Modeling and Control of SCIG based variable-Speed with Power ...

International Review of Modelling and Simulations (I.R.E.M.O.S), Vol. 4, n.3

Modeling and Control of SCIG based variable-Speed with Power Factor Control M. Benchagra1, M. Hilal2, Y. Errami3, M. Ouassaid4, M. Maaroufi5

Abstract – This paper presents a new model for steady- state and dynamic-study of a gridconnected SCIG. The system consisting of Squirrel Cage Induction Generators (SCIG); the generator is driven by wind turbine through a gearbox. The studied wind turbine is connected to distribution system through Power Electronics Converters (PECs), filters and step-up transformers. The mathematical models of the studied SCIG generation system including wind speed, filter, turbine system, gearbox, SCIG, PECs, DC-link, step-up transformer, etc. are established and implemented using MATLAB/SIMULINK software. The paper presents the vector control strategy of SCIG that allows the independent control of flux and electromagnetic torque on the PWM converter, and extracting maximum power (MPPT). On the PWM inverter, the vector control strategy is implemented to regulate the DC-voltage and the reactive power from the grid, to have a Power Factor Control (PFC). The simulation results verify the effectiveness of the controls strategies, so it can be concluded that the proposed control of the studied SCIG system can be effectively utilized to study wind farm based on SCIG under any selected operating conditions. Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved. Keywords: Wind Power, SCIG, PECs, MPPT, PFC, PI Controller, Simulink

Nomenclature Pm : Mechanical power of the wind turbine Cp : Power coefficient δ : Tip speed ratio β : Blade pitch angle ρ : Air density A : Rotor blades area v : Wind speed R : Blade radius Pm-opt : Optimal mechanical power Tem : Electromagnetic torque Tm : Mecanical torque ωm : Generator speed ωs : Stator electrical speed ωr : Rotor electrical speed vds : Direct stator voltage vqs : Quadrate stator voltage vdr : Direct rotor voltage vqr : Quadrature rotor voltage λds : Direct stator flux λqs : Quadrature stator flux λdr : Direct rotor flux λqr : Quadrature rotor flux ids : Direct stator current iqs : Quadrature stator current idr : Direct rotor current

Manuscript received Mars 2011, revised April 2011

iqr : Rs : Rr : Ls : Lr : Lm : J : : Jt Jg : Ps : Udc : is : ig : C : vg123 : ig123 : vi123 : Rt : Lt : Pg : Qg : Pg-ref : Qg-ref : vgdq : igdq : vrdq : s : Tr :

Quadrature rotor current Resistance per phase of a stator winding Resistance per phase of a rotor winding Inductance per phase of a stator winding Inductance per phase of a rotor winding Mutual inductance Total inertia Turbine inertia Generator inertia SCIG active power DC-link voltage SCIG side current Grid side current DC-link capacitor Terminal distribution-system voltages Terminal distribution system line currents Output VSI voltages Resistance of the grid-side transmission line Inductance of the grid-side transmission line Output active power of the wind generator Output reactive power of the wind generator Active power absorbed by the VSI Reactive power command on the VSI Direct and quadrate distribution voltages Direct and quadrate distribution line currents Direct and quadrate output VSI voltages Laplace operator Rotor time constant

Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved

M. Benchagra1, M. Hilal, Y. Errami, M. Ouassaid, M. Maaroufi

Wind turbine VSC SCIG

Wind

ࢼ࢘ࢋࢌ

࣓࢓ MPPT

ig

ig1

idc

Gear box

v

VSI is

isa

abc/dq idqs Tem-ref ࣅ࢘ࢋࢌ

ࢁࢊࢉ

PWM

Vector control strategy

ࢁࢊࢉି࢘ࢋࢌ ࡽࢍି࢘ࢋࢌ

ࡾࢌ ࡸࢌ

Grid vg1

T

abc/dq

PWM idqg

Vector control strategy

vdqg

Fig. 1. Schematic diagram of control strategy for a SCIG wind generation system

I.

