978-1-4799-7947-9/15/$31.00 ©2015 IEEE

Predictive current control of a wind energy conversion system based DFIG via direct matrix

converter Said Chikha Kamel Barra Abdellatif Reama

Electrical Engineering and Electrical Engineering and Embedded systems department Automatic Laboratory LGEA Automatic Laboratory LGEA ESIEE Paris, Cité Descartes University of Oum El Bouaghi University of Oum El Bouaghi, 93162 Noisy le Grand cedex, France Oum El Bouaghi, 04000. Algeria Oum El Bouaghi, 04000. Algeria chikhasaid@hotmail.fr barakamel@yahoo.fr a.reama@esiee.fr

Abstract— The paper presents a predictive direct power

control of a Doubly Fed Induction Generator (DFIG) via a Direct Matrix Converter (DMC) for use in variable speed Wind Energy Conversion System (WECS). The proposed control method combines the merits of Finite States Model Predictive Control (FSMPC) in term of flexibility to the ones of DFIG control in term of maximum power extraction over a large range of wind speeds. The proposed control algorithm selects the switching state of the Direct Matrix Converter (DMC) that minimizes the error between rotor currents predictions to their computed values for all different voltage vectors. The optimal voltage vector that minimizes a cost function is then applied to the DFIG rotor terminal. Moreover, the proposed predictive control is easily extended to minimize the stator and rotor reactive power with unity power factor operation. Simulation results show that the proposed control method is intuitive since it is simple, multi-objective, avoids inner loops and provides best dynamic performance.

Keywords— Direct Matrix Converter, Predictive Current Control (PCC); Doubly Fed Induction Generator; Wind Energy Conversion System.

I. INTRODUCTION Over the two last decades, wind energy conversion systems

(WECS) have attracted more and more attention for maintaining the continuously growing energy needs of humanity. Wind energy systems using a doubly fed induction generator (DFIG) is the most popular configuration due to the advantages of variable speed operation range and its four quadrants active and reactive power capabilities. Generally, the stator of DFIG is directly connected to the grid whereas the rotor is connected to the grid via two back to back bidirectional converters where the Rotor Side Converter (RSC) controls the active and reactive powers of the generator that flow between the stator and the ac grid while the Grid Side Converter (GSC) controls the DC link voltage and ensures operation of high power factors. As the rotor speed is fluctuating due to wind speed variations, the electric power of the rotor is reversible depending on whether the machine operates in either sub-synchronous mode or super-synchronous mode. Note that the main advantage of the WECS based DFIG machine is the perfect decoupling between active and reactive power control by controlling rotor currents [1][2][3].

Since power converters have a discrete nature, Finite-States Model Predictive Control (FS-MPC) appears as an attractive alternative that offers a completely different and powerful approach to control power converters. Several advantages of this control method can be cited such as its fast dynamic response; it does not need for linear controllers in inner loops, flexible method, good performance and can be implemented with standard commercial microprocessors. The method is based on the fact that a finite number of possible switching states can be generated by power converter ( 8 states for a two-level three- phase inverter, 27 states for a three-level VSI, 27 states for a DMC,…). For the selection of the appropriate switching state to be applied to the system, a quality function must be defined and then evaluated for the predicted values on each sampling interval and the optimal switching state that minimizes the quality function is selected to be applied during the next sampling time [4][5][6][7].

Direct Matrix Converters (DMC) have recently received a considerable attention because of their numerous merits on traditional AC-DC-AC converters such as no DC-link capacitor, the bi-directional power flow control (the capability of regeneration), the sinusoidal input-output waveforms and adjustable input power factor, but the biggest drawback of this technology is the high control complexity [7][8].

In this paper, a predictive control method is used to control simultaneously the DFIG rotor currents and rotor reactive power without use neither linear controllers nor inner loops. Simulation results are presented to confirm the effectiveness of the predictive control method.

