CN110852492A - Photovoltaic power ultra-short-term prediction method for finding similarity based on Mahalanobis distance - Google Patents

Photovoltaic power ultra-short-term prediction method for finding similarity based on Mahalanobis distance Download PDF

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CN110852492A
CN110852492A CN201911021479.6A CN201911021479A CN110852492A CN 110852492 A CN110852492 A CN 110852492A CN 201911021479 A CN201911021479 A CN 201911021479A CN 110852492 A CN110852492 A CN 110852492A
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杨茂
冯帆
杨滢璇
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State Grid Corp of China SGCC
China Electric Power Research Institute Co Ltd CEPRI
Northeast Electric Power University
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Abstract

According to the photovoltaic power ultra-short term prediction calculation method based on similarity finding of the Mahalanobis distance, the weather type division based on the original data is adopted; analyzing main meteorological factors influencing the photovoltaic power under various weathers by utilizing the grey correlation degree; selecting 34 similar days with the shortest distance based on the Mahalanobis distance and comparing the similar days with the traditional Euclidean distance; and inputting the main meteorological factor data of similar days into a radial basis function neural network for ultra-short-term prediction and the like. The prediction method is scientific and reasonable, the prediction process is simple, the prediction precision is high, the physical significance is clear, the prediction result is effective, and the practicability is high.

