A novel adaptive approach for hourly solar radiation forecasting

Renewable Energy 87 (2016) 628e633

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Renewable Energy journal homepage: www.elsevier.com/locate/renene

A novel adaptive approach for hourly solar radiation forecasting Emre Akarslan a, b, *, Fatih Onur Hocaoglu a, b a b

Afyon Kocatepe University, Department of Electrical Engineering, Afyonkarahisar, Turkey Solar and Wind Energy Research and Application Center, Afyonkarahisar, Turkey

a r t i c l e i n f o

a b s t r a c t

Article history: Received 1 July 2015 Received in revised form 15 September 2015 Accepted 30 October 2015 Available online xxx

Solar radiation forecasting is an important part of planning and sizing of a photovoltaic power plant. Yearly measured hourly solar radiation data on the surface of a region include both stochastic and deterministic behaviors. The deterministic part comes from the solar geometry whereas the stochastic part is occurred due to random atmospheric events such as the motion of clouds etc. Moving from these facts, in this paper two different adaptive approaches are developed and tested for hourly solar radiation forecasting. In first approach, the data is separated into seasons. For winter and summer season it is thought that linear predictors work better due to rare alterations for short time periods. For these seasons linear prediction approach is adopted and used. On the other hand bigger alterations are most probable for spring and fall seasons. Therefore, for these seasons an empirical method is employed. In second approach, clearness index is considered as a decision maker to decide whether linear or empirical method will be used as a predictor. This decision is adopted for each prediction. It is obtained from the results that such an adoptive method outperforms non adoptive ones. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Solar radiation forecasting Linear prediction filter Empiric model Adaptive method

1. Introduction Increasing energy demands together with rising conventional fuel costs and environmental awareness made renewable energy sources very popular in this decade [30]. Among others solar energy is one of the most important renewable energy sources. While it is possible to generate clean energy production from the solar radiation at the surface of a region, the variability of surface radiation levels caused by atmospheric processes decreases the reliability of the solar power production and increases the associated integration costs to the power grid [9]. In recent times the number of larger solar installations; both large scale photovoltaic and also concentrated solar thermal plants are considerably increased due to financial support of the governments. In order to first influence financial backers to participate in their development, and also to potentially compete in the electricity markets, better solar energy prediction models are required [16]. Furthermore, accommodating higher penetration levels of solar power into a new generation of power grid portfolios requires the use of increasingly more accurate forecasting systems in order to reduce backup reserves and

* Corresponding author. Afyon Kocatepe University, Department of Electrical Engineering, Afyonkarahisar, Turkey. E-mail address: [email protected] (E. Akarslan). http://dx.doi.org/10.1016/j.renene.2015.10.063 0960-1481/© 2015 Elsevier Ltd. All rights reserved.

improve unit commitment associated with power generation variability [8,18,23]. To improve the accuracy of prediction, a huge number of studies are performed. Among them, Artificial Neural Networks (ANN) [29], Adaptive Neuro-Fuzzy Inference System (ANFIS) [25], Autoregressive (AR) [3], Autoregressive Moving Average (ARMA) [20], Hidden Markov Model [13], Fuzzy Logic [6], Lasso [38], AngstromePrescott equations [19,21,24], Linear Prediction Filters [14] and Multi-Dimensional Linear Prediction Filters [1] can be good examples for time series prediction approaches. On the other hand, the use of hybrid models has gained popularity as it takes advantage of different models [22,37]. The basic idea of the model combination in forecasting is to use each model's unique feature to capture different patterns in the data. Both theoretical and empirical finding suggests that combining different models can be an efficient way to improve the forecast performance [37]. Developed hybrid methods in the literature are exemplified as following Wu and Chan [37]: proposed a new hybrid model that contains two different methods in the prediction phase. Firstly, ARMA model is used to predict the stationary residual series and then the controversial Time Delay Neural Network (TDNN) is applied to do the prediction. Their simulation results showed that this hybrid model can take the advantages of both ARMA and TDNN and gives better results [37]. Voyant et al. [34] presented a novel technique to predict global radiation using a hybrid ARMA/ANN model. This model has been used to forecast the hourly global