II. WIND TURBINE CHARACTERISTICS The turbine allows converting the aerodynamic energy into

mechanical energy. The wind speed v applied to the blades of the turbine causes its rotation, and creates mechanical power on the shaft of the turbine, symbolized Pt and given by:

32...).,(.21

vRCP pt πρβλ= (1)

Where, is the air density (kg/m3), R is the blade radius (in m), Cp is the performance coefficient of the turbine which is a

2015 6th International Renewable Energy Congress (IREC)

function of the pitch angle of rotor blades (in degrees) and v is the wind speed in m/s. The tip-speed ratio is given by:

v

Rt .Ω=λ (2)

where t is the wind turbine rotor speed (rad/s). The power coefficient Cp( , ) is the aerodynamic efficiency of the wind turbine also depends on the characteristic of the turbine. This coefficient has a theoretical limit, called the Betz limit, equal to 0.593 and which is never achieved in practice. In this work we used an approximate expression of the power coefficient as a function of the relative speed and the pitch angle of the blades

[1],[2],[3]:

)2).(3.(00184.0

)2.(3,034,14

)1,0.(sin))2.(00167,035.0(),(

−−−

−−

+−−=

βλ

β

λπββλpC

(3)

The Cp( , ) characteristic (3) is illustrated in Fig.1 where it shows the aerodynamic efficiency Cp of the used 2 MW turbine versus the tip speed ratio for different values of the pitch angle .

05

1015

2025

0

5

10

150

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Pitch angle (B°)Tips speed ratio (lamda)

Pow

er c

oeffi

cien

t (C

p)

Fig. 1. 3D plot of power coefficient Cp ( , )

A. DFIG Model By choosing a d-q reference frame synchronized with the

stator flux, also,by setting the quadratic component of the stator flux to the null value and by neglecting the stator resistance, the electrical equations of the DFIG are written as follows [1][2]:

−−−=

+−=

).

.......(.1

).....(.1

s

smdrrsqrrqr

r

dr

qrrsdrrdrr

dr

LvL

giLgiRVLdt

di

iLgiRVLdt

di

σωσ

σωσ

(4)

Where (Vdr, Vqr) are rotor voltage components, m is the stator-rotor transformation ratio, (idr,iqr) are rotor current components, (Rr, Lr, Lm) are rotor resistance, rotor inductance and mutual inductance respectively. The expressions of stator active and reactive powers are then given by:

−=

−=

drs

ms

s

sss

qrs

mss

iL

LmvL

vQ

iLLm

vP

....

..

.

φ (5)

B. Direct matrix converter Despite some drawbacks such as high number of power

semiconductor devices, the limitation of maximum load voltage to 86% of the supply voltage, no need for energy storage element, the matrix converters have received recently a wide attention especially in motion control. The three-phase to three-phase matrix converter has been extensively researched due to its potential as a replacement for the traditional AC-DC-AC converter in AC motor drives for the following benefits [6][7][8]: • Adjustable input displacement factor, irrespective of the load • The capability of regeneration (Four-quadrant operation) • High quality input and output waveforms • The lack of bulky and limited lifetime energy storage components, such as electrolytic capacitors.

Consider a three phase to three phase matrix converter consisting of 9 bi-directional switches. The switching function SjJ(t) takes the value ‘0’ when it is open and ‘1’ when it is closed as given by the following expressions:

{ } { }CBAJandcbajforopenedjJS

closedjJStjJS ,,,,,,

0

1)( ∈∈= (6)

Due to the direct connection with voltage sources, the input lines must never be shorted. If the switches cause a short circuit between the input voltage sources, infinite current flows through the switches and damages the circuit. Also, due to the inductive nature of typical loads, the output terminals must not be open-circuited. If any output terminal is open-circuited, the voltage across the inductor (and consequently across the switches) is infinite and switches will be damaged due to the over-voltage. As a result, switches for each output phase must be controlled based on the following expression by:

1=++ jCSjBSjAS (7)

With these constraints, the bidirectional switches can assume only twenty-seven (27) allowed switching combination modes.

