## 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 md.rana@unsw.edu.au

Irena Koprinska

School of Information Technologies The University of Sydney

NSW, Australia irena.koprinska@sydney.edu.au Vassilios G Agelidis

Australian Energy Research Institute University of New South Wales

NSW, Australia
vassilios.agelidis@unsw.edu.au
**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 30 minutes **
**intervals from the previous values, without 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 with 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 grid-connected 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, without 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 *Pi *is a
vector of half-hourly PV power outputs for day *i*, i.e.

, … , , 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 with 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, without using any exogenous variables. They compared the performance of four methods: ARIMA, k nearest neighbor, NN trained with the backpropagation algorithm and NN trained with 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 with the genetic algorithm was the most accurate

prediction model. The two NN approaches obtained Mean Absolute Error (MAE) in the range of 42.96 - 61.92 kW for 1 hour ahead prediction and 62.53 - 87.76 kW 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 (MRE) was between 4.85%
(for sunny day) and 12.42% (for cloudy day).

Chow *et al.* [8] applied NNs for predicting the PV power
output 10 and 20 minutes ahead. As inputs to the NNs they
used solar irradiation, temperature, solar elevation angle and
solar azimuth angle. They developed multi-layer perceptron
with one hidden layer, trained with the backpropagation
algorithm, with 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
with 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, with the
combination of wavelet transform and RBFNN outperforming
RBFNN without 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 [10] 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

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

*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 5000 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, 2013. The data represents the power output of the PV arrays at the given location, in 30 minutes intervals. We only consider the data between 7:00 am to 5:00 pm as most of the data values outside this time window are either zero or not available. Thus, there are 7,300 data points (365 days × 20 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 10th February, 2013. We can see that the range of solar power varies for the different case studies – it is highest for case study 1 (0.09-430 kW) and lowest for case study 2 (0.03-90 kW). 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.

Fig. 1. PV power output for each case study for one week (from Monday 4th February to Sunday 10th February, 2013)

*C.* *Training, Validation, and Testing Sets *

We divided the data for each case study into three
non-overlapping subsets: training *(Dtrain), *validation* (Dvalid), *and
testing* (Dtest)*. The data split was 50%-25%-25%, following the
recommendation in [19], resulting in 183 instances in *Dtrain,* 91
in *Dvalid* and 91 in *Dtest*. One instance is 20-dimensional vector,
where each value corresponds to the half-hourly PV power
output for a single day from 7:00 am to 5:00 pm.

0 100 200 300 400 500 1 20 39 58 77 96 115 134 Solar Power [k W]

Time Lag (1 lag = 30 min) a) Case study 1 0 20 40 60 80 100 1 20 39 58 77 96 115 134 Solar Power [k W]

Time Lag (1 lag = 30 min) b) Case study 2 0 50 100 150 200 250 300 350 400 1 20 39 58 77 96 115 134 Solar Power [k W]

Time Lag (1 lag = 30 min) c) Case study 3 0 50 100 150 200 250 300 350 1 20 39 58 77 96 115 134 Solar Power [k W]

Time Lag (1 lag = 30 min) d) Case study 4

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TABLE I
**Case **
**Study **
**MAE**
** kW**
1 72.55
2 16.19
3 58.34
4 59.66
Avg. 51.69
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. ACCURACY OF T
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9 17.92 17
4 17.24 63
6 17.65 61
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PPROACHES
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15.61 17.27
58.10 17.17
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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 A1 and A3 needed less time than the

less accurate A2. This is because A1 and A3 create one

prediction model, while A2 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 A2 was about 3

times higher than the time for A1 and A3 (10 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 with the performance of a single NN, using the same experimental setting. The accuracy results for A1, A2,and A3 with a single NN are shown in Table II. A

graphical comparison of the MRE 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 MRE averaged over all case studies are 9.43%, 36.48% and 7.18% for A1, A2,and

A3, respectively. The computational cost of training an

ensemble is higher than for a single NN, but suitable for both offline and online practical applications: 3-10 minutes for training an ensemble, compared to 10-30 sec for training a single NN.

