Inter-hour direct normal irradiance forecast with multiple data types and time-series
Boosted by a strong solar power market, the electricity grid is exposed to risk under an increasing share of fluctuant solar power. To increase the stability of the electricity grid, an accurate solar power forecast is needed to evaluate such fluctuations. In terms of forecast, solar irradiance is the key factor of solar power generation, which is affected by atmospheric conditions, including surface meteorological variables and column integrated variables. These variables involve multiple numerical time-series and images. However, few studies have focused on the processing method of multiple data types in an inter-hour direct normal irradiance (DNI) forecast. In this study, a framework for predicting the DNI for a 10-min time horizon was developed, which included the nondimensionalization of multiple data types and time-series, development of a forecast model, and transformation of the outputs. Several atmospheric variables were considered in the forecast framework, including the historical DNI, wind speed and direction, relative humidity time-series, and ground-based cloud images. Experiments were conducted to evaluate the performance of the forecast framework. The experimental results demonstrate that the proposed method performs well with a normalized mean bias error of 0.41% and a normalized root mean square error (nRMSE) of 20.53%, and outperforms the persistent model with an improvement of 34% in the nRMSE.
KeywordsInter-hour forecast Direct normal irradiance Ground-based cloud images Multiple data types Multiple time-series
Solar energy is an important renewable energy resource, but is intermittent in the short period owing to the fluctuations of solar radiation. Dramatic fluctuations cause the energy output of a solar power plant to rapidly decrease from hundreds of megawatts to zero output within a few minutes, and bring about huge risk to the stability of the electrical grid . Therefore, an accurate forecast of solar power is the premise and key technology of the grid-connection for photovoltaic (PV) or concentrated solar thermal (CST) plants [2, 3]. For various power system operations, the geographical and temporal requirements differ in a solar power forecast [4, 5].
Solar power significantly depends on the solar irradiance, such as the global horizontal irradiance (GHI) for PV plants and the direct normal irradiance (DNI) for CST plants , and thus the solar power output forecast can be transformed into a solar irradiance (GHI or DNI) forecast [7, 8, 9]. In this study, we focus on a DNI forecast. The DNI is mainly affected by surface meteorological variables and column integrated variables, such as clouds and water vapor. Except for clouds, these atmospheric variables have been considered in most clear-sky models for a DNI estimation  or numerical weather prediction for a day-ahead solar irradiance forecast [11, 12] and long-term solar irradiance estimation . However, for an inter-hour DNI forecast in all sky conditions, clouds have been the only factor considered in certain forecast models, and other atmospheric variables have been ignored [14, 15, 16, 17, 18, 19]. Recently, the majority of all-sky DNI forecast models have employed two main parts: clear-sky DNI forecast and cloud fraction forecast [20, 21, 22]. In this way, except for clouds, the effectiveness of other atmospheric variables is considered in a clear-sky DNI estimation. However, the accuracy of clear-sky forecast is limited by the immeasurability of most clear-sky atmospheric variables under all-sky conditions, and thus most clear-sky models applied in all-sky forecast are empirical with few atmospheric variables [23, 24, 25].
To achieve a higher accuracy of an inter-hour DNI forecast,  modified a clear sky model by considering the variation of the atmospheric components. Reference  also developed a forecast method using adaptive clear-sky models. However, the improvement in accuracy was limited by adjusting these models. In this study, a framework of an inter-hour DNI forecast was developed by directly considering the atmospheric variables, including the historically measured relative humidity, wind speed and direction, DNI, and clouds, presented through a numerical time-series or images. To fuse different types of data and avoid some inputs overwhelmed by the large magnitude of other variables, all inputs were transformed into dimensionless variables. Firstly, a ground-based cloud image was in-painted and corrected to obtain more accurate all-sky information, and the cloud covers in six key areas were then extracted separately, each of which was set as the input of the forecast model. Secondly, the measured historical DNI was transformed into a clear-sky index using a clear-sky model, and was set as an input of the forecast model. Finally, a support vector regression (SVR) model was employed to predict the DNI for the following 10 minutes, with multiple inputs including the cloud cover, clear-sky index, wind speed, and relative humidity (instead of water vapor).
The remainder of this paper is constructed as follows. The instrument and data collection are introduced in Section 2. A forecast framework based on multiple data types and time-series is described in Section 3. Experiments carried out to evaluate the performance of the proposed method, along with the results and a discussion, are detailed in Section 4. Finally, some concluding remarks are provided in Section 5.
2 Data collection
All ground-based cloud (GBC) images and measured data employed were downloaded from the open database of the Solar Radiation Research Laboratory (39.74°N, 105.18°W, at 1828.8 m above sea level), which was provided by the National Renewable Energy Laboratory (NREL) .
