IEEE TRANSACTIONS ON SMART GRID 1 Simultaneous Optimal ...

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IEEE TRANSACTIONS ON SMART GRID 1

Simultaneous Optimal Design of Measurementand Communication Infrastructures in Hierarchical

Structured WAMSFariborz Haghighatdar Fesharaki, Rahmat-Allah Hooshmand, Member, IEEE, and

Amin Khodabakhshian, Member, IEEE

Abstract—The ability of data recovery during communicationalfailures is one of the significant advantages of the wide area mea-surement system (WAMS) with hierarchical structure. For thispurpose, in addition to the proper partitioning of the WAMS, therelative location of phasor measurement units (PMUs) and phasordata concentrators (PDCs) should be selected so as tomaximize thereliability of the communication network. The aim of this paperis to develop an organized method for partitioning the WAMS aswell as proposing a new algorithm for the simultaneous optimalplacement of PMUs and PDCs. In the proposed method, first itis assumed that PMUs are installed at all of the system buses.Then, redundant PMUs will be omitted sequentially to providethe system observability with the maximum communication relia-bility. The IEEE 30-, and 118-bus systems are used to demonstratethe proposed algorithm. Contingencies such as PMU loss and lineoutage are considered in power system observability achievement.Finally, to show the applicability of proposed methods to realdimensional power systems, the IEEE 300-bus power system isalso analyzed in the normal operating condition.

Index Terms—Phasor data concentrator (PDC), phasor mea-surement unit (PMU), reliability, survival mechanisms, wide areameasurement system (WAMS).

I. INTRODUCTION

R ELIABLE monitoring of the power network is onepromising feature of the modern synchrophasor-based

measurement system. This system is called wide area mea-surement system (WAMS). In contrary with the measurementsin the well-known supervisory control and data acquisition(SCADA) system, the phasor measurements in a WAMS aresynchronous values with high sample rate (30 samples/s).Hence, the WAMS can improve the performance of modernpower systems in various fields including, state estimation(SE), voltage stability assessment, on-line fault location andadaptive protection, line outage detection, power system sta-bility assessment, measurement based control, and remedialactions [1]–[7].However, SE is a key function in modern power systems by

providing a complete, consistent, and accurate database as aninput to all other on-line applications [8]. The power system isto be fully observable prior to SE. Because of the economical

Manuscript received August 18, 2012; revised December 22, 2012 andMarch06, 2013; accepted April 20, 2013. Paper no. TSG-00505-2012.The authors are with the Department of Electrical Engineering, Uni-

versity of Isfahan, Isfahan, Iran (e-mail: [email protected]; [email protected]; [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TSG.2013.2260185

concern, PMUs should be installed so that the system observ-ability would be provided with the minimum number of usedPMUs. Since the system observability lies within the electricalanalysis, many of power system engineers and researchers dealwith the problem of optimal PMU placement only by consid-ering the observability constraint [9]–[12]. The contribution andimplementation details for a plenty of papers published in thisfield can be found in [8].In addition to PMUs, phasor data concentrators (PDCs) and

communication network are the other main components of aWAMS. In the hierarchical structured WAMS, the measureddata by PMUs would be transferred to the PDC which sorts thephasors according to the GPS time stamps. Finally, when a setof data with the same time stamp is completed, it will be passedthrough the communication network to the power system con-trol center for required processing and applications.The above-mentioned correlations between the three main

components, reveals that in optimal design of the WAMS,all components should be considered simultaneously. Just afew papers deal with the simultaneous optimal design of theWAMS components [13]. Moreover, various aspects whichshould be considered in the optimal design of the WAMS arehighly dependent upon the used structure for the WAMS. Forinstance, two different control strategies for the WAMS, i.e.,centralized, and decentralized strategies are introduced in [14].In these strategies, PMUs are directly communicated with eachother and with the control center through the communicationspanning tree. The problem of finding the optimal spanningtree, called the minimum spanning tree, is investigated for thecentralized and the decentralized strategies, in [15] and [16],respectively. Reference [13] shows that by simultaneous place-ment of PMUs and design of the spanning tree, the number ofused PMUs will be increased to some extent but the cost ofcommunication infrastructure will be decreased.In this paper, the hierarchical structure presented in [17] is

opted for the WAMS. In this structure, as it is shown in Fig. 1, aWAMS is divided into multiple regional networks. The gathereddata by PMUs will be submitted through every regional com-munication network to the corresponded PDC. All the PDCs aswell as the control center are correlated [through the ring inter-face units (RIUs)] within a highly reliable ring structure, calledthe back-bone network. Hence, the reliability of the data trans-mission in the hierarchical structured WAMS is extremely de-pendent on the relative location of PMUs and PDCs in regionalnetworks.

1949-3053 © 2013 IEEE


2 IEEE TRANSACTIONS ON SMART GRID

Fig. 1. Hierarchical structure of a WAMS [17].

In a communication network, when a fiber optic link en-counters failure, a survival mechanism should be employedto recover the normal data transfer. The survival mechanismscan be divided into two different methods including staticpath protection, and dynamic path restoration. Of these twomechanisms, the static path protection is faster. Thus, in thispaper this mechanism is employed. In the static path protec-tion, a link-disjoint backup path is dedicated to every primarypath [18]. Hence, only two link-disjoint predetermined pathsare available between every PMU and the associated PDC.Considering this fact, a simple and straightforward method isproposed in [17] for evaluating the reliability of the regionalnetworks. This method is employed in this paper to reducethe computational burden instead of using the well-knowncut-set or tie-set methods [19] with considerable complexitiesand computational burdens. Formulation of the problems ofreliability evaluation and the path finding in regional commu-nication networks can be found in [17] and [18], respectively.In this paper, a new method is proposed for simultaneous op-

timal placement of PMUs and PDCs. Using this method, theoptimal placement will be performed in order to guarantee thepower system observability besides providing the highest reli-ability for the communication network. Thus, considering pre-vious published papers in the field of optimal PMU placementin power systems, the new contributions given in this paper canbe listed as follows:1) An organized method is developed for proper partitioningof the WAMS.

2) By incorporating the reliability factor with the observ-ability constraint, a new heuristic method is presented forsimultaneous optimal placement of PMUs and PDCs inthe hierarchical structured WAMS.

3) The proposed placement method, in terms of computa-tional burden, is adapted to real dimensional electric powernetworks.

Moreover, in this paper the power system observability is in-vestigated in condition as well as in the case of consid-ering the effect of a single line outage, in addition to the normaloperation of the power system.

Fig. 2. Single-line diagram of the nine-bus power system.

The rest of this paper is organized as follows. In Section II,an organized method is developed for the WAMS partitioning.The proposed method for simultaneous optimal placement ofPMUs and PDCs is presented in Section III. Simulation resultsare provided in Section IV to show the feasibility of the pro-posed methods.

II. PARTITIONING OF THE WAMS INTO REGIONAL NETWORKS

In [20] a sectionalizing method is presented which can beused in power system restoration after a complete blackout. Theprerequisite for employing the mentioned method is that the lo-cations of PMUs are given prior to power system sectionalizing.In other words, that method is applicable after PMU placement.In this paper, the mentioned method is modified so as to beadopted with the problem of WAMS partitioning prior to the si-multaneous placement of PMUs and PDCs. However, the orig-inal method can also be used for power system restoration afterthis placement. For more illustrations, the partitioning methodis described over the nine-bus power system depicted in Fig. 2.Consider the network connectivity matrix defined

as follows:

(1)

For sectionalizing the WAMS, first we should select thenumber of regional networks, . Moreover, a central nodewould be allocated to every regional network. With respect tothe central bus numbers, the initial or the first order regionalmatrix, , which is an binary matrix can be defined.Each row in is correlated with one regional network. Allthe entries in every row are set to 0, but the one correspondedto the central bus would be adjusted by 1. In this regard, byconsidering with buses 4 and 7 as the central nodes inthe nine-bus power system, is as follows:

(2)

Now, let as the th order regional network matrix whichis defined by (3),

(3)

where is after correction and . For higherorder regional matrices the correction, if needed, will be accom-plished in two steps explained in the following.


HAGHIGHATDAR FESHARAKI et al.: SIMULTANEOUS OPTIMAL DESIGN OF MEASUREMENT AND COMMUNICATION INFRASTRUCTURES 3

For more illustrations, consider the second order regional ma-trix, , which would be obtained by multiplying the initialregional matrix by the network connectivity matrix. The newnon-zero entries appeared on the th row of , compared with, indicate the connected buses directly to the th central node.

Thus, every regional network will be extended by grouping thedirectly connected nodes with the corresponded central node, atthe second step. For instance, is represented for the nine-buspower system as follows:

(4)

According to , the buses 1, 5, and 9 are added into theregional network 1 while the bus 6 as well as 8 are merged withthe regional network 2, at the second step.Continuing this procedure, more nodes will be incorporated

into every regional network. This process should be carried ontill the last ungrouped node would be merged with a specific re-gional network. At the resumption of this procedure the value ofsome entries in the higher order regional matrices might becomebigger than 1. These values should be converted into 1 (the firstcorrection step).Moreover, in some merging steps it is possible that by per-

forming the multiplication given in (3), one node be appearedin two or more regional networks (two or more rows of the ob-tained regional matrix). Thus, the regional matrix should be cor-rected. In the original method presented in [20] the correctionwould be done according to the system restoration consider-ations. However, here, based on the following two rules (thesecond correction step):1) If one node is appeared in two or more regional networks,that node should be incorporated into the regional networkthat has the highest number of connections to it.

2) If there were multiple regional networks with the equalhighest number of connections, the mentioned nodeshould be incorporated into the one which has the min-imum number of nodes up to this stage.

Using the first rule, it is tried to increase the nodal degreeas much as possible. This improves the chance of having twolink-disjoint paths for PMUs. However, the second rule impliesthe uniform expansion of the regional networks.For instance, the third order regional matrix before correc-

tion, , is as follows:

(5)

As it can be seen the buses 5, 6, 8, and 9 are situated in bothregional networks. According to the corresponded entries, thebuses 5 and 9 have two connections with the first regional net-work while have one connection with the second regional net-work. Hence, these buses should be merged with the regionalnetwork 1. However, the bus 6 as well as 8 should be incorpo-rated into the regional network 2.Moreover, as it wasmentionedbefore, non-zero entries should be converted into 1. Thus, thecorrected matrix is as shown in (6).

(6)

Obviously, the solution of the developed method is highlydependent on the selected central buses. Hence, the locations ofcentral buses should be optimized. By looking ahead, as it canbe understood form the simultaneous optimal placement methodproposed in Section III as follows:1) The dependency of the solution to the power system parti-tioning will be minimized if the number of boundary lines

between various regional networks is minimized.2) The reliability of the communication network will bemaxi-mized if the total number of radial nodes in variousregional networks is minimized.

3) The amount of computations will be minimized if thesystem buses are distributed equally between variousregional networks.

Hence, the goal function is selected as follows:

(7)

where is the number of system buses in the th regional net-work. Moreover, , , and are weighting factors.Here, since we deal with a non-linear and non-convex

problem, the evolutionary and intelligent optimization algo-rithms can be employed effectively to obtain the optimal solu-tion. Among the different intelligent algorithms, a well-knownand powerful one, called “real-coded genetic algorithm [21],”which can easily be coordinated with the problem, is opted. Inthis algorithm, the initial population contains random locationsselected for the central nodes. Then, by applying the geneticoperators, including: selection, mutation, and crossover, on thechromosomes, the optimal solution is searched by the popu-lation in sequential generations. In this algorithm the lengthof each chromosome is selected equal to . Every gene, asdiscussed above, contains the location of a central node.Some practical factors which can be considered in selecting

the number of partitions, , in real power systems are include:1) geographical and topological properties of the power system,2) the capabilities of data transmission system in terms of secu-rity, reliability, and so on, 3) the expansion purposes and powersystem planning.

III. PROPOSED METHOD FOR SIMULTANEOUS OPTIMALPLACEMENT OF PMUS AND PDCS

As it is discussed in [17], the reliability of the communica-tion network is a function of the relative location of installedPMUs and PDCs. Hence, the optimal location of PMUs andPDCs should be determined simultaneously. For this purpose, atthe following, first the optimal placement of PMUs only for pro-viding the power system observability will be reviewed briefly.Then, the proposed multi-step elimination method for simulta-neous optimal placement of PMUs and the PDCs will be de-scribed in details.

A. PMU Placement for Maintaining the System Observability

Here, placement of PMUs with the aim of power system ob-servability achievement will be addressed. By installing a PMUon a system bus, in addition to the voltage phasor of that bus,the current phasors of all its incident lines will be measured.Hence, the voltage phasors of all connected buses to that bus can



be calculated. Therefore, a system bus is observable if a PMUis installed on that bus or on one of its adjacent buses. More-over, if the injection to a bus is zero, a linear algebraic equationbased on the voltage phasor of this bus and its adjacent buseswill be obtained. This equation can be solved with at most oneunknown voltage phasor. Thus, among a set of connected busesincluding a zero-injection, one bus can be unobserved. There-fore, by knowing the zero-injection buses, for a given arrange-ment of PMUs, the system observability can be evaluated by astructural survey on the power network.To guarantee the system observability in condition,

the phasor voltage of every bus must be accessible at least intwo ways. In other words, every system bus must be observabletwice. In this situation, by malfunctioning of a PMU, the acces-sibility to some node voltages will be lost at most in one way.Hence, the power system will still be observable.In this paper, to evaluate the power system observability in

condition, the installed PMUs would be eliminated oneat a time, followed by the mentioned structural survey in a loop.The power system would be observable in condition, ifthe system observability were provided in all iterations of thisloop. A similar loop should be accomplished while the systemlines are eliminated one at a time, to evaluate the power systemobservability in the case of a single line outage.

B. Simultaneous Optimal Placement of PMUs and PDCs

In order to determine the optimal locations for installingPMUs as well as PDCs in a WAMS containing buses andregional networks, first it is supposed that PMUs are installedon all of the system buses. The power system is evidentlyobservable in this situation but regarding the presented de-scriptions in the previous subsection, some of these PMUs areredundant. Hence, the redundant PMUs are eliminated using amulti-step elimination algorithm such that besides maintainingthe power system observability, the maximum reliability wouldbe yielded for the communication network. For this purpose,the binary placement vector whose length is equal tois used. Indeed, there is a one by one correspondence betweenthe power system nodes and the entries of this vector. Eachof 1s in this vector indicates the installation of a PMU at thecorresponded bus. Therefore, at the beginning of the algorithm,as it is shown in (8), all the entries of are equal to 1.

(8)

Then, all the possible arrangements of PMUs are allocated,which will be obtained by eliminating one PMU from ,to new placement vectors as follows:

...

(9)

It should be noted that every PMU placement vector canbe decomposed into sub-vectors. Each sub-vector is cor-responded to one of the regional networks according to the

WAMS partitioning. The decomposition of the vectors in (9)can typically be represented as (10).

...

(10)

Now, let be the reliability of the th regional networkwhen a PDC is installed on the th bus of this network, for agiven PMU placement vector. As it is mentioned in Section I,this value can be calculated using the formulas presented in [17].It is reminded that is the number of system buses in the thregional network. Assuming as the maximum reliabilityobtained by replacing the PDC on all of the buses in this regionalnetwork, there will be

(11)

Thus, the objective function can be defined as (12).

(12)

In the following, the value of the objective function, whichwill be referred to as the fitness value, is represented by forthe th PMU placement vector. Now, among the PMU place-ment vectors given in (9), the one which leads to the max-imum fitness value as well as providing the system observabilitywould be assigned to . The corresponded PDC locationswould be saved into another vector, named .In order to eliminate the next redundant PMU, the above-

mentioned procedure should be applied on all of the arrange-ments obtained by eliminating one PMU from the new .This process would be continued till none of the derived ar-rangements can provide the power system observability. In thissituation, the last saved indicates the optimal locationsof PMUs while the last saved denotes the optimal loca-tions of PDCs.It is possible, but with a very low probability, to have more

than one PMU placement vector with the same or very closemaximum reliabilities in some of the above sequential elimina-tion loops. Hence, there will be a multiple . The above-mentioned procedure should be implemented on all the arrange-ments obtained by eliminating a single PMU from all vectors inthe multiple .Let be the number of arrangements obtained by eliminating

a single PMU from . Obviously, is not constant andchanges in accordance with the number of 1s (PMUs) in .Thus, the proposed simultaneous optimal placement of PMUsand PDCs can be represented by the flowchart shown in Fig. 3.In this flowchart the variable counter resets to zero at the begin-ning of every elimination loop. If the value of counter at the endof this loop is still equal to zero, it reveals that none of the PMUplacement vectors can provide the power system observability.Hence, the process will be terminated.



Fig. 3. Flowchart of simultaneous optimal placement of PMUs and PDCs.

C. Adapting the Proposed Method to Large Scale Systems

To reduce the amount of calculations in large scale powersystems, first, every regional network will be considered as aseparated electrical network. Then, the proposed algorithm inSection III-B will be applied to every network separately. Indoing so, a PMU placement vector will be divided into sev-eral smaller sub-vectors. Thus, the total number of arrange-ments which would be obtained by eliminating a single PMU

Fig. 4. Regions of the WAMS in IEEE 30-bus system.

in (9) will be decreased intensively. It is clear that in this con-dition, for every regional network the effect of PMUs installedin neighboring regions is not taken into account in terms of ob-servability. Hence, there will be some redundant PMUs in thesolution at the first step. Thus, at the second step, by applyingthe multi-step elimination algorithm to the obtained solution atthe first step, the redundant PMUs can be eliminated.It should be noted that in a power system with buses

and regional networks, by using the proposed method inSection III-B, at the first iteration, combinations, at thesecond iteration, combinations, and so on, are tobe evaluated. Hence, the number of combinations that must beevaluated is approximately equal to .However, when the number of boundary lines between

regions is low, the overlap between PMUs installed in variousregions and subsequently the number of redundant PMUs,which should be eliminated after combining the regions, isinsignificant. As a result, computations at the second step ofthe proposed method in Section III-C can be ignored againstthe computations at the first step. Thus, suppose that the systembuses are distributed equally in various regions, an approximatevalue for the number of required evaluations is then equal to

. Hence, in the IEEE118-bus power system with 7 regional networks, the approxi-mate number of evaluations, by using the method presented inSection III-B, is equal to 828 478 while it is reduced to 17 760by using the proposed method in Section III-C.It should be noted that the partitioning of the WMAS as well

as the measurement placement is an off-line design procedurewhich are to be done once prior to the implementation of theWAMS. However, it is still expected that the amount of com-putations in a very large scale power system becomes consider-ably high. Thus, the authors will try to improve their presentedmethod in the sense of computational burden in their futurework.

IV. SIMULATION RESULTS

To demonstrate the efficiency of the proposed method, it isapplied to the 30-, and 118-bus IEEE test systems. The regionalpartitioning is represented in Figs. 4 and 5, respectively.The failure rate and the repair time of per unit length for a

typical optic fiber link are given in [17]. Moreover, the length ofan optic fiber link can be approximated by the length of its par-allel transmission line. Hence, having the length of transmission



Fig. 5. Regions of the WAMS in IEEE 118-bus system.

TABLE IRELIABILITY OF REGIONAL NETWORKS AND OPTIMAL LOCATION OF PMUS AND PDCS IN THE BASE CASE

lines [22], the required parameters for evaluating the reliabilityof regional networks can be derived.In Table I, in addition to the optimal location of PMUs and

PDCs, the fitness values, reliabilities and the number of usedPMUs are represented for the base case. Table II shows the pri-mary and backup paths between every PMU and the associatedPDC in this case. As it can be seen in Table II, all the PMUs,except two of them in IEEE 118-bus system, have two link-dis-joint paths to the PDC. Looking closely at Fig. 5, the reasoncan be found. In both cases, a set of system buses are situatedon a radial configuration. In order to provide the system observ-ability, two PMUs are to be installed on two of the mentioned ra-dial nodes. Hence, the backup path could not be found for thosePMUs. The radial configuration in both cases is due to originalsystem topology. Hence, the lack of the backup path is not dueto the system partitioning.Moreover, by looking closely at Tables I and II, it can be seen

that the most important reason for reducing the reliability of thecommunication network is the installation of the PMUs on theradial nodes. In this case, because the secondary path cannot befound from the PMU to the corresponded PDC, the reliabilitywill be degraded. Another factor which degrades the reliabilityof the communication network is the existence of fiber opticlinks with low availability values. Hence, it seems that the reli-ability of the communication network, can be increased in twoways: 1) new optic fiber links can be constructed from the radialnodes equipped with PMUs to the corresponded PDC and 2) the

critical optic fiber links can possibly be substituted by more re-liable links.In addition, as it can be seen in Figs. 4 and 5, the average

number of system buses in the IEEE 30-bus power system(which is equal to 10) is lower than the average number ofsystem buses in the IEEE 118-bus power system (which isequal to 17). Hence, as it is expected based on the approximateformula presented in Section III-C, the computation time in theIEEE-118 bus power system grows intensively.In Table III the optimal location of PMUs and PDCs together

with the fitness values and reliabilities in conditionare presented. The same specifications are given in Table IV,when the effect of the line outage is considered in under studyproblem. Because of the space limitation, the citation of paths isignored in these two cases. However, in these cases, unlike thebasic case, PMUs are to be installed on radial buses because,by the outage of the PMU installed on the adjacent bus or bythe outage of the connecting line, such nodes will absolutelybecome unobservable. Hence, it is expected that the reliabilityof the communication network be degraded intensively. How-ever, as it can be seen in Tables III and IV, the proper WAMSpartitioning prevents such degradation.In all of the above mentioned simulations, the effect of zero-

injections is considered in the power system observability as-sessment. Moreover, the computation time is provided in allof the cases at the last column of the corresponded table. Asit was expected, the computation time in the base case is higher



