CN104102832A - Wind power ultrashort-term prediction method based on chaotic time series - Google Patents

Abstract

The invention relates to a wind power ultrashort-term prediction method based on chaotic time series. The method is characterized by including determining a time delay tau and embedded dimension m of a chaotic system, establishing a wind power prediction model based on the chaotic time series, and evaluating wind power prediction error by a wind power prediction error evaluation system. The wind power ultrashort-term prediction method based on the chaotic time series is scientific and reasonable, allows wind power output of a wind farm to be accurately predicted under the prediction precision which is lower than the requirement of China national energy administration for wind power prediction error 20%, and has good engineering application effect.

Description

A kind of ultrashort-term wind power prediction method based on chaos time sequence

Technical field

The present invention is a kind of ultrashort-term wind power prediction method based on chaos time sequence.

Background technology

Along with becoming increasingly conspicuous of the energy and environmental problem, wind-powered electricity generation is subject to people's attention day by day as a kind of clean regenerative resource.In China, installed capacity of wind-driven power improves year after year, and by the end of the end of the year 2013, Wind Power In China installed capacity has reached 91412.89MW.Because wind power has undulatory property, after large-scale wind power access electrical network, can bring adverse effect to security and the economy of regional power system operation.If can exert oneself and carry out accurate forecast wind power, to contribute to dispatching of power netwoks department to grasp in advance the wind power that is about to networking, improve economy and the security of Operation of Electric Systems, seeking a kind of can be that various equivalent modifications is wanted the technical barrier solving always to the wind power method of carrying out effectively prediction of exerting oneself for this reason.

Summary of the invention

Technical matters to be solved by this invention is, for wind power probabilistic feature of exerting oneself, analyze wind power power producing characteristics, according to the power producing characteristics result of analyzing, constructive chaos time sequence is introduced to wind power prediction, utilize chaology to disclose the wind power simple rule that seemingly random phenomenon may hide of exerting oneself behind, built the wind power forecast model based on chaos time sequence theory, and in conjunction with wind power wave characteristic proposition correction rule.

Solving the technical scheme that its technical matters takes is: a kind of ultrashort-term wind power prediction method based on chaos time sequence, it is characterized in that, and it comprises following content:

1) the time-lag τ of chaos system and embedding dimension m parameter determines

In to the reconstruct of wind power time series, it is the key link that guarantees precision of prediction that the rationality of the time-lag τ of chaos system and embedding dimension m is selected, if τ is too little, can cause the correlativity between reconstruct attractor consecutive point too strong, for the analysis of attractor, be easy to be disturbed by noise sequence; If τ is too large, in system, adjacent states become uncorrelated in cause-effect relationship, if m is too low, can cause occurring between attractor selfing; If m is too high, make between points distant; Consider chaos time sequence x={x _i| i=1,2 ..., N}, with time delay τ, embeds dimension m, phase space reconstruction X={X _i, X _ifor the point in phase space, embed seasonal effect in time series correlation integral and be

$C(m,N,r,\mathrm{\&tau;})=\frac{2}{M(M-1)}\underset{1\&le;i<j\&le;M}{\mathrm{\&Sigma;}}\mathrm{\&theta;}(r-d_{\mathrm{ij}})---\left(1\right)$

D wherein _ij=|| X _i-X _j|| _(∞)if, x < 0, θ (x)=0, if x>=0, θ (x)=1, correlation integral is that a class integration distributes, represent in phase space that distance between any two points is less than the probability of r, distance between points represents with the Infinite Norm of the difference of vector here, defines test statistics

S ₁(m,N,r,τ)＝C(m,N,r,τ)-C ^m(1,N,r,τ) (2)

The computation process of actual (2) formula is: by time series x={x _i| i=1,2 ..., N} resolves into τ mutual nonoverlapping subsequence, and τ is reconstruct time delay,

x ¹＝{x _i|i＝1,t+1,...,N-τ+1}

x ²＝{x _i|i＝2,t+2,...,N-τ+2} (3)

···

x ^t＝{x _i|i＝t,2τ,...,N}

Here the integral multiple that N is τ, the statistic of calculating the definition of (2) formula adopts the average strategy of piecemeal,

$S_2(m,N,r,\mathrm{\&tau;})=\frac{1}{t}\underset{s=1}{\overset{\mathrm{\&tau;}}{\mathrm{\&Sigma;}}}[C_s(m,N/\mathrm{\&tau;},r,\mathrm{\&tau;})-C_s^m(1,N/\mathrm{\&tau;},r,\mathrm{\&tau;})]---\left(4\right)$

