Θ K }。
According to the steps, the method is not limited by the number of the wind power plants, and the generation of the predicted output scene of a plurality of wind power plants can be performed simultaneously.
In the embodiment, 2 wind farms are selected for testing by the proposed method, and the Gaussian hidden Markov model is trained by adopting output prediction error data of 15 minutes in the whole year. FIG. 3 illustrates a plot of actual output at 96 points on a day, point predicted output, and 10 generated wind power output predictions for two wind farms. The point-plus-solid line is the actual output curve, the point-plus-solid line is the point predicted output curve, and the rest solid lines are the 10 predicted output scene curves. The result shows that the predicted output scenes of the two wind power plants can both be better covered with the predicted output and the actual predicted output, and the effectiveness of the method is verified.
The correlation of the prediction errors among the wind farms is described by adopting a cross-correlation coefficient, the cross-correlation coefficient describes the correlation coefficient of two time sequences at different time intervals, and the change condition of the correlation of the two time sequences along with time can be reflected. FIG. 4 shows the cross-correlation coefficient results for two wind farm actual outputs, point predicted outputs and 10 predicted output scenarios. The thickened solid line is the cross-correlation coefficient of the actual output force, the line formed by connecting hollow boxes is the cross-correlation coefficient of the point predicted output force, and the rest dotted lines are the cross-correlation coefficients of 10 predicted output force scenes. The result shows that the cross-correlation coefficients of 10 predicted output scenes can better cover the change range of the cross-correlation coefficients of the predicted output and the actual output of the points, the change trend of the cross-correlation coefficients along with time is consistent, and the deviation between the cross-correlation coefficients and the cross-correlation coefficients of the actual predicted output is smaller. The prediction output scene generated by the method provided by the patent well reflects the correlation of prediction errors among wind power plants, and the effectiveness of the method is verified.
Example 2:
1) The prediction error data of all wind power plants are read, and normalization processing is carried out by using the installed capacity;
2) According to the modeling method of the step 101, establishing Gaussian hidden Markov model parameters which take all wind power plant output prediction errors as observables and the correlation relationship among wind power plants as state quantities;
3) Estimating parameters of a Gaussian hidden Markov model according to a Baum Welch algorithm in the step 102 based on wind farm output prediction error historical data;
4) Calculating an accumulated state transition probability matrix of the established Gaussian hidden Markov model based on the method in the step 103;
5) Given the time and the number of the scenes required to be generated and the point predicted output results of each wind power plant, based on the Gaussian hidden Markov model obtained through training, a Monte Carlo simulation method in step 201 is adopted to randomly generate the predicted output scene set of all the wind power plants.
Example 3
Based on the same inventive concept, the invention also provides a system for generating the multi-wind power plant output scene, which comprises:
the processing module is used for obtaining multidimensional Gaussian distribution and accumulated state transition probability matrixes based on output prediction error data of a plurality of wind power plants and a pre-constructed Gaussian hidden Markov model;
the prediction error module is used for determining the prediction error of each wind power plant at each moment in a preset period based on the multidimensional Gaussian distribution and the cumulative state transition probability matrix;
And the generating scene module is used for predicting the force value and the prediction error of the wind power plant based on the points of each wind power plant to obtain the predicted force scenes of all the wind power plants.
In an embodiment, the processing module includes:
the power output prediction error data generation sub-module is used for obtaining power output prediction error data of each wind power plant based on actual power output values of the plurality of wind power plants and the corresponding points;
the correlation state submodule is used for determining the correlation state among the plurality of wind power plants according to the output prediction error data of each wind power plant;
the setting submodule is used for setting the correlation state as a hidden state in the Gaussian hidden Markov model and setting the number of the hidden states;
the iteration sub-module is used for training the Gaussian hidden Markov model based on the output prediction error data of each wind power plant and the number of the hidden states, and iteratively calculating a state transition matrix of the Gaussian hidden Markov model, and a mean vector and a covariance matrix of Gaussian distribution corresponding to each hidden state through a forward-backward algorithm;
the multidimensional Gaussian distribution submodule is used for determining multidimensional Gaussian distribution based on mean vectors and covariance matrixes of Gaussian distribution corresponding to each hidden state;
An accumulated state transition probability sub-module for calculating an accumulated state transition probability based on the state transition matrix;
wherein the cumulative state transition probability matrix consists of cumulative state transition probabilities.
In an embodiment, the prediction error module includes:
a correlation state sub-module, configured to determine correlation states of the plurality of wind farms at each moment in a preset period based on the cumulative state transition probability matrix;
and the prediction error sub-module is used for generating the prediction error of each wind power plant at each moment through random sampling based on the correlation states of the wind power plants at each moment and the corresponding multidimensional Gaussian distribution.
