CN103544362B - A kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction - Google Patents

Abstract

The present invention relates to a kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction, the method comprises the following steps: 1) obtain at least one monitoring point history power quality index data in setting the time period in forecast interval, line number of going forward side by side Data preprocess, it is thus achieved that historical data sequence；2) judge whether there is new breath value year to be predicted, the most then perform step 3), if it is not, then historical data sequence is adjusted, and perform step 3 with the historical data sequence after adjusting)；3) according to historical data sequence, to the moon, the monthly developmental sequence of tolerance carries out timing curve prediction, it is thus achieved that the lateral prediction sequence in year to be predicted；4) according to historical data sequence, to the moon, the annual developmental sequence of tolerance carries out timing curve prediction, it is thus achieved that longitudinal forecasting sequence in year to be predicted；5) weighted average, it is thus achieved that the two-dimensional prediction sequence in year to be predicted.Compared with prior art, the present invention has the advantages such as precision of prediction is high, anti-interference, principle is simple.

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 based on two-dimensional curve prediction humorous Ripple medium-and long-term forecasting method.

Background technology

The quality of power supply is related to the safety and stability of electrical network, economical operation, along with modern power network supplies to high reliability and high-quality Electricity transformation, improve the electrical network quality of power supply become ensure power system safety and stability run in the urgent need to.

On the one hand the electrical network quality of power supply constantly accesses tend to disliking because of non-linear, Large Copacity and the strong load equipment of impact Change, on the other hand improved because of its control measures and the continuous extension to increase capacity of electrical network.Also there are some uncertain factors simultaneously, as The trend of the quality of power supply is all made by the change etc. of protection and the normal operating mode automatically of natural phenomena and power equipment and device Become serious interference.

Power transmission network, as the chief component of power system, carries jumbo electric power transformation task, its electric energy matter Amount problem influence area is big, therefore most important to the safety of whole electrical network.If the quality of power supply can be predicted, analyze Its development trend, finds the problem that the quality of power supply maybe will deteriorate early, takes corresponding measure to be improved and administer, thus reducing Even avoid the loss thereby resulted in, provide strong foundation and decision support for network optimization, have important theory value and Realistic meaning.Therefore it is the most necessary for being predicted the quality of power supply, and the requirement to quality of power supply prediction is more and more higher, right Medium-and long-term forecasting also has urgent demand.Within medium-term forecast refers to 1～2 year, the moon or the prediction in season, long-term forecast refers to 1～10 year The moon, season, the prediction in year.

Summary of the invention

Defect that the purpose of the present invention is contemplated to overcome above-mentioned prior art to exist and provide a kind of precision of prediction high, anti- Simply based on two-dimensional curve prediction the harmonic wave medium-and long-term forecasting method of interference, principle.

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

A kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction, the method comprises the following steps:

1) at least one monitoring point history power quality index data in setting the time period in forecast interval are obtained, and Carry out data prediction, it is thus achieved that historical data sequence；

2) judge whether there is new breath value year to be predicted, i.e. judge whether there is known electric energy quality index data year to be predicted, The most then perform step 3), if it is not, then historical data sequence is adjusted, and perform with the historical data sequence after adjusting Step 3)；

3) according to historical data sequence, to the moon, the monthly developmental sequence of tolerance carries out timing curve prediction, it is thus achieved that to be predicted The lateral prediction sequence in year

4) according to historical data sequence, to the moon, the annual developmental sequence of tolerance carries out timing curve prediction, it is thus achieved that to be predicted Longitudinal forecasting sequence in year

5) lateral prediction sequence and longitudinal forecasting sequence are weighted averagely, it is thus achieved that the two-dimensional prediction sequence in year to be predictedAnd add in historical data sequence:

$y_t^{\mathrm{hv}}=w_1{y}_t^{\mathrm{hor}}+w_2{y}_t^{\mathrm{ver}}$

In formula, w₁、w₂The weight of predicted value horizontal, longitudinal respectively.

The described setting time period is more than 1 year.

Described data prediction particularly as follows:

The power quality index data obtaining each monitoring point are weighted averagely obtaining the comprehensive history number of forecast interval According to sequence, computing formula is as follows:

Y_region=wy_point

w_i=p_i/p_sum, i=1,2 ..., N

Wherein, w_iFor the i-th element of weight vectors w, represent the weight of i-th monitoring point, p_iFor i-th monitoring point Power, p_sumFor the general power of monitoring point each in forecast interval, Y_tegionFor the comprehensive historical data sequence of forecast interval, y_pointFor The power quality index matrix of each monitoring point in forecast interval.

Described step 3) particularly as follows:

301) being predicted the characteristic parameter of the horizontal curve in year to be predicted, described characteristic parameter includes averagely marking one Value ρ and minimum perunit value β；

302) closest to year on the basis of the time in year to be predicted on the time, according to the monthly perunit value sequence of standard year With step 301) characteristic parameter that records in advance obtains the monthly perunit value sequence in year to be predicted；

303) newly cease famousization according to the monthly perunit value sequence in year to be predicted and the new breath value in year to be predicted to process, Obtain lateral prediction value.

