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Abstract—This paper proposes a control methodology for in-terfacing medium and large photovoltaic (PV) arrays to the pow-er system distribution grid. First, the structure of the PV system in grid-connected mode is introduced. It consists of a PV array in addition to a power conditioning system for grid interfacing pur-poses. The power conditioning system is composed of a DC-DC boost converter, followed by a current controlled Voltage Source Inverter (VSI). The system was controlled to inject a clean sinu-soidal current into the grid. Maximum power point tracking (MPPT) and PV cell modeling will be discussed as well. After that, simulation results of the system using MATLAB SIMULINK are presented. Finally, a case study was conducted to examine the effect of the interfacing transformer topology on the system during fault conditions.

Index Terms—Control, Photovoltaic power systems, Pulse width modulated inverters, Maximum Power Point Tracking.

I. INTRODUCTION ISTRIBUTED Generation is one of the fastest growing areas of research in today’s evolving power system. Al-

though the concept of generating power from multiple dis-persed locations is not new, the introduction of renewable energy sources and small capacity fossil fuel generators to the centralized power grid is a relatively new concept. Several reasons have caused the shift towards a more decentralized power system. Those reasons include but are not limited to: electricity market privatization and the increased environmen-tal concerns regarding greenhouse gases [1]. Photovoltaic ar-rays are one of the DG sources that have been growing steadi-ly in the last few years. This is primarily due to its increasing power conversion efficiency and the decreasing costs of instal-ling new PV modules. A survey report published by the Inter-national Energy Agency (IEA) has indicated that approximate-ly 5.68 GW of PV power was installed in year 2008 [2]. About 75% of that additional capacity was installed in Spain and Germany alone. The growth trend of PV power installations since 1992 is shown in figure 1 to get an understanding of that increase. Grid connected PV systems form the majority of the installed PV power capacity as compared to stand-alone sys-tems. In order to encourage investments in PV systems, some governments provide contracts for buying power from the system owner for a specified period of time. For instance, the government of Ontario, Canada, has started the Feed-in Tariff (FIT) program, enabled by the Green Energy and Green Economy Act passed in 2009 [3]. Ontario Power Authority (OPA) is the entity in charge of implementing the FIT pro-

The authors are with the Department of Electrical and Computer Engineer-

ing at the University of Waterloo, ON, Canada N2L 3G1, (email: akhali-fa@uwaterloo.ca, ehab@hivolt.uwaterloo.ca)

gram. The program provides investors with a steady income that justifies the high capital cost of PV systems. Under the FIT program, PV power is sold back to the power system grid following a predetermined price scheme. Roof mounted PV systems below 10 kW receive a contract price of 80.2 ¢/kWh for a contract period of 20 years. Ground mounted PV systems with capacity between 10 kW and 10 MW receive a contract price of 44.3 ¢/kWh for the same period.

0

2000

4000

6000

8000

10000

12000

14000

16000

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

Year

PV P

ower

Inst

alle

d (M

W)

Fig. 1. Total installed PV power in IEA participating countries by year (in-cluding both grid connected and stand alone PV arrays). Source: International Energy Agency. With the increase in the number of grid connected PV sys-tems, comes the challenge of implementing an effective power conversion system (PCS). The DC output power from the ar-ray needs to be converted into AC power for it to be injected into the grid. IEEE Std. 929-2000 [4] requires current injected by PV systems into the distribution network to have a total harmonic current distortion below 5% at rated inverter output. From that, the power conversion system has to perform two important functions: 1) extract maximum power output from the PV array and 2) inject an almost harmonic free sinusoidal current into the grid. This paper focuses on the control of the PCS and presents a control methodology to address the previously mentioned is-sues. The PV cell equivalent circuit model is presented in sec-tion II to be used in simulating the system. Section III de-scribes the structure of a grid connected PV system and its associated control blocks. Control of the PCS is divided into two parts: controlling the DC converter to extract maximum power from the array while boosting the terminal voltage, and controlling the VSI to inject 3 phase sinusoidal currents into the grid. Simulation results obtained using SIMULINK are presented in section IV. Section V discusses the effect of the interfacing transformer topology on the propagation of zero sequence currents between the PV system and the grid. Final-ly, a brief conclusion follows in section VI.

