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Energy 66 (2014) 202e215

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Energy

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A new approach for optimum simultaneous multi-DG distributedgeneration Units placement and sizing based on maximization ofsystem loadability using HPSO (hybrid particle swarm optimization)algorithm

M.M. Aman a,*, G.B. Jasmon a, A.H.A. Bakar b, H. Mokhlis a,b

aDepartment of Electrical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, MalaysiabUM Power Energy Dedicated Advanced Centre (UMPEDAC) Level 4, Wisma R&D, University of Malaya, Jalan Pantai Baharu, 59990 Kuala Lumpur, Malaysia

a r t i c l e i n f o

Article history:Received 7 February 2013Received in revised form13 December 2013Accepted 16 December 2013Available online 18 January 2014

Keywords:Distributed generationReactive powerSystem loadabilityHybrid particle swarm optimization (HPSO)

* Corresponding author. Tel.: þ60 3 7967 5348.E-mail address: mohsinaman@gmail.com (M.M. A

0360-5442/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.energy.2013.12.037

a b s t r a c t

This paper presents a new approach for optimum simultaneous multi-DG (distributed generation)placement and sizing based on maximization of system loadability without violating the system con-straints. DG penetration level, line limit and voltage magnitudes are considered as system constraints.HPSO (hybrid particle swarm optimization) algorithm is also proposed in this paper to find the optimumsolution considering maximization of system loadability and the corresponding minimum power losses.The proposed method is tested on standard 16-bus, 33-bus and 69-bus radial distribution test systems.This paper will also compare the proposed method with existing Ettehadi method and present theeffectiveness of the proposed method in terms of reduction in power system losses, maximization ofsystem loadability and voltage quality improvement.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Power utilities are facing major challenges as the demand ofpower system is growing exponentially. The existing transmissionline infra-structure is unable to support such a huge power de-mand. The present need is either to invest in transmission systemto increase the capacity or provide the consumer demand locally byDG (distributed generation). Electric power generation integratedwithin the distribution systems is known as “distributed” or“dispersed” generation. The DG source can be a traditional com-bustion generator (such as diesel reciprocating generator and nat-ural gas-turbine) and non-traditional generator including fuel cell,storage device and renewable energy source (such as wind turbineand photovoltaic) [1,2].

DG has many advantages over centralized power generationincluding power losses reduction, voltage profile improvement,system stability improvement, pollutant emission reduction,relieving transmission and distribution congestion and others [3e7]. The optimum placement of DG is necessary to achieve themaximum benefits with less investment cost [8]. After deregulationof power system, non-utility companies are investing in

man).

All rights reserved.

distribution system to meet the active power demand (MW) andget the maximum profit. For example in United States the per-centage of nonutility generators in distribution system hasincreased from 40 GW tomore than 150 GW in ten years from 1990to 2000 [9].

In deregulated operation of distribution system, the DNO(distribution network operator) is responsible in providing goodquality service to consumer and maintain the security and effi-ciently utilize the existing infrastructure under different un-certainties including load changes, available generation andoperating schedule of DG Units, particularly in case of intermit-tent energy source (e.g. wind and solar). Different artificialintelligent based techniques have been proposed in literature forsmooth operation of distribution system under various opera-tional scenarios [10e15]. In some countries, the DNOs are allowedto invest DG Units based on its interests and requirements.However, in some other countries, the DNOs are not allowed toown DG Units [10].

Researchers have solved the problem of optimum DG place-ment problem on the basis of minimization of power losses [16e20] and voltage stability [21e27] approach. Authors have alsoconsidered DG placement as a multi-objective function, consid-ering reduction in power losses, improved voltage regulations andvoltage stability in fitness function [28]. It has also been seen in

τ1

Point ofCollapse

Loading Factor (λ )

Vol

tage

Mag

nitu

de(p

erun

it)

τ2

AB

Fig. 1. Effect of maximum loadability of the system on voltage profile improvement.

M.M. Aman et al. / Energy 66 (2014) 202e215 203

Ref. [29] that the DG placement also improves the reliability andvoltage profile of the system. DG with reactive power control alsohelps in better network voltage profile and lower power losses.The DG penetration level versus power losses present a U-trajec-tory, thus the non-optimum placement of DG may increase thepower losses [30].

The impact of DG on loadability of distribution network hasalso been investigated in Refs. [25,31] and concluded that thepresence of DG increases the loadability of the distribution system.System loadability is related with voltages of the system, theweakest voltage buses result in poor loadability of the system.Different approaches have been proposed to increase the load-ability of the system by improving the voltages of the system andthe DG is placed on the selected weakest voltage bus. The weakestvoltage bus is determined using eigen value determination foroptimum DG location and the maximum loading margin isconsidered for optimum DG size in Ref. [27]. CPF (continuationpower flow) method is used for weakest voltage bus determina-tion as an optimum bus for DG placement [21]. Further authors inRef. [21] have also extended the work for multi-DG Unit placementafter first DG Unit has been placed. Authors have consideredmaximum loading up to the voltage constraint in fitness functionfor optimum DG placement using genetic algorithm in Ref. [25].Successive modal analysis and CPF are utilized for optimum multi-DG Units placement in Ref. [22]. However techniques based onsuccessive selection of DG position, when one DG Unit has beenplaced, cannot lead to the global optimum solution of maximumloadability of the system.

In this paper, a new approach for optimum simultaneousmulti-DG unit placement is presented based on maximization ofsystem loadability. System loadability (l) is defined as the ca-pacity of the system with which the maximum load could beconnected without violating the system and operating con-straints. In this paper, bus voltage and line current limit areconsidered as operating and system constraints respectively. Inpractice, it is highly needed to utilize the existing infrastructurewithout high investment to increase the capacity of existingsystem. In literature, it has been seen that the system capacity orloadability is usually limited by two factors, thermal limits andvoltage limits. Thermal limit or thermal capacity is the ampacityor maximum current carrying capacity limit of the conductor. Thecurrent carrying capacity is limited by the conductor’s maximumdesign temperature, which is determined by the insulation classuse [32]. However the voltage limit is the allowable minimume

maximum voltage variation for safe operation of power systemand connected load [33]. The study [33] has concluded that themaximum loadability of the distribution system is limited by thevoltage limit rather than the thermal limit. The higher loadingfactor results in large current in the distribution line which re-sults in high voltage drop and thus presents the poor voltageregulation. From continuation power flow (CPF) theorem [34] andresults of Ref. [21], it can be concluded that increasing themaximum loadability (lmax) improves the overall voltage profile,as shown in Fig. 1.

From Fig. 1, it can be observed that curve A will have overallbetter voltage profile than curve B at each loading. Here in Fig. 1, s isrepresenting the tangent (predictor vector) at different point ofloading.

