Optimal selection of distributed generating units and its ...

Ain Shams Engineering Journal (2015) xxx, xxx–xxx

Ain Shams University

Ain Shams Engineering Journal

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ELECTRICAL ENGINEERING

Optimal selection of distributed generating units

and its placement for voltage stability enhancement

and energy loss minimization

* Corresponding author. Tel.: +91 7567513461.

E-mail address: [email protected] (P. Bhatt).

Peer review under responsibility of Ain Shams University.

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http://dx.doi.org/10.1016/j.asej.2015.10.0092090-4479 � 2015 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article in press as: Mehta P et al., Optimal selection of distributed generating units and its placement for voltage stability enhancement and enminimization, Ain Shams Eng J (2015), http://dx.doi.org/10.1016/j.asej.2015.10.009

Pankita Mehtaa, Praghnesh Bhatt

a,*, Vivek Pandyab

aDepartment of Electrical Engineering, C.S. Patel Institute of Technology, CHARUSAT, Changa, Gujarat, IndiabDepartment of Electrical Engineering, School of Technology, PDPU, Gandhinagar, Gujarat, India

Received 31 July 2015; revised 24 October 2015; accepted 31 October 2015

KEYWORDS

Continuation power flow

(CPF);

Distributed generation (DG);

Eigenvalue;

Modal analysis;

Participation factor

Abstract The integration of distributed generation (DG) in distribution network may significantly

affect its performance. Transmission networks are no longer accountable solely for voltage security

issues in distribution networks with penetration of DGs. The reactive power support from the DG

sources greatly varies with the type of DG units and may potentially distress the larger portion of

the network from the voltage stability aspects. This paper presents the analysis for the selection of

the best type of DG unit among different categories and its optimal location that can enhance the

voltage stability of distribution network with simultaneous improvement in voltage profile. Voltage

sensitivity index and bus participation factors derived from continuation power flow and Modal

Analysis, respectively, are used together for voltage stability assessment and placement of DGs.

Changes in mode shapes and participation factors with the placement of DGs are comprehensively

analyzed for 33 and 136 nodes radial distribution network.� 2015 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an

open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

The integration of DG is expected to play an increasinglyimportant role in the electric power system infrastructure plan-ning and market operations. The integration of DG at the dis-

tribution network results in operating situations that do not

occur in a conventional system without generation directly

connected at the distribution level [1]. Attention must be paidto effectively eliminate the potentially adverse impacts thatDG penetration could impress on the electric delivery system.

Inappropriate DG placement and sizing may increase systemlosses and network capital and operating costs. Hence, system-atic studies and planning are required to locate and operate theDGs at the distribution level in order to improve voltage pro-

file, to reduce system losses, and to enhance the stability [1–3].Power systems are expected to become more heavily loaded

in the forthcoming years as the demand for electric power rises

sharply. The economic and environmental concerns limit theconstruction of new transmission and generation capacity.This may result in deficit of local reactive power support in

ergy loss

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2 P. Mehta et al.

heavily loaded system which in turn causes the progressivevoltage decline [4–6]. The decline in voltage level is one ofimportant factors which restrict the increase of load served

by distribution companies. Therefore, it is necessary to con-sider voltage stability constraints for planning and operationof distribution systems. The shortage of reactive power can

be compensated by an increased share of DGs in distributionsystems to improve voltage stability. These DG sources possessdifferent reactive power generation capability and their impact

on the voltage stability should be studied distinctly. However,these types of studies are least reported in the literature.

The reactive power support using capacitor is one of themethods to reduce the power losses [7]; it is also shown that

placement of many capacitors at the incorrect positions willfurther increase line losses. The minimization of losses doesnot give any assurance of the maximization of benefits unless

the problem is well formulated [7–9]. However, the activepower support from the capacitors cannot be possible whichhave significant impact on system performance. Like capacitors

placement, higher penetration of the DG at the suboptimallocation may increase losses in distribution lines. Hence, it issignificantly essential to decide the size, location and type of

DG unit to be placed. Authors in [10,11] revealed that subopti-mal location for DG placement and improper sizing, wouldlead to higher losses as compared to the system without DG.

The issue of loss minimization in the distribution network is

reported in [12] where an analytical expression and the method-ology based on the exact loss formula are being used for theestimation of the optimal size and location of DG for reducing

the total power losses in primary distribution systems. How-ever, the proposed methodology is limited to DG type whichis capable of delivering real power only. Multiple DG units

placement using an improved analytical (IA) method to iden-tify the best location for DG for high loss reduction in large-scale primary distribution network is given in [13]. The tradi-

tional problem of minimizing losses in distribution networkshas been investigated using a single, deterministic demand levelwith the help of OPF in [14]. A new long term scheduling foroptimal allocation and sizing of different types of DG units

in the distribution networks in order to minimize power lossesare presented in [15]. In [16], author discussed the iterativesearch method for optimal sizing and siting of single DG for

minimization of cost and loss. The issue of voltage stability indistribution networks and the impact of DG units on it drawattention in recent period. A meta-heuristic technique based

on backtracking search optimization algorithm (BSOA) is pre-sented in [17] with objectives to reduce power loss and improvevoltage profile in RDN considering the DG type which caninject active and reactive power both. In [18], BSOA and set

of fuzzy expert roles using loss sensitivities factors and bus volt-ages are used to identify the DG locations. The Optimal sizeand location of multiple DGs are determined with particle

swarm optimization using constriction factor approach in [19]considering predetermines annual load growth with voltageregulation as constraint. Simultaneous placement of DG and

fixed capacitor in radial distribution network with time varyingload in order to decrease reactive power loss, energy and powerloss reduction, improvement of voltage profile and voltage sta-

bility has been discussed in [20].A new voltage stability index is introduced in [21] by

simplified load flow equations to seek the most sensitive buses

Please cite this article in press as: Mehta P et al., Optimal selection of distributed genminimization, Ain Shams Eng J (2015), http://dx.doi.org/10.1016/j.asej.2015.10.009

to voltage collapse in radial networks. A method for DGplacement in radial distribution network based on Voltagesecurity margin (VSM) enhancement and loss reduction is

presented in [22], which use CPF to identify the most sensitivebus to voltage collapse. The work in [23] is suggested thatvoltage magnitude is not a suitable indicator for the proximity

to voltage collapse. Author [24] has described a technique forselection of buses in a subtransmission system for location ofDG and determination of their optimum capacities by

minimizing transmission losses and improvement in voltageprofile.

