Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Wind power forecasting using artificial neural networks with numerical prediction : a case study for… Bolouri Afshar, Banafsheh 2016

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
24-ubc_2016_september_bolouriafshar_banafsheh.pdf [ 2.77MB ]
Metadata
JSON: 24-1.0308789.json
JSON-LD: 24-1.0308789-ld.json
RDF/XML (Pretty): 24-1.0308789-rdf.xml
RDF/JSON: 24-1.0308789-rdf.json
Turtle: 24-1.0308789-turtle.txt
N-Triples: 24-1.0308789-rdf-ntriples.txt
Original Record: 24-1.0308789-source.json
Full Text
24-1.0308789-fulltext.txt
Citation
24-1.0308789.ris

Full Text

 i   Wind Power Forecasting Using Artificial Neural Networks with Numerical Prediction – A Case Study for Mountainous Canada   by   Banafsheh Bolouri Afshar  B.ASc. Mechanical Engineering, KNToosi University of Technology, 2009  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF SCIENCE  in  The Faculty of Graduate and Postdoctoral Studies  (Atmospheric Science)   THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)   August 2016   © Banafsheh Bolouri Afshar, 2016      ii Abstract Wind is a free and easily available source of energy. Several countries, including Canada, have already incorporated wind power into their electricity supply system.  Forecasting wind power production is quite challenging because the wind is variable and depends on weather conditions, terrain factors and turbine height. In addition to traditional physical and statistical methods, some advanced methods based on artificial intelligence have been investigated in recent years to achieve more reliable wind-power forecasts. The aim of this work is to exploit the ability of artificial neural network (ANN) models to find the most effective parameters to estimate generated power from predicted wind speed at a wind farm in mountainous Canada. The historical data of both observations and forecasts of weather characteristics along with turbine availabilities and the reported power production are used for this purpose. Experiments are done first with the observations (perfect-prog technique) to find the optimum architecture for the artificial neural network. Next to obtain a day-ahead forecast of the wind power, weather forecasts from a numerical weather prediction model was input to the optimum ANN as the predictors (model output statistics method). The results from ANN models are compared to linear-model fits in order to show the ability of ANN models to capture the nonlinearity effects. Also, another comparison is made between the results from artificial neural network models and the current approach used operationally by a utility company. The selected architecture is a three-layered feed-forward back-propagation ANN model with 8 hidden neurons.  Verification results using an independent dataset show that the ANN method improves the day-ahead wind-power forecasts by up to 56% compared to the current operational approach.      iii Preface The author performed all work pertaining to case study data quality control, model configuration, and data analysis. Dr. Roland Stull offered guidance, editing, and refinement of procedures.       iv  Table of Contents Abstract ................................................................................................................................. ii Preface ..................................................................................................................................iii Table of Contents .............................................................................................................. iv List of Tables ....................................................................................................................... vi List of Figures .................................................................................................................... vii Acknowledgements ......................................................................................................... xii 1 Introduction .................................................................................................................. 1 1.1 General Context ......................................................................................................................................... 1     1.1.1 Energy Demand ............................................................................................................................................ 1     1.1.2 Wind Energy .................................................................................................................................................. 2     1.1.3 Wind Power Forecasts .............................................................................................................................. 3     1.1.4 Forecasting Models ..................................................................................................................................... 5 1.2 Thesis Objective......................................................................................................................................... 7 1.3 Thesis Outline ............................................................................................................................................. 7 2 Artificial Neural Network Fundamentals ........................................................... 9 2.1 Artificial Neural Network Structure .................................................................................................. 9 2.2 Activation Function ............................................................................................................................... 10 2.3 Training, Validation, and Testing Datasets ................................................................................. 12 2.4 Normalization of the Data .................................................................................................................. 12 2.5 Objective Function and Optimization Process ........................................................................... 12 2.6 Optimization Algorithms .................................................................................................................... 13 2.7 Selecting the Artificial Neural Network Structure ................................................................... 15 3 Methods and Available Data ................................................................................ 17 3.1 Data Pre-processing .............................................................................................................................. 17      3.1.1 Data Quality Control ................................................................................................................................ 17      3.1.2 Input Selection and Preparation ........................................................................................................ 19      3.1.3 Normalization ............................................................................................................................................. 20   v      3.1.4 Training, Validation, and Testing Datasets .................................................................................. 20 3.2 Forecasting Techniques ...................................................................................................................... 21      3.2.1 Regression ..................................................................................................................................................... 22      3.2.2 Empirical Operational Methods ......................................................................................................... 22      3.2.3 Designing the Artificial Neural Network ........................................................................................ 22      3.2.4 Frequency of ANN Training and Speed of Forecasting ............................................................ 24 4 Algorithm Development ......................................................................................... 27 4.1 Perfect-prog (PP) Method .................................................................................................................. 27      4.1.1 PP Polynomial Regression Model Using Observed Wind Speed ........................................... 27      4.1.2 PP Empirical Operational Method Using Observed Wind Speed ......................................... 30      4.1.3 PP Artificial Neural Network Models Using Observed Weather .......................................... 31 4.2 Model Output Statistics (MOS) ANN Models Using NWP Data ............................................ 46 5 Results .......................................................................................................................... 52 5.1 Application of Models to Other Time Periods ............................................................................ 52      5.1.1    June - July ................................................................................................................................................... 53      5.1.2    July - August ............................................................................................................................................. 54      5.1.3    August - September ............................................................................................................................... 55      5.1.4    September - October ............................................................................................................................. 56      5.1.5    October - November .............................................................................................................................. 57      5.1.6    December - January .............................................................................................................................. 58      5.1.7    January - February ................................................................................................................................ 59      5.1.8    February - March ................................................................................................................................... 60      5.1.9    March - April ............................................................................................................................................ 61      5.1.10    April - May .............................................................................................................................................. 62      5.1.11    May - June ............................................................................................................................................... 63 5.2 Comparison of Forecasts for a Common Month from Two Training Datasets ............. 66 5.3 An Ensemble Average ANN for Wind Power .............................................................................. 67 5.4 ANN-MOS and LUT Models for the Whole Year ........................................................................ 68 6 Conclusions and Discussion .................................................................................. 71 6.1 Conclusions .............................................................................................................................................. 71 6.2 Recommendations ................................................................................................................................. 72 Bibliography ..................................................................................................................... 74 Appendix ............................................................................................................................ 77   vi  List of Tables Table 1.1. Time-horizons for wind-power forecasting applications. ......................................................................... 4 Table 2.1. The most commonly used activation functions. ......................................................................................... 11 Table 3.1. The optimum ANN design properties. ............................................................................................................ 26 Table 4.1. Comparison of performance of different PP-ANN experiments ........................................................... 44 Table 4.2. Performance comparison of polynomial regression model, empirical operational method (LUT), and optimum ANN, all using PP technique. ......................................................................................................... 45 Table 4.3. Performance comparison of the empirical operational method (LUT) and the optimum ANN, both using the MOS technique. ................................................................................................................................................ 51 Table 5.1. Summary of the LUT and ANN model results for all time periods ...................................................... 65      vii List of Figures Figure 1.1. Idealized curve of output power P vs. wind speed v for a single hypothetical wind turbine ..... 3 Figure 2.1. Schematic of an artificial neural network with one hidden layer. ................................................... 10 Figure 3.1. Schematic of the designed artificial neural network. ............................................................................ 26 Figure 4.1. Polynomial regression model of the wind speed observations vs. wind power (Nov/Dec). .... 28 Figure 4.2. Wind-power forecasts by polynomial regression model with the wind-speed observations as the predictor (Nov/Dec). ........................................................................................................................................................... 29 Figure 4.3. Wind-power forecasts by the LUT method with the wind-speed observations as the predictor (Nov/Dec). ....................................................................................................................................................................................... 30 Figure 4.4. Wind-power forecasts by single hidden neuron ANN with the wind-speed observations as the predictor (Nov/Dec). ................................................................................................................................................................... 31 Figure 4.5. Wind-power forecasts by single hidden neuron ANN with the wind-speed and temperature observations as the predictor (Nov/Dec). ........................................................................................................................... 32 Figure 4.6. Wind-power forecasts by single hidden neuron ANN with the wind-speed and temperature observations, and time of the day as the predictor (Nov/Dec). ................................................................................. 