CN109919353B - Distributed photovoltaic prediction method of ARIMA model based on spatial correlation - Google Patents

Distributed photovoltaic prediction method of ARIMA model based on spatial correlation Download PDF

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CN109919353B
CN109919353B CN201910028384.0A CN201910028384A CN109919353B CN 109919353 B CN109919353 B CN 109919353B CN 201910028384 A CN201910028384 A CN 201910028384A CN 109919353 B CN109919353 B CN 109919353B
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weather
correlation
power
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CN109919353A (en
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章坚民
胡瑛俊
赵羚
姜驰
杨宁
孔历波
王伟峰
林英鹤
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State Grid Corp of China SGCC
State Grid Zhejiang Electric Power Co Ltd
Hangzhou Dianzi University
Zhejiang Huayun Information Technology Co Ltd
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State Grid Corp of China SGCC
State Grid Zhejiang Electric Power Co Ltd
Hangzhou Dianzi University
Zhejiang Huayun Information Technology Co Ltd
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Abstract

The invention discloses a distributed photovoltaic prediction method of an ARIMA model based on spatial correlation, and relates to the field of electric power. At present, the distributed photovoltaic prediction precision is low. The method comprises the steps of calculating rank correlation coefficients of historical output data of a power station to be predicted and other power stations based on photovoltaic output data of different weather types; selecting N power stations with rank correlation coefficients larger than a set value and/or best correlation as correlation slave stations, and incorporating the power stations into an ARIMA model based on spatial correlation to establish prediction models of different weather types; combining the weather types of the daily forecast given by the meteorological department, selecting a prediction model corresponding to the weather for output prediction, and if no correlation power station is matched, performing ARIMA modeling according to the weather types by using the data of the power station to be predicted; and matching according to forecast information provided by a weather forecast department, and realizing photovoltaic ultra-short-term power prediction by using a corresponding model. The technical scheme has high prediction accuracy and has self-adaptability in responding to weather changes.

Description

Distributed photovoltaic prediction method of ARIMA model based on spatial correlation
Technical Field
The invention relates to the field of electric power, in particular to a distributed photovoltaic prediction method of an ARIMA model based on spatial correlation.
Background
Compared with a centralized photovoltaic power station, the distributed photovoltaic power prediction has the following problems: 1) the components occupy small area, are distributed dispersedly, and have irregular running states due to incomplete operation and maintenance; 2) Due to the influence of meteorological factors, the photovoltaic output presents randomness and volatility; 3) a single photovoltaic user lacks actually measured meteorological data, and prediction accuracy is not high. Therefore, the distributed photovoltaic prediction difficulty is high, and the prediction method cannot completely move the hard set according to the prediction method of the centralized photovoltaic power station.
The existing distributed photovoltaic prediction method mainly comprises a direct prediction method and an indirect prediction method, wherein the indirect prediction method is used for predicting weather data indirectly so as to predict photovoltaic output, and mainly comprises methods such as numerical weather forecast and foundation cloud pictures. The indirect prediction method is to predict the photovoltaic on the basis of the related meteorological data, but the accuracy required by numerical weather forecast is higher, the meteorological monitoring points with high accuracy in China are fewer at present, while the direct prediction method is to discover a certain rule by utilizing the statistical analysis of the actual output data, and comprises a time series method, a multiple linear regression method, a grey theory prediction method and the like.
Disclosure of Invention
The technical problem to be solved and the technical task provided by the invention are to perfect and improve the prior technical scheme, and provide a distributed photovoltaic prediction method of an ARIMA model based on spatial correlation, so as to achieve the purpose of accurately predicting the output of distributed photovoltaic. Therefore, the invention adopts the following technical scheme.
A distributed photovoltaic prediction method based on an ARIMA model of spatial correlation comprises the following steps:
1) acquiring actual output data of the distributed photovoltaic, and intercepting historical output data of the photovoltaic output effective time;
2) per-unit processing the actual output data of each user;
3) dividing weather types according to the average level of the daily output;
4) calculating rank correlation coefficients of historical output data of the power station to be predicted and other power stations based on photovoltaic output data of different weather types;
5) selecting N power stations with rank correlation coefficients larger than a set value and/or best correlation as correlation slave stations and incorporating the power stations into ARIMA models based on spatial correlation to establish prediction models of different weather types;
6) combining the weather types of the daily forecast given by the meteorological department, selecting a prediction model corresponding to the weather for output prediction, and if no correlation power station is matched, performing ARIMA modeling by using the data of the power station to be predicted according to the weather types without considering the correlation;
7) acquiring forecast information provided by a weather forecast department in a photovoltaic output area to be forecasted; and matching is carried out according to forecast information provided by a weather forecast department, and photovoltaic ultra-short term power prediction is realized by utilizing a corresponding model.
The technical scheme is based on the proposed large-scale regional photovoltaic clustering method, the photovoltaic power stations which have spatial correlation with the power station to be predicted in the clustering power stations are further screened, ARIMA models are established according to weather types and are matched with the forecast information provided by a weather forecast department, and the photovoltaic ultra-short-term power prediction is realized by using the corresponding models. On the basis of introducing relevant power station data, classifying weather by historical output data, selecting a corresponding weather model for power forecasting by referring to weather forecasts given by a weather department, and having self-adaptability in responding to weather changes.
