visible human utilization to render induced electric field and current density images inside the...

CONTRIBUTEDP A P E R

Visible Human Utilization toRender Induced Electric Fieldand Current Density ImagesInside the HumanEffects of exposure to high voltage on the brains and other body tissues and

organs of people standing close to electric transmission lines

are being explored with computer models.

By Nabil Mohamed Maalej, Member IEEE, Chokri Ahmed Belhadj,

Tarek K. Abdel-Galil, Member IEEE, and Ibrahim O. Habiballah

ABSTRACT | The external and internal exposure to power

frequency electromagnetic field, generated by high-voltage

power transmission lines, raises serious safety concerns. Since

we cannot measure the induced electric fields and current

densities inside the human body, we used the Visible Human

(VH) to investigate the induced electric fields and currents in

human body tissues and organs of a worker standing 2 m away

from conductor phase C of a double-circuit 132 kV transmission

line. The double circuit 132 kV 60 Hz transmission line has a

power rating of 293 MVA and a maximum recorded peak load

current of 603 A. Charge simulation method and the Biot–

Savart law have been used for computation of external electric

and magnetic fields. Finite-difference time-domain technique

was used to calculate the organs’ internal induced electric field

and circulating current densities in more than 40 different

tissues of the VH with 3 mm voxel size. The simulation indicates

that, at 2 m away from a 132 kV transmission line, the computed

external electric field is 6.485 kV/m and the external magnetic

field is 66.4 �T, which are below the limits set by the IEEE

standards for external exposure for live-line workers. The

maximum induced electric fields in the brain and heart are

23 and 14 mV/m, respectively. These values are below the IEEE

standard recommended limits of 53 mV/m for the brain and

943 mV/m for the heart. The VH data allowed us to obtain

two- and three-dimensional images of the induced electric

field and current density distribution in different organs,

tissues, and cross-sections of the human body.

KEYWORDS | Biomagnetics; current density; dosimetry; elec-

tromagnetic fields; imaging; transmission lines

I . INTRODUCTION

The exposure of the general public and power-line workers

to high-voltage transmission lines at extremely low fre-

quency (ELF) of 50 or 60 Hz is a very important health

concern. Significant research has been conducted to deter-mine the short- and long-term effects of ELF exposure on

the human body. While no conclusive results were reached

for the long-term health effects, many national and inter-

national organizations have issued regulations to prevent

short-term effects such as nerve or muscle stimulation. The

IEEE recommended ELF exposure limits in IEEE Standard

C95.6-2002 [1]. The recommended limits for occupational

external electric and magnetic field are 20 kV/m and2.71 mT for power frequency. The International Commis-

sion on Non-Ionizing Radiation Protection (ICNIRP) also

published guidelines for EMF exposure limits [2]. The

Manuscript received February 28, 2009; revised July 3, 2009, and August 20, 2009.

Current version published November 18, 2009. This work was supported by the King

Fahd University of Petroleum and Minerals through the Center of Engineering Research

and by the Saudi Electric Company under Grant CER02260.

N. M. Maalej is with the Department of Physics, King Fahd University of

Petroleum and Minerals, Dhahran 321261, Saudi Arabia (e-mail: [email protected];

[email protected]).

C. A. Belhadj, T. K. Abdel-Galil, and I. O. Habiballah are with the

Department of Electrical Engineering, King Fahd University of Petroleum and

Minerals, Dhahran 321261, Saudi Arabia (e-mail: [email protected];

[email protected]; [email protected]).

Digital Object Identifier: 10.1109/JPROC.2009.2031668

Vol. 97, No. 12, December 2009 | Proceedings of the IEEE 20530018-9219/$26.00 �2009 IEEE

ICNIRP recommended occupational external electric andmagnetic field limits as 8.3 kV/m and 4.2 mT.

In recent years, a number of laboratories have devel-

oped heterogeneous models of the human body with an

anatomical shape and numerous tissues to study EMF

exposure. Most of these models have been developed by

computer segmentation of data from magnetic resonance

imaging (MRI) and allocation of proper tissue type [3]–[6].

These groups and others have used high-resolution humanbody models to study EMF exposures of the human body to

low and high frequencies.

High-resolution models and advanced numerical

methods have been used to calculate EMF exposure at

high frequencies [6], [10], [11]. Recently, Kuhn investi-

gated radio-frequency exposure and absorption character-

istics for various anatomies ranging from a 6-year-old child

to a large adult male by numerical modeling [12]. Handreviewed the different calculation method and anatomical

models for high-frequency electromagnetic exposure [13].

Several methods have also been developed to study

electric fields and current densities induced in anatomic

models of the human body for low-frequency exposure

[7]–[9], [14]–[16]. Gandhi used the quasi-static impedance

method to calculate the currents induced in the nominal

2 � 2 � 3 and 6 mm resolution anatomically basedmodels of the human body for exposure to magnetic fields

at 60 Hz from homogeneous and nonhomogeneous

magnetic fields [14]. Dawson used the scalar potential

finite-difference method approach that resulted in a high

computational efficiency for a 3.6 mm voxel model [8].

Dimbylaw used both the impedance method and the scalar

potential finite-difference method in a fine-resolution

(2 mm) anatomically realistic voxel model [9].This paper investigates the induced electric fields and

currents in human body tissues and organs of a live-line

worker standing 2 m away from conductor phase C of a

double-circuit 132 kV transmission line. The results are

compared with the IEEE and ICNIRP exposure limits to

verify compliance and safety from the possible short-term

effects from extremely high voltages and ELF. This paper

also focuses on the two-dimensional (2-D) and three-dimensional (3-D) visualization of the induced internal

exposure in body tissues and organs of the Visible Human

Project (VHP). Particular attention is given to brain tissue

since the relationship between EMF exposure and changes

in brain activity has been demonstrated in animal and

human subjects [17].

II . METHODS

A. Exposure Scenario and ExternalExposure Calculation

A 132 kV double-circuit transmission line located in the

Riyadh region of Saudi Arabia was selected. Its power

rating is 293 MVA, and the peak load current was 603 A.

The study was conducted for a worker standing 2 m away

from phase C. The worker is standing in a bucket facing

the power line with his hands on the side of his body(Fig. 1). The human body was assumed to be standing in

free space and not in contact with electrical ground.

The charge simulation method (CSM) [18] was used to

calculate the external electric fields, while the Biot–Savarat

law was used to calculate the external magnetic field inten-

sity at the location of the worker. EMF WORKSTATION

software developed by the Electric Power Research Institute

[19], which is based on CSM and Biot–Savart law, was usedto compute the external electric and magnetic fields. The

computation accuracy has been verified analytically [19].

The electric and magnetic fields produced by the transmis-

sion line were modeled using the subroutine EXPOCALC of

EMF WORKSTATION, Version 2.51.

B. Internal Exposure CalculationWe have adopted the finite-difference time-domain

(FDTD) method to solve Maxwell’s equations to calculateinternal field. The FDTD was first introduced by Yee in

1966 as a numerical technique to solve Maxwell’s equation

for electromagnetic field interaction with materials [20].

This method is based on the discretization of Maxwell’s

equations and involves spatially sampling the electric and

magnetic fields distributions in space and time. The simu-

lation results were validated by comparing the results with

the analytical solutions for simple geometries. The resultsfor the human body were also validated with previously

published data [11].

EMPIRE Software (IMST GmbH, Germany, 3D-FDTD

Simulator), which is a powerful FDTD solver, has been

utilized to calculate induced electric field and average

current densities (ACDs). At 2 m away from conductor C

of the power transmission line, the external electric and

Fig. 1. Simulated scenario: a worker standing 2 m away and

facing phase C of a double-circuit 132 kV power line.

Maalej et al. : Visible Human to Render Induced Electric Field and Current Density Images

2054 Proceedings of the IEEE | Vol. 97, No. 12, December 2009

magnetic field variation along the human body were from6.2 to 6.5 kV/m and 63 to 66.5 �T, respectively. Hence,

we used a plane-wave excitation with the highest values of

the electric and magnetic fields to simulate the worst case

scenario. For the low-frequency calculation, we assumed

quasi-static condition. The FTTD calculations were done at

10 MHz; then the results were scaled back to 60 Hz using

Gandhi’s frequency-scaling method for ELF [3]. The

induced ACDs, averaged over a square centimeter, dueto the exposure to an external electric field and magnetic

field are added vectorially to determine the resultant

values. The corresponding induced electric fields are cal-

culated by dividing the ACD by the conductivity (at 60 Hz)

of the tissue at that voxel.

C. Visible Human and Image RenderingIn this paper, we use the anatomical human body from

the VHP. The VH1 of the U.S. National Library of

Medicine has created digital image data sets of a human

male and female for use in education and research. The

body model is obtained from computerized tomography

and MRI slices from a human cadaver. The heterogeneous

model has more than 40 different tissues and is available in6, 3, and 1 mm voxel sizes. Previously, we used the 6 mm

voxel size to determine the induced EMF exposures for a

person standing under the power line [22]. In this paper,

we use the 3 mm voxel size with a total of 114� 196 �626 ¼ 13987344 voxels. For the 3 mm voxel size, the

FDTD simulation time and memory required us to store

the data for one layer (2–3 cm thick) of the body at a time.

After, storing the data for all the layers, the data for thewhole body was compiled using MATLAB programming.

For this heterogeneous model, we used the human tissue

conductivity ð�Þ, permittivity ð"Þ, and permeability ð�Þpublished by Gabriel [23].

The VHP data are available in a raw indexed file of

numbers corresponding to different tissues. The data were

converted to a 3-D voxel matrix that served as a 3-D map to

analyze the ACD and electric field for different organs andtissues. MATLAB programs were developed for data post-

processing to determine the maximum and average current

densities and electric fields for any desired tissue or organ,

any body transversal, and coronal or sagittal cross-sections.

III . RESULTS AND DISCUSSION

A. External Fields ExposureAt 2 m away from conductor phase C of a double-circuit

132 kV transmission line, the magnitude of the external

electric field and magnetic fields was 6.485 kV/m and

66.4 �T, respectively. The electric field value is below the

controlled environment limit of 20 kV/m. The magneticfield value is below the external magnetic field limits of

2.71 mT for the head and torso for a controlled environment.

B. Induced Electric Fields and ACD inBody Organs and Tissues

To obtain the induced electric field and ACD inside the

body, we assumed a uniform plane-wave excitation withexternal E-field from the front of the VHP to the back of

the body ðEy ¼ �6:485 kV/m) and an external B field

from head to feet ðBz ¼ �66:4 �T). Fig. 2 shows the

distribution of electric field and current density distribu-

tion in the same sagittal cross-section of the body torso.

The color spectrum from blue to red used here reflects the

minimum to maximum amplitude variation. The electric

field is highest at the skin and mucous membranes, whichare at the boundary between the nonconducting air and the

highly conducting body soft tissues. The skin has the

lowest body-tissue conductivities of 0.0002 S/m, and

hence the highest induced electric fields. In fact, the

electric field values in the skin are two to three orders of

magnitude higher than the E-field in the soft body tissues.

Table 1 shows the tissue conductivities at 60 Hz,

induced ACD ðJavgÞ, maximum current density ðJmaxÞ,induced average electric field ðEavgÞ, and induced maxi-

mum electric field ðEmaxÞ for selected body tissues and

organs. The hands and feet are composed of different

tissues and do not have a single conductivity. The cal-

culated values for the hands and feet include all the tissues

in these body parts except the skin. The values for all the

voxels in each organ are used to calculate the maximum and

average values of the current density and electric field. Theratio of maximum ACD to average ACD ranges from 2.4 for

the pancreas to about 18 for the lung. The maximum

induced electric field for all tissues was in the fat of the toes

and was 1.37 V/m. The maximum induced ACD in all the

tissues is 3.11 mA/m2 in the cortical bone of the big toe.

Fig. 3 shows the average and maximum induced ACD

profile along the height of the human body. Each average1http://www.nlm.nih.gov/research/visible/visible_human.html.

Fig. 2. (a) Electric field and (b) current density distributions in

the same sagittal cross-section of the upper body.

Maalej et al.: Visible Human to Render Induced Electric Field and Current Density Images

Vol. 97, No. 12, December 2009 | Proceedings of the IEEE 2055

value is the average for all the voxels in the axial cross-

section (layer) of the body, excluding the skin and mucous

membrane. The voxels in each layer correspond to

different tissues with different conductivities. Fig. 4 shows

the layer average and maximum induced electric fieldalong the height of the body, excluding the skin and

mucous membrane. The layer maximum electric field can

be as much as 167 times the layer average electric field.

The large difference is due to the large difference between

the conductivities of different body tissues. For exam-

ple, the conductivity of cerebral spinal fluid (2 S/m) is

a hundred times that for the cortical bone (0.02 S/m).

