Solar Irradiance Forecasting Based on the ...

Solar Irradiance Forecasting Based on the Combination of Radial Basis Function Artificial Neural Network and Genetic Algorithm Hamidreza, Jahangir Faculty of Electrical Engineering, K. N. Toosi University, Tehran, Iran, [email protected], ORCID: 0000-0003-44621370

Ali Ahmadian College of Engineering, University of Bonab, Bonab, & College of Engineering, University of Waterloo, Waterloo, Canada, [email protected], ORCID: 0000-0003-4565-5089

Masoud Aliakbar Golkar Faculty of Electrical Engineering, K. N. Toosi University, Tehran, Iran, [email protected]

Ali Elkamel College of Engineering, University of Waterloo, Waterloo, Canada, & College of Engineering, Khalifa University of Science and Technology, the Petroleum Institute, Abu Dhabi, UAE, [email protected]

Ali Almansoori College of Engineering, University of Waterloo, Waterloo, Canada, & College of Engineering, Khalifa University of Science and Technology, the Petroleum Institute, Abu Dhabi, UAE, [email protected]

Cite this paper as:

Abstract:

Keywords:

Jahangir, H. and etl. Solar irradiance forecasting based on the combination of Radial Basis Function Artificial Neural Network and Genetic Algorithm. 6th Eur. Conf. Ren. Energy Sys. 25-27 June 2018, Istanbul, Turkey. Nowadays, the use of solar energy is very common with regard to the limitation of fossil fuels, environmental pollution standards and the advancement of solar panel technology. Due to the stochastic behavior of the Solar Irradiance (SI), the power of solar panels is uncertain. In order to improve the reliability of using solar energy in the power grid, the SI should be predicted with high precision. Artificial Neural Networks (ANNs) are very effective in predicting uncertainty phenomena. In this research, environmental data and previous values of SI are used to predict the SI. Radial Basis Function (RBF) ANNs are precise method because Gaussian functions are used in their activation function. In ANNs, connection between different layers is created through weights. In conventional ANNs initial weights are randomly determined and this can affect the performance of the ANNs. In this study, the initial weights are determined by meta-heuristic optimization algorithm such as Genetic Algorithm (GA). In this method, a GA is used during the training of the ANN and the SI is predicted over a week. To evaluate the proposed method, different error calculation methods are applied. Artificial Neural Network- Forecasting-Genetic Algorithm- Solar Irradiance- Uncertainty.

© 2018 Published by ECRES Nomenclature Wijm d

𝑋0 𝑓 E 𝑑 e 𝑓 𝑋 𝑗 𝑁𝑒𝑡𝑖 SI

Weight of m-th layer and j-th neuron to the i-th data sample Desired output vector Bias of the first layer Activation function Sum square error Desired output vector Error vector Activation function Input vector Activation function input of the i-th neuron of the j-th layer Solar Irradiance

THE 6TH EUROPEAN CONFERENCE ON RENEWABLE ENERGY SYSTEMS Istanbul/Turkey 25-27 June 2018

ANN GA RBF MAE MAPE RMSE ML

Artificial Neural Networks Genetic Algorithm Radial Basis Function Mean Absolute Error Mean Absolute Percentage Error Root Mean Square Error Machine Learning

