CN106156892A - A kind of method for building up of grid line loss rate forecast model - Google Patents

Abstract

The present invention relates to the method for building up of a kind of grid line loss rate forecast model, initially set up p unit linear regression model (LRM), then carry out the significance test of the significance test of linear regression, regression coefficient successively to model.It is finally predicted Estimating Confidence Interval.Present configuration is simple, it was predicted that speed is fast, and extrapolation characteristic is good.

Description

A kind of method for building up of grid line loss rate forecast model

Technical field

The present invention relates to electric power system dispatching technology, power system safety and stability running technology field, particularly a kind of electricity The method for building up of netting twine loss rate forecast model.

Background technology

The technical scheme of prior art: level trend Predicting Technique, linear extrapolation.

(1) level trend Predicting Technique

Level trend Predicting Technique mainly has the full method of average, the method for moving average and exponential smoothing.Here one is mainly introduced Secondary exponential smoothing, because it is a kind of method conventional in production forecast, is also used for line loss per unit trend prediction.The simple full phase The method of average is that the past data one to time series is not all utilized with not leaking on an equal basis；Rolling average rule does not consider farther out The data of phase, and give recent data bigger weight in the method for weighted moving average；And the exponential smoothing rule compatible full phase Average and the rolling average chief, does not give up the data pass by, but is given only the influence degree gradually weakening, i.e. with data Away from imparting gradually converges to the flexible strategy of zero.

The fundamental formular of Single Exponential Smoothing:

s_t=α x_t+(1-α)s_t-1

Wherein, s₀=x₁, 0 ＜ α ＜ 1.With the smooth value s of t phase_tThe value of prediction t+1 phaseParticularly

(2) linear extrapolation

Linear trend extrapolation is simplest extrapolation.This method can be used to study and becomes by constant growth rate in time The things changed.In the coordinate diagram with the time as abscissa, the change of things is close to straight line.According to this straight line, permissible Infer the change in things future.Mainly include secondary moving average method, Secondary Exponential Smoothing Method and second order self-adaptive coefficient prediction Method.The common ground of these methods is to utilize data x in t₁,x₂,…,x_t, provide predicted value

In order to determineIt is crucial that obtainWithHere secondary moving average method is mainly introduced.

The first step: calculate once, secondary sliding average

Second step: calculate intercept and slope

3rd step: make a prediction

Existing Predicting Technique, according only to data itself, carries out corresponding Future Data prediction by a large amount of historical datas, Be mathematical analysis Forecasting Methodology purely, do not inquire into the inner link of data, not have analysis cause different pieces of information because have Which, and these factors are for the impact that target data is forward or negative sense.

Content of the invention

In view of this, the purpose of the present invention is to propose to the method for building up of a kind of grid line loss rate forecast model, simple in construction, Predetermined speed is fast, and extrapolation characteristic is good.

The employing below scheme of the present invention realizes: the method for building up of a kind of grid line loss rate forecast model, specifically include with Lower step:

Step S1: set up p unit linear regression model (LRM):

Wherein, x₁,x₂,…x_pBeing the controlled variable of p (p > 1) individual linear independence, y is stochastic variable, b₀,b₁,…,b_p,σ² Being all unknown parameter to be asked, ε is random error；

Step S2: to variable x₁,x₂,…x_pMake n independent observation with y, obtain the sample that capacity is n:

(x_i1,x_i2…,x_ip,y_i) (i=1,2 ..., n)；

And then obtain:

Above formula matrix form is represented, p unit linear regression model (LRM) is rewritten into: Y=XB+ ε；

Wherein remember:

Note Β estimate vector is

Step S3: obtainBy obtain Substitute into the p unit linear regression model (LRM) in step S1, obtain p unit equation of linear regression:WhereinIt is referred to as the coefficient of this p unit equation of linear regression；

Step S4: test model, first carries out the significance test of linear regression, then carries out the aobvious of regression coefficient The inspection of work property；

Step S5: be predicted Estimating Confidence Interval: when sample size n sample range is bigger, and the coordinate x of future position_0jCloseWhen, by y₀Prediction confidence intervals be expressed as:

Expression is the upper of stochastic variable X of Normal DistributionQuantile, it is an entirety, and representative is one Number, so-called onQuantile refers to

Utilize the principle of normal distribution 2 σ, obtain:

Further, the significance test of linear regression described in step S4 specifically includes following steps:

Step S411: set: H₀:b₁=b₂=...=b_p=0, H₁:b₁,b₂,…,b_pIt is not all zero；

According to sample (x_i1,x_i2…,x_ip,y_i) test；If refusing H under level of significance α₀, then it is assumed that linearly return It is significant for returning；

