CN103544362A - Harmonic medium and long term prediction method based on two-dimensional curve prediction - Google Patents

Harmonic medium and long term prediction method based on two-dimensional curve prediction Download PDF

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CN103544362A
CN103544362A CN201310539260.1A CN201310539260A CN103544362A CN 103544362 A CN103544362 A CN 103544362A CN 201310539260 A CN201310539260 A CN 201310539260A CN 103544362 A CN103544362 A CN 103544362A
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sequence
year
prediction
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value
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CN103544362B (en
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金家培
陈甜甜
罗祾
杨洪耕
高云
潘爱强
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State Grid Shanghai Electric Power Co Ltd
East China Power Test and Research Institute Co Ltd
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State Grid Shanghai Electric Power Co Ltd
East China Power Test and Research Institute Co Ltd
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Abstract

The invention relates to a harmonic medium and long term prediction method based on two-dimensional curve prediction. The method includes the following steps: 1) acquiring historical electric energy quality index data of at least one monitoring point in a set time period in a prediction interval and conducting data preprocessing to obtain a historical data series; 2) judging whether a year to be predicted has an innovation value, executing the step 3) on yes judgment, adjusting the historical data series on no judgment and executing the step 3) with the adjusted historical data series; 3) conducting time series curve prediction on a monthly development series of monthly quantity according to the historical data series to obtain a transverse prediction series of the year to be predicted; 4) conducting time series curve prediction on a yearly development series of the monthly quantity according to the historical data series to obtain a vertical prediction series of the year to be predicted; 5) conducting weighted average calculation to obtain the two-dimensional prediction series of the year to be predicted. Compared with the prior art, the method has the advantages of being high in prediction accuracy, anti-jamming, simple in principle and the like.

Description

A kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction
Technical field
The present invention relates to a kind of electrical network quality of power supply Forecasting Methodology, especially relate to a kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction.
Background technology
The quality of power supply is being related to safety and stability, the economical operation of electrical network, along with the transformation of modern power network to high reliability and quality supply, improve the electrical network quality of power supply become guarantee power system safety and stability operation in the urgent need to.
The electrical network quality of power supply on the one hand because of non-linear, large capacity and the strong load equipment of impact constantly access aggravate, on the other hand because its control measures and the continuous extension to increase capacity of electrical network improve.Also there are some uncertain factors, as the automatic protection of spontaneous phenomenon and power equipment and device and the change of normal operating mode etc. have all caused serious interference to the trend of the quality of power supply simultaneously.
Power transmission network, as the chief component of electric system, is being born jumbo electric power transfer task, and its power quality problem influence area is large, therefore most important to the safety of whole electrical network.If can the quality of power supply be predicted, analyze its development trend, find that early the quality of power supply is maybe by the problem worsening, take corresponding measure to be improved and administer, thereby the loss causing thus is even avoided in reduction, for network optimization provides strong foundation and decision support, there is important theory value and realistic meaning.Therefore the quality of power supply is predicted to be very necessary, also more and more higher to the requirement of quality of power supply prediction, medium-and long-term forecasting is also had to urgent demand.Medium-term forecast refers in 1~2 year, month or the prediction in season, long-term forecasting refers to moon, the season of 1~10 year, the prediction in year.
Summary of the invention
Object of the present invention is exactly to provide in order to overcome the defect of above-mentioned prior art existence a kind of harmonic wave medium-and long-term forecasting method that precision of prediction is high, anti-interference, principle is simply predicted based on two-dimensional curve.
Object of the present invention can be achieved through the following technical solutions:
A harmonic wave medium-and long-term forecasting method for two-dimensional curve prediction, the method comprises the following steps:
1) obtain the historical power quality index data of at least one monitoring point in setting-up time section in forecast interval, the line number of going forward side by side Data preprocess, obtains historical data sequence;
2) whether have new breath value, whether have known electric energy quality index data, if so, perform step 3 if judging to be predicted year if judging to be predicted year), if not, historical data sequence is adjusted, and with the historical data sequence execution step 3 after adjusting);
3) according to historical data sequence, to the moon, the monthly developmental sequence of tolerance carries out timing curve prediction, obtains the lateral prediction sequence of to be predicted year
Figure BDA0000407918750000021
4) according to historical data sequence, to the moon, the annual developmental sequence of tolerance carries out timing curve prediction, obtains longitudinal forecasting sequence of to be predicted year
Figure BDA0000407918750000022
5) lateral prediction sequence and longitudinal forecasting sequence are weighted on average, obtain the two-dimensional prediction sequence of to be predicted year
Figure BDA0000407918750000023
and add in historical data sequence:
y t hv = w 1 y t hor + w 2 y t ver
In formula, w 1, w 2the weight of horizontal, the longitudinal predicted value of difference.
Described setting-up time section is greater than 1 year.