1. INTRODUCTION Nowadays, the use of renewable energy sources in modern societies is very common. With regard to environmental pollution and the limitation of fossil fuel resources, the use of renewable energy in many countries is increasing substantially. Solar power is one of the most popular energy sources in countries with good solar radiation due to its easy and comprehensive access [1]. In spite of all its advantages, solar energy has a stochastic behavior and it is strongly influenced by the changing environmental conditions [2]. The prediction of SI is done by different methods and among different methods, ANNs have a significant accuracy. In using ANNs for better training various coefficients and initial weights are determined by Meta heuristic optimization algorithms [3-6]. This method significantly improves the accuracy of the results and convergence speed of ANN [7]. In this paper, RBF artificial neural networks based on Rough structure and the GA have been used to predict the SI for a period of one day to a week. In this method, during the network training, the coefficients are determined by the GA. It should be noted that the use of the Rough structure is due to the uncertainty in the behavior of the SI which is fully and thoroughly investigated in this paper. With regard to the SI’s prediction period, its results can be used for the various cases shown in Fig. 1 [8]. As shown in Fig. 1, shortterm intervals for operation purposes and long-term intervals are used for planning purposes. According to the works done in relation to the prediction of SI based on past data these methods can be classified in two ways, time series and machine learning (ML) [9]. One of the most popular time series techniques is the ARIMA method which has been used in many studies in this field [10-11]. This method like other time series methods loses its accuracy in the presence of noise in the data and according to the analysis it is less accurate than the ML methods. Nowadays, with the advances made in the computing tools, the use of ML methods is very common. ML is widely used in various applications of classification, forecasting and feature selection. ANNs are one of the most popular ML tools that have been applied by many researchers to predict SI [12]. In previous studies, the constant coefficients and random initial weights of the ANN were commonly used [13]. In this paper, the GA has been used to determine the optimal amount of training coefficients and initial weights. In addition, Rough ANNs are considered in this work to be very effective in predicting uncertain data such as SI. The main features of this article are as follows:  Use of ANNs with Rough structure due to data uncertainty  Use of GA to determine ANN coefficients and initial weights  Use of radial basis activation functions in ANNs  High precision prediction The paper structure is as follows: In the section 2, the formulation of the applied method is described in details and then in the section 3, the simulation results and analysis are presented. Finally, the conclusions of the above research are presented in the section 4.

Load Flowing Stability and Regulation Seconds

Minutes

Unit Commitment Hours

Days

Months and Years Time

Reserve Management and Dispatching

Planning

Figure 1. Purposes of different time resolution prediction

THE 6TH EUROPEAN CONFERENCE ON RENEWABLE ENERGY SYSTEMS Istanbul/Turkey 25-27 June 2018

2. PROBLEM STATEMENT In this section, ANNs with RBF based on Rough structure and the combination of ANNs with GA are fully introduced and finally, the proposed method is described. -ANNs with RBF based on Rough structure ANNs are an important branch of statistical ML method that are used extensively in prediction applications of various phenomena and have high ability to analysis the different nonlinear models. Traditional ANNs lose their precision with increasing uncertainty in input data. Using Rough ANNs will increase the accuracy of results in these situations. Given the Rough structure, the ANN is resistant to noise and uncertainty in input data. Rough Neuron consists of a combination of traditional neurons and Rough set. In fact, by using Rough Neurons, the input data is considered as an interval mode in place of the single mode [14]. This is very useful in using data such as SI, ambient temperature or rainfall and other phenomena that have a maximum and minimum value. In these situations, if traditional ANNs applied, the error value is increased and the accuracy of the results is not favorable. But using the Rough neurons, these phenomena can be carefully examined. RBF neural network has been identified among researchers in this field as an effective tool for various applications [15]. Some of the benefits of RBF networks such as fast training and global approximation capability with local responses have made many researchers interested in using them in a variety of fields. In this paper, the combination of ANNs and RBF has been used. The structure of the Rough neuron is shown in Fig. 2 and formulations with the Rough structure are presented as follows: Upper Bound

𝑊𝑈

𝑂𝑈

α

X

𝑊𝐿

Input

𝑂𝐿

β

Output

Lower Bound

Figure 1. Rough neuron configuration

Feedforward equations of Rough structure neuron [14]: 𝑛

0 𝑛𝑒𝑡𝐿𝑚𝑗 (𝑘) = ∑𝑖=1 𝑤𝐿𝑚𝑗𝑖 (𝑘)𝑥𝑖 (𝑘)

(1)

𝑛

0 𝑛𝑒𝑡𝑈𝑚𝑗 (𝑘) = ∑𝑖=1 𝑤𝑈𝑚𝑗𝑖 (𝑘)𝑥𝑖 (𝑘)

(2)

𝑂𝐿𝑚𝑗 = 𝑚𝑖𝑛⁡(𝑓𝑗𝑚 (𝑛𝑒𝑡𝐿𝑚𝑗 (𝑘)) , 𝑓𝑗𝑚 (𝑛𝑒𝑡𝑈𝑚𝑗 (𝑘))⁡

(3)

