CN102867225A - Safety monitoring and predicting method for hourly power loads by aid of chaos and linear regression model - Google Patents

Safety monitoring and predicting method for hourly power loads by aid of chaos and linear regression model Download PDF

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CN102867225A
CN102867225A CN2012103554876A CN201210355487A CN102867225A CN 102867225 A CN102867225 A CN 102867225A CN 2012103554876 A CN2012103554876 A CN 2012103554876A CN 201210355487 A CN201210355487 A CN 201210355487A CN 102867225 A CN102867225 A CN 102867225A
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electric power
dimension
sequence
chaos
correlation
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李眉眉
柯玲
第宝锋
黄正文
丁晶
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Sichuan University
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Sichuan University
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Abstract

The invention relates to a safety monitoring and predicting method for hourly power loads by the aid of a chaos and linear regression model. The hourly power loads are used as research objects, power load phase-space is reconstructed on the basis of a chaos theory, a nonlinear prediction scheme for the load phase-space is studied, and the method is a physical modeling and analyzing method applicable to actual prediction and safety monitoring. The technical scheme includes that the safety monitoring and predicting method comprises steps of A, extracting power loads at integral points of 24 hours everyday for 365 days in the whole year to form a time sequence of the hourly power loads; B, solving an autocorrelation function of the sequence; C, solving saturation correlation dimensions of the sequence; D, solving a Kolmogorov measure entropy of the sequence; and E, predicting a state after a time step T according to the linear regression model. The safety monitoring and predicting method indicates that the hourly power loads have a chaos characteristic, prediction precision of the chaos and linear regression model is satisfactory, and change rules of the hourly power loads can be effectively monitored, so that safe and economical running of a power system is guaranteed.

