Modeling, Control and Simulation of DFIG for Maximum Power Point

Modeling, Control and Simulation of DFIG for Maximum Power Point Tracking

Mohammad Sleiman1,2, Bachir Kedjar3, Abdelhamid Hamadi3, Kamal Al-Haddad3 and Hadi Y. Kanaan2 1

2

Lebanese University, Faculty of Engineering – Branch III, Al Hadath, P.O. Box 14-6573, Beirut, Lebanon Saint-Joseph University, Faculty of Engineering – ESIB, Mar Roukoz, B.P. 11-0514, Beirut 1107 2050, Lebanon 3 Ecole de Technologie Supérieure, 1100 Rue Notre-Dame West, Montreal, Quebec, H3C 1K3, Canada E-mails: [email protected], [email protected], [email protected]

Abstract—This paper deals with the modeling, analysis, control and simulation of a doubly-fed induction generator (DFIG) driven by a wind turbine. This grid connected wind energy conversion system (WECS) is composed of DFIG and two back-to-back PWM voltage-source converters in the rotor circuit. A mathematical model of the machine, derived in an appropriate dq reference frame is established. The grid voltage oriented vector control is used for the grid side converter (GSC) in order to maintain a constant DC bus voltage and to compensate for reactive power at the power network. The stator voltage orientated vector control is adopted in the rotor side converter (RSC) control strategy, providing efficient handling of active and reactive power at the stator, as well as a maximum power point tracking (MPPT) method for the DFIG-based wind turbine. The proposed system is simulated for different operating conditions to illustrate the reliability of the control technique. Corresponding system simulation results under nonlinear load variations and wind speed transients are presented to demonstrate the significance of MPPT in WECS, and the effectiveness of adopted control technique. Index Terms—Doubly-Fed Induction Generator (DFIG), Modeling, Grid voltage oriented vector control (GVOVC), Stator voltage oriented vector control (SVOVC), MPPT.

I.

NOMENCLATURE

v sd , vsq , vrd , vrq

Stator and rotor voltages in dq frame.

i sd , isq , i rd , irq

Stator and rotor currents in dq frame.

R s , Rr , ω s , ω r

Stator and rotor resistances, voltage speeds. Stator and rotor fluxes in dq frame.

Ψ sd , Ψ sq , Ψ rd , Ψ rq

Rf , Lf

Stator, magnetizing, rotor inductances. Electromagnetic torque, mechanical speed DFIG pair of poles, slip ratio Grid filter resistance and inductance

Pg , Qg , Ps , Qs

Grid and stator, active and reactive powers

Vˆs

Grid maximum voltage amplitude

θs , θm , θr

Stator voltage, rotor electrical, slip angles

Lss , Lm , Lrr

Tem , Ωm p, s

II.

installations [1]. Today, wind power can compete with any other source of energy as a free of cost and non-polluting method of harnessing natural energy. Recently, intensive research has being carried out increasingly in most of the countries, resulting in various WECS configurations. One of these popular systems is the grid connected DFIG-based wind turbine. This variable speed DFIG system was adopted to improve the efficiency, power rating, cost benefit effectiveness etc. [2-4]. Variable speed DFIG-based wind turbines are an efficient solution for wind energy harvesting, due to the high variability nature of wind [5]. Such systems have many advantages including maximum power capture, smoothness of power transmission and less mechanical stresses [6]. This provides more flexibility in power conversion and also better stability in frequency and voltage control in the power systems to which such generators are connected [7]. However, due to variable speed operation, total energy output is much more in case of DFIG-based WECS, so capacity utilization factor is improved and cost of per unit energy is reduced [8]. A wind energy conversion system using DFIG is shown in Fig. 1.

INTRODUCTION

The total installed wind capacity around the world has crossed 254 GW, where it’s expected to reach 273 GW by the end of 2012. However, despite the annual growth records for the past few years, namely in 2008 by 29%, and in 2009 by 31%, an expected annual growth reduction due to slowdown in the Chinese market beside political uncertainties in several key markets, was observed consecutively, in 2010 by 25%, and 2011 by 20%, as a global decrease in wind energy systems’

Fig. 1.

Grid-connected DFIG with back-to-back converter and loads.

