Improved convolutional neural network‐based quantile regression for regional photovoltaic generation probabilistic forecast

IET Renewable Power GenerationVolume 14, Issue 14 p. 2712-2719 Research ArticleFree Access Improved convolutional neural network-based quantile regression for regional photovoltaic generation probabilistic forecast Yixiao Yu, Key Laboratory of Power System Intelligent Dispatch and Control, Shandong University, Jinan, 250061 People's Republic of ChinaSearch for more papers by this authorMengxia Wang, Corresponding Author wangmx@sdu.edu.cn Key Laboratory of Power System Intelligent Dispatch and Control, Shandong University, Jinan, 250061 People's Republic of ChinaSearch for more papers by this authorFangqing Yan, Laiwu Electric Power Supply Company of State Grid Shandong Electric Power Company, Laiwu, 271100 People's Republic of ChinaSearch for more papers by this authorMing Yang, orcid.org/0000-0002-0020-8683 Key Laboratory of Power System Intelligent Dispatch and Control, Shandong University, Jinan, 250061 People's Republic of ChinaSearch for more papers by this authorJiajun Yang, State Grid Shaanxi Electric Power Research Institute, Xi'an, 710054 People's Republic of ChinaSearch for more papers by this author Yixiao Yu, Key Laboratory of Power System Intelligent Dispatch and Control, Shandong University, Jinan, 250061 People's Republic of ChinaSearch for more papers by this authorMengxia Wang, Corresponding Author wangmx@sdu.edu.cn Key Laboratory of Power System Intelligent Dispatch and Control, Shandong University, Jinan, 250061 People's Republic of ChinaSearch for more papers by this authorFangqing Yan, Laiwu Electric Power Supply Company of State Grid Shandong Electric Power Company, Laiwu, 271100 People's Republic of ChinaSearch for more papers by this authorMing Yang, orcid.org/0000-0002-0020-8683 Key Laboratory of Power System Intelligent Dispatch and Control, Shandong University, Jinan, 250061 People's Republic of ChinaSearch for more papers by this authorJiajun Yang, State Grid Shaanxi Electric Power Research Institute, Xi'an, 710054 People's Republic of ChinaSearch for more papers by this author First published: 24 September 2020 https://doi.org/10.1049/iet-rpg.2019.0949Citations: 1AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat Abstract Nowadays, an increasing number of photovoltaic (PV) plants are becoming integrated into one regional power grid. Under this circumstance, the probabilistic forecast of regional PV power generation is of significance for the regional power system operation and control. This study presents a novel probabilistic forecast method for regional PV generation that integrates the convolutional neural network (CNN) with non-linear quantile regression (QR). In this method, the CNN structure is enhanced to extract the non-linear features of the input data and generate the non-linear QR function. As a result, the improved CNN can effectively process high-dimensional and complex input data and the non-linear QR model can provide quantile forecast information of regional PV power. The validity of the proposed method is verified by using it to forecast the regional PV generation from the clustered PV plants in the Weifang region of China. 1 Introduction Owing to the continuous increase in global energy consumption and shortage of fossil fuels, the development of photovoltaic (PV) generation has been promoted in recent years. According to the statistics of the International Energy Agency, the worldwide PV power generation capacity has reached a milestone of 616 GW in 2019 [1]. Due to the rapid growth of PV generation capacity in China, it becomes more and more common that many PV plants are integrated into one regional power grid, and some researchers have focused on the issue that how to forecast regional PV power, thus providing necessary information for system operators to make control decisions [2]. The bottom-up and upscaling are two widely used methods recorded in the literature for the regional PV generation forecast [3]. The bottom-up method first forecasts the generation of each individual PV plant in the region, and then the regional PV generation can be obtained by adding up the forecasted generation of each PV plant [4]. The upscaling method first selects representative PV plants in the region, and then forecasts their outputs and the linear combination coefficients to the total generation of all the PV plants in the region. Finally, the total generation can be obtained by the linear combination of the forecasted results of the representative PV plants [5-7]. Compared with the bottom-up method, the upscaling method does not need to forecast the generation for every PV plant in the region, which considerably reduces its training time and input information. However, the forecast accuracy of the upscaling method