brainstorming

Applied Soft Computing 35 (2015) 291309

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Applied Soft Computing

j ourna l h o mepage: www.elsev ier .com/ locate /asoc

Securit ngusing h ing

BelkacemDepartment of

a r t i c l

Article history:Received 10 SeReceived in reAccepted 24 JuAvailable onlin

Keywords:Optimal poweFirey algorithPattern searchBrainstormingObjective funcSVC

em prposetive otive ithmled anposectivepensaviatiohe p

two practical test systems IEEE 14-Bus and IEEE 30-Bus. Simulation results conrm the effectiveness ofthis hybrid strategy for solving the security optimal power ow.

2015 Elsevier B.V. All rights reserved.

1. Introdu

The secutool for powobjective ofof power systate of mulrelated to aconstraintsity are threpower systethese objecperformancconrmed tplex multi strategy to under normhas been wmization te(LP, NLP) [2

CorresponE-mail add

http://dx.doi.o1568-4946/ ction

rity optimal power ow (OPF) is the most importanter system planning, operation and control. The main

OPF tool which considered as an important sub problemstem planning is to determine the optimal operationti dispersed units by optimizing multi control variables

specied objective function considering multi practical. Active power loss, voltage deviation and voltage stabil-e important tasks which interest expert specialized inm planning operation and control. The optimization oftive functions affect directly and indirectly the dynamices of practical power system [1]. Many research resultshat optimization of these objective functions is a com-objective problem which require robust and exibleenhance the performance of practical power systemsal and at critical situations. The standard OPF problemidely solved using several classical mathematical opti-chniques such as linear and non linear programming], gradient based method [3], quadratic programming

ding author. Tel.: +213 665084111.ress: [email protected] (B. Mahdad).

(QP) [4], Newton-based method [5,6], and interior point meth-ods [7]. A recent survey of the major contributions related tothis category based mathematical methods is presented in [8].Based on a large number of papers proposed to solving variousproblems related to power system planning, operation and con-trol, we can conclude that the deterministic optimization methodsconverge to local optimal solution and can not guarantee globalsolution when considering practical generator constraints (Pro-hibited zones, valve point effect, and multi-fuel options) due tosensibility to initial conditions and to the form of the objectivefunction. These major drawbacks have contributed to the devel-opment of new stochastic based optimization techniques suchas, evolutionary programming [9], improved evolutionary pro-gramming [10], enhanced genetic algorithm (EGA) [11], improvedgenetic algorithms (IGA) [12], adapted genetic algorithm (AGA)[13], particle swarm optimization (PSO) [14,15], differential evo-lution (DA) [1619], improved harmony search algorithm [20],Imperialist competitive algorithm (ICA) [21], gravitational searchalgorithm (GSA) [22], articial bee colony algorithm (ABC) [23,24],rey algorithm (FFA) [25,26], brain storm optimization algorithm(BSA) [27], Application of brainstorming strategy for enhancementdynamic teaching based LMD education system [28]. In generalview, we can conclude that the main difference between thesemethods is related to the robustness of their mechanism search

rg/10.1016/j.asoc.2015.06.0372015 Elsevier B.V. All rights reserved.y optimal power ow considering loadiybrid FFAPS assisted with brainstorm

Mahdad , K. SrairiElectrical Engineering, Biskra University, Algeria

e i n f o

ptember 2014vised form 2 April 2015ne 2015e 2 July 2015

r owm

processtions

a b s t r a c t

This paper presents a new power systpattern search algorithm (PS). The putotal voltage deviation, with the objecpower system security. A new interacproposed that allows FFA and PS algorStatic VAR compensator (SVC) is modeing the voltage stability index. The provariables at the same time, namely, aand the reactive power of shunt comtotal power loss and total voltage deand competitive search mechanism. T margin stability rules

lanning strategy which combines rey algorithm (FFA) with is minimizing total fuel cost, total power loss and reducingf enhancing the loading margin stability and consequently theand simple mechanism, inspired in brainstorming process, iss to explore new regions of the search space. In this study thed integrated in an efcient location which is chosen consider-

d algorithm is interactive and tries to optimize a set of control power generations, voltage of generators, tap transformers,tors to optimize three objective functions such as: fuel cost,n. These variables are optimized using a exible interactiveroposed planning strategy has been examined and applied to

292 B. Mahdad, K. Srairi / Applied Soft Computing 35 (2015) 291309

determined by the number of parameters to be adjusted, an opti-mization method with simple and interactive mechanism searchand with less parameter to control is preferred.

Recently, many research results clearly conrmed that eachglobal optiHybrid metion to comhybrid metfor solvingpower systeniques are,modied teferential ev[31], hybridalgorithm (imperialist SQP) algori[35], new tive algorithoptimizatiosive teachin[39] and hiliterature rhow adjustbetween vaances of eatime. The mmethods is nication prexploration

Flexible Hingorani atechnologytechnologysource prodgin stabilitydevices suctrollers (TCthe electricpower systgies have bow considmulti objecmulti FACTand Nageshoptimal powow controtion algoritconsidering[47] a hybadapted anfor congestproposed fosecurity.