Taking into account the valid switching states, the output voltages and the input currents can be calculated by:

ki

kjJPHL

ko vSTv ).(= (8)

kr

TkjJPHPH

ki iSTi .)(= (9)

Where vo is the output voltage defined as vok [voa

k vobk voc

k]T, vi is the converter input voltage vi

k [viak vib

k vick]T, ir is the load

current (rotor current) irk [ira

k irbk irc

k]T, iie is the converter input current ie

k [iAk iB

k iCk]T. T(SkjJ) is the direct instantaneous

commutation matrix of the DMC as a function of the switches SjJ in the k sampling time, defined as [11]:

−−−−−−−−−

=

aCScCSaBScBSaAScAScCSbCScBSbBScASbASbCSaCSbBSaBSbASaAS

PHLT

=

cCcBcA

bCbBbA

aCaBaA

PHPH

SSSSSSSSS

T (10)

Fig. 2. Wind energy conversion system based DFIG controlled by a DMC in

the rotor side.

III. CONTROL STRATEGY Several control algorithms of the WECS have been reported

recently through the literature whether for a wind system feeding an isolated load, or the network. The configuration of the present work is given by fig.2 where the rotor of the DFIG is connected to the grid via a DMC and a RLC filter assuming that +/- 30% of DFIG nominal power is exchanged with the grid whereas the rest of this power is directly generated by the stator to the grid. The RLC filter is used to avoid overvoltages and current harmonics. The Maximum Power Point Tracker

MPPT controller is used to track closely the maximum power point of the wind turbine (turbine rotor works closely on the Optimal Regime Characteristic ORC).

A. MPPT control strategy In order to obtain the maximum captured energy from the

wind, the designed controller should guarantee that the turbine is kept on the MPPT curve as the wind velocity changes. The based control is to adjust the electromagnetic torque on the shaft of the DFIG in order to fix the rotational speed to a reference value.

The electromagnetic reference torque C*em is obtained at the

output of the speed PI controller as it is shown by fig.4. This controller allows the tracking of the DFIG rotational speed and mitigates the effect of mechanical torque Cm considered as a perturbation. For a given operating point (fixed speed wind), it is desired that the mechanical power is maximum, which corresponds to the maximum value of the coefficient Cpmax. This is obtained if the relative velocity reaches its optimal value opt (for a pitch angle constant and equal to 2° in our case study). The reference rotational speed of the turbine *

t is then obtained from the equation (2) and it is defined by:

R

voptt

.* λ=Ω (11)

Fig. 3. MPPT controller.

B. Control of DFIG Generally, the field Oriented Control (FOC) concept of the

DFIG is based on stator active-reactive power control, however this solution is suitable only when the machine operates in normal regime, but when the grid is affected by disturbances and faults, the measure of stator powers is not appropriate, so the rotor currents are chosen to be directly controlled in the studied system. The references for rotor current components should be imposed in the assumption of constant stator flux module as:

Roptλ

G +-

PI

β

v

*tΩ

*mΩ

*emC

mΩ

0 500 1000 1500 200 0 2500 3000 35000

0. 5

1

1. 5

2

2. 5x 1 06

vRtΩ

G1

pCvR 232

ρλ

π G1

+- fJs +

1

mΩ

tΩ

λ

pC

tC

mC

MPPT controller

Turbine model

iar ibr icr

DFIG

Direct Matrix Converter

voa

voc

via

vib

vic

Rf,Lf

Cf

ias

ibs ics

Rotor power

o

Gear box

Aeroturbine

Grid

Stator power

Input filter

Wind

vob

iA

iB

iC

iga

igb

igc

** .... em

sm

sqr C

LmpL

iφ

−= (12)

Fig. 4. DFIG rotor current predictive control block diagram.