A method is presented for locating and sizing of DGs toenhance voltage stability and to reduce network losses simulta-

neously in [25], where Modal analysis and continuous powerflow are used for DG placement in the event of reactive powerdeficit. The enhancement of voltage profile, loadability with

simultaneous reduction distribution losses considering voltagerelated constraint is discussed in [26].

Based on the literature review discussed above, it has been

observed that the different issues in the field of distributed gen-eration are covered which are based on optimal location andsizing of DG, loss minimization, voltage stability enhancement

and reconfiguration of distribution network after the integra-tion of DG resources. This paper is mainly focused on voltagestability analysis with different types of distributed generatingunits which were not addressed earlier in the literature. The

impact of DG operating in a voltage regulation mode withvarying reactive power support has been analyzed for the volt-age stability enhancement. Further, the optimal location of

DG is ascertained at the weakest bus which is determined byCPF and modal analysis. The variation in mode shapes withthe variation in DG types and its locations have been compre-

hensively studied for the analysis of voltage stability. Themode shapes and participation factors are used to identifythe weakest region where placement of DG may have the ben-

eficiary effect to enhance the voltage stability. The objectivesof this paper are as follows:

(1) To perform power flow analysis on a Test systems (33-

nodes radial distribution network [18] and 136-nodesradial distribution [35]) without considering any DGunits. These systems are considered as base case test

system.(2) To identify the weakest bus for the base case test systems

by performing continuation power flow and Modal

analysis.(3) To determine and rank the buses which are more prone

to voltage instability based on the mode shapes partici-pation factors obtained through the Modal analysis.

(4) To ascertain the type of DG units and its placementmethodology in a system to enhance voltage stabilitymargin.

(5) To compare the impact of different types of DG units toimprove the performance of distribution system.

2. DG technologies and their impact on voltage stability

DG technologies are classified based on their capability ofinjecting real and/or reactive power in the system. Accord-ingly, DG technologies are grouped in the following manner.

erating units and its placement for voltage stability enhancement and energy loss


Optimal selection of generating units and its placement 3

2.1. Type 1: DG capable of injecting both active power (P) andreactive power (Q)

DG units that are based on synchronous machine for smallhydro, geothermal, and combined cycles fall in Type 1 cate-

gory. The DG with the synchronous generators may be mod-eled either with constant terminal voltage control (voltagecontrol mode) or with constant power factor control (powerfactor control). The DGs with the voltage control mode are

considered as PV nodes and DGs with the power factor con-trol mode are considered as PQ nodes [27]. In this work, theDG with synchronous generator of Type 1 category is modeled

as PV nodes.

2.2. Type 2: DG capable of injecting active power (P) only

Photovoltaic (PV), micro turbines, fuel cells, which are inte-grated to the main grid with the help of converters/inverters[28,29] are the examples of Type 2 category. In this work, it

is assumed that DG units in this category neither absorb nordeliver reactive power to system and operate with unity powerfactor only.

2.3. Type 3: DG capable of injecting reactive power (Q) only

The DG units equipped with synchronous compensator areconsidered as Type 3 category.

2.4. Type 4: DG capable of injecting active power (P), but

consuming reactive power (Q)

Fixed speed squirrel cage induction generator (SQIG) used forwind turbine generating (WTG) system falls under this cate-gory. SQIG in super-synchronous mode is capable of injecting

real power in the system whereas it demands reactive powerfrom the system.

Thus, it is worthwhile to note that the type of DG technol-ogy adopted will have a significant bearing on the performance

of distribution network. The installation of synchronousmachine-based DG units that are close to the loads can leadto beneficial impact on system voltage stability margin; on

another end, the case with an induction generator may havedetrimental impact on the system stability margin. Therefore,it is an utmost requirement to analyse the effect of different

types of DG technologies on the voltage stability to enjoythe system wide benefits.

3. Modal analysis and continuation power flow for voltage

stability analysis

The penetration of different types of DGs at the distribution

network greatly affects the voltage profile and voltage stabilitylimits due to their different reactive power generation capabil-ity. While integrating DGs in the system, it is not only impor-tant to maintain acceptable voltage magnitudes, but it is also

crucial to ensure that the steady-state loading should not reachthe critical state at which voltage collapse may occur.

Modal analysis is a static approach that captures the snap-

shots of the system conditions at various time frames along thetime domain trajectories. It gives the voltage stability related

Please cite this article in press as: Mehta P et al., Optimal selection of distributed geneminimization, Ain Shams Eng J (2015), http://dx.doi.org/10.1016/j.asej.2015.10.009

information from a system wide perspective and clearly identi-fies the areas that are prone to voltage instability. In addition,it gives the information about the voltage instability character-

istic, what are the key factors influencing the voltage instabilityand which measures are the most effective to enhance the volt-age stability [30–32].

Continuation power flow (CPF) is a tool for steady statevoltage stability analysis which reformulates the conventionalpower flow equations so that they remain well-conditioned at

all possible loading conditions. The CPF can successfullydetermine a distance from an operating point to a voltage col-lapse which may be measured in terms of physical quantitiessuch as load level, active power flow and reactive power gener-

ation/absorption capability of network [33].

3.1. Modal analysis

Incremental voltage of the buses from voltage stability view

point is of great importance, and also useful to identify thebuses for addition of DG. The incremental power flow equa-tions are used for obtaining incremental voltage sensitivities

[30,34] as given in (1) where elements of Jacobian matrix givesthe sensitivity between power flow bus voltage changes.

DP

DQ

� �¼ JPh JPV

JQh JQV

� �Dh

DV

� �ð1Þ

where DP = incremental change in bus real power;DQ = incremental change in bus reactive power injection;Dh = incremental change in bus voltage angle; DV= incre-

mental change in bus voltage magnitude. JPh ¼ @P@h, JPV ¼ @P

@V,

JQh ¼ @Q@h and JQV ¼ @Q

@Vare the elements of Jacobian. Voltage

stability of system is affected by both active and reactive

power. However at each operating point active power P is keptconstant and voltage stability is evaluated by considering theincremental relationship between reactive power Q and busvoltage magnitude V.