Description

Photovoltaic power ultra-short-term prediction method for finding similarity based on Mahalanobis distance
Technical Field
The invention relates to the field of photovoltaic power prediction, in particular to a photovoltaic power ultra-short-term prediction method based on similarity found by Mahalanobis distance.
Background
Photovoltaic power generation has become a new growing point for renewable energy power generation following wind power generation. Photovoltaic power generation is to convert solar energy resources into electric energy required by people by utilizing equipment. The sunlight has day and night periodicity, and is easily influenced by weather and meteorology, so the photovoltaic power has the characteristics of intermittence, fluctuation and randomness. The accurate prediction of the photovoltaic power directly influences the safe and economic operation of the power grid.
The photovoltaic power ultra-short-term prediction refers to prediction from a prediction moment to the future of 15 minutes to 4 hours, and the time resolution is 15 minutes. The significance of the ultra-short term prediction lies in that a plan curve is corrected in a rolling mode, and active output is adjusted in time.
The existing ultra-short term prediction generally establishes a mapping relation between historical input data and future power output, and can directly predict future power values according to the historical data, so that higher prediction accuracy is obtained. For the artificial intelligence method, the method has great advantages for processing the nonlinear time sequence, but cannot reflect the dynamic characteristics of the system. Overall, the prediction cannot track future power trends and is affected by the training data set.
Disclosure of Invention
The invention aims to provide a photovoltaic power ultra-short-term prediction method which is scientific and reasonable, clear in physical significance, capable of calculating numerical weather forecast, simple and practical, higher in precision and capable of finding similarity based on the Mahalanobis distance.
The technical scheme adopted for realizing the aim of the invention is as follows: a photovoltaic power ultra-short term prediction method based on similarity finding of Mahalanobis distance is characterized by comprising the following steps: it comprises the following steps:
1) division of weather types
The weather types are divided into three categories by utilizing k-means clustering analysis, namely sunny days, cloudy days and rainy days,
the optimization objective of k-means clustering is defined as formula (1):
Figure BDA0002247360340000011
in the formula, xnFor each meteorological datum; mu.skIs a clustering center;
Figure BDA0002247360340000012
j is minimized through several iterations;
2) gray correlation analysis calculation
Respectively selecting power sequences as reference sequences X under corresponding weather types0＝{x0(1),x0(2),…,x0(n) }; each meteorological factor sequence is a comparison sequence Xi＝{xi(1),xi(2),…,xi(n)}，
The sequence of differencing is formula (2)
Δi＝|x0(k)-xi(k)| (2)
Calculating the maximum and minimum values of the two poles and recording the maximum and minimum values as
Figure BDA0002247360340000021
The correlation coefficient is the formula (3)
Figure BDA0002247360340000022
Wherein ξ is a resolution factor, generally 0.5,
calculating the degree of correlation of gray
The larger the grey correlation value is, the higher the representative correlation is, and four meteorological factors with larger correlation are selected as main factors influencing the photovoltaic power;
3) finding optimal similar day based on Mahalanobis distance and Euclidean distance
Assume that the two sample sequences are:
Figure BDA0002247360340000024
the method for finding the optimal similar day by using the Euclidean distance is shown as the formula (5):
Figure BDA0002247360340000025
respectively adding the Euclidean distances of the main influence factors corresponding to the prediction day and the historical sample day, searching 34 sampling days with the shortest distance, regarding the sampling days as the optimal similar days,
the method for finding the optimal similar day by using the mahalanobis distance is as follows:
first, a sample is calculated
Figure BDA0002247360340000026
And
Figure BDA0002247360340000027
covariance of formula (6)
In the formula, mux、μyRespectively represent
Figure BDA0002247360340000029
And
Figure BDA00022473603400000210
mean value of (a)x＝E(xi),μy＝E(yi)；
Then two samples from the same distribution
Figure BDA00022473603400000211
Andthe similarity of (d) is expressed by mahalanobis distance as formula (7):
Figure BDA00022473603400000213
wherein Σ isAnd
Figure BDA00022473603400000215
the covariance of (a);
respectively adding the Mahalanobis distances of the main influence factors corresponding to the prediction day and the historical sample day, searching 34 sampling days with the shortest distance, and taking the sampling days as the optimal similar days;
4) reconstruction of training set matrix using similar days
Screening the similar days meeting the requirements day by day to ensure that no abnormal data section exists, and taking NWP data corresponding to the similar days to form a new input matrix:
in the formula (I), the compound is shown in the specification,
Figure BDA0002247360340000032
the radiation vector is short-wave radiation vector,
Figure BDA0002247360340000033
is a temperature vector ofThe relative humidity vector of the water in the water tank,
Figure BDA0002247360340000035
is a wind speed vector;
5) simulation calculation
Simulation input quantity: analyzing the measured data of the electric field to determine the total installed capacity of the electric field; inputting historical data: total radiation, temperature, humidity, wind speed; inputting predicted current day NWP data: short wave radiation, temperature, humidity, wind speed; the data sampling interval is 15 min; obtaining a photovoltaic power ultra-short term prediction result of the daily prediction time period according to the steps 1) to 4);
6) error analysis
The accuracy of the prediction result is defined as formula (11):
in the formula, PMTo predict photovoltaic power; pPActual photovoltaic power; n is the number of the predicted points; the Cap is the starting capacity of the photovoltaic power station,
the yield is defined by the formula (10):
Figure BDA0002247360340000037
in the formula, if
Figure BDA0002247360340000038
Then B isk1 is ═ 1; if it is
Figure BDA0002247360340000039
Then B isk＝0，
The root mean square error of the prediction result is formula (11):
Figure BDA00022473603400000310
the mean absolute error is formula (12):
Figure BDA00022473603400000311
inputting simulation input quantity according to the step 5), carrying out error calculation on the predicted power calculated by the model and the actual measured power through the error evaluation standard formula (9) -formula (12) in the step 5), and obtaining the predicted root mean square error, the average absolute error, the qualification rate and the accuracy rate.