Control of Three Phase Grid Connected Photo-voltaic Power Systems

Ahmed S. Khalifa and Ehab F. El-Saadany, Senior Member, IEEE

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978-1-4244-7245-1/10/$26.00 ©2010 IEEE

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II. PV CELL EQUIVALENT CIRCUIT MODEL The equivalent circuit model of a PV cell is needed in order

to simulate its real behavior. One of the models proposed in literature is the double exponential model [5] depicted in fig-ure 2. Using the physics of p-n junctions, a PV cell can be modeled as a DC current source in parallel with two diodes that represent currents escaping due to diffusion and charge recombination mechanisms. Two resistances, Rs and Rp, are included to model the contact resistances and the internal PV cell resistance respectively.

Fig. 2. Double exponential PV cell circuit model.

The relationship between the PV cell output current and terminal voltage is governed by:

1 2

1 01

2 02

( )exp 1

( )exp 1

sph D D

p

sD

sD

V IRI I I I

R

q V IRI I

akT

q V IRI I

akT

+= − − −

⎡ + ⎤⎛ ⎞= −⎢ ⎥⎜ ⎟⎝ ⎠⎣ ⎦

⎡ + ⎤⎛ ⎞= −⎢ ⎥⎜ ⎟⎝ ⎠⎣ ⎦

(1)

Where Iph is the PV cell internal generated photocurrent, ID1 and ID2 are the currents passing through diodes D1 and D2, a is the diode ideality factor, k is the Boltzmann constant (1.3806503 × 10−23 J/K), T is the PV cell temperature in Kel-vin, q is the electron charge (1.60217646 × 10−19 C), I01 and I02 are the reverse saturation currents of each diode respective-ly.

Assuming that the current passing in diode D2 due to charge recombination is small enough to be neglected, a sim-plified PV cell model can be reached as shown in figure 3. That model provides a good compromise between accuracy and model complexity and has been used in several previous works [7], [8]. In that case, equation (1) can be simplified to:

0( )

exp 1s sph

p

q V IR V IRI I I

akT R⎡ + ⎤ +⎛ ⎞= − − −⎢ ⎥⎜ ⎟

⎝ ⎠⎣ ⎦ (2)

The PV cell characteristics vary with external factors in-

cluding temperature and solar irradiation level. To incorporate these effects into the model, two additional relations are used.

Fig. 3. Simplified PV cell circuit model.

The PV cell output current varies with solar irradiation and temperature through:

( )n In

GI I K TG

= + Δ (3)

Where In is the nominal PV cell output current (at 25 °C and 1000 W/m2), KI is the current/temperature variation coefficient (A/K), ΔT is the variation from the nominal temperature (25 °C) and Gn is the nominal solar irradiation (1000 W/m2). The current/temperature variation coefficient, KI, has a relatively small value. Therefore, changes in the cell operating tempera-ture have a slight impact on the short circuit current as op-posed to solar irradiation.

The PV cell reverse saturation current, I0 in (2), is strongly dependent on temperature. The following relation can be used to model that effect [7]:

,0

,exp( ( ) / ) 1sc n I

oc n V

I K TI

q V K T akT+ Δ

=+ Δ −

(4)

Where Isc,n is the nominal short circuit current of the PV cell, Voc,n is the nominal open circuit voltage, KI and KV are the cur-rent and voltage temperature variation coefficients respective-ly. Figure 4 shows the I-V characteristic of a PV cell under different solar irradiance levels and at different temperatures. The short circuit current varies linearly with solar irradiance while temperature variations have more effect on the cell open circuit voltage.

0 0.1 0.2 0.3 0.4 0.5 0.60

2

4

6

8

10

PV cell terminal voltage (V)

PV

cel

l cu

rren

t (A

)

1000 W/m2

800 W/m2

500 W/m2

T = 50 C

T = 75 C

Fig. 4. PV cell I-V characteristic for different solar irradiation levels (conti-nuous lines) and different temperatures (dashed lines).

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Fig. 5. Schematic diagram of the grid connected PV system showing its main control blocks.

III. STRUCTURE OF THE GRID CONNECTED PV SYSTEM Figure 5 shows the structure of a grid connected PV sys-

tem. It is composed of a 100 kW (maximum output power) PV array connected to a DC-DC boost converter. A DC link capa-citor was connected to the converter and served as a relatively constant voltage DC bus for the three-phase voltage source inverter (VSI). Its voltage was regulated at a constant value by using a DC link controller.