Preferably, in step 4), the Spearman rank correlation coefficient is used to measure the correlation between two power stations, the formula being as follows:
Figure BDA0001943331990000031
extracting historical output data of all power stations with the same dimension in the same area, respectively calculating correlation coefficients of the historical output data and the historical output data of the power stations to be predicted based on data samples of different weather classifications, and screening N power stations with the highest correlation number or the power stations with the correlation coefficients larger than a certain set threshold value as correlation slave stations of the power stations to be predicted.
Preferably, in step 5), the photovoltaic power station with the correlation value larger than 0.8 is extracted as the dependent photovoltaic slave station.
Preferably, the power station X output prediction model to be predicted is:
Figure BDA0001943331990000032
wherein epsilontIs random interference at the current moment, and the coefficient gamma is (alpha)0(l,x)(l,x)(l,i)(l,i)), 1≤i≤N,0≤l≤Ls(ii) a N is the number of photovoltaic power stations with correlation, L is the parameter training sample length, p and q are the model orders of ARIMA,
the coefficient gamma is calculated by a least square estimation method:
LSE=||Px-Xγ||2
Figure BDA0001943331990000033
is the actual output data of the power station X to be predicted, X ═ E, Xx,X1,X2,…XN]Is a coefficient matrix composed of N related power stations and the power station to be predicted, wherein E ═ 1,1, …,1]TIs a unit column vector of L x 1,
Figure BDA0001943331990000041
1≤i≤N;
Figure BDA0001943331990000042
preferably, in step 3), the photovoltaic output level of the whole day is represented by the photovoltaic daily average output, and the calculation formula is as follows:
Figure BDA0001943331990000043
n is the length of the power generation time period, PiThe output value of the photovoltaic is the output value of the photovoltaic at the ith moment;
when P is presentaverageJudging whether the weather type is sunny when the weather type is more than or equal to 0.4; when P is more than or equal to 0.3averageIf the weather type is less than 0.4, judging the weather type to be multiple days; when P is more than or equal to 0.2averageIf the weather type is less than 0.3, judging the weather type is cloudy; when P is more than or equal to 0averageIf the weather is less than 0.2, judging the weather type to be rainy.
Preferably, the prediction model adopts an ARIMA (p, d, q) model, and the prediction model is a combination of d-order difference and ARMA (p, q); during data preprocessing, stability detection needs to be carried out on a sequence, and a non-stable time sequence can form a stable time sequence through finite difference and then is modeled; using AIC (Akaike information criterion) information criterion to carry out order determination, selecting p and q with minimum AIC value as model order, wherein the AIC calculation formula is as follows
Figure BDA0001943331990000044
The model parameters can be calculated by a least square estimation method, namely, for an objective function:
Figure BDA0001943331990000045
minimized to obtain
Figure BDA0001943331990000046
I.e. parameters obtained by least squares estimation.
Finally checking the residual sequence [ epsilon ]tAnd e, if the residual error sequence is a white noise sequence, namely useful information of the sequence is completely extracted by the model parameters, the residual error sequence is an effective model, and if the residual error sequence is not the white noise sequence, the residual useful information in the sequence is to be extracted and the model needs to be fitted again.
Preferably, before distributed photovoltaic prediction is carried out, large-scale regional photovoltaic clustering is carried out on distributed photovoltaic, then photovoltaic power stations which have spatial correlation with power stations to be predicted in clustered power stations are further screened, ARIMA models are established according to weather types and matched with forecast information provided by a weather forecast department, and short-term power prediction of the photovoltaic is realized by utilizing corresponding models.
Preferably, the large-scale regional photovoltaic clustering of distributed photovoltaics comprises the following steps:
a) taking the data per hour as a sample, performing per unit processing on the data, intercepting historical output data of 5:00-20:00 points for 15 hours, performing weather type matching identification on the photovoltaic historical output data according to regions, wherein each single power station uses 15-moment weather type indexes to represent the output historical data, and the weather types are as follows: sunny days, cloudy days, rain, thunderstorm rain, light rain, heavy rain, and heavy rainstorm;
b) sequentially carrying out cluster analysis on the data of each integral point to generate a distributed photovoltaic geographical position distribution map under five weather types, and partitioning the geographical position of the photovoltaic output data under each weather type through K-means clustering;
c) under each weather type, the magnitude of the photovoltaic output force belongs to an interval, namely the photovoltaic output forces have similarity with each other; the geographical position blocks of each photovoltaic power station are positioned according to a table look-up method, if the photovoltaic power stations belong to a geographical position block under the five weather types, only a proper power station is selected from the same geographical block to serve as a primary reference power station, namely under any weather type, the output of the photovoltaic power station follows the reference power station and is called a harmonious power station; if the photovoltaic power station belongs to different geographical blocks under different weather types, namely belongs to different reference power stations, namely called dissonant power stations, the photovoltaic power station needs to be additionally selected as a reference power station;
d) calculating the ratio of the number of the dissonant power stations to the total power stations in the classification K value setting range, and determining the optimal K value of the clustering analysis according to the ratio;
e) and performing cluster analysis on all distributed photovoltaic geographic positions again according to the K value to obtain a result, namely the result is the regionalized display of the wide-area distributed photovoltaic division group with spatial correlation, and a photovoltaic power generation user group division result is obtained.
Preferably, during the matching of the weather types, classifying the weather according to the proportion value k of the actual daily generated energy and the daily rated generated energy reference value, distributing the intervals and corresponding five types of weather types, and when k is more than or equal to 1 and less than 0.8, determining that the weather type is sunny and cloudy in sunny days; when k is more than or equal to 0.8 and less than 0.6, the weather type is cloudy and cloudy in the shade; when k is more than or equal to 0.6 and less than 0.4, the weather type is considered as cloudy; when k is more than or equal to 0.4 and less than 0.2, the weather type is considered as rain fall, thunderstorm rain and light rain; when k is more than or equal to 0.2 and less than 0, the weather type is considered as heavy rain and heavy rainstorm;
when discrete sampling is carried out, the daily actual power generation amount is a sampling value of a daily interval of 15 minutes, and then:
Figure BDA0001943331990000061
wherein i is the serial number of the photovoltaic user, j is the number of photovoltaic daily collection points, P (i, j) is the discrete sampling value of the ith photovoltaic user at the moment j, and PmaxThe daily rated power generation reference value is estimated from the historical maximum value of the daily power generation discrete sampling value due to the lack of the rated power generation data; when data is collected every 15 minutes, the day has 4 × 24 ═ 96 points, i.e. j ═ 1,2, …, 96.
Preferably, the cluster analysis result fluctuates depending on the initial cluster center and the cluster number, and has certain instability; selecting a proper initial clustering center position is important for analyzing a clustering result; suppose the dataset to be clustered is X ═ Xi|xi∈RPI is 1,2, …, n, and K initial positions are centered at C1,C2,…,CKBy W1,W2,…,WKRepresenting the sample sets contained in the K classes, wherein all the sample sets are W;
define 1 sample xi,xjEuclidean distance between:
Figure BDA0001943331990000071
define 2 samples xiAverage of distances to all samples:
Figure BDA0001943331990000072
defining 3 mean distances of data set samples
Figure BDA0001943331990000073
Define 4 data points xiDensity (x) ofi)
density(x)={p∈C|d(x,p)≤cmean*θ}
Theta is a density radius coefficient;
firstly, the density of each sample data in the data set is calculated according to the definitions 3-4, and the sample with the maximum density is found
Figure BDA0001943331990000074
As initial centre C of the first class1Deleting samples lying in the density radius, i.e.
Figure BDA0001943331990000075
W=W-W1
Repeating the above principle, and searching the sample with the maximum density in W again
Figure BDA0001943331990000076
Take it as the initial center of the C category, and order it
Figure BDA0001943331990000077
And so on until finding K initial clustering centers C1,C2,…,CK
Using the euclidean distance between vectors as the basis for classification, the calculation formula is as follows:
Figure BDA0001943331990000078
wherein d isijAnd n is the dimension of each standard vector, wherein the Euclidean distance is between the ith standard vector and the jth standard vector.
Has the beneficial effects that:
the technical scheme is that photovoltaic electric stations which have spatial correlation with power stations to be predicted in the grouped power stations are screened, ARIMA models are established according to weather types, the ARIMA models are matched with forecast information provided by a weather forecast department, and photovoltaic ultra-short-term power prediction is achieved by utilizing corresponding models. On the basis of introducing relevant power station data, classifying weather by historical output data, referring to weather forecast given by a weather department, selecting a corresponding weather model for power forecast, and having self-adaptability in terms of weather change.
According to the technical scheme, the user photovoltaic under each type of weather is partitioned according to the region by using a cluster analysis method, the output consistency of different regions is analyzed, the clustering position of the user photovoltaic is optimized, the most representative reference power station is selected as the construction position of a weather monitoring point or the reference position of a weather station for purchasing weather data, and the power of each user photovoltaic in the cluster is predicted by using the least weather data, so that the position selection of the weather station is optimized to ensure the photovoltaic prediction precision, the cost for introducing the weather data is reduced, and the economy is improved; in addition, even if no meteorological station is added, the meteorological consistency of the large-scale distributed power station is grouped, and the time-space photovoltaic prediction of the grouping can be established by the meteorological-consistent distributed power stations. The accuracy of prediction is effectively improved. .
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is an ARIMA modeling flow of the present invention.
Fig. 3 is a flow chart of photovoltaic power generation user group division according to the present invention.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the drawings in the specification.
According to the technical scheme, firstly, based on the proposed large-scale regional photovoltaic clustering method, photovoltaic power stations which have spatial correlation with power stations to be predicted in the clustering power stations are further screened, ARIMA models are established according to weather types and are matched with forecast information provided by a weather forecast department, and ultra-short-term power prediction of photovoltaic power for 15 minutes is achieved by using corresponding models.
As shown in fig. 1, a distributed photovoltaic prediction method based on an ARIMA model of spatial correlation includes the following steps:
1) acquiring actual output data of the distributed photovoltaic, and intercepting historical output data of the photovoltaic output effective time;
2) per-unit processing the actual output data of each user;
3) dividing weather types according to the average level of the daily output;
4) calculating rank correlation coefficients of historical output data of the power station to be predicted and other power stations based on photovoltaic output data of different weather types;
5) selecting N power stations with rank correlation coefficients larger than a set value and/or best correlation as correlation slave stations and incorporating the power stations into ARIMA models based on spatial correlation to establish prediction models of different weather types;
6) combining the weather types of the daily forecast given by the meteorological department, selecting a prediction model corresponding to the weather for output prediction, and if no correlation power station is matched, performing ARIMA modeling by using the data of the power station to be predicted according to the weather types without considering the correlation;
7) acquiring forecast information provided by a weather forecast department in a photovoltaic output area to be forecasted; and matching is carried out according to forecast information provided by a weather forecast department, and photovoltaic ultra-short term power prediction is realized by utilizing a corresponding model.
