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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 2, NO. 4, OCTOBER 2011 423

A Control Design Approach for Three-PhaseGrid-Connected Renewable Energy Resources

S. Ali Khajehoddin , Member, IEEE , Masoud Karimi-Ghartemani , Senior Member, IEEE ,Praveen K. Jain , Fellow, IEEE , and Alireza Bakhshai , Senior Member, IEEE

Abstract— This paper presents a method to design a controlsystem for a three-phase voltage source converter (VSC) that

connects a renewable energy source to the utility grid throughan output -type or -type filter. The well-known /transformation method creates coupling terms that are visible andcan readily be canceled in the -type filter. Such terms, however,

are very complicated when an filter is used. This paper,

first revisits the derivation of the decoupling control method foran -type output filter and then, for the first time, derives thedecoupling terms for an -type filter. Having successfullydecoupled the real and reactive power loops, feedback controllersare presented and designed to achieve desirable performance.

The proposed controller provides active damping of theresonance mode, robustness with respect to grid frequency, andimpedance uncertainty. Moreover, a new controller is designed toimprove the startup transient of the system. The methodology usedin this paper is inspired from the feedback linearization theory

and it provides a clear design method for the nonlinear systems.Simulation results are presented to confirm the analytical results.

Index Terms— Active damping, decoupling, grid-connection,, renewable energy.

I. I NTRODUCTION

R ENEWABLE energy resources have attracted public,

governmental, and academic attention due to the globalenergy crisis. An important technical challenge is the integra-

tion of renewable resources into the existing utility grid such

that reliable power is injected without violating the grid codes

and standards.

For three-phase grid-connected inverter applications, the

system is implemented to deliver active power as well as

desired reactive power to the grid. In such systems, there are

usually two control loops, one for active and another for reac-

tive power control which are preferably decoupled from each

other. Grid-connected rectifiers use topologies similar to the

grid-connected inverter systems with the difference of power

fl

ow direction from grid to the dc link. Usually rectifi

ers needto operate at unity power factor, i.e., no reactive power should

be drawn from the grid. Therefore, control methods developed

for one can be extended to the other one.

Manuscript received October 10, 2010; revised February 21, 2011; acceptedApril 17, 2011. Date of publication June 02, 2011; date of current versionSeptember 21, 2011.

The authors are with the Department of Electrical and Computer Engineering, Queens University, Kingston, ON, K7L 3N6, Canada(e-mail: [email protected]; [email protected]; praveen. [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TSTE.2011.2158457

A commonly used grid-connected converter topology is

a voltage source converter (VSC) with an output -type or

-type filter. -type filters are superior in terms of filter

size and weight, however, they introduce undesirable high-fre-

quency resonances at the output current. Passive damping of

those resonances cause losses and their active damping often

requires measurement of multiple signals used in a complicated

control method.

There are two general approaches to design the control sys-

tems for three-phase grid-connected converters: in stationary

domain [1], [2] or in synchronous referencedomain [3]–[6]. Thestationary frame has the advantage of avoiding coupling terms

and also the possibility of controlling harmonics but it suffers

from higher order control, more complicated design, sensitivity

of the design to the grid frequency [7], and digital implemen-

tation dif ficulties known for resonant controllers [8]. The great

advantage of the synchronous reference method is in mapping

the ac variables into dc quantities and thus, possibility of em-

ploying simple PI controllers. A side effect of this transforma-

tion is, however, introduction of mutual coupling terms into

equations. Conventionally, input decoupling terms are used to

decouple active and reactive power control loops and simple PI

controllers are used to close the loops. This strategy is well un-

derstood and is widely used for -type output filters [3], [4].In an -type filter, the decoupling terms are complicated

and have not been formulated so far. Instead, the -type de-

coupling terms have been applied to -type filters for the

sake of controller design [9], [10]. This is an approximate so-

lution which can create performance and stability problems for

higher values of switching frequency to resonance frequency ra-

tios [10]. The problem has been mitigated in [10] by adding fur-

ther second-order transfer functions in the control loops. More-

over, such methods do not guarantee damping of the resonance

mode. In [5], an alternative approach to tackle the problem is

introduced based on a linear full state feedback and deadbeat

control which does not consider the nonlinear dynamics of thedc link voltage.