𝑂𝑈𝑚𝑗 = 𝑚𝑎𝑥⁡(𝑓𝑗𝑚 (𝑛𝑒𝑡𝐿𝑚𝑗 (𝑘)) , 𝑓𝑗𝑚 (𝑛𝑒𝑡𝑈𝑚𝑗 (𝑘))⁡

(4)

𝑗

𝑂𝑗𝑚 (𝑘) =

𝑚 𝛼𝑂𝐿𝑚 +𝛽𝑂𝑈 𝑗

𝑗

(5)

2

Feedback equations of Rough structure neuron: 𝜕𝐸 𝜕𝑤𝑈 𝜕𝐸 𝜕𝑤𝐿

(𝑘) =

𝜕𝐸

(𝑘) =

𝜕𝐸

𝜕𝑒

𝜕𝑒

× ×

𝜕𝑒 𝜕𝑦 𝜕𝑒 𝜕𝑦

× ×

𝜕𝑦 2 𝜕𝑜𝑢

𝜕𝑦 𝜕𝑜𝐿2

× ×

2 𝜕𝑜𝑢

(𝑘)

(6)

(𝑘)

(7)

𝜕𝑤𝑢 𝜕𝑜𝐿2 𝜕𝑤𝐿

THE 6TH EUROPEAN CONFERENCE ON RENEWABLE ENERGY SYSTEMS Istanbul/Turkey 25-27 June 2018

The radial neural network based on Rough is shown in Fig. 3. The related formulas are as follows: Feedforward equations of RBF neural network:

φ(𝑛𝑒𝑡𝑗 ) = 𝑒

1 𝑛𝑒𝑡𝑗 2 ) 2 𝜎𝑗

− (

=𝑒

1 ‖𝑥−𝑐𝑗 ‖ 2 ) 2 𝜎𝑗

− (

(8)

‖𝑥 − 𝑐𝑗 ‖ = √(𝑥1 − 𝑐1𝑗 )2 + (𝑥2 − 𝑐2𝑗 )2 + (𝑥3 − 𝑐3𝑗 )2 + ⋯ + (𝑥𝑛 − 𝑐𝑛𝑗 )2

(9)

Feedback equations of RBF neural network: 𝑐𝑗 (𝑘 + 1) = 𝑐𝑗 (𝑘) − 𝜂𝑐 ×

𝜕𝐸 𝜕𝑐𝑗

𝜎𝑗 (𝑘 + 1) = 𝜎𝑗 (𝑘) − 𝜂𝜎 ×

(𝑘)

𝜕𝐸 𝜕𝜎𝑗

(10)

(𝑘)

(11) 𝜎1

𝑂11 1 𝑊1𝑈

𝐶1

1

1 𝑊1𝐿

X1

𝜎2

𝑂21

𝑊𝑗𝑈1

𝐶2

X2

α

y 𝑊𝑗𝐿1

𝜎𝑗

𝑂𝐿2

β

𝑂𝑗1

𝐶𝑗

Xn

𝑂𝑈2

1 𝑊𝑛𝑈 1 𝑊𝑛𝐿

𝜎𝑛 𝐶𝑛

𝑂𝑛1

Figure 3. Rough RBF neural network

Regarding the Rough structure of the RBF neural network, the learning method of mean and standard deviation values are as follows: 𝜕𝐸 𝜕𝐶𝑗 𝜕𝐸 𝜕𝜎𝑗

