CN109886452B - Wind power ultra-short term probability prediction method and system based on empirical dynamic modeling - Google Patents
Wind power ultra-short term probability prediction method and system based on empirical dynamic modeling Download PDFInfo
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Abstract
The invention discloses a wind power ultra-short term probability prediction method and system based on empirical dynamic modeling, wherein the method comprises the following steps: standard normalization processing is carried out on the time sequence to be measured, and nonlinear polymerization degree calculation is carried out on the data after the standard normalization processing so as to investigate the nonlinear degree of a given dynamic system; calculating an optimal embedding dimension E and delay time tau by adopting a particle swarm optimization algorithm; further, performing phase space reconstruction on the time sequence to be measured; and (3) constructing an empirical dynamic model, and predicting a given dynamic system by adopting a simplex projection method in a reconstruction phase space to obtain a prediction result of the quantity to be predicted. The prediction result shows that the wind power ultra-short term probability prediction method based on the empirical dynamic modeling can realize the objective description of the wind power generation dynamic process completely according to data, and the effectiveness of probability prediction is obviously improved.
Description
Technical Field
The invention belongs to the technical field of wind power prediction in a new energy power generation process, and particularly relates to a wind power ultra-short term probability prediction method and system based on empirical dynamic modeling.
Background
Wind power generation is the most developed renewable energy power generation form at present, has been connected to a modern power grid in a large scale, and is making important contribution to the energy-saving and emission-reducing industry of the whole society. Wind power is taken as a representative of new energy power generation, and has strong development momentum and wide market prospect by relying on unique geographical characteristics and policy advantages of China. Meanwhile, due to the fluctuation and intermittency of the output power of the wind power plant, the large-scale access of wind power brings huge challenges to the operation scheduling of the power system. The power prediction of the wind power plant is an effective means for relieving peak load and frequency modulation pressure of a power system and improving wind power receiving capacity, and is an effective way for guiding the wind power plant to make a maintenance plan, improving the wind energy utilization rate and improving economic benefits.
According to different prediction periods, wind power prediction can be divided into medium-long term prediction, short term prediction and ultra-short term prediction. The long-term prediction of the wind power takes years as timeliness, and is mainly used for planning a wind power plant and making an annual power generation plan; the medium-term prediction of the wind power takes week or month as the aging, and is mostly used for making maintenance plans of wind power plants. The requirements of the medium-long term prediction on the prediction accuracy are not strict, but long-time operation data needs to be accumulated. The short-term prediction of the wind power is generally performed in a prediction period of 1-3 days, and in order to reduce or even avoid wind abandon, the short-term prediction has high requirements on precision and is often used for optimizing daily power generation plans and cold and hot standby of conventional power supplies, adjusting maintenance plans and other activities. The ultra-short term prediction refers to wind power prediction for 0-4 hours in the future, and the ultra-short term prediction is beneficial to optimizing the rotating reserve capacity and the frequency and voltage modulation of a power system, so that the combination of a unit and the economic load scheduling are optimized on line.
According to different prediction result forms, wind power prediction methods can be divided into single-value (or deterministic) prediction and probability (or uncertainty) prediction. The currently used wind power prediction technology is mostly a single-value prediction method, only one condition-expected future wind power plant output power is obtained through prediction, and the prediction is deterministic prediction. In order to improve the accuracy of the single-value prediction method, a great deal of research has been carried out by domestic and foreign scholars, but the deterministic prediction method has a great difficulty in breaking through the prediction accuracy because it is unrealistic to obtain all data of a future event. Thus, any prediction method has its inherent uncertainty and irreducibility, making it impossible to obtain all the information of future events, achieving accurate predictions, especially of varying atmospheric behavior. Compared to deterministic predictions, uncertainty prediction methods that provide probability information of future events have advantages over achieving accurate predictions. Probabilistic or non-deterministic predictions have advanced significantly with the development of theoretical predictions.