is very sensitive to the selection of representative PV plants. The forecast accuracy will decrease if an inappropriate PV plant is selected for analysis [5, 6]. The point forecast on the power output of the individual PV plant is the basis of the bottom-up and upscaling methods. There is much research concerned with the point forecast of individual PV generation. In [8], numerical weather prediction (NWP) information is used to forecast the PV generation based on the formulated mathematical model that characterises the relationship between weather conditions and the PV power. In [9], the auto-regressive integrated moving average time series model is used to forecast the PV power for one-day ahead using air temperature, precipitation amount, insolation duration and humidity as input. In [10], the PV power in the 24 h horizon is forecasted based on the artificial neural network (ANN) using the historical PV power, solar irradiance, humidity and temperature as an input. In [11], the support vector machine (SVM) is employed to forecast the power output of individual PV plant, and the influence of the forecast time horizon on forecast accuracy is analysed. In [12], hybrid models (self-organising map, learning vector quantisation network, and support vector regression) are used for the point forecast of PV power; the obtained results show that the forecast of the hybrid models is better than the accuracy of every single model. Based on the point forecast on the power output of the individual PV plant, the bottom-up and upscaling methods can provide the point forecast of regional PV power. However, due to the high variability and intermittency of the PV power output, point forecast is difficult to accurately and comprehensively forecast the PV power. In comparison, the probabilistic forecast can provide operators with the prediction interval (PI) and the probability distribution of PV power, thus guiding operators to make control decisions considering the uncertainty of PV power. Several probabilistic forecast methods have been proposed to forecast the probability density function (PDF), confidence intervals or quantiles of the power output of the individual PV plant. In [13], a probabilistic forecast method based on the higher-order Markov chain is used to forecast the PDF of the PV power for 15-minute ahead. In [14], a statistical method combining extreme machine learning and quantile regression (QR) is developed to forecast the confidence intervals of the PV power. In [15], the weighted Gaussian process regression approach is employed to forecast the confidence intervals of the PV power. In [16], the CNN-based QR (CNN-QR) method is proposed to forecast the quantiles of PV power for 30-minute ahead. So far, the research on the probabilistic forecast of PV power is mainly focused on the power output of the individual PV plant, and few studies have focused on the probabilistic forecast of regional PV power. For the forecast of regional PV power, it requires the forecast method can efficiently mine the effective information from massive input data of multiple PV plants in the region (e.g. the NWP information and historical generation of PV plants), including the correlations of the power output and the correlations of weather information among the regional PV plants [5]. CNN is an efficient technique for feature extraction in deep learning (DL). In [16], the high efficiency of the deep feature extraction by the CNN-QR method has been proved; the method is also proved to be effective for the probabilistic forecast of the output power of individual PV plant. As the core of that model, CNN is employed to learn the non-linear QR function that formulates the mapping relationship between the input information and quantiles of individual PV power. In this paper, the CNN is used to conduct the probabilistic forecast of the regional PV generation. To enhance the CNN extraction of deep features from the massive input data obtained for multiple PV plants and regional PV power, an improved CNN-QR (ICNN-QR) method is proposed. The contributions of this paper can be summarised as follows: (i) An ICNN-QR probabilistic forecast model for regional PV generation is developed. Compared with the commonly used bottom-up and upscaling methods, the proposed ICNN-QR method can provide more accurate and comprehensive probabilistic forecast information for system operators. (ii) The CNN structure is considerably improved by introducing multiple Conv-pool structures for regional PV plants (each Conv-pool structure includes a set of convolutional and pooling layers). The ICNN is capable of conducting feature extraction from the input data of individual PV plant and extracting the correlation features for the input data of regional PV plants. As a result, the ICNN-QR method exhibits higher forecast accuracy and lower calculation time as compared with those of the traditional CNN-QR approach. (iii) The proposed ICNN-QR model is used to conduct the forecast of the PV power generated by ten clustered PV plants in the Weifang region of China, thus verifying the validity of the ICNN-QR model. The remaining parts of this paper are organised as follows. In Section 2, the DL process and CNN are described in detail. The proposed forecast model of regional PV power generation is outlined in Section 3. Section 4 discusses the evaluation methods of the forecast results. Case studies are performed in Section 5, and Section 6 summarises the conclusions drawn from the results of this paper. 