Modelling and control of wind turbine doubly fed induction generator with MATLAB simulink

This paper describes the modelling and control system of a wind turbine, using a doubly fed induction generator. This configuration makes the wind turbine suitable for variable speed wind energy application. The power captured by the wind turbine is converted into electrical power by the induction generator, and it is transmitted to the grid by the stator and the rotor windings. The control system generates voltage command signals for rotor converter and grid converter, respectively, in order to control the power of the wind turbine. Reactive power exchanged with the network through the converters is set to 0 VAr. The control strategy has been developed using MATLAB/Simulink. The simulation results are presented and discussed in the conclusions.


Introduction
Recently, wind energy has become the most promising of renewable energy sources and has expanded rapidly throughout the world.With the advancement of aerodynamic designs, wind turbines that can capture several megawatts of power are available.When such wind energy conversion systems (WECSs) are integrated to the grid, they produce a substantial amount of power, which can supplement the base power generated by thermal, nuclear or hydro power plants.
A WECS can vary in size from several megawatts to a few hundred kilowatts.The largest series production units today are specified to deliver 1.5-MW output power.It is anticipated that in the near future, the power rating of wind turbines will increase further, especially in offshore applications.For example, the prototype of a Nordex N80 with a rated power of 2.5 MW was installed in March 2000 near Aachen.The choice of the generator and converter system was determined by the size of the WECS.Among electrical rotating machines, induction machines are of special importance due to their simplicity and robustness.In comparison with alternative schemes, the doubly fed induction machine for variable speed constant frequency generation systems is nowadays an established technology.Other solutions based on direct-driven permanent magnet synchronous machines are proposed on the market.
There exists a large range of possible wind turbine configurations.Most commonly, wind turbines are of two major categories: 'fixed speed turbines' and 'variable speed turbines'.There is a wide range of topologies classified into these groups.A comparison and discussion of a few concepts can be found in [1][2][3][4][5].
The most commonly used concepts are fixed speed wind turbines equipped with asynchronous or induction generators directly connected to the grid.One of the oldest and simplest concepts was first used in Denmark, and therefore known as the 'Danish concept'.
Variable speed turbines with induction or synchronous generator, directly or indirectly connected to the grid have become more and more important in recent years.Possibilities such as mechanical load reduction and more efficient energy production, due to intelligent control strategies, make these concepts a beneficial economic solution.Furthermore, these types are better grid-compliant compared to fixed speed turbines.The possibility to independently control the speed decoupled from the grid gives the possibility to decouple frequencies resulting from wind fluctuations from the grid, which reduces flicker contribution.The converter integrated in a variable speed wind turbines gives the possibility to actively control the power output of the wind turbine, which is increasingly important for integration of wind turbines into the grid [6,7].
The fixed speed wind turbine is a self-controlled concept.With increasing wind speed, the laminar wind current flow around the fixed blade profile breaks and the turbine loses the possibility to obtain energy from the wind and stalls.The squirrel cage induction generator, which transforms the obtained mechanical energy into electrical energy, is directly connected to the grid.The speed of the generator may differ from the grid frequency due to the slip variation of the generator, which is up to 1%.
The variable speed wind turbine is usually equipped with a pitch control, where the blade can be turned to increase or decrease lift forces on the blade profile and, thereby, continuously control energy absorption from the wind.The active pitch control is designed to optimize the power obtained from the wind by changing the rotation speed of the rotor and the pitch angle, and therefore gain an optimum current flow around the blade.This achieved variable speed range at the turbine shaft or generator axes is different from the fixed frequency of the power system by 50 or 60 Hz.A direct coupling of a synchronous generator to the grid is therefore not possible, and a squirrel cage induction machine is too small in speed variation possibilities (<1%), which would limit power production only in a synchronism of the shaft speed and grid frequency.To enable efficient power production at a huge range of different wind speeds, the mechanical speed has to be decoupled from the grid frequencies.One method to decouple the two systems is to use a full-scale power converter between the generator and the grid.This may give a speed variation of up to 120%.The success of this concept has been limited over many years due to technical development in the area of power electronics and the associated costs.Another way to connect a variable speed wind turbine to the grid is to use a doubly fed induction generator (DFIG).Wind turbines equipped with DFIG have become more and more common in the recent years.They combine the advantages of pitch control with efficient transmission of power to the grid and the possibility of dynamic control of active and reactive power.Wind turbine technology benefits from developments in the area of drive control.Essential progress in the dynamical control of machines brought the introduction of field-oriented control by Blaschke.In the following years until today, research to improve the principle has been done [8][9][10][11][12].
In a system with DFIG, the converter is placed to feed into the rotor of the machine while the stator is directly connected to the grid.Through the converter, it is possible to control the supply, or extract the energy to the rotor of the induction machine.
Thus, the machine can be controlled to run between sub-synchronous speed and over synchronous speed (speed higher than synchronous speed).Usually, a variation from −40% to +30% of synchronous speed is chosen.The total speed variation is between 60% and 70%.Under these conditions, the power converter has a size of 30, or a maximum of 40 of the rated power, which is beneficial both economically and technically.
The WECS configuration used in this work is a DFIG with converters cascade and a capacity energy storage system in the dc link.This paper is structured as follows.First, we illustrate the importance of a wind turbine system, with different configurations existing for fixed, variable speed and several progresses in control.In Section 2, we describe the configuration proposed in this paper.Section 3 is devoted to modelling the wind turbine.Section 4 presents the modelling of the DFIG system.The detailed control strategy is discussed in Section 5. Section 6 presents and discusses the simulation and results, followed by the conclusions in Section 7.