Make N → ∞ have

$S_2(m,r,\mathrm{\&tau;})=\frac{1}{\mathrm{\&tau;}}\underset{s=1}{\overset{\mathrm{\&tau;}}{\mathrm{\&Sigma;}}}[C_s(m,r,\mathrm{\&tau;})-C_s^m(1,r,\mathrm{\&tau;})]---\left(5\right)$

If time series x={x _iindependent same distribution, so to fixing m, τ, when N → ∞, for all r, all has S ₂(m, r, τ) is worth identically vanishing, but real time sequence is to have between limit for length and element to have correlativity, the actual S obtaining ₂(m, r, τ) is generally not equal to zero, S ₂(m, r, τ)～τ has reacted seasonal effect in time series autocorrelation performance, copies the correlation method principle of asking time delay, optimum time delay τ _ddesirable S ₂first zero point of (m, r, τ)～τ, or get S ₂the time point of (m, r, τ)～τ to the mutual difference minimum of all radius r, now represents the most approaching being uniformly distributed of point in phase space reconstruction, and reconstruct attracts track to launch completely in phase space, selects two minimum and maximum radius r, definition residual quantity

ΔS ₂(m,τ)＝max{S ₂(m,r _j,τ)}-min{S ₂(m,r _j,τ)} (6)

Δ S ₂(m, t) measured S ₂the maximum deviation of (m, r, τ)～τ to all radius r, to sum up, optimum time delay τ _ddesirable S ₂first zero point or the S of (m, r, τ)～τ ₂first local minimum point of (m, τ)～τ, can obtain N and m according to BDS statistical conclusions, and the reasonable estimation of r, gets N=3000 here, m=2,3,4,5, r _i=i * 0.5 σ, σ=std (x) (σ is seasonal effect in time series standard deviation), i=1,2,3,4, calculate

${\stackrel{\&OverBar;}{S}}_2\left(\mathrm{\&tau;}\right)=\frac{1}{16}\underset{m=2}{\overset{5}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{4}{\mathrm{\&Sigma;}}}{S}_2(m,r_i,\mathrm{\&tau;})---\left(7\right)$

$\mathrm{\&Delta;}{\stackrel{\&OverBar;}{S}}_2\left(\mathrm{\&tau;}\right)=\frac{1}{4}\underset{m=2}{\overset{5}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{S}_2(m,\mathrm{\&tau;})---\left(8\right)$

Find first zero point or first local minimum point be optimum time delay τ _d, in addition, because normalized set formula (4) adopts the average strategy of piecemeal, for the time series that the cycle is T, when τ=kT, k is greater than zero integer, with be zero, consider with definition index

$S_{2\mathrm{car}}\left(\mathrm{\&tau;}\right)=\mathrm{\&Delta;}{\stackrel{\&OverBar;}{S}}_2\left(\mathrm{\&tau;}\right)+\left|{\stackrel{\&OverBar;}{S}}_2\left(\mathrm{\&tau;}\right)\right|---\left(9\right)$

Find S _2car(τ) overall smallest point can obtain and embed window τ _w, can determine time delay τ, by the method for determining time-lag τ and embedding dimension m, be CC method,

2) the wind power forecast model based on chaos time sequence

To wind power time series { x _k: k=1,2 ..., n} carries out phase space reconfiguration, and reconstruct wind power phase space is as shown in the formula shown in (10):

X ₁＝[x ₁,x _τ+1,x _2τ+1,……,x( _m-1) _τ+1] ^T

X ₂＝[x ₂,x _τ+2,x _2τ+2,……,x _(m-1)τ+2] ^T (10)

……

X _n-( _m-1) _τ＝[x _n-( _m-1) _τ,x _n-( _m-2) _τ,……,x _n]T

Wherein, n-(m-1) τ is the length of wind power time vector serial after reconstruct;

Local method is using the last point in trajectory of phase space as central point, decentering is put to nearest a plurality of tracing points as reference point, reference point is made to matching, estimate track trend, from the tracing point doping, isolate the value of future position, the object of phase space reconfiguration will be found " the most close part in history " exactly, first order local area method refers to X (t+1)=a+bX (t) carrys out matching n point small neighbourhood around, wherein X (t) is the wind power column vector after phase space reconfiguration, establishes n neighborhood of a point and comprises a t ₁, t ₂..., t _p, formula mistake! Do not find Reference source.Can be expressed as

$\left[\begin{array}{c}X(t_1+1)\\ X(t_2+1)\\ .\\ .\\ .\\ X(t_p+1)\end{array}\right]=a+b\left[\begin{array}{c}X\left(t_1\right)\\ X\left(t_2\right)\\ .\\ .\\ .\\ X\left(t_p\right)\end{array}\right]---\left(11\right)$

