A 5-day wind speed & power forecasts using a layer recurrent neural network (LRNN)

Sustainable Energy Technologies and Assessments 6 (2014) 1–24

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Original Research Article

A 5-day wind speed & power forecasts using a layer recurrent neural network (LRNN) Zaccheus O. Olaofe ⇑ Faculty of Engineering and Built Environment, University of Cape Town, Rondebosch, Cape Town, South Africa

a r t i c l e

i n f o

Article history: Received 9 August 2012 Revised 19 November 2013 Accepted 2 December 2013

Keywords: Synthetic data Layer recurrent neural network (LRNN) Paarl station Wind forecasts Symmetric mean absolute percentage error (sMAPE)

a b s t r a c t This article presents the long term wind speed and power output of a 40 kW wind turbine based on a layer recurrent neural network as the predictor. The forecast model utilized the levenberg marquardt back propagation (BP) algorithm with a tap delay for prediction of the wind speed and power generation at 5-min steps of up to 5 days ahead at station A. In addition, the BP algorithm was considered for prediction of the wind potential at station B using 10-min samples at the same tower height. For accuracy comparisons, the 10-min synthetic samples were generated from the sampled 5-min measurements at station A; and the wind predictions were compared with the 5-min predictions. To prepare the forecast model, a one month weather samples were obtained at the 20 m tower height on both wind stations. The first day data was used to train the model and forecast began at the second day for maximum period of 5 days. A usable total electricity generation of 1322.61 kWh using the sampled 5-min measurements, and 4485.56 kWh using the sampled 10-min measurements were predicted for the period of 30 days for the stations A and B, respectively. Using the generated synthetic samples at station A, a usable total electricity generation of 1320.55 kWh was predicted. The wind forecast shows a very small deviation between the use of the 5-min measurements, and the 10-min synthetic samples at station A. Furthermore, the forecast model was assessed to test how well the LRNN performed with the selected network parameters. A new weather sample was obtained from a remote station at a 20 m tower height to test the forecast model accuracy. The estimated errors were used to determine the closeness of the wind predictions to its acceptable or actual value at both stations. Accuracy test results using independent samples show close relationship with the validation results using the weather samples at station A. Ó 2013 Elsevier Ltd. All rights reserved.

Introduction Around the world, the wind among other forms of renewable resources such as the hydropower, bio-energy, solar energy, tidal wave etc. has been considered as one of the fastest growing source of electricity generation due to its economical way of harnessing the kinetic energy of the wind. In addition, the conversion of the kinetic energy of the wind has shown in recent years as the most cost effective method of energy generation in locations with sufficient wind [1,2]. However, the impact of climate change on the environment such as the changing precipitation patterns, increasing frequency and intensity of droughts, wildfires, increasing flooding and sea level rising, increasing air temperature etc. has affected the large scale exploitation of renewable energy resources. The wind energy systems based on their sizes, and rated power can be classified as small scale, medium scale and large scale energy systems. The small scale wind energy system is one of the most

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cost-effective home-based renewable energy systems which is efficient at remote locations with fairly wind potentials. As a result, this energy system can be utilized as an alternative electricity source or compensator in developing locations or communities with no grid connected system, or compensator during limited electricity supply from the grid [3]. For a medium scale energy system, wind energy has found applications in remote locations and small islands as a result of its social and economic potentials [4]. For the large scale energy systems, they are utilized for utility scale electricity generation and widely used for grid-tie energy applications. The electric power generated by a wind energy system changes rapidly with the continuous fluctuation of the prevailing wind and direction at an area under consideration. The site factors which often affect the power outputs include the weather conditions (the air temperature and atmospheric pressure, ice, bugs, velocity of the air), terrain structure and obstruction, wind turbulence, layout of the wind energy system etc. [5,6]. Other factors include the design/shape and strength of the rotor-blades, gear-box assembly, drag force, alternator/dynamo, speed and windings of the electrical generator), environmental factor of the site etc. For a stand-alone

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wind energy application, this could result into an electricity imbalance between the generation supply and demand by the end users if not adequately managed. As a result, it is crucial to the utility that an accurate wind prediction be made which can be utilized for estimating the long term electricity generation potential ahead of time. In addition, knowing the potential of a wind turbine ahead of time can help in handling the one of the problems associated with the intermittency of the wind energy by scheduling the operations of other electric power plants or utilization of energy storage technologies during limited generation [7]. In this article, the electricity generation of a small scale 40 kW wind energy system is predicted in discrete time steps based on the use of artificial neural network (ANN). The layer recurrent neural network (LRNN) based on the ANN is utilized to forecast the wind speed and power generation using the historical time series weather samples obtained at a 20 m height on the Paarl (station A), and Vredenburg (station B). The layer recurrent neural network (LRNN) is a recurrent neural network (RNN) with a tap delay which allows the network to have an infinite dynamic response to the time series input samples. A total of 1-month time series samples (wind speed, wind direction, wind gust, humidity, air temperature, atmospheric pressure) sampled at the 5-min and 10-min steps on the Paarl and Vredenburg wind stations, respectively were obtained. It is believed that the wind variations at any site can be observed using 5-min measurements, as well as a sampled 10-min wind measurement. The sampled 5-min measurement at station A was used to generate a synthetic wind samples at 10-min steps, and the predictions were compared with the 10-min wind predictions at station B. Furthermore, the synthetic 10-min samples were considered at station A for comparisons of the wind prediction error associated with the use of 5-min and 10-min measurements. However, the forecast results proved that only a small deviation exists in the use of sampled 5-min measurement, as compared with the 10-min synthetic data at station A. Moreover, the use of synthetic 10-min samples for the wind prediction at station A when compared with the 10-min actual measurement at station B shows that the strength of the wind reaching both locations differ, and require different LRNN architectures for optimal wind prediction. The use of 24-hidden neurons LRNN optimally predicted the wind potential at station A while the use of 24-hidden neurons over-generalized the wind potential at 20 m height on station B. The 1st day sample of the measurements at the stations A and B were used for training of the LRNN for the 30 days prediction. Thereafter, the prediction of the wind speed and power output begins on the second day for a maximum period of 5 days for the 30 days in the month. A 5-day prediction of the prevailing wind speed and the power output of the 40 kW wind turbine at time steps t + k, t + 2k, t + 3k. . .t + nk are made, where k is the constant value of the desired forecast time step. At station A, the value of k = 5, and at station B, the value of k = 10. In addition, the wind power forecasts were compared with the wind power output obtained from the statistical-based technique. At the station A, a usable total electricity generation of 1322.61 kWh using the 5min measurement samples were available; and 1320.55 kWh were available using the generated 10-min synthetic samples. A usable total electricity of 4485.41 kWh using a sampled 10-min measurements at station B were available for the period of 30 days in the month. Comparing the sampled 5-min and generated 10-min synthetic data at station A, an electricity generation variation of 2.076 kWh (0.157%) was predicted for the period of 30 days. The forecast results proved that only a small deviation exists between the use of sampled 5-min measurements, and the generated 10min synthetic data at station A. The validation results of wind speed forecasts return an overall root symmetric mean absolute percentage error (sMAPE) value of 0.028%, mean absolute scaled error (MASE) value of 4.217%, and a standard deviation of absolute