From a physics point of view, a wind farm can be considered as an artificial physical system with determined dynamics. Nevertheless, there is a strong uncertainty in the output power of the wind farm, and the fundamental reasons are the nonlinearity and complexity of the dynamic system of the wind farm itself and the uncertainty of the boundary conditions of the system, which are collectively shown in the following aspects. Firstly, wind power plants are complex in structure and have obvious nonlinear characteristics. Under a certain meteorological condition, the output power of the wind power plant is related to various factors such as the internal landform, the fan layout and the fan output characteristics, and obvious nonlinear association relations exist among the influencing factors and between the influencing factors and the output power of the wind power plant (for example, it is generally believed that a high-order and discontinuous mapping relation exists between the wind speed and the output power of the fan). Therefore, the wind power plant dynamic system is determined to have high complexity, the output power of the wind power plant dynamic system is sensitive to boundary meteorological conditions along with nonlinear characteristics, and even for the meteorological conditions which seem to be the same, the output power of the wind power plant dynamic system fluctuates obviously due to slight differences which are difficult to account. Secondly, due to the complex and nonlinear characteristics of the atmospheric system, the boundary meteorological conditions of the wind power plant are difficult to accurately acquire. It is easy to understand that the atmospheric system is a complex system with strong nonlinearity and chaos phenomenon, and strong uncertainty exists in the prediction of the future development trend of the atmospheric system. However, the estimation of the state variable change trajectory in the wind farm dynamic system needs to be based on the boundary condition provided by the atmospheric system, and the estimation of the boundary condition is inaccurate, so that the complexity and the nonlinear characteristics of the atmospheric system are reserved and amplified in the wind farm dynamic system. Therefore, it is easy to know that for a wind power plant dynamic system with high uncertainty, it is extremely difficult to describe the wind power plant dynamic system by using a model with fixed equations, and the fixed equations limit the mining of effective information, so that when the meteorological conditions change, accurate prediction is difficult to give.
However, during the construction, commissioning and operation of the wind farm, a large amount of meteorological and operation and maintenance data are accumulated, and the sufficient dynamic characteristics of the system are already contained in the behavioral data of the wind farm. Therefore, the dynamic feature mining based on the measured data without the prior model assumption is important for the understanding and prediction of the nonlinear dynamic system of the wind power plant. Therefore, the method adopts the equation-free prediction based on the empirical dynamic model, aims to fully mine the hidden characteristics of the data and draw the development track of the data, and accordingly carries out ultra-short-term probability prediction on the wind power.
Disclosure of Invention
The invention provides a wind power ultra-short term probability prediction method and system based on empirical dynamic modeling, and aims to solve the technical problems that a wind power plant dynamic system is high in complexity, model deviation is not beneficial to effective information mining in data, and a high-precision wind power prediction result is difficult to provide in practice.
In order to solve the technical problem, the invention provides a wind power ultra-short term probability prediction method based on empirical dynamic modeling, which comprises the following steps:
step (1): carrying out standard normalization processing on the time sequence to be measured and calculating the nonlinear polymerization degree of the well-regulated data so as to investigate the nonlinear degree of the system;
step (2): optimizing by adopting a particle swarm optimization algorithm to obtain an embedding dimension E and a delay time tau;
and (3): according to the embedding dimension E and the delay time tau obtained in the steps (1) and (2), carrying out phase space reconstruction on the time sequence to be measured;
and (4): constructing an empirical dynamic model, and predicting in a reconstruction phase space to obtain the prediction probability distribution of the wind power;
and (5): and obtaining the upper and lower bounds of the wind power predicted output, namely the wind power predicted output interval result according to the selected confidence coefficient.
The standard normalization in the step (1) is to convert the time series of the measurement to be predicted into a time series which follows a standard normal distribution, even if it is expected to be 0, and the variance is 1:
Vt'＝(Vt-μ(Vt))/σ(Vt) (1)
in the formula, VtMu (V) as the original time series to be pre-measuredt) To expect this time series, σ (V)t) Is the standard deviation of the time series, Vt' is a time series after standard normalization.
The nonlinear polymerization degree in the step (1) is calculated by adopting an S mapping method. The S-map is computed as a local linear mapping between the lagged coordinate vector and the target variable, and includes an adjustment factor θ that controls the weight of the link between each vector: when theta is 0, S is mapped into a linear autoregressive model; and theta > 0 gives more weight to neighboring state quantities when calculating the local linear mapping, thereby exhibiting nonlinearity.
The embedding dimension E and the delay time tau are calculated in the step (2) by adopting a particle swarm optimization algorithm, and in the particle swarm optimization algorithm, the solution of each optimization problem is a particle in a search space. Each particle has an initial velocity and position, an adaptation value determined by an adaptation function. Each particle is assigned a memory function that keeps track of the best position sought, and furthermore the velocity of each particle determines the direction and distance they seek so that the particle can search in the optimal solution space. Optimizing at each iterationIn the process, the particles update their speed and position by comparing the fitness value with two extreme values: the optimal solution (individual extremum p) found by the particle itselfbest) And the best solution (global extreme g) currently found for the whole populationbest) I.e. by
xi(t+1)＝xi(t)+vi(t+1) (3)
Where t represents the t-th iteration, viRepresents the velocity, x, of the ith particleiRepresents the position of the ith particle, and omega is the inertia weight; c. C1And c2As a cognitive factor, R1And R2Is [0,1 ]]Two random numbers within the range. In the step, the optimization goal of the particle swarm algorithm is to minimize the coverage bandwidth index (CWC), which is also a method for evaluating the population fitness of the particles.
