CN111612244A - QRA-LSTM-based method for predicting nonparametric probability of photovoltaic power before day - Google Patents

QRA-LSTM-based method for predicting nonparametric probability of photovoltaic power before day Download PDF

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CN111612244A
CN111612244A CN202010418956.9A CN202010418956A CN111612244A CN 111612244 A CN111612244 A CN 111612244A CN 202010418956 A CN202010418956 A CN 202010418956A CN 111612244 A CN111612244 A CN 111612244A
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CN111612244B (en
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梅飞
江玉寒
陆继翔
陆进军
顾佳琪
张家堂
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Hohai University HHU
NARI Group Corp
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Abstract

The invention discloses a QRA-LSTM-based photovoltaic power nonparametric probability prediction method, which trains a group of mutually independent long-term and short-term memory network (LSTM) deterministic prediction models by adopting photovoltaic historical data and numerical weather forecast data (NSW), and integrates each independent LSTM prediction model through a quantile regression average algorithm (QRA) to generate a photovoltaic power nonparametric probability prediction model. The nonparametric probability prediction can describe the uncertainty problem which is difficult to reflect by the pure deterministic prediction, and the result has higher reliability. The method can effectively avoid the problems that deterministic prediction and probabilistic prediction are separately seen, and the like, provides important basis for decision scheduling of scheduling personnel, and has great application value and prospect.

Description

QRA-LSTM-based method for predicting nonparametric probability of photovoltaic power before day
Technical Field
The invention belongs to the technical field of photovoltaics, and particularly relates to a method for predicting nonparametric probability of photovoltaic power in the day ahead.
Background
In recent years, the power generation of new energy resources such as photovoltaic and wind power is rapidly developed, and the installed photovoltaic capacity worldwide is increased year by year. However, as the permeability of photovoltaics in the power grid increases, the inherent uncertainty and volatility of photovoltaic power generation presents challenges to the safe operation and power quality of the power grid. In order to absorb the grid-connected power of the photovoltaic as much as possible, the dispatcher needs to fully know the output characteristics of the photovoltaic. The photovoltaic output prediction in the short-term day ahead can give a photovoltaic output prediction value in the future day, and an important basis is provided for decision scheduling of scheduling personnel. The traditional photovoltaic output prediction is mainly based on deterministic prediction and mainly comprises the following steps according to different adopted methods: statistical models, machine learning prediction models, prediction models based on numerical weather forecasts, and prediction models based on sky or satellite clouds. The statistical model mainly comprises a multiple regression model and a time sequence model, the machine learning model mainly comprises a neural network, a support vector machine, a random forest, a long-term memory network (LSTM) and other models, the prediction model based on Numerical weather forecast mainly utilizes information such as horizontal irradiance given by Numerical weather forecast (NWP) and combines the corresponding relation of photovoltaic output and irradiance to obtain photovoltaic output prediction, and the prediction model based on a sky or a satellite cloud picture gives short-term and medium-term prediction of the photovoltaic output through the distribution condition of the cloud picture.
With the occurrence of power system algorithms taking parameter uncertainty into account, such as probability power flow and power system robust optimization scheduling, the traditional deterministic photovoltaic output point prediction has the problem that a reasonable prediction interval and probability density cannot be provided. Probability prediction is an uncertainty prediction, and compared with the traditional prediction, probability prediction can give not only a specific predicted value but also the probability distribution condition of each point. However, the existing method mainly starts from a probability prediction model, and the deterministic prediction and the probability prediction are respectively considered in isolation. In order to combine deterministic prediction and probabilistic prediction, an integrated photovoltaic output probability prediction model is to be proposed.
Disclosure of Invention
In order to solve the technical problems mentioned in the background art, the invention provides a QRA-LSTM-based method for predicting the probability of the nonparametric photovoltaic power before the day.
