Accurate prediction of photovoltaic power output based on long short‐term memory network

IET OptoelectronicsVolume 14, Issue 6 p. 399-405 Research ArticleFree Access Accurate prediction of photovoltaic power output based on long short-term memory network Nan-Run Zhou, Department of Electronic Information Engineering, Nanchang University, Nanchang, 330031 People's Republic of ChinaSearch for more papers by this authorYi Zhou, Department of Electronic Information Engineering, Nanchang University, Nanchang, 330031 People's Republic of ChinaSearch for more papers by this authorLi-Hua Gong, Department of Electronic Information Engineering, Nanchang University, Nanchang, 330031 People's Republic of ChinaSearch for more papers by this authorMin-Lin Jiang, Corresponding Author minlinjiang@ncu.edu.cn Institute for Advanced Study, Nanchang University, Nanchang, 330031 People's Republic of ChinaSearch for more papers by this author Nan-Run Zhou, Department of Electronic Information Engineering, Nanchang University, Nanchang, 330031 People's Republic of ChinaSearch for more papers by this authorYi Zhou, Department of Electronic Information Engineering, Nanchang University, Nanchang, 330031 People's Republic of ChinaSearch for more papers by this authorLi-Hua Gong, Department of Electronic Information Engineering, Nanchang University, Nanchang, 330031 People's Republic of ChinaSearch for more papers by this authorMin-Lin Jiang, Corresponding Author minlinjiang@ncu.edu.cn Institute for Advanced Study, Nanchang University, Nanchang, 330031 People's Republic of ChinaSearch for more papers by this author First published: 01 December 2020 https://doi.org/10.1049/iet-opt.2020.0021AboutSectionsPDF 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 An accurate power output prediction of the photovoltaic system is pivotal to eliminate the extra cost and the negative impact in the utility grid integrated with photovoltaic power sources. The power output of a photovoltaic system is predicted by introducing a long short-term memory method. Moreover, the influence of noise data on prediction results is eliminated with the empirical mode decomposition. To further improve the accuracy and stability of the prediction method, the parameters of long short-term memory neural networks are determined with a sine cosine algorithm. The performances of the long short-term memory method in terms of root mean square error, mean absolute error, and coefficient of determination in January and August are analysed, respectively. Compared with other prediction schemes, the long short-term memory method provides superior accuracy for photovoltaic power output prediction. 1 Introduction The consumption of traditional energy sources such as coal, oil, and gas has caused serious pollution to the earth [1–4], therefore, the development and utilisation of renewable energy technologies is an urgent task. Photovoltaic (PV) technology has drawn increasing attention because it can turn sunlight into electricity directly [5–7]. In 2018, the installed capacity of global PV power generation systems increased by ∼100 GW and the total installed capacity reached 500 GW [8]. It is estimated that the global installed capacity of PV power generation systems would reach 1700 GW in 2030 [9]. The installed capacity of PV systems has grown rapidly in recent years because of the improvement of component efficiency and the reduction of maintenance and operating costs [10]. In the past decade, the construction cost of PV power generation systems has dropped by 59% owing to the improvement of technology and the introduction of new materials [11]. However, the intermittency and variability of solar energy would result in voltage instability and power uncertainty, which limits the large-scale application of PV technology [12–14]. Therefore, an accurate PV power prediction is of great significance to reduce the negative impact of solar energy and improve the reliability of the PV system [15, 16]. Traditional time series prediction methods, such as autoregressive model [17] and autoregressive moving average [18], are commonly employed in PV power output prediction and many researchers took lots of effort to improve the performance of time series prediction model. However, most of these prediction methods are linear prediction models, which cannot entirely analyse the factors affecting the PV power output because of the time-varying and inherent non-linear characteristics [19]. Recently, it has been proved that the machine learning method has superior performance in time series processing. Artificial neural network and support vector regression (SVR) are two widely applied machined learning techniques because of their strong non-linearity regression capacity. For instance, Liu et al. accurately predicted the next 24 h PV power output by a backpropagation neural network with the inputs of aerosol index data, wind speed, humidity, and temperature [20]. An Elman neural network PV power output prediction method based on kernel principal component analysis and association rules was invented to enhance the generalisation ability and improve the prediction accuracy [21]. Compared with the artificial neural network model, the training of SVR