CN104318334A - Short-time power load forecasting method based on long-range dependence FARIMA model - Google Patents

Abstract

The invention relates to a short-time power load forecasting method based on a long-range dependence FARIMA model. The method includes the following steps that (1) forecasting sample data are obtained according to power load data before a forecasting day; (2) the forecasting sample data are preprocessed, singular points and zero-mean-value are eliminated to obtain a power load sequence {Xt}; (3) an estimated value H of a Hurst index of the power load sequence {Xt} is calculated by means of a rescaled range analysis method; (4) whether the power load sequence meets the requirement of a long-range dependence process is judged according to the obtained estimated value H of the Hurst index, if the answer is positive, a fractional difference parameter d is calculated, and if the answer is negative, the step (1) is repeated; (5) according to the obtained fractional difference parameter d, the FARIMA model of the power load sequence {Xt} is built; (6) according to the FARIMA model, a power load value is forecasted, and an actual forecast value is obtained by carrying out inverse difference on the forecasted power load value to adjust a power scheduling scheme. Compared with the prior art, the method has the advantages of being accurate in result, high in practicality and the like.

Description

A kind of Short-Term Load Forecasting Method closing FARIMA model based on appearance

Technical field

The present invention relates to a kind of Methods of electric load forecasting, especially relate to a kind of Short-Term Load Forecasting Method closing FARIMA model based on appearance.

Background technology

The prediction of electric load plays a significant role in electric system production planning and power grid operation, unit maintenance scheduling, interzone power transfer scheme, load scheduling scheme etc.The stable operation of electric system requires that generated energy can immediately following the change of system loading, electric energy must can balanced circuit load, if in advance predict load or load prediction inaccurate, a large amount of waste of energy will be caused, therefore Accurate Prediction load not only plays an important role to system cloud gray model and the production schedule, and to determining the method for operation, power system optimal dispatch also has key effect.

Short-term electric load prediction provides the variation tendency of following a period of time electric load, ensure power grid security, realize enterprise's Power System Intelligent to control, run and the rational Transaction algorithm of plan, Automatic Generation Control (AGC) prerequisite, but because electric load is by outside the impact of the natural cause such as weather, temperature, load itself also has random nature, therefore short-term electric load prediction is a complicated problem.The domestic and international research to short-term load forecasting at present mainly contains trend extrapolation, regression analysis, Grey Theory Forecast method, neural network prediction, time series forecasting etc., the emphasis of each research is different, but because loading effects factor is a lot, a lot of Forecasting Methodology is restricted by precision of prediction and estimation range and can not promotes the use of.

Summary of the invention

Object of the present invention is exactly to overcome the defect that above-mentioned prior art exists and the Short-Term Load Forecasting Method closing FARIMA model based on appearance providing a kind of result accurate, practical.

Object of the present invention can be achieved through the following technical solutions:

Close a Short-Term Load Forecasting Method for FARIMA model based on appearance, comprise the following steps:

1) according to the Power system load data before prediction day, forecast sample data are obtained;

2) pre-service is carried out to forecast sample data, reject dissimilarity and zero-mean, obtain electric load sequence { X _t;

3) Rescaled range analysis is utilized to calculate electric load sequence { X _tthe estimated value H of Hurst index;

4) according to the estimated value H of the Hurst index obtained, judge whether electric load sequence meets long correlated process, if meet, then calculate mark differential parameter d, the calculating formula of d is:

d＝H-0.5，

If do not meet, then return step 1);

5) electric load sequence { X is set up according to the mark differential parameter d obtained _tfARIMA model;

FARIMA model is mark difference autoregressive moving-average model, and arma modeling is autoregressive moving-average model, is a basic theory of random processes model.

Arma modeling is for sample electric load sequence { X _texpression formula is:

X _t＝φ ₁X _t-1+φ ₂X _t-2+…+φ _pX _t-p+ε _t-θ ₁ε _t-1-θ ₂ε _t-2-…-θ _qε _t-q，

Wherein, X _t=φ ₁x _t-1+ φ ₂x _t-2+ ... + φ _px _t-pfor { X _taR model,

X _t=ε _t-θ ₁ε _t-1-θ 2 ε _t-2-...-θ _qε _t-qfor { X _tmA model.