The grid was modeled as a Y connected voltage source fol-lowed by a resistance, Rg, and inductance Lg. An RL load and an adjustable speed drive were connected to the system to model some of the typical loads connected to a distribution network.

The current controlled voltage source inverter was used to convert the DC power stored in the DC link capacitor and in-jected sinusoidal currents into the grid. Lf and Cf formed an LC filter to get rid of undesirable harmonics in the injected current. If the leakage inductance, Lt, of the interfacing trans-former, T1, was referred to the low voltage side (the PV array side), an LCL filter was formed and a much cleaner current waveform could be obtained. Total harmonic current distor-tion (THDI) is an important measure that defines how clean a current waveform is.

The system had multiple control blocks that worked togeth-er to ensure that maximum power was extracted from the PV array and then converted it to AC power to be injected into the grid. The details of each control block in the system are dis-cussed in the next few subsections.

A. DC-DC boost converter control The DC-DC boost converter was used to extract maximum

power output from the PV array and also increased the termin-al voltage to a level suitable for interfacing with the grid. A schematic diagram of the converter is shown in figure 6.

The PV array was connected at the input side of the conver-

ter while the DC link capacitor was connected at the output. The switching control law, u, applied at the gate of transistor Q is defined as:

1 0

0 0PV mp

PV mp

V Vu

V V

− >⎧⎪= ⎨ − <⎪⎩ (5)

Where Vpv is the terminal voltage of the PV array and Vmp is the voltage of the array at maximum power point in volts. A switching position equals to 1 meant that the switch was closed; while a value of 0 meant that the switch was open. By implementing that control law, maximum power output from the array could be obtained assuming that both solar irradia-tion and temperature did not change during the control inter-val. Several techniques for maximum power point tracking in PV arrays were covered in good detail in [9]. Of those tech-niques, perturb and observe (P&O) and incremental conduc-tance are widely used due to their good performance and ease of implementation.

Fig. 6. DC-DC boost converter schematic diagram.

The value of Vmp can be found by either using an algorithm

like perturb and observe, or by assuming it is a constant frac-tion of the open circuit voltage of the PV array at certain irrad-iation and temperature.

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B. Voltage source inverter (VSI) The voltage source inverter was used to convert the DC

output of the PV array to AC power. Figure 7 shows a sche-matic diagram of a two-level, three phase VSI. The voltage source inverter derives its name from the fact that it uses a relatively constant DC voltage source to generate three phase voltages and currents. Pulse width modulation techniques are an effective and efficient way of generating the switching pulses at the gate terminals of each transistor. The aim of the control strategy in this paper is to regulate the current output from the inverter to follow a specified reference signal. A possible way of doing so is to convert the three phase output current of the inverter to a rotating reference frame (dq0) and then shape the output current as desired.

Fig. 7. Two level, three phase voltage source inverter.

C. Current control in the rotating reference frame (dq0) Assuming the system is balanced; the dq transformation

can be used to convert the three phase currents injected by the inverter, into three constant DC components defined as the direct, quadrature and zero components: Id, Iq and I0 respec-tively. The relation between the natural (abc) and the rotating frames (dq0) is:

0

cos ( ) cos ( 2 / 3) cos ( 2 / 3)

sin ( ) sin ( 2 / 3) sin ( 2 / 3)

1 2 1 2 1 2

23

d a

q b

c

t t t

t t t

I II T II I

Tω ω π ω π

ω ω π ω π

− +

− − − − +

⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥= × ×⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

⎡ ⎤⎢ ⎥

= ⎢ ⎥⎢ ⎥⎣ ⎦

(6)

Where T is the transformation matrix and ω is the frequency of rotation of the reference frame in rad/sec. Real and reactive powers injected by the inverter can be calculated in dq frame by using:

d d q q

d q q d

P V I V I

Q V I V I

= +

= + (7)

Where Vd, Vq are the dq voltages at the point of common coupling, Id and Iq are the dq components of the injected cur-rent. A phase locked loop was used to lock on the grid fre-quency in such a way that Vq was set to zero [12]. In that case,

calculations of real and reactive powers were decoupled and simplified to:

d d

d q

P V IQ V I

==

(8)

Which means that if the grid voltage is relatively constant, Id and Iq can control real and reactive power injections from the PV array. The block diagram representing the PLL is shown in figure 8.

