The Capacitive Coupling Between EHV Lines and ... - IEEE Xplore

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 19, NO. 3, JULY 2004

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The Capacitive Coupling Between EHV Lines and Nearby Pipelines Mohamed M. Saied, Senior Member, IEEE

Abstract—This paper addresses the effect of the electrostatic field due to extra high voltage (EHV) overhead transmission lines on pipelines in the vicinity of those power lines. Two measures for this effect are used: the maximum electric field on the pipe surface and the total electric charge on the pipeline per unit length. A mathematical model is presented for assessing these two measures. The results of applying the model to a situation involving a single-circuit, six-bundle, three-phase, 750-kV EHV line with flat conductor configuration are presented and discussed. The first set of results refers to a parallel pipeline of radius 0.5 m. The dependence of both the maximum electric field (at the top of the pipe) and the charge per meter on the distance between the pipeline and the tower center is similar to the distribution of the electric field beneath the tower at the ground surface. It shows maxima of both quantities if the pipe is exactly under one of the outer phases of the power line. At a distance of about 35 m from the tower center, both the electric field and the charge per unit length drop to 50% of their maximum values. The electric field is found to increase almost linearly with the clearance between the pipeline and the ground surface. The charge changes in a more complicated way with the clearance. It decreases if the pipe clearance increases from 0 to 0.2 m, then increases steadily beyond this value. For a given distance from the 750-kV line and for a fixed clearance from the ground, both the electric field and the electric charge per unit length on the pipeline will increase with the pipe radius. This paper will deal also with the impact of the pipeline on the nearby EHV power line and its associated network. The results will show that for a solidly earthed power network, the presence of the pipeline will be accompanied by a slight increase in the neutral current. On the other hand, for a power network with an inductively earthed neutral, there will be a tendency toward a parallel resonance that can occur for particular values of the neutral inductance and pipe radius. This resonance will result in an increase in the system’s neutral potential, which will be primarily limited by the network losses. Index Terms—Capacitive coupling, electrostatic interference, extra high voltage (EHV) lines, pipelines.

I. INTRODUCTION

T

HE ever increasing cost for right of ways suitable for erecting extra high voltage (EHV) power lines and pipelines as well as the noticeable current public awareness toward the visual and environmental impact of those lines have led to exploring the possibility of using the close or even common corridors for both power and pipelines. This, of course, reduces the land cost considerably. Nevertheless, several technical problems will arise from the close proximity of those lines. One of those problems is the issue of interference between the power and pipelines, during normal opera-

Manuscript received March 6, 2003. The author is with the Electrical Engineering Department, Kuwait University, Safat 13060, Kuwait (e-mail: [email protected]). Digital Object Identifier 10.1109/TPWRD.2003.823211

tion as well as in emergency conditions [1]–[5], [8]. If we focus on the possible concerns regarding the effect of power lines on nearby pipelines, the electromagnetic coupling represents one of the possible reasons for endangering the personnel and equipment dealing with the pipelines. Basically, it has two components: inductive and capacitive. The first one is due to the magnetic field generated by the currents in the power line. Since this effect is proportional to the line currents, steady-state magnetic coupling can assume dangerous values especially during fault conditions. The objective of [1], which is one of two volumes jointly issued by the Electric Power Research Institute (EPRI) and the Pipeline Research Committee (PRC) of the American Gas Association (A.G.A), was threefold: documenting available data on mutual interaction between electric power lines and parallel natural gas pipelines, procedures for evaluating the power frequency voltages and currents electromagnetically induced on the gas pipelines, and procedures to reduce these effects on both components and personnel. Reference [2] reports on a study dealing with a 525-kV power line, railroad, and pipeline sharing a common corridor for an exposure length of about 62 mi. Primary concern was given to both the magnetic induction due to current in the transmission line conductors (during normal and faulty conditions) and the electrostatic induction due to voltage on these conductors. The impact on the safety considerations for railroad and pipeline operation or maintenance personnel as well as on the compatible operation of electrical and electronic equipment associated with the pipeline and railroad system were discussed. Two main criteria were suggested: the magnetically induced voltage to earth on an individual conductor, or the accessible voltage difference between two conductors at an equipment location was limited to 60 V [5], and the electrostatically induced available short circuit current to earth from a conductor was limited to 6 mA. In [3] and [4], a study specializing in the areas of inductive and conductive coupling between power lines and natural gas pipelines was presented. A computer package, called ECCAPP, was described. Its problem-solving abilities and applications are demonstrated. This paper summarizes also some of the results of parametric analysis examining the role of various factors affecting the electrical interference levels caused in pipelines by nearby transmission lines under fault conditions. Reference [8] acknowledges that the problem of ac interference has been known for more than 30 years, and discusses the three types of interference between ac lines and nearby pipelines: electrostatic capacitive, resistive ohmic, and electromagnetic inductive interference. With regard to the capacitive component, the significance of grounding welded pipe sections lengths exceeding a few hundred to 1000 ft is discussed. It is further stated that with practical pipe coating, this type of coupling is of minor significance after construction.

