Derek Kearney

Analysis of Wind Velocity and the Quantification of Wind Turbulence in Rural and Urban Environments Using the Levy Index and Fractal Dimension

This paper is concerned with a quantitative and comparative analysis of wind velocities in urban and rural environments. It is undertaken to provide a route to the classification of wind energy in a rural and urban setting. This is a common problem and the basis of a significant focus of research into wind energy. In this paper, we use a non-Gaussian statistical model to undertake this task, and, through a further modification of the data analysis algorithms used, extend the model to study the effect of wind turbulence, thereby introducing a new metric for this effect that is arguably superior to a more commonly used and qualitatively derived measure known as the Turbulence Intensity. Starting from Einstein’s evolution equation for an elastic scattering process, we consider a stochastic model for the wind velocity that is based on the Generalised Kolmogorov Feller Equation. For a specific ‘memory function’ the Mittag-Leffler function it is shown that, under specified conditions, this model is compatible with a non-Gaussian processes characterised by a Levy distribution that, although previously used in wind velocity analysis, has been introduced phenomenologically. By computing the Levy index for a range of wind velocities in both rural and urban environments using industry standard cup anemometers, wind vanes and compatible data collection conditions (in terms of height and sampling rates), we show that the intuitive notion that the ‘quality’ of wind velocity in an urban environment is poor compared to a rural environment is entirely quantifiable. This quantifies the notion that a rural wind resource is, on average, of higher yield when compared to that of the urban environment in the context of the model used. In this respect, results are provided that are based on five rural and urban locations in Ireland and the UK and illustrate the potential value of the model in the consideration of locating suitable sites for the development of wind farms (irrespective of the demarcation between an urban and rural environment). On this basis, the paper explores an approach whereby the same model is used for evaluating wind turbulence based on the Fractal Dimension using the ‘polar wind speed’ obtained from three-dimensional data sets collected in urban environments.

Non-Gaussian Analysis of Wind Velocity Data for the Determination of Power Quality Control

The quality of power (i.e. the sustainable power output as a function time) of any wind dependent energy converter (including wind turbines and wave energy converters) is determined by many design and environmental factors but timedependent variations in the wind speed are arguably the most important. In this paper we consider a non-Gaussian model for analysing and then simulating wind velocity data. In particular, we consider a Levy distribution for the statistical characteristics of wind velocity and show how this distribution can be used to derive a stochastic fractional diffusion equation for the wind velocity as a function of time whose solution is characterised by the Levy index. A Levy index based numerical analysis is then performed on wind velocity data for both rural and urban areas where, in the latter case, the index is shown to have a larger value. Finally, an empirical relationship is derived for the power output from a wind turbine in terms of the Levy index using Betz law and a similar relationship obtained for a wave energy converter. In both cases, it is shown how the average power output as a function of time is (inversely) related to the Levy index for the wind velocity. It is concluded that these relationships may have value in determining the optimal geographical locations for the construction of wind and wave farms and for monitoring their performance in terms of power quality control.

A Techno-Economic Analysis of Photovoltaic System Design as Specific ally Applied to Commercial Buildings in Ireland

This paper evaluates the viability of installing photovoltaic (PV) systems in existing commercial buildings in Dublin. Data collected from previously installed photovoltaic systems at the Dublin Institute of Technology was analysed in order to determine the potential solar resource available in Ireland. A 1.1 kWp photovoltaic system installed in Dublin can produce over 900 kWh of electricity in a given year depending on the available solar resource for that year. A feasibility study was conducted in Dublin city centre in order to evaluate the technical, financial and environmental aspects of integrating a PV system into an existing building. The intention is that the results from this work will help in demonstrating the benefits and challenges associated with installing PV systems in existing commercial buildings in Ireland.

Wind turbine power quality estimation using a Lévy model for wind velocity data

The power quality of a wind turbine is determined by many factors but time-dependent variation in the wind velocity are arguably the most important. In this paper a non-Gaussian model for the wind velocity is introduced that is based on a Lévy distribution. It is shown how this distribution can be used to derive a stochastic fractional diffusion equation for the wind velocity as a function of time whose solution is characterised by the Lévy index. A numerical method for computing the Lévy index from wind velocity time series is introduced and applied to example wind velocity data for both rural and urban areas where, in the latter case, the index is observed to have a larger value. Finally, an empirical relationship is derived for the power output from a wind turbine in terms of the Lévy index using Betz law.

INVERTER PERFORMANCE FOR SMALL WIND TURBINES WHEN CONNECTED IN PARALLED WITH THE LOW-VOLTAGE DISTRIBUTION SYSTEM

Small wind turbines have been installed in urban and turbulent locations with surprisingly poor performance and this has been backed up by data from a trial at the Dublin Institute of Technology. In order to develop the small wind turbine industry a careful examination of assessment methods for the wind resource is required. Small wind turbines connected in parallel with the grid use inverters. As the wind turbine is not always at max output, a Weighted Average Efficiency for wind inverters is proposed. Pitfalls associated with developing an accurate weighted average efficiency for an inverter are identified and this will enable a more accurate sizing of the inverter for the turbine. The methodology for determining the performance of inverters and small wind turbines can be applied to any location.

Estimation of Wave Energy from Wind Velocity

The aim of this paper is to report on a possible correlation between the Levy index for wind velocity and the mean Energy Density of sea surface waves in the same location. The result is based on data obtained from 6 buoys located around the coast of Ireland and maintained by the Marine Institute of Ireland and a further 144 buoys located at various locations off the coast of the United States of America and maintained by the National Data Buoy Centre. These buoys provide historical data on the wind velocity, wave height and wave period as well as other data on an hourly interval. Using this data, we consider the relationship between a stochastic model for the time variations in wave height that in turn, is based on a non-Gaussian model for the wind force characterised by the Levy index. The results presented in this paper indicate the possibility of developing a method of estimating the energy and power densities of sea waves from knowledge of the wind velocity alone.