Introduction

The renewable energy is urged on promotion by the countries in the world, the wind power is the most common and development priorities now. Developing the wind generation is a good choice and many wind farms are constructed continuously, for example, gridconnected Squirrel Cage Induction Generators (SCIGs) are important alternative for large-scale wind farm because of its rotor structure, simplicity of construction and maintenance-free operation [1]-[6]. The existing software for the simulation of power system operation was mainly developed and analyzed of conventional systems, for example, SCIG at fixed speed in MATLAB/simulink, PSCAD and DIGSILENT. New forms of power generation, like wind farm based on SCIG with power electronics converters cannot be analyzed effectively with these software [7]-[10]. In this paper a new SGIGs wind turbine model for steady-state and dynamic analysis is studied and described. The paper proposes a SCIG wind turbine system consisting of a SCIG driven by wind turbine through a gearbox. The output terminals of the SCIG are connected to a distribution system through a step-up transformer, connection cables, and PECs with appropriate controls [11]-[14]. A combined mathematical model including wind speed, wind turbine, gearbox, SCIG, DC-link voltage, PECs, step-up transformer, and grid system to simulate the steady-state and dynamics of SCIG wind turbine system, the model is established and implemented using SIMULINK software. This paper is organized as below. Section II introduces the employed mathematical models of the proposed SCIG wind farm system with wind turbine set connected to a distribution system through PECs and connection lines. Section III shows the procedure and results of designing the PI controllers using vector control strategy. Section IV presents some dynamic simulation results of the studied wind turbine with the designed PI controller Manuscript received April 2011, revised June 2011

subject to various wind speed disturbance conditions. Specific important conclusions of this paper are drawn in section V.

II.

Modeling of the studied SCIG Wind Farm System II.1.

System Configuration

The schematic diagram of the studied wind turbine with a turbine-SCIG set connected to distribution system through transmission lines and PECs is shown in Fig. 1. The rotor shaft of the studied squirrel cage induction generator is coupled to the hub of a turbine through a gearbox for transforming low rotational speeds of the turbine to the required higher rotational speeds of the SCIG. The PECs consisting of a voltage-source converter (VSC), a DC-link, and a voltage-source inverter (VSI) are used to convert the variable generated voltage of the SCIG to a stable voltage that used to connect to the distribution system. The three-phase stator windings of the studied SCIG are connected to the input terminals of the VSC [15]-[18]. The output terminals of the VSI are connected to the 15-kV distribution system through a step-up transformer of 230/15 kV and a transmission line. The combined equivalent impedance of the step-up transformer, the transmission line, and the internal equivalent impedance of the 15-kV distribution system is Rf+jLf . As shown in Fig. 1, the pulses width modulation of the VSC, PWM, control the SCIG’s output voltage vs and output active power Ps. The PWM of the VSI, control the DC-link voltage Udc and the output reactive power Q g. II.2.

Characteristics of Wind Turbine

The captured mechanical power Pm of the studied wind turbine can be expressed by the following equation [1].

Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved

M. Benchagra1, M. Hilal, Y. Errami, M. Ouassaid, M. Maaroufi 1 (1) ‫ߜ( ܥ‬, ߚ)ߩ‫ ݒܣ‬ଷ 2 ௣ This paper considers a generic equation to model the power coefficient Cp, based on the modeling turbine characteristics described by [19]: ܲ௠ =

116 −21 − 0.4ߚ − 5൰ exp ൬ ൰ ߜ௜ ߜ௜ (2) + 0.0068ߜ 1 0.035 ߜூିଵ = ൤ − ൨ (ߜ + 0.08ߚ) (ߚ ଷ + 1) A relationship between Cp and δ for various values of the pitch angle β is illustrated in Fig. 2. The maximum value of Cp, that is CPmax= 0.47, is achieved for β=0° and for δ=8.1. If the electromagnetic torque reference is estimated and the mechanical characteristics of the wind turbine are known, it is possible to deduce in real time the optimal mechanical power Pm-opt (3) which can be generated using the MPPT [20]. The typical mechanical power is illustrated in Fig (3). ‫ܥ‬௣ (ߜ, ߚ) = 0.5109 ൬

ܲ௠ି௢௣௧ = II.3.

