1

Abstract-- At a given wind velocity, the mechanical power

available from a wind turbine is a function of its shaft speed. To maximize the power captured from the wind, the shaft speed has to be controlled. In low-cost wind energy conversion systems, the turbine shaft speed is not regulated and a squirrel-cage induction generator is used to convert the turbine mechanical power to electric power. Power electronic converters are used to interface the induction generator with the grid and maximize the power captured from the wind. In this paper, a wind energy conversion scheme based on the matrix converter topology is proposed. As the commutation problems in the conventional nine-bidirectional switch matrix converter topology impairs its performance in industrial applications, an improved topology which does not have any commutation problems, has been adopted for the system presented in this paper. Through matrix converter, the terminal voltage and frequency of the induction generator can be controlled in such a way that the wind turbine is operating at its maximum power point for all wind velocities. The power factor at the interface with the grid is also controlled by the matrix converter to ensure purely active power injection into the grid for optimal utilization of the installed wind turbine capacity. Furthermore, the reactive power requirements of the induction generator are satisfied by the matrix converter to avoid self-excitation capacitors. Theoretical analysis and simulation results are used to support the claims made on the advantages of the proposed scheme.

Index Terms-- Wind energy, squirrel cage Induction generator, matrix converter, maximum power point tracking.

I. INTRODUCTION

UE to the increasing demand on electrical energy and environmental concerns, a considerable amount of effort

is being made to generate electricity from renewable sources of energy. The major advantages of using renewable sources are abundance and lack of harmful emissions. Wind is one of the most abundant renewable sources of energy in nature. The wind energy can be harnessed by a wind energy conversion system (WECS), composed of a wind turbine, an electric

S. M. Barakati is with the Department of Electrical & Computer

Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada (e-mail: smbaraka@engmail.uwaterloo.ca).

M. Kazerani is with the Department of Electrical & Computer Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada (e-mail: M.Kazerani@ece.uwaterloo.ca).

X. Chen is with the Department of Electrical & Computer Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada, as a visiting scholar from Harbin Institute of Technology, China (e-mail: chenxiyou@hotmail.com).

generator, a power electronic converter and the corresponding control system.

Based on the types of components used, different WECS structures can be realized. However, the objective in all structures is the same, i.e., the wind energy at varying wind velocities has to be converted to electric power at the grid frequency [1].

Wind turbine configurations for extracting energy from the wind are categorized based on horizontal or vertical axis, number of blades and power rating. Modern wind turbines are of horizontal-axis type, normally have three blades, and their output power can be as high as 2MW per machine [2].

To choose other components of WECS, the strategy of speed control should be known. It has been shown that, for grid connected wind turbine systems, the efficiency of constant-speed systems is lower than that of variable-speed systems. Therefore, despite the extra cost of power electronics, the life-cycle cost is lower. Many different configurations of variable-speed wind turbines have been introduced in the literature [3],[4],[5]. Reference [3] introduces a high-performance configuration, commonly known as Scherbius drive, composed of a doubly-fed induction generator (DFIG) and a PWM AC/DC/AC converter connected between the stator and rotor terminals to implement variable speed operation. Another configuration for variable-speed wind turbines has been introduced in [4]. This system is composed of a DFIG with a matrix converter connected between the stator control winding and the main stator terminals. Variable speed is implemented through control of the matrix converter. The main advantage of the configurations reported in [3] and [4] is in employing a pilot converter to perform shaft speed control. The main disadvantage of these schemes is the high cost of the doubly-fed induction generator.

Recently, the use of squirrel-cage induction generator (SCIG) for direct grid-connection of WECS has been well established, due to the low cost in comparison with other types of electric machines [6],[7],[8]. The most common configuration of power converters for WECS based on variable-speed wind turbine and SCIG is that composed of two back-to-back voltage source converters with a large capacitor on the dc-link. The power flow of the grid side converter is controlled in order to keep the dc-link voltage constant, while the control of the generator side is set to satisfy the SCIG magnetization demand and control the speed or torque. A technical advantage of this topology is the capacitor decoupling between the grid converter and the

A New Wind Turbine Generation System Based on Matrix Converter

S. M. Barakati, M. Kazerani, Senior Member, IEEE, and X. Chen

D

2

generator converter. Besides providing some protection, this decoupling facilitates independent control of the two converters, allowing compensation of asymmetries on both the generator and the grid sides. However, the dc-link capacitor is bulky and exhibits relatively reduced lifetime [7].