In general, the average and maximum current densities and

electric fields reach the highest values in the parts of thebody that have the smallest cross-sectional area, such as the

hands and feet, fingers, and toes.

Fig. 3. Layer average and maximum ACD profile along the height

of the human body.

Fig. 4. Layer average and maximum electric field profile along

the height of the body.

Table 1 Induced Average and Maximum Current Densities and

Electric Fields in Selected Parts of the Body, Excluding the Skin

Fig. 5. The ACD distribution for an axial cross-section of the head.

The arrow indicates where the maximum ACD occurs for the

brain tissues.



C. Induced ACD and Electric Field in the BrainThe exact locations at which the maximum ACD or

electric fields occur for any organ or tissue were alsoobtained. For most organs, the maximum values occurred

at the boundary with adjacent tissues. Fig. 5 shows the ACD

distribution for an axial cross-section of the head at which

the maximum ACD occurs in the brain tissues. Fig. 6 shows

the electric field distribution in the same axial cross-section

showing only the voxels of the brain tissues (cerebellum,

white matter, and gray matter). It is very clear that the

maximum electric field value occurs at the voxels bordering

the brain.

The 3-D distribution of the ACD in the brain tissues can

also be represented as shown in Fig. 7. The visualized

transversal and sagittal cross-section reveal the intensitydistribution intensities of the brain tissues. The maximum

values of current densities and electric field occur at the

periphery of the organ as indicated by the arrow. The max-

imum ACD value is 1.39 mA/m2. The bulk of the voxels

deeper inside the organ have much lower ACD values.

Fig. 8 shows the histogram of the ACD for the brain tissue

voxels. Most voxels (99.7%) in the brain have an ACD less

than 0.1 mA/m2. The remaining small number of voxelswith relatively larger value of ACD are located at outer

volume layer of the tissue, as shown in Figs. 6 and 7.

D. Compliance With Internal Exposure LimitsTable 2 summarizes the results of the studied EMF

exposure scenario for the induced electric field and

Fig. 6. The electrical field distribution in the brain tissues

(cerebellum, white matter, and gray matter).

Fig. 7. A 3-D representation of the brain tissues showing the

ACD distribution and the location of maximum ACD.

Fig. 8. The histogram of the brain voxels versus induced

average current density.

Table 2 Comparison of Internal Exposure Limits and the

FTDT Simulation Results for ACD and Electric Fields



current densities. All the induced electric field values forthe brain, the heart, the hands and feet, and all other

tissues (excluding the skin) are below the IEEE limits [1].

The current density values shown in Table 2 are also

below the ICNIRP limit of 10 mA/m2 [2]. It is important

to note that we considered only one orientation of the

maximum external electric and magnetic fields for the

described scenario.

IV. CONCLUSION

The results of the study described in this paper indicate

that for a worker standing 2 m away conductor phase C of

a double-circuit 132 kV transmission line, the computed

external electric field is 6485 V/m and the external mag-

netic field is 66.4 �T. These values are below the limits

set by IEEE standards for external exposure for live-lineworkers. The induced maximum current density in all the

tissues was below the ICNIRP limit of 10 mA/m2. The

maximum current density, spatially averaged over 1 cm2,

was 1.4 mA/m2 for the brain and 1.2 mA/m2 for the heart

tissue. All the induced electric field values were below the

IEEE limits for a controlled environment. The maximum

induced electric fields in the brain and heart were 22.0

and 13.8 mV/m, respectively. The maximum inducedelectric field for all human tissues, excluding the skin,

was at the toes and was 1.37 V/m. This value is lower than

the IEEE Standard limit of 2.1 V/m for extremities. We

were able to use the VHP data and FDTD method to

obtain 2-D and 3-D visualization of the induced current

density and electric fields in any body part, organ, or

tissue.

REF ERENCE S

[1] IEEE Standard for Safety Levels With Respect toHuman Exposure to Electromagnetic Fields,0–3 kHz, IEEE Std. C95.6, 2002.

[2] ICNIRP, BGuidelines limiting exposure totime-varying electric, magnetic, andelectromagnetic fields (up to 300 GHz),[Health Phys., vol. 74, no. 3, pp. 494–522, 1998.

[3] O. P. Gandhi and J. Y. Chen, BNumericaldosimetry at power line frequencies usinganatomically based models,[ Bioelectromagn.J. Supp., vol. 1, pp. 43–60, 1992.