This paper is organized as follows: In Section 2, the need forreactive power compensation in presence of DG will be discussed.In Section 3, an optimization algorithm HPSO (hybrid particleswarm optimization) will be proposed for optimum simultaneousmulti-DG Unit placement. In DG Unit placement based on maxi-mization of system loadability, different DG location and DG sizecombinations may result into same maximum loadability. Thus in

order to reach the optimum solution, the K-matrix in HPSO algo-rithm will sort the best result on the basis of minimum powerlosses and select the best results. In Section 4, the proposed algo-rithm for multi-DG Unit placement will be presented. In Section 5,the proposed algorithmwill be tested on 16-bus, 33-bus and 69-busradial distribution test systems. The present approach of optimummulti-DG Unit placement will also be compared with Ref. [22] inthe same section.

2. Impact of distributed generation on voltage stability

Previously DGs were mainly considered as an active source ofenergy [1], however at higher system loading with maximum DGpenetration, the poor voltage profile can be a big challenge for thesystem operator thus the reactive power compensation approachmust be utilized to maintain the voltages in allowable limits [35].DG presence in the system also affects the reactive power man-agement plan. For example in case of wind generation, asynchro-nous induction generators are used. Such generators need reactivepower from the system to which they are connected. Differentmethods of reactive compensations are stated in literature [36]including synchronous generator, shunt capacitor banks and end-user reactive power compensation within the reactive power con-sumption equipment. The growing trend of using non-conventionalpower generation (using wind and solar energy) has also led to thebounding that the renewable energy generation must play theirrole in improving the voltage profile and providing necessaryreactive power support.

Now-a-day state of the art technologyhas comeout to control theactive andreactivepower fromDG.Thewindgeneration isnowusingdoubly fed induction generator and PV inverters are using specialself-commutated line inverter, capable of absorbing and supplyingreactive power at different system loading. The reactive powercapability of solar andwindpower plants canbe further enhancedbythe addition of SVC, STATCOMS and other reactive support equip-ment at the plant level. Currently, inverter-based reactive capabilityis more costly compared to the same capability supplied by syn-chronousmachines [37e39]. The author in Ref. [40] has analysed theimportance of reactive power in presence of DG and concluded thatthe presence of DG results into better voltage profile. However atlight load in distribution system in presence of DG, the problem ofvoltage risemayarise, thus thevoltage regulatingdevicemust alsobepresented in the system. The energy curtailment from DG is not agood solution as this will result in revenue lost. DG has beenconsidered as an active source of energy in Refs. [18e20,41e43],

Fig. 2. Effect of DG placement on kVA margin to maximum loadability (KMML).

M.M. Aman et al. / Energy 66 (2014) 202e215204

however DG has been considered as an active as well as reactivesource of energy in Refs. [16,17,21,22,24,44]. Three different types ofDGs are mainly considered in literature [17].

Type 1: DG injects active power (P) only, e.g. photovoltaicsystem.Type 2: DG injects reactive power (Q) only, e.g. synchronouscompensators.Type 3: DG injects active power (P) but absorbs reactive power,e.g. induction generator.Type 4: DG injects both active (P) and reactive (Q) power e.g.synchronous generator.

In this paper DG will be considered as a PQ (activeereactivepower) source of energy (Type 4). Following definitions are usedin this paper to see the potential effect of DG on distribution system.

1. DG penetration level is defined as the ratio of the total DGpower generation (SDG) over the system demand (SLoad) as givenby Eqn. (1).

DG penetration levelð%Þ ¼ SDGðkVAÞSLoadðkVAÞ

� 100 (1)

Table 1DG placement evaluation indices [22,42].

Parameters Formulae

Active line-loss reduction (ALLR) TLLR% ¼ ReflossesRe

Reactive line-loss reduction (RLR) RLR% ¼ ImflossesgImf

Qualified Load-index Improvement (QLI) QLI% ¼ ðPnbus

i¼1ViLiðP

System loadability improvement (SLI) SLI% ¼ lmaxð0Þ�lmax

lmaxð0Þ

kVA margin to maximum loadability improvement (KMMLI) KMMLI% ¼ KMMLK

Voltage profile improvement (VPI) VPI% ¼ Pnbusi¼1ðVi

Number of bus violating voltage limit (NBVV) NBVV ¼ 0

for i ¼ 1:nbusif Vi < 0.95 or Vi

NBVV ¼ NBVV þendend

2. KMML (kVAmargin tomaximum loadability) is defined in Ref.[45] to represent the additional load from the operating point ‘O’to the point of voltage collapse, as shown in Fig. 2.

From Fig. 2, it can be observed that the curve A (with optimumDG placement) will have a better voltage profile than curve B ateach loading. Further it can also be noted that using the optimumDG placement, the operating point of the system (lV) can also beincreased fromO1 to O2 (within the allowable branch current limits(ILimit) and voltage limits VLimits).

The effect of DG placement on system performances is evaluatedby calculating the indices defined in Table 1.

3. Hybrid particle swarm optimization (HPSO)

PSO (particle swarm optimization) is introduced by Kennedy[46] to solve the optimization problem, based on socialepsycho-logical metaphor behaviour. A particle i is represented as positionvector xi (xi ¼ xi1, xi2, xi3, xi4, .. xid). In each iteration, the i-thparticle fitness value is calculated. The best fitness position asso-ciated with the best particles (pbest) is considered as particles bestposition (pposition). The overall best fitness (gposition) of the popula-tion associated with the overall best particles gbest is recorded asoptimum result. During the iteration procedure, the velocity andthe position of ith particles are updated according to the Eqns. (2)and (3). The rate of position vector of ith particle is representedas velocity vector vi (vi ¼ vi1, vi2, vi3, vi4,..vid).

vðtþ1Þid ¼ w,v

ðtÞid þ c1,r1,ðpbestid � xidÞ þ c2,r2,ðgbest� xidÞ

(2)

xðtþ1Þid ¼ xðtÞid þ v

ðtþ1Þid (3)

where t is number of iterations, d is a total number of initial par-ticles, c1 and c2 are acceleration constants, set at 2.0, r1 and r2 arerandom numbers, w is inertia weight given by Eqn. (4).

w ¼ wmax þwmax �wminitermax

� t (4)

where,

wmax and wmin are 0.9 and 0.4 respectively. HPSO parametersettings (c1, c2, wmin, wmax) are defined in accordance withstandard PSO parameters [17].

Abbreviations

g0�ReflossesgDGflossesg0 � 100 � Subscript (0) is representing the base case when

no DG(s) is present in the system.0�ImflossesgDGlossesg0 � 100 � Subscript (DG) is representing the case when

DG(s) is present in the system.Þð0Þ�ð

Pnbusi¼1

ViLiÞðDGÞnbusi¼1

ViLiÞðDGÞ� 100 � nbus is total number of buses.

ðDGÞ � 100 � Vi is voltage magnitude at bus i.

ð0Þ�KMMLðDGÞMMLð0Þ

� 100 � Li is active load at bus i pu.

ð0Þ � ViðDGÞÞ2 � lmax is maximum loadability of the system.

> 1.051

� KMML is kVA margin to maximum loadabilityof the system.

No

YesLmb==Lmb(max)

Start

Read System DataBusdata, Linedata, Base Voltage, Base MVA,

Desired Accuracy (ep=1x10-4)

Form BIBC Matrix

Set LimitsCutoff=1000, Lmb=1, Lmb(max)=10000

M.M. Aman et al. / Energy 66 (2014) 202e215 205

In the proposed method of optimum DG placement and sizing,HPSO is used to find the fitness function, given by Eqn. (5).

f ¼ Maxflmaxg (5)

where,

f is the fitness function and lmax is maximum loadability orloading factor of the system.

In the present case of solving multi-DG Units’ placement on thebasis of maximization of system loadability, two major problemsarise.

1. Due to multiple combinations of DG positions and DG size(particularly in two DG Unit and three DG Unit case), it ispossible that the simple PSO may stuck in local minima, thus toobtain the global best solution, the good results will againiterated with new random solution (like a scout bees in ABCalgorithm).

2. One or more DG positions and DG size may result in the samemaximum loading factor (lmax). Thus in order to obtain theoptimum DG placement, a new K-matrix variable is definedwhich will contain the DG position(s), DG size(s), loadability andpower losses, as shown in Eqn. (6). The good results are sortedout on the basis of minimum power losses and the first rowsolution will be treated as the best solution. In proposed HPSO,K-matrix variable will be formed from the updated gbest posi-tions and will help in finding the optimum DG placement basedon system maximum loadability as well as minimum powerlosses. The utilization of K-Matrix in solving multi-DG Unitplacement will be explained in next section.

26x x x x l

zfflffl}|fflffl{Fitness

Pzfflfflffl}|fflfflffl{Sorting Criteria

37

End

Lm

b=L

mb+

0.01

Accuracy>ep

It==Cutoff

Compute Accuracy Using Eq. (A-3)

Forward Loop:Compute I using Eq. (A-1)

Backward Loop:Compute V using Eq. (A-2)

P=Po+Lmb x PoQ=Qo+Lmb x Qo

It=0Accuracy=1

It=It+1 ; Vpr=V

Print ResultsLoading Factor (λ)

Break

Stored Lmb and Vmin

Yes

No

Yes

No

Fig. 3. Flow chart for calculation of maximum loadability of the system (lmax).

K-Matrix ¼

66666666664

11 12 13 14 max1 losses1

x21 : : : lmax2 Plosses2: : : : lmax3 Plosses3: : : : lmax4 Plosses4: : : : : :

xn1 : : : lmaxn Plossesn

77777777775

(6)

Due to above two reasons, a modified form of original PSO isproposed and referred as hybrid particle swarm optimization(HPSO). The HPSO algorithm is inspired from Artificial Bee Colonyalgorithm, in terms of scout bees’ behaviour, thus it is referred as‘hybrid’. The detail of ABC (Artificial Bee Colony) algorithm can beseen in Ref. [47]. Here it is noticed that HPSO differs from multi-objective approach, multi-objective approach is commonly usedin solving two independent quantities (e.g. cost and minimumpower losses). HPSO is particularly useful when two quantities arehighly dependent on each other and the improvement in onequantity will also result in better solution of other quantity (e.g.loadability, voltage profile or minimum power losses). The appli-cation of HPSO in solving multi-DG Unit placement will beexplained in next section.

4. Proposed algorithm for optimum DG placement and sizing

In this section, a new algorithm for optimum multi-DG Units’placement will be proposed on the basis of maximization of systemloadability, given by Eqn. (5). Thukaram radial load flow used involtage stability and optimization tool will be used to compute themaximum loading of the system [48]. The generalize steps offinding maximum loadability are given below.

4.1. Fitness function calculations

To find the maximum loadability or loading factor (l) of thesystem, the active and reactive load is increased on all buses, usingEqn. (7), with equal loading factor of 0.01, till the divergence isobserved in load flow analysis.

Pnew ¼ P0 � Loading FactorðlÞ (7a)

Qnew ¼ Q0 � Loading FactorðlÞ (7b)

where

l is a loading factor, Po and Qo are initial active and reactivepower load, connected with ith bus. Pnew and Qnew are finalactive and reactive power load, connected with ith bus.

The complete block diagram for fitness function calculation isshown in Fig. 3.

M.M. Aman et al. / Energy 66 (2014) 202e215206

4.2. Problem formulation

HPSO method is used to find the optimum fitness based onmaximization of system loadability and minimum power losses.The initial particle (xi) is a 1 � 2 vector (PDG1, PDG1), 1 � 4 vector(PDG1, PDG1, PDG2, PDG2) or 1 � 6 vector (PDG1, PDG1, PDG2, PDG2, PDG3,PDG3), representing random DG positions (PDG) and DG sizes (PDG).Following constraints, given in Eqns. (8)e(10), related to DGplacement are considered in problem formulation.

Size of DG : 0 �Xnk¼1

PDG �X

Pload ðn ¼ No: of DG unitsÞ

(8)

Position of DG : 2 � DG position � nbuses (9)

Position of DG : PDG1sPDG2sPDG3 (10)

The placement of DG may increase the line current in some ofthe branches and bus voltages on some of the buses. Thus the line

Start

Set best of pbests as gbest

Cycle=Cycle+1

End

Yes

Is Cycle==Max_Cycle?

Yes

No

If fitness(p)==fitness(gbest) then construcK-matrix=[p fitness(p) losses(

Initialize HPSO; Pop Size=70; It_MaxMax_Cycle=3; It=1; Cycle=0

Initialize random particles, following thegiven in Eqns. (8) to (12)

Calculate fitness of each particles po

It=It+1

Update particles(p) using Eqns. (2)

Sort K-matrix:If K[fitness(p)]==gbest(fitness) then constru

K-matrix(new)=[p fitness(p) losse

If fitness(p) is better thanfitness(pbest) than pbest=p

Select the first best particles of K-matrix(new) a

Is It==It_max?

Sort K-matrix(new):Sort K-matrix(new) on the basis of los

such that losses(p1)<losses(p2)<losses(p3

Fig. 4. Flow Chart of Proposed Algorithm for optimum simultaneous multi DG

amperage limits and bus voltage constraints are also introduced inproblem formulation, given in Eqns. (11) and (12) respectively.