only requires a small amount of experimental data in solving non-linear problems [22]. The power output of a grid-connected PV system was predicted by combining the SVR with the weather classification method, which achieves a mean relative error of 8.64% [23]. Zeng and Qiao investigated the next hour PV power output prediction model based on a least-square support vector machine with the inputs of wind speed, sky-cover, atmospheric transmissivity, and relative humidity (RH) [24]. The performance of their adopted model is better than that of autoregressive or radial basis function neural networks. However, the performance of SVR depends largely on many parameters, such as penalty, tube radius, and the parameters of the kernel function. The adjustment of these parameters is complicated and time-consuming. Long short-term memory (LSTM), as an advanced recurrent neural network, was applied extensively in the fields of artificial language forecast, speech recognition, and handwriting generation [25]. The LSTM can reserve relevant information and discard irrelevant features by maintaining a memory unit during training. This characteristic makes LSTM networks very suitable for the PV power output prediction. Recently, a day-ahead PV power forecast method based on LSTM and weather classification approach was designed, which reached a root mean square error (RMSE) of 4.62% under ideal weather conditions [26]. Ospina et al. forecasted the power output values of large-scale and small-scale PV systems based on four LSTM neural networks [27]. After that, Han et al. provided a mid-to-long-term wind and PV power generation prediction approach combining copula function with LSTM and the results indicate their proposed approach outperforms the persistence model and the support vector machine model [28]. Wang et al. also gave a hybrid model based on LSTM and convolutional network for PV power prediction, where the temporal features of data are extracted by LSTM and the spatial features of data are extracted by a convolutional network [29]. Moreover, Zheng et al. devised an algorithm combining LSTM with a particle optimisation algorithm to predict the power output of multi-region solar power plants [30], in which the hyper-parameters of LSTM are searched with the particle optimisation algorithm. Although some studies on PV power output prediction based on LSTM have been conducted, there is still room to improve the prediction accuracy by optimising the LSTM model. Meanwhile, many scholars focused on improving the performance of the model without consideration of the impact of data noise on the prediction results. Motivated by these, an accurate prediction method of PV power output based on the LSTM network has been investigated and the impact of data quality and parameter setting on prediction results are considered in this study. The major achievements and innovations are summarised as follows: (i) The introduced LSTM prediction model is trained and validated by using the historical dataset from a read-world PV system. Five influence factors, i.e. global horizontal irradiance (GHI), diffuse horizontal irradiance (DHI), RH, air temperature (AT), and history PV power output are considered as the inputs of the LSTM network to predict the future PV power output. (ii) To explore the effect of seasons on the forecast horizon, the proposed prediction scheme is carried out in two typical months, i.e. January and August, where RMSE, mean absolute error (MAE), and coefficient of determination are regarded as evaluation metrics. (iii) To optimise the performance of the LSTM model, a sine cosine algorithm (SCA) is employed to search the parameters of LSTM and a data denoising method based on empirical mode decomposition (EMD) is designed to reduce the influence of noise data on prediction results. The outline of this paper is organised as follows. The architecture of the LSTM prediction model is described in Section 2. The implementation procedure is given in Section 3. The prediction results and analyses are provided in Section 4 and a brief conclusion is drawn in Section 5. 2 Architecture of the LSTM prediction model 2.1 Empirical mode decomposition (EMD) The EMD can decompose the input time series into several intrinsic mode functions (IMFs) and a residual component. Suppose is the input time series signal, the detailed procedures of EMD can be explained as follows. Step 1: The local minima and maxima of can be identified. Step 2: The lower envelope and upper envelope are fitted by the cubic spline interpolation of the local minima and local maxima. Step 3: The mean value of lower and upper envelopes can be calculated (1) Step 4: A new series signal can be obtained by (2) Step 5: Steps 2–4 are repeated until one of the following criteria is satisfied: (i) approaches 0; (ii) the number of zeroes and extreme points of is equal or differ by one; and (iii) the maximal iteration is reached. Step 6: is treated as a new IMF and the residual signal is (3) Step 7: is replaced by . Step 8: Steps 1–7 are repeated until all IMFs are obtained. 