In an embodiment, the correlation status submodule includes:
the initial time unit is used for randomly generating a positive integer based on the number of hidden states to serve as the correlation state of the plurality of wind power plants at the initial time in the preset period;
and the rest time unit is used for obtaining the correlation states of the plurality of wind power plants at rest time in a preset period based on the iterative computation of the correlation states of the plurality of wind power plants at the initial time and the cumulative state transition probability matrix.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing is illustrative of the present invention and is not to be construed as limiting thereof, but rather as providing for the use of additional embodiments and advantages of all such modifications, equivalents, improvements and similar to the present invention are intended to be included within the scope of the present invention as defined by the appended claims.
Claims (2)
1. The method for generating the multi-wind power plant output scene is characterized by comprising the following steps of:
obtaining a multidimensional Gaussian distribution and cumulative state transition probability matrix based on output prediction error data of a plurality of wind power plants and a pre-constructed Gaussian hidden Markov model;
determining a prediction error of each wind power plant at each moment in a preset period based on the multidimensional Gaussian distribution and the cumulative state transition probability matrix;
based on the point predicted force value of each wind power plant and the prediction error of the wind power plant, obtaining predicted force scenes of all the wind power plants;
The method for obtaining the multidimensional Gaussian distribution and cumulative state transition probability matrix based on the output prediction error data of a plurality of wind power plants and a pre-constructed Gaussian hidden Markov model comprises the following steps:
based on the actual output values of the wind power plants and the predicted output values of the corresponding points, output prediction error data of each wind power plant are obtained;
determining a correlation state among the plurality of wind power plants according to the output prediction error data of each wind power plant;
setting the correlation state as a hidden state in the Gaussian hidden Markov model, and setting the number of the hidden states;
training a Gaussian hidden Markov model based on output prediction error data of each wind power plant and the number of hidden states, and iteratively calculating a state transition matrix of the Gaussian hidden Markov model, and a mean vector and a covariance matrix of Gaussian distribution corresponding to each hidden state through a forward-backward algorithm;
determining multidimensional Gaussian distribution based on mean vector and covariance matrix of Gaussian distribution corresponding to each hidden state;
calculating an accumulated state transition probability based on the state transition matrix;
wherein the cumulative state transition probability matrix consists of cumulative state transition probabilities;
Training the Gaussian hidden Markov model based on the output prediction error data of each wind power plant and the number of hidden states, and iteratively calculating a state transition matrix of the Gaussian hidden Markov model, and a mean vector and a covariance matrix of Gaussian distribution corresponding to each hidden state through a forward-backward algorithm, wherein the training comprises the following steps:
step 101, setting initial values for a state transition matrix, a mean value vector of Gaussian distribution, a covariance matrix of Gaussian distribution and a probability distribution vector of hidden states in a Gaussian hidden Markov model;
102, calculating forward probabilities of hidden states at initial moments in a training period, and sequentially calculating forward probabilities of hidden states at all other moments in the training period;
step 103, calculating backward probabilities of hidden states at the ending time in the training period, and sequentially calculating backward probabilities of hidden states at all other time points in the training period;
104, calculating the conditional probability of the hidden state at any moment based on an observation sequence formed by output prediction error data of a plurality of wind power plants, the forward probability of each hidden state and the backward probability of each hidden state;
step 105, calculating joint conditional probabilities of hidden states at any moment and hidden states at the next moment at any moment based on an observation sequence formed by output prediction error data of a plurality of wind power plants, forward probabilities of hidden states and backward probabilities of the hidden states;
Step 106, updating a state transition matrix, a mean vector of Gaussian distribution, a covariance matrix of Gaussian distribution and a probability distribution vector of hidden states in the Gaussian hidden Markov model based on the conditional probability and the joint conditional probability;
step 107, if the state transition matrix, the mean value vector of the gaussian distribution, the covariance matrix of the gaussian distribution and the probability distribution vector of the hidden state in the updated gaussian hidden markov model meet a preset convergence condition, the cycle is ended, the gaussian hidden markov model is set according to the current parameters, otherwise, step 102 is executed;
the forward probability is calculated as follows:
wherein: alpha t+1 (j) The method comprises the following steps Forward probability of the hidden state j at t+1; pi j : the hidden state of the wind power plant is theta j Probability of (2); b j (. Cndot.): probability distribution obeyed by an observation sequence with a hidden state of j; o (O) 1 : a historical observation sequence of the output of each wind power plant at the initial moment; n: the number of hidden states; alpha t (j) The method comprises the following steps the forward probability of the hidden state j at the time t; a, a ij : the hidden state at the moment t of the jth column of the ith row in the state transition matrix A is theta i The hidden state at time t+1 is converted to θ j Probability of (2); o (O) t+1 : a historical observation sequence of the output of each wind power plant at the time of t+1;