TABLE II. ACCURACY USING A SINGLE NN INSTEAD OF ENSEMBLE OF NNS

**A1 ** **A2 ** **A3 **
**Case **
**Study **
**MAE **
** kW **
**MRE **
**% **
**MAE **
**kW **
**MRE **
**% **
**MAE **
**kW **
**MRE **
** % **
1 77.76 18.08 112.19 26.08 77.64 18.05
2 16.62 18.38 26.38 29.19 16.94 18.74
3 71.37 21.09 76.51 22.61 64.42 19.04
4 63.17 18.69 81.59 24.14 61.04 18.06
Avg. 57.23 19.06 74.17 25.51 55.01 18.47

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

approaches. A1, A2,and A3 achieved better prediction accuracy

using an ensemble at acceptable computational cost.

*D.* *Comparative Study *

We compared the performance of our approach with two persistence models (baselines) and a SVR based iterative approach.

The first persistence model, Bpday, 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, Bweek, considers the

half-hourly 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, 10]. In
order to develop the SVR prediction model, we used the
Weka’s implementation of the SMOreg algorithm with RBF
kernel as described by Shevade *et al.* [24]. We generated the
predictions iteratively, as in approach A3 (see Section IV-C).

Table III shows the performance of the three methods used for comparison. Fig. 6 visually compares the MRE results from Table I and Table III, for all methods.

TABLE III. ACCURACY OF METHODS USED FOR COMPARISON

** SVR** **Bpday ** **Bweek **
**Case **
**Study **
**MAE **
** kW **
**MRE **
**% **
**MAE **
**kW **
**MRE **
**% **
**MAE **
**kW **
**MRE **
** % **
1 77.63 18.04 79.39 18.45 88.12 20.48
2 16.25 17.98 17.37 19.21 19.01 21.03
3 59.17 17.49 61.44 18.16 68.63 20.28
4 58.22 17.22 60.07 17.77 68.36 20.22
Avg. 52.82 17.68 54.57 18.40 61.03 20.50

Fig. 6. Comparison of MRE for different methods

We can see that A3 compares favorably with SVR in all

case studies except case study 4, where the performance of the two methods is similar. A3 also outperformed the two baselines

0.00 5.00 10.00 15.00 20.00 25.00 30.00 A1 A2 A3 MRE (%) ensemble single NN 0 5 10 15 20 25

Case study 1 Case study 2 Case study 3 Case study 4

MRE

(%)

Bpday and Bpweek, achieving an improvement in MRE of6.32%

and 15.94%, respectively. The second best approach overall is A1, closely followed by the iterative SVR, and then Bpday, A2

and Bpweek. A2 is outperformed by the iterative SVR and also

slightly outperformed by the Bpday baseline. This highlights that

A2 did not performed well enough.

VI. CONCLUSIONS

In this paper, we presented three approaches (A1, A2, and

A3) for forecasting the half-hourly PV power output for the

next day. A1 uses an ensemble of NNs to predict all 20 outputs

for the next day at the same time. A2 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. A3 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 A1, A2 and A3 using four Australian solar datasets

for one year, and compared their performance with an iterative SVR approach and two baselines.

We found that A3 was the most accurate approach, and that

A1 also showed promising results. The MRE of A1 and A3

averaged for 1-20 steps ahead prediction was 16.86% - 17.92% and 16.92% - 17.58%, respectively. A2, on the other hand,

showed relatively poor performance and was outperformed by the baseline Bpday for 3 out of 4 case studies. However, the

accuracy of A2 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.

The iterative SVR also achieved good accuracy; its MRE was between 17.22% and 18.04%. The good performance of the two iterative approaches, A3 and SVR, indicates that

iterative approaches are better option for multiple step ahead prediction than non-iterative approaches.

In conclusion, considering both accuracy and time to train the prediction model, we found that A3 was the most promising

method for practical applications. Our future studies will investigate the application of wavelet based approaches for solar power forecasting.

ACKNOWLEDGMENT

This research was partially supported by a research award from the Clean Energy and Intelligent Networks Research Cluster at the University of Sydney.

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