error (Std.) of 2.872% using a 5-hidden neurons LRNN. Using 15hidden neurons LRNN, the validation results return sMAPE value of 0.015%, MASE value of 2.055%, and Std. value of 1.893%. For 24-hidden neurons, the validation results return sMAPE value of 0.003%, MASE value of 0.460%, and Std. value of 0.968%. Furthermore, the new weather measurements sampled at 5min steps for the period of 31 days were obtained from another station at a 20 m height to test the accuracy of the forecast wind model. These new samples were fed as inputs to the forecast model to obtain the wind speed predictions for the new station. The wind predictor returns an overall sMAPE of 0.025%, MASE of 4.736%, and a standard deviation of absolute error of 2.664% using a 5-hidden neuron. Using 15-hidden neurons LRNN, the tested results return sMAPE value of 0.008%, MASE value of 1.552%, and Std. value of 1.526%. For 24-hidden neurons, the tested results return sMAPE value of 0.003%, MASE value of 0.676%, and Std. value of 1.129%. These tested results show close values with the validation results obtained using the previous samples derived from the pearl station.

Wind data processing In the development of an algorithm for any machine learning application, the following steps were involved: data extraction and collection; input samples preparation in usable format; analyzation of the input samples; designing and configuration of the proposed network architecture; initialization of the weights and biases as well as training of the algorithm or network; validation or/and testing of the algorithm performance etc. Often times, the prevailing wind at a specific site which varies with the time and season, as well as the weather conditions are usually considered as the main factor which affects the power output of a wind turbine [8]. In developing an accurate forecast model for the wind prediction at the stations A and B shown in Fig. 1, the most important tasks are the selection of the input samples, and the network parameters which determine the system architecture of the forecast wind model. The important weather parameter samples are chosen as the inputs for the forecast wind model, while the power output obtained from the statistical-based approach as defined in Eq. (1) is used for comparisons with the wind power prediction obtained from the LRNN. Though, a total of 1-month weather records which include the wind speed, wind direction, wind gust, humidity, air temperature and atmospheric pressure were obtained at both stations; however, the four parameter samples which were processed from the collected 1-month weather as shown in Fig. 2 include: the wind

Fig. 1. Illustration of the wind stations at a 20 m height.

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Fig. 2. Schematic representation of the statistical-based and the forecast model.

speed (X1), wind direction (X2), air temperature (X3), and atmospheric pressure (X4). To ensure the LRNN performs well for the proposed wind prediction at the considered stations, a large dataset is required and fed as input samples for the training of the model. The wind speed distribution (X5) from the modeling of the wind is fed as additional input into the forecast model (LRNN) as shown in Fig. 2. In addition, the wind speed distribution (X5) was also included in the forecast model because of the limited 1-month weather data available for the proposed task. The network convergence requires adequate input samples to learn. A total of 53,568 weather data points were collected for the period of 31 days at a 20 m tower height on station A. Since only 5-parameter samples (X1–X5) where considered for forecast wind model as shown in Fig. 2, a total of 44,640 samples were used at station A. At station B, a total of 26,784 weather samples were collected for the period of 1-month at a 20 m tower height. Since only 5-parameter (X1–X5) were considered for the forecast model, a total of 22,320 samples was used for at the station B. Furthermore at the station A, a total of 26,784 weather samples was collected for the period of 1-month at a 20 m tower height using the generated synthetic samples. Since only 5-parameter (X1–X5) were considered for this forecast model, a total of 22,320 samples was used for this task.

Wind power estimation

For an accurate estimation of the wind power output of the turbine, the statistical wind model is developed based on the knowledge of the prevailing site conditions alongside with the wind turbine parameters. The relationship between the site wind measurements, turbine parameters and the power output of the turbine is defined by Eq. (1), and known as the average power output of the turbine. Eq. (1) is defined as the electrical power output of the turbine for each wind speed value multiplied by the probability of the specified wind speed, integrated over all the possible wind speed [9].

1 PAV ðmÞ ¼ cp g qðhÞA 2

Z

m2

m1

ðm3 Þf ðmÞdv

ð1Þ

where PAV(m) is the average power output of the wind turbine, CP is the power coefficient of the rotor blades, g is the mechanical and electrical efficiency of the wind turbine, A is the swept area of the wind turbine, q(h) is the time varying air density as a function of a given height (kg/m3), f(m) is the wind speed distribution, and m is the wind speed at the site. The summary of the 5-day mean wind speed, time varying air density, average power and energy output of the 40 kW wind turbine at both stations are shown in the Table 1. The usable mean wind speed, varied air density, power output and the aggregated energy generation of the turbine from the 2nd to 31st day of the month, using 5-min measurement, 10-min synthetic data and 10-min measurements, respectively are shown in Table 1a–c.

The statistical-based technique The layer recurrent neural network (LRNN) There are several factors which influence the power output of a wind site such as the location and positioning of the turbine, the mechanical and electrical efficiency of the wind turbine (e.g. the design/shape and strength of the rotor-blades, gear-box assembly, drag force, alternator/dynamo, speed and windings of the electrical generator), environmental factor (such as the wind turbulence, ice, bugs, velocity of the air) etc. The conventional statistical wind technique used for estimating the wind power output of the 40 kW turbine was based on the turbine parameters specification, and the existing 1-month weather measurement recorded at a 20 m height. The wind turbine specifications at both stations include: the rotor efficiency CP; the swept area of the wind turbine at 78.55 m2, efficiency of the wind turbine at 98.5%, cut-in-speed at 3.0 m/s, nominal speed at 12.5 m/s, and cut-out-speed at 25.0 m/s, rated power output of 40 kW, 3-bladed rotor etc.