0885-8977/04$20.00 © 2004 IEEE

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TABLE I COORDINATES OF THE SUBCONDUCTORS OF PHASE a

Fig. 1. Considered 750-kV, single-circuit, six-bundle transmission line together with the pipeline.

The presence of the pipelines will change the charge distribution on the power line conductors as well as at the ground surface. The pipeline itself will be also electrically charged. The new charge distribution will depend on the geometrical data of both the power and pipelines, as well as on the separation between them. Moreover, the charge and hence the field distribution will also depend on the neutral treatment of the power line, since some of the system capacitive currents will have the characteristics of zero sequence components. Although the capacitive coupling is basically a voltage-related phenomenon, it can increase significantly during unsymmetrical faults because of the resulting asymmetrical voltages on the line conductors. During sudden disturbances in either the electrical or the geometrical arrangement, fast electromagnetic transient phenomena will take place involving both the capacitive as well as the inductive coupling components simultaneously. This paper focuses on the steady-state capacitive coupling between the electrical power line and a parallel pipeline sharing the same corridor. The analysis will start with formulating the relationship between both the electric potential of the electric line conductors and the pipeline in terms of the conductors’ charges using the concept of potential coefficients. As a typical example, the case of the exposure of a pipeline to a 750-kV, three-phase, single-circuit, six-bundle EHV line will be considered. For given phase voltages, the solution of a set of simultaneous linear equations will yield the charges on all subconductors as well as on the earthed pipeline. It will then be possible to calculate the electrostatic field at any point of interest. Special attention will be paid to the maximum field as well as the electric charge on the pipeline. II. METHOD OF ANALYSIS The analysis starts with giving the and coordinates of the middle points of the three active bundled conductors , and for the three phases , and , respectively. They give the centers of the circles passing through the subconductors of the respective phases. Required also are the coordinates locating the center of the pipeline; see Fig. 1. The next step is to derive the coordinates of all the 18 subconductors (6 for each phase) in terms of the coordinates of their corresponding middle point, the radius of the bundle circuit , and the radius of each subconductor. For example, the coordinates of the subconductors of phase a, numbered from 1 to 6, can be given by Table I. The coordinates of the subconductors (7, 8, 12) corresponding to phase can be obtained using

Fig. 2.

Distances between the conductors m; n. TABLE II ABSOLUTE POTENTIALS OF CONDUCTORS

Table I after putting , and instead of and . Similarly, the coordinates of subconductors (13, 14, 18) can be derived by replacing and in Table I by and , respectively. coordinates of the conductors, it is possible to With the by calculate the distances between any two conductors (1) Moreover, the distance between the conductor and mirror of the conductor (denoted ) with respect to the ground surface is

(2) as depicted in Fig. 2. Using the above distances among the actual conductors and their images with respect to the ground surface, it is possible to determine the potential coefficients as given in [6], [7]. The absolute potentials of the different conductors are shown in Table II. The values in Table II are given assuming that the line is a part of a solidly earthed neutral network. denotes the peak phase voltage V, with the voltage of phase taken as a reference for all phasor quantities.

SAIED: CAPACITIVE COUPLING BETWEEN EHV LINES AND NEARBY PIPELINES

Fig. 3. Field components at the point Q .