The technical scheme is based on the proposed large-scale regional photovoltaic clustering method, the photovoltaic power stations which have spatial correlation with the power station to be predicted in the clustering power stations are further screened, ARIMA models are established according to weather types and are matched with the forecast information provided by a weather forecast department, and the photovoltaic ultra-short-term power prediction is realized by using the corresponding models. On the basis of introducing relevant power station data, classifying weather by historical output data, selecting a corresponding weather model for power forecasting by referring to weather forecasts given by a weather department, and having self-adaptability in responding to weather changes.
The following problems in distributed photovoltaic prediction are further explained below:
first, weather type division
The daily average photovoltaic output belongs to the category of average values, and refers to the average value of photovoltaic output during the period of generating power. Actual photovoltaic statistical data shows that an ideal photovoltaic output curve is subject to symmetrical distribution, so that the daily average photovoltaic output can be used for representing the photovoltaic output level all day, and the daily average photovoltaic output is expressed by a formula:
Figure BDA0001943331990000101
where n is the length of the period during which power can be generated, PiFor the output value of the photovoltaic at the ith moment and for wide-area distributed photovoltaic users, in order to remove the difference caused by different installed capacity dimensions and the like, P should be dealt with firstlyiAnd (5) per unit processing. The average photovoltaic daily output directly reflects the weather conditions of the day, the average photovoltaic daily output can be used as a basis for dividing the weather types, if the level value of the daily output is large, the weather is clear, the daily illumination amplitude is high, the opposite is true, and if the level value of the daily output is low, the weather condition is poor, and the daily illumination amplitude is low. The daily average output threshold corresponding to the weather type is set as shown in table 1.
TABLE 1 weather types and corresponding model parameters
Figure BDA0001943331990000102
Second, volt output spatial correlation matching
The spatial correlation refers to the correlation between output tracks of different photovoltaic power stations in the same dimension, and measures the correlation closeness degree of two variable factors, in the technical scheme, a Spearman rank correlation coefficient is used for measuring the correlation between the two power stations, and the formula is as follows:
Figure BDA0001943331990000111
extracting historical output data of all power stations with the same dimension in the same area, respectively calculating correlation coefficients of the historical output data and the historical output data of the power stations to be predicted based on data samples of different weather classifications, and screening N power stations with the highest correlation number or the power stations with the correlation coefficients larger than a certain set threshold value as correlation slave stations of the power stations to be predicted.
Modeling of three, ARIMA model
The autoregressive moving average model is a commonly used model for fitting a stationary time sequence at present, and is a memory of a system for history self state and noise entering the system, namely, the value of the sequence at the time t is a multivariate linear function of previous p historical observed values and previous q random interferences, and is simply recorded as ARMA (p, q):
xt=α01xt-12xt-2+…+αpxt-pt1εt-12εt-2-…βqεt-q
wherein the error term εtIs random interference at time t and is a white noise sequence with a mean value of zero. Whereas the ARIMA (p, d, q) model is a combination of the d-order difference and ARMA (p, q). During data preprocessing, stability detection needs to be carried out on a sequence, and a non-stable time sequence can form a stable time sequence through finite difference and then is modeled. Using AIC (Akaike information criterion) information criterion to carry out order determination, selecting p and q with minimum AIC value as model order, wherein the AIC calculation formula is as follows
Figure BDA0001943331990000112
The model parameters can be calculated by a least square estimation method, namely, for an objective function:
Figure BDA0001943331990000121
minimized to obtain
Figure BDA0001943331990000122
I.e. the parameters obtained by the least squares estimation.
Finally checking the residual sequence [ epsilon ]tAnd e, if the residual error sequence is a white noise sequence, namely useful information of the sequence is completely extracted by the model parameters, the residual error sequence is an effective model, and if the residual error sequence is not the white noise sequence, the residual useful information in the sequence is to be extracted and the model needs to be fitted again.
ARIMA model based on spatial correlation
According to the technical scheme, the photovoltaic power stations with spatial correlation are introduced to improve the ARIMA model of the power station to be predicted, and the ARIMA model of the power station to be predicted is established by utilizing actual output data of the photovoltaic power stations with correlation so as to improve the prediction accuracy of the model.
Assuming that X power station to be predicted has N photovoltaic power stations with correlation, p and q are the model orders of ARIMA, and the output prediction model is defined as follows:
Figure BDA0001943331990000123
wherein epsilontIs random interference at the current moment, and the coefficient gamma is (alpha)0(l,x)(l,x)(l,i)(l,i)), 1≤i≤N,0≤l≤Ls(ii) a Can be calculated by a least square estimation method:
LSE=||Px-Xγ||2
let the length of the parameter training sample be L,
Figure BDA0001943331990000124
is the actual output data of the power station X to be predicted, X ═ E, Xx,X1,X2,…XN]Is a coefficient matrix composed of N related power stations and the power station to be predicted, wherein E ═ 1,1, …,1]TIs a unit column vector of L x 1,
Figure BDA0001943331990000125
1≤i≤N
Figure BDA0001943331990000131
in order to simplify model calculation, the number of correlation slave stations can be controlled by changing the threshold value of the correlation coefficient when a correlation power station is matched, and the problem that the X matrix dimension is too high to cause the complexity of model calculation is avoided.