2.1 GBC images
A total of 73 clear-sky GBC images were selected from 2013 to construct a clear-sky image dataset (CSID). All clear-sky images correspond to a solar zenith ranging from 89° to 17° (step size of 1°). The CSID set was constructed for the following preprocessing of the image inpainting to detect error pixels around the sun, as discussed in Section 3.1.
2.2 Measured numerical data
3 DNI forecast based on multiple data types and time-series
3.1 GBC image processing
After determining the error pixels, distinguishing them from the surrounding clouds is the greatest difficulty. Various cloud detection algorithms have been proposed, each of which has shown a satisfactory performance under a specific situation. Among them, the clear-sky background different (CSBD) algorithm outperforms other methods in a circumsolar area when the sun is not obstructed by clouds, but it fails to detect cloud which blocked the sun or is optically thick and dark . The red-blue ratio (R/B) algorithm achieves better results when the clouds are optically thick and dark, but it fails to distinguish clouds from clear sky when cirrus or stratus clouds are present . Combining the advantages of the CSBD and R/B algorithms in cloud detection, the error pixels in a GBC image (It) are marked using the following steps.
Step 1: search a clear-sky GBC image Ic based on the closest solar zenith from the constructed CSID introduced in Section 2.1.
Step 2: rotate the image Ic to make its azimuth angle the same as the target image It.
Step 3: calculate the green-channel histograms of the two images (Ic and It).
Step 4: adjust the green channel of the clear-sky image (Ic) by multiplying a ratio to make its green distribution the same as that of It.
Step 5: mark the pixel whose difference between the two green channels is greater than threshold Tg as a cloud (M1).
Step 6: mark the pixel as a cloud (M2) using the R/B algorithm.
Step 7: remove the error pixels (M2⊕M1) around the position of the sun.
Finally, the distortion of the inpainted GBC image was corrected using the spherical orthogonal distortion correction method , and the pre-processing of the GBC image was completed.
3.2 Input nondimensionalization
The key point in predicting the inter-hour DNI is to predict the cloud motion, including the speed and direction. Because GBC images were sampled every 10 min, it is difficult to accurately identify the direction and speed of the cloud from two consecutive images. Considering the relationship between the cloud motion and wind, the wind speed and direction were used to estimate the cloud motion.
However, the cloud speed does not have a clear relationship with the wind speed owing to the difficulty of cloud boundary detection and the lack of information regarding the cloud base height. Therefore, six cloud cover features were extracted from 20 × 20 pixel areas along the opposite direction of the wind (cloud), as shown in Fig. 2, to address the cloud effect on the DNI. The wind speed was set as one of the model inputs to adjust the weight of the cloud cover in the forecast model. Therefore, the GBC image was transformed to six cloud covers in 20 × 20 pixel areas dimensionlessly.
3.3 DNI inter-hour forecast model
In view of the advantage of handling non-linear problems, SVR was applied as the DNI forecast model. The structure of the SVR model was introduced in detail in . In this study, the kernel function of the SVR is the radial basis function. There are three model parameters: cost C, the tolerance of termination criterion ε and attenuation parameter ν. The three model parameters are adjusted using the cross-validation method  with the training and validation sets. The extensive grid search method was used to determine the three hyperparameters, where C was set in [1, 5] at a step size of 0.5, ε was set in [0.001, 0.1] at a step size of 0.001, and ν was set in [1, 3] at a step size of 0.2, respectively. The range of these hyperparameters was set based on the experimental results and previous experience.
4 Results and discussion
Performance of different models using only numerical DNI time-series as inputs for 10-min DNI forecast
Performance of different models with different inputs for 10-min DNI forecast
A framework for predicting the inter-hour DNI was proposed, including the nondimensionalization of the input variables, employment of a forecast model based on the SVR, and transformation of outputs. Multiple input variables, involving the historical measured DNI, relative humidity, ground-based cloud image, and wind speed, were employed in the developed forecast model. The data from the NREL dataset for the entire year of 2013 were used to train the forecast model using a cross-validation method. The experimental results demonstrated that the proposed model was comparable to other models in terms of the forecast accuracy, and achieved a 34% improvement in the nRMSE over the persistent model.
The performance of the proposed forecast model is affected by the ramp rate of the DNI time-series, with a higher accuracy when the monthly DNI changes more gently, and vice versa. Therefore, considering the ramp rate and thereby constructing different forecast models will further improve the forecast accuracy, and should be investigated in the future studies.
The authors acknowledge the National Renewable Energy Laboratory for providing the data used in this study. This research was supported by the National Key Research and Development Program of China (No. 2018YFB1500803), National Natural Science Foundation of China (No. 61773118, No. 61703100), and Fundamental Research Funds for Central Universities.
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