The arrangement of neurons with N-input (number of elements in the input vector), and the pattern of connection between network layers are called the neural network architecture. The artificial neural network (ANN) is made up of highly interconnected processing units called the neurons, each of which performs the following tasks: accepts training samples through the input unit(s) of the connection link (weight), sums the input signals to the neuron and generates an output from the neurons through an activation function. Each input sample is weighted appropriately, and the sum of the weighted inputs with the bias formed the input to the transfer function. The ANN has the layers of processing elements which make parallel computations on the input samples they received via the connection links (synapses) and passes it to the neurons of subsequent layer to determine the output of the network [10,11]. The behavior of a neural model is determined

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Table 1 Summary of the 5-day usable mean wind speed, time varying air density, average power (kW), and the energy output of the 40 kW turbine for 30 days. Days

v(m/s)

q(kg/m3)

PAV(kW)

E0(kW)

(a) Using 5-min measurement data at station A 2–6 5.13 1.173 7–11 6.02 1.158 12–16 5.37 1.156 17–21 5.44 1.176 22–26 5.58 1.163 27–31 5.09 1.185

1.433 2.918 1.536 1.387 2.440 1.309

171.92 350.17 184.28 166.43 292.75 157.06

Aver/sum

1.837

1322.60

(b) Using 10-min synthetic data at station A 2–6 5.07 1.173 7–11 6.04 1.158 12–16 5.38 1.156 17–21 5.40 1.176 22–26 5.53 1.163 27–31 4.99 1.185

5.44

1.431 2.914 1.533 1.385 2.435 1.308

171.78 349.66 183.95 166.25 292.19 156.93

Aver/sum

1.834

1320.77

6.755 10.052 6.202 4.648 4.686 5.036

810.64 1206.29 744.21 557.62 562.36 604.28

6.230

4485.41

5.40

1.168

1.168

(c) Using 10-min measurement data at station B 2–6 6.93 1.202 7–11 7.14 1.195 12–16 6.70 1.197 17–21 6.51 1.206 22–26 6.61 1.195 27–31 6.69 1.208 Aver/sum

6.76

1.200

by its connection weights and the choice of the transfer or activation function(s). For a multilayer neural model, the log-sigmoid, tan-sigmoid (sigmoid output neuron is used for pattern recogni-

tion problem), and the linear (linear output neurons is used for function fitting problem) transfer functions are the most commonly used transfer functions for this network design, but other differentiable transfer functions can be created and used if desired. Other available transfer functions in the neural model include the: radial basis, saturating linear, triangular basis, inverse etc. Furthermore, there are several neural algorithms available for training the network with the weight and bias learning rules, with sequential updating. The sequence of input sample as presented to the network updates according to its learning function after each time step. The available training functions for the neural model include the: Levenberg Marquardt BackPropagation (trainlm), Scaled Conjugate Gradient BackPropagation (trainscg), BFGS Quasi-Newton BackPropagation (trainbfg), Gradient Descent with Momentum BackPropagation (traindm), Bayesian Regularization (trainbr), Batch Unsupervised Weight/Bias Training (trainbu), Gradient Descent with Adaptive Learning Rate BackPropagation (trainda) etc. In addition, the following network functions are available for measuring the performance of the model based on the specified training function: Mean Square Error (mse), Mean Square Error with Regularization (msereg), Sum Squared Error (sse), Mean Absolute Error (mae) etc. Any of these performance functions can be set during the network configuration of the neural model [12]. The Layer recurrent neural network (LRNN) is a recurrent neural network (RNN) similar to the feedforward neural network (FNN), except that each layer (either the hidden or the output) has a recurrent connection with a tap delay associated with it. The associated tap delay allows the network to have an infinite dynamic response to time series input samples [13]. In addition, this network is similar to the time delay network and distributed delay neural network with the finite input responses. Furthermore, the time

Fig. 3. System architecture of a FNN.

Fig. 4. System architecture of a LRNN.

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delay neural network is similar to the FNN, except that the input weight has an associated tapped delay line at the input which allows the network to have a finite dynamic responses to the time series input samples. Hence, the dynamics appear only at the input units of a static multilayer feedforward neural network. Similar to the time delay network, the distributed delay neural network has additional delay(s) on the layer weight(s). Fig. 3 shows the architecture of a 2-layer feedforward neural network trained with Levenberg Marquardt BP algorithm, with no tap delay layer weight as compared with Figs. 4 and 5. The network configuration shown in Fig. 3 is similar with Figs. 4 and 5, except that the input weights connect to the hidden layer 1 from the input units. The layer weights from layer 1 connect directly to the layer 2 (network output) without dynamic response to the time series samples. Fig. 4 shows the processing of the input samples in the LRNN architecture. The first layer ‘‘hidden’’ has a connection from the LRNN inputs and the subsequent layer which produces the network’s output has a connection from the previous layer. The hidden layer has it weights coming from the input samples, and the subsequent layer has a weight coming from the previous layer (hidden layer). The LRNN has the following connections: 5 input units, a hidden layer with a tan-sigmoid transfer function, and a linear transfer function in the second layer of the network which produces the output. Though, the hidden layer(s) do not directly interfere with the external environment, they have tremendous influence on the subsequent layer or output layer of the ANN. The selection of appropriate network parameters such as the number of neurons in each layer, the number of hidden layers, and the transfer function types were the most important network parameters considered for this architecture. The following network parameters were considered for the LRNN architecture: 5 hidden neurons was used and due to poor performance of the predictor, the number of hidden neurons were later increased to 15 and to 24-hidden neurons to stabilize the network; 2000 number of iterations (epochs) to train for network convergence; bias value of 1 is used for the shifting of transfer function curve to the left or right for successful learning pattern; the network training with mean squared error (mse) performance goal of 1e-5 etc. The bias value is associated with each node in the intermediate and output layers of a network whose activation is always 1. The LRNN above is characterised by the presence of a backward connection providing feedback loop from the output of the hidden layer into one of the weights of the input layer via the context unit. In addition, the feedback loop from the hidden layer as shown in Figs. 4 and 5 is taken from the real output during the training of the LRNN. The network has a feedback loop with a single tap delay in the hidden layer of the network. The default time delay value of this network layer was set to one, and can be varied depending on the network response to the input samples. In addition, the LRNN design has no input tap delay but a delay on the layer weight. The LRNN in Figs. 4 and 5 was trained using the Levenberg Marquardt back propagation (BP) alogrithm for the wind prediction at stations A and B [14–16]. The Levenberg Marquardt BP alogrithm is a network training function that updates its weight and bias values according to the Levenberg–Marquardt optimization [17]. This training function is the fastest BP algorithm of an ANN among other training functions but requires more memory to store the historical input sequence. Furthermore, the LRNN using Levenberg Marquardt back propagation has an advantage over the scaled conjugate gradient BP due to its convergence rate, computation time, and memory capability to store the learnt pattern during training of the model. The steps used in the back propagation algorithm have been explained in several ANN literature such as Sreelakshmi et al. [18]. Using the back propagation algorithm, the error derivatives are fed back from the hidden layer through the context unit of the input units as shown in Figs. 4 and 5. The network connection

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(a) Designed LRNN with 5-Hidden Neurons

Validation of the LRNN with 5-Hidden Neurons

Error estimation of the forest wind model using 5-hidden neurons

(b) Designed LRNN with 15-Hidden Neurons

Validation of the LRNN with 15-Hidden Neurons

Error estimation of the forest wind model using 15-hidden neurons Fig. 5. Performance comparisons of the LRNN using 5, 15 and 24 hidden neurons.

weights are adjusted depending on the computed error values of the weights function. These errors are back-propagated if they