Firey ation methodapplied by to power syis preferredparametersevolutionaring many prcontrol. Thethe rules pprocess wauals workin

is rstly developed and formulated as an optimization problem byShi in 2011 [27]. To date, the BSO algorithm has not been appliedintensively to solving the complex problems related to power sys-tem planning and control, very recently in [50], Rezaee Jordehi

ed an efcient algorithm based brain storm optimizationhm (rove viatioant athis rd ore ad

experedmpled cmued inant o

loss SVCpropgencstemering

urity

urity systetimave fustraitructs:

izatit denal ithmybridsted nizedods.r ows in of poof coithmctive

opttiond indmunial anqualiess d.

his wA cone the

mecwo md fromization method has its advantages and drawbacks.thods considered as an alternative and robust solu-bine different methods. In the recent literature varioushods have been proposed and applied with success

many complex and combined problems related tom planning, operation and control, some of these tech-

Evolving ant direction differential evolution [29], Aachinglearning based optimization [30], hybrid dif-olution (DE) with particle swarm optimization (PSO)

fuzzy particle swarm optimization and NedlerMeadHFPSO-NM) [32], chaotic improved PSO [33], hybridcompetitive-sequential quadratic programming (HIC-thm [34], A modied shufe frog leaping algorithmmodied and hybrid modied imperialist competi-ms [36], adaptive biogeography based predatorpreyn technique [37], self-evolving brain-storming inclu-glearning-based algorithm [38], A hybrid GAPSSQPerarchical adaptive PSO [40]. As well described in theeview, the structure of these methods is based oning dynamically their parameters and on combinationrious methods to exploit efciently the best perform-ch method to achieve the global solution at a reducedain idea introduced in the mechanism search of theseto provide an intelligent adaptive and exible commu-ocess to guide efciently the processes search during

and exploitation stages.AC transmission Systems (FACTS) rst introduced bynd Gyugyi [41], is relatively considered as one of recent

installed in many practical electrical networks. FACTS is an alternative solution to ensure balance betweenuction and power demand particularly at loading mar-. In recent years many types of controllers based FACTSh as: shunt Controllers (SVC, STATCOM), series Con-SC, SSSC) and hybrid Controllers (UPFC) integrated inity market to improve the performances of the practicalem [42]. In the literature many techniques and strate-een proposed to enhance the security optimal powerering the integration of FACTS devices [43]. An efcienttive strategy based differential evolution consideringS technology is presented in [44]. Venkateswara Rao

Kumar [45] proposed a BAT search algorithm baseder ow for generation reallocation with unied powerller, in [46] a multi-objective adaptive clonal selec-hm is proposed for the solving optimal power ow

multi-type FACTS devices and load uncertainty, inrid bacterial foraging and NelderMead algorithm isd applied for optimal location of series FACTS devicesion management, and in [48] a strategy based PSO isr dynamic control of UPFC to enhance power system

lgorithm is one of the recent metaheuristic optimiza-s proposed by author in [25], this method adapted andresearchers to solve many complex problems relatedstem planning operation and control. In this work FFA

for its simplicity to adapt and program and has a few to adjust. Pattern search algorithm is also an efcienty technique, adapted and applied with success to solv-actical problems related to power system operation and

brainstorming concept rst introduced by Osborn [49],roposed by Osborn demonstrated that brainstormings more effective in generating new ideas than individ-g. The adaptation of brainstorming principle and rules

proposalgoritto impage deimport

In standarules acess, toconsidto accoproposble comproposimportpowerof oneof the convertest syconsid

2. Sec

Secpowerthe opobjectiity conbasic sfollow

Optimegy, the algoror hadjuorgameth

Poweworkrole tion algor

Objeto bedeviamize

Comglobtion procused

In tthe FFachievsearchthese tinspireBSOA) for optimal location and control of FACTS devicesvarious objective functions such as power loss and volt-n and overload minimization, the results achieved arend competitive.work and to enhance the performances of the twoptimization methods (FFA and PS), the brainstormingapted and used to assist FFA and PS during search pro-loit with efciently the search space. In this study, FFA is

as a global optimization technique and the PS is adaptedish the task of local search, the main particularity of theombined optimization method is related to the exi-nication rules inspired from brainstorming process. Theteractive hybrid approach applied to optimize threebjective functions: reduce the total fuel cost, the total

and voltage deviations by considering the integration compensator at efcient location, The performancesosed planning strategy in term of solution quality ande characteristic have been tested on the two practicals, IEEE 14-Bus and IEEE 30-Bus at normal condition and

loading margin stability.