According to the photovoltaic power ultra-short term prediction calculation method based on similarity finding of the Mahalanobis distance, the weather type division based on the original data is adopted; analyzing main meteorological factors influencing the photovoltaic power under various weathers by utilizing the grey correlation degree; selecting 34 similar days with the shortest distance based on the Mahalanobis distance and comparing the similar days with the traditional Euclidean distance; and inputting the main meteorological factor data of similar days into a radial basis function neural network for ultra-short-term prediction and the like. The prediction method is scientific and reasonable, the prediction process is simple, the prediction precision is high, the physical significance is clear, the prediction result is effective, and the practicability is high.
Drawings
FIG. 1 shows two methods to obtain a comparison graph of the similar daily power and the predicted daily power;
FIG. 2 is a block diagram of a similar photovoltaic power ultra-short term prediction based on Mahalanobis distance;
FIG. 3 is a diagram illustrating comparison between predicted results and actual values for finding similar days based on two distances.
Detailed Description
The following further explains a photovoltaic power ultra-short term prediction calculation method based on similarity found by mahalanobis distance in the present invention with reference to the accompanying drawings and specific embodiments.
With reference to fig. 1 to fig. 3, the ultrashort-term prediction method for finding similar photovoltaic power based on mahalanobis distance in the present invention includes the following steps:
1) division of weather types
The weather types are divided into three categories by utilizing k-means clustering analysis, namely sunny days, cloudy days and rainy days,
the optimization objective of k-means clustering is defined as formula (1):
Figure BDA0002247360340000041
in the formula, xnFor each meteorological datum; mu.skIs a clustering center;
j is minimized through several iterations;
2) gray correlation analysis calculation
Respectively selecting power sequences as reference sequences X under corresponding weather types0＝{x0(1),x0(2),…,x0(n) }; each meteorological factor sequence is a comparison sequence Xi＝{xi(1),xi(2),…,xi(n)}，
The sequence of differencing is formula (2)
Δi＝|x0(k)-xi(k)| (2)
Calculating the maximum and minimum values of the two poles and recording the maximum and minimum values as
Figure BDA0002247360340000051
The correlation coefficient is the formula (3)
Figure BDA0002247360340000052
Wherein ξ is a resolution factor, generally 0.5,
calculating the degree of correlation of gray
Figure BDA0002247360340000053
The larger the grey correlation value is, the higher the representative correlation is, and four meteorological factors with larger correlation are selected as main factors influencing the photovoltaic power;
3) finding optimal similar day based on Mahalanobis distance and Euclidean distance
Assume that the two sample sequences are:
the method for finding the optimal similar day by using the Euclidean distance is shown as the formula (5):
Figure BDA0002247360340000055
respectively adding the Euclidean distances of the main influence factors corresponding to the prediction day and the historical sample day, searching 34 sampling days with the shortest distance, regarding the sampling days as the optimal similar days,
the method for finding the optimal similar day by using the mahalanobis distance is as follows:
first, a sample is calculatedAndcovariance of formula (6)
Figure BDA0002247360340000058
In the formula, mux、μyRespectively representAnd
Figure BDA00022473603400000510
mean value of (a)x＝E(xi),μy＝E(yi)；
Then two samples from the same distribution
Figure BDA00022473603400000511
And
Figure BDA00022473603400000512
the similarity of (d) is expressed by mahalanobis distance as formula (7):
Figure BDA00022473603400000513
wherein Σ isAndthe covariance of (a);
respectively adding the Mahalanobis distances of the main influence factors corresponding to the prediction day and the historical sample day, searching 34 sampling days with the shortest distance, and taking the sampling days as the optimal similar days;
4) reconstruction of training set matrix using similar days
Screening the similar days meeting the requirements day by day to ensure that no abnormal data section exists, and taking NWP data corresponding to the similar days to form a new input matrix:
in the formula (I), the compound is shown in the specification,
Figure BDA0002247360340000062
the radiation vector is short-wave radiation vector,
Figure BDA0002247360340000063
is a temperature vector of
Figure BDA0002247360340000064
The relative humidity vector of the water in the water tank,
Figure BDA0002247360340000065
is a wind speed vector;
5) simulation calculation
Simulation input quantity: analyzing the measured data of the electric field to determine the total installed capacity of the electric field; inputting historical data: total radiation, temperature, humidity, wind speed; inputting predicted current day NWP data: short wave radiation, temperature, humidity, wind speed; the data sampling interval is 15 min; obtaining a photovoltaic power ultra-short term prediction result of the daily prediction time period according to the steps 1) to 4);
6) error analysis
The accuracy of the prediction result is defined as formula (11):
Figure BDA0002247360340000066
in the formula, PMTo predict photovoltaic power; pPActual photovoltaic power; n is the number of the predicted points; the Cap is the starting capacity of the photovoltaic power station,
the yield is defined by the formula (10):
Figure BDA0002247360340000067
in the formula, ifThen B isk1 is ═ 1; if it is
Figure BDA0002247360340000069
Then B isk＝0，
The root mean square error of the prediction result is formula (11):
the mean absolute error is formula (12):
Figure BDA00022473603400000611
inputting simulation input quantity according to the step 5), carrying out error calculation on the predicted power calculated by the model and the actual measured power through the error evaluation standard formula (9) -formula (12) in the step 5), and obtaining the predicted root mean square error, the average absolute error, the qualification rate and the accuracy rate.
Detailed description of the invention
The method takes the measured data and the NWP data of a certain photovoltaic power station as an example for analysis, and the sampling interval is 15 min. The installed capacity of the power station is 30 MW; the evaluation indexes of the prediction results are as follows:
TABLE 1 prediction accuracy statistics
Tab.1 prediction accuracy statistics
The description of the present invention is not intended to be exhaustive or to limit the scope of the claims, and those skilled in the art will be able to conceive of other substantially equivalent alternatives, without inventive step, based on the teachings of the embodiments of the present invention, within the scope of the present invention.