And (3) reconstructing the phase space in the step (3) refers to reconstructing the original nonlinear power system by using a single-dimensional time sequence observation value so as to describe the evolution rule and the development situation of the original nonlinear power system. According to the Tarkens theorem and the Whitney embedding theorem, for a one-dimensional observation sequence of the chaotic system, as long as the embedding dimension E meets the condition that E is more than or equal to 2M +1(M is the dimension of the original power system), a reconstruction system which is identical to the original system differential can be obtained, namely the original power system can be reconstructed from a time sequence observation value of the single-dimensional observation quantity. Therefore, the original dynamic system can be reconstructed into a high-dimensional phase space by only selecting a proper embedding dimension E and a proper delay time tau, and the original system is analyzed in the reconstructed space.
The prediction process of the step (4) uses a simplex projection method. The simplex projection method is to embed time delay into a single time sequence to generate attractor reconstruction, and performs prediction in reconstruction phase space, and its principle is briefly as follows: the simplex projection method predicts the motion trail of the current state quantity which may appear next step by calculating the motion trail of the adjacent points of the state quantity. Given a reconstruction phase space and a state quantity XsFirst, find XsB neighboring points around (b + E1 is usually set, and E is the embedding dimension), and these neighboring points are denoted as state quantities Xn(s,i)Wherein n (s, i) represents the distance XsThe ith near time series observation, namely Xn(s,1)Is a distance XsNearest point, Xn(s,2)Is a distance XsThe second nearest point, and so on; then observing and recording the variation tracks of the adjacent points, wherein the track of each adjacent point can be regarded as the state quantity XsPossible future motion trajectory, thus position X after h time steps for each adjacent pointn(s,i)+hAll have a certain probability of being XsPosition X after h time stepss+hWherein each X isn(s,i)+hIs:
wherein d (X)s,Xn(s,i)) Is a state quantity XsAnd the state quantity Xn(s,i)The Euclidean distance between the adjacent points is N, the number of the adjacent points is N equals to b, and b equals to E + 1. According to each future value and the occurrence probability thereof, a power probability distribution table after h step lengths can be obtained; further, when the number of neighboring points is large enough, the power probability distribution after h time steps can be approximated.
And (5) obtaining upper and lower intervals of the predicted power from the power probability distribution obtained in the step (4) according to a pre-selected confidence level (for example: 90%), and selecting different confidence levels to obtain upper and lower intervals of different powers so as to obtain confidence bands with different widths.
Advantageous technical effects
1. As a prediction method based on data mining, the historical time sequence to be predicted is used as training data, and wide area measurement information in a wind power plant can be fully utilized; meanwhile, the model considers the influence effect of the adjacent nodes on the nodes to be predicted in the learning process, so that the time-space correlation characteristics of the power system can be reflected, the change rule and the operation situation of the state quantity can be accurately described, the prediction error is reduced, and a more reliable prediction result is obtained.
2. As a dynamic modeling method, the method is not limited by a fixed parameter equation, and the model can be continuously adjusted according to the change trend of the state quantity, so that the model has strong adaptability. Therefore, under the steady-state condition, the model can be automatically adjusted to the optimal state according to the change of the data, so that the high-precision prediction result is ensured.
3. As a probability prediction method, on the basis of realizing the prediction of the single expected value of the future generated energy of the wind power plant, the method can reliably predict the fluctuation interval of the prediction error under the specified confidence coefficient, and provides more comprehensive prediction information for the power grid scheduling and the reliable operation of the power system.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, are provided to further illustrate the application and, together with the description, serve to explain the application and not to limit the application.
FIG. 1 is a block diagram of a wind power ultra-short term probability prediction method based on empirical dynamic modeling;
FIG. 2 is a schematic diagram of the phase space reconstruction of the present invention;
FIG. 3 is a process diagram of a wind power ultra-short term probability prediction method based on empirical dynamic modeling;
FIG. 4 is a schematic diagram of simplex projection prediction according to the present invention;
FIG. 5 is a graph illustrating the results of wind field interval prediction according to an example of the present invention;
FIG. 6 is a graph of probabilistic predictions in a validation of an example of the present invention;
FIG. 7 is a schematic structural diagram of the wind power ultra-short term probability prediction system based on empirical dynamic modeling.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The embodiment of the invention carries out the ultra-short-term probability prediction of the wind power of a Penglai wind farm in the Shandong tobacco platform area in the future for fifteen minutes, and the invention is further explained by combining the attached drawings and the embodiment.
