2. Mathematical model for DFIG

In this section, we deal with the mathematical modeling of the DFIG-based wind energy system, we will only describe the wind turbine (also called drive train), and the asynchronous generator (also called induction generator) because this chapter focuses on estimating of the parameters and dynamic states of the DFIG Figure 1. Two frames of reference are used in this model: stator voltage (d-q) reference frame and mutual flux (d-q) reference frame. In Tables 1 and 2, all parameters and constants are given.

#### 2.1 Modeling of the wind turbine

From the wind, the power extracted can give the mechanical torque. The energy from the wind is extracted from the wind turbine and converted into mechanical power [14]. The wind turbine model is based on the output power characteristics, as Eqs. (1) and (2), [15].

Pm ¼ Cpð Þ λ; β

1 2 ρAν<sup>3</sup>

<sup>λ</sup>TS <sup>¼</sup> <sup>R</sup>ω<sup>t</sup> νw

Parameters Values

Number of blade 3 Radius of blade (R)/m 35.25 Gearbox gain (G) 91

) 12

) 1000

) 0.0024

Parameters Values Rated active power (Ps)/(MW) 1.5 Rated voltage (line to line) (Vs)/(V) 575 Rated DC-link voltage (Vdc)/(V) 1200 Number of poles 4 Frequency (f)/(Hz) 60 Stator resistance (Rs)/(pu) 0.00707 Rotor resistance (Rr)/(pu) 0.005 Stator leakage inductance (Ls)/(pu) 0.171 Rotor leakage inductance (Lr)/(pu) 0.156 Magnetizing inductance (Lm)/(pu) 2.9 DC-link capacitance (C)/(F) 0.04

where the aerodynamic extracted power is Pm, which depends on CP, the efficiency coefficient,the air density ρ, the turbine swept area A, and the wind speed νw. The kinetic energy contained in the wind at a particular wind speed is given by Ew. The blade radius and angular frequency of rotational turbine are R and wt, respectively. CP(λ; β) the efficiency coefficient depends on tip speed ratio λTS and blade pitch angle β, determines the amount of wind kinetic energy that can be

λi

<sup>λ</sup>TS <sup>þ</sup> <sup>0</sup>:08<sup>β</sup> � <sup>0</sup>:<sup>035</sup>

� 0:4β � 5 <sup>e</sup>

captured by the wind turbine system [13]. CP(λ; β) can be described as:

<sup>¼</sup> <sup>1</sup>

Cpð Þ¼ <sup>λ</sup>; <sup>β</sup> <sup>0</sup>:<sup>5</sup> <sup>116</sup>

1 λi

where

25

Table 1.

Table 2.

Parameters of the DFIG.

Rated wind speed (vw)/(m s�<sup>1</sup>

Advanced Monitoring of Wind Turbine DOI: http://dx.doi.org/10.5772/intechopen.84840

Moment of inertia (Jeq)/(kg m<sup>2</sup>

Parameters of the wind turbine.

Viscosity factor (feq)/(N m s rad�<sup>1</sup>

<sup>w</sup> ¼ Cpð Þ λ; β Ew (1)

�21=λ<sup>i</sup> (3)

<sup>β</sup><sup>3</sup> <sup>þ</sup> <sup>1</sup> (4)

(2)

Figure 1. Configuration of DFIG-based wind turbine system [13].