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(c) Designed LRNN with 24-Hidden Neurons

Validation of the LRNN with 24-Hidden Neurons Error estimation of the forest wind model using 24-hidden neurons

Fig. 5 (continued)

exceed the threshold or tolerance value as specified in the architecture of the network. The training network continues but automatically stops at a point of generalization, and the criteria used to stop the training process depend on whether the network is poorly, accurately or over-trained (over-generalized) during this learning process [19–22]. A premature halt to training will result in a network that is not trained to its highest potential, while a late halt to training can result in a network whose operation is characterized by over-generalization [19,21]. As explained by Reed et al. in literature, one of the approaches that can be used to prevent over-generalization is the termination of training network before over-generalization occurs. That is, for a given network training samples and learning algorithm, there may be an optimal amount of training model that can produce the best generalization. However, the network learning process stops when any of the following conditions are met: (1) the maximum number of epochs (iterations) is reached; (2) the performance is minimized to the goal; (3) the performance gradient falls below minimum gradient; (4) the maximum amount of time for training is exceeded; (5) validation performance has increased more than maximum failure times since the last time it decreased. To prepare the forecast model based on the LRNN architecture in Fig. 4, the 5-min samples for the period of 31 days were obtained at a 10 m height on station A, and divided into training and validating data samples. The first day data points were used as training samples and the remaining 30 days samples were used for determining the performance of the fully-trained LRNN using the vary-

ing number of 5, 15 and 24-hidden neurons. In addition, the 30 days samples were used to estimate the error rate of the chosen LRNN parameters, and for tuning of the forecast model for the proposed wind prediction at the 20 m height on the stations A and B in Fig. 1. Fig. 5a–c shows the comparisons of different number of hidden neurons and their responses from the poor generalization to the stabilization of the LRNN. Fig. 5a shows poor convergence of the LRNN using 5-hidden neurons; the number of neurons were later increased to 15 neurons as shown in Fig. 5b; and finally stabi-

Fig. 6. Description of a 5-day wind forecast of the LRNN.

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lized using maximum of 24 hidden neurons as shown in Fig. 5c. The training time of the forecast model using 5-hidden neurons stopped at 00:02:21 min after 7 iterations as shown in Fig. 5a. For 15-hidden neurons, the training stopped at 00:06:07 min after 9 iterations as seen in Fig. 5b. Using the 24-hidden neurons as shown in Fig. 5c, the training time increases for maximum of 00:12:36 min at 13 iterations. The LRNN returns sMAPE values of 0.028%, 0.015% and 0.003% using 5, 15 and 24 hidden neurons.

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The MASE of 4.217%, 2.055% and 0.460%, respectively; and the Std. values of 2.872%, 1.893%, and 0.968%, respectively. Upon stabilization of the forecast model using 24-hidden neurons, the LRNN architecture remains unaltered for the wind prediction at station A, except at station B that utilized 15-hidden neurons architecture due to over-generalization of the forecast model when utilized for the wind potential at 20 m height. The LRNN produced the future wind speed and power output of the 40 kW turbine for the

Fig. 7. Wind speed forecasts using 5-min samples at station A.

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period of 30-day based on the first day training samples fed into the forecast model as illustrated in Fig. 6. Data entry To generate a 5-day wind prediction at the stations A and B, the weather variables samples (X1–X5) were considered. A total of 44,640 samples (X1–X5) was fed through the input units into the

LRNN at station A. Using the generated 10-min synthetic data at station A, a total of 22,320 data points (X1–X5) were considered. At the station B, a total of 22,320 samples (X1–X5) at 10-min steps was fed through the input units into the LRNN for wind prediction. The first day samples were considered as historical training samples as illustrated in Figs. 7–12a. The wind forecasts for the second day of the month 02/03/2012 (00:00 am) began on the 01/03/2012 at exactly 23:55 pm for station A. For the station B, the forecast be-

Fig. 7 (continued)

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Fig. 8. Wind power forecasts using 5-min samples at station A.

gan on the same day 01/03/2012 at exactly 23:50 pm for the days ahead forecast. Furthermore using the generated 10-min synthetic samples at station A, the forecast began on the same day 01/03/ 2012 at exactly 23:50 pm for the days ahead wind forecast. To obtain the wind prediction as shown in Figs. 7–12, the LRNN in Fig. 4 used the Levenberg Marquardt back propagation (BP) algorithm. This backpropagation training algorithm computes the value of the error derivative of the weights or function, and these errors were used to adjust the weights of the layer(s) based on

the levenberg marquardt optimization. The weight adjustment of the hidden layer alters the steepness of the tan-sigmoid activation function. Furthermore, the estimated error function is fed back to the network, and the Levenberg Marquardt BP algorithm adjusts the weights associated with the input connections. This allows the neural network to learn patterns during training of the neural network. For each epoch, the input samples are presented to the network and the associated weights with the input samples are adjusted each time. The network learns by adjusting the

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Fig. 8 (continued)

weights for optimum class labeling of the input samples. The network iterative learning process continues for the maximum of 2000 epochs for convergence, and automatically stops at a point of network generalization. The criteria used for stopping the network are crucial depending on whether the neural model is poorly, accurately or over-trained using the selected network parameters. The choice of a 15-hidden neurons at station A and

24-hidden neurons at station B were considered for the network architecture due to the response of the forecast model to different weather samples at the stations. The predictions were compared to validate the LRNN for poor, accurate and over prediction of the wind potentials at both stations. Figs. 7–12 show the summary of the 5 days prediction of the prevailing wind speed and power outputs of the 40 kW turbine

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Fig. 9. wind speed forecasts using synthetic samples at station A.

at the stations A and B. In Figs. 7a–12a, the 1st day training samples (historical samples) were shown in color blue, while the 2nd day of up to 5 days ahead wind prediction are shown in the color red. In Figs. 7b–12b, the past 6th days samples became the historical samples as shown in color blue, while the 7th day of up to 5 days ahead wind prediction are shown in the color red. In Figs. 7c–12c, the past 11th days samples became the historical

samples as shown in color blue, while the 12th day of up to 5 days ahead wind prediction are shown in the color red. In Figs. 7d–12d, the past 16th days samples became the historical samples as shown in color blue, while the 17th day of up to 5 days ahead wind prediction are shown in the color red. In Figs. 7e–12e, the past 21st days samples became the historical samples as shown in color blue, while the 22nd day of up to 5 days ahead wind prediction

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Fig. 9 (continued)

are shown in the color red. In Figs. 7f–12f, the past 26th days samples became the historical samples as shown in color blue, while the 27th day of up to 5 days ahead wind prediction are shown in the color red. Furthermore, Figs. 9 and 10 show the summary of the 5 days prediction of the prevailing wind speed and turbine power output using the generated synthetic samples at station A.