6) according to FARIMA model prediction power load charge values, and contrast is carried out to prediction power load charge values divide and obtain actual prediction value, in order to adjust electricity consumption scheduling scheme.

Described step 3) specifically comprise the following steps:

31) for electric load sequence { X _t: t=1,2,3 ... the calculating formula of n}, its R/S statistics is:

$\frac{R\left(n\right)}{S\left(n\right)}=\frac{1}{S\left(n\right)}(\max (0,w_1,w_2,...,w_n)-\min (0,w_1,w_2,...,w_n))$

$w_k=(x_1+x_2+...+x_k)-k\stackrel{\‾}{x}\left(n\right),k=\mathrm{1,2,3}...,n$

Wherein, R (n) is the extreme difference of sample electric load sequence, and S (n) is the standard deviation of sample electric load sequence, for the mean value of electric load sequence, n is sample size, x _kfor electric load sequence { X _ta middle kth element;

32) according to the calculating formula of R/S statistics, under logarithmic coordinate, R/S curve is drawn;

33) least square fitting is carried out to R/S curve, obtain the estimated value H of Hurst index.

Described step 5) specifically comprise the following steps:

51) the auto-regressive parameter vector φ [φ of the AR model of arma modeling is calculated according to Yule-Walker equation ₁, φ ₂..., φ _p]:

$\left(\begin{array}{c}-{\mathrm{\φ}}_1\\ -{\mathrm{\φ}}_2\\ ...\\ -{\mathrm{\φ}}_p\end{array}\right){\left(\begin{array}{c}r\left(0\right),r\left(1\right),...,r(p-1)\\ r\left(1\right),r\left(0\right),...,r(p-2)\\ ...\\ r(p-1),r(p-2),...,r\left(0\right)\end{array}\right)}^{-1}\left(\begin{array}{c}r\left(1\right)\\ r\left(2\right)\\ ...\\ r\left(p\right)\end{array}\right)$

Wherein, r (p) is electric load sequence { X _tautocorrelation function;

52) try to achieve the autoregressive coefficient p of AR model and the moving average coefficient q of MA model according to AIC criterion, and set up AR model, the calculating formula of AIC criterion is:

$\min \mathrm{AIC}=n\ln \hat{{{\mathrm{\σ}}_{\mathrm{\ϵ}}}^2}+2(p+q+1)$

AR (φ, the p) model set up is:

X _t＝φ ₁X _t-1+φ ₂X _t-2+…+φ _pX _t-p+ε _t

Wherein, ε _tfor zero-mean, variance are stationary white noise, be estimated value;

53) electric load sequence { X is set up _tmA model, specifically comprise the following steps:

531) according to mark differential parameter d to electric load sequence { X _t: t=... ,-1,0,1 ... carry out mark Difference Calculation difference sequence Y, the calculating formula of Y is:

Y＝{Y _t，t＝1，2，3…，N}

$Y_t={\mathrm{\Δ}}^d{X}_t={(1-B)}^d{X}_t=\underset{k=0}{\overset{\∞}{\mathrm{\Σ}}}\left(\begin{array}{c}d\\ k\end{array}\right){(-B)}^k{X}_t=\underset{k=0}{\overset{\∞}{\mathrm{\Σ}}}{\mathrm{\π}}_k{X}_{t-k}(k=\mathrm{1,2,3}...N)$

${\mathrm{\Δ}}^d={(1-B)}^d=1-\left(\begin{array}{c}d\\ 1\end{array}\right)B+\left(\begin{array}{c}d\\ 2\end{array}\right)B^2+...+{(-1)}^{d-1}\left(\begin{array}{c}d\\ d-1\end{array}\right)B^{d-1}+{(-1)}^d{B}^d$

${\mathrm{\π}}_k=\frac{\mathrm{\Γ}(d+1)}{\mathrm{\Γ}(k+1)\mathrm{\Γ}(d-k+1)}$

Wherein, Δ ^dfor d rank difference operator, B is lag operator, and N is the total sample number of difference sequence Y;