IiDG < IiLimit i ¼ 1 to nbr (11)

0:95 � Vkbus � 1:05 k ¼ 1 to nbus (12)

where

nbr is total number of branches, nbus is total number of buses andVbus is bus voltage.

The amount of reactive power from DG is given by Eqn. (13).

QDG ¼ PDG � tan�cos�1ðpower factorÞ

�; (13)

In case of fixed DG penetration, the amount of active and reac-tive power from a single DGUnit can be calculated using Eqns. (14a)and (14b) respectively.

No

t the K-matrixp)]

=70;

constrains

sition (p)

and (3)

ct K-matrix(new)s(p)]

s optimum result

Join new set of Particleswith K-matrixnew(p)

Initialize random particles,following the constrainsgiven in Eqns. (8)-(12)

ses(p))….losses(pn)

unit Placement based on maximization of system loadability using HPSO.

Table 2cMaximum loadability calculations under different DG penetration and operating power factor for 69-bus radial distribution test system.

PFY No. of DGs ¼ 1 No. of DGs ¼ 2 No. of DGs ¼ 3

DG penetration (%) DG penetration (%) DG penetration (%)

80 60 40 20 80 60 40 20 80 60 40 20

1 4.63 4.3 3.96 3.6 4.65 4.32 3.97 3.6 4.65 4.32 3.96 3.60.95 4.88 4.48 4.08 3.66 4.91 4.5 4.08 3.66 4.91 4.5 3.84 3.660.9 4.92 4.51 4.1 3.67 4.96 4.53 4.1 3.67 4.96 4.53 4.1 3.670.85 4.93 4.52 4.1 3.67 4.97 4.54 4.1 3.67 4.97 4.53 4.1 3.670.8 4.91 4.51 4.1 3.67 4.96 4.53 4.09 3.67 4.95 4.52 4.1 3.660.75 4.89 4.49 4.08 3.66 4.93 4.51 4.08 3.66 4.93 4.5 4.08 3.66

Highlighted result shows the maximum loadability of the system at different level of DG penetration.PF ¼ power factor.

Table 2bMaximum loadability calculations under different DG penetration and operating power factor for 33-bus radial distribution test system.

PFY No. of DGs ¼ 1 No. of DGs ¼ 2 No. of DGs ¼ 3

DG penetration (%) DG penetration (%) DG penetration (%)

80 60 40 20 80 60 40 20 80 60 40 20

1 4.3 4.18 4.04 3.84 4.69 4.43 4.15 3.84 4.66 4.43 4.16 3.840.95 4.43 4.28 4.11 3.88 4.99 4.65 4.28 3.89 4.9 4.6 4.28 3.910.9 4.45 4.3 4.12 3.89 5.05 4.69 4.31 3.89 4.95 4.64 4.3 3.920.85 4.45 4.3 4.12 3.89 5.07 4.71 4.31 3.89 4.97 4.65 4.31 3.920.8 4.45 4.3 4.12 3.89 5.07 4.7 4.31 3.89 4.97 4.65 4.31 3.920.75 4.43 4.29 4.11 3.88 5.05 4.69 4.3 3.88 4.95 4.64 4.3 3.91

Highlighted result shows the maximum loadability of the system at different level of DG penetration.PF ¼ power factor.

Table 2aMaximum loadability calculations under different DG penetration and operating power factor for 16-bus radial distribution test system.

PFY No. of DGs ¼ 1 No. of DGs ¼ 2 No. of DGs ¼ 3

DG penetration (%) DG penetration (%) DG penetration (%)

80 60 40 20 80 60 40 20 80 60 40 20

1 9.63 9.14 8.62 8.1 9.41 8.96 8.5 8.03 9.32 8.88 8.45 8.010.95 9.69 9.18 8.66 8.12 9.52 9.04 8.56 8.06 9.44 8.98 8.51 8.040.9 9.64 9.15 8.64 8.11 9.51 9.03 8.55 8.06 9.43 8.98 8.51 8.040.85 9.58 9.11 8.61 8.1 9.47 9 8.53 8.05 9.4 8.95 8.5 8.030.8 9.51 9.05 8.58 8.08 9.42 8.97 8.51 8.04 9.36 8.92 8.48 8.020.75 9.43 9 8.54 8.07 9.36 8.93 8.48 8.03 9.3 8.88 8.45 8.01

Highlighted result shows the maximum loadability of the system at different level of DG penetration.PF ¼ power factor.

Table 316-Bus, 33-bus and 69-bus radial distribution test system’s details.

Testsystem

Total Activeload inkW (P)

Total reactiveload inkVAR (Q)

Total apparentload inkVAS ¼ Sqrt(P2 þ Q2)

System powerfactor(PF ¼ P/S)

16-Bus 28 700 5900 29 300.17 0.9795

M.M. Aman et al. / Energy 66 (2014) 202e215 207

PDG ¼ SDG � PF (14a)

QDG ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiS2DG � P2DG

q(14b)

where

SDG ¼ SLoad � DG_penetration_level� 1=No: of DG Units

(14c)

SLoad ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXnbus

i¼2

P2i þXnbus

i¼2

Q2i

vuut (14d)

The complete flow chart of proposed algorithm of multi-DG Unitplacement is shown in Fig. 4.

system33-Bus

system3715 2300 4369.35 0.8502

69-Bussystem

3801.9 2694.1 4659.67 0.8159

where Sqrt ¼ square root; PF ¼ power factor.

4.3. Selection of DG operating power factor

In this section, the maximization of system loadability iscomputed for 16-bus, 33-bus and 69-bus radial distribution test

systems under different power factors and different level of DGpenetration, using HPSO method. The DG operating power factor isvaried from 1.0 to 0.75 (in step of 0.05) and the DG penetration levelhas been changed from 20% up to 80% (in step of 20%). The obtainedresults of maximum loadability of the system are summarized inTable 2.

Table 3 shows the system details of 16-bus, 33-bus and 69-busradial distribution system.

Fig. 5. Single line diagram of modified 16-bus radial distribution test systems.

M.M. Aman et al. / Energy 66 (2014) 202e215208

By comparing, Tables 2 and 3, it can be seen that the most op-timum (maximum loadability) results are achieved when the DGoperating power factor is nearer to the system power factor. Thus0.95 operating power-factor of DG is considered in case of 16-bustest system, and 0.85 power-factor of DG is considered in case of33-bus and 69-bus test systems. From Table 2, it can also be noticedthat higher DG penetration will result in higher system loadability,thus the amount of DG penetration level can be decided on eco-nomic grounds.