2 DL and CNN DL is a special branch of machine learning [17, 18]. As compared with the traditional machine learning algorithm, the DL process consists of multiple layers, which can automatically extract more complex features from input data without the manual extraction step (Fig. 1). Fig. 1Open in figure viewerPowerPoint Comparison of (a) DL, (b) Traditional machine learning processes Compared with the power output of the individual PV plant forecast, there are much more input data for the regional PV generation forecast, including the NWP and historical generation data of every PV plant in the region. Therefore, features that are more complex must be extracted from the input data, and multiple parameters of the DL structure should be optimised. As one of the most effective DL methods in terms of feature extraction, CNN [19-21] is used to establish a non-linear QR model and forecast various quantiles of regional PV power generation. Compared with the traditional NN [22, 23], CNN has fewer parameters because of its weight sharing technique, which can significantly shorten the training time. The advantages of CNN indicate its suitability for extracting features from the massive input data collected for the regional PV power generation forecast. The CNN architecture generally includes an input layer, convolutional layers, pooling layers, fully connected layers, and an output layer. For the regional PV generation forecast, the functions of each layer can be described as follows. 2.1 Convolutional layer In the proposed model, the convolutional layer is designed to extract the hidden features from the NWP and historical PV generation data by performing the convolutional operation. Owing to the high dimensionality of the input data, a relatively large number of network parameters must be trained. In the DL process, the CNN weight sharing procedure is applied to solve this issue by sharing the parameters of the convolutional kernel. Here, each convolutional kernel has a receptive field for extracting local neurons from the previous layer. However, the neurons between different layers are locally connected, as shown in Fig. 2. Fig. 2Open in figure viewerPowerPoint Connections between different neurons in the convolutional layer A feature map of the convolutional layer is obtained by calculating the dot product between the feature maps of the previous layer and the convolutional kernel, and then non-linearised by an activation function as follows: (1) where is the activation function, commonly using the sigmoid function and ReLU function. Compared with the sigmoid function, the ReLU function exhibits a higher convergence rate and is used as the activation function in this paper. denotes the feature map i in the (l − 1)th layer, ⊗ is the convolutional operation, denotes the input set of the feature maps, is the weight of feature map i in the (l − 1)th layer with respect to the feature map j in the l th layer, denotes the bias of the feature map i in the (l − 1)th layer toward the feature map j in the l th layer, and is the feature map j in the l th layer. 2.2 Pooling (sub-sampling) layer The pooling layer is located behind the convolutional layer. It is used for the further extraction of non-linear features and dimension reduction of the input data. The pooling layer first divides the input feature maps into a set of subareas and then converts these subareas into smaller feature maps by the pooling function, which generates their average or maximum values as the output. Thus, the pooling layer can effectively reduce the number of CNN structural parameters and calculation complexity. The feature map of the pooling layer can be computed as (2) where denotes feature map i in the (l − 1)th layer, is the weight coefficient of the feature map j in the l th layer, denotes the pooling function, and represents the feature map j in the l th layer. In this paper, the maximum pooling function is adopted. After the Conv-pool structure, the input data are flattened into a one-dimensional vector and then input into the fully connected layers. 