The matrix converter (MC) provides direct AC-AC conversion and is considered an emerging alternative to the conventional two-stage AC-DC-AC converter topology [9],[10]. A matrix converter provides a large number of control levers that allows for independent control on the output voltage magnitude, frequency and phase angle, as well as the input power factor. When compared with the AC-DC-AC converter system, the bold feature of MC is elimination of the DC-link reactive elements, e.g., bulky capacitors and/or inductors. However, this topology has not yet found its appropriate place in industrial applications. The main reasons behind this are the potential commutation problems, requiring complex control and snubber circuits, unavailability of monolithic bi-directional switches, lack of decoupling between the two ac sides of the converter, and low voltage gain.

A novel MC topology with advantages over the conventional nine-bidirectional-switch topology has been developed by Wei and Lipo [11]. The improved topology has the same performance as the conventional MC, but does not have any commutation problems. In addition, voltage gain is improved and control is simplified.

This paper proposes a new wind energy conversion system in which the AC-DC-AC converter has been replaced by an improved MC topology and the doubly-fed induction machine has been replaced by a less costly SCIG machine. In this paper, first, a brief description of WECS is provided. Then, it is demonstrated how the wind energy can be optimally captured and converted to electric energy using a wind turbine, a SCIG and a matrix converter. Finally, some simulation results based on the proposed WECS are presented to support the theoretical expectations.

II. THE PROPOSED SCHEME

Fig. 1 shows a block diagram of the proposed wind energy conversion scheme. As the entire power generated by the wind turbine is transferred through the matrix converter, this work targets low-to-medium-power wind turbines. For medium-to-high-power wind turbines, doubly-fed induction generator with a pilot converter connected to the auxiliary winding will be more appropriate. The wind turbine is followed by a gear box which steps up the shaft speed. Note that working at a low shaft speed translates into a low induction generator terminal frequency which can result in core saturation unless a low terminal voltage is imposed. At low terminal voltages, the operating current will be high, making the scheme impractical. The matrix converter interfaces the SCIG with the grid and implements shaft speed control to achieve maximum power point tracking at varying wind velocities. It also performs power factor control at the grid interface and satisfies the Var demand at the induction generator terminals. The proposed scheme allows for

connecting individual wind turbines to the grid. It also permits paralleling the outputs of several wind turbine generation units at the grid interface. The power handling capability of the system can be enhanced by adopting a multi-converter approach. In the following sections, different elements of the system will be described.

GearBox

SCIGMatrix

Converter

Grid

Fig. 1 Schematic diagram of proposed wind energy conversion scheme.

III. WIND TURBINE

The mechanical power generated by a wind turbine is given by Equation (1) [12].

31

2 p r wP C A Vρ= (1)

where P is the power in W, ρ the air density in g/m3, Cp a dimensionless factor called power coefficient, Ar the turbine

rotor area in m2 ( 2r rA Rπ= , where Rr is the rotor blade radius)

and Vw the wind speed in m/s. The power coefficient is related to the tip speed ratio λ and rotor blade pitch angle θ according to Equation (2) [12].

18.4 /2.14151( , ) 0.73 0.58 0.002 13.2 i

pi

C e λλ θ θ θλ

−⎛ ⎞= − − −⎜ ⎟

⎝ ⎠ (2)

where

3

11 0.0030.02 1

iλ

λ θ θ

=−

− +

(3)

and

r r

w

R

V

ωλ = (4)

In (4), ωr is the angular speed of the turbine shaft. The theoretical limit for Cp is 0.59 according to Betz’s Law [13], but its practical range of variation is 0.2-0.4. In this paper, the rotor pitch angle is assumed to be fixed. Fig. 2 shows a typical Cp versus λ curve [6].

0 1 2 3 4 5 6 7 8 9 10

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

POWER COEFFICIENT Cp( )

Tip Speed Ratio ( )

l

λ

λ

Fig. 2 A typical Cp versus λ curve

As Equations (1)-(4) suggest, the mechanical power generated by the wind turbine at a given wind velocity is a function of the shaft speed. In this paper, a wind turbine

3

model has been created in PSIM simulation package based on the equations (1)-(4) [6]. The block diagram of the model is shown in Fig. 3 and a typical P versus ωr curve produced by the model is shown in Fig. 4.

