504 IEEE Transactions on Power Systems, Vol. 11, No. 1, February 1996

Distribution System Reconfiguration for Loss Reduction: An Algorithm Based on Network Partitioning Theory

R.J. SBrfi, M.M.A. Salama Dept. of Elec. and Comp. Eng.

University of Waterloo Waterloo, Ontario Canada, N2L 3G1

Abstract - The algorithm proposed in this paper provides the facility to achieve on-line distribution system reconfiguration for loss reduction. Based on partitioning the distribution network into groups of load busses, such that the line section losses between the groups of nodes are minimized, the proposed method overcomes the size restrictions imposed by previously described reconfiguration techniques. By dividing the distribution network into groups of busses, the combinatorial nature of the reconfiguration problem is overcome, while simultaneously minimizing losses. Computer simulations, of the proposed method, demonstrate the numerous benefits that are offered by the proposed reconfiguration algorithm.

Keywords: distribution automation, loss minimization, system reconfiguration, network partitioning theory.

I. INTRODUCTION

In 1975, Merlin and Back introduced the concept of distribution system reconfiguration for system loss reduction [l]. The technique proposed by Merlin and Back exploited the radial topology, typical of urban distribution systems. Due to the fact that the configuration of distribution networks is designed to be most efficient for a specific demand condition, the algorithm of Merlin and Back determined a new network topology that would minimize I 2R losses for the prevailing system diversity and load.

The concept of reconfiguring the topology of the distribution network to minimize losses can immediately be recognized as being cost efficient, and consequently of interest to efficiency conscious electric utilities. In view of the increasing use of supervisory control and data acquisition systems (SCADA), and distribution automation and control (DAC), distribution system reconfiguration becomes a more viable alternative for loss reduction. Distribution systems

This paper was presented at the 1995 IEEE Power Industry Computer Applications Conference held in Salt Lake City, Utah, May 7-12, 1995.

A.Y. Chikhani Dept. of Elec. and Comp. Eng.

Royal Military College of Canada Kingston, Ontario Canada. K7K 5LO

equipped with SCADA and DAC already possess the necessary automated switches and remote monitoring facilities.

Unfortunately, utilities have been reluctant to implement distribution system reconfiguration in on-line schemes, despite the fact that pilot projects and feasibility studies have demonstrated the potential savings associated with reconfiguration for loss reduction [2], [3]. Utilities express concern over the time consuming nature of the existing reconfiguration algorithms, the effect on system reliability and continuity of supply, and the switching sequence to bring about the reconfiguration. The large number of nodes in distribution systems offer considerable flexibility in possible topology changes, but also contribute to the short-coming of previously proposed reconfiguration algorithms due to the computational burden presented by he reconfiguration problem.

From the initial introduction of the concept of reconfiguration for loss reduction by Merlin and Back, to the most recently documented reconfiguration algorithms, it is apparent that, with the existing algorithms, on-line, real-time implementations are not feasible. The combinatorial nature of the reconfiguration problem dictates that reconfiguration algorithms based on optimization are too time consuming for on-line use. Algorithms based on heuristics offer only a reduction in the losses and do not offer detailed models of the non-linear loads typical at the distribution level. Reference 141 offers a comprehensive survey of the previously proposed reconfiguration methods, and their characteristics.

The algorithm proposed in this paper represents a novel method of overcoming the size limitations of previously proposed reconfiguration algorithms, consequently permitting on-line reconfiguration of the distribution network. Although network partitioning theory has been employed in other power system applications, the method introduced by this paper makes use of partitioning in a novel manner. In the proposed algorithm, the line sections of the distribution system are weighted according to the associated losses, and partitioned into blocks of busses. The partition is made such that the most efficient line sections are grouped together within the blocks and the least efficient: form the CUtSet. The worth of the proposed method is derived from the fact that it commences the search for a minimal loss network configuration while the distribution system is partitioned into sub-systems. An initial version of the proposed algorithm was previously described by the authors in [5].