2.2 Sine cosine algorithm (SCA) SCA is a new optimisation algorithm based on sine and cosine functions, which is invented by Mirjalili in 2016 [31]. The position of each agent is updated by (4)where represents the position of the ith solution at the tth iteration, is the optimal position at the tth iteration, , , and are random numbers, is the control parameter, i.e. (5)where a is a constant and represents the maximal number of iterations. The pseudo code of the SCA is shown in Table 1. Table 1. Pseudo-code of the SCA 1: Initialise N solutions. 2: Set the initial iteration number . 3: Repeat 4: Evaluate each solution by objection function. 5: Determine the best solution. 6: Update , , , and . 7: Update the position of search agents with (4). 8: Set . 9: Until . 10: Return the best solution obtained as global optimum solution. 2.3 LSTM neural network The architecture of a single LSTM cell at time step t is replotted in Fig. 1 [32]. , , , and are update gate, input gate, forget gate, and output gate, respectively. The LSTM cell receives the input data from the current time step and the previous time step . The forget gate, as a key element of the LSTM cell, determines how much information should be discarded from the memory. In (6) and (7), the hard sigmoid activation is served as the transmission function. Equations (7) and (8) provide the working mechanism of input and update gates, respectively. The cell state is updated recursively as rendered in (9). Finally, the output gate is calculated with (10), and then the final cell output can be obtained by (11). and denote the weight matrices of input and output, respectively, and is a bias vector and . represents the Hadamard product (6) (7) (8) (9) (10) (11)The predicted target is projected by (12)where is a projection matrix. As exhibited in (13), the training of LSTM with the backpropagation of gradient descent is to minimise the usual squared error objection function f(13)where denotes the actual target. This procedure can be accomplished by an offline task. Therefore, the PV prediction with LSTM can be completed at a rapid rate. Fig. 1Open in figure viewerPowerPoint Structure of a LSTM cell To evaluate the performance of the LSTM prediction model, RMSE, MAE, and are employed as the evaluation indexes. The mathematical forms of RMSE, MAE, and are defined as (14) (15) (16)where N is the total hour, and are the actual and predicted PV power output values at the ith hour, respectively. 3 Implementation procedure of the LSTM prediction model The operational flowchart of the LSTM prediction model is displayed in Fig. 2 and the detailed process is as follows. Step 1: The historical PV power output data and meteorological data are collected as input data. Fig. 2Open in figure viewerPowerPoint Operational flowchart of the proposed LSTM prediction model Step 2: The input data is decomposed into IMFs and residual components with EMD. Step 3: To reduce the influence of high-frequency noise on prediction results, the high-frequency IMFs are removed and the medium-frequency and low-frequency IMFs are recombined. Step 4: The recombined data is standardised by (17)where n is the number of samples, and are the standardised sample and original one, respectively. Step 5: The initial parameters of LSTM, i.e. neural units, learning rate, and batch size are randomly assigned, where the value ranges of neural units, learning rate, and batch size are , , and , respectively. Step 6: The LSTM network is trained with the training dataset. Step 7: The RMSE between the predicted PV power value and the measured PV one in the validation dataset is utilised as a fitness function and the fitness value of each agent is calculated. Step 8: The values of , , and are regenerated randomly. Step 9: The value of is updated with (5). Step 10: The position of each agent is updated with (4). Step 11: Steps 4–9 are repeated until the maximal number of iterations or the pre-set accuracy is reached. Step 12: The optimal values of neural units, learning rate, and batch size in the LSTM can be obtained. Step 13: The LSTM is retrained with the data samples consisting of the training dataset and validation dataset. Step 14: The PV power output for the next day is predicted by the LSTM network. 4 Prediction results and analysis 4.1 Theory analysis The accuracy of the data-driven based prediction model mainly depends on the quality of the collected data. During the data acquisition, the quality of the data is affected by various external factors, such as measurement errors, transmission failures, and so on. In the proposal, the impact of noise data on the prediction results is eliminated with EMD. Compared with Fourier decomposition and wavelet decomposition, EMD has better time-frequency concentration and can decompose any type of signal without hypothesis. Thus EMD is a quite effective method to deal with the noise signal. The accuracy of the prediction model can be improved by denoising historical meteorological data with EMD. The performance of LSTM is affected by neural units, learning rates, and batch size. The increase in the number of neural units would make the network more complicated. Conversely, the decrease of the number of neural units makes the network lack the necessary learning and information processing capacities. Similarly, an excessively high learning rate will result in the network to skip the optimal