Forecasting Solar Power Generated by Grid Connected PV Systems Using Ensembles of Neural Networks

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1 Forecasting Solar Power Generated by Grid Connected PV Systems Using Ensembles of Neural Networks Mashud Rana Australian Energy Research Institute University of New South Wales NSW, Australia Irena Koprinska School of Information Technologies The University of Sydney NSW, Australia Vassilios G Agelidis Australian Energy Research Institute University of New South Wales NSW, Australia [email protected] Abstract Forecasting solar power generated from photovoltaic systems at different time intervals is necessary for ensuring reliable and economic operation of the electricity grid. In this paper, we study the application of neural networks for predicting the next day photovoltaic power outputs in 3 minutes intervals from the previous values, out using any exogenous data. We propose three different approaches based on ensembles of neural networks - two non-iterative and one iterative. We evaluate the performance of these approaches using four Australian solar datasets for one year. This includes assessing predictive accuracy, evaluating the benefit of using an ensemble, and comparing performance two persistence models used as baselines and a prediction model based on support vector regression. The results show that among the three proposed approaches, the iterative approach was the most accurate and it also outperformed all other methods used for comparison. Keywords solar power forecasting; renewable energy; neural networks; ensemble of classifiers; clustering; iterative prediction I. INTRODUCTION Solar power generated from photovoltaic (PV) systems is one of the fastest growing and most promising sources of renewable energy [1]. PV systems produce electricity directly by utilizing the absorbed solar irradiance. Many countries have built large-scale PV plants and connected them to the electricity grid [2, 3]. In Australia, the solar irradiance per square meter is the highest compared to any other continent in the world [4], which has led to a rapid increase of gridconnected and standalone PV systems. However, the power produced by a PV system is highly variable and intermittent, which makes the integration of the produced solar energy into the electricity transmission and distribution networks a challenging task. The power produced by a PV system depends on the solar irradiance, cloud cover and other weather and environmental conditions, and also on the parameters of the PV systems. To ensure reliable and economic operation of the power grid, it is essential to forecast the power output from PV systems accurately at short time intervals (from minutes to a day ahead). This is needed not only for maintaining the stability of the grid, but also for supporting the transactions of electricity suppliers, providers and traders at competitive electricity markets. Solar power forecasting has received an increased attention recently due to new legislations encouraging the deployment of solar power plants. The most prominent approaches are based on statistical methods such as auto regression, moving average and their combinations [5, 6], computational intelligence methods such as Neural Networks (NNs) [2, 3, 5, 7, 8], nearest neighbor [5] and Support Vector Regression (SVR) [9-11], and also fuzzy inference Most of the existing approaches predict the PV power output indirectly by firstly predicting the solar irradiance (or using predictions provided by meteorological centers) and then converting the predicted solar irradiance into PV power output by considering the characteristics of the PV plant such as area and efficiency. However, obtaining local weather forecasts of solar irradiance, cloud coverage and other meteorological variables for the site of the PV plant is not always possible. In this paper, we consider the task of directly predicting the PV power output from previous PV output data only, out using any exogenous environmental and meteorological variables. While the majority of previous work focuses on one step ahead prediction, i.e. at time t, the task is to predict the power output at time t+1, we consider multiple step ahead prediction our goal is to predict all half-hourly PV power outputs for the next day. More formally, given a time sequence of PV power outputs up to the day d,,,,,, where P i is a vector of half-hourly PV power outputs for day i, i.e.

