CN104992246A - Improved-least-square-method-based prediction method of load electric quantity for transformer substation - Google Patents

Abstract

The invention discloses an improved-least-square-method-based prediction method of a load electric quantity for a transformer substation. The method comprises the following steps: analyzing an influence factor of a load electric quantity of a transformer substation; obtaining a training sample set and a testing sample set; establishing matrixes of transformer substation load electric quantities and influence factors of the training sample set; establishing a matrix form of an improved least square equation set; introducing a particle swarm optimization algorithm to solve the improved least square equation set, thereby obtaining a regression equation of the transformer substation load electric quantities; and carrying out transformer substation load electric quantity prediction. According to the invention, influences on load electric quantities of the transformer substation from January to December by all potential influence factors are used as variable constant terms of the classical least square method; and thus the improved least square equation set is formed and the particle swarm optimization algorithm is introduced to carry out solving. With the prediction method, the prediction precision of the load electric quantity of the transformer substation can be effectively improved.

Description

A kind of Substation Station power load Forecasting Methodology based on improving least square method

Technical field

The present invention relates to power prediction field, particularly a kind of Substation Station power load Forecasting Methodology based on improving least square method.

Background technology

In recent years, along with the propelling of energy-saving and emission-reduction work, the station management of power use of transformer station is paid attention to.But because large multi-Substation is not stood the special metering of power consumption, certain difficulty is existed to the direct research of station power consumption, and the primary equipment such as disconnector, isolating switch in the electricity consumption of station relates to safety and the reliability of conveying electricity, its kwh loss caused is normal and necessary, and controllability is not strong, station load in transformer station comprises air-conditioning system, illuminator, field dynamic power system etc., the electricity consumption of Substation Station load belongs to a part for Substation Station power consumption, and it is strong to have artificial controllability, the features such as data are complete, strengthen the prediction of Substation Station power load, realization becomes more meticulous, the scientific station load management of power use, effectively can reduce Substation Station load power consumption, thus reduce Substation Station power consumption, improve Substation Station management of power use level, line loss is reduced to power grid enterprises, realize target for energy-saving and emission-reduction and there is positive facilitation.

Current power predicating method mainly can be divided into: traditional prediction method and artificial intelligence approach.Traditional prediction method is based on trend time series method, extrapolation method, gray forecast approach etc., and these are calculated, and ratio juris is simple, speed fast, but for complication system, is difficult to set up effective mathematical model, and the precision that predicts the outcome is not high.Artificial intelligence approach mainly comprises expert system, fuzzy logic method and Artificial Neural Network etc., and these methods have ripe theoretical foundation, have application, but their algorithms is complicated, not easily promote in practical power systems prediction field.Least square method (becoming least square method again) is a kind of mathematical optimization techniques, it finds the optimum matching function of data by minimum error quadratic sum, because its algorithm is simple, calculate fast, all have a wide range of applications in various fields such as parameter estimation, System Discrimination, prediction, forecasts, therefore consider practicality and replicability, the forecast model setting up Substation Station power load based on least square method should be selected.But only can consider electricity, temperature codominance influence factor when using Classical Least-Squares to carry out the prediction of Substation Station power load, be difficult to consider the underlying factors such as transformer station fixing maintenance, equipment test, precision of prediction is not high.

Summary of the invention

The object of the invention is to overcome the shortcoming of prior art and deficiency, proposing a kind of Substation Station power load Forecasting Methodology based on improving least square method.

Object of the present invention is achieved through the following technical solutions:

Based on the Substation Station power load Forecasting Methodology improving least square method, comprise the following steps:

S1. Substation Station power load influence factor is analyzed;

S2. training sample set and test sample book collection is obtained;

S3. the N=12*n that the training sample setting up training sample set concentrates the matrix B of transformer station's each Nakshatra power load composition and training sample to concentrate each influence factor of Substation Station power load to form is capable, the matrix A of 10 row;

S4. the matrix form improving least square normal equation system is set up: the fixed constant item in Classical Least-Squares system of equations is improved to the variable with each Monthly changes, and uses c ₀₁~ c ₁₂represent the value in 1 ~ Dec; Then based on set up improvement least square normal equation system, coefficient vector X in Classical Least-Squares and influence factor matrix A are improved, improve the matrix form that least square normal equation system is write as A ' X '=B the most at last, wherein A ' is influence factor matrix, and X ' is coefficient vector;

S5. introduce PSO Algorithm and improve least square normal equation system, obtain the regression equation of Substation Station power load;

S6. Substation Station power load is predicted: according to the regression equation described in step S5, the corresponding influence factor value of input test collection carries out the prediction of Substation Station power load, and according to the relative error E predicted the outcome _r, square error E and coefficient of determination R ²evaluate build the performance of regression equation.

Described step S3 is specific as follows:

(21) number from 1 ~ n the time of training sample set, the initial value of definition k=1 ~ n, k is 1,

(22) kth year Substation Station power load and each influence factor value be described below:

221) define j=1 ~ 12, the initial value of j is 1;

222) defining training sample concentrates the Substation Station power load in j month in kth year to be b _kj, influence factor value is: conveying electricity a _k1j, 110kV bus exports electricity a _k2j, 10kV bus active energy a _k3j, 10kV bus capacity of idle power a _k4j, circuit electricity a _k5j, electric capacity electricity a _k6j, monthly maximum temperature a _k7j, monthly minimum temperature a _k8j, monthly mean of daily maximum temperature a _k9j, mean monthly maximum temperature a _k10j;

213) judge whether j equals 12, if so, enters next step, if not j=j+1, returns step 222);

(23) judge whether k equals n, if so, enters next step, if not k=k+1, returns step (22);

(24) setting up training sample concentrates the sample matrix of Substation Station power load and influence factor thereof as follows:

B＝[b _1,1b _1,2… b _1,12b _2,1b _2,2… b _2,12… b _n,12]′，

$A=\left[\begin{array}{cccc}{a}_{1,1,1}& a_{1,2,1}& \mathrm{...}& a_{1,10,1}\\ a_{1,1,2}& a_{1,2,2}& \mathrm{...}& a_{1,10,2}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ a_{1,1,12}& a_{1,2,12}& \mathrm{...}& a_{1,10,12}\\ a_{2,1,1}& a_{2,2,1}& \mathrm{...}& a_{2,10,1}\\ a_{2,1,2}& a_{2,2,2}& \mathrm{...}& a_{2,10,2}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ a_{2,1,12}& a_{2,2,12}& \mathrm{...}& a_{2,10,12}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ a_{n,1,12}& a_{n,2,12}& \mathrm{...}& a_{n,10,12}\end{array}\right].$

Described step S4 is specific as follows:

(31) improvement least square normal equation system is set up as follows:

c ₀₁+a _1,1,1x ₁+a _1,2,1x ₂+…a _1,10,1x ₁₀＝b _1,1

c ₀₂+a _1,1,2x ₁+a _1,2,2x ₂+…a _1,10,2x ₁₀＝b _1,2

·

·

·

c ₁₂+a _1,1,12x ₁+a _1,2,12x ₂+…a _1,10,12x ₁₀＝b _1,12

c ₀₁+a _2,1,1x ₁+a _2,2,1x ₂+…a _2,10,1x ₁₀＝b _2,1，

c ₀₂+a _2,1,2x ₁+a _2,2,2x ₂+…a _2,10,2x ₁₀＝b _2,2

·

·

·

c ₁₂+a _2,1,12x ₁+a _2,2,12x ₂+…a _2,10,12x ₁₀＝b _2,12

·

·

·

c ₁₂+a _n,1,12x ₁+a _n,2,12x ₂+…a _n,10,12x ₁₀＝b _n,12

Wherein c ₀₁~ c ₁₂be represent the impact of transformer station's underlying factor on transformer station's station in 1 ~ Dec power load, it take year as loop cycle;

(32) improvement least square normal equation system is rewritten into matrix form:

Underlying factor in 1 ~ Dec is affected c to transformer station's Nakshatra power load ₀₁~ c ₁₂decompose as follows:

C＝[c ₀₁c ₀₂… c ₁₂] ^T＝x ₀C′＝x ₀[c′ ₀₁c′ ₀₂… c′ ₁₂] ^T

Wherein C ' is called Substation Station power load underlying factor factoring; x ₀it is Substation Station power load underlying factor coefficient of dissociation;

By C ' obtained above and x ₀be merged into the influence factor matrix A in Classical Least-Squares system of equations and coefficient vector X respectively, the influence factor matrix A of the least square normal equation system that is improved ' and coefficient vector X ' as follows:

$A^{\′}=\left[\begin{array}{ccccc}{c}_{01}^{\′}& a_{1,1,1}& a_{1,2,1}& \mathrm{...}& a_{1,10,1}\\ c_{02}^{\′}& a_{1,1,2}& a_{1,2,2}& \mathrm{...}& a_{1,10,2}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ c_{12}^{\′}& a_{1,1,12}& a_{1,2,12}& \mathrm{...}& a_{1,10,12}\\ c_{01}^{\′}& a_{2,1,1}& a_{2,2,1}& \mathrm{...}& a_{2,10,1}\\ c_{02}^{\′}& a_{2,1,2}& a_{2,2,2}& \mathrm{...}& a_{2,10,2}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ c_{12}^{\′}& a_{2,1,12}& a_{2,2,12}& \mathrm{...}& a_{2,10,12}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ c_{12}^{\′}& a_{n,1,12}& a_{n,2,12}& \mathrm{...}& a_{n,10,12}\end{array}\right]$

X′＝[x ₀x ₁x ₂x ₃x ₄x ₅x ₆x ₇x ₈x ₉x ₁₀]′，

Then the above least square normal equation system that improves can be write as following matrix form:

A′X′＝B。

The concrete steps introducing the least square normal equation system that PSO Algorithm improves described in step S5 are as follows:

(41) population initialization: at 12 dimension space stochastic generation M particle, the initial position of i-th particle is expressed as x _i=(x _i1, x _i2, x _i3, x _i4, x _i5, x _i6, x _i7, x _i8, x _i9, x _i10, x _i11, x _i12), wherein i=1,2 ... M, initial velocity is v _i=(v _i1, v _i2, v _i3, v _i4, v _i5, v _i6, v _i7, v _i8, v _i9, v _i10, v _i11, v _i12), setting particle iterations, aceleration pulse C ₁, C ₂, particle rapidity restriction [-Vmax, Vmin], the optimal location p of each particle _bestrepresent, all particle optimal location g _bestrepresent;

(42) particle fitness is calculated:

421) defining i=1 ~ M, i is positive integer, and the initial value of i is 1;

422) with the current location parameter x of the i-th particle _i1~ x _i12replace Substation Station power load underlying factor factoring c ' ₀₁~ c ' ₁₂, the influence factor matrix A of the least square method that can be improved _i', Substation Station power load each influence factor coefficient row X can be tried to achieve by the solution formula of following formula Classical Least-Squares _i':

$X_i^{\′}={(A_i^{\′T}\×A_i^{\′})}^{-1}\×A_i^{\′-T}\×B,$

Thus the predicted value that can obtain Substation Station power load is:

${\hat{B}}_i=A_i^{\′}{X}_i^{\′};$

423) using the fitness of the Prediction sum squares of Substation Station power load as particle, the fitness of i-th particle is:

$P_i=\underset{k=1}{\overset{N}{\Σ}}{({\hat{B}}_{ik}-B_k)}^2$

424) judge whether i equals M, is, enters next step, otherwise i=i+1, return step 422);

(43) individual and global optimum is upgraded: respectively by the current fitness of each particle and its individual optimal value p _bestand global optimum g _bestrelatively, if currency is better than p _best, then p _bestbe updated to currency, otherwise remain unchanged; If currency is better than g _bestrelatively, then g _bestbe updated to currency, otherwise remain unchanged;

(44) position and speed is upgraded: first, according to the following formula the minimax speed of more new particle:

$\left\{\begin{array}{cc}{v}_i>v_{max}& v_{max}=v_i\\ v_i<v_{min}& v_{min}=v_i\end{array}\right.,$

Secondly, judge whether particle rapidity is positioned in speed restriction [-Vmax, Vmin] scope, and be then for each particle, its d ties up, wherein 1≤d≤12, speed v _id, position x _idmore new formula is as follows:

v _id ^k+1＝v _id ^k+c ₁×rand ₁×(p _best-x _id ^k)+c ₂×rand ₂×(g _best-x _id ^k)，

x _id ^k+1＝x _id ^k+v _id ^k+1，

Wherein c ₁and c ₂two aceleration pulses, rand ₁, rand ₂it is the random function of value in [0,1] scope; Otherwise upgrade position according to maximal rate restriction;

(45) end condition judges: check whether and reach iterations or fitness value is restrained, be, calculates and terminates and export location parameter and Substation Station power load each influence factor coefficient row X ' of optimal particle; Otherwise return step (42) to continue to calculate;

The concrete steps obtaining the regression equation of Substation Station power load described in step S5 are as follows:

(51) B is used respectively _j, A _1j, A _2j, A _3j, A _4j, A _5j, A _6j, T _1j, T _2j, T _3j, T _4jrepresent that Substation Station power load, conveying electricity, 110kV bus export electricity, 10kV bus active energy, 10kV bus capacity of idle power, circuit electricity, electric capacity electricity, the jth value of individual month of monthly maximum temperature, monthly minimum temperature, monthly mean of daily maximum temperature and mean monthly maximum temperature, wherein, j=1 ~ 12;

(52) with solving the location parameter x improving the optimal particle that least square normal equation system obtains ₁~ x ₁₂replace Substation Station power load underlying factor factoring c ' ₀₁~ c ' ₁₂, obtain Substation Station power load underlying factor factoring Matrix C ', obtain underlying factor coefficient of dissociation x by the first row of each influence factor coefficient row X ' ₀; The then underlying factor C in Substation Station power load each month;

(53) regression equation setting up Substation Station power load is as follows:

B _j=x ₁a _1j+ x ₂a _2j+ x ₆a _6j+ x ₇t _1j+ x ₈t _2j+ x ₁₀t _4j+ C _j, wherein j=1 ~ 12.

Error E described in step S6 _r, square error E and coefficient of determination R ²adopt following formulae discovery:

$\begin{array}{cc}{E}_r=\frac{(B_i-{\hat{B}}_i)}{B_i}& i=1,\mathrm{2...}L,E=\frac{1}{L}\underset{i=1}{\overset{L}{\&Sigma;}}{(B_i-{\hat{B}}_i)}^2,R^2=\frac{\underset{i=1}{\overset{L}{\&Sigma;}}{\hat{B}}_i^2}{\underset{i=1}{\overset{L}{\&Sigma;}}{B_i}^2},\end{array}$

Wherein L is test set number of samples, B _i, wherein i=1,2...L is actual value and predicted value, wherein the relative error E of the station power load of i-th test sample book respectively _rless with square error E, coefficient of determination R ²more close to 1, then the estimated performance of model is more excellent, and generalization ability is better.

Compared with prior art, tool has the following advantages and beneficial effect in the present invention:

1, a kind of Substation Station power load Forecasting Methodology based on improving least square method is proposed, set up the forecast model of Substation Station power load, contribute to work about electric power personnel to the planning of Substation Station load electricity consumption and regulation and control, to the science, the fine-grained management that realize the electricity consumption of Substation Station load, the optimum allocation of resource, reducing transformer station's loss etc. has positive facilitation;

2, the underlying factor such as fixing maintenance, equipment test of transformer station is considered, Classical Least-Squares is improved, the algorithm that the method is inheriting Classical Least-Squares is simple, calculate the advantage such as quick while, greatly can improve the accuracy rate of forecast model, reduce the predicated error of Substation Station power load, and realize improving solving of least square normal equation system in conjunction with the ability of searching optimum that particle cluster algorithm is powerful, effectively can improve the precision of prediction of Substation Station power load;

3, the Substation Station power load Forecasting Methodology based on improvement least square method proposed by the invention, can be applicable to other power prediction fields, has stronger practicality and generalization.

Accompanying drawing explanation

Fig. 1 is a kind of Substation Station power load Forecasting Methodology process flow diagram based on improving least square method of the present invention;

The PSO Algorithm that utilizes that Fig. 2 adopts for method of the present invention improves the process flow diagram of least square normal equation system;

Fig. 3 is that in the embodiment of the present invention, Substation Station power load predicts the outcome figure;

Fig. 4 is Substation Station power load Relative Error E in the embodiment of the present invention _rdistribution plan.

Embodiment

Below in conjunction with embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are not limited thereto.

Accompanying drawing 1 is the Substation Station power load Forecasting Methodology process flow diagram based on improving least square method, and its step is as follows:

S1. Substation Station power load influence factor is analyzed;

The each influence factor of described Substation Station power load comprises: conveying electricity, 110kV bus export electricity, 10kV bus active energy, 10kV bus capacity of idle power, circuit electricity, electric capacity electricity, monthly maximum temperature, monthly minimum temperature, monthly mean of daily maximum temperature, mean monthly maximum temperature.

