CN111222680A - Wind power station output ultra-short-term prediction method based on least square support vector machine - Google Patents

Wind power station output ultra-short-term prediction method based on least square support vector machine Download PDF

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CN111222680A
CN111222680A CN201911033654.3A CN201911033654A CN111222680A CN 111222680 A CN111222680 A CN 111222680A CN 201911033654 A CN201911033654 A CN 201911033654A CN 111222680 A CN111222680 A CN 111222680A
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沈润杰
华丹琼
邢瑞敏
张建卜
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Abstract

The invention relates to a method for ultra-short output prediction of a wind power station based on a least square support vector machine, which specifically comprises the following steps: step S1: decomposing the wind speed time series into N modal components with different scales by utilizing variational modal decomposition; step S2: respectively establishing an LSSVM prediction model of a least square support vector machine for each modal component; step S3: dividing a data set of the wind speed historical sequence into a training set, a cross validation set and a test set, and carrying out normalization processing on the data; step S4: and rolling the LSSVM prediction model through a training set, optimizing the kernel width and penalty factors of the LSSVN prediction model on a cross validation set by utilizing a particle swarm optimization algorithm, and then testing errors on a test set to obtain the optimal LSSVM prediction model smaller than an error threshold. Compared with the prior art, the method has the advantages of reducing the influence of wind speed non-stationarity, improving prediction precision and the like.

Description

Wind power station output ultra-short-term prediction method based on least square support vector machine
Technical Field
The invention relates to the field of big data prediction, in particular to a wind power station output ultra-short-term prediction method based on a least square support vector machine.
Background
The Support Vector Machine (SVM) is a data-based machine learning method which is established by Vapnik on the basis of a statistical learning theory, the Least Square Support Vector Machine (LSSVM) is the expansion and improvement of the Support Vector Machine (SVM), a least square linear system is used as a loss function, an equality constraint replaces an inequality constraint of a conventional SVM, a quadratic programming problem is converted into a solving problem of a linear equation set, and the convergence rate of an algorithm is improved.
Wind farm power prediction models can be divided into three categories: physical prediction models, statistical prediction models, and combined prediction models. The physical prediction model firstly obtains weather information such as wind speed, wind direction, air temperature, air pressure and the like of a wind power plant by using a numerical weather forecast NWP system, then obtains the weather information at the height of a hub of each wind generating set on the basis of fully considering the aggregation effects of a wind generating set group such as a tower shadow effect, a wake effect and the like according to the physical and geographic information of the wind power plant, and then calculates and calculates the output power of the wind generating set by using the power curve of a single fan; the essence of the statistical prediction model is that a mapping model is established between input and output, the input content comprises historical data, numerical weather forecast and other information, the output content comprises wind power plant power, and then the model is applied to prediction. The combined prediction model comprehensively considers more than two kinds of single predictions, and obtains the global optimal prediction performance by utilizing the advantages of each single prediction model.
China has large land area and long coastline, and land and offshore wind energy resources are abundant, and the wind power industry is vigorously developed by China governments in the last two decades. With the gradual expansion of the scale of the wind power station, the problems to be solved appear in the aspects of self management control, high power incorporation into the power grid and the like, and compared with the conventional power supply, the wind power station is difficult to play the roles in the aspects of peak regulation, frequency regulation, voltage regulation, standby and the like in the power system, so that the safe and stable operation risk of the power grid is increased. Due to characteristics of wind randomness, uncertainty, volatility and the like, impact on a power grid can be caused by power access of large-scale wind power generation, and the risk of stable operation of the power grid is increased. The influence on the safe and stable operation of the system comprises the influence on both static safety and dynamic safety. Static safety is mainly reflected in the influence of the change of wind power generation capacity on the static voltage of a system, and when the wind power generation capacity is small, the line of a wind power plant access system runs under light load, so that the voltage of the system is increased; when the wind power generation capacity is increased, the reactive loss of the wind power plant and the power transmission line is increased, and the voltage of the system is reduced. The dynamic safety mainly comprises the influence of wind power generation on the stability of transient voltage and a transient power angle, and when a power grid fails, the transient voltage of a wind power node continuously drops, and finally the phenomenon of voltage collapse and high-frequency oscillation occurs. In order to solve the problem, the theoretical output of the wind power plant needs to be analyzed and researched, a model capable of actually reflecting the theoretical output of the wind power plant is found, and ultra-short-time prediction is carried out on the theoretical output of the wind power plant.
Disclosure of Invention
The invention aims to overcome the defects that wind power change impacts a power grid and the stable operation risk of the power grid is increased in the prior art, and provides a wind power station output ultra-short-term prediction method based on a least square support vector machine.
The purpose of the invention can be realized by the following technical scheme:
a super-short-term wind power station output prediction method based on a least square support vector machine comprises the following steps:
step S1: decomposing the wind speed sequence into N modal components with different scales by utilizing variational modal decomposition;
step S2: respectively establishing LSSVM prediction models of a least square support vector machine by the wind speed sequences corresponding to the N modal components;
step S3: dividing a data set of the wind speed sequence into a training set, a cross validation set and a test set, and carrying out normalization processing on the data;
step S4: and rolling the LSSVM prediction model through a training set, optimizing the kernel width and penalty factors of the LSSVN prediction model on a cross validation set by utilizing a particle swarm optimization algorithm, and then testing errors on a test set to obtain the optimal LSSVM prediction model smaller than an error threshold.
The modal components are finite bandwidths with center frequencies, the sum of the estimated bandwidths of each modal component is minimized through a modal function, and the sum is equal to a non-stationary signal corresponding to a wind speed sequence.
Performing Hilbert transform on the analysis signal of the modal function to obtain a single-sided frequency spectrum of the modal function, specifically:
Figure BDA0002250842260000021
Figure BDA0002250842260000022
where δ (t) is an impulse function, t is time, uk(t) is the mode function, j is the imaginary symbol;
mixing the analytic signals of the mode functions and modulating the frequency spectrum of each mode to a corresponding base frequency band by taking the estimated center frequency as a reference, wherein the method specifically comprises the following steps:
Figure BDA0002250842260000031
wherein the content of the first and second substances,
Figure BDA0002250842260000032
vector description of the center frequency on the complex plane;
calculating the square L2 norm of the corresponding fundamental frequency band of the demodulation signal, and estimating the bandwidth of each modal signal, wherein the constrained variation expression is as follows:
Figure BDA0002250842260000033
wherein the content of the first and second substances,
Figure BDA0002250842260000034
partial derivatives of t, w, as a functionkIs the frequency center of each mode function.
The constrained variation expression is converted into an unconstrained variation expression by introducing a secondary penalty factor and a Lagrange multiplier, and the unconstrained variation expression is specifically as follows:
Figure 100002_1
wherein, C is a secondary penalty factor, lambda (t) is a Lagrange multiplication operator, k is the number of mode functions, and f (t) is an input non-stationary signal.
The variation modal decomposition adopts an alternating direction multiplier algorithm, modal components are converted into a frequency domain through Fourier equidistant conversion, and the integration form of non-negative frequency intervals of the modal components is as follows:
Figure BDA0002250842260000036
where ω is a random frequency, ωkIs the frequency center, u, of each mode functionk(w) is a modal function in the frequency domain,
Figure BDA0002250842260000037
is a mode function in the (n + 1) th iteration, lambda (w) is a Lagrange multiplication operator on a frequency domain, and f (w) is a non-stationary signal on the frequency domain;
according to the frequency domain expression of the modal component, the parameters of the alternating direction multiplier algorithm are updated as follows:
Figure 100002_2
wherein the content of the first and second substances,
Figure BDA0002250842260000039
is the current surplus
Figure 100002_3
Wiener filtering of (1);
the center frequency is converted into the frequency domain and then expressed as:
Figure BDA0002250842260000041
according to the frequency domain expression of the center frequency, the parameters of the alternative direction multiplier algorithm are updated as follows:
Figure BDA0002250842260000042
wherein the content of the first and second substances,
Figure BDA0002250842260000043
is the center of gravity of the power spectrum of the modal function.
The LSSVM prediction model for rolling training of the training set specifically comprises the steps of adding a true value of a moment into the training set after the moment is predicted, and removing a data point at the front end of the training set, which is farthest from the next predicted moment.
The particle swarm optimization algorithm specifically comprises the steps of updating by tracking individual extremum values and global extremum values, and searching an optimal value through multiple iterations.
The individual extremum is an optimal position through which one particle has passed, and the global extremum is an optimal one of optimal positions reached by all particles in the individual particle swarm.
The specific process of the particle swarm optimization algorithm is as follows:
step S401: initializing a particle swarm;
step S402: according to the population size N of the particle group and the position x of each particleiAnd viCalculating a fitness value F for each particlen[i]；
Step S403: fitness value Fn[i]And individual extremum pbest(i) Global extreme value gbestBy comparison, if Fn[i]>pbest(i) Then use Fn[i]Replacement of pbest(i) If F isn[i]>gbestThen use Fn[i]G is replaced bybest；
Step S404: updating the velocity v of the particles according to the individual extrema and the global extremaiAnd position xi；
Step S405: and exiting when the error of the updated LSSVM prediction model is smaller than the threshold value or reaches the maximum iteration number, otherwise, returning to the step S402 to continue the optimization.
Compared with the prior art, the invention has the following beneficial effects:
1. according to the method, the unstable wind power output sequence is decomposed into a plurality of stable sequences by utilizing the variational modal decomposition aiming at the characteristics of the wind speed, so that the influence of non-stationarity on the prediction precision is reduced.
2. The invention divides the data set into a training set, a cross validation set and a test set, and trains through a rolling training mode, thereby ensuring the stability of the number of the training sets, continuing the correlation of the time sequence and the authenticity of the data, and improving the prediction precision.
3. The combined prediction models of different methods are used for carrying out prediction on the non-stationary sequence, and the prediction has better generalization capability.
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FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a schematic diagram of training set partitioning according to the present invention;
FIG. 3 is a schematic flow chart of the rolling training of the present invention;
FIG. 4 is a schematic flow chart of the particle swarm optimization algorithm of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
As shown in fig. 1, a method for ultra-short term prediction of wind power plant output based on a least square support vector machine is characterized by comprising the following steps:
step S1: decomposing the wind speed sequence into N modal components with different scales by utilizing variational modal decomposition;