Adopt least square method to obtain

$\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{(X_{\mathrm{ki}+1}-a-{\mathrm{bX}}_{\mathrm{ki}})}^2=\min ---\left(12\right)$

To unknown number a, b in (12) formula, ask local derviation abbreviation to obtain

$\left\{\begin{array}{c}a+b\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{x}_{\mathrm{ki}}=\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{x}_{\mathrm{ki}+1}\\ a\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{x}_{\mathrm{ki}}+b\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{x}_{\mathrm{ki}}^2=\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{x}_{\mathrm{ki}}{x}_{\mathrm{ki}+1}\end{array}\right.---\left(13\right)$

Solving equations (13) is obtained a, b, can obtain predictor formula;

3) wind-powered electricity generation predicated error appraisement system

The definition of predicated error is conducive to the superiority-inferiority of Forecasting Methodology to be evaluated, and the predicated error index of employing has root-mean-square error MSE, mean absolute error MAE and mean absolute percentage error MAPE, and following formula (14) is shown in the definition of MAPE

$e_{\mathrm{MAPE}}=\frac{1}{n+1}\underset{t=s}{\overset{s+n}{\mathrm{\&Sigma;}}}\left|\frac{{\hat{P}}_t-p\left(t\right)}{P_N}\right|\&times;100\%---\left(14\right)$

Wherein, for t wind power predicted value constantly, s is for predicting the zero hour, and n is that total prediction is counted,

Tolerance interval evaluation index containing degree of confidence: its implication is given confidence level ε, with predicted value centered by, calculate radius r, wind-powered electricity generation real power falls into interval in given confidence level the key step of its calculating is as follows:

(1) by wind power data (x ₁, x ₂..., x _n) be divided into history data set (x ₁, x ₂..., x _m), forecast set (x _m+1, x _m+2..., x _l) and checksum set (x _l+1, x _l+2..., x _n),

(2) by history data set, through chaos time sequence model, calculate wind power predicted value the predicated error of wind power is i=1,2 ..., k, k=l-m, statistics e _iin be greater than the number num of r, level of confidence ε and num have following relation: 1-ε=r/ (k+1), predict that domain representation is the probability that new predicted value belongs to this forecast interval is ε,

(3) utilize checksum set to verify accuracy and the rationality of tolerance interval under given confidence level.

Accompanying drawing explanation

Active power in Fig. 1 wind energy turbine set one month;

Wind power fluctuation under Fig. 2 different time yardstick;

Output of wind electric field 1 rank differential variation under Fig. 3 different time yardstick;

The prediction curve of Fig. 4: 15min, 30min and 1h predetermined period;

Embodiment

Utilize drawings and Examples to be described further a kind of ultrashort-term wind power prediction method based on chaos time sequence of the present invention below.

A kind of ultrashort-term wind power prediction method based on chaos time sequence of the present invention, comprises following content:

1) the time-lag τ of chaos system and embedding dimension m parameter determines

In to the reconstruct of wind power time series, it is the key link that guarantees precision of prediction that the rationality of the time-lag τ of chaos system and embedding dimension m is selected, if τ is too little, can cause the correlativity between reconstruct attractor consecutive point too strong, for the analysis of attractor, be easy to be disturbed by noise sequence; If τ is too large, in system, adjacent states become uncorrelated in cause-effect relationship, if m is too low, can cause occurring between attractor selfing; If m is too high, make between points distant; Consider chaos time sequence x={x _i| i=1,2 ..., N}, with time delay τ, embeds dimension m, phase space reconstruction X={X _i, X _ifor the point in phase space, embed seasonal effect in time series correlation integral and be

$C(m,N,r,\mathrm{\&tau;})=\frac{2}{M(M-1)}\underset{1\&le;i<j\&le;M}{\mathrm{\&Sigma;}}\mathrm{\&theta;}(r-d_{\mathrm{ij}})---\left(1\right)$

D wherein _ij=|| X _i-X _j|| _(∞)if, x < 0, θ (x)=0, if x>=0, θ (x)=1, correlation integral is that a class integration distributes, represent in phase space that distance between any two points is less than the probability of r, distance between points represents with the Infinite Norm of the difference of vector here, defines test statistics

S ₁(m,N,r,τ)＝C(m,N,r,τ)-C ^m(1,N,r,τ) (2)