In order to achieve the technical purpose, the technical scheme of the invention is as follows:
a QRA-LSTM-based method for predicting nonparametric probability of photovoltaic power in the day ahead comprises the following steps:
(1) respectively adopting range normalization on the photovoltaic output data set P, the irradiation data set I and the temperature data set T, and storing respective maximum value and minimum value;
(2) directly connecting the normalized data sets P, I and T in the step (1) in series to form a data set [ P, I, T ], and dividing the data set after being connected in series into a training set and a verification set by taking days as a unit;
(3) constructing a group of LSTM networks with different hidden layer neuron numbers and mutually independent, training by adopting the training sets divided in the step (2), adjusting partial hyper-parameters by utilizing cross validation to obtain a trained LSTM prediction model, and predicting the validation set divided in the step (2) by using the trained LSTM prediction model;
(4) establishing objective functions of quantiles under various probability conditions by using a QRA algorithm and the verification set prediction results obtained in the step (3), and solving each objective function to obtain weight vectors of each independent LSTM prediction model under each quantile;
(5) performing a day-ahead photovoltaic output certainty prediction by using a trained group of independent LSTM prediction models in combination with meteorological data and historical photovoltaic output data, and solving a normalized day-ahead photovoltaic output quantile prediction by using a predicted value and the weight vector obtained in the step (4);
(6) and (4) carrying out reverse normalization on the quantile prediction obtained in the step (5) based on the maximum value and the minimum value stored in the step (1) to obtain a quantile prediction result, so as to realize nonparametric probability prediction.
Further, in the step (3), a group of independent LSTM networks adopts photovoltaic output data of the day before the day to be predicted, irradiation data and air temperature data of the day to be predicted as characteristic inputs, photovoltaic output prediction of the day to be predicted as an output result, and defines
Figure BDA0002496115900000031
The prediction results for each independent LSTM prediction model for the validation set day j data,
Figure BDA0002496115900000032
wherein
Figure BDA0002496115900000033
And representing the prediction results of the independent LSTM prediction models at the ith sampling time of the jth day on the verification set, wherein i is 1,2, …, n represents the sampling times of photovoltaic output in one day, and k represents the number of the independent LSTM prediction models.
Further, in step (4), applying a QRA algorithm to each independent LSTM prediction model to obtain an integrated probabilistic prediction model, where the expression of the model is as follows:
Figure BDA0002496115900000034
in the above formula, the first and second carbon atoms are,
Figure BDA0002496115900000035
the quantile predictive value of the photovoltaic output probability distribution predictive result under the probability q condition is 0<q<1，
Figure BDA0002496115900000036
A vector formed by prediction values of each independent prediction model, wherein t represents a sampling time, and t is 1,2, …, n, wq,tPrediction model for each independent LSTM in q quantilesThe weight vector of (2).
Further, in step (4), an objective function of the q quantile is established:
Figure 4
in the above formula, the first and second carbon atoms are,
Figure 2
solving the objective function for the real value of the verification set at the jth day t sampling moment to obtain wq,tThe optimum value of (c).
Further, in the step (5), a group of trained independent LSTM prediction models is utilized to combine meteorological data and historical photovoltaic output data to carry out prediction on the photovoltaic output certainty before the day to obtain a predicted value
Figure BDA0002496115900000039
Will predict the value
Figure BDA00024961159000000310
And w obtained in step (4)q,tSubstitution into
Figure BDA00024961159000000311
And obtaining the quantile prediction of the normalized photovoltaic output before the day.
Adopt the beneficial effect that above-mentioned technical scheme brought:
(1) the invention provides a novel photovoltaic output nonparametric probability prediction model, the method utilizes photovoltaic output historical data and NWP data to obtain a group of independent LSTM deterministic prediction models, and a quantile regression average algorithm is adopted to realize the establishment of the photovoltaic output nonparametric probability prediction, thereby effectively avoiding the problems of isolated waiting for deterministic prediction and probability prediction;
(2) in the embodiment of the invention, the relation between the pinball loss function of the quantile regression average algorithm integrated probability prediction model and the average absolute error MAE of each independent deterministic model is established;
(3) the method can provide the nonparametric probability predicted value of photovoltaic output before the day, provides an important basis for decision scheduling of scheduling personnel, and has great application value and prospect.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a schematic of a data set at day j in the present invention;
FIG. 3 is a graph showing the predicted results of models in example 2018, 9, 10;
FIG. 4 is a graph of a pre-day photovoltaic output nonparametric probability prediction obtained by using the model of the present invention in an example;
fig. 5 is a graph of the prediction of the photovoltaic output interval before the day (NC 90%) obtained by using the model of the present invention in the example.
Detailed Description
The technical scheme of the invention is explained in detail in the following with the accompanying drawings.