Validation phase A validation rule is a criterion used in the process of data validation, which involve a data validation algorithm. In addition, the validation samples are used to stop the training early if the network performance on the validation fails to improve or

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Fig. 10. Wind power forecasts using synthetic samples at station A.

remains the same for maximum failure epochs. In a multilayer perception (MLP) where the model selection and the error estimates (differences between the predicted and the actual) are to be computed simultaneously, the sampled data from the wind site are often divided into three disjoint sets: training set where the training samples are used for learning; validation set are used to tune the parameters of the network model; and the testing

dataset are used to assess the performance of a fully-trained network. Upon the completion of the wind prediction, the error rate of the predictions is estimated. The estimated errors were used to determine the closeness of the wind predictions to its acceptable or actual value at both stations. The error metrics used for estimating the amount of error(s) introduced into the wind prediction var-

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Fig. 10 (continued)

ies, depending on the interest of the user. Example of the scale dependent metrics often used in error measurements are based on the absolute or square error analysis and include the mean absolute error (MAE), root mean square error (RMSE), and the standard deviation of the absolute error (Std.). These are often been considered as the validation criteria. In validation of the accuracy of the wind forecasts, the statistical error metrics usually used are defined in Eqs. (2)–(4) [23].

MAE ¼

N 1X jPLRNN  PA j  100% N i¼1 PR

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X RMSE ¼ t ðPLRNN  P A Þ2 N i¼1

ð2Þ

ð3Þ

Z.O. Olaofe / Sustainable Energy Technologies and Assessments 6 (2014) 1–24

15

Fig. 11. Wind speed forecasts using 10-min samples at station B.

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PN i¼1 jAE  MAEj Std: ¼ N1

ð4Þ

where AE is the amount of physical error or uncertainty in the forecast; MAE is used to measure the closeness between the predicted and the actual power output at period t; N is the number of samples used in computing the usable wind prediction, PR is the rated power of the wind turbine. The error metrics such as the AE, MAE, MSE and RMSE are not sufficient to reliably assess the performances of the forecasting model (predictor). They have the disadvantage that they put a heavier penalty on positive errors than on negative errors (i.e.

give extreme values or greater weight to larger error values) [24–26]. As a result, the other error metrics considered for the assessment or evaluation of the wind predictor is defined in Eqs. (5) and (6). The symmetrical MAPE (sMAPE) was proposed by Makridakis [24] to deal with some of the limitations of the MAPE. By using the symmetric MAPE, the problem of large errors when the actual wind power values are close to zero are avoided. The sMAPE is defined by Eq. (5) [27]:

sMAPE ¼

1 XN jP LRNN  PA j PLRNN P   100% i¼i A N 2

ð5Þ

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Z.O. Olaofe / Sustainable Energy Technologies and Assessments 6 (2014) 1–24

Fig. 11 (continued)

sMAPE is the symmetric mean absolute percentage error known to be the most appropriate metric for evaluating the errors of the wind predictor. In addition, the sMAPE is an average of the absolute percent errors but these errors are computed using a denominator representing the average of the forecast and actual values. The mean absolute scaled error (MASE) was proposed by Hyndman and Koehler [28] as a generally applicable measurement of forecast accuracy. The literature proposed the scaled errors based

on the in-sample MAE from the naïve forecast method. Unlike, the scale dependent metrics, the scaled error is independent of the scale of the data. The scaled error of the MASE is defined by Eq. (6).

qt ¼

1 N1

P LRNN  PA PN i¼2 jP Ai  P Ai1 j

The mean absolute scaled error is simply by Eq. (7)

ð6Þ

Z.O. Olaofe / Sustainable Energy Technologies and Assessments 6 (2014) 1–24

17

Fig. 12. Wind power forecasts using 10-min samples at station B.

MASE ¼ meanðjqt jÞ

ð7Þ

The MASE was proposed by Hyndman et al. to be the best accurate metric for forecast accuracy comparisons acros series on the different scales. Because of its scale free, ease interpretation, non-degeneracy problems etc., the MASE has found its wide applicability in comparisons of the forecast methods on a single series as well as

in comparisons of forecast accuracy between series. As explained by Hyndman et al., the only scenario which the MASE would be infinite or undefined is when all historical observations are equal. Other error metrics available for forecast accuracy include: the Median Absolute Percentage Error (MdAPE), the Median Relative Absolute Error (MdRAE), the Geometric Means of Square Error (GMMSE) etc. [29,30].

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Z.O. Olaofe / Sustainable Energy Technologies and Assessments 6 (2014) 1–24

Fig. 12 (continued)

Testing phase The testing phase is the last phase after the completion of the training/prediction, and the validation phase (using the validation sample set) in case of the MLP. The testing samples are used as a further check to ensure the network is well generalized, but do not have any effect on training phase. The testing results of the

forecast model are different from the validation results obtained during the training phase. The validation results are associated with the prediction accuracy of the forecast, and for determining the amount of forecast error introduced by the predictor. However, in the evaluation of performance of the LRNN using the levenberg marquardt back propagation (BP) algorithm with the chosen network parameters, an independent weather samples were used to

Z.O. Olaofe / Sustainable Energy Technologies and Assessments 6 (2014) 1–24

test how well the LRNN performed at both stations for the wind prediction. The performance of the forecast model was evaluated using an independent samples collected at the Darling station. The new weather samples were obtained at a 20 m height for the month of March 2010. These samples were used only for testing the accuracy of the prediction model in forecasting the wind speed and power output of the 40 kW turbine as shown in Fig. 13. Fig. 13a and b shows the accuracy test result of the forecast model using the weather samples obtained at Darling Station; while Fig. 14a and b shows the actual wind power for the same month at Darling Station. Figs. 13 and 14 show that the LRNN was able to predict the wind potentials at the stations A and B based on the trained 1-day historical wind samples at the station. Figs. 13 and 14 show strong agreement with each other, indicating the importance of artificial neural network as a useful tool in wind energy application when compared with the conventional time series models used in wind forecasting. The deviations of the wind speed and power prediction by the LRNN from the actual records are plotted in Fig. 15. 4. Discussion The LRNN has been used to forecast the long term wind speed and power output of a 40 kW turbine at the two stations, and compared with the statistical-based technique. In addition, the use of 5,

19

15 and 24-hidden neurons architecture have been proposed for the selection and tuning of the forecast wind model. The training time of the LRNN increases with the number of hidden neurons as well as the input samples used for the network design. The accuracy of the wind forecast using these numbers of hidden neurons was compared and the use of 15-hidden neurons was more accurate as compared with the 24-hidden neurons for the wind prediction at station B. Thus, the use of 24-hidden neuron for the 10-min weather samples at the station B over-generalized the wind prediction. In addition, the use of 5-hidden neurons LRNN under-estimated the wind potentials at station B. At the station A, the 5 and 15-hidden neurons of the LRNN performed poorly with the 5-min and the generated 10-min synthetic samples at a 20 m height. However, the 24-hidden neurons LRNN predicted the wind potential to a close value. Another surveillance in the wind forecast at station A was the increase forecast errors at different time steps, using the 10-min synthetic samples as summarized in Table 2a and b. The reasons for decrease in wind forecast accuracy may be due to the characteristics of the generated synthetic samples and the number of available wind samples. It is believed that the 5-min wind samples at station A if compressed into an hourly or daily synthetic samples, the wind forecast error may increase beyond these error values. Hence the performance of this forecast model would be dependent on the quality of wind samples available for the defined task as well as the architecture of the model.