As shown in FIG. 1, the method for predicting the ultra-short term probability of the power of the wind power plant based on the empirical dynamic modeling mainly comprises the following steps:
step (1): data preparation and processing, namely performing standard normalization processing on a time sequence of a quantity to be predicted, such as power, voltage amplitude, phase angle and the like, and performing nonlinear polymerization degree calculation on the data after the standard normalization processing so as to examine the nonlinear degree of a given dynamic system.
Firstly, according to the step (1), the time series to be measured is subjected to standard normalization processing. Wherein the standard normalization is to convert the time series of the measurement to be predicted into a time series that follows a standard normal distribution, even if it is expected to be 0, with a variance of 1:
Vt'＝(Vt-μ(Vt))/σ(Vt) (5)
in the formula, VtMu (V) as the original time series to be pre-measuredt) To expect this time series, σ (V)t) Is the standard deviation of the time series, Vt' is a time series after standard normalization.
And then, carrying out nonlinear aggregation calculation on the time series to be measured after the standard normalization.
The nonlinear polymerization degree is calculated by adopting an S mapping method. The S-map calculates a local linear mapping between the lagged coordinate vector and the target variable, including an adjustment factor θ, which is used to control the weight of the link between each vector: when theta is 0, S is mapped into a linear autoregressive model; and theta > 0 gives more weight to neighboring state quantities when calculating the local linear mapping, thereby exhibiting nonlinearity. And theta is more than 0 through calculation, and the power time series has the nonlinear characteristic.
Step (2): and calculating the optimal embedding dimension E and the delay time tau by adopting a particle swarm algorithm.
The idea of the particle swarm optimization is derived from the research on the predation behavior of a bird swarm, the flying foraging behavior of the bird swarm is simulated, and the birds achieve the optimal colony through collective cooperation, so that the optimization method is based on 'colony intelligence'. In particle swarm optimization, the solution of each optimization problem is a "particle" in the search space. Each particle has an initial velocity and position, an adaptation value determined by an adaptation function. Each particle is assigned a memory function that remembers the best position found and shares it with the population, and the velocity of each particle determines the direction and distance they are searching for so that the particle can search in the optimal solution space. During each iterative optimization, the particle updates its velocity and position by comparing the fitness value with two extreme values: the optimal solution (individual extremum p) found by the particle itselfbest) And the best solution (global extreme g) currently found for the whole populationbest) I.e. by
xi(t+1)＝xi(t)+vi(t+1) (7)
Where t represents the t-th iteration, viRepresents the velocity, x, of the ith particleiRepresents the position of the ith particle, and omega is the inertia weight; c. C1And c2As a cognitive factor, R1And R2Is [0,1 ]]Two random numbers within the range.
In the step, the optimization goal of the particle swarm algorithm is to minimize the coverage bandwidth index (CWC), which is also a method for evaluating the population fitness of the particles. The embedding dimension E and the delay time τ corresponding to the minimum CWC are obtained.
The coverage bandwidth index is a common comprehensive index for measuring the quality of the prediction interval, and the smaller the value of the coverage bandwidth index is, the better the prediction interval is. The coverage bandwidth index consists of two parts: inter-zone coverage capability (PICP) and inter-zone width (PINAW).
The interval coverage capability refers to the capability of the obtained prediction interval containing a true value, and the larger the value of the capability is, the higher the reliability of the prediction interval is, the calculation formula is as follows:
wherein, c (i) is an indication function of the coverage, and the expression is as follows:
wherein, yiIs the ith observation, [ Li,Ui]Is the upper/lower boundary of the ith prediction interval, and M is the number of the prediction intervals.
The interval width means the sharpness of the interval, and the smaller the interval width is, the more abundant the reflected information is, and the better the sharpness is. The interval width is calculated by the formula:
wherein M is the number of prediction intervals.
The calculation formula of the coverage bandwidth index is as follows:
CWC＝PINAW(1+γ(PICP)e-η(PICP-μ)) (11)
where μ is a predetermined confidence level, 0.9 in the present example, η is a penalty factor, 10 in the present example, γ (PICP) is a step function, and the expression is:
x obtained from the above calculation by the formula (7)i(t +1) is a position of the particle, which is two-dimensional, i.e. consisting of two parameters, E and τ; according to the particle xiReconstructing phase space of E and tau at (t +1), predicting in reconstruction space, and obtaining the result of prediction and observed value yiComparing and judging by using a CWC; different E and tau form different phase spaces, so the prediction result and the CWC score are different, and E and tau with the optimal prediction effect (namely, the CWC is the minimum) are selected as the optimal solution.
And (3): and performing phase space reconstruction on the time sequence to be measured according to the optimal embedding dimension E and the delay time tau.