In the above system, the variable speed DFIG stator is directly connected to the grid/load and the rotor connected to a back-toback partially rated (20-30% of machine rating) voltage source power converter [9]. Vector oriented control enables decoupled control of active and reactive power flowing between the DFIG and the grid [10]. Traditionally the converter connected to the grid is called grid side converter (GSC), and the converter connected to the DFIG rotor circuit is called rotor side converter (RSC). Basically, the main role of the GSC is to control the DC bus voltage and the reactive power at the grid, and the RSC to control active and reactive power production at the stator. This is done by implementing an MPPT algorithm in the RSC, e.g. the optimal tip speed method, which ensures harvesting of maximum available mechanical power at a unity power factor. Both stator and rotor are capable of power

978-1-4673-5769-2/13/$31.00 ©2013 IEEE

generation, however the direction of active power flow through the rotor circuit is dependent on the wind speed and accordingly the generator speed, which can operate within ±33% around the synchronous speed [11]. III.

MODELING OF DFIG

The DFIG can be regarded as a traditional induction generator with a nonzero rotor voltage, with its stator windings directly connected to the grid [12]. Unlike short-circuited rotor induction machines, the DFIG’s rotor windings are connected to the grid through power converters. However, due to DFIG’s wounded rotor nature, mutual inductances change as the machine turns, resulting in a time varying mathematical model equations [13]. In fact, time varying model equations bring burden for the machine control; therefore an efficient axis transformation into the dq synchronous reference frame (Park’s reference frame) not only simplifies model equations into timeinvariant ones, but also reduces model mathematical representation from 3 axes to 2 axes, as shown in Fig. 2.

is dedicated to the power converter which consists of a back-toback converter, divided into a GSC and a RSC. The grid voltage oriented vector control as presented experimentally on a DFIG in [15], is used to control the GSC in order to maintain a constant DC bus voltage and to compensate for reactive power at the grid side. Whereas, stator voltage orientated vector control provides stable operation of the DFIG as stated in [16], which is used to control the RSC for active and reactive power control at the stator side.

Fig. 3.

A.

Fig. 2.

Equivalent d-q model of the DFIG in synchronous frame.

As derived in [14], stator and rotor dq voltage equations are obtained from DFIG equivalent circuit of Fig. 2, as follow: ⎧⎪ d Ψ sd ⎪⎪⎪ vsd = Rs isd + dt − ω s Ψ sq (1) ⎨ ⎪⎪ d Ψ sq + ω s Ψ sd ⎪⎪ vsq = Rs isq + ⎪⎩ dt ⎧⎪ d Ψ rd ⎪⎪ vrd = Rr ird + − ωr Ψ rq dt ⎪ (2) ⎨ ⎪⎪ d Ψ rq + ωr Ψ rd ⎪⎪ vrq = Rr irq + ⎪⎩ dt Stator and rotor flux space dq vector equations are given by (3) and (4): Ψsd = Lss isd + Lmird and Ψsq = Lss isq + Lmirq (3)

Ψrd = Lmisd + Lrr ird and Ψrq = Lmisq + Lrr irq

(4)

where Lss = Lm + Ls and Lrr = Lm + Lr . Torque expression in the generator convention, as discussed in [12], becomes: 3 L (5) Tem = p m (Ψ sq ird − Ψ sd irq ) 2 Lss IV. CONTROL STRATEGY Oriented vector control technique is adopted to control the DFIG-based WECS as depicted in Fig. 3. This control strategy

Vector control of DFIG with grid and rotor side converters.

Grid Side Converter Control

The adopted vector control strategy must fulfill the two main objectives of the grid side converter. 1) Regulate DC bus voltage. 2) Control reactive power exchanged bidirectionally between the rotor of the machine and the grid. Thus, by aligning the grid voltage vector with synchronous frame direct axis, its indirect axis component becomes null. Hence, the GSC control equations and grid power expressions are yet simplified, as shown in (6) and (7). ⎧ didg ⎪ ⎪ ) + vsd + ω s L f iqg v = −( R f idg + L f ⎪ ⎪ fd dt (6) ⎨ ⎪ diqg ⎪ ⎪ v = −( R f iqg + L f ) − ω s L f idg ⎪ ⎪ dt ⎩ fq ⎧ 3 3 ⎪ ⎪ Pg = ( vsd idg + vsq iqg ) become JJJJJJJG Pg = 2 vsd idg ⎪ 2 ⎪ (7) ⎨ ⎪ 3 3 ⎪ Qg = ( vsq idg − vsd iqg ) become Q = − v i ⎪ JJJJJJJG g ⎪ 2 2 sd qg ⎩ where v fd and v fq are GSC output voltage vector components,