λ C(λ)ω r

V

PwρR

Tw

Fig. 3 Block diagram of the wind turbine model in PSIM: ω r: shaft speed, V: wind velocity, R: radius of the shaft, ρ :Air Density.

0 1 2 3 4 5 6 7 80

20

40

60

80

100

120

140

TURBINE POWER (KWat)

SPEED(rad/Sec.)

Vw3

Vw2

Vw1

*

*

*

Vw3>Vw2>Vw1

Fig. 4 Typical P versus ωr curves for different wind velocities (* = PMax).

As seen from Fig. 4, at any given wind velocity, maximum power can be captured from the wind if the shaft speed is adjusted at the value corresponding to the peak power. The idea in this paper is to change the terminal frequency of the induction generator through matrix converter frequency control to track the shaft speed corresponding to the maximum turbine power at all times. The maximum power tracking can be achieved through perturbing the shaft speed in small increments or decrements and observe the direction of changes in the power till the maximum power, at which dP/dωr=0, is reached. The method suggested in this paper for maximum power tracking is perturbation and Observation which is commonly used in photovoltaic energy conversion systems for capturing the maximum power from the solar array under different insolation levels.

IV. SQUIRREL-CAGE INDUCTION GENERATOR

Fig. 5 shows a typical torque-speed curve for a SCIG. In Fig. 5, Te is the induced torque in the induction machine. The sign of the torque in the motoring and generating regions has been specified based on the convention that: Tmotor > 0 and Tgenerator < 0. The magnitude of the counter torque that is developed in the induction generator as a result of the load connected at the machine’s stator terminals is then Tc = - Te. The theoretical range of operation in the generator mode is limited between the synchronous angular speed ωs and the ωr

corresponding to the pushover torque. ωs is related to the induction generator terminal frequency fe dictated by the matrix converter through Equation (5).

0 50 100 150 200 250 300 350 400

-500

-400

-300

-200

-100

0

100

200

300

wm

Operating Region

Torque

Nm

Fig. 5 A Typical Te versus ωr curve for SCIG.

4

s efp

πω = (5)

where p is the number of poles of the induction generator. Fig. 6 shows the Pw - ωr and Tw - ωr curves of the wind turbine, as well as a family of Tc - ωr curves for the induction generator for different ωs values. As shown in Fig. 6, by varying fe and thus ωs, the Tc - ωr curve can be shifted to the right or left with respect to the torque-speed curve of the wind turbine to assume a wide range of possible steady-state operating points defined by the intersections of the two curves. Obviously, one of the operating points corresponds to maximum power. To move from one operating point to another, fe is changed in steps (small enough to maintain generating mode) and the difference between the wind turbine torque Tw and the new counter torque of the induction generator Tc at the operating speed will accelerate or decelerate the shaft according to Equation (6) until the new steady-state operating point is reached.

rw c

dT T J

dt

ω− = (6)

0 .33 .66 1 1.33 1.66

-1.5

-1

-.5

0

.5

1

1.5

2

2.5

wr

Tw

Tc

Torque (pu)

Pw

Power(pu)

P w

T w OP1

OPm OP2 1

(PU)

ws1 wsm w

s2

wr /wrm

Wind Velocity Vw

*

Fig. 6 Maximizing captured wind power by shifting Te - ωr curve.

4

A. Accelerating Shaft Towards Maximum Power Point

In Fig. 6, OPm is the operating point corresponding to maximum power captured from wind at the wind velocity of Vw

*. At this point, Pw =1 pu, Tw =1 pu, and ωr = ωrm =1 pu, where ωrm is the angular shaft speed corresponding to maximum power point.

Assuming the present operating point to be OP1, corresponding to ωs1, the shaft should speed up so that the operating point OPm can be assumed by the system. This can be achieved by increasing ωs from ωs1 to ωsm through an increase in the SCIG terminal frequency. The SCIG terminal voltage is also adjusted by the matrix converter according to the constant V/f strategy. The frequency adjustment is performed in steps small enough for the induction machine to keep operating as a generator throughout the transition period. This action makes Tw-Tc>0 and accelerates the shaft according to Equation (6) towards maximum power point.