The invention designs a method for predicting nonparametric probability of photovoltaic power in the day ahead, which comprises the following steps as shown in figure 1:
step 1: respectively adopting range normalization on the photovoltaic output data set P, the irradiation data set I and the temperature data set T, and storing respective maximum value and minimum value;
step 2: connecting the data sets P, I and T in series to form a data set, and dividing the data set after being connected in series into a training set and a verification set by taking days as a unit;
and step 3: constructing a group of LSTM networks with different hidden layer units and independent from each other, training by adopting the training set divided in the step 2, adjusting partial hyper-parameters by using cross validation to obtain a trained LSTM prediction model, and predicting the validation set divided in the step 2 by using the trained LSTM prediction model;
and 4, step 4: establishing objective functions of quantiles under various probability conditions by using a Quantile Regression Averaging (QRA) algorithm and the verification set prediction results obtained in the step (3), and solving the objective functions to obtain weight vectors of independent LSTM prediction models under different quantiles;
and 5: carrying out photovoltaic output certainty prediction before the day by using a trained group of independent LSTM prediction models and combining meteorological data and historical photovoltaic output data, and obtaining quantile prediction of photovoltaic output before the day by using a predicted value and the weight vector obtained in the step (4);
step 6: and (4) performing inverse normalization on the quantile prediction obtained in the step (5) based on the maximum value and the minimum value stored in the step (1) to obtain a quantile prediction result, and realizing nonparametric probability prediction.
In step 2, take the data set of the j-th day as an example, as shown in FIG. 2, wherein p1-pnRepresenting the photovoltaic output at n sampling moments, wherein n represents the number of sampling times of the photovoltaic output in one day, and if the sampling interval is 1h, n is 24, i1-i24And T1-T24Representing the hourly horizontal irradiance and temperature prediction given by NWP.
In step 3 above, a set of independent LSTM networks uses photovoltaic output data p for the day before the day to be predicted1,p2,…,pn]Irradiation data [ i ] of the day to be predicted1,i2,…,i24]And gas temperature data [ T1,T2,…,T24]As characteristic input, the photovoltaic contribution prediction of the day to be predicted is taken as output result, as shown in fig. 2. Definition of
Figure BDA0002496115900000051
The prediction results for each independent LSTM prediction model for the validation set day j data,
Figure BDA0002496115900000052
wherein
Figure BDA0002496115900000053
And representing the prediction results of the independent LSTM prediction models at the ith sampling time of the jth day on the verification set, wherein i is 1,2, …, n represents the sampling times of photovoltaic output in one day, and k represents the number of the independent LSTM prediction models.
In step 4, applying QRA to each independent LSTM prediction model to obtain an integrated probabilistic prediction model, where the expression of the model is as follows:
Figure BDA0002496115900000061
in the formula (1), the reaction mixture is,
Figure BDA0002496115900000062
quantile prediction value 0 of photovoltaic output probability distribution prediction result under probability q condition<q<1，
Figure 3
Vector (regression factor) formed by predicted values of each independent prediction model, t represents sampling time, wq,tIs the weight vector of each independent LSTM prediction model in q quantile, w is more than or equal to 0q,t≤1。
Based on QRA algorithm and the prediction result of the verification set in step 3, an objective function of the following q quantiles is established:
Figure 5
in the formula (2), the reaction mixture is,
Figure BDA0002496115900000065
to verify the true value of the set at day j and time t (t ═ 1,2, …, n), w is obtained by minimizing the above equationq,tThe optimum value of (c). Because the QRA is a non-convex optimization problem, an accurate theoretical optimal solution is difficult to provide for the non-convex optimization problem, and the QRA is usually solved by means of a solver or an element heuristic algorithm.
In the step 5, a group of trained independent LSTM prediction models is combined with meteorological data and historical photovoltaic output data to predict the photovoltaic output certainty in the day ahead to obtain a predicted value
Figure BDA0002496115900000066
Will predict the value
Figure BDA0002496115900000067
And step 4, optimizing the obtained wq,tAnd (3) substituting the formula (1) to obtain quantile prediction of photovoltaic output before the day. With the change of q, the complete nonparametric probability prediction and non-parametric probability prediction can be obtainedPrediction Interval (PI) of same Nominal Coverage (NC).
The invention will be illustrated by the following specific examples.