Described step 301) in, the characteristic parameter Forecasting Methodology of employing includes the dynamic method of average, regression analysis or index Exponential smoothing.

Described step 302) including:

A) the monthly perunit value sequence to standard yearCarry out generation process:

WillSequence is become after descending sequenceIf monthly perunit value sequence d in year to be predicted_tSequence postscript isIt is labeled as h under sequence corresponding original of context_j, per days, number scale was T, then have a following relation:

$1=y_{k,1}^{\left(0\right)}\≥y_{k,2}^{\left(0\right)}\≥\·\·\·\≥y_{k,T}^{\left(0\right)}>0$

$1=y_{t,1}^{*}\≥y_{t,2}^{*}\≥\·\·\·\≥y_{t,T}^{*}=\mathrm{\β}>0$

$y_{k,j}^{\left(0\right)}=d_{k,h_j}^{\left(0\right)},j=\mathrm{1,2},...,T$

$y_{t,j}^{*}=d_{t,h_j},j=\mathrm{1,2},...,T$

WillAdjacent two of sequence asks difference to obtain sequenceAnd x_t, obtain:

$x_{k,j}^{\left(0\right)}=y_{k,j}^{\left(0\right)}-y_{k,j+1}^{\left(0\right)}\≥0,j=\mathrm{1,2},...,T-1$

$x_{t,j}=y_{t,j}^{*}-y_{t,j+1}^{*}\≥0,j=\mathrm{1,2},...,T-1$

$y_{k,j}^{\left(0\right)}=1-\underset{i=1}{\overset{j-1}{\mathrm{\Σ}}}{x}_{k,j}^{\left(0\right)},j=2,...,T$

$y_{t,j}^{*}=1-\underset{i=1}{\overset{j-t}{\mathrm{\Σ}}}{x}_{t,i},j=2,...,T$

x_{T, i}With the relational expression of characteristic parameter ρ, β it is:

$\mathrm{\ρ}=\frac{1}{T}\underset{j=1}{\overset{T}{\mathrm{\Σ}}}{y}_{t,j}^{*}=\frac{1}{T}\underset{j=1}{\overset{T}{\mathrm{\Σ}}}(1-\underset{i=1}{\overset{j-1}{\mathrm{\Σ}}}{x}_{t,i})=\frac{1}{T}(T-\underset{j=1}{\overset{T}{\mathrm{\Σ}}}\underset{i=1}{\overset{j-1}{\mathrm{\Σ}}}{x}_{t,i})=\frac{1}{T}[T-\underset{i=1}{\overset{T-1}{\mathrm{\Σ}}}(T-i)x_{t,i}]$

$\mathrm{\β}=y_T=1-\underset{i=1}{\overset{T-1}{\mathrm{\Σ}}}{x}_{t,i};$

B) founding mathematical models:

$\left\{\begin{array}{c}\min z=\frac{1}{2}{(x-x^{\left(0\right)})}^T(x-x^{\left(0\right)})\\ s.t.\mathrm{Ax}=b\\ x\≥0\\ \end{array}\right.$

Wherein, $x^{\left(0\right)}=\left[\begin{array}{c}{x}_{k,1}^{\left(0\right)}\\ .\\ .\\ .\\ x_{k,T-1}^{\left(0\right)}\end{array}\right],$ $x=\left[\begin{array}{c}{x}_{t,1}\\ .\\ .\\ .\\ x_{t,T-1}\end{array}\right],$ $A=\left[\begin{array}{cccc}T-1& T-2& ...& 1\\ 1& 1& ...& 1\end{array}\right],$ $b=\left[\begin{array}{c}T(1-\mathrm{\ρ})\\ 1-\mathrm{\β}\end{array}\right];$

C) be iterated solving to the Mathematical Modeling in step b), iterative process particularly as follows:

C1) Lagrange multiplier w is introduced^T=[w₁, w₂..., w_T-1] and v^T=[v₁, v₂], and remember W₀=diag{w_i, then W₀E=w, e^T=[1,1 ..., 1]；Put initial value W₀=0, iterations q=1, given condition of convergence ε (ε ＞ 0)；

C2) v:v=(AA is calculated^T)^-1□[b-A(x⁽⁰⁾+W₀e)]；

C3) x is calculated^(*)=x⁽⁰⁾+W₀e+A^TV, it is judged that x^(*)In each componentIfThen put w_i=0；Otherwise, order Thus obtain x^(*)、W₀；

C4) judge | | Ax^(*)||₂/||b||₂Whether ＜ ε sets up, the most then stop iteration, obtain optimal solution x^(*)；If it is not, then Put q=q+1, return step c2)；

D) optimal solution x that step c) is obtained^(*)Carry out inverse generation to process:

First unfavourable balance number process is carried out, it is thus achieved that sequenceWherein

$y_{t,1}^{*}=1.0$

$y_{t,i+1}^{*}=y_{t,i}^{*}-x_{t,i}^{(*)},i=\mathrm{1,2},...,T-1$

RightCarry out inverse sequence and obtain sequence d_t, i.e.