Considering, DP ¼ 0; the incremental relationship betweenreactive power Q and bus voltage magnitude V is given as (2):

DV ¼ J�1R DQ ð2Þ

where the reduced Jacobian Matrix ðJRÞ is given by (3):

JR ¼ ½JQV � JQhJ�1PhJPV� ð3Þ

Let,

JR ¼ nKg ð4Þwhere n and g are right and left eigenvector matrices of JR,respectively. K is diagonal eigenvalue matrix of JR; Inverting(4) yields

J�1R ¼ nK�1g ð5Þ

and substituting (5) in (2) results in

DV ¼ nK�1gDQ ð6Þ

DV ¼Xi

nigiki

DQ ð7Þ

where gi is the ith row of the left eigenvector of JR, and ni isthe ith column of the right eigenvector. The ith mode of theQ–V response is defined by the ith eigenvalue ki and the corre-sponding left and right eigenvectors gi&ni.

rating units and its placement for voltage stability enhancement and energy loss


4 P. Mehta et al.

Since, n�1 ¼ g, equation (6) may be written as follows:

gDV ¼ K�1gDQ ð8ÞDefine v ¼ gDV as the vector of modal voltage variations

and q ¼ gDQ as the vector of modal reactive power variations,

so (8) can be written as follows:

v ¼ K�1q ð9Þ

Thus for the ith mode, the vector for the modal voltagevariations can be written as

vi ¼ 1

kiqi ð10Þ

The magnitude of ki determines the degree of stability of

the ith modal voltage. The smaller the magnitude of positiveki, ith modal voltage is much closer to be unstable. The relativecontribution of the power at bus k in mode i is given by the bus

participation factor:

Pki ¼ nkigki ð11ÞPki indicates the contribution of the ith eigenvalue to the V-Qsensitivity at bus k. The participation factors determine the

most critical areas which lead the system to instability.

3.2. Continuation power flow

The continuation power flow is an iterative process that

employs a predictor–corrector scheme as shown in Fig. 1a tofind a solution path of a set of power flow equations that havebeen reformulated to include a load parameter [33,34]. The

process starts from a known solution (i.e. from Point A corre-sponding to base case loading kk) and uses a tangent predictorto estimate a subsequent solution corresponding to a different

value of the load parameter (i.e. point B). This estimate is thencorrected using a conventional power flow method with a sys-tem load assumed to be fixed (i.e. Point C). The CPF method

stresses the system up to kcriticalk which corresponds to critical

loading in the system where the voltage instability occurs. In

this paper, the increase in active and reactive load takes theform as given in (12) and (13):

Predictor

Corrector

Critical Point

Exact Solution

Bus

Vol

tage

Loading, λ

A

EDC

B

FG

Figure 1a Sequence of calculations in CPF [5].


PL ¼ kPL0 ð12Þ

QL ¼ kQL0 ð13Þwhere k is the loading parameter which ranges from

0 6 k 6 kcriticalk . PL0 and QL0 are active and reactive loads,

respectively, in the base case. The generated active power

(PG) by the generators is also increased simultaneously withthe same scaling factor to cater the increased load demandand it is given by (14):

PG ¼ kPG0 ð14Þ

4. Optimal placement of DG units based on voltage stability

enhancement

The 33- and 136-node radial distribution systems given in[18,35], respectively, are used for the power flow analysis andto propose a methodology for placement of the different typesof DG units with the objectives to reduce power losses,

improve voltage profile and enhance the voltage stability mar-gin of the system. The total active and reactive loads for 33-node RDN are 3715 kW and 2300 kvar, respectively. For

136-node RDN, the active and reactive loads are 18214 kWand 7933 kvar, respectively.

4.1. Steps for DG placement

The placement of different types of DG in distribution net-work greatly affects the voltage profile at the different busesand power flow in feeders, thus alters the active and reactive

power losses in a system. The variation in voltage profile andlosses in a system also varies with the different types of DGtechnologies discussed in Section 2. Hence, the attention must

be paid not only to decide the location for DG placement butthe types of DG technologies need to be considered. In thiswork, voltage stability enhancement is considered to be the

major criteria for the DG placement to ensure the stable oper-ation of the system with acceptable voltage levels at the con-sumer nodes. The procedure adopted to find out the optimal

locations for DG placement along with selection of different

Critical PointBus

Vol

tage

Loading, λ

A

C

B

Base Case Loading

Stressed Loading

Figure 1b Typical PV curve.



Table 1 Indices for the performance measurement of test

system.

Penetration level of DG % Penetration Level ¼ PDG

PLoad� 100%

Voltage sensitivity index VSI for bus k ¼ Vbase casek �Vcritical

kPn

i¼1Vbase casei �Vcritical

ið ÞActive power loss indices APLI ¼ PLoss�PDG

Loss

PLoss� 100%

Reactive power loss indices QPLI ¼ QLoss�QDGLoss

QLoss� 100%

Aggregate voltage deviation

indexAVDI ¼ Pn

i¼1jVDGi � 1j

Voltage stability margin VSM ¼ kmaxj � kk

Active power transfer

capabilityAPTC ¼ PBase�PDGþPL�PDGL

PBase� 100

Reactive power transfer

capabilityRPTC ¼ QBase�QDGþQL�QDGL

QBase� 100


types of DG technologies in a given test system is shown inFig. 2.

5. Definition of indices for performance assessment of test

systems

To investigate the impact of placement of different types of

DG units on the power losses, voltage profile and voltage sta-bility, different performance indices have been defined and aresummarized in Table 1 as follows.

5.1. Penetration level of DG

In a radial distribution system, the load demand is supplied

only by the source at one end (i.e. Sub-station). With the inte-gration of DG at any node in a distribution network, the netdemand from the source is reduced and it affects the perfor-

mance of distribution network. Authors in [16] discussed theeffect of penetration level of DG on the voltage profile ofthe buses whereas authors in [12] addressed the issue of sizeselection of DG and its placement on the basis of loss

Is this a last candidate bus?

Run PF, CPF and Modal Analysis without DG

Start

Ranking of weakest buses based on CPF and Modal

Analysis

Place either Type1 or Type 2 or Type 3 DG on Candidate Bus

Run PF, CPF and Modal Analysis with DG

Are all DG Type Considered?

Calculate All Indices and Stop

Next candidate bus

ReplaceDG Type

Yes

No

Yes

No

Suggest location and type of DG with highest VSM for voltage

stability enhancement

Figure 2 Flowchart for selection of DG type and location for

voltage stability enhancement.


minimization. The ratio of active power generated by DGðPDGÞ to total active power demand ðPLoadÞ is defined as pene-

tration level of DG in a distribution network and it is given by(15):

% Penetration Level ¼ PDG

PLoad

� 100% ð15Þ

5.2. Active and reactive power loss indices

The impact of DG placement on active power loss indexðAPLIÞ and reactive power loss index ðQPLIÞ can be assessedwith the use of (16) and (17), respectively [22]. Optimal DGplacement should result in higher loss indices.

