Search

This article aims to obtain and evaluate medium-term operating policies for the hydrothermal scheduling problem by using the stochastic dual dynamic programming (SDDP) approach. To this end, to feed the mathematical model and build the probability distribution functions that best fit each month of the actual inflow volume, monthly inflow data recorded from 1938 to 2018 for the Infiernillo reservoir located in Mexico were employed. Moreover, we simulated inflow volume scenarios using the Monte Carlo method for each month of a one-year planning period. The SDDP approach to solving the optimization problem consisted of the simulation of one forward scenario per iteration and the stabilization of the total operating cost as a convergence criterion, which results in an operating policy. We then assessed its quality by estimating the one-sided optimality gap. It is worth mentioning that the best operation policy required scenario trees of up to 17,000 inflow realizations per stage. Additionally, to study the evolution of the expected value along the planning horizon of the main variables involved in the medium-term hydrothermal scheduling problem, we simulated the best operation policy over 10,000 inflow scenarios. Finally, to show the practical value of the proposed approach, we report its computational complexity. [ABSTRACT FROM AUTHOR]

This paper deals with the effect of layer height randomness on the seismic response of a layered soil. These parameters are assumed to be lognormal random variables. The analysis is carried out via Monte Carlo simulations coupled with the stiffness matrix method. A parametric study is conducted to derive the stochastic behavior of the peak ground acceleration and its response spectrum, the transfer function and the amplification factors. The input soil characteristics correspond to a site in Mexico City and the input seismic accelerations correspond to the Loma Prieta earthquake. It is found that the layer height heterogeneity causes a widening of the frequency content and a slight increase in the fundamental frequency of the soil profile, indicating that the resonance phenomenon is a concern for a large number of structures. Variation of the layer height randomness acts as a variation of the incident angle, i.e., a decrease of the amplitude and a shift of the resonant frequencies. [ABSTRACT FROM AUTHOR]

The main purpose is to build a wind speed model to assess its impact on the power output estimate of a wind turbine. This modelling is based on stochastic differential equations and memoryless transformations, considering a stable numerical scheme capable to optimize the computational complexity. According to statistical characteristics of a wind speed dataset recorded at a given location in Mexico, the model is parameterized for six probability density functions (PDF), showing exponential decay of the autocorrelation function. The suitability of the model for wind speed modelling and power output estimate is evaluated through a comparative analysis between the real dataset and the simulations; moreover, the quality of the findings have been assessed employing statistical measures criteria. Finally, and contrary to what has been reported, that is, the Weibull PDF is the best one to characterize wind speed in many regions of the world including Mexico, it turns out that among the six PDFs considered in this work, the probability density functions Beta and Log-Pearson 3 represent the best fit to the real wind speed data as well as providing an estimate of less than 1% of the semiannual produced energy by a wind turbine. • Analysis of a wind speed model based on the Ornstein-Uhlenbeck process. • The Beta and Log-Pearson 3 distributions present the best performance. • Computational complexity and stability analysis are developed. • A fixed initial condition can significantly affect the evaluation criteria. [ABSTRACT FROM AUTHOR]

• Wind power estimation using a wind speed model based on the Fokker-Planck equation. • Eight probability distributions evaluated to estimate wind resources. • Beta distribution has the best performance in short-term. • Long-term energy estimation by the MCP algorithm and the mathematical model. The main purpose of this article is to estimate the wind power generation in Juchitan de Zaragoza-Mexico based on stochastic analysis of the average wind speed. This estimation is carried out by simulating numerically a stochastic differential equation (SDE) for a set of randomly generated trajectories of the Wiener process and a particular probability density function (PDF). Due to the fact that wind power is formulated as an explicit function of wind speed, then a good selection of the appropriate PDF can significantly reduce the wind power estimation error. Moreover, and in order to get more insights into the statistical behavior of the wind power output, we propose eight different PDFs to evaluate its suitability to characterize wind speed and wind power as well. The challenging step is to find the drift and volatility of the SDE, which in this work are determined in closed form via the solution of the stationary Fokker–Planck equation. To assess the practical value and competitiveness of the proposed approach, computational complexity, stability analysis and different measures of accuracy have been addressed. Finally, the results show that among the eight PDFs evaluated in this particular study, the three-parameter Beta distribution has the best performance in estimating wind resources in the short-term, while for long-term closed results are obtained between the three-parameter generalized Gamma, three-parameter Beta and Log-Pearson 3 distributions. [ABSTRACT FROM AUTHOR]