Described data pre-service is specially:
The power quality index data that each monitoring point is obtained are weighted the comprehensive historical data sequence that on average obtains forecast interval, and computing formula is as follows:
Y region=wy point
w i=p i/p sum,i=1,2,...,N
Wherein, w ifor i the element of weight vectors w, represent the weight of i monitoring point, p ibe the power of i monitoring point, p sumfor the general power of each monitoring point in forecast interval, Y tegionfor the comprehensive historical data sequence of forecast interval, y pointpower quality index matrix for each monitoring point in forecast interval.
Described step 3) be specially:
301) characteristic parameter of the horizontal curve in year to be predicted is predicted, described characteristic parameter comprises average perunit value ρ and minimum perunit value β;
302) take on the time close to time of to be predicted year be standard year, according to monthly perunit value sequence and the step 301 of standard year) characteristic parameter recording in advance obtains the monthly perunit value sequence of to be predicted year;
303) according to the monthly perunit value sequence of to be predicted year and the new breath value of to be predicted year, carry out newly ceasing famousization processing, obtain lateral prediction value.
Described step 301), in, the characteristic parameter Forecasting Methodology of employing comprises the moving method of average, regression analysis or exponential smoothing.
Described step 302) comprising:
A) the monthly perunit value sequence to standard year
Figure BDA0000407918750000031
generate processing:
Will
Figure BDA0000407918750000032
after descending sequence, become sequence
Figure BDA0000407918750000033
if the monthly perunit value sequence d of to be predicted year tsequence postscript is
Figure BDA0000407918750000034
before and after sequence, under corresponding original of sequence, be labeled as h j, per days, number scale was T, had following relation:
1 = y k , 1 ( 0 ) ≥ y k , 2 ( 0 ) ≥ · · · ≥ y k , T ( 0 ) > 0
1 = y t , 1 * ≥ y t , 2 * ≥ · · · ≥ y t , T * = β > 0
y k , j ( 0 ) = d k , h j ( 0 ) , j = 1,2 , . . . , T
y t , j * = d t , h j , j = 1,2 , . . . , T
Will
Figure BDA0000407918750000039
adjacent two of sequence asks difference to obtain sequence and x t, obtain:
x k , j ( 0 ) = y k , j ( 0 ) - y k , j + 1 ( 0 ) ≥ 0 , j = 1,2 , . . . , T - 1
x t , j = y t , j * - y t , j + 1 * ≥ 0 , j = 1,2 , . . . , T - 1
y k , j ( 0 ) = 1 - Σ i = 1 j - 1 x k , j ( 0 ) , j = 2 , . . . , T
y t , j * = 1 - Σ i = 1 j - t x t , i , j = 2 , . . . , T
X t, iwith the relational expression of characteristic parameter ρ, β be:
ρ = 1 T Σ j = 1 T y t , j * = 1 T Σ j = 1 T ( 1 - Σ i = 1 j - 1 x t , i ) = 1 T ( T - Σ j = 1 T Σ i = 1 j - 1 x t , i ) = 1 T [ T - Σ i = 1 T - 1 ( T - i ) x t , i ]
β = y T = 1 - Σ i = 1 T - 1 x t , i ;
B) set up mathematical model:
min z = 1 2 ( x - x ( 0 ) ) T ( x - x ( 0 ) ) s . t . Ax = b x ≥ 0
Wherein, x ( 0 ) = x k , 1 ( 0 ) . . . x k , T - 1 ( 0 ) , x = x t , 1 . . . x t , T - 1 , A = T - 1 T - 2 . . . 1 1 1 . . . 1 , b = T ( 1 - ρ ) 1 - β ;
C) to step b) in mathematical model carry out iterative, iterative process is specially:
C1) introduce Lagrange multiplier w t=[w 1, w 2..., w t-1] and v t=[v 1, v 2], and remember W 0=diag{w i, W 0e=w, e t=[1,1 ..., 1]; Put initial value W 0=0, iterations q=1, given condition of convergence ε (ε > 0);
C2) calculate v:v=(AA t) -1[b-A (x (0)+ W 0e)];
C3) calculate x (*)=x (0)+ W 0e+A tv, judgement x (*)in each component
Figure BDA00004079187500000320
if
Figure BDA00004079187500000321
put w i=0; Otherwise, order
Figure BDA0000407918750000041
Figure BDA0000407918750000042
obtain thus x (*), W 0;
C4) judgement || Ax (*)|| 2/ || b|| 2whether < ε sets up, and if so, stops iteration, obtains optimum solution x (*); If not, put q=q+1, return to step c2);
D) to step c) the optimum solution x that obtains (*)carrying out contrary generation processes:
First carry out unfavourable balance and count processing, obtain sequence
Figure BDA0000407918750000043
wherein
y t , 1 * = 1.0
y t , i + 1 * = y t , i * - x t , i ( * ) , i = 1,2 , . . . , T - 1
Right
Figure BDA0000407918750000046
carry out contrary sequence and obtain sequence d t,
Figure BDA0000407918750000047
Described step 303), in, newly cease famousization processing and be specially:
If the power quality index data of the front m of to be predicted year month are known, the new breath value sequence of to be predicted year is { y t, 1, y t, 2, y t, m, the lateral prediction value in to be predicted year residue month is
y t , j hor = y t , k d t , j d t , k , j = m + 1 , m + 2 , . . . , T
Wherein, d t, j,d t, kbe respectively the perunit value of the to be predicted year j month, the k month, y t, kmeet { y t, k| min (v (k)), v (k)computing formula as follows
v ( k ) = 1 m &Sigma; j = 1 m ( y ^ t , j ( k ) - y t , j ) 2
y ^ t , j ( k ) = y t , k d t , j d t , k , k , j = 1,2 , . . . , m
Obtain thus the lateral prediction sequence of to be predicted year
Figure BDA00004079187500000411
Described step 4), in, when known annual developmental sequence is greater than three values, longitudinally predicted value is identical with the computing method of lateral prediction value.