Active power loss reduction;APLI

¼ PLoss � PDGLoss

PLoss

� 100% ð16Þ

Reactive power loss reduction; QPLI

¼ QLoss �QDGLoss

QLoss

� 100% ð17Þ

5.3. Voltage sensitivity index (VSI)

VSI gives the direct indication of maximum bus voltage devi-ation at the point of voltage collapse. The bus with highestVSI could be identified as the ‘‘weakest bus” in a system.

VSI for bus k ¼ Vbase casek � Vcritical

kPni¼1ðVbase case

i � Vcriticali Þ ð18Þ

5.4. Voltage stability margin (VSM)

The VSM gives the relative distance from the current operatingpoint to the point of voltage collapse. Higher values of VSMensure that the system is capable of carrying more loading

without losing its stability. The VSM can be represented by(19) as follows:

VSM ¼ kcritical � kk ð19Þ



6 P. Mehta et al.

Here, kk is the reference loading, which is assumed to bezero. kcritical is the loading at the point of voltage instability.

5.5. Aggregate voltage deviation index (AVDI)

AVDI gives the aggregate bus voltage deviation after the opti-mal DG placement in test system. The lowest value of AVDI

indicates more improvement in bus voltage profile at all thebuses after the placement of DG as compared to base case.AVDI is given by (20):

AVDI ¼Xn

i¼1

jVDGi � 1j ð20Þ

5.6. Power transfer capacity (PTC) of distribution network

The increase in electric demand requires to enhance the powertransfer capability of the existing distribution network tomaintain reliability and continuity of supply. Otherwise the

new construction of distribution lines is required, which isnot a practical solution always. Distributed generation canonly provide the alternatives to strengthen the existing distri-

bution network without addition of new lines. The powertransfer capacity of distribution network with the placementof DG units can be assessed as follows [22]. The active andreactive power transfer capacities are given by (21) and (22),

respectively:

APTC ¼ PBase � PDG þ PLoss � PDG;Loss

PBase

� 100 ð21Þ

RPTC ¼ QBase �QDG þQLoss �QDG;Loss

QBase

� 100 ð22Þ

where PBase, QBase are active and reactive power of the slack busin base case, respectively; PDG, QDG are active and reactivepower of the slack bus with DG unit, respectively; PLoss,

QLoss are active and reactive power losses in the distributionlines in base case, respectively; PDG;Loss, QDG;Loss are active

and reactive power losses in distribution lines with DG units,respectively.

6. Results and discussions

In this work, placements of different types of DG discussed inSection 2 are considered for the analysis. Power flow, continu-

ation power flow and Modal analysis are performed to selectthe best type among different DG units and to ensure itsoptimal location that can enhance the voltage stability. The

penetration level of 26% is considered for both test systems.i.e. 33-nodes and 136-nodes RDNs.

6.1. Determination of optimal location for DG placement

The CPF is carried out by assuming base case loading equal tozero. The active and reactive power loads are increased withconstant power factor until the voltage collapse. Fig. 3 shows

the bus voltage profile of the 33- and 136-node RDN obtainedwith CPF, where all bus voltages correspond to voltagecollapse point. Bus 18 is found to be the most critical bus in

33-nodes RDN with a voltage of 0.35954 pu corresponding


to critical loading of kcritical ¼ 3:40045. For 136-nodes RDN,Bus 118 is found to be the most critical bus with a voltageof 0.5171 pu corresponding to critical loading of

kcritical ¼ 3:68643.The results of the Modal analysis in the base case for both

test systems are given in Table 2 along with the eigenvalues for

the most associated buses corresponding to three operatingpoints A, B and C as shown in Fig. 1b. It is observed that withthe increment in loading, the eigenvalues start reducing and the

least eigenvalues are obtained for most stressed condition atpoint C. The buses with minimum eigenvalue are ranked forboth RDNs and they are determined as the most critical busesfrom voltage stability point of view. The top ten bus participa-

tion factors contributed in these most critical modes in basecase for both systems corresponding to point C are listed inTables 3 and 4. The bus participation factors present their per-

centage contribution to the respective modes; thus, they clearlyreveal the order of buses which need more attention for voltagestability enhancement.

It can be observed that some of the buses repeatedly con-tribute to critical modes which represent the non-localizedbehavior of the modes and determine the weak region in the

system. The existence of such a weak region clearly indicatesthat the reactive power support to this region is exhaustedand attention must be given to ensure availability of reactivepower for maintaining voltage stable operation of the system.

The comparison between Voltage Sensitive Index (VSI)obtained with CPF and the bus participation factors corre-sponding to the least stable modes (i.e. Point C) is represented

in Table 5 for the base case test system. The results of CPF andModal analysis follow the same order of the voltage sensitivity;thus, the ranking of the buses suggested by both analyses

together can be confirmed to identify the buses which are mostprone to voltage instability. Hence, Bus 18 and Bus 118 areidentified as the best choice for DG unit placement to enhance

the voltage stability for 33- and 136-node RDN, respectively.Further, the aim of this paper is to determine the optimal loca-tion of DG units that can improve the overall performance ofthe system in terms of indices given in Table 1. Hence, place-

ment of DG units is also analysed for the subsequent busesin the ranking with comparative lower voltage sensitivity inorder to evaluate overall system performance.

6.2. Determination of type of DG units

The characteristic of three types of DG units for reactive

power compensation in order to enhance the voltage stabilityhas been discussed in Section 2. Type 1 and Type 3 DG unitscomprised of synchronous generators and synchronous com-pensators, respectively, are modeled to deliver reactive power

in normal and emergency condition. They will operate in volt-age regulation mode and maintain their voltage to nominalvalue. Type 2 DG units comprise of PV cell which will neither

supply nor absorb any reactive power.Any one type of DG unit is placed at the candidate buses

determined by CPF and Modal analysis at a time and its influ-

ence on the variation of critical modes have been analysed.Figs. 4 and 5 show the comparison between eigenvalueobtained for both the systems without and with the placement

of different types of DG units on the candidate buses. Theresults clearly show that the placement of any type of DG unit



(a ) 33-Nodes RDN (b) 136-Nodes RDN

0 5 10 15 20 25 30 35

0.4

0.5

0.6

0.7

0.8

0.9

1

Bus Numbers

Bus

Vol

tage

s (p

u)at

Crit

ical

Loa

ding

0 20 40 60 80 100 120 1400.5

0.6

0.7

0.8

0.9

1

Bus Numbers

Bus

Vol

tage

s (p

u)at

Crit

ical

Loa

ding

33-Nodes RDN

136-Nodes RDN

Figure 3 Bus voltages profile of test systems corresponding to critical loading without placement of DG.