Photovoltaic output data:
in the embodiment, data collected by a self-built photovoltaic power generation system of a certain enterprise in China is adopted, the installation capacity of the photovoltaic system is 2.8MW, the collected data comprises historical photovoltaic output, GHI and air temperature, the collection time is from 2017, 9 and 14 days to 2018, 9 and 13 days, the sampling interval of the photovoltaic output power is 15min, and the time interval of irradiance and temperature data is 1 h. The collected data is screened by abnormal data, and extreme abnormal values are removed. This example runs the following calculations in a MATLAB2018a environment.
And (3) prediction evaluation indexes:
for deterministic prediction, MAPE is usually adopted to measure the effect of prediction, but since the actual value of the photovoltaic output contains more zero or minimal values, when these values are used as denominators, MAPE appears as a maximum or even infinite value. The present invention therefore measures the effect of deterministic predictions using Mean Absolute Error (MAE) and Root Mean Square Error (RMSE), the expressions for MAE and RMSE being defined as follows:
Figure BDA0002496115900000071
Figure BDA0002496115900000072
in the formula, n is the sampling frequency of photovoltaic output, piAnd
Figure BDA0002496115900000073
the real value and the predicted value of the photovoltaic output at the i-th sampling moment are respectively.
Because the probability prediction generates a prediction curve of each quantile, evaluation indexes such as MAE (maximum likelihood estimation) and RMSE (maximum likelihood estimation) in the traditional deterministic prediction obviously cannot be used for measuring the performance of the probability prediction. The pinball loss function is typically used to measure the error of the probabilistic predictions. For q quantile prediction, the pinball loss function is defined as:
Figure BDA0002496115900000074
in the formula ptThe actual value of the photovoltaic output at the moment t,
Figure BDA0002496115900000075
is the predicted value of q quantile at the time t. And L (-) is an evaluation index of the quantile prediction at the time t q, and the smaller L (-) is, the more accurate the probability prediction is obtained.
Winkler score can also be used to measure the error of the probabilistic prediction. Unlike pinball loss function Winklerscore, it focuses more on the evaluation of probability intervals and can simultaneously evaluate the width of the interval and the coverage of the actual value. For a (1- α) × 100% prediction interval, Winkler score is defined as:
Figure BDA0002496115900000081
in the formulat＝Ut-LtWherein U istAnd LtUpper and lower bounds, p, of the prediction interval at time ttAnd the actual photovoltaic output value at the moment t is obtained. A smaller Winkler score represents a prediction interval with higher actual value coverage and smaller interval width.
LSTM-QRA prediction:
the data set is collected for 364 days in total, the data from 1 st to 300 th days are selected as a training set, the data from 301 st and 332 th days are selected as a verification set, and the data from 333 st and 364 th days are selected as a test set. In this embodiment, a set of independent LSTM prediction models is constructed by using 10 different hidden layer unit numbers (hidden unit is 0.25a,0.5a, a,2a,3a,4a,5a,6a,7a,8a, where a represents the dimension of the LSTM input feature). The sampling interval of the data is 15min, n is 96, and the characteristic dimension of the input of the LSTM is 144. The parameters of 10 mutually independent LSTM networks are shown in table 1.
TABLE 1
Number of input units 144
Number of hidden layer units 36,72,144,288,432,576,720,864,1008,1152
Number of output units 96
Learning rate 0.01
Minimum number of iterations 500
The 10 independent LSTM networks were trained using training set data and used to make deterministic predictions of photovoltaic contribution on the validation and test sets, and the effects of deterministic predictions were measured using mae (pu) and rmse (pu), with the test results shown in table 2.
TABLE 2
Prediction model MAE(％) RMSE(％)
LSTM1 31.8874 58.9834
LSTM2 33.1326 63.2188
LSTM3 36.8061 68.5956
LSTM4 34.3431 64.2149
LSTM5 37.6755 71.1089
LSTM6 36.6594 67.8151
LSTM7 36.9296 68.6016
LSTM8 34.2934 64.3060
LSTM9 34.2084 65.3501
LSTM10 32.9212 61.6342
LSTM in Table 21-LSTM10The number of hidden layer units is 36,72,144,288,432,576,720, 864,1008 and 1152. LSTM in Table 21The prediction model has the smallest MAE and RMSE of all independent prediction models, apparently LSTM1The overall prediction performance in the test set is superior to other models. To further study the predicted performance, data of 9/10/2018 was selected as the study subject, and the prediction results of the models are shown in fig. 3 (a) and (b).