Described step 4) in, when known annual developmental sequence only has two values, adopt growth ratio method to calculate longitudinal predicted value, its formula is as follows:
y t , j ver = y t - 1 , j y t , k y t - 1 , k
Wherein, k=1,2 ..., m, j=m+1, m+2 ..., T.
Described step 5) in, the weight w of horizontal, longitudinal predicted value 1, w 2meet
J ( w 1 , w 2 ) = &Sigma; i = 1 m [ z i - ( w 1 y t , i hor + w 2 y t , i ver ) ] 2
Wherein, z ibe the actual value of i month, for sequence
Figure BDA00004079187500000415
in i element,
Figure BDA00004079187500000416
for sequence
Figure BDA00004079187500000417
in i element.
Compared with prior art, the present invention has the following advantages:
1. the inventive method has adopted the large value of moon tolerance 95% probability of Detecting Power Harmonics point to predict, has weakened thus harmonic wave random factor to the harmful effect predicting the outcome.
2. the inventive method adopts the interval integrated value of harmonic wave to predict, has weakened the impact that each monitoring point random variation produces.
3. the inventive method has considered harmonic wave moon tolerance the same year (monthly development trend is also horizontal trend) and trend that the same period (annual development trend, i.e. longitudinal development trend), two dimension developed over the years month by month, has used for reference the method for load prediction.Because measuring two-way trend the moon, formed the netted development relation in its space, within each month, tolerance is on the point of crossing of the netted comprehensive development trend in space, therefore take into account the two while predicting, takes full advantage of its natural law.Month tolerance annual developmental sequence point between be spaced apart 1 year, embodied the development and change rule under its overall background improving constantly at social development levels; And interval between its monthly developmental sequence point is 1 month, has embodied its rule with seasonal variations.The present invention adopts the method for curve prediction to utilize respectively these two kinds of rules to predict it, according to the weight of asking for, Two-way measured value is weighted and on average obtains two-dimensional prediction result.
4. the inventive method can accurately provide the development trend of the quality of power supply, and principle is simple.
Accompanying drawing explanation
Fig. 1 is the principle schematic of correction sequence of the present invention;
Fig. 2 is schematic flow sheet of the present invention;
Fig. 3 is per-unit curve model solution process schematic diagram of the present invention;
Fig. 4 is the inventive method and error comparison diagram horizontal, longitudinally independent Forecasting Methodology.
Embodiment
Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.The present embodiment be take technical solution of the present invention and is implemented as prerequisite, provided detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment.
A harmonic wave medium-and long-term forecasting method for two-dimensional curve prediction, for harmonic wave control, the deterioration of the prevention quality of power supply provide strong foundation.The method take the Monitoring Data of harmonic wave as basis, take into account its development trend same period over the years (annual development trend) and the same year month by month development trend (monthly development trend) carry out two-dimensional prediction.First for harmonic wave year developmental sequence and monthly developmental sequence predict respectively, then according to Least Square Theory, ask for weight, finally respectively annual trend and monthly trend prediction value are weighted and on average obtain two-dimensional prediction result.
The method is theoretical based on normal distribution model.Least square method is to determine the common method of forecast model function expression unknown parameter.Its model is:
J ( w ) = ( z - z ^ ) ( z - z ^ ) T = ( z - wY ) ( z - wY ) T - - - ( 1 )
aw T=1 (2)
1≥w≥0 (3)
Wherein, z, a, Y is known quantity,
Figure BDA0000407918750000062
w is unknown quantity.This model is constrained linear least-squares problem.In the situation that data volume is less, can adopt process of iteration.
While predicting, if there is no known power quality index data in year to be predicted, original series does not meet predicted condition, needs to adjust.For famousization of the new breath of the inventive method prediction step, proposed the concept of correction sequence, adjusted original series and make it meet the realization that Forecasting Methodology requires to facilitate this step.
Known array is y j=[y i, 1y i, 2y i, T], i=1,2 ..., t-1 (t>=2).Forecasting sequence is: y t=[y t, 1y t, 2 ... y t, T], y wherein t, k(k=1,2 ..., m) known.Initial month of original series is respectively: January and Dec, the i.e. natural division in year.When known 2 years and above data (being t >=2) and while within to be predicted year, there is no new breath value (being m=0), need first adjust sequence, redefine start-stop month, make m ≠ 0, thereby obtain a new sequence, be called correction sequence, its schematic diagram is as shown in Figure 1.