5. Application of proposed DG placement algorithm on radialdistribution system

In this section, the proposed algorithm of optimum multi-DGUnit placement will be applied on 3-phase, 12.66 kV standard 16-bus [49], 33-bus [50] and 69-bus [51] radial distribution test sys-tems. The system details including bus and line data are given inAppendix A. In the proposed, DG will be considered as a ePQ loadand the DG will provide active and reactive power. The DG oper-ating power factor is set at 0.95 for 16-bus system and 0.85 for 33-bus and 69-bus radial distribution system. Following two casestudies are presented:

Case 1 (with maximum DG penetration): In case 1, DG pene-tration is considered as maximum as possible, without violating DGconstraints, line amperage constraint and bus voltage constraint,given in Eqns. (8)e(12). In case 1, it is highly possible, the busvoltages and line current may cross the maximum limit, thus lineamperage constraint and bus voltage constraint are introduced inproblem formulation.

Table 4Application of proposed algorithm for optimum single and multi-DG Units placement on

No. of DG Units DG size in kVA / (DG position) Active powerlosses (kW)

Reactive plosses (kV

Base caseWithout DG e 511.40 590.33Proposed method (case 1)Single DG Unit 21859.62 / (8) 315.02 407.66Two DG Units 7921.98 / (7) 492.59 585.49

22058.09 / (8)Three DG Units 11506.39 / (11) 536.56 635.06

14430.99 / (9)9654.92 / (8)

Proposed method (case 2)Single DG Unit 11720.1 / (08) 176.54 227.58Two DG Units 11720.1 � (1/2) / (11) 200.63 248.69

11720.1 � (1/2) / (10)Three DG Units 11720.1 � (1/3) / (11) 178.36 225.17

11720.1 � (1/3) / (08)11720.1 � (1/3) / (10)

Case 2 (with 40% DG penetration): In case 2, the DG pene-tration is considered 40% of total load (SLoad). The DG constraintsgiven in Eqns. (9) and (10) and line amperage constraint given inEqn. (12) are introduced in problem formulation. Case 2 isconsidered in order to compare the proposed method with [22]method where author has considered 40% DG penetration leveland have applied the proposed method on 33-bus radial distri-bution test system.

The applications of proposed multi-DG Unit placement ondifferent radial distribution system are as follows.

5.1. 16-Bus radial distribution test system

16-Bus system is a standard 12.66 kV network, having 3 feeders[49]. The system details are given in appendix Table A-1. In order tosolve the 3 feeder system, the system has been transformed to asingle feeder, 15-bus radial distribution test system, as shown inFig. 5. When the proposed algorithm of DG Unit placement isapplied on modified 16-bus radial distribution test system, resultspresented in Table 4 are obtained. The base load of modified 16-bussystem is 29 300.17 kVA.

From Table 4, following points can be concluded:

1. Using the proposed method of optimum DG placement, systemmaximum loadability, kVA margin to maximum loadability(KMML) and voltage quality has been significantly improved.However the power losses have been increased with maximumDG penetration and reduced with limited 40% DG penetration.Thus the amount of DG penetration must be decided on

16-bus test system.

owerAR)

Maximumsystemloadability

KMML QLI VPI NBVV lV

7.55 192 209.12 28.1496 e 0 1.05

9.13 238 210.39 28.8557 0.0895 0 1.339.4 246 121.43 29.0211 0.1131 0 1.34

9.64 253 153.4 29.0695 0.1025 0 1.71

8.4 216 821.26 28.5396 0.0438 0 1.308.55 221 216.29 28.5723 0.0445 0 1.45

8.50 219 751.28 28.5623 0.0418 0 1.45

-20

-10

0

10

20

30

40

50

60

70

PLR RLR KMMLI SLI QLII PLR RLR KMMLI SLI QLII

Proposed Method (With maximum DG penetration)

Proposed Method (With 40% DG penetration)

Perc

enta

ge Im

prov

emen

t

Single DG Unit Two DG Units Three DG Unit

Fig. 6. Comparison of DG Evaluation indices in presence of DG Unit(s) for modified 16-bus radial distribution system.

M.M. Aman et al. / Energy 66 (2014) 202e215 209

economic as well as on technical grounds. The DG placementevaluation indices defined in Table 1 are used to develop theeffectiveness of proposed method in quantitative form and theobtained results are shown in Fig. 6.

Fig. 7. System maximum loading curve for 16-bus radial distribution system (case 1).

Fig. 8. Single line diagram

2. To show the advantage of the proposed method of DG place-ment, the loading margin factor (l) is also calculated from 0 upto the voltage limit (lV), satisfying the line and bus voltageconstraints also. The higher value of lV will allow the operator toadd more load with the same existing infrastructure. It wasfound that the base case can carry only 30 765.18 kVA (lV¼ 1.05)without violating the voltage and line constraints. However theproposed method with 40% DG penetration can carry up to38 969.23 kVA (lV ¼ 1.33), 39 262.23 kVA (lV ¼ 1.34) and50 103.29 kVA (lV ¼ 1.71) in case of single, two and three DGUnits respectively. These results have been summarized in Fig. 7.Similar results are achieved in case 2.

From above results and discussion of 16-bus test system, it canalso be observed that the performance of one DG Unit, two DGUnit and three DG Unit placement are approximately the same.Thus the optimum number of DG Units in case 16-bus systemmust be 1, in order to reduce the installation and maintenance costof DG.

5.2. 33-Bus radial distribution test system

When the proposed algorithm of DG Unit placement is appliedon 33-bus radial distribution test system (shown in Fig. 8), results

of 33-bus test system.

Table 5Application of proposed algorithm for optimum single and multi-DG Units placement on 33-bus test system (case 1).

No. of DG Units DG size in kVA / (DG position) Active powerlosses (kW)

Reactive powerlosses (kW)

Maximumsystemloadability

KMML QLI VPI NBVV

Base caseWithout DG e 210.99 143.01 3.41 10 530.40 3.5228 e 21Proposed methodSingle DG Unit 3623.9 / (8) 131.85 113.03 4.31 14 462.55 3.7213 0.1757 0Two DG Units 1313.9 / (16) 87.65 73.32 5.00 17 477.40 3.7609 0.0700 0

2212.3 / (22)Three DG Units 444.0 / (29) 84.16 68.02 5.04 17 652.18 3.7713 0.0643 0

1364.1 / (15)1973.0 / (31)

5 10 15 20 25 30 33

0.88

0.9

0.92

0.940.950.96

0.98

1

1.02

1.041.051.06

1.08

Bus No.

Vol

tage

Mag

nitu

de(p

u)

Base case (Without DG)Single DG (8)Two DGs (16 & 32)Three DGs (15,29 & 31)

Fig. 10. Voltage profile curve of 33-bus radial system (case 1).