Described step 303) in, new breath famousization process particularly as follows:

If the power quality index data of the front m in year to be predicted month are it is known that the new breath value sequence in year the most to be predicted is {y_{T, 1}, y_{T, 2}..., y_{T, m}, the lateral prediction value in residue month in year the most to be predicted is

$y_{t,j}^{\mathrm{hor}}=y_{t,k}\frac{d_{t,j}}{d_{t,k}},j=m+1,m+2,...,T$

Wherein, d_{T, j,}d_{T, k}It is respectively the month in year j to be predicted, the perunit value of the k month, y_{T, k}Meet { y_{T, k}|min(v^(k)), v^(k)'s Computing formula is as follows

$v^{\left(k\right)}=\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{({\hat{y}}_{t,j}^{\left(k\right)}-y_{t,j})}^2$

${\hat{y}}_{t,j}^{\left(k\right)}=y_{t,k}\frac{d_{t,j}}{d_{t,k}},k,j=\mathrm{1,2},...,m$

Thus obtain the lateral prediction sequence in year to be predicted

Described step 4) in, when known annual developmental sequence is more than three values, longitudinal predicted value and lateral prediction value Computational methods identical.

Described step 4) in, when known annual developmental sequence only has two values, use growth ratio method to calculate longitudinally Predicted value, its formula is as follows:

$y_{t,j}^{\mathrm{ver}}=y_{t-1,j}\frac{y_{t,k}}{y_{t-1,k}}$

Wherein, k=1,2 ..., m, j=m+1, m+2 ..., T.

Described step 5) in, weight w of predicted value horizontal, longitudinal₁、w₂Meet

$J(w_1,w_2)=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{[z_i-(w_1{y}_{t,i}^{\mathrm{hor}}+w_2{y}_{t,i}^{\mathrm{ver}})]}^2$

Wherein, z_iFor the actual value of the i-th moon,For sequenceMiddle i-th element,For sequenceMiddle i-th Element.

Compared with prior art, the invention have the advantages that

1. the inventive method have employed the 95% big value of probability of measuring by the moon of Detecting Power Harmonics point and is predicted, and thus weakens humorous The harmful effect to predicting the outcome of the ripple random factor.

2. the inventive method uses harmonic range integrated value to be predicted, and weakens what each monitoring point change at random produced Impact.

3. the inventive method considered measure by the harmonic wave moon the same year (monthly development trend, namely laterally trend) month by month and The trend of the same period over the years (annual development trend, i.e. longitudinal development trend) two dimension development, the method having used for reference load prediction.Because of the moon Measuring two-way trend and constitute the development relationship of its spatial networks, each moon measures the intersection being in spatial networks comprehensive development trend On point, therefore take into account the two during prediction and take full advantage of its natural law.Month tolerance annual developmental sequence point between be spaced apart 1 Year, embody its development and change rule under the overall background that social development levels improves constantly；And its monthly developmental sequence point Between interval be 1 month, embody its rule with seasonal variations.The present invention use the method for curve prediction be utilized respectively this two Plant rule it is predicted, be weighted averagely obtaining two-dimensional prediction result by Two-way measured value according to the weight asked for.

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 the schematic flow sheet of the present invention；

Fig. 3 is per-unit curve model solution process schematic of the present invention；

Fig. 4 is the inventive method and error comparison diagram horizontal, the most individually Forecasting Methodology.

Detailed description of the invention

The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.The present embodiment is with technical solution of the present invention Premised on implement, give detailed embodiment and concrete operating process, but protection scope of the present invention be not limited to Following embodiment.

A kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction, deteriorates for harmonic wave control, the prevention quality of power supply Strong foundation is provided.The method takes into account its development trend same period (year development trend) over the years based on the Monitoring Data of harmonic wave Two-dimensional prediction is carried out with development trend month by month in the same year (monthly development trend).First against harmonic wave year developmental sequence and monthly Exhibition sequence is predicted respectively, then asks for weight according to Least Square Theory, the most respectively to year trend and monthly trend Predicted value is weighted averagely obtaining two-dimensional prediction result.

The method is theoretical based on normal distribution model.Least square method determines that forecast model function expression unknown parameter Common method.Its model is:

$J\left(w\right)=(z-\hat{z}){(z-\hat{z})}^T=(z-\mathrm{wY}){(z-\mathrm{wY})}^T---\left(1\right)$

aw^T=1 (2)

1≥w≥0 (3)

Wherein, z, a, Y are known quantity,W is unknown quantity.This model is that constrained linear least-squares is asked Topic.In the case of data volume is less, iterative method can be used.

