A combined method for predicting total solar radiation under different quantiles

Abstract

This paper presents a method for combined prediction of total solar radiation at different quantiles, belonging to the field of photovoltaic power generation technology. Existing numerical weather prediction methods suffer from insufficient dispersion and poor accuracy. This method trains different calibration models using a training dataset to determine the model parameters of the corresponding calibration models at different quantiles. The ensemble forecast of total solar radiation from the retraining dataset is input into the calibration model after determining the model parameters, outputting a post-processed forecast value of total solar radiation. The post-processed forecast value of total solar radiation and the measured values ​​of total solar radiation from the retraining dataset are then input into the combined calibration model, and the weights of the calibration models with different determined model parameters are obtained through optimization. Based on the model parameters and weights of the corresponding calibration models at different quantiles, when the ensemble forecast of total solar radiation simulated for the next time period is input into the combined calibration model, the combined forecast value of total solar radiation at different quantiles will be output. This method is used to accurately obtain total solar radiation.

Description

Technical Field

[0001] This invention relates to obtaining total solar radiation and belongs to the field of photovoltaic power generation technology. Background Technology

[0002] To support the development of the photovoltaic industry, the European Centre for Medium-Range Weather Forecasts (ECMWF) releases numerical weather predictions (NWPs) every six hours daily, including ensemble forecasts of total solar radiation, which is crucial for predicting photovoltaic output. This publicly shared data has powerfully promoted the development of photovoltaic technology in both research and industry, leading to various successes. However, experts in the solar energy field generally believe that numerical weather predictions lack decentralization. From this perspective, ensemble forecasting correction has become a common practice in using numerical weather predictions to forecast photovoltaic power.

[0003] Current correction techniques include ensemble model output statistics (EMOS) and quantile regression (QR), representing parametric and nonparametric statistical perspectives describing the predicted distribution, respectively. For forecasters, accurately predicting the distribution of forecast variables in advance is not easy; therefore, nonparametric methods exhibit better correction performance, thereby improving prediction accuracy, a fact confirmed by numerous existing studies. Furthermore, unlike ordinary least squares regression, which aims to reduce the sum of squared errors between forecasts and observations, quantile regression uses asymmetric piecewise linear loss as its objective, characterizing the probability distribution of forecast variables from a holistic perspective (at different quantiles) and exhibiting better robustness to outliers or anomalies in the sample. On the other hand, since ensemble model output statistics already assumes the distribution of forecast variables, estimating forecasts at any quantile is not difficult.

[0004] Given the variety of calibration techniques available, the question of model selection arises when calibrating ensemble forecasts of total solar radiation issued by the European Centre for Medium-Range Weather Forecasts (ECMWF). In other words, which model should be chosen for ensemble forecast calibration? It is easy to understand that, in most cases, one calibration technique is not always superior to others. In such situations, combining forecasts from multiple competing or complementary calibration models, especially those at different quantiles, to improve forecast performance is a highly attractive strategy.

[0005] Against this backdrop, there is a need for a technique that can effectively improve the under-dispersion of numerical weather forecasts in order to obtain better prediction results for total solar radiation. Summary of the Invention

[0006] The purpose of this invention is to solve the problems of insufficient dispersion and poor accuracy in existing numerical weather forecasts, and to propose a method for predicting total solar radiation using a combination of different quantiles.

[0007] A method for predicting total solar radiation using a combination of different quantiles, the method comprising:

[0008] Step 1: Obtain the measured total solar radiation values ​​at each moment within a certain time period and the ensemble forecast of total solar radiation at each moment within the corresponding time period;

[0009] Step 2: Divide the total solar radiation measurements at each moment within a certain time period and the ensemble forecasts of total solar radiation at each moment within the corresponding time period into two parts in equal proportions. The total solar radiation measurements and ensemble forecasts in the first part are called the training dataset, and the total solar radiation measurements and ensemble forecasts in the second part are called the retraining dataset.

[0010] Step 3: Use the training dataset to train different calibration models to determine the model parameters of the corresponding calibration model at different fractional positions;

[0011] Step 4: Input the total solar radiation ensemble forecast from the retraining dataset into the calibration model after determining the model parameters, and output the post-processed total solar radiation forecast value; input the obtained post-processed total solar radiation forecast value and the measured total solar radiation value from the retraining dataset into the combined calibration model, and obtain the weights of the calibration model after different determined model parameters through optimization;

[0012] Step 5: Based on the model parameters and weights of the corresponding calibration model at different fractional levels, when the combined calibration model is input with the ensemble forecast of total solar radiation for the next time period, the combined forecast value of total solar radiation at different fractional levels will be output.