Fig. 8. Phase locked loop (PLL) block diagram.

In order to inject real power from the inverter, Id was con-trolled to follow a specified reference signal Id

*. Reactive power injection was set to zero and thus Iq

* = 0. The reference current Id

* was extracted from the dynamics of the DC link capacitor. A constant DC voltage across the capacitor meant that the power that went into it from the PV array matched the power going out to the inverter. The relationship is depicted as:

( )2 2DC in out

d V P Pdt C

= − (9)

Where VDC is the DC link capacitor voltage. The input power Pin to the capacitor was controlled to be the maximum PV array output power by the DC-DC converter. It was the task of the inverter, however, to control the output power Pout from the capacitor to keep its voltage constant. A proportional-integral (PI) controller was used to extract the reference cur-rent Id

* from the error mismatch between Pin and Pout:

( ) ( )( )* 1d P in out I in out

d

I K P P K P P dtV

= − + −∫ (10)

Having this information, the command voltages vd

* and vq*

for the inverter gates PWM can be obtained from:

( ) ( )( ) ( )

* * *

* * *

d P d d I d d f q d

q P q q I q q f d q

v K I I K I I dt L I V

v K I I K I I dt L I V

ω

ω

= − + − − +

= − + − + +

∫∫

(11)

Where KP and KI are the PI controller constants. The com-

mand voltages are transformed back to the natural abc frame where they will be used as the SPWM modulating signals for the inverter. These signals are normalized with respect to the DC link voltage to have maximum amplitude of 1 V for com-parison with a high frequency carrier signal.

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(a) (b)

(c) (d)

(e) (f)

Fig. 9. Simulation results of the PV grid connected system: (a) 3 phase current injected into the grid, (b) dq components of the injected current, (c) Total har-monic distortion of the injected current (THDI), (d) real and reactive powers transferred from the PV system to the grid, (e) DC link capacitor voltage and (f) modulating signals used for generating the sinusoidal PWM gating pulses for the 3 phase VSI.

IV. SIMULATION RESULTS The PV grid connected system in figure 5 was simulated

using MATLAB Simulink to verify the control methodology discussed earlier. A 100 kW PV array was interfaced to the grid and the control was set to inject maximum active power to the grid. The adjustable speed drive was controlled using direct field oriented control (FOC) to reach a constant speed of 2000 rpm. A 500/6600 VLL delta-Wye grounded transformer was used to step up the output voltage of the inverter. Figure 9 shows some of the waveforms obtained during the simulation.

The PV system was operating in constant current control mode. Figure 9(a) shows the 3 phase currents injected to the grid, which reached a stable value following some initial tran-sients caused by changes in the DC link voltage. This is con-firmed by the dq components of the injected current shown in figure 9(b) which follow closely the references Id

* and Iq*.

Total harmonic distortion was also recorded as shown in figure 9(c), to make sure that it is below the limits set by the IEEE Std. 929-2000. The effect of the motor acceleration caused some distortion in the injected current as it was accele-rating. However, the THDI level was still below 5%. Real and reactive powers injected from the PV system are shown in figure 9(d). The injected real power was about 92 kW while reactive power was set to zero. The DC link capacitor voltage was controlled at a steady state value of about 1.05 kV as shown in figure 9(e). Finally, the modulating signals used to generate the sinusoidal PWM pulses for the inverter switches are shown in figure 9(f). The switching frequency was set to 99 × 60 Hz = 5940 Hz to eliminate even harmonics. The per-formance of the proposed control methodology was confirmed by simulation in terms of injected power quality and the speed of finding the approximate maximum power point.

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V. BEHAVIOR OF THE SYSTEM DURING FAULT CONDITIONS The operation of the distribution system protection devices

can be disrupted when distributed generation (DG) sources are connected. Protection relays in radial distribution systems are set to respond to a certain magnitude of fault current, which is determined by the short circuit level at the fault location. If a DG source happens to be located between a distribution subs-tation and a fault, it can contribute to the fault current. If the fault current contribution from the grid decreases, the protec-tion relay may not be able to detect the fault and a “relay un-der-reach” situation occurs. The situation is depicted in figure 10.