When being predicted, if not having known power quality index data year to be predicted, i.e. original series does not meets prediction Condition, need to adjust.Propose the concept of correction sequence for the inventive method prediction new breath famousization step, adjust original Sequence complies with Forecasting Methodology and requires with the realization facilitating this step.

Known array is y_j=[y_{I, 1}y_{I, 2}…y_{I, T}], i=1,2 ..., t-1 (t >=2).Forecasting sequence is: y_t=[y_{T, 1}y_t, 2…y_{T, T}], wherein y_{T, k}(k=1,2 ..., m) known.Original series initiates the nature being respectively as follows: January and December, i.e. year month Divide.As known 2 years and above data (i.e. t >=2) and year to be predicted newly breath value (i.e. m=0), need to first adjust sequence Row, redefine start-stop month, make m ≠ 0, thus obtain new sequence, referred to as a correction sequence, and its schematic diagram is as shown in Figure 1.

The foundation having main steps that transverse and longitudinal two-dimensional curve forecast model of the inventive method and solving and the asking of weight Take.Curve prediction model mainly uses the foundation of existing Day Load Curve Forecasting model and method for solving to obtain, further according to tool Body situation carries out famousization.Owing to the index amount of the quality of power supply exists feature with year as mechanical periodicity, therefore required data are Should be the power quality index value of a year less.The following prediction process first introducing known more than 1 year historical data.

As in figure 2 it is shown, the harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction of the present invention comprises the following steps:

1) at least one monitoring point history quality of power supply in setting the time period (more than 1 year) in forecast interval is obtained Achievement data, line number of going forward side by side Data preprocess, it is thus achieved that historical data sequence；

2) judge whether there is new breath value year to be predicted, the most then perform step 3), if it is not, then historical data sequence is entered Row sum-equal matrix, and perform step 3 with the historical data sequence after adjusting)；

3) according to historical data sequence, to the moon, the monthly developmental sequence of tolerance carries out timing curve prediction, it is thus achieved that to be predicted The lateral prediction sequence in year

4) according to historical data sequence, to the moon, the annual developmental sequence of tolerance carries out timing curve prediction, it is thus achieved that to be predicted Longitudinal forecasting sequence in year

5) lateral prediction sequence and longitudinal forecasting sequence are weighted averagely, it is thus achieved that the two-dimensional prediction sequence in year to be predictedAnd add in historical data sequence:

$y_t^{\mathrm{hv}}=w_1{y}_t^{\mathrm{hor}}+w_2{y}_t^{\mathrm{ver}}$

In formula, w₁、w₂The weight of predicted value horizontal, longitudinal respectively.

Hereinafter 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, is i.e. predicted the overall trend of sequence, claims For lateral prediction.To the moon, the annual developmental sequence of tolerance carries out timing curve prediction, is referred to as longitudinally prediction.Transverse and longitudinal prediction is all adopted By the method for curve prediction.Mainly it is introduced with the process of horizontal curve prediction.Owing to the index amount of harmonic wave exists with year it is The feature of mechanical periodicity, therefore it is believed that its per-unit curve each year basically identical.

1.1 data prediction

If carried out interval comprehensive electric energy quality prediction, need initial data is carried out the pretreatment of following steps.Single prison This step it is made without when measuring point is predicted.

Because the ratio of interval impact with its power with general power is proportionate by each electric energy quality monitoring point.Therefore according to prison The power of measuring point accounts for the ratio of general power and is weighted each data of monitoring point of forecast interval averagely obtaining interval comprehensive electric energy Figure-of-merit curve.The power quality index data obtaining each monitoring point are weighted averagely obtaining the comprehensive history number of forecast interval According to sequence, computing formula is as follows:

Y_region=wy_point (4)

w_i=p_i/p_sum, i=1,2 ..., N (5)

Wherein, w_iFor the i-th element of weight vectors w, represent the weight of i-th monitoring point, p_iFor i-th monitoring point Power, p_sumFor the general power of monitoring point each in forecast interval, Y_regionFor the comprehensive historical data sequence of forecast interval, y_pointFor The power quality index matrix of each monitoring point in forecast interval.For interval censored data relatively one point data, enchancement factor is weakened, Regular enhancing.It is predicted improving the degree of accuracy of prediction with interval comprehensive electric energy quality data.

1.2 curve prediction

Curve prediction is divided into two steps: curvilinear characteristic parameter prediction and per-unit curve are predicted.Its lateral prediction result is monthly The horizontal per-unit curve of amount.

(1) prediction of curvilinear characteristic parameter

The prediction of curvilinear characteristic parameter can use the dynamic method of average, regression analysis, exponential smoothing etc..Here use dynamic flat All methods obtain year characteristic parameter to be predicted average perunit value ρ and minimum perunit value β (0 ＜ β ＜ ρ ＜ 1).