In the case of distribution systems of more modest proportions, the proposed algorithm can determine a network configuration that reduces the system line losses in one step.

0885-8950/96/$05.00 0 1995 IEEE

505

factor, such as cable ampacity or the amount of use to which the associated switch has been subjected. A heuristic has been developed to determine a weighting measure for open line sections. The third section of this paper outlines the weighting measures in considerable detail.

In the context of distribution systems of larger proportions, any previously defined reconfiguration method can be employed to minimize the intra-block losses, with the benefit of a considerably reduced computational burden. The proposed algorithm has been implemented using a fast heuristic technique for partitioning the system, and the method of Civanlar et al., for the inter-block reconfiguration. The proposed method is particularly suited to parallel implementations and permits real-time reconfiguration of even large distribution systems.

This paper is divided into six sections. In the second section, an overview of the proposed algorithm is presented. The third section describes the partitioning scheme in detail. A review of the mathematical basis of an implementation of the proposed algorithm is provided in the fourth section. Examples that demonstrate the efficiency of the proposed algorithm are provided in the fifth section. The sixth section offers concluding remarks.

11. THE PROPOSED ALGORITHM

A distinct advantage of distribution system reconfiguration over the numerous other methods of reducing line losses is the fact that it can be implemented at a minimal expense. An electric utility or large industrial facility that is equipped with automatic tie and sectionalizing switches, and remote monitoring facilities, can introduce reconfiguration algorithms through software integration. The proposed algorithm lends itself favourably to installation on even a PLC based control system, due to the minimum computation required. In view of the time required to effect the switching operations, and the relatively slow variations in load, a reconfiguration algorithm is thought to be suitable for on- line implementation if it can provide a robust solution within a short time, for example 10 minutes.

Figure 1 outlines the reconfiguration algorithm proposed in this paper. Stages 1 and 9 require inpudoutput with the system. Stage 1 of the algorithm requires the prevailing demand information from the network’s SCADA system. Based on the demand at monitoring points of the distribution system, the line section power flow and losses are calculated through a load flow analysis ( stage 2).

A shortcoming of many of the previously described reconfiguration algorithms is that they require a load flow analysis to be performed at each iteration of the reconfiguration. Although performing a load flow analysis of even a large distribution network can be performed with a minimal time requirement, the repetitive load flows make real-time implementation unfeasible. In the best-case scenario, the proposed reconfiguration algorithm only requires a load flow solution of the entire distribution system twice. Iterative load flow analysis is required only on the partitioned sub-systems: the reduction in solution time is dependent on the order of the load flow algorithm employed.

The third stage of the solution algorithm ihvolves assignment of a weighting factor to each line section considered in the reconfiguration. The weighting factor represents not only information related to the efficiency of a particular line section, but can also be biased by some other

INITIAL STATUS OF 1 DISTRlBUTlON SYSTEM

2+ LOAD FLOWANALYSE

FACTOR TO FEEDERS

4 PARTITION I

I DISTRIBUTION SYSTEM I

RECONFIGURE

RECONNECTED

AS A WHOLE

CRITERIA FOR SYSTEM CONVERSION

9 PROCEEDWTH

RECONFIGURATION

Figure 1: The proposed reconfiguration algorithm

The fourth stage of the proposed reconfiguration algorithm involves partitioning of the distribution system into multiple sub-systems. Not only does the partitioning operation reduce the computational burden of the reconfiguration problem, in addition, it performs a minimization of the losses for the line sections joining the sub-systems. By employing a fast partitioning method, the time required for partitioning the distribution network is reduced to an acceptable margin, for even large networks. Efforts have been made to identify the number of sub-system into which the network is partitioned: while all tests indicate that the losses are not increased by a less desirable selection of block size, a more appropriate selection of block size and number will result in a near optimal solution.

The fifth stage of the algorithm represents the reconfiguration of the individual sub-networks. Future work involves the use of external equivalency to consider the effect

506

of the other sub-networks. A strong point of the proposed method is that any previously described reconfiguration algorithm can be employed to reconfigure the individual blocks of demand points: size restrictions of the previous algorithms can consequently be overcome. If we consider that for a network equipped with n switches there are n2 possible switching combinations, one quickly gains an appreciation for the valuable contribution of the proposed algorithm. The reconfiguration method selected for this stage must, as a minimal requirement, ensure that voltage drop and line ampacity constraints are met.

Stages 6 and 7 of the proposed reconfiguration algorithm require reconnection of the individual sub-systems, and analysis of the system as a whole. Step 7 serves as a measure of redundancy, ensuring that the behaviour of the system as a whole compares favourably to what can be extrapolated from analysis of the individual sub-systems.

The eighth stage of the proposed reconfiguration algorithm serves to determine whether or not the proposed reconfiguration is to take place. In an actual implementation, conversion criteria must include a comparison of the monetary cost of the reconfiguration to the actual savings of reduced losses. In an industrial context, this criteria might consider the increase in surplus power to be sold to a utility, and the released capacity. Should the conversion criteria be met, the reconfiguration is brought about, otherwise, another virtual reconfiguration of the distribution system may performed based on other criteria ( a change in block size and numbers is highlighted as a possibility).

III. THE PARTITIONING MODEL

Prior to partitioning the distribution system into sub- systems, it is necessary to model the distribution line sections as the branches of a hypergraph. In the proposed algorithm, each line section of the distribution system is to be assigned a weight based on the its efficiency. In order to provide a weight to line sections that are open during the prevailing demand condition, an approximation formula is described for the efficiency of the system if the line section were closed. By making this assumption about the weight of open line sections, the radial system can be characterized by a pseudo-meshed topology. Other authors have considered the distribution system to be initially in a meshed configuration to ensure the independence of the final configuration from the prevailing switch status [21, [61.

Equation 1 describes a proposed weighting scheme that biases a line section based on its efficiency, and not total losses. This distinction is important as the reconfiguration algorithms previously proposed consider not the efficiency of the line, but rather the associated losses. In this manner, a heavily loaded line section that is efficient is not eliminated from the candidate pool due to high relative losses.

i andj represent the end nodes of a specific line section; m.. is the weighting factor assigned to line section ij ; v p.. is the real power flow calculated for line sectionij ;

v I .. is the line current calculated for line section ij ; v R e . is the resistivity of line section ij .

II

From equation 1, it becomes apparent that the more efficient the line section, the greater the weighting €actor (m). The partitioning operation collects the nodes joined by the line sections with a heavier weighting together, and minimizes the summed weight of the line sections joining the blocks of busses. The losses between the different sub- systems is minimized by the process of decoupling the distribution network. Due to the high power factor typical of a well compensated, modem distribution system, only the real component of the power is considered.

In the instance of an open line section, the weighting measure must take into account, not only the losses of the line section itself, but as well the increase in losses on the lines that are to supply it. The effect of the load transfer accounts for the losses on the line section, and its influence on the total system losses. The approximation for the power and losses due to the closure of an open line section is based on equation 2 [7], and assumes a constant voltage.

0.001 x R;j c.. = ' kV2

In equation 2, the terms are the same as those defined for equation 1, with the addition of:

is the loss associated with line section i j ; P

kV IS the nominal system voltage. L g

For a line section that is open, S is the set of line sections that provide the path of greatest resistance from a common source node to the last bus in the chain of line sections. It is assumed that by effecting a switching option, the transferred load wiU extend from the previously open section, to the load point that results in the summed demands to be within a small margin of the member line section's capacity. P is

defined as a member of the set of open line sections. The increase in the losses on the supplying line sections due to the closing of a previously opened line section is represented by equation 3.

0, ij

In equation 1, the following expressions are defmed: In equation 3, the following new symbols are defined:

507

scheme. The time required to accomplish the partitioning is acceptable for even large distribution systems.

Reference [9] reports that a time of 39.18 seconds was required to partition a VLSI sample system of 904 nets and 833 nodes into 6 blocks: the graph represented by this sample system is easily on the same order of magnitude as a typical

@L,oG is the change in losses due to the closing of a line section formerly open; k is the a member of the set Of nodes, K ,that is inferior to the end point of line sections in W ; Db is the real power demand at node k ; n

CWG represents the loss coefficients for the members of the set W : W is the subset S that are superior in the chain of nodes to the f is t node in K.

Through extension of equations 2 and 3, the weighting factor for the open line sections is defined in equation 4. The use of equation 4 to determine the weighting factor for open line sections ensures that the partition is not dependent of the initial configuration of the system.

Should operational restraints be placed on a switch such that it cannot be operated, it is possible to artificially bias the weight to ensure that the switch is not included in cutset. In the same manner, the cost of the switching operation can be calculated from the expected number of switching operations possible in the lifetime of the switch, the amount of usage to date, and the replacement cost of the unit. Non-automated switches can be included in the algorithm, and if a study of predicted load patterns determines an operation to be beneficial, the switching can be performed manually at a pre- determined frequency ( i.e. on a seasonal basis).

(4) - Vk fed by open section

m0.q -

IV. THE MATHEMATICAL BASIS

The numerical methods employed in an implementation of the proposed reconfiguration method are described. One of the main advantages of the proposed reconfiguration technique is that any combination of load flow, partitioning, and reconfiguration methods can be employed in conjunction with this method.

For the purposes of demonstrating the efficiency of the proposed algorithm, load flow calculations were performed using a modified version of Kersting’s ladder network method as described in [81. Results of the load flow calculations were validated using a recognized commercial distribution system analysis package ( EDSA Design Master v27.81, EDSA- Micro Corporation).

The partitioning of the distribution system was performed employing an eigenvector based technique to generate a good start partition, followed by the Sanchis iterative improvement technique [9]. The details of the heuristic partitioning method are developed in [9]. The use of the heuristic partitioning method overcomes the combinatorial nature of the problem and can be used to obtain near-optimal results. The accuracy of the solution depends on the number of iterations performed during the iterative improvement

urban distribution system. The time saved in the solution of the partitioned system is no doubt greater than the time consumed for the partitioning operation, and convergence is assured in instances where it previously could not have been.

Through the use of the weighting factors described by equations 1 and 4, the distribution system is represented as a hypergraph. A netlist matrix ( C ) is constructed to represent the connections of the graph, and consequently an adjacency matrix ( A ) can be determined. The connectivity matrix is formed by placing the weighting measure for a given line section in the position corresponding to the index of its end nodes: the resultant matrix is symmetrical with a zero diagonal and of the dimensions n x n ( n being the total number of demand points in the system). Several means of calculating the adjacency matrix were employed, but one equation described in [9] was found to be the most effective:

In equation 5, the following symbols are employed: c . represents the j lh row of C ;

a .. represents the i j lh entry in A. 1

II Reconfiguration of the individual sub-systems is performed

in accordance to the heuristic method outlined by Civanlar et al. [lo]. The method of Civanlar et al., was selected as it has been used as a basis of comparison in subsequently proposed reconfiguration algorithms. This heuristic reconfiguration technique represented considerable innovation as it employed an empirical formula to estimate the relative loss reduction associated with a proposed switching combination, and it used two “rules of thumb” to reduce the total number of permissible switching options. The two “rules of thumb” of Civanlar et al. were based on voltage drop constraints: i) In the case of a normally open tie switch, loss

reduction can only be achieved if the load is transferred from the side of the greatest voltage drop from the sub- station to switch, over to the side with the lower voltage drop from sub-station to switch;

ii) If the voltage drop across an open switch is substantial, a reduction in losses will result.

V. AN ILLUSTRATIVE EXAMPLE

The validity of the proposed algorithm was verified using the sample three feeder distribution system described in [lo]. The initial network topology of the sample three feeder

508

system is provided in figure 2, and the line section data in table 1. Despite the diminutive size of the sample system, it possesses many characteristics of a system of realistic proportions.

Figure 2 Sample Three Feeder System

Table 1: Initial Sample System Data

I I I I I 1 i StartEnd Section Data (pu) End Load End Bus Line Loss End Bus V

Bus Resistance Reactance Mw MVAr C w k ) (kW) (Nore 1) I

" No& 2: Ba'se Values: lo0 kVA, 23kV.

The sample system is used to demonstrate the effect of the sub-system size and numbers on the subsequent reconfiguration. Of note is the fact that in no instance did a less appropriate selection of block size result in an appreciable increase in losses. Although it is most desirable to pfoduce a reconfiguration that minimizes the system losses, time constraints many dictate that only a sub-opptimal reduction in losses can only be brought about. In the case of large distribution systems, previously described

reconfiguration algorithms may become trapped in a local optimal due to the non-linear nature of the problem, or witness combinatorial explosion and never converge to a solution. Exhaustive search philosophies are inappropriate for larger networks.

Due to the small size of the sample distribution system, it is not appropriate to consider the absolute time required to reconfigure the distribution system using the proposed algorithm. For the system in question, benefit of the partitioning is not fully appreciated: the proposed method is better suited to systems of greater magnitude. A better basis for comparison is the number of possible switching combinations existing initially, and the number following the partitioning. The loss reductions brought about by the reconfigurations through partitioning are compared to those obtained in 1101.

The development of a method to determine the most appropriate block sizes and number would increase the value of the proposed method. Figure 3 illustrates the partitioning of the sample distribution system into 2 sub-systems: 5 nodes in one sub-system, and 11 in the other. The unpartitioned sample system contains a maximum of 16 possible switching combinations, assuming that every combination is feasible and will not result in thermal or voltage drop violations. From the decomposition of the sample system into two sub-systems, the maximum possible number of switching combinations is reduced to 10 combinations.

2

2

...........................................

FEEDER1 j FEEDER 3

. . . . . . ".:._ 7 ......................................................................

Figure 3: 5/11 Bus Sub-Systems

The partition of the system determined in the 5/11 bus example of figure 3, indicates that all the branches within the 5 bus sub-system should remain connected, and that one must only consider reconfiguration within the 11 bus sub-system. Although the behaviour of the distribution system in this model is considered to be static for the purposes of the partitioning, results have shown that this heuristic is efficient in decoupling the system. In a larger network, the partition

509

systems, it is possible to determine if the proposed reconfiguration reduces the losses and satisfies a l l operational factors.

may not be as effective as in this example, where one feeder is isolated to form the radial system, but a significant reduction in the computational burden can certainly be expected.

In order to gain a better appreciation for the proposed technique, the nine stages of the partitioning based reconfiguration algorithm are to be reviewed through examination of the 5/11 partition. For the purposes of this illustrative example we assume that the initial status of the distribution system has been determined and that a load flow analysis has been performed in order to obtain the power flow through the initially closed line sections. It is of note that in the proposed algorithm, the load flow is performed on the radial network, and it is in the partitioning procedure that the system is represented as a meshed network. Considering a meshed network ensures that the final solution is not dependent on the initial system status.

The assignment of weighting factors is subsequently performed in stage three of the proposed algorithm. The weighting of the line sections is performed for the initially closed line sections in accordance with equation 1. The system is consequently represented as a meshed graph by heuristicaIIy determining a weighting factor for open line sections based on equation 4. For the sample system detailed in figure 2, equation 1 is employed to assign weighting measures for all line sections, with the exception of 5-11,lO- 14, and 7-16 which are initially open and consequently employ equation 4.

The partitioning algorithm employed in the proposed method permits one to “fix” specific nodes of the graph into a specified block. In order bias the partitioning scheme such that it will influence the solution towards a radial system and have each sub-system supplied by a feeder, it is desirable to “fix” the feeders into distinct blocks. The user having specified the number of blocks and the size of each block, the system is partitioned using the heuristic method of [SJ. In the 5/11 block example, following the partitioning, the 5 node block is considered to be reconfigured and only the 11 node block configuration must be investigated. In this example, the radial nature of the system precludes analysis of the two blocks together as there is no connectivity at this level. When reconfiguring a system of considerably larger proportions, the proposed algorithm may have to consider the external networks if the partition does not provide the tree structure of a radial graph.

The fifth stage of the algorithm considers reconfiguration of the individual sub-systems. We must only examine the 11 node block in the example provided. For the proposes of this paper, the method of Civanlar et al. 1101 is utilized to reconfigure the individual blocks. It becomes apparent that the number of possible switching combinations is reduced considerably through the partitioning. In the example provided, the sixth stage of the algorithm becomes redundant as the partitioning and subsequent reconfiguration have isolated the three feeders into a radial network. This stage would be considered only in the instance of a larger network where, due to some operational parameter or feature of the topology, it is not possible to isolate the particular section. Following the load flow analysis of the individual sub-

c

a s t - 0 8 ” s

10

0 Benchmarks 2 Sub-systems 3 Sub-systems

Figure 4 Loss Reductions Associated with Block Size

In the partitioning algorithm employed, a block size tolerance is specified: the initial size of the sub-systems specified may be violated if a reduction in the cut nets will result. If, due to an operational criteria such as reliability, it is required that a bus remain within a specific sub-system, measures can be taken within the interchange algorithm to fix the bus in a specific block. For a small system such as the one proposed, the partitioning based algorithm may be used on its own to determine a configuration that reduces the system losses.

Figure 4 illustrates the effect of different sub-system sizes on the resultant loss reduction: the loss reduction brought about by the original algorithm of Civanlar et al.. is used to demonstrate the efficiency of the proposed reconfiguration technique. The numbers above the bars of the chart in figure 4 indicate the number of buses in each partition. Due to the diminutive size of the sample system, the partitioning was limited to a maximum of three blocks. The proposed method of partitioning the distribution system into sub-systems to permit individual reconfiguration is shown to achieve loss reductions very comparable to those achieved by Civanlar et al..

In instances where the system was partitioned into two sub-systems, the proposed algorithm demonstrated that it had the potential to yield the same loss reductions as achieved by Civanlar et al. In the case of partitioning the sample network into 3 sub-systems, the full potential of the proposed method was not employed as the partitioning isolated the nodes such that no reconfiguration within a sub-system was possible.

VI. CONCLUSIONS

A novel method of performing distribution system reconfiguration for loss reduction has been proposed. The proposed method offers numerous advantages over those previously described in literature. The proposed method has no limitations on the maximum size of distribution system that can be reconfigured in real-time. The partitioning operation serves not only to reduce the computational burden of the reconfiguration, but as well, minimizes the losses on the line sections that form the cutset.

The proposed partitioning method serves to reduce the number of possible switching combinations by isolating demand points into groups that should be supplied via the same source. The method outlined in this paper offers the additional advantage that it can easily be integrated into existing reconfiguration methods and presents a minimal computational burden. Reconfiguration of a sample distribution system and comparison to the results obtained from other reconfiguration algorithms lends to the validity of the proposed algorithm.

The proposed reconfiguration algorithm is suitable for use in industrial as well as electric utility applications. If one considers the monetary value of the released capacity, brought about by the loss reductions, the installation of additional automated switches, to offer increased flexibility in reconfiguration, may be justified. As a greater number of utilities install SCADA systems, the advantages offered by reconfiguration for loss reduction becomes more apparent.

REFERENCES

A. Merlin and H. Back, “Search for a Minimal-Loss Operating Spanning Tree Configuration in an Urban Power Distribution System”, Proc. Fijth Power Systems Computer Conference ( PSCC ) , Cambridge,

P.A. Gnadt and J.S. Lawler, Automating Electric Utility Distribution Systems: The Athens Automation and Control Experiment, Englewood Cliffs: Prentice- Hall, 1990. N.S. Markushevich, I.C. Herejk, and R.E. Nielson, “Functional Requirements and Cost-Benefit Study for Distribution Automation at B.C. Hydro”, Proc. PICA

R.J. Sarfi, M.M.A. Salama, and A.Y. Chikhani, “A survey of the state of the art in distribution system reconfiguration for system loss reduction”, Electric Power Systems Research, Vol. 31, No. 1, 1994, pp.

R.J. Sarfi , M.M.A. Salama, A.Vannelli, and A.Y. Chikhani, “Loss Reduction in Distribution Systems: A New Approach Using Partitioning Techniques”, Proc. IEEE IAS Annual Meeting , Toronto, October

D.Shirmohammadi and H.W. Hong, “Reconfiguration of Electric Distribution Networks for Resistive Line Loss Reduction”, IEEE T-PWRD , Vol. 4, No. 2,

1975, pp.1-18.

1993, pp. 169-178.

61-70.

1993, pp. 1439-1444.

April 1989, pp. 1492-1498.

T.Gonen, Transmission System Engineering, Norwich: Wiley-Interscience, 1988. M.M.A. Salama and A.Y. Chikhani, “A Power Flow Algorithm for Unbalanced Radial Distribution Systems”, Proc. 25th North American Power Symposium, Washington, 1993, pp. 490-495. S.W. Hadley, B.L. Mark, and A. Vannelli, “An Efficient Eigenvector Approach for Finding Netlist Partitions”, IEEE T-CAD, Vol. 11, No. 7, July 1992,

S.Civanlar, J.J. Grainger, H. Yin, and S.S.H. Lee, “Distribution Reconfiguration for Loss Reduction”, IEEE T-PWRD, Vol. 3, No. 2, May 1988, pp. 1217- 1223.

pp. 885-892.

Robert Sarfi received a B.Eng. in Electrical Engineering from the Royal Military College of Canada in 1991. Following service as a naval officer in the Canadian Forces, he entered the graduate program in Power Systems at the University of Waterloo, Canada, where he is presently studying towards a Ph.D. He has worked extensively on analytical studies for both utilities and large industrial facilities. His interests are in distribution system optimization and automation, transient modeling and simulation, and artificial intelligence applied to power systems.

Magdy Salama received B.Sc. and M.Sc. degrees Electrical Engineering from Cairo University, Egypt in 1971 and 1973 respectively. He received a Ph.D. Degree in Electrical Engineering from the University of Waterloo, Canada in 1977. He joined the Department of Electrical Engineering, Ain-Shams University, Cairo, Egypt in 1978, where he became Full Professor in 1989. Currently, he is a Professor and Associate Chair for Undergraduate Studies in Electrical Engineering at the University of Waterloo, Canada. His interests are in high voltage, insulation, cables and distribution systems, and power systems control and operation.

Aziz Chikhani received a B.Sc. degree in Electrical Engineering from Cairo University, Egypt in 1971, M.A.Sc. and Ph.D. degrees in Electrical Engineering from the University of Waterloo in 1976 and 1981, respectively. He joined the Department of Electrical of the Royal Military College of Canada in Kingston, Ontario in 1980, and is currently a Professor and Dean of Engineering. He has been an Adjunct Professor at the University of Windsor since 1985. Dr. Chikhani is a past chairman of the IEEE Kingston Section. His interests include the operation and control of distribution systems, cables and microprocessor applications in power systems. Dr. Chikhani is a Registered Professional Engineer in the Province of Ontario.