Dynamic Model and Control of DFIG Wind Energy Systems Based on Power Transfer Matrix

Dynamic Model and Control of DFIG Wind EnergySystems Based on Power Transfer Matrix Esmaeil Rezaei, Ahmadreza Tabesh, Member, IEEE, and Mohammad Ebrahimi Abstract—This paper presents a p

Dynamic Model and Control of DFIG Wind Energy

Systems Based on Power Transfer Matrix

Esmaeil Rezaei, Ahmadreza Tabesh, Member, IEEE, and Mohammad Ebrahimi

Abstract—This paper presents a power transfer matrix model

and multivariable control method for a doubly-fed induction

generator (DFIG) wind energy system The power transfer matrix

model uses instantaneous real/reactive power components as the

system state variables It is shown that using the power transfer

matrix model improves the robustness of controllers as the power

waveforms are independent of a frame of reference The

sequential loop closing technique is used to design the controllers

based on the linearized model of the wind energy system The

designed controller includes six compensators for capturing the

maximum wind power and supplying the required reactive power

to the DFIG A power/current limiting scheme is also presented

to protect power converters during a fault The validity and

per-formance of the proposed modeling and control approaches are

investigated using a study system consisting of a grid-connected

DFIG wind energy conversion system This investigation uses

the time-domain simulation of the study system to: 1) validate

the presented model and its assumptions, 2) show the tracking

and disturbance rejection capabilities of the designed control

system, and 3) test the robustness of the designed controller to the

uncertainties of the model parameters.

Index Terms—Doubly fed induction generator (DFIG),

dy-namics modeling, instantaneous power, multivariable control,

wind energy systems, wind power control, wind turbine generator.

I INTRODUCTION

among economically available and viable renewable

energy systems which have experienced rapid growth in recent

years Increasing the penetration level of wind farms highlights

the grid integration concerns including power systems stability,

power quality (PQ), protection, and dynamic interactions of

the wind power units in a wind farm [1]–[3] Wind energy

systems based on doubly fed induction generators (DFIGs)

have been dominantly used in high-power applications since

they use power-electronic converters with ratings less than the

rating of the wind turbine generators [4]–[8] The scope of this

paper is dynamic modelling and control of DFIG wind turbine

generators

Modeling and control of DFIGs have been widely

investi-gated based on well-established vector control schemes in a

Manuscript received July 31, 2011; revised April 02, 2012; accepted April

13, 2012 Date of publication May 30, 2012; date of current version June 20,

2012 Paper no TPWRD-00653-2011.

The authors are with the Department of Electrical and Computer Engineering,

Isfahan University of Technology, Isfahan 84156, Iran (e-mail: rezaei58@ec.

iut.ac.ir; a.tabesh@cc.iut.ac.ir; mebrahim@cc.iut.ac.ir).

Digital Object Identifier 10.1109/TPWRD.2012.2195685

stator field-oriented frame of reference [7]–[9] The vector con-trol is a fast method for independent concon-trol of the real/reactive power of a machine The method is established based on con-trol of current components in a frame of reference using an

transformation Since the components are not phys-ically available, the calculation of these components requires a phase-locked loop (PLL) to determine synchronous angle [10], [11] The dynamics of transformations are often ig-nored in the procedure of control design Thus, any control de-sign approach must be adequately robust to overcome the certainties in estimation of machine parameters as well as un-accounted dynamics of the overall system The proposed power transfer matrix model for DFIG in this paper presents an alter-native modeling and control approach which is independent of

transformations

Direct torque control (DTC) and direct power control schemes (DPC) have been presented as alternative methods which directly control machine flux and torque via the selection

of suitable voltage vectors [12]–[14] It has been shown that DPC is a more efficient approach compared to modified DTC [15]–[17] However, the DPC method also depends on the estimation of machine parameters and it requires a protection mechanism to avoid overcurrent during a fault in the system This paper presents a modelling and control approach which uses instantaneous real and reactive power instead of compo-nents of currents in a vector control scheme The main features

of the proposed model compared to conventional models in the frame of reference are as follows

1) Robustness: The waveforms of power components are

in-dependent of a reference frame; therefore, this approach

is inherently robust against unaccounted dynamics such as PLL

2) Simplicity of realization: The power components (state

variables of a feedback control loop) can be directly ob-tained from phase voltage/current quantities, which simplifies the implementation of the control system Using power components instead of current in the model of the system, the control system requires an additional protection algorithm to prevent overcurrent during a fault Such an algo-rithm can be simply added to the control system via measuring the magnitude of current The sequential loop closing technique

is adopted to design a multivariable control system including six compensators for a DFIG wind energy system The designed control system captures maximum wind power via adjusting the speed of the DFIG and injects the required reactive power to the system via a grid-side converter

0885-8977/$31.00 © 2012 IEEE

Fig 1 Schematic diagram of the DFIG-based wind generation system.