The proposed approach uses a transformed set of variables

that transforms the control system into a linear system despite

the nonlinearity of the original equations. This linear system is

further decoupled into two subsystems. The two resulted linear

subsystems correspond to active and reactive power control

loops. The active power loop is also controlled by the dc link

variable that turns out to be the dc link energy rather than dc

link voltage. The final control loop includes one integrating

controller for each loop in order to achieve zero steady state

er ror and also to achieve robustness to system uncertainties

and disturbances. The design of such integrating controllers is

performed using standard root-locus method without resorting

1949-3029/$26.00 © 2011 IEEE



424 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 2, NO. 4, OCTOBER 2011

Fig. 1. Block diagram of a typical three-phase grid-connected renewable en-ergy system using a two-stage conversion topology.

to any trial and error. This is possible thanks to the perfect

decoupling of the two loops. Another advantage of having two

decoupled loops is minimization of undesirable transients of

reactive current caused by changes of active power and vice

versa. This, for example, can become more important when

a sensitive dc load is connected to the dc link of the system.

Moreover, active damping of the resonance mode is automati-

cally achieved by appropriate selection for the location of the

closed-loop poles. Moreover, the proposed method is inher-

ently adaptive with respect to grid frequency, a characteristic

that cannot easily be achieved in other approaches. This paper

also introduces a method to design, formulate, and control the

startup transients of the system by using additional terms in the

control structure. Such terms are formulated and designed for

both -type and -type converters.

The paper is organized as follows. The study system is in-

troduced in Section II and the problem formulation is formally

presented in Section III. The proposed technique of decoupling

and control is explained in Section IV. The startup control

is presented in Section V. Section VI presents some perfor-

mance evaluation results and Section VII concludes the paper.

Those materials of more mathematical nature are provided in

Appendix.

II. STUDY SYSTEM

Block diagram of a typical three-phase grid-connected re-

newable energy system is shown in Fig. 1. The conversion

system may comprise of 1) a first-stage converter whose main

objectives are maximum power point tracking (MPPT) and

performing a voltage boost, 2) a VSC that converts the dc power

stored in the dc link into ac, and 3) an output filter that serves

as the interface between the inverter and the grid to attenuate

switching noises. The power generated by the renewable source

is , and the current injected to the grid is while the dc link

capacitance is and its voltage is . This structure is called

the two-stage conversion system. It is possible to remove the

first stage and connect the renewable source directly to the dc

link. In such a structure, called a single-stage structure, the

inverter performs the MPPT as well.

III. SYSTEM EQUATIONS AND PROBLEM DEFINITION

A. L-Type Output Filter

Fig. 2 (top) shows the single line block diagram of a three-

phase grid-connected converter with an output -typefilter. The

system equations in terms of phases , , and are

(1)

Fig. 2. Single line converter block diagram with an output -type filter (top)or -type filter (bottom).

The system equations are transformed to using

. Moreover, the system istrans-

formed to frame using transformation.

The resulted set of equations is

(2)

where the -transformation is performed using the grid voltage

angle as the reference. In (2), is the grid frequency and is

the grid voltage magnitude. We assume a purely sinusoidal and

balanced grid voltage in this study. The power balance equation

can be used to derive an equation for the dc-link voltage as

follows:

(3)

In (3), denotes the inverter instantaneous output power

(4)

where stands for the instantaneous power of the filter

which is zero (in balanced three-phase case). Notice that internal

system losses are neglected. Thus, (3) is

(5)

Equations (2) and (5) describe the dynamic of thesystem state

variables . Since the converter uses PWM tech-

nique, and , where and are thecontrol signals. As a result, the nonlinear state space equations

are

(6)

where the input power is in general a nonlinear function

of the state variables. This is a third-order nonlinear multivari-

able system.