optimal power ow

optimal power ow is a fundamental sub-problem ofm planning, the main objective of this strategy is to ndl settings of control variables in terms of one or morenction while satisfying operating equality and inequal-nts [1]. Fig. 1 shows the strategy of security OPF, theure of security OPF may be presented and described as

ion method: represent the core of the optimization strat-pends on the complexity of the problem to be solved,results achieved depend on the particularity of the

used such as standard algorithms (GA, PSO, ABC), method, how the initial parameters are chosen andduring search process, how the control variables are, and how the global method is hybridized with other

(PF) based NewtonRaphson algorithm: this second taskcoordination with the optimization method, the mainwer ow is to determine the state variables and viola-nstraints. The equality constraints are veried using PF.functions: in general, the well known objective functionsimized are: fuel cost, emission, power losses, voltage, and voltage stability, these objective functions are opti-ividually or simultaneously.cation process: is related to the interaction betweend local optimization methods to enhance the solu-ty and convergence characteristics. The communicationepends on the global and local optimization methods

ork, we have used two simple optimization methods,sidered as a global optimization method adapted to

exploration phase and the PS considered as a localhanism coordinated to enhance the exploitation search,ethods are coordinated using exible practical rules

m brainstorming process.

B. Mahdad, K. Srairi / Applied Soft Computing 35 (2015) 291309 293

jectiv

In generconsideringusing the fo

Minimize J

Subject t

g(x, u) = 0

h(x, u) 0

where J is thtives. g is thsecurity ineables, u repstate vectortudes VL, slapower Qg.

x = [(1,...,NThe cont

generator tedynamic co

u = [Pg(1,...,

2.1. Objecti

2.1.1. MinimMinimiz

considered operation. T

presws:

= m

NG iFig. 1. Strategy of security multi ob

al the basic mathematical formulation of security OPF one or more objective function may be representedllowing generalized expressions:

i(x, u) i = 1, . . ., Nobj (1)

o:

cost exas follo

J1(x, u)

where(2)

(3)

e ith objective function, and Nobj is the number of objec-e equality constraints, h is the system operation andquality constraints. x represents the vector of state vari-resents the vector of control variables. In general, the

includes bus voltage angles , load bus voltage magni-ck bus real power generation Pgs and generator reactive

L), VL(1,...,NL), Pgs, Qg(1,...,NG)]T (4)

rol variable vector consists of real power generation Pg,rminal voltage Vg, shunt capacitors/reactors Bsh, shuntmpensators (SVC) Bsvc and transformers tap ratio t.

NG1), Vg(1,...,NG), Bsh(1,...,Nsh), Bsvc(1,...,Nsvc), t(1,...,Nt)]T

(5)

ve functions

ization of total fuel costation of fuel cost is an important task for expert andas an important index for power system planning andhe simplied objective function f is the total generation

generation ith generato

2.1.2. MinimThe obje

total voltagequation:

J2(x, u) = m

where Vref i

2.1.3. MinimThe obje

to be optim

J3(x, u) = m

2.2. Constra

2.2.1. EquaThe equ

equilibriume OPF.

sed as a quadratic function, mathematically formulated

in fi = min(

NGi=1

(ai + biPgi + ciP2gi))

(6)

s the number of thermal units, Pgi is the active power

at unit i and ai, bi and ci are the cost coefcients of ther.

ization of voltage deviationctive function associated to the minimization of thee deviation at all load buses is described by the following

in VD = min(

iNL|Vi Vref |

)(7)

s the desired voltage at all load buses.

ization of power lossesctive function associated to the total active power lossized is formulated by the following equation:

in Ploss = min(

NLk=1

gk[(tkVi)2 + V2j 2tkViVj cos ij]

)(8)

ints

lity constraintsality constraints g(x) of the OPF reect the physical

of active and reactive power between production and


demand at all buses. In other term, the principle of energy conser-vation must be veried at each bus. The following two generalizedequations reect the equilibrium and conservation of active andreactive power at all buses:

Pgi Pdi V

Qgi Qdi

where N is ttive power power demrespectivelyj respectiveadmittance

2.2.2. InequThese ar

ational powcompensatothese constfollows:

2.2.2.1. Gen

Limits on

Vmingi Vg Limits on

Pmingi Pg Limits on

Qmingi Qg

2.2.2.2. Tra

Limits on

tmini ti

2.2.2.3. FAC

Parametetheir limi

Xmin XF

2.2.2.4. Secsumer instaTo achieve tbuses) and tconstraints

Sli Smaxli ,

VminLi VLi

where NBRof loading b

2.2.3. Constraints managementIn order to take in consideration the violation of security con-

straints, a modied tness function is adapted using the penaltyfunction. The inequality constraints are immerged within the

ve funtedsion:

u) =

=

(PGs

v, e occtudestion ible ndlin{

VL

VL{

Q

Q{PmG

PmG

Smaxbri

adin

loadlity ocritic

nddinaltage

load poinentatation

P Q

Pbase Qbaseding

ltage

to systor caonsenormancei

Nj=1

Vj(gij cos ij + bij sin ij) = 0 (9)