(a) Forecast Wind Speed

(b) Forecast Wind Power

Fig. 13. Performance evaluation of the LRNN using an independent samples at darling station.

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Z.O. Olaofe / Sustainable Energy Technologies and Assessments 6 (2014) 1–24

(a) Actual Wind Speed

(b) Actual Wind Power

Fig. 14. Actual wind speed and power output at darling station.

For prediction of the 30 days wind potential using different samples at the stations A and B, the LRNN as a powerful tool was preferred because of it robustness and memory features when compared with the static feedforward network. The network can be trained to learn or map the sequence of time varying weather samples to the power output of the turbine. The ability of the LRNN to map or recognize the existing patterns of the non-linear weather samples to the wind power outputs on different time horizons, at different stations has made the use of ANN a powerful tool not only in wind application but also in various applications such as: Science and Engineering in modeling of linear and nonlinear dynamic systems; recognition of patterns among input and output signals; fault detection; in control systems and filtering; optimization and signal processing in communication line etc. [31–33]; hydrology in predictions of the quality of water on the earth surface [34– 35]; Financial asset allocation; stock market prices prediction and control [36,37]; medical research in prediction of patient recovery state based on known medical records over a period of time; learning and controlling of joint arm movements; processing and detection of image in ultrasound and X-rays etc. [38,39]. Upon the completion of the wind speed and power output forecast of the 40 kW turbine, only the wind power outputs within the range of the cut-in-speed ‘‘3.00 m/s’’ and rated speed ‘‘12.50 m/s’’ were usable at the ststions. The wind speed recorded for this study range between 0.33 m/s and 15.92 m/s. However, above the rated speed of the turbine, the efficiency of the wind turbine drops pro-

portionally with respect to the strength of the wind. The wind prediction below the cut-in-speed and cut-in-power were filtered. This was as a result of the in-ability of the wind turbine to produce usable power below these wind speed values. Beyond the rated speed of the turbine, the power output of the turbine drops significantly to maintain the aerodynamic efficiency of the entire system. Table 1 shows the summary of the usable mean wind speed, the varied air density, the average power and energy output for 30 working days of the 40 kW turbine. Table 2 shows the summary of usable average power and energy output of the turbine obtained from the LRNN and the estimated error values such as the standard deviation of the absolute error (Std.), the symmetric mean absolute percentage error (sMAPE) and the mean absolute scaled error (MASE). The usable average power and energy outputs prediction in Table 1 shows strong agreement with the average power and energy outputs estimates summarized in Table 2. The comparisons of the average power, energy outputs of the 40 kW turbine, the estimated cumulative error of the prediction at both stations were made as shown in Table 2a–c. The wind energy generation comparisons at station A were made between the sampled 5-min measurements (actual) and 10-min synthetic samples (generated) to determine the cumulative effect of error propagation which might affect the wind forecast for longer time horizons. As shown in column 3 of Table 2a and b, only a small energy variation exists in the forecast of the wind samples. However, if the forecast time horizon was increased beyond 10-min steps

Z.O. Olaofe / Sustainable Energy Technologies and Assessments 6 (2014) 1–24

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(a) Wind Speed

(b) Wind Power

Fig. 15. Estimated error (deviation) of the LRNN using an independent samples at darling station.

such as 1-h, daily etc., the cumulative effect of the error propagation will be observed in the wind energy prediction. The columns 4–6 of Table 2a and b show the cumulative effect of the error propagation introduced into the wind energy forecast. The cumulative error of the prediction at 10-min steps on the stations A and B, and as summarized in Table 2b and c cannot be compared because of the distance apart and the operating weather conditions which differ at both stations. As a result, the forecast model performance at both stations differs with input samples as shown in the columns 4–6 of Table 2b and c. Comparing the energy generation at the stations A and B, the following were observed at the stations: (1) the highest wind power potential were recorded on the 7th–11th days of the month with differences in the power generation forecast at both stations. During this period using the 5-min weather samples, the model recorded the highest wind power forecast error at station A. Also, this is applicable in the use of 10-min synthetic samples at station A. As summarized in Table 2a and b, these days have the highest wind potential for utilization with mean wind speeds of 6.021 m/s and 6.036 m/s using the 5-min and 10-min synthetic samples, respectively. It was observed in the wind samples at 5-min steps that the wind speed range from 0.331 m/s to 12.641 m/s. Using the generated 10-min synthetic samples at station A, the wind speeds

range from 0.358 m/s to 12.144 m/s. In addition, the 40 kW turbine using the 5-min wind samples began power generation at the cutin-speed of 3.036 m/s. Using the 10-min synthetic samples, the turbine began wind power generation at the cut-in-speed of 3.008 m/s. It was observed that the 5-min samples had more usable wind potential for a longer period of time as compared with the 10-min synthetic samples for the wind power generation. (2) The lowest wind power generation was recorded on the 27th– 31st days of the month but with differences in the wind power forecast error. The lowest forecast error using the sampled 5-min measurements were observed on the 2nd–6th days of the month and 22nd–26th days of the month using the 10-min synthetic samples. The wind power forecast errors show the response of the forecast model to different time varying weather samples at the same station. It can be seen that the behavior of the forecast model differs significantly with different sampling measurements at the same station for the same period of time. At station B using the sampled 10-min measurements, the highest wind power generation was recorded on the 7th–11th days while the lowest wind power generation was recorded on the 17th–21st days of the month. The lowest forecast error was observed on the 17th–21st days of the month and the highest forecast error was observed on the 7th–11th days of the month. The

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Table 2 Summary of the usable average power and energy output of the 40 kW wind turbine using the LRNN, the estimated errors for the 30 days prediction. Days

PAV (kW)

ELRNN (kWh)

sMAPE (%)

MASE (%)

Std. (%)

(a) Using the sampled 5-min measurements at station A 2–6 1.433 171.92 0.080 7–11 2.918 350.17 0.110 12–16 1.536 184.28 0.087 17–21 1.387 166.43 0.102 22–26 2.439 292.75 0.101 27–31 1.309 157.06 0.098