33 Figure 4.7. Wind-power forecasts by single hidden neuron ANN with the wind-speed and wind-direction observations as the predictor (Nov/Dec). ........................................................................................................................... 34 Figure 4.8. Wind-power forecasts by single hidden neuron ANN with the wind-speed, wind-direction, temperature, relative humidity, and air-density observations, and time of day as the predictor (Nov/Dec). ....................................................................................................................................................................................... 35 Figure 4.9.Wind-power forecasts by single hidden neuron ANN with the wind-speed, wind-direction, wind shear, temperature, relative humidity, and air-density observations, and time of day as the predictor (Nov/Dec). ................................................................................................................................................................... 36 Figure 4.10. Wind-power forecasts by single hidden neuron ANN with the wind-speed, wind-direction, wind shear, temperature, relative humidity, and air-density observations, reported turbine availability, and time of day as the predictor (Nov/Dec). ..................................................................................................................... 37 Figure 4.11. Wind-power forecasts by single hidden neuron ANN with the wind-speed, wind-direction, wind shear, temperature, relative humidity, and air-density observations, and reported turbine availability as the predictor (Nov/Dec)............................................................................................................................... 38   viii Figure 4.12. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind shear, temperature, relative humidity, and air-density observations, reported turbine availability, and time of day as the predictor (Nov/Dec). ..................................................................................................................... 39 Figure 4.13. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind shear, temperature, relative humidity, and air-density observations, and reported turbine availability as the predictor (Nov/Dec)............................................................................................................................... 40 Figure 4.14. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind shear, temperature, relative humidity, and air-density observations as the predictor (Nov/Dec). . 41 Figure 4.15. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind shear, temperature, relative humidity, and air-density observations, and yesterday’s average turbine availability as the predictor (Nov/Dec). ............................................................................................................. 42 Figure 4.16. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind shear, temperature, relative humidity, and air-density observations, and yesterday’s average turbine availability as the predictor (Nov/Dec).. ............................................................................................................ 46 Figure 4.17. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Nov/Dec)............................................................................................................................... 47 Figure 4.18. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Nov/Dec). ....................................................................................................................................................................................... 48 Figure 4.19. Polynomial regression model of the wind speed forecasts vs. wind power (Nov/Dec). ......... 49 Figure 4.20. Wind-power forecasts by polynomial regression model with the wind-speed forecasts as the predictor (Nov/Dec). ........................................................................................................................................................... 50 Figure 5.1. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Jun/Jul). .......................................................................................................................................................................................... 53 Figure 5.2. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Jun/Jul). ................................................................................................................................. 53 Figure 5.3. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Jul/Aug). ......................................................................................................................................................................................... 54   ix Figure 5.4. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Jul/Aug). ................................................................................................................................ 54 Figure 5.5. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Aug/Sep). ....................................................................................................................................................................................... 55 Figure 5.6. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Aug/Sep). .............................................................................................................................. 55 Figure 5.7. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Sep/Oct). ........................................................................................................................................................................................ 56 Figure 5.8. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Sep/Oct). ............................................................................................................................... 56 Figure 5.9. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Oct/Nov). ........................................................................................................................................................................................ 57 Figure 5.10.Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Oct/Nov). .............................................................................................................................. 57 Figure 5.11. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Dec/Jan). ........................................................................................................................................................................................ 58 Figure 5.12. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Dec/Jan). ............................................................................................................................... 58 Figure 5.13. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Jan/Feb). ........................................................................................................................................................................................ 59 Figure 5.14. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Jan/Feb). ............................................................................................................................... 59   x Figure 5.15. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Feb/Mar). ....................................................................................................................................................................................... 60 Figure 5.16. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Feb/Mar). ............................................................................................................................. 60 Figure 5.17. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Mar/Apr). ....................................................................................................................................................................................... 61 Figure 5.18. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Mar/Apr). ............................................................................................................................. 61 Figure 5.19. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Apr/May). ...................................................................................................................................................................................... 62 Figure 5.20. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Apr/May). ............................................................................................................................. 62 Figure 5.21. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (May/Jun). ....................................................................................................................................................................................... 63 Figure 5.22. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (May/Jun). .............................................................................................................................. 63 Figure 5.23. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor for December using two training datasets Nov-Dec and Dec-Jan. ................... 66 Figure 5.24. Ensemble-averaging weights for overlapping pairs of months. ..................................................... 67 Figure 5.25. Ensemble-average forecasts for December using weighted forecasts of Nov-Dec and Dec-Jan training datasets. .................................................................................................................................................................. 68 Figure 5.26. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, air-density forecasts, time of day, month of year, and yesterday’s average turbine availability as the predictor (whole year). ................................................................ 69   xi Figure 5.27. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor 70      xii Acknowledgements I would like to acknowledge the support from the BC Hydro and Power Authority for funding this project. I wish to express my sincere thanks to my supervisor Prof. Roland Stull and committee members, Dr. Magdalena Rucker, Dr. Doug McCollor, and Dr. Phil Austin for their guidance and for providing me with all necessary facilities. I would also like to thank Dr. Valentina Radic for her recommendations. I take this opportunity to record my sincere gratitude to my friends at UBC Weather Forecast Research Team who have lent their helping hands and for their encouragements in this venture, especially Maggie Campbell, David Siuta, Dr. Rosie Howard, Dr. Greg west, and Pedro Odon. I will always remember all the good memories we made together.  I also thank my father who has been my first and best teacher and my dear mother for their unceasing encouragement and support. Last but not the least, a special thanks to my beloved husband, Mahdiar, for his unwavering moral and emotional support and his priceless advice.        1 1   Introduction 1.1 General Context 1.1.1 Energy Demand High demand for power in today's modern life necessitates searching for alternative sources of energy. Utilizing renewable energy resources is a high priority within energy production and management policies in many countries. The growing rate of demand for energy and the global warming phenomenon, which has raised a lot of concern about carbon dioxide emissions along with the high price of fossil fuel, has led governments to consider the utilization of new sources of energy. Several nuclear power-plant disasters and their long-term effects on the next generations’ health and environment have also initiated a series of debates on eliminating nuclear power from the future energy policies for some countries [1]&[2].   Wind is a free and easily available source of energy and appears to be the fastest growing of renewable energy resources [3]. Several countries, including Canada, have already considered the wind as a worthwhile and clean alternative, and have added wind power to their electricity supply system.  The Canadian Wind Energy Association (CanWEA) reported that Canada was in seventh place in the world for total installed wind energy capacity with 11,205 MW, and sixth in the world for the amount of capacity added in 2015 [4]. Wind energy provides approximately five percent of Canada’s total electricity now and is projected to generate 20 percent or more of the electricity demand by 2025.   2 1.1.2 Wind Energy A wind turbine generates wind power by converting the kinetic energy of the wind into the electricity. The theoretical power available from the wind is given by [5],   (  )                                 Where   represents the density of air and   is the turbine efficiency, which is usually 30% to 45% [5].   and   are the turbine-blade radius and hub-height wind velocity, respectively. Wind speed is assumed to be uniform along the diameter of the blade. Figure 1.1 shows an idealized wind-power curve relating power output (P) to wind speed magnitude ( ).  Three key wind-speed values are the cut-in speed (   ), rated-power wind speed (  ), and cut-out speed (    ). Cut-in speed is the speed at which the turbine starts to generate power. Power generation increases until it gets to its rated value then it remains constant until wind speed reaches the cut-out value. The turbine produces the maximum rated power (  ) for wind speeds in the range          . At its rated wind speed, the turbine produces the maximum amount of electricity that the generators can handle. As wind speed increases further, the aerodynamics of the blades are designed to change (via feathering the blades to reduce their pitch, or causing aerodynamic stalling), to keep the shaft rotation rate and electrical power generation nearly constant [5]. Finally, there is zero power generation for winds faster than the cut-out speed, because the turbine is shut down to prevent damaging thrust forces on bearings and bending forces on the blades.  Hypothetical idealized turbines have a cubic (  ) increase in power vs. wind speed for the rising part of the curve (        ), as is sketched in Figure 1.1.  However, actual collections of wind turbines at a wind farm can have total output with a wind-speed exponent (b) less than 3. Thus:     3      (           )                                                                                                                                                                                            Figure ‎1.1. Idealized curve of output power P vs. wind speed v for a single hypothetical wind turbine with maximum rated power of 1 MW Figure 1.1 shows a theoretical power curve. However, in modern wind farms, instead of a sharp cut-out of power, the power generation decreases gradually at the cut-out speed. 1.1.3 Wind Power Forecasts The amount of energy produced in a wind farm directly depends on the composition of the wind farm, characteristics of the wind, and the meteorological conditions. Forecasting the wind-power production is quite challenging since the wind is extremely variable and depends on terrain factors and turbine height. Different weather conditions could make a wind turbine generate from zero power to its maximum capacity. Besides, wind power is not storable and must be transported once is generated. The high dependency of the wind-power generation on weather conditions motivates the designing of a reliable power-forecasting system. Such a v (m/s) cut-out    4 forecasting system is required in order to estimate the amount of wind energy that can be extracted from the wind farms and to anticipate what proportion of the demanded power in the power grid can be provided by the wind. Numerous studies in many scientific areas have been conducted in the attempt to find a sufficient solution to cope with this issue, and various methods have been developed.  The time-horizon for wind-power forecasting can be classified into 3 main scales, immediate-short-term, short-term, and long-term forecasts. Immediate-short-term forecasts are made eight hours ahead of the desired time in order to help make decisions for real-time grid operations and regulations. To manage the transmission loads and maintain the operational security in the electricity market, a forecast is also required the day before, which is called a short-term forecast. For maintenance purposes and calculating the optimal operating cost, long-term forecasts are needed several days ahead [6]. Table 1.1 lists the time-horizons for wind-power forecasting [6]. Table ‎1.1. Time-horizons for wind-power forecasting applications. Time scale Forecast range Applications Immediate-short-term Eight-hours-ahead  Real-time grid operations  Regulation actions Short-term One-day-ahead  Economic load dispatch planning  Load decision-making  Operational security in the electricity market Long-term Multiple-days-ahead  Maintenance planning  Operation management  Optimizing operating cost Wind-power forecasting methods can be classified into two main categories, physical and statistical methods. The former usually performs better in short and long-term prediction whilst the latter shows advantages in immediate-short-term prediction [7]. More advanced methods based on artificial intelligence, namely artificial neural networks (ANN), fuzzy logic, neuro-fuzzy, evolutionary algorithms,   5 and some hybrid methods have also been widely investigated in recent years [8]. These recent methods have shown considerable improvements in immediate-short-term and short-term predictions of the wind power [6].   1.1.4 Forecasting Models For physical techniques, numerical weather prediction (NWP) models collect meteorological and geographical information as the input and predict the wind speed accordingly. An advantage of NWP models is that their forecasts are made using full dynamic and thermodynamic equations that show the atmosphere’s behaviour. Wind power can then be estimated using the existing power curves of the wind farm [9].  It is also possible to improve the wind-speed forecast and relate it to the prospective power generation through existing power curves for the wind farm.  Statistical models work with historical data and by statistical approaches such as pattern identification and parameter estimation, try to make a mathematical model of the problem. Such models include the autoregressive model (AR), moving average model (MA), autoregressive moving average model (ARMA), or autoregressive integrated moving average model (ARIMA) [7]. Some studies suggest that wind-turbine power forecasts should be based on the wind-speed forecast rather than directly on a wind-power time series [10]. The spatial relationship of the wind speed among different locations could also be considered toward achieving a more accurate model to forecast wind power. Such an approach is called a spatial correlation model [7].  Since every model works with a certain series of input data, either from dynamical-model outputs or historical data, along with various physical, statistical, and mathematical techniques with specific approximations, a precise comparison of their performances would not be feasible. However, some studies suggest that artificial intelligence-based models, such as an artificial neural network, have shown good performance in short-term predictions [8].     6 There are a number of advantages for artificial neural network models over the other statistical methods that can be summarized as follows [11]:  Neural network models require less formal statistical training to develop.  Neural networks can implicitly detect complex nonlinear relationships between independent and dependent variables.  Neural networks have the ability to detect all possible interactions between predictor variables.  Neural networks can be developed using multiple different training functions. There are also a number of disadvantages that are cited in the literature [11], some of them (e.g. limited ability to explicitly identify possible causal relationships, and being prone to overfitting) are easily resolvable by creating several models with every possible combination of input variables and utilizing appropriate training and testing datasets. Computationally intensive procedures in training the artificial neural networks have also become less concerning because of the fast-paced improvements in technology and computational resources. Many attempts were made by others for short-term wind-power forecasting using artificial neural networks. Wind speed, wind components as a representative for the wind direction along with the time of the day and week of the year were used as predictors. It was shown that time of the day and week of the year indicated seasonal and daily trends in the dataset [1]. Another study took the variability in air density into account. This study suggests that using wind speed along with air density as the inputs for the ANN could decrease the root mean squared error (RMSE) of the wind power forecast by up to 16% [12]. A study in China also demonstrated the success of a back-propagation artificial neural network in forecasting the wind power using wind speed, wind direction, temperature, pressure, and relative humidity as its predictors [13].     7 1.2 Thesis Objective The aim of this work is to exploit the ability of artificial neural network models to find the most effective parameters to estimate generated power from predicted wind speed at a wind farm. The historical data of both observations and forecasts of weather characteristics along with turbine availabilities and the related power productions are used for this purpose. Wind power is forecast for every overlapped pair of months during a year and for the whole year. The reason for using the overlapped months is to make a smoother transition between the forecasts made from the different training datasets. Also, dividing the data into 12 groups of two-month periods instead of 12 single months was not only for increasing each sample size, but also for making a broader variable range for each training period. Each pair of months was trained independently. Experiments are done first with the observations and then with the forecasts as the predictors that are input to the ANN. The best model with the most accurate forecast is found for each period. The results from the best models are compared to linear-model fits in order to show the ability of artificial neural network models to capture the nonlinearity effects. Also, another comparison is made between the results from artificial neural network models and the current empirical approach used operationally by a utility company. 1.3 Thesis Outline Chapter 2 discusses the fundamental knowledge required for designing artificial neural network models by introducing the network parameters, structure, and model characteristics. Data pre-processing and preparation methods are also explained in this chapter.  Chapter 3 includes the methods and materials utilized for the current work. Data pre-processing and data-sampling methods are presented. Applied forecasting techniques are explained and the properties of the designed models are discussed. In chapter 4 different algorithms are tested. This chapter shows the results from several models that are designed in this work and compares their performance. It   8 also discusses the improvement of the wind-power forecast provided by every model. Chapter 5 uses the resulting best algorithms to evaluate ANN forecasts for every pair of months in this case study. These results are compared with a linear method and with the method currently used operationally by a utility company.  Conclusion and discussion are in chapter 6.     9 2   Artificial Neural Network Fundamentals 2.1 Artificial Neural Network Structure An artificial neural network (ANN) is an information-processing system that adopts the neural structure of the human brain for analyzing data, finding patterns, classification, and prediction through a learning process using a series of mathematical equations [11]. There are multiple layers of neurons (nodes) in an artificial neural network. Each layer receives multiple inputs to its nodes and, after applying some mathematical calculations, passes the information to the next layer. Thus, each layer feeds the next layer with information – this is the basic concept of a feed-forward neural network. There are three main categories of layers in an artificial neural network: input, hidden, and output layers. The main advantage of an artificial neural network with multiple layers over a single-layer model is the ability to resolve nonlinear problems [1]. Figure 2.1 is a schematic of a single-hidden-layer ANN model.     10  Figure ‎2.1. Schematic of an artificial neural network with one hidden layer.  The input variables,   , are mapped to the hidden layer neurons,   , and then to the output variables,   , by,     (∑           )                              (∑           )                              Where f and g are activation functions,     and     are weight matrices, and     and     are offset parameters [14].  2.2 Activation Function The activation function could be chosen from the following list: logistic sigmoidal function, hyperbolic tangent function, or linear function. It is also possible to create a hybrid artificial neural network with different activation functions in different   11 layers. However, there should be at least one non-linear activation function used in an ANN structure in order to retain its ability to solve non-linear problems. The most commonly used activation-function features are shown in Table 2.1.  Table ‎2.1. The most commonly used activation functions. Activation Function Mathematical Equation Graphical Representation Linear         Logistic sigmoidal                Hyperbolic tangent                   It was shown by others that the activation function plays a very important role in the accuracy of artificial neural network results, but if a network could be trained successfully with a particular activation function, it would be highly probable that other activation functions would also result in an acceptable training [15]. Linear activation functions have been used by some investigators in input and output layers. For the hidden and output layers, non-linear activation functions are used [16]. Some studies show that the linear activation function in the output layer combined with a nonlinear activation function for a single hidden layer has positive effects on the performance of the ANN [16]. This work adopts that ANN structure.   12 2.3 Training, Validation, and Testing Datasets The data used in an ANN model must be divided into training and testing datasets. The ANN processes the training dataset in order to find the optimum model parameters. The training dataset is also divided into training and validation datasets. The validation dataset is used for tuning the model parameters of the ANN during the training process to prevent overfitting, and to better handle outliers [17].  The most commonly used technique for validating the model during the training phase is the cross-validation method. In this approach the training dataset is partitioned into several folds, where first, one fold is reserved as the validation set and the rest of the folds are considered as the training dataset. This procedure is then repeated for every fold acting as the validation set. The performance of the model would be the average performance of all folds [18]. The independent testing dataset would then be used to evaluate the forecasting ability of the trained model. 2.4 Normalization of the Data The data used in an artificial neural network model should be normalized first. Normalization of the data minimizes the impact of the scale of variables on the model [19]. Normalization scales the input values of different variables to be in the same range, and to minimize the ANN bias of one variable relative to another [20]. It could also speed up the training procedure [20]. The variables should be normalized either between -1 and 1 or between 0 and 1, depending on the variable’s actual range. The output results must then be denormalized in order to get the actual forecast values. 2.5 Objective Function and Optimization Process ANNs are able to learn the relationship between the predictors (input variables) and the corresponding predictands (output variables) by adjusting the internal weights and offset parameters during the training process [11], so that the forecast values   13 would be as close as possible to the real available observed data. In pursuance of this, a defined objective function (also referred to as the cost function, error function, or loss function) has to be minimized. The most commonly used form of the objective function, E, in nonlinear regression problems is the mean-squared error, MSE, between the model forecast and the real data or target values,     ∑                                      where,    is the forecast data (model forecast),     is the target data (observations), and N is the number of observations [14].  