B. Decelerating Shaft Towards Maximum Power Point

Assuming the present operating point to be OP2, corresponding to ωs2, the shaft should slow down so that the system assumes the operating point OPm. This can be accomplished by decreasing ωs from ωs2 to ωsm through a decrease in the SCIG terminal frequency and voltage according to constant V/f strategy, in steps small enough to restrict operation within the stable generating region. This action makes Tw-Tc<0 and decelerates the shaft according to Equation (6) towards maximum power point.

V. MAXIMUM POWER POINT TRACKING ALGORITHM

Instead of a closed-loop control that finds the SCIG terminal frequency based on the error between the actual and reference values of power, for capturing maximum power from the wind [6,7,8], in this paper, Perturbation and Observation method [14] has been adopted to track the maximum power point. In this method, the SCIG terminal frequency is incremented or decremented in small steps as long as the signs of ∆f and ∆P/∆f are the same, as an indication for moving towards the maximum power point. When ∆P/∆f=0, maximum power point has been reached. If incrementing or decrementing the frequency results in opposite signs for ∆f and ∆P/∆f, the direction of frequency change is reversed. This method which has been successfully used for maximum power point tracking of photovoltaic energy conversion systems, has three advantages over the closed-loop control approach with PI- controller:

1. Perturbation and Observation method does not need priori knowledge of maximum wind turbine power Pw,max at different wind velocities and the induction machine parameters. In closed-loop control approach, this priori knowledge is required to calculate the maximum power on the induction generator side, which is used as the reference for power.

2. Perturbation and Observation method works

successfully irrespective of the location of the present operating point with respect to the maximum power point. Closed-loop control approach can be made to work successfully only if the present operating point is to the left or right hand side of the maximum power point, not in both cases. The reason for this is that the variations of Pw with f is not monotonic and closed-loop controller based on PI-controller woks for monotonic variations only.

3. Perturbation and Observation method works based on small increments and decrements of frequency. This ensures smooth acceleration and deceleration towards the maximum power point without overshoot and undershoot in speed. It also maintains operation in the stable generating region of induction machine during transitions. Closed-loop control based on PI-controller is not immune to these problems unless a very slow controller is used.

VI. MATRIX CONVERTER

Matrix Converter represents a new generation of AC-AC converters with a compact design due to the lack of large energy storage elements.

A. Conventional Matrix Converter Topology

The conventional matrix converter topology is composed of an array of nine bi-directional switches connecting each phase of the input to each phase of the output. By properly operating the switches in the matrix converter, one can achieve control on the output voltage magnitude, frequency and phase angle, as well as control on the input displacement angle. Matrix converter is a bi-directional power flow device with the capability of producing high quality input and output waveforms. Fig. 7 shows the schematic diagram of a conventional matrix converter [9,10].

Ai

Ci

Bi

A

B

C

a b c

ai bi ci

n

N

Three-phase ac system 2

Three-phase ac system 1

≡

Fig. 7 Schematic diagram of a conventional matrix converter.

5

A serious drawback attributed to the conventional matrix converter topology is the commutation problems associated with the operation of the four-quadrant switches. Safe operation of the switches require complicated switching strategies impairing the elegance of the topology.

B. Improved Matrix Converter Topology

Fig. 8 shows the schematic diagram of the improved matrix converter topology [11].

p

n

dci

Ai Bi Ci

sav

sbv

scv

avbv

cv Av Bv Cv

ai

bi

ci

+

-fC

n

NController

1 φ 2 θ2 V 2 f

Side 1

Side 2

Gating Pulses

Fig. 8 Schematic diagram of the improved matrix converter.

The improved matrix converter is based on the concept of “fictitious dc link” used in controlling the conventional matrix converter. However, there is no energy storage element between the line-side and load-side converters.

The improved matrix converter topology has the following advantages with respect to the conventional matrix converter topology:

1. The commutation problems associated with the switches have been solved.

2. All the switches at the line-side turn on and turn off at zero current.

As shown in Fig. 8, matrix converter offers four control levers that can be used to control the input displacement angle and output voltage magnitude, frequency and phase angle.