step S2: respectively establishing LSSVM prediction models of a least square support vector machine by the wind speed sequences corresponding to the N modal components;
step S3: dividing a data set of the wind speed sequence into a training set, a cross validation set and a test set, and carrying out normalization processing on the data;
step S4: and rolling the LSSVM prediction model through a training set, optimizing the kernel width and penalty factors of the LSSVN prediction model on a cross validation set by utilizing a particle swarm optimization algorithm, and then testing errors on a test set to obtain the optimal LSSVM prediction model smaller than an error threshold.
The modal components are finite bandwidths with center frequencies, and the sum of the estimated bandwidths of each modal component is minimized through a modal function and is equal to the non-stationary signal corresponding to the wind speed sequence.
Performing Hilbert transform on an analytic signal of the modal function to obtain a unilateral frequency spectrum of the modal function, specifically:
Figure BDA0002250842260000051
Figure BDA0002250842260000052
where δ (t) is an impulse function, t is time, uk(t) is the mode function, j is the imaginary symbol;
mixing the analytic signals of the mode functions and modulating the frequency spectrum of each mode to a corresponding base frequency band by taking the estimated center frequency as a reference, wherein the method specifically comprises the following steps:
Figure BDA0002250842260000061
wherein the content of the first and second substances,
Figure BDA0002250842260000062
vector description of the center frequency on the complex plane;
calculating the square L2 norm of the corresponding fundamental frequency band of the demodulation signal, and estimating the bandwidth of each modal signal, wherein the constrained variation expression is as follows:
Figure BDA0002250842260000063
wherein the content of the first and second substances,
Figure BDA0002250842260000064
partial derivatives of t, w, as a functionkIs the frequency center of each mode function.
The constrained variable expression is converted into an unconstrained variable expression by introducing a secondary penalty factor and a Lagrangian multiplier, wherein the secondary penalty factor can ensure the reconstruction accuracy of the signal in the presence of Gaussian noise, the Lagrangian maintains the strictness of constraint conditions, and the expanded Lagrangian expression is specifically as follows:
Figure 4
wherein, C is a secondary penalty factor, lambda (t) is a Lagrange multiplication operator, k is the number of mode functions, and f (t) is an input non-stationary signal.
The variation modal decomposition adopts an alternating direction multiplier algorithm, modal components are converted into a frequency domain through Fourier equidistant conversion, and the integration form of non-negative frequency intervals of the modal components is as follows:
Figure BDA0002250842260000066
where ω is a random frequency, ωkFor the frequency center, u, of each mode functionk(w) is a modal function in the frequency domain,
Figure BDA0002250842260000067
is a mode function in the (n + 1) th iteration, lambda (w) is a Lagrange multiplication operator on a frequency domain, and f (w) is a non-stationary signal on the frequency domain;
according to the frequency domain expression of the modal components, the parameters of the alternating direction multiplier algorithm are updated as follows:
Figure 5
wherein the content of the first and second substances,
Figure BDA0002250842260000069
is the current surplus
Figure 6
Wiener filtering of (1);
the center frequency is converted into the frequency domain and then expressed as:
Figure BDA00022508422600000611
according to the frequency domain expression of the center frequency, the parameters of the alternating direction multiplier algorithm are updated as follows:
Figure BDA0002250842260000071
wherein the content of the first and second substances,
Figure BDA0002250842260000072
is the center of gravity of the power spectrum of the modal function.
As shown in fig. 2, a part of the training set is used as a cross validation set, the training set of the previous part is used for training the model, the cross validation set is used for validating errors, so as to select different model parameters according to the error magnitude, and train the optimal model with the parameter with the minimum error.
As shown in fig. 3, the LSSVM prediction model is specifically trained by rolling the training set, in which a true value at a time is added to the training set after the time is predicted, and a data point at the front end of the training set, which is farthest from the next predicted time, is removed.
The particle swarm optimization algorithm specifically comprises the steps of updating by tracking an individual extreme value and a global extreme value, and searching an optimal value through multiple iterations, wherein the individual extreme value is an optimal position through which a particle passes, and the global extreme value is an optimal position in the optimal positions reached by all the particles in an individual particle swarm.
As shown in fig. 4, the specific flow of the particle swarm optimization algorithm is as follows:
step S401: initializing a particle swarm;
step S402: according to the population size N of the particle group and the position x of each particleiAnd viCalculating a fitness value F for each particlen[i]；
Step S403: fitness value Fn[i]And individual extremum pbest(i) Global extreme value gbestMaking a comparison if Fn[i]>pbest(i) Then use Fn[i]Replacement of pbest(i) If F isn[i]>gbestThen use Fn[i]G is replaced bybest；
Step S404: updating the velocity v of the particles according to the individual extrema and the global extremaiAnd position xi；
Step S405: and exiting when the error of the updated LSSVM prediction model is smaller than the threshold value or reaches the maximum iteration number, otherwise, returning to the step S402 to continue the optimization.

