**2. Methodology of data processing**

Several investigations aiming at handling the uncertain nature of wind and solar energy re‐ sources have been reported. Basically, the methods found in the literature can be classified into three groups: methods that deal with the prediction of uncertain variables as an input data pre-processing, methods that use stochastic scenario-based approach within the optimi‐ zation procedure to cover all the outcomes per the probable range of uncertain variables, and methods based on a combination of these two approaches. The studies presented in [5-7] can be mentioned as one of the most recent efforts lying in the first group. In [5-6] an Artificial Neural Network (ANN) forecast technique is employed and followed by risk anal‐ ysis based on the error in the forecast data. Then, the so called pre-processed data is directly taken as the input to the optimization process. Relying on the forecast tools, such methods suffer from high inaccuracy or ex-ante underestimation of the available power which in‐ creases the scheduled generation and reserve costs. Anyway, this approach is useful as it ac‐ counts for the temporal correlation between the random variables representative of each time step of the scheduling period, in terms of time-series models. On the other hand, in [8-9] which belong to the second group, the focus is on the stochastic scenario analysis rath‐ er than the forecasting methods. The usage of this approach also has its own advantages, as it tries to model the likely range of values for the random variables. However, the efficiency of this approach largely depends on the accuracy and reliability of their probabilistic analy‐

The most effective approach is associated with the third group, which applies the advantag‐ es of both forecast techniques and scenario-based optimization approach. Reference [10] presents a computational framework for integrating a numerical weather prediction (NWP) model in stochastic unit commitment/economic dispatch formulations that describes the wind power uncertainty. In [11], the importance of stochastic optimization tools from the viewpoint of the profit maximization of power generation companies is investigated. The exposed financial losses regarding the wind speed forecast errors are discussed. A stochastic model is also presented in [12]which uses a heuristic optimization method for the reduction of random wind power scenarios. The wind speed data is assumed to follow the normal PDF. A similar approach is introduced in [13] whereas the wind speed error distribution is considered as a constant percentage of the forecasted data. In [14], the Auto-Regressive Moving Average (ARMA) time series model was chosen to estimate the wind speed volatili‐ ty. Based on the model, the temporal correlation of wind speed at a time step with respect to

In this chapter, the authors present a framework for stochastic modeling of random process‐ es including wind speed and solar irradiation which are involved in the power generation scheduling optimization problems. Based on a thorough statistical analysis of the accessible historical observations of the random variables, a set of scenarios representing the available level of wind and solar power for each time step of scheduling are estimated. To this aim, the Kernel Density Estimation (KDE) method is proposed to improve the accuracy in model‐ ing the Probability Distribution Function (PDF) of wind and solar random variables. In ad‐ dition, the concept of aggregation of multi-area wind/solar farms is analyzed using Copula method. Taking the advantage of this method, we can reflect the interdependency and spa‐

sis; based on which the potential scenarios are built.

102 New Developments in Renewable Energy

the prior time steps is well analyzed.