During the optimization process, the gradient of the objective function with respect to the parameters is needed in order to minimize E, using the back-propagation algorithm. The back-propagation procedure includes two major steps. First, in the forward step, the parameters are randomly initialized and output values are predicted. The objective function is then calculated using Equation (2.3). During the backward step, the network tries to update the parameters so that the objective function is minimized. To do so, the gradient of E with respect to the parameters is used to calculate the new parameters by,                                                is called the learning rate and is an optional factor that affects the accuracy and speed of the learning. A greater learning rate results in a faster training, but a smaller learning rate provides a higher accuracy. The optimization process continues until the optimum parameters are achieved.  2.6 Optimization Algorithms There are a number of nonlinear least-square optimization algorithms that can be used. Some of the most commonly used algorithms are gradient descent, Gauss-Newton, and Levenberg-Marquardt methods. All these methods present an iterative   14 algorithm to find a perturbation h to the parameters p that reduces error    to its minimum.        ∑                                      In fitting a function         of an independent variable   (i.e. predictors) and a vector of   parameters   (i.e. model weights and biases) to a set of   data points        (i.e. number of instances), it is convenient to minimize the sum of the weighted squares of the errors (weighted residuals) between the observed data    and the curve-fit (model-forecast) function    [21].  The gradient descent method reduces the sum of the squared errors in the objective function by updating the parameters in the steepest-descent (negative gradient) direction. The gradient of the chi-squared objective function with respect to the parameters is [21],         (        )                            Where   is the     Jacobian matrix       ⁄   that represents the local sensitivity of    to variations of parameters   [21].   The parameter update h that moves the parameters in the direction of the steepest descent is given by [21],        (        )                                 The Gauss-Newton method approximates the least-squares function as being locally quadratic, and seeks its minimum. The parameter update h that minimizes    is calculated by [21],            (        )                            15 Levenberg-Marquardt algorithm adaptively varies the parameter updates between the gradient descent update and the Gauss-Newton update [21],               (        )                 This method interpolates both gradient descent and Gauss-Newton methods, meaning it acts more like gradient descent when the parameters are far from their optimal values with small values of  , but is like Gauss-Newton with large values of  , otherwise. The Levenberg-Marquardt algorithm tends to be the fastest training function, but it is not effective in large networks since it requires more memory and computation power. The method is more robust than gradient descent, meaning it could converge to the final minimum even if it starts very far off from it. However, in the presence of multiple local minima, the initial guess for the parameters must be fairly close to the final answer so that algorithm can converge to the global minimum. It is also more suited for nonlinear regression problems than for pattern recognition. Marquardt’s suggested update relationship is also given by [21] as:                        (        )                           2.7 Selecting the Artificial Neural Network Structure Another critical step in designing an artificial neural network is selecting the number of hidden layers and their neurons. The number of hidden layers and neurons highly depends on the size of the input and output layers, the characteristics of the sample database, the complexity of the activation function, the training algorithm, the desired accuracy, and the time limitations [22]. The optimum architecture of the ANN is usually found empirically. However, some studies have shown that an artificial neural network with only one hidden layer can approximate any continuous function         arbitrarily well if there are enough neurons in the hidden layer [23]. Also, it is suggested in the literature that the number of hidden nodes should be between the number of input and output nodes and less than twice   16 of the number of neurons in the input layer [22], in order to reduce overfitting (i.e., fitting the noise in the dataset). This constraint is used in this thesis.     17 3   Methods and Available Data This chapter describes the purpose and the motivations for the current study. Available data and the pre-processing steps are explained. The chapter also contains a description of the designed artificial neural network, including its structure, characteristics, and implemented optimization algorithm. It also provides details on the data sampling methods and applied forecast-verification metrics. 3.1 Data Pre-processing The data is from a wind farm in Canada containing the non-quality-controlled hourly observations of weather characteristics including wind speed, wind direction, temperature, relative humidity, and pressure for one year from June 2014 to May 2015. The data also includes the related power generation and turbine availabilities.  The exact location of wind farm and the data are withheld from publications due to a confidentiality agreement signed with the utility company. Also, the wind power has the units of MW but it is normalized for confidentiality.  Forecasts by a numerical weather prediction system that is the average of 16 different ensemble members are also available for the same period. 3.1.1 Data Quality Control The first essential step before starting any data-analysis study is the quality control of the available data. There are a series of proposed guidelines on quality-control approaches [20].  The quality control procedure of the observed data for the current work is explained below:   Finding missing values or periods of times when the measurement system was down for any reason and indicating them by “NaN” (Not a Number).   18  Filtering the data by comparing the recorded values with the manufacturer specification sheet of the instrument measurement range and eliminating out-of-range values.   Removing any value that is not physically possible for a variable; e.g., wind speed less than zero.   Filtering the data by considering the reasonable values for each season. Historical meteorological measurements for the area are obtained from the nearest airport station. Minimum lowest temperature and maximum highest temperature for each month during the desired period were used. The predictor data was compared to the historical values to dismiss any out-of-range measurements.  Refining the data by examining the time consistency of the temperature, i.e. the maximum variability allowed between specific timestamps. To do so, the change in temperature in 5-minute-windows was calculated. Also, for the times when there was a sudden jump in the temperature, the change in other variables, i.e. wind speed, wind direction, relative humidity, and pressure were checked in order to find any available correlation. If no such a correlation was found, the measured temperature was considered as an outlier and discarded.    Filtering the data by examining the time consistency of the wind speed. The histogram of the wind speed trend was made. For the periods when there was a large change in wind speed in a specific height, the recorded wind speed difference by sensors on other levels was controlled to find any probable correlation. The data was discarded in case such a correlation did not exist.     Examining the time consistency of the measured values of the relative humidity using a standard-deviation method. In order to do this, the averaged relative humidity in 10-minute-windows was required. Equation (3.1) was used to examine if the changes in relative humidity were reasonable.                                                        19 where   is the standard deviation of the relative humidity. After quality control, 8641 hourly data instances were available out of the maximum possible 8760 hours in a year. 3.1.2 Input Selection and Preparation  As discussed earlier, wind-power production by a wind turbine is related to the wind speed and density of the air. Also, previous studies suggest that the amount of wind-power generation depends on the wind direction, air temperature, and relative humidity. This study aims to take into account all the mentioned predictors along with some additional variables, i.e. wind shear and turbine availability to obtain a more reliable forecast for the wind power. Also, considering the ideal gas law, two independent variables are needed to show the state of a gas, i.e. temperature and pressure. Thus, the designed artificial neural network considers several combinations of the variables. These variables are wind speed, wind direction, wind shear, temperature, density, relative humidity, time of day, month of year, and turbine availability as the inputs and wind power as the output. Some of the variables were already available whilst air density and wind shear were calculated as explained next. Air Density  Assuming dry conditions, the ideal gas law was applied to estimate the air density.                                  where P and T represent the pressure and the temperature, respectively.    is the gas constant , which for dry air is equal to 0.287053 kPaK-1m3kg-1. The dry-condition assumption will not affect the results since the relative humidity is also used as a predictor for wind power. Since temperature was already considered as a predictor for wind power, density was used as the representative of pressure in this study.   20 Wind Shear Wind shear is the change of horizontal wind speed and/or wind direction with altitude, Z [5]. Shear depends partly on the atmospheric static stability. The wind shear was calculated using the wind speed components (U,V) at two different heights by,                                                            3.1.3 Normalization The data was normalized before using it in the forecasting system. There are various techniques for normalizing a dataset. The method applied in the current work, is called min-max normalization. This method normalizes the values of element A according to their minimum and maximum values. It converts a value of a in vector A into  ̂ in the range [low, high] [27]. All the variables except for temperature were normalized to the [0,1] range. Temperature was normalized to the [-1,1] range.   ̂                                                           For normalizing wind speed, the maximum value was considered to be equal to the cut-out wind speed, despite the fact that the cut-out wind speed might never be reached or that some wind speeds might be faster. The maximum power and maximum turbine availability were assumed to be the maximum designed capacity of the wind farm; again despite the fact that this might never be reached in reality.  Wind direction data was normalized using the sine and cosine of its values.   3.1.4 Training, Validation, and Testing Datasets A critical step in preparing the data for a forecasting system is dividing the available data into two completely separate groups, i.e. training and testing datasets. The   21 testing dataset must not be used in the training process in any form, to let the forecasting system be evaluated by a totally independent dataset.  In the present work, the data was divided into 12 groups of overlapped periods, e.g. June-July, July-August, August-September, …, May-June. For this part of the study the day of the year was not used as an input and all the days were considered to be the same. This assumption seems to be reasonable since each group contains two subsequent months with similar weather characteristics. For each group, two-thirds of the data were randomly picked to form the training dataset, and the remainder were put in the testing dataset. For the artificial neural network models, the training dataset itself is also divided into two different sets for training and validation. 70% of the training dataset was employed for training and the remaining 30% served for validation purpose. All the studies were also repeated for another dataset containing the data for the whole year (June 2014-May 2015) in which time of day and month of the year were considered as two extra predictors. All the discussed approaches towards preparing the data were implemented on every data set.  3.2 Forecasting Techniques For every model designed in this work, the root mean squared error (RMSE) of the wind power forecast was used to compare the accuracy of the different approaches.        √∑                                        where    is the model forecast and    is the real observation for each time step. For each pair of months and for the whole year, three approaches were tested to estimate wind power: (1) regression; (2) empirical operational methods; and (3) artificial neural networks.   22 3.2.1 Regression In order to investigate how the forecast would be influenced by the nonlinearity, first a regression model was fitted to the training dataset. The regression model fit could be a 4th order (or more) polynomial, depending on the data sample. Since in the current operational approach wind speed is the only predictor, the polynomial model in this work is also a simple linear regression model that predicts the wind power using only the wind speed as its predictor.  The model fit was then evaluated using testing dataset, and the root-mean-squared error (RMSE) of the forecast in MW was calculated. Although a polynomial regression fits a nonlinear function to the data, from the statistics point of view, it lies under the category of “linear regression”, in the sense that the regression function is linear in the system parameters; i.e., linear in the weights and biases, not linear in the predictors [24].  3.2.2 Empirical Operational Methods In order to calculate the amount of expected power generation in a wind farm, several empirical techniques are currently being used operationally by the local utility company. These methods anticipate the wind power using a tabulated relationship (i.e., a look-up table, LUT) between the wind speed and wind power based on previous observations. In case the actual power output does not match the estimated power generation, a calibration factor in real-time might be applied to adjust the forecast. However, this calibration factor is not used very often. Wind speed forecasts used in this study are bias-corrected. We also compared the RMSE of the results from empirical methods with the forecasts from the artificial neural network.  