Similarly, the direct rotor current component is used to control the generated stator reactive power and can be given by:

** .... s

ms

s

m

sdr Q

LmvL

Lmi −=

φ (13)

C. Predictive Control The proposed predictive control strategy is based on the

fact that only a finite number of possible switching states can be generated by a Direct Matrix Converter. The finite set of states of the switches SaA,SbA,…,ScC contains only twenty seven (27) different voltage active vectors that can be applied on terminal rotor of the DFIG. The dynamic model of the studied

system is given by the dynamics of the rotor current components expressed in relations (4).

The predicted values of rotor current components are used to evaluate a cost function F that minimizes the quadratic error between predicted values and their references and the switching state that produces the minimum value of this cost function is selected to be applied on machine terminals in the next sampling time according to receding horizon control. Assuming that it is possible to define a first order approximation for the derivatives due to the first order nature of the state equations of DFIG model, where Ts is the sampling period. These predictions are given by:

+

+−−−=+

++−=+

)(

).

...)(....)(.)((

.)1(

)())(....)(.)((.

)1(

kiL

vLmgkiLgkiRkv

LT

ki

kikiLgkiRkvL

Tki

qr

s

smdrrsqrrqr

r

sqr

drqrrsdrrdrr

sdr

σωσ

σωσ

(14) The quality function is then defined to satisfy the dynamic

performance of the control system. This quality function is computed every sampling time for each possible commutation state of the converter to select the one with the smallest error in order to be applied at the beginning of the next sampling period. This quality function can be defined as:

2*2*]27..1[ ))1()1(())1()1(( +−+++−+= kikikikig qrqrdrdr (15)

IV. MINIMIZATION OF THE REACTIVE POWER One of the most benefits of DMC converter is the possibility to control the displacement factor in the grid side by minimizing the input reactive power transited via the rotor. The input filter model can be described by the following continuous-time equations [4][7][8]:

dttdv

Ctiti

tvdt

tdiLtiRtv

ifeg

is

fsfs

)()()(

)()(

)()(

+=

++= (16)

Where Lf, Rf and Cf are the inductance, resistance and capacitance of the line filter respectively. The filter input side can be represented by state space model as:

)()()( tuBtxAtx cc +=•

(17)

where: =)()(

)(titv

txg

i , =)()(

)(titv

tue

s

−−=

fff

fc LRL

CA

//1/10 −

=0/1/10

f

fc L

CB

Direct Matrix

converter

iar

ibr

icr DFIG

0 500 1000 1500 2000 2500 3000 35000

0. 5

1

1. 5

2

2. 5 x 106

op t / R

*

Cem*

MPPT controller

s.mp.m.LsL

−

iqr*

Grid

SaA… ScC

abc dq

Qs*

m.m.LsvsL

*s.Qmm.L

s −

idr*

iqr idr

voa

vob

voc

Predictive model

Cost function

minimization

idr(k+1)

via vib

vic

Rf

Lf

Cf Cf

iqr(k+1)

igabc currents

ias ibs ics

n

Wind

Gear box

Aero turbine

stator power

Cf

Lf Lf

Rf Rf

The discrete-time state space model is determined as:

+=+

+)()(

)()(

1()1(

kikv

Bkikv

Atkikv

e

sq

g

iq

g

i (18)

Where:

scTAq e

AAAA

A ==2221

1211 ,

cqcq BIAABBBB

B )( 221

2221

1211×

− −== (19)

Finally, we compute the filter input current ig and the capacitance voltage vi by the following relations:

)()()()()1( 12111211 kiBkvBkiAkvAkv esgii +++=+ (20)

)()()()()1( 22212221 kiBkvBkiAkvAki esgig +++=+ (21)

The instantaneous reactive input power that flows between the grid and the rotor via the DMC can be predicted, based on predictions of the input voltage (stator voltage) and grid current as:

)1()1()1()1()1( ++−++=+ kikvkikvkQ gqsdgdsqg (22)

Due to the flexibility of the FS-MPC, multiple objectives can be achieved at the same time by adding more functions in the global cost function g. A third term is added in the cost function to correct the power factor in the grid side by the following modified quality function:

2*

2*2*]27..1[

))1()1((

))1()1(())1()1((

+−++

+−+++−+=

kQkQ

kikikikig

gg

qrqrdrdr

λ (23)

where is a weighting factor.