idg , iqg and vsd are grid current and voltage respectively, as vsq = 0 . Based on the sign of a non-zero slip ratio ( s ), a part of DFIG’s generated active power is interchanged with the grid through the rotor, which can deliver/absorb grid’s power in super-/subsynchronous modes, respectively. Equation (7), states that active power and consequently DC bus voltage can be controlled via idg , whereas iqg can control reactive power flow in the grid. This strategy is depicted in Fig. 4. Thus the design of the current controllers follows directly from (8). ⎧⎪ v * = −K Δi − K pi dg ii ∫ Δidg dt + (vsd + ωs L f iqg ) ⎪⎪ fd (8) ⎨ ⎪⎪ v * = −K Δi − K Δ i dt − ( ω L i ) fq pi qg ii qg s f dg ∫ ⎩⎪ * * where Δidg = idg −idg and Δiqg = iqg −iqg . K pi , and Kii

are the proportional and integral factor of the inner current loop

respectively. Tii =

K pi is the integration time constant of the Kii

controller.

cross−term ⎧⎪

 ⎪⎪ di L rd ⎪⎪ vrd = Rr ird + σ Lrr − (σω r Lrr irq + ω r m Ψ sq ) ⎪ dt Lss ⎨ ⎪⎪ ⎪⎪ v = R i + σ L dirq + σω L i r rq rr r rr rd  

⎪⎪ rq dt ⎪⎩ cross−term

(11)

Lm2 ) is the machine’s leakage coefficient. Lss It is clear from the stator power expressions (10), that stator active power is controlled by ird , while irq controls stator reactive power. However, by introducing MPPT, the desired optimal electro-magnetic torque will force the DFIG to bring maximum available power to grid. The torque expression (5) becomes: where σ = ( Lrr −

3 Lm (12) p Ψ i 2 Lss sq rd The RSC control strategy is illustrated in Fig. 5. For the stator to operate at unity power factor, the flow of reactive power Tem =

Fig. 4.

Grid voltage oriented vector control block diagram.

The angular position of the grid voltage is detected using a PLL [17], which has good quality in terms of stability and of transient response [18]. This locked angle will be used to transform system variables to the dq reference frame. The DC bus voltage is maintained constant via the outer voltage PI controller which processes the error between reference and *

* from the stator side to grid is set to zero, thus irq can be determined from (10).

*

measured DC bus voltage and yields idg . While iqg is set to zero to compensate for reactive power at the grid side, the GSC provides needed magnetizing energy through the rotor for the DFIG. Finally the measured grid currents ( idg , iqg ) and *

*

reference currents ( idg , iqg ) are compared then processed by inner current PI controllers, in order to generate appropriate signals for the GSC. Furthermore, for the sake of future implementation of this work, processing and dead-time switching delays were accounted in controllers design, as introduced in [19].

Turbine Pow er Characteristics

Rotor Side Converter Control

12 m/s

1

In grid connected DFIG-based WECS, the RSC is responsible for controlling the DFIG in order to harvest the maximum available and affordable mechanical power at the wind turbine and to maintain a unity power factor at the stator. Thus by neglecting the stator resistance and under a balanced grid voltage assumption, the stator magnetic flux is considered to be constant and imposed by the grid. Thus, with stator voltage vector aligned with the direct axis, we get the stator fluxvoltage relations (9) as following:

vsd = Vˆs ≈−ωsΨsq and vsq = 0 ≈ ωsΨsd

Stator voltage oriented vector control block diagram

To track the optimal power operating points, which are in fact, peaks of the turbine’s power characteristics curve shown in Fig. 6. The optimal tip speed ratio method is adopted [20].

(9)

Now, with Ψ sd ≈ 0 and solving for ird in (3), then replacing in (7) and using (9) yields: 3L 3 vsd 2 3 Lm Ps = − m vsd ird and Qs = + v i (10) 2 Lss 2 ωs Lss 2 sd Lss rq The steady state rotor voltage expressions become:

Turbine output power (pu of nominal mechanical power)

B.