Table 2 Eigenvalues for most critical buses at different operating points.

33 node RDN 136 node RDN

Bus no. Eigenvalues at different operating points Bus no. Eigenvalues at different operating points

Point A Point B Point C Point A Point B Point C

Bus 18 0.21498 0.1807 0.08446 Bus 118 0.02264 0.01904 0.00753

Bus 33 0.69787 0.645 0.4572 Bus 38 0.04461 0.04255 0.03896

Bus 18 2.25493 2.06237 1.53569 Bus 62 0.04546 0.04364 0.04050

Bus 22 2.74458 2.71166 2.65266 Bus 97 0.05750 0.05517 0.05124

Bus 25 4.17262 3.95781 3.38813 Bus 15 0.06110 0.05809 0.05265

Table 3 Bus participation factors for most critical buses obtained with modal analysis for 33-nodes RDN.

Bus participation factors for most critical buses obtained with modal analysis

k1 ¼ 0:08446 k2 ¼ 0:4572 k3 ¼ 1:53569 k4 ¼ 2:65266 k5 ¼ 3:38813

Bus 18 Bus 33 Bus 18 Bus 22 Bus 25

Bus 18 0.1279 Bus 33 0.1824 Bus 18 0.1954 Bus 22 0.4504 Bus 25 0.1668











on any of the candidate buses significantly increases themagnitude of the critical modes in positive direction which

helps the system to keep away from the voltage instability.The ranking for the most associated buses in critical modesin Figs. 4 and 5 with the placement of different DGs can be

identified as given in Table 6.To determine the best types of DG for voltage stability

enhancement, different types of DGs are placed at the critical

buses and the improvement in VSM has been observed. Thecomparison between VSM values after the placement of


different DGs at the selected candidate buses is shown inFig. 6. It is noticed that the placement of any type of DG at

any of the candidate bus can successfully improve the VSM.But improvements in VSM are quite noticeable only whenDGs are placed at first two candidate buses as determined

by CPF and Modal analysis. On another end, the improve-ments in VSM are marginal when DGs are placed at lowerranked buses. Hence, it is proposed to place the DGs unit at

the bus with the least mode shape in the base case to gainthe maximum benefit of the voltage stability enhancement.



Table 4 Bus participation factors for most critical buses obtained with modal analysis for 136-nodes RDN.

Bus participation factors for most critical buses obtained with modal analysis

k1 ¼ 0:00753 k2 ¼ 0:04050 k3 ¼ 0:03896 k4 ¼ 0:05124 k5 ¼ 0:05265

Bus 118 Bus 38 Bus 62 Bus 97 Bus 15











Table 5 Comparison of results obtained with CPF and modal analysis for base case system.

33-nodes RDN 136-nodes RDN

CPF analysis Modal analysis CPF analysis Modal analysis

Bus no. VSI Bus no. BPF Bus no. VSI Bus no. BPF

Bus 18 0.05920 Bus 18 0.12793 Bus 118 0.0301 Bus 118 0.0725

Bus 17 0.05870 Bus 17 0.12458 Bus 117 0.0301 Bus 117 0.0722

Bus 16 0.05701 Bus 16 0.11002 Bus 116 0.0293 Bus 116 0.0691

Bus 15 0.05589 Bus 15 0.10268 Bus 110 0.0293 Bus 110 0.0688

Bus 14 0.05475 Bus 14 0.09461 Bus 115 0.0293 Bus 115 0.0686

Bus 13 0.05296 Bus 13 0.08266 Bus 109 0.0289 Bus 109 0.0670

Bus 12 0.04823 Bus 12 0.06029 Bus 114 0.0285 Bus 114 0.0661

Bus 11 0.04712 Bus 11 0.05694 Bus 113 0.0285 Bus 113 0.0658

Bus 10 0.04650 Bus 10 0.05511 Bus 112 0.0284 Bus 112 0.0648

Bus 33 0.04432 Bus 09 0.04036 Bus 111 0.0283 Bus 111 0.0638

8 P. Mehta et al.

Also, Fig. 6 shows that VSM has been enhanced greatlywith the placement of synchronous generator on the most volt-

age sensitive buses. This indicates that the selection of syn-chronous generator as DG units on most voltage sensitivebuses can carry more load before becoming voltage unstable.

The capability of synchronous generator of delivering bothactive and reactive power makes it more promising for enhanc-ing the voltage stability margin. On the other end, the VSM

with synchronous compensator is less due to its inability tosupply active power. The load relies only on the source gener-ation (i.e. sub-station); hence, larger value of the current fedright from the source has been responsible for greater real

and reactive power losses in the distribution feeders. Thus,the system becomes voltage unstable earlier as compared tothat of synchronous generator.

Figs. 7a and 7b and Figs. 8a and 8b show the comparativebus voltage profile with the placement of all types of DGs oneach candidate bus for the normal as well as stressed loading

condition, respectively. For the stressed loading condition inFigs. 8a and 8b, the bus voltage profile are plotted nearer tokcritical ¼ 3:4005 and kcritical ¼ 3:6863, respectively, for 33-nodes and 136-nodes RDNs. These given values of k corre-

spond to kcritical for the base case test systems without anyDGs. For 33-nodes RDN, the placement of DGs on the firsttwo candidate buses can significantly improve the bus voltages

profile in comparison with base case which can be seen inFig. 7a whereas improvement is not much noticeable with


placement of DGs at buses with lower ranking of voltage sen-sitivity. The placement of synchronous generator depicts the

best performance for improvement in voltage profile amongall DG types.

For 136-nodes RDN, the improvement in bus voltage pro-

file almost equally affected for the nodes in lateral feeder whereDG has been placed. For the main and other lateral feeders,the placement of DGs cannot alter the voltage profile much.