B. LCL-Type Output Filter

A single line diagram of a three-phase filter connection

is shown in Fig. 2 (bottom portion). The differential equations



KHAJEHODDIN et al.: CONTROL DESIGN APPROACH FOR THREE-PHASE GRID-CONNECTED RENEWABLE ENERGY RESOURCES 425

governing this system in the -frame can be written as

(7)

where the -transformation is performed using the grid voltage

angle as the reference. With the definition of state-variables as

, the control signals as

, the system of (7) is a multivariable nonlinear system

of order seven.

C. Control Objectives

For both converters with -type or -type output filters,

the control objectives are (i) injecting the (maximum real and

controlled reactive) powers to the grid, (ii) maintaining a pure

sinusoidal form for the injected current, and (iii) controlling the

peak inrush current at the startup stage. In the two-stage struc-

ture, the MPPT is performed by the first-stage converter and the

VSC transfers the maximum power to the grid by means of reg-

ulating the dc link voltage at a constant prespecified value. In

the single-stage structure, however, the dc link voltage directly

reflects the source voltage and therefore, the dc link voltage ref-

erence is obtained from a MPPT algorithm and it is not constant

anymore. In other words, the objective (i) can be further decom- posed into two objectives: (i-1) regulating the dc link voltage

to its reference value, and (i-2) controlling the flow of reactive

power. There are few challenges in the control of such systems

that are the coupling between the outputs of the system, the non-

linearities in the system equations, and grid voltage distortions.

Such challenges are much more pronounced in the -type

inverter.

IV. PROPOSED CONTROL SYSTEM

A. Proposed Method for L-Type Filters

The reactive power control loop, formulated by the second

equation in (2), can be decoupled from the dc-link control loop

by introducing a new input variable .

The equation thus becomes which is rep-

resented by the transfer function . In other

words, from the new input variable to the output reactive cur-

rent, the system is decoupled and SISO. Now, in order to en-

sure zero steady-state error in the presence of uncertainties, we

use a simple integrating ( ) controller for this loop as

. The control signal will then be equal to

(8)

With this control, the closed-loop will have the following

transfer function:

The constants and can easily be selected to achieve a de-sirable transient response.

The dc-link control loop can be linearized using

transformation that is the energy stored in the

dc-link. This change of coordinates can be obtained using a

full state feedback linearization technique as explained briefly

in Appendix A. However, in this case due, to simplicity of the

-filter case, the solution is found intuitively. Using the output

feedback linearization technique, the dc-link control loop can

be represented as

(9)

This form allows decoupling and also feedback linearization of

the equations by choosing

The resulted equations will be

(10)

that has a transfer function .

To ensure zero steady state error in the presence of uncertainties,

an controller is used. The closed-looptransfer function is

which can have a desirable transient response provided that the

constants and are properly selected.

The control signal for the dc-link control loop is given by

(11)

In the above equations, the input power is a nonlinear

time varying variable whose derivative is shown in the equa-

tions. In renewable energy applications, this quantity is slow

varying compared to the dynamics of the controller and more-

over, if maximum power point tracking is utilized, the input

power derivative variations will be around zero. Furthermore,

the integral controller in the system will compensate any slow

variations of the quantity as a disturbance signal. As a result, in




Fig. 3. Control system block diagram of the -type converter.

Fig. 4. Control system block diagram of the -type converter (reconfigured according to conventional approach).

Fig. 5. Root locus of the reactive current control loop for -type converter.

the final implementation of the controller the power derivative

term is not considered.

Fig. 3 shows the control system block diagram of the -type

converter using the proposed method. The main decoupling

terms are and that are well known in the liter-

ature [3]. The term also helps generating a better startup

transient. However, the proposed method is different from the

conventional method in three aspects: 1) the system is globally

linear from controllers point of view; 2) the introduction of

terms make the control system design as simple as designing an

integral controller; and 3) a feed-forward (or decoupling) term

associated with the input power is also included in the real

Fig. 6. Root locus of the dc-link energy control loop for -type converter.

power loop. This latter term is also from the same nature

of and it mainly helps avoiding large startup transients. The

integrating controller ensures compensation of these two terms

in the steady state anyway. Fig. 4 shows a reconfigured version

of Fig. 3 in a way that it resembles the conventional structure.

The design process can be done by selecting and obtaining

(or ) using the root-locus method. Figs. 5 and 6 show

the root locus of the decoupled control loops of the proposed

system. The system parameters are , mH,

, . The controller gains for the desired lo-

cation of closed-loop poles are and

.




B. Proposed Method for LCL-Type Filters

Control design for the -type converter is more compli-

cated than the -type converter because the number of equa-

tions is higher and the decoupling terms are not visible. In the

approach proposed in [9], the capacitor in the output filter is

neglected and the filter is treated like a simple filter

with . To take advantage of -type filters,the tendency is to operate at switching frequencies and subse-

quently sampling frequency much higher than the resonant fre-

quency [1]. However, this approximation of with , can

easily cause performance deterioration or even instability as the

switching (sampling) frequency increases beyond four times the

resonant frequency [10].

In this paper, the decoupling terms and controller design are

accomplished without any approximation and as a result the sta-

bility and performance of the system are not affected by the

switching (sampling) frequency.

The system equations using the filter are given by (7).

The reactive power is equal to , thus, can solely be used to control the reactive power. Using the feedback lin-

earization technique (see Appendix A) one can write

(12)

where and is the new input signal. Thus, from

to the output reactive current , the system is SISO and

decoupled. As a result, the open-loop transfer function will be

A simple selection is , , that

results in , where is a properly

chosen positive number. Then, a controller as simple as

results in the following closed-loop transfer function:

that yields a desirable transient response should and are properly selected. Therefore, the control law can be written as

(13)

Similar to the filter, the active power control loop is de-

signed via the dc-link voltage (or energy) control. Based on the

feedback linearization technique and with respect to (7), write

(14)

In deriving the above equations, the time derivatives of are

neglected based on the justification made for the filter. Thus,

the open-loop transfer function is

which can be simplified to

with the selection of , , ,




Fig. 7. Control system block diagram of the -type converter.

, where is a positive real number. Using an con-

troller , the closed-loop system will have the fol-

lowing transfer function:

The coef ficients and can readily be selected to place the

poles at a desired location and to achieve desirable transient

response. Therefore, the control law can be written as

(15)

Fig. 7 shows the control system block diagram of the

-type converter using the proposed method. It can be

observed that the system is linear from to and from

to . The decoupling terms are shown in terms of tothat are explained above. It is worth mentioning that these

terms are linear combination of the system state variables and

there are no time derivatives involved. The design procedure

comprises selection of and obtaining (and ) using a

simple root-locus curve. Figs. 8 and 9 show the root locus of the

decoupled control loops of the proposed system. The system

parameters are , mH, H,

F, , . The controller gains

for the desired location of closed-loop poles are

and , where and are shown in Fig. 7.

V. STARTUP CONTROL

The initial startup stage of the system depends very much on

the initial conditions of the system and their interaction with the

control algorithm. This can cause harsh behavior at the startup

stage leading to system failures. In this paper, it is proposed to

include constant terms to the control loops, shown by and

in Fig. 3 to smooth such behavior. This section proposes a

method to optimally design such constants.

Assume that the command signal is set to zero and the linear

loop dynamics is described by where the scalar

is the startup smoothing term. The objective is to design

the term such that the startup behavior of

is controlled. The response of this system can be expressed as

, where

is the vector of initial conditions, is the system’s

Fig. 8. Root locus of thereactive current control loop for -type converter.

Fig. 9. Root locus of the dc-link energy control loop for -type converter.

response to the initial conditions (with no constant input),

and is the system’s response to the unity constant input

(with no initial conditions). By defining the following norm:

, where is a positive semidefi-

nite matrix, one can conclude

. By solving

the time derivative equation with respect to , results in

(16)




Fig. 10. Impact of startup controller for the -type filter.

