CN103854073A - Method for comprehensively predicting generation capacity of multi-radial flow type small hydropower station group area - Google Patents

Method for comprehensively predicting generation capacity of multi-radial flow type small hydropower station group area Download PDF

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CN103854073A
CN103854073A CN201410108969.0A CN201410108969A CN103854073A CN 103854073 A CN103854073 A CN 103854073A CN 201410108969 A CN201410108969 A CN 201410108969A CN 103854073 A CN103854073 A CN 103854073A
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generated energy
model
predicted value
value
correlative factor
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刘志坚
黄蓉
周术明
杨志华
宋琪
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Kunming University of Science and Technology
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Abstract

The invention relates to a method for comprehensively predicting the generation capacity of a multi-radial flow type small hydropower station group area, and belongs to the technical field of power. The method comprises the following steps: firstly, obtaining a linear multiple regression equation of the generation capacity of the multi-radial flow type small hydropower station group area and the mutual factors which can influence the generation capacity by using a partial least square model, meanwhile modeling the relevant factor sequences by using an improved gray prediction model to obtain a relevant factor prediction value, subsequently substituting the obtained relevant factor prediction value into the linear multiple regression equation obtained from the partial least square model, so as to obtain a prediction value of the generation capacity of the multi-radial flow type small hydropower station group area, and finally obtaining relative errors according to the prediction value of the generation capacity. The method is high in prediction precision and remarkable in prediction effect.

Description

A kind of multipath streaming group of small power station area generated energy Comprehensive Prediction Method
Technical field
The present invention relates to a kind of multipath streaming group of small power station area generated energy Comprehensive Prediction Method, belong to power technology field.
Background technology
Year, month generating online plan that under Power Market, generally all can require the considerable scale dispersed generators of participating in Electricity Market Operation to assign according to planning authorities of Utilities Electric Co., participate in load prediction and peaking generation plan.Wherein monthly prediction is the important process of power project department, electricity consumption sales department, the economical operation of precision of prediction direct relation electricity market.But, in the majority with small power station in dispersed generators, owing to there is no natural storage capacity, major part is wherein all the radial-flow type small power stations that do not possess regulating power, its generating capacity is subject to the restriction of many factors and affects, between the wet season, electric mass of small hydropower cannot be at local power network net internal consumption, on a large amount of electric weight more than needed, economize net, and low water season is because of little electric undercapacity, need be from economizing net supply electric weight off the net, therefore the precision of prediction of the multipath streaming group of small power station area generated energy is directly connected to the precision of prediction of the quantity of electricity indexs such as electricity sales amount He Xia province net electric weight, and these predicted value precision are all as the performance assessment criteria in power marketing department demand Side Management.
Affect the many factors of radial-flow type small power station generated energy, and between many factors and small power station's generated energy, have the problem of multicollinearity, conventional linear homing method is difficult to accurately describe the relation between variable.For the processing of influence factor, due to the most remote mountain area of radial-flow type small power station, obtain and collect hydrometeorological data and have great difficulty, and due to the backwardness of operations staff's quality and management system, cause the scarcity of historical summary.For small sample data problem, traditional statistical method is difficult to find its Changing Pattern.
Summary of the invention
The invention provides a kind of multipath streaming group of small power station area generated energy Comprehensive Prediction Method, contingency causes the not high deficiency of many small power stations' area generated energy precision of predictions be difficult to find statistical law, the influence factor multicollinearity of things under small sample capacity during for solving, to be difficult to accurately describe that relation, radial-flow type small power station water between independent variable and dependent variable sent out etc.
Technical scheme of the present invention is: a kind of multipath streaming group of small power station area generated energy Comprehensive Prediction Method, first adopt partial least square model, obtain the multipath streaming group of small power station area generated energy and affect the linear multiple regression equation between the correlative factor of generated energy; Adopt improved grey model forecast model to carry out modeling to each correlative factor ordered series of numbers simultaneously, obtain correlative factor predicted value; Then by the linear multiple regression equation of the correlative factor predicted value substitution partial least square model gained obtaining, obtain the multipath streaming group of small power station area generated energy predicted value; Finally draw relative error according to generated energy predicted value.