It is observed from Fig. 7b that the type of DG units bringsdifferent variations in bus voltage profile. The placements ofDGs at location other than Bus 118 are not capable to preventthe drastic voltage drop in valley near buses 100–120. The per-

formances of fuel cell and synchronous compensators havecaused more variations in bus voltages as compared to syn-chronous generator. The DGs with reactive power generation

capability are modeled in voltage regulation mode; hence, theytry to maintain nominal voltage of 1.0 pu at its node by sup-plying/absorbing reactive power. Therefore, the reactive power

generation by DG units which affect the performance of sys-tem is noted in Table 7. For 136-nodes RDN, the synchronousgenerator at Bus 118 absorbs (�1348) kvar to maintain its ter-minal voltage to nominal value of 1.0 pu; hence, its result is

inferior as compared to synchronous compensator and fuelcell. The synchronous compensator provides reactive powersupport of 2059 kvar to maintain the terminal voltage of 1.0

pu. Even if the fuel cell neither generates nor absorbs any reac-tive power, its placement raises the voltage up to 1.0478 which



1 2 3 4 50

1

2

3

4

5

Critical Modes with Placement of DGs at Bus 18

Eig

enva

lue

0 1 2 3 4 5 60

1

2

3

4

5


Eig

enva

lue

0 1 2 3 4 5 60

1

2

3

4

5


Eig

enva

lue

0 1 2 3 4 5 60

1

2

3

4

Critical Modes with Placement of DGs at Bus 25E

igen

valu

e

Without DGWith Syn GenWith Syn ComWith Fuel Cell

Figure 4 Eigenvalues obtained with the placement of different DG units at the candidate buses for 33-nodes RDN.

1 2 3 4 50

0.01

0.02

0.03

0.04

0.05

0.06


Eig

enva

lue

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

0.01

0.02

0.03

0.04

0.05

0.06


Eig

enva

lue

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

0.01

0.02

0.03

0.04

0.05

0.06


Eig

enva

lue

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

0.01

0.02

0.03

0.04

0.05

0.06


Eig

enva

lue

Without DGSyn GenSyn ComFuel Cell

Figure 5 Eigenvalues obtained with the placement of different DG units at the candidate buses for 136-nodes RDN.


is also not a desirable condition. This comprehensive analysissuggests that while selecting the DG units to achieve the par-ticular objectives, the constraints must be designed very care-

fully and more powerful solution techniques should beadopted. The size of the distribution network, number of lat-eral branches, loading on different nodes, load models and

active and reactive power generation capability of DG unitssignificantly affect the performance of the system. The benefi-cial impact of placement of DGs on Bus 18 and Bus 118,


respectively, for 33- and 136-nodes RDNs on voltage stabilityenhancement are clearly depicted in Figs. 8a and 8b where thereductions in bus voltages are limited even for the stressed

loading conditions.

6.3. Determination of multiple location and type of DG

The placement of first DG unit on the most voltage sensitivebus determined by CPF and Modal analysis results in greater



Table 6 Identification of critical modes for most associated buses with the placement of DG.

33 RDN 136 RDN 33 RDN 136 RDN 33 RDN 136 RDN 33 RDN 136 RDN 33 RDN 136 RDN

Without

DG

Without

DG

DG at Bus

18

DG at Bus

118

DG at Bus

33

DG at Bus

38

DG at Bus

22

DG at Bus

62

DG at Bus

25

DG at Bus

97

18 118 33 38 18 118 18 118 18 118

33 38 12 35 18 62 33 38 33 38

18 62 22 37 22 97 18 97 18 97

22 97 25 34 28 15 25 15 22 15

25 15 25 39 25 73 25 73 27 73

Bus 18 Bus 33 Bus 22 Bus 250

1

2

3

4

5

6

7

Vol

tage

Sta

bilit

y M

argi

n (V

SM

)

Bus 118 Bus 38 Bus 62 Bus 970

2

4

6

8

10

12

Vol

tage

Sta

bilit

y M

argi

n (V

SM

)

Without DG

With Syn GenWith Syn Com

With Fuel Cell


Figure 6 Comparative voltage stability margin (VSM) without and with DG units for 33- and 136-nodes RDNs.

0 5 10 15 20 25 30 350.9

0.92

0.94

0.96

0.98

1

Bus Numbers

Bus

Vol

tage

s (p

u)

DG Placed at 18

0 5 10 15 20 25 30 350.9

0.92

0.94

0.96

0.98

1

Bus Numbers

Bus

Vol

tage

s (p

u)

DG Placed at 33

0 5 10 15 20 25 30 350.9

0.92

0.94

0.96

0.98

1

Bus Numbers

Bus

Vol

tage

s (p

u)

DG Placed at 22

0 5 10 15 20 25 30 350.9

0.92

0.94

0.96

0.98

1

Bus Numbers

Bus

Vol

tage

s (p

u)

DG Placed at 25

Without DGSyn GenSyn ComFuel Cell

Figure 7a Comparative bus voltage profile of 33-nodes RDN without and with DGs for normal loading condition.

10 P. Mehta et al.

Please cite this article in press as: Mehta P et al., Optimal selection of distributed generating units and its placement for voltage stability enhancement and energy lossminimization, Ain Shams Eng J (2015), http://dx.doi.org/10.1016/j.asej.2015.10.009


0 20 40 60 80 100 120 140

0.92

0.94

0.96

0.98

1

1.02

1.04

Bus Numbers

Bus

Vol

tage

(pu)

DG Placed at Bus 118

0 20 40 60 80 100 120 1400.9

0.95

1

Bus Numbers

Bus

Vol

tage

(pu)

DG Placed at Bus 38

0 20 40 60 80 100 120 1400.9

0.95

1

Bus Numbers

Bus

Vol

tage

(pu)

DG Placed at Bus 62

0 20 40 60 80 100 120 140

0.92

0.94

0.96

0.98

1

1.02

Bus Numbers

Bus

Vol

tage

(pu)

DG Placed at Bus 97


Figure 7b Comparative bus voltage profile of 136-nodes RDN without and with DGs for normal loading condition.

0 5 10 15 20 25 30 350.2

0.4

0.6

0.8

1

Bus Numbers

Bus

Vol

tage

s w

ithS

tress

ed L

oadi

ng (p

u)

DG Placed at Bus 18

0 5 10 15 20 25 30 350.2

0.4

0.6

0.8

1

Bus Numbers

Bus

Vol

tage

s w

ithS

tress

ed L

oadi

ng (p

u)

DG Placed at Bus 33

0 5 10 15 20 25 30 350.2

0.4

0.6

0.8

1

Bus Numbers

Bus

Vol

tage

s w

ithS

tress

ed L

oadi

ng (p

u)

DG Placed at Bus 22

0 5 10 15 20 25 30 350.2

0.4

0.6

0.8

1

Bus Numbers

Bus

Vol

tage

s w

ithS

tress

ed L

oadi

ng (p

u)

DG Placed at Bus 25


Figure 8a Comparative bus voltage profile of 33-nodes RDN without and with DGs for stressed loading condition.