The matrix must be properly chosen to ensure the best re-

sponse. The following is the summary of results for and

filters, respectively.

A. L-Type Filter

Thereactive power loop (in the absence of a command signal)

is described by , . The initial

conditions are , . Therefore, the response to

initial conditions, i.e., , is identically zero. This results in

that no smoothing term is required and thus .The dc link energy loop (in the absence of a command signal)

is described by , ,

. The initial conditions are ,

, . The expression (16) will be equal

to about for the numerical values of mH,

F, V, and . The matrix is a di-

agonal matrix with diagonal elements equal to 0 and 1, respec-

tively. Fig. 10 shows that the startup controller can significantly

smooth the initial stage of the responses. In this figure, a jump

from 1 to 2 kW (in the input power ) is applied at s

and a jump from zero to 2.5 A in reactive current is applied

at s. As mentioned, the reactive power loop needs nostartup control. It is also worth mentioning that the startup co-

ef ficient does not depend on the value of and thus, it can

be designed independent from the system operating point.

B. LCL-Typefilter

The dc link energy control loop is described by the following

equations: , , ,

, , where . The initial

conditions are , ,

, where . Calculating from (16)

(for the numerical values of mH F,

F, , , F) results in .

The matrix is chosen to be diagonal with elements zero except

for the last one that is unity.

Fig. 11. Impact of startup controller for the -type filter.

The reactive power control loop is described by the following

equations: , , ,

, where . The initial conditions are, , , . The same method

(used above) for startup control is applied and it failed to satis-

factorily improve the startup control. Therefore, we generalized

the startup controller from a constant value to a full state feed-

back as follows. The startup controller is equal to .

The gain vector is calculated using the LQR technique that

minimizes the cost function . Selection

of matrix is crucial in this process. It is performed by varying

diagonal elements over some positive range and observing the

root-locus as well as the startup response. Fig. 11 shows the

closed-loop system response to a command of real power at

s and a command of reactive power at s.Highly satisfactory startup transient is observed. Without this

controller, the startup responses are very harsh and intolerable

(not shown).

VI. PERFORMANCE EVALUATION R ESULTS

The proposed method is realized on a 3-kW solar photo-

voltaic (PV) system that is directly connected to the dc link and

a three-phase PWM inverter is used. The switching frequency

is 20 kHz and the power system parameters are mH,

F, mH, F. The controller

gains are designed using the proposed technique for and

-typefi

lters. The whole system is simulated in PSIM soft-ware. Several simulation results are presented in this section to

verify static and dynamic performances and robustness of the

proposed method.

A simulation scenario is defined as follows: the system starts

from zero to full irradiation level and the irradiation level drops

50% at 0.05 s and the command for reactive current steps from

zero to 20 A at s. Fig. 12 shows the graphs of grid

current components and (top portion), the dc-link voltage

(middle portion) and the grid currents in frame (bottom

portion) for the -typefilter. It is observed that the and

waveforms follow their commands closely. The dc link voltage

is regulated to 500 V with small transients at the jump instants.

The same simulation scenario is applied to the -type

filter and the resultsare shown in Fig. 13. Desirable performance




Fig. 12. Performance of the -type controller: d and q axes grid current (top),dc link voltage (middle) and grid currents (bottom).

Fig. 13. Performance of the -type controller: d and q axes grid current(top), dc link voltage, grid currents and input power (bottom).

of the controller in tracking the power commands and in regu-

lating the dc link voltage is observed. The very bottom portion

in Fig. 13 shows variations of the PV power. It confirms smooth

variations of this variable.

Fig. 14. Performance of the -type controller with 250 H uncertainty inthe grid impedance: d and q axes grid current (top), dc link voltage, gridcurrents and input power (bottom).