And (4) reconstructing the phase space in the step (3) refers to reconstructing the original nonlinear power system by using a single-dimensional time sequence observation value so as to describe the evolution rule and the development situation of the original nonlinear power system. According to the Takens theorem, a given dynamic system can be reconstructed from the time sequence observed value of the single-dimensional observed quantity as long as the optimal embedding dimension E meets the condition that E is more than or equal to 2M +1(M is the dimension of the prime power system). As shown in fig. 2, fig. 2(a) is a trajectory curve of a dynamic system in a three-dimensional state space, and the whole curve forms a manifold of the system in the state space, and the manifold can be reconstructed by time-series observed values of single-dimensional observed quantities in the system according to the takens theorem. FIG. 2(b) is a manifold of a prime dynamic system reconstructed from time series observations of a single dimensional variable y, where τ is the small time interval described in the Tarkens theorem. Fig. 2(c) shows the manifold of the dynamic system reconstructed from the time-series observations of the observations y, z. As shown in FIG. 2, the original system can be reconstructed into a high-dimensional phase space by selecting an appropriate optimal embedding dimension E and delay time τ, and the original system can be analyzed in the reconstructed space.
According to the embedding dimension E and the delay time tau, phase space reconstruction is carried out on the power time sequence of the tobacco station Penglai wind power plant, and the model expression is as follows:
Xt＝<Vt> (13)
wherein XtAs observed by the time sequence { xtConstructed E-dimensional vector, Xt＝<xt,xt-τ,xt-2τ,...,xt-(E-1)τ>T is the measurement time, VtThe power observation sequence is a power observation sequence of the tobacco terrace Penglai wind power plant.
And (4): and (3) constructing an empirical dynamic model, and predicting the power of the tobacco station Penglai wind power plant in a reconstruction phase space to obtain a prediction result.
In the process of predicting a given dynamic system in a reconstruction phase space, the motion tracks of adjacent points of the state quantity are calculated by utilizing a simplex projection method, the probability of occurrence of each track is estimated, and the motion track of the given dynamic system state is predicted.
Simplex projection is a method of predicting by embedding time delays into a single time series to produce an attractor reconstruction. Specifically, power probability distribution of the wind power at the future moment is predicted by calculating the occurrence probability of motion tracks of adjacent points of state quantity.
Given a reconstruction phase space and a state quantity XsFirst, find XsThe surrounding b neighbors (b is usually set to E +1, E is the embedding dimension) are denoted as vector Xn(s,i)Wherein n (s, i) represents the distance XsThe ith near time series observation, namely Xn(s,1)Is a distance XsNearest point, Xn(s,2)Is a distance XsThe second nearest point, and so on; then observing and recording the variation tracks of the adjacent points, wherein the track of each adjacent point can be regarded as the state quantity XsPossible future motion trajectory, thus position X after h time steps for each adjacent pointn(s,i)+hAll have a certain probability of being XsPosition X after h time stepss+hWherein each X isn(s,i)+hIs:
wherein d (X)s,Xn(s,i)) Is a state quantity XsAnd the state quantity Xn(s,i)The euclidean distance between; n is the number of adjacent points, N equals b, b equals E + 1. According to each future value and the occurrence probability thereof, a power probability distribution table after h step lengths can be obtained; further, when the number of neighboring points is large enough, the power probability distribution after h time steps can be approximated.
Further, according to a confidence level selected in advance (for example: 90%), upper and lower intervals of the predicted power are obtained from the power probability distribution obtained in the above steps, and different confidence levels are selected to obtain different upper and lower intervals of the power, so as to obtain confidence bands with different widths.
Fig. 3 shows a prediction process of performing wind power ultra-short term probability prediction on a tobacco station plaza wind farm by using the method: firstly, reconstructing a phase space of a time sequence to be predicted, predicting a given dynamic system in the reconstructed phase space by adopting a simplex projection method, and predicting the power probability distribution of the wind power at the future moment by calculating the occurrence probability of motion tracks of adjacent points of state quantity.
Fig. 4 further illustrates the prediction process of the simplex projection method.
And selecting a power time sequence of the tobacco terrace Penglai wind power plant as a sample, wherein the length of the sample is 8000 points, and the time interval is 5 minutes. The samples were predicted for the next 5 minutes, 15 minutes, and 30 minutes, respectively, and tested in a cross-validation manner. In this example, the samples were subjected to seasonal prediction, in which 12-2 months were winter, 3-5 months were spring, 6-8 months were summer, and 9-11 months were autumn.
Cross-validation means that in a given sample, a large portion of the sample is taken for modeling, and a small portion is used to verify the accuracy of the model built and to record prediction errors. The embodiment of the invention adopts a quadruple cross validation scheme for the model: the data are evenly divided into four sections, 2000 points are arranged on each section, three sections are sequentially selected for training the model, the rest sections are used for prediction, and in the process, the model predicts each section of samples once.