1 ܴ߱௠ ଷ ‫ܥ‬௣ ߩ‫ ܣ‬൬ ൰ = ܶ௘௠ ߱௠ 2 ߜ

Fig. 2. Characteristics Cp vs λ, for various values of pitch angle β

(3) Fig. 3. Typical mechanical power vs generator speed at various wind speeds

Induction Generator Model

The electromagnetic torque can be calculated as ܶ௘௠ = ߣ௤௦ ݅ௗ௦ − ߣௗ௦ ݅௤௦

The classical electrical equations of the SCIG in the PARK frame are written as follows

݀ߣௗ௦ − ߱௦ ߣ௤௦ ݀‫ݐ‬ ݀ߣ௤௦ ‫ݒ‬௤௦ = ܴ௦ ݅௤௦ + + ߱௦ ߣௗ௦ ݀‫ݐ‬
(4) ‫ = ݒ۔‬0 = ܴ ݅ + ݀ߣௗ௥ − (߱ − ߱ )ߣ ௥ ௗ௥ ௦ ௥ ௤௥ ۖ ௗ௥ ݀‫ݐ‬ ۖ ݀ߣ ۖ ௤௥ ‫ݒ ە‬௤௥ = 0 = ܴ௥ ݅௤௥ + ݀‫ ݐ‬+ (߱௦ − ߱௥ )ߣௗ௥ where subscripts ‘s’ and ‘r’ refer to the stator and rotor side respectively, subscripts ‘d’ and ‘q’ refer to the d-axis and q-axis respectively The stator and rotor flux can be expressed as ‫ۓ‬ ۖ ۖ ۖ

‫ݒ‬ௗ௦ = ܴ௦ ݅ௗ௦ +

ߣௗ௦ = ‫ܮ‬௦ ݅ௗ௦ + ‫ܮ‬௠ ݅ௗ௥ ‫ ݅ ܮ = ߣۓ‬+ ‫݅ ܮ‬ ௤௦ ௦ ௤௦ ௠ ௤௥
ߣ = ‫ܮ‬ ݅ + ‫ܮ‬ ௥ ௗ௥ ௠ ݅ௗ௦ ‫ ۔‬ௗ௥ ߣ = ‫ܮ‬ ݅ + ‫ܮ‬ ‫ ە‬௤௥ ௥ ௤௥ ௠ ݅௤௦

(6)

The voltage and flux equations can be supplemented by the mechanical equation for the drive train given by (7) to complete the model of SCIG used in this paper ‫ܬ‬

݀߱௠ = ܶ௠ − ܶ௘௠ ݀‫ݐ‬

where J is total inertia, it can be calculated as ‫ܬ‬௧ ‫ = ܬ‬ଶ + ‫ܬ‬௚ ‫ܩ‬

(7)

(8)

The active and reactive power transmitted through the stator can be expressed as Pୱ = vୢୱ ݅ௗ௦ + ‫ݒ‬௤௦ ݅௤௦
൜ ܳ௦ = ‫ݒ‬ௗ௦ ݅௤௦ − ‫ݒ‬௤௦ ݅ௗ௦

(5)

II.4.

(9)

Power-Balance Equation between VSC and VSI

The voltage-current equation of the DC-link capacitor C can be expressed by

Manuscript received April 2011, revised June 2011

Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved

M. Benchagra1, M. Hilal, Y. Errami, M. Ouassaid, M. Maaroufi

࣓࢓

MPPT

ࣅ࢘ࢋࢌ

ࢀࢋ࢓ି࢘ࢋࢌ

࢏ࢊ࢙ Current calculation

PI

࢏࢙ࢗି࢘ࢋࢌ

࢏࢙ࢗ

࢏ࢊ࢙ି࢘ࢋࢌ

Flux estimator

࢙࢜ࢗି࢘ࢋࢌ

PI Decoupling system (Eqs 4&5) PI

࢜ࢊ࢙ି࢘ࢋࢌ

࢙࢜ࢇି࢘ࢋࢌ

dq/ abc

VSC

࢙࢜࢈ି࢘ࢋࢌ

PWM

࢙࢜ࢉି࢘ࢋࢌ

Current controller

Fig. 4. Block diagram of the proposed VSC control system with vector control strategy

‫ܥ‬

ܷ݀ௗ௖ = ݅௦ − ݅௚ ݀‫ݐ‬

Therefore, active and reactive power can be controlled by controlling direct and quadrature current components idg-ref, iqg-ref, which is given as: (10)

‫ݒ‬ௗ௚ ݅ௗ௚ି௥௘௙ 1 ൤ ൨= ଶ ቂ‫ݒ‬ ଶ ݅௤௚ି௥௘௙ ൫‫ݒ‬ௗ௚ + ‫ݒ‬௤௚ ൯ ௤௚

−‫ݒ‬௤௚ ܲ௚ି௥௘௙ ‫ݒ‬ௗ௚ ቃ ൤ܳ௚ି௥௘௙ ൨

(16)

where is is the SCIG-side current and ig is the grid-side transmission-line current. II.5.

III. Control of Power Electronics Converters

Grid-Side Transmission-Line Model

The voltage-current equations of the grid-side transmission line can be expressed by ݅௚ଵ ݅ ‫ݒ‬௚ଵ ‫ݒ‬௜ଵ ݀ ௚ଵ ൥‫ݒ‬௚ଶ ൩ = ܴ௧ ቎݅௚ଶ ቏ + ‫ܮ‬௧ ቎݅௚ଶ ቏ + ൥‫ݒ‬௜ଶ ൩ ݀‫ݐ‬ ‫ݒ‬௚ଷ ‫ݒ‬௜ଷ ݅௚ଷ ݅௚ଷ

(11)

Transforming the voltage equation (11) using dq transformation in the rotating reference frame at the grid frequency gives: ݀݅ௗ௚ + ߱‫ܮ‬௧ ݅௤௚ ݀‫ݐ‬ ݀݅௤௚ = ‫ݒ‬௤௜ − ܴ௧ ݅௤௚ − ‫ܮ‬௧ − ߱‫ܮ‬௧ ݅ௗ௚ ݀‫ݐ‬

‫ݒ‬ௗ௚ = ‫ݒ‬ௗ௜ − ܴ௧ ݅ௗ௚ − ‫ܮ‬௧ ‫ݒ‬௤௚

(12)

III.1. Control of VSC

(13)

The squirrel cage induction generator is connected to the power system through PWM inverter and PWM converter. One of the primary requirements for controlling the VSC is to extract maximum power of the SCIG [21]. The SCIG is controlled using vector control strategy, with currents and voltages referred to a dq synchronous frame with the d axis aligned along the rotor flux vector position. This allows decoupled control of electromagnetic torque and flux, by setting the quadrature component of the rotor to the null value as follows:

Using dq transformation, the active and reactive powers are given by: ܲ௚ି௥௘௙ = ‫ݒ‬ௗ௚ ݅ௗ௚ + ‫ݒ‬௤௚ ݅௤௚

ܳ௚ି௥௘௙ = ‫ݒ‬ௗ௚ ݅௤௚ − ‫ݒ‬௤௚ ݅ௗ௚

For normal operation of the VSC and the VSI of the studied wind power generation system, the DC-link voltage Udc must be properly maintained at a constant value under all operation conditions. A constant DC voltage for Udc indicates a balanced condition of the active-power flow between the VSC and the VSI. To achieve this balanced condition, the VSI is designed to control the DC-link voltage to ensure that the energy collected by the VSC is transmitted to the distribution system. The VSC is assigned to control the active power generated by the SCIG.

(14) (15)

‫ܮ‬௠ ݅ 1 + ܶ௥ . ‫ ݏ‬௦ௗ and ߣ௤௥ = 0

ߣௗ௥ =

Manuscript received April 2011, revised June 2011

(17)

Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved

M. Benchagra1, M. Hilal, Y. Errami, M. Ouassaid, M. Maaroufi

Then the electromagnetic torque is simplified as indicated below: ‫ܮ‬௠ (18) ܶ௘௠ = ‫݌‬ ߣ ݅ ‫ܮ‬௥ ௗ௥ ௦௤ Where p is the pole-pair number The PI control method is used to regulate the flux and electromagnetic torque. The control scheme of the SCIG is shown in Fig.4.

shown in Fig. 5(b). The corresponding results are presented in Fig.6. ݅‫ݏ‬ ܷ݀ܿି௥௘௙

PI

݅݃

ܲ‫ݏ‬

/ ݅ܿ

1 ‫ܥݏ‬

*

ܷ݀ܿ ܲ݃−‫݂݁ݎ‬

Fig. 5.a. DC-link control ࡼࢍି࢘ࢋࢌ

ࡽࢍି࢘ࢋࢌ

࢜ࢊࢍ ࢜ࢗࢍ

࢏ࢗࢍି࢘ࢋࢌ Current calculation Eq (16)

࢏ࢗࢍ PI

࢏ࢊࢍି࢘ࢋࢌ

PI

࢏ࢊࢍ

Decoupling system (Eqs 12&13)