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radiation for five places in Mediterranean area and gave better results than the conventional one [34]. Bhardwaj et al. [5] proposed the combination of Hidden Markov Model (HMM) and Generalized Fuzzy Model (GFM) for solar radiation forecasting. In this work continuous density, HMM with Pearson R model is utilized for the extraction of shape based clusters from the input meteorological parameters and it is then processed by the GFM to accurately estimate the solar radiation [5]. Huang et al. [16] described a new and efficient method capable of forecasting 1-h ahead solar radiation during cloudy days. The method combines an autoregressive (AR) model with a dynamical system model and gives better results than both [16]. Mostafavi et al. [26] introduced a hybrid approach to predict global solar radiation. The solar radiation was formulated in terms of several climatological and meteorological parameters and monthly data collected for 6 years in two cities of Iran were used to develop GP/SA-based (genetic programming (GP) and simulated annealing (SA)) models. They showed that this method notably outperform the existing models [26]. Benmouiza and Cheknane [4] presented a hybrid model that includes k-means and nonlinear autoregressive neural network models. k-means algorithm is used to extract useful information from the data with the aim of modeling the time series behavior and find patterns of the input space by clustering the data. Nonlinear autoregressive (NAR) neural networks are powerful computational models for modeling and forecasting nonlinear time series. In this approach, the advantages of both methods are used to obtain more successful approach to predict solar radiation [4]. Chu et al. [9] introduced novel smart forecasting models for Direct Normal Irradiance (DNI). These models combine sky image processing with Artificial Neural Network (ANN) optimization schemes. The forecasting models, are used to predict 1 min average DNI for specific time horizons of 5 and 10 min. The hybrid forecast models proposed in this work achieve statistically robust forecasting skills in excess of 20% over persistence for both 5 and 10 min ahead forecasts [9]. Marquez et al. [23] described a new hybrid method that combines information from processed satellite images with ANNs for predicting global horizontal irradiance (GHI) at temporal horizons of 30, 60, 90, and 120 min. The forecasting approach uses information gathered from satellite image analysis including velocimetry and cloud indexing as inputs to the ANN models [23]. Voyant et al. [35] proposed an original technique to model the insolation time series based on combining ANN and AR and ARMA model. While ANN by its non-linear nature is effective to predict cloudy days, ARMA techniques are more dedicated to sunny days without cloud occurrences [35]. Dong et al. [11] presented a new hybrid method that uses satellite image analysis and a hybrid exponential smoothing state space (ESSS) model together with ANN. Geostationary satellite images provide cloud information, allowing a cloud cover index to be derived and analyzed using selforganizing maps (SOM) while the ESSS model is used to forecast cloud cover index. Solar irradiance values are predicted via ANN by using cloud cover index [11]. Wang et al. [36] developed an optimized hybrid method by CS (Cuckoo Search) on the basis of the OP-ELM (Optimally Pruned Extreme Learning Machine), for predict clear sky and real sky global horizontal radiation. Experimental results show that the optimized hybrid method has a good prediction performance [36]. Chu et al. [10] introduced a standalone, real-time solar forecasting computational platform that integrates cloud tracking techniques using a low-cost fisheye network camera and ANN algorithms. They trained and validated the forecasting methodology with measured irradiance and sky imaging data collected for a six-month period, and applied it operationally to forecast both global horizontal irradiance and direct normal irradiance at two separate locations. Results show that the forecasting platform outperforms the