Operating Principle of the Wind Turbine DFIG System
The wind turbine and DFIG are represented in Figure 1.Two cascaded voltage source converters (VSCs) make the transfer.The first is linked to the network called the grid converter (C grid ), which operates as a rectifier and the second is called the rotor converter (C rotor ), which operates as an inverter connected to the rotor of the generator.
The rotor windings are powered via bidirectional PWM VSCs by slip rings and brushes.The converters use forced-commutated power electronic devices (IGBTs) to generate an AC voltage from a DC voltage source assured by a capacitor on the DC side.The rotor converter is connected to the grid via a coupling inductor L. The conversion of the mechanical power captured by the wind turbine in electrical power is done by the induction generator and it is carried out to the grid by stator and rotor winding.
Another advantage of the DFIG technology is the ability for power electronic converters to generate or absorb reactive power, thus eliminating the need for installing capacitor banks as in the case of squirrel-cage induction generators.

Wind Turbine Model
A 1.5-MW wind turbine uses a DFIG that consists of a wound rotor induction generator and an AC/DC/AC IGBT-based PWM converter.The stator winding is connected directly to the 60-Hz grid, while the rotor is fed at variable frequency through the AC/DC/AC converter.The DFIG technology allows extracting the maximum energy from the wind for low wind speeds by optimizing the turbine speed, while minimizing mechanical stresses on the turbine during gusts of wind.
The aerodynamic model of a wind turbine is determined by its power speed characteristics [3].The friction factor and the inertia of the turbine must be combined with those of the generator associated to the turbine.For a horizontal axis wind turbine, the mechanical power output P m (w) that a turbine can produce is given as where ρ is the air density (in kg/m 3 ), v is the wind speed (in m/s), A is the turbine swept area (m 2 ) and C p is the power coefficient, which is a function of both tip speed ratio λ and blade pitch angle β (in degrees).In this work, the C P equation is approximated using a non-linear function according to [3]   The tip speed ratio λ is where Ω is the angular velocity of wind turbine and R is the blade radius.In this paper, we consider the pitch angle β equal to 0° (in this case, the power coefficient is the maximum) (see Figure 2(a)).
The turbine power characteristics are in Figure 2(b).At wind speed equal to 12 m/s, the turbine output power per unit of nominal mechanical power is equal to 0.73 for 1.2 turbine speed in per unit of nominal generator speed turbine speed.
In the per unit system, we have with mean v as the mean value of the expected wind speed in metre per second and p k (less than or equal to 1) as the power gain for 1 p pu C   pu and