S2. training sample set and test sample book collection is obtained;

Obtain station power load and the influence factor numerical value thereof in certain transformer station nearest 1 ~ Dec of several years, using N=12*n the sample of wherein n as training sample set, using the L=12*l of a l sample as test sample book collection;

S3. the Substation Station power load of training sample set and the matrix of influence factor thereof is set up; Its step is as follows:

(21) number from 1 ~ n the time of training sample set, the initial value of definition k=1 ~ n, k is 1,

(22) kth year Substation Station power load and each influence factor value be described below:

221) define j=1 ~ 12, the initial value of j is 1;

222) defining training sample concentrates the Substation Station power load in j month in kth year to be b _kj, influence factor value is: conveying electricity a _k1j, 110kV bus exports electricity a _k2j, 10kV bus active energy a _k3j, 10kV bus capacity of idle power a _k4j, circuit electricity a _k5j, electric capacity electricity a _k6j, monthly maximum temperature a _k7j, monthly minimum temperature a _k8j, monthly mean of daily maximum temperature a _k9j, mean monthly maximum temperature a _k10j;

213) judge whether j equals 12, if so, enters next step, if not j=j+1, returns step 222);

(23) judge whether k equals n, if so, enters next step, if not k=k+1, returns step (22);

(24) setting up training sample concentrates the sample matrix of Substation Station power load and influence factor thereof as follows:

B＝[b _1,1b _1,2… b _1,12b _2,1b _2,2… b _2,12… b _n,12]′ (1)

$A=\left[\begin{array}{cccc}{a}_{1,1,1}& a_{1,2,1}& \mathrm{...}& a_{1,10,1}\\ a_{1,1,2}& a_{1,2,2}& \mathrm{...}& a_{1,10,2}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ a_{1,1,12}& a_{1,2,12}& \mathrm{...}& a_{1,10,12}\\ a_{2,1,1}& a_{2,2,1}& \mathrm{...}& a_{2,10,1}\\ a_{2,1,2}& a_{2,2,2}& \mathrm{...}& a_{2,10,2}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ a_{2,1,12}& a_{2,2,12}& \mathrm{...}& a_{2,10,12}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ a_{n,1,12}& a_{n,2,12}& \mathrm{...}& a_{n,10,12}\end{array}\right]---\left(2\right)$

B is the column vector that training sample concentrates each Nakshatra power load composition of transformer station, and A is that the N=12*n that training sample concentrates each influence factor of Substation Station power load to form is capable, the matrix of 10 row.

S4. set up the matrix form improving least square normal equation system, owing to considering the underlying factor of Substation Station power load, the fixed constant item in Classical Least-Squares system of equations is improved to the variable with each Monthly changes, and uses c ₀₁~ c ₁₂represent the value in 1 ~ Dec; Then based on set up improvement least square normal equation system, coefficient vector X in Classical Least-Squares and influence factor matrix A are improved, improve the matrix form that least square normal equation system is write as AX=B the most at last, so that apply the relevant solution formula of Classical Least-Squares in solution procedure.Its concrete steps are as follows:

(1) improvement least square normal equation system is set up as follows:

c ₀₁+a _1,1,1x ₁+a _1,2,1x ₂+…a _1,10,1x ₁₀＝b _1,1

c ₀₂+a _1,1,2x ₁+a _1,2,2x ₂+…a _1,10,2x ₁₀＝b _1,2

·

·

·

c ₁₂+a _1,1,12x ₁+a _1,2,12x ₂+…a _1,10,12x ₁₀＝b _1,12

c ₀₁+a _2,1,1x ₁+a _2,2,1x ₂+…a _2,10,1x ₁₀＝b _2,1(3)

c ₀₂+a _2,1,2x ₁+a _2,2,2x ₂+…a _2,10,2x ₁₀＝b _2,2

·

·

·

c ₁₂+a _2,1,12x ₁+a _2,2,12x ₂+…a _2,10,12x ₁₀＝b _2,12

·

·

·

c ₁₂+a _n,1,12x ₁+a _n,2,12x ₂+…a _n,10,12x ₁₀＝b _n,12

Wherein c ₀₁~ c ₁₂be represent transformer station to fix the underlying factors such as maintenance, equipment test to the impact of transformer station's station in 1 ~ Dec power load, it take year as loop cycle;

(2) improvement least square normal equation system is rewritten into matrix form

Underlying factor in 1 ~ Dec is affected c to transformer station's Nakshatra power load ₀₁~ c ₁₂decompose as follows:

$C=\left[\begin{array}{c}{c}_{01}\\ c_{02}\\ c_{03}\\ c_{04}\\ c_{05}\\ c_{06}\\ c_{07}\\ c_{08}\\ c_{09}\\ c_{10}\\ c_{11}\\ c_{12}\end{array}\right]=x_0{C}^{\&prime;}=x_0\left[\begin{array}{c}{c}_{01}^{\&prime;}\\ c_{c2}^{\&prime;}\\ c_{03}^{\&prime;}\\ c_{04}^{\&prime;}\\ c_{05}^{\&prime;}\\ c_{06}^{\&prime;}\\ c_{07}^{\&prime;}\\ c_{08}^{\&prime;}\\ c_{09}^{\&prime;}\\ c_{10}^{\&prime;}\\ c_{11}^{\&prime;}\\ c_{12}^{\&prime;}\end{array}\right]$

C=[c can be write a Chinese character in simplified form into ₀₁c ₀₂c ₁₂] ^t=x ₀c '=x ₀[c ' ₀₁c ' ₀₂c ₁' ₂] ^t(4)

$A^{\&prime;}=\left[\begin{array}{ccccc}{c}_{01}^{\&prime;}& a_{1,1,1}& a_{1,2,1}& \mathrm{...}& a_{1,10,1}\\ c_{02}^{\&prime;}& a_{1,1,2}& a_{1,2,2}& \mathrm{...}& a_{1,10,2}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ c_{12}^{\&prime;}& a_{1,1,12}& a_{1,2,12}& \mathrm{...}& a_{1,10,12}\\ c_{01}^{\&prime;}& a_{2,1,1}& a_{2,2,1}& \mathrm{...}& a_{2,10,1}\\ c_{02}^{\&prime;}& a_{2,1,2}& a_{2,2,2}& \mathrm{...}& a_{2,10,2}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ c_{12}^{\&prime;}& a_{2,1,12}& a_{2,2,12}& \mathrm{...}& a_{2,10,12}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ c_{12}^{\&prime;}& a_{n,1,12}& a_{n,2,12}& \mathrm{...}& a_{n,10,12}\end{array}\right]---\left(5\right)$

X′＝[x ₀x ₁x ₂x ₃x ₄x ₅x ₆x ₇x ₈x ₉x ₁₀]′ (6)

Wherein C ' is called Substation Station power load underlying factor factoring; x ₀it is Substation Station power load underlying factor coefficient of dissociation;