3.2.3 Designing the Artificial Neural Network Perfect-prog Method vs. Model Output Statistics In the perfect-prog (PP) method, predictors are the observed weather characteristics; e.g., wind speed and temperature, in order to forecast other   23 variables, namely wind power in this context. This approach develops equations based on the previous observations and does not make any correction for probable biases in the system. PP also does not take into account errors in the NWP model forecasts of weather variables [25].  The model output statistics (MOS) method was developed to modify the PP system’s forecast. This technique develops the relationship equations between the observed predictand (wind power) and the predictors, which are the forecasts from the NWP system instead of the observations [25]. The ANN in the current work was first designed using the observed values to obtain the perfect model fit to help finding the optimum structure of the network. Then in order to estimate the ability of the model to forecast the power using the day-ahead NWP weather forecasts (MOS), a series of meteorological forecasts of the input variables along with the yesterday’s average turbine availability for the same period of time were used as the predictors. The available weather-forecast dataset is the average of 16 different WRF1 ensemble members with different combinations of PBL2 schemes and the initial conditions; i.e., GFS3 and NAM4. Data Sampling  It is possible to improve the accuracy of a machine-learning algorithm (e.g. an artificial neural network) by implementing some sampling techniques. One of these methods is called bagging or bootstrap aggregation, which also reduces the probability of overfitting. Bagging-predictors method can generate multiple predictor sets from a single dataset [26]. As it was discussed before in section 2.3, the other approach to cope with the overfitting issue is the cross-validation technique, which should be applied after sampling the data via bagging method. However, this technique is computationally intensive and, given the already implemented approach to prevent overfitting and the reasonably accurate acquired                                                         1 Weather Research and Forecasting Model 2 Planetary Boundary Layer  3 Global Forecast System (from the US National Centers for Environ. Prediction, NCEP) 4 North American Mesoscale Forecast system (from NCEP)   24 results, only slight improvements can be expected. Thus, the cross-validation technique was not considered in this work. In this work the bagging-predictors method was utilized to make 10 different random subsets from each training dataset.  Since during each neural network run, the initial parameters are chosen randomly, the forecasts could be slightly different and, as a result, RMSE would change in each run. In order to minimize the random error, the model runs 10 times and outputs the arithmetic mean of the 10 runs as its forecast. Several ANN models were designed with different combinations of inputs as a sensitivity study to find the most effective predictors, as will be described in chapter 4 on algorithm development. Selecting System Characteristics As discussed earlier in chapter 2, a single-hidden-layered artificial neural network can forecast sufficiently well, if the number of hidden nodes is defined carefully. It was also mentioned some empirically derived rules of thumb suggest that the optimal size of the hidden layer is usually between the sizes of input and output layers. For our study, that reasonable maximum number of hidden nodes is 8. The model in this work is a back-propagation multi-layer perceptron (MLP) with one hidden layer. As a sensitivity study, the number of hidden nodes were chosen to be 1, 2, 3, …, 8. Adding more hidden nodes beyond 8 did not seem to improve the results significantly. The MLP also has hybrid architecture with the hyperbolic tangent activation function for its hidden layer and a linear transfer function in the output layer. The objective function is the mean squared error (MSE) and optimization method was chosen to be Levenberg-Marquardt algorithm. This design is summarized in Figure 3.1 and Table 3.1. 3.2.4 Frequency of ANN Training and Speed of Forecasting Once the ANN is trained for a specific period of time, i.e. using data from every hour for two months or for a whole year, it is ready for operational application.   25 If desired, the ANN for each two-month period can be retrained every year. Normalized weather forecast variables from NWP models along with the average turbine availability from the previous day are given to the saved trained ANN as predictors, allowing the ANN to forecast the wind power. This process can be scripted to run automatically, and the computation time is only a few seconds on modern desktop computers and laptops. Hence, it is an operationally viable method for utility companies.     26  Figure ‎3.1. Schematic of the designed artificial neural network.   Table ‎3.1. The optimum ANN design properties.   Number of hidden layers 1 Number of nodes in input layer 8-10 Number of nodes in hidden layer 8 Number of nodes in output layer 1 Activation function in hidden layer Logistic sigmoidal Activation function in output layer Linear Objective function Mean-squared error (MSE) Optimization algorithm Levenberg-Marquardt Data-sampling method Bagging      27 4   Algorithm Development In this section, two months were selected for algorithm development to investigate the ability of various models to make wind-power forecasts. Since stronger winds usually occur in winter, choosing the November-December pair is sensible. We examined two different approaches and compares the results. First, all the models [regression of a polynomial, empirical method, and feed-forward back-propagation artificial neural networks (ANN)], were designed by applying the “perfect prog” technique that used weather observations as inputs. To test realistic real-time forecasts, outputs from the operationally-used look-up tables (LUT) and the best-structured ANN model were further refined by employing a model output statistics (MOS) method that used weather forecasts as inputs. A comparison between the results from both approaches is also presented. In each part (PP and MOS), the available data was divided into training and testing datasets, and the same datasets were used for each forecast model. For every model the root-mean-squared error between the forecast and corresponding observed wind power were calculated and the results from each model were compared.  4.1 Perfect-prog (PP) Method 4.1.1 PP Polynomial Regression Model Using Observed Wind Speed The simplest model tested here is a polynomial regression model. A 4th order polynomial was fit to the data in order to relate the wind-speed observations to the observed wind powers for the training dataset (Figure 4.1).    28  Figure ‎4.1. Polynomial regression model of the wind speed observations vs. wind power (Nov/Dec).   00.10.20.30.40.50.60.70.80.910 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Normalized wind power Normalized wind speed Nov/Dec 4th order polynomial regression model   29 The polynomial function was then used to forecast the wind power from the existing wind-speed observations in the independent testing dataset (Figure 4.2).   Figure ‎4.2. Wind-power forecasts by polynomial regression model with the wind-speed observations as the predictor (Nov/Dec). RMSE units for normalized wind power are dimensionless.   00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Nov/Dec Polynomial regression model (predictor: wind speed) Real ObservationsModel ForecastR2=0.95 RMSE=4.63 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation   30 4.1.2 PP Empirical Operational Method Using Observed Wind Speed This section shows the results of an empirical look-up table (LUT) method utilized to forecast the expected wind power using wind-speed observations as the predictor. The results in Figure 4.3 present the best forecast the empirical model was able to produce. The root mean squared error shows 29.5% improvement over the linear-regression method. Since this LUT is the method currently in use operationally by the local utility company, a goal of this research is to see if it is possible to develop a more accurate method based on ANN.  Figure ‎4.3. Wind-power forecasts by the LUT method with the wind-speed observations as the predictor (Nov/Dec). Performance improvement compared to the regression method: 29.5%.   00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Nov/Dec Operational method (predictor: wind speed) Real ObservationsModel ForecastsR2=0.96 RMSE=3.27 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation    31 4.1.3 PP Artificial Neural Network Models Using Observed Weather In this section several candidate feed-forward back-propagation artificial neural network (ANN) models working with different sets of predictors and various structures are tested and their performances are compared. The simplest ANN with single hidden neuron and the wind-speed observations as the only predictor delivers 9% improvement in RMSE performance over the empirical operational method (Figure 4.4).   Figure ‎4.4. Wind-power forecasts by single hidden neuron ANN with the wind-speed observations as the predictor (Nov/Dec). Performance improvement compared to the LUT method: 9%.   00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Nov/Dec ANN with 1 hidden neuron (predictor: wind speed) Real ObservationsModel ForecastsR2=0.97 RMSE=2.98 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation    32 As it might be expected, adding more relevant predictors and utilizing more complex architectures can possibly enhance the performance of the ANNs. Some experiments with more predictors are described in the following figures. In the next experiment, wind speed and temperature are the predictors (Figure 4.5). Performance improvements are given in the figure captions.  Figure ‎4.5. Wind-power forecasts by single hidden neuron ANN with the wind-speed and temperature observations as the predictor (Nov/Dec). Performance improvement compared to the basic ANN: 6%. Performance improvement compared to the LUT method: 14.5%.     00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Nov/Dec ANN with 1 hidden neuron (predictors: wind speed, temperature) Real ObservationsModel ForecastsR2=0.97 RMSE=2.80 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation    33 It seems that time of day might not be a proper predictor for the wind power as the RMSE slightly decreases by adding the time to the list of predictors (Figure 4.6). The reason behind this can be that the effects of time such as change in air density and wind shear due to the changes in boundary layer have already been taken into account. Thus, considering the time as an independent predictor might not be necessary anymore. However, time of day might have some other effects that were not considered. Some of the following results show the wind forecast with and without using time of day as a predictor.   Figure ‎4.6. Wind-power forecasts by single hidden neuron ANN with the wind-speed and temperature observations, and time of the day as the predictor (Nov/Dec). Performance improvement compared to the basic ANN: 5%. Performance improvement compared to the LUT method: 13.5%.     00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Nov/Dec ANN with 1 hidden neuron (predictors: wind speed,  temperature, time of day) Real ObservationsModel ForecastsR2=0.97 RMSE = 2.83 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation    34 The results from the ANN that uses wind direction and wind speed as its inputs could forecast the wind power 14% more accurately than the basic ANN with wind speed as the only predictor (Figure 4.7).  Figure ‎4.7. Wind-power forecasts by single hidden neuron ANN with the wind-speed and wind-direction observations as the predictor (Nov/Dec). Performance improvement compared to the basic ANN: 14%. Performance improvement compared to the LUT method: 22%.   00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Nov/Dec ANN with 1 hidden neuron  (predictors: wind speed, wind direction) Real ObservationsModel ForecastsR2=0.98 RMSE = 2.56 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation    35 As mentioned earlier, a number of studies already focused on the effects of different predictors of the wind-power production using artificial neural networks. Figure 4.8 below demonstrates the results of combining all the predictors that the previous studies took into account, i.e. wind speed, wind direction, temperature, relative humidity, density, and time of the day.  Figure ‎4.8. Wind-power forecasts by single hidden neuron ANN with the wind-speed, wind-direction, temperature, relative humidity, and air-density observations, and time of day as the predictor (Nov/Dec). Performance improvement compared to the basic ANN: 16.5%. Performance improvement compared to the LUT method: 24%.   00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Nov/Dec ANN with 1 hidden neuron (predictors: wind speed, wind direction, temperature, relative humidity, density, time of day) Real ObservationsModel ForecastsR2=0.98 RMSE = 2.49 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation    36 We hypothesized that the wind shear could be an effective factor in forecasting the wind power. Adding the wind shear to the ANN slightly improved the results (Figure 4.9).   Figure ‎4.9.Wind-power forecasts by single hidden neuron ANN with the wind-speed, wind-direction, wind shear, temperature, relative humidity, and air-density observations, and time of day as the predictor (Nov/Dec). Performance improvement compared to the basic ANN: 18%. Performance improvement compared to the LUT method: 25%.   00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Nov/Dec  ANN with 1 hidden neuron (predictors: wind speed, wind direction, wind shear, temperature, relative humidity, density, time of day) Real ObservationsModel ForecastsR2=0.98 RMSE = 2.44 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation    37 Also, the data acquired in this work suggest that adding the reported turbine availability to the list of the predictors would give more reliable wind-power forecasts. This indeed significantly improved the results (Figure 4.10). Removing the time-of-day predictor reduced RMSE slightly (Figure 4.11).  Figure ‎4.10. Wind-power forecasts by single hidden neuron ANN with the wind-speed, wind-direction, wind shear, temperature, relative humidity, and air-density observations, reported turbine availability, and time of day as the predictor (Nov/Dec). Performance improvement compared to the basic ANN: 38.5%. Performance improvement compared to the LUT method: 44%.   