CN105447594A - Electric power system grey load prediction method based on exponential smoothing - Google Patents

Abstract

The invention relates to the electric power system load prediction field and especially relates to a grey load prediction method based on exponential smoothing. Aiming at conditions of randomness and uncertainty possessed by an original date sequence of a traditional grey model, the invention provides an improved method combining the exponential smoothing. Through using the exponential smoothing, weighting is performed on the original date sequence to generate a new sequence. Historical data which has large volatility and easily generates a large error is smoothed so that the sequence becomes a sequence which has a high regularity and shows an exponential function. Simultaneously, a background value of a grey model is optimized and a prediction error of the model is further reduced. Through combining the two prediction models, prediction precision is greatly increased; and the method is suitable for correlation departments of an electric power system and the like and is used to solve a load prediction problem in an electric power program.

Description

A kind of electric system Grey Load Prediction method based on exponential smoothing

Technical field

The present invention relates to Load Prediction In Power Systems field, particularly a kind of electric system Grey Load Prediction method based on exponential smoothing.

Background technology

Flourish along with power industry, along with the continuous intensification of electric system reform, more and more important to the research of load forecast theoretical method.Load prediction is historical data according to load and Correlative Influence Factors thereof, the Changing Pattern of analysis load, consider the reason affecting load variations, use certain load forecasting model and research method, estimate the process of the load value in following section sometime.Its main task is the room and time distribution of prediction future electrical energy load.The fundamental purpose of load forecast is exactly carry out predicting by a large amount of historical datas the development and level thereof that provide load, formulates the following corresponding production schedule and development plan provides basic foundation for electrical production department and administrative authority.Determine that each service area respectively plans a year delivery, supplies electricity consumption peak load and plans regional total electric power development level, determine the basic comprising of each planning year power load.Correctly predict electric load, being to ensure that supply without cost (obligation) each department of national economy and people's lives are with the demand of the electric power of abundance, is also the needs of power industry own health sustainable development.

Exponential smoothing is a kind of method conventional in production forecast, in all Forecasting Methodologies, and maximum one that exponential smoothing is.Exponential smoothing is a kind of Time Series Analysis Forecasting method grown up on method of moving average basis, and it used gauge index smooth value, coordinates regular hour sequential forecasting models to predict the future to phenomenon.The weighted mean of its principle to be the exponential smoothing value of arbitrary phase be all current period actual observation value and last phase index smooth value.

Grey system theory is widely used in processing data in modeling, and error is little, and computation process is easy.Irregular historical data after cumulative, become the series of increase, utilizes differential equation matching, thus carry out the prediction of Future Data by gray theory." uncertain, poor information, sample " problem that it studies emphatically fuzzy mathematics, probability statistics cann't be solved, and cover according to information, generated by sequence and seek real rule.Its principal feature is few data modeling.

Because known need for electricity is by the impact of the correlative factors such as politics, economy, weather, makes observation data sequence have randomness and uncertainty, cause the precision of grey forecasting model to reduce.Therefore exponential smoothing and grey forecasting model combine by this patent, utilization index smoothing method is weighted original data sequence and generates new sequence, smooth out comparatively large, the easy historical data produced compared with big error of some undulatory propertys, it is made to be transformed into the regular strong sequence exponentially changed, and the background value of gray model is optimized, thus increase substantially the precision of prediction of grey forecasting model.

Along with the continuous application of grey forecasting model in load forecast, propose the Grey Load Prediction method of multiple Optimization-type, power industry is significant.

Summary of the invention

The object of the present invention is to provide a kind of Grey Load Prediction method based on exponential smoothing, this improved model largely improves randomness and the uncertainty of its original observed data sequence, improve the precision of prediction of this load forecasting model, effective foundation can be provided for electric system power planning.

