In this section, the WTGS and its functional operation are discussed. Figure 1 shows the one-line diagram of a wind turbine generation system connected to an infinite grid.
The WTGS is model such that maximum power (torque) is extracted from the turbines for a given wind speed using a maximum power point tracking (MPPT) algorithm.
The torque is then applied to a 2 MVA doubly fed induction generator (DFIG), with rotor-side and grid-side controllers. Therefore, representing a type 3 WTGS.

Figure 1: Wind Turbine Generation System

System Configuration and DFIG Modeling

The system configuration of a grid-connected doubly fed induction generator is shown in Figure 2.
The system comprises a wind turbine, a DFIG, a DC-link capacitor, and the back-to-back (Type of devices: IGBTs) three-phase pulse width modulated (PWM) voltage source converter with their respective controllers.
The stator of the DFIG is supplied by the three-phase voltages directly from the grid at constant amplitude and frequency, creating the stator magnetic field.
The rotor of the DFIG is supplied by three-phase voltages that takes a different amplitude and frequency at steady state to reach different operating condition of the machine (speed, torque).

Figure 2: Investigated DFIG Wind Turbine System Configuration

With,

: Wind speed in m/s

: Turbine angular speed in rad/s

: Torque produced by the turbine in N.m.

: Mechanical power produced by the turbine in W. 

: Rotor angular speed in rad/s

: Torque received by the rotor in N.m.

: Mechanical power received by the rotor in W. 

: Reduction ratio of the gear box. 

: Efficiency ratio of the gear box.  

: Active and reactive power of the stator and rotor sides.

: Active and reactive power of the grid side.

 Wind Turbine Modeling

The kinetic energy of the wind is converted to rotational energy in the form of a mechanical torque by a wind turbine (WT).
The power extracted by the turbine from available power in the wind is given in equation (1), as follows:

Where,

: Tip speed ratio.

: Blade radius (m).

: Wind speed (m/s).

: Air density.

: Pitch angle.

: Power coefficient, and it is a function of the tip speed ratio  and the the pitch angle .

The equation of the power coefficient is given in (3), and it reflects the efficiency if the conversion form wind energy to mechanical energy.

Where, through  are the characteristic coefficients of the wind turbine, and is the rotational speed of the wind turbine (rad/s) as in [3].
The characteristic curve ( vs ) for different values of the pitch angle () is shown in Figure 3; and it can be observed that the optimum power coefficient is obtained when  is equal to zero degree (curve in blue). 
The maximum power extraction from the WT can be achieved when the turbine operates at the optimum .
Figure 4 illustrates the maximum power tracking curve for the DFIG. The optimum power to be extracted from the WTGS can be expressed as follows:

Figure 3: vs Characteristics of the Wind Turbine for Various Pitch Angles

Figure 4: WTGS Characteristics for DFIG with Maximum Power Point Tracking

DFIG Modeling

In synchronous  reference frame rotating at a speed, the modeling of the DFIG is given by the following equations:

• Stator voltage components

• Rotor voltage components

With,

: Angular speed of dq reference frame relative to the stator.

: Angular speed of dq reference frame relative to the rotor.

: Number of pole pair.

: Electrical speed of the rotor in rad/s. , and .

• Stator flux components

• Rotor flux components

From the above equations, the equivalent electric circuit in d-q reference frame is obtained as presented in Figure 5.

Figure 5: DFIG modeling: d and q Axes Equivalent Circuits.

Where,

:  Stator voltages and current in dq axis.

: Rotor voltages and current in dq axis.

: Stator leakage inductance, rotor leakage inductance, and magnetizing inductance.

: Stator and rotor resistances.

: Stator and rotor fluxes in dq axis.

Using the dq parameters for the DFIG, its electromagnetic and mechanical torques are calculated as follows:

The active and reactive power equations of the stator and rotor are given by the equations (10) and (11) below:

Vector Control of the DFIG

To control the DFIG, the RSC and GSC of the system must be properly designed. RSC and GSC structures are designed using the transformation equations and equivalent circuits mentioned in the previous section.
Among the existing control methods for the DFIG that have been developed in literature, the vector control technique is implemented in this work, which is probably the most extended and established one.
The overall vector control structure used is shown in Figure 6. The role of the RSC is to control generated power by regulating the dq-axis rotor currents .
The duty of the GSC is to control the bi-directional transfer of power flow from the grid to the rotor or from the rotor to the grid by keeping the DC bus voltage constant.

Figure 6: Overall Closed-Loop Control Scheme of the DFIG

Control of the Rotor-Side Converter (RSC)

The active and reactive powers absorbed by the rotor side are respectively controlled by the torque component  and the excitation component  of the rotor current.
The reference torque  value is produced via the Speed PI controller. 

Figure 7: Control Scheme of the Rotor-Side Converter

Control of the Grid-Side Converter (GSC)

The GSC control strategy is used to control the power flow of the DFIG.
Two critical components to consider when controlling the power flow are the DC link voltage and reactive power exchange with the grid.
The expression of the grid exchange active and reactive powers is given in Equation (12).

Equation (12) reveals that the current  component controls the , while the current component  controls the value of .
A capacitor forms the DC-Link; active power flows through RSC-Capacitor-GSC to the grid.
Therefore, maintaining to a constant value will ensure both RSC and GSC work properly during active power flow.
In the same manner, reactive power flow in the grid is ensured. The control strategy for the GSC is shown in Figure 8.

Figure 8: Control Scheme of the Grid-Side Converter

Simulation Parameters

The simulation parameters are provided in Table 1. These parameters can be found in DFIM tutorial 1 developed by Prof. Gonzalo Abad [2]. 

DFIG Nameplate Ratings
Apparent Nominal Power	2 MVA
Power Factor	0.9
Nominal Line-to-line Stator Voltage	690 V
Nominal Line-to line Rotor Voltage	2070 V
Nominal Stator Current	1760 A
Nominal Rotor Current	590 A
Nominal Speed	1500 rpm
Nominal Torque	12732 N.m
Number of Pole Pair	2
Stator Resistance	2.6 mΩ
Stator Inductance	0.087 mH
Rotor Resistance	2.9 mΩ
Rotor Inductance	0.087 mH
Magnetizing Inductance	2.5 mH
Moment of Inertia	63.5 kg.m2
Friction Factor	0.001 N.m.s
Gear Box Ratio	100
Gear Box Efficiency Ratio	0.98
Three-phase Two-level Back-to-Back Converter Nameplate Ratings
DC Voltage	1150 V
DC-Link Capacitor	80 mF
PWM Frequency	5 kHz
Fundamental Frequency	50 Hz

Table 1: Simulation Parameters of the WTGS