1.245 2.593 1.750 2.249 2.513 2.033

2.555 4.238 2.798 2.715 3.590 3.533

Aver/sum

2.064

3.238

2.435 15.393 13.811 1.638 1.462 4.186

7.006 11.836 10.621 5.151 3.759 6.077

1.837

1322.61

0.096

(b) Using the 10-min synthetic samples at station A 2–6 1.431 171.71 0.378 7–11 2.913 349.59 2.132 12–16 1.533 183.96 1.506 17–21 1.386 166.29 0.361 22–26 2.434 292.13 0.295 27–31 1.307 156.87 0.617 Aver/sum

6.488

7.408

(c) Using the sampled 10-min measurements at station B 2–6 6.755 810.64 0.071 7–11 10.052 1206.29 0.091 12–16 6.202 744.21 0.076 17–21 4.647 557.62 0.036 22–26 4.686 562.36 0.075 27–31 5.036 604.28 0.069

1.834

0.659 0.794 0.751 0.588 0.677 0.666

2.419 3.341 2.989 1.962 2.404 2.236

Aver/sum

0.689

2.559

6.230

1320.55

4485.41

0.882

0.069

comparisons of the forecast errors trend in Table 2a–c showed the performance of the LRNN with varying number of hidden neurons. The forecast errors in the Table 2a and c followed the same trend as compared with the forecast errors trend in Table 2b, except in the 17th–21st days of the month. Using 24-hidden neurons LRNN for the wind power prediction at station B, the forecast error of the model tends to zero due to over-training or over-generalization of the network. Thus, only a 15-hidden neurons was found accurate for stabilization of the LRNN for the wind prediction at station B. In addition, comparing the forecast error values as summarized in the Table 2b and c (using 10-min samples), the lowest forecast error was observed on the same 22nd–26th days of the month using the synthetic samples at station A, and on 17th–21st days using the actual samples at the station B. The highest forecast error was observed on the same 7th–11th days of the month at both stations using the same time samples. Table 2a–c shows a close approximation to the results summarized in Table 1a–c. However, the 5 days wind power forecasts as summarized in Table 2 had some cumulative errors propagation as these appear to have close values with the expected power outputs of the 40 kW turbine. The cumulative errors propagation of the forecast at different time samples were as a result of poor convergence and decrease in the generalization capabilities of the LRNN. Though, the wind potential were not accurately predicted for some time steps due to the learning behavior of the forecast model when presented with different noisy samples at different stations in the same time horizons, however, based on the number of input samples, selection of the network parameters and the chosen training algorithm, the LRNN was able to generate an acceptable wind power prediction from the prevailing weather input samples fed into the model. Fig. 16a and b shows the comparisons of the usable mean wind speed as well as the power output of the 40 kW turbine using the 5-min samples, 10-min synthetic samples and the 10-min samples at stations A and B. The highest wind speed potential was observed on the 7th–11th days of the month at both stations. The lowest wind speed potential was on the 27th–31st days at station A,

Fig. 16. Comparisons of the usable mean wind speed and power output of the 40 kW turbine.

and 17th–21st days of the month as shown in Fig. 16a. The 10min synthetic samples at station A followed the same wind pattern with the 5-min actual measurements at the station. Though stations A and B were farther apart, the 1st–3rd weeks of the month show similar wind trend indicating the strength and direction of the wind reaching both stations at the same time horizons. In addition, both stations had regular wind in each week of the month except in the second week where the prevailing wind reached its peak at 15.92 m/s at station B and 12.64 m/s at station A. Beyond the rated speed of the turbine (12.50 m/s), not all the prevailing wind were converted into electricity as some of the wind power were lost during the conversion process to maintain the aerodynamic efficiency of the turbine (i.e. minimal rotor for minimization of the drag force on the blades), hence sustaining the aerodynamic efficiency of the turbine during the high wind. The usable mean wind speed and power output of the 40 kW turbine as shown in Fig. 16a and b were estimated at 5.438 m/s, 5.402 m/s and 6.761 m/s using the 5-min, 10-min synthetic and 10-min samples, respectively at the stations A and B. The mean wind power outputs of the 40 kW turbine for the period of 30 days were estimated at 1.837 kWh, 1.834 kWh and 6.230 kWh, respectively.

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Furthermore, the forecast model accuracy has been tested using 5-min new weather records at a 20 m height on the Darling station, and comparisons were made with the validation results of the wind forecast at Paarl station. The validation results at station A and the accuracy test results of the forecast model are summarized below: The validation results of wind speed forecasts return an overall root symmetric mean absolute percentage error (sMAPE) value of 0.003%, MASE value of 0.460%, and Std. value of 0.968% at a 10 m height on station A. Using the new weather samples at Darling location, the forecast wind speed model returns an overall sMAPE value of 0.003%, MASE value of 0.676%, and Std. value of 1.129% at a 20 m height based on the chosen 24-hidden neurons LRNN. The accuracy tested result shows a close value (strong agreement) with the validation result using the previous samples derived from station A.

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increased and hence the network complexity increased rapidly. Furthermore, due to robustness of the recurrent neural network when utilized for wind prediction, it should be considered only for highly varying noisy samples, non-linear problems, real time systems etc. Acknowledgement The author would like to extend gratitude to the South African Weather Services and Ms E.A. Adebowale for their supports toward the completion of this study. Thanks to the peer reviewers who evaluated this article, and provided insight into the evaluation of the forecast model. The financial support of Ekiti State Government, NG towards this study is appreciated. References

5. Conclusion The usable wind speed and power output of the 40 kW turbine at Paarl and Vredenburg Stations for the period of 30 days have been predicted. In addition, the usable wind speed and power output from the generated 10-min synthetic samples have been predicted. These usable wind energy outputs from the predictor have been compared with the wind energy output from the statistical-based technique. The wind speed and power output forecast at different operating conditions of the stations, and the accuracy of tested forecasts model proved that the performance of LRNN is dependent on the quality of input samples, the architecture of the forecast model, as well as the forecast time steps. Though, it was desired to have a single trained Levenburg Marquardt BP algorithm with the same number of hidden neurons at the considered stations. However, the performance of the forecast model using the LM algorithm differs with the same number of hidden neurons at the two stations. The forecast model based on the LM algorithm for the same number of hidden neurons and different weather samples at the stations shows a large variation in the wind prediction. Using the sampled 5-min measurements at Paarl Station, the mean absolute scaled error (MASE) values were estimated at 3.514% and 2.064% for the chosen 15 and 24-hidden neurons network, respectively. At the same station using the generated 10min synthetic samples, the MASE was estimated at 18.506% and 6.488%, respectively. Furthermore, at the Vredenburg station using the sampled 10-min measurements, the MASE was estimated at 0.689% and 0.016%, respectively. The forecast error of the wind model observed in this study showed that the Layer Recurrent Neural Networks built on the LM algorithm with 24-hidden neurons appeared to be unsuitable for the wind forecast at Vredenburg station due to over-generalization of the forecast model. The 24hidden neurons LRNN at station B could not terminate the network training before over-generalization occurred. Instead of using the algorithm to train the network for optimal prediction, the network was over-trained. The 24-hidden neurons network was optimally trained for the wind prediction based on the prevailing weather conditions at Paarl station. At Vredenburg station where the weather conditions differ from Paarl station for the same time horizons, the 15-hidden neurons were chosen to avoid overgeneralization. In summary, the applicability of ANNs are mostly found in the functional prediction and system modeling where the physical processes are not understood or/are highly complex. The disadvantage of ANN application is that they require a lot of input samples for network convergence and right choice of the network parameters to give good confidence outputs, so they are not accurate when utilized with small input samples for network training. Also, with higher numbers of input samples, the number of layer connections