The computation process of actual (2) formula is: by time series x={x _i| i=1,2 ..., N} resolves into τ mutual nonoverlapping subsequence, and τ is reconstruct time delay,

x ¹＝{x _i|i＝1,t+1,...,N-τ+1}

x ²＝{x _i|i＝2,t+2,...,N-τ+2} (3)

···

x ^t＝{x _i|i＝t,2τ,...,N}

Here the integral multiple that N is τ, the statistic of calculating the definition of (2) formula adopts the average strategy of piecemeal,

$S_2(m,N,r,\mathrm{\&tau;})=\frac{1}{t}\underset{s=1}{\overset{\mathrm{\&tau;}}{\mathrm{\&Sigma;}}}[C_s(m,N/\mathrm{\&tau;},r,\mathrm{\&tau;})-C_s^m(1,N/\mathrm{\&tau;},r,\mathrm{\&tau;})]---\left(4\right)$

Make N → ∞ have

$S_2(m,r,\mathrm{\&tau;})=\frac{1}{\mathrm{\&tau;}}\underset{s=1}{\overset{\mathrm{\&tau;}}{\mathrm{\&Sigma;}}}[C_s(m,r,\mathrm{\&tau;})-C_s^m(1,r,\mathrm{\&tau;})]---\left(5\right)$

If time series x={x _iindependent same distribution, so to fixing m, τ, when N → ∞, for all r, all has S ₂(m, r, τ) is worth identically vanishing, but real time sequence is to have between limit for length and element to have correlativity, the actual S obtaining ₂(m, r, τ) is generally not equal to zero, S ₂(m, r, τ)～τ has reacted seasonal effect in time series autocorrelation performance, copies the correlation method principle of asking time delay, optimum time delay τ _ddesirable S ₂first zero point of (m, r, τ)～τ, or get S ₂the time point of (m, r, τ)～τ to the mutual difference minimum of all radius r, now represents the most approaching being uniformly distributed of point in phase space reconstruction, and reconstruct attracts track to launch completely in phase space, selects two minimum and maximum radius r, definition residual quantity

ΔS ₂(m,τ)＝max{S ₂(m,r _j,τ)}-min{S ₂(m,r _j,τ)} (6)

Δ S ₂(m, t) measured S ₂the maximum deviation of (m, r, τ)～τ to all radius r, to sum up, optimum time delay τ _ddesirable S ₂first zero point or the S of (m, r, τ)～τ ₂first local minimum point of (m, τ)～τ, can obtain N and m according to BDS statistical conclusions, and the reasonable estimation of r, gets N=3000 here, m=2,3,4,5, r _i=i * 0.5 σ, σ=std (x) (σ is seasonal effect in time series standard deviation), i=1,2,3,4, calculate

${\stackrel{\&OverBar;}{S}}_2\left(\mathrm{\&tau;}\right)=\frac{1}{16}\underset{m=2}{\overset{5}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{4}{\mathrm{\&Sigma;}}}{S}_2(m,r_i,\mathrm{\&tau;})---\left(7\right)$

$\mathrm{\&Delta;}{\stackrel{\&OverBar;}{S}}_2\left(\mathrm{\&tau;}\right)=\frac{1}{4}\underset{m=2}{\overset{5}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{S}_2(m,\mathrm{\&tau;})---\left(8\right)$

Find first zero point or first local minimum point be optimum time delay τ _d, in addition, because normalized set formula (4) adopts the average strategy of piecemeal, for the time series that the cycle is T, when τ=kT, k is greater than zero integer, with be zero, consider with definition index

$S_{2\mathrm{car}}\left(\mathrm{\&tau;}\right)=\mathrm{\&Delta;}{\stackrel{\&OverBar;}{S}}_2\left(\mathrm{\&tau;}\right)+\left|{\stackrel{\&OverBar;}{S}}_2\left(\mathrm{\&tau;}\right)\right|---\left(9\right)$

Find S _2car(τ) overall smallest point can obtain and embed window τ _w, can determine time delay τ, by the method for determining time-lag τ and embedding dimension m, be CC method,

2) the wind power forecast model based on chaos time sequence

To wind power time series { x _k: k=1,2 ..., n} carries out phase space reconfiguration, and reconstruct wind power phase space is as shown in the formula shown in (10):

X ₁＝[x ₁,x _τ+1,x _2τ+1,……,x( _m-1) _τ+1] ^T

X ₂＝[x ₂,x _τ+2,x _2τ+2,……,x _(m-1)τ+2] ^T (10)

……

X _n-( _m-1) _τ＝[x _n-( _m-1) _τ,x _n-( _m-2) _τ,……,x _n] ^T

Wherein, n-(m-1) τ is the length of wind power time vector serial after reconstruct;