Fig. 5.

Max. power at base wind speed (12 m/s)

0.8 10.8 m/s

0.6 9.6 m/s

0.4

8.4 m/s

7.2 m/s

0.2

6 m/s 1 pu

0

-0.2

-0.4 0

Fig. 6.

0.2

0.4 0.6 0.8 1 Turbine speed (pu of nominal generator speed)

1.2

1.4

The turbine power characteristics curve

In this method, MPPT is achieved by keeping the tip speed ratio, which is the ratio of the turbine speed at the tip of a blade to wind velocity, to its optimal value, i.e. by setting the optimal rotor speed reference ( Ωm* ) to its corresponding measured wind speed ( Vw ), which can be done by using a look-up table. Now back to the adopted control law, once Ωm* is obtained

Initially the wind speed is 12 m/s, and the generator speed is pushed to a non-maximum power operating point (point A, 2340 rpm). The MPPT algorithm sets the reference rotational speed Ωm* to its optimal value, and the system starts to track its optimal path, as shown in Transition 1; then the system stabilizes and reaches its optimal speed after passing through a deceleration phase (point B, 11.7N.m , t=1.5 sec), as shown in Fig. 8. At this point, the electromagnetic and mechanical torques are equal to 11.7 N.m, which to be the machine optimal torque at this speed, if frictional losses were neglected. At t = 2 sec, a sudden change in wind speed from 12 m/s to 10 m/s causes a drop in the available wind energy and consequently a sudden drop in the mechanical torque applied on the machine from 11.7 N.m to 7.8 N.m (point C, 1800 rpm, 6 N.m). However, the mechanical speed of the turbine and generator cannot change instantaneously due to the moment of inertia, as shown in Transition 2. As a result, the speed reference Ωm* calculated by the MPPT block, is reflected on the torque reference Tem* by forcing the machine to decelerate, and thus the rotor speed decreases accordingly toward its new optimal point (point D, 1550 rpm, 7.8 N.m, t = 4 sec).

and compared with actual rotor mechanical speed, Tem* is processed using a classical PI controller [8], so ird * can be calculated from (12). Now the actual rotor currents ird and irq * are compared with the reference rotor currents ird * and irq

before being processed using inner PI current controllers, in a similar manner to the ones used for GSC, then added with cross-terms, to finally generate the control signals for the RSC.

RESULTS AND DISCUSSION

V.

The model of the WECS shown in Fig. 1 is developed and simulated in Simulink environment and SimPowerSystems blockset MATLAB’s graphical modeling and simulation environment. The DFIG studied in this WECS is a 2KW machine coupled with a squirrel-cage induction dynamometer from Lab-Volt (Model 8505). The parameters used in this work are listed in Table 1: Table 1.

Simulated WECS specifications

Grid

Vs ( LN , rms) f s ( Hz ) Lg (mH )

GSC 120 60 1

Pn (W ) R f (Ω) 0.1 N ( rpm) Vdc (V ) 400 Vs (V ) C (mF ) 1.32 Vr (V ) Non-Linear Load η L f (mH )

NA Linear Load (P, Q)(W, Var) (700, 500) Current (A)

NA

12

2/6

J m ( Kg .m 2 )

DFIG 2000 Ls (mH ) 1720 120 360 77% 0.05

Rs (Ω) Lm (mH ) Lr (mH ) Rr (Ω ) Dm ( N .m.s )

4 1.18 46 38 10 0.005

This DFIG coupled system can be used to emulate a DFIG-based wind turbine with various wind patterns, due to its capability to drive the DFIG in torque mode. The power convention is given in Table 2: Table 2.

Adopted power convention

Power Convention

Grid

Stator & Rotor

P&Q > 0

generating

receiving

P&Q < 0

receiving

generating

GSC

Loads

receiving receiving generating

NA

Fig. 8.

The following trials will reveal system’s behavior during various operating conditions, such as wind speed variations in which MPPT algorithm performance was validated, step load variations, and step wind speed transients. A.

Torques Tem, Tm, and Speed during transition

Finally the system reaches its steady-state (optimal) operating point, after 2 seconds from the sudden wind speed drop, where both electromagnetic and mechanical torques are equal, (point D, 7.8 N.m, t = 4 sec).