The key step of the inventive method is the foundation of transverse and longitudinal two-dimensional curve forecast model and solves and the asking for of weight.Curve prediction model mainly adopts the foundation of existing Day Load Curve Forecasting model and method for solving to obtain, then carry out famousization as the case may be.Because existing, the index amount of the quality of power supply take the feature that year as the cycle changes, therefore required minimum data should be the power quality index value of a year.The following forecasting process of first introducing known 1 year above historical data.
As shown in Figure 2, the harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction of the present invention comprises the following steps:
1) obtain the historical power quality index data of at least one monitoring point in setting-up time section (being greater than a year) in forecast interval, the line number of going forward side by side Data preprocess, obtains historical data sequence;
2) whether have new breath value, if so, perform step 3 if judging to be predicted year), if not, historical data sequence is adjusted, and with the historical data sequence execution step 3 after adjusting);
3) according to historical data sequence, to the moon, the monthly developmental sequence of tolerance carries out timing curve prediction, obtains the lateral prediction sequence of to be predicted year
Figure BDA0000407918750000063
4) according to historical data sequence, to the moon, the annual developmental sequence of tolerance carries out timing curve prediction, obtains longitudinal forecasting sequence of to be predicted year
Figure BDA0000407918750000064
5) lateral prediction sequence and longitudinal forecasting sequence are weighted on average, obtain the two-dimensional prediction sequence of to be predicted year and add in historical data sequence:
y t hv = w 1 y t hor + w 2 y t ver
In formula, w 1, w 2the weight of horizontal, the longitudinal predicted value of difference.
Below this method is specifically introduced.
1 transverse and longitudinal curve prediction
To the moon, the monthly developmental sequence of tolerance carries out timing curve prediction, the overall trend of sequence is predicted, is called lateral prediction.To the moon, the annual developmental sequence of tolerance carries out timing curve prediction, is called longitudinal prediction.Transverse and longitudinal prediction all adopts the method for curve prediction.Mainly the process with horizontal curve prediction is introduced.Because existing, the index amount of harmonic wave take the feature that year as the cycle changes, therefore can think that its per-unit curve each year is basically identical.
1.1 data pre-service
If carry out interval comprehensive electric energy quality prediction, need to carry out to raw data the pre-service of following steps.Single monitoring point does not need to carry out this step while predicting.
Because each electric energy quality monitoring point is proportionate on the ratio of interval impact and its power and general power.Therefore account for the ratio of general power is weighted each data of monitoring point of forecast interval on average to obtain interval comprehensive electric energy quality curve according to the power of monitoring point.The power quality index data that each monitoring point is obtained are weighted the comprehensive historical data sequence that on average obtains forecast interval, and computing formula is as follows:
Y region=wy point (4)
w i=p i/p sum,i=1,2,...,N (5)
Wherein, w ifor i the element of weight vectors w, represent the weight of i monitoring point, p ibe the power of i monitoring point, p sumfor the general power of each monitoring point in forecast interval, Y regionfor the comprehensive historical data sequence of forecast interval, y pointpower quality index matrix for each monitoring point in forecast interval.Interval censored data is compared with one point data, and enchancement factor is weakened, regular enhancing.With interval comprehensive electric energy quality data, predict the accuracy that can improve prediction.
1.2 curve prediction
Curve prediction is divided into two steps: curvilinear characteristic parameter prediction and per-unit curve prediction.Its lateral prediction result is a month horizontal per-unit curve for tolerance.
(1) prediction of curvilinear characteristic parameter
The prediction of curvilinear characteristic parameter can adopt the moving method of average, regretional analysis, exponential smoothing etc.Here adopt the moving method of average to obtain the year average perunit value ρ of characteristic parameter to be predicted and minimum perunit value β (0 < β < ρ < 1).
Make T=12 (being annual moon number), first with the annual laterally maximal value y of sequence 0, ito y i(i=1,2 ..., t-1) carry out standardization, obtain corresponding year per-unit curve d i(i=1,2 ..., t-1), there is following relation:
y 0 , i = max 1 &le; j &le; T y t , j - - - ( 7 )
d t,j=y i,j/y 0,i,j=1,2,…,T (8)
Feature and shape that the average perunit value ρ of main characteristic parameters of monthly developmental sequence per-unit curve and minimum perunit value β can reflect curve, it changes the variation that has substantially reflected monthly developmental sequence curve.The curve of known t-1, its average perunit value and minimum perunit value are respectively ρ iand β i(i=1,2 ..., t-1).