M.M. Aman et al. / Energy 66 (2014) 202e215210

presented in Table 5 are obtained. The base load of 33-bus system is4369.35 kVA. The 33-bus system details are given in appendixTable A-2.

From Table 5, following points can be concluded:

1. Using the proposed method of optimum DG placement, powerlosses have been reduced, while system maximum loadability,kVA margin to maximum loadability (KMML), and voltagequality has been significantly improved. The DG placementevaluation indices defined in Table 1 are used to develop theeffectiveness of proposed method in quantitative form and theobtained results are shown in Fig. 9.

2. The overall voltage profile curve for 33-bus radial distributionsystem in presence of DG Unit(s) is shown in Fig. 10.

3. To show the advantage of the proposed method of DGplacement, the loading margin factor (l) is also calculatedfrom 0 up to the voltage limit (lV), satisfying line constraintsalso. It was found that the base case can carry only2403.14 kVA (lV ¼ 0.55) without violating the voltage and lineconstraints. However the proposed method can carry up to5898.62 kVA (lV ¼ 1.35), 8520.23 kVA (lV ¼ 1.95) and8738.70 kVA (lV ¼ 2.00) in case of single, two and three DGUnits respectively. These results have been summarized inFig. 11.

4. Fig. 12 shows iteration versus maximum loadability of the sys-tem convergence plot of proposed HPSO algorithm for single DGUnit placement. From Fig. 9, it can be observed that the pro-posed method reaches to the maximum loadability of the sys-tem in less number of iterations with corresponding minimumpower losses. In cycle 1, proposed algorithm results in optimumDG placement at bus-8 with DG size 3623.1 kVA having mini-mum power loss 132.08 kW. However, in cycle 2, the power

0

10

20

30

40

50

60

70

80

PLR RLR KMMLI SLI QLII

Perc

enta

ge Im

prov

emen

t

Single DG Unit Two DG Units Three DG Units

Fig. 9. Comparison of DG Evaluation indices in presence of DG Unit(s) for 33-bus radialdistribution system (case 1).

losses have been reduced to 131.90 kW with optimum DGplacement at bus-8 and DG size of 3625.2 kVA. In last cycle(cycle 3), the best result withmaximum loadability (lmax¼ 4.31)and corresponding minimum power losses (131.85 kW) is

Fig. 11. System maximum loading curve for 33-bus radial distribution system (case 1).

01020304050607080

Proposed Method

Ettheadi Method

Proposed Method

Ettheadi Method

Proposed Method

Ettheadi Method

Single DG Unit Case Two DG Units Case Three DG Units Case

Perc

enta

ge Im

prov

emen

t

PLR QLR KMMLI SLI QLII

Fig. 13. Comparison of proposed method and Ettehadi method for the same level of DGpenetration (case 2).

4.25

4.26

4.27

4.28

4.29

4.3

4.31

4.32

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70

Max

imum

Loa

dabi

lity

of th

e Sy

stem

( λm

ax)

No. of Iterations

Cycle 1 Cycle 2 Cycle 3

Cycle 1 (8, 3623.1 kVA)λmax=4.31

Plosses=132.08 kW

Cycle 3 (8,3623.9 kVA)λmax=4.31

Plosses=131.85 kW

Cycle 2 (8, 3625.2 kVA)λmax=4.31

Plosses=131.90 kW

Fig. 12. Convergence plot of proposed HPSO algorithm.

M.M. Aman et al. / Energy 66 (2014) 202e215 211

obtained with optimum DG placement at bus-8 and DG size of3623.9 kVA.

The proposed approach of optimum DG placement is alsocompared with Ettehadi method with 40% DG penetration(1747.7 kVA). In Ettehadi method [22], the author has consideredthe voltage stability approach (based on eigen value determination)for optimum DG placement. A fixed DG with 40% DG penetration(1747.7 kVA) is placed on selected weakest voltage buses. Thecomparative results of proposed method with Ettehadi method aresummarized in Table 6.

From Table 6, following points can be concluded:

1. It can be seen that in terms of active and reactive power lossesreduction, system loadability improvement, voltage profileimprovement and quality load index improvement the perfor-mance of proposed method is found better than the Ettehadimethod. The DG placement evaluation indices defined in Table 1are used to compare the proposed method with Ettehadimethod in quantitative terms and the comparative results arepresented in Fig. 13.

2. From Table 6, it can also be observed that the number ofbuses violating voltage limits (NBVV) has been reduced from9-buses (in case of Ettehadi method) to 3 buses (proposedmethod).

3. The loading margin factor up to the voltage limit (lV) is alsofound better than the Ettehadi method in all three scenarios ofDG placement.

Table 6Comparison of proposed algorithm with Ettehadi method [22] for optimum single and m

No. of DG Units DG size in kVA / (DG position) Active powerlosses (kW)

Reactive powlosses (kVAR

Ettehadi methodSingle DG Unit 1747.7 / (33) 148.46 116.29Two DG Units 1747.7 � (1/2) / (33) 103.38 75.25

1747.7 � (1/2) / (18)Three DG Unit 1747.7 � (1/3) / (33) 99.00 70.75

1747.7 � (1/3) / (18)1747.7 � (1/3) / (32)

Proposed methodSingle DG Unit 1747.7 / (14) 112.80 81.92Two DG Units 1747.7 � (1/2) / (17) 52.72 38.15

1747.7 � (1/2) / (31)Three DG Unit 1747.7 � (1/3) / (14) 59.59 41.38

1747.7 � (1/3) / (18)1747.7 � (1/3) / (32)

On the basis of above discussion it can be concluded that the DGplacement based on maximization of system loadability worksbetter than the Ettehadi method either for single or multi-DG Unitplacement. From above results and discussion of 33-bus test sys-tem, it can also be observed that the performance of two DG Unitplacement and three DG Unit placements are approximately thesame in both cases, either in case of maximum DG penetration or40% DG penetration. Thus the optimum number of DG Units in case33-bus system must be 2, in order to reduce the installation andmaintenance cost.

5.4. 69-Bus radial distribution test system

When the proposed algorithm of DG Unit placement is appliedon 69-bus radial distribution test system (shown in Fig. 14), resultspresented in Table 7 are obtained. The base load of 69-bus system is4659.67 kVA. The 69-bus system details are given in appendixTable A-3.

From Table 7, following points can be concluded:

1. Using the proposed method of optimum DG placement on 69-bus radial distribution test system, power system losses havebeen reduced, system maximum loadability, quality load index,kVA margin to maximum loadability and overall voltage profilehas been significantly improved, as compared to the base case.The DG placement evaluation indices defined in Table 1 are alsocalculated and results are presented in Fig. 15.