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reference persistence model for both locations [10]. Gala et al. [12] applied Support Vector Regression (SVR), Gradient Boosted Regression (GBR), Random Forest Regression (RFR) as well as a hybrid method to combine them to downscale and improved 3h accumulated radiation forecasts provided by Numerical Weather Prediction (NWP) systems for seven locations in Spain. Their results show that hybrid artificial intelligence systems are quite effective and, hence, relevant for solar radiation prediction [12]. In this paper, a novel alternative adaptive method that combines the linear prediction filters and an empirical model is developed. Two different combining strategies are applied and effects of these strategies on prediction performances are investigated. In the first strategy, the method to be used is determined according to season. In winter and summer times linear prediction filters can be a good choice due to strong correlation with extraterrestrial radiation. This correlation foregrounds linear prediction filter for prediction. In the second strategy, on the other hand, the clearness index values are employed as decision maker. If the clearness index value is greater than a specified value, linear prediction filters otherwise empirical models are decided as the predictor. To test the performance of the approaches developed, solar radiation data of different regions (Afyonkarahisar, Ankara and Çanakkale) are used. The organization of the paper is as follows. The data used for this study are described in Section 2. The novel adaptive hybrid approach is explained in Section 3. Experimental results are given in Section 4. Finally, conclusions are explained in Section 5. 2. The description and evaluation of the data In this study, solar radiation data from different regions (Afyonkarahisar, Ankara and Çanakkale) in Turkey are used. The regions used to test the performance of the proposed approaches are depicted in Fig. 1. The global solar radiations data belong to these regions are taken from Turkish State Meteorological Service (DMI). Some data (<1% of all data) were wrong measured (the values were bigger than calculated extraterrestrial values) or missing due to different external reasons. Such data are predicted using previous and future values of the data as a preliminary analysis. In the empirical method (see Section 3), extraterrestrial solar radiation values are critical. By definition, extraterrestrial radiation is the intensity of the sun at the top of the Earth's atmosphere and can be calculated using solar geometry for the region. It varies throughout the year because of the Earth's elliptical orbit, which results in an Earth-Sun varying distance during the year in a predictable way [1]. In this study, hourly extraterrestrial global solar radiations are calculated using the MDIC SOLPOS Calculator, which is available from the NREL website (http://www.nrel.gov/). To apply linear prediction filters, the data to be used are converted into a 2-D matrix. Hocaoglu et al. [14] first proposed this 2-D representation of solar radiation data. The 2-D image obtained from the solar radiation data provides the tool for the image processing techniques on solar data. Fig. 2 illustrates the one year solar radiation time series and data are rendered as a two-dimensional matrix (Eq. (1)) and plotted as a surface mesh in Fig. 3, where the dimensions x, y, z, are hours of days, days of year, and solar radiation magnitudes, respectively.

2

Xrad

x11 6 : ¼4 : xm1

:::::: : : ::::::

3 x1n : 7 5 : xmn

(1)

Illustration in Fig. 3 provides significant insight about the radiation pattern as a function of time. The informational insight is apparent from the sample surface plots and image visualizations

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Fig. 1. Insolation map of Turkey (Cities marked were used in this study) (www.eie.gov.tr).

Fig. 4. Image view of solar radiation data rendered in 2-D form.

solar radiation falling on the horizontal surface is increasing or decreasing. Fig. 2. Solar radiation time series for Afyonkarahisar in time period 1st Jan-31st Dec 2013.

3. Novel adaptive approaches In this study novel adaptive approaches are proposed. These approaches include combination of linear prediction filters and an empiric model. In this section detailed description of this approach is explained. For this aim, the linear prediction filters will be presented. The use of the linear prediction filters for solar radiation forecasting is firstly introduced by Hocaoglu et al. [14]. In this approach, 2-D linear filters were applied to overall the image that consists of the solar radiation data and optimal filter coefficients were determined. Consider the 2-D linear prediction filter in (2).

(2) Fig. 3. Hourly solar radiation data presented in 2-D surface.

presented in Figs. 3 and 4. These two plots correspond to the same rendering style with different visualizations [14]. By inspecting the image version of the data in Fig. 4, it is easy to interpret daily and seasonal behavior of solar radiation. Blue (in the web version) regions of the image indicate that there is no sun shine on the horizontal surface. The transition between blue and red indicates that

The prediction pixel was determined by using past pixels with the Formula (3).

 Z i;jþ1 ¼ Zi;j :a

(3)

i,j and Zi,j are identify the row and column number of the pixel and the pixel value, respectively. In 2-D solar radiation data, i denotes the days, j denotes the hours and Zi,j denotes the solar radiation at day i and hour j. Prediction is made for all possible (i,j) coordinates with past samples [15]. In 2-D linear filter approach, the estimation

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Ẑiþ1,jþ1 is considered as a linear combination of past samples and the combination coefficients were optimized in the sense of minimum squared error between the estimation and real value. The error at a particular coordinate (i,j) was calculated from Equation (4).