(𝑘) =

𝜕𝐸

(𝑘) =

𝜕𝐸

𝜕𝑒

𝜕𝑒

×

×

𝜕𝑒 𝜕𝑦

𝜕𝑒 𝜕𝑦

×

×

𝜕𝑦 2 𝜕𝑜𝑈

𝜕𝑦 2 𝜕𝑜𝑈

×

×

2 𝜕𝑜𝑈

𝜕𝑜𝑗1 2 𝜕𝑜𝑈

𝜕𝑜𝑗1

×

×

𝜕𝑜𝑗1 𝜕𝑐𝑗 𝜕𝑜𝑗1 𝜕𝜎𝑗

(𝑘) +

𝜕𝐸

(𝑘) +

𝜕𝐸

𝜕𝑒

𝜕𝑒

×

×

𝜕𝑒 𝜕𝑦

𝜕𝑒 𝜕𝑦

×

×

𝜕𝑦 𝜕𝑜𝐿2 𝜕𝑦 𝜕𝑜𝐿2

×

×

𝜕𝑜𝐿2 𝜕𝑜𝑗1 𝜕𝑜𝐿2 𝜕𝑜𝑗1

×

×

𝜕𝑜𝑗1 𝜕𝑐𝑗 𝜕𝑜𝑗1 𝜕𝜎𝑗

(𝑘)

(12)

(𝑘)

(13)

-The combination of ANNs and GA In conventional ANNs, the initial values of weights are randomly selected and their value influences the convergence rate and the behavior of the ANN. In the combined method of the ANN and the GA, the initial values are optimized by the GA algorithm. This causes the ANN to perform better and the calculation error is reduced. In fact, this method makes it possible to reduce the dependence of the results to the initial values of the randomly selected ANN parameters. The comparison of the convergence rate of the combined method of GA-ANN and independent methods is shown in Fig. 4. The compounding method significantly improves the convergence rate and accuracy of the results. The main idea of the combination of GA and ANN is shown in Fig. 5.

THE 6TH EUROPEAN CONFERENCE ON RENEWABLE ENERGY SYSTEMS Istanbul/Turkey 25-27 June 2018

Figure 4. The convergence rate of the different methods [16] Generating Initial Weights and coeffient

Generating Different ANNs

Training ANNs

Mutation

Crossover

Evaluating ANNs

Ranking and Selecting the Best

Figure 5. Flowchart of the proposed method

3. SIMULATION RESULTS In this paper, using the combination of the GA and the ANNs, the SI for a period of one day to one week is predicted. The last 4 years data has been used to train the ANN [17]. In this paper, environmental data such as SI and ambient temperature with their maximum and minimum values are used to train the ANN. The simulation results are shown in Fig.6. Fig. 6 shows the results of SI predictions for a day from all the seasons. As the figures show, the accuracy of the results is improved with the combination algorithm. In the summer, when the SI rate is significantly increased, the difference between the results of the combined method and the standalone ANN is more than winter. For accurate analysis of the results, the error value is calculated using three well-known measurement methods [18]. The formulas for these three error criteria are presented below. 1 ̂ 𝑀𝐴𝐸 = ∑𝑁 𝑖=1(|𝑌⁡ − 𝑌𝑖 |) 𝑁

1

̂⁡ −𝑌𝑖 ) (𝑌

𝑁

𝑌𝑖

𝑀𝐴𝑃𝐸 = ∑𝑁 𝑖=1 |

𝑅𝑀𝑆𝐸 = √

1 𝑁−1

|

2 ̂ ∑𝑁 𝑖=1(𝑌⁡ − 𝑌𝑖 )

(14) (15)

(16)

The error value obtained from the three introductory methods for the one-week period in the summer is given in Table 1.

THE 6TH EUROPEAN CONFERENCE ON RENEWABLE ENERGY SYSTEMS Istanbul/Turkey 25-27 June 2018

Table 1. Different error criteria values for simulation results Error Criteria ANN with GA ANN without GA MSE (W/m2) 0.29 0.53 MAPE (%) 4.5 7.6 2 RMSE (W/m ) 0.37 0.62

(a)

(b)

(c)

(d)

Figure 6. Solar irradiance prediction with different methods for one day duration

(a): Spring – (b): Summer – (c): Fall – (d): Winter

4. CONCLUSION In this paper, a method for predicting the solar irradiance was introduced in light of the importance of renewable energy sources in modern energy supply. By accurately predicting the intensity of the sun's radiation in each area, more reliable solar energy can be used in distribution networks. Due to the high uncertainty of the sun's radiation and the high probability of noise in environmental data, Rough Artificial Neural Networks are used in this paper. Rough Artificial Neural Networks have acceptable performance against noise and data uncertainty. The simulation results in this paper showed that using the combination of Genetic Algorithm and Artificial Neural Network causes the results to be more