2.3 Fully connected layer Several fully connected layers are added behind the Conv-pool structure. Each neuron in the fully connected layer is connected to all neurons in the previous layer. The neurons of the fully connected layer can be calculated as (3) where denotes the neurons in the l th layer. 3 ICNN-QR model for regional PV power generation forecast As mentioned above, the input data of the model for forecasting regional PV generation is very complex and larger. If the data are directly input into the CNN structure, it will be difficult to accurately extract the features of regional PV plants. In order to solve this problem, the CNN structure is considerably enhanced in this paper by adding multiple specific input layers and Conv-pool structures. Moreover, the ICNN is further combined with the non-linear QR for the probabilistic forecast of regional PV generation. 3.1 Non-linear QR model QR is a typical regression model for estimating the influence of the explanatory variable on the response variable in different quantiles [24, 25]. The traditional linear QR is only applicable to linear relationships existing between the input and output data. On the contrary, the non-linear QR model has a much wider range of possible applications [26]. A simplified expression of the non-linear QR model can be written as (4) where denotes the quantile, the range of is [0, 1], is the conditional quantile of response variable Y corresponding to explanatory variable X, and denote the weight vectors, and represents the non-linear function whose value depends on the explanatory variable and weight vectors. The estimation of the weight parameters in the non-linear QR model is transformed into an optimisation problem of minimising the loss function, which can be described as (5) where and denote the weights, and and are the penalty parameters. In order to avoid overfitting, the parameters are estimated by cross-validation. As shown in (5), the influences of the explanatory variables on response variables at different quantiles can be calculated if the weight vectors are obtained. Moreover, the conditional distribution of the response variables is obtained by continuously increasing from 0 to 1. 3.2 ICNN-QR architecture The relationship between the NWP data of each PV plant and the regional PV generation is complex and non-linear; it is also difficult to express via exact mathematical equations [27, 28]. Therefore, the non-linear QR model can use CNN to learn and fit the non-linear and complex relationships between the input and output data, instead of accurate mathematical equations. The traditional CNN-QR model has only one Conv-pool structure. The input data of all PV plants are input into the same Conv-pool structure via one input layer. After that, the extracted features are put into the fully connected layers to forecast the probabilistic PV generation of the region. It is easy to see that the feature extraction of an individual PV plant and the correlation feature extraction between the PV plants in the region are implemented simultaneously of the traditional CNN-QR model. All feature extractions are employed simultaneously in the traditional CNN-QR model, which may lead to the loss of representative features. In this paper, a new ICNN-QR probabilistic forecast model is established (see Fig. 3). The structure of the ICNN-QR model generally includes the input layers, convolutional layers, pooling layers, flattening layer, fully connected layers, and output layer. Compared with the structure of the traditional CNN-QR model, the ICNN-QR model contains several input layers and Conv-pool structures. Each PV plant has its own Conv-pool structure for inputting data and feature extraction. The features of the input data extracted by the Conv-pool structures are integrated, and then flattened into a vector through the flattening layer, then input to the fully connected layer for the forecast. The correlation features of all PV plants in the region are further extracted from the fully connected layers. Finally, the output layer produces the quantile forecast results of regional PV generation. Fig. 3Open in figure viewerPowerPoint Architecture of the ICNN-QR model To summarise this procedure, the ICNN-QR model first extracts representative features from the input data of individual PV plant using multiple Conv-pool structures and then comprehensively extracts the correlation information of the regional PV plants by the fully connected layers. The existence of two distinct feature extraction levels in the ICNN-QR model makes its forecast more accurate, efficient, and comprehensive as compared with the traditional CNN-QR model. 3.3 Training the ICNN-QR model The input data of the ICNN-QR model for the regional PV generation forecast include the historical PV generation, irradiance, and ambient temperature data obtained for each PV plant in the selected region. The output of the model contains different quantiles of regional PV power generation. The training method of the ICNN-QR model is identical to that of the traditional CNN model, which generally uses gradient descent techniques based on the batch gradient descent and stochastic gradient descent methods [29]. Because the batch gradient descent method considers all samples in the parameter updating process, the training speed decreases as the number of samples increases. In contrast, the stochastic gradient descent method randomly selects a set of samples and then updates the model parameters, which considerably increases the training speed [30]. Therefore, the stochastic gradient descent method is used for training the ICNN-QR model in this paper. The training process of the ICNN-QR model is illustrated in Fig. 4. First, the weights and bias of the ICNN are initialised, after which input data are transmitted forward through the ICNN. In the next step, the error of the output value of the ICNN-QR model is computed with respect to the target value. If the calculated error is larger than the predetermined threshold value, the error is transmitted back to the ICNN-QR model. The errors of the fully connected layers, pooling layers, and convolutional layers are obtained successively. The weights and biases of each layer are updated by minimising the loss function, and the training process returns to the data forward transmission step. If the calculated error value does not exceed the threshold value, the training process ends. Fig. 4Open in figure viewerPowerPoint Training process of the ICNN-QR model 4 Forecast evaluation criteria 4.1 Deterministic forecast evaluation criteria In this paper, the mean absolute error (MAE) and root mean square error (RMSE) are selected as the deterministic forecast evaluation criteria, which can be expressed as (6) (7) where N denotes the number of samples; and represent the actual PV power and forecasted PV power of the i th sample, respectively; and denotes the nominal capacity of the PV plant where the i th sample is located. 4.2 Probabilistic forecast evaluation criteria Probabilistic forecast results can be evaluated in terms of the reliability and sharpness [31] as described below. 4.2.1 Reliability Reliability refers to the ability of a model to match the forecasted data distribution with the actual observations. The reliability index R ACE can be calculated from the PI coverage probability P ICP at a given confidence level as follows: (8) The P ICP value is expressed as (9) where N denotes the number of samples, and is the indication function (10) where is the PI calculated by the forecast model at the confidence level . The smaller is the absolute value of R ACE, the more reliable is the probabilistic forecast. Ideally, R ACE should be equal to 0. 4.2.2 Sharpness The sharpness is measured by the width of the PIs and reflects the concentration of the forecasted distribution. It can be evaluated by calculating the PI-normalised average width of P INAW : (11) where R represents the difference between the maximum and minimum sample values. The probabilistic forecast should be sharp, and the PI width should be as narrow as possible. The smaller is the P INAW value, the sharper is the forecasted distribution. 4.2.3 Comprehensive evaluation In this paper, the pinball score is used to comprehensively evaluate the quantile forecast results in terms of reliability and sharpness. The pinball score can be calculated as follows: (12) where denotes the actual PV power, and is the forecasted PV power in the quantile. The smaller pinball score corresponds to the higher forecast accuracy. 5 Case study In this section, the ICNN-QR probabilistic forecast model is used to forecast the regional PV power generation. The proposed method is validated by comparing the forecast results with several benchmarks. 5.1 Data description and pre-processing The 6-month historical data, including the PV power and NWP data of each PV plant (over the period from October 2017 to March 2018 with a 15-min resolution) are collected. The collected data are divided into two datasets: the training dataset (including the first 5-month data) and the test dataset (the last-month data). The training dataset is used to train the ICNN-QR model, and the test dataset is used to verify the effectiveness of the model. The forecast models employed in the case study are constructed using the TensorFlow software library written in the Python programming language. The locations of the selected PV plants are shown in Fig. 5, and their nominal capacities are listed in Table 1. Fig. 5Open in figure viewerPowerPoint Locations of the PV plants in Weifang, Shandong Province, China Table 1. Nominal capacities of the studied PV plants PV plants Nominal capacity, MW PV plant 1 20 PV plant 2 50 PV plant 3 20 PV plant 4 25 PV plant 5 25 PV plant 6 20 PV plant 7 25 PV plant 8 25 PV plant 9 20 PV plant 10 20 regional PV plants 250 Before the network training procedure, the input data are normalised to eliminate the forecast error caused by the different forms of raw data according to the formula (13) where represents the normalised value of the i th sample, denotes the value of the i th sample, and and represent the maximum and minimum sample values, respectively. The range of the normalised data is [0, 1] in this paper. 