Further, in order to verify robustness of the proposed method

with respect to different parameters, the following three sets

of simulations are performed using the same simulation sce-

nario defined above. In one simulation, an uncertainty in the

grid impedance with the value of 250 H is considered. Thesimulation results are shown in Fig. 14. The control system tol-

erates this large uncertainty and only small impacts on transient

responses are observed. Another simulation considers the im-

pact of one sample delay corresponding to calculation time. The

sampling frequency is 20 kHzfor this simulation. Theresults are

shown in Fig. 15 which confirm desirable operation of the con-

trol system with only minor impacts on the transient response

due to this delay. Oneadvantage of the proposed control method

is that its control gains are derived in terms of the system fre-

quency. Therefore, the same control design can be used for sys-

tems with different values of frequency. Fig. 16 shows a simu-

lation where the system frequency is 80 Hz. The performance isalmost identical with that of the 60-Hz system shown in Fig. 13.

VII. CONCLUSION

For three-phase grid-connected inverter systems, control

methods are proposed 1) to accurately formulate the decou-

pling terms in and -type outputfilters, 2) to design its

controller gains, and 3) to control the startup transient of the

system. Advantages of the methods are 1) systematic treatment

of the problem using known control theories, 2) globally

linear control loops using appropriate change of coordinates,

3) systematic design procedure, and 4) robustness against

grid uncertainties. The proposed method obviates the need for




Fig. 15. Performance of the -type controller with the same control design(performed for 60 Hz) working at a system frequency of 80 Hz: d and q axesgrid current (top), dc link voltage, grid currents and input power (bottom).

Fig. 16. Performance of the -type controller with the same control design(performed for 60 Hz) working at a system frequency of 80 Hz: and axesgrid current (top), dc link voltage, grid currents and input power (bottom).

incorporating additional filters to partially compensate for in-

stabilities caused by approximate decoupling in high switching

frequencies.

Fig. 17. Diagram of output feedback linearization technique used in this paper.

APPENDIX A

R EVIEW OF FEEDBACK LINEARIZATION TECHNIQUE

The feedback linearization technique [11], [12] is a useful

concept of nonlinear control theory. Consider a single-input

single-output (SISO) system described by the following

state-space equations:

(17)

where is the -dimensional state vector, is thecontrolsignal,

and is the output. The full-state feedback linearization tech-nique involves a coordinate transformation on the state vector

such as and also on the control signals

such that the state-space equations transform to the linear rep-

resentation . For the -type and -type con-

verter, the linearizing coordinate is obtained by defining the dc

link energy as the new state variable.

The output feedback linearization is a special case of the

state feedback linearization in the sense that the new coordi-

nates consists of the output and its time-derivatives up to a

certain degree. Such a degree is called the relative degree of

the system. The time-derivative of the output signal is

, where is the Liederivative and is defined as . Assume that

and calculate the second derivation of with re-

spect to time as , where by definition

. We keep taking time derivatives until the

factor in front of becomes nonzero. Assume that this occurs

for , i.e., and .

Define the new input and thus the

system becomes that is a linear system of order .

This linear system has all its poles at origin and has no zero. Let

where for is an algebraic function of the

system state variables and does not use any time differentiation

of the state variables.

Then the transfer function from to is

and its poles can be arbitrarily placed by selecting ’s. When

the command is a constant signal, a simple integrating ( )

controller can be used to achieve desired response. Block dia-

gram of the whole system is shown in Fig. 17. The scalar is

the relative degree of system and this method of control leaves

state




In case a multi-input multi-output (MIMO) system is con-

cerned, the same process can be performed on every output of

thesystem. If thenumber of control inputs is equal to the number

of outputs (a square system), then it is possible to arrive at a

new system of coordinates and new set of inputs that make the

system decompose into multi-SISO systems. This is indeed the

case with grid connection of three-phase inverters as it is dis-

cussed in this paper.

