Universidade do Algarve Photovoltaic Power Forecast Modeling with Arti(cid:28)cial Neural Networks Joªo AndrØ Martinho Bolas Soares Disserta(cid:231)ªo Mestrado Integrado em Engenharia Eletr(cid:243)nica e Telecomunica(cid:231)ıes Trabalho efectuado sob a orienta(cid:231)ªo de: Prof. Doutor Ant(cid:243)nio Eduardo de Barros Ruano Prof. Doutor Cristiano Louren(cid:231)o Cabrita 2015 Universidade do Algarve Photovoltaic Power Forecast Modeling with Arti(cid:28)cial Neural Networks Joªo AndrØ Martinho Bolas Soares Disserta(cid:231)ªo Mestrado Integrado em Engenharia Eletr(cid:243)nica e Telecomunica(cid:231)ıes Trabalho efectuado sob a orienta(cid:231)ªo de: Prof. Doutor Ant(cid:243)nio Eduardo de Barros Ruano Prof. Doutor Cristiano Louren(cid:231)o Cabrita 2015 (cid:16)Declara(cid:231)ªo de autoria de trabalho(cid:17) Declaro ser o autor deste trabalho, que Ø original e inØdito. Autores e trabalhos consul- tados estªo devidamente citados no texto e constam da listagem de referŒncias inclu(cid:237)da. (Joªo Bolas Soares) Copyright ' A Universidade do Algarve tem o direito, perpØtuo e sem limites geogrÆ(cid:28)cos, de arquivar e publicitar este trabalho atravØs de exemplares impressos reproduzidos em papel ou forma digital, ou por qualquer outro meio conhecido ou que venha a ser inventado, de o divulgar atravØs de reposit(cid:243)rios cient(cid:237)(cid:28)cos e de admitir a sua c(cid:243)pia e distribui(cid:231)ªo com objectivos educacionais ou de investiga(cid:231)ªo, nªo comerciais, desde que seja dado crØdito ao autor e editor . i Acknowledgments I would like to show my greatest appreciation to Prof. Doutor Ant(cid:243)nio Ruano for the guidance, support and availability, without them this dissertation would not be a reality. I would like to express to my gratitude to Prof. Doutor Cristiano Cabrita, for the avail- ability of the data set needed to accomplish this work, for the insights and good advices on this project. Being arti(cid:28)cial neural networks an analogy from real neurons. And being these only capable of learning through experience. I would like to thank to my friends and my family with whom i have shared most of my experiences. Making me who i am today. Lastly but with my greatest appreciation i would like to show my gratitude to my parents, ElsaandJoªoSoaresfortheconstanthelpandinspiringsupportthroughmyacademiccareer. ii Resumo Com uma crescente preocupa(cid:231)ªo relativamente ao consumo energØtico global, a energia fotovoltaica surge como uma fonte energia renovÆvel promissora. Esta disserta(cid:231)ªo Ø con- stru(cid:237)da sob a premissa de que a capacidade de previsªo de potŒncia fotovoltaica produzida possibilita o aumento de performance da rede elØtrica local atravØs de um controlo e(cid:28)ciente da mesma. O trabalho desenvolvido propıe uma estrutura com a capacidade de previsªo de potŒncia produzida por um sistema fotovoltaico ligado a rede elØtrica presente na Universi- dade do Algarve. A estrutura de previsªo proposta Ø composta por dois modelos din(cid:226)micos, nªo lineares, de previsªo e um modelo estÆtico nªo linear. Redes Neuronais Arti(cid:28)ciais foram usadas como modelos. Os modelos de previsªo tŒm como objectivo fazer previsıes da tem- peratura do ar e irradia(cid:231)ªo solar em passos incrementais de 5 minutos para um horizonte de previsªo de 4 horas. O modelo estÆtico Ø constru(cid:237)do para estimar a potŒncia gerada pelo sis- tema fotovoltaico e Ø otimizado atravØs de compara(cid:231)ªo entre vÆrios tipos de redes neuronais como o perceptrªo multicamadas e fun(cid:231)ıes de base radial, e modelos com escalas temporais diferentes, aplicados a diferentes esta(cid:231)ıes do ano, bem como um modelo anual. Palavras-Chave: Energia Fotovoltaica, Redes Neuronais Arti(cid:28)ciais, Previsªo iii Abstract In a growing concern for the world energy consumption, photovoltaic energy sources are a reliable renewable energy alternative. This thesis is built upon the premise that the forecast of photovoltaic power production can increase performance of local electric network through an e(cid:30)cient network management. The work developed proposes a power production forecast structure based on a grid-connected photovoltaic system in the University of Algarve. The proposed forecast structure is composed of two non-linear dynamic forecasting models and one non-linear static model. Arti(cid:28)cial Neural Networks were used in the development of these models which are intended to forecast solar irradiance and air temperature using Radial Basis Functions with 5 minutes time steps within a prediction horizon of 4 hours. The static model on the structure was created to estimate the power generated by the photovoltaic system and it was optimized through comparison between several network architectures (MLP and RBF) and several seasonal models, as well as a annual model. Keywords: Photovoltaic Energy, Arti(cid:28)cial Neural Networks, Forecast iv Contents "Declara(cid:231)ªo de autoria de trabalho" i Acknowledgments ii Resumo iii Abstract iv Table of Contents v List of Figures viii List of Tables x Acronyms and Abbreviations xi 1 Introduction 1 1.1 Motivation and Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Thesis scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Theoretical Background 3 2.1 Arti(cid:28)cial Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Arti(cid:28)cial Neural Networks properties . . . . . . . . . . . . . . . . . . . . . . 4 2.2.1 Single Input-Neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.2 Neuron with an input vector . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.3 Activation function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Neural Networks architecture . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3.1 Single-Layer Feedforward Neural Networks . . . . . . . . . . . . . . . 7 2.3.2 Multilayer FeedForward Neural Networks . . . . . . . . . . . . . . . . 8 2.3.2.1 Hidden Layers . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.3 Radial Basis Function . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Training Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4.1 Generalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4.1.1 Overtraining . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4.2 Training Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4.2.1 Steepest Descent . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4.2.2 Newton’s Method . . . . . . . . . . . . . . . . . . . . . . . . 14 v 2.4.2.3 Gauss-Newton Method . . . . . . . . . . . . . . . . . . . . . 15 2.4.2.4 Levenberg-Marquardt method . . . . . . . . . . . . . . . . . 16 2.4.3 Network Performance Evaluation . . . . . . . . . . . . . . . . . . . . 18 2.5 Photovoltaic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.5.1 Air Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.5.2 Solar Irradiance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.5.3 Photovoltaic Technology . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.5.4 Grid-Connected Photovoltaic Systems . . . . . . . . . . . . . . . . . . 24 2.5.5 Standalone Photovoltaic Systems . . . . . . . . . . . . . . . . . . . . 25 2.6 Forecasting with Arti(cid:28)cial Neural Networks . . . . . . . . . . . . . . . . . . 25 2.6.1 Multiobjective Evolutionary Algorithms . . . . . . . . . . . . . . . . 26 3 Electric Power production forecast with Arti(cid:28)cial Neural Networks 29 4 Methodology Applied 31 4.1 Structure of the forecasting approach . . . . . . . . . . . . . . . . . . . . . . 31 4.2 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.3 Data Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.3.1 Outlier Removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.3.2 Power Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.3.3 Data Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.3.4 Sampling Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.4 Data Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.4.1 Characteristic days . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.4.2 Seasonal Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.4.3 Yearly Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.5 Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.5.1 Multi-Layered Perceptron learning procedure . . . . . . . . . . . . . 48 4.5.2 Radial Basis Function learning procedure . . . . . . . . . . . . . . . 49 4.5.3 Testing and Validation sets . . . . . . . . . . . . . . . . . . . . . . . 50 4.6 Forecasting Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.6.1 MOEA approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.7 Evaluation criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5 Results 56 5.1 Seasonal models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.1.1 Multi-Layer Perceptrons Results . . . . . . . . . . . . . . . . . . . . . 56 5.1.2 Radial Basis Functions Results . . . . . . . . . . . . . . . . . . . . . 60 vi 5.2 Yearly model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 5.3 Comparison between static models . . . . . . . . . . . . . . . . . . . . . . . 66 5.4 Forecasting models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5.5 Global model results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6 Conclusion and Future work 86 6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 6.2 Di(cid:30)culties and future work . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 References 88 vii List of Figures 2.1 Analogy of signal interaction between n arti(cid:28)cial neuron and n biologic neuron in a single layer con(cid:28)guration [4] . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Arti(cid:28)cial Neuron with single Input diagram . . . . . . . . . . . . . . . . . . 4 2.3 Arti(cid:28)cial neuron with input vector diagram [5] . . . . . . . . . . . . . . . . . 5 2.4 Sigmoid function [5]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.5 Threshold function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.6 Hyperbolic tangent function[5] . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.7 Feedforward single layer Arti(cid:28)cial Neural Network [5]. . . . . . . . . . . . . . 7 2.8 Multilayer feedforward neural network, with topology [3,2,1] . . . . . . . . . 8 2.9 Radial Basis Function Network[8] . . . . . . . . . . . . . . . . . . . . . . . . 9 2.10 Supervised learning diagram[5] . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.11 Illustration of the early-stopping method based on cross-validation[5] . . . . 13 2.12 Output power versus voltage of a single crystalline silicon solar cell at various temperatures [13]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.13 RelativeEarth-SunpositionatnoononwinterdayintheNorthernHemisphere [14] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.14 Sun’s position relative to earth de(cid:28)ned by two angles, ψ (azimuth) and θ S ZS (solar zenith). γ represents the altitude on the Earth’s surface[14]. . . . . . 21 S 2.15 Receiver PV panel (tilt β, azimuth α) and sun beam incidence angle [14]. . 22 2.16 Physical structure of Photovoltaic Cell [17]. . . . . . . . . . . . . . . . . . . 23 2.17 Example of a schematic of a grid-connected PV system [19]. . . . . . . . . . 25 2.18 Example of a schematic of a standalone PV system [19]. . . . . . . . . . . . 25 2.19 Concept of Pareto optimality [23]. . . . . . . . . . . . . . . . . . . . . . . . . 27 2.20 Generic (cid:29)ow of operation of most MOEAs [22]. . . . . . . . . . . . . . . . . . 28 4.1 Flowchart of forecasting approach . . . . . . . . . . . . . . . . . . . . . . . . 32 4.2 Photograph of PV array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.3 Characteristic sunny days . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.4 Characteristic partially clouded days . . . . . . . . . . . . . . . . . . . . . . 38 4.5 Characteristic overcast cloudy days . . . . . . . . . . . . . . . . . . . . . . . 39 4.6 Comparison between theoretical and measured solar irradiance values. . . . . 41 4.7 Characteristic day distribution according to MRAE. . . . . . . . . . . . . . 42 4.8 TrainingsetdataforSpringmodelexhibitinggeneratedpower,airtemperature and solar irradiance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.9 Training set data for Summer model exhibiting generated power, air temper- ature and solar irradiance. . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 viii
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