Claims (9)

1. A super short-term wind power station output prediction method based on a least square support vector machine is characterized by comprising the following steps:
step S1: decomposing the wind speed time series into N modal components with different scales by utilizing variational modal decomposition;
step S2: respectively establishing an LSSVM prediction model of a least square support vector machine for each modal component;
step S3: dividing a data set of the wind speed historical sequence into a training set, a cross validation set and a test set, and carrying out normalization processing on the data;
step S4: and rolling the LSSVM prediction model through a training set, optimizing the kernel width and penalty factors of the LSSVN prediction model on a cross validation set by utilizing a particle swarm optimization algorithm, and then testing errors on a test set to obtain the optimal LSSVM prediction model smaller than an error threshold.
2. The method of claim 1, wherein the modal components are finite bandwidths with a center frequency, and the sum of the estimated bandwidths of each modal component is minimized by a modal function and is equal to the non-stationary signal corresponding to the wind speed sequence.
3. The ultra-short-term wind power plant output prediction method based on the least square support vector machine according to claim 2, wherein hilbert transform is performed on an analytic signal of the modal function to obtain the modal function single-sided spectrum, specifically:
Figure FDA0002250842250000011
Figure FDA0002250842250000012
where δ (t) is an impulse function, t is time, uk(t) is the mode function, j is the imaginary symbol;
mixing the analytic signals of the mode functions and modulating the frequency spectrum of each mode to a corresponding base frequency band by taking the estimated center frequency as a reference, wherein the method specifically comprises the following steps:
Figure FDA0002250842250000013
wherein the content of the first and second substances,
Figure FDA0002250842250000014
vector description of the center frequency on the complex plane;
calculating the square L2 norm of the corresponding fundamental frequency band of the demodulation signal, and estimating the bandwidth of each modal signal, wherein the constrained variation expression is as follows:
Figure FDA0002250842250000021
wherein the content of the first and second substances,
Figure FDA0002250842250000022
partial derivatives of t, w, as a functionkIs the frequency center of each mode function.
4. The ultra-short term wind power plant output prediction method based on the least square support vector machine according to claim 3, wherein the constrained variable expression is converted into an unconstrained variable expression by introducing a secondary penalty factor and a Lagrangian multiplier, specifically as follows:
Figure 1
wherein, C is a secondary penalty factor, lambda (t) is a Lagrange multiplication operator, k is the number of mode functions, and f (t) is an input non-stationary signal.
5. The ultra-short-term wind power plant output prediction method based on the least square support vector machine according to claim 4, wherein the variation modal decomposition adopts an alternating direction multiplier algorithm, a modal component is converted into a frequency domain through Fourier equidistant transformation, and the integration form of a non-negative frequency interval of the modal component is as follows:
Figure FDA0002250842250000024
where ω is a random frequency, ωkIs the frequency center, u, of each mode functionk(w) is a modal function in the frequency domain,
Figure FDA0002250842250000025
is a mode function in the (n + 1) th iteration, lambda (w) is a Lagrange multiplication operator on a frequency domain, and f (w) is a non-stationary signal on the frequency domain;
according to the frequency domain expression of the modal component, the parameters of the alternating direction multiplier algorithm are updated as follows:
Figure 2
wherein the content of the first and second substances,
Figure FDA0002250842250000027
is the current surplus
Figure 3
Wiener filtering of (1);
the center frequency is converted into the frequency domain and then expressed as:
Figure FDA0002250842250000029
according to the frequency domain expression of the center frequency, the parameters of the alternative direction multiplier algorithm are updated as follows:
Figure FDA00022508422500000210
wherein the content of the first and second substances,
Figure FDA0002250842250000031
is the center of gravity of the power spectrum of the modal function.
6. The ultra-short term wind power plant output prediction method based on the least square support vector machine according to claim 1, wherein the rolling training LSSVM prediction model of the training set specifically includes adding a true value of a moment into the training set after the moment is predicted, and removing a data point at the front end of the training set which is farthest from the next prediction moment.
7. The ultra-short term wind power plant output prediction method based on the least square support vector machine according to claim 1, wherein the particle swarm optimization algorithm is specifically updated by tracking individual extrema and global extrema, and an optimal value is searched through multiple iterations.
8. The ultra-short term wind power plant output prediction method based on the least square support vector machine as claimed in claim 7, wherein the individual extreme value is an optimal position where a particle has passed, and the global extreme value is an optimal one of the optimal positions reached by all the particles in the individual particle swarm.
9. The ultra-short term wind power plant output prediction method based on the least square support vector machine according to claim 7, wherein the particle swarm optimization algorithm comprises the following specific procedures:
step S401: initializing a particle swarm;
step S402: according to the population size N of the particle group and the position x of each particleiAnd viCalculating a fitness value F for each particlen[i]；
Step S403: fitness value Fn[i]And individual extremum pbest(i) Global extreme value gbestBy comparison, if Fn[i]>pbest(i) Then use Fn[i]Replacement of pbest(i) If F isn[i]>gbestThen use Fn[i]G is replaced bybest；
Step S404: updating the velocity v of the particles according to the individual extrema and the global extremaiAnd position xi；
Step S405: and exiting when the error of the updated LSSVM prediction model is smaller than the threshold value or reaches the maximum iteration number, otherwise, returning to the step S402 to continue the optimization.
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CN112906967A (en) * 2021-02-24 2021-06-04 大唐环境产业集团股份有限公司 Desulfurization system slurry circulating pump performance prediction method and device
CN113449920A (en) * 2021-06-30 2021-09-28 上海电机学院 Wind power prediction method, system and computer readable medium
CN114239412A (en) * 2021-12-21 2022-03-25 许昌许继风电科技有限公司 Real-time wind speed calculation method and system for complex terrain wind turbine generator position based on mixed multi-class algorithm

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CN112906967A (en) * 2021-02-24 2021-06-04 大唐环境产业集团股份有限公司 Desulfurization system slurry circulating pump performance prediction method and device
CN113449920A (en) * 2021-06-30 2021-09-28 上海电机学院 Wind power prediction method, system and computer readable medium
CN114239412A (en) * 2021-12-21 2022-03-25 许昌许继风电科技有限公司 Real-time wind speed calculation method and system for complex terrain wind turbine generator position based on mixed multi-class algorithm

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