For achieving the above object, technical scheme of the present invention is: a kind of electric system Grey Load Prediction method based on exponential smoothing, realizes as follows:

Step S1: obtain raw data row x ⁽⁰⁰⁾=[x ⁽⁰⁰⁾(1), x ⁽⁰⁰⁾(2), x ⁽⁰⁰⁾(3) ... x ⁽⁰⁰⁾(n)];

Step S2: the number of times selecting exponential smoothing according to time series trend feature, for the selection of exponential smoothing number of times, according to following rule: when time series is smoothed trend, adopts Single Exponential Smoothing; When time series linearly trend time, adopt Secondary Exponential Smoothing Method; When time series is nonlinear trend, then estimated by third index flatness; Three kinds of exponential smoothing model are respectively:

S _t ⁽¹⁾＝αX _t+(1-α)S _t-1 ⁽¹⁾

S _t ⁽²⁾＝αS _t ⁽¹⁾+(1-α)S _t-1 ⁽²⁾

S _t ⁽³⁾＝αS _t ⁽²⁾+(1-α)S _t-1 ⁽³⁾

Wherein: X _tfor raw data row; α is coefficent of exponential smoothing; S _t ⁽ⁿ⁾be n the exponential smoothing value in t cycle;

Step S3: choose coefficent of exponential smoothing α, the historical data of getting 0.05,0.3,0.6 and 0.95 pair of electric load is respectively smoothing, sets up mathematical prediction model according to different α value;

Step S4: the initial value of selected smoothing computation, if seasonal effect in time series observation period n>15, because the Influence on test result of initial value to prediction is less, desirable x ₀as initial value; If seasonal effect in time series observation period n<15, for reducing error, get the mean value of first three observed reading as initial value;

Step S5: obtaining new sequence after using exponential smoothing computing is:

x ⁽⁰⁾＝[x ⁽⁰⁾(1),x ⁽⁰⁾(2),x ⁽⁰⁾(3)…x ⁽⁰⁾(n)]

To x ⁽⁰⁾make one-accumulate, obtaining generation ordered series of numbers is: x ⁽¹⁾=[x ⁽¹) (1), x ⁽¹⁾(2), x ⁽¹⁾(3) ... x ⁽¹⁾(n)].

Wherein, $x^{\left(1\right)}\left(k\right)=\underset{i=0}{\overset{k}{\&Sigma;}}{x}^{\left(0\right)}\left(i\right);$

Step S6: the background value z calculating grey forecasting model ⁽⁰⁾:

z ⁽⁰⁾(k)＝0.5x ⁽¹⁾(k)+0.5x ⁽¹⁾(k-1)，k＝2,3,...,n

Step S7: Grey Differential Equation is: x ⁽⁰⁾(k)+az ⁽¹⁾(k)=b;

Its albinism differential equation is: $\frac{{\mathrm{dx}}^{\left(1\right)}}{dt}+{\mathrm{ax}}^{\left(1\right)}=b$

Wherein, a, b are parameter, are designated as $P=\left[\begin{array}{c}a\\ b\end{array}\right];$

Step S8: utilize least square method to ask for parameter P:

$P=\left[\begin{array}{c}a\\ b\end{array}\right]={\left(B^{T}B\right)}^{-1}{B}^T{y}_n$

Wherein, $B=\left[\begin{array}{cc}-z^{\left(0\right)}\left(2\right)& 1\\ -z^{\left(0\right)}\left(3\right)& 1\\ ...& ...\\ -z^{\left(0\right)}\left(n\right)& 1\end{array}\right]$

$y_n={\left[\begin{array}{cccc}{x}_0\left(2\right)& x_0\left(3\right)& ...& x_0\left(n\right)\end{array}\right]}^T$

Step S9: the background value in step S6 is optimized, if adjustment parameter θ is:

Step S10: recalculate background value: z ⁽¹⁾(k)=θ x ⁽¹⁾(k)+(1-θ) x ⁽¹⁾(k-1), k=2,3 ..., n

Step S11: after the background value after being optimized, repeats step S8, again solves a, b;

Wherein: $B=\left[\begin{array}{cc}-z^{\left(1\right)}\left(2\right)& 1\\ -z^{\left(1\right)}\left(3\right)& 1\\ ...& ...\\ -z^{\left(1\right)}\left(n\right)& 1\end{array}\right]$