Vi

Nj=1

Vj(gij sin ij bij cos ij) = 0 (10)

he number of buses, Pgi, Qgi are the active and the reac-generation at bus i; Pdi, Qdi are the real and the reactiveand at bus i; Vi, Vj, the voltage magnitude at bus i, j,; ij is the phase angle difference between buses i andly, gij and bij are the real and imaginary part of the

(Yij).

ality constraintse the sets of physical constraints associated to all oper-er system elements (generator, transformer, lines, andrs), from production source to load bus. Generally,raints are organized and mathematically expressed as

erator constraints.

the generator bus voltage magnitude:

i Vmaxgi , i = 1, 2, . . ., NPV (11)

the output of active power generation:

i Pmaxgi , i = 1, 2, . . ., NPV (12)

the output of reactive power generation:

i Qmaxgi , i = 1, 2, . . ., NPV (13)

nsformer constraints.

the tap ratio (t) of transformer.

tmaxi , i = 1, 2, ..., NT (14)

TS controllers constraints.

rs of shunt FACTS controllers must be restricted withints.

ACTS Xmax (15)

urity limits. Energy produced must be delivered to con-ntaneously and within the admissible security values.his task, the constraints on voltage at loading buses (PQransmission line loadings are considered. These security

are expressed as follows:

i = 1, 2, . . ., NBR (16)

VmaxLi , i = 1, 2, . . ., NPQ (17)

and NPQ are the number of branches and the numberuses respectively.

objectiaugmeexpres

Jmod(x,

Penalty

+ P

wheretion armagnigeneraadmissthe ha

V limLi =

Q limGi =

PlimGs =

Slimbri =

2.3. Lo

Thethe abiunder used toin coorand vo

Thetem torepresthe rel

Pnew =Qnew =where

Pnew, Qnew,: loa

2.4. Vo

DuepowerOperatity to cunder disturbnction. The mathematical formulation of the proposed objective function can be expressed by the following

J(x, u) + Penalty (18)

v

NLi=1

(VLi V limLi )2 + Q

NGi=1

(QGi Q limGi )2

PlimGs )2 + br

NBRi=1

(Sbri Slimbri )2

(19)

Q, P and br are penalty factor terms, if limits viola-urred at dependent variables such as: load bus voltage, real power generation at slack bus, reactive poweroutput and transmission loading, they are xed to theirlimits (max or min). The following expressions illustrateg of constraints violations:

mini

if VLi < VminLimaxi

if VLi > VmaxLi(20)

minGi

if QGi < QminGimaxGi

if GGi > QmaxGi(21)

ins if PGs < P

minGs

axs if PGs > P

maxGs

(22)

if Sbri > Smaxbri (23)

g margin stability

ing margin stability is an important index which reectsf the system to deliver dynamically power to consumeral situations. In this study loading margin stability is

the best location of SVC controller and also optimizedtion with other objective functions such as power loss

deviation.ing margin stability is determined by pushing the sys-t of collapse by load increase at all load bus. Based onion shown in Fig. 2, the following equation describes

between load increase and loading margin stability.

base (24)

base (25)

: the new and basic active power demands: the new and basic reactive power demands

margin stability

stability index

economical and environment constraints, practicalem must to operate close to their admissible limits.n estimate the reliability of a power system by its abil-rve constantly acceptable voltage delivered to consumeral condition and also at critical situations (load increase,s) [51]. L-index is one of the efcient voltage stability


index propobus indicatbus; L-indesponding toequations dage stability

First, thebuses expre[

IL

IG

]= [Yb

where YLL, YSecond, [

VL

IG

]= [H

where H maHGL and HGGPV buses an

The H m

[H] =[

ZL

YGL

Finally, tfollows:

Lj =1

NGi=

For stabstable zone

3. Modelin

The statidevices largin Fig. 3, thparallel Thyhigh voltagtogether widynamicallyically capac

howle of

SVCcontrons d

jBSVC

reased a

BSVCi

tima

he litn, siz

stud efcion oering

folloed lo

ticaRun stabiSort valueFig. 2. Loading margin stability.

sed by Kessel and Glavitch [52]. L-index of a speciedes the proximity of voltage collapse condition of thatx varies between two extreme values, 0 and 1 corre-

no load and voltage collapse situation. The followingescribe the mathematical formulation of L-index volt-.

buses are separated into two parts: PV buses and PQssed as follows

us] .

[VL

VG

]=[

YLL YLG

YGL YGG

].

[VL

VG

](26)

LG, YGL and YGG are sub matrix of Ybus.the following transformation can be written:

] .

[IL

VG

]=[

HLL HLG

HGL HGG

].

[IL

VG

](27)

trix is generated by the partial inversion of Ybus, HLL, HLG,are sub matrix of H, are voltage and current vector of

d PQ buses, respectively.atrix is given as follows:

L ZLLYLGZLL YGG YGL.ZLLYLG

](28)

he L-index corresponding to each bus is expressed as

Fig. 4 sprincip

Theshunt equati

ISVC = The

expres

QSVCi =

3.1. Op

In tlocatioIn thisexploitreductconsid

Thepropos

1. Iden1.1

1.2 1

HLGji ViVj

j = 1, 2, . . ., NL (29)le situations the value of Lj at each bus must be in the

Lj < 1.

g of static VAR compensator (SVC)

c VAR controller (SVC) [1,57] is one of the shunt FACTSely exploited and installed in the world. As well showne basic structure of SVC consists of connected anti-ristors to provide controllability. Air core reactors ande AC capacitors are the reactive power elements usedth the Thyristor valves. The SVC has the ability to control

the voltage at critical buses by exchanging dynam-itive or inductive reactive power with the network.

cons2. Select th

buses NB3. Identify

example4. Locate th5. Locate th

bus C is SVC is sh

4. Overvie

Firey rmetaheurisShe Yang aadapted anbinatorial oFig. 3. Basic circuit schema of SVC.

s the SVC steady-state model representation and basic SVC.

model used in this study is based on representing theoller as variable susceptance; the following simpliedescribe the susceptance SVC model.

V (30)

ctive power QSVCi

exchanged with the bus i can bes:

V2i (31)

l location strategy of SVC controllers

erature various techniques were proposed for optimaling and control of multi type of FACTS devices [1,57].y a simple and exible location strategy is proposed toiently the integration of SVC controller to maximize thef power losses and voltage deviation under normal and

loading margin stability.wing steps summarize in brief the methodology of thecation strategy.

tion of critical buses based on voltage stability index.continuation power ow to determine loading marginlitythe buses based on their minimal voltage stability index. The buses with low voltage stability index value are

idered as the rst best candidate for SVC location.e weak bus with low voltage stability index from all, based on Fig. 5, k is the candidate bus.all branches associated to the rst candidate bus: for

i-j-m as well shown in Fig. 6.e branch associated to the related weak bus.e SVC compensator in the middle of the selected branch,the best location. The owchart for optimal location ofown in Fig. 7.

w of FFA

esearch algorithm is one of the new Biology inspiredtic algorithms which have recently introduced by Xin-t Cambridge University in 2007 [25]. FFA has beend applied with success to solving many complex com-ptimization problems FFA [26]. The main advantages of


Fig. 4. Steady-state model representation and basic principle of shunt compensation.

the rey asubgroups, enhance thwith anotheFFA are premechanismrules which[26,53,54],

1. All reies are unisex, the sex of reies has no effect on theirmovement in the environment, they will move only toward moreattractive and brighter ones.

2. The degree of attractiveness of a rey is proportional to itsbrightness which decreases as the distance from the other reyincreases due to the fact that the air absorbs light. If there is nota brighter or more attractive rey than a particular one, it willthen move randomly [26,53].

level of light intensity of a rey is determined by the valuee ob

ctive basbetw

= 03. Theof th

AttraTh

tion

(r) Fig. 5. Optimal location of SVC: step 1.

lgorithm is its ability to divide initial population intothis pertinent propriety is exploited in this study toe robustness of the mechanism search in coordinationr local search algorithm. The basic steps of the standardsented in the schematic diagram shown in Fig. 8. The

search of FFA has three particular idealized interactive are inspired from ashing characteristics of real reiesthe particularity of these rules described as follows:

where r isattractivecontrols t

DistanceIn the s

positions

rij = ||xi

where xi,kd is the n

MovemeThe mo

tive re

xt+1i

= xti

Fig. 6. Steps for optimal location of SVC Comjective function related to a specied problem.

enessic mathematical formulation of the attractiveness func-een reies is expressed by the following equation:

exp(rm), with m 1, (32)

the distance between any two reies, 0 is the initialness at r = 0, and is an absorption coefcient whichhe decrease of the light intensity.

earch space, the distance between two reies i and j at xi and xj can be dened by the following relation:

xj|| =

dk=1

(xi,k xj,k)2 (33)

is the ith component of the spatial coordinate xi, xj andumber of dimension.ntvement of a rey i which is attracted by a more attrac-y j is given by the following equation [53,54].

+ 0. exp(r2ij ) (xj xi) + (rand 0.5), (34)pensator.


where theond termintensity random mones. Ii anthat is assbe evaluadescriptio

ParameteLike ma

initial valgreatly th

Fig. 9. Basic pseudo code for the proposed rey algorithm.

ithm. These parameters depend on the nature and particu- of t

[0, 1omp= 1;e att

rvie

pattccesy coFig. 7. Basic ow chart for optimal location of SVC.

rst term is the current position of a rey, the sec- is used for considering a reys attractiveness to lightseen by adjacent reies, and the third term is for the

algorlarity

the c

0Th

5. Ove

Thewith suto manovement of a rey in case there are not any brighterd Ij are two variables which reect the light intensityociated with a specied tness function of particles toted. The pseudo code depicted in Fig. 9 gives a briefn about the standard rey algorithm.rs settingsny metaheuristic optimization methods, choosing theues of parameters is an important task which affectse efciency of results and convergence behaviors of the

global optimadvantage oputationallto the initiato be used optimizatio

As well iing a set of p[1 0], [0

Fig. 8. Mechanism search of the rey alghe problem to be solved.]: is a randomization parameter determined based onlexity of the problem to be solved.

ractiveness or absorption coefcient = 1.

w of pattern search (PS)

ern search (PS) is an evolutionary algorithm applieds for solving a variety of optimization problems relatednstrained complex research areas. Compared to manyization methods, pattern search (PS) method has thef being very simple in concept, easy to implement, com-y competitive, the drawback of this algorithm is relatedl conditions, for this reason this method is very suitableas a local search routine in coordination with a globaln method [39,57].llustrated in Fig. 10b, the algorithm starts by establish-oints called mesh, around the initial point X0. [1 0], [0 1],1], the determination of the next position representedorithm.


gorith

by directiofunction. Dothers direcbe found in

The basiIn this studtion factorsnumber of complexityand dynamsearch proc

6. The pro

The matrapping intration and PS algorithmconsidered mal regionsfunctions (fied stage nd new soto generatixed shuntcesses is rereached.

6.1. Method

As well ithe method

1. Identica2. Specify t

F2 (poweoptimal s2.1 Activ

variaF3

2.2 Savetive f

optimcontrVoltaSave

Restrattrol follobinat FFA

optixedmizeTap tSave

optimtranss areReacSaveFig. 10. Flow chart of the PS al

n and step size is based on the evaluation of tnessetails description and graphic representation of PS andt search methods for unconstrained optimization may

[36,57].c research steps of PS algorithm are shown in Fig. 10a.y, the mesh size and the mesh expansion and contrac-

are selected as 1, 2 and 0.5 respectively; the maximumgeneration is taken between 50 and 150 based on the

of the problem. The vector of initial points X0 is selectedically updated based on communication process duringess.

posed dynamic power system planning strategy

in task of this proposed hybrid method is to avoido a local optimum by dynamically balancing the explo-exploitation capability of the two standard FFA ands. Initially only active power of generating units are

and optimized using FFA to explore the best sub opti- by identifying critical units considering three objectiveuel cost, power loss and voltage deviation). At a spec-the partial solution found are communicated to PS to

3. Theing 3.1 3.2

4. Theare opti4.1 4.2

5. Thetap able5.1 5.2 lution by optimizing two control variables associatedng voltages, tap transformers and reactive power of

compensators and SVC Controllers. The search pro-peated until a number of minimum specied trails are

ology of the proposed combined algorithm

llustrated in Fig. 11, the following points describe brieyology of the proposed combined algorithm.

tion of critical buses.he objective function to be optimized: F1 (fuel cost),r loss) or F3 (voltage deviation). Generate initial sub-olution, this task achieved using FFA1e power generation is considered as the rst controlble to be optimized to minimize individually F1, F2 and

the sub-optimal solution corresponding to each objec-unction.

6.2. Coordi

6.2.1. OverThe pro

reasoning usummarizetion betweebrainstormproposed bmore effectThe Osbornterm qualitipate and gindividualsexible anding rules arbetween diVery recentthe followilows:m.

al active power generation is xed: Run PS, the follow-ol variables are to be optimized:ge of generation units

the new best solutionmark: the main advantage of the proposed exibleegy is that expert can choose the sequence of con-variables associated to each optimization stage, thewing description are a sample of basic and possible com-ion.1, FFA2, FFA3 or FFA2, FFA3, FFA1 or FFA3, FFA1, FFA2

mal active power generation and voltage of generators: Run FFA2: the following control variables are to bed:ransformer,

the new best solutional active power generation and voltage of generators,

former are xed: Run FFA3: the following control vari- to be optimized:tive power of SVC compensator.

the new best solution.nation based on brainstorming process

viewposed interactive hybrid method is based on humansing brainstorming process; the following descriptions the particularity and importance of the communica-n experts to achieve the desired optimal objectives. Theing process rst introduced by Osborn [49], the rulesy Osborn demonstrated that brainstorming process wasive in generating new ideas than individuals working.s rules have the particularity to generate new ideas iny and quantity, it gives chance to all individuals to partic-enerate original idea. Experience conrmed that some

have excellent idea, but needs to be exploited using interactive mechanism. In this study the brainstorm-e adapted and applied at specied stages to coordinatefferent solutions found using FFA and PS algorithms.ly, many optimization algorithms developed based onng basic rules named Osborns rules formulated as fol-


1. Focus on to particiand prod

2. Suspendigenerateviduals pideas witevaluatio

3. Welcomefacilitatevariety o

4. Go to quacombine

In indusdifcult prosolution prosons (experbrain stormin term of s

Fig. 12 ilnication baprocess unAs well claeach globalA perfect soperformancbeing applipractical reFig. 11. Mechanism parallel search using FFA and PS assisted

quantity [49]: This rule gives chance to all individualspate and to generate new ideas which allow generatingucing a greater number of ides.ng judgment [49]: In brainstorming, criticism of ideasd should be put on hold by suspending judgment, indi-articipating will have the chance to generate unusualhout judgment. Criticism is reserved for a later stage forn.

unusual ideas [49]: The particularity of this rule is to and allows working in an environment with a goodf ideas, unusual ideas are welcomed.ntify [49]: A strong evaluation mechanism selects ands ideas to form good idea.

trial area, experience conrmed that when we face ablem which every single expert cannot solve or theposed fail to attain the desired objective, a group of per-ts), especially with different experience, get together to, the problem can usually be solved with high efciencyolution quality and time required [23].lustrates the basic principle of the interactive commu-sed on brainstorming process. During communication-expectable intelligence and original idea can occur.ried and conrmed in many recent research results,

optimization method has advantages and drawbacks.lution is to hybrid these methods to achieve the beste. The optimization based on brainstorming processed to solving many complex problems related to manysearch areas. Details description about brainstorming

mechanismin using thethe main iduniversity iintroducedrmed the ienhance th

6.2.2. BrainThe ada

developed 2011 [27]. Tsively to soplanning anproposed aand controlsuch as pozation. As wBSOA propooperations.

Initializatthe initiaof searchbrainstor

Clusteringclusters (K-means s with brainstorming rules.

search can be found in [38,50]. Our rst contribution brainstorming concept was rst investigated in [28],ea proposed is to enhance the teaching quality in ourn Algeria within the educational system named LMD

recently in our universities. Teaching experience con-mportance of introducing the brainstorming process toe educational level of our students.

storm optimization algorithmptation of brainstorming principle and rules is rstlyand formulated as an optimization problem by Shi ino date, the BSO algorithm has not been applied inten-lving the complex problems related to power systemd control, very recently in 2015, Rezaee Jordehi [50]n efcient algorithm based BSOA for optimal location

of FACTS devices to improve various objective functionswer loss and voltage deviation and overload minimi-ell depicted in Fig. 13, the basic mechanism search ofsed by Shi [27] is formulated based on the following 4

ion: like the majority of global optimization techniques,l population is generated randomly in feasible region

space. In BSOA, individuals are analogous to ideas inming.: this operation divides the population into differentbrainstorming groups) according to individual features.trategy is used for clustering [50].


Fig. 12. Interactive communication based on brains

Fig. 13. Basic mechanism search of BSOA.

Cluster ceideas of bbility P1, aindividuaindex to b

Individuauals (ideaindex P2 ithe follow

Xid(t) = Xwhere N(and standand is up

S(t) = log

where tmrespectiv

The operrepeated

6.2.3. PropoIn this w

and PS durifunction F1ability P1 drelated to ocommunicabation operexploitationexible hybbetween di

1. For thePS.torming process.

nter perturbation: cluster centers are analogous to bestrainstorming groups, during this stage and with proba-

cluster center is selected and is replaced with a randoml [50]. P1 is control parameter and considered as analance between exploration and exploitation capability.l perturbation: in order to improve the quality of individ-s) during search process, a second specied probabilistics introduced to create perturbation to individuals usinging equation:

id(t) + S(t)N(0, 1) (35)

0, 1) represents Gaussian distribution with mean zeroard deviation of one. S(t) is the perturbation step sizedated using the following equation:

sig(

(tmax/2)tK

) r (36)

ax and t represent the maximum and current iterationely, K is a scale factor.ations of the mechanism search are evaluated anduntil a number of maximum generations is reached.

sed brainstorming rulesork, the brainstorming rules are used to assist FFA

ng search process, for each specied principal objective, the individuals of population are perturbed with prob-ened by experience, the sub optimal vector decisionther secondary objective functions such as F2, and F3 areted to the principal objective function F1, this pertur-ation is important to balance between exploration and

capability. Fig. 14 shows the owchart of the proposedrid method. The following steps describe the interactionfferent methods during search process.

next trail, communicate the best solution found to


Fig.

2. Brainstowithin operatiosuch asworst idate diveCommu

At spetrol varfunctionsolutionsidered

0.92

0.94

0.96

0.98

1

1.02

1.04

1.06

.u)Vol

atge

Mag

nitu

des

(p 14. Flowchart of the proposed interactive hybrid method.

Fig. 15. Perturbation during brainstorming process.

rming process: The basic idea introduced and adaptedthe brain storming process is based on perturbationn, the best idea found from other objective functions

F2, and F3 at specied stages which considered as theeas from the objective function F1 are exploited to cre-rsity in search space to improve the near global solution.nication process at specied stages is shown in Fig. 15.cied stage (iteration), communicate the optimal con-

iables (Pgi, Vgi, Ti, Qci) corresponding to other objectives (F2, F3) to PS, it is important to clarify that the best

found considering for example F2 (power loss), con- as the worst solution when considering the objective

Fig.

functioexplore

3. Generaand woa speci

4. Conver4.1 For eac

stopped4.1 The pro

achieve

7. Case stu

In this sdeveloped iThe propossystems. Onbe retrievedinvestigateteristics corgiven.

7.1. Test sy

This test1-2-3-6-8, one shunt Vthe total lothe values limits for acTable 1

Case 1: FThe tota

ing total p0.3479 p.u. the SVC comvoltages at

Case 2: PTable 2

function vacondition (Pwith the pthe results age deviatiexchanged line 13-14 ivoltages at 0 5 10 15Number of Buses

16. Distribution of optimized voltages at all buses: case 1.

n F1 (fuel cost optimization), this stage is important to new feasible regions (ideas) during process search.te new database: Save the new solution (best solutionrst solution): repeat the communication processes untiled Ntrail.

genceh algorithm (partial solution), the search process

if a specied number of generation is reached (Gmax).cesses search stopped if a specied number of trails ared.

dies and numerical results

ection, the proposed interactive planning strategy isn the Matlab programming language using 7.8 version.ed approach applied to many electrical practical test

the standard IEEE 14-Bus and IEEE 30-Bus, data can from [55,56], in this study only one SVC controller is

d. Due to paper length limit, the convergence charac-responding to the different objective functions are not

stem 1: IEEE 14-Bus

system consists of 5 generating units located at buses:two transformers located at lines 4-7, 4-9 and 5-6 andAR compensation installed at bus 9. At normal conditionad demand to satisfy is 259.0 MW, the generator data,of fuel cost coefcients, the minimum and maximumtive and reactive power of generating units are given in

uel cost minimization

l fuel cost achieved is 8078.63 $/h, the correspond-ower loss and voltage deviation are: 9.221 MW, andrespectively. The optimized reactive power delivered bypensator is 5.98 MVAR. The distribution of optimized

all buses is shown in Fig. 16.ower loss minimizationshows the optimized control variables and objectivelues with real power loss minimization at base loadD = 259.0 MW). The minimum real power loss obtainedroposed strategy is 0.634 MW which is better thanfound on case 1 (9.221 MW), the corresponding volt-on achieved is 0.3816 p.u. The optimal reactive powerby the SVC and the network installed in the middle of thes 5.93 MVAR. For this case the distribution of optimizedall buses is shown in Fig. 17.


Table 1Technical admissible paramaters of generators and the fuel cost coefcients: IEEE 14-Bus.

Bold font with red color has been used to indicate the limits of control variables.

Table 2Optimized control variables for IEEE 14-bus system: cases 2 and 3.

Bold font with blue color has been used to indicate best results of the proposedplanning strategy.

0 5 10 150.92

0.94

0.96

0.98

1

1.02

1.04

1.06

Vol

atge

Mag

nitu

des (

p.u)

Number of Buses

Fig. 17. Distribution of optimized voltages at all buses: case 2.

0 0.92

0.94

0.96

0.98

1

1.02

1.04

1.06

Vol

atge

Mag

nitu

des (

p.u)

Fig.

Case 3: VIn this c

compared trespondingpower exch13-14 is 6 Mfor minimuobjective fusator are shat all buses

Case 4: Pimization

To test egy, the towith increatotal powerity = 1.6 p.ucorrespondinjected at security counits, branlimits. Fig. buses, Tablsponding stin all brancvariables an

Table 3The best results for three optimized objective functions: IEEE 14-Bus: PD = 259 MW.

Bold font with blue color has been used to indicate best results of the proposed strategy.5 10 15Number of Buses

0.065

18. Distribution of optimized voltages at all buses: case 3.

oltage deviation minimizationase the total voltage deviation is reduced to 0.0465 p.u.o case 1 (0.3479 p.u.) and case 2 (0.3816 p.u.), the cor-

total power loss is 1.2516 MW. The optimal reactiveanged by the SVC installed in the middle of the lineVAR. Table 2 shows the optimized control variables

m voltage deviation. The best results of three optimizednctions considering the installation of one SVC compen-own in Table 3. The distribution of optimized voltages

is shown in Fig. 18.ower loss minimization and loading margin stability max-the feasibility and robustness of the proposed strat-tal active power loss is minimized in coordinationsing load to the limit of margin stability. The optimal

loss achieved is 3.0912 MW at loading margin stabil-. which correspond to the new load PD = 414.4 MW, theing voltage deviation is 0.2672 p.u. The reactive powerthe middle of branch 13-14 by the SVC is 6 MVAR. Allnstraints in term