Nonlinear and Nonparametric Stochastic Model to Represent Uncertainty of Renewable Generation in Operation and Expansion Planning Studies of Electrical Energy Systems

Abstract:

The uncertainties of wind and solar generation patterns tends to be a critical factor in operation and expansion planning studies of electrical energy systems, as these generations are highly dependent on atmospheric variables which are difficult to predict. Traditionally, the uncertainty of renewable generation has been represented through scenarios generated by autoregressive parametric models (ARMA, PAR(p), SARIMA, etc.), that have been widely used for simulating the uncertainty of inflows and electrical demand. These methods have 3 disadvantages: (i) it is assumed that the random variables can be modelled through a known probability distribution, usually Weibull, log-normal, or normal, which are not always adequate; (ii) the temporal and spatial coupling of the represented variables are generally constructed from the Pearson Correlation, strictly requiring the hypothesis of data normality, that in the case of wind and solar generation is not met; (iii) there is an exponential increase in the model complexity due to its dimensionality. This work proposes the use of a stochastic model built from the combination of a non-parametric approach of a probability density function (the kernel density estimation method) with a dynamic Bayesian network framework. The kernel density estimation method is used to obtain the probability density function of the random variables directly from historical records, eliminating the need of choosing prior distributions. The Bayesian network allows the representation of nonlinearities in the temporal coupling of the time series, since they allow reproducing a compact probability distribution of a variable, subject to preceding stages. The proposed model was used to the generate wind power scenarios in long-term operation studies of the Brazilian Electric System, in which inflows of major rivers were also represented. The results show a considerable quality gain when compared to scenarios generated by traditional approaches.