Description

The chaos linear regression model (LRM) security monitoring Forecasting Methodology of a kind of electric power hour load
Technical field
The present invention relates to the chaos linear regression model (LRM) security monitoring Forecasting Methodology of a kind of electric power hour load, namely take electric power hour load as research object, based on chaology, reconstruct electric load phase space, how research extracts the dynamic information feature of electric load, inquire into the nonlinear prediction scheme in the load phase space, then be applied to the physical modeling analytical approach in actual prediction and the safety monitoring, belong to power domain.
Background technology
Power system load data as water resources development, distribute rationally, the important evidence of reservoir operation.Load forecast plays a very important role the safety and economic operation of electric system.Generation schedule, system security assessment and energy exchange plan etc. need the short-term load forecasting data as decision-making foundation.The electric load time series that obtains in the practice presents complicacy, uncertainty, nonlinear characteristics.Based on chaology, reconstruct electric load phase space, how research extracts the dynamic information feature of electric load, inquires into the nonlinear prediction scheme in the load phase space, and it is very significant being applied in actual prediction and the safety monitoring again.
Summary of the invention
The chaos linear regression model (LRM) security monitoring Forecasting Methodology of a kind of electric power that the present invention proposes hour load, its technical scheme is as follows.
1, according to annual integral point extraction 365 day 24 hours every day electric load, form electric power hour Load Time Series, unit is megawatt.
2, ask for the autocorrelation function of electric power hour load sequence.For length be nTime series , time span is J τAutocorrelation function be:
Figure 2012103554876100002DEST_PATH_IMAGE003
Choose the autocorrelation function first time corresponding time when zero crossing of electric power hour load sequence, be the optimum delay time of phase space reconstruction τ
3, ask for the saturated correlation dimension of electric power hour load sequence.
(1) choosing time delay is the required time of autocorrelation function method τ, embed dimension mInitial value is 1, reconstruct hour sequence phase space;
(2) select the suitable radius of a ball rBe different values, calculate the right Euclidean distance of all phase points in the phase space, account for total ratio of counting mutually less than the number of radius, thereby obtain correlation integral C( r);
Correlation integral Expression phase space phase point pair
Figure 2012103554876100002DEST_PATH_IMAGE005
In, distance
Figure 761794DEST_PATH_IMAGE006
Less than given positive number rThe ratio (N is total counting mutually) that in all phase points, accounts for of number
Figure 466445DEST_PATH_IMAGE008
fBe the Heaviside unit function,
Figure 8285DEST_PATH_IMAGE010
(3) paint the ln of sequence by the correlation integral point that obtains C( r)-ln rRelation curve is analyzed Scaling Whether exist, the straight-line segment in relation curve partly is without Scaling Range;
Objective definite without Scaling Range length, simulate straight line after its slope be defined as correlation dimension D 2
(4) increase phase space and embed dimension, repeat said process, obtain different correlation integral and the correlation dimensions that embed under the dimension D 2( m);
(5) paint correlation dimension D 2( m) with embedding dimension mRelation curve, corresponding correlation dimension was saturated correlation dimension when curve entered the saturation region, corresponding space dimensionality is suitable minimum the embedding dimension.
(6) from ln C( r)-ln rIn the graph of a relation, remove slope and be 0 and slope be the straight-line segment of ∞, determine best-fitting straight line therebetween, the slope of straight line is correlation dimension D 2Along with the phase space dimension mRising, it is saturated that correlation dimension occurs, and namely obtains saturated correlation dimension, corresponding ATTRACTOR DIMENSIONS is D 2(m).
4, ask for the Kolmogorov entropy (measure entropy) of electric power hour load.Measure entropy is another feature amount of identification chaos sequence, is used for the degree of confusion of gauging system motion.Consider one mThe phase space of cone motive system is divided into the length of side and is r mDimension cube box is for an attractor and track that drops in the basin of attraction of state space x( t), getting the time interval is a smaller value τ,
Figure 789290DEST_PATH_IMAGE012
Expression initial time system track is the i 0 In the individual grid, t= τThe time be engraved in i 1 In the individual grid, t= K τThe time be engraved in i k Joint probability in the individual grid, the Kolmogorov entropy is expressed as:
Figure 416580DEST_PATH_IMAGE014
Usually use K 2As an estimation of Kolmogorov entropy, For mThe radius of a ball is in the dimension embedded space rCorrelation integral:
For chaotic motion, its Kolmogorov entropy be greater than zero less than infinitely-great one on the occasion of.
5, for electric power hour Load Time Series be:
Figure 2012103554876100002DEST_PATH_IMAGE019
With aforesaid saturated correlation dimension mAnd time delay τ, its phase space of reconstruct is:
Figure 2012103554876100002DEST_PATH_IMAGE021
Wherein N=n-( M-1) * τLength for sequence vector.
6, a prediction initial state point being set is
Figure 820645DEST_PATH_IMAGE022
, with
Figure 669653DEST_PATH_IMAGE022
The principle of the most similar (vicinity) phase point is followed following principle:
Figure 450527DEST_PATH_IMAGE024
In historical phase point, seek out it with distance-taxis kIndividual similar phase point, the state phasor of similar phase point is
Figure 2012103554876100002DEST_PATH_IMAGE025
(wherein i=1 ~ k).
7, in electric power hour load phase space, state point is
Figure 248850DEST_PATH_IMAGE022
kIndividual similar phase point
Figure 89767DEST_PATH_IMAGE025
, with process evolution step-length TAfter state
Figure 691649DEST_PATH_IMAGE026
Between in a local scope, satisfy linear relationship:
Figure 2012103554876100002DEST_PATH_IMAGE027
A, BEstimate with least square method.
8, state point is Evolution also satisfy similar like this rule:
Figure 663464DEST_PATH_IMAGE028
Linear regression model (LRM) thus measurablely goes out initial state
Figure 675283DEST_PATH_IMAGE022
The later state of elapsed time step-length T.
 
Beneficial effect of the present invention:
ⅰ. the present invention illustrates that an electric power hour load has chaotic characteristic.Electric power hour Load Time Series is along with the rising that embeds dimension, and saturated phenomenon appears in correlation dimension, and its attractor has dimension; And the measure entropy of hour load be greater than zero less than infinitely-great one on the occasion of, illustrate that electric power hour loads and to have the feature of chaos.Thereby available Chaotic Analysis Method, the phase space of reconstruct hour load is carried out short-term forecasting in phase space.
ⅱ. the chaos linear regression model (LRM) security monitoring Forecasting Methodology of a kind of electric power that the present invention proposes hour load, excavate the development law of phase space phase point, higher to hour short-term forecasting precision of load, thus can effectively monitor the safety and economic operation that electric power hour load variations rule ensures electric system.
ⅲ. the chaos linear regression model (LRM) security monitoring Forecasting Methodology of electric power hour load is to seek Changing Pattern in historical phase point, if strengthen the adaptability of safe prediction model, needs to increase the fresh information that sequence develops.
 
(4) description of drawings:
The autocorrelation function graph of Fig. 1 Sichuan province in 2000 electric system hour load sequence.
The saturated correlation dimension figure of Fig. 2 Sichuan province in 2000 electric system hour load.
Kolmogorov entropy (measure entropy) value of Fig. 3 Sichuan province in 2000 electric power hour load.
The chaos linear regression model (LRM) of Fig. 4 Sichuan province in 2000 electric power hour load figure that predicts the outcome.
 