2 ,,, our goal is to forecast,,, all half-hourly power outputs for day d+1. As prediction models we developed and applied ensembles of NNs. Although feed-forward NNs have been successful for forecasting time series in various applications, their performance is sensitive to many parameters, including the network architecture and random initialization of weights. Combining several NNs in an ensemble can reduce this sensitivity. Ensembles of NNs have been shown to be successful for multiple steps ahead prediction of electricity load data [12, 13]. The contributions of this paper are: 1. We propose three different NN ensemble based approaches for forecasting the half-hourly PV power outputs for the next day, using only previous power data. The first two approaches predict all power outputs for the next day simultaneously and the third one does this iteratively by using the previously predicted values. 2. We comprehensively evaluate the performance of the proposed approaches using four datasets of Australian PV power half-hourly data, for one year. We compare their performance two persistence models used as baselines, and a SVR based prediction model. This paper is organized as follows. Section II provides an overview of the related work. Section III describes the data used in our study. Section IV presents our proposed approaches for forecasting the solar power output. Section V presents and discusses the results, and Section VI concludes the paper. II. RELATED WORK Forecasting solar power output from PV systems is a relatively new topic that is receiving significant attention due to the growing production and use of solar energy. In this section we briefly review the previous work on PV power prediction. Most of the existing approaches predict the solar irradiance and use it to estimate the power output (indirect prediction) but there are also some recent approaches that directly predict the PV power output. Inman et al. [14] reviewed methods for solar power forecasting and classified them into five main groups: statistical (regressive) methods (e.g. auto regressive, moving average, and combinations of them such as ARIMA), methods based on artificial intelligence techniques (e.g. NNs, nearest neighbor), numerical weather prediction methods, remote sensing methods (e.g. satellite and statistical satellite) and local sensing methods (e.g. sky-imager). Pedro and Coimbra [5] predicted the solar power 1 and 2 hours ahead from a time series of previous solar power values only, out using any exogenous variables. They compared the performance of four methods: ARIMA, k nearest neighbor, NN trained the backpropagation algorithm and NN trained a genetic algorithm. They conducted an evaluation using data for two full years and found that the two NN based methods outperformed the other methods, and that the NN trained the genetic algorithm was the most accurate prediction model. The two NN approaches obtained Mean Absolute Error () in the range of for 1 hour ahead prediction and for 2 hours ahead prediction for a 1 MW PV power plant. Chen et al. [2] introduced a new approach for 1 to 24 hours ahead solar power prediction based on Radial Basis Function NN (RBFNN). At first, they categorized the days into sunny, cloudy and rainy using self-organizing map NNs and based on the weather predictions of solar irradiance and cloudiness. Then, a separate RBFNN prediction model for each group was trained to predict the 24 hourly PV power outputs for the next day. Shi et al. [9] proposed a similar approach the days were clustered into four groups (clear-sky, cloudy, foggy and rainy) and a separate SVR prediction model was built for each group. The obtained Mean Relative Error () was between 4.85 (for sunny day) and (for cloudy day). Chow et al. [8] applied NNs for predicting the PV power output 1 and 2 minutes ahead. As inputs to the NNs they used solar irradiation, temperature, solar elevation angle and solar azimuth angle. They developed multi-layer perceptron one hidden layer, trained the backpropagation algorithm, early stopping criterion based on validation set to avoid overtraining. The results were promising and showed that NNs can successfully model the nonlinear relationship between the meteorological parameters and the PV solar power output. Mandal et al. [7] used wavelet transform in conjunction RBFNNs. They firstly decomposed the highly fluctuating PV power time series data into multiple time-frequency components. The one hour ahead decomposed PV power output was then predicted using the decomposed components, as well as previous solar irradiation and temperature data. The final prediction was generated by applying the inversed wavelet transform. The results showed good accuracy, the combination of wavelet transform and RBFNN outperforming RBFNN out wavelets. Mellit et al. [15] presented a different wavelet based approach, called wavelet network. Instead of decomposing the data and applying NNs to predict each component, they used wavelets as activation functions in the NNs. The approach was effective, achieving Mean Absolute Percentage Error (MAPE) of about 6. Zeng and Qjao [1] studied the application of SVR for solar power forecasting. They applied SVR to predict the atmospheric transmissivity using historical transmissivity and other meteorological data. The predicted transmissivity was then converted back to solar power according to the latitude of the PV site and time of the day. The evaluation showed that SVR was more accurate compared to ARIMA and RBFNN. Approaches based on fuzzy logic were also proposed. Jararzadeh et al. in [16] investigated the application of interval type-2 Takagi-Sugeno-Kang fuzzy systems. Using temperature and solar irradiance as inputs, they predicted the output of PV plants under different operating conditions, and showed better results than ARIMA. Yona et al. [17] proposed a hybrid approach by combing NNs and fuzzy theory. They first applied a fuzzy model to estimate the hourly insolation using different