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S. Ali Khajehoddin (S’04–M’10) received the B.Sc.degree in electrical engineering and the M.Sc. degreefrom Isfahan University of Technology, Iran, in 1997and 2000, and the Ph.D. degree from Queens Univer-

sity, Kingston, ON, Canada, in 2010.After completing his Masters, he established a

company where he developed and produced digitalmeters and high-tech power system analyzers for fiveyears. For his doctoral research at Queens, he workedon the design and implementation of compact anddurable micro-inverters for photovoltaic (PV) grid

connected systems. Since 2010, he has been working at SPARQ systemsInc. toward mass-production and commercialization of micro-inverters. Hisresearch interests include power electronics, control systems, power quality,and renewable energy systems mainly PV systems.

Dr. Khajehoddin has filed four patents and was awarded several scholar-ships, including the MITACS Industrial Postdoctoral Fellowship and the On-tario Graduate Scholarship.

Masoud Karimi Ghartemani (M’01–SM’09)received the B.Sc. and M.Sc. degrees in electrical

engineering in 1993 and 1995 from Isfahan Uni-versity of Technology, Iran. He received the Ph.D.degree in electrical engineering from University of Toronto in 2004.

He was a faculty member at Sharif Universityof Technology from 2005 to 2008. He is currentlya researcher with the Queen’s Centre for Energyand Power Electronics Research (ePOWER) at theQueens University, ON, Canada. His research inter-

ests include power system stability and control, grid-integration of renewableenergy systems, and power quality.

Praveen K. Jain (S’86–M’88–SM’91–F’02) re-ceived the B.E. degree (with honors) from the

University of Allahabad, India, and the M.A.Sc.and Ph.D. degrees from the University of Toronto,Canada in 1980, 1984, and 1987, respectively, all inelectrical engineering.

Currently he is a Professor and Canada ResearchChair at the Department of Electrical and Computer Engineering, Queen’s University, Kingston, Canada,and the Director of the Queen’s Centre for Energyand Power Electronics Research (ePOWER). He has

received over $20M cash and $20M in-kind in external research funding to con-duct research in the field of power electronics. He has supervised more than 75graduate students, postdoctoral fellows, and research engineers. He has pub-lished over 350 technical papers (including more than 90 IEEE Transactions papers) and has over 50 patents (granted and pending). He is also a Founder of CHiL Semiconductor in Tewksbury, MA (recently a cquired by IR); and SPARQSystem in Kingston, ON, Canada. Prior to joining Queen’s, he has worked as aProfessor at Concordia University (1994–2000), a Technical Advisor at Nortel

(1990–1994), a Senior Space Power Electronics Engineer at Canadian Astro-nautics Ltd. (1987–1990), a Design Engineer at ABB (1981), and a ProductionEngineer at Crompton Greaves (1980). In addition, he has consultedwith Astec,Ballard Power, Freescale, General Electric, Intel, and Nortel.

Dr. Jain is an Associate Editor of the IEEE TRANSACTIONS ON POWER

ELECTRONICS and an Editor of International Journal of Power Electronics.He is also a Distinguished Lecturer of IEEE Industry Applications Society.He is a Fellow of the Engineering Institute of Canada (EIC) and the CanadianAcademy of Engineering (CAE). He is also the recipient of the 2011 IEEE Newell Award–the highest field award in Power Electronics.

Alireza Bakhshai (M’03–SM’09) received theB.Sc. and M.Sc. degrees from the Isfahan Universityof Technology, Isfahan, Iran, in 1984 and 1986,

respectively, and the Ph.D. degree from ConcordiaUniversity, Montreal, QC, Canada, in 1997.

From 1986 to 1993 and from 1998 to 2004, hewas on the faculty of the Department of Electricaland Computer Engineering, Isfahan University of Technology. He was a Postdoctoral Fellow from1997 to 1998 at Concordia University. Currently, heis with the Department of Electrical and Computer

Engineering, Queens University, Kingston, ON, Canada. His research interestsinclude high-power electronics, distributed generation, wind energy, smartgrid, control systems, and flexible ac transmission systems.

a control design approach for three-phase

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