As can be seen from FIG. 3, LSTM1May not perform optimally. In order to more intuitively represent the predicted performance of each model in 2018, 9, 10 and the like, the MAE and RMSE of each independent model in 2018, 9, 10 and the like are calculated, as shown in table 3.
TABLE 3
Prediction model MAE(％) RMSE(％)
LSTM1 27.6967 48.9718
LSTM2 28.7594 54.7220
LSTM3 28.8541 54.9748
LSTM4 25.5805 48.8954
LSTM5 26.3695 49.0645
LSTM6 28.4778 56.0087
LSTM7 27.6826 52.5477
LSTM8 27.5668 52.1010
LSTM9 26.8539 53.0722
LSTM10 27.4205 50.8909
As can be seen from Table 3, LSTM for 9, 10 and 20184The model has better prediction effect, LSTM1The predicted effect of the model can only be ranked to the seventh of 10 independent models (in MAE order), even in RMSE orderLSTM1The predictive effect of the model can only rank to 2 nd. The results in table 3 explain the reason that the integrated prediction model usually has better prediction performance, the model with good overall prediction performance does not necessarily have higher prediction precision at a certain day, and the integrated model makes up for the deficiency by a reasonable integration algorithm so as to enhance the generalization capability of the prediction model.
To describe the probability density of prediction, this embodiment selects a probability q every 0.05 from 0.05-0.95, so there are 19 quantiles of prediction, and obtains the optimal weight w by QRA, the measured value of photovoltaic output of the verification set and the prediction result of each independent LSTM model on the verification setq,t. By the optimum weight wq,tAnd formula
Figure 6
The results of 10 independent LSTM model predictions were integrated to form a nonparametric probabilistic prediction of photovoltaic output on the test set.
Fig. 4 shows the probability prediction results of the LSTM-QRA model on 6 days (corresponding to (a) - (f) in the figure, respectively) on the test set, and since the interval prediction of high NC is important for power system planning and economic scheduling, fig. 5 shows the Prediction Interval (PI) of NC 90% by two quantile prediction lines under the conditions of q 0.05 and q 0.95. In fig. 5, it can be seen that the PI with NC equal to 90% covers most of the actual photovoltaic output values, and the interval prediction has higher reliability in sunny days, while the prediction effect on rainy days and cloudy days is worse than that on sunny days. In order to more fully understand the probability prediction effect of the model provided by the invention under each weather, the Winkler score of the Prediction Interval (PI) when NC is 90% in fig. 5 and the sum of pinball loss functions under the conditions of q being 0.05-0.95 and t being 0-24 (sampling interval 15min) on each day in fig. 4 are calculated respectively.
Pinball loss function L of the model proposed by the invention for each day of 6 days on the test setPinballThe average of Winklerscore (NC ═ 90%) and all independent deterministic prediction models MAE per day are shown in table 4.
TABLE 4
Date 8 month and 25 days 8 month and 26 days 8 month and 30 days 8 month and 31 days 9 month and 7 days 9 month and 12 days
LPinball 38.4824 50.5243 34.1139 36.8520 44.2796 47.1391
Winkler(90％) 50.5942 39.5677 39.7596 44.1908 31.5589 34.8484
MAE(％) 26.0160 54.6273 18.5522 21.3477 36.7824 52.2600
As can be seen from Table 4, the pinball loss function L is usedPinballThe results are significantly different for both indices Winkler (90%). The phenomenon is caused by LPinballMore attention is paid to the overall effect of probability prediction, strict requirements on the width of the PI are not required, and when NC is 90%, the actual value is basically in the PI, so Winkler (90%) is simplified into the superposition of the PI width, and the prediction with the smaller PI width has greater advantage. In addition, L can be foundPinballThe method is consistent with the MAE change trend of a deterministic prediction model, the deterministic prediction model has smaller MAE in sunny days, and the probabilistic prediction model provided by the invention also obtains smaller LPinballL corresponding to cloudy and rainy daysPinballAnd MAE both increased somewhat.
