Grid-scale Fluctuations and Forecast Error in Wind Power

The fluctuations in wind power entering an electrical grid (Irish grid) were analyzed and found to exhibit correlated fluctuations with a self-similar structure, a signature of large-scale correlations in atmospheric turbulence. The statistical structure of temporal correlations for fluctuations in generated and forecast time series was used to quantify two types of forecast error: a timescale error ($e_{\tau}$) that quantifies the deviations between the high frequency components of the forecast and the generated time series, and a scaling error ($e_{\zeta}$) that quantifies the degree to which the models fail to predict temporal correlations in the fluctuations of the generated power. With no $a$ $priori$ knowledge of the forecast models, we suggest a simple memory kernel that reduces both the timescale error ($e_{\tau}$) and the scaling error ($e_{\zeta}$)

Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements

Copyright @ 2012 ElsevierIn this paper, the extended Kalman filtering problem is investigated for a class of nonlinear systems with multiple missing measurements over a finite horizon. Both deterministic and stochastic nonlinearities are included in the system model, where the stochastic nonlinearities are described by statistical means that could reflect the multiplicative stochastic disturbances. The phenomenon of measurement missing occurs in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over the interval [0,1]. Such a probability distribution is allowed to be any commonly used distribution over the interval [0,1] with known conditional probability. The aim of the addressed filtering problem is to design a filter such that, in the presence of both the stochastic nonlinearities and multiple missing measurements, there exists an upper bound for the filtering error covariance. Subsequently, such an upper bound is minimized by properly designing the filter gain at each sampling instant. It is shown that the desired filter can be obtained in terms of the solutions to two Riccati-like difference equations that are of a form suitable for recursive computation in online applications. An illustrative example is given to demonstrate the effectiveness of the proposed filter design scheme.This work was supported in part by the National 973 Project under Grant 2009CB320600, National Natural Science Foundation of China under Grants 61028008, 61134009 and 60825303, the State Key Laboratory of Integrated Automation for the Process Industry (Northeastern University) of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Transaction fees and optimal rebalancing in the growth-optimal portfolio

The growth-optimal portfolio optimization strategy pioneered by Kelly is based on constant portfolio rebalancing which makes it sensitive to transaction fees. We examine the effect of fees on an example of a risky asset with a binary return distribution and show that the fees may give rise to an optimal period of portfolio rebalancing. The optimal period is found analytically in the case of lognormal returns. This result is consequently generalized and numerically verified for broad return distributions and returns generated by a GARCH process. Finally we study the case when investment is rebalanced only partially and show that this strategy can improve the investment long-term growth rate more than optimization of the rebalancing period.Comment: 17 pages, 7 figure

A new kernel-based approach to system identification with quantized output data

In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods to provide an estimate of the system. In particular, we design two methods based on the so-called Gibbs sampler that allow also to estimate the kernel hyperparameters by marginal likelihood maximization via the expectation-maximization method. Numerical simulations show the effectiveness of the proposed scheme, as compared to the state-of-the-art kernel-based methods when these are employed in system identification with quantized data.Comment: 10 pages, 4 figure