3 weather variables such as clouds, humidity and temperature. The output of the fuzzy model was then fed to a recurrent NN, to predict the hourly power output of the PV plant. Yang et al. [11] integrated SOM, SVR, and fuzzy inference to develop a hybrid approach for one day ahead solar power prediction. SOM and SVR were applied to classify the historical input data and to develop the prediction model, respectively. The fuzzy inference was used to select the best model from a group of trained SVRs, depending on the available weather predictions. An evaluation using one year of solar data showed that the hybrid method outperformed NN and SVR. III. DATA Solar Power [] a) Case study Time Lag (1 lag = 3 min) b) Case study 2 A. Case Studies We use data collected from the 1.22 MW PV system installed at the St. Lucia campus of the University of Queensland in Brisbane, Australia, and available from [18]. This is the largest PV system in Australia and consists of more than 5 polycrystalline silicon solar panels across four different sites. We use data from all four sites and consider the data from each site as a separate case study. For each case study, we use the data from 1st January to 31st December, 213. The data represents the power output of the PV arrays at the given location, in 3 minutes intervals. We only consider the data between 7: am to 5: pm as most of the data values outside this time window are either zero or not available. Thus, there are 7,3 data points (365 days 2 points per day) available for each case study. The data was normalized between -1 and 1. B. Data Characteristics Fig. 1 shows the PV power output for the four case studies for one week from Monday 4th February to Sunday 1th February, 213. We can see that the range of solar power varies for the different case studies it is highest for case study 1 (.9-43 ) and lowest for case study 2 (.3-9 ). This is due to the different capacity of the solar panel arrays installed at the four sites (e.g. the number of modules installed at site 1 is about five times higher compared to the number of modules at site 2). We can also observe that the four graphs show relatively similar patterns for the same day. This is as expected since the four sites are located close to each other and receive similar amount of solar irradiation. In general, for a typical sunny day (such as the first day in Fig. 1), the solar power starts to increase at the beginning of the day, reaches its peak around midday when the solar irradiance is highest and then gradually declines until the end of the day. By comparing the solar power profiles of different days for a given case study, we can see that the solar power is highly volatile it changes rapidly following the variations of the factors affecting its production, such as solar irradiance, cloud coverage, rainfall, temperature, humidity etc. The variable nature of the data makes the prediction task very challenging. Solar Power [] Solar Power [] Solar Power [] Time Lag (1 lag = 3 min) c) Case study Time Lag (1 lag = 3 min) d) Case study Time Lag (1 lag = 3 min) Fig. 1. PV power output for each case study for one week (from Monday 4th February to Sunday 1th February, 213) C. Training, Validation, and Testing Sets We divided the data for each case study into three nonoverlapping subsets: training (D train ), validation (D valid ), and testing (D test ). The data split was , following the recommendation in [19], resulting in 183 instances in D train, 91 in D valid and 91 in D test. One instance is 2-dimensional vector, where each value corresponds to the half-hourly PV power output for a single day from 7: am to 5: pm.

4 The training set was used to develop and trainn the prediction models, the validation set was used to identify the best architecture for the NN ensemble, and the t testing sett was used to evaluate the accuracy of the prediction models. IV V. PROPOSED APPROACHESS This section describes our three proposed NN based approaches for forecasting the day ahead half-hourly PV power outputs. A. Approach 1 (A 1 ) The first approach, A 1, applies an ensemble of NNs to build the prediction model. The motivation of using an ensemble of NNs instead of a single NN is to reduce the sensitivity of f NNs to the random initializationn of weights and network architecture. Adeodatoa et al. [ 13] and Ferreira et al. [2] have showed that ensembles of NNs were more accurate than single NN for time seriess prediction, especially for more than onee step ahead prediction. The key idea of A 1 is to simultaneously predict the twenty half-hourlnext day by using the power outputs from the previous day. PV power outputs from 7: am to 5: pm for the Thus, a single NNN from the ensemble has 2 input nodes for the half-hourly PV power output in day d, one hidden layer V nodes in it, and 2 output nodes providingg the predictions for day d+1, as shown in Fig. 2. Fig. 2. Architecture of a single NN, part of the NNN ensemble, for the proposed approaches A 1 and A 2. A 3 has the same architecture but one output node. We first constructed V different NN structures by varying the number of neurons in the hidden layer from 1 to V. For each structure, we then built an ensemble that