&rho; i = 1 T &Sigma; j - 1 T d i , j - - - ( 9 )
&beta; i = min 1 &le; j &le; T d i , j - - - ( 10 )
The prediction of curvilinear characteristic parameter can adopt the moving method of average, regretional analysis, exponential smoothing etc.Here adopt the moving method of average.The characteristic parameter of predicting the monthly developmental sequence curve of to be predicted year is respectively:
&rho; ^ = 1 t - 1 &Sigma; i = 1 t - 1 &rho; i - - - ( 11 )
&beta; ^ = 1 t - 1 &Sigma; i = 1 t - 1 &beta; i - - - ( 12 )
(2) per-unit curve prediction
First per-unit curve prediction will determine datum curve.Can select historical each year curve to make generalized analysis, as weighted comprehensive (near big and far smaller principle), determine and represent curve.Also can select certain year actual curve with typicalness as datum curve.On the employing time of the present invention close to certain year interval comprehensive harmonic curve of to be predicted year as datum curve.Foundation and method for solving according to existing Day Load Curve Forecasting model obtain the quality of power supply per-unit curve of to be predicted year.
Suppose that monthly developmental sequence curve post youngest of known reference year value sequence is
Figure BDA0000407918750000086
with to be predicted year characteristic parameter ρ, in the situation of β (0 < β < ρ < 1) (being obtained by upper step prediction), carry out the prediction of this year curve.Suppose to be predicted year curve post the one value sequence d t, j with
Figure BDA0000407918750000087
there is similar shape.
1. Raw Data Generation is processed
In order to weaken the randomness of raw data, and provide intermediate information for setting up mathematical model, introduce the thought of gray system, to raw data
Figure BDA0000407918750000088
generate processing:
A. sequence is processed
Will after descending sequence, become sequence
Figure BDA00004079187500000810
if the monthly perunit value sequence d of to be predicted year isequence postscript is
Figure BDA00004079187500000811
before and after sequence, under corresponding original of sequence, be labeled as h j, per days, number scale was T, T=12, has following relation:
1 = y k , 1 ( 0 ) &GreaterEqual; y k , 2 ( 0 ) &GreaterEqual; &CenterDot; &CenterDot; &CenterDot; &GreaterEqual; y k , T ( 0 ) > 0 - - - ( 13 )
1 = y t , 1 * &GreaterEqual; y t , 2 * &GreaterEqual; &CenterDot; &CenterDot; &CenterDot; &GreaterEqual; y t , T * = &beta; > 0 - - - ( 14 )
y k , j ( 0 ) = d k , h j ( 0 ) , j = 1,2 , . . . , T - - - ( 15 )
y t , j * = d t , h j , j = 1,2 , . . . , T - - - ( 16 )
B. difference is processed
Will adjacent two of sequence asks difference to obtain sequence
Figure BDA0000407918750000097
and x t, obtain:
x k , j ( 0 ) = y k , j ( 0 ) - y k , j + 1 ( 0 ) &GreaterEqual; 0 , j = 1,2 , . . . , T - 1 - - - ( 17 )
x t , j = y t , j * - y t , j + 1 * &GreaterEqual; 0 , j = 1,2 , . . . , T - 1 - - - ( 18 )
y k , j ( 0 ) = 1 - &Sigma; i = 1 j - 1 x k , t ( 0 ) , j = 2 , . . . , T - - - ( 19 )
y t , j * = 1 - &Sigma; i = 1 j - 1 x t , i , j = 2 , . . . , T - - - ( 20 )
X t, iwith the relational expression of characteristic parameter ρ, β be:
&rho; = 1 T &Sigma; j = 1 T y t , j * = 1 T &Sigma; j = 1 T ( 1 - &Sigma; i = 1 j - 1 x t , i ) = 1 T ( T - &Sigma; j = 1 T &Sigma; i = 1 j - 1 x t , i ) = 1 T [ T - &Sigma; i = 1 T - 1 ( T - i ) x t , j ] - - - ( 21 )
&beta; = y T = 1 - &Sigma; i = 1 T - 1 x t , i - - - ( 22 )
2. mathematical model
By generation, process, problem is converted into and makes sequence x twith
Figure BDA00004079187500000914
difference as far as possible little, mathematical model is:
min z = 1 2 &Sigma; i = 1 T - 1 ( x t , i - x k , i ( 0 ) ) 2 - - - ( 23 )
s . t . &Sigma; i = 1 T - 1 ( T - i ) x t , i = T ( 1 - &rho; ) - - - ( 24 )
&Sigma; i = 1 T - 1 x t , i = 1 - &beta; - - - ( 25 )
x t,i≥0,i=1,2,…,T-1 (26)
Order x ( 0 ) = x k , 1 ( 0 ) . . . x k , T - 1 ( 0 ) , x = x t , 1 . . . x t , T - 1 , A = T - 1 T - 2 . . . 1 1 1 . . . 1 , b = T ( 1 - &rho; ) 1 - &beta; , The matrix form of problem is:
min z = 1 2 ( x - x ( 0 ) ) T ( x - x ( 0 ) ) - - - ( 27 )
s.t.Ax=b (28)
x≥0 (29)
3. model solution
This model is a typical quadratic programming problem, can adopt the method for solving of quadratic programming.Given this problem has following feature: the gloomy matrix in sea of objective function is unit matrix, and equality constraint is linear restriction.Succinct method for solving is as follows.
