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The major drawback of wind energy relies in its variability in time, which necessitates specific strategies to be settled. One such strategy can be the coordination of wind power production with a co-located power generation of dispatchable energy source (DES), e.g., thermal power station, combined heat and power plant, gas turbine or compressed air energy storage. In this paper, we consider an energy producer that generates power by means of a wind park and of a DES and sells the produced energy to an isolated grid. We determine the optimal quantity of energy produced by a DES, given the unit cost of this energy, that a power producer should buy and use to hedge against the risk inherent in the production of energy through wind turbines. We determine the optimal quantity by solving a static optimization problem taking into account the possible dependence between the amount of energy produced by wind turbines and electricity prices by using a copula function. Several particular cases are studied that allow the determination of the optimal solution in an analytical closed form. Finally, a numerical example concerning a real 48 MW wind farm located in Poland and Polish Power Exchange shows the possibility of implementing the model in real-life problems.

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Because of the stochastic nature of wind turbines, the output power management of wind power generation (WPG) is a fundamental challenge for the integration of wind energy systems into either power systems or microgrids (i.e., isolated systems consisting of local wind energy systems only) in operation and planning studies. In general, a wind energy system can refer to both one wind farm consisting of a number of wind turbines and a given number of wind farms sited at the area in question. In power systems (microgrid) planning, a WPG should be quantified for the determination of the expected power flows and the analysis of the adequacy of power generation. Concerning this operation, the WPG should be incorporated into an optimal operation decision process, as well as unit commitment and economic dispatch studies. In both cases, the probabilistic investigation of WPG leads to a multivariate uncertainty analysis problem involving correlated random variables (the output power of either wind turbines that constitute wind farm or wind farms sited at the area in question) that follow different distributions. This paper advances a multivariate model of WPG for a wind farm that relies on indexed semi-Markov chains (ISMC) to represent the output power of each wind energy system in question and a copula function to reproduce the spatial dependencies of the energy systems’ output power. The ISMC model can reproduce long-term memory effects in the temporal dependence of turbine power and thus understand, as distinct cases, the plethora of Markovian models. Using copula theory, we incorporate non-linear spatial dependencies into the model that go beyond linear correlations. Some copula functions that are frequently used in applications are taken into consideration in the paper; i.e., Gumbel copula, Gaussian copula, and the t-Student copula with different degrees of freedom. As a case study, we analyze a real dataset of the output powers of six wind turbines that constitute a wind farm situated in Poland. This dataset is compared with the synthetic data generated by the model thorough the calculation of three adequacy indices commonly used at the first hierarchical level of power system reliability studies; i.e., loss of load probability (LOLP), loss of load hours (LOLH) and loss of load expectation (LOLE). The results will be compared with those obtained using other models that are well known in the econometric field; i.e., vector autoregressive models (VAR).