Fig. 2 illustrates modeling steps of an ARIMA model, which is the core of the technical scheme, and performs data analysis modeling on the basis of a photovoltaic historical output time sequence to realize photovoltaic power prediction. The ARIMA (p, d, q) model is a combination of the d-order difference and ARMA (p, q). During data preprocessing, stability detection needs to be carried out on the sequence firstly, and the non-stationary time sequence can form a stationary time sequence through finite difference and then be modeled.
As shown in fig. 3, the step of photovoltaic power generation user group division includes
a) Taking the data per hour as a sample, performing per unit processing on the data, intercepting historical output data of 5:00-20:00 points for 15 hours, performing weather type matching identification on the photovoltaic historical output data according to regions, wherein each single power station uses 15-moment weather type indexes to represent the output historical data, and the weather types are as follows: sunny days, cloudy days, rain, thunderstorm rain, light rain, heavy rain, and heavy rainstorm;
b) sequentially carrying out cluster analysis on the data of each integral point to generate a distributed photovoltaic geographical position distribution map under five weather types, and partitioning the geographical position of the photovoltaic output data under each weather type through K-means clustering;
c) under each weather type, the magnitude of the photovoltaic output force belongs to an interval, namely the photovoltaic output forces have similarity with each other; the geographical position blocks of each photovoltaic power station are positioned according to a table look-up method, if the photovoltaic power stations belong to a geographical position block under the five weather types, only a proper power station is selected from the same geographical block to serve as a primary reference power station, namely under any weather type, the output of the photovoltaic power station follows the reference power station and is called a harmonious power station; if the photovoltaic power station belongs to different geographical blocks under different weather types, namely belongs to different reference power stations, namely called dissonant power stations, the photovoltaic power station needs to be additionally selected as a reference power station;
d) calculating the ratio of the number of the dissonant power stations to the total power stations in the classification K value setting range, and determining the optimal K value of the clustering analysis according to the ratio;
e) and performing cluster analysis on all distributed photovoltaic geographic positions again according to the K value to obtain a result, namely the result is the regionalized display of the wide-area distributed photovoltaic division group with spatial correlation, and a photovoltaic power generation user group division result is obtained.
The technical scheme provides a basis for the least deployment of meteorological sites or the power prediction of multi-photovoltaic users based on space-time association; firstly, the influence of weather on photovoltaic output is divided into two types of atmospheric climate and microclimate: the atmospheric climate is mainly influenced by sunshine or five types of weather types and is divided according to the proportion of the actual photovoltaic output to the rated output, so that the historical data time period is divided into five types of weather type sample groups; the microclimate is regarded as generalized microclimate influences such as photovoltaic installation elevation, temperature, humidity and surrounding geographic environment, and the five historical weather type sample groups are subjected to spatial correlation cluster analysis to obtain photovoltaic region division of the user; and determining an optimal region blocking scheme as a user photovoltaic grouping strategy by integrating the number of user photovoltaic points which are not grouped in the blocks and the weather consistency of the sub-regions. According to the technical scheme, the user photovoltaic under each type of weather is partitioned according to regions by using a cluster analysis method, the output consistency of different regions is analyzed, the clustering position of the user photovoltaic is optimized, the most representative reference power station is selected as the construction position of a weather monitoring point or the reference position of a weather station for purchasing weather data, and the power of each user photovoltaic in a cluster is predicted by using the least weather data, so that the position selection of the weather station is optimized to ensure the photovoltaic prediction precision, the cost for introducing the weather data is reduced, and the economy is improved; in addition, even if no meteorological station is added, the meteorological consistency of the large-scale distributed power station is grouped, and the time-space photovoltaic prediction of the grouping can be established by the meteorological-consistent distributed power stations.
The photovoltaic power generation user group division mainly adopts a K-means clustering method, data are divided into a plurality of groups according to the distance or similarity of the data, and the division principle is that samples in the groups are minimized and the distance between the groups is maximized. The specific steps of the algorithm are as follows:
1) and (3) data cleaning, namely performing quality analysis on the original data, including data missing value analysis, data abnormal value processing and the like.
2) And (4) preprocessing the data, normalizing and standardizing the data, and eliminating the difference between the dimensions.
3) And (4) extracting the clustering features, namely extracting the most effective clustering features from the data and converting the most effective clustering features into feature vectors.
4) And clustering, namely selecting the optimal clustering number and distance function aiming at the characteristic vector, and performing clustering or grouping.
5) And (4) clustering evaluation, namely selecting a proper evaluation function for evaluating the clustering effect.
The following problems in the division of photovoltaic power generation user groups are further explained below:
the correlation principle of the photovoltaic output process and weather is as follows:
1) climatic effect
Due to numerous photovoltaic output influence factors, the prediction accuracy of the photovoltaic output influence factors is closely related to the weather state. The solar irradiance and the photovoltaic output in the photovoltaic power generation capacity influence factor have the largest correlation, even linear correlation, and are the main influence factors, namely the atmospheric climate influence.
2) Influence of geographical microclimate
Under the same climatic conditions, microclimate factors such as temperature, humidity and the terrain where the photovoltaic is located have an irrespective effect on the photovoltaic output, under the same climatic conditions, the output process characteristics of the photovoltaic belonging to a certain region are similar, and due to the influence of the geographical characteristics microclimate, the photovoltaic process characteristics of different regions have deviation, so that the microclimate influence is formed.