TABLE IIPRIMARY AND BACKUP PATHS IN VARIOUS REGIONS OF THE WAMS

TABLE IIIRELIABILITY OF REGIONAL NETWORKS AND OPTIMAL LOCATION OF PMUS AND PDCS IN CONDITION

TABLE IVRELIABILITY OF REGIONAL NETWORKS AND OPTIMAL LOCATION OF PMUS AND PDCS WITH CONSIDERING THE LINE OUTAGE

than the other two cases because, more PMUs should be elimi-nated by using the proposed multi-step optimization algorithm.In all of the above simulations the proposedmethod presented inSection III-C is employed. To investigate the efficiency of thismethod, the numerical simulations are also performed by usingthe method presented in Section III-B. It is found that there isno difference between the optimal solutions obtained by usingthe suggested method in Sections III-B and the one proposed inIII-C. Having no difference is due to the appropriate partitioningof theWAMS in which it is apt to minimize the overlap betweenregional networks as much as possible.Moreover, the simulation times are compared with each other

in Table V. As it can be seen in this table, the computation timefor large scale power systems might become unacceptably highby using the presented method in Section III-B. The computerused for simulation had an Intel Core 2 Duo CPUT9600 runningat 2.80 GHz with 4.0 GB of RAM.

TABLE VCOMPARING THE SIMULATION TIMES ASSOCIATED WITH PRESENTED METHODS

IN SECTIONS III-B AND III-C

Finally, the IEEE 300-bus power system [23] is sectional-ized into 20 regions using the presented method in Section II.The system observability is provided by 69 PMUs using the si-multaneous optimal placement method proposed in Section III.In doing so, the reliability of regions is obtained as: 0.8764,0.9998, 0.9903, 0.8908, 0.9904, 0.9777, 0.8956, 0.8868, 0.9929,0.9563, 0.7349, 0.8412, 0.9988, 0.9483, 0.9367, 0.8301, 0.9996,



0.7911, 0.9415, and 0.7444. Moreover, the execution time isabout 6621.0(s).

V. CONCLUSION

In this paper, a new method is developed for partitioning theWAMS with hierarchical structure. Moreover, a new methodfor simultaneous optimal placement of PMUs and PDCs isproposed. Using this method, along with providing the powersystem observability, the location of PMUs as well as PDCswhich leads to the highest reliability for the communicationnetwork will be obtained. In doing so, the WAMS would beoptimally designed in the view point of all three main compo-nents, i.e. PMUs, PDCs, and communication network. In powersystem observability achievement, various contingencies suchas the measurement loss as well as the line outage are also con-sidered. The simulation results show that however by using theproposed method the number of PMUs will insignificantly beincreased, but the reliability of the communication network willbe improved as much as possible. Moreover, these simulationsdemonstrate the feasibility and applicability of the proposedmethod in practical power systems.

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Fariborz Haghighatdar Fesharaki was born in Is-fahan, Iran, in 1981. He received the B.Sc. degree inelectrical engineering from Islamic Azad Universityof Najaf Abad, Iran, in 2005 and the M.Sc. (Honors)degree in electrical engineering from University ofIsfahan, Iran, in 2008, where he is pursuing the Ph.D.degree.His research interests include power system

quality assessment and computational methods inpower system monitoring and operation.

Rahmat-Allah Hooshmand (M’10) received theB.Sc. degree from University of Mashhad, Iran, in1989, the M.Sc. degree from University of Tehran,Iran, and Ph.D. degree from Tarbiat ModarresUniversity, Iran, in 1990 and 1995, respectively allin electrical engineering.He is currently Professor in Electrical Engineering

Department, University of Isfahan, Isfahan, Iran. Hismain area of research interests are modeling of powersystems and distribution networks.

AminKhodabakhshian (M’05) was born in Isfahan,Iran. He received the B.Sc. andM.Sc. degrees in elec-trical engineering from University of Tehran, Tehran,Iran in 1986 and 1988, respectively, and the Ph.D. de-gree in 1995 from University of Wollongong, Aus-tralia.He is currently Associate Professor in Electrical

Engineering Department, University of Isfahan, Is-fahan, Iran. His research interests are in the area ofpower system dynamic stability, control applicationsin power systems, and dispersed generations.

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