Step S12: try to achieve x ⁽¹⁾the analogue value:

Step S13: to x ⁽¹⁾k () carries out inverse accumulated generating reduction, obtain x ⁽⁰⁾the predicted value of (k), regressive equation is:

Step S14: adopt the precision of prediction of residual test method to the forecast model improving front and back to assess:

$e\left(k\right)=\&lsqb;x^{\left(0\right)}\left(k\right)-{\hat{x}}^{\left(0\right)}\left(k\right)\&rsqb;/x^{\left(0\right)}\left(k\right),(k=2,3,...,n)$

Step S15: according to the degree of accuracy of the predicted value inspection model to known historical data, selects optimum alpha parameter in step S3, determines final forecast model.

In an embodiment of the present invention, in described step S5, using the data rows that obtains after the exponential smoothing original data sequence as grey forecasting model.

Compared to prior art, the present invention has following beneficial effect: a kind of Grey Load Prediction method based on exponential smoothing proposed by the invention, utilization index smoothing method is smoothing to raw data, by choosing suitable level and smooth number of times and smoothing factor, make it be transformed into the regular strong sequence exponentially changed, reduce randomness and the uncertainty of raw data; Simultaneously for unreasonable being optimized of the background value setting in gray model, further increase the precision of prediction of this forecast model, for the load prediction part in electric system provides effective ways.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the Grey Load Prediction method that the present invention is based on exponential smoothing.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is specifically described.

As shown in Figure 1, a kind of electric system Grey Load Prediction method based on exponential smoothing of the present invention, realizes as follows:

Step S1: obtain raw data row x ⁽⁰⁰⁾=[x ⁽⁰⁰⁾(1), x ⁽⁰⁰⁾(2), x ⁽⁰⁰⁾(3) ... x ⁽⁰⁰⁾(n)];

Step S2: the number of times selecting exponential smoothing according to time series trend feature, for the selection of exponential smoothing number of times, according to following rule: when time series is smoothed trend, adopts Single Exponential Smoothing; When time series linearly trend time, adopt Secondary Exponential Smoothing Method; When time series is nonlinear trend, then estimated by third index flatness; Three kinds of exponential smoothing model are respectively:

S _t ⁽¹⁾＝αX _t+(1-α)S _t-1 ⁽¹⁾

S _t ⁽²⁾＝αS _t ⁽¹⁾+(1-α)S _t-1 ⁽²⁾

S _t ⁽³⁾＝αS _t ⁽²⁾+(1-α)S _t-1 ⁽³⁾

Wherein: X _tfor raw data row; α is coefficent of exponential smoothing; S _t ⁽ⁿ⁾be n the exponential smoothing value in t cycle;

Step S3: choose coefficent of exponential smoothing α, the historical data of getting 0.05,0.3,0.6 and 0.95 pair of electric load is respectively smoothing, sets up mathematical prediction model according to different α value;

Step S4: the initial value of selected smoothing computation, if seasonal effect in time series observation period n>15, because the Influence on test result of initial value to prediction is less, desirable x ₀as initial value; If seasonal effect in time series observation period n<15, for reducing error, get the mean value of first three observed reading as initial value;

Step S5: obtaining new sequence after using exponential smoothing computing is:

x ⁽⁰⁾＝[x ⁽⁰⁾(1),x ⁽⁰⁾(2),x ⁽⁰⁾(3)…x ⁽⁰⁾(n)]

To x ⁽⁰⁾make one-accumulate, obtaining generation ordered series of numbers is: x ⁽¹⁾=[x ⁽¹⁾(1), x ⁽¹⁾(2), x ⁽¹⁾(3) ... x ⁽¹⁾(n)].