Coefficient vector X in Classical Least-Squares system of equations and influence factor matrix A are improved, as above shown in X ', A ';

Then the above least square normal equation system that improves can be write as following matrix form:

A′X′＝B (7)

S5. introduce PSO Algorithm and improve least square normal equation system, obtain the regression equation of Substation Station power load.The concrete steps wherein introducing the least square normal equation system that PSO Algorithm improves are as follows, see accompanying drawing 2:

(41) population initialization: at 12 dimension space stochastic generation M particle, the i-th (i=1,2 ... M) initial position of individual particle is expressed as x _i=(x _i1, x _i2, x _i3, x _i4, x _i5, x _i6, x _i7, x _i8, x _i9, x _i10, x _i11, x _i12), initial velocity is v _i=(v _i1, v _i2, v _i3, v _i4, v _i5, v _i6, v _i7, v _i8, v _i9, v _i10, v _i11, v _i12), setting particle iterations, aceleration pulse C ₁, C ₂, particle rapidity restriction [-Vmax, Vmin], the optimal location p of each particle _bestrepresent, all particle optimal location g _bestrepresent;

(42) particle fitness is calculated

421) defining i=1 ~ M, i is positive integer, and the initial value of i is 1;

422) with the current location parameter x of the i-th particle _i1~ x _i12replace Substation Station power load underlying factor factoring c ' ₀₁~ c ' ₁₂, the influence factor matrix A of the least square method that is improved by formula (5) _i', Substation Station power load each influence factor coefficient row X can be tried to achieve by the solution formula of following formula Classical Least-Squares _i':

$X_i^{\&prime;}={(A_i^{\&prime;T}\&times;A_i^{\&prime;})}^{-1}\&times;A_i^{\&prime;-T}\&times;B---\left(8\right)$

The predicted value that can obtain Substation Station power load is:

${\hat{B}}_i=A_i^{\&prime;}{X}_i^{\&prime;}---\left(9\right)$

423) using the fitness of the Prediction sum squares of Substation Station power load as particle, the fitness of i-th particle is:

$P_i=\underset{k=1}{\overset{N}{\&Sigma;}}{({\hat{B}}_{ik}-B_k)}^2---\left(10\right)$

424) judge whether i equals M, is, enters next step, otherwise i=i+1, return step 2);

(43) individual and global optimum is upgraded: respectively by the current fitness of each particle and its individual optimal value p _bestand global optimum g _bestrelatively, if currency is better than p _best, then p _bestbe updated to currency, otherwise remain unchanged; If currency is better than g _bestrelatively, then g _bestbe updated to currency, otherwise remain unchanged;

(44) position and speed is upgraded: first according to formula (11) more new particle minimax speed; Secondly judging whether particle rapidity is positioned at speed and limits in [-Vmax, Vmin] scope, is then according to formula (12) (13) the more speed of new particle, position; Otherwise upgrade position according to maximal rate restriction;

$\{\begin{array}{cc}{v}_i>v_{\max }& v_{\max }=v_i\\ v_i<v_{\min }& v_{\min }=v_i\end{array}---\left(11\right)$

For each particle, its d ties up (1≤d≤12) speed v _id, position x _idmore new formula is as follows:

v _id ^k+1＝v _id ^k+c ₁×rand ₁×(p _best-x _id ^k)+c ₂×rand ₂×(g _best-x _id ^k) (12)

x _id ^k+1＝x _id ^k+v _id ^k+1(13)

Wherein c ₁and c ₂two aceleration pulses, rand ₁, rand ₂it is the random function of value in [0,1] scope;

(45) end condition judges: check whether and reach iterations or fitness value is restrained, be, calculates and terminates and export location parameter and Substation Station power load each influence factor coefficient row X ' of optimal particle; Otherwise return step (52) to continue to calculate.

The concrete steps obtaining the regression equation of Substation Station power load are as follows:

(51) B is used respectively _j, A _1j, A _2j, A _3j, A _4j, A _5j, A _6j, T _1j, T _2j, T _3j, T _4jrepresent that Substation Station power load, conveying electricity, 110kV bus export electricity, 10kV bus active energy, 10kV bus capacity of idle power, circuit electricity, electric capacity electricity, jth (j=1 ~ 12) value of individual month of monthly maximum temperature, monthly minimum temperature, monthly mean of daily maximum temperature and mean monthly maximum temperature;

(52) with solving the location parameter x improving the optimal particle that least square normal equation system obtains ₁~ x ₁₂replace Substation Station power load underlying factor factoring c ' ₀₁~ c ' ₁₂, obtain Substation Station power load underlying factor factoring Matrix C ', obtain underlying factor coefficient of dissociation x by the first row of each influence factor coefficient row X ' ₀; Then the underlying factor C in Substation Station power load each month can formula (4) try to achieve

(53) regression equation setting up Substation Station power load is as follows:

B _j＝x ₁A _1j+x ₂A _2j...+x ₆A _6j+x ₇T _1j+x ₈T _2j...+x ₁₀T _4j+c _j(j＝1～12) (14)

In the above-mentioned Substation Station power load Forecasting Methodology based on improvement least square method, step (5) is described utilizes relative error E _r, square error E and coefficient of determination R ²evaluate the performance of institute's established model, relative error E _r, square error E and coefficient of determination R ²adopt following formulae discovery:

$E_r=\frac{(b_i-{\hat{b}}_i)}{b_i},i=1,\mathrm{2...}L---\left(15\right)$

$E=\frac{1}{L}\underset{i=1}{\overset{L}{\&Sigma;}}{({\hat{y}}_i-y_i)}^2---\left(16\right)$

$R^2=\frac{\underset{i=1}{\overset{L}{\&Sigma;}}{\hat{b}}_i^2}{\underset{i=1}{\overset{L}{\&Sigma;}}{b_i}^2}---\left(17\right)$

L is test set number of samples, b _i, (i=1,2...L) is actual value and predicted value, wherein the relative error E of the station power load of i-th test sample book respectively _rless with square error E, coefficient of determination R ²more close to 1, then the estimated performance of model is more excellent, and generalization ability is better.