Introduce Lagrange multiplier w t=[w 1, w 2..., w t-1] and v t=[v 1, v 2], and remember W 0=diag{w i, make e t=[1,1 ..., 1],
W 0e=w (30)
Set up following Lagrangian function:
L ( x , W 0 , v ) = 1 2 ( x - x ( 0 ) ) T ( x - x ( 0 ) ) - ( W 0 e ) T x - v T ( Ax - b ) - - - ( 31 )
Quadratic programming is as the special case of convex programming, and K-T condition, as sufficient and necessary condition, can be expressed as, at optimum point x (*)place:
x (*)-x (0)-W 0e-A Tv=0 (32)
Ax (*)-b=0 (33)
W 0x (*)=0 (34)
x (*)≥0,W 0≥0 (35)
By above-mentioned, obtained:
v=(AA T) -1□[b-A(x (0)+W 0e)] (36)
(AA wherein t) -1for constant matrices.
As shown in Figure 3, the iterative process of model is:
A. put initial value W 0=0, iterations q=1, given condition of convergence ε (ε > 0);
B. according to formula (36), calculate v;
C. calculate x (*)=x (0)+ W 0e+A tv, judgement x (*)in each component
Figure BDA0000407918750000102
if
Figure BDA0000407918750000103
put w i=0; Otherwise, order
Figure BDA0000407918750000105
obtain thus x (*)w 0;
D. whether judgement (33) formula is set up, and is converted into the judgement condition of convergence || Ax (*)|| 2/ || b|| 2whether < ε sets up, and if so, stops iteration, obtains optimum solution x (*); If not, put q=q+1, return to step a.
4. contrary generation of result processed
A. unfavourable balance number is processed
y t , 1 * = 1.0 - - - ( 37 )
y t , i + 1 * = y t , i * - x t , i ( * ) , i = 1,2 , . . . , T - 1 - - - ( 38 )
B. contrary sequence is processed
d t , h j = y t , j * - - - ( 39 )
1.3 new famousization of breath
According to the value in the known month (1~m month) of to be predicted year, new breath value is carried out the famous value that minimum variance estimate obtains prediction curve, is called famousization of information.Sequence { the y that the known month in time to be predicted is worth t, 1, y t, 2..., y t, m,
y ^ t , j = y t , k d t , j d t , k , j = m + 1 , m + 2 , . . . , T - - - ( 40 )
Wherein, d t, j, d t, kbe respectively the t j month, the perunit value of the k month, y t, kmeet { y t, k| min (v (k)), v (k)for take k month numerical value m before famousization of benchmark curve mean square deviation of individual month, by formula (42), calculated.
Figure BDA0000407918750000113
The lateral prediction value of t m+1~T month is
Figure BDA0000407918750000114
this method takes full advantage of new breath value.
The data that obtain by virtual year method by the value prediction of whole year calendar year not out, if desired can according to the estimation of prediction in virtual year newly breath value re-start prediction and famousization of calendar year per-unit curve, draw annual value.
In next the method that can not adopt of situation that only known a year and a day, data were predicted the data of Second Year to famousization of prediction curve.Need to predict and make famousization of prediction curve the maximal value in prediction year.Can rule of thumb determine maximal value, prediction accuracy in the case reduces.
While only knowing the data of a year, longitudinally prediction cannot realize.When if known longitudinal sequence only has two values, because the longitudinal iterative process of model solution does not restrain, should not adopt curve prediction model.Now adopt growth ratio method, its formula is as follows:
y t , j ver = y t - 1 , j y t , k y t - 1 , k - - - ( 43 )
Wherein, k=1,2 ..., m, j=m+1, m+2 ..., T.
2 two-dimensional predictions
Given data is carried out two-dimensional prediction by weighted mean during more than 1 year, makes full use of its month to measure horizontal trend and longitudinal trend correlativity separately.
The criterion that weight is chosen is to make predicated error meet least-squares estimation.Make two-dimensional estimation value be
Figure BDA0000407918750000117
, weight is ww=(w 1, w 2), have:
z ^ i = w 1 y t , i hor + w 2 y t , i ver - - - ( 44 )
Wherein, i=1,2 ..., m, the actual value of i month and the error of its estimated value are:
e i = z i - z ^ i - - - ( 45 )
Criterion of least squares is exactly to wish that required weight can make the quadratic sum of evaluated error reach minimum, even performance index:
J ( w 1 , w 2 ) = &Sigma; i = 1 m [ z i - ( w 1 y t , i hor + w 2 y t , i ver ) ] 2 - - - ( 46 )
Reach minimum weight, wherein, z ibe the actual value of i month, for sequence
Figure BDA0000407918750000124
in i element,
Figure BDA0000407918750000125
for sequence
Figure BDA0000407918750000126
in i element.According to the process of iteration of Constrained least square method, solve.Given initial value: w (0)=[0 1], select suitable iteration step length to carry out iterative.
Therefore the estimated value for the t m+1 month is:
y t , m + 1 hv = w 1 y t , m + 1 hor + w 2 y t , m + 1 ver - - - ( 47 )
When only knowing the data of a year, longitudinally prediction cannot be carried out, therefore directly using lateral prediction result as two-dimensional prediction result.