Current controller

࢜ࢗࢍି࢘ࢋࢌ

࢜ࢍ૚ି࢘ࢋࢌ dq/ abc

࢜ࢊࢍି࢘ࢋࢌ

࢜ࢍ૛ି࢘ࢋࢌ

࢜ࢍ૜ି࢘ࢋࢌ

VSI

PWM

Fig. 5.b. Block diagram of the proposed VSI control

III.2. Control of VSI Normal operation of the VSI requires that both idg and iqg must follow the time –varying reference points while the DC-link voltage Udc must also be maintained at a preset value. Two separate control loops, i.e., an inner fast current-control loop and an outer slow DC-voltage control loop, are used to control the required transmission-line current and the DC-link voltage, respectively [22]-[23]. With respect to the reference frame oriented along the grid voltage vector position, the control allows the independent control of active and reactive power exchanges between the grid and the VSI. The d-current is utilized to control the DC voltage and the q-current is to regulate the reactive power. The control schemes are illustrated in Fig.5. In Fig. 5(a), C is the DC link capacitor, Udc-ref is the DC voltage command and Ps is the active power delivered from the VSC, In Fig. 5(b), Pg-ref is the active power absorbed by the VSI, Qg-ref is the reactive power command on the VSI, and the block of “Current calculation” functions to calculate out the references of the dq current components idg-ref , iqg-ref. Because the output reactive power of the VSI is directly determined by the q-axis current, its reference value can come from either the required reactive power or the AC voltage-control loop [7]. By setting the q-axis reference current of the transmission line to be zero, a unity-power-factor control of the VSI can be established. The block diagram of the proposed VSI control system is Manuscript received April 2011, revised June 2011

IV.

SIMULATIONS RESULTS

The model of the SCIG based variable speed wind turbine system of figure 1 is built using MATLAB/SIMULINK dynamic system simulation software. The simulation model is developed based on a GE 300 kW industrial squirrel cage induction machine. The parameters of the Turbine and SCIG used are given in appendix, respectively in Table I and II. The power converter and the control algorithm are also implemented and included in the model. The PWM inverter is operated at 10 kHz. The sampling time used for simulation 10 us. Figure (6) shows the response of the system for a step change of wind speed from 10 m/s to 12 m/s to 9 m/s and then comes back to 10 m/s. it is seen from Fig 6(a), Fig(b) and Fig.6(c) that in power optimization section for the low and moderate wind the generator speed has to change to keep maximum power coefficient. Fig.6(d) and Fig.6(e) shows that the vector control strategy of VSC is very effective on decoupling electromagnetic torque and flux of SCIG.

Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved

M. Benchagra1, M. Hilal, Y. Errami, M. Ouassaid, M. Maaroufi

Fig. 6.a

Fig.6.d

Fig. 6.b Fig.6.e

Fig.6.c Fig.6.f

Fig.6.g. Fig.6. SCIG simulation responses to variable wind speed

Manuscript received April 2011, revised June 2011

Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved

M. Benchagra1, M. Hilal, Y. Errami, M. Ouassaid, M. Maaroufi

Fig.7.a.

Figure (7) shows the responses of the inverter to DCvoltage and reactive power reference. Fig7(a) and Fig.7(b) shows that the control strategy of VSI is very effective on reactive power, the response of the inverter to a step change in reactive power demand. Fig.7(c) shows DC-link voltage, as desired, the DC-link voltage reaches a steady state value of 760 V. The flow of real power from inverter to the grid tracks the reference as shown in Fig.7(d). Fig.7(e) shows the line-transmission phase voltage (vg1) and current (ig1), illustrating that the change in phase takes place within one cycle. This waveform shows the capability of the inverter to supply reactive power to, or receive reactive power from the grid. In other words, the power factor control is possible by setting reactive power to zero. The simulation results demonstrate that the SCIG model control works very well and shows very good dynamic and steady state performance. The control algorithm can be used to extract maximum power from the variable speed wind turbine under fluctuating wind, and simulate the exchange of power with grid.

Fig.7.b

V.