(5) embodiment:
1, the electric system of Sichuan province in 2000 annual every day of 24 hours integral points hour load makeup time sequence, sequence length n=8760.
2, ask for the autocorrelation function of this sequence, select optimum delay time τBe 10h, (see figure 1).
3, ask for hour saturated correlation dimension of load.Along with the phase space dimension mRising, approximately work as mSaturated, corresponding ATTRACTOR DIMENSIONS appearred in correlation dimension in=8 o'clock D 2(8)=2.562(sees Fig. 2).Select space dimensionality corresponding to this moment 8The best embedding dimension for phase space reconstruction.
4, ask for the Kolmogorov entropy (measure entropy) of electric power hour load.Along with mIncrease K 2Tend towards stability the Kolmogorov entropy KBe about 0.0483, (see figure 3).
5, theoretical based on phase space reconstruction, set up hour phase space of load, the best of getting phase space embeds dimension m=8, time delay τ=10, consist of more than 8000 phase point, all phase points are expressed as
Figure 2012103554876100002DEST_PATH_IMAGE029
?。
6, in electric power hour load phase space reconstruction, the integral point load of predicting 24 hours every days of on Dec 1st ~ 7,2000.Take 1 ~ 7945 phase point as material point, 7946 ~ 8113 phase points utilize the phase space linear regression model (LRM) to carry out short-term forecasting for having predicted the newspaper point.
7, in known data phase point, estimate A and B with least square method.
8, use model
Figure 30041DEST_PATH_IMAGE028
Since the 7946th phase point prediction, predict the 8113rd phase point.Select step-length T=1h.
9, the chaos phase space linear regression model (LRM) is to the (see figure 4) that predicts the outcome of Sichuan Province's electric power hour load, and maximum relative error is 16.7%, and average relative error is 5.78%, and it is 83.93% that precision of prediction is higher than 90% ratio.

Claims (4)