Wherein, $x^{\left(1\right)}\left(k\right)=\underset{i=0}{\overset{k}{\&Sigma;}}{x}^{\left(0\right)}\left(i\right);$

Step S6: the background value z calculating grey forecasting model ⁽⁰⁾:

z ⁽⁰⁾(k)＝0.5x ⁽¹⁾(k)+0.5x ⁽¹⁾(k-1)，k＝2,3,...,n

Step S7: Grey Differential Equation is: x ⁽⁰⁾(k)+az ⁽¹⁾(k)=b;

Its albinism differential equation is:

Wherein, a, b are parameter, are designated as $P=\left[\begin{array}{c}a\\ b\end{array}\right];$

Step S8: utilize least square method to ask for parameter P:

$P=\left[\begin{array}{c}a\\ b\end{array}\right]={\left(B^{T}B\right)}^{-1}{B}^T{y}_n$

Wherein, $B=\left[\begin{array}{cc}-z^{\left(0\right)}\left(2\right)& 1\\ -z^{\left(0\right)}\left(3\right)& 1\\ ...& ...\\ -z^{\left(0\right)}\left(n\right)& 1\end{array}\right]$

$y_n={\left[\begin{array}{cccc}{x}_0\left(2\right)& x_0\left(3\right)& ...& x_0\left(n\right)\end{array}\right]}^T$

Step S9: the background value in step S6 is optimized, if adjustment parameter θ is:

Step S10: recalculate background value: z ⁽¹⁾(k)=θ x ⁽¹⁾(k)+(1-θ) x ⁽¹⁾(k-1), k=2,3 ..., n

Step S11: after the background value after being optimized, repeats step S8, again solves a, b;

Wherein: $B=\left[\begin{array}{cc}-z^{\left(1\right)}\left(2\right)& 1\\ -z^{\left(1\right)}\left(3\right)& 1\\ ...& ...\\ -z^{\left(1\right)}\left(n\right)& 1\end{array}\right]$

Step S12: try to achieve x ⁽¹⁾the analogue value:

Step S13: to x ⁽¹⁾k () carries out inverse accumulated generating reduction, obtain x ⁽⁰⁾the predicted value of (k), regressive equation is:

Step S14: adopt the precision of prediction of residual test method to the forecast model improving front and back to assess:

$e\left(k\right)=\&lsqb;x^{\left(0\right)}\left(k\right)-{\hat{x}}^{\left(0\right)}\left(k\right)\&rsqb;/x^{\left(0\right)}\left(k\right),(k=2,3,...,n)$

Step S15: according to the degree of accuracy of the predicted value inspection model to known historical data, selects optimum alpha parameter in step S3, determines final forecast model.

In above-mentioned steps, in described step S5, using the data rows that obtains after the exponential smoothing original data sequence as grey forecasting model.

Be more than preferred embodiment of the present invention, all changes done according to technical solution of the present invention, when the function produced does not exceed the scope of technical solution of the present invention, all belong to protection scope of the present invention.

Claims (2)

1. based on an electric system Grey Load Prediction method for exponential smoothing, it is characterized in that: realize as follows:

Step S1: obtain raw data row x ⁽⁰⁰⁾=[x ⁽⁰⁰⁾(1), x ⁽⁰⁰⁾(2), x ⁽⁰⁰⁾(3) ... x ⁽⁰⁰⁾(n)];

Step S2: the number of times selecting exponential smoothing according to time series trend feature, for the selection of exponential smoothing number of times, according to following rule: when time series is smoothed trend, adopts Single Exponential Smoothing; When time series linearly trend time, adopt Secondary Exponential Smoothing Method; When time series is nonlinear trend, then estimated by third index flatness; Three kinds of exponential smoothing model are respectively:

S _t ⁽¹⁾＝αX _t+(1-α)S _t-1 ⁽¹⁾

S _t ⁽²⁾＝αS _t ⁽¹⁾+(1-α)S _t-1 ⁽²⁾

S _t ⁽³⁾＝αS _t ⁽²⁾+(1-α)S _t-1 ⁽³⁾

Wherein: X _tfor raw data row; α is coefficent of exponential smoothing; S _t ⁽ⁿ⁾be n the exponential smoothing value in t cycle;