[1] Celik AN. Weibull representative compressed wind speed data for energy and performance calculations of wind energy systems. Energy Convers Manage 2003;44:3057–72. [2] Patel MR. Wind and solar power system. 1st ed. New York: CRC Press; 1999. pp. 283–288. [3] Olaofe ZO, Folly KA. Economic viability of a 3 kW wind conversion system for home energy management, power electronics and machines in wind applications (PEMWA2012), July 16–18, Colorado, USA. [4] Kaldellis JK, Gavras ThJ. The economic viability of commercial wind plants in Greece: a complete sensitivity analysis. Energy Policy 2000;28:509–17. [5] Bhattacharya P, Bhattacharjee R. A study on Weibull distribution for estimating the parameters. J Appl Quantitat Methods 2010;5(2):234. [6] Bhatti SST, Kothari D. Wind power estimation using artificial neural network. J Energy Eng 2007;133(1):46–52. [7] Olaofe ZO, Folly KA, Energy storage technologies for small scale wind conversion system, power electronics and machines in wind applications (PEMWA2012), July 16–18, Colorado, USA. [8] Jhon Z, Baily B, Brower M. Wind energy forecasting: the economic benefits of accuracy, AWS True Wind LLC NY, USA. [9] Manwell JF, McGowan JG, Roger AL. Wind energy explained theory, design and application. New York: Wiley; 2002. [10] Nayak MA, Deo MC. Wind speed prediction by different computing techniques. BALWOIS 2010, Ohrid, Republic of Macedonia, 25–29 May, 2010. [11] Jain AK, Mao J, Mohiuddin KM. Artificial neural networks: a tutorial. USA: Michigan State University; 1996. [12] Matlab. V7.14, Neural Network Toolbox/Functions/Network Initialization Functions; 2012. [13] Matlab. Neural Network Toolbox/Functions/New Network Functions/ Layrecnet; 2012. [14] Lera G, Pinzolas M. Neighborhood based Levenberg–Marquardt algorithm for neural network training. IEEE Trans Neural Network 2002;13(5):1200–3. [15] Kermani Bahram G, Schiffman Susan S, Troy Nagle H. Performance of the Levenberg–Marquardt neural network training method in electronic nose applications. Sens Actuat B Chem 2005;110(1):13–22. [16] Wilamowski BM, Iplikci S, Kaynak O, Efe MO. An algorithm for fast convergence in training neural networks, Neural Networks. In: Proceedings. IJCNN ‘01. International Joint Conference on Neural, Network, 3; 2001, pp. 1778–82. [17] Matlab. V7.14, Neural Network Toolbox/Functions/Training Functions/trainlm; 2012. [18] Sreelakshmi K, Ramakanthkumar P. Neural Networks for short-term wind speed prediction. World Acad Sci Eng Technol 2008;42. [19] Reed RD, Marks II. Neural smithing. Cambridge, MA: MIT Press; 1999. [20] Bishop CM. Neural networks for pattern recognition. New York: Oxford University Press; 1995. [21] Leverington D. A Basic Introduction toFeedforward Backpropagation Neural Networks’’, Available Online: ; 2009. [22] Lawrence S, Giles CL, Tsoi AC, Lessons in neural network training: overfitting may be harder than expected. In: Proceeding of the 14th National Conference on Artificial Intelligence, California; 1997, pp. 540–45. [23] Kusiak A, Zheng H, Song Z. Wind farm power prediction: a data-mining approach. Wind Energy 2009;12:275–93. [24] Makridakis S. Accuracy measures: theoretical and practical concerns. Int J Forecast 1993;9:527–9. [25] Swanson DA, Tayman J, Barr CF. A Note on the measurement of accuracy for subnational demographic estimates. Demography 2000;37:193–201. [26] Makridakis S, Chatfield C, Hibon M, Lawrence M, Mills T, Ord K, Simmons LF. The M-2 several European and American institutions; as a research competition: a real-time judgmentally based forecasting study. Int J Forecast 1993;9:5–23. [27] Makridakis S, Hibon M. The M3-competition: results, conclusions and implications. Int J Forecast 2000;16:451–76.

24

Z.O. Olaofe / Sustainable Energy Technologies and Assessments 6 (2014) 1–24

[28] Hyndman RJ, Koehler AB. Another look at measures of forecast accuracy. Int J Forecast 2006;22(4):679–88. [29] Armstrong JS, Collopy F. Error measures for generalizing about forecasting methods: empirical comparisons. Int J Forecast 1992;8:69–80. [30] Fildes R. Evaluation of extrapolative forecasting methods. Int J Forecast 1992;8:81–98. [31] Cun LY, Boser B, Denker JS, Henderson D, Howard RE, Hubbard W, et al. Handwritten Digit Recognition with a back-propagation network, In Touretsky DS, editor. Advances in Neural Information Processing Systems 2, San Mateo, CA; 1990, p. 396–404. [32] Nguyen D Widrow B. The Truck Backer-Upper: An example of Self-Learning in Neural Networks. In: International Joint Conference on Neural Networks, Washington DC II; 1989, p. 357–63. [33] Widrow B, Stearns SD. Adaptive signal processing. Englewood, Cliffs, NJ: Prentice Hall; 1985.

[34] Jain P, Deo MC. Neural Networks in ocean engineering. SAOS 2006, vol. 1. Woodhead Publishing Ltd.; 2006. p. 25–35. [35] Govindaraju RS, Rao AR. Artificial neural networks in hydrology. Water science and technology library, vol. 36. Springer; 2000, ISBN 978-0-7923-6226-5. p. 348. [36] Rao AR, Hsu EC. Hilbert–Huang transform analysis of hydrological and environmental time series. Water Sci Technol Library 2008;60(12):248. ISBN 978-1-4020-6453-1.. [37] Hamid SA, Iqbal Z. Using neural networks for forecasting volatility of S&P 500 Index futures prices. J Business Res 2004;57(10):1116–25. [38] Stock JH, Watson MW. New indexes of coincident and leading economic indicators. Handbook of the national bureau of economic research, vol. 4. MIT Press; 1989. ISBN: 0-262-02296-6. pp. 351 – 409. [39] Lan N. Neural network generation of muscle stimulation patterns for control of arm movements. IEEE Trans Rehab Eng 1994;2(4):213–24.