Local method is using the last point in trajectory of phase space as central point, decentering is put to nearest a plurality of tracing points as reference point, reference point is made to matching, estimate track trend, from the tracing point doping, isolate the value of future position, the object of phase space reconfiguration will be found " the most close part in history " exactly, first order local area method refers to X (t+1)=a+bX (t) carrys out matching n point small neighbourhood around, wherein X (t) is the wind power column vector after phase space reconfiguration, establishes n neighborhood of a point and comprises a t ₁, t ₂..., t _p, formula mistake! Do not find Reference source.Can be expressed as

$\left[\begin{array}{c}X(t_1+1)\\ X(t_2+1)\\ .\\ .\\ .\\ X(t_p+1)\end{array}\right]=a+b\left[\begin{array}{c}X\left(t_1\right)\\ X\left(t_2\right)\\ .\\ .\\ .\\ X\left(t_p\right)\end{array}\right]---\left(11\right)$

Adopt least square method to obtain

$\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{(X_{\mathrm{ki}+1}-a-{\mathrm{bX}}_{\mathrm{ki}})}^2=\min ---\left(12\right)$

To unknown number a, b in (12) formula, ask local derviation abbreviation to obtain

$\left\{\begin{array}{c}a+b\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{x}_{\mathrm{ki}}=\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{x}_{\mathrm{ki}+1}\\ a\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{x}_{\mathrm{ki}}+b\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{x}_{\mathrm{ki}}^2=\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{x}_{\mathrm{ki}}{x}_{\mathrm{ki}+1}\end{array}\right.---\left(13\right)$

Solving equations (13) is obtained a, b, can obtain predictor formula;

3) wind-powered electricity generation predicated error appraisement system

The definition of predicated error is conducive to the superiority-inferiority of Forecasting Methodology to be evaluated, and the predicated error index of employing has root-mean-square error MSE, mean absolute error MAE and mean absolute percentage error MAPE, and following formula (14) is shown in the definition of MAPE

$e_{\mathrm{MAPE}}=\frac{1}{n+1}\underset{t=s}{\overset{s+n}{\mathrm{\&Sigma;}}}\left|\frac{{\hat{P}}_t-p\left(t\right)}{P_N}\right|\&times;100\%---\left(14\right)$

Wherein, for t wind power predicted value constantly, s is for predicting the zero hour, and n is that total prediction is counted,

Tolerance interval evaluation index containing degree of confidence: its implication is given confidence level ε, centered by predicted value x^i, calculates radius r, and wind-powered electricity generation real power falls into interval in given confidence level the key step of its calculating is as follows:

(1) by wind power data (x ₁, x ₂..., x _n) be divided into history data set (x ₁, x ₂..., x _m), forecast set (x _m+1, x _m+2..., x _l) and checksum set (x _l+1, x _l+2..., x _n),

(2) by history data set, through chaos time sequence model, calculate wind power predicted value the predicated error of wind power is i=1,2 ..., k, k=l-m, statistics e _iin be greater than the number num of r, level of confidence ε and num have following relation: 1-ε=r/ (k+1), predict that domain representation is the probability that new predicted value belongs to this forecast interval is ε,

(3) utilize checksum set to verify accuracy and the rationality of tolerance interval under given confidence level.

1, wind power wave characteristic is analyzed

Raw data in the present invention is the Northeast's wind energy turbine set actual measurement wind power data of 1 month (sampling interval 6 seconds), and as shown in Figure 1, this wind energy turbine set total installation of generating capacity is P _n=49.3MW.

In order to portray the fluctuation characteristic of wind power, calculated the mean value of power swing amplitude, number percent and the power standard of the mean value of fluctuating range, mean variation amount are poor.If wind energy turbine set t constantly wind power is p (t), n is total sampling number.

To the wind power data analysis in Fig. 1, shown in the following Fig. 2 of result of calculation and Fig. 3.

From Fig. 2 and Fig. 3, along with reducing of time scale, the fluctuating range of wind power also reduces, and the variation of the interior wind power of dozens of minutes is less, means that it is feasible according to the historical data of wind power, carrying out the prediction of ultra-short term wind power.Fig. 3 shows that wind power surpasses 10% probability very little (lower than 3%) of installed capacity with interior variation at 1h.

2, wind power chaotic Property Analysis

Chaos refers in non-linear deterministic system, a kind of aperiodic behavior producing due to internal system nonlinear interaction.Forecasting Methodology for chaos time sequence has universe method, local method, weighting zeroth order local method, weighing first order local area method and the Forecasting Methodology based on Lyapunov index etc.Whether the wind power with randomness, undulatory property is chaos time sequence, and maximum Lyapunov exponent is the strong foundation of differentiating.The present invention utilizes small data sets to the calculating that force data has carried out maximum Lyapunov exponent that goes out under the wind energy turbine set different time yardstick of northeast.The advantage of this algorithm be reliable to small data group, calculated amount is little, relatively easy to operate etc.