Step S3: choose coefficent of exponential smoothing α, the historical data of getting 0.05,0.3,0.6 and 0.95 pair of electric load is respectively smoothing, sets up mathematical prediction model according to different α value;

Step S4: the initial value of selected smoothing computation, if seasonal effect in time series observation period n>15, because the Influence on test result of initial value to prediction is less, desirable x ₀as initial value; If seasonal effect in time series observation period n<15, for reducing error, get the mean value of first three observed reading as initial value;

Step S5: obtaining new sequence after using exponential smoothing computing is:

x ⁽⁰⁾＝[x ⁽⁰⁾(1),x ⁽⁰⁾(2),x ⁽⁰⁾(3)…x ⁽⁰⁾(n)]

To x ⁽⁰⁾make one-accumulate, obtaining generation ordered series of numbers is: x ⁽¹⁾=[x ⁽¹⁾(1), x ⁽¹⁾(2), x ⁽¹⁾(3) ... x ⁽¹⁾(n)];

Wherein, $x^{\left(1\right)}\left(k\right)=\underset{i=0}{\overset{k}{\&Sigma;}}{x}^{\left(0\right)}\left(i\right);$

Step S6: the background value z calculating grey forecasting model ⁽⁰⁾:

z ⁽⁰⁾(k)＝0.5x ⁽¹⁾(k)+0.5x ⁽¹⁾(k-1)，k＝2,3,...,n

Step S7: Grey Differential Equation is: x ⁽⁰⁾(k)+az ⁽¹⁾(k)=b;

Its albinism differential equation is: $\frac{{\mathrm{dx}}^{\left(1\right)}}{dt}+{\mathrm{ax}}^{\left(1\right)}=b$

Wherein, a, b are parameter, are designated as $P=\left[\begin{array}{c}a\\ b\end{array}\right];$

Step S8: utilize least square method to ask for parameter P:

$P=\left[\begin{array}{c}a\\ b\end{array}\right]={\left(B^{T}B\right)}^{-1}{B}^T{y}_n$

Wherein, $B=\left[\begin{array}{cc}-z^{\left(0\right)}\left(2\right)& 1\\ -z^{\left(0\right)}\left(3\right)& 1\\ ...& ...\\ -z^{\left(0\right)}\left(n\right)& 1\end{array}\right]$

y _n＝[x ₀(2)x ₀(3)…x ₀(n)] ^T

Step S9: the background value in step S6 is optimized, if adjustment parameter θ is:

Step S10: recalculate background value: z ⁽¹⁾(k)=θ x ⁽¹⁾(k)+(1-θ) x ⁽¹⁾(k-1), k=2,3 ..., n

Step S11: after the background value after being optimized, repeats step S8, again solves a, b;

Wherein: $B=\left[\begin{array}{cc}-z^{\left(1\right)}\left(2\right)& 1\\ -z^{\left(1\right)}\left(3\right)& 1\\ ...& ...\\ -z^{\left(1\right)}\left(n\right)& 1\end{array}\right]$

Step S12: try to achieve x ⁽¹⁾the analogue value:

Step S13: to x ⁽¹⁾k () carries out inverse accumulated generating reduction, obtain x ⁽⁰⁾the predicted value of (k), regressive equation is:

Step S14: adopt the precision of prediction of residual test method to the forecast model improving front and back to assess:

$e\left(k\right)=\&lsqb;x^{\left(0\right)}\left(k\right)-{\hat{x}}^{\left(0\right)}\left(k\right)\&rsqb;/x^{\left(0\right)}\left(k\right),(k=2,3,...,n)$

Step S15: according to the degree of accuracy of the predicted value inspection model to known historical data, selects optimum alpha parameter in step S3, determines final forecast model.

2. a kind of electric system Grey Load Prediction method based on exponential smoothing according to claim 1, is characterized in that: in described step S5, using the data rows that obtains after the exponential smoothing original data sequence as grey forecasting model.