[0013] Preferably, the specific process of step 3 is as follows:

[0014] The total solar radiation ensemble forecasts from the training dataset are input into different calibration models. The pinball loss between the calibration model output and the total solar radiation measurements from the training dataset is used as the objective function to obtain the model parameters of the corresponding calibration models at different fractional levels.

[0015] Preferably, the pinball loss function S τ (y,x) can be represented as:

[0016]

[0017] In the formula, x is the output value of the calibration model under different quantiles, that is, the post-processed forecast value of total solar radiation, y is the measured value of total solar radiation in the training dataset, and τ is the quantile.

[0018] Preferably, the combined correction model is:

[0019]

[0020] In the formula, i is the number of data points in the retraining dataset; n is the number of data points in the retraining dataset; τ0 is the number of selected quantiles; y i The total solar radiation measurement at point i in the retraining dataset; ω represents the combined predicted total solar radiation at data point i under different calibration models at quantile τ, i.e., the model output value of the combined calibration model; m.τ The weight of the out-of-sample post-processed total solar radiation forecast of the m-th calibration model at quantile τ in the combined total solar radiation forecast; Let be the post-processed forecast of total out-of-sample solar radiation at the i-th data point for the m-th calibration model under quantile τ.

[0021] The beneficial effects of this invention are:

[0022] This application proposes a method for combined prediction of total solar radiation at different quantiles. The core of this method is to utilize combined calibration models to obtain the weights of different calibration models at different quantiles. When the weight of a calibration model at a certain quantile is zero, the post-processed forecast of total solar radiation from that calibration model is discarded from the combined forecast of total solar radiation at that quantile. This application introduces optimization techniques into total solar radiation prediction for the first time, improving the prediction performance by retaining (discarding) calibration models with good (poor) post-processing effects. By combining the advantages of multiple calibration models, this application obtains a total solar radiation forecast with higher accuracy than a single optimal calibration model or a simple quantile averaging (SQA) model (where the combined forecast equals the average of the post-processed forecasts of total solar radiation from each calibration model). This application has significant practical implications for improving the accuracy of total solar radiation and photovoltaic power output prediction, enhancing the power system's ability to absorb photovoltaic power, and ultimately reducing overall carbon emissions. Attached Figure Description

[0023] Figure 1 This is a flowchart of a combined method for predicting total solar radiation under different quantiles. Detailed Implementation

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0026] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0027] Example 1:

[0028] A method for predicting total solar radiation using a combination of different quantiles, the method comprising:

[0029] Step 1: Obtain the measured total solar radiation values ​​at each moment within a certain time period and the ensemble forecast of total solar radiation at each moment within the corresponding time period;

[0030] Step 2: Divide the total solar radiation measurements at each moment within a certain time period and the ensemble forecasts of total solar radiation at each moment within the corresponding time period into two parts in equal proportions. The total solar radiation measurements and ensemble forecasts in the first part are called the training dataset, and the total solar radiation measurements and ensemble forecasts in the second part are called the retraining dataset.

[0031] Step 3: Use the training dataset to train different calibration models to determine the model parameters of the corresponding calibration model at different fractional positions;

[0032] Step 4: Input the total solar radiation ensemble forecast from the retraining dataset into the calibration model after determining the model parameters, and output the post-processed total solar radiation forecast value; input the obtained post-processed total solar radiation forecast value and the measured total solar radiation value from the retraining dataset into the combined calibration model, and obtain the weights of the calibration model after different determined model parameters through optimization;

[0033] Step 5: Based on the model parameters and weights of the corresponding calibration model at different fractional levels, when the combined calibration model is input with the ensemble forecast of total solar radiation for the next time period, the combined forecast value of total solar radiation at different fractional levels will be output.

[0034] In this embodiment, the present application can obtain a verification measurement set in the time period following the acquisition of the total solar radiation measurement value, and obtain a verification forecast set in the same time period as the verification measurement set. The verification measurement set and the verification forecast set are referred to as the verification dataset.

[0035] The total solar radiation measurements in the training dataset, retraining dataset, and validation dataset are all total solar radiation measurements downloaded from a weather station by the Surface Radiation Budget Network (SURFRAD), and the ratio of the training dataset, retraining dataset, and validation dataset is 2:1:1.

[0036] The total solar radiation ensemble forecasts in the training dataset, retraining dataset, and validation dataset are all downloaded from the same weather station's total solar radiation ensemble forecasts from the Meteorological Archival and Retrieval System (MARS) of the European Centre for Medium-Range Weather Forecasts, and the ratio of the training dataset, retraining dataset, and validation dataset is 2:1:1.

