A cyclic time-dependent Markov process to model daily patterns in wind turbine power production

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 state-space (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

Wind speed forecasting at different time scales: a non parametric approach

The prediction of wind speed is one of the most important aspects when dealing with renewable energy. In this paper we show a new nonparametric model, based on semi-Markov chains, to predict wind speed. Particularly we use an indexed semi-Markov model, that reproduces accurately the statistical behavior of wind speed, to forecast wind speed one step ahead for different time scales and for very long time horizon maintaining the goodness of prediction. In order to check the main features of the model we show, as indicator of goodness, the root mean square error between real data and predicted ones and we compare our forecasting results with those of a persistence model

Performance and economic analysis of hybrid microhydro systems

Microhydro (MHP) systems usually employ unregulated turbines and an electronic load controller, a demand-side control device. Existing analytical models for such systems are lacking details, especially supply-side flow control, for performance simulation at hourly or sub-hourly scales. This work developed stochastic models for downscaling of streamflow and an empirical model of MHP systems. We integrated these models within the framework of Hybrid2 tool to simulate the long-term performance of a tri-hybrid system consisting of hydropower, solar PV and wind turbine. Based on an additive model of time series decomposition, we develop a Multiple Input Single Output (MISO) model in order to synthesize an hourly time series of streamflow. The MISO model takes into account daily precipitation dataset as well as regional hydrological characteristics. The model employs a constrained Monte-Carlo Markov Chain (MCMC) algorithm which is validated against an hourly time series of flow data at Blue River at Blue, Oklahoma. A non-dimensional performance model of MHP systems is developed based on empirical data from Nepal. Three design configurations are presented for a case study. The results show that, along with a small pond that can store water for an hour at the rated capacity of MHP system, a hybrid system with half the size of the battery bank can supply the load year around at Thingan Project in Nepal. This system meets the availability requirements of the Multi-Tier Framework for measuring energy access for household supply. The new proposed system is marginal in the economic sense as well. This project can never recover the initial capital cost at a current rate of the tariff which is about 7 cents/kWh. Other O&M risks aside, the sensitivity analysis suggests that the system may barely recover the initial capital cost, excluding the subsidy, at twice the existing rate of tariff and half the interest rate. This study aspires to come up with better techniques to simulate hybrid microhydro systems and enhance their design and operation through more effective utilization of resources

First and second order semi-Markov chains for wind speed modeling

The increasing interest in renewable energy, particularly in wind, has given rise to the necessity of accurate models for the generation of good synthetic wind speed data. Markov chains are often used with this purpose but better models are needed to reproduce the statistical properties of wind speed data. We downloaded a database, freely available from the web, in which are included wind speed data taken from L.S.I. -Lastem station (Italy) and sampled every 10 minutes. With the aim of reproducing the statistical properties of this data we propose the use of three semi-Markov models. We generate synthetic time series for wind speed by means of Monte Carlo simulations. The time lagged autocorrelation is then used to compare statistical properties of the proposed models with those of real data and also with a synthetic time series generated though a simple Markov chain.Comment: accepted for publication on Physica

Coupled coarse graining and Markov Chain Monte Carlo for lattice systems

We propose an efficient Markov Chain Monte Carlo method for sampling equilibrium distributions for stochastic lattice models, capable of handling correctly long and short-range particle interactions. The proposed method is a Metropolis-type algorithm with the proposal probability transition matrix based on the coarse-grained approximating measures introduced in a series of works of M. Katsoulakis, A. Majda, D. Vlachos and P. Plechac, L. Rey-Bellet and D.Tsagkarogiannis,. We prove that the proposed algorithm reduces the computational cost due to energy differences and has comparable mixing properties with the classical microscopic Metropolis algorithm, controlled by the level of coarsening and reconstruction procedure. The properties and effectiveness of the algorithm are demonstrated with an exactly solvable example of a one dimensional Ising-type model, comparing efficiency of the single spin-flip Metropolis dynamics and the proposed coupled Metropolis algorithm.Comment: 20 pages, 4 figure