S6. Substation Station power load is predicted.According to the Substation Station power load regression equation based on improvement least square method that upper step is set up, the corresponding influence factor value of input test collection carries out the prediction of Substation Station power load, and according to the relative error E predicted the outcome _r, square error E and coefficient of determination R ²evaluate build the performance of regression equation.

Real data below in conjunction with concrete transformer station is further described

(1) training sample set and test sample book collection is set up

For certain 220kV transformer station, obtain the data of the station power load in 2008 ~ 2014 years annual 1 ~ Dec of this transformer station, conveying electricity, 110kV bus output electricity, 10kV bus active energy, 10kV bus capacity of idle power, circuit electricity, electric capacity electricity, monthly maximum temperature, monthly minimum temperature, monthly mean of daily maximum temperature, mean monthly maximum temperature; Using 2008 ~ 2013 each month numerical value totally 72 samples as training sample set, using 2014 each month numerical value totally 12 samples as test set;

(2) set up improvement least square normal equation system and solve

The improvement least square normal equation system setting up this Substation Station power load is as follows:

A′X′＝B (7)

Wherein $A^{\&prime;}=\left[\begin{array}{ccccc}{c}_{01}^{\&prime;}& a_{1,1,1}& a_{1,2,1}& \mathrm{...}& a_{1,10,1}\\ c_{02}^{\&prime;}& a_{1,1,2}& a_{1,2,2}& \mathrm{...}& a_{1,10,2}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ c_{12}^{\&prime;}& a_{1,1,12}& a_{1,2,12}& \mathrm{...}& a_{1,10,12}\\ c_{01}^{\&prime;}& a_{2,1,1}& a_{2,2,1}& \mathrm{...}& a_{2,10,1}\\ c_{02}^{\&prime;}& a_{2,1,2}& a_{2,2,2}& \mathrm{...}& a_{2,10,2}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ c_{12}^{\&prime;}& a_{2,1,12}& a_{2,2,12}& \mathrm{...}& a_{2,10,12}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ c_{12}^{\&prime;}& a_{6,1,12}& a_{6,2,12}& \mathrm{...}& a_{6,10,12}\end{array}\right]---\left(18\right)$

X′＝[x ₀x ₁x ₂x ₃x ₄x ₅x ₆x ₇x ₈x ₉x ₁₀]′ (6)

At 12 dimension space stochastic generation, 30 particles, setting particle iterations 200 times, aceleration pulse C ₁=C ₂=2, particle maximal rate restriction [-2,2], the step improving least square normal equation system according to above-mentioned PSO Algorithm can obtain:

Each influence factor coefficient row X ':

X′＝[14.4697，-0.0051，0.0052，0.0052，0.0002，-0.0003，-0.0054，-0.1077，0.1174，0.0872，-0.0473]；

Particle optimal location parameter, i.e. underlying factor factoring C ':

C′＝[c′ ₀₁c′ ₀₂c′ ₀₃c′ ₀₄c′ ₀₅c′ ₀₆c′ ₀₇c′ ₀₈c′ ₀₉c′ ₁₀c′ ₁₁c′ ₁₂]′＝[0.338522，0.354931，0.349257，0.327123，0.44252，0.480017，0.441175，0.447892，0.440923，0.410664，0.377636，0.332811]’；

The underlying factor C in Substation Station power load each month:

C＝x ₀C′＝[c ₀₁c ₀₂c ₀₃c ₀₄c ₀₅c ₀₆c ₀₇c ₀₈c ₀₉c ₁₀c ₁₁c ₁₂]′＝[4.89831，5.135744，5.053647，4.733375，6.403127，6.945698，6.383672，6.480866，6.380019，5.942191，5.464279，4.815681]’；

(3) regression equation of Substation Station power load is set up

Use Y respectively _j, A _1j, A _2j, A _3j, A _4j, A _5j, A _6j, T _1j, T _2j, T _3j, T _4jrepresent that Substation Station power load, conveying electricity, 110kV bus export electricity, 10kV bus active energy, 10kV bus capacity of idle power, circuit electricity, electric capacity electricity, jth (j=1 ~ 12) value of individual month of monthly maximum temperature, monthly minimum temperature, monthly mean of daily maximum temperature and mean monthly maximum temperature, then set up Y _jas follows with the regression equation of each influence factor:

Y _j＝-0.0051*A _1j+0.0052*A _2j+0.0052*A _3j+0.0002*A _4j+(-0.0003)*A _5j

+(-0.0054)*A _6j+(-0.1077)*T _1j+0.1174*T _2j+0.0872*T _3j+(-0.0473)*T _4j+c _j

(4) Substation Station power load is predicted

Each influence factor value in 1 ~ Dec of test set is substituted into the above-mentioned regression equation based on improving the Substation Station power load that least square method is set up respectively, obtain the predicted value of transformer station's station power load of each month, and Relative Error, square error and the coefficient of determination can be obtained.Table 1 is transformer station's station power load of each month and the influence factor value thereof of test set.

Transformer station's station power load of each month of table 1 test set and influence factor value thereof

Unit: ten thousand kWh; DEG C

Fig. 3 is that Fig. 4 is station power load Relative Error E based on the improvement Substation Station power load predicted value of least square method and the comparison diagram of actual value _rdistribution plan; Can see based on improving the Substation Station power load Relative Error of least square method substantially within 3%, square error is 0.0211, the coefficient of determination reaches 0.9924, shows that the set up Substation Station power load forecast model based on improvement least square method has higher precision of prediction and extraordinary generalization ability.

Above-described embodiment is the present invention's preferably embodiment; but embodiments of the present invention are not restricted to the described embodiments; change, the modification done under other any does not deviate from Spirit Essence of the present invention and principle, substitute, combine, simplify; all should be the substitute mode of equivalence, be included within protection scope of the present invention.

Claims (5)

1., based on the Substation Station power load Forecasting Methodology improving least square method, it is characterized in that, comprise the following steps:

S1. Substation Station power load influence factor is analyzed;

S2. training sample set and test sample book collection is obtained;

S3. the N=12*n that the training sample setting up training sample set concentrates the matrix B of transformer station's each Nakshatra power load composition and training sample to concentrate each influence factor of Substation Station power load to form is capable, the matrix A of 10 row;

S4. the matrix form improving least square normal equation system is set up: the fixed constant item in Classical Least-Squares system of equations is improved to the variable with each Monthly changes, and uses c ₀₁~ c ₁₂represent the value in 1 ~ Dec; Then based on set up improvement least square normal equation system, coefficient vector X in Classical Least-Squares and influence factor matrix A are improved, improve the matrix form that least square normal equation system is write as A ' X '=B the most at last, wherein A ' is influence factor matrix, and X ' is coefficient vector;

S5. introduce PSO Algorithm and improve least square normal equation system, obtain the regression equation of Substation Station power load;

S6. Substation Station power load is predicted: according to the regression equation described in step S5, the corresponding influence factor value of input test collection carries out the prediction of Substation Station power load, and according to the relative error E predicted the outcome _r, square error E and coefficient of determination R ²evaluate build the performance of regression equation.

2. the Substation Station power load Forecasting Methodology based on improving least square method according to claim 1, it is characterized in that, described step S3 is specific as follows:

(21) number from 1 ~ n the time of training sample set, the initial value of definition k=1 ~ n, k is 1,

(22) kth year Substation Station power load and each influence factor value be described below:

221) define j=1 ~ 12, the initial value of j is 1;

222) defining training sample concentrates the Substation Station power load in j month in kth year to be b _kj, influence factor value is: conveying electricity a _k1j, 110kV bus exports electricity a _k2j, 10kV bus active energy a _k3j, 10kV bus capacity of idle power a _k4j, circuit electricity a _k5j, electric capacity electricity a _k6j, monthly maximum temperature a _k7j, monthly minimum temperature a _k8j, monthly mean of daily maximum temperature a _k9j, mean monthly maximum temperature a _k10j;

213) judge whether j equals 12, if so, enters next step, if not j=j+1, returns step 222);

(23) judge whether k equals n, if so, enters next step, if not k=k+1, returns step (22);

(24) setting up training sample concentrates the sample matrix of Substation Station power load and influence factor thereof as follows:

B＝[b _1,1b _1,2… b _1,12b _2,1b _2,2… b _2,12… b _n,12]′，

$A=\left[\begin{array}{cccc}{a}_{1,1,1}& a_{1,2,1}& ...& a_{1,10,1}\\ a_{1,1,2}& a_{1,2,2}& ...& a_{1,10,2}\\ ...& ...& ...& ...\\ a_{1,1,12}& a_{1,2,12}& ...& a_{1,10,12}\\ a_{2,1,1}& a_{2,2,1}& ...& a_{2,10,1}\\ a_{2,1,2}& a_{2,2,2}& ...& a_{2,10,2}\\ ...& ...& ...& ...\\ a_{2,1,12}& a_{2,2,12}& ...& a_{2,10,12}\\ ...& ...& ...& ...\\ a_{n,1,12}& a_{n,2,12}& ...& a_{n,10,12}\end{array}\right].$

3. the Substation Station power load Forecasting Methodology based on improving least square method according to claim 1, it is characterized in that, described step S4 is specific as follows:

(31) improvement least square normal equation system is set up as follows:

c ₀₁+a _1,1,1x ₁+a _1,2,1x ₂+…a _1,10,1x ₁₀＝b _1,1

c ₀₂+a _1,1,2x ₁+a _1,2,2x ₂+…a _1,10,2x ₁₀＝b _1,2

.

.

.

c ₁₂+a _1,1,12x ₁+a _1,2,12x ₂+…a _1,10,12x ₁₀＝b _1,12

c ₀₁+a _2,1,1x ₁+a _2,2,1x ₂+…a _2,10,1x ₁₀＝b _2,1，

c ₀₂+a _2,1,2x ₁+a _2,2,2x ₂+…a _2,10,2x ₁₀＝b _2,2

.

.

.

c ₁₂+a _2,1,12x ₁+a _2,2,12x ₂+…a _2,10,12x ₁₀＝b _2,12

.

.

.

c ₁₂+a _n,1,12x ₁+a _n,2,12x ₂+…a _n,10,12x ₁₀＝b _n,12

Wherein c ₀₁~ c ₁₂be represent the impact of transformer station's underlying factor on transformer station's station in 1 ~ Dec power load, it take year as loop cycle;

(32) improvement least square normal equation system is rewritten into matrix form:

Underlying factor in 1 ~ Dec is affected c to transformer station's Nakshatra power load ₀₁~ c ₁₂decompose as follows:

C＝[c ₀₁c ₀₂… c ₁₂] ^T＝x ₀C′＝x ₀[c′ ₀₁c′ ₀₂… c′ ₁₂] ^T

Wherein C ' is called Substation Station power load underlying factor factoring; x ₀it is Substation Station power load underlying factor coefficient of dissociation;

By C ' obtained above and x ₀be merged into the influence factor matrix A in Classical Least-Squares system of equations and coefficient vector X respectively, the influence factor matrix A of the least square normal equation system that is improved ' and coefficient vector X ' as follows:

$A^{\&prime;}=\left[\begin{array}{ccccc}{c}_{01}^{\&prime;}& a_{1,1,1}& a_{1,2,1}& ...& a_{1,10,1}\\ c_{02}^{\&prime;}& a_{1,1,2}& a_{1,2,2}& ...& a_{1,10,2}\\ ...& ...& ...& ...& ...\\ c_{12}^{\&prime;}& a_{1,1,12}& a_{1,2,12}& ...& a_{1,10,12}\\ c_{01}^{\&prime;}& a_{2,1,1}& a_{2,2,1}& ...& a_{2,10,1}\\ c_{02}^{\&prime;}& a_{2,1,2}& a_{2,2,2}& ...& a_{2,10,2}\\ ...& ...& ...& ...& ...\\ c_{12}^{\&prime;}& a_{2,1,12}& a_{2,2,12}& ...& a_{2,10,12}\\ ...& ...& ...& ...& ...\\ c_{12}^{\&prime;}& a_{n,1,12}& a_{n,2,12}& ...& a_{n,10,12}\end{array}\right],$