Conclusion

Control strategy for variable speed wind turbine with a SCIG is completely studied in this paper. A vector control strategy for the generator side converter and grid side converter to extract and exchange maximum power are discussed and implemented using MATLAB/Simulink. From the simulation results, the proposed model and controls can be used to study and simulate wind turbine based on SCIG. Fig.7.c

Appendix PARAMETRS OF TURBINE-GENERATOR TABLE I PARAMETERS OF THE TURBINE

Fig.7.d

Parameters

Values

Density of Air Area swept by blades, A Speed-up gear ratio, G Base wind speed Turbine inertia

1.22 kg/m3 615.8 m2 23 12 m/s 50 kg.m2

TABLE II PARAMETERS OF THE SCIG Parameters

Fig.7.e Fig.7. Grid-connected SCIG simulation results Manuscript received April 2011, revised June 2011

Rated power No. of poles Rated speed Stator resistance Stator inductance Mutual inductance Rotor resistance Rotor inductance Generator inertia

Values 300 kW 2 158.7 rad/s 0.0063 Ω 0.0118 H 0.0116 H 0.0048 Ω 0.0116 H 10 kg/m2

Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved

M. Benchagra1, M. Hilal, Y. Errami, M. Ouassaid, M. Maaroufi

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Authors’ information 1,2,3,5

Department of electrical Engineering, Ecole Mohammadia d’ingénieurs, Mohammed V University, Rabat, Morocco. E-mail: [email protected] , [email protected] [email protected], [email protected] @emi.ac.ma 4 Department of industrial Engineering, National School of Application Sciences - Safi, Cadi Aayad University, Morocco. E-mail: [email protected], [email protected]

Mohamed. Benchagra was born in BeniMellal, Morocco, in 20/03/1982. 20/03/1982 He received the diplôme d’ingénieur d’application d’ degree from the Faculty Facult of Technical Sciences, BéniMellal, Morocco, in 2004 and the DESA in 2006 in electrical and power electronics engineering from Mohammadia School of Engineering (Mohamed V University) RabatRabat Morocco, where he pursues his doctoral program. His research is interested in the modeling and control of wind farm based on asynchronous generators.. He is also interested in all electrical energy research. M. Benchagra is a graduate student member of the IEEE. Mohamed HILAL was born in AssoulErrachidia, Morocco. Morocco He received this diploma in Electrical Engineering from Ecole Normal Supérieur de l’Enseignement Technique, Rabat, in 1993, and his DESA in Electrical Engineering from Ecole Mohammadia d’Ingénieur, Université Mohamed V , Rabat, Morocco, in 2008. He is currently rrently Professor at high School of technologies, Salé, Sal Morocco. His research interests are electric drives, power electronics, power systems and renewable energy.

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M. Benchagra1, M. Hilal, Y. Errami, M. Ouassaid, M. Maaroufi

Youssef Errami received the Agregation in electrical engineering from Ecole Normale Supérieure périeure de Rabat, Morocco in 2001 and the DESS from laboratory of physical, Chouab Doukkali Doukkali. University,Eljadida,Morocco, in 2005. In 2009, he joined electric machines Laboratory at the Department of Electrical Engineering of Ecole Mohammadia d’Ingénieur, Rabat, Morocco .He is pursuing Ph.D His research interests are in the areas of Power Electronics Systems, electric drives, power systems and Wind Power Energy. Youssef Errami is a graduate student member of the IEEE Mohammed Ouassaid was born in Rabat, Morocco, in 1970. He received the « Diplôme d’agrégation » in Electrical Engineering from Ecole Normal Supérieur de l’Enseignement Technique, Rabat, in 1999, and the M.Sc.A. and Ph. D. degrees, in Electrical Engineering from Ecole Mohammadia d’Ingén d’Ingénieur, Université Mohamed V , Rabat, Morocco, in 2002 and 2006, respectively. He is currently an Assistant Professor at National School of Application Sciences (ENSA(ENSA Safi) Cadi Aayad University, Morocco.. His research interests are electric drives, power electronics, ctronics, power systems and renewable energy. Dr. Ouassaid is a member of the IEEE. Mohammed Maaroufi was born in Marrakech, Morocco, in 1955. He received the diplôme d’ingénieur d’état degree from the Ecole Mohammadia, Rabat, Morocco, in 1979 and the Ph.D. degrees from the Liége University, Belgium, in 1990, in Electrical Engineering. In 1990, he joined the Department of Electrical Engineering, Ecole Mohammadia, Rabat, Morocco, where is currently a Professor and University Research Professor. His current rent research interests include electrical network, renewable energy, motor drives and power systems.

Manuscript received April 2011, revised June 2011

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