V. SIMULATION RESULTS The proposed predictive control for WECS of fig.4 is

tested in Matlab environment with a sampling time of 10 s, considering a DFIG of 2MW for high power generation system whose parameters are given in the Appendix. The first test is used to control only the rotor currents without minimization of the reactive power Qg ( =0) by using the cost function (15) for minimization. In fig.5, we illustrate the rotor line currents versus the wind speed profile for both sub synchronous and super synchronous regimes.

The generated stator active and reactive powers are illustrated by fig.6 for a stator reactive power reference settled to 0 VAR. The tracking performance shows high dynamic performance for both stator powers and electromagnetic torque since the powers are perfectly decoupled and track their references accurately and precisely. As a consequence, the stator current in fig.7 appears highly sinusoidal and is achieved

in opposite phase with the grid-stator voltage because the machine operates in generating mode.

Fig. 5 Rotor currents versus speed generator variations

Fig.6. Stator active power Ps, reactive power Qs and electromagnetic torque of the DFIG

The harmonic spectrum of the stator current is shown in Fig .8. We can see that the THD of this current is less than 4.6%, meaning that the predictive current control gives a good current quality although the switching frequency is variable; the THD is calculated up to 4000 Hz.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-2000

-1500

-1000

-500

0

500

1000

1500

2000

Time [s]

Stat

or c

urre

nt [A

]an

d S

tato

r vol

tage

[V]

VoltageCurrent

Fig.7. Stator current in opposite phase with the stator voltage

0 0.5 1 1.5 2 2.5 3 3.5 4-1000

-500

0

500

1000

1500

2000

Time [s]

Gen

erat

or sp

eed

[tr/m

in]

and

Rot

or c

urre

nt [A

]

super-synchronous

mode

sub-synchronous

mode

synchronous speed

0 0.5 1 1.5 2 2.5 3 3.5 4

-2

-1

0

x 10 6

0 0.5 1 1.5 2 2.5 3 3.5 4-15000

-10000

-5000

0

Time [s]

TeT*e

Ps

P*sQsQ*s

Stat

or a

ctiv

e [W

] an

d re

activ

e pow

er [V

AR

]

Elec

trom

agne

tic

torq

ue [N

.m]

The second test is performed now by minimizing the cost function (236). Fig.9 illustrates the profile of reactive power Qg without minimization ( =0) in the range [0-2]s and with minimization ( =0.1) in the range [2-4]s. The tracking performance of rotor currents and powers are similar to those of fig.5, fig.6 and fig.7. One can see that before activating the reactive power minimization process in [0-2]s, Qg is fluctuating and the input current ig presents high distortion and different phase with the related grid voltage, however, when the minimization process is activated at t=2s, the reactive power Qg tends to zero that makes the input current ig in sinusoidal form and in phase with the grid voltage during the sub-synchronous mode, whereas, when the machine operates in super-synchronous mode, this current is also sinusoidal but achieved in opposite phase with the grid voltage as can be seen in fig.10.

0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27-2000

-1000

0

1000

2000

Time (s)

0 500 1000 1500 2000 2500 3000 3500 4000

1

2

3

4

Frequency (Hz)

Fundamental (50Hz) = 1437 , THD= 4.55%

Mag

(% of F

unda

men

tal)

Fig.8. stator current spectrum

0 0.5 1 1.5 2 2.5 3 3.5 4-1

-0.5

0

0.5

1 x 106

Time [s]

Rea

ctiv

e po

wer

m

inim

izat

ion

[Var

]

Fig.9 Reactive power Qg without minimization ( =0) and with minimization ( =0.1) applied at t=2s.