 εiþ1;jþ1 ¼ Z iþ1;jþ1  Ziþ1;jþ1

(4)

The energy of total prediction error was calculated with:

ε¼

m X n X

ε2i;j

(5)

i¼2 j¼2

where m and n identify the size of image. The filter coefficients which minimize this function can be calculated with the Eq. (6)

vε ¼0 va1

(6)

The solution to Eq. (7) yields the following equation:

R$a ¼ r

(7)

where R is the correlation value between the past values, a is the linear filter coefficient and r is the correlation between the past and predicted pixel. The optimal filter coefficient can be obviously found from:

a ¼ R1 $r

(8)

It was proven that 2-D prediction approach improves the prediction performance in solar radiation forecasting [14], considerably. However since this approach is linear in the sense of coefficient, it gives more accurate results in case it is applied on clear sky solar radiation data. Due to the weather conditions such as rain, wind, cloud etc., solar radiation has a stochastic behavior in time. Therefore to consider this behavior, a different strategy is considered. In this strategy it is thought to use an adaptive method. In this adaptive method, combinations of two different models are employed as predictors, instead of a single predictor. An empiric model is used as the second predictor. The empiric model was previously proposed elsewhere [2]. This model (Equation (9)) is based on extraterrestrial radiation and utilizes from the strong correlation between extraterrestrial and solar radiation values. It is thought that hourly variations between consecutive samples of both measured and extraterrestrial radiations can be similar.

Sðt þ 1Þ ¼ SðtÞ þ ðEðt þ 1Þ  EðtÞÞ

(9)

where S(t) represent the solar radiation and E(t) represent the extraterrestrial radiation in time instance t. Extraterrestrial radiation is the upper limit of the solar radiation value that measured on a horizontal surface on the earth. Thus, this criterion should be considered on forecasting application [2]. To convert the findings above into beneficial prediction models, two different combination strategies are built. In the first strategy, a seasonal approach is proposed. Since the variation of measured solar radiation on a horizontal surface is more coincide with the extraterrestrial radiation in summer and winter than the other seasons for the selected regions of Turkey, in these seasons linear prediction filters are employed as a predictor. In spring and fall seasons, on the other hand, some random atmospheric events such as rain, fog, wind etc. can be observed much more than the other seasons. Furthermore, the variation of measured solar radiation will be changed in a nonlinear way in these seasons. Therefore empirical model is employed as a predictor for these seasons.

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In the second strategy, clearness index (the ratio of solar radiation to the extraterrestrial radiation in a certain time) value is employed to decide which method will be used in prediction. Clearness index can be expressed as follows:

ciðtÞ ¼ SðtÞ=EðtÞ

(10)

The clearness index value is smaller than 1 and provide information about the weather condition. In the proposed strategy, if the clearness index value is smaller than 0.5, the next prediction is made by empiric model otherwise; the linear prediction filters are employed. In linear prediction filter method, only past samples of solar radiation data are used to predict 1 h later solar radiation value. The empiric model used in this study is utilized from the extraterrestrial radiation and this provides additional information to predict solar radiation. Furthermore linear prediction filter's performance decreases if the correlation of data reduces. Therefore, to overcome this weakness of the linear prediction filter approach, an empiric model is integrated to this approach with different strategies. By this way, it is thought that the new approach will increase the prediction performance due to these strategies make it more robust to different conditions. 4. Experimental results In this section, performances of the previously mentioned combine strategies are tested on different solar radiation data measured from three different regions of Turkey. RMSE, RMSE (%) and MBE assessment criteria are employed to evaluate the performance of the adaptive strategies. The Root Mean Square Error is a commonly used measure of the differences between the values extracted by a forecasting model or an estimator and the realobserved values. The RMSE has the same units as the measured variable-parameter, which is forecasted by the model. The value of RMSE provides information on the short term performance [28]. A lower RMSE indicates better performance. The RMSE (%) is used to evaluate the performances in different regions which have different solar radiation values in different range. The MBE provides information in the long term performance of the correlations by allowing a comparison of the actual deviation between predicted and measured values term by term. The MBE is used to describe whether a model over-(positive value) or under-(negative value) predicts the observation and has the same units as the measured variable-parameter, which is forecasted by the model. The ideal value of MBE is ‘zero’ [27,28]. The experimental results are shown in Table 1. As seen in Table 1, in all regions Strategy 1 provides better prediction performance than the linear prediction filter in the sense of RMSE and RMSE (%) criteria. An improvement about the 10e15% in prediction performance is achieved in case Strategy 1 is used. If the MBE results are examined, it is obvious that Strategy 1 outperform the linear prediction filter approach. The predictions with linear prediction filters are over the measured values while the values are very close to measured ones in case Strategy 1 is used. In the second strategy, the predictor is decided according to the calculated clearness index values for each time instances. If the clearness index value at time t is smaller than 0.5 (abnormal change on weather condition case), the empiric model, otherwise the linear prediction filter is employed as predictor. To better illustrate the proposed Strategy 2, a flowchart is built in Fig. 5. The experiment results obtained from Strategy 2 are also illustrated in Table 1. As seen in Table 1, for all regions, adaptive method with Strategy 2 provides better performance than the others. Nearly, 30% improvement is achieved in case Strategy 2 is used