Below with instantiation explanation the inventive method.
The interval integrated voltage total percent harmonic distortion (VTHD) of four monitoring point 2009-2011s and the data of total harmonic current of table 1 for calculating according to formula (4), its weight is as shown in table 2.What the inventive method adopted is the large value of monthly data 95% probability, to weaken the impact of quality of power supply undulatory property.Predicting the outcome of correspondingly obtaining is also 95% probable value.
Integrated data between table 1 monitoring occupied area
Figure BDA00004079187500001210
Each monitoring point weight of table 2
Figure BDA0000407918750000129
Figure BDA0000407918750000131
The known No. 2 monitoring points value of 2009 and the total percent harmonic distortion data of voltage of 4 months before 2010, predict the value in residue month in 2010.The result of prediction is as shown in table 3, and error as shown in Figure 4.
Table 3 predicts the outcome
Figure BDA0000407918750000132
In table 4, list absolute average and the variance of each method predicated error, evaluated respectively its prediction accuracy and stability.From predicting the outcome and Error Graph and table 4, the result of two-dimensional prediction is with respect to laterally or longitudinally predicting the outcome separately, and its error is less than both, and the poor minimum of mean square of error illustrates that two-dimensional prediction accuracy and stability are better than single directional prediction.
Table 4 comparison that predicts the outcome
Figure BDA0000407918750000133

Claims (10)

1. the harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction, is characterized in that, the method comprises the following steps:
1) obtain the historical power quality index data of at least one monitoring point in setting-up time section in forecast interval, the line number of going forward side by side Data preprocess, obtains historical data sequence;
2) whether have new breath value, whether have known electric energy quality index data, if so, perform step 3 if judging to be predicted year if judging to be predicted year), if not, historical data sequence is adjusted, and with the historical data sequence execution step 3 after adjusting);
3) according to historical data sequence, to the moon, the monthly developmental sequence of tolerance carries out timing curve prediction, obtains the lateral prediction sequence of to be predicted year
Figure FDA0000407918740000011
4) according to historical data sequence, to the moon, the annual developmental sequence of tolerance carries out timing curve prediction, obtains longitudinal forecasting sequence of to be predicted year
Figure FDA0000407918740000012
5) lateral prediction sequence and longitudinal forecasting sequence are weighted on average, obtain the two-dimensional prediction sequence of to be predicted year
Figure FDA0000407918740000013
and add in historical data sequence:
y t hv = w 1 y t hor + w 2 y t ver
In formula, w 1, w 2the weight of horizontal, the longitudinal predicted value of difference.
2. a kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction according to claim 1, is characterized in that, described setting-up time section is greater than 1 year.
3. a kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction according to claim 1, is characterized in that, described data pre-service is specially:
The power quality index data that each monitoring point is obtained are weighted the comprehensive historical data sequence that on average obtains forecast interval, and computing formula is as follows:
Y region=wy point
w i=p i/p sum,i=1,2,...,N
Wherein, w ifor i the element of weight vectors w, represent the weight of i monitoring point, p ibe the power of i monitoring point, p sumfor the general power of each monitoring point in forecast interval, Y tegionfor the comprehensive historical data sequence of forecast interval, y pointpower quality index matrix for each monitoring point in forecast interval.
4. a kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction according to claim 1, is characterized in that described step 3) be specially:
301) characteristic parameter of the horizontal curve in year to be predicted is predicted, described characteristic parameter comprises average perunit value ρ and minimum perunit value β;
302) take on the time close to time of to be predicted year be standard year, according to monthly perunit value sequence and the step 301 of standard year) characteristic parameter recording in advance obtains the monthly perunit value sequence of to be predicted year;
303) according to the monthly perunit value sequence of to be predicted year and the new breath value of to be predicted year, carry out newly ceasing famousization processing, obtain lateral prediction value.
5. a kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction according to claim 4, is characterized in that described step 301) in, the characteristic parameter Forecasting Methodology of employing comprises the moving method of average, regression analysis or exponential smoothing.