The concrete steps of described method are as follows:
A, according to the multipath streaming group of small power station area generated energy ywith mthe individual correlative factor variable that affects generated energy x 1, x 2..., x m , choose nindividual sample observation station, obtains x=[ x 1, x 2..., x m ] n× m , y=[ y] n× 1 , according to partial least square model, set up linear multiple regression equation and be:
Figure 2014101089690100002DEST_PATH_IMAGE002
（1）
Wherein, i=1, m, mfor the number of correlative factor of hypothesis; c 0for the error system of regression equation, c 1, c 2, c m for regression coefficient;
Figure 2014101089690100002DEST_PATH_IMAGE004
,
Figure DEST_PATH_IMAGE006
...,
Figure 2014101089690100002DEST_PATH_IMAGE008
for xin the value of each standard parameter inverse process;
Figure DEST_PATH_IMAGE010
for yin the value of each standard parameter inverse process;
B, employing improved grey model forecast model carry out modeling to each correlative factor ordered series of numbers, obtain correlative factor predicted value: the concrete steps of described improved grey model forecast model are as follows:
B1, original data series is carried out to running mean processing, obtain the ordered series of numbers after slipping smoothness is processed;
B2, the ordered series of numbers after slipping smoothness is processed is carried out to one-accumulate generate one-accumulate ordered series of numbers, use one-accumulate ordered series of numbers structure differential equation of first order specified data matrix;
The solve for parameter of B3, employing least-squares estimation linear first-order differential equation;
B4, calculating are without inclined to one side
Figure DEST_PATH_IMAGE012
the parameter of model
Figure DEST_PATH_IMAGE014
,
Figure DEST_PATH_IMAGE016
;
B5, basis
Figure DEST_PATH_IMAGE018
, aestimated value
Figure 982202DEST_PATH_IMAGE014
,
Figure 420136DEST_PATH_IMAGE016
set up original data sequence model:
Figure DEST_PATH_IMAGE020
（2）
Wherein, 0≤ k≤ n-1 o'clock
Figure DEST_PATH_IMAGE022
for the match value of original data sequence, k>= ntime
Figure 466852DEST_PATH_IMAGE022
for the predicted value of original data sequence;
C, by the linear multiple regression analysis formula of the correlative factor predicted value substitution partial least square model gained obtaining, obtain the multipath streaming group of small power station area generated energy predicted value;
D, the absolute value of the difference of the actual value of generated energy and generated energy predicted value is obtained to relative error divided by the actual value of generated energy.
Principle of work of the present invention is:
1, establish the known radial-flow type group of small power station area generated energy ywith mindividual Correlative Influence Factors variable x 1, x 2..., x m . x=[ x 1, x 2..., x m ] n× m , y=[ y] n× 1 , in order to study the statistical relationship between small power station's mass-sending electric weight and Correlative Influence Factors, choose nindividual sample observation station, carry out as follows standardization:
Figure DEST_PATH_IMAGE024
, i=1,2,… n； j=1,2,… m
Figure DEST_PATH_IMAGE026
, i=1,2,… n
In formula, x ij represent independent variable matrix xin jindividual variable iindividual sample value, y i representing matrix y iindividual sample value,
Figure DEST_PATH_IMAGE028
for matrix xin jthe mean value of row all elements, for column vector matrix ythe average of middle all elements, s j for matrix xin jthe standard deviation of row all elements, s y for column vector matrix ythe standard deviation of middle all elements.Therefore after standardization, obtain:
Figure DEST_PATH_IMAGE032
In formula, i=1,2, n; j=1,2, m.
To influence factor matrix e 0carry out principal component analysis (PCA), extract the first leading factor t 1= e 0 w 1, t 1it is each factor of influence
Figure 811858DEST_PATH_IMAGE004
, ...,
Figure 414320DEST_PATH_IMAGE008
linear combination, w 1for e 0the first main shaft, wherein,
Figure DEST_PATH_IMAGE034
.Requirement t 1large as far as possible carries e 0in variation information, and with f 0degree of correlation maximum.Can represent well like this e 0, again can be right f 0there is the strongest interpretability.