00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Nov/Dec  ANN with 1 hidden neuron (predictors: wind speed, wind direction, wind shear, temperature, relative humidity, density, turbine availability, time of the day) Real ObservationsModel ForecastsR2=0.99 RMSE = 1.83 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation    38  Figure ‎4.11. Wind-power forecasts by single hidden neuron ANN with the wind-speed, wind-direction, wind shear, temperature, relative humidity, and air-density observations, and reported turbine availability as the predictor (Nov/Dec). Performance improvement compared to the basic ANN: 39%. Performance improvement compared to the LUT method: 44.5%    00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Nov/Dec  ANN with 1 hidden neuron (predictors: wind speed, wind direction, wind shear, temperature, relative humidity, density, turbine availability) Real ObservationsModel ForecastsR2=0.99 RMSE = 1.81 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation    39 In another experiment, the number of nodes on the hidden layer of the ANN was increased sequentially from 1 to 8. The optimum number of hidden nodes appeared to be 8 (Figure 4.12), as this resulted in 53% improvement in the forecast compared to the basic ANN with only one hidden node (Figure 4.11). As discussed in chapter 3, adding more hidden nodes beyond 8 appeared not to improve the results significantly, and runs the risk of fitting the noise more than the desired signal.  Figure ‎4.12. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind shear, temperature, relative humidity, and air-density observations, reported turbine availability, and time of day as the predictor (Nov/Dec). Performance improvement compared to the basic ANN: 53%. Performance improvement compared to the LUT method: 57%.  00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Nov/Dec ANN with 8 hidden neurons  (predictors: wind speed, wind direction, wind shear,  temperature, relative humidity, density, turbine availability, time of day) Real ObservationsModel ForecastsR2=0.99 RMSE = 1.40 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation   40   Figure ‎4.13. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind shear, temperature, relative humidity, and air-density observations, and reported turbine availability as the predictor (Nov/Dec). Performance improvement compared to the basic ANN: 56%. Performance improvement compared to the LUT method: 60%.  Eliminating the time of day as predictor for wind-power forecasting improves the results (Figure 4.13). Thus, the most relevant predictors are: wind speed, wind direction, temperature, relative humidity, air density, and turbine availability. This was the best of the perfect-prog (PP) experiments, which used weather observations as inputs.     00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Nov/Dec ANN with 8 hidden neurons  (predictors: wind speed, wind direction, wind shear,  temperature, relative humidity, density, turbine availability) Real ObservationsModel ForecastsR2=0.99 RMSE = 1.30 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation   41 To mimic real operational situations where the wind-power forecasts are needed before actual turbine availability is reported, turbine availability was eliminated from the predictors list while continuing to utilize 8 hidden nodes in the ANN (Figure 4.14). As expected, forecast accuracy decreased.  Figure ‎4.14. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind shear, temperature, relative humidity, and air-density observations as the predictor (Nov/Dec). Performance improvement compared to the basic ANN: 34%. Performance improvement compared to the LUT method: 40%.   00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Nov/Dec ANN with 8 hidden neurons  (predictors: wind speed, wind direction, wind shear, temperature, relative humidity, density) Real ObservationsModel ForecastsR2=0.99 RMSE=1.97 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation   42 Next, the average turbine availability of the previous day was included as a predictor, because this would be known in an operational environment. The results (Figure 4.15) still show 35% improvement comparing to the basic ANN.  Figure ‎4.15. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind shear, temperature, relative humidity, and air-density observations, and yesterday’s average turbine availability as the predictor (Nov/Dec). Performance improvement compared to the basic ANN: 35%. Performance improvement compared to the LUT method: 41%.    00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Nov/Dec ANN with 8 hidden neurons (predictors: wind speed, wind direction,  wind shear, temperature, relative humidity, density, yesterday's average  turbine availability) Real ObservationsModel ForecastsR2=0.99 RMSE = 1.93 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation   43 Table 4.1 summarises the performance of different PP-ANN models that use observations as inputs. Table 4.2 compares the results from PP polynomial regression, PP empirical operational method, and the optimum PP-ANN. The abbreviations used in the tables are listed below:  WS: wind speed  WD: wind direction  WSH: wind shear  T: temperature  D: density  RH: relative humidity  TA: turbine availability  PTA: previous-day’s average turbine availability  t: Time of day  R2: r-squared correlation coefficient between the forecast and observed wind power  RMSE: root-mean-squared error of the wind power forecast     44  Table ‎4.1. Comparison of performance of different PP-ANN experiments. Larger R2 and smaller RMSE are better. Predictors Number of hidden nodes R2 RMSE (MW) Figure WS 1 0.97 2.98 4.4 WS, T 1 0.97 2.77 4.5 WS, T, t 1 0.97 2.83 4.6 WS, WD 1 0.98 2.56 4.7 WS, WD, T, RH, D, t 1 0.98 2.49 4.8 WS, WD, WSH, T, RH, D, t 1 0.98 2.44 4.9 WS, WD, WSH, T, RH, D, TA, t 1 0.99 1.83 4.10 WS, WD, WSH, T, RH, D, TA 1 0.99 1.81 4.11 WS, WD, WSH, T, RH, D, TA, t 8 0.99 1.40 4.12 WS, WD, WSH, T, RH, D, TA 8 0.99 1.30 (Best) 4.13 WS, WD, WSH, T, RH, D 8 0.99 1.97 4.14 WS, WD, WSH, T, RH, D, PTA 8 0.99 1.93 4.15      45  Table ‎4.2. Performance comparison of polynomial regression model, empirical operational method (LUT), and optimum ANN, all using PP technique. Model name Predictors R2 RMSE (MW) Figure Polynomial regression WS observations 0.95 4.63 4.2 LUT WS observations 0.96 3.27 4.3 ANN WS, WD, WSH, T, RH, D, TA (observations) 0.99 1.30 4.13  The previous experiments all used a perfect-prog (PP) approach where weather observations were used as inputs to the wind-power forecast algorithms.  Next, a model output statistics (MOS) approach was tested where ANN input is from the NWP-model forecasts. Although NWP is known a priori to have errors compared to observations, the NWP approach allows day-ahead estimates of wind power to be made.     46 4.2 Model Output Statistics (MOS) ANN Models Using NWP Data The day-ahead average forecasts that were output from of an ensemble weather forecast system for the wind speed, wind direction, wind shear, temperature, air density, and relative humidity, along with time of day and the previous day’s average turbine availability were used as inputs into the best wind-power forecast model, i.e. the eight-hidden-neuron ANN trained by the observations. The model then was tested with the forecast weather inputs. As expected, this resulted in significantly less accurate forecast due to the inaccuracy in weather forecasts (Figure 4.16). The two inset figures show forecast vs. observed relationships for wind speed (an input to the ANN) and wind power (the output from ANN).  Figure ‎4.16. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind shear, temperature, relative humidity, and air-density observations, and yesterday’s average turbine availability as the predictor (Nov/Dec). RMSE of the model tested with the ensemble forecast variables = 14.63.   00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Nov/Dec ANN with 8 hidden neurons (predictors: wind speed, wind direction, wind shear,  temperature, relative humidity, density, yesterday's turbine availability ) Real ObservationsModel ForecastsRMSE = 14.63 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind speed forecast Normalized wind speed observation R2=0.42 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation R2=0.49   47  As mentioned earlier, in the perfect-prog technique, the model outputs (the numerical weather prediction forecasts in this case) are considered perfect, which is not true. Thus, in this context, the major utility of the perfect prognostic technique was to help find the optimum ANN structure.  Hypothetically the accuracy of the wind-power forecast might be improved if the ANN was trained using weather forecasts, instead of observed weather data. The weather forecast data was divided into separate testing and training datasets. The eight-hidden-neuron ANN was then trained with the NWP forecast variables. The results for the independent testing dataset (Figure 4.17) showed 35.5% improvement using MOS method compared to the previous case when the observed variables were used in training process (perfect-prog). Although the NWP forecasts used in this work are bias-corrected, it seems that there is a bias in how the forecast variables affect each other, which the ANN captures and removes. This consequently improves the results significantly.  Figure ‎4.17. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Nov/Dec). RMSE of the model tested with the ensemble forecast variables = 9.44. Performance improvement compared to the ANN trained with the observations: 35.5%. 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Nov/Dec ANN with 8 hidden neurons (predictors: wind speed, wind direction, wind shear,  temperature, relative humidity, density, yesterday's turbine availability ) Real ObservationsModel ForecastsR2=0.67 RMSE = 9.44 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation   48   The results indicate that it is possible to forecast the wind power one day ahead of the desired time with an acceptable error. The accuracy of the wind-power forecast system directly depends on the accuracy of the weather-forecast system. In order to estimate the skilfulness of the ANN in forecasting the wind power, a comparison with the current operational method was also made. In order to do so, the wind-speed forecast on a day ahead of the desired time was used as input to the LUT operational method to forecast the wind power. The results showed 65% less accuracy in the LUT operational approach compared to the MOS-ANN outputs. In fact, using the wind-speed forecasts is the usual practice to forecast the wind power in industry and using wind-speed observations to forecast wind power was only considered in this work as a basis for comparison and validation of the developed algorithm.  Figure ‎4.18. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Nov/Dec). Performance decrease compared to the ANN trained with forecasts: 65%.   00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Nov/Dec LUT operational method (predictor: wind speed) Real ObservationsModel ForecastsR2=0.47 RMSE = 15.57 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation   49   For completeness, tests were also made using day-ahead NWP wind speed as input to a polynomial regression. It seems that the wind-speed data is too spread out for a polynomial regression model to fit it properly. The polynomial fits the data for smaller values properly but it cannot forecast larger wind powers. Results are in Figure 4.19 and Figure 4.20.   Figure ‎4.19. Polynomial regression model of the wind speed forecasts vs. wind power (Nov/Dec).  00.10.20.30.40.50.60.70.80.910 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Normalized wind power Normalized wind speed Nov/Dec 4th order polynomial regression model   50  Figure ‎4.20. Wind-power forecasts by polynomial regression model with the wind-speed forecasts as the predictor (Nov/Dec). Performance decrease compared to the ANN trained with forecasts: 39%. The results in Figure 4.20 show that the polynomial regression model’s forecasts are 15.5% more accurate than the LUT operational method. The clustering of wind-power forecast below about 0.3 in the inset Figure 4.20 is explained by the best-fit curve in Figure 4.19, which never reaches the middle and high wind-power values.  00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Nov/Dec Polynomial regression model (predictor: wind speed) Real ObservationsModel ForecastsR2=0.43 RMSE = 13.16 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation   51 In summary, the best method to forecast wind power a day ahead is the ANN method with 8 hidden nodes and with inputs from NWP forecasts and from the previous-day’s average turbine availability. Table 4.3 shows the summary of the results from MOS technique. Table ‎4.3. Performance comparison of the empirical operational method (LUT) and the optimum ANN, both using the MOS technique. Larger R2 and smaller RMSE are better. Model name Predictors R2 RMSE (MW) Figure Polynomial Reg. WS forecasts 0.43 13.16 4.20 LUT WS forecasts 0.47 15.57 4.18 ANN WS, WD, WSH, T, RH, D, PTA (forecasts) 0.67 9.44 4.17     52 5   Results 5.1 Application of Models to Other Time Periods In this section wind-power forecasts from the optimum ANN-MOS model and the LUT operational method for all overlapped months (except for Nov-Dec that has already been discussed in detail) are presented. The results from both models are compared for each time period in Figures 5.1 – 5.22.     53 5.1.1    June - July   Figure ‎5.1. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Jun/Jul).  Figure ‎5.2. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Jun/Jul). Performance improvement compared to the LUT method: 56%. 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Jun/Jul Operational method (predictor: wind speed) Real ObservationsModel ForecastsRMSE = 17.23  R2 = 0.15 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Jun/Jul ANN with 8 hidden neurons (predictors: wind speed, wind direction,  wind shear, temperature, relative humidity, density, yesterday's average  turbine availability) Real ObservationsModel ForecastsR2 = 0.61 RMSE = 7.59 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation  00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation    54 5.1.2    July - August  Figure ‎5.3. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Jul/Aug).   Figure ‎5.4. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Jul/Aug). Performance improvement compared to the LUT method: 54%. 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Jul/Aug Operational method (predictor: wind speed) Real ObservationsModel ForecastsR2 = 0.23 RMSE = 17.01 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Jul/Aug ANN with 8 hidden neurons (predictors: wind speed, wind direction,  wind shear, temperature, relative humidity, density, yesterday's average  turbine availability)  Real ObservationsModel ForecastsR2 = 0.63 RMSE = 7.79 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation  00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation    55 5.1.3    August - September    Figure ‎5.5. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Aug/Sep).   Figure ‎5.6. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Aug/Sep). Performance improvement compared to the LUT method: 38%. 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Aug/Sep Operational method (predictor: wind speed) Real ObservationsModel ForecastsR2 = 0.46 RMSE = 13.71 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Aug/Sep ANN with 8 hidden neurons (predictors: wind speed, wind direction,  wind shear, temperature, relative humidity, density, yesterday's average  turbine availability) Real ObservationsModel ForecastsR2 = 0.66 RMSE = 8.53 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecast Normalized wind power observation  00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecasts Normalized wind power observation    56 5.1.4    September - October  Figure ‎5.7. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Sep/Oct).   Figure ‎5.8. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Sep/Oct). Performance improvement compared to the LUT method: 30%. 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Sep/Oct Operational method (predictor: wind speed) Real ObservationsModel ForecastsR2 = 0.46 RMSE = 15.85 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Sep/Oct ANN with 8 hidden neurons (predictors: wind speed, wind direction,  wind shear, temperature, relative humidity, density, yesterday's average  turbine availability) Real ObservationsModel ForecastsR2 = 0.69 RMSE = 11.12 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecasts Normalized wind power observation  00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecasts Normalized wind power observation    57 5.1.5    October - November  Figure ‎5.9. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Oct/Nov).   Figure ‎5.10.Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Oct/Nov). Performance improvement compared to the LUT method: 36%. 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Oct/Nov Operational method (predictor: wind speed)  Real ObservationsModel ForecastsR2 = 0.41 RMSE = 15.94 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Oct/Nov ANN with 8 hidden neurons (predictors: wind speed, wind direction,  wind shear, temperature, relative humidity, density, yesterday's average  turbine availability) Real ObservationsModel ForecastsR2 = 0.74 RMSE = 10.24 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecasts  Normalized wind power observation  00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecasts Normalized wind power observation    58 5.1.6    December - January  Figure ‎5.11. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Dec/Jan).  Figure ‎5.12. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Dec/Jan). Performance improvement compared to the LUT method: 20%. 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Dec/Jan Operational method (predictor: wind speed) Real ObservationsModel ForecastsR2 = 0.61 RMSE = 16.27 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Dec/Jan ANN with 8 hidden neurons (predictors: wind speed, wind direction,  wind shear, temperature, relative humidity, density, yesterday's average  turbine availability) Real ObservationsModel ForecastsR2 = 0.76 RMSE = 13.06 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecasts Normalized wind power observation   00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecasts Normalized wind power observation    59 5.1.7    January - February  Figure ‎5.13. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Jan/Feb).   Figure ‎5.14. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Jan/Feb). Performance improvement compared to the LUT method: 29%. 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Jan/Feb Operational method (predictor: wind speed) Real ObservationsModel ForecastsR2 = 0.65 RMSE = 15.22 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Jan/Feb ANN with 8 hidden neurons (predictors: wind speed, wind direction,  wind shear, temperature, relative humidity, density, yesterday's average  turbine availability) Real bservationsModel ForecastsR2 = 0.83 RMSE = 10.80 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecasts Normalized wind power observations 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecasts Normalized wind power observations   60 5.1.8    February - March  Figure ‎5.15. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Feb/Mar).  Figure ‎5.16. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Feb/Mar). Performance improvement compared to the LUT method: 23%. 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Feb/Mar Operational method (predictor: wind speed) Real ObservationsModel ForecastsR2 = 0.76 RMSE = 15.64 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Feb/Mar ANN with 8 hidden neurons (predictors: wind speed, wind direction,  wind shear, temperature, relative humidity, density, yesterday's average  turbine availability) Real ObservationsModel ForecastsR2 = 0.72 RMSE = 12.08 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecasts Normalized wind power observations 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecasts Normalized wind power observations   61 5.1.9    March - April  Figure ‎5.17. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Mar/Apr).   Figure ‎5.18. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Mar/Apr). Performance improvement compared to the LUT method: 22%. 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Mar/Apr Operational method (predictor: wind speed) Real ObservationsModel ForecastsR2 = 0.53 RMSE = 17.95 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Mar/Apr ANN with 8 hidden neurons (predictors: wind speed, wind direction,  wind shear, temperature, relative humidity, density, yesterday's average  turbine availability) Real ObservationsModel ForecastsR2 = 0.72 RMSE = 14.10 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power observations Normalized wind power observations 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecasts Normalized wind power observations   62 5.1.10    April - May Figure ‎5.19. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (Apr/May).   Figure ‎5.20. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (Apr/May). Performance improvement compared to the LUT method: 43%. 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Apr/May Operational method (predictor: wind speed) Real ObservationsModel ForecastsR2 = 0.48 RMSE = 16.20 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Apr/May ANN with 8 hidden neurons (predictors: wind speed, wind direction,  wind shear, temperature, relative humidity, density, yesterday's average  turbine availability) Real ObservationsModel ForecastsR2 = 0.83 RMSE = 9.18 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecasts Normalized wind power observations 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecasts Normalized wind power observations   63 5.1.11    May - June  Figure ‎5.21. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor (May/Jun). Figure ‎5.22. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor (May/Jun). Performance improvement compared to the LUT method: 43%. 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset May/Jun Operational method (predictor: wind speed) Real ObservationsModel ForecastsR2 = 0.33 RMSE = 13.22 00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset May/Jun ANN with 8 hidden neurons (predictors: wind speed, wind direction,  wind shear, temperature, relative humidity, density, yesterday's average  turbine availability)  Real ObservationsModel ForecastsR2 = 0.64 RMSE = 7.57 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecasts Normalized wind power observations 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecasts Normalized wind power observations   64 Since the available data is for one year from June to May, there is no sequential May-June pair of months. Instead, the months May 2015 and June 2014 were used for May-June period (Figure 5.21 and 5.22). The results show forecasts from the LUT method have increased accuracy during the winter compared to summer, while ANN models have increased accuracy in summer months. RMSE for ANN models increases from fall to spring due to the less accurate NWP forecasts of weather characteristics, but for all months, ANN is more accurate (has less RMSE) than LUT. The greatest improvement for wind-power forecast by ANN (compared to the LUT method) was in June-July when ANN model forecasted the wind power 56% more accurately than LUT method. Also, for the whole study period, the ANN model, forecasts wind power at least 20% better than the LUT operational method.  Table 5.1 summarizes all results from both ANN and LUT approaches for every time period.     65  Table ‎5.1. Summary of the LUT and ANN model results for all time periods. Lower RMSE and higher R2 is better. Time Period LUT RMSE (MW) LUT R2 ANN RMSE (MW) ANN R2 RMSE Improvement Figure Jun-Jul 17.23 0.15 7.59 0.61 56% 5.1 & 5.2 Jul-Aug 17.01 0.23 7.78 0.63 54% 5.3 & 5.4 Aug-Sep 13.71 0.46 8.53 0.66 38% 5.5 & 5.6 Sep-Oct 15.85 0.46 11.12 0.69 30% 5.7 & 5.8 Oct-Nov 15.94 0.41 10.24 0.74 36% 5.9 & 5.10 Nov-Dec 15.57 0.47 9.44 0.67 39% 4.17 & 4.18 Dec-Jan 16.27 0.61 13.06 0.76 20% 5.11 & 5.12 Jan-Feb 15.22 0.65 10.80 0.83 29% 5.13 & 5.14 Feb-Mar 15.64 0.76 12.08 0.72 23% 5.15 & 5.16 Mar-Apr 17.95 0.53 14.10 0.72 22% 5.17 & 5.18 Apr-May 16.20 0.48 9.18 0.83 43% 5.19 & 5.20 May-Jun 13.22 0.33 7.57 0.64 43% 5.21 & 5.22     66 5.2 Comparison of Forecasts for a Common Month from Two Training Datasets In this section two different training datasets that have one month in common are used separately to forecast the wind power for an independent test dataset from the common month.  The training datasets are November-December and December-January and the forecasts are made for an independent test dataset for their common month December (Figure 5.23).    Figure ‎5.23. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, and air-density forecasts, and yesterday’s average turbine availability as the predictor for December using two training datasets Nov-Dec and Dec-Jan. 00.10.20.30.40.50.60.70.80.91Normalized wind power  Random hours from the testing dataset Forecast by Nov-Dec DatasetForecast by Dec-Jan DatasetReal Observations00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power observations Normalized wind power observations Nov-Dec Dataset R2 = 0.62 RMSE = 10.55 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power observations Normalized wind power observations Dec-Jan Dataset   R2 = 0.71 RMSE = 10.10   67 Results in Figure 5.23 show that wind-power forecasts by the Dec-Jan dataset are closer to the observations for very strong wind events. One reason can be that stronger wind events usually occur during Dec-Jan rather than Nov-Dec. Therefore Dec-Jan dataset appears to be more successful in handling such conditions. For other situations, forecasts from both training sets show no significant difference. 5.3 An Ensemble Average ANN for Wind Power One reason for training the ANN on overlapping pairs of months is to avoid discontinuities or jump of the wind-power forecast across the month boundaries. One way to achieve this is to combine overlapping months into a 2-model ensemble, where each ensemble member is weighted with a linear ramp function as sketched in Figure 5.24.   Figure ‎5.24. Ensemble-averaging weights for overlapping pairs of months. For example, on 14 Feb, the ensemble-average forecast is 0.5 times the Jan-Feb-trained model plus 0.5 times the Feb-Mar-trained model. By the end of Feb, the Jan-Feb model has a weight of zero and the Feb-Mar model has a weight of one. Figure 5.25 shows an example of this weighted ensemble average for December. The RMSE of ensemble-average forecast for December is 8.659 while it is 10.437 and 8.912 using Nov-Dec and Dec-Jan training sets, respectively. 00.510 2 4 6 8 10 12 14weight     Jan     Feb      Mar    Apr    May     Jun       Jul       Aug     Sep     Oct      Nov    Dec   68 Figure ‎5.25. Ensemble-average forecasts for December using weighted forecasts of Nov-Dec and Dec-Jan training datasets. 5.4 ANN-MOS and LUT Models for the Whole Year In this section an eight-hidden-neuron ANN was trained with the NWP forecast data from the whole year instead of a two-month period dataset. Several combinations of predictors were tested. The most accurate MOS forecast was achieved by using the following variables as predictors: wind speed, wind direction, wind shear, temperature, relative humidity, air density, time of day, month of year, and previous day’s average turbine availability. Results are presented in Figure 5.26. The LUT method was also applied on the same dataset to forecast wind power. Figure 5.27 shows the results. The results show the ANN model improves wind-power forecast of the whole year by 46% comparing to the LUT operational method.     00.10.20.30.40.50.60.70.80.91Normalized wind power Hours of month December Ensemble-average forecasts for December Real ObservationsEnsemble Model ForecastsR2 = 0.77 RMSE = 8.66 00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecasts Normalized wind power observations   69   Figure ‎5.26. Wind-power forecasts by eight-hidden neuron ANN with the wind-speed, wind-direction, wind-shear, temperature, relative humidity, air-density forecasts, time of day, month of year, and yesterday’s average turbine availability as the predictor (whole year).   00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Whole year ANN with 8 hidden neurons (predictors: wind speed, wind direction,  wind shear, temperature, relative humidity, density, time of day, month of year, yesterday's average turbine availability) Real ObservationsModel Forecasts00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecasts Normalized wind power observations RMSE = 10.83      R2 = 0.71   70     Figure ‎5.27. Wind-power forecasts by the LUT method with the wind-speed forecasts as the predictor  (whole year). Performance decrease compared to the ANN trained with forecasts: 46%.   00.10.20.30.40.50.60.70.80.91Normalized wind power Random hours from the testing dataset Whole year Operational LUT method (predictor: wind speed) Real ObservationsModel Forecasts00.20.40.60.810 0.2 0.4 0.6 0.8 1Normalized wind power forecasts Normalized wind power observations RMSE = 15.87     R2 = 0.48   71 6   Conclusions and Discussion In this work, the ability of artificial neural network (ANN) models in wind-power forecasting for a wind farm located in mountainous western Canada was studied.  Wind-power forecasts were produced using three different techniques; i.e., polynomial regression, look-up-table operational method, and ANN models, and the results were compared. Experiments were made for every two-month period (12 overlapped training datasets) and for the whole year. Also, two statistical methods, i.e. perfect-prog (PP) and model output statistics (MOS) were utilized. Perfect-prog method uses the observed variables as predictors and it was applied to find the optimum ANN structure.  