Secondly, determining the weather state:
because the photovoltaic power station lacks historical meteorological data, the characteristic vector of the type of the meteorological data extracted by the historical data of photovoltaic output is the key of clustering. The illumination intensity directly influences the photovoltaic output, and the illumination intensity is at the maximum value due to less cloud amount in fine days, so that the maximum ratio of the reference value of the actual daily power generation amount and the daily rated power generation amount of the photovoltaic output can be reflected to a certain extent, and the ratio of the reference value of the actual daily power generation amount and the daily rated power generation amount of the photovoltaic output gradually decreases along with the decrease of the illumination intensity. Therefore, the ratio of the daily actual power generation amount to the daily rated power generation amount is provided as a weather type index K, and during discrete sampling, the daily actual power generation amount is a sampling value with a daily interval of 15 minutes, and then:
Figure BDA0001943331990000161
wherein i is a serial number of a photovoltaic user, j is a photovoltaic daily collection point number, P (i, j) is a discrete sampling value of the ith photovoltaic user at the moment j, and PmaxIs a reference value of daily rated power generation, and is estimated from a historical maximum value of a daily power generation discrete sampling value due to the lack of rated power generation data. Assuming data is collected every 15 minutes, there are 4 × 24-96 points in a day, i.e., j-1, 2, …, 96.
Classifying the weather according to the ratio of the actual daily generated energy to the daily rated generated energy reference value, wherein the distribution intervals and the corresponding five weather types are shown in the table 1:
TABLE 1 weather type index vs. weather type
Figure BDA0001943331990000162
Figure BDA0001943331990000171
Thirdly, selecting an initial central position:
the cluster analysis result fluctuates depending on the initial cluster center and the cluster number, and has a certain instability.The selection of an appropriate initial clustering center position is crucial to the analysis of clustering results. Suppose the dataset to be clustered is X ═ Xi|xi∈RPI is 1,2, …, n, and the center of K initial positions is C1,C2,…,CKBy W1,W2,…,WKRepresents the sample sets contained in the K classes, and all sample sets are W.
Define 1 sample xi,xjEuclidean distance between:
Figure BDA0001943331990000172
define 2 samples xiAverage of distances to all samples:
Figure BDA0001943331990000173
defining 3 an average distance of data set samples
Figure BDA0001943331990000174
Define 4 data points xiDensity (x) ofi)
density(x)={p∈C|d(x,p)≤cmean*Theta is the density radius coefficient
Firstly, the density of each sample data in the data set is calculated according to the definitions 3-4, and the sample with the maximum density is found
Figure BDA0001943331990000175
As initial centre C of the first class1Deleting samples lying in the density radius, i.e.
Figure BDA0001943331990000176
W=W-W1
Repetition ofBased on the principle, the sample with the highest density in W is searched again
Figure BDA0001943331990000177
Take it as the initial center of the C category, and order it
Figure BDA0001943331990000181
And so on until finding K initial clustering centers C1,C2,…,CK
Four, clustering basis
The clustering criterion is a condition for data classification. Herein, the euclidean distance between vectors is used as a basis for classification, and the calculation formula is as follows:
Figure BDA0001943331990000182
wherein d isijAnd n is the dimension of each standard vector, wherein the Euclidean distance is between the ith standard vector and the jth standard vector.
Fifth, area division process
And (3) providing the historical output data of distributed photovoltaic users in a certain city in 2017, 6-8 months and 92 days, and intercepting the historical data of 8 hours with an interval of 1 hour from 9 am to 5 pm as a data source.
In the morning of 11: for example 00, firstly, weather type indexes are subjected to weather type matching identification on photovoltaic historical output data according to regions; then dividing sub-regions for the geographic position of the photovoltaic output data under each type of weather type through K-means clustering; the cluster number range is set to K ═ 3, 10. The geographical position distribution of the photovoltaic users after clustering under each weather type is shown, wherein the number of the geographical position clustering blocks is 6; each sub-region is numbered 1-6 for ease of distinction.
The magnitude of the photovoltaic contribution for each weather type is subordinate to a geographic region, i.e., the photovoltaic contributions for that region have similarities to each other. The geographical position area of each user photovoltaic is respectively positioned, if the user photovoltaic belongs to a determined geographical position area under the five weather types, only a proper power station is selected from the same geographical area to serve as a primary reference power station, namely under any weather type, the output of the user photovoltaic follows the same reference power station, and the power station is called a harmonious power station. If the weather types are different, the user photovoltaic is subordinate to different geographical areas, namely, the user photovoltaic is subordinate to different reference power stations, and the user photovoltaic is called an inharmonic power station; for an anharmonic power station, it is difficult to follow the same reference power station for different weather types. And calculating the number ratio of the photovoltaic slave stations covered by each area and the number ratio of the discordant power stations in all the power stations, as shown in the table 2.
Ratio of harmonious power station to discordant power station in period 211: 00
Figure BDA0001943331990000191
As the number of geographical location block classes increases, the proportion of the anharmonic power station does not necessarily increase (or decrease) as the number of cluster classes increases; according to the analysis of the county case, the fluctuation is shown, for example, the number of the discordant power stations with K equal to 8 is smaller than that with K equal to 7.
With the increase of the number of the geographical position block classes, the area of the region is reduced, the variance of the weather type index is gradually reduced, and the weather in the region tends to be uniform, so that the area of the divided sub-region is not suitable to be too large by considering the influence of micro-terrain and micro-weather. Therefore, the proportion of incoordination power stations and the consistency of weather conditions are comprehensively considered, in the data samples of 15 minutes, the photovoltaic groups of users with the clustering number of 8 are the optimal division, and the method for selecting the representative stations from the data samples at other moments is the same as that described above, so that the optimal division numbers obtained through optimization are K-7, K-8 and K-9 under the condition that the data samples at different moments are obtained.