0

P

of (x; y ) due to

Q

and its image

A system of simultaneous complex equations can then be foras mulated linking the charges on the conductors well as on the image conductors with the given voltages, in terms of the different potential coefficients. The above system of equations can be easily reduced to a simpler one since the charges of the image conductors are exactly the negative values of those existing on the conductors. It was then possible to use a Mathematica program to solve these equations in order to get the complex charges , and their images. The capacitive current through any conductor is equal to . Accordingly, the capacitive currents through the different phases are

(3) The neutral current is then (4) Having determined the individual complex charges , it is possible to determine the electric fields at any arbitrary point due to and its imageand

(5)

in the directions indicated in Fig. 3, where

(6) and , In order to get the resultant electric field due to both the horizontal and vertical components of and , should be determined and added. This process will be repeated for all charges and the corresponding negative images in order to get the total electric field at any point of coordinates . It should be noted that the so-determined electrostatic fields are two-dimensional, and have no axial or longitudinal compo-

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nents, since the issue of the electromagnetic or inductive coupling is not taken into account. Two approaches will be used in order to demonstrate the impact of the pipeline on the high voltage power line. The first approach deals with results describing the effect of the presence of the pipeline on the electric potential distribution in the vicinity of the power line. Several graphs illustrating the pipeline surface gradient will also be presented. They will enable us to assess these gradient in comparison with the typical values of the undisturbed field on the surfaces of the active phase conductors, on the ground wires, and on the ground surface. The second approach is based on a circuit analysis comprising impact of the pipeline on the values of both the potential assumed by the neutral point and the current through the earthing impedance (if applicable), for different kinds of neutral treatment. III. RESULTS The above method is applied to a 750-kV single-circuit, 50-Hz, six-bundle overhead transmission line with flat horizontal conductor configuration. The line has the following geometrical data: cm; • radius of each bundle subconductor • average height of the active 18 subconductors m; • -coordinate of the center of phase ; • -coordinate of the center of phase m; • -coordinate of the center of phase m; • radius of the circle passing through subconductors cm. The coordinates and geometrical data of the pipeline will be given later for each case study. Several computer runs have been done to validate the described model. The potential at the ground level was computed and plotted as a function of the horizontal coordinate . The potential was found constant . Then the horizontal component of the electric field was computed along the same path and found also to be zero, as expected. At any active conductor, the potential was calculated and found to be equal to the corresponding phase voltage. The neutral current (per unit length) of the power line can then be obtained using (4). Assuming a neutral impedance , the neutral voltage is (7) First, a pipeline of radius 0.5 m is assumed. Its axis is 1 m above the ground level, and is at a horizontal distance 35 m to the right of phase . Fig. 4 is given to illustrate the impact of the pipeline on the potential distribution around the EHV power line. The -axis gives the coordinate, in meters, measured from phase a. The distributions are shown for four horizontal planes with the indicated vertical distances. The originally symmetrical curves (with respect to m of phase b) will be strongly distorted by the presence of the pipeline. All four curves are seen to be pulled down in the vicinity of m in order to satisfy the condition of zero potential of the earthed pipeline. The potential distribution along two vertical planes at horizontal distances 34.5 m (i.e., touching the left side of the pipe) and 35.5 m (i.e., touching the right side of the pipeline) is indicated in Fig. 5. The two curves

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Fig. 4. Potential distribution along four horizontal planes (with the indicated heights above ground). The x-axis gives the coordinate in meters measured from phase a.


Fig. 6. Effect of the pipeline on the electric field distribution on the ground surface.

Fig. 7. Electric field on the pipe surface as a function of the angle measured from the direction of the positive x-axis. Fig. 5. Potential distribution in kilovolts (max) along two vertical planes of the indicated horizontal distances in meters, measured from phase a.

give the electric potential versus the height in meters measured from the ground level. In the absence of the pipeline, the two curves will be nearby straight lines (for heights between 0 and 2.5 m). Again here, the presence of the pipeline will distort the potential distribution in the way depicted in Fig. 5, in order to satisfy a zero pipe m for both curves). potential (at Fig. 6 depicts the (vertical) field distribution on the ground surface versus the -coordinate in meters measured from phase . The originally symmetrical distribution of the field magnitude will be modified indicating the strong shielding effect of the earthed pipeline, hi particular, beneath the pipe. The field is seen to reverse its direction, so that there will be two locations (i.e., two parallel straight lines) on the ground surface having zero electric field. These zero-field parallel lines correspond, approximately, to the intersections of the two vertical planes mentioned in the context of Fig. 5 with the ground surface. Directly under the axis of the pipelines, the field reverses its sign and drops in magnitude m) from about 0.07 kV/cm (as seen from Fig. 6 at to about 0.03 kV/cm. The distribution of the electric field on the pipe surface is illustrated in Fig. 7. The field in kilovolts (max)/cm is given in dependence on the angle measured from the positive direction of the horizontal -axis. The field direction is always normal to the surface of the pipeline. The curve is indicating that the