Modelling of DFIG
The DFIG model is based on the following assumptions.The equations are derived in the synchronous reference frame using direct (d) and quadrature (q) axis representation.
The rotor voltages are where the flux linkages are expressed as To obtain an independent control of the powers produced from the wind system, we achieve a decoupled control of active and reactive power by the stator flux orientation.Controls of the electromagnetic torque and stator reactive power will be obtained by controlling the dq-axe rotor currents of the DFIG.
The stator field rotates in steady state at the synchronous speed.This field is symbolised by the stator flux vector, which gives a visual idea of the phase and flux amplitude.By choosing the twophase d, q related to rotating stator field, and placing the stator flux vector on the d-axis [13][14][15], we can write This choice is not random but is justified by the fact that the machine is often coupled with a powerful network voltage and constant frequency, which leads to finding the stator flux of the machine.Neglecting the resistance of the stator windings is the often accepted hypothesis for high power machines: The systems of Eqs. ( 8) and ( 10) can be simplified as follows: The stator active and reactive power in the orthogonal coordinate system can be written as Under the assumption of a stator flux oriented, this system of equations can be simplified as The stator currents can be derived in the following form: By introducing these expressions in Eq. ( 6 where σ is the dispersion coefficient between the two axes d and q, and g is the slip The rotor side converter is a two-level inverter, which controls the active and reactive powers generated by the stator of the DFIG.

Model Description
Decoupled control of active and reactive powers based on vector control is used.The control strategy provides the pitch angle, the command signals for rotor converter and grid converter, respectively, in order to control the active and reactive powers at the grid terminals.
The mechanical power and the stator electric power are given as The mechanical equation is In steady state at fixed speed without power losses in generator, we have where s is the slip of the generator From Eq. ( 22), we can deduce that the electrical rotor power is a fraction of electrical stator power.is negative for speed generator lower than synchronous speed (sub-synchronous speed operation) and positive for speed generator greater than synchronous speed (super-synchronous speed operation).

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The rotor converter C rotor and the grid converter C grid are used to control the active powers flow r p and gc p in order to keep the DC voltage constant.In addition, the rotor converter and the grid converter attribute directly in production or absorption of reactive power at the grid.The reactive power at grid (see Figure 1) is controlled by the reactive current flowing in the rotor converter C rotor .The reactive power control loop is illustrated in Figure 4.
The reactive power at the grid is given as The grid voltage and the grid current vectors are expressed as It is controlled by adjusting the direct current component delivered by the rotor converter.A proportional-integral (PI) regulator is used to regulate the direct I dr component current to its reference value.The output of this regulator is the direct voltage control V drc-control generated by the rotor converter.
The active power measured at the grid terminals of the wind turbine is given as It is added to the power losses, which represent the Joule effect losses in rotor, stator and grid converter winding and power friction given as is the resistance of grid-side converter coupling inductor to the grid and friction

T
is the friction torque of the generator.
These powers are subtracted from the reference power obtained from the tracking turbine power characteristic.In order to reduce the power error to zero, a PI regulator is used.The output of this regulator is the reference rotor current Then we can deduce that the active power at the grid is regulated with the quadratic current component generated by the rotor converter.Hence, this control loop allows obtaining a decoupled control of active and reactive power at the grid.87

Model Description
The converter C grid generates the grid voltage signals to the IGBTs, constituting the grid converter in order to regulate the voltage of the DC bus capacitor and control the production and absorption of reactive power at the grid.The control system is illustrated in Figure 5  .The grid voltages control are converted from d-q axis to the abc axis and compared with the actual voltages grid converter in order to generate the PWM switching signals to the IGBTs that constitute the grid converter.