1. the chaos linear regression model (LRM) security monitoring Forecasting Methodology of an electric power hour load, it is characterized in that: the concrete steps that described method sequentially comprises are:
A, according to annual 365 day 24 hours every day integral point extract electric load, form electric power hour Load Time Series;
B, ask for the autocorrelation function of electric power hour load sequence;
C, ask for the saturated correlation dimension of electric power hour load sequence;
D, ask for the Kolmogorov measure entropy of electric power hour load;
E, for electric power hour Load Time Series be:
Figure 2012103554876100001DEST_PATH_IMAGE001
Figure 2012103554876100001DEST_PATH_IMAGE002
With aforesaid saturated correlation dimension mAnd time delay τ, its phase space of reconstruct is:
Figure 2012103554876100001DEST_PATH_IMAGE003
Wherein N=n-( M-1) * τLength for sequence vector;
F, arrange one the prediction initial state point be , with
Figure 995823DEST_PATH_IMAGE004
The principle of the most similar (vicinity) phase point is followed following principle:
Figure 2012103554876100001DEST_PATH_IMAGE005
In historical phase point, seek out it with distance-taxis kIndividual similar phase point, the state phasor of similar phase point is
Figure 2012103554876100001DEST_PATH_IMAGE006
(wherein i=1 ~ k);
G, in electric power hour load phase space, state point is
Figure 162231DEST_PATH_IMAGE004
kIndividual similar phase point
Figure 145231DEST_PATH_IMAGE006
, with process evolution step-length TAfter state
Figure 2012103554876100001DEST_PATH_IMAGE007
Between in a local scope, satisfy linear relationship:
Figure 2012103554876100001DEST_PATH_IMAGE008
A, BEstimate with least square method;
H, state point are
Figure 58216DEST_PATH_IMAGE004
Evolution also satisfy similar like this rule:
Figure 2012103554876100001DEST_PATH_IMAGE009
Linear regression model (LRM) thus measurablely goes out initial state
Figure 701950DEST_PATH_IMAGE004
The later state of elapsed time step-length T.
2. the chaos linear regression model (LRM) security monitoring Forecasting Methodology of a kind of electric power according to claim 1 hour load is characterized in that: when described B step is asked for the autocorrelation function of electric power hour load sequence, for length be nTime series
Figure 2012103554876100001DEST_PATH_IMAGE010
, time span is J τAutocorrelation function be:
?
Figure 2012103554876100001DEST_PATH_IMAGE011
Choose the autocorrelation function first time corresponding time when zero crossing of electric power hour load sequence, be the optimum delay time of phase space reconstruction τ
3. the chaos linear regression model (LRM) security monitoring Forecasting Methodology of a kind of electric power according to claim 1 hour load is characterized in that: when described C step is asked for the saturated correlation dimension of electric power hour load sequence, comprise the steps:
A, to choose time delay be the required time of autocorrelation function method τ, embed dimension mInitial value is 1, reconstruct hour sequence phase space;
B, the suitable radius of a ball of selection rBe different values, calculate the right Euclidean distance of all phase points in the phase space, account for total ratio of counting mutually less than the number of radius, thereby obtain correlation integral C( r);
Correlation integral
Figure 2012103554876100001DEST_PATH_IMAGE012
Expression phase space phase point pair
Figure 2012103554876100001DEST_PATH_IMAGE013
In, distance Less than given positive number rThe ratio (N is total counting mutually) that in all phase points, accounts for of number
fBe the Heaviside unit function,
Figure 2012103554876100001DEST_PATH_IMAGE016
C, paint the ln of sequence by the correlation integral point that obtains C( r)-ln rRelation curve is analyzed Scaling
Figure 2012103554876100001DEST_PATH_IMAGE017
Whether exist, the straight-line segment in relation curve partly is without Scaling Range; Objective definite without Scaling Range length, simulate straight line after its slope be defined as correlation dimension D 2
D, increase phase space embed dimension, repeat said process, obtain different correlation integral and the correlation dimensions that embed under the dimensions D 2( m);
E, point are painted correlation dimension D 2( m) with embedding dimension mRelation curve, corresponding correlation dimension was saturated correlation dimension when curve entered the saturation region, corresponding space dimensionality is suitable minimum the embedding dimension;
F, from ln C( r)-ln rIn the graph of a relation, remove slope and be 0 and slope be the straight-line segment of ∞, determine best-fitting straight line therebetween, the slope of straight line is correlation dimension D 2, along with the phase space dimension mRising, it is saturated that correlation dimension occurs, and namely obtains saturated correlation dimension, corresponding ATTRACTOR DIMENSIONS is D 2(m).
4. the chaos linear regression model (LRM) security monitoring Forecasting Methodology of a kind of electric power according to claim 1 hour load, it is characterized in that: when described D step is asked for the Kolmogorov measure entropy of electric power hour load, measure entropy is another feature amount of identification chaos sequence, be used for the degree of confusion of gauging system motion, consider one mThe phase space of cone motive system is divided into the length of side and is r mDimension cube box is for an attractor and track that drops in the basin of attraction of state space x( t), getting the time interval is a smaller value τ, Expression initial time system track is the i 0 In the individual grid, t= τThe time be engraved in i 1 In the individual grid, t= K τThe time be engraved in i k Joint probability in the individual grid, the Kolmogorov measure entropy is expressed as:
Figure 2012103554876100001DEST_PATH_IMAGE019
Usually use K 2As an estimation of Kolmogorov measure entropy,
Figure 603041DEST_PATH_IMAGE012
For mThe radius of a ball is in the dimension embedded space rCorrelation integral:
Figure 2012103554876100001DEST_PATH_IMAGE020
For chaotic motion, its Kolmogorov measure entropy be greater than zero less than infinitely-great one on the occasion of.
CN2012103554876A 2012-09-21 2012-09-21 Safety monitoring and predicting method for hourly power loads by aid of chaos and linear regression model Pending CN102867225A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105488335A (en) * 2015-11-23 2016-04-13 广东工业大学 Lyapunov exponent based power system load prediction method and apparatus
CN107771278A (en) * 2015-06-26 2018-03-06 德国弗劳恩霍夫应用研究促进协会 For providing device, cell instrument, the method and computer program of the information at least one sequence

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
李眉眉等: "基于混沌理论的电力负荷预测", 《四川水利发电》 *
李眉眉等: "电力日负荷的混沌特性分析及短期预测", 《水电能源科学》 *
李眉眉等: "电网短期负荷预测的混沌方法", 《四川电力技术》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107771278A (en) * 2015-06-26 2018-03-06 德国弗劳恩霍夫应用研究促进协会 For providing device, cell instrument, the method and computer program of the information at least one sequence
CN105488335A (en) * 2015-11-23 2016-04-13 广东工业大学 Lyapunov exponent based power system load prediction method and apparatus

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Application publication date: 20130109