II MODEL OF ADFIG WINDENERGYSYSTEMUSING

INSTANTANEOUSPOWERCOMPONENTS

A Definitions and Assumptions

The schematic diagram of a DFIG wind turbine generator is

depicted in Fig 1 The power converter includes a rotor-side

converter (RSC) to control the speed of generator and a grid-side

converter (GSC) to inject reactive power to the system Using

a passive sign convention, the instantaneous real and reactive

power components of the grid-side converter, and ,

in the synchronous reference frame, are [18]

(1)

where and are components of the stator voltages

and GSC currents in the synchronous reference frame,

respec-tively Solving (1) for and , we obtain

(2) where

(3)

Similarly, the instantaneous real/reactive power components of

DFIG can be obtained in terms of stator currents as

(4) and the stator current components are given by

(5)

The negative sign in (5) complies the direction of the stator

power flow on Fig 1 The exact dynamic model of an induction

machine is conventionally expressed by voltage and torque

equations [18] Herein, we develop a simplified model for the

DIFG-based wind turbine of Fig 1 by substituting currents

in the exact model in terms of instantaneous real and reactive

power The key assumption to simplify the model is assuming

an approximately constant stator voltage for DFIG This

as-sumption can be only used under a steady-state condition where

the grid voltage at the point of common coupling (PCC) varies

in a narrow interval, typically less than 0.05 p.u Using this

The voltage and flux equations of a doubly fed induction ma-chine in the stator voltage synchronous reference frame can be summarized as [18]

(6)

(7)

(8) where and are the stator and rotor resistances, and is the synchronous (stator) frequency Subscripts and signify the stator and rotor variable, and and are the stator, rotor, and magnetization inductances, respectively The com-plex quantities and represent the voltage, current, and flux vectors, and is the slip frequency defined as

(9)

where is the rotor speed of the induction machine To obtain

a model of DFIG in terms of and , the rotor flux and current are obtained from (8) as

(10)

and from (10) in (7) and then by solving (6) and (7) for , we obtain

(11)

Using (5) to replace components of in (11) and by rearranging the equation, we obtain

(12)

(13) where

(14)

The state equation of the stator flux can be obtained by

substi-tuting for and from (5) in (6) Solving the stator voltage

equations for yields

(15) (16) The electromechanical dynamic model of the machine is [18]

(17)

where and are the number of pole pairs, inertia of the

rotor, and mechanical torque of the machine, respectively The

electric torque is given by [18]

(18)

In (17), the mechanical torque is input to the model and ,

based on (18), can be expressed in terms of instantaneous real

and reactive power Substituting for and from (5) in (18)

and then replacing in (17), we deduce

(19) where

(20)

The simplified model of the induction machine is presented in

(12)–(16) and (19) which is summarized as

(21)

The model of DFIG in (21) is a nonlinear dynamic model since

the coefficients of the state variables are functions of the state

variables

Fig 2 Equivalent circuit of the grid-side filter.

C Grid-Side Converter and Filter Model

Fig 2 shows the representation of the grid-side converter and its filter in the synchronous reference frame The model of the grid-side converter and filter is

(22) where and are the resistance and inductance of the filter, respectively, and subscript signifies the variables at the grid-side converter [19] Substituting for from (2) in (22) yields

(23) where

(24) (25)

The dc-link model can be deduced from the balance of real power at the converter dc-link node as given by

(26) where is the real power that the converter delivers to the rotor and represents the total power loss, including con-verter switching losses and copper losses of the filter The de-livered real power to the rotor is [18]

(27) Using (10) and (5), can be expressed as

(28)

In the high-power converter, the power loss is often less than 1%

of the total transferred power, and the impact of in (26) can

the model of the dc link is deduced as follows:

(29) Using (28), the right-hand-side quantities in (29) can be

where are the wind turbine radius, air mass density,

and wind speed, respectively is the wind turbine power

co-efficient which is a function of the tip speed ratio

and the pitch angle of the turbine blades, For a high-power

wind turbine, the maximum mechanical power captured at

ranges from 6 to 8 Theoretically, it can be shown that 0.6

wind turbines [1]