[0037] Based on the model parameters and weights of different calibration models, a combined solar radiation forecast value applicable to practical scenarios—represented in this application using the validation dataset—is calculated; this is the final total solar radiation. An average quantile score (AQS) is proposed to evaluate the post-processing and combination effects of this application. The definition is as follows:

[0038]

[0039] In the formula, t is the data index of the validation dataset; n' is the number of data points in the validation dataset; y t To verify the measurements taken for dataset t; The total solar radiation combination forecast value at time t is given by the quantile τ.

[0040] As can be seen from the definition, if the mean quantile score is lower, the post-processing and combination effect of the combined correction model will be better, that is, the forecast accuracy will be higher.

[0041] In the preferred embodiment, step 3 is as follows:

[0042] The total solar radiation ensemble forecasts from the training dataset are input into different calibration models. The pinball loss between the calibration model output and the total solar radiation measurements from the training dataset is used as the objective function to obtain the model parameters of the corresponding calibration models at different fractional levels.

[0043] In a preferred embodiment, the pinball loss function S τ (y,x) can be represented as:

[0044]

[0045] In the formula, x is the output value of the calibration model under different quantiles, that is, the post-processed forecast value of total solar radiation in the sample, y is the measured value of total solar radiation in the training dataset, and τ is the quantile.

[0046] In this implementation, it is worth noting that Formula 1—the calculation formula for the pinball loss function—applies to all the following cases, but it should be noted that x and y may belong to different datasets.

[0047] In a preferred embodiment, the combined correction model is as follows:

[0048]

[0049] In the formula, i is the data index of the retraining dataset; n is the number of data points in the retraining dataset; τ0 is the number of selected quantiles; y i The total solar radiation measured at point i in the retraining dataset; ω represents the combined predicted value of total solar radiation at data point i under different correction models at quantile τ, i.e., the model output value of the combined correction model; m.τ The weight of the out-of-sample post-processed total solar radiation forecast of the m-th calibration model at quantile τ in the combined total solar radiation forecast; Let be the post-processed forecast of total out-of-sample solar radiation at the i-th data point for the m-th calibration model under quantile τ.

[0050] In this implementation, ensemble forecast refers to data directly released by ECMWF, which can be obtained directly; post-processed forecast refers to the model output value after applying a calibration model to the ensemble forecast; combined forecast refers to the model output value after applying a combined calibration model to the post-processed forecast obtained from multiple calibration models. In-sample refers to the training process, and out-of-sample refers to the estimated value calculated using the trained model parameters on a new dataset.

[0051] The combined total solar radiation forecast value of the combined calibration model is equal to the linear weighted sum of the out-of-sample total solar radiation post-processed forecast values ​​of each calibration model, as shown in the second formula in Formula 2; the combined calibration model should satisfy the constraint that the sum of the weights of each calibration model at each quantile is one, as shown in the third formula in Formula 2.

[0052] Considering that Formula 2 is a piecewise function, which is not conducive to solving the model, this application uses the non-negative vector ξ. + and ξ - These represent the positive and negative parts of the measured total solar radiation minus the predicted total solar radiation combination, respectively. At this point, the linearized form of the combined correction model can be obtained as follows:

[0053]

[0054] st

[0055]

[0056]

[0057] The GUROBI solver is called to solve the established combined correction model, and the weights of different correction models at each quantile are obtained.

[0058] In a preferred embodiment, there are a total of ten calibration models.

[0059] In a preferred embodiment, the ten calibration models include an EMOS model with five different model parameters, a regular quantile regression, a quantile regression with Lasso penalty, a quantile regression neural network model with two different model parameters, and a quantile regression forest.

[0060] Experimental verification:

[0061] The dataset used total solar radiation measurements from 2017 to 2020, recorded at the Goodwin Creek, MS (GCM) weather station in SURFRAD, and the corresponding ensemble forecasts of total solar radiation for the next 12–35 hours issued daily at 12Z by the ECMWF for the same period. The GCM dataset has a longitude of -89.873°, a latitude of 34.255°, and a time zone parameter TZ of -7. Missing data points account for 3.76% of the total solar radiation measurements, while the ECMWF dataset is complete. The selected calibration models included five EMOS models with different optimization objectives and preset prediction distributions, ordinary quantile regression (QR), 1-penalized quantile regression (QRL), a quantile regression neural network model with two different parameters (QRNN), and a quantile regression forest (QRF), for a total of ten calibration models. There are 13 quantiles, i.e., τ = {0.01, 0.05, 0.1, 0.2, ..., 0.9, 0.95, 0.99}. The measurement and forecast datasets are divided into training, retraining, and validation datasets in a 2:1:1 ratio.