532) by difference sequence Y through FIR filter filtering, obtains and exports Z={Z _t, t=1,2,3 ..., N}, and the m rank AR model setting up Z;

533) try to achieve its AR parameter according to the m rank AR model of Z, and calculate the inversely related coefficient of Z, obtain the q rank AR model of Z;

534) according to the q rank AR model of Z, electric load sequence { X is calculated according to Yule-Walker equation _tthe moving average coefficient [θ of MA model ₁, θ ₂..., θ _q].

54) electric load sequence { X is set up _tfARIMA model.

Described step 4) in judge that the method whether electric load sequence meets long correlated process is:

As 0.5 < H < 1, electric load sequence meets long correlated process;

As H=0.5, electric load sequence does not have self-similarity, discontented foot length correlated process.

Compared with prior art, the present invention has the following advantages:

One, result is accurate, The present invention reduces the despatching work amount of dispatcher, and prediction effect is more accurate than the artificial result estimated.

Two, practical, by research of the present invention, large enterprise, industrial sector according to the load-following capacity of house generator, can reduce critical point flow on the basis of the result of short-term forecasting, reduce electric cost, for enterprise brings larger economic benefit.

Accompanying drawing explanation

Fig. 1 is method flow diagram of the present invention.

Fig. 2 is that the present invention closes Hurst index map to the appearance of electric load.

Fig. 3 is long correlation model load prediction curve and the actual curve comparison diagram of Forecasting Methodology of the present invention.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.

Embodiment:

As shown in Figure 1, a kind of Short-Term Load Forecasting Method closing FARIMA model based on appearance, comprises the following steps:

1) according to the Power system load data before prediction day, obtain forecast sample data, select first Saturday (on July 5th, 1997), second July 12 1997 Saturday, this meets load variations and there is certain rule and periodic feature, select the 3rd Friday (on July 18th, 1997), because the 3rd Friday from Saturday (on July 19th, 1997) is nearest, the variation tendency of load indirectly can be reflected.Adopt front 144 sample points to predict front 24 sample points in Saturday (on July 19th, 1997), three groups of daily load values are as shown in table 1,

Table 1 three groups of daily load values (unit: MW)

Time	First Saturday load value	Second Saturday load value	3rd Saturday load value
				00：30	473	429	471
01：00	470	433	459
				01：30	462	423	451
02：00	424	407	413
				02：30	420	391	418
03：00	421	358	411
				03：30	420	388	401
04：00	395	353	403
				04：30	381	335	398
05：00	374	361	402

05：30	391	347	418
				06：00	372	350	432
06：30	397	393	475
				07：00	420	393	504
07：30	453	404	509
				08：00	454	415	504
08：30	456	431	541
				09：00	458	446	547
09：30	458	442	551
				10：00	479	439	560
10：30	499	470	551
				11：00	495	460	555
11：30	502	469	559
				12：00	504	462	537
12：30	484	463	525
				13：00	479	451	549
13：30	469	454	547
				14：00	465	443	519
14：30	471	442	525
				15：00	461	450	524
15：30	494	447	530
				16：00	482	447	523
16：30	483	452	500
				17：00	478	424	511
17：30	486	429	511
				18：00	475	440	503
18：30	483	440	495
				19：00	478	424	517
19：30	468	448	522
				20：00	487	448	521
20：30	486	430	516
				21：00	486	454	518
21：30	504	458	479
				22：00	513	479	473
22：30	500	458	477
				23：00	481	449	456
23：30	478	421	464
				24：00	455	419	435

2) pre-service is carried out to forecast sample data, reject dissimilarity and zero-mean, obtain electric load sequence { X _t; get the daily load data of the first two Saturday before day is predicted in one month in certain city and the 3rd Friday as forecast sample; data interval sampling in units of 30 minutes of load; predict the load variations of half a day of the 3rd Saturday; pre-service is carried out to historical load data, adopts following formula to be normalized.