The probability of the hidden state at the initial moment of the wind power plant forms a probability distribution vector of the hidden state;
the backward probability is calculated according to the following formula:
wherein: beta t (j) The method comprises the following steps the backward probability of the hidden state j at the time t; a, a ji : the hidden state at the moment t of the jth row and the ith column in the state transition matrix A is theta j The hidden state at time t+1 is converted to θ i Probability of (2); b i (. Cndot.): probability distribution obeyed by an observation sequence with hidden state i; beta t+1 (i) The method comprises the following steps the backward probability that the hidden state is i at the time of t+1; o (O) t+1 : a historical observation sequence of the output of each wind power plant at the time of t+1; t: the termination time of the training period; n: the number of hidden states;
the conditional probability of the hidden state at any moment is calculated according to the following formula:
wherein: gamma ray t (j) The method comprises the following steps Conditional probability of the hidden state j at t; alpha t (j) The method comprises the following steps the forward probability of the hidden state j at the time t; beta t (j) The method comprises the following steps the backward probability of the hidden state j at the time t; alpha t (i) The method comprises the following steps the forward probability of the hidden state i at the time t; beta t (i) The method comprises the following steps time tThe backward probability of the hidden state is i; n: the number of hidden states;
the joint conditional probability is calculated as follows:
wherein: zeta type toy t (i, j): joint conditional probability of hidden state j at time t; alpha t (j) The method comprises the following steps the forward probability of the hidden state j at the time t; a, a ij : the hidden state at the moment t of the jth column of the ith row in the state transition matrix A is theta i The hidden state at time t+1 is converted to θ j Probability of (2); b j (. Cndot.): probability distribution obeyed by an observation sequence with a hidden state of j; o (O) t+1 : a historical observation sequence of the output of each wind power plant at the time of t+1; beta t+1 (j) The method comprises the following steps Backward probability of the hidden state j at the time of t+1; alpha t (r): the forward probability that the hidden state is r is at the t moment; a, a rs : the hidden state at the time t of the ith row and the ith column in the state transition matrix A is theta r The hidden state at time t+1 is converted to θ s Probability of (2); b s (. Cndot.): probability distribution obeyed by an observation sequence with the hidden state s; beta t+1 (s): backward probability that the hidden state is s at t+1; n: the number of hidden states;
the state transition matrix, the mean vector of the Gaussian distribution, the covariance matrix of the Gaussian distribution and the probability distribution vector of the hidden state in the Gaussian hidden Markov model are updated based on the conditional probability and the joint conditional probability, and the state transition matrix, the mean vector of the Gaussian distribution, the covariance matrix of the Gaussian distribution and the probability distribution vector of the hidden state are updated according to the following steps:
π j ＝γ 1 (j),j＝1,2,...,N
wherein: pi j : the relevant state of the wind power plant is theta j Probability of (2); gamma ray 1 (j) The method comprises the following steps Conditional probability of the hidden state j at the initial moment; n: the number of hidden states;
wherein: a, a ij : the hidden state at the moment t of the jth column of the ith row in the state transition matrix A is theta i The hidden state at time t+1 is converted to θ j Probability of (2); zeta type toy t (i, j): joint conditional probability of hidden state j at time t; gamma ray t (j) The method comprises the following steps Conditional probability of the hidden state j at t;
wherein: mu (mu) j : a mean vector of Gaussian distribution with hidden state j; o (O) t : a historical observation sequence of the output of each wind power plant at the time t;
wherein: sigma and method for producing the same j : covariance matrix of Gaussian distribution with hidden state j;
the cumulative state transition probability is calculated as follows:
wherein: c ij : the accumulated state transition probability of the ith row and the jth column in the accumulated state transition probability matrix C; a, a ik : the hidden state at the moment t of the kth column of the ith row in the state transition matrix A is theta i The hidden state at time t+1 is converted to θ k Probability of (2);
the multidimensional gaussian distribution is calculated according to the following formula:
b j (O)＝N(μ j ,Σ j ),1≤j≤N
wherein: b j (. Cndot.): a plurality of wind power plants are distributed in a multi-dimensional Gaussian mode with a hidden state j; o: a historical observation sequence formed by output data of each wind power plant;
mean vectorIs->
Covariance matrix +.>
Is a multi-dimensional gaussian distribution of (a);
the determining the prediction error of each wind power plant at each moment in a preset period based on the multidimensional Gaussian distribution and the cumulative state transition probability matrix comprises the following steps:
determining the correlation states of the plurality of wind power plants at each moment in a preset period based on the cumulative state transition probability matrix;
Generating a prediction error of each wind power plant at each moment by random sampling based on the correlation states of the wind power plants at each moment and the corresponding multidimensional Gaussian distribution;
the determining the correlation states of the plurality of wind farms at each moment in a preset period based on the cumulative state transition probability matrix includes:
