Characterisation of wind speed series and power in Durban

Abstract

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...

Model predictive control of a doubly fed induction generator

“…)𝐼 𝑞𝑟 (3)(4)(5)(6) Substituting these into the rotor voltage equations, the following is obtained [27], [48], [85]: )𝑤 𝑟 (3)(4)(5)(6)(7)(8) Where:…”

“…In (3)(4)(5)(6)(7)(8)(9)(10), it is seen that if the stator resistance is neglected, the stator active power is dependent on the rotor quadrature current. In (3)(4)(5)(6)(7)(8)(9)(10)(11), it is seen that the stator reactive power is dependent on the rotor direct current. The last terms in (3.7) and (3.8) are known as the coupling terms and are added at the output of the proportional-integral controllers.…”

“…𝛷 𝑞𝑠 = −𝛷 𝑠 = 𝐿 𝑠 𝐼 𝑞𝑠 + 𝐿 𝑚 𝐼 𝑞𝑟 (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) Rewriting these, making the stator currents the subject of the formula yields:…”

“…Equations (3-18) - (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22) form the basis for indirect FOC using SVOC. In (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21), it is seen that if the stator resistance is neglected, the stator active power is dependent on the rotor direct current.…”

“…Furthermore, the use of coal in the generation of electrical power emits harmful by-products which damage our precious ozone layer. Is there for these reasons that the world is turning towards the production of electrical energy from sustainable power sources [1], [2], [3]. One such source is the sun, which can effectively be used in small scale electrical power generation [4].…”