Maximum Lyapunov exponent under table 1 different time yardstick

It is to differentiate a sufficient and necessary condition that time series is chaos system that maximum Lyaponov index is greater than 0, as shown in Table 1, the maximum Lyaponov index of the wind-powered electricity generation data under 3 time scales is all greater than 0, so the wind-powered electricity generation of above 3 time scales is exerted oneself, sequence is chaos time sequence.

In to the reconstruct of wind power time series, it is the key link that guarantees precision of prediction that the rationality of the time-lag τ of chaos system and embedding dimension m is selected.If τ is too little, can cause the correlativity between reconstruct attractor consecutive point too strong, for the analysis of attractor, be easy to be disturbed by noise sequence; If τ is too large, in system, adjacent states become uncorrelated in cause-effect relationship.If m is too low, can cause occurring between attractor selfing; If m is too high, make between points distant.

The present invention adopts CC method can calculate τ and m simultaneously, and the method forms statistic by the correlation integral of sequence, and statistic has represented the correlativity of Nonlinear Time Series, by the graph of a relation of statistic and time delay, determines τ and m.The method easily operates, and calculated amount is little, reliable and have a stronger noise resisting ability to small data group.τ under different predetermined period that use CC method calculates and m are in Table 2.

Time delay under the different predicted time yardsticks of table 2 and embedding dimension

3 embodiment analyses

3.1 embodiment explanations

The present invention utilize proposition based on chaos time sequence wind power forecasting method, northeast wind energy turbine set wind power is carried out to the prediction of different time yardstick, check Forecasting Methodology validity.

Adopt chaos single order forecast model and method, this wind energy turbine set wind power is carried out to the prediction of different time yardstick, the validity of checking Methods of Chaotic Forecasting.Finally provided and predicted radius to specifying under the error fiducial interval that predicts the outcome, for the reasonable use of Forecasting Methodology is laid a good foundation.

3.2 predict the outcome and analyze

Respectively the wind power of following 15min, 30min and 1h time scale is carried out to point prediction, as shown in Figure 4, error statistics is in Table 3 for result.Visible, along with the increase of predetermined period, the precision of prediction of single employing wind power Time Series Method declines, and precision of prediction requirement to wind power prediction error 20% lower than National Energy Board, has higher using value.

The error that the different predetermined period of table 3 predict the outcome

The probability distribution of 3.3 predicated errors

On the basis of point prediction, adopt probabilistic forecasting, can determine the possible fluctuation range that predicts the outcome.Wind-powered electricity generation probabilistic forecasting is the forecast interval providing on existing point prediction basis under certain confidence level.Error statistics to different time scale prediction result counts prediction radius under given degree of confidence, as shown in table 4.

Forecast interval radius (perunit value) under the different confidence levels of table 4

Along with the change of predetermined period is large, under same confidence level, it is large that the interval radius predicting the outcome constantly becomes as can be seen from Table 4; Along with diminishing of degree of confidence, under same predetermined period, the interval radius predicting the outcome constantly diminishes.Along with the increase of predetermined period, corresponding prediction accuracy can decline, and will guarantee that confidence level is constant, and corresponding interval radius must increase; And along with the diminishing of degree of confidence, be equivalent to reduce the degree of accuracy requirement of prediction, under same predetermined period, the interval radius predicting the outcome will inevitably diminish.

By above sample calculation analysis, strong proof the wind power forecasting method based on chaos time sequence of the present invention prediction that the wind power of wind energy turbine set is exerted oneself there is good precision, meet the requirement of National Energy Board to wind energy turbine set wind power predicated error, there is good practical value.

Design conditions in the embodiment of the present invention, legend, table etc. are only for the present invention is further illustrated; and non exhaustive; do not form the restriction to claim protection domain; the enlightenment that those skilled in the art obtain according to the embodiment of the present invention; without creative work, just can expect that other is equal in fact alternative, all in protection domain of the present invention.