$\hat{L}=\frac{L_t-L_{\min }}{L_{\max }-L_{\min }},t=\mathrm{1,2},...24$

Wherein: L _max, L _minbe respectively maximum, the minimum value of load in sample; for the normalized value of the load in sample, t is moment value, and its scope is [0,24], and Lt is the load value of t;

3) Rescaled range analysis is utilized to calculate electric load sequence { X _tthe estimated value H of Hurst index, as shown in Figure 2, specifically comprise the following steps:

31) for electric load sequence { X _t: t=1,2,3 ... the calculating formula of n}, its R/S statistics is:

$\frac{R\left(n\right)}{S\left(n\right)}=\frac{1}{S\left(n\right)}(\max (0,w_1,w_2,...,w_n)-\min (0,w_1,w_2,...,w_n))$

$w_k=(x_1+x_2+...+x_k)-k\stackrel{\&OverBar;}{x}\left(n\right),k=\mathrm{1,2,3}...,n$

Wherein, R (n) is the extreme difference of sample electric load sequence, and S (n) is the standard deviation of sample electric load sequence, for the mean value of electric load sequence, n is sample size, x _kfor electric load sequence { X _ta middle kth element;

32) according to the calculating formula of R/S statistics, under logarithmic coordinate, R/S curve is drawn, as shown in Figure 2;

33) least square fitting is carried out to R/S curve, obtain the estimated value H (in this example H=0.8505) of Hurst index, and judge whether electric load sequence meets long correlated process.

4) according to the estimated value H of the Hurst index obtained, judge whether electric load sequence meets long correlated process, if meet, then calculate mark differential parameter d, the calculating formula of d is:

d＝H-0.5，

If do not meet, then return step 1), judge that the method whether electric load sequence meets long correlated process is:

As 0.5 < H < 1, electric load sequence meets long correlated process;

As H=0.5, electric load sequence does not have self-similarity, discontented foot length correlated process.

5) electric load sequence { X is set up according to the mark differential parameter d obtained _tfARIMA model, specifically comprise the following steps:

51) the auto-regressive parameter vector φ [φ of the AR model of arma modeling is calculated according to Yule-Walker equation ₁, φ ₂..., φ _p]:

$\left(\begin{array}{c}-{\mathrm{\&phi;}}_1\\ -{\mathrm{\&phi;}}_2\\ ...\\ -{\mathrm{\&phi;}}_p\end{array}\right){\left(\begin{array}{c}r\left(0\right),r\left(1\right),...,r(p-1)\\ r\left(1\right),r\left(0\right),...,r(p-2)\\ ...\\ r(p-1),r(p-2),...,r\left(0\right)\end{array}\right)}^{-1}\left(\begin{array}{c}r\left(1\right)\\ r\left(2\right)\\ ...\\ r\left(p\right)\end{array}\right)$

Wherein, r (p) is electric load sequence { X _tautocorrelation function;

52) try to achieve the autoregressive coefficient p of AR model and the moving average coefficient q of MA model according to AIC criterion, and set up AR model, the calculating formula of AIC criterion is:

$\min \mathrm{AIC}=n\ln \hat{{{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}}^2}+2(p+q+1)$

AR (φ, the p) model set up is:

X _t＝φ ₁X _t-1+φ ₂X _t-2+…+φ _pX _t-p+ε _t

Wherein, ε _tfor zero-mean, variance are stationary white noise, be estimated value;

53) electric load sequence { X is set up _tmA model, specifically comprise the following steps:

531) according to mark differential parameter d to electric load sequence { X _t: t=... ,-1,0,1 ... carry out mark Difference Calculation difference sequence Y, the calculating formula of Y is:

Y＝{Y _t，t＝1，2，3…，N}

$Y_t={\mathrm{\&Delta;}}^d{X}_t={(1-B)}^d{X}_t=\underset{k=0}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\left(\begin{array}{c}d\\ k\end{array}\right){(-B)}^k{X}_t=\underset{k=0}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{\mathrm{\&pi;}}_k{X}_{t-k}(k=\mathrm{1,2,3}...N)$