point during training. A too low learning rate would reduce the training speed of the network. In addition, the larger batch size makes the network more accurately move towards an extreme value. However, the scale of batch size is limited by the hardware resources of computers. Therefore, the adjustments of neural units, learning rate, and batch size have a decisive influence on prediction results. The trial-and-error method is a traditional method to determine the LSTM parameters, which is time-consuming and cannot guarantee the optimal parameter value can be found. SCA is an excellent intelligent optimisation algorithm, which can balance the global search and local mining capabilities by the adaptability and randomness of parameters. Many studies indicate that SCA has a better search capacity than a particle swarm algorithm, a genetic algorithm, and a cuckoo search algorithm [33]. Thus, the accuracy and stability of the LSTM prediction model are improved with SCA to search neural units, learning rate, and batch size. 4.2 Data analysis The 2017 PV power output and meteorological data with the resolution of 5 min were collected from the 25 desert knowledge australia solar centre (DKASC), Alice Spring PV system [34]. The specification of this PV system is listed in Table 2 and the meteorological data include GHI, DHI, RH, and AT. The PV system with a peak power of 5.83 kW consists of 22 modules and each module has a capacity of 265 W. Fig. 3 presents the correlation coefficient between the PV power output and four weather variables (GHI, DHI, RH, and AT). Obviously, GHI is pretty positively correlated with the PV power output, while DHI and AT are moderately positively correlated with the PV power output. There is a negative correlation between PV power output and RH. By taking these meteorological factors as the inputs of the LSTM model, the prediction accuracy can be enhanced to some extent. Fig. 3Open in figure viewerPowerPoint Correlation coefficient between each of the weather variables and PV power output in 2017 Table 2. Properties of the PV system Property Specification PV cell poly-Si array structure fixed ground mount array rating 5.83 kW module rating 265 WP number of modules 22 inverter type/size SMA SMC/6000 A installation completed 2 July 2016 array tilt/azimuth 20°/0° (solar north) Fig. 4 shows the monthly average PV power output curve in 2017. As can be observed from Fig. 4, the fluctuation of the PV power output curves in summer (December to February) is obvious, while the fluctuation of the PV power output curves in winter (June to August) is relatively smooth. Fig. 5 shows the distribution of the PV power output values at noon for each month in 2017. Owing to the local seasonal characteristic, the fluctuation of PV power values in January is more volatile than those in other months, while the fluctuation in August is the least. Thus, the history data in January and August are selected to train the LSTM model for performance comparison. Fig. 4Open in figure viewerPowerPoint Monthly average PV power output curves in 2017 Fig. 5Open in figure viewerPowerPoint Distribution of PV power output at noon (12:00) for each month in 2017 Fig. 6 exhibits the distribution of hourly PV power output data throughout 2017. Apparently, the PV power values are highly correlated with the moment of each day. The peak power occurs between 12:00 and 13:00, while the PV power output values are relatively low at the beginning and end of each day. Some red outliers appear below the first quartile because of some terrible weather conditions. Therefore, the data samples from 8:00 to 18:00 in January and August 2017 are considered for the training of the LSTM model. Fig. 6Open in figure viewerPowerPoint Distribution of hourly PV power output data in 2017 4.3 Parameter setting analysis The influence on the prediction results is analysed in terms of input meteorological variables, dataset division, and the parameter setting of SCA. The prediction accuracy can be improved by selecting the key input variables and the training effect is affected by different dataset divisions. Besides, the performance of the LSTM is influenced by the parameter setting of the SCA. Five different cases are designed to test the influence of different weather variables on the prediction results and the detailed test results are shown in Table 3. As can be observed from Table 3, the proposed LSTM prediction model has a higher accuracy with the inputs of PV power output values and GHI, in which the RMSE and MAE values are 0.5241 and 0.3025 kW, respectively. Therefore, the historical PV power output values and GHI are considered as the input parameters of the proposed LSTM prediction model. Table 3. RMSE and MAE results by feeding different input variables Input variable RMSE, kW MAE, kW case 1 PV power output values and GHI 0.5283 0.3066 case 2 PV power output values, GHI and DHI 0.5533 0.3270 case 3 PV power output values, GHI, DHI, and AT 0.6657 0.4196 case 4 PV power output values, GHI, DHI, AT, and RH 0.7877 0.4483 case 5 GHI, DHI, AT, and RH 0.6099 0.4064 The RMSE and MAE results with different data divisions are shown in Table 4. On the whole, the RMSE and MAE values are not significantly different from the change of dataset division. The proposed LSTM prediction model possesses slightly better accuracy while the percentages of training dataset and validation dataset are and , respectively. Thus, the percentages of the training dataset, validation dataset, and testing dataset for the prediction model are , , and , respectively. Table 4. RMSE and MAE results with different data divisions Training dataset Validation dataset Testing dataset RMSE, kW MAE, kW case 1 80% 10% 10% 0.5241 0.3025 case 2 75% 15% 10% 0.5428 0.3324 case 3 70% 20% 10% 0.5268 0.3242 In the SCA, it is easier to find the global optimal solution with a larger population size. However, the calculation speed is greatly reduced with the increase of the population size. The appropriate population size and number of iterations are of great significance in balancing the efficiency and the accuracy of the SCA. The RMSE and MAE results with different population sizes and iteration times are shown in Table 5. Obviously, the prediction results have not decreased significantly with the increase in population size or the number of iterations. Therefore, the population size and number of iterations in the proposed LSTM model are 10 and 30, respectively. Table 5. RMSE and MAE results with the different parameters of SCA Size of group Number of iterations RMSE, kW MAE, kW case 1 10 30 0.5241 0.3025 case 2 10 50 0.5172 0.3081 case 3 20 30 0.5167 0.3149 case 4 30 30 0.5256 0.3050 case 6 30 50 0.5632 0.3157 4.4 Prediction results Fig. 7 shows the correlation distributions between forecasted power output values and actual power output values in two typical months, i.e. January and August. The correlation distribution in Figs. 7b is similar to linear distribution, which demonstrates that the predicted power output values for the LSTM model are consistent with the actual PV power output values in August. Whereas, a larger discrepancy between forecasted power output values and actual power output values can be noticed in January. Fig. 7Open in figure viewerPowerPoint Correlation distribution between forecasted and actual power values in two typical months (a) January, (b) August The predicted PV power output results in two typical months are displayed in Figs. 8. Obviously, the LSTM model has a better prediction effect in August, since the predicted PV power output values in August are closer to the actual power values than those in January. As shown in Figs. 8a, the LSTM model can also accurately predict the PV power output to some extent even if the fluctuation of the actual PV power output curves is obvious in January. Overall, the LSTM model can achieve a satisfactory prediction result under different seasons. Fig. 8Open in figure viewerPowerPoint Predicted PV power output curve in two typical months (a) January, (b) August 4.5 Comparison experiment Several other prediction schemes are employed to verify the superiority of the proposed prediction model. The abbreviation of each prediction model is shown in Table 6. For the month with fickle weather conditions, the prediction results obtained by different prediction models are quite different. To verify the accuracy of the proposed model in fickle weather conditions, the comparison experiment is conducted in January and the prediction results by different models are shown in Fig. 9. Compared with the other prediction models, the predicted curve by the proposed model is closer to the actual power curve. The prediction errors by different models in terms of RMSE and MAE are presented in Table 7. The RMSE and MAE of the proposed ELM-SCA-ELM model are less than those of other models, and their values are 0.5283 and 0.3063 kW, respectively, obtained by the ELM-SCA-ELM model is 0.9210, which demonstrates that there is a good correlation between the actual value and the corresponding predicted one. Therefore, the proposed model has higher accuracy than the other prediction models. Fig. 9Open in figure viewerPowerPoint Prediction results by different prediction models (a) LSTM, (b) AGPR, (c) EMD-SCA-ELM, (d) EMD-SCA-LSTM Table 6. Abbreviation of each prediction model Abbreviation Full name LSTM prediction model based on LSTM neural network [35] AGPR prediction model based on Gaussian process regression with active learning [36] EMD-SCA-ELM prediction model based on EMD, SCA, and ELM [33] EMD-SCA-LSTM proposed prediction model Table 7. Prediction errors by different models Models RMSE, kW MAE, kW LSTM 0.7031 0.4473 0.8600 AGPR 0.5894 0.3105 0.9016 EMD-SCA-ELM 0.6281 0.3817 0.8883 EMD-SCA-LSTM 0.5283 0.3063 0.9210 5 Conclusion An accurate PV power output prediction scheme based on the LSTM network is investigated with the inputs of GHI and history PV power values. Based on empirical model decomposition, a denoising method is designed to improve the prediction accuracy and reduce the influence of data noise on prediction results. Moreover, to further improve the accuracy and stability of the prediction model, the number of neural units, the learning rate, and the batch size are determined by the SCA. The prediction results indicate the proposed prediction can accurately predict PV power output under different seasons. 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