Claims (1)

1. A photovoltaic power ultra-short term prediction method based on similarity finding of Mahalanobis distance is characterized by comprising the following steps: it comprises the following steps:
1) division of weather types
Dividing the weather types into three categories, namely sunny days, cloudy days and rainy days by utilizing k-means clustering analysis, and defining the optimization target of k-means clustering as a formula (1):
Figure FDA0002247360330000011
in the formula, xnFor each meteorological datum; mu.skIs a clustering center;
Figure FDA0002247360330000012
j is minimized through several iterations;
2) gray correlation analysis calculation
Respectively selecting power sequences as reference sequences X under corresponding weather types0＝{x0(1),x0(2),…,x0(n) }; each meteorological factor sequence is a comparison sequence Xi＝{xi(1),xi(2),…,xi(n)}，
The sequence of differencing is formula (2)
Δi＝|x0(k)-xi(k)| (2)
Calculating the maximum and minimum values of the two poles and recording the maximum and minimum values as
Figure FDA0002247360330000013
The correlation coefficient is the formula (3)
Figure FDA0002247360330000014
Wherein ξ is a resolution factor, generally 0.5,
calculating the degree of correlation of gray
Figure FDA0002247360330000015
The larger the grey correlation value is, the higher the representative correlation is, and four meteorological factors with larger correlation are selected as main factors influencing the photovoltaic power;
3) finding optimal similar day based on Mahalanobis distance and Euclidean distance
Assume that the two sample sequences are:
Figure FDA0002247360330000016
the method for finding the optimal similar day by using the Euclidean distance is shown as the formula (5):
Figure FDA0002247360330000017
respectively adding the Euclidean distances of the main influence factors corresponding to the prediction day and the historical sample day, searching 34 sampling days with the shortest distance, regarding the sampling days as the optimal similar days,
the method for finding the optimal similar day by using the mahalanobis distance is as follows:
first, a sample is calculated
Figure FDA0002247360330000021
Andcovariance of formula (6)
Figure FDA0002247360330000023
In the formula, mux、μyRespectively representAnd
Figure FDA0002247360330000025
mean value of (a)x＝E(xi),μy＝E(yi)；
Then two samples from the same distribution
Figure FDA0002247360330000026
And
Figure FDA0002247360330000027
the similarity of (d) is expressed by mahalanobis distance as formula (7):
Figure FDA0002247360330000028
wherein Σ isAnd
Figure FDA00022473603300000210
the covariance of (a);
respectively adding the Mahalanobis distances of the main influence factors corresponding to the prediction day and the historical sample day, searching 34 sampling days with the shortest distance, and taking the sampling days as the optimal similar days;
4) reconstruction of training set matrix using similar days
Screening the similar days meeting the requirements day by day to ensure that no abnormal data section exists, and taking NWP data corresponding to the similar days to form a new input matrix:
Figure FDA00022473603300000211
in the formula (I), the compound is shown in the specification,
Figure FDA00022473603300000212
the radiation vector is short-wave radiation vector,
Figure FDA00022473603300000213
is a temperature vector of
Figure FDA00022473603300000214
The relative humidity vector of the water in the water tank,
Figure FDA00022473603300000215
is a wind speed vector;
5) simulation calculation
Simulation input quantity: analyzing the measured data of the electric field to determine the total installed capacity of the electric field; inputting historical data: total radiation, temperature, humidity, wind speed; inputting predicted current day NWP data: short wave radiation, temperature, humidity, wind speed; the data sampling interval is 15 min; obtaining a photovoltaic power ultra-short term prediction result of the daily prediction time period according to the steps 1) to 4);
6) error analysis
The accuracy of the prediction result is defined as formula (11):
Figure FDA00022473603300000216
in the formula, PMTo predict photovoltaic power; pPActual photovoltaic power; n is the number of the predicted points; the Cap is the starting capacity of the photovoltaic power station,
the yield is defined by the formula (10):
Figure FDA0002247360330000031
in the formula, ifThen B isk1 is ═ 1; if it is
Figure FDA0002247360330000033
Then B isk＝0，
The root mean square error of the prediction result is formula (11):
Figure FDA0002247360330000034
the mean absolute error is formula (12):
Figure FDA0002247360330000035
inputting simulation input quantity according to the step 5), carrying out error calculation on the predicted power calculated by the model and the actual measured power through the error evaluation standard formula (9) -formula (12) in the step 5), and obtaining the predicted root mean square error, the average absolute error, the qualification rate and the accuracy rate.
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Application publication date: 20200228