III LINEARIZEDDYNAMICMODEL OF A DFIG

WINDTURBINEGENERATOR

A DFIG and Wind Turbine Model

For a high-power machine, the stator resistant is small;

there-fore, based on (6), a constant stator voltage under normal

oper-ation yields slow-varying flux components Thus, the

com-ponents of the stator flux of a DFIG in a field-oriented frame of

reference with 0 can be obtained from (15) and (16) as

(31)

Substituting for from (31) in (12), (13), and (19), then

by linearizing the equations about an operating point, the

small-signal model of DFIG can be expressed as

(32) (33) (34) where denotes small-signal quantities, and

(35)

In the linearized model, superscript 0 denotes the quantities at

an operating point To calculate , the power torque equation

is linearized by assuming a constant wind speed

as

(36) where is obtained via linearizing in (30) as given by

(37) where

(38) Using (37), the dynamic model of DFIG and the wind turbine

in Laplace domain can be expressed based on a power transfer function as

(39)

where can be readily obtained from the solution of (37) for

B Model of the Grid-Side Filter and DC Link

The model of the grid-side filter in Laplace domain can be obtained by transferring (23) into the Laplace domain as

(40) where

(41)

Solving (40) for and , the grid-side filter model in the Laplace domain is

(42) where

(43)

(44)

Using (29), the linearized model of dc link can be obtained as

(45) where

(46)

Fig 3 Schematic diagram of the feedback control system for the machine-side

and grid-side converters.

From (45), the dc bus model in the Laplace domain is

(47)

Equations (39), (42), and (47) represent the linearized

multi-variable model of a DFIG wind turbine generator

IV MULTIVARIABLECONTROLLERDESIGN FOR A

DFIG WINDTURBINEGENERATOR

A Controller Design Scheme

Fig 3 depicts the suggested multivariable feedback control

system for the machine- and grid-side control schemes In this

scheme, the control inputs of the linearized model of the system

are to control real/reactive power of the rotor; and

to adjust the dc-link voltage and injected reactive

power to the system The outputs (feedbacks) of the system are

the rotor speed, dc-link voltage, and the instantaneous

real/reac-tive power of the rotor- and grid-side converters The feedback

control system includes six compensators which are used in two

where the required reactive power of the machine and grid

are directly controlled via and control loops as shown

Fig 3 The outer control loops include for regulating the

rotor speed and for adjusting the dc-link voltage level

The sequential loop closing (SLC) method [20] is adopted to

design six controllers based on the multivariable model of the

system developed in Section III In the SLC method, based on

physical relevance of the inputs and outputs, the input-output

pairs are determined Then, a controller is designed for the first

pair of the input-output by treating the system as a single-input

single-output (SISO) system The second controller is designed

for the next pair of input-output variables using the first

con-troller as an integral part of the system Based on the theory of

the SLC design method [20], the multivariable system is stable

if all of the designed subsystems during the sequential controller design procedure are stable

B Design of the Machine-Side Controllers 1) Stator Real and Reactive Power Controllers: Considering

as the first pair in (39) and, thus, imposing ,

we obtain the first SISO subsystem for controller design as

(48) The first controller to be designed is

(49) Substituting from (49) in (48), the closed-loop model of the first subsystem in Laplace domain is

(50)

Thus, must be designed so that all poles of (50) remain in the left-half plane (LHP) The design of can be simply per-formed via SISO system design methods, such as frequency re-sponse or root locus To design for reactive power control, the first controller is considered as a part of the system, then

in (39), the closed-loop model of the second subsystem is obtained

(51) where

Thus, must be designed so that the second subsystem in (51) remains stable

2) Rotor Speed Controller: Speed control of the

turbine-gen-erator rotor is performed via control of the real power of the stator Therefore, the speed controller uses as the con-trol input Using the concon-trol scheme of Fig 3, is

(52) Embedding and controllers in the model of the system, the transfer function of rotor speed can be calculated as

(53) where

Substituting for from (52) in (53) yields

(54)

troller design procedure for and is quite similar to

that of the rotor-side converter since both controllers have the

same structure Therefore, and can be simply

ob-tained by repeating the design procedure as explained in (48)

Also, both subscripts and should be re-placed with subscript For brevity, the details of the design

procedure have been omitted

2) DC-Link Voltage Controller: Substituting for ,

and into (46), we obtain

(55)

where detailed expressions for and are given in the

Appendix Based on (47) and (55), can regulate

at its reference value using the dc-link controller in

Therefore, the closed-loop system for

is deduced as

(56)

where detailed expressions for and are given in the

Appendix Finally, must be designed to stabilize the

dc-link closed-loop system in (56)