0 20 40 60 80 100 120 1400.4

0.6

0.8

1

Bus Numbers

Bus

Vol

tage

sw

ith S

tress

ed L

oadi

ng (p

u)

DG Placed at Bus 118

0 20 40 60 80 100 120 1400.4

0.6

0.8

1

Bus Numbers

Bus

Vol

tage

sw

ith S

tress

ed L

oadi

ng (p

u)

DG Placed at Bus 38

0 20 40 60 80 100 120 1400.4

0.6

0.8

1

Bus Numbers

Bus

Vol

tage

sw

ith S

tress

ed L

oadi

ng (p

u)

DG Placed at Bus 62

0 20 40 60 80 100 120 1400.4

0.6

0.8

1

Bus Numbers

Bus

Vol

tage

sw

ith S

tress

ed L

oadi

ng (p

u)

DG Placed at Bus 97


Figure 8b Comparative bus voltage profile of 136-nodes RDN without and with DGs for stressed loading condition.

Table 7 Active and reactive power generation without and with DGs for 33- and 136-nodes RDNs.

Synchronous generator Synchronous compensator Fuel cell

P (kW) Q (kvar) V (pu) P (kW) Q (kvar) V (pu) P (kW) Q (kvar) V (pu)

DG placed at Bus 18 (33-nodes RDN)

1115 139 1 0 1592 1 1115 0 0.99091

DG Placed at Bus 118 (136-nodes RDN)

4761 �1348 1 0 2059 1 4761 0 1.0478

Table 8 VSI with placement of different types of DG units on candidate buses for 33-nodes RDN.

VSI with DG placed at Bus 18 VSI with DG placed at Bus 33

Bus no. Syn gen Syn com Fuel cell Bus no. Syn gen Syn com Fuel cell

Bus 33 0.0841 0.0632 0.0639 Bus 18 0.0822 0.0663 0.0656

Bus 32 0.0837 0.063 0.0636 Bus 17 0.0813 0.0658 0.065

Bus 31 0.0823 0.0623 0.0627 Bus 16 0.0782 0.0641 0.0629

Bus 30 0.0762 0.0591 0.0584 Bus 15 0.0762 0.063 0.0616

Bus 29 0.0712 0.0563 0.055 Bus 14 0.0741 0.0619 0.0603



Bus 18 0.0585 0.0596 0.0592 Bus 18 0.062 0.0599 0.0591

Bus 17 0.0581 0.0591 0.0587 Bus 17 0.0615 0.0594 0.0586

Bus 16 0.0565 0.0574 0.0571 Bus 16 0.0596 0.0578 0.057

Bus 15 0.0554 0.0562 0.056 Bus 15 0.0584 0.0567 0.0559

Bus 14 0.0543 0.0551 0.0549 Bus 14 0.0572 0.0556 0.0548

12 P. Mehta et al.



Table 9 BPF with placement of different types of DGs for 33-nodes RDN.

BPF with DG placed at Bus 18 BPF with DG placed at Bus 33


Bus 33 0.1518 0.1606 0.148 Bus 18 0.1459 0.14311 0.1459

Bus 32 0.1459 0.1541 0.1424 Bus 17 0.1422 0.13938 0.1422

Bus 31 0.1372 0.1446 0.1339 Bus 16 0.1239 0.12205 0.1239

Bus 30 0.1048 0.1095 0.1025 Bus 15 0.1153 0.11363 0.1153

Bus 29 0.0933 0.0973 0.0913 Bus 14 0.1054 0.10416 0.1054

Bus 28 0.0641 0.0658 0.0629 Bus 13 0.0905 0.09 0.0905

BPF with DG placed at Bus 22 BPF with DG placed at Bus 25


Bus 18 0.1278 0.1279 0.1278 Bus 18 0.1283 0.12826 0.1283

Bus 17 0.1245 0.1246 0.1245 Bus 17 0.1251 0.12499 0.1251

Bus 16 0.11 0.11 0.11 Bus 16 0.1105 0.11039 0.1105

Bus 15 0.1027 0.1027 0.1027 Bus 15 0.1032 0.10311 0.1032

Bus 14 0.0946 0.0946 0.0946 Bus 14 0.0952 0.09503 0.0952

Bus 13 0.0827 0.0827 0.0827 Bus 13 0.0831 0.083 0.0831

Table 10 VSI with placement of different types of DG units on candidate buses for 136-nodes RDN.


Syn gen Syn com Fuel cell Bus no. Syn gen Syn com Fuel cell

0.01794 (106)# 0.01120 (15) 0.0222 (113) Bus 117 0.03186 0.03339 0.03190

0.01733 (107) 0.01104 (17) 0.0222 (114) Bus 118 0.03186 0.03339 0.03190

0.01669 (113) 0.01102 (13) 0.0221 (107) Bus 110 0.03104 0.03252 0.03108

0.01669 (114) 0.01097 (85) 0.0221 (112) Bus 115 0.03099 0.03247 0.03103

0.01654 (112) 0.01090 (16) 0.0221 (106) Bus 116 0.03099 0.03247 0.03103


Bus no. Syn gen syn com Fuel cell Bus no. Syn gen Syn com Fuel cell

Bus 117 0.03015 0.03279 0.03029 Bus 117 0.0334 0.0308 0.0338

Bus 118 0.03015 0.03279 0.03029 Bus 118 0.0334 0.0308 0.0338

Bus 110 0.02937 0.03195 0.02951 Bus 110 0.0325 0.0300 0.0330

Bus 115 0.02933 0.03189 0.02946 Bus 115 0.0325 0.0300 0.0329

Bus 116 0.02933 0.03189 0.02946 Bus 116 0.0325 0.0300 0.0329

# Numbers in bracket indicate bus number.

Table 11 Evaluation of indices for the performance measurement of 33-nodes RDN.