VII. SIMULATION RESULTS

Fig. 9 shows the block diagram of the proposed wind energy conversion system together with the maximum power point tracking control. In this section, the simulation results obtained for the system of Fig. 8 will be presented. In order to assess the capability of the system in tracking maximum power point at varying wind velocity, a step change in the wind velocity is applied to the system. The system is first operating at the wind velocity of Vw1=8m/s. At this velocity, the maximum power captured from the wind turbine is 37.5kW. At t=6 seconds, the wind velocity is decreased to 6m/s. The maximum power corresponding to this velocity is 15.9kW. Again, at t=7.5 seconds, the wind velocity is

GearBox

SCIGMatrix

Converter

Grid

MaximumPower Point

TrackingController

2f

P

K2V

Fig. 9 Proposed wind energy conversion system together with maximum power point tracking control.

increased back to 8 m/s. Fig. 10 illustrates successful tracking of maximum power during the changes made to the wind velocity. This tracking has been accomplished by implementing the Perturbation & Observation technique. Fig. 11 shows the variations in the matrix converter output frequency set-point that results in necessary changes in the induction generator terminal frequency and thus the shaft speed in attempt to track the maximum power point. Fig. 12 illustrates the variation in the shaft speed as a result of induction generator terminal frequency adjustments. Fig. 13 shows the output voltages of matrix converter which is imposed on the induction generator stator terminals. As seen, the magnitude of the induction generator terminal voltage has been varied with frequency according to the constant V/f strategy. It has to be noted that the displacement power factor at the interface with the grid has been maintained at unity during steady-state, using matrix converter control.

6 6.5 7 7.5 8 8.5 9 1

1.5

2

2.5

3

3.5

4x 10

4

PTurbine

PMAX

VW

=6m/ s

VW

=8m/ s

Time

P out-Turbine

KW

(Sec)

Fig.10 Maximum power point tracking control at varying wind velocity.

6

6 6.5 7 7.5 8 8.5 9 30

32

34

36

38

40

42

44

Time (Sec)

Set-poit frequency of Matrix Converter

HZ

Fig. 11 Frequency set point variations during maximum power point tracking.

6 6.5 7 7.5 8 8.5 9 25

30

35

40

45

50

Speed (Shaft of Wind Turbine)

Time (Sec)

RPM

Fig. 12 Turbine shaft speed variations during maximum power point tracking.

6 6.5 7 7.5 8 8.5 9 -500

-400

-300

-200

-100

0

100

200

300

400

500

Line-Line Voltage (Output of Matrix converter)

Volt

Time (Sec)

Fig. 13 Matrix converter terminal voltage variations according to constant V/f control during maximum power point tracking.

VIII. CONCLUSIONS

In this paper, a wind energy conversion scheme based on an improved matrix converter topology with no commutation problems is proposed. The matrix converter controls the terminal voltage and frequency of the induction generator in such a way that the wind turbine is operating at its maximum power point for all wind velocities. The matrix converter also implements unity power factor at the interface with the grid

for optimal utilization of the installed wind turbine power and satisfies the reactive power demand of the induction generator to avoid self-excitation capacitors. The maximum power point tracking is performed through perturbation and observation method. This method is superior to the commonly used PI-controller-based closed-loop control in that it does not require priori knowledge of the maximum wind turbine power at different wind velocities and induction machine parameters. Also, using this method, maximum power point can be reached irrespective of the present operating point, while maintaining the operation in the stable generating region during transitions. The proposed scheme targets small-to-medium power wind turbines without speed regulator that are connected to the grid individually or in groups through low-cost squirrel-cage induction generators. Simulation results show successful tracking of maximum power from the wind at all wind velocities.

IX. APPENDIX

Wind Turbine and Induction Generator Parameters

3

2

: 1.25 / , 10

: 0.294 , 1.39 , 0.156

0.74 , 41 , 6, 4

air wind turbine

s s r

r m

Wind Turbine kg m R m

Induction Generator R L mH R

L mH L mH p J kgm

ρ = =

= Ω = = Ω

= = = =

X. REFERENCES [1] L.L. Freries, Wind Energy Conversion Systems, Prentice Hall,1990. [2] S. Heier, Grid Integration of Wind Energy Conversion Systems, New

York: Wiley, 1998. [3] L Zhang, C Watthanasarn, and W. Shepherd, "Application of a matrix

converter for the power control of a variable-speed wind-turbine driving a doubly-fed induction generator" IECON 97,Vol.2, pp.906 – 911, Nov. 1997.