Fig. 8. Electric field at the top of the pipeline as a function of the pipe’s horizontal distance measured in meters from the tower center.

field on the pipe upper surface is much stronger than that of the lower half. At an angle of 90 (i.e., on the top of the pipeline), the field is 0.148 kV/cm, whereas at an angle of 270 (i.e., at the pipe bottom), the field is 0.06 kV/cm. This is because both the earthed pipeline and the ground have zero potential. The dependence of the maximum pipe electric field (i.e., on the top of the pipeline) on the horizontal distance between the pipe and the tower center is given in Fig. 8. The maximum electric field has its highest value of about 0.175 kV/cm if the pipe is placed at m measured from phase b. The field then decreases steadily to almost zero if the pipeline is about 100 m far from the tower center (or phase ). These values assume constant pipe radius (0.5 m) and height (1 m).


Fig. 9. Charge/meter on the pipeline versus its horizontal distance from the tower center.

Fig. 10. ground.

Charge/meter on the pipeline as a iunction of the pipe clearance to

A similar behavior is seen in Fig. 9 depicting the relationship between the magnitude of the charge per meter on the pipeline (in 10 C/m) and its separation from the tower center. Again here, the charge on the pipe will be extremely small if the pipe is placed at a distance of more than 100 m (for the given pipe radius and height). The effect of the clearance between the pipe bottom and the ground (in meters) on the charge on the pipeline (in 10 C/m) is depicted in Fig. 10. If the pipe (of 0.5 m radius) is almost touching the ground surface (i.e., zero clearance), a charge of 2.8 10 C/m will result. Increasing the clearance from zero will be accompanied by a decrease of the charge, until it assumes its least value of 2.6 10 C/m at a clearance of about 0.2 m. The charge then increases steadily with the clearance, reaching 3.52 10 C/m at a clearance of 1.3 m. The pipe radius is unchanged m and is located at a fixed distance 23 m from the tower center. As for the maximum electric field on the top of the pipeline, so for clearances less than 0.15 m, the field will remain almost constant 0.132 kV/m. As the clearance increases beyond 0.15 m, the field increases almost linearly to reach about 0.180 kV/cm at a clearance of 1.3 m. Changing the radius of the pipeline will affect the charge per unit length as shown in Fig. 11. Here, it is assumed that both the height and the horizontal distance of the pipe from the tower center are fixed, namely 1 and 23 m, respectively. For pipe radii

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Fig. 11.

Charge/meter on the pipeline as a function of its radius.

Fig. 12.

Effect of the pipeline radius on its maxim electric field.

less than 0.65 m, the charge/meter increases almost linearly with the radius. Beyond 0.65 m, the charge increases at a faster rate. The effect of the pipe radius on the maximum electric field (at the top of its surface) is given in Fig. 12, in which the radius varies between almost zero to 1 m. It is noticed that the field assumes large values for small pipe radii. From Fig. 6, it could be seen that at a point 23 m from the tower center the magnitude of the undisturbed field at the ground level in the absence of the pipeline will be about 0.07 kV/cm. Fig. 12 shows, however, that a pipe of a radius of 0.5 m placed at the same location will assume a maximum electrostatic field of about 0.15 kV/cm (i.e., more than double the value of the undisturbed field). Since the clearance to ground is assumed fixed (1 m), pipelines of radii greater than 1 m could not be represented in Fig. 12. In the following part, the impact of the pipeline on the EHV power line will be investigated. The considered power line is a part of a solidly earthed network and the axis of the pipeline is assumed 2 m above the ground level. The neutral current in mA/km, as obtained using (4), will be discussed. In the absence of the pipeline, i.e., its radius is zero, the neutral current is 194 mA/km. This “intrinsic” neutral current is due to the unsymmetrical flat conductor configuration of the intransposed power line. The presence of the pipeline increases the neutral current slightly. The effect increases with the pipe radius. For a pipe radius of 2 m, the neutral current will increase only by about 1.8% to reach 197.5 mA/km. Without any loss of generality, and in order to reduce the computational burden, the following results refer to a simpler 750-kV, two-phase power line with flat configuration, i.e., the conductors of the two phases and have the same height

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V

and

Fig. 15. Neutral voltage V as a function of both the neutral reactance (in

1m) and the pipe radius (in meters) of a compensated network.