Carry out
Figure DEST_PATH_IMAGE036
, to the first leading factor
Figure DEST_PATH_IMAGE040
recurrence:
Figure DEST_PATH_IMAGE042
In above formula, e 1, f 1for residual matrix:
b 1, a 1that regression coefficient vector is:
Figure DEST_PATH_IMAGE046
In formula,
Figure DEST_PATH_IMAGE048
what represent is matrix e 0transposed matrix,
Figure DEST_PATH_IMAGE050
what represent is matrix f 0transposed matrix.
Carry out convergence judgement, if yright t 1regression accuracy reached requirement, finish the extraction to composition.Otherwise use residual matrix e 1with f 1replace e 0with f 0, then repeat above-mentioned steps, extract the second leading factor t 2= e 1 w 2, so composition is extracted in circulation.Suppose to have extracted altogether in the time meeting accuracy requirement kindividual composition t 1, t 2..., t k , right f 0 t 1, t 2..., t k enterprising line retrace, has:
Figure DEST_PATH_IMAGE052
Due to
Figure DEST_PATH_IMAGE054
be x=[ x 1, x 2..., x m ] linear combination, and
Figure 573381DEST_PATH_IMAGE036
be xmatrix after standardization, therefore above formula can be expressed as:
Figure DEST_PATH_IMAGE056
In formula,
Figure DEST_PATH_IMAGE058
, ifor unit matrix, 1≤ h≤ k,
Figure DEST_PATH_IMAGE060
it is column vector matrix b j transposed matrix, w h derivation with
Figure 260977DEST_PATH_IMAGE034
.
By above formula standardization reduction inverse process, be reduced to
Figure DEST_PATH_IMAGE062
right
Figure DEST_PATH_IMAGE064
regression equation be:
Figure DEST_PATH_IMAGE066
In formula, regression coefficient
Figure DEST_PATH_IMAGE068
, kfor the final number of extracting composition, for column vector jrow component, 1≤ j≤ m, and 1≤ h≤ k.
Conventionally, need in regression equation, introduce an error coefficient, be designated as c 0, full scale equation becomes:
Figure DEST_PATH_IMAGE074
From analyzing above, partial least squares regression equation does not need to select whole compositions to carry out regression modeling, in partial least squares regression modeling, choosing how many compositions is advisable, can increase after a new composition by investigation, can have obvious improvement to consider to the forecast function of model.Based on this, define intersection validity principle, that is:
Figure DEST_PATH_IMAGE076
Wherein,
Figure DEST_PATH_IMAGE078
,
Figure DEST_PATH_IMAGE080
; y i represent the ithe actual value of individual sample,
Figure DEST_PATH_IMAGE082
represent with except the ithe model that all sample fittings outside individual sample obtain is ipredicted value on individual sample, represent that model that all sample fittings obtain is ipredicted value on individual sample.When
Figure DEST_PATH_IMAGE086
time, t h the contributrion margin of composition is significant.At this moment increase composition t h forecast model is significantly improved.
2, establishing hydrometeorological original data sequence is:
Figure DEST_PATH_IMAGE088
Process through running mean:
Figure DEST_PATH_IMAGE090
Wherein:
Figure DEST_PATH_IMAGE092
Consider the stochastic volatility of hydrometeorological data, running mean can weaken the impact of raw data fluctuation for precision of forecasting model.Hydrometeorological data after slipping smoothness is processed are carried out after one-accumulate generation, form ordered series of numbers:
Figure DEST_PATH_IMAGE094
In formula, .