Optimal classification of consumer photovoltaic groups
The calculation results of different classification quantities K based on the photovoltaic historical data of the user are shown in a table 3; it can be seen that when the optimal classification K is 7, both errors are minimum values, which indicates that the preferred representative power plant historical output data in such a region distribution is closest to the fluctuation situation of the region.
TABLE 3 results of two error comparisons
Figure BDA0001943331990000201
The distributed photovoltaic prediction method based on the ARIMA model of the spatial correlation shown in fig. 1 to 3 is a specific embodiment of the present invention, has embodied the substantial features and advantages of the present invention, and can be modified equivalently in shape, structure and the like according to the practical use requirements and under the teaching of the present invention, which are within the protection scope of the present solution.

Claims (8)

1. A distributed photovoltaic prediction method based on an ARIMA model of spatial correlation is characterized by comprising the following steps:
1) acquiring actual output data of the distributed photovoltaic, and intercepting historical output data of the photovoltaic output effective time;
2) per-unit processing the actual output data of each user;
3) dividing weather types according to the average level of the daily output;
4) calculating rank correlation coefficients of historical output data of the power station to be predicted and other power stations based on photovoltaic output data of different weather types;
5) selecting N power stations with rank correlation coefficients larger than a set value or the best correlation as correlation slave stations, and incorporating the power stations into an ARIMA model based on spatial correlation to establish prediction models of different weather types;
6) combining the weather types of the daily forecast given by the meteorological department, selecting a prediction model corresponding to the weather for output prediction, and if no correlation power station is matched, dividing the weather types by using the data of the power station to be predicted to perform ARIMA modeling without considering the correlation;
in step 4), Spearman rank correlation coefficients are used to measure the correlation between two stations, the formula is as follows:
Figure RE-FDA0003536783050000011
extracting historical output data of all power stations with the same dimension in the same area, respectively calculating correlation coefficients of the historical output data and historical output data of power stations to be predicted based on data samples classified by different weather, and screening N power stations with the highest correlation coefficients or the power stations with the correlation coefficients larger than a certain set threshold value as correlation slave stations of the power stations to be predicted;
the power station X output prediction model to be predicted is as follows:
Figure RE-FDA0003536783050000021
wherein epsilontIs random interference at the current moment, and the coefficient gamma is (alpha)0(l,x)(l,x)(l,i)(l,i)),1≤i≤N,0≤l≤Ls(ii) a N is the number of photovoltaic power stations with correlation, L is the parameter training sample length, p and q are the model orders of ARIMA,
the coefficient gamma is calculated by a least square estimation method to obtain:
LSE=||Px-Xγ||2
Figure RE-FDA0003536783050000022
is the actual output data of the power station X to be predicted, X ═ E, Xx,X1,X2,…XN]Is a coefficient matrix composed of N related power stations and the power station to be predicted, wherein E ═ 1,1, …,1]TIs a unit column vector of L x 1,
Figure RE-FDA0003536783050000023
1≤i≤N;
Figure RE-FDA0003536783050000024
2. the distributed photovoltaic prediction method based on the ARIMA model of spatial correlation as claimed in claim 1, characterized in that: in step 5), the photovoltaic power station with the correlation value larger than 0.8 is extracted as a correlation photovoltaic slave station.
3. The distributed photovoltaic prediction method based on the ARIMA model of spatial correlation as claimed in claim 1, characterized in that: in the step 3), the photovoltaic daily average output is used for representing the photovoltaic output level of the whole day, and the calculation formula is as follows:
Figure RE-FDA0003536783050000025
n is the length of the power generation time period, PiThe output value of the photovoltaic is the output value of the photovoltaic at the ith moment;
when P is presentaverageJudging whether the weather type is sunny when the weather type is more than or equal to 0.4; when P is more than or equal to 0.3averageIf the weather type is less than 0.4, judging that the weather type is cloudy; when P is more than or equal to 0.2averageIf the weather type is less than 0.3, judging the weather type is cloudy; when P is more than or equal to 0averageIf the weather type is less than 0.2, judging that the weather type is rainy.
4. The distributed photovoltaic prediction method based on the ARIMA model of spatial correlation as claimed in claim 1, characterized in that: the prediction model adopts an ARIMA (p, d, q) model, and is a combination of d-order difference and ARMA (p, q); during data preprocessing, stability detection needs to be carried out on a sequence, and a non-stable time sequence can form a stable time sequence through finite difference and then is modeled; using AIC (Akaike information criterion) information criterion to carry out order determination, selecting p and q with minimum AIC value as model order, wherein the AIC calculation formula is as follows
Figure RE-FDA0003536783050000031
The model parameters can be calculated by a least square estimation method, namely, for an objective function:
Figure RE-FDA0003536783050000032
minimized to obtain
Figure RE-FDA0003536783050000033
Namely parameters obtained by least square estimation;
finally checking the residual sequence [ epsilon ]tAnd e, if the residual error sequence is a white noise sequence, namely useful information of the sequence is completely extracted by the model parameters, the residual error sequence is an effective model, and if the residual error sequence is not the white noise sequence, the residual useful information in the sequence is to be extracted and the model needs to be fitted again.