Claims (1)

1. the ultrashort-term wind power prediction method based on chaos time sequence, is characterized in that, it comprises following content:

1) the time-lag τ of chaos system and embedding dimension m parameter determines

In to the reconstruct of wind power time series, it is the key link that guarantees precision of prediction that the rationality of the time-lag τ of chaos system and embedding dimension m is selected, if τ is too little, can cause the correlativity between reconstruct attractor consecutive point too strong, for the analysis of attractor, be easy to be disturbed by noise sequence; If τ is too large, in system, adjacent states become uncorrelated in cause-effect relationship, if m is too low, can cause occurring between attractor selfing; If m is too high, make between points distant; Consider chaos time sequence x={x _i| i=1,2 ..., N}, with time delay τ, embeds dimension m, phase space reconstruction X={X _i, X _ifor the point in phase space, embed seasonal effect in time series correlation integral and be

$C(m,N,r,\mathrm{\&tau;})=\frac{2}{M(M-1)}\underset{1\&le;i<j\&le;M}{\mathrm{\&Sigma;}}\mathrm{\&theta;}(r-d_{\mathrm{ij}})---\left(1\right)$

D wherein _ij=|| X _i-X _j|| _(∞)if, x < 0, θ (x)=0, if x>=0, θ (x)=1, correlation integral is that a class integration distributes, represent in phase space that distance between any two points is less than the probability of r, distance between points represents with the Infinite Norm of the difference of vector here, defines test statistics

S ₁(m,N,r,τ)＝C(m,N,r,τ)-C ^m(1,N,r,τ) (2)

The computation process of actual (2) formula is: by time series x={x _i| i=1,2 ..., N} resolves into τ mutual nonoverlapping subsequence, and τ is reconstruct time delay,

x ¹＝{x _i|i＝1,t+1,...,N-τ+1}

x ²＝{x _i|i＝2,t+2,...,N-τ+2} (3)

···

x ^t＝{x _i|i＝t,2τ,...,N}

Here the integral multiple that N is τ, the statistic of calculating the definition of (2) formula adopts the average strategy of piecemeal,

$S_2(m,N,r,\mathrm{\&tau;})=\frac{1}{t}\underset{s=1}{\overset{\mathrm{\&tau;}}{\mathrm{\&Sigma;}}}[C_s(m,N/\mathrm{\&tau;},r,\mathrm{\&tau;})-C_s^m(1,N/\mathrm{\&tau;},r,\mathrm{\&tau;})]---\left(4\right)$

Make N → ∞ have

$S_2(m,r,\mathrm{\&tau;})=\frac{1}{\mathrm{\&tau;}}\underset{s=1}{\overset{\mathrm{\&tau;}}{\mathrm{\&Sigma;}}}[C_s(m,r,\mathrm{\&tau;})-C_s^m(1,r,\mathrm{\&tau;})]---\left(5\right)$

If time series x={x _iindependent same distribution, so to fixing m, τ, when N → ∞, for all r, all has S ₂(m, r, τ) is worth identically vanishing, but real time sequence is to have between limit for length and element to have correlativity, the actual S obtaining ₂(m, r, τ) is generally not equal to zero, S ₂(m, r, τ)～τ has reacted seasonal effect in time series autocorrelation performance, copies the correlation method principle of asking time delay, optimum time delay τ _ddesirable S ₂first zero point of (m, r, τ)～τ, or get S ₂the time point of (m, r, τ)～τ to the mutual difference minimum of all radius r, now represents the most approaching being uniformly distributed of point in phase space reconstruction, and reconstruct attracts track to launch completely in phase space, selects two minimum and maximum radius r, definition residual quantity

ΔS ₂(m,τ)＝max{S ₂(m,r _j,τ)}-min{S ₂(m,r _j,τ)} (6)

Δ S ₂(m, t) measured S ₂the maximum deviation of (m, r, τ)～τ to all radius r, to sum up, optimum time delay τ _ddesirable S ₂first zero point or the S of (m, r, τ)～τ ₂first local minimum point of (m, τ)～τ, can obtain N and m according to BDS statistical conclusions, and the reasonable estimation of r, gets N=3000 here, m=2,3,4,5, r _i=i * 0.5 σ, σ=std (x) (σ is seasonal effect in time series standard deviation), i=1,2,3,4, calculate

${\stackrel{\&OverBar;}{S}}_2\left(\mathrm{\&tau;}\right)=\frac{1}{16}\underset{m=2}{\overset{5}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{4}{\mathrm{\&Sigma;}}}{S}_2(m,r_i,\mathrm{\&tau;})---\left(7\right)$

$\mathrm{\&Delta;}{\stackrel{\&OverBar;}{S}}_2\left(\mathrm{\&tau;}\right)=\frac{1}{4}\underset{m=2}{\overset{5}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{S}_2(m,\mathrm{\&tau;})---\left(8\right)$