VI. CONCLUSION

The paper presents a predictive direct rotor current control of wind energy conversion system using a DFIG machine via a direct matrix converter DMC. The flexibility of

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2-1000

-500

0

500

1000

1500

2000

Time [s]

Inpu

t cur

rent

[A] a

nd in

put v

olta

ge [V

]

DFIG speedsuper synchrounos mode

Sub synchrounos mode

Fig.10. Input current ig and grid voltage for both sub-synchronous and super-synchronous mode when activating the reactive power minimization process ( =0.1).

predictive control strategy allows the minimization of the reactive power that flows between the rotor and the grid. The method avoids the use of any linear or nonlinear controllers in inner loops except for the external speed loop. The control scheme is very simple and powerful since it uses discrete model of the converter to predict the behavior of the system. The optimal suited converter switching state is obtained from the 27 possible combinations by considering a cost function that includes the current errors. Simulation results show accurate and precise tracking performance; also a unity power factor in the grid side can be achieved by minimizing the rotor reactive power for both sub-synchronous and super-synchronous modes. The FS-MPC method shows that multiple objectives can be obtained simultaneously by adding more terms in the global cost function.

VII. REFERENCES [1] S. El Aimani, “Modelling and control structures for variable speed wind

turbine”, Multimedia Computing and Systems (ICMCS), 2011 International Conference on, pp 1-5, April 2011.

[2] T. Mesbahi, T. Ghennam, T. ; E. M. Berkouk, “A Doubly Fed Induction Generator for wind stand-alone power applications (Simulation and experimental validation)”, Electrical Machines (ICEM), 2012 XXth International Conference on, pp 2028-2033, 2-5 Sept 2012.

[3] A. Bouharchouche, E. M. Berkouk, ; T. Ghennam, B. Tabbache, “Modeling and control of a Doubly fed induction generator with battery-supercapacitor hybrid energy storage for wind power applications”, Power Engineering, Energy and Electrical Drives (POWERENG), 2013 Fourth International Conference on , pp 1392 – 1397, 13-17 May 2013.

[4] J. Rodriguez et al.,“Predictive Torque and Flux Control of an Induction Machine fed by an Indirect Matrix Converter with Reactive Power Minimization ”; IEEE Transactions on power Electronics , Vol. 978-1-4244-6392, March 2010.

[5] M. E. Rivera, René E. Vargas José R. Espinoza José R. Rodríguez “Behavior of the Predictive DTC based Matrix Converter under Unbalanced AC Supply”, 42nd IAS Annual Meeting. Conference Record of the 2007 IEEE pp. 202-207.

[6] R. Vargas, J. Rodriguez, U. Ammann, and P. Wheeler, "Predictive Current Control of a Induction Machine Fed by a Matrix Converter with Reactive Power Control", IEEE Trans. on Industrial Electronics, vol. 55, no. 12, pp. 4362-4371, June 2008.

[7] M. Rivera, R. Vargas, J. Espinoza, J. Rodr´ guez, P. Wheeler, C. Silva, Current Control in Matrix Converters connected to Polluted AC Voltage Supplies, in Proc. of IEEE PESC 2008, 15-19 June 2008, pp. 412-417.

[8] R. Vargas et al., “Predictive Current Control of an Induction Machine Fed by a Matrix Converter With Reactive Power Control “, IEEE Transactions on power Electronics , Vol. 55, No. 12, Dec. 2008.

TABLE I. SYSTEM PARAMTERS

Variables Description Simulation

values

Source Vs

fs

Input Filter Lf Cf Rf

DFIG Rr Rs

Lm

Lfs Lfr

RMS supply stator phase voltage

Supply Frequency

Input Filter Inductance Input Filter Capacitance Input Filter Resistance

Rotor Resistance Stator Resistance

Mutual Inductance The Leakage Stator Inductance The Leakage rotor Inductance

690 (V) 50(Hz)

400(uH) 120(uf) 0,5( )

54,44(m ) 4,45(m ) 4,41(m H) 134(uH) 1,6(m H)