5. The distributed photovoltaic prediction method based on the ARIMA model of spatial correlation as claimed in claim 1, characterized in that: before distributed photovoltaic prediction is carried out, large-scale regional photovoltaic clustering is carried out on distributed photovoltaic, photovoltaic power stations which have spatial correlation with power stations to be predicted in clustered power stations are further screened, weather types are divided, ARIMA models are built, the ARIMA models are matched with forecast information provided by a weather forecast department, and short-term power prediction of the photovoltaic is realized by utilizing corresponding models.
6. The distributed photovoltaic prediction method based on the ARIMA model of spatial correlation as claimed in claim 5, characterized in that: the large-scale regional photovoltaic clustering of distributed photovoltaics comprises the following steps:
a) taking the data per hour as a sample, performing per unit processing on the data, intercepting historical output data of 5:00-20:00 points for 15 hours, performing weather type matching identification on the photovoltaic historical output data according to regions, wherein each single power station uses 15-moment weather type indexes to represent the output historical data, and the weather types are as follows: first, sunny day, cloudy in sunny day, second, cloudy in cloudy day, third, cloudy day, fourth, gusty rain, thunderstorm rain, light rain, fifth, heavy rain, and heavy rain;
b) sequentially carrying out cluster analysis on the data of each integral point to generate a distributed photovoltaic geographical position distribution map under five weather types, and partitioning the geographical position of the photovoltaic output data under each weather type through K-means clustering;
c) under each weather type, the magnitude of the photovoltaic output is subordinate to an interval, namely the photovoltaic outputs have similarity with each other; the geographical position blocks of each photovoltaic power station are positioned according to a table look-up method, if the photovoltaic power stations belong to one geographical position block under the five weather types, only a proper power station is selected from the same geographical block to serve as a primary reference power station, namely under any weather type, the output of the photovoltaic power station follows the reference power station and is called a harmonious power station; if the photovoltaic power station belongs to different geographical blocks under different weather types, namely belongs to different reference power stations, namely called dissonant power stations, the photovoltaic power station needs to be additionally selected as a reference power station;
d) calculating the ratio of the number of the dissonant power stations to the total power stations in the classification K value setting range, and determining the optimal K value of the clustering analysis according to the ratio;
e) and performing cluster analysis on all distributed photovoltaic geographic positions again according to the K value to obtain a result, namely the regional display of the wide-area distributed photovoltaic compartment groups with spatial correlation, and obtaining photovoltaic power generation user group division results.
7. The distributed photovoltaic prediction method based on the ARIMA model of spatial correlation as claimed in claim 6, characterized in that:
when the weather types are matched, classifying the weather according to the proportion value k of the actual daily generated energy and the daily rated generated energy reference value, distributing the intervals and corresponding five types of weather types, and when k is more than or equal to 1 and less than 0.8, determining that the weather type is sunny and cloudy in sunny days; when k is more than or equal to 0.8 and less than 0.6, the weather type is determined to be cloudy and cloudy; when k is more than or equal to 0.6 and less than 0.4, the weather type is considered as cloudy; when k is more than or equal to 0.4 and less than 0.2, the weather type is considered as rain fall, thunderstorm rain and light rain; when k is more than or equal to 0.2 and less than 0, the weather type is considered as heavy rain and heavy rainstorm;
when discrete sampling is carried out, the daily actual power generation amount is a sampling value of a daily interval of 15 minutes, and then:
Figure RE-FDA0003536783050000051
wherein i is a serial number of a photovoltaic user, j is a photovoltaic daily collection point number, P (i, j) is a discrete sampling value of the ith photovoltaic user at the moment j, and PmaxThe daily rated power generation reference value is estimated from the historical maximum value of the daily power generation discrete sampling value due to the lack of the rated power generation data; when data is collected every 15 minutes, there are 4 × 24 ═ 96 points in one day, i.e., j ═ 1,2, …, 96.
8. The method according to claim 6, wherein the distributed photovoltaic prediction based on the ARIMA model of spatial correlation comprises: the clustering analysis result fluctuates depending on the initial clustering center and the clustering number, and has certain instability; selecting a proper initial clustering center position is important for analyzing a clustering result; suppose the dataset to be clustered is X ═ Xi|xi∈RPI is 1,2, …, n, and the center of K initial positions is C1,C2,…,CKBy W1,W2,…,WKRepresenting the sample sets contained in the K classes, wherein all the sample sets are W;
define 1 sample xi,xjEuclidean distance between:
Figure RE-FDA0003536783050000061
define 2 samples xiAverage of distances to all samples:
Figure RE-FDA0003536783050000062
defining 3 mean distances of data set samples
Figure RE-FDA0003536783050000063
Define 4 data points xiDensity (x) ofi)
density(x)={p∈C|d(x,p)≤cmean*θ}
Theta is a density radius coefficient;
firstly, the density of each sample data in the data set is calculated according to the definitions 3-4, and the sample with the maximum density is found
Figure RE-FDA0003536783050000064
As initial centre C of the first class1Deleting samples lying in the density radius, i.e.
Figure RE-FDA0003536783050000065
W=W-W1
Repeating the above principle, and searching the sample with the maximum density in W again
Figure RE-FDA0003536783050000066
Take it as the initial center of the C category, and order it
Figure RE-FDA0003536783050000067
And so on until finding K initial clustering centers C1,C2,…,CK
Using the euclidean distance between vectors as a basis for classification, the calculation formula is as follows:
Figure RE-FDA0003536783050000068
wherein d isijAnd n is the dimension of each standard vector, wherein the Euclidean distance is between the ith standard vector and the jth standard vector.
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