Most utilities require DG sources to disconnect within a few cycles of detecting a fault in the system. That could be difficult to implement especially when DG sources comprise a major part of the generated power. In Denmark for example, about 20% of the country’s total electricity supply in 2007 was generated from renewable energy sources like wind turbines [6]. That’s why it is important to study how fault conditions affect the system when renewable energy sources are installed.

Fig. 10. Effect of DG fault current contribution on the protection system.

Single line to ground faults (SLG) are the most probable

type of faults to occur. Ground protection relays are used to detect this type of faults by continuously monitoring zero se-quence currents in the system. The contribution of zero se-quence currents (ZSC) from the DG to the grid is affected by the topology of the interfacing transformer. In this paper, two different transformer topologies were considered, namely: Delta-Delta (Δ-Δ) and Delta (DG side)-Wye grounded (grid side).

Delta-Delta transformers offer good isolation of ZSC be-tween the DG and the grid, but there is a risk of phase over- voltages when the grid circuit breaker trips for a permanent fault [18]. Delta-Y grounded transformers, on the other hand, could allow the DG to contribute zero sequence currents to the grid. The zero sequence circuit equivalent of both transformer topologies is shown in figure 11.

A simulation was conducted for a single line to ground fault F1 at the grid side in figure 5. The fault was a temporary fault that lasted for 0.2 seconds. The zero sequence current contribution of the PV array system was monitored for each transformer topology used. The fault current magnitude and the zero sequence current contribution of the PV array for the delta-delta transformer are shown in figure 12. It is clear that no zero sequence current was detected from the PV system to

the grid during the fault. On the other hand, the delta-Y grounded topology allowed zero sequence current to pass from the PV system to the fault. That is a case during which the DG could disrupt the ground relays correct operation. The results for that case are shown in figure 13.

Fig. 11. DG zero sequence current contribution for a SLG grid fault when using (a) delta-delta and (b) delta-wye grounded transformers.

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8-3000

-2000

-1000

0

1000

2000

3000

Time (s)

Fau

lt cu

rren

t (A

)

(a)

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8-10

-5

0

5

10

Time (s)

Zer

o se

quen

ce c

urre

nt (

A)

(b)

Fig. 12. (a) Single line to ground fault current F1 for phase A and (b) zero sequence current injected by the PV system to feed the fault for the delta-delta transformer.

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0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8-3000

-2000

-1000

0

1000

2000

3000

Time (s)

Fau

lt cu

rren

t (A

)

(a)

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

-800

-600

-400

-200

0

200

400

600

800

Time (s)

Zer

o se

quen

ce c

urre

nt (

A)

(b)

Fig. 13. (a) Single line to ground fault current F1 for phase A and (b) zero sequence current injected by the PV system to feed the fault for the delta-Y grounded transformer.

VI. CONCLUSION This paper presented a control technique for grid connected

PV array systems. The main objectives were to achieve maxi-mum power output from the PV array and to inject a high quality AC current into the grid to transfer that power. To that aim, the PV cell equivalent circuit model was obtained to con-struct the system and then focus was directed towards the power conditioning system (PCS) and its controls. The first stage of the PCS was a DC-DC boost converter responsible for extracting maximum power from the PV array and increasing its output voltage. The second stage of the PCS was a current controlled voltage source inverter (VSI) that converted the DC power of the array into AC power and injected it into the grid. The control technique relied on transforming the three phase currents and voltages into a rotating reference frame and then regulated the resulting dq current components. After that, si-mulation results obtained using MATLAB Simulink were pre-sented to confirm the system operation. Finally, the system behavior under fault conditions was illustrated through a case study on two interfacing transformer topologies: delta - delta and delta (PV) – Y grounded (grid).

VII. REFERENCES [1] Pepermans, G., Driesen, J., Haeseldonekx, D., Belmans, R., and

D’haeseleer, W., 2005. Distributed generation: definition, benefits and issues. Energy Policy 33, 787-798.

[2] IEA-PVPS. (2009, Sept.). Trends in photovoltaic applications. [Online]. Available: www.iea-pvps.org

[3] Ontario Power Authority (2009). Feed-in Tariff Program. [Online]. Available: fit.powerauthority.on.ca

[4] “IEEE Recommended Practice for Utility Interface of Photovoltaic (PV) Systems," IEEE Std 929-2000, p. i, 2000.