Find first zero point or first local minimum point be optimum time delay τ _d, in addition, because normalized set formula (4) adopts the average strategy of piecemeal, for the time series that the cycle is T, when τ=kT, k is greater than zero integer, with be zero, consider with definition index

$S_{2\mathrm{car}}\left(\mathrm{\&tau;}\right)=\mathrm{\&Delta;}{\stackrel{\&OverBar;}{S}}_2\left(\mathrm{\&tau;}\right)+\left|{\stackrel{\&OverBar;}{S}}_2\left(\mathrm{\&tau;}\right)\right|---\left(9\right)$

Find S _2car(τ) overall smallest point can obtain and embed window τ _w, can determine time delay τ, by the method for determining time-lag τ and embedding dimension m, be CC method,

2) the wind power forecast model based on chaos time sequence

To wind power time series { x _k: k=1,2 ..., n} carries out phase space reconfiguration, and reconstruct wind power phase space is as shown in the formula shown in (10):

X ₁＝[x ₁,x _τ+1,x _2τ+1,……,x _(m-1)τ+1] ^T

X ₂＝[x ₂,x _τ+2,x _2τ+2,……,x _(m-1)τ+2] ^T (10)

……

X _n-(m-1)τ＝[x _n-(m-1)τ,x _n-(m-2)τ,……,x _n] ^T

Wherein, n-(m-1) τ is the length of wind power time vector serial after reconstruct;

Local method is using the last point in trajectory of phase space as central point, decentering is put to nearest a plurality of tracing points as reference point, reference point is made to matching, estimate track trend, from the tracing point doping, isolate the value of future position, the object of phase space reconfiguration will be found " the most close part in history " exactly, first order local area method refers to X (t+1)=a+bX (t) carrys out matching n point small neighbourhood around, wherein X (t) is the wind power column vector after phase space reconfiguration, establishes n neighborhood of a point and comprises a t ₁, t ₂..., t _p, formula mistake! Do not find Reference source.Can be expressed as

$\left[\begin{array}{c}X(t_1+1)\\ X(t_2+1)\\ .\\ .\\ .\\ X(t_p+1)\end{array}\right]=a+b\left[\begin{array}{c}X\left(t_1\right)\\ X\left(t_2\right)\\ .\\ .\\ .\\ X\left(t_p\right)\end{array}\right]---\left(11\right)$

Adopt least square method to obtain

$\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{(X_{\mathrm{ki}+1}-a-{\mathrm{bX}}_{\mathrm{ki}})}^2=\min ---\left(12\right)$

To unknown number a, b in (12) formula, ask local derviation abbreviation to obtain

$\left\{\begin{array}{c}a+b\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{x}_{\mathrm{ki}}=\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{x}_{\mathrm{ki}+1}\\ a\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{x}_{\mathrm{ki}}+b\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{x}_{\mathrm{ki}}^2=\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{x}_{\mathrm{ki}}{x}_{\mathrm{ki}+1}\end{array}\right.---\left(13\right)$

Solving equations (13) is obtained a, b, can obtain predictor formula;

3) wind-powered electricity generation predicated error appraisement system

The definition of predicated error is conducive to the superiority-inferiority of Forecasting Methodology to be evaluated, and the predicated error index of employing has root-mean-square error MSE, mean absolute error MAE and mean absolute percentage error MAPE, and following formula (14) is shown in the definition of MAPE

$e_{\mathrm{MAPE}}=\frac{1}{n+1}\underset{t=s}{\overset{s+n}{\mathrm{\&Sigma;}}}\left|\frac{{\hat{P}}_t-p\left(t\right)}{P_N}\right|\&times;100\%---\left(14\right)$

Wherein, for t wind power predicted value constantly, s is for predicting the zero hour, and n is that total prediction is counted,

Tolerance interval evaluation index containing degree of confidence: its implication is given confidence level ε, with predicted value centered by, calculate radius r, wind-powered electricity generation real power falls into interval in given confidence level the key step of its calculating is as follows:

(1) by wind power data (x ₁, x ₂..., x _n) be divided into history data set (x ₁, x ₂..., x _m), forecast set (x _m+ ₁, x _m+ ₂..., x _l) and checksum set (x _l+ ₁, x _l+ ₂..., x _n),

(2) by history data set, through chaos time sequence model, calculate wind power predicted value the predicated error of wind power is i=1,2 ..., k, k=l-m, statistics e _iin be greater than the number num of r, level of confidence ε and num have following relation: 1-ε=r/ (k+1), predict that domain representation is the probability that new predicted value belongs to this forecast interval is ε,

(3) utilize checksum set to verify accuracy and the rationality of tolerance interval under given confidence level.