Step S412: find test statistics, by total variance quadratic sum Q_TIt is decomposed into:

Owing to right-hand member Section 3 is zero, so:

Wherein, the right-hand member Section 1 of equation is denoted asClaim Q_EFor deviation from regression quadratic sum, it is by line Property return and cause；The right-hand member Section 2 of equation is denoted asClaim Q_eFor residual sum of squares (RSS), it is to be drawn by test The error rising；Above formula can be write a Chinese character in simplified form into:

Q_T=Q_E+Q_e；

This formula shows, total variance quadratic sum Q of y_TCan be analyzed to linear regression plane pairDeviation from regression quadratic sum Q_EWith Residual sum of squares (RSS) Q to linear regression plane equation for the y_eThis two-part and；

Step S413: obtaining test statistics F is

For given level of signifiance α, look into F distribution table and can obtain～F (p, n-p-1)；

If F >=F_α(p, n-p-1), then refuse H₀, i.e. think that overall linear returns notable；

If F is ＜ F_α(p, n-p-1), then accept H₀, i.e. think that linear regression is not notable.

Further, under total linear relations is notable, regression coefficientIt is not all zero.But, not It is to say that the coefficient of each independent variable is notable, therefore, it is also desirable to carry out the significance test of respective variation coefficient；Institute in step S4 State the significance test of regression coefficient and specifically include following steps:

Step S421: assume

H₀: b_j=0；H₁:b_j≠0；

Step S422: obtain test statistics and be distributed as

Wherein, C_jjRepresent decision-making correct when cost；

The judgement D being provided as out_i, i.e. data assert H when producing_iIt is assumed to be true, and in fact now H_jAssume to be only correct determining Plan.If i=j, then the decision-making made is correct, has then made the judgement of mistake as i ≠ j.

C_ijIt is defined as assuming H_jSelect H for true time_iCost, and the cost of erroneous decision is more than the cost of correct decisions. That is: C_i≠j,j＞ C_jj, to all i, j all sets up.

According to bayesian criterion, given C_ij, P (H_jUnder the conditions of), the minimum decision rule of average cost.

Made by the division of decision rule to observation space: Z ∈ Z₀, then obtain assuming H₀Set up, on the contrary Z ∈ Z₁, then obtain Assume H₁Set up.

IfThen refuse H₀, i.e. think b_jIt is significantly not equal to zero, namely independent variable x_jY is had significantly Impact；

IfThen accept H₀, i.e. think b_jIt is significantly equal to zero, namely independent variable x_jTo y without notable shadow Ring.

Compared with prior art, the present invention carries out regression analysis by dependent variable with the causality of multiple independents variable and solves Regression equation, tests to regression equation and draws predicted value.The present invention affects load variations according to historical data with some Variable factors infers the numerical value of future time, has principle, simple in construction, it was predicted that speed is fast, and extrapolation characteristic waits well significantly Advantage, for grid line loss rate, this object being associated with many factors has preferably prediction performance.

Detailed description of the invention

Below in conjunction with embodiment, the present invention will be further described.

Present embodiments provide the method for building up of a kind of grid line loss rate forecast model, specifically include following steps:

Step S1: set up p unit linear regression model (LRM):

Wherein, x₁,x₂,…x_pBeing the controlled variable of p (p > 1) individual linear independence, y is stochastic variable, b₀,b₁,…,b_p,σ² Being all unknown parameter to be asked, ε is random error；

Step S2: to variable x₁,x₂,…x_pMake n independent observation with y, obtain the sample that capacity is n:

(x_i1,x_i2…,x_ip,y_i) (i=1,2 ..., n)；

And then obtain:

Above formula matrix form is represented, p unit linear regression model (LRM) is rewritten into: Y=XB+ ε；

Wherein remember:

Note Β estimate vector is

Step S3: obtainBy obtain Substitute into the p unit linear regression model (LRM) in step S1, obtain p unit equation of linear regression:WhereinIt is referred to as the coefficient of this p unit equation of linear regression；

Step S4: test model, first carries out the significance test of linear regression, then carries out the aobvious of regression coefficient The inspection of work property；

Step S5: be predicted Estimating Confidence Interval: when sample size n sample range is bigger, and the coordinate x of future position_0jCloseWhen, by y₀Prediction confidence intervals be expressed as:

Expression is the upper of stochastic variable X of Normal DistributionQuantile, it is an entirety, and representative is one Number, so-called onQuantile refers to

Utilize the principle of normal distribution 2 σ, obtain:

In the present embodiment, the significance test of linear regression described in step S4 specifically includes following steps:

Step S411: set: H₀:b₁=b₂=...=b_p=0, H₁:b₁,b₂,…,b_pIt is not all zero；

According to sample (x_i1,x_i2…,x_ip,y_i) test；If refusing H under level of significance α₀, then it is assumed that linearly return It is significant for returning；

Step S412: find test statistics, by total variance quadratic sum Q_TIt is decomposed into:

Owing to right-hand member Section 3 is zero, so:

Wherein, the right-hand member Section 1 of equation is denoted asClaim Q_EFor deviation from regression quadratic sum, it is by line Property return and cause；The right-hand member Section 2 of equation is denoted asClaim Q_eFor residual sum of squares (RSS), it is to be drawn by test The error rising；Above formula can be write a Chinese character in simplified form into:

Q_T=Q_E+Q_e；

This formula shows, total variance quadratic sum Q of y_TCan be analyzed to linear regression plane pairDeviation from regression quadratic sum Q_E With residual sum of squares (RSS) Q to linear regression plane equation for the y_eThis two-part and；

Step S413: obtaining test statistics F is

For given level of signifiance α, look into F distribution table and can obtain～F (p, n-p-1)；

If F >=F_α(p, n-p-1), then refuse H₀, i.e. think that overall linear returns notable；

If F is ＜ F_α(p, n-p-1), then accept H₀, i.e. think that linear regression is not notable.

In the present embodiment, under total linear relations is notable, regression coefficientIt is not all zero.But, It is not to say that the coefficient of each independent variable is notable, therefore, it is also desirable to carry out the significance test of respective variation coefficient；Step S4 Described in the significance test of regression coefficient specifically include following steps:

Step S421: assume

H₀: b_j=0；H₁:b_j≠0；

Step S422: obtain test statistics and be distributed as

Wherein, C_jjRepresent decision-making correct when cost.

The judgement D being provided as out_i, i.e. data assert H when producing_iIt is assumed to be true, and in fact now H_jAssume to be only correct determining Plan.If i=j, then the decision-making made is correct, has then made the judgement of mistake as i ≠ j.

C_ijIt is defined as assuming H_jSelect H for true time_iCost, and the cost of erroneous decision is more than the cost of correct decisions. That is: C_i≠j,j＞ C_jj, to all i, j all sets up.

According to bayesian criterion, given C_ij, P (H_jUnder the conditions of), the minimum decision rule of average cost.

Made by the division of decision rule to observation space: Z ∈ Z₀, then obtain assuming H₀Set up, on the contrary Z ∈ Z₁, then obtain Assume H₁Set up.

IfThen refuse H₀, i.e. think b_jIt is significantly not equal to zero, namely independent variable x_jY is had aobvious Write impact；

IfThen accept H₀, i.e. think b_jIt is significantly equal to zero, namely independent variable x_jTo y without notable shadow Ring.

In the present embodiment, as a example by Fuzhou City, by analysis result it is recognised that affect the factor master of Fuzhou City's line loss per unit 35kV sale of electricity accounting to be had, 10kV sale of electricity accounting and maximum load, given future position is (x₁₁,x₁₂,x₁₃), it was predicted that value is by three Unit's equation of linear regression is given, i.e.

In formula, X₁₁: first 35kV sale of electricity accounting；

X₁₂: first month 10kV sale of electricity accounting；

X₁₃: first month maximum load；

First month line loss per unit；

According to the historical data of 35kV sale of electricity accounting, 10kV sale of electricity accounting and maximum load, substitute intoCoefficient formulas in, drawValue.At grey forecasting model In, according to moon delivery, maximum monthly load, the historical data of monthly power demand, draw X₁₁、X₁₂、X₁₃Predicted value.Finally by X₁₁、 X₁₂、X₁₃Predicted value substitute intoIn, finally can obtain the predicted value of first month line loss per unit

The foregoing is only presently preferred embodiments of the present invention, all impartial changes done according to scope of the present invention patent with Modify, all should belong to the covering scope of the present invention.

Claims (3)

1. the method for building up of a grid line loss rate forecast model, it is characterised in that comprise the following steps:

Step S1: set up p unit linear regression model (LRM):

$\left\{\begin{array}{c}y=b_0+b_1{x}_1+...+b_p{x}_p+\mathrm{\ϵ}\\ \mathrm{\ϵ}~N(0,{\mathrm{\σ}}^2)\end{array}\right.;$

Wherein, x₁,x₂,...x_pBeing the controlled variable of p (p > 1) individual linear independence, y is stochastic variable, b₀,b₁,…,b_p,σ²It is all Unknown parameter to be asked, ε is random error；

Step S2: to variable x₁,x₂,…x_pMake n independent observation with y, obtain the sample that capacity is n:

(x_i1,x_i2…,x_ip,y_i) (i=1,2 ..., n)；

And then obtain:

$\left\{\begin{array}{c}{y}_1=b_0+b_1{x}_{11}+...+b_p{x}_{1p}+{\mathrm{\ϵ}}_1\\ y_2=b_0+b_1{x}_{21}+...+b_p{x}_{2p}+{\mathrm{\ϵ}}_2\\ ......\\ y_n=b_0+b_1{x}_{n1}+...+b_p{x}_{np}+{\mathrm{\ϵ}}_n\end{array}\right.;$

Above formula matrix form is represented, p unit linear regression model (LRM) is rewritten into: Y=XB+ ε；

Wherein remember:

Note Β estimate vector is

Step S3: obtainBy obtainSubstitute into In step S1 p unit linear regression model (LRM), obtain p unit equation of linear regression:WhereinIt is referred to as the coefficient of this p unit equation of linear regression；

Step S4: test model, first carries out the significance test of linear regression, then carries out the conspicuousness of regression coefficient Inspection；

Step S5: be predicted Estimating Confidence Interval: by y₀Prediction confidence intervals be expressed as:

$(\hat{y}-Z_{\frac{\mathrm{\α}}{2}}\widehat{\mathrm{\σ}},\hat{y}+Z_{\frac{\mathrm{\α}}{2}}\widehat{\mathrm{\σ}});$

Expression is the upper of stochastic variable X of Normal DistributionQuantile；

Utilize the principle of normal distribution 2 σ, obtain:

2. the method for building up of a kind of grid line loss rate forecast model according to claim 1, it is characterised in that: in step S4 The significance test of described linear regression specifically includes following steps:

Step S411: set: H₀:b₁=b₂=...=b_p=0, H₁:b₁,b₂,…,b_pIt is not all zero；

According to sample (x_i1,x_i2…,x_ip,y_i) test；If refusing H under level of significance α₀, then it is assumed that linear regression is Significantly；

Step S412: find test statistics, by total variance quadratic sum Q_TIt is decomposed into:

$\begin{array}{c}{Q}_T=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left(y_i-\stackrel{\‾}{y}\right)}^2=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\[\left(y_i-{\hat{y}}_i\right)+\left({\hat{y}}_i-\stackrel{\‾}{y}\right)\]}^2\\ =\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left({\hat{y}}_i-\stackrel{\‾}{y}\right)}^2+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left(y_i-{\hat{y}}_i\right)}^2+2\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\left(y_i-{\hat{y}}_i\right)\left({\hat{y}}_i-\stackrel{\‾}{y}\right)\end{array}$

Owing to right-hand member Section 3 is zero, so:

$Q_T=\underset{i=1}{\overset{n}{\Σ}}{\left({\hat{y}}_i-\stackrel{\‾}{y}\right)}^2+\underset{i=1}{\overset{n}{\Σ}}{(y_i-{\hat{y}}_i)}^2;$

Wherein, the right-hand member Section 1 of equation is denoted asClaim Q_EFor deviation from regression quadratic sum, it is by linearly returning Return and cause；The right-hand member Section 2 of equation is denoted asClaim Q_eFor residual sum of squares (RSS), it is caused by test Error；Above formula can be write a Chinese character in simplified form into:

Q_T=Q_E+Q_e；

This formula shows, total variance quadratic sum Q of y_TCan be analyzed to linear regression plane pairDeviation from regression quadratic sum Q_EWith y to line Residual sum of squares (RSS) Q of property plane of regression equation_eThis two-part and；

Step S413: obtaining test statistics F is

$F=\frac{Q_E/p}{Q_e/(n-p-1)}~F(p,n-p-1);$

For given level of signifiance α, look into F distribution table and can obtain～F (p, n-p-1)；

IfThen refuse H₀, i.e. think that overall linear returns notable；

IfThen accept H₀, i.e. think that linear regression is not notable.

3. the method for building up of a kind of grid line loss rate forecast model according to claim 1, it is characterised in that: in step S4 The significance test of described regression coefficient specifically includes following steps:

Step S421: assume

H₀: b_j=0；H₁:b_j≠0；

Step S422: obtain test statistics and be distributed as

$t_j=\frac{{\hat{b}}_j}{\sqrt{c_{jj}}\sqrt{Q_e/(n-p-1)}}~t(n-p-1)$

Wherein, C_jjRepresent decision-making correct when cost；

Therefore, ifThen refuse H₀, i.e. think b_jIt is significantly not equal to zero, namely independent variable x_jY is had aobvious Write impact；

IfThen accept H₀, i.e. think b_jIt is significantly equal to zero, namely independent variable x_jY is not made significant difference.