Nonlinear Modeling of Temporal Wind Power Variations

Modeling wind speed time series (WSTS) is an essential part of network planning studies in order to generate synthetic wind power time series (WPTS). Hence, this paper proposes a methodology to equip planners with accurate simulation of wind speed and power variations as well as complete temporal dependence structure based on the copula theory. Unlike traditional autoregressive and Markov chain methods, the suggested technique is well-prepared to deal with “nonlinear long-memory temporal dependence” and “non-Gaussian empirical probability distributions” of the WSTS. Meanwhile, the proposed statistical modeling framework is compatible with the scenario-based analysis of active networks as well. Furthermore, a case study for optimal sizing of an autonomous wind/photovoltaic/battery system is presented. The purpose of the presented study is to fully examine the accuracy and effectiveness of the copula-based model of wind generation for planning nonmemoryless power systems. Among a list of commercially available system devices, the optimal number and type of units are calculated ensuring both a minimum 20-year round total system cost and a perfect reliability. The genetic algorithm is used in four wind generation scenarios consisting of real and simulated WPTS. Then, considering the corresponding optimal solutions, the autoregressive moving average (ARMA), nonparametric Markov and proposed copula-based simulations are compared against real data.