${\mathrm{\&Delta;}}^d={(1-B)}^d=1-\left(\begin{array}{c}d\\ 1\end{array}\right)B+\left(\begin{array}{c}d\\ 2\end{array}\right)B^2+...+{(-1)}^{d-1}\left(\begin{array}{c}d\\ d-1\end{array}\right)B^{d-1}+{(-1)}^d{B}^d$

${\mathrm{\&pi;}}_k=\frac{\mathrm{\&Gamma;}(d+1)}{\mathrm{\&Gamma;}(k+1)\mathrm{\&Gamma;}(d-k+1)}$

Wherein, Δ ^dfor d rank difference operator, B is lag operator, and N is the total sample number of difference sequence Y;

532) by difference sequence Y through FIR filter filtering, obtains and exports Z={Z _t, t=1,2,3 ..., N}, and the m rank AR model setting up Z;

533) try to achieve its AR parameter according to the m rank AR model of Z, and calculate the inversely related coefficient of Z, obtain the q rank AR model of Z;

534) according to the q rank AR model of Z, electric load sequence { X is calculated according to Yule-Walker equation _tthe moving average coefficient [θ of MA model ₁. θ ₂. ..., θ _q].

54) electric load sequence { X is set up _tfARIMA model.

6) as shown in Figure 3, figure is long correlation model load prediction curve and the actual curve comparison diagram of Forecasting Methodology, according to FARIMA model prediction power load charge values, and contrast is carried out to prediction power load charge values divide and obtain actual prediction value, in order to adjust electricity consumption scheduling scheme.

Claims (4)

1. close a Short-Term Load Forecasting Method for FARIMA model based on appearance, it is characterized in that, comprise the following steps:

1) according to the Power system load data before prediction day, forecast sample data are obtained;

2) pre-service is carried out to forecast sample data, reject dissimilarity and zero-mean, obtain electric load sequence { X _t;

3) Rescaled range analysis is utilized to calculate electric load sequence { X _tthe estimated value H of Hurst index;

4) according to the estimated value H of the Hurst index obtained, judge whether electric load sequence meets long correlated process, if meet, then calculate mark differential parameter d, the calculating formula of d is:

d＝H-0.5，

If do not meet, then return step 1);

5) electric load sequence { X is set up according to the mark differential parameter d obtained _t: t=1,2,3 ... the FARIMA model of n};

6) according to FARIMA model prediction power load charge values, and contrast is carried out to prediction power load charge values divide and obtain actual prediction value, in order to adjust electricity consumption scheduling scheme.

2. a kind of Short-Term Load Forecasting Method closing FARIMA model based on appearance according to claim 1, is characterized in that, described step 3) specifically comprise the following steps:

31) for electric load sequence { X _t: t=1,2,3 ... the calculating formula of n}, its R/S statistics is:

$\frac{R\left(n\right)}{S\left(n\right)}=\frac{1}{S\left(n\right)}(\max (0,w_1,w_2,\&CenterDot;\&CenterDot;\&CenterDot;,w_n)-\min (0,w_1,w_2,\&CenterDot;\&CenterDot;\&CenterDot;,w_n))$

$\begin{array}{cc}{w}_k=(x_1+x_2+\&CenterDot;\&CenterDot;\&CenterDot;+x_k)-k\stackrel{\&OverBar;}{x}\left(n\right)& k=\mathrm{1,2,3}\&CenterDot;\&CenterDot;\&CenterDot;,n\end{array}$

Wherein, R (n) is the extreme difference of sample electric load sequence, and S (n) is the standard deviation of sample electric load sequence, for the mean value of electric load sequence, n is sample size, x _kfor electric load sequence { X _ta middle kth element;

32) according to the calculating formula of R/S statistics, under logarithmic coordinate, R/S curve is drawn;

33) least square fitting is carried out to R/S curve, obtain the estimated value H of Hurst index.