[5] J.A. Gow, C. Manning, "Development of a photovoltaic array model for use in power-electronics simulation studies," in proc. IEE Electric power applications, vol 146, issue 2, pp.193-200, March 1999.

[6] Danish Energy Authority (2008). Facts about wind power. [Online]. Available: http://www.ens.dk/en-US/Sider/forside.aspx

[7] M. G. Villalva, et al., "Comprehensive Approach to Modeling and Simu-lation of Photovoltaic Arrays," Power Electronics, IEEE Transactions on, vol. 24, pp. 1198-1208, 2009.

[8] Shengyi Liu; Dougal, R.A.; , "Dynamic multiphysics model for solar array," Energy Conversion, IEEE Transactions on , vol.17, no.2, pp.285-294, Jun 2002

[9] T. Esram and P. L. Chapman, "Comparison of Photovoltaic Array Max-imum Power Point Tracking Techniques," Energy Conversion, IEEE Transactions on, vol. 22, pp. 439-449, 2007.

[10] F. Blaabjerg, et al., "Overview of Control and Grid Synchronization for Distributed Power Generation Systems," Industrial Electronics, IEEE Transactions on, vol. 53, pp. 1398-1409, 2006.

[11] M. P. Kazmierkowski and L. Malesani, "Current control techniques for three-phase voltage-source PWM converters: a survey," Industrial Elec-tronics, IEEE Transactions on, vol. 45, pp. 691-703, 1998.

[12] Kroutikova, N.; Hernandez-Aramburo, C.A.; Green, T.C.; , "State-space model of grid-connected inverters under current control mode," Electric Power Applications, IET , vol.1, no.3, pp.329-338, May 2007

[13] M. K. Mishra, et al., "Operation of a DSTATCOM in Voltage Control Mode," Power Engineering Review, IEEE, vol. 22, pp. 79-79, 2002.

[14] S. B. Kjaer, J. K. Pedersen, and F. Blaabjerg, “A review of single-phase grid-connected inverters for photovoltaic modules,” IEEE Trans. Ind. Appl., vol. 41, no. 5, pp. 1292–1306, Sep./Oct. 2005.

[15] Y. Mohamed and E. F. El-Saadany, "Adaptive Decentralized Droop Controller to Preserve Power Sharing Stability of Paralleled Inverters in Distributed Generation Microgrids," Power Electronics, IEEE Transac-tions on, vol. 23, pp. 2806-2816, 2008.

[16] A. Timbus, et al., "Evaluation of Current Controllers for Distributed Power Generation Systems," Power Electronics, IEEE Transactions on, vol. 24, pp. 654-664, 2009.

[17] Wu, Bin High-Power Converters and AC Drives. John Wiley & Sons, 2006. Pg: 296

[18] Natural Resources Canada (2007). Protection Coordination Planning with Distributed Generation. [Online]. Available: canmetenergy-canmetenergie.nrcan-rncan.gc.ca/fichier.php/codectec/En/2007-149/ 2007-149e.pdf

[19] I. Atlas, A. Sharaf "A photovoltaic array simulation model for Matlab Simulink GUI environment," in international Conf. on Clean Electrical Power, pp.341-345, May 2007.

Ahmed S. Khalifa was born in Giza, Egypt, in 1985. He received the B.Sc. degree in electrical and electronic engineering from the United Arab Emirates University (UAEU). He is currently pursuing the M.A.Sc. degree in electrical and computer engineering at the University of Waterloo since August 2008. His current research interests include renewable energy sources and control of PWM drives. Ehab F. El-Saadany (M’01---SM’05) was born in Cairo, Egypt, in 1964. He received the B.Sc. and M.Sc. degrees in electrical engineering from Ain Shams University, Cairo, Egypt, in 1986 and 1990, respectively, and the Ph.D. degree in electrical engineering from the University of Waterloo, Waterloo, ON, Canada, in 1998. Currently, he is an Associate Professor in the Depart-ment of Electrical and Computer Engineering, University of Waterloo. His current research interests include distribution system control and operation, power quality, power electronics, digital signal processing applications to power systems, and mechatronics.

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