[4] T. W. Dawson, J. DeMoerloose, andM. A. Stuchly, BComparison of magneticallyinduced ELF fields in humans computed byFDTD and scalar potential FD codes,[Appl. Comput. Electromagn. Soc., vol. 11,pp. 63–71, 1996.

[5] I. G. Zubal, C. R. Harrell, E. O. Smith,Z. Rattner, G. R. Gindi, and P. H. Hoffer,BComputerized three-dimensional segmentedhuman anatomy,[ Med. Phys. Biol., vol. 21,pp. 299–302, 1994.

[6] P. J. Dimbylow, BFDTD calculations of thewhole-body averaged SAR in an anatomicallyrealistic voxel model of the human body from1 MHz to 1 GHz,[ Phys. Med. Biol., vol. 42,pp. 479–490, 1997.

[7] C. M. Furse1 and O. P. Gandhi, BCalculationof electric fields and currents induced in amillimeter resolution human model at 60 Hzusing the FDTD method,[ Bioelectromagnetics,vol. 19, pp. 293–299, 1998.

[8] T. W. Dawson and M. A. Stuchly,BHigh-resolution organ dosimetry for humanexposure to low-frequency magnetic fields,[IEEE Trans. Magn., vol. 34, no. 3, pp. 708–771,1998.

[9] P. J. Dimblylow, BInduced current densitiesfrom low-frequency magnetic fields in a 2 mmresolution, anatomically realistic model of thebody,[ Phys. Med. Biol., vol. 43, pp. 221–230,1998.

[10] P. J. Dimbylow, BFine resolution calculationsof SAR in the human body for frequenciesup to 3 GHz,[ Phys. Med. Biol., vol. 47,pp. 2835–2846, 2002.

[11] O. P. Gandhi, Y. G. Gu, J. Y. Chen, andH. I. Bassen, BSpecific absorption ratesand induced current distributions in ananatomically based human model forplane-wave exposures,[ Health Phys.,vol. 63, pp. 281–290, 1992.

[12] S. Kuhn, W. Jennings, A. Christ, andN. Kuster, BAssessment of inducedradio-frequency electromagnetic fields invarious anatomical human body models,[Phys. Med. Biol., vol. 54, pp. 875–889, 2009.

[13] J. W. Hand, BModeling the interaction ofelectromagnetic fields (10 MHz–10 GHz)with the human body: Methods andapplications,[ Phys. Med. Biol., vol. 53,pp. R243–R286, 2008.

[14] O. P. Gandhi, BSome numerical methods fordosimetry: Extremely low frequencies tomicrowave frequencies,[ Radio Sci., vol. 30,pp. 161–177, 1995.

[15] O. P. Gandhi, G. Kang, D. Wu, and G. Lazzi,BCurrents induced in anatomic modelsof the human for uniform and nonuniformpower frequency magnetic fields,[Bioelectromagnetics, vol. 22, pp. 112–121,2001.

[16] T. W. Dawson, K. Caputa, and M. A. Stuchly,BNumerical evaluation of 60 Hz magneticinduction in the human body in complex

occupational environments,[ Phys. Med. Biol.,vol. 44, pp. 1025–1040, 1999.

[17] S. Carrubba and A. A. Marino, BThe effectsof low-frequency environmental-strengthelectromagnetic fields on brain electricalactivity: A critical review of the literature,[Electromagn. Biol. Med., vol. 27, no. 2,pp. 83–101, 2008.

[18] H. Singer, H. Steinbigler, and P. Weiss,BA charge simulation method for thecalculation of high voltage fields,[ IEEE Trans.Power App. Syst., vol. PAS-93, pp. 1660–1668,1974.

[19] Electric and Magnetic Fields Workstation(EMF WORKSTATION), ver. 2.5,Electric Power Research Institute, 2007.

[20] K. S. Yee, BNumerical solution of initialboundary value problems involving Maxwell’sequations in isotropic media,[ IEEE Trans.Antennas Propag., vol. AP-14, pp. 302–307,1966.

[21] M. Stuchly and O. P. Gandhi,BInter-laboratory comparison ofnumerical dosimetry for humanexposure to 60 Hz electric and magneticfields,[ Bioelectromagnetics, vol. 21,pp. 167–174, 2000.

