Review and Improvement of Several Optimal Intelligent Pitch Controllers and Estimator of WECS via Artificial Intelligent Approaches - Complex System Modelling and Control Through Intelligent Soft Computations - page 499

3 WECS Modelling

3.1 Wind Modelling

Wind time model has been created founded on the ARMA series in this section.
The wind speed v w ð t Þ has two parts declared as:

v w ð t Þ¼ v m þ v t ð t Þ ð 1 Þ

where v m is the signify wind speed at hub height and v t ð t Þ is the instantaneous

turbulent part, whose linear model is composed by a filter disturbed by

Gaussian noise. The instantaneous turbulence component of wind speed is obtained
as Endusa and Aki ( 2009 ):

rst-order

v t ð t Þ¼d t # t ð 2 Þ

where d t is the standard deviation and # t is the ARMA time series model, which

may be expressed as:

# t ¼ d 1 # t 1 þ d 2 # t 2 þþd n # t n þ g t h 1 g t 1 h m g t m ð 3 Þ

where g t is the white noise process with zero mean, d i ð i ¼ 1 ; 2 ; ...; n Þ and h j ð j ¼

1 are the autoregressive parameters and moving average parameters,

respectively. Wind speed by the ARMA model is presented in Simulink environ-
ment as Fig. 1 b.

; 2 ; ...; m Þ

3.2 Simulation of Wind Model

The main parameters of wind turbine have been simulated in this section. First the
wind speed is modeled by the ARMA series in MATLAB simulation. The mean
wind speed is determined based on spectral energy distribution of the wind and a
superimposed noise signal. Figure 2 shows the response of the wind turbine to a
wind speed pro

le above and below rated wind.

3.3 Wind Turbine Modeling

Considered wind turbines in this work, operate at variable speed in wind farms.
They can be represented by the modeling of rotor, drive train and generation system
with generator and power-factor-correction capacitors. The aerodynamic power
captured by the rotor is given by the nonlinear expression: