Research Article Gravitational Search Algorithm and ...downloads.hindawi.com/journals/jam/2015/894758.pdfResearch Article Gravitational Search Algorithm and Selection Approach for

Research ArticleGravitational Search Algorithm and Selection Approach forOptimal Distribution Network Configuration Based on DailyPhotovoltaic and Loading Variation

Koong Gia Ing1 H Mokhlis12 H A Illias12 M M Aman1 and J J Jamian3

1Department of Electrical Engineering Faculty of Engineering University of Malaya 50603 Kuala Lumpur Malaysia2University of Malaya Power Energy Dedicated Advanced Centre (UMPEDAC) Level 4 Wisma RampD UMJalan Pantai Baharu University of Malaya 59990 Kuala Lumpur Malaysia3Faculty of Electrical Engineering Universiti Teknologi Malaysia 81310 Johor Bahru Johor Malaysia

Correspondence should be addressed to H Mokhlis hazliumedumy

Received 13 March 2015 Revised 14 June 2015 Accepted 21 June 2015

Academic Editor Mengqi Hu

Copyright copy 2015 Koong Gia Ing et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Network reconfiguration is an effective approach to reduce the power losses in distribution system Recent studies have shown thatthe reconfiguration problem considering load profiles can give a significant improvement on the distribution network performanceThis work proposes a novel method to determine the optimal daily configuration based on variable photovoltaic (PV) generationoutput and the load profile data A good combination and coordination between these two varying data may give the lowestpower loss in the system Gravitational Search Algorithm (GSA) is applied to determine the optimum tie switches positions for33-Bus distribution system GSA based proposed method is also compared with Evolutionary Programming (EP) to examine theeffectiveness of GSA algorithm Obtained results show that the proposed optimal daily configuration method is able to improvethe distribution network performance in term of its power loss reduction number of switching minimization and voltage profileimprovement

1 Introduction

Over the last few decades the power loss of distributionsystem has raised attention of researchers to increase theefficiency of the existing network Different researchers haveproposed different approaches for minimization of powersystem losses [1] One of the common approaches is throughnetwork reconfiguration

Network reconfiguration is defined as altering the topo-logical structures of the distribution feeders by changing theposition of tie and sectionalizing switches however undernormal operation medium voltage distribution networksoperate in radial manner [2 3] During normal conditionnetwork reconfiguration is used to improve the power qualitymaintain the voltage stability and reduce power loss whilefor fault condition it is used for service restoration Oncethe source of fault is removed by opening all the switchessurrounding the affected portions the service can be restoredwithin a very short time

In the past various algorithms have been proposed fornetwork reconfiguration Merlin and Back were the pioneersin proposing network reconfiguration as a tool for power lossreduction [4] in 1975 The network reconfiguration problemwas solved by closing all tie switches in the system (resultingin mesh network) then the switches are successively openedone at a time until a new radial networkwithminimumpowerlosses is obtained Later on Shirmohammadi and Hongimproved the Merlin method by avoiding the approximationmade in [4] Shirmohammadi theorem starts by closingall tie switches which are then opened by anther basedon optimum power flow results [5] This method was alsofound efficient in terms of computation time as comparedto Merlin method Reference [2] introduced the ldquofeederexchange approachrdquo and calculated the loss reduction due toload transfer between two feeders A year later Baran andWu improved the branch exchange method [2] by proposingtwo approximated power flow equations and solved theproblem of lossminimization and loss reduction as an integer

Hindawi Publishing CorporationJournal of Applied MathematicsVolume 2015 Article ID 894758 11 pageshttpdxdoiorg1011552015894758

2 Journal of Applied Mathematics

programming problem [6] In the same year Lin and Chin[7] have considered service restoration in addition to lossminimization in solving network reconfiguration problemZhu et al performed the network reconfiguration based onmodified heuristic solution and experience system operationrules [8] In a latest research Mohd Zin et al in [9] have usedthe heuristic search algorithm to find the minimum powerlosses as an objective function introduced by the authorin [6] The update principle of heuristic search is made byfinding the branch having minimal current till the optimumsolution is obtained

Most of the methods discussed above require exhaustivesearch mechanism by considering all possible solutions froma predetermined set and subsequently pick the best oneHowever such methods are considered as nonefficient interms of computation time and space requirement Intelli-gent greedy and nature observed heuristic techniques havealso been proposed in the literature and they are commonlyknown as Artificial Intelligent (AI) methods [10] ArtificialIntelligent methods are a special class of heuristic searchmethods [10] Intelligent based optimization methods havealso been utilized in finding optimum tie switch combina-tions in network reconfiguration problem Authors have usedGenetic Algorithms (GA) [11] fuzzy [12ndash14] neural network[15 16] fuzzy-GA [17] Particle Swarm Optimization (PSO)[18] Matroid Theory [19] Hybrid Evolutionary algorithm[20] Ant Colony Search (ACS) algorithm [21 22] HarmonySearch Algorithm [23] and Bacterial Foraging Algorithm[24] Das [12] and Savier and Das [25] have proposedfuzzy based multiobjective approach for loss reduction andconsidered voltage limit and line limits as well in fuzzyset Penalty based multiobjective-single-fitness approacheshave been utilized in [21] to combine power losses withsystem constraints including voltage limits and line limitThemultiobjective problem is solved using ACS algorithm

Besides network reconfiguration Distributed Generation(DG) such as minihydro photovoltaic and wind is installedin distribution system to solve the power loss problem dueto voltage drop However the placement and size of DGare essential as they have a great impact on the power loss[26] Many researchers have proposed different methodsfor optimum DG location and size separately [26ndash28] orsimultaneously [29 30] However all the aforementionedworks have considered a constant load and fixed DG outputIn practical load pattern and DG generation output dynam-ically change with time Therefore some studies have alsoconsidered a variable load pattern in their researches Forexample a gradual approaching method is proposed in [31]to solve dynamic reconfiguration In [32] researchers solvedthe network reconfiguration problemwith daily variable loadimplementation as well These studies have proven that thenetwork performance was improved when the time-varyingload profiles were taken into consideration

Apart from that there are few works on network recon-figuration with the presence of DG considering variableload profile For example network reconfiguration with thepresence of wind and photovoltaic generation for total dailypower loss reduction using improved genetic algorithm isproposed in [33] Network reconfiguration with photovoltaic

generation for power loss reduction considering the DGpenetration and three different load levels is presented in [34]

In this work a novel method is proposed to solvethe network reconfiguration problem based on daily PVgeneration output and variable load profiles GravitationalSearch Algorithm (GSA) proposed in [35] is used in thispaper to determine the best daily system configurationThe proposed method can be viewed in two parts In thefirst part hourly optimal configuration considering the PVgeneration and load profile is carried out using GSA Inthe second part a selective approach is used to determinethe best configuration that gives the lowest power loss forthe whole day (24 hrs) or optimal daily configuration Theproposed method is implemented on 33-bus distributionsystemThe proposed method results are also compared withEvolutionary Programming (EP) to show the effectiveness ofGSA

This paper is organized as follows In Section 2 mathe-matical model for network reconfiguration is described Theproposedmethod including application of GSA and selectionapproach is provided in Section 3 Selection of PV moduleis presented in Section 4 while load modelling and PVgeneration are presented in Section 5 In Section 6 analysisof the performance of the proposed method is discussedFinally the conclusions are presented in Section 7

2 Mathematical Model for DistributionNetwork Reconfiguration Problem

Network reconfiguration is used tominimize the distributionsystem power loss The new configuration selected mustfulfil the constraints and maintain the radial structure of thedistribution system In this study themain objective is to gainminimum power loss of the distribution system Thus theobjective function can be formulated as follows

Min

119875loss =119879

sumℎ

119873

sum119891=1

10038161003816100381610038161003816119868119891100381610038161003816100381610038162

119897119891119877119891

(1)

where119873 is total line in the system 119868119891is real active current of

line 119891 119877119891is resistance of line 119891 119891 is line number 119897

119891is the

topology status of line 119891 (1 = close 0 = open)119879 is the total hour considered in the time frame and ℎ

is the current time considered In this work (1) is used toanalyse the power loss for every hour (ℎ) of a day with theload data of hour (ℎ) and PV generation of hour (ℎ)

The power system constraints that are also being consid-ered in the study are as follows

(a) Voltage Bus Constraint The value of the bus voltage 119881busat each nodemust be within the acceptable limits to maintainthe power quality For example in this work the minimumvoltage (119881min) used is 095 pu and maximum voltage (119881max)is 105 pu

119881min lt 119881bus lt 119881max (2)

Journal of Applied Mathematics 3

(b) Radial Configuration Constraint The radial configurationof the network must be maintained after the reconfigurationprocess In order to ensure this requirement graph theory isused to determine the radiality of the network In this work aMATLAB function is used to check the radiality of a networkas follows

TF = graphisspantree (119866) (3)

where119866 is the distribution system If the network is radial TFequals 1 (true) else it is 0 (false) A radial distribution systemmust connect all the buses and it contains no loop In orderto maintain the radial structure of the distribution system anetwork with loop form one of the switches from that loopmust be opened to retain the radial structure

There are several methods for radial power flow analysissuch as backward-forward method However in this workthe proposed method uses Newton-Raphson load flow forpower flow analysis to calculate the power lossThis load flowis selected to avoid fussy requirements on radial structureand prevent complicated computation [36] It can handle theDG in the calculation more effectively as compared to otherdistribution load flow methods Furthermore this methodprovides high convergence with low storage required whichcan be easily applied with any metaheuristic optimizationmethod

The real power of bus 119891 119875119891 reactive power of bus 119891 119876

119891

the differences in real power Δ119875119891 the differences in reactive

power Δ119876119891 rectangular Newton-Raphson and power loss

can be computed as

119875119891=119873

sum119896=1

10038161003816100381610038161003816119881119891100381610038161003816100381610038161003816100381610038161003816119881119896

100381610038161003816100381610038161003816100381610038161003816119884119891119896

10038161003816100381610038161003816 cos (120579119891119896 minus 120575119891+ 120575119896) (4)

119876119891=119873

sum119896=1

10038161003816100381610038161003816119881119891100381610038161003816100381610038161003816100381610038161003816119881119896

100381610038161003816100381610038161003816100381610038161003816119884119891119896

10038161003816100381610038161003816 sin (120579119891119896 minus 120575119891+ 120575119896) (5)

Δ119875119891= 119875sp119891

minus 119875119891 (6)

Δ119876119891= 119876sp119891minus 119876119891 (7)

[Δ119875

Δ119876] =

[[[[

[

120597119875120597120575

120597119875120597119881

120597119876120597120575

120597119876120597119881

]]]]

]

[Δ120597

Δ |119881|] (8)

119875loss =119873

sum119891=1

119860119891119896

(119875119891119875119896+ 119876119891119876119896)

+ 119861119891119896

(119876119891119875119896minus 119875119891119876119896)

(9)

119860119891119896

=119877119891119896

cos (120575119891minus 120575119896)

119881119891119881119896

(10)

119861119891119896

=119877119891119896

sin (120575119891minus 120575119896)

119881119891119881119896

(11)

End

Start

Create configuration and corresponding power loss matrix

Find the nonsimilar effective configurations

Compute total power losses for all nonsimilar effective configurations

Select the optimal daily configuration from the evaluation

Part

2

Sele

ctio

n pa

rtPa

rt 1

GSA

Obtain ldquohrdquo hour configuration

Figure 1 Flowchart of the proposed method

where 119881119891and 119881

119896are voltage magnitude of bus 119891 and bus

119896 respectively 119884119891119896

and 120579119891119896

are magnitude and angel of 119884119891119896

element in the bus admittance matrix respectively 120575119891and 120575119896

are voltage angel of bus 119891 and bus 119896 respectively 119875sp119891and119876sp

119891

are specified real and reactive power at bus 119891 respectively 119875119896

and 119876119896are real and reactive power of bus 119896 respectively and

119877119891119896

is line resistance between bus 119891 and bus 119896

3 Proposed Method

The proposed method for finding the best configurationbased on daily PV generation and load profiles is presentedin this section The proposed algorithm consists of two mainparts as shown in Figure 1 In the first part a day is dividedinto ℎ hours where ℎ equals 24 hours in this work UsingGSA and graph theory optimal configuration is obtained foreach hour while the distribution network is maintained to beradial Hence a total of ℎ effective configurations are obtainedfor the network In part two the optimal daily configurationis obtained with a selective approach

Part 1 Finding Effective Configuration Using GravitationalSearch Algorithm (GSA) Gravitational Search Algorithm(GSA) is first introduced by Rashedi et al in [35] GSA isthe newest stochastic search algorithm which is based onNewtonian laws and mass interactions In this algorithmthe population individuals are referred to as masses andtheir performances are measured by their position massesEach mass will have four particulars its position its inertialmass its active gravitational mass and passive gravitationalmass The position of the mass represented a solution whileits gravitational and inertial masses are corresponding tothe fitness function According to Newtonian laws all theseobjects will attract each other due to the gravity force Due to


this force all these objects will move towards the object withheavier mass In other words heavy masses equaled goodsolutions and they move slower than the lighter masses thatequaled bad solutions In this way the exploitation step of thealgorithm is guaranteed

The details of the proposed method to reduce power lossare based on the following steps

Step 1 (input data and parameters) Input data are insertedin the program This includes bus data line data PV outputbase MVA base voltage predefined voltage bus range radialconfiguration constraint maximum iteration and accuracyThe parameter needed to be set in GSA is the number ofmasses (119873mass)

Step 2 (generating initial masses) The initial population isdetermined by selecting random switches to be opened inthe distribution network to form the masses The number ofswitches to be opened is 119873opened The set of switches to beopened is written as follows

Mass119894= lfloor11987811 11987822 119878119889

119873openedrfloor for 119894 = 1 2 119873mass (12)

where Mass119894represents the position of 119894th mass in the 119889th

dimension or 119889th component in 119894th mass 11987811 11987822 and 119878119889

119873opened

are the switches to be opened in 119889th dimension Only theset of switches to be opened that satisfy all the constraintswill be generated as the mass At the end of this step all theelements in the masses for network reconfiguration are thenconverted to whole number by rounding the decimal numberto the nearest positive number

Step 3 (evaluate fitness of each mass) In the fitness functionpower loss is calculated in the current mass population usingNewton-Raphson load flow analysis

Step 4 (update gravitational constant best mass worst massand inertia mass of each iteration) In order to control thesearching accuracy the gravitational constant119866 is initializedat the beginning and is reduced with iteration Hencegravitational constant 119866 is a function of initial value ofgravitational constant 119866

119900 and iteration iter as follows

119866 (iter) = 119866119900ℓminus120572(itermax iter) (13)

where 120572 is a user specified constant iter is the currentiteration and max iter is the total number of iterations

The active gravitational mass 119872119886 passive gravitational

mass 119872119901 and inertial mass of mass 119894 119872

119894119894 are computed

using fitness evaluation According to Newtonrsquos law and lawof motion a heavier mass has higher attractions and movemore slowly Hence in GSA a heavier mass is represented asgood solution and the pattern of movement is represented bythe explorations The inertia mass 119872

119894 is updated as follows

by assuming all masses are equal

119872119886119894= 119872119901119894= 119872119894119894= 119872119894

119898119894 (iter) =

fit119894 (iter) minus worst (iter)

best (iter) minus worst (iter)

119872119894 (iter) =

119898119894 (iter)

sum119873mass119895=1

119898119895 (iter)

(14)

where fit119894(iter) represents the power loss of the mass 119894 at

iteration iter and best(iter) and worst(iter) represent thestrongest and weakest masses with respect to the lowestand highest power losses in current iteration The mass 119895 ofcurrent iteration is represented as119898

119895(iter) For minimization

problem the best(iter) and worst(iter) are defined as

best (iter) = min119895isin1119873ma

fit119895 (iter)

worst (iter) = max119895isin1119873mass

fit119895 (iter)

(15)

Step 5 (calculation of the total force in different directions)The gravitational force 119865

119894119895 of mass 119894 due to mass 119895 at current

iteration iter can be computed as follows

119865119894119895 (iter) = 119866 (iter)

119872119894 (iter) times 119872

119895 (iter)119877119894119895 (iter) + 120576

(Mass119895 (iter)

minusMass119894 (iter))

(16)

where 119872119894is the inertial mass of the mass 119894 119872

119895is the

inertial mass of mass 119895 120576 is a small constant and 119877119894119895(iter)

is the Euclidian distance between 119894 and 119895 masses specified asfollows

119877119894119895 (iter) =

10038171003817100381710038171003817Mass119894 (iter) Mass

119895 (iter)100381710038171003817100381710038172 (17)

Step 6 (calculation of acceleration and velocity) The acceler-ation of the mass 119894 at current iteration iter in 119889th dimensionand 119886119889119894(iter) is defined as follows

119886119889119894(iter) =

119865119889119894(iter)

119872119894119894 (iter)

(18)

where 119865119889119894(iter) is the total force that acts on mass 119894 of 119889th

dimension and is calculated as follows

119865119889119894(iter) =

119873mass

sum119895isin119896best 119895 =119894

rand119895119865119889119894119895(iter) (19)

The random number between interval [0 1] rand119895is intro-

duced in GSA In order to compromise between explorationand exploitation in this algorithm the exploration must fadeout and exploitation must fade in with lapse of iterationsIn other words all masses apply force to each other in thebeginning and only onemass applies force to others in the endof the algorithm Based on the aforementioned concept119870besta function of iteration which is the set of first 119870masses withthe lowest power loss and biggest mass is introduced to thisalgorithm119870o the initial value of119870best is set at the beginninganddecreasedwith iterationsThus119870best is decreased linearlywith iterations as well In this way a smaller value of119870best willresult in less interaction between the masses by gravitationalforce Hence themovement and computational of power loss


are reduced and lead to convergence [37]The next velocity ofa mass is given as follows

V119889119894(iter + 1) = rand

119894times V119889119894(iter) + 119886119889

119894(iter) (20)

Step 7 (update massesrsquo position) The next position of a masscan be expressed as follows

Mass119889119894(iter + 1) = Mass119889

119894(iter) + V119889

119894(iter + 1) (21)

Step 8 (convergence) Steps 3 to 8 are repeated until thestopping criterion is reached

Step 9 (matrix of ℎ feasible configurations) Amatrix consistsof ℎ feasible configuration and its power loss is created Eachconfiguration consists of 119873opened switch to be opened whichdepends on the chosen test systemConfiguration ℎ is the bestconfiguration with the minimum power loss at hour ℎ Forexample configuration 1 is the best configuration at 0100 andso on as illustrated in

1198781

1198782

1198783

sdot sdot sdot 119878119873opened

Power loss for ℎ hour

Configuration 1Configuration 2

Configuration ℎ

[[[[[[

[

11987811

11987821

119878ℎ1

11987812

11987822

119878ℎ2

11987813

11987823

119878ℎ3

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

1198781119873opened

1198782119873opened

119878ℎ119873opened

119875loss1199041119875loss1199042

119875loss119904ℎ

]]]]]]

]

(22)

Part 2 A Selective Approach for Optimal Daily ConfigurationIn the steps above 119873

119911number of configurations will be

obtained for total time 119879 Since most of the PV generationsand the load of certain ℎ hour in total time 119879 are approxi-mately the same most of the obtained configurations in (22)are similar The similar configurations 119873similar are removedfrom the matrix Hence only the nonsimilar effective con-figurations are left in the matrix119873left (119873119911 minus 119873similar = 119873left)

The first nonsimilar effective configuration in the matrixrepresents the set switch 1 and so forth until the lastnonsimilar effective configuration and set switch 119910 Hence amatrix consists of all nonsimilar effective configurations andis obtained as illustrated in

Power loss for each set switch at ℎ hour

Set Switch 1Set Switch 2

Set Switch 119910

[[[[[[[

[

1198831

1198832

119883119910

]]]]]]]

]

119875loss1198831119875loss1198832

119875loss119883119910

(23)

Each set switch obtained in Part 2 is used to calculate thetotal power loss for a day using Newton-Raphson load flowanalysis Then the total daily power losses of the distributionsystem for all sets of the switch are obtained and the switchset with the minimum total daily power loss is selected as theoptimum configuration of the day as illustrated in

Set switch Total daily power loss

[[[[[[[

[

1198831

1198832

119883119910

TotDaily119875loss1198831TotDaily119875loss1198832

TotDaily119875loss119883119910

]]]]]]]

]

(24)

where optimal daily configuration = min(TotDaily119875loss)

4 Selection of PV Module

ThePVgeneration in this study is dependent on the solar irra-diance and ambient temperature ofMalaysianMeteorologicalDepartment for year 2008 at Kuantan siteThe capacity factor(CF) is calculated using four PVmodules from [38] based onthe solar irradiance mentioned as above for a day As shownin Figure 2 module D has the highest CF (02223) thereforemodule D is selected for this study The PV output for 10000units and each ℎ time interval are calculated using (8) to (12)The PV generation is shown in Figure 3

119879CZ (ℎ) = 119879119886+ 119904az (ℎ119903) (

119873OT (module) minus 2008

)

119868119885 (ℎ) = 119904az (ℎ)

sdot [119868SC (module) + 119870119894 (module) (119879CZ (ℎ) minus 25)]


0

01

02

03

A B C D

CF

PV module

Figure 2 CF of the PV module

0

02

04

06

08

1

12

minus01

01

03

05

07

09

1 3 5 7 9 11 13 15 17 19 21 23

Load

pro

file (

pu)

PV g

ener

atio

n (M

W)

Hour

PV generationLoad profile

Figure 3 PV generation and load profile of a day

119881119885 (ℎ) = 119881OC (module) minus (119870

119881 (module) times 119879CZ (ℎ))

FF (module) =(119881MPP (module) times 119868MPP (module))119881OC (module) times 119868SC (module)

119875Sz (ℎ) = 119873PV times FF (module) times 119881119885 (ℎ) times 119868

119885 (ℎ)

(25)

where 119879CZ(ℎ) is cell temperature [∘C] during ℎ current time119879119886is ambient temperature [∘C] 119870

119881(module) is voltage tem-

perature coefficient of the PV module [V∘C] 119870119894(module) is

current temperature of the PVmodule [A∘C]119873OT(module)is nominal operating temperature of cell of the PV module[∘C] FF(module) is fill factor of the PVmodule 119868SC(module)is short circuit current of the PV module [A] 119881OC(module)is open circuit voltage of the PV module [V] 119868MPP(module)is current at maximum power point of the PV module [A]119881MPP(module) is voltage at maximum power point of the PVmodule [V]119875SZ(ℎ) is output generation of PVmodule duringℎ current time and 119904az(ℎ) is average solar irradiance during ℎcurrent time

5 Load Modelling and PV Generation

The load profiles were received fromTenaga Nasional Berhad(TNB) [39] as shown in Figure 3 This study provides hourlypeak load per unit of the daily peak load

6 Analysis of Proposed Method

The test system for this study consists of 1266 kV 33-busradial distribution The single line diagram of the system isshown in Figure 2 The system consists of three DGs fivelabelled tie switches 32 unlabelled sectionalizing switchesand 33 labelled buses The line between bus 1 and bus 2 isreferred to as switch 1 line between bus 2 and bus 3 is referredto as switch 2 and so forth until switch 32Thefive tie switchesare referred to as switches 33 34 35 36 and 37 as shownin Figure 4 The line and load data are taken from [6] Foranalysis purpose theDGs are assumed to be installed at buses6 18 and 22 However the locations can be changed based onthe actual site data or using other placement methods such asin [29]The parameters of GSA used in the simulation are setto 119873mass = 100 max iter = 100 and 119866

0= sum of all active

power in the system and 120572 = 10 The simulations are carriedout on a computer with Intel Duo Core 30GHz and 30GBRAM

The 119878base equals 100MVA and all the calculations areperformed per unit In the simulation of the network fourscenarios were considered to analyse the capability of theproposed method They are as follows

Scenario 1 The system is without reconfiguration and varia-tion of the load and PV generation are considered

Scenario 2 The system is with optimal hourly reconfigu-ration and variation of the load and PV generation areconsidered

Scenario 3 The system is with optimal daily configurationobtained from the proposed method

Scenario 4 The system is with optimal daily configurationobtained by considering 24 demand levels and PV generationas whole

The results of a matrix consist of ℎ feasible configurationsand their power loss obtained in Part 1 of the study isshown in Table 4 The highlighted configurations in Table 4represent repeated configurations that will be removed inselection approach in Part 2 to obtain the nonsimilar effectiveconfigurations matrix in Part 2 The remaining are the non-imilar effective configurations The results of nonsimilareffective configurations matrix in Part 2 of the study areshown in Table 5

Then for each set of the switch in Table 5 their total dailypower loss is obtained by carrying out Newton-Raphson loadflow analysisThe results of the total power loss evaluation forall sets switch obtained in Part 2 are shown in Table 1

From Table 1 the total daily power loss of set switch19 which is represented with lowast is the lowest among the20 sets switch Even set switch 16 with the lowest powerloss at 1300 does not yield the lowest total daily powerlosses Hence set switch 19 is chosen as the optimal dailyconfiguration which is the best configuration for the dayThe real results of the four scenarios are summarised inTable 2 The proposed method is carried out using EP forthese four scenarios as well as for comparison as shown in


26 33323130292827

Mai

nsu

bsta

tion

23 2524

1 32 4 65 12 181716151413

19 222120

DG

7 8 9 10 11

DG

DG

Figure 4 33-bus test system with DG at buses 6 18 and 22

Table 1 Results of total power loss evaluation for all sets switch obtained in Part 2

Set switch 1 2 3 4 5 6 7 8 9 10Total dailypower loss (kW) 272430 277007 263854 275283 296039 256408 221949 290931 237565 214908

Set switch 11 12 13 14 15 16 17 18 19lowast 20Total dailypower loss (kW) 224901 230323 233055 320201 208832 225625 272187 225625 207551 247359

Table 2 EP is selected for comparison since it is a commonand well-established optimization methodThe optimal dailyconfiguration obtained in Scenario 4 is 37 10 7 13 and 17withGSA and 6 8 17 10 and 5 with EP

From Table 2 the total daily power loss is reduced by5036 in Scenario 2 4840 in Scenario 3 and 4802in Scenario 4 using GSA as optimizing tool and 4477 inScenario 2 4197 in Scenario 3 and 4100 in Scenario4 using EP as optimizing tool compared with Scenario 1with same load profile and PV generation The total dailypower loss reduction using Scenario 2 is 196 (GSA) and280 (EP) more compared with Scenario 3 and 234(GSA) and 377 (EP) more compared with Scenario 4However no switching is required for Scenarios 3 and 4For example 24 times switching are requested in Scenario2 while no switching is requested in Scenarios 3 and 4Scenarios 3 and 4 far outweigh Scenario 2 with an acceptabletotal power loss reduction less than Scenario 2 Apart fromthat Scenario 3 gives slightly higher total daily power lossreduction compared with Scenario 4 This is because moreconstraints need to be consideredwhen 24 demand levels andPV generation are considered as whole Hence this limitedthe solution options

The DG installation location and number are assumed inthis work Altering DG installation location and number willautomatically effect the power loss The performance of theproposed method is not affected since the algorithm still thesame just altering the load data In other words more powerloss can be reduced with optimal DG installation locationand number for a distribution network An optimal daily

configuration still can be obtainedwith the proposedmethodSimilarly for different type of DG with their typical outputgeneration

The performance of Scenario 2 is reduced when changingthe hour slots from 1 hour to 2 hours or 4 hours and soforth In this case lower total daily power loss is obtainedin Scenario 3 compared to Scenario 2 if the hour slot isincreased The total daily power loss for Scenarios 2 and 3and optimal daily configuration obtained from Scenario 3 forhour slots of one two and four are presented in Table 3 It canbe noticed that the total daily power loss in Scenario 3 is lessthan Scenario 2 for two- and four-hour slots However theseresults are the optimal results since the load demand and PVgeneration are changing with time Therefore the analysis inthis work is carried out based on hourly basis

From this analysis it clearly shows that the proposedmethod is effective to determine optimal daily configura-tion based on PV generation and load profiles for a dayApart from that GSA with selection approach gives thebest solution compared with EP with selection approachFigure 5 illustrates the optimal configuration obtained fromthe proposed method

The voltage profiles for all scenarios are shown inFigure 6 All the scenarios show the similar shape of thevoltage profiles with slight change in the magnitude Theproposedmethod also improves the overall voltage profiles ofthe distribution system besides generating lower power loss

From Figure 6 all bus voltages in Scenario 1 are belowthe 095 pu voltage constraint in a day Although all the busvoltages satisfy the minimum voltage constraint only from


Table 2 Comparison of the total daily power loss among the four scenarios

Scenario 1 (withoutreconfiguration)

Scenario 2 (with optimalhourly reconfiguration)

Scenario 3 (withproposed method)

Scenario 4 (with optimaldaily configuration of 24demand levels as whole)

GSA and selection approachTotal daily power loss(kW) 402230 199658 207551 209078

EP and selection approachTotal daily power loss(kW) 402230 222152 233428 237317

26 33323130292827

23 2524

1 32 4 65 12 181716151413

19 222120

DG

DG

DG

7 8 9 10 11

Mai

nsu

bsta

tion

Figure 5 Optimal daily configuration

Table 3 Comparison of the total daily power loss among one twoand four hoursrsquo slots

Hour slots(hr) Scenario 2 Scenario 3

Optimal dailyconfiguration in

Scenario 31 199658 207551 28 14 7 17 102 220475 208897 31 6 37 34 104 213267 209909 28 10 7 17 13

time 0200 to 1800 the overall voltage profiles are improvedclearly for all the buses in Scenarios 2 3 and 4 The voltageprofiles at time 1800 for all the buses for Scenarios 1 2 3 and4 are shown in Figure 7

FromFigure 7 it can be seen that at time 1800 the voltageprofiles for Scenarios 1 2 3 and 4 are almost the same forall buses Scenarios 2 3 and 4 improve the voltage profilesof all the buses and the voltages are within acceptable rangeespecially for buses 28 to 33This implies that reconfigurationconsidering PV generation and load profiles yields desiredresults of minimizing the power loss reducing the numberof switching and improving the voltage profiles MeanwhileFigure 8 shows the ability of the GSA with proposed methodin finding the optimum configuration at times 0100 0800and 1800 which required less than 10 numbers of iterationsto reach the optimal point It is to note that the large the

09091092093094095096097098

1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Volta

ge p

rofil

es (p

u)

Time of a day

Min voltage for Scenario 1 Min voltage for Scenario 2Min voltage for Scenario 3 Min voltage for Scenario 4

Figure 6 Performance of voltage profile for all scenarios of a day

number of iterations the longer computing time requiredas the iteration is counted based on the fixed looping inprogramming Thus in this work the number of iterationsis set to 100

7 Conclusion

In this work a novel method to determine the best config-uration based on the daily PV generation and load profilesin the distribution network has been successfully proposedExperimental results indicate that the proposed method is


Table 4 Results of matrix consists of ℎ feasible configurations andtheir power loss obtained in Part 1

Currenttime (h) 119878

11198782

1198783

1198784

1198785

Power lossesfor ℎ hour(kW)

01 11 7 27 32 14 885602 11 7 28 14 36 800803 28 14 33 9 32 753904 28 9 33 32 14 713105 9 34 37 32 7 707406 32 28 34 7 11 716507 33 36 10 28 34 712108 37 34 9 32 7 707309 37 17 9 14 7 756310 21 31 37 7 13 704111 11 14 30 7 28 700112 8 33 28 13 16 702213 10 7 37 30 14 571714 37 9 30 7 13 623015 37 7 30 10 13 672816 21 34 31 37 7 831717 14 11 7 28 17 869218 10 7 37 14 31 791919 7 11 34 32 28 980120 10 7 14 27 32 1261421 10 37 31 14 7 1238022 28 14 7 17 10 1184223 9 14 28 32 33 1084524 7 37 13 32 9 9978

Total daily power losses for Scenario 2 199658

093094095096097098099

1101

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33Bus number

Voltage for Scenario 1 at 1800 Voltage for Scenario 2 at 1800Voltage for Scenario 3 at 1800 Voltage for Scenario 4 at 1800

Volta

ge p

rofil

es (p

u)

Figure 7 Voltage profiles for all buses for all scenarios with load andPV generation at 1800

simple and effective to minimize total daily power loss withno switching required with the optimal daily configurationobtained Hence same method can be applied for a yearIt also improves the voltage profiles A 33-bus distribu-tion system with three photovoltaic DGs different sets ofPV generation and load profiles are successfully used to

Table 5 Results of nonsimilar effective configurations matrixobtained in Part 2

1198781

1198782

1198783

1198784

1198785

Set switch 1 11 7 27 32 14Set switch 2 11 7 28 14 36Set switch 3 28 9 33 32 14Set switch 4 32 28 34 7 11Set switch 5 33 36 10 28 34Set switch 6 37 34 9 32 7Set switch 7 37 17 9 14 7Set switch 8 21 31 37 7 13Set switch 9 11 14 30 7 28Set switch 10 8 33 28 13 16Set switch 11 10 7 37 30 14Set switch 12 37 9 30 7 13Set switch 13 37 7 30 10 13Set switch 14 21 34 31 37 7Set switch 15 14 11 7 28 17Set switch 16 10 7 37 14 31Set switch 17 10 7 14 27 32Set switch 18 10 37 31 14 7Set switch 19 28 14 7 17 10Set switch 20 7 37 13 32 9

6065707580859095

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Pow

er lo

ss (k

W)

Iteration

Power loss obtained Power loss obtained

Power loss obtainedat time 0100 at time 0800

at time 1800

Figure 8 Convergence performance of GSAwith proposedmethodat selected time of a day

demonstrate the effectiveness of the proposed method Acomparison between GSA and EP with selection approachis carried out and the result proven GSA outperforms EP interms of producing lower total daily power loss

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors thank the University of Malaya and MalaysianMinistry of Education (MOE) for supporting this workthrough High Impact Research Grant (HIR-MOHE


D000004-16001) and Universiti Teknologi Malaysia(QJ130000272300K88)

References

[1] S Kalambe and G Agnihotri ldquoLoss minimization techniquesused in distribution network bibliographical surveyrdquo Renew-able and Sustainable Energy Reviews vol 29 pp 184ndash200 2014

[2] S Civanlar J J Grainger H Yin and S S H Lee ldquoDistributionfeeder reconfiguration for loss reductionrdquo IEEE Transactions onPower Delivery vol 3 no 3 pp 1217ndash1223 1988

[3] A Gonzalez F M Echavarren L Rouco T Gomez and JCabetas ldquoReconfiguration of large-scale distribution networksfor planning studiesrdquo International Journal of Electrical Power ampEnergy Systems vol 37 no 1 pp 86ndash94 2012

[4] A Merlin and H Back ldquoSearch for a minimal-loss operatingspanning tree configuration in an urban power distributionsystemrdquo in Proceedings of the 5th Power System Conference(PSCC rsquo75) Cambridge UK 1975

[5] D Shirmohammadi and H W Hong ldquoReconfiguration ofelectric distribution networks for resistive life losses reductionrdquoIEEE Transactions on Power Delivery vol 4 no 2 pp 1492ndash1498 1992

[6] M E Baran and F F Wu ldquoNetwork reconfiguration in distri-bution systems for loss reduction and load balancingrdquo IEEETransactions on Power Delivery vol 4 no 2 pp 1401ndash1407 1989

[7] W-M Lin and H-C Chin ldquoA new approach for distributionfeeder reconfiguration for loss reduction and service restora-tionrdquo IEEE Transactions on Power Delivery vol 13 no 3 pp870ndash875 1998

[8] J Zhu X Xiong J Zhang G Shen Q Xu and Y Xue ldquoA rulebased comprehensive approach for reconfiguration of electricaldistribution networkrdquo Electric Power Systems Research vol 79no 2 pp 311ndash315 2009

[9] A A Mohd Zin A K Ferdavani A B Khairuddin andM M Naeini ldquoReconfiguration of radial electrical distribu-tion network through minimum-current circular-updating-mechanism methodrdquo IEEE Transactions on Power Systems vol27 no 2 pp 968ndash974 2012

[10] N Kokash An Introduction to Heuristic Algorithms Depart-ment of Informatics and Telecommunications 2005

[11] J Z Zhu ldquoOptimal reconfiguration of electrical distributionnetwork using the refined genetic algorithmrdquo Electric PowerSystems Research vol 62 no 1 pp 37ndash42 2002

[12] D Das ldquoA fuzzy multiobjective approach for network recon-figuration of distribution systemsrdquo IEEE Transactions on PowerDelivery vol 21 no 1 pp 202ndash209 2006

[13] Y Song G Wan A Johns and P Wang ldquoDistribution networkreconfiguration for loss reduction using fuzzy controlled evo-lutionary programmingrdquo IEE ProceedingsmdashGeneration Trans-mission and Distribution vol 144 no 4 pp 345ndash350 1997

[14] J S Savier and D Das ldquoImpact of network reconfiguration onloss allocation of radial distribution systemsrdquo IEEETransactionson Power Delivery vol 22 no 4 pp 2473ndash2480 2007

[15] H Kim Y Ko and K-H Jung ldquoArtificial neural-networkbased feeder reconfiguration for loss reduction in distributionsystemsrdquo IEEE Transactions on Power Delivery vol 8 no 3 pp1356ndash1366 1993

[16] M A Kashem G B Jasmon A Mohamed and MMoghavvemi ldquoArtificial neural network approach to networkreconfiguration for lossminimization in distribution networksrdquo

International Journal of Electrical Power and Energy Systemsvol 20 no 4 pp 247ndash258 1998

[17] K Prasad R Ranjan N C Sahoo and A Chaturvedi ldquoOptimalreconfiguration of radial distribution systems using a fuzzymutated genetic algorithmrdquo IEEE Transactions on Power Deliv-ery vol 20 no 2 I pp 1211ndash1213 2005

[18] M Assadian M M Farsangi and H Nezamabadi-PourldquoGCPSO in cooperation with graph theory to distributionnetwork reconfiguration for energy savingrdquo Energy Conversionand Management vol 51 no 3 pp 418ndash427 2010

[19] B Enacheanu B Raison R Caire O Devaux W Bienia andN HadjSaid ldquoRadial network reconfiguration using geneticalgorithm based on the matroid theoryrdquo IEEE Transactions onPower Systems vol 23 no 1 pp 186ndash195 2008

[20] T Niknam E Azadfarsani and M Jabbari ldquoA new hybridevolutionary algorithm based on new fuzzy adaptive PSO andNM algorithms for distribution feeder reconfigurationrdquo EnergyConversion and Management vol 54 no 1 pp 7ndash16 2012

[21] C-T Su C-F Chang and J-P Chiou ldquoDistribution networkreconfiguration for loss reduction by ant colony search algo-rithmrdquo Electric Power Systems Research vol 75 no 2-3 pp 190ndash199 2005

[22] Y-K Wu C-Y Lee L-C Liu and S-H Tsai ldquoStudy ofreconfiguration for the distribution system with distributedgeneratorsrdquo IEEE Transactions on Power Delivery vol 25 no3 pp 1678ndash1685 2010

[23] R Srinivasa Rao S V L Narasimham M Ramalinga Raju andA Srinivasa Rao ldquoOptimal network reconfiguration of large-scale distribution system using harmony search algorithmrdquoIEEE Transactions on Power Systems vol 26 no 3 pp 1080ndash1088 2011

[24] K S Kumar and T Jayabarathi ldquoPower system reconfigurationand loss minimization for an distribution systems using bacte-rial foraging optimization algorithmrdquo International Journal ofElectrical Power amp Energy Systems vol 36 no 1 pp 13ndash17 2012


[26] M M Aman G B Jasmon H Mokhlis and A H A BakarldquoOptimal placement and sizing of a DG based on a new powerstability index and line lossesrdquo International Journal of ElectricalPower amp Energy Systems vol 43 no 1 pp 1296ndash1304 2012

[27] Z Yasin and T Rahman Network Reconfiguration in a PowerDistribution System under Fault Condition with the Presence ofDistributed Generation Universiti Tenaga Nasional SelangorMalaysia 2006

[28] J Olamaei T Niknam and G Gharehpetian ldquoApplication ofparticle swarm optimization for distribution feeder reconfigu-ration considering distributed generatorsrdquoAppliedMathematicsand Computation vol 201 no 1-2 pp 575ndash586 2008

[29] W M Dahalan H Mokhlis A H A Bakar and J J JamianldquoThe simultaneous application of optimum network reconfigu-ration and distributed generation sizing using PSO for powerloss reductionrdquo Przeglad Elektrotechniczny vol 89 no 4 pp137ndash141 2013

[30] M M Aman G B Jasmon A H A Bakar and H Mokhlis ldquoAnew approach for optimum simultaneousmulti-DG distributedgeneration Units placement and sizing based on maximizationof system loadability using HPSO (hybrid particle swarmoptimization) algorithmrdquo Energy vol 66 pp 202ndash215 2014

[31] Y HuPing P YunYan and X Ning ldquoGradual approachingmethod for distribution network dynamic reconfigurationrdquo in


Proceedings of the Workshop on Power Electronics and Intel-ligent Transportation System (PEITS rsquo08) pp 257ndash260 IEEEGuangzhou China August 2008

[32] A E Milani and M R Haghifam ldquoAn evolutionary approachfor optimal time interval determination in distribution networkreconfiguration under variable loadrdquo Mathematical and Com-puter Modelling vol 57 no 1-2 pp 68ndash77 2013

[33] T Hao L Lin and W Yanhan ldquoResearch of distribution net-work reconfiguration with renewable energy power generationunitrdquo in Proceedings of the IEEE International Conference onPower System Technology (POWERCON rsquo14) pp 2680ndash2685IEEE Chengdu China October 2014

[34] A S Bouhouras T A Papadopoulos G C Christoforidis GK Papagiannis and D P Labridis ldquoLoss reduction via networkreconfigurations in Distribution Networks with PhotovoltaicUnits Installedrdquo in Proceedings of the 10th International Con-ference on the European Energy Market (EEM rsquo13) pp 1ndash8Stockholm Sweden May 2013

[35] E Rashedi H Nezamabadi-pour and S Saryazdi ldquoGSA agravitational search algorithmrdquo Information Sciences vol 179no 13 pp 2232ndash2248 2009

[36] H Yang F Wen and L Wang ldquoNewton-Raphson on powerflow algorithm andBroydenmethod in the distribution systemrdquoin Proceedings of the IEEE 2nd International Power and EnergyConference (PECon rsquo08) pp 1613ndash1618 December 2008

[37] B Shaw V Mukherjee and S P Ghoshal ldquoA novel opposition-based gravitational search algorithm for combined economicand emission dispatch problems of power systemsrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 35no 1 pp 21ndash33 2012

[38] Y M Atwa E F El-Saadany M M A Salama and RSeethapathy ldquoOptimal renewable resourcesmix for distributionsystem energy loss minimizationrdquo IEEE Transactions on PowerSystems vol 25 no 1 pp 360ndash370 2010

[39] N H B Jalal Operating Code 1 Demand Forecast The Ma-laysian Grid Code Awareness Programme Kuala LumpurMalaysia 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


programming problem [6] In the same year Lin and Chin[7] have considered service restoration in addition to lossminimization in solving network reconfiguration problemZhu et al performed the network reconfiguration based onmodified heuristic solution and experience system operationrules [8] In a latest research Mohd Zin et al in [9] have usedthe heuristic search algorithm to find the minimum powerlosses as an objective function introduced by the authorin [6] The update principle of heuristic search is made byfinding the branch having minimal current till the optimumsolution is obtained

Most of the methods discussed above require exhaustivesearch mechanism by considering all possible solutions froma predetermined set and subsequently pick the best oneHowever such methods are considered as nonefficient interms of computation time and space requirement Intelli-gent greedy and nature observed heuristic techniques havealso been proposed in the literature and they are commonlyknown as Artificial Intelligent (AI) methods [10] ArtificialIntelligent methods are a special class of heuristic searchmethods [10] Intelligent based optimization methods havealso been utilized in finding optimum tie switch combina-tions in network reconfiguration problem Authors have usedGenetic Algorithms (GA) [11] fuzzy [12ndash14] neural network[15 16] fuzzy-GA [17] Particle Swarm Optimization (PSO)[18] Matroid Theory [19] Hybrid Evolutionary algorithm[20] Ant Colony Search (ACS) algorithm [21 22] HarmonySearch Algorithm [23] and Bacterial Foraging Algorithm[24] Das [12] and Savier and Das [25] have proposedfuzzy based multiobjective approach for loss reduction andconsidered voltage limit and line limits as well in fuzzyset Penalty based multiobjective-single-fitness approacheshave been utilized in [21] to combine power losses withsystem constraints including voltage limits and line limitThemultiobjective problem is solved using ACS algorithm

Besides network reconfiguration Distributed Generation(DG) such as minihydro photovoltaic and wind is installedin distribution system to solve the power loss problem dueto voltage drop However the placement and size of DGare essential as they have a great impact on the power loss[26] Many researchers have proposed different methodsfor optimum DG location and size separately [26ndash28] orsimultaneously [29 30] However all the aforementionedworks have considered a constant load and fixed DG outputIn practical load pattern and DG generation output dynam-ically change with time Therefore some studies have alsoconsidered a variable load pattern in their researches Forexample a gradual approaching method is proposed in [31]to solve dynamic reconfiguration In [32] researchers solvedthe network reconfiguration problemwith daily variable loadimplementation as well These studies have proven that thenetwork performance was improved when the time-varyingload profiles were taken into consideration

Apart from that there are few works on network recon-figuration with the presence of DG considering variableload profile For example network reconfiguration with thepresence of wind and photovoltaic generation for total dailypower loss reduction using improved genetic algorithm isproposed in [33] Network reconfiguration with photovoltaic

generation for power loss reduction considering the DGpenetration and three different load levels is presented in [34]

In this work a novel method is proposed to solvethe network reconfiguration problem based on daily PVgeneration output and variable load profiles GravitationalSearch Algorithm (GSA) proposed in [35] is used in thispaper to determine the best daily system configurationThe proposed method can be viewed in two parts In thefirst part hourly optimal configuration considering the PVgeneration and load profile is carried out using GSA Inthe second part a selective approach is used to determinethe best configuration that gives the lowest power loss forthe whole day (24 hrs) or optimal daily configuration Theproposed method is implemented on 33-bus distributionsystemThe proposed method results are also compared withEvolutionary Programming (EP) to show the effectiveness ofGSA

This paper is organized as follows In Section 2 mathe-matical model for network reconfiguration is described Theproposedmethod including application of GSA and selectionapproach is provided in Section 3 Selection of PV moduleis presented in Section 4 while load modelling and PVgeneration are presented in Section 5 In Section 6 analysisof the performance of the proposed method is discussedFinally the conclusions are presented in Section 7

2 Mathematical Model for DistributionNetwork Reconfiguration Problem

Network reconfiguration is used tominimize the distributionsystem power loss The new configuration selected mustfulfil the constraints and maintain the radial structure of thedistribution system In this study themain objective is to gainminimum power loss of the distribution system Thus theobjective function can be formulated as follows

Min

119875loss =119879

sumℎ

119873

sum119891=1

10038161003816100381610038161003816119868119891100381610038161003816100381610038162

119897119891119877119891

(1)

where119873 is total line in the system 119868119891is real active current of

line 119891 119877119891is resistance of line 119891 119891 is line number 119897

119891is the

topology status of line 119891 (1 = close 0 = open)119879 is the total hour considered in the time frame and ℎ

is the current time considered In this work (1) is used toanalyse the power loss for every hour (ℎ) of a day with theload data of hour (ℎ) and PV generation of hour (ℎ)

The power system constraints that are also being consid-ered in the study are as follows

(a) Voltage Bus Constraint The value of the bus voltage 119881busat each nodemust be within the acceptable limits to maintainthe power quality For example in this work the minimumvoltage (119881min) used is 095 pu and maximum voltage (119881max)is 105 pu

119881min lt 119881bus lt 119881max (2)







119891



can be computed as

119875119891=119873

sum119896=1

10038161003816100381610038161003816119881119891100381610038161003816100381610038161003816100381610038161003816119881119896

100381610038161003816100381610038161003816100381610038161003816119884119891119896

10038161003816100381610038161003816 cos (120579119891119896 minus 120575119891+ 120575119896) (4)

119876119891=119873

sum119896=1

10038161003816100381610038161003816119881119891100381610038161003816100381610038161003816100381610038161003816119881119896

100381610038161003816100381610038161003816100381610038161003816119884119891119896

10038161003816100381610038161003816 sin (120579119891119896 minus 120575119891+ 120575119896) (5)

Δ119875119891= 119875sp119891

minus 119875119891 (6)

Δ119876119891= 119876sp119891minus 119876119891 (7)

[Δ119875

Δ119876] =

[[[[

[

120597119875120597120575

120597119875120597119881

120597119876120597120575

120597119876120597119881

]]]]

]

[Δ120597

Δ |119881|] (8)

119875loss =119873

sum119891=1

119860119891119896

(119875119891119875119896+ 119876119891119876119896)

+ 119861119891119896

(119876119891119875119896minus 119875119891119876119896)

(9)

119860119891119896

=119877119891119896

cos (120575119891minus 120575119896)

119881119891119881119896

(10)

119861119891119896

=119877119891119896

sin (120575119891minus 120575119896)

119881119891119881119896

(11)

End

Start





Part

2

Sele

ctio

n pa

rtPa

rt 1

GSA



where 119881119891and 119881


119896 respectively 119884119891119896

and 120579119891119896




119891



119877119891119896


3 Proposed Method








Mass119894= lfloor11987811 11987822 119878119889




119873opened













119872119886119894= 119872119901119894= 119872119894119894= 119872119894

119898119894 (iter) =



119872119894 (iter) =

119898119894 (iter)

sum119873mass119895=1

119898119895 (iter)

(14)






fit119895 (iter)


fit119895 (iter)

(15)




119865119894119895 (iter) = 119866 (iter)

119872119894 (iter) times 119872

119895 (iter)119877119894119895 (iter) + 120576

(Mass119895 (iter)


(16)


119895is the



119877119894119895 (iter) =

10038171003817100381710038171003817Mass119894 (iter) Mass

119895 (iter)100381710038171003817100381710038172 (17)


119886119889119894(iter) =

119865119889119894(iter)

119872119894119894 (iter)

(18)



119865119889119894(iter) =

119873mass

sum119895isin119896best 119895 =119894

rand119895119865119889119894119895(iter) (19)





V119889119894(iter + 1) = rand

119894times V119889119894(iter) + 119886119889

119894(iter) (20)


Mass119889119894(iter + 1) = Mass119889

119894(iter) + V119889

119894(iter + 1) (21)



1198781

1198782

1198783




Configuration ℎ

[[[[[[

[

11987811

11987821

119878ℎ1

11987812

11987822

119878ℎ2

11987813

11987823

119878ℎ3

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

1198781119873opened

1198782119873opened

119878ℎ119873opened

119875loss1199041119875loss1199042

119875loss119904ℎ

]]]]]]

]

(22)







Set Switch 119910

[[[[[[[

[

1198831

1198832

119883119910

]]]]]]]

]

119875loss1198831119875loss1198832

119875loss119883119910

(23)



[[[[[[[

[

1198831

1198832

119883119910



]]]]]]]

]

(24)




119879CZ (ℎ) = 119879119886+ 119904az (ℎ119903) (


)

119868119885 (ℎ) = 119904az (ℎ)



0

01

02

03

A B C D

CF

PV module


0

02

04

06

08

1

12

minus01

01

03

05

07

09

1 3 5 7 9 11 13 15 17 19 21 23

Load

pro

file (

pu)

PV g

ener

atio

n (M

W)

Hour



119881119885 (ℎ) = 119881OC (module) minus (119870




119885 (ℎ)

(25)




















26 33323130292827

Mai

nsu

bsta

tion

23 2524

1 32 4 65 12 181716151413

19 222120

DG

7 8 9 10 11

DG

DG





















26 33323130292827

23 2524

1 32 4 65 12 181716151413

19 222120

DG

DG

DG

7 8 9 10 11

Mai

nsu

bsta

tion





Scenario 31 199658 207551 28 14 7 17 102 220475 208897 31 6 37 34 104 213267 209909 28 10 7 17 13



09091092093094095096097098

1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Volta

ge p

rofil

es (p

u)

Time of a day




7 Conclusion





11198782

1198783

1198784

1198785


01 11 7 27 32 14 885602 11 7 28 14 36 800803 28 14 33 9 32 753904 28 9 33 32 14 713105 9 34 37 32 7 707406 32 28 34 7 11 716507 33 36 10 28 34 712108 37 34 9 32 7 707309 37 17 9 14 7 756310 21 31 37 7 13 704111 11 14 30 7 28 700112 8 33 28 13 16 702213 10 7 37 30 14 571714 37 9 30 7 13 623015 37 7 30 10 13 672816 21 34 31 37 7 831717 14 11 7 28 17 869218 10 7 37 14 31 791919 7 11 34 32 28 980120 10 7 14 27 32 1261421 10 37 31 14 7 1238022 28 14 7 17 10 1184223 9 14 28 32 33 1084524 7 37 13 32 9 9978


093094095096097098099

1101

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33Bus number


Volta

ge p

rofil

es (p

u)




1198781

1198782

1198783

1198784

1198785


6065707580859095

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Pow

er lo

ss (k

W)

Iteration



at time 1800





Acknowledgments




References


















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















119891



can be computed as

119875119891=119873

sum119896=1

10038161003816100381610038161003816119881119891100381610038161003816100381610038161003816100381610038161003816119881119896

100381610038161003816100381610038161003816100381610038161003816119884119891119896

10038161003816100381610038161003816 cos (120579119891119896 minus 120575119891+ 120575119896) (4)

119876119891=119873

sum119896=1

10038161003816100381610038161003816119881119891100381610038161003816100381610038161003816100381610038161003816119881119896

100381610038161003816100381610038161003816100381610038161003816119884119891119896

10038161003816100381610038161003816 sin (120579119891119896 minus 120575119891+ 120575119896) (5)

Δ119875119891= 119875sp119891

minus 119875119891 (6)

Δ119876119891= 119876sp119891minus 119876119891 (7)

[Δ119875

Δ119876] =

[[[[

[

120597119875120597120575

120597119875120597119881

120597119876120597120575

120597119876120597119881

]]]]

]

[Δ120597

Δ |119881|] (8)

119875loss =119873

sum119891=1

119860119891119896

(119875119891119875119896+ 119876119891119876119896)

+ 119861119891119896

(119876119891119875119896minus 119875119891119876119896)

(9)

119860119891119896

=119877119891119896

cos (120575119891minus 120575119896)

119881119891119881119896

(10)

119861119891119896

=119877119891119896

sin (120575119891minus 120575119896)

119881119891119881119896

(11)

End

Start





Part

2

Sele

ctio

n pa

rtPa

rt 1

GSA



where 119881119891and 119881


119896 respectively 119884119891119896

and 120579119891119896




119891



119877119891119896


3 Proposed Method








Mass119894= lfloor11987811 11987822 119878119889




119873opened













119872119886119894= 119872119901119894= 119872119894119894= 119872119894

119898119894 (iter) =



119872119894 (iter) =

119898119894 (iter)

sum119873mass119895=1

119898119895 (iter)

(14)






fit119895 (iter)


fit119895 (iter)

(15)




119865119894119895 (iter) = 119866 (iter)

119872119894 (iter) times 119872

119895 (iter)119877119894119895 (iter) + 120576

(Mass119895 (iter)


(16)


119895is the



119877119894119895 (iter) =

10038171003817100381710038171003817Mass119894 (iter) Mass

119895 (iter)100381710038171003817100381710038172 (17)


119886119889119894(iter) =

119865119889119894(iter)

119872119894119894 (iter)

(18)



119865119889119894(iter) =

119873mass

sum119895isin119896best 119895 =119894

rand119895119865119889119894119895(iter) (19)





V119889119894(iter + 1) = rand

119894times V119889119894(iter) + 119886119889

119894(iter) (20)


Mass119889119894(iter + 1) = Mass119889

119894(iter) + V119889

119894(iter + 1) (21)



1198781

1198782

1198783




Configuration ℎ

[[[[[[

[

11987811

11987821

119878ℎ1

11987812

11987822

119878ℎ2

11987813

11987823

119878ℎ3

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

1198781119873opened

1198782119873opened

119878ℎ119873opened

119875loss1199041119875loss1199042

119875loss119904ℎ

]]]]]]

]

(22)







Set Switch 119910

[[[[[[[

[

1198831

1198832

119883119910

]]]]]]]

]

119875loss1198831119875loss1198832

119875loss119883119910

(23)



[[[[[[[

[

1198831

1198832

119883119910



]]]]]]]

]

(24)




119879CZ (ℎ) = 119879119886+ 119904az (ℎ119903) (


)

119868119885 (ℎ) = 119904az (ℎ)



0

01

02

03

A B C D

CF

PV module


0

02

04

06

08

1

12

minus01

01

03

05

07

09

1 3 5 7 9 11 13 15 17 19 21 23

Load

pro

file (

pu)

PV g

ener

atio

n (M

W)

Hour



119881119885 (ℎ) = 119881OC (module) minus (119870




119885 (ℎ)

(25)




















26 33323130292827

Mai

nsu

bsta

tion

23 2524

1 32 4 65 12 181716151413

19 222120

DG

7 8 9 10 11

DG

DG





















26 33323130292827

23 2524

1 32 4 65 12 181716151413

19 222120

DG

DG

DG

7 8 9 10 11

Mai

nsu

bsta

tion





Scenario 31 199658 207551 28 14 7 17 102 220475 208897 31 6 37 34 104 213267 209909 28 10 7 17 13



09091092093094095096097098

1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Volta

ge p

rofil

es (p

u)

Time of a day




7 Conclusion





11198782

1198783

1198784

1198785


01 11 7 27 32 14 885602 11 7 28 14 36 800803 28 14 33 9 32 753904 28 9 33 32 14 713105 9 34 37 32 7 707406 32 28 34 7 11 716507 33 36 10 28 34 712108 37 34 9 32 7 707309 37 17 9 14 7 756310 21 31 37 7 13 704111 11 14 30 7 28 700112 8 33 28 13 16 702213 10 7 37 30 14 571714 37 9 30 7 13 623015 37 7 30 10 13 672816 21 34 31 37 7 831717 14 11 7 28 17 869218 10 7 37 14 31 791919 7 11 34 32 28 980120 10 7 14 27 32 1261421 10 37 31 14 7 1238022 28 14 7 17 10 1184223 9 14 28 32 33 1084524 7 37 13 32 9 9978


093094095096097098099

1101

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33Bus number


Volta

ge p

rofil

es (p

u)




1198781

1198782

1198783

1198784

1198785


6065707580859095

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Pow

er lo

ss (k

W)

Iteration



at time 1800





Acknowledgments




References


















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra














Mass119894= lfloor11987811 11987822 119878119889




119873opened













119872119886119894= 119872119901119894= 119872119894119894= 119872119894

119898119894 (iter) =



119872119894 (iter) =

119898119894 (iter)

sum119873mass119895=1

119898119895 (iter)

(14)






fit119895 (iter)


fit119895 (iter)

(15)




119865119894119895 (iter) = 119866 (iter)

119872119894 (iter) times 119872

119895 (iter)119877119894119895 (iter) + 120576

(Mass119895 (iter)


(16)


119895is the



119877119894119895 (iter) =

10038171003817100381710038171003817Mass119894 (iter) Mass

119895 (iter)100381710038171003817100381710038172 (17)


119886119889119894(iter) =

119865119889119894(iter)

119872119894119894 (iter)

(18)



119865119889119894(iter) =

119873mass

sum119895isin119896best 119895 =119894

rand119895119865119889119894119895(iter) (19)





V119889119894(iter + 1) = rand

119894times V119889119894(iter) + 119886119889

119894(iter) (20)


Mass119889119894(iter + 1) = Mass119889

119894(iter) + V119889

119894(iter + 1) (21)



1198781

1198782

1198783




Configuration ℎ

[[[[[[

[

11987811

11987821

119878ℎ1

11987812

11987822

119878ℎ2

11987813

11987823

119878ℎ3

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

1198781119873opened

1198782119873opened

119878ℎ119873opened

119875loss1199041119875loss1199042

119875loss119904ℎ

]]]]]]

]

(22)







Set Switch 119910

[[[[[[[

[

1198831

1198832

119883119910

]]]]]]]

]

119875loss1198831119875loss1198832

119875loss119883119910

(23)



[[[[[[[

[

1198831

1198832

119883119910



]]]]]]]

]

(24)




119879CZ (ℎ) = 119879119886+ 119904az (ℎ119903) (


)

119868119885 (ℎ) = 119904az (ℎ)



0

01

02

03

A B C D

CF

PV module


0

02

04

06

08

1

12

minus01

01

03

05

07

09

1 3 5 7 9 11 13 15 17 19 21 23

Load

pro

file (

pu)

PV g

ener

atio

n (M

W)

Hour



119881119885 (ℎ) = 119881OC (module) minus (119870




119885 (ℎ)

(25)




















26 33323130292827

Mai

nsu

bsta

tion

23 2524

1 32 4 65 12 181716151413

19 222120

DG

7 8 9 10 11

DG

DG





















26 33323130292827

23 2524

1 32 4 65 12 181716151413

19 222120

DG

DG

DG

7 8 9 10 11

Mai

nsu

bsta

tion





Scenario 31 199658 207551 28 14 7 17 102 220475 208897 31 6 37 34 104 213267 209909 28 10 7 17 13



09091092093094095096097098

1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Volta

ge p

rofil

es (p

u)

Time of a day




7 Conclusion





11198782

1198783

1198784

1198785


01 11 7 27 32 14 885602 11 7 28 14 36 800803 28 14 33 9 32 753904 28 9 33 32 14 713105 9 34 37 32 7 707406 32 28 34 7 11 716507 33 36 10 28 34 712108 37 34 9 32 7 707309 37 17 9 14 7 756310 21 31 37 7 13 704111 11 14 30 7 28 700112 8 33 28 13 16 702213 10 7 37 30 14 571714 37 9 30 7 13 623015 37 7 30 10 13 672816 21 34 31 37 7 831717 14 11 7 28 17 869218 10 7 37 14 31 791919 7 11 34 32 28 980120 10 7 14 27 32 1261421 10 37 31 14 7 1238022 28 14 7 17 10 1184223 9 14 28 32 33 1084524 7 37 13 32 9 9978


093094095096097098099

1101

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33Bus number


Volta

ge p

rofil

es (p

u)




1198781

1198782

1198783

1198784

1198785


6065707580859095

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Pow

er lo

ss (k

W)

Iteration



at time 1800





Acknowledgments




References


















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











V119889119894(iter + 1) = rand

119894times V119889119894(iter) + 119886119889

119894(iter) (20)


Mass119889119894(iter + 1) = Mass119889

119894(iter) + V119889

119894(iter + 1) (21)



1198781

1198782

1198783




Configuration ℎ

[[[[[[

[

11987811

11987821

119878ℎ1

11987812

11987822

119878ℎ2

11987813

11987823

119878ℎ3

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

1198781119873opened

1198782119873opened

119878ℎ119873opened

119875loss1199041119875loss1199042

119875loss119904ℎ

]]]]]]

]

(22)







Set Switch 119910

[[[[[[[

[

1198831

1198832

119883119910

]]]]]]]

]

119875loss1198831119875loss1198832

119875loss119883119910

(23)



[[[[[[[

[

1198831

1198832

119883119910



]]]]]]]

]

(24)




119879CZ (ℎ) = 119879119886+ 119904az (ℎ119903) (


)

119868119885 (ℎ) = 119904az (ℎ)



0

01

02

03

A B C D

CF

PV module


0

02

04

06

08

1

12

minus01

01

03

05

07

09

1 3 5 7 9 11 13 15 17 19 21 23

Load

pro

file (

pu)

PV g

ener

atio

n (M

W)

Hour



119881119885 (ℎ) = 119881OC (module) minus (119870




119885 (ℎ)

(25)




















26 33323130292827

Mai

nsu

bsta

tion

23 2524

1 32 4 65 12 181716151413

19 222120

DG

7 8 9 10 11

DG

DG





















26 33323130292827

23 2524

1 32 4 65 12 181716151413

19 222120

DG

DG

DG

7 8 9 10 11

Mai

nsu

bsta

tion





Scenario 31 199658 207551 28 14 7 17 102 220475 208897 31 6 37 34 104 213267 209909 28 10 7 17 13



09091092093094095096097098

1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Volta

ge p

rofil

es (p

u)

Time of a day




7 Conclusion





11198782

1198783

1198784

1198785


01 11 7 27 32 14 885602 11 7 28 14 36 800803 28 14 33 9 32 753904 28 9 33 32 14 713105 9 34 37 32 7 707406 32 28 34 7 11 716507 33 36 10 28 34 712108 37 34 9 32 7 707309 37 17 9 14 7 756310 21 31 37 7 13 704111 11 14 30 7 28 700112 8 33 28 13 16 702213 10 7 37 30 14 571714 37 9 30 7 13 623015 37 7 30 10 13 672816 21 34 31 37 7 831717 14 11 7 28 17 869218 10 7 37 14 31 791919 7 11 34 32 28 980120 10 7 14 27 32 1261421 10 37 31 14 7 1238022 28 14 7 17 10 1184223 9 14 28 32 33 1084524 7 37 13 32 9 9978


093094095096097098099

1101

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33Bus number


Volta

ge p

rofil

es (p

u)




1198781

1198782

1198783

1198784

1198785


6065707580859095

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Pow

er lo

ss (k

W)

Iteration



at time 1800





Acknowledgments




References


















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0

01

02

03

A B C D

CF

PV module


0

02

04

06

08

1

12

minus01

01

03

05

07

09

1 3 5 7 9 11 13 15 17 19 21 23

Load

pro

file (

pu)

PV g

ener

atio

n (M

W)

Hour



119881119885 (ℎ) = 119881OC (module) minus (119870




119885 (ℎ)

(25)




















26 33323130292827

Mai

nsu

bsta

tion

23 2524

1 32 4 65 12 181716151413

19 222120

DG

7 8 9 10 11

DG

DG





















26 33323130292827

23 2524

1 32 4 65 12 181716151413

19 222120

DG

DG

DG

7 8 9 10 11

Mai

nsu

bsta

tion





Scenario 31 199658 207551 28 14 7 17 102 220475 208897 31 6 37 34 104 213267 209909 28 10 7 17 13



09091092093094095096097098

1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Volta

ge p

rofil

es (p

u)

Time of a day




7 Conclusion





11198782

1198783

1198784

1198785


01 11 7 27 32 14 885602 11 7 28 14 36 800803 28 14 33 9 32 753904 28 9 33 32 14 713105 9 34 37 32 7 707406 32 28 34 7 11 716507 33 36 10 28 34 712108 37 34 9 32 7 707309 37 17 9 14 7 756310 21 31 37 7 13 704111 11 14 30 7 28 700112 8 33 28 13 16 702213 10 7 37 30 14 571714 37 9 30 7 13 623015 37 7 30 10 13 672816 21 34 31 37 7 831717 14 11 7 28 17 869218 10 7 37 14 31 791919 7 11 34 32 28 980120 10 7 14 27 32 1261421 10 37 31 14 7 1238022 28 14 7 17 10 1184223 9 14 28 32 33 1084524 7 37 13 32 9 9978


093094095096097098099

1101

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33Bus number


Volta

ge p

rofil

es (p

u)




1198781

1198782

1198783

1198784

1198785


6065707580859095

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Pow

er lo

ss (k

W)

Iteration



at time 1800





Acknowledgments




References


















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










26 33323130292827

Mai

nsu

bsta

tion

23 2524

1 32 4 65 12 181716151413

19 222120

DG

7 8 9 10 11

DG

DG





















26 33323130292827

23 2524

1 32 4 65 12 181716151413

19 222120

DG

DG

DG

7 8 9 10 11

Mai

nsu

bsta

tion





Scenario 31 199658 207551 28 14 7 17 102 220475 208897 31 6 37 34 104 213267 209909 28 10 7 17 13



09091092093094095096097098

1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Volta

ge p

rofil

es (p

u)

Time of a day




7 Conclusion





11198782

1198783

1198784

1198785


01 11 7 27 32 14 885602 11 7 28 14 36 800803 28 14 33 9 32 753904 28 9 33 32 14 713105 9 34 37 32 7 707406 32 28 34 7 11 716507 33 36 10 28 34 712108 37 34 9 32 7 707309 37 17 9 14 7 756310 21 31 37 7 13 704111 11 14 30 7 28 700112 8 33 28 13 16 702213 10 7 37 30 14 571714 37 9 30 7 13 623015 37 7 30 10 13 672816 21 34 31 37 7 831717 14 11 7 28 17 869218 10 7 37 14 31 791919 7 11 34 32 28 980120 10 7 14 27 32 1261421 10 37 31 14 7 1238022 28 14 7 17 10 1184223 9 14 28 32 33 1084524 7 37 13 32 9 9978


093094095096097098099

1101

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33Bus number


Volta

ge p

rofil

es (p

u)




1198781

1198782

1198783

1198784

1198785


6065707580859095

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Pow

er lo

ss (k

W)

Iteration



at time 1800





Acknowledgments




References


















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra

















26 33323130292827

23 2524

1 32 4 65 12 181716151413

19 222120

DG

DG

DG

7 8 9 10 11

Mai

nsu

bsta

tion





Scenario 31 199658 207551 28 14 7 17 102 220475 208897 31 6 37 34 104 213267 209909 28 10 7 17 13



09091092093094095096097098

1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Volta

ge p

rofil

es (p

u)

Time of a day




7 Conclusion





11198782

1198783

1198784

1198785


01 11 7 27 32 14 885602 11 7 28 14 36 800803 28 14 33 9 32 753904 28 9 33 32 14 713105 9 34 37 32 7 707406 32 28 34 7 11 716507 33 36 10 28 34 712108 37 34 9 32 7 707309 37 17 9 14 7 756310 21 31 37 7 13 704111 11 14 30 7 28 700112 8 33 28 13 16 702213 10 7 37 30 14 571714 37 9 30 7 13 623015 37 7 30 10 13 672816 21 34 31 37 7 831717 14 11 7 28 17 869218 10 7 37 14 31 791919 7 11 34 32 28 980120 10 7 14 27 32 1261421 10 37 31 14 7 1238022 28 14 7 17 10 1184223 9 14 28 32 33 1084524 7 37 13 32 9 9978


093094095096097098099

1101

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33Bus number


Volta

ge p

rofil

es (p

u)




1198781

1198782

1198783

1198784

1198785


6065707580859095

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Pow

er lo

ss (k

W)

Iteration



at time 1800





Acknowledgments




References


















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












11198782

1198783

1198784

1198785


01 11 7 27 32 14 885602 11 7 28 14 36 800803 28 14 33 9 32 753904 28 9 33 32 14 713105 9 34 37 32 7 707406 32 28 34 7 11 716507 33 36 10 28 34 712108 37 34 9 32 7 707309 37 17 9 14 7 756310 21 31 37 7 13 704111 11 14 30 7 28 700112 8 33 28 13 16 702213 10 7 37 30 14 571714 37 9 30 7 13 623015 37 7 30 10 13 672816 21 34 31 37 7 831717 14 11 7 28 17 869218 10 7 37 14 31 791919 7 11 34 32 28 980120 10 7 14 27 32 1261421 10 37 31 14 7 1238022 28 14 7 17 10 1184223 9 14 28 32 33 1084524 7 37 13 32 9 9978


093094095096097098099

1101

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33Bus number


Volta

ge p

rofil

es (p

u)




1198781

1198782

1198783

1198784

1198785


6065707580859095

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Pow

er lo

ss (k

W)

Iteration



at time 1800





Acknowledgments




References


















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











References


















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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