MPPT in action, during step wind speed variation.

Grid Active and Reactive Power

A step change in wind speed from 12 m/s to 10 m/s is investigated. The torque and speed behavior during this transition is studied as shown in Fig. 7.

(W, Var)

0 -500 W Var

-1000 -1500 -2000 1.5

2

2.5

3

3.5

4

Sum of Stator and GSC Active and Reactive Power

(W, Var)

0 -1000 W Var

-2000 1.5

2

2.5

3

3.5

4

3.5

4

Available Mechanical Power

(W)

0 -1000 -2000 1.5

2

2.5

3

Load Active and Reactive Power

(W, Var)

500

Fig. 7.

Torque vs. speed during wind speed transients

400

W Var

300 200 1.5

2

2.5

3 Time

Fig. 9.

Power balance during the wind speed transition

3.5

4

During this wind speed transition, a unity power factor operation was maintained. Active power delivered to grid dropped from -1100W to -500W, concurrently, with a drop in DFIG’s generated power from -1500W to -900W. This drop is a consequence of mechanical power drop from -2000W to 1100W. DFIG provided the RL load (400W, 280Var) with the needed reactive power, as shown Fig. 9. The net power balance is attained in this trial.

During this trial, the stator generates 2KW; the rotor consumes 600W, while the GSC compensates for the RL load of 500Vars, as shown in Fig. 11. The load variation is reflected in the power balance plots. It is clear that whenever the load consumption increases, the grid received power decreases; initially the grid received 700W when no nonlinear load connected, but it delivers 100W when the load consumption increases to 1500W (800W+700W).

B.

C.

Non-Linear Load variations

In Fig. 12, a sudden generator speed variation (from 1700 rpm till 2370 rpm) was investigated. During this step change the rotor current faced a phase shift, and the DFIG encounters a transition from sub- to super-synchronous operation mode. The DC voltage is maintained at 400V, and rotor current frequency stepped from 3.3 Hz to -19 Hz. 0 -200 2

Grid Current (A)

10 Stator Current (A)

200

Stator Current (A)

Grid Voltage (V)

In Fig. 10, non-linear load variations are investigated. Initially a linear RL load of (700W, 500Var) was connected. Then a variable current controlled non-linear load was connected and (increased from 0W till 600W, then till 800W, after that it was decreased to 600W, then to 0W) at periods (t = 0.4 sec, 0.5 sec, 0.6 sec, and 0.7 sec) respectively. During this transition, the GSC compensated for the current harmonics caused by the nonlinear load. The grid received power dropped as the load current increased, while maintaining a sinusoidal grid current wave form. Also the DC voltage was maintained at 400V, disregarding the negligible over- and under-voltages within the ± 1% limits, during this load variations.

Sub- to Super-synchronous step speed transition

0 -5 0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.7

0 -5 0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.7

Rotor Current (A)

Load Current (A)

4 2 0 -2 -4 0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.7

GSC Current (A)

5

0

-5 0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.7

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.7

0.4

0.45

0.5

0.55 Time

0.6

0.65

0.7

0.7

3.5

4

4.5

5

5.5

6

2.5

3

3.5

4

4.5

5

5.5

6

2.5

3

3.5

4

4.5

5

5.5

6

2.5

3

3.5

4

4.5

5

5.5

6

2.5

3

3.5

4

4.5

5

5.5

6

10 0 -10 2

GSC Current (A)

5

DC Bus Voltage (V)

Grid Current (A)

-10 0.35

3

0 -10 2

Load Current (A)

5

2.5

10

2 0 -2 2 5 0 -5 2 20

Sub-Synchronous

Super-Synchronous

0 -20 2

2.5

3

3.5

4

4.5

5

5.5

6

2.5

3

3.5

4 Time

4.5

5

5.5

6

410 400 390 2

Fig. 12.

System voltages and currents during speed transitions.

Rotor Current (A)

20

0

-20 0.35 DC Bus Voltage (V)

405

400

395 0.35

Fig. 10.

System voltages and currents during load variations. Grid Active & Reactive Power

500

This sudden speed reference change from 1700 rpm till 2370 rpm, due to wind speed variation, led to a step change in the mechanical torque, whereas the electromechanical torque was yet unchanged. This torque difference caused the machine to decelerate until reaching its optimal speed reference at 2370 rpm, as shown in Fig. 13. It’s worth noting that the little difference between mechanical and electromechanical torque is due to friction.

(W, Var)

0

Mechanical and Electromechanical Torques -8 Tm Tem

-500 -10

-1000 0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.7

0 (W, Var)

-12 (N.m)

Stator Active & Reactive Power

-14 -16

-1000

Friction effect -18

-2000 0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

-20

0.7

2

2.5

3

3.5

4

4.5

5

5.5

6

GSC Active & Reactive Power

(W, Var)

500 DFIG mechanical speed response to a step speed reference 2500

0

2400

-500 2300

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.7

(W, Var)

1500

2200 (RPM)

Load Active & Reactive Power P Q

2100 2000 1900

1000

Mech. Speed Reference Speed

1800

500 0.35

Fig. 11

1700

0.4

0.45

0.5

0.55 Time

0.6

0.65

System active and reactive power during load variations.

0.7

0.7

1600

2

Fig. 13

2.5

3

3.5

4 Time

4.5

Torques Tem, Tm, and Speed during transition.

5

5.5

6

REFERENCES [1]

Before the sudden speed reference took place, DFIG was generating 1700 W and the grid was receiving 1000 W. At t = 3 sec, the available mechanical power increased from 2000 W to 3100 W, whereas the DFIG generated power raised to 2500 W, as shown in Fig. 14. In fact this step change didn’t perturb the unity power factor operation at the grid. Note that this case represents an over-rating operation of the DFIG. Grid Active and Reactive Power (W, Var)

0 -1000 -2000 2

2.5

3

3.5

4

4.5

5

5.5

6

4.5

5

5.5

6

4.5

5

5.5

6

4.5

5

5.5

6

Sum of Stator and GSC Active and Reactive Power (W, Var)

0 -1000 -2000 -3000

2

2.5

3

3.5

4

Available Mechanical Power (W, Var)

-1500 -2000 -2500 -3000 -3500

2

2.5

3

3.5

4

Load Active and Reactive Power (W, Var)

500 400 300 200

2

Fig. 14.

2.5

3

3.5

4 Time

Power balance during speed reference transition.

VI.

CONCLUSION

The modeling, control and simulation of a 2KW-DFIG coupled with a wind turbine emulator from Lab-Volt has been carried out for grid connected WECS. The oriented vector control techniques and the 2 back-to-back voltage source converters has been found capable to compensate for grid reactive power, and to drive the DFIG to track the maximum power points from the available wind regime. The DFIG operation principles were illustrated in the simulation results. A case study was provided for system in-depth analysis; the DFIG was simulated under nonlinear load and sudden wind speed variations, where the MPPT algorithm had shown an expected reliable performance. The DFIG has been operated at unity power factor while delivering maximum power to the grid. The DFIG’s rotor could share power generation up to 30% of the machine’s rating with a 30% rated power converter of machine’s rated power, so losses in converters are reduced because only a fraction of the total power is handled by the converter. In general the DFIG-based WECS are efficient and can capture maximum power from the available wind. Therefore, DFIG-based WECS are one of the best solutions to harness wind energy. ACKNOWLEDGEMENT The authors gratefully thank the Agence Universitaire de la Francophonie (AUF), the Research Council of Saint-Joseph University, the National Council for Scientific Research (CNRS), and Canada Research Chair in Energy Conversion and Power Electronics for their financial support.