Specified data matrix b, y n (why need to determine that these two matrix of coefficients are the solve for parameters in order to ask linear first-order differential equation here
Figure DEST_PATH_IMAGE098
, .Because application is through the ordered series of numbers of running mean and one-accumulate generation
Figure 815103DEST_PATH_IMAGE094
modeling, describes the evolution of thing, builds following differential equation of first order
Figure DEST_PATH_IMAGE102
):
Figure DEST_PATH_IMAGE104
Figure DEST_PATH_IMAGE106
Adopt the solve for parameter of least-squares estimation linear first-order differential equation
Figure 916045DEST_PATH_IMAGE098
,
Figure 944044DEST_PATH_IMAGE100
:
Figure DEST_PATH_IMAGE108
Calculate without inclined to one side
Figure 187944DEST_PATH_IMAGE012
the parameter of model:
Figure DEST_PATH_IMAGE110
Set up original data sequence model:
Figure DEST_PATH_IMAGE112
In formula, 0≤ k≤ n-1 o'clock
Figure 502251DEST_PATH_IMAGE022
for the match value of original data sequence, k>= ntime
Figure 962925DEST_PATH_IMAGE022
for the predicted value of original data sequence.
The invention has the beneficial effects as follows:
1, the in the situation that of in advance supposition, accurately described that the group of radial-flow type small power station exerts oneself and its influence factor between complex relationship, with simple linear fit the relationship of the two, precision of prediction is higher.
2,, while processing the Correlative Influence Factors such as hydrometeorology, improved grey model prediction has solved the problem that sample size is limited and random fluctuation is larger, has improved precision of prediction.
3, by comprehensive to partial least squares algorithm and improved grey model prediction, the two is learnt from other's strong points to offset one's weaknesses, and prediction effect is remarkable.
Brief description of the drawings
Fig. 1 is prediction steps block diagram of the present invention;
Fig. 2 is the prediction effect figure of embodiment 2 in the present invention.
Embodiment
Embodiment 1: as shown in Figure 1-2, a kind of multipath streaming group of small power station area generated energy Comprehensive Prediction Method, first adopt partial least square model, obtain the multipath streaming group of small power station area generated energy and affect the linear multiple regression equation between the correlative factor of generated energy; Adopt improved grey model forecast model to carry out modeling to each correlative factor ordered series of numbers simultaneously, obtain correlative factor predicted value; Then by the linear multiple regression equation of the correlative factor predicted value substitution partial least square model gained obtaining, obtain the multipath streaming group of small power station area generated energy predicted value; Finally draw relative error according to generated energy predicted value.
The concrete steps of described method are as follows:
A, according to the multipath streaming group of small power station area generated energy ywith mthe individual correlative factor variable that affects generated energy x 1, x 2..., x m , choose nindividual sample observation station, obtains x=[ x 1, x 2..., x m ] n× m , y=[ y] n× 1 , according to partial least square model, set up linear multiple regression equation and be:
Figure DEST_PATH_IMAGE114
（1）
Wherein, i=1, m, mfor the number of correlative factor of hypothesis; c 0for the error system of regression equation, c 1, c 2, c m for regression coefficient;
Figure DEST_PATH_IMAGE116
,
Figure DEST_PATH_IMAGE118
...,
Figure DEST_PATH_IMAGE120
for xin the value of each standard parameter inverse process;
Figure DEST_PATH_IMAGE122
for yin the value of each standard parameter inverse process;
B, employing improved grey model forecast model carry out modeling to each correlative factor ordered series of numbers, obtain correlative factor predicted value: the concrete steps of described improved grey model forecast model are as follows:
B1, original data series is carried out to running mean processing, obtain the ordered series of numbers after slipping smoothness is processed;
B2, the ordered series of numbers after slipping smoothness is processed is carried out to one-accumulate generate one-accumulate ordered series of numbers, use one-accumulate ordered series of numbers structure differential equation of first order specified data matrix;
The solve for parameter of B3, employing least-squares estimation linear first-order differential equation;
B4, calculating are without inclined to one side
Figure DEST_PATH_IMAGE124
the parameter of model
Figure DEST_PATH_IMAGE126
,
Figure DEST_PATH_IMAGE128
;
B5, basis
Figure 342085DEST_PATH_IMAGE018
, aestimated value
Figure 706071DEST_PATH_IMAGE126
, set up original data sequence model:
Figure DEST_PATH_IMAGE130
（2）
Wherein, 0≤ k≤ n-1 o'clock
Figure DEST_PATH_IMAGE132
for the match value of original data sequence, k>= ntime
Figure 76933DEST_PATH_IMAGE132
for the predicted value of original data sequence;
C, by the linear multiple regression analysis formula of the correlative factor predicted value substitution partial least square model gained obtaining, obtain the multipath streaming group of small power station area generated energy predicted value;
D, the absolute value of the difference of the actual value of generated energy and generated energy predicted value is obtained to relative error divided by the actual value of generated energy.