Make T=12 (the most annual moon number), first with maximum y of annual laterally sequence_{0, i}To y_i(i=1,2 ..., t- 1) carry out standardization, obtain corresponding year per-unit curve d_i(i=1,2 ..., t-1), then there is a following relation:

$y_{0,i}=\underset{1\≤j\≤T}{\max }{y}_{t,j}---\left(7\right)$

d_{T, j}=y_{I, j}/y_{0, i}, j=1,2 ..., T (8)

The main characteristic parameters average perunit value ρ of monthly developmental sequence per-unit curve and minimum perunit value β can reflect song The feature of line and shape, its change reflects the change of monthly developmental sequence curve substantially.The curve of known t-1, it is average Perunit value and minimum perunit value are respectively ρ_iAnd β_i(i=1,2 ..., t-1).

${\mathrm{\ρ}}_i=\frac{1}{T}\underset{j-1}{\overset{T}{\mathrm{\Σ}}}{d}_{i,j}---\left(9\right)$

${\mathrm{\β}}_i=\underset{1\≤j\≤T}{\min }{d}_{i,j}---\left(10\right)$

The prediction of curvilinear characteristic parameter can use the dynamic method of average, regression analysis, exponential smoothing etc..Here use dynamic flat All methods.Then predict that the characteristic parameter of the monthly developmental sequence curve in year to be predicted is respectively as follows:

$\widehat{\mathrm{\ρ}}=\frac{1}{t-1}\underset{i=1}{\overset{t-1}{\mathrm{\Σ}}}{\mathrm{\ρ}}_i---\left(11\right)$

$\widehat{\mathrm{\β}}=\frac{1}{t-1}\underset{i=1}{\overset{t-1}{\mathrm{\Σ}}}{\mathrm{\β}}_i---\left(12\right)$

(2) per-unit curve prediction

Per-unit curve prediction first has to determine datum curve.History each year curve can be selected to make generalized analysis, as Weighted comprehensive (near big and far smaller principle), determines and represents curve.Certain year actual curve with typicalness can also be selected as base Directrix curve.The present invention uses on the time closest to certain year of year to be predicted interval comprehensive harmonic curve as datum curve.Depend on The quality of power supply per-unit curve in year to be predicted is obtained according to the foundation of existing Day Load Curve Forecasting model and method for solving.

Assume that known reference year monthly developmental sequence curve post the one value sequence isSpecial with year to be predicted Levy parameter ρ, in the case of β (0 ＜ β ＜ ρ ＜ 1) (being obtained by the prediction of upper step), carry out the prediction of this year curve.Assume year to be predicted Curve post the one value sequence d_{T, j with} There is similar shape.

1. Raw Data Generation processes

In order to weaken the randomness of initial data, and provide average information for founding mathematical models, introduce gray system Thought, to initial dataCarry out generation process:

A. sequence processes

WillSequence is become after descending sequenceIf monthly perunit value sequence d in year to be predicted_iSequence postscript isIt is labeled as h under sequence corresponding original of context_j, per days, number scale was T, T=12, then have a following relation:

$1=y_{k,1}^{\left(0\right)}\≥y_{k,2}^{\left(0\right)}\≥\·\·\·\≥y_{k,T}^{\left(0\right)}>0---\left(13\right)$

$1=y_{t,1}^{*}\≥y_{t,2}^{*}\≥\·\·\·\≥y_{t,T}^{*}=\mathrm{\β}>0---\left(14\right)$

$y_{k,j}^{\left(0\right)}=d_{k,h_j}^{\left(0\right)},j=\mathrm{1,2},...,T---\left(15\right)$

$y_{t,j}^{*}=d_{t,h_j},j=\mathrm{1,2},...,T---\left(16\right)$

B. difference processes

WillAdjacent two of sequence asks difference to obtain sequenceAnd x_t, obtain:

$x_{k,j}^{\left(0\right)}=y_{k,j}^{\left(0\right)}-y_{k,j+1}^{\left(0\right)}\≥0,j=\mathrm{1,2},...,T-1---\left(17\right)$

$x_{t,j}=y_{t,j}^{*}-y_{t,j+1}^{*}\≥0,j=\mathrm{1,2},...,T-1---\left(18\right)$

$y_{k,j}^{\left(0\right)}=1-\underset{i=1}{\overset{j-1}{\mathrm{\Σ}}}{x}_{k,t}^{\left(0\right)},j=2,...,T---\left(19\right)$

$y_{t,j}^{*}=1-\underset{i=1}{\overset{j-1}{\mathrm{\Σ}}}{x}_{t,i},j=2,...,T---\left(20\right)$

x_{T, i}With the relational expression of characteristic parameter ρ, β it is:

$\mathrm{\ρ}=\frac{1}{T}\underset{j=1}{\overset{T}{\mathrm{\Σ}}}{y}_{t,j}^{*}=\frac{1}{T}\underset{j=1}{\overset{T}{\mathrm{\Σ}}}(1-\underset{i=1}{\overset{j-1}{\mathrm{\Σ}}}{x}_{t,i})=\frac{1}{T}(T-\underset{j=1}{\overset{T}{\mathrm{\Σ}}}\underset{i=1}{\overset{j-1}{\mathrm{\Σ}}}{x}_{t,i})=\frac{1}{T}[T-\underset{i=1}{\overset{T-1}{\mathrm{\Σ}}}(T-i)x_{t,j}]---\left(21\right)$