D Current Limiting During a Fault

The target of the controller design procedure is to improve

performance of wind energy conversion while maintaining

the stability of the system under normal operating conditions

Therefore, the design procedure mainly deals with stability,

tracking performance for capturing maximum wind power,

disturbance rejection, and robustness against uncertainties and

unaccounted dynamics

During a fault and/or sever transients, additional protection

algorithms, such as fault ride through (FRT) and startup

al-gorithms, must be added to the control system Various

algo-rithms, including active crowbar [21], series dynamic restorer

[22], and dynamic voltage restorer [23] have been suggested for

FRT These algorithms are independent of the control approach

during the normal operation; therefore, they can be used with

the proposed transfer power matrix method herein as well

In addition to FRT algorithms and to mitigate overcurrent

during a transient, an extra feedback loop can be used to

sense the converter currents and reduce the power reference

commands during transients This extra loop only requires the

magnitude of the current and it merely becomes operational

during a fault condition An example of such a current loop

for the protection of the converter is elaborated in [19] and

[23] This loop does not impact the performance of controllers

Fig 4 Schematic diagram of the study system.

TABLE I

S TUDY S YSTEM ’ S W IND T URBINE G ENERATOR D ATA

during the normal operation of the system and, therefore, it will not be included in the design procedure of the controllers

V MODELVALIDATION ANDPERFORMANCEEVALUATION OF

THEMULTIVARIABLECONTROLSYSTEM Fig 4 shows the schematic of a study system for validation

of the proposed modelling and control approaches The study system includes a 1.5-MW DFIG wind turbine-generator con-nected to a grid The electrical and mechanical parameters of the turbine generator are adopted from [24] and summarized

in Table I Using the proposed designed method, the following per-unitized controllers were designed for the study system

(57)

(58)

(59) (60)

The performance of these controllers was investigated based on time-domain simulations of the study system using the Matlab/ Simulink software tool

A Tracking and Disturbance Rejection Capabilities

Fig 5(a) and (b) shows a trapezoidal pattern for wind speed and a step change in the reactive reference which are applied to

Fig 5 Reference commands for wind and the stator reactive power.

Fig 6 Tracking performance of real and reactive stator powers.

the controllers of the study system The trapezoidal pattern was

selected to examine the system behavior following variation in

the wind speed with both negative and positive slopes The

se-lected wind speed pattern spans an input mechanical wind power

from 0.7 to 1 p.u (70 to 100% of the turbine-generator rated

power) The reactive power command is a step change of 0.25

p.u and occurs at 3 s when the real power is about 0.6 p.u

Fig 6 compares real/reactive power quantities of the DFIG

against their command signals Due to the coupling

phenom-enon, the variation of each power quantity can be considered as

a disturbance to the other one For instance, the effect of

cou-pling can be seen in Fig 6(a) at 3 s, where the step

com-mand in reactive power causes a small deviation in real power

However, as Fig 6 shows, both real and reactive power

quan-tities accurately track their command signals which means the

controllers successfully mitigate the impact of coupling effect in

the tracking of commands signals Fig 7(a) and (b) depicts the

dc-link voltage and the rms values of the machine

voltage/rent quantities These figures show that the stator and rotor

cur-rents are changing as the real/reactive power changes whereas

the dc link and stator voltages remained fixed as expected from

the control strategy Specifically, the and current curves

show a step change at 3 s, corresponding to the 0.25-p.u

step command in the reactive power Fig 7 shows that as the

Fig 7 RMS values of the stator voltage and currents.

Fig 8 Robustness of the controllers to variations in L

Fig 9 Robustness of the controllers to a 40 error in the PLL angle.

power reference commands are within the rated power of the turbine generator, the voltage/current of the machine and con-verter will remain within their limits