5.2 Model verification The proposed probabilistic forecast model of regional PV power generation combines the ICNN with non-linear QR. The ICNN extracts features from the input data and maps the non-linear correlation between the input and output data, and the non-linear QR method quantitatively estimates the uncertainty of the regional PV generation forecast. In this case study, the ambient temperature, irradiance and the power output of the individual PV plant of the ten selected PV plants are input into ten Conv-pool structures, respectively. The extracted features of each Conv-pool structure are integrated, and input into the fully connected layers to further excavate the features of all PV plants. The output layer outputs the forecast results under different quantiles. In the convolutional layer, the convolutional kernel is set as 3 × 3, and the filters are set to 8. In the pooling layer, the pooling kernel is designed as 2 × 2. The pooling function of the pooling layer is the maximum pooling and the fully connected layers are as the two-layer structure. Fig. 6 shows the PIs of the three-day ahead probabilistic forecast, which are obtained by the proposed method for 13–15 March 2018 and the forecast time resolution is 15 min. The actual regional PV power generation curve is also plotted in Fig. 6. Since the output power of regional PV plants is null at night, only the PV generation from 7:00 a.m. to 5:00 p.m. are considered in the study. It can be seen that the actual regional PV generation curve can be well covered by the PIs obtained by the proposed model, which intuitively demonstrates that the effectiveness of the proposed method on the regional PV power probabilistic forecast. Fig. 6Open in figure viewerPowerPoint PIs of the three-day ahead probabilistic forecast obtained by the proposed method for 13–15 March 2018 Fig. 7 shows the PDF curves recorded for the three time periods of 13 March 2018 (at 8:00 a.m., 12:00 p.m., and 2:00 p.m.). Here, the output quantiles of the ICNN-QR model are used as the input, and the PDF of regional PV power generation is obtained by the kernel density estimation [32]. All the actual regional PV power generation values are located in the middles of the corresponding PDF curves, which indicates that the forecasted value with the highest probability is close to the actual PV power generation. Fig. 7Open in figure viewerPowerPoint Probability density curves generated by the proposed method on 13 March 2018 at (a) 8:00 a.m., (b) 12:00 p.m., (c) 2:00 p.m 5.3 Comparison of different forecast models In order to further assess the performance of the proposed model, several benchmarks, including point forecast methods and probabilistic forecast methods, are presented and compared with the proposed method. 5.3.1 Point forecast method Here, the middle values of the proposed model (50% quantiles) are selected as the point forecast results, which are compared with the results produced by the bottom-up and upscaling forecast methods. Regional PV power generation of the ten PV plants is forecasted by the bottom-up method, while the SVM and NN forecast methods are used for the individual PV plant. The SVM approach uses the Gaussian function as the kernel function. The NN in the case study is designed as one input layer, two hidden layers and one output layer. The hidden layers use ReLU function as the activation function. And the training method uses the stochastic gradient descent method. The forecast results of the individual PV plant are added up to obtain the regional PV power generation. Meanwhile, the upscaling method first selects the most relevant PV plants by analysing the existing correlation between different PV plants in the study region and then applies the SVM and NN techniques to forecast the power for the representative PV plants. The regional PV generation is obtained by upscaling the forecast generation of the representative PV plant. The calculated MAE and RMSE (Table 2) are used to evaluate the performance of regional PV power point forecast methods. According to Table 2, the MAE and RMSE of the proposed method are much smaller than those of the bottom-up and upscaling forecast methods which use the NN and SVM to forecast the power outputs of the individual PV plant. Therefore, the forecast accuracy of the proposed method is superior to the accuracies of the widely used