Precision evaluation index: the invention uses the coverage bandwidth index as an accuracy evaluation index, and the calculation formula is shown in (11).
Table 1 shows the optimal embedding dimension E and the delay time τ obtained by the particle swarm optimization, and E is 7 and τ is 5.
TABLE 1 particle swarm calculation results
The prediction results using the method of the invention are shown in table 2:
table 2 example of the invention prediction results show
For the coverage capability PICP, the larger the value is, the stronger the coverage capability of the prediction interval is represented; for the interval width PINAW, the smaller the value is, the narrower the width of the prediction interval is represented, and the better the practicability of the prediction interval is indicated; for the comprehensive coverage bandwidth index CWC, the smaller the value is, the better the comprehensive performance of the prediction interval is. As can be seen from table 2, the value of the CWC increases with the extension of the prediction scale, which is mainly because the uncertainty of the wind power increases with the extension of the prediction scale, the prediction interval becomes wider, so that the PINAW score increases, and the CWC value increases.
The comparison of the prediction results of the method of the present invention with other prediction methods is shown in table 3:
TABLE 3 comparison of predicted results
As can be seen from table 3, the CWC value of the prediction interval obtained by the method is the smallest, which indicates that a more reliable prediction result can be obtained by using the method of the present invention to perform prediction, and therefore, data mining on effective measurement information in a wind farm is beneficial to improving the accuracy of load prediction. The embodiment of the invention only predicts the active power of the wind power plant, and actually, the method can be widely applied to prediction of other electrical quantities (voltage amplitude and phase angle) in the power grid, and an ideal prediction result can be obtained.
As a prediction method based on data mining, the historical time sequence to be predicted is used as training data, and wide area measurement information in a wind power plant can be fully utilized; meanwhile, the model considers the influence effect of the adjacent nodes on the nodes to be predicted in the learning process, so that the time-space correlation characteristics of the power system can be reflected, the change rule and the operation situation of the state quantity can be accurately described, the prediction error is reduced, and a more reliable prediction result is obtained.
As a dynamic modeling method, the method is not limited by a fixed parameter equation, and the model can be continuously adjusted according to the change trend of the state quantity, so that the model has strong adaptability. Therefore, under the steady-state condition, the model can be automatically adjusted to the optimal state according to the change of the data, so that the high-precision prediction result is ensured.
As a probability prediction method, on the basis of realizing the prediction of the single expected value of the future generated energy of the wind power plant, the method can reliably predict the fluctuation interval of the prediction error under the specified confidence coefficient, and provides more comprehensive prediction information for the power grid scheduling and the reliable operation of the power system.
According to the grasped historical power data of the tobacco station plagiary wind power plant, the samples are respectively predicted for 5 minutes in the future, 15 minutes in the future and 30 minutes in the future according to different seasons, and the prediction results are shown in fig. 5 and fig. 6. Fig. 5(a) shows a prediction interval of 5 minutes, fig. 5(b) shows a prediction interval of 15 minutes, fig. 5(c) shows a prediction interval of 30 minutes, the prediction season is autumn, and the time resolution of the data is 5 minutes. As can be seen from fig. 5, as the prediction scale increases, the prediction interval becomes increasingly wider, which is caused by the enhancement of the wind power uncertainty. Fig. 6(a) and 6(b) are predicted probability distributions for summer and winter, respectively, with a prediction scale of 15 minutes. As can be seen from FIG. 6, the predicted probability distribution obtained by the method of the present invention can well contain the real output curve, further proving the effectiveness of the method.
Compared with probability prediction methods such as a continuous method, sparse Bayesian learning and kernel density estimation, relative prediction error indexes are compared, and the effectiveness and the practicability of the wind power ultra-short term probability prediction method based on the empirical dynamic modeling are verified.
FIG. 7 is a schematic structural diagram of the wind power ultra-short term probability prediction system based on empirical dynamic modeling.
As shown in fig. 7, the ultra-short-term probability prediction system for wind power based on empirical dynamic modeling of the present invention includes:
(1) and the nonlinear polymerization degree calculation module is used for performing standard normalization processing on the time sequence to be measured and calculating the nonlinear polymerization degree of the data after the standard normalization so as to investigate the nonlinear degree of the given dynamic system.
Wherein the standard normalization is to convert the time series of the measurement to be predicted into a time series that follows a standard normal distribution, even if it is expected to be 0, with a variance of 1:
Vt'＝(Vt-μ(Vt))/σ(Vt) (20)
in the formula, VtMu (V) as the original time series to be pre-measuredt) To expect this time series, σ (V)t) Is the standard deviation of the time series, Vt' is a time series after standard normalization.
In the nonlinear polymerization degree calculation module, the nonlinear polymerization degree of the data after the standard normalization is calculated by adopting an S mapping method. The S-map is computed as a local linear mapping between the lagged coordinate vector and the target variable, and includes an adjustment factor θ that controls the weight of the link between each vector: when theta is 0, S is mapped into a linear autoregressive model; and theta > 0 gives more weight to neighboring state quantities when calculating the local linear mapping, thereby exhibiting nonlinearity.
(2) And the particle swarm optimization module calculates the optimal embedding dimension E and the delay time tau by adopting a particle swarm algorithm.
(3) And the high-dimensional phase space reconstruction module is used for performing phase space reconstruction on the time sequence to be measured according to the optimal embedding dimension E and the delay time tau.
In the phase space reconstruction module, according to the Tarkens theorem, when the optimal embedding dimension E meets the condition that E is more than or equal to 2M +1, a given dynamic system is reconstructed by a time sequence observation value of the single-dimensional observation quantity; where M is the prime mover system dimension.
The phase space reconstruction means reconstructing an original nonlinear power system by using a single-dimensional time sequence observation value so as to describe the evolution rule and the development situation of the original nonlinear power system. According to the Takens theorem, a given dynamic system can be reconstructed from the time sequence observed value of the single-dimensional observed quantity as long as the optimal embedding dimension E meets the condition that E is more than or equal to 2M +1(M is the dimension of the prime power system). Therefore, the original dynamic system can be reconstructed into a high-dimensional phase space by only selecting the appropriate optimal embedding dimension E and the delay time tau, and the original system can be analyzed in the reconstructed space.
(4) And the prediction module is used for constructing an empirical dynamic model, predicting a given dynamic system in a reconstruction phase space and obtaining a prediction result of the quantity to be predicted.
In the prediction module, the motion tracks of the adjacent points of the state quantity are calculated by utilizing a simplex projection method, the probability of each track is estimated, and the motion track of the given dynamic system state is predicted.
The simplex projection method is to embed time delay into a single time sequence to generate attractor reconstruction, and predicts the power probability distribution of the wind power at the future moment by calculating the occurrence probability of motion trails of adjacent points of state quantity.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.
Claims (14)
1. A wind power ultra-short term probability prediction method based on empirical dynamic modeling is characterized by comprising the following steps:
step (1), the nonlinearity degree of a given dynamic system is inspected based on time series data to be measured;
step (2), calculating the optimal embedding dimension E and delay time tau of the time sequence to be measured;
step (3), according to the optimal embedding dimension E and the delay time tau, carrying out phase space reconstruction on the time sequence to be measured;
step (4), an empirical dynamic model is constructed, a given dynamic system is predicted in a reconstruction phase space, and a prediction result of the quantity to be predicted is obtained;
in the step (2), the optimal embedding dimension E and the delay time tau of the time sequence to be measured are calculated by adopting a particle swarm optimization algorithm; wherein E satisfies E is more than or equal to 2M +1, M is the dimension of the prime power system, and the optimization goal of the particle swarm optimization algorithm is to minimize the coverage bandwidth index (CWC);
in the step (4), in the process of predicting the given dynamic system in the reconstruction phase space, the motion tracks of the adjacent points of the state quantity are calculated by using a simplex projection method, the probability of each track is estimated, and the motion track of the given dynamic system state is predicted, wherein in the simplex projection method, the state quantity X issAdjacent point X ofn(s,i)Position X after h time stepsn(s,i)+hIs a state quantity XsPosition X after h time stepss+hThe probability of (p), (i) is:
wherein n (s, i) represents a distance XsIth near time series observation, Xn(s,1)Is a distance XsState quantity of nearest point, Xn(s,i)Is a distance XsState quantity of i-th nearest point, d (X)s,Xn(s,i)) Is a state quantity XsAnd the state quantity Xn(s,i)The euclidean distance between; n is the number of adjacent points, N is b, b is E + 1;
and obtaining power probability distribution after h step lengths according to the future value and the occurrence probability of each state quantity.
2. The wind power ultra-short term probability prediction method based on empirical dynamic modeling as claimed in claim 1, wherein the step (1) specifically includes:
step (1.1) standard normalization processing is carried out on time series data to be measured;
and (1.2) carrying out nonlinear polymerization degree calculation on the data after the standard normalization.
3. The wind power ultra-short term probability prediction method based on empirical dynamic modeling as claimed in claim 2, characterized in that in step (1.2), an S mapping method is adopted to calculate the nonlinear polymerization degree.