Rotor Speed Control
The control system uses a torque controller in order to maintain the speed at 1.2 pu.A PI regulator is introduced to achieve this goal (see Figure 6).

Pitch Angle Control System
A PI controller is used to control the blade pitch angle in order to limit the electric output power to the nominal mechanical power.The pitch angle is maintained constant at zero degree when the measured electric output power is under its nominal value.When it increases above its nominal value, the PI controller increases the pitch angle to keep the measured power to its nominal value.The pitch angle  is proportional to the speed deviation.The control system is illustrated in Figure 7.

Simulation Results
The simulations were performed using MATLAB/Simulink software.In order to validate the control approach discussed in this paper, we present an operating point when the wind speed is constant equal to 15 m/s.For this simulation, we consider the parameters of generator, converters (Table 1), turbine (Table 2) and control parameters in Table 3.  Q ) exchanged with the network through the converters is set to (0 VAr), which guarantees a power factor close to unity.The switching frequency of the power switches of the grid converter and rotor converter is set to 5 kHz.
Figures 8(a) and 8(b) show the three phase voltages and currents at the grid.We also observe in Figure 8(c) that the DC bus voltage is well regulated to 1150 V. Figures 8(d) and 8(e) show the active and reactive power.Note that the DFIG wind system produces 1.5 MW.The turbine output power is 1 pu of its rated power, and the reactive power is controlled to 0 Var.In this paper, the wind speed is maintained constant at 15 m/s.The control system uses a torque controller in order to maintain the speed at 1.2 pu (see Figure 8(f)).The pitch angle is 8.7° as shown in Figure 8(g).

Conclusion
This paper has addressed the modelling and control of a wind system based on a DFIG.First, we explained why this wind system is most used now, including the economy realized through the design of static converters implemented.
Then we discussed the modelling of various components of the wind system.The aerodynamic and mechanical models of the turbine have been developed.Then, in order to establish different controllers for two converters, we developed models of DFIG.The controls of C grid and C rotor were detailed to provide independent control of active and reactive power while ensuring optimal operation of the turbine.
To validate the model and control of the global wind system, we performed simulation for an operating point at constant wind speed.The results showed that the active and reactive power of the wind system based on DFIG could be controlled independently while ensuring optimal active power supplied to the grid.

Figure 1 .
Figure 1.The wind turbine and the doubly fed induction generator system i

6 W
ind Turbine Cp Characteristic (pitch angle increases by step of 2 deg.)Cp Lambda Pitch angle 0 degree

Figure 4 .
Figure 4. Rotor-side converter control system for reactive power control error produced between the actual qr i component and the reference qr-ref i component is reduced to zero by a PI regulator.The output of this current regulator is qgc-control V , the quadratic voltage control generated by the rotor converter.The rotor voltages control are converted from d-q axis to the abc axis and compared to the actual voltages rotor in order to generate the PWM switching signals to the IGBTs constitute the rotor converter.
. An outer regulation loop regulates the DC voltage regulator at the DC bus bar capacitor.The output of the DC voltage regulator is the reference current dgc-ref i .This current is compared to the actual direct current generated by the grid converter dgc i in order to control active power flow.A PI regulator is introduced to the inner current regulation loop which controls the reactive power absorption or production via the quadratic current generated by the grid converter qgc i .

Figure 5 .
Figure 5. Grid-side converter control system

Figure 6 .
Figure 6.Rotor speed control system

Figure 8 .
Simulation results.(a) Three-phase voltages (pu) at the grid.(b) Three-phase currents (pu) at the grid.(c) DC bus voltage.(d) Active power in the grid.(e) Reactive power in the grid.(f) Rotor speed (pu) of DFIG.(g) Pitch angle Simulink.Global Journal of Computer Sciences: Theory and Research.7(2), 77-91.91 ), the rotor voltages are equal to

Table 2 .
Turbine parameters Parameter Value

Table 3 .
Control parameters Parameter