[4] R.Pena, J.C.Clare, and G.M.Asher, " A doubly fed induction generator using back-to-back PWM converters supplying an isolated load from a variable speed wind turbine" IEE Proc., Electric Power Applications, Volume: 143 , Issue: 5 , Sept. 1996 pp.:380 – 387.

[5] R. Spee, S. Bhowmik, J.H.R. Enslin, " Adaptive control strategies for variable-speed doubly-fed wind power generation systems ", IEE Industry Applications Society Annual Meeting, Vol.1,Oct. 1994 pp. 545 - 552.

[6] M. G. Simoes, B. K. Bose, and R. J. Spiegel, "Fuzzy logic based intelligent control of a variable speed cage machine wind generation system", IEEE Trans. On Power Electronics, Vol. 12, NO. 1, JANUARY 1997,pp 87-95.

[7] R. Teodorescu, and F. Blaabjerg, "Flexible Control of Small Wind Turbines With Grid Failure Detection Operating in Stand-Alone and Grid-Connected Mode",IEEE Trans. On Power Electronics, Vol. 19, NO. 5, SEP. 2004,pp 1323,1332.

[8] W. Lu and B. T. Ooi, "Multiterminal LVDC system for optimal acquisition of power in wind-farm using induction generators", IEEE Tran. On Power Electronics Vol. 17, NO. 4, JULY 2002, pp. 558-563.

[9] M. Venturini and A. Alesina, "The generalized transformer: A new bidirectional sinusoidal waveform frequency converter with continuously adjustable input power factor " in Proc. IEEE PESC’80, 1980, pp. 242–252.

[10] P. W. Wheeler, IEEE, J. Rodríguez, J. Clare,L. Empringham, and A. Weinstein, " Matrix Converters: A Technology Review " , IEEE Trans. On Industrial elctronicas, Vol. 49, NO. 2, APRIL 2002,pp 276-289.

[11] L. Wei, T.A. Lipo, " A Novel Matrix Converter Topology with simple Commutation".

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[12] J. G. Slootweg, S. W. H. de Haan, H. Polinder, and W. L. Kling, "General Model for Representing Variable SpeedWind Turbines in Power System Dynamics Simulations", IEEE Trans. On Power Systems, Vol. 18, NO. 1, FEB.2003, pp. 144-151.

[13] L.S.T. Ackermann, "Wind Energy Technology and current status. A Review", Renewable and Sustainable Energy Review, 4:315-375, 2000.

[14] C. Hua and C. Shen “Comparative study of Peak Power Tracking Techniques for Solar Storage System," Applied powe Electronics Conference and Exposition, vol.2,pp.679-685,Feb.1998.

XI. IOGRAPHIES

S. Masoud Barakati received the B.Eng. degree from Mashhad University, Mashhad, Iran, and M. Eng. degree from Tabriz University, Tabiz, Iran, in 1993 and 1996, respectively. From 1996 to 1997, he was with the Department of Electrical Engineering at S&B University, Iran, as a lecturer. He is presently a PhD student in the Department of Electrical and Computer Engineering at the University of Waterloo, Waterloo, Ontario, Canada. His research interests are in the areas

of control systems and applications of power electronics.

Mehrdad Kazerani (S’88, M’96, SM’02) received the B.Sc. degree from Shiraz University, Iran, M. Eng. degree from Concordia University, Montreal, Canada, and Ph.D. degree from McGill University, Montreal, Canada, in 1980, 1990, and 1995, respectively. From 1982 to 1987, he was with the Energy Ministry, Iran. He is presently Associate Professor with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario, Canada. His research interests are in the areas of power electronic circuits and systems design, active power

filters, matrix converters, distributed power, and FACTS. Xiyou Chen received the B.Sc., M.Sc. and PhD degrees from Harbin Institute of Technology, Harbin, China, in 1982, 1985, and 2000, respectively. He is a professor at Harbin Institute of Technology. Currently, he is with the Department of Electrical & Computer Engineering at the University of Waterloo, as a visiting scholar. His research interests are in applications of power electronics in power systems, matrix converters, and chaos phenomena in power systems and power electronics..