X′＝[x ₀x ₁x ₂x ₃x ₄x ₅x ₆x ₇x ₈x ₉x ₁₀]′，

Then the above least square normal equation system that improves can be write as following matrix form:

A′X′＝B。

4. the Substation Station power load Forecasting Methodology based on improving least square method according to claim 1, is characterized in that, the concrete steps introducing the least square normal equation system that PSO Algorithm improves described in step S5 are as follows:

(41) population initialization: at 12 dimension space stochastic generation M particle, the initial position of i-th particle is expressed as x _i=(x _i1, x _i2, x _i3, x _i4, x _i5, x _i6, x _i7, x _i8, x _i9, x _i10, x _i11, x _i12), wherein i=1,2 ... M, initial velocity is v _i=(v _i1, v _i2, v _i3, v _i4, v _i5, v _i6, v _i7, v _i8, v _i9, v _i10, v _i11, v _i12), setting particle iterations, aceleration pulse C ₁, C ₂, particle rapidity restriction [-Vmax, Vmin], the optimal location p of each particle _bestrepresent, all particle optimal location g _bestrepresent;

(42) particle fitness is calculated:

421) defining i=1 ~ M, i is positive integer, and the initial value of i is 1;

422) with the current location parameter x of the i-th particle _i1~ x _i12replace Substation Station power load underlying factor factoring c ' ₀₁~ c ' ₁₂, the influence factor matrix A of the least square method that can be improved ' _i, Substation Station power load each influence factor coefficient row X ' can be tried to achieve by the solution formula of following formula Classical Least-Squares _i:

$X_i^{\&prime;}={(A_i^{\&prime;T}\&times;A_i^{\&prime;})}^{-1}\&times;A_i^{\&prime;-T}\&times;B,$

Thus the predicted value that can obtain Substation Station power load is:

${\hat{B}}_i=A_i^{\&prime;}{X}_i^{\&prime;};$

423) using the fitness of the Prediction sum squares of Substation Station power load as particle, the fitness of i-th particle is:

$P_i=\underset{k=1}{\overset{N}{\&Sigma;}}{({\hat{B}}_{ik}-B_k)}^2$

424) judge whether i equals M, is, enters next step, otherwise i=i+1, return step 422);

(43) individual and global optimum is upgraded: respectively by the current fitness of each particle and its individual optimal value p _bestand global optimum g _bestrelatively, if currency is better than p _best, then p _bestbe updated to currency, otherwise remain unchanged; If currency is better than g _bestrelatively, then g _bestbe updated to currency, otherwise remain unchanged;

(44) position and speed is upgraded: first, according to the following formula the minimax speed of more new particle:

$\left\{\begin{array}{cc}{v}_i>v_{max}& v_{max}=v_i\\ v_i<v_{min}& v_{min}=v_i\end{array}\right.,$

Secondly, judge whether particle rapidity is positioned in speed restriction [-Vmax, Vmin] scope, and be then for each particle, its d ties up, wherein 1≤d≤12, speed v _id, position x _idmore new formula is as follows:

v _id ^k+1＝v _id ^k+c ₁×rand ₁×(p _best-x _id ^k)+c ₂×rand ₂×(g _best-x _id ^k)，

x _id ^k+1＝x _id ^k+v _id ^k+1，

Wherein c ₁and c ₂two aceleration pulses, rand ₁, rand ₂it is the random function of value in [0,1] scope; Otherwise upgrade position according to maximal rate restriction;

(45) end condition judges: check whether and reach iterations or fitness value is restrained, be, calculates and terminates and export location parameter and Substation Station power load each influence factor coefficient row X ' of optimal particle; Otherwise return step (42) to continue to calculate;

The concrete steps obtaining the regression equation of Substation Station power load described in step S5 are as follows:

(51) B is used respectively _j, A _1j, A _2j, A _3j, A _4j, A _5j, A _6j, T _1j, T _2j, T _3j, T _4jrepresent that Substation Station power load, conveying electricity, 110kV bus export electricity, 10kV bus active energy, 10kV bus capacity of idle power, circuit electricity, electric capacity electricity, the jth value of individual month of monthly maximum temperature, monthly minimum temperature, monthly mean of daily maximum temperature and mean monthly maximum temperature, wherein, j=1 ~ 12;

(52) with solving the location parameter x improving the optimal particle that least square normal equation system obtains ₁~ x ₁₂replace Substation Station power load underlying factor factoring c ' ₀₁~ c ' ₁₂, obtain Substation Station power load underlying factor factoring Matrix C ', obtain underlying factor coefficient of dissociation x by the first row of each influence factor coefficient row X ' ₀; The then underlying factor C in Substation Station power load each month;

(53) regression equation setting up Substation Station power load is as follows:

B _j=x ₁a _1j+ x ₂a _2j+ x ₆a _6j+ x ₇t _1j+ x ₈t _2j+ x ₁₀t _4j+ C _j, wherein j=1 ~ 12.

5. the Substation Station power load Forecasting Methodology based on improving least square method according to claim 1, is characterized in that: the error E described in step S6 _r, square error E and coefficient of determination R ²adopt following formulae discovery:

$E_r=\frac{(B_i-{\hat{B}}_i)}{B_i},i=1,2...L,E=\frac{1}{L}\underset{i=1}{\overset{L}{\&Sigma;}}{(B_i-{\hat{B}}_i)}^2,R^2=\frac{\underset{i=1}{\overset{L}{\&Sigma;}}{\hat{B}}_i^2}{\underset{i=1}{\overset{L}{\&Sigma;}}{B_i}^2},$

Wherein L is test set number of samples, B _i, wherein i=1,2...L is actual value and the predicted value of the station power load of i-th test sample book respectively, E _rfor relative error, E is square error, R ²for the coefficient of determination.