Embodiment 2: as shown in Figure 1-2, a kind of multipath streaming group of small power station area generated energy Comprehensive Prediction Method, the concrete implementation step of described method is as follows:
The fraction of the year of choosing the group of somewhere radial-flow type small power station 2009～2011, the moon, generated energy data were as historical data, and the moon, generated energy was predicted to 2012 fraction of the year.Choose the Hydrology flow, hydrology quantity of precipitation, the meteorological quantity of precipitation that are closely related with generated energy and carry out forecast analysis as independent variable factor, known, sample observation station is 3, and the number of correlative factor is 3.Utilize Matlab7.0 simulation software, be predicted as example in March, 2012 describe with the group of this small power station, raw data is as shown in table 1.
Figure DEST_PATH_IMAGE134
First, choose above three groups of data and carry out PLS(offset minimum binary, Partial Least Square) modeling, obtain regression equation and be:
Then adopt improved grey model prediction algorithm to process respectively each correlative factor, each factor prediction ordered series of numbers is as shown in table 2.
Figure DEST_PATH_IMAGE138
Finally, by the improved grey model predicted value substitution PLS equation of linear regression of each correlative factor, obtain the monthly generated energy predicted value group of radial-flow type small power station of this area in March, 2012.By that analogy, adopt based on PLS and improvement GM integrated forecasting algorithm, can obtain 1～12 month generated energy predicted value in 2012, contrast prediction effect as shown in Figure 2 with actual value.Relative Error is analyzed as shown in table 3.
Figure DEST_PATH_IMAGE140
In 2012, in totally 12 month predicted values, maximum error was 14.02%, and least error is 0.17%, and average forecasting error is 5.43%.Obviously herein the Comprehensive Model for the monthly generated energy in the group of radial-flow type small power station area proposing has very high precision of prediction, and the hydrometeorological data such as Hydrology flow, hydrology quantity of precipitation are easy to obtain.Correctly effective by simulating, verifying the present invention.
By reference to the accompanying drawings the specific embodiment of the present invention is explained in detail above, but the present invention is not limited to above-mentioned embodiment, in the ken possessing those of ordinary skill in the art, can also under the prerequisite that does not depart from aim of the present invention, make various variations.

Claims (2)

1. the group of a multipath streaming small power station area generated energy Comprehensive Prediction Method, is characterized in that: first adopt partial least square model, obtain the multipath streaming group of small power station area generated energy and affect the linear multiple regression equation between the correlative factor of generated energy; Adopt improved grey model forecast model to carry out modeling to each correlative factor ordered series of numbers simultaneously, obtain correlative factor predicted value; Then by the linear multiple regression equation of the correlative factor predicted value substitution partial least square model gained obtaining, obtain the multipath streaming group of small power station area generated energy predicted value; Finally draw relative error according to generated energy predicted value.
2. the multipath streaming group of small power station according to claim 1 area generated energy Comprehensive Prediction Method, is characterized in that: the concrete steps of described method are as follows:
A, according to the multipath streaming group of small power station area generated energy ywith mthe individual correlative factor variable that affects generated energy x 1, x 2..., x m , choose nindividual sample observation station, obtains x=[ x 1, x 2..., x m ] n× m , y=[ y] n× 1 , according to partial least square model, set up linear multiple regression equation and be:
Figure 9568DEST_PATH_IMAGE001
（1）
Wherein, i=1, m, mfor the number of correlative factor of hypothesis; c 0for the error system of regression equation, c 1, c 2, c m for regression coefficient;
Figure 532953DEST_PATH_IMAGE002
,
Figure 25114DEST_PATH_IMAGE003
...,
Figure 329057DEST_PATH_IMAGE004
for xin the value of each standard parameter inverse process; for yin the value of each standard parameter inverse process;
B, employing improved grey model forecast model carry out modeling to each correlative factor ordered series of numbers, obtain correlative factor predicted value: the concrete steps of described improved grey model forecast model are as follows:
B1, original data series is carried out to running mean processing, obtain the ordered series of numbers after slipping smoothness is processed;
B2, the ordered series of numbers after slipping smoothness is processed is carried out to one-accumulate generate one-accumulate ordered series of numbers, use one-accumulate ordered series of numbers structure differential equation of first order specified data matrix;
The solve for parameter of B3, employing least-squares estimation linear first-order differential equation;
B4, calculating are without inclined to one side
Figure 811433DEST_PATH_IMAGE006
the parameter of model
Figure 146599DEST_PATH_IMAGE007
, ;
B5, basis
Figure 78969DEST_PATH_IMAGE009
, aestimated value
Figure 576947DEST_PATH_IMAGE007
,
Figure 410910DEST_PATH_IMAGE008
set up original data sequence model:
（2）
Wherein, 0≤ k≤ n-1 o'clock for the match value of original data sequence, k>= ntime
Figure 219707DEST_PATH_IMAGE011
for the predicted value of original data sequence;
C, by the linear multiple regression analysis formula of the correlative factor predicted value substitution partial least square model gained obtaining, obtain the multipath streaming group of small power station area generated energy predicted value;
D, the absolute value of the difference of the actual value of generated energy and generated energy predicted value is obtained to relative error divided by the actual value of generated energy.
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Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106548285A (en) * 2016-11-04 2017-03-29 广西电网有限责任公司电力科学研究院 The bulk sale power predicating method that meter and small power station exert oneself
CN108154268A (en) * 2017-12-25 2018-06-12 国网福建省电力有限公司 The method of quick estimation Small Hydropower Stations generated energy
CN109102110A (en) * 2018-07-23 2018-12-28 云南电网有限责任公司临沧供电局 A kind of radial-flow type small power station goes out force prediction method and device in short term
CN110969297A (en) * 2019-11-26 2020-04-07 国网浙江省电力有限公司 Power load prediction method and device based on backward interval partial least square method
CN113610288A (en) * 2021-07-28 2021-11-05 华北电力大学 Power demand prediction method, device and storage medium

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
吉培荣等: "电网负荷预测的无偏灰色预测模型", 《三峡大学学报（自然科学报）》 *
牛东晓 等: "基于灰色和偏最小二乘方法的年度负荷预测", 《华东电力》 *

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106548285A (en) * 2016-11-04 2017-03-29 广西电网有限责任公司电力科学研究院 The bulk sale power predicating method that meter and small power station exert oneself
CN108154268A (en) * 2017-12-25 2018-06-12 国网福建省电力有限公司 The method of quick estimation Small Hydropower Stations generated energy
CN108154268B (en) * 2017-12-25 2022-07-05 国网福建省电力有限公司 Method for rapidly estimating group power generation quantity of small hydropower stations
CN109102110A (en) * 2018-07-23 2018-12-28 云南电网有限责任公司临沧供电局 A kind of radial-flow type small power station goes out force prediction method and device in short term
CN109102110B (en) * 2018-07-23 2022-03-22 云南电网有限责任公司临沧供电局 Method and device for predicting short-term output of runoff small hydropower station
CN110969297A (en) * 2019-11-26 2020-04-07 国网浙江省电力有限公司 Power load prediction method and device based on backward interval partial least square method
CN113610288A (en) * 2021-07-28 2021-11-05 华北电力大学 Power demand prediction method, device and storage medium

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