THE 6TH EUROPEAN CONFERENCE ON RENEWABLE ENERGY SYSTEMS Istanbul/Turkey 25-27 June 2018

accurate. In addition, the use of combination of these methods improves the convergence speed of the Artificial Neural Network. In fact, in traditional Artificial Neural Networks, initial values are determined randomly, but in the combination method using the Genetic Algorithm the initial values are optimally selected that improve the performance of the Artificial Neural Network. According to the results of this paper, the use of the combined method is recommended. REFERENCES [1] Jahangir H, Ahmadian A, Aliakbar Golkar M. Multi-Objective Sizing of Grid-Connected Micro-Grid Using Pareto Front Solutions.In: IEEE PES International Conference on Innovative Smart Grid Technologies; 4-6 November 2015, Bangkok Convention Center, Bangkok, Thailand. [2] Jahangir H. Ahmadian A. Aliakbar Golkar M. Optimal Design of Stand Alone Microgrid Resources Based on Proposed Monte-Carlo Simulation. In: IEEE PES International Conference on Innovative Smart Grid Technologies; 4-6 November 2015, Bangkok Convention Center, Bangkok, Thailand. [3] Mohanraj, M , Jayaraj, S , Muraleedharan, C . Performance prediction of a direct expansion solar assisted heat pump using artificial neural networks. Applied Energy 2009; 86: 1442-1449 [4] Chang, G , Lu, H , Chang , Lee . An improved neural network-based approach for short-term wind speed and power forecast. Renewable Energy 2017; 105:301-11. [5] Chou, T , Zhang, G , Lin, Z , Song , C. Global optimization of absorption chiller system by genetic algorithm and neural network Energy and Buildings 2002; 34:103-109. [6] Kishore, B , Sathyanarayana, M ,Sujatha ,K . Intelligent condition monitoring of air blower using artificial neural network and genetic algorithm, International Journal of Engineering Research and Technology 2012; ISSN 2278-0181. [7] Changyu, L , Quian. Optimization of injection molding process parameters using combination of artificial neural network and genetic algorithm method, Journal of Material Processing Technology 2007; 183:412-418. [8] Bhatti, S , Kothari, D. Wind power estimation using artificial neural network. Journal of Energy Engineering 2007;133: 46– 52. [9] Ampazis , N , Perantonis, S . Two highly efficient second-order algorithms for training feedforward networks. IEEE Transactions on Neural Networks and Learning Systems 2002;13:1064–74. [10] Olavi, K . ARIMA representation for daily solar irradiance and surface air temperature time series. Journal of Atmospheric and Solar Terrestrial Physics 2009; 71: 841-847. [11] Yanting, Li , Yan, Su , Lianjie, Shu . An ARMAX model for forecasting the power output of a grid connected photovoltaic system. Renewable Energy 2014;66:78-89. [12] Siecker, J , Kusakana, K , Numbi, B. A review of solar photovoltaic systems cooling technologies. Renewable and Sustainable Energy Reviews 2017; 79:192-203. [13] Weldekidan, H , Vladimir, S , Town, G . Review of solar energy for biofuel extraction 2018; 88:184-192. [14] Ahmadi, Gh , Teshnehlab, M. Designing and Implementation of Stable Sinusoidal Rough-Neural Identifier. IEEE Transactions on Neural Networks and Learning Systems 2017;28:1774 –86. [15] Zeng, W, Zhang, Z , Ga, Ch. A Levenberg-Marquardt Neural Network Model with Rough Set for Protecting Citrus from Frost Damage. In: 8th International Conference on Semantics, Knowledge and Grids, Beijing, China, 2012. [16] Hiroaki, Kitano . Designing Neural Networks Using Genetic Algorithms with Graph Generation Systems, in: Complex Systems 1990; 4:461-476. [17] [Online]. Available: http://www.suna.org.ir. [18]Yu, Ch , Li, Y , Zhang, M. Comparative study on three new hybrid models using Elman Neural Network and Empirical Mode Decomposition based technologies improved by Singular Spectrum Analysis for hour-ahead wind speed forecasting. Energy Conversion and Management 2017;147:75–85.