[22] N. M. Maalej, T. K. Abdel-Galil,M. A. Abdul-Majeed, and I. O. Habiballah,BOrgan dosimetry for a worker standing undera 132 kV power line,[ in Proc. World Congr.Med. Phys. Biomed. Eng. 2006, Seoul,South Korea, 2007, vol. 14, pp. 2660–2663.

[23] S. R. Gabriel, W. Lau, and C. Gabriel,BThe dielectric properties of biologicaltissues: Measurements in the frequency range10 Hz–20 GHz,[ Phys. Med. Biol., vol. 41,pp. 2251–2269, 1996.

ABOUT THE AUT HORS

Nabil Mohamed Maalej (Member, IEEE) received

the B.S. degree in electrical engineering from the

University of Rochester, Rochester, NY, in 1985. He

received the M.S. degree in electrical engineering

and the M.S. and Ph.D. degrees in medical physics

from the University of Wisconsin, Madison, WI, in

1987, 1990, and 1994, respectively.

He did his postdoctoral training with the

Madison Cardiovascular Research Group, Univer-

sity of Wisconsin, from 1994 to 1998. He was

with Arthur D. Little, Inc., Boston, MA, as a Consultant in design and

development of medical devices (1998–2001). Since 2001, he has been

an Associate Professor of medical physics at King Fahd University of

Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia. He helped

establish the first master’s program in medical physics in the Middle

East. He was a Visiting Professor at the National University of

Singapore in summer of 2007. He has 80 journal and conference

publications. His research interests include bioinstrumentation, car-

diovascular research, diagnostic imaging, radiation therapy, and

bionanotechnology.

Dr. Maalej is a member of the American Association of Medical

Physicists. He received the SATURN award for achievement from the

University of Wisconsin, Madison, in 1994. He received the Best Teacher

and Advisor Award from KFUPM in 2005.



Chokri Ahmed Belhadj received the B.Sc. degree

from King Saud University, Riyadh, Saudi Arabia,

in 1985, the M.Sc. degree from King Fahd Univer-

sity of Petroleum and Minerals (KFUPM), Dhahran,

Saudi Arabia, in 1988, and the Ph.D. degree from

Ecole Polytechnique of Montreal, University of

Montreal, Montreal, PQ, Canada, in 1996, all in

electrical engineering.

He was with the Research Institute, KFUPM,

working on several power system projects. He was

involved with the Hydro-Quebec Research Institute, Montreal, on several

power system analysis projects. Since 1996, he has been an Assistant

Professor in the Electrical Engineering Department, KFUPM. His areas of

interest are high-voltage engineering, electric and magnetic fields

studies and impact on human health, electromagnetic transient investi-

gations analysis, and power system analysis and modeling.

Tarek K. Abdel-Galil (Member, IEEE) received the B.Sc. and M.Sc.

degrees from Ain-Shams University, Egypt, in 1992 and 1998, respec-

tively, and the Ph.D. degree from the University of Waterloo, Waterloo,

ON, Canada, in 2003, all in electrical engineering.

During 2004, he was a Research Assistant in the Electrical and

Computer Engineering Department, University of Waterloo. Presently, he

is a Research Engineer with the Research Institute, King Fahd University

of Petroleum and Minerals, Dhahran, Saudi Arabia. His research interests

are in the area of the operation and control of distribution systems,

power quality analysis, application of artificial intelligence algorithms in

power system, high voltage, and insulation systems.

Ibrahim O. Habiballah received the B.S. degree

from King Abdul-Aziz University, Saudi Arabia, in

1984, the M.S. from King Fahd University of

Petroleum and Minerals (KFUPM), Dhahran, Saudi

Arabia, in 1987, and the Ph.D. degree from the

University of Waterloo, Waterloo, ON, Canada,

in 1993.

He is an Associate Professor and Chairman of

the Electrical Engineering Department, KFUPM.

Since joining KFUPM in 1984, he has supervised

and co-supervised more than 50 summer training and co-op students.

Since 2000, he has been involved in more than ten funded projects for

local and international clients. His areas of interest include power sys-

tems in general, power system state estimation, power system opti-

mization and partitioning of large power networks, power quality, HV

insulators, and energy conservation. He has published more than

25 journal and conference papers and authored or coauthored more

than seven technical reports.



visible human utilization to render induced electric field and current density images inside the...

Documents