[0062] In programming, the R package is used to obtain the model parameters of each calibration model based on the training dataset. Then, the GUROBI solver is called on the Spyder platform to obtain the weights of each calibration model at different quantiles. Finally, the average quantile scores of each calibration model, the simple average calibration model, and the combined calibration model proposed in this paper are calculated. The weights of each calibration model at the 50th quantile are shown in Table 1, and the average quantile scores of each model are shown in Table 2.

[0063] Table 1. Weights of each calibration model at the 50th quantile in this embodiment.

[0064] Model EMOS1 EMOS2 EMOS3 EMOS4 EMOS5 QR QRL QRNN1 QRNN2 QRF Weight 0 0 0.72 0.07 0 0 0 0.13 0 0.08

[0065] Table 2 shows the mean quantile scores of each model in this embodiment.

[0066]

[0067] As shown in Table 1, only four calibration models—EMOS3, EMOS4, QRNN1, and QRF—were selected at the 50th percentile, indicating that not all calibration models are needed in the final combined solar total radiation forecast. In this case, simply averaging the post-processed solar total radiation forecasts from each model would result in a relatively poor forecast quality, as evidenced by the SQA average quantile score of 25.4 in Table 2, which is higher than the 21.9 of this application. Furthermore, Table 2 shows that the average quantile score of this invention is lower than that of each calibration model and the simple average calibration model, fully validating the advantages of this invention in correcting the under-dispersion of numerical weather prediction and improving the accuracy of solar total radiation forecasts. Therefore, compared with each calibration model and the simple average calibration model, the combined calibration model proposed in this application can obtain a solar total radiation forecast with better prediction accuracy.

[0068] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method for predicting total solar radiation using a combination of different quantiles, characterized in that, The method includes: Step 1: Obtain the measured total solar radiation values ​​at each moment within a certain time period and the ensemble forecast of total solar radiation at each moment within the corresponding time period; Step 2: Divide the total solar radiation measurements at each moment within a certain time period and the total solar radiation ensemble forecasts at each moment within the corresponding time period into two parts in equal proportions. The total solar radiation measurements and the total solar radiation ensemble forecasts in the first part are called the training dataset, and the total solar radiation measurements and the total solar radiation ensemble forecasts in the second part are called the retraining dataset. Step 3: Use the training dataset to train different calibration models to determine the model parameters of the corresponding calibration model at different fractional positions; Step 4: Input the total solar radiation ensemble forecast from the retraining dataset into the calibration model after determining the model parameters, and output the post-processed total solar radiation forecast value; input the obtained post-processed total solar radiation forecast value and the measured total solar radiation value from the retraining dataset into the combined calibration model, and obtain the weights of the calibration model after different determined model parameters through optimization; Step 5: Based on the model parameters and weights of the corresponding calibration model at different fractional levels, when the combined calibration model is input with the ensemble forecast of total solar radiation for the next time period, the combined forecast value of total solar radiation at different fractional levels will be output.

2. The method for predicting total solar radiation using a combination of different quantiles according to claim 1, characterized in that, The specific process of step 3 is as follows: The total solar radiation ensemble forecasts from the training dataset are input into different calibration models. The pinball loss between the calibration model output and the total solar radiation measurements from the training dataset is used as the objective function to obtain the model parameters of the corresponding calibration models at different fractional levels.

3. The method for predicting total solar radiation using a combination of different quantiles according to claim 2, characterized in that, pinball loss function S τ (y,x) can be represented as: In the formula, x is the output value of the calibration model under different quantiles, that is, the post-processed predicted value of total solar radiation in the sample, y is the measured value of total solar radiation in the training dataset, and τ is the quantile.

4. The method for predicting total solar radiation using a combination of different quantiles according to claim 1, characterized in that, The combined correction model is as follows: In the formula, i is the data index of the retraining dataset; n is the number of data points in the retraining dataset; τ0 is the number of selected quantiles; y i The total solar radiation measured at point i in the retraining dataset; ω represents the combined predicted value of total solar radiation at data point i under different correction models at quantile τ, i.e., the model output value of the combined correction model; m.τ The weight of the out-of-sample post-processed total solar radiation forecast of the m-th calibration model at quantile τ in the combined total solar radiation forecast; Let be the post-processed forecast of total out-of-sample solar radiation at the i-th data point for the m-th calibration model under quantile τ.

5. The method for predicting total solar radiation using a combination of different quantiles according to claim 1, characterized in that, There are a total of ten calibration models.

6. The method for predicting total solar radiation using a combination of different quantiles according to claim 5, characterized in that, The ten calibration models include five EMOS models with different model parameters, one ordinary quantile regression, one quantile regression with Lasso penalty, two quantile regression neural network models with different model parameters, and one quantile regression forest.

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