B Control System Robustness

Fig 8 shows the tracking and disturbance rejection perfor-mances of real/reactive power when the leakage inductance of

the machine is changed using the same reference commands

as shown in Fig 5 Since Fig 8 shows the responses accurately

track the commands for and , therefore, the designed

controller is robust to a variation of this parameter

Fig 9 compares tracking performance of the proposed

con-trol system with the conventional vector concon-trol method as

de-scribed in [25] The PI controllers of the vector control method

were first tuned for best performance at 0.1 and 2

Then, the synchronous signal of the phase-locked loop (PLL)

was deviated via biasing the PLL angle with 40 As Fig 9

shows, the proposed method accurately follows the reference

commands for real and reactive power whereas the vector

con-trol method fails to track the commands The reason is that the

vector control method is significantly sensitive to the frame

of reference whereas the proposed control system is less

inde-pendent to the reference frame

VI SUMMARY ANDCONCLUSION

An alternative modeling and controller design approach

based on the notion of the instantaneous power transfer matrix

is described for a DFIG wind energy system The waveforms

of the power components remain intact at different reference

frames and can be easily calculated using the phase voltages

and currents Therefore, this approach facilitates the

imple-mentation of the controllers and improves the robustness of the

control system Furthermore, the proposed model can be

po-tentially used to simplify the control issues of the wind energy

system under an unbalanced condition since feedback variables

are independent of -components in positive, negative, and

zero sequences

The proposed approach is verified using the time-domain

simulation of a study system for DFIG wind energy systems

The simulation results show that the suggested model and

con-trol scheme can successfully track the rotor speed reference for

capturing the maximum power and maintain the dc-link voltage

of the converter regardless of disturbances due to changes in

real and reactive power references

APPENDIX Details of , and in (55) and (56) are shown in the equations at the top of the page

REFERENCES

[1] M Patel, Wind and Solar Power Systems: Design, Analysis, and

Oper-ation. Boca Raton, FL: CRC, 2006.

[2] K Xie and R Billinton, “Determination of the optimum capacity and type of wind turbine generators in a power system considering

reli-ability and cost,” IEEE Trans Energy Convers., vol 26, no 1, pp.

227–234, Mar 2011.

[3] T Zhou and B François, “Energy management and power control of a hybrid active wind generator for distributed power generation and grid

integration,” IEEE Trans Ind Electron., vol 58, no 1, pp 95–104, Jan.

2011.

[4] J Hu, H Nian, H Xu, and Y He, “Dynamic modeling and improved

control of DFIG under distorted grid voltage conditions,” IEEE Trans.

Energy Convers., vol 26, no 1, pp 163–175, Mar 2011.

[5] L Fan, H Yin, and Z Miao, “On active/reactive power modulation of

DFIG-based wind generation for interarea oscillation damping,” IEEE

Trans Energy Convers., vol 26, no 2, pp 513–521, Jun 2011.

[6] S Muller, M Deicke, and R De Doncker, “Doubly fed induction

gen-erator systems for wind turbines,” IEEE Ind Appl Mag., vol 8, no 3,

pp 26–33, May/Jun 2002.

[7] E Tremblay, S Atayde, and A Chandra, “Comparative study of control strategies for the doubly fed induction generator in wind energy

con-version systems: A DSP-based implementation approach,” IEEE Trans.

Sustain Energy, vol 2, no 3, pp 288–299, Jul 2011.

[8] M Mohseni, S Islam, and M Masoum, “Enhanced hysteresis-based

current regulators in vector control of DFIG wind turbines,” IEEE

Trans Power Electron., vol 26, no 1, pp 223–234, Jan 2011.

[9] Z Wang, G Li, Y Sun, and B Ooi, “Effect of erroneous position

mea-surements in vector-controlled doubly fed induction generator,” IEEE

Trans Energy Convers., vol 25, no 1, pp 59–69, Mar 2010.

[10] P Rodríguez, A Luna, I Candela, R Mujal, R Teodorescu, and F Blaabjerg, “Multiresonant frequency-locked loop for grid

synchroniza-tion of power converters under distorted grid condisynchroniza-tions,” IEEE Trans.

Ind Electron., vol 58, no 1, pp 127–138, Jan 2011.

[11] G Escobar, M Martinez-Montejano, A Valdez, P Martinez, and

M Hernandez-Gomez, “Fixed reference frame phase-locked loop (FRF-PLL) for grid synchronization under unbalanced operation,”

IEEE Trans Ind Electron., vol 58, no 5, pp 1943–1951, May 2011.

[12] R Datta and V Ranganathan, “Direct power control of grid-connected

wound rotor induction machine without rotor position sensors,” IEEE

Trans Power Electron., vol 16, no 3, pp 390–399, May 2001.

[13] S Chen, N Cheung, K Wong, and J Wu, “Integral sliding-mode di-rect torque control of doubly-fed induction generators under

unbal-anced grid voltage,” IEEE Trans Energy Convers., vol 25, no 2, pp.

356–368, Jun 2010.