2. The overall voltage profile of 69-bus test system in presence ofDG is shown in Fig. 16.

ulti-DG Units placement with 40% DG penetration level (case 2).

er)

System loadabilitymargin

KMML QLI VPI lV NBVV

3.73 11 928.33 3.6141 0.1022 0.8 94.14 13 719.76 3.6290 0.0451 1.2 0

4.07 13 413.91 3.6257 0.0318 1.15 0

4.12 13 632.37 3.6562 0.2168 1.0 34.31 14 462.55 3.6529 0.0587 1.35 0

4.31 14 462.55 3.6559 0.0973 1.25 0

36 37 38 39 40 41 42 43 44 45 46Main

Substation

47 48 49 50

66 6751 52

68 69

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

28 29 30 31 32 33 34 35

53 54 55 56 57 58 59 60 61 62 63 64 65

Fig. 14. Single line diagram 69-bus test system.

Table 7Application of proposed algorithm for optimum single and multi-DG Units placement on 69-bus test system.

No. of DG DG size in kVA / (DG position) Active powerlosses

Reactive powerlosses

Maximumsystemloadability

KMML QLI VPI lV NBVV

Base caseWithout DG e 224.95 102.15 3.22 10 344.47 3.6189 e 0.6 9Proposed method with maximum DG penetration (case 1)Single DG Unit 3684.7 / (61) 87.13 38.34 4.91 18 219.32 3.8713 0.1459 1.75 0Two DG Units 3685.1 / (61) 86.68 37.17 4.91 18 219.32 3.8719 0.1459 1.75 0

547.6 / (48)Three DG Units 3652.5 / (61) 87.00 38.18 4.91 18 219.32 3.8715 0.1459 1.75 0

32.2 / (63)152.9 / (46)

Proposed method with 40% DG penetration (case 2)Single DG Unit 1863.9 / (64) 41.94 24.09 4.1 14 444.98 3.7582 0.0981 1.45 0Two DG Units 1863.9 � (1/2) / (64) 29.98 18.01 4.1 14 444.98 3.7573 0.0968 1.45 0

1863.9 � (1/2) / (61)Three DG Units 1863.9 � (1/3) / (62) 28.78 17.40 4.1 14 444.98 3.7569 0.0967 1.45 0

1863.9 � (1/3) / (64)1863.9 � (1/3) / (61)

0102030405060708090

100

PLR RLR KMMLI SLI QLII PLR RLR KMMLI SLI QLII

Proposed Method (With Maximum DG penetration)

Proposed Method (With 40% DG penetration)

Perc

enta

ge Im

prov

emen

t

Single DG Unit Two DG Units Three DG Unit

Fig. 15. Comparison of DG Evaluation indices in presence of DG unit(s) with maximum DG penetration (Case 1) and 40% DG penetration (Case 2) for 69-bus radial distributionsystem.

M.M. Aman et al. / Energy 66 (2014) 202e215212

10 20 30 40 50 60 690.9

0.92

0.940.950.96

0.98

1

1.02

1.041.051.06

Bus No.

Vol

tage

Mag

nitu

de(p

u)

Base case (Without DG)Single DG (61)Two DGs (61 & 48)Three DGs (61,63 & 46)

Fig. 16. Voltage profile curve of 69-bus radial system (case 1).

M.M. Aman et al. / Energy 66 (2014) 202e215 213

3. From Table 7, it can also be seen that the loading margin factorconsidering voltage and line limit (lV) for base case (when noDG is present) is only 2795.80 kVA (lV ¼ 0.6). However theproposed method can carry up to 8154.42 kVA (lV ¼ 1.75) and6756.52 kVA (lV ¼ 1.45) in case of maximum DG penetrationand 40% DG penetration respectively, in all scenario of DGplacement (single DG Unit, two DG Units and three DG Units).These results are also presented in Fig. 17.

4. From above results it can also be observed that in both caseseither maximum DG penetration or 40% DG penetration, theperformance of one, two and multi-DG Unit placement isfound approximately the same in terms of power loss reduction,maximum loadability improvement and voltage qualityimprovement. Thus in present case of 69-bus test system, op-timum number of DG placement must be ‘one’ in order to getthe maximum benefit with minimum installation and operationcost of DG.

The proposed algorithm of optimum multi-DG Unit placementhas been well tested on 16-bus, 33-bus and 69-bus radial distri-bution test system and improved results are obtained in all cases.The other advantage of proposed method is simplicity and practical

Fig. 17. System maximum loading curve for 69-bus radial distribution system.

consideration of line and voltage limit constraints which allows theplanning engineers to well handle the problem of DG placement.From 16-bus, 33-bus and 69-bus test system results, it was alsofound that the optimum number of DG Unit select is also subjective(w.r.t. the distribution system), a detailed study must be carried outat planning stage, otherwise higher number of DG Unit placementwill result in loss of investment only.

6. Conclusion

This paper has presented a new approach for optimumsimultaneous multi-distributed generation (DG) Units’ placementand sizing on the basis of maximization of system loadability.Hybrid particle swarm optimization (HPSO) algorithm is alsoproposed to solve the single objective and multi-constraintsproblem. HPSO will help in getting the best result consideringloadability as well as minimum power losses, when two or moreDG combinations will result in the same maximum loadability.The application of proposed algorithm on 16-bus, 33-bus and 69-bus test system shows that with 40% DG penetration only, powerlosses can be reduced up to 60e75% and maximum loadability ofthe system can increase up to 15e40% and overall voltage qualitysignificantly improves. The proposed method was also comparedwith Ettehadi method and it was found that the proposed methodworks better than the existing method in terms of maximizationof system loadability, reduction in power system losses, improvingthe KVA margin to maximum loadability (KMML) and improve-ment in voltage quality.

Acknowledgements

This work was supported by the Bright Spark Programme andthe Institute of Research Management and Monitoring Fund-IPPP(Grant Code: PV144/2012A) of University of Malaya and HIR/MOHE Research Grant (Grant Code: D000004-16001) of Ministry ofHigher Education, Malaysia.

Appendix

D. Thukaram RLF method [52]

Thukaram load flow is used in the present paper to carry out theload flow analysis. Thukaram load flow method is based on for-wardebackward sweep. In backward sweep, the load current iscomputed for nth loads in the network, using the followingrelation.

Ii ¼ conjðSi=ViÞ i ¼ 1;2;3;.n (A-1)

where S is the connected load, V is the voltage at ith bus in nth bussystem.

However, in forward sweep, the receiving end voltage (Vr) iscalculated using the difference of sending end voltage (Vs) and linedrop, as given by Eqn. (A-2).

Vr ¼ Vs � IðRþ jXÞ (A-2)

where I is branch current, R is line resistance and X is line reactance.The current in each branch is formulated as a function of equivalentcurrent injections and thematrix is known as BIBC (bus-injection tobranch-current) [53]. Apply the same approach to nth buses in theradial system. The convergence criteria proposed is given by thefollowing relation.