World Wind Energy Association (WWEA) Half-year Report 2012 (accessed on Nov. 20, 2012) [Online]. Available: http://www.wwindea.org/home/index.php [2] M. Ghofrani, A. Arabali, and M. Etezadi-Amoli, "Modeling and simulation of a DFIG-based wind-power system for stability analysis," in Power and Energy Society General Meeting, 2012 IEEE, 2012, pp. 18. [3] H. S. Kim and D. D. C. Lu, "Review on wind turbine generators and power electronic converters with the grid-connection issues," in Universities Power Engineering Conference (AUPEC), 2010 20th Australasian, 2010, pp. 1-6. [4] B. Shen, B. Mwinyiwiwa, Y. Zhang, and B.-T. Ooi, "Sensorless Maximum Power Point Tracking of Wind by DFIG Using Rotor Position Phase Lock Loop (PLL)," IEEE Trans. Power Electron., vol. 24, no. 4, pp. 942-951, 2009. [5] H. Li and Z. Chen, "Overview of different wind generator systems and their comparisons," Renewable Power Generation, IET, vol. 2, no. 2, pp. 123-138, 2008. [6] J. Hu, J. Zhu, D. G. Dorrell, Q. Ma, Y. Zhang, and W. Xu, "Control strategies of variable-speed wind system under new grid code requirement-A survey," in IECON 2010 - 36th Annual Conference on IEEE Industrial Electronics Society, 2010, pp. 3061-3066. [7] M. Tazil, V. Kumar, R. C. Bansal, S. Kong, Z. Y. Dong, W. Freitas, and H. D. Mathur, "Three-phase doubly fed induction generators: an overview," Electric Power Applications, IET, vol. 4, no. 2, pp. 75-89, 2010. [8] B. Singh, S. K. Aggarwal, and T. C. Kandpal, "Performance of Wind Energy Conversion System Using a Doubly Fed Induction Generator for Maximum Power Point Tracking," in Industry Applications Society Annual Meeting (IAS), 2010 IEEE, 2010, pp. 1-7. [9] A. Tapia, G. Tapia, J. X. Ostolaza, and J. R. Saenz, "Modeling and control of a wind turbine driven doubly fed induction generator," IEEE Trans. on Energy Conversion, vol. 18, no. 2, pp. 194-204, 2003. [10] S. Li and T. A. Haskew, "Analysis of Decoupled d-q Vector Control in DFIG Back-to-Back PWM Converter," in Power Engineering Society General Meeting, 2007. IEEE, 2007, pp. 1-7. [11] R. Datta and V. T. Ranganathan, "Variable-speed wind power generation using doubly fed wound rotor induction machine-a comparison with alternative schemes," IEEE Trans. on Energy Conversion, vol. 17, no. 3, pp. 414-421, 2002. [12] Y. Lei, A. Mullane, G. Lightbody, and R. Yacamini, "Modeling of the wind turbine with a doubly fed induction generator for grid integration studies," IEEE Trans. on Energy Conversion, vol. 21, no. 1, pp. 257264, 2006. [13] E. Tremblay, S. Atayde, and A. Chandra, "Comparative Study of Control Strategies for the Doubly Fed Induction Generator in Wind Energy Conversion Systems: A DSP-Based Implementation Approach," IEEE Transactions on Sustainable Energy, vol. 2, no. 3, pp. 288-299, 2011. [14] G. Abad, J. Lopez, M. A. Rodriguez, L. Marroyo, and G. Iwanski, in Doubly Fed Induction Machine: Modeling and Control for Wind Energy Generation, First ed: John Wiley & Sons, Inc., 2011. [15] R. Pena and J. C. Clare, "Doubly fed induction generator using back-toback PWM converters and its application to variable-speed wind-energy generation," Proc. IEEE, Electric Power Applications, vol. 143, no. 3, pp. 231-241, 1996. [16] S. Chondrogiannis and M. Barnes, "Stability of doubly-fed induction generator under stator voltage orientated vector control," Renewable Power Generation, IET, vol. 2, no. 3, pp. 170-180, 2008. [17] V. Kaura and V. Blasko, "Operation of a phase locked loop system under distorted utility conditions," IEEE Trans. Ind. Applicat., vol. 33, no. 1, pp. 58-63, 1997. [18] S. Rahmani, K. Al-Haddad, and F. Fnaiech, "A new control technique based on the instantaneous active current applied to shunt hybrid power filters," in IEEE 34th Annual Power Electronics Specialist Conference, PESC '03., 2003, pp. 808-813 vol.2. [19] V. Blasko and V. Kaura, "A novel control to actively damp resonance in input LC filter of a three-phase voltage source converter," IEEE Trans. Ind. Applicat., vol. 33, no. 2, pp. 542-550, 1997. [20] M. Soliman, O. P. Malik, and D. T. Westwick, "Multiple Model Predictive Control for Wind Turbines With Doubly Fed Induction Generators," IEEE Transactions on Sustainable Energy, vol. 2, no. 3, pp. 215-225, 2011.