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Fatih Onur Hocaoglu (Anadolu University Eskisehir, Turkey), Ömer Nezih Gerek (Anadolu University Eskisehir, Turkey) and Mehmet Kurban (Anadolu University Eskisehir, Turkey)

DOI: 10.4018/978-1-59904-849-9.ch210

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TopThe prediction of hourly solar radiation data has important consequences in many solar applications (Markvart, Fragaki & Ross, 2006). Such data can be regarded as a time series and its prediction depends on accurate modeling of the stochastic process. The computation of the conditional expectation, which is in general non-linear, requires the knowledge of the high order distribution of the samples. Using a finite data, such distributions can only be estimated or fit into a pre-set stochastic model. Methods like Auto*-*Regressive (AR) prediction, Fourier Analysis (Dorvlo, 2000) Markov chains (Jain & Lungu, 2002) (Muselli, Poggi, Notton & Louche, 2001) and ARMA model (Mellit, Benghanem, Hadj Arab, & Guessoum, 2005) for designing the non-linear signal predictors are examples to this approach. The neural network (NN) approach also provides a good to the problem by utilizing the inherent adaptive nature (Elminir, Azzam, Younes, 2007). Since NNs can be trained to predict results from examples, they are able to deal with non*-*linear problems. Once the training is complete, the predictor can be set to a fixed value for further prediction at high speed. A number of researchers have worked on prediction of global solar radiation data (Kaplanis, 2006) (Bulut & Buyukalaca, 2007). In these works, the data is treated in its raw form as a 1-D time series, therefore the inter-day dependencies are not exploited. This article introduces a new and simple approach for hourly solar radiation forecasting. First, the data are rendered in a matrix to form a 2-D image-like model. As a first attempt to test the 2-D model efficiency, optimal linear image prediction filters (Gonzalez, 2002) are constructed. In order to take into account the adaptive nature for complex and non-stationary time series, NNs are also applied to the forecasting problem and results are discussed.

This article presents a two-dimensional model approach for the prediction of hourly solar radiation. Before proceeding with the prediction results, the following technical background is provided. Using the described tools, the approach is tested with optimal coefficient linear filters and artificial NNs (Hocaoglu, Gerek & Kurban, 2007).

The collected hourly solar radiation data is a 1-D discrete-time signal. In this work, we render this data in a 2-D matrix form as given in equation 1.

By inspecting the image version of the data in Fig. 1, it is easy to interpret daily and seasonal behavior of solar radiation. Dark regions of the image indicate that there is no sun shine on horizontal surface. The transition from black to white indicates that solar radiation fall on horizontal surface is increasing or decreasing. During winter time, the dawn to dusk period is shorter, producing a narrower protruding blob. Conversely, the white blob is wider during summer times, indicating that the day-time is longer. The width behavior of the white blob clearly indicates the seasonal changes of sun-light periods. The horizontal *and* vertical correlations within the 2-D data are quite pronounced. This implies that, given the vertical correlation among the same hours of consecutive days, it is beneficial to use 2-D prediction for hourly forecasting. The prediction efficiency of the proposed model is illustrated with 2-D optimum linear prediction filters and NNs.

Solar Radiation: Radiant energy emitted by the sun from a nuclear fusion reaction that creates electromagnetic energy.

Prediction Error: Difference between the actually measured and previously forcasted value of a time-series data. Commonly represented in terms of RMSE.

RMSE: Root-Mean-Squared Error. A quantitative error measure that defines the error between two sets of data as one-by-one differencing, squaring each difference, adding the squared terms, and finally taking the square root.

Optimal Coefficient Linear Filters: A linear predictor takes a linear combination of past values in a time series, and assigns this combination as the prediction value. While taking the linear combination, the scales of each past sample should be calculated in a way that the prediction error has minimum amount of energy. Such a set of scales are called optimal coefficients of a linear filter.

Backpropagation algorithm: Learning algorithm of ANNs, based on minimising the error obtained from the comparison between the outputs that the network gives after the application of a set of network inputs and the outputs it should give (the desired outputs).

2-D Data Representation: A matrix containing vertical and horizontal indexes can also be considered as a 2-D image. A 2-D representation does not have to correspond to an image acquired by a camera or an imaging device. Here, the representation is used for the compact visualization of the solar data.

Artificial Neural Networks: A network of many simple processors (“units” or “neurons”) that imitates a biological neural network. The units are connected by unidirectional communication channels, which carry numeric data. Neural networks can be trained to find nonlinear relationships in data, and are used in applications such as robotics, speech recognition, signal processing or medical diagnosis.

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