$\mathrm{\β}=y_T=1-\underset{i=1}{\overset{T-1}{\mathrm{\Σ}}}{x}_{t,i}---\left(22\right)$

2. Mathematical Modeling

Being processed by generation, problem is converted into and makes sequence x_tWithDifference the least, then Mathematical Modeling is:

$\min z=\frac{1}{2}\underset{i=1}{\overset{T-1}{\mathrm{\Σ}}}{(x_{t,i}-x_{k,i}^{\left(0\right)})}^2---\left(23\right)$

$s.t.\underset{i=1}{\overset{T-1}{\mathrm{\Σ}}}(T-i)x_{t,i}=T(1-\mathrm{\ρ})---\left(24\right)$

$\underset{i=1}{\overset{T-1}{\mathrm{\Σ}}}{x}_{t,i}=1-\mathrm{\β}---\left(25\right)$

x_{T, i}>=0, i=1,2 ..., T-1 (26)

Order $x^{\left(0\right)}=\left[\begin{array}{c}{x}_{k,1}^{\left(0\right)}\\ .\\ .\\ .\\ x_{k,T-1}^{\left(0\right)}\end{array}\right],$ $x=\left[\begin{array}{c}{x}_{t,1}\\ .\\ .\\ .\\ x_{t,T-1}\end{array}\right],$ $A=\left[\begin{array}{cccc}T-1& T-2& ...& 1\\ 1& 1& ...& 1\end{array}\right],$ $b=\left[\begin{array}{c}T(1-\mathrm{\ρ})\\ 1-\mathrm{\β}\end{array}\right],$ The then matrix of problem Form is:

$\min z=\frac{1}{2}{(x-x^{\left(0\right)})}^T(x-x^{\left(0\right)})---\left(27\right)$

S.t.Ax=b (28)

x≥0 (29)

3. model solution

This model is a typical quadratic programming problem, can use the method for solving of quadratic programming.Given this problem There is following feature: the gloomy matrix in sea of object function is unit matrix, and equality constraint is linear restriction.Then succinct method for solving is such as Under.

Introduce Lagrange multiplier w^T=[w₁, w₂..., w_T-1] and v^T=[v₁, v₂], and remember W₀=diag{w_i, make e^T= [1,1 ..., 1], then

W₀E=w (30)

Set up following Lagrangian:

$L(x,W_0,v)=\frac{1}{2}{(x-x^{\left(0\right)})}^T(x-x^{\left(0\right)})-{\left(W_{0}e\right)}^{T}x-v^T(\mathrm{Ax}-b)---\left(31\right)$

Quadratic programming is as the special case of convex programming, and K-T condition, as sufficient and necessary condition, can be expressed as, in optimum point x^(*) Place:

x^(*)-x⁽⁰⁾-W₀e-A^TV=0 (32)

Ax^(*)-b=0 (33)

W₀x^(*)=0 (34)

x^(*)>=0, W₀≥0 (35)

Obtained by above-mentioned:

V=(AA^T)^-1□[b-A(x⁽⁰⁾+W₀e)] (36)

Wherein (AA^T)^-1For constant matrices.

As it is shown on figure 3, the iterative process of model is:

A. initial value W is put₀=0, iterations q=1, given condition of convergence ε (ε ＞ 0)；

B. v is calculated according to formula (36)；

C. x is calculated^(*)=x⁽⁰⁾+W₀e+A^TV, it is judged that x^(*)In each componentIfThen put w_i =0；Otherwise, order Thus obtain x^(*)W₀；

D. judge whether (33) formula is set up, be converted into the judgement condition of convergence | | Ax^(*)||₂/||b||₂Whether ＜ ε sets up, if It is then to stop iteration, obtain optimal solution x^(*)；If it is not, then put q=q+1, return step a.

4. the inverse generation of result processes

A. unfavourable balance number processes

$y_{t,1}^{*}=1.0---\left(37\right)$

$y_{t,i+1}^{*}=y_{t,i}^{*}-x_{t,i}^{(*)},i=\mathrm{1,2},...,T-1---\left(38\right)$

B. process against sequence

$d_{t,h_j}=y_{t,j}^{*}---\left(39\right)$

1.3 newly cease famousization

The value in the known month (the 1～m month) according to year to be predicted, i.e. new breath value carries out minimum variance estimate and obtains prediction song The famous value of line, referred to as information famousization.Sequence { the y of the known month value in time to be predicted_{T, 1}, y_{T, 2}..., y_{T, m},

${\hat{y}}_{t,j}=y_{t,k}\frac{d_{t,j}}{d_{t,k}},j=m+1,m+2,...,T---\left(40\right)$

Wherein, d_t,_j, d_{T, k}It is respectively the t j month, the perunit value of the k month, y_{T, k}Meet { y_{T, k}|min(v^(k)), v^(k)For with kth On the basis of individual month numerical value, the mean square deviation of m month before famousization curve, is calculated by formula (42).