Indices kw losses kvar losses APLI RPLI AVDI VSI % APTC % RPTC VSM

Without DG 211 143 – – 1.80 9.19 – – 3.40

DG at Bus 18 Syn gen 140 101 33.59 29.53 0.88 5.77 1.92 1.74 4.70

Syn comp 286 220 �35.41 �53.67 1.01 2.22 �1.91 �2.99 3.57

Fuel cell 151 108 28.49 24.19 0.96 7.83 1.64 2.83 4.69

DG at Bus 33 Syn gen 92 72 39.11 33.23 0.95 6.55 3.15 2.99 4.67

Syn comp 262 209 �24.34 �46.29 1.06 3.50 �1.31 �2.46 3.74

Fuel cell 117 90 44.66 37.01 1.27 7.40 2.95 1.77 3.42

DG at Bus 22 Syn gen 230 165 �9.05 �15.24 1.77 8.43 �0.37 �0.95 3.42

Syn comp 212 145 �0.40 �1.14 1.78 9.12 �5.37 �5.86 3.40

Fuel cell 219 155 �3.95 �8.19 1.78 8.49 1.98 1.77 3.42

DG at Bus 25 Syn gen 170 121 19.39 15.24 1.59 8.85 1.15 0.97 3.58

Syn comp 255 182 �21.06 �26.99 1.63 8.12 0.74 �1.33 3.50

Fuel cell 180 126 14.68 11.98 1.65 8.21 0.90 0.703 3.56




Table 12 Evaluation of indices for the performance measurement of 136-nodes RDN.

Indices kw losses kvar losses APLI RPLI AVDI VSI % APTC % RPTC VSM

Without DG 320 703 3.408 0.030 3.686

DG at Bus 118 Syn gen 675 928 �1.11 �0.32 3.047 0.018 21.74 �20.83 8.170

Syn comp 364 705 �0.14 0.00 2.483 0.011 �0.47 23.81 4.230

Fuel cell 545 736 �0.70 �0.05 2.566 0.022 23.14 �0.88 4.548

DG at Bus 38 Syn gen 442 830 �0.38 �0.18 0.111 0.032 24.24 �16.80 3.687

Syn comp 328 702 �0.02 0.00 0.107 0.033 �0.08 21.44 3.686

Fuel cell 407 771 �0.27 �0.10 0.108 0.032 24.62 �1.59 3.687

DG at Bus 62 Syn gen 616 983 �0.92 �0.40 0.120 0.030 22.38 �31.35 3.688

Syn comp 334 706 �0.04 0.00 0.109 0.033 �0.14 17.05 3.686

Fuel cell 501 825 �0.56 �0.17 0.112 0.030 23.61 �2.84 3.688

DG at Bus 97 Syn gen 503 1000 �0.57 �0.42 0.114 0.033 23.59 �20.68 3.687

Syn comp 323 704 �0.01 0.00 0.113 0.031 �0.03 13.70 3.686

Fuel cell 460 917 �0.44 �0.31 0.114 0.034 24.05 �4.98 3.687

14 P. Mehta et al.

VSM for any type of DG unit which can be observed fromFig. 6 and Tables 11 and 12. The ranking of the weakest buses

suggested by VSI and BPF can provide better insight to deter-mine the next location of DG placement as well as its type. For33-nodes RDN, Bus 33 can be identified as the next candidate

bus for the placement of DG in order to enhance voltage sta-bility as indicated by Tables 8 and 9. For this system, the syn-chronous generators will provide the better results as it gives

highest VSI. The careful observation of VSI for 136-nodesgiven in Table 10 reveals the fact that the placements of differ-ent types of DG leave the system with different degrees of volt-age sensitivity. Hence, the problem of multiple DG placement

becomes much more complex in order to have system widebenefits.

The different performance indices given in Table 1 are eval-

uated and given in Tables 11 and 12 for 33-nodes and 136-nodes RDNs, respectively. The impacts of DG units placementat different candidate buses on real and reactive losses and

their indices, aggregate voltage deviation index, power transfercapabilities are calculated. It is observed that losses have beenreduced to greater extent with placement of synchronous gen-erator on Bus 33 as compared to Bus 18. But more emphasis

has been given to higher value of VSM and lower value ofAVDI while placing DGs. For 136-nodes RDN, placementof synchronous generator greatly increases the voltage stability

margin. But it has detrimental impact on active and reactivepower losses. Hence, weightage should be decided to strikethe balance between enhancement of VSM and minimization

of losses.

7. Conclusion

The paper has proposed a methodology to find the optimallocation and type of DG unit among different types whichcan enhance the voltage stability. The comprehensive analysis

with the use of CPF and Modal analysis are carried out onwell-known 33-nodes and 136-nodes radial distribution net-work for assessment of voltage stability characteristic withthe placement of different DG units. The ranking of the volt-

age sensitive buses are determined with extensive studies. Thechanges in mode shapes and bus participation factors afterthe placement of different types of DG units at different


locations have been presented. It is observed that the DG unitsoperating in voltage control mode and having reactive power

regulation capability effectively enhance the voltage stabilitymargin irrespective of the system size. The DG units with onlyactive power generation capability give better results as com-

pared to DG units with only reactive power generation capa-bility. The placement of any type of DG unit results involtage profile improvement as compared to the system with-

out DG in normal as well as stressed loading condition.

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[34] Milano F. Power system analysis toolbox (PSAT), Version 1.3.4,

User Manual; 2005, Available <http://www.power.uwaterloo.ca/

fmilano>.

[35] Mantovani JRS, Casari F, Romero RA. Reconfigurac�ao de

sistemas dedistribuic� ao radiais utilizando o criterio de queda de

tensao. SBA Controle Autom 2000;11(2):150–9.

Pankita Mehta completed her BE degree in

Electrical Engineering in 2003, from

Saurashtra University, Rajkot, India, and her

M.E. degree in Electrical Power System in

2006 from Sardar Patel University of Vallabh

Vidhyanagar, India. Currently she is working

as Assistant Professor in Charotar University

of Science and Technology and pursuing PhD.

Her main research interests include Electrical

machines and power system.

Dr. Praghnesh Bhatt did his PhD from S V

National Institute of Technology, Surat, India

in 2012. He is working as Professor in

Department of Electrical Engineering at C S

Patel Institute of Technology, Charusat,

India. His research areas of interests are

Power System Analysis, Power system

Dynamics and Stability, Grid integration of

wind power generation, Power System Pro-

tection and Distributed Generation.

Dr. Vivek J. Pandya has completed his B.E.

(Electrical Engineering, Sardar Patel Univer-

sity), 1995, M.E. (Electrical Power Systems,

Sardar Patel University), 2003, and Ph.D.

(Power System Protection (Electrical Engi-

neering), from Maharaja Sayajirao Univer-

sity, Vadodara, India. His areas of interests

are Electrical Machines, Electrical power sys-

tem and Power system protection. He had

published several papers in reputed journals

and conferences. Currently he is working as Associate Professor at

PDPU, School of Technology, Raysan, India.





































































http://www.power.uwaterloo.ca






http://www.power.uwaterloo.ca/fmilano

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