randomly generating a positive integer based on the number of hidden states to serve as a correlation state of a plurality of wind power plants at initial moments in a preset period;
obtaining the correlation states of the plurality of wind power plants at the rest time in a preset period based on the iterative computation of the correlation states of the plurality of wind power plants at the initial time and the cumulative state transition probability matrix;
the obtaining the correlation states of the plurality of wind farms in the rest time in the preset period based on the iterative computation of the correlation states of the plurality of wind farms in the initial time and the cumulative state transition probability matrix comprises the following steps:
step 201, taking the initial time as a known time;
step 202, generating random numbers in the interval [0,1 ];
step 203, comparing the random number with all elements of a row corresponding to a known time in the cumulative state transition probability matrix, and determining that the correlation states of a plurality of wind power plants at the next time are values corresponding to a previous column in two adjacent columns of the row corresponding to the known time when the size of the random number is between two adjacent columns of elements of the row corresponding to the known time;
Step 204, when the next time is the ending time of the preset period, the cycle is ended, and the correlation states of the plurality of wind power plants corresponding to all the times in the preset period are output; otherwise, executing step 202 with the next time as a known time;
the predicted force scenes of all wind power plants are shown as the following formula:
wherein: theta (theta) k : the k group of M wind power plants predicts the output scene;
m wind farms at t T Predicting a vector composed of forces at a point of time; epsilon M (t T )：t T Prediction errors of M wind power plants at moment; />
M. wind farm at t T Predicting output at moment; m: the number of wind farms; t: predicting a period;
the method for obtaining the predicted output scenes of all wind power plants based on the predicted output values of the points of each wind power plant and the predicted errors of the wind power plants further comprises the following steps:
generating a preset number of predicted power scenes of all wind power plants in a circulating mode based on the predicted power scenes of all wind power plants;
the generating of the predicted power scenes of all wind power plants based on the predicted power scenes of all wind power plants in a circulating way comprises the following steps:
when the number of the predicted output scenes of all the wind power plants is equal to the preset number, obtaining the predicted output scenes of all the wind power plants with the preset number;
When the number of the predicted power scenes of all the wind power plants is smaller than the preset number, continuously determining the prediction error of each wind power plant at each moment in a preset period based on the multidimensional Gaussian distribution and the cumulative state transition probability matrix, and generating the predicted power of the scenes based on the point predicted power value of each wind power plant and the prediction error of the wind power plant until the predicted power scenes of all the wind power plants with the preset number are obtained;
wherein the predicted output scenes of all the wind power plants with the preset quantity are { Θ } 1 ,Θ 2 ,...,Θ K }；
Wherein: theta (theta) K : predicting the force of the K group of M wind power plants; k: the preset predicted output group number.
2. A system for generating a multi-wind farm output scenario for implementing a method for generating a multi-wind farm output scenario as claimed in claim 1, comprising:
the processing module is used for obtaining multidimensional Gaussian distribution and accumulated state transition probability matrixes based on output prediction error data of a plurality of wind power plants and a pre-constructed Gaussian hidden Markov model;
the prediction error module is used for determining the prediction error of each wind power plant at each moment in a preset period based on the multidimensional Gaussian distribution and the cumulative state transition probability matrix;
The generating scene module is used for predicting the force value and the prediction error of the wind power plant based on the points of each wind power plant to obtain the predicted force scenes of all the wind power plants;
the processing module comprises:
the power output prediction error data generation sub-module is used for obtaining power output prediction error data of each wind power plant based on actual power output values of the plurality of wind power plants and the corresponding points;
the correlation state submodule is used for determining the correlation state among the plurality of wind power plants according to the output prediction error data of each wind power plant;
the setting submodule is used for setting the correlation state as a hidden state in the Gaussian hidden Markov model and setting the number of the hidden states;
the iteration sub-module is used for training the Gaussian hidden Markov model based on the output prediction error data of each wind power plant and the number of the hidden states, and iteratively calculating a state transition matrix of the Gaussian hidden Markov model, and a mean vector and a covariance matrix of Gaussian distribution corresponding to each hidden state through a forward-backward algorithm;
the multidimensional Gaussian distribution submodule is used for determining multidimensional Gaussian distribution based on mean vectors and covariance matrixes of Gaussian distribution corresponding to each hidden state;
An accumulated state transition probability sub-module for calculating an accumulated state transition probability based on the state transition matrix;
wherein the cumulative state transition probability matrix consists of cumulative state transition probabilities.
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