6.1 Conclusions The optimum ANN is a three-layered feed-forward back-propagation network with 8 hidden neurons. The optimum model was then trained by the NWP ensemble forecasts (MOS method), to produce the day-ahead forecast of the wind power.  This work achieved more accurate forecasts by introducing wind shear and turbine availability as two important factors in wind-power forecasting. It is shown that wind speed, wind direction, wind shear, temperature, relative humidity, air density, and turbine availability are the most relevant predictors for two-month period training datasets. For the whole-year forecasts, adding time of day and month of year to the list of predictors slightly improved the results.  The ANN method improved the day-ahead wind-power forecasts by up to 56% compared to the current operational approach.  A comparison was also made between the forecasts from two training datasets for the month they had in common. To further smooth the results and avoid discontinuities or jumps of the wind-power forecast across the month boundaries, an ensemble-average model was produced in which each ensemble member (two   72 different datasets with one month in common) was weighted with a linear ramp function. 6.2 Recommendations 1. This study showed that turbine availability has a considerable effect on wind-power forecasting and the utility company could likely improve their LUT approach by taking this effect into account. 2. Additional improvements might be possible by finding more appropriate predictors for the ANN model. 3. It might be possible to either train the ANN model for each feeder in the wind farm or adding the feeder number to the model inputs. 4. Atmospheric static stability could also be tested as a predictor for wind-power forecasting. Lapse rate can act as a representative for the static stability. 5. The proposed ANN method could also be applied for wind-power forecasting for 2-7 days ahead. To do so, the model would need to be retrained by appropriate datasets, i.e. 2-7 days NWP forecasts. 6. It might also be possible to retrain the ANN model for immediate-short-term forecasts of the wind power (eight hours ahead). 7. The ANN model would be retrained for other wind farms using the historical data from the desired wind farm. 8. It might be worthwhile to test different objective functions in the ANN model. 9. Applying the bootstrapping method to estimate the uncertainty in the ANN forecasts is also recommended.  10. A different approach could be training the ANN model using generated power per turbine as a predictor. Namely divide the total power by the number of available turbines. Then the predicted power could be multiplied by the estimated number of available turbines.  11. It might also be worthwhile to apply the ANN method to wind-speed forecasting. 12. This work suggests that the developed algorithm can be coded to produce short-term wind-power forecasts operationally. The Weather Forecast   73 Research Team (WFRT) at the University of British Columbia is planning to produce these forecasts operationally in the near future.     74 Bibliography 1. Svensson, M. 2015. Short-term wind-power forecasting using artificial neural networks. Master’s thesis, School of Computer Science and Communication, Royal Institute of Technology KTH. Stockholm, Sweden. 2. Tastu, J. 2013. Short-term wind-power forecasting: probabilistic and space-time aspects. PhD thesis, Department of Applied Mathematics and Computer Science, Technical University of Denmark DTU. Kongens Lyngby, Denmark. 3. Pinson, P. 2006. Estimation of the uncertainty in wind-power forecasting. PhD thesis, Mines Paris Tech. Paris, France. 4. The Canadian Wind Energy Association. 16th August 2016. http://canwea.ca/ 5. Stull, R. 2011. Meteorology for Scientists and Engineers. 3rd edition. Springer. The University of British Columbia, Vancouver, Canada. 6. Wang, X., Guo, P., and Huang, X. 2011. A review of wind-power forecasting models. Energy Procedia 12, pp. 770-778. Chengdu, China. 7. Lei, M., Shiyan, L., Chuanwen, J., Hongling, L., and Yan, Z. 2009. A review on the forecasting of wind speed and generated power. Renewable and Sustainable Energy Reviews 13, pp. 915-920. Shanghai, China. 8. Catalao, J. P. S., Pousinho, H. M. I., Mendes, V. M. F. 2009. An artificial neural network approach for short-term wind-power forecasting in Portugal. IEEE. Portugal. 9. Landberg, L. 1999. Short-term prediction of the power production from wind farms. Journal of Wind Engineering and Industrial Aerodynamics 80, pp. 207-220. Roskilde, Denmark. 10. Alexiadis, M. C., Dokopoulos, P. S., Sahsamanoglou, H. S., and Manousaridis, I. M. 1998. Short-term forecasting of wind speed and related electrical power. Solar Energy. Vol. 63, No. 1, pp. 61-68. Thessaloniki, Greece. 11. Tu, J. V. 1996. Advantages and disadvantages of using artificial neural networks versus logistic regression for predicting medical outcomes. J Clin Epidemiol. Vol. 49, No. 11, pp. 1225-1231. Boston, USA. 12. Farkas, Z. 2011. Considering air density in wind-power production. Department of Physics of Complex Systems, Eotvos University. Budapest, Hungary.  13. Wang, S., Liu, X., Jin, Y., and Qu, K. 2015. Wind-power short-term forecasting based on back propagation neural network. International Journal of Smart Home. Vol. 9, No. 7, pp. 231-240. Shenyang, China.   75 14. Hsieh W., W., 2009. Machine learning methods in the environmental sciences neural networks and kernels. Cambridge University Press. 15.  Sibi, P., Allwyn J., S., and Siddarth, P. 2013. Analysis of different activation functions using back propagation neural network. Journal of Theoretical and Applied Information Technology. Vol. 47 No.3. Kumbakonam, India. 16. Ozkan, C., and Sunanr Erbek, F. 2003. The comparison of activation functions for multispectral landsat TM image classification. Photogrammetric Engineering & Remote Sensing. Vol. 69, No. 11, pp. 1225-1234. Turkey. 17. Ward Powers, D. M., and Atyabi, A. 2012. The problem of cross-validation: averaging and bias, repetition and significance. Engineering and Technology Conference. China. 18. Hernandez, M., Zaribafiyan, A., Aramon M., and, Naghibi, M. 2016. A novel graph-based approach for determining molecular similarity. 1QBit. Vancouver, Canadda. 19. Francis, L. 1999. Neural networks demystified. Salford Systems’ Course on Advanced CART. San Diego, USA. 20. Zahumensky, I. 2004. Guidelines on quality control procedures for data from automatic weather stations. World Meteorological Organization. Geneva, Switzerland. 21. Gavin, H. P. 2016. The Levenberg-Marquardt method for nonlinear least squares curve-fitting problems. Department of Civil and Environmental Engineering, Duke University. USA. 22. Karsoliya, S. 2012. Approximating number of hidden layer neurons in multiple hidden layer BONN architecture. International Journal of Engineering Trends and Technology. Vol. 3 Issue 6. Bhopal, India. 23. Hornik, K., Stinchcombe M. B., and White, H. 1989. Multilayer feed-forward networks are universal approximators. Journal of Neural Networks. Vol. 2 Issue 5, pp. 359-366. Austin, USA. 24. Statistics course: Regression methods. The Pennsylvania State University, Department of Statistics. 16th August 2016.       https://onlinecourses.science.psu.edu/stat501/node/324 25. Vislocky, R. L., and Young, G. S. 1989. The use of perfect prog forecasts to improve model output statistics forecasts of precipitation probability. Weather and Forecasting. Vol. 4. Pennsylvania, USA. 26. Breiman, L. 1994. Bagging predictors. Technical Report No. 421. Department of Statistics, University of California. Berkeley, USA.   76 27. Nayak, S. C., Misra, B. B., Behera, H. S. 2014. Impact of data normalization on stock index forecasting. International Journal of Computer Information Systems and Industrial Managements Applications. Vol. 6, pp. 257-269. USA.      77 Appendix MATLAB code: %% wind-power forecast by Banafsheh Bolouri Afshar %% combining raw data raw_matrix = xlsread('Final_data_notAveraged_notNormalized.xlsx'); Final_matrix_averaged = zeros(8760,12);   %% create the full matrix of all time steps (1 hour) for the desired period (June 2014-May 2015) >> Cal MonthDays = [31 28 31 30 31 30 31 31 30 31 30 31]; %% Cal=zeros(Lines,4);   %% counters used: n, i, j, k, p p=1; %% line counter   for i=6:12 %% Jun-Dec         for j=1:MonthDays(i)                 for k=0:23                             Cal(p,1)=2014;                 Cal(p,2)=i;                 Cal(p,3)=j;                 Cal(p,4)=k;                                p=p+1;             end         end end   for i=1:5 %% Jan-May         for j=1:MonthDays(i)                 for k=0:23                             Cal(p,1)=2015;                 Cal(p,2)=i;                 Cal(p,3)=j;                 Cal(p,4)=k;                 p=p+1;             end         end end   %% averaging 5-minute data to get hourly data temperature = nanmean(reshape(raw_matrix(:,7),12,[]))'; RH = nanmean(reshape(raw_matrix(:,8),12,[]))'; density = nanmean(reshape(raw_matrix(:,9),12,[]))'; shear = nanmean(reshape(raw_matrix(:,10),12,[]))'; availability = nanmean(reshape(raw_matrix(:,11),12,[]))'; wind_speed = nanmean(reshape(raw_matrix(:,12),12,[]))'; wind_direction = nanmean(reshape(raw_matrix(:,13),12,[]))'; wind_power = nanmean(reshape(raw_matrix(:,14),12,[]))'; % Final_matrix_averaged(:,1:12) = [Cal(:,1:4) temperature(:,1) RH(:,1) density(:,1) shear(:,1) availability(:,1) wind_speed(:,1) wind_direction(:,1) wind_power(:,1)]; % filename1 = 'Final_matrix_averaged.xlsx'; % xlswrite(filename1,Final_matrix_averaged);     78 %% normalizing data [y1,PS] = mapminmax((temperature)'); temperature_norm = y1'; [y2,PS] = mapminmax((RH)',0,1); RH_norm = y2'; [y3,PS] = mapminmax((density)',0,1); density_norm = y3'; [y4,PS] = mapminmax((shear)',0,1); shear_norm = y4'; [y5,PS] = mapminmax((availability)',0,1); availability_norm = y5'; [y6,PS] = mapminmax((wind_speed)',0,1); wind_speed_norm = y6'; wind_direction_norm1(:,1) = sin(wind_direction(:,1)*pi/180); wind_direction_norm2(:,1) = cos(wind_direction(:,1)*pi/180); [y7,PS] = mapminmax((wind_power)',0,1); wind_power_norm = y7'; [y8,PS] = mapminmax((Cal(:,4))',0,1); time_norm = y8'; [y9,PS] = mapminmax((Cal(:,2))',0,1); month_norm = y9'; [y10,PS] = mapminmax((Cal(:,3))',0,1); day_norm = y10';   % Final_matrix_averaged_normalized(:,1:13) = [Cal(:,1:4) temperature_norm(:,1) RH_norm(:,1) density_norm(:,1) shear_norm(:,1) availability_norm(:,1) wind_speed_norm(:,1) wind_direction_norm1(:,1) wind_direction_norm2(:,1) wind_power_norm(:,1)]; % filename2 = 'Final_matrix_averaged_normalized.xlsx'; % xlswrite(filename2,Final_matrix_averaged_normalized);   % ModelOut_normalized(:,1:13) = [Cal(:,1) month_norm(:,1) day_norm(:,1) time_norm(:,1) temperature_norm(:,1) RH_norm(:,1) density_norm(:,1) shear_norm(:,1) availability_norm(:,1) wind_speed_norm(:,1) wind_direction_norm1(:,1) wind_direction_norm2(:,1) wind_power_norm(:,1)]; % filename3 = 'ModelOut_normalized.xlsx'; % xlswrite(filename3,ModelOut_normalized);   %% ANN data = xlsread('ModelOut_normalized'); data_train = zeros(5840,12); data_test = zeros(2920,12); p=1; for k=1:length(data_test)     data_test(k,:) = data(p,2:13); p=p+3; end data_test = data_test(~any(isnan(data_test),2),:); m=2; for n=1:2:length(data_train);     data_train(n,:) = data(m,2:13);     data_train(n+1,:) = data(m+1,2:13); m=m+3; end for q=1:10     eval(['x_test' num2str(q) '=data_test(:,q);']); end     79 % test with month, time, and everything else except day  x_test = [x_test1 x_test3 x_test4 x_test5 x_test6 x_test7 x_test8 x_test9 x_test10 x_test11];   % test with month and everything else except day and time % x_test = [x_test1 x_test4 x_test5 x_test6 x_test7 x_test8 x_test9 x_test10 x_test11];   % test the network with temperature, wind speed, and wind direction as predictor % x_test = [x_test4 x_test9 x_test10 x_test11];   % test the network with wind speed, and wind direction as predictor % x_test = [x_test9 x_test10 x_test11];   % test the network with temperature and wind speed as predictor % x_test = [x_test4 x_test9];   % test the network with wind speed as predictor % x_test = x_test9;   y_test = data_test(:,12);   rmse = zeros(10,1); for r=1:10   for j=1:10     eval(['x' num2str(j) '=data_train(:,j);']); end   y = data_train(:,12);   %% bagging 10 sets of 4088 numbers out of 5840   for i=1:10     index=randi(5840,4088,1);     x_train1 = x1(index);     x_train2 = x2(index);     x_train3 = x3(index);     x_train4 = x4(index);     x_train5 = x5(index);     x_train6 = x6(index);     x_train7 = x7(index);     x_train8 = x8(index);     x_train9 = x9(index);     x_train10 = x10(index);     x_train11 = x11(index);          % train with month, time, and everything else except day      x_train = [x_train1 x_train3 x_train4 x_train5 x_train6 x_train7 x_train8 x_train9 x_train10 x_train11];           % train with month and everything else except day and time     % x_test = [x_train1 x_train4 x_train5 x_train6 x_train7 x_train8 x_train9 x_train10 x_train11];          % train the network with temperature, wind speed, and wind   80 direction as predictor     % x_train = [x_train4 x_train9 x_train10 x_train11];          % train the network with wind speed, and wind direction as predictor     % x_train = [x_train9 x_train10 x_train11];          % train the network with temperature and wind speed as predictor     % x_train = [x_train4 x_train9];          % train the network wind speed as predictor     % x_train = x_train9;               y_train = y(index);          net = feedforwardnet(8,'trainlm');     net.trainParam.epochs = 300;     net = train(net,x_train',y_train');     y_model(i,:) = net(x_test');     y_model_mean = mean(y_model);     y_forecast = (y_model_mean)';   end   %% without bagging  %     x_test = [x_test1 x_test2 x_test3 x_test4 x_test5 x_test6 x_test7 x_test8 x_test9 x_test10 x_test11]; %     y_test = data_test(:,12); %     x_train = [x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11]; %     y_train = y; %      %     net = feedforwardnet(8,'trainlm'); %     net.trainParam.epochs = 300; %     net = train(net,x_train',y_train'); %     y_model(1,:) = net(x_test'); %     y_forecast = (y_model)';   for i=1:length(y_forecast) if (y_forecast(i) < 0) == 1     y_forecast(i) = 0; end end     %% getting the actual data from normalized data for test data set MAX = **confidential**; MIN = 0; y_test_nonnormalized = **confidential**.*(y_test); y_forecast_nonnormalized = **confidential**.*(y_forecast); rmse(r,1)  = sqrt(mse(y_forecast_nonnormalized-y_test_nonnormalized)); end   rmse_average = mean(rmse(:,1));     

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.24.1-0308789/manifest

Comment

Related Items