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Using a method for stochastic data analysis borrowed from statistical physics, we analyze synthetic data from a Markov chain model that reproduces measurements of wind speed and power production in a wind park in Portugal. We show that our analysis retrieves indeed the power performance curve, which yields the relationship between wind speed and power production, and we discuss how this procedure can be extended for extracting unknown functional relationships between pairs of physical variables in general. We also show how specific features, such as the rated speed of the wind turbine or the descriptive wind speed statistics, can be related to the equations describing the evolution of power production and wind speed at single wind turbines.

Wind energy is becoming a top contributor to the renewable energy mix, which raises potential reliability issues for the grid due to the fluctuating nature of its source. To achieve adequate reserve commitment and to promote market participation, it is necessary to provide models that can capture daily patterns in wind power production. This paper presents a cyclic inhomogeneous Markov process, which is based on a three-dimensional statespace (wind power, speed and direction). Each time-dependent transition probability is expressed as a Bernstein polynomial. The model parameters are estimated by solving a constrained optimization problem: The objective function combines two maximum likelihood estimators, one to ensure that the Markov process long-term behavior reproduces the data accurately and another to capture daily fluctuations. A convex formulation for the overall optimization problem is presented and its applicability demonstrated through the analysis of a case-study. The proposed model is capable of reproducing the diurnal patterns of a three-year dataset collected from a wind turbine located in a mountainous region in Portugal. In addition, it is shown how to compute persistence statistics directly from the Markov process transition matrices. Based on the case-study, the power production persistence through the daily cycle is analysed and discussed.The EC European Parliament objective to achieve 20% of the consumed 2 energy from the renewable energy sector by 2020 introduced a serious chal-3 lenge to the planning and operating of power systems. Wind energy is be-4 coming a top contributor to the renewable energy mix due to rather high 5 capacities and generation costs that are becoming competitive with conven-6 tional energy sources [28]. However, wind energy systems suffer from a major 7 drawback, the fluctuating nature of their source, which affects the grid secu-8 rity, the power system operation and market economics. There are several 9 tools to deal with these issues, such as the knowledge of wind power persis-10 tence and wind speed or power simulation. Persistence is related to stability 11 properties and can provide useful information for bidding on the electricity 12 market or to maintain reliability, e.g. by setting reserve capacity. 13Wind power or speed simulation can be used to study the impact of wind 14 generation on the power system. For this task, a sufficiently long time series 15 of the power output from the wind plants should be used. However, real 16 data records are commonly of short length and thus synthetic time series 17 are generated by stochastic simulation techniques to model wind activity 18 [16]. Shamshad et al. [23] used first and second-order Markov chain mod-19 els for the generation of hourly wind speed time series. They found that a 20 model with 12 wind speed states (1 m/s size) can capture the shape of the 21 probability density function and preserve the properties of the observed time 22 series. Additionally, they concluded that a second-order Markov chain pro-23 duce...

This paper presents a direct method to obtain the deterministic and stochastic contribution of the sum of two independent sets of stochastic processes, one of which is composed by Ornstein-Uhlenbeck processes and the other being a general (non-linear) Langevin process. The method is able to distinguish between all stochastic process, retrieving their corresponding stochastic evolution equations. This framework is based on a recent approach for the analysis of multidimensional Langevin-type stochastic processes in the presence of strong measurement (or observational) noise, which is here extended to impose neither constraints nor parameters and extract all coefficients directly from the empirical data sets. Using synthetic data, it is shown that the method yields satisfactory results.

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