Table A-369-Bus test system data [51].

From To P (kW) Q (kW) R (ohms) X (ohms) Imax

1 2 0 0 0.0005 0.0012 4002 3 0 0 0.0005 0.0012 4003 4 0 0 0.0015 0.0036 400

M.M. Aman et al. / Energy 66 (2014) 202e215214

MaxhVki � Vk�1

i

iDtolerance i ¼ 1;2;3;.n (A-3)

where, k is no. of iteration and n is total number of buses.

Table A-116-Bus test system data [49].

From To P (kW) Q (kVAR) R (ohms) X (ohms) Imax

1 2 0 0 1.0E-10 1.0E-10 25002 3 2000 1600 0.1202 0.1603 14003 4 3000 400 0.1282 0.1763 5003 5 2000 �400 0.1442 0.2885 5005 6 1500 1200 0.0641 0.0641 5002 7 4000 2700 0.1763 0.1763 14007 8 5000 1800 0.1282 0.1763 10007 9 1000 900 0.1763 0.1763 5008 10 600 �500 0.1763 0.1763 5008 11 4500 �1700 0.1282 0.1763 5002 12 1000 900 0.1763 0.1763 140012 13 1000 �1100 0.1442 0.1923 50012 14 1000 900 0.1282 0.1763 50014 15 2100 �800 0.0641 0.0641 500

Imax is assumed maximum line current limit in Amperes. SB ¼ 100 MVA;VB ¼ 12.66 kV.

Table A-233-Bus test system data [50].

From To P (kW) Q (kVAR) R (ohms) X (ohms) Imax

1 2 100 60 0.0922 0.0470 4002 3 90 40 0.4930 0.2510 4003 4 120 80 0.3661 0.1864 4004 5 60 30 0.3811 0.1941 4005 6 60 20 0.8190 0.7070 4006 7 200 100 0.1872 0.6188 3007 8 200 100 1.7117 1.2357 3008 9 60 20 1.0299 0.7400 2009 10 60 20 1.0440 0.7400 20010 11 45 30 0.1967 0.0651 20011 12 60 35 0.3744 0.1237 20012 13 60 35 1.4680 1.1549 20013 14 120 80 0.5416 0.7129 20014 15 60 10 0.5909 0.5260 20015 16 60 20 0.7462 0.5449 20016 17 60 20 1.2889 1.7210 20017 18 90 40 0.7320 0.5739 2002 19 90 40 0.1640 0.1564 20019 20 90 40 1.5042 1.3555 20020 21 90 40 0.4095 0.4784 20021 22 90 40 0.7089 0.9373 2003 23 90 50 0.4512 0.3084 20023 24 420 200 0.8980 0.7091 20024 25 420 200 0.8959 0.7010 2006 26 60 25 0.2031 0.1034 30026 27 60 25 0.2842 0.1447 30027 28 60 20 1.0589 0.9338 30028 29 120 70 0.8043 0.7006 20029 30 200 600 0.5074 0.2585 20030 31 150 70 0.9745 0.9629 20031 32 210 100 0.3105 0.3619 20032 33 60 40 0.3411 0.5302 200

Imax is maximum line current limit in Amperes, given in Ref. [54]. SB ¼ 100 MVA;VB ¼ 12.66 kV.

4 5 0 0 0.0251 0.0294 4005 6 2.6 2.2 0.366 0.1864 4006 7 40.4 30 0.381 0.1941 4007 8 75 54 0.0922 0.047 4008 9 30 22 0.0493 0.0251 4009 10 28 19 0.819 0.2707 40010 11 145 104 0.1872 0.0619 20011 12 145 104 0.7114 0.2351 20012 13 8 5 1.03 0.34 20013 14 8 5.5 1.044 0.345 20014 15 0 0 1.058 0.3496 20015 16 45.5 30 0.1966 0.065 20016 17 60 35 0.3744 0.1238 20017 18 60 35 0.0047 0.0016 20018 19 0 0 0.3276 0.1083 20019 20 1 0.6 0.2106 0.069 20020 21 114 81 0.3416 0.1129 20021 22 5 3.5 0.014 0.0046 20022 23 0 0 0.1591 0.0526 20023 24 28 20 0.3463 0.1145 20024 25 0 0 0.7488 0.2475 20025 26 14 10 0.3089 0.1021 20026 27 14 10 0.1732 0.0572 2003 28 26 18.6 0.0044 0.0108 20028 29 26 18.6 0.064 0.1565 20029 30 0 0 0.3978 0.1315 20030 31 0 0 0.0702 0.0232 20031 32 0 0 0.351 0.116 20032 33 14 10 0.839 0.2816 20033 34 19.5 14 1.708 0.5646 20034 35 6 4 1.474 0.4873 2003 36 26 18.55 0.0044 0.0108 20036 37 26 18.55 0.064 0.1565 20037 38 0 0 0.1053 0.123 20038 39 24 17 0.0304 0.0355 20039 40 24 17 0.0018 0.0021 20040 41 1.2 1 0.7283 0.8509 20041 42 0 0 0.31 0.3623 20042 43 6 4.3 0.041 0.0478 20043 44 0 0 0.0092 0.0116 20044 45 39.22 26.3 0.1089 0.1373 20045 46 39.22 26.3 0.0009 0.0012 2004 47 0 0 0.0034 0.0084 30047 48 79 56.4 0.0851 0.2083 30048 49 384.7 274.5 0.2898 0.7091 30049 50 384.7 274.5 0.0822 0.2011 3008 51 40.5 28.3 0.0928 0.0473 20051 52 3.6 2.7 0.331 0.1114 2009 53 4.35 3.5 0.174 0.0886 30053 54 26.4 19 0.203 0.1034 30054 55 24 17.2 0.2842 0.1447 30055 56 0 0 0.2813 0.1433 30056 57 0 0 1.59 0.5337 30057 58 0 0 0.7837 0.263 30058 59 100 72 0.3042 0.1006 30059 60 0 0 0.3861 0.1172 30060 61 1244 888 0.5075 0.2585 30061 62 32 23 0.0974 0.0496 30062 63 0 0 0.145 0.0738 30063 64 227 162 0.7105 0.3619 30064 65 59 42 1.041 0.5302 30011 66 18 13 0.2012 0.0611 20066 67 18 13 0.0047 0.0014 20012 68 28 20 0.7394 0.2444 20068 69 28 20 0.0047 0.0016 200

Imax is maximum line current limit in Amperes, SB ¼ 100 MVA, VB ¼ 12.66 kV.

M.M. Aman et al. / Energy 66 (2014) 202e215 215

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