[14] S Chen, N Cheung, K Wong, and J Wu, “Integral variable structure

direct torque control of doubly fed induction generator,” IET Renew.

Power Gen., , vol 5, no 1, pp 18–25, 2011.

[15] D Zhi, L Xu, and B Williams, “Model-based predictive direct power

control of doubly fed induction generators,” IEEE Trans Power

Elec-tron., vol 25, no 2, pp 341–351, Feb 2010.

[16] P Zhou, W Zhang, Y He, and R Zeng, “Improved direct power

con-trol of a grid-connected voltage source converter during network

un-balance,” J Zhejiang Univ.-Sci C, vol 11, no 10, pp 817–823, 2010.

[17] J Hu, H Nian, B Hu, Y He, and Z Zhu, “Direct active and reactive

power regulation of DFIG using sliding-mode control approach,” IEEE

Trans Energy Convers., vol 25, no 4, pp 1028–1039, Dec 2010.

[18] P Krause, O Wasynczuk, S Sudhoff, and I P E Society, Analysis of

Electric Machinery and Drive Systems. Piscataway, NJ: IEEE, 2002.

[19] A Tabesh and R Iravani, “Multivariable dynamic model and robust

control of a voltage-source converter for power system applications,”

IEEE Trans Power Del., vol 24, no 1, pp 462–471, Jan 2009.

[20] J Maciejowski, Multivariable Feedback Design, ser Electron Syst.

Eng Ser Reading , MA: Addison-Wesley, 1989, vol 1.

[21] G Pannell, D Atkinson, and B Zahawi, “Minimum-threshold crowbar

for a fault-ride-through grid-code-compliant DFIG wind turbine,”

IEEE Trans Energy Convers., vol 25, no 3, pp 750–759, Sep 2010.

[22] J Yang, J Fletcher, and J O’Reilly, “A series-dynamic-resistor-based

converter protection scheme for doubly-fed induction generator during

various fault conditions,” IEEE Trans Energy Convers., vol 25, no 2,

pp 422–432, Jun 2010.

[23] C Wessels, F Gebhardt, and F Fuchs, “Fault ride-through of a DFIG

wind turbine using a dynamic voltage restorer during symmetrical and

asymmetrical grid faults,” IEEE Trans Power Electron., vol 26, no 3,

pp 807–815, Mar 2011.

[24] R Fadaeinedjad, M Moallem, and G Moschopoulos, “Simulation of a

wind turbine with doubly fed induction generator by fast and simulink,”

IEEE Trans Energy Convers., vol 23, no 2, pp 690–700, Jun 2008.

[25] R Pena, J Clare, and G Asher, “Doubly fed induction generator using

back-to-back PWM converters and its application to variable-speed

wind-energy generation,” in Proc Inst Elect Eng., Elect Power Appl.,

1996, vol 143, no 3, pp 231–241, IET.

Esmaeil Rezaei was born in Isfahan, Iran in 1979 He

received the B.Sc degree in electronics and the M.Sc degree in electrical engineering from Isfahan Univer-sity of Technology (IUT), Isfahan, Iran, in 2001 and

2004, respectively, where he is currently pursuing the Ph.D degree in electrical engineering.

He was a Technical Designer with the Information and Communication Technology Institute (ICTI), Isfahan University of Technology, from 2004 to

2007 His current research interests include electrical drives and energy conversion systems for renewable energy resources.

Ahmadreza Tabesh (M’12) received the B.Sc

de-gree in electronics and the M.Sc dede-gree in systems control from Isfahan University of Technology, Is-fahan, Iran, in 1995 and 1998, respectively, and the Ph.D degree in energy systems from the University

of Toronto, Toronto, ON, Canada, in 2005 From 2006 to 2009, he was Postdoctorate at the Microengineering Laboratory for MEMS, Depart-ment of Mechanical Engineering, Université de Sherbrooke, Sherbrooke, QC, Canada Currently,

he is an Assistant Professor with the Department of Electrical and Computer Engineering, Isfahan University of Technology His areas of research include renewable energy systems and micropower energy harvesters (power MEMS).

Mohammad Ebrahimi received the B.Sc and M.Sc.

degrees in electrical engineering from Tehran Univer-sity, Tehran, Iran, in 1984 and 1986, respectively, and the Ph.D degree in power systems from the Tarbiyat Modarres University, Tehran, Iran, in 1996 Currently, he is an Associate Professor at the Isfahan University of Technology (IUT), Isfahan, Iran His research interests include electrical drives, renewable energy, and energy savings.