Then the lateral prediction value of t m+1～the T month isThis method takes full advantage of new breath value.

The value that calendar year is annual is not predicted out by the data obtained by the method in virtual year, the most then can foundation The new breath value of estimation of prediction of virtual year re-starts prediction and famousization of calendar year per-unit curve, draws the value of the whole year.

The method then can not be used in advance in the case of the data of Second Year are predicted by data in the most known a year and a day Survey curve famousization.Need to be predicted making prediction curve famousization to the maximum in prediction year.Can empirically determined maximum Value, the prediction accuracy in the case of this reduces.

When only knowing the data of a year, longitudinally prediction cannot realize.If known longitudinal sequence only has two values, because of longitudinal direction The iterative process of model solution does not restrains, and should not use curve prediction model.Now using growth ratio method, its formula is as follows:

$y_{t,j}^{\mathrm{ver}}=y_{t-1,j}\frac{y_{t,k}}{y_{t-1,k}}---\left(43\right)$

Wherein, k=1,2 ..., m, j=m+1, m+2 ..., T.

2 two-dimensional predictions

Given data more than 1 year time carry out two-dimensional prediction by weighted average, make full use of its month measure horizontal trend and Longitudinal respective correlation of trend.

The criterion that weight is chosen is to make predicated error meet least-squares estimation.The two-dimensional estimation value is made to be, weight is ww =(w₁, w₂), then have:

${\hat{z}}_i=w_1{y}_{t,i}^{\mathrm{hor}}+w_2{y}_{t,i}^{\mathrm{ver}}---\left(44\right)$

Wherein, i=1,2 ..., m, the actual value of the i-th moon with the error of its estimate is:

$e_i=z_i-{\hat{z}}_i---\left(45\right)$

Criterion of least squares is just desirable to required weight can make the quadratic sum of evaluated error reach minimum, even if performance refers to Mark:

$J(w_1,w_2)=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{[z_i-(w_1{y}_{t,i}^{\mathrm{hor}}+w_2{y}_{t,i}^{\mathrm{ver}})]}^2---\left(46\right)$

Reach minimum weight, wherein, z_iFor the actual value of the i-th moon,For sequenceMiddle i-th element, For sequenceMiddle i-th element.Iterative method according to least square with equality constraint method solves.Given initial value: w (0)=[0 1], suitable iteration step length is selected to be iterated solving.

Therefore the estimate for the t m+1 month is:

$y_{t,m+1}^{\mathrm{hv}}=w_1{y}_{t,m+1}^{\mathrm{hor}}+w_2{y}_{t,m+1}^{\mathrm{ver}}---\left(47\right)$

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.

With instantiation, the inventive method is described below.

Table 1 is that the total harmonic wave of interval integrated voltage of four monitoring point 2009-2011 that foundation formula (4) calculates is abnormal Variability (VTHD) and the data of total harmonic current, its weight is as shown in table 2.The inventive method uses monthly data The 95% big value of probability, to weaken the impact of quality of power supply fluctuation.Predicting the outcome of correspondingly obtaining also is 95% probable value.

Integrated data between occupied area monitored by table 1

Table 2 each monitoring point weight

The known No. 2 monitoring points value of 2009 and the voltage total harmonic distortion factor data of 4 months before 2010, it was predicted that 2010 The value in residue month in year.The result of prediction is as shown in table 3, and error is as shown in Figure 4.

Table 3 predicts the outcome

Table 4 lists absolute average and the variance of each method predicated error, evaluate respectively its prediction accuracy and Stability.From predicting the outcome and Error Graph and table 4, the result of two-dimensional prediction is relative to the most individually predicting As a result, its error is less than both, and mean square of error difference is minimum, illustrates that the two-dimensional prediction degree of accuracy and stability are better than single directional prediction.

Table 4 predicts the outcome and compares

Claims (10)

1. a harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction, it is characterised in that the method comprises the following steps:

1) obtain at least one monitoring point history power quality index data in setting the time period in forecast interval, and carry out Data prediction, it is thus achieved that historical data sequence；

2) judge whether there is new breath value year to be predicted, i.e. judge whether there is known electric energy quality index data year to be predicted, if so, Then perform step 3), if it is not, then historical data sequence is adjusted, and perform step with the historical data sequence after adjusting 3), described is adjusted specifically redefining start-stop month to historical data sequence, makes there is new breath value year to be predicted；

3) according to historical data sequence, to the moon, the monthly developmental sequence of tolerance carries out timing curve prediction, it is thus achieved that year to be predicted Lateral prediction sequence

4) according to historical data sequence, to the moon, the annual developmental sequence of tolerance carries out timing curve prediction, it is thus achieved that year to be predicted Longitudinal forecasting sequence

5) lateral prediction sequence and longitudinal forecasting sequence are weighted averagely, it is thus achieved that the two-dimensional prediction sequence in year to be predicted And add in historical data sequence:

In formula, w₁、w₂The weight of predicted value horizontal, longitudinal respectively.

A kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction the most according to claim 1, it is characterised in that The described setting time period is more than 1 year.

A kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction the most according to claim 1, it is characterised in that Described data prediction particularly as follows:

The power quality index data obtaining each monitoring point are weighted averagely obtaining the comprehensive historical data sequence of forecast interval Row, computing formula is as follows:

Y_region=wy_point

w_i=p_i/p_sum, i=1,2 ..., N

Wherein, w_iFor the i-th element of weight vectors w, represent the weight of i-th monitoring point, p_iFor the power of i-th monitoring point, p_sumFor the general power of monitoring point each in forecast interval, Y_regionFor the comprehensive historical data sequence of forecast interval, y_pointFor prediction The power quality index matrix of each monitoring point in interval.

A kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction the most according to claim 1, it is characterised in that Described step 3) particularly as follows:

301) being predicted the characteristic parameter of the horizontal curve in year to be predicted, described characteristic parameter includes average perunit value ρ With minimum perunit value β；

302) closest to year on the basis of the time in year to be predicted on the time, according to monthly perunit value sequence and the step of standard year Rapid 301) characteristic parameter recorded in advance obtains the monthly perunit value sequence in year to be predicted；

303) newly cease famousization according to the monthly perunit value sequence in year to be predicted and the new breath value in year to be predicted to process, it is thus achieved that Lateral prediction value.

A kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction the most according to claim 4, it is characterised in that Described step 301) in, the characteristic parameter Forecasting Methodology of employing includes the dynamic method of average, regression analysis or exponential smoothing.

A kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction the most according to claim 4, it is characterised in that Described step 302) including:

A) the monthly perunit value sequence to standard yearCarry out generation process:

WillSequence is become after descending sequenceIf monthly perunit value sequence d in year to be predicted_tSequence postscript isRow It is labeled as h under corresponding original of sequence context_j, per days, number scale was T, then have a following relation:

WillAdjacent two of sequence asks difference to obtain sequenceAnd x_t, obtain:

x_t,iWith the relational expression of characteristic parameter ρ, β it is:

B) founding mathematical models:

Wherein,

C) be iterated solving to the Mathematical Modeling in step b), iterative process particularly as follows:

C1) Lagrange multiplier w is introduced^T=[w₁,w₂,…,w_T-1] and v^T=[v₁,v₂], and remember W₀=diag{w_i, then W₀E= W, e^T=[1,1 ..., 1]；Put initial value W₀=0, iterations q=1, given condition of convergence ε (ε ＞ 0)；

C2) v:v=(AA is calculated^T)^-1·[b-A(x⁽⁰⁾+W₀e)]；

C3) x is calculated^(*)=x⁽⁰⁾+W₀e+A^TV, it is judged that x^(*)In each componentIfThen put w_i= 0；Otherwise, orderThus obtain x^(*)、W₀；

C4) judge | | Ax^(*)||₂/||b||₂Whether ＜ ε sets up, the most then stop iteration, obtain optimal solution x^(*)；If it is not, then put q =q+1, returns step c2)；

D) optimal solution x that step c) is obtained^(*)Carry out inverse generation to process:

First unfavourable balance number process is carried out, it is thus achieved that sequenceWherein

RightCarry out inverse sequence and obtain sequence d_t, i.e.

A kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction the most according to claim 6, it is characterised in that Described step 303) in, new breath famousization process particularly as follows:

If the power quality index data of the front m in year to be predicted month are it is known that the new breath value sequence in year the most to be predicted is { y_t,1, y_t,2,…,y_t,m, the lateral prediction value in residue month in year the most to be predicted is

Wherein, d_t,j、d_t,kIt is respectively the month in year j to be predicted, the perunit value of the k month, y_t,kMeet { y_t,k|min(v^(k)), v^(k)Calculating Formula is as follows

Thus obtain the lateral prediction sequence in year to be predicted

A kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction the most according to claim 7, it is characterised in that Described step 4) in, when known annual developmental sequence is more than three values, longitudinal predicted value and the calculating side of lateral prediction value Method is identical.

A kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction the most according to claim 1, it is characterised in that Described step 4) in, when known annual developmental sequence only has two values, use growth ratio method to calculate longitudinal predicted value, its Formula is as follows:

Wherein, k=1,2 ..., m, j=m+1, m+2 ..., T.

A kind of harmonic wave medium-and long-term forecasting method based on two-dimensional curve prediction the most according to claim 1, its feature exists In, described step 5) in, weight w of predicted value horizontal, longitudinal₁、w₂Meet

Wherein, z_iFor the actual value of the i-th moon,For sequenceMiddle i-th element,For sequenceMiddle i-th element.