4. The method for predicting the ultra-short term probability of the wind power based on the empirical dynamic modeling as claimed in claim 1, wherein in the step (3), the process of reconstructing the phase space of the time series to be predicted is to reconstruct the given dynamic system into a high-dimensional phase space according to the optimal embedding dimension E and the delay time τ obtained in the step (2).
5. The wind power ultra-short term probability prediction method based on empirical dynamic modeling as claimed in claim 4, wherein the model expression of the reconstructed high-dimensional phase space is:
Xt＝<Vt>
wherein, XtBased on the time-series observed value { x }of the quantity to be predictedtConstructed E-dimensional vector, Xt＝<xt,xt-τ,xt-2τ,...,xt-(E-1)τ>T is the measurement time, VtFor the wind farm power observation sequence, XtThe sequence value of (2).
6. The method of claim 5, further comprising obtaining upper and lower intervals of predicted power from the power probability distribution according to a pre-selected confidence level.
7. The method as claimed in claim 6, further comprising selecting different confidence levels to obtain different upper and lower power intervals to obtain confidence bands of different widths.
8. A wind power ultra-short-term probability prediction system based on empirical dynamic modeling is characterized by comprising the following steps:
the nonlinear polymerization degree calculation module is used for carrying out standard normalization processing on the time sequence to be measured and carrying out nonlinear polymerization degree calculation on the data after the standard normalization so as to investigate the nonlinear degree of a given dynamic system;
the particle swarm optimization module is used for calculating the optimal embedding dimension E of the time sequence to be predicted and the delay time tau by adopting a particle swarm algorithm;
the high-dimensional phase space reconstruction module is used for performing phase space reconstruction on the time sequence to be measured according to the optimal embedding dimension E and the delay time tau;
the prediction module is used for constructing an empirical dynamic model and predicting a given dynamic system in a reconstruction phase space to obtain a prediction result of the quantity to be predicted;
the particle swarm optimization module adopts a particle swarm optimization algorithm to calculate the optimal embedding dimension E and the delay time tau of the time sequence to be predicted; wherein E satisfies E is more than or equal to 2M +1, M is the dimension of the prime power system, and the optimization goal of the particle swarm optimization algorithm is to minimize the coverage bandwidth index (CWC);
the high-dimensional phase space reconstruction module calculates motion tracks of adjacent points of state quantity by utilizing a simplex projection method, estimates the probability of occurrence of each track and predicts the motion track of the given dynamic system state, wherein in the simplex projection method, the state quantity X issAdjacent point X ofn(s,i)Position X after h time stepsn(s,i)+hIs a state quantity XsPosition X after h time stepss+hThe probability of (p), (i) is:
wherein n (s, i) represents a distance XsIth near time series observation, Xn(s,1)Is a distance XsState quantity of nearest point, Xn(s,i)Is a distance XsState quantity of i-th nearest point, d (X)s,Xn(s,i)) Is a state quantity XsAnd the state quantity Xn(s,i)The euclidean distance between; n is the number of adjacent points, N is b, b is E + 1;
and obtaining power probability distribution after h step lengths according to the future value and the occurrence probability of each state quantity.
9. The ultra-short-term probability prediction system for wind power based on empirical dynamic modeling of claim 8, wherein the nonlinear degree of polymerization calculation module further comprises a standard normalization processing sub-module for performing standard normalization processing on the time series to be predicted before calculating the nonlinear degree of polymerization of the given dynamic system.
10. The ultra-short-term probability prediction system for wind power based on empirical dynamic modeling of claim 9, wherein in the nonlinear degree of polymerization calculation module, an S-mapping method is used to calculate the nonlinear degree of polymerization of the given dynamic system.
11. The ultra-short-term probability prediction system for wind power based on empirical dynamic modeling of claim 10, wherein the high-dimensional phase space reconstruction module reconstructs a given motive dynamic system into a high-dimensional phase space based on the optimal embedding dimension E and the delay time τ.
12. The ultra-short-term probability prediction system for wind power based on empirical dynamic modeling of claim 11, wherein the model expression for reconstructing the high-dimensional phase space is:
Xt＝<Vt>
wherein, XtAs observed by the time sequence { xtConstructed E-dimensional vector, Xt＝<xt,xt-τ,xt-2τ,...,xt-(E-1)τ>，VtFor the wind farm power observation sequence, XtT is the measurement time.
13. The ultra-short-term wind power probability prediction system based on empirical dynamic modeling of claim 12, further comprising deriving upper and lower intervals of predicted power from the power probability distribution based on a pre-selected confidence level.
14. The ultra-short-term probability prediction system for wind power based on empirical dynamic modeling of claim 13, further comprising selecting different confidence levels to obtain different upper and lower power intervals to obtain confidence bands of different widths.
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