In conclusion, the invention provides an integrated LSTM nonparametric probability prediction model based on QRA for the photovoltaic probability prediction problem in the future, the proposed model trains a group of mutually independent LSTM deterministic prediction models by adopting photovoltaic historical data and NWP data, and the QRA integrates each independent LSTM prediction model to generate the nonparametric probability prediction of photovoltaic output. In order to verify the effectiveness of the proposed model and the feasibility of QRA, the invention adopts the proposed method to predict the measured data. In order to rapidly obtain nonparametric probability prediction, a probability prediction model does not need to be established independently, and the method can be obtained by QRA integration by adopting a plurality of existing deterministic predictions.
The embodiments are only for illustrating the technical idea of the present invention, and the technical idea of the present invention is not limited thereto, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the scope of the present invention.

Claims (5)

1. A QRA-LSTM-based method for predicting nonparametric probability of photovoltaic power in the day ahead is characterized by comprising the following steps:
(1) respectively adopting range normalization on the photovoltaic output data set P, the irradiation data set I and the temperature data set T, and storing respective maximum value and minimum value;
(2) directly connecting the normalized data sets P, I and T in the step (1) in series to form a data set [ P, I, T ], and dividing the data set after being connected in series into a training set and a verification set by taking days as a unit;
(3) constructing a group of LSTM networks with different hidden layer neuron numbers and mutually independent, training by adopting the training sets divided in the step (2), adjusting partial hyper-parameters by utilizing cross validation to obtain a trained LSTM prediction model, and predicting the validation set divided in the step (2) by using the trained LSTM prediction model;
(4) establishing objective functions of quantiles under various probability conditions by using a QRA algorithm and the verification set prediction results obtained in the step (3), and solving each objective function to obtain weight vectors of each independent LSTM prediction model under each quantile;
(5) performing a day-ahead photovoltaic output certainty prediction by using a trained group of independent LSTM prediction models in combination with meteorological data and historical photovoltaic output data, and solving a normalized day-ahead photovoltaic output quantile prediction by using a predicted value and the weight vector obtained in the step (4);
(6) and (4) carrying out reverse normalization on the quantile prediction obtained in the step (5) based on the maximum value and the minimum value stored in the step (1) to obtain a quantile prediction result, so as to realize nonparametric probability prediction.
2. The QRA-LSTM-based method for predicting non-parametric probability of photovoltaic power before day according to claim 1, wherein in step (3), a set of independent LSTM networks uses the photovoltaic output data of the day before the day to be predicted, the irradiation data and the air temperature data of the day to be predicted as characteristic inputs, the photovoltaic output prediction of the day to be predicted as an output result, and defines
Figure FDA0002496115890000011
The prediction results for each independent LSTM prediction model for the validation set day j data,
Figure FDA0002496115890000021
wherein
Figure FDA0002496115890000022
And representing the prediction results of the independent LSTM prediction models at the ith sampling time of the jth day on the verification set, wherein i is 1,2, …, n represents the sampling times of photovoltaic output in one day, and k represents the number of the independent LSTM prediction models.
3. The QRA-LSTM-based method for predicting non-parametric probability of photovoltaic power before day according to claim 2, wherein in step (4), QRA algorithm is applied to each independent LSTM prediction model to obtain an integrated probability prediction model, and the expression of the model is as follows:
Figure FDA0002496115890000023
in the above formula, the first and second carbon atoms are,
Figure FDA0002496115890000024
the quantile predictive value of the photovoltaic output probability distribution predictive result under the probability q condition is 0<q<1，
Figure FDA0002496115890000025
A vector formed by prediction values of each independent prediction model, wherein t represents a sampling time, and t is 1,2, …, n, wq,tThe weight vector for each independent LSTM prediction model in the q quantile.
4. A method of QRA-LSTM based nonparametric probabilistic predictive of photovoltaic power before day according to claim 3, characterized in that in step (4) the objective function of the q quantile is established:
Figure 1
in the above formula, the first and second carbon atoms are,
Figure FDA0002496115890000027
solving the objective function for the real value of the verification set at the jth day t sampling moment to obtain wq,tThe optimum value of (c).
5. The method according to claim 1, wherein in step (5), the photovoltaic output certainty prediction before day is performed by using a trained set of independent LSTM prediction models in combination with meteorological data and historical photovoltaic output data to obtain a predicted value
Figure FDA0002496115890000028
Will predict the value
Figure FDA0002496115890000029
And w obtained in step (4)q,tSubstitution into
Figure FDA00024961158900000210
And obtaining the quantile prediction of the normalized photovoltaic output before the day.
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