Fig. 14. Neutral current, in amps per meter for a 750-kV, two-phase line as a function of the pipe radius. The EHV network is assumed solidly earthed.

Fig. 16. Plot illustrating the parallel resonance which will occur at a certain value of the neutral reactance, due to the presence of a parallel pipeline of radius 1 m.

above ground, 20.2 m. Furthermore, no bundling is considered. Each of the two phases has a single solid circular conductor of 35.8–cm radius (which is chosen equal to the geometrical mean radius of the previously considered three-phase line). The conductors of phases and are assumed 11.8 m apart. The pipeline is assumed located at a horizontal distance of 11.2 m to the right of the power line. The phase voltages of the two-phase line are 750 2 and 750 2 kV for phase and , respectively. Fig. 14 depicts the effect of the pipe radius on the neutral current for the untransposed two-phase line, in amps per meter. Here, in the absence of the pipeline (i.e., its radius is zero), the neutral current is zero. There is no “intrinsic” neutral current because the two-phase line with its flat conductor configuration is geometrically symmetrical with respect to the ground surface. In the presence of a pipeline of a radius 2 m, and placed 2 m above ground, this symmetry will be disturbed, resulting in a neutral current of about 10 A/m or 10 mA/km. Another situation for a possible adverse effect of the pipeline on a nearby power network assumes a compensated network, i.e., a network inductively earthed via Petersen coils (i.e., in Fig. 13). These inductors are used to compensate for the stray capacitive currents during earth faults and hence facilitate the duty of the circuit breakers involved. Since the stray capacitances increase with the network geometrical dimensions, the required inductive reactance will decrease with the line length. Fig. 15 depicts a three-dimensional plot giving the magnitude in volts, as a function of of the steady state neutral voltage,

both the radius of the pipeline in meters and the reactance of the neutral reactance in meters. It is seen that even in the absence of the pipeline (i.e., for a pipe with almost zero radius) there is a particular value of the neutral inductive reactance (about m) at which parallel resonance occurs. This will 1.7 10 be accompanied by a considerable displacement of the neutral voltage. The presence of the pipeline is seen to “detune” the parallel resonance, i.e., the resonance will occur at smaller values of the neutral inductance. This can be attributed to the fact that the pipe will increase the effective network capacitance. Therefore, smaller inductance will be needed for a parallel resonance to occur at the power frequency. This effect increases with the pipe radius as see in Fig. 15. The neutral voltage during this situation will be limited primarily by the network losses. Theoretically, this voltage can reach an infinite value, if the network is assumed lossless, as seen in Fig. 16, giving the neutral voltage for the case of a pipe of 1 m radius placed 2 m above . ground, in terms of the power network’s neutral reactance Fig. 17 depicts the magnitude of the neutral voltage for a parm ticular neutral reactance of the power network 1.51 10 as a function of the pipe radius. It is seen that there is a critical value for the radius of the pipeline (around 1.8 m in this case) at which the neutral voltage will assume dangerously high values (limited by the network losses). Since the losses are not taken into consideration in its analysis, Fig. 17 shows an infinite neutral voltage for this critical pipe radius.

Fig. 13. Equivalent circuit used for calculating the neutral potential the neutral current I .


Fig. 17. Neutral voltage versus the pipe radius for a particular neutral reactance.

IV. CONCLUSION 1) The problem of the mutual capacitive coupling between EHV power lines and nearby pipelines sharing the same corridor is pointed out. The issue is of paramount significance especially in oil-producing countries such as the Gulf states. 2) A mathematical model is given for the computation of the electrostatic effect of the power line on the pipelines. Two indexes are used to assess this effect: the maximum electrostatic field and the electric charge per unit length of the pipe. The impact of the pipeline on the potential and field distributions around the power line is also discussed. 3) For a 750-kV, three-phase power line, and a pipeline of a radius 0.5 m, it is seen that the electric field on the pipe can reach 0.175 kV/cm, for a horizontal separation of about 16 m between them. Both the field and the charge on the pipe will decrease to almost zero if the pipeline is 100 m from the power line. 4) The relationship between the pipe charge and the clearance between the pipeline and the ground is rather complicated. Increasing the clearance from zero will be accompanied by a decrease of the charge, until it assumes its least value of 2.6 10 C/m at a clearance of about 0.2 m. The charge will then steadily increase with the clearance, reaching 3.52 10 C/m at a clearance of 1.3 m. 5) For clearances less than 0.15 m, the field on the pipe surface will remain almost constant 0.132 kV/cm. As the pipe clearance increases beyond 0.15 m, the field increases linearly with the clearance, reaching about 0.180 kV/cm at a clearance of 1.3 m. 6) For pipe radii less than 0.65 m, the charge/m on the pipeline increases almost linearly with the radius. Beyond 0.65 m, the charge increases at a faster rate.

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7) Several parameter studies have been done to investigate the impact of the pipelines on the EHV power line. It is noticed, for example, that the presence of the pipeline will result in a slight increase (around 1.8%) in the neutral current, if the power line is part of a solidly earthed power network. 8) For the case of inductively earthed neutral, the results of analyzing a case involving a 750-kV, two-phase power line show that even in the absence of the pipeline, there is a particular value of the neutral inductance at which parallel resonance will occur, accompanied by a considerable shift of the network’s neutral voltage. The pipeline will detune the parallel resonance, i.e., the resonance will occur at a smaller neutral inductance. This effect increases with the pipe radius. 9) Results show also that for a particular power network’s neutral inductance, there will be a critical value for the pipe radius, at which the above mentioned resonance phenomenon will occur. On the other hand, there exists a critical neutral reactance that will result in this resonance for a given pipeline radius. REFERENCES [1] J. Dabkowski and A. Taflove, “Mutual design considerations for overhead ac transmission lines and gas transmission pipelines,” Electric Power Research Institute (EPRI), Volume 1: Engineering Analysis, Sept. 1978. [2] M. Frazier, P. Thomas, H. Roberton, J. Dunlap, and T. Morgan, “Transmission line, railroad and pipeline common corridor study,” IEEE Trans. Power Delivery, vol. PWRD-1, pp. 294–300, July 1986. [3] F. P. Dawalibi and R. D. Southey, “Analysis of electrical interference from power lines to gas pipelines—Part I: Computation methods,” IEEE Trans. Power Delivery, vol. 4, pp. 1840–1846, July 1989. [4] , “Analysis of electrical interference from power lines to gas pipelines: Part II: Parametric analysis,” IEEE Trans. Power Delivery, vol. 5, pp. 415–421, Jan. 1990. [5] , Principles and practices for inductive coordination of electric supply and railroad communications/signal systems, Association of American Railroads and Edison Electric Institute, Sept. 1977. [6] Transmission Line Reference Book, 345 kV and Above, 1982. [7] J. A. Grainger and W. D. Stevenson, Power System Analysis, 1st ed. New York: McGraw-Hill, 1994, ch. 5. [8] J. Smart III, D. van Costendrop, and W. Wood, “Induced AC creates problems for pipelines in utility corridors,” J. Corrison Technol., vol. 82, no. 6, pp. 1–12, June 1999.

Mohamed M. Saied (M’80–SM’84) was born in Egypt in 1945. He received the B.Sc. degree (Hons.) in electrical engineering from Cairo University, Cairo, Egypt, in 1965 and the Diplom-Ingenieur and Doktor-Ingenieur degrees from Rheinisch-Westfaelische Technische Hochschule (RWTH), Aachen, Germany, in 1970 and 1974, respectively. From 1965 to 1967, he was a Research and Teaching Assistant at Cairo University. From 1974 to 1983, he was a Faculty Member at Assiut University, Egypt. In 1983, he joined Kuwait University, Safat, Kuwait, where he is now a full Professor of electrical power engineering. He spent a one-year sabbatical leave (1998) as a Visiting Professor at Cairo University. Prof. Saied is a Senior Member of Forschungs-Gesellschaft Energie in Germany and CIGRE’ in France.