6. a kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction according to claim 4, is characterized in that described step 302) comprising:
A) the monthly perunit value sequence to standard year
Figure FDA0000407918740000021
generate processing:
Will
Figure FDA0000407918740000022
after descending sequence, become sequence if the monthly perunit value sequence d of to be predicted year tsequence postscript is
Figure FDA0000407918740000024
before and after sequence, under corresponding original of sequence, be labeled as h j, per days, number scale was T, had following relation:
1 = y k , 1 ( 0 ) &GreaterEqual; y k , 2 ( 0 ) &GreaterEqual; &CenterDot; &CenterDot; &CenterDot; &GreaterEqual; y k , T ( 0 ) > 0
1 = y t , 1 * &GreaterEqual; y t , 2 * &GreaterEqual; &CenterDot; &CenterDot; &CenterDot; y t , T * = &beta; > 0
y k , j ( 0 ) = d k , h j ( 0 ) , j = 1,2 , . . . , T
y t , j * = d t , h j , j = 1,2 , . . . , T
Will
Figure FDA0000407918740000029
adjacent two of sequence asks difference to obtain sequence
Figure FDA00004079187400000211
and x t, obtain:
x k , j ( 0 ) = y k , j ( 0 ) - y k , j + 1 ( 0 ) &GreaterEqual; 0 , j = 1,2 , . . . , T - 1
x t , j = y t , j * - y t , . j + 1 * &GreaterEqual; 0 , j = 1,2 , . . . , T - 1
y k , j ( 0 ) = 1 - &Sigma; i = 1 j - 1 x k , i ( 0 ) , j = 2 , . . . , T
y t , j * = 1 - &Sigma; i = 1 j - 1 x t , i , j = 2 , . . . , T
X i, jwith the relational expression of characteristic parameter ρ, β be:
&rho; = 1 T &Sigma; j = 1 T y t , j * = 1 T &Sigma; j = 1 T ( 1 - &Sigma; i = 1 j - 1 x t , i ) = 1 T ( T - &Sigma; j = 1 T &Sigma; i = 1 j - 1 x t , i ) = 1 T [ T - &Sigma; i = 1 T - 1 ( T - i ) x t , i ]
&beta; = y T = 1 - &Sigma; i = 1 T - 1 x t , i ;
B) set up mathematical model:
min z = 1 2 ( x - x ( 0 ) ) T ( x - x ( 0 ) ) s . t . Ax = b x &GreaterEqual; 0
Wherein, x ( 0 ) = x k , 1 ( 0 ) . . . x k , T - 1 ( 0 ) , x = x t , 1 . . . x t , T - 1 , A = T - 1 T - 2 . . . 1 1 1 . . . 1 , b = T ( 1 - &rho; ) 1 - &beta; ;
C) to step b) in mathematical model carry out iterative, iterative process is specially:
C1) introduce Lagrange multiplier w t=[w 1, w 2..., w t-1] and v t=[v 1, v 2], and remember W 0=diag{w j, W 0e=w, e t=[1,1 ..., 1]; Put initial value W 0=0, iterations q=1, given condition of convergence ε (ε > 0);
C2) calculate v:v=(AA t) -1[b-A (x (0)+ W 0e)];
C3) calculate x (*)=x (0)+ W 0e+A tv, judgement x (*)in each component
Figure FDA0000407918740000033
if
Figure FDA0000407918740000034
put w i=0; Otherwise, order
Figure FDA0000407918740000035
Figure FDA0000407918740000036
obtain thus x (*), W 0;
C4) judgement || Ax (*)|| 2/ || b|| 2whether < ε sets up, and if so, stops iteration, obtains optimum solution x (*); If not, put q=q+1, return to step c2);
D) to step c) the optimum solution x that obtains (*)carrying out contrary generation processes:
First carry out unfavourable balance and count processing, obtain sequence
Figure FDA0000407918740000037
wherein
y t , 1 * = 1.0
y t , i + 1 * = y t , i * - x t , i ( * ) , i = 1,2 , . . . , T - 1
Right
Figure FDA00004079187400000310
carry out contrary sequence and obtain sequence dt,
7. a kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction according to claim 6, is characterized in that described step 303) in, newly cease famousization processing and be specially:
If the power quality index data of the front m of to be predicted year month are known, the new breath value sequence of to be predicted year is { y t, 1, y t, 2..., y t, m, the lateral prediction value in to be predicted year residue month is
y t , j hor = y t , k d t , j d t , k , j = m + 1 , m + 2 , . . . , T
Wherein, d t, j, d t, kbe respectively the perunit value of the to be predicted year j month, the k month, y t, kmeet { y t, k| min (v (k)), v (k)computing formula as follows
v ( k ) = 1 m &Sigma; j = 1 m ( y ^ t , j ( k ) - y t , j ) 2
y ^ t , j ( k ) = y t , k d t , j d t , k , k , j = 1,2 , . . . , m
Obtain thus the lateral prediction sequence of to be predicted year
8. a kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction according to claim 7, is characterized in that described step 4) in, when known annual developmental sequence is greater than three values, longitudinally predicted value is identical with the computing method of lateral prediction value.
9. a kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction according to claim 1, it is characterized in that described step 4) in, when known annual developmental sequence only has two values, adopt growth ratio method to calculate longitudinal predicted value, its formula is as follows:
y t , j ver = y t - 1 , j y t , k y t - 1 , k
Wherein, k=1,2 ..., m, j=m+1, m+2 ..., T.
10. a kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction according to claim 1, is characterized in that described step 5) in, the weight w of horizontal, longitudinal predicted value 1, w 2meet
J ( w 1 , w 2 ) = &Sigma; i = 1 m [ z i - ( w 1 y t , i hor + w 2 y t , i ver ) ] 2
Wherein, z ibe the actual value of i month,
Figure FDA0000407918740000044
for sequence in i element,
Figure FDA0000407918740000046
for sequence
Figure FDA0000407918740000047
in i element.
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