Both the planning and operating of a wind farm demand an appropriate wind speed model of its location. The model also helps predict the dynamic behaviour of wind turbines and wind power potential in the location. This study characterises the wind speed series and power in Durban (29.9560°S, 30.9730°E) IntroductionDepletion of fossil fuel reserves, global warming, security concerns, and rising commodity prices are pushing the world to go green. Much attention is currently given to the development of renewable energy, among which harnessing wind energy is the cheapest alternative [1][2][3]. Feasibility studies related to wind power require an appropriate wind speed model of a site [4,5]. These models are also important in planning and operating wind turbines. Hence, the wind speeds of a specified site should be appropriately characterised to determine wind energy potential and attain comprehensive results in the investigations of the dynamics of the wind turbines [4,6,7]. Moreover, a good characterisation of wind speed helps transmission system operators in scheduling their power dispatch [4]. Wind is a random stochastic process whose dynamic behaviour can be represented by a stochastic model [8]. Naturally, it depends on pressure gradient, waves, jet streams, and local weather conditions [9]. Its stochastic modelling is a complicated task because of its strong variability in time and land terrains. Over a year, wind speed is periodic, showing seasonal variations; however, hourly average wind speed is a stochastic process with a Weibull probability density function; whereas within minutes, it follows a Gaussian distribution [10].Different methods have been employed for time series characterisation of wind processes. Traditionally Weibull distribution is widely used to represent wind speed series at a given site [4,[11][12][13]. Normal, Gamma, Lognormal or combination of these distributions with Weibull distribution [4,7,[14][15][16], empirical wavelet [17] or Kernel density method [18] can also be used to model wind speed series. Shokrzadeh et al. [19] and Kazemi and Goudarzi [20] employed advanced parametric and nonparametric and least square approximation methods to forecast wind power. A typical distribution may not necessarily represent the cumulative wind behaviour of all locations in a region [7]. Thus, the wind speed for a particular location needs to be modelled. The above distributions cannot be used, however, when chronology is considered [4]. A rough observation on the raw wind speed data from Durban demonstrated that the current wind speed depended on the previous wind speed, indicating that chronology should be considered in modelling the wind speeds. Evolutionary algorithms such as genetic algorithm and local search technique are also used in wind speed modelling [21] despite their time consuming procedure [4]. The Markov chain model, which retains chronology and consumes less time, could, therefore, be employed to synthesise wind speed time series for dynamic simulation and wind power f...

Abstract-Damping local oscillations is vital in the operation of a direct-drive permanent magnet synchronous generator wind turbine as well as its integration into a grid. Currently, these oscillations are controlled by proportional-integral controllers. This paper proposes the inclusion of virtual resistors to improve the performance of the wind turbine further. Simulation results show that virtual resistors, connected in series to stator windings, have a positive impact on the damping of local oscillations. They significantly reduce the rise and settling times of the rotor speed, electromagnetic torque, active power and reactive power and increase the corresponding damping ratios. In contrast, the ones, connected in parallel to stator windings, have a negative impact on the damping of local oscillations. This indicates that an appropriate selection and connection of virtual resistors improves the dynamic and small-signal performances of a PMSG wind turbine.Keyword-Damping local oscillations, permanent magnet synchronous generator, wind turbine, dynamic performance, small-signal stability, virtual resistors I. INTRODUCTION For the past two centuries, rapidly growing populations and modernization trends have accelerated the demand for energy. Today, the world heavily depends on fossil fuels such as oil, coal, and natural gas for its increasing energy requirements. However, this fossil-fuelled economy is facing challenges including depletion of reserves, global warming, security concerns, and rising cost [1]. In tackling these challenges, much attention is given to the development of renewable energy, among which harnessing wind energy is the cheapest alternative [2,3].Three types of wind energy technologies-squirrel-cage induction generator (SCIG), doubly fed induction generator (DFIG) and permanent magnet synchronous generator (PMSG) wind turbines-are widely adopted in the wind industry. Compared to SCIG, DFIG and PMSG are popular for two reasons [4]. Firstly, they offer the opportunity to operate the machine at maximum power for various wind speeds, and secondly, they have less mechanical stress on their shafts. These days, the popular variable-speed wind turbines employed in large-scale wind parks are DFIG wind turbines [5]. Nevertheless, recently, direct-drive PMSG wind turbines are gaining momentum among researchers, engineers and turbine manufacturers for their high efficiency, low power loss and smaller size [6 -11].The integration of wind power into grids is rapidly growing. In some European countries, the level of penetration has reached as high as 21% [12]. However, due to this high penetration and the intermittent nature of the wind, there are concerns such as generation reserve, power system stability and reliability [13]. Furthermore, wind turbines themselves have stability problems, which surely challenge transmission system operators. In large grids, the ability of both local and system-wide power system oscillation damping plays a crucial role [14].A range of efforts have been made to damp local ...