consists of n NNs (we used n=2) as shown in Fig. 3. Each member of the ensemble has the same structure, i.e. the same number of hidden neurons, but is initialized to different random weights. Each of the n members of ensemble was trained separately on the training data using the Levenberg Marquardt (LM) algorithm [21]. We chose LM over thee standard steepest gradient descent backpropagation algorithm because of its faster convergence. The LM algorithm combines the steepest gradient descent and the Gauss-Newton algorithm, switching between them based on the complexity of the error surface. It preserves the advantages a of both algorithms: the fast convergence of the Gauss-Newton algorithm and the stability of the steepest gradient descent when used a small learning rate. Fig. 3. An ensemble of NNs EV We used the following NN parameters: tangent sigmoid transfer function for the hidden neurons and a linear transfer function for the output o neurons; the maximum training epoch was set to 3 and the regularization parameter was set to.9. To predict thee half-hourly power outputs for a given day, the individual predictions p off the ensemble members are combined by taking their median value (see Fig. 3), i.e. the prediction for time (half an hour) h for day d+1 is: =,,,,, where, is the prediction for h generated by an ensemble e member, h=1,...,2 and j=1,,...,n. The performance of each ensemble was evaluated on the validation set. The best performing ensemble, i.e. the one the lowest prediction error (), was then selected and used to predict the testing data. B. Approach 2 (AA 2 ) The main ideaa of A 2 is to first group the data into several clusters, and thenn build a separate NN prediction model for each cluster. The use of clustering is motivated by the different PV output for different types of days. In particular, the PV power output has different characteristics under different meteorological and environmental conditions [2] and shows significant variations during rainy days, cloudy days and days clear sky [9]. Fig. 4 presentss the main steps of approach A 2. The first step is partitioning thee available training data into k clusters using the X-Means algorithm [22]. X-Means is an extended version of the popular k-means algorithm. In contrast to k-means, X- means doesn t equire the number of clusters and the initial

5 centroids to be supplied by the user, but estimates them from the data. The application of X-Means generated the same number of clusters for each case study 3. This result is consistent the expected 3 types of days (clear sky, cloudy, and rainy) that have the most influence on the PV power output. Fig. 4. Main steps of approach A The second step is assigningg a cluster label to the instances from the training, validation and testing sets, and separating the instances that belong to each cluster. The third step is developing a prediction model for each cluster. To do this, A 2 applies the same method as A 1 it creates an ensemble of f NNs to predict simultaneously all half-hourly power outputs for the next day. To predict a new instance from the testing data, A 2 first identifies the NNs ensemble trained for the cluster c label of the new instance, and then uses this ensemble to producee the prediction. C. Approach 3 (A 3 ) In contrast to approaches A 1 and A 2 that predict simultaneously the half-hourly PV power outputs for the next day, A 3 does this iteratively. A prediction model (an ensemble of NNs one output node) is built for a single step ahead prediction. At time h, it makes a prediction for time h+1, and this prediction is then used to make the prediction for time h+2 and so on. This means that the predicted data for time h is considered as actual data and is appended to the end of the available actual data. The last twenty samples from the appendedd data are used to make prediction for time h+1, and this continues for all time A 2 points from the forecasting f horizon. This means that to make the prediction for the time h+1 of day d+1, where h>1, we use the previously recorded actual data till day d and the previously forecasted data for times 1 to h for day d+1. A similar iterative approach has been shown to be effective for forecasting of electricity load in [23]. The NNs ensemble is built t in the same way as for A 1 and A 2. The only difference is in the architecture of the ensemble member it has one o output node, not 2 as in A 1 and A 2. V. RESULTS AND DISCUSSION This section presents p and discusses the results for alll case studies. All reported results are results on thee testing data. A. Evaluation Metrics M To assess thee predictive accuracy, we used two standard performance measures, Mean Absolute Errorr () and Mean Relative Error (), as defined below: where: andd are the actual and predicted power output for day d at time h, respectively; D is the number of instances (days) in the test data; d H is the total number of predicted power outputs for a day (H=2( for ourr task) and R is the data range. B. Performance Evaluation E Table I presents the forecasting accuracy, averaged over all 2 hours from the forecasting horizon, for the t three proposed approaches. The results show that overall the iterative approach, A 3, is most accurate, followed by the non-iterative A 1 and A 2. In terms of average, M A 3 outperformed A and A 1 1.5, and the relative results for are similar. A comparison across A 1, A 2, andd A 3 for each case study shows that A 3 outperformed both A 1 and A 2 for all case studies except A 1 for case studyy 1. The E for the four case studies are in the range of for A 1, for A 2, and for A 3. TABLE I. ACCURACY OF THE PROPOSED APPROACHES A 1 Case Study E Avg A possible reason for the lower accuracy of A 2 is the small size of the clusters. The number of training examples assigned to each cluster was: 48 for cluster 1, 51 for cluster c 2 and 81 for A 2 A

6 cluster 3, for the first case study. Using a larger training data is likely to improve the clustering results, and in turn, the predictive accuracy results In terms of time required to build the prediction models, the more accurate approaches A 1 and A 3 needed less time than the less accurate A 2. This is because A 1 and A 3 create one prediction model, while A 2 first clusters the data and then creates a separate prediction model for each cluster (3 clusters and 3 prediction models for our data). Thus, as expected, the time required to build a prediction model for A 2 was about 3 times higher than the time for A 1 and A 3 (1 minutes compared to 3 minutes). This time includes the training time for all n ensemble members and the aggregation of their outputs. C. Ensemble of NNs vs single NN To assess the benefit of using an ensemble of NNs, we compared its performance the performance of a single NN, using the same experimental setting. The accuracy results for A 1, A 2, and A 3 a single NN are shown in Table II. A graphical comparison of the results for the ensemble (Table I) and single NN (Table II) is presented in Fig. 5. The results show that using an ensemble of NNs resulted in higher accuracy than using a single NN, for all three approaches. The improvements in terms of averaged over all case studies are 9.43, and 7.18 for A 1, A 2, and A 3, respectively. The computational cost of training an ensemble is higher than for a single NN, but suitable for both offline and online practical applications: 3-1 minutes for training an ensemble, compared to 1-3 sec for training a single NN. TABLE II. ACCURACY USING A SINGLE NN INSTEAD OF ENSEMBLE OF NNS A 1 A 2 A 3 Case Study Avg approaches. A 1, A 2, and A 3 achieved better prediction accuracy using an ensemble at acceptable computational cost. D. Comparative Study We compared the performance of our approach two persistence models (baselines) and a SVR based iterative approach. The first persistence model, B pday, considers the half-hourly PV power outputs from the previous day d, as the predictions for the next day d+1, i.e. the predictions for,, are given by,,. The second persistence model, B week, considers the halfhourly PV power outputs from the same day, one week before as the predictions for the next day, i.e. the predictions for,, are given by,,. SVR, on the other hand, is one of the state-of-the art machine learning algorithms for solving regression problems. SVR based prediction models have been shown to achieve promising accuracy for solar power prediction in [9, 1]. In order to develop the SVR prediction model, we used the Weka s implementation of the SMOreg algorithm RBF kernel as described by Shevade et al. [24]. We generated the predictions iteratively, as in approach A 3 (see Section IV-C). Table III shows the performance of the three methods used for comparison. Fig. 6 visually compares the results from Table I and Table III, for all methods. 25 TABLE III. ACCURACY OF METHODS USED FOR COMPARISON SVR B pday B week Case Study Avg A1 A2 A3 SVR Bpday Bpweek 3. ensemble single NN 2 () () A1 A2 A3 Fig. 5. Ensemble of NNs vs single NN in the proposed approaches Hence, we can conclude that the use of ensemble of NNs instead of a single NN is beneficial for our proposed 5 Case study 1 Case study 2 Case study 3 Case study 4 Fig. 6. Comparison of for different methods We can see that A 3 compares favorably SVR in all case studies except case study 4, where the performance of the two methods is similar. A 3 also outperformed the two baselines

7 B pday and B pweek, achieving an improvement in of 6.32 and 15.94, respectively. The second best approach overall is A 1, closely followed by the iterative SVR, and then B pday, A 2 and B pweek. A 2 is outperformed by the iterative SVR and also slightly outperformed by the B pday baseline. This highlights that A 2 did not performed well enough. VI. CONCLUSIONS In this paper, we presented three approaches (A 1, A 2, and A 3 ) for forecasting the half-hourly PV power output for the next day. A 1 uses an ensemble of NNs to predict all 2 outputs for the next day at the same time. A 2 also predicts all outputs for the next day simultaneously, but firstly partitions the data into a set of clusters using the X-Means algorithm and then builds an ensemble of NNs for each cluster. A 3 uses an iterative methodology, where an ensemble of NNs forecasts one output at a time, which is then used for the predictions of the next points from the forecasting horizon. We conducted a comprehensive evaluation of the proposed approaches A 1, A 2 and A 3 using four Australian solar datasets for one year, and compared their performance an iterative SVR approach and two baselines. We found that A 3 was the most accurate approach, and that A 1 also showed promising results. The of A 1 and A 3 averaged for 1-2 steps ahead prediction was and , respectively. A 2, on the other hand, showed relatively poor performance and was outperformed by the baseline B pday for 3 out of 4 case studies. However, the accuracy of A 2 is likely to be improved by increasing the number of training instances for each cluster. We also investigated the effect of using an ensemble of NNs instead of a single NN, and showed that the use of ensemble improved accuracy. 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