3. a kind of Short-Term Load Forecasting Method closing FARIMA model based on appearance according to claim 1, is characterized in that, described step 5) specifically comprise the following steps:

51) the auto-regressive parameter vector φ [φ of the AR model of arma modeling is calculated according to Yule-Walker equation ₁, φ ₂..., φ _p]:

$\left(\begin{array}{c}-{\mathrm{\&phi;}}_1\\ -{\mathrm{\&phi;}}_2\\ \&CenterDot;\&CenterDot;\&CenterDot;\\ -{\mathrm{\&phi;}}_p\end{array}\right)={\left(\begin{array}{c}r\left(0\right),r\left(1\right),\&CenterDot;\&CenterDot;\&CenterDot;,r(p-1)\\ r\left(1\right),r\left(0\right),\&CenterDot;\&CenterDot;\&CenterDot;,r(p-2)\\ \&CenterDot;\&CenterDot;\&CenterDot;\\ r(p-1),r(p-2),\&CenterDot;\&CenterDot;\&CenterDot;,r\left(0\right)\end{array}\right)}^{-1}\left(\begin{array}{c}r\left(1\right)\\ r\left(2\right)\\ \&CenterDot;\&CenterDot;\&CenterDot;\\ r\left(p\right)\end{array}\right)$

Wherein, r (p) is electric load sequence { X _tautocorrelation function;

52) try to achieve the autoregressive coefficient p of AR model and the moving average coefficient q of MA model according to AIC criterion, and set up AR model, the calculating formula of AIC criterion is:

$\min \mathrm{AIC}=n\ln {\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^{{^}_2}+2(p+q+1)$

AR (φ, the p) model set up is:

X _t＝φ ₁X _t-1+φ ₂X _t-2+…+φ _pX _t-p+ε _t

Wherein, ε _tfor zero-mean, variance are stationary white noise, σ _ε ²estimated value;

53) electric load sequence { X is set up _tmA model, specifically comprise the following steps:

531) according to mark differential parameter d to electric load sequence { X _t: t=... ,-1,0,1 ... carry out mark Difference Calculation difference sequence Y, the calculating formula of Y is:

Y＝{Y _t，t＝1，2，3…，N}

$Y_t={\mathrm{\&Delta;}}^d{X}_t={(1-B)}^d{X}_t=\underset{k=0}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\left(\begin{array}{c}d\\ k\end{array}\right){(-B)}^k{X}_t=\underset{k=0}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{\mathrm{\&pi;}}_k{X}_{t-k}(k=\mathrm{1,2,3}\&CenterDot;\&CenterDot;\&CenterDot;N)$

${\mathrm{\&Delta;}}^d={(1-B)}^d=1-\left(\begin{array}{c}d\\ 1\end{array}\right)B+\left(\begin{array}{c}d\\ 2\end{array}\right)B^2+\&CenterDot;\&CenterDot;\&CenterDot;+{(-1)}^{d-1}\left(\begin{array}{c}d\\ d-1\end{array}\right)B^{d-1}+{(-1)}^d{B}^d$

${\mathrm{\&pi;}}_k=\frac{\mathrm{\&Gamma;}(d+1)}{\mathrm{\&Gamma;}(k+1)\mathrm{\&Gamma;}(d-k+1)}$

Wherein, Δ ^dfor d rank difference operator, B is lag operator, and N is the total sample number of difference sequence Y;

532) by difference sequence Y through FIR filter filtering, obtains and exports Z={Z _t, t=1,2,3 ..., N}, and the m rank AR model setting up Z;

533) try to achieve its AR parameter according to the m rank AR model of Z, and calculate the inversely related coefficient of Z, obtain the q rank AR model of Z;

534) according to the q rank AR model of Z, electric load sequence { X is calculated according to Yule-Walker equation _tthe moving average coefficient [θ of MA model ₁, θ ₂..., θ _q].

54) electric load sequence { X is set up _tfARIMA model.

4. a kind of Short-Term Load Forecasting Method closing FARIMA model based on appearance according to claim 1, is characterized in that, described step 4) in judge that the method whether electric load sequence meets long correlated process is:

As 0.5 < H < 1, electric load sequence meets long correlated process;

As H=0.5, electric load sequence does not have self-similarity, discontented foot length correlated process.