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Table 1 Experimental results with Linear Prediction Filter and Hybrid (Strategy-1 and 2) approaches.

AFYONKARAHISAR

Filter Adaptive Adaptive Filter Adaptive Adaptive Filter Adaptive Adaptive

ANKARA

ÇANAKKALE

(Strategy-1) (Strategy-2) (Strategy-1) (Strategy-2) (Strategy-1) (Strategy-2)

RMSE (Wm2)

RMSE (%)

MBE

104.3124 93.2761 77.9310 100.3597 87.3610 72.0405 96.6095 83.0648 68.4132

54.1387 48.4108 40.4466 53.4094 46.4917 38.3385 49.2350 42.3322 34.8654

9.2265 0.9525 11.1524 8.5801 ¡0.4747 4.7626 7.6784 1.1381 17.4450

Bold values indicate the best results.

rather than the linear prediction filter is used, alone. If the results are examined in terms of RMSE (%), the proposed approach gives the best results on Çanakkale data. This means proposed approach is better on regions which have worse insulation characteristics. To show the effectiveness of the proposed approach deeply, measured and predicted values of solar radiations for Çanakkale region are plotted in Fig. 6.

It is clear from Fig. 6 that, the predicted values are strongly correlated with the measured solar radiation data. In order to place the work with other published works developed models with proposed approach are compared in the sense of RMSE (%) error measure. For this aim, results with proposed approach (Strategy-2) on Çanakkale region's data and results from different studies of others are compared in Table 2. It is obvious from Table 2 that the proposed adaptive approach outperforms the conventional methods.

Start

5. Conclusions Calculate the LPF coefficients for all months

Calculate the Clearness Index (ci) for me (t-1)

ci(t-1)>0.5

Make the predic on with LPF

YES

NO

In this study, novel adaptive approach with two different Strategies is proposed for hourly solar radiation forecasting. It is aimed to improve the prediction accuracy of previously developed linear prediction filter models. In the first strategy, a seasonal approach is considered. In summer and winter, linear prediction filters are employed whereas, in spring and fall the empirical model is employed as the predictor. In the second strategy, the clearness index value is employed as a decision maker to decide which method will be used. It is obtained that, the proposed adoptive method with the both strategies outperforms the linear prediction filter approach. An improvement in the range of 10e30% is achieved for different regions. It can be concluded that, proposed approach is open for improvement. Further strategies can be adopted and used for solar radiation forecasting. Such studies are considered as future works.

S(t)=S(t-1)+E(t)-E(t-1)

YES

Predic on (t)

t=t+1

t<8760 NO

Finish

Fig. 5. Flowchart of the hybrid model based on clearness index.

Fig. 6. The correlation between the measured and predicted values for Çanakkale region.

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Table 2 Comparison between the best result obtained in this study and conventional methods. Reference

Model type

Location of data used

RMSE (%)

Lee et al. [17] Brabec et al. [7] Voyant et al. [33] Voyant et al. [33] Voyant et al. [33] Trapero et al. [32] This study

Angstrom type equations Heteroscedastic model (HR) Multi-Layer Perceptron (MLP) Autoregressive and Moving Average (ARMA) Hybrid (MLP-ARMA) Autoregressive Integrated Moving Average (ARIMA) Proposed Adaptive Approach

South Korea (Seoul) Romania (Timisoara) France (Ajaccio, Corsica) France (Ajaccio, Corsica) France (Ajaccio, Corsica) Spain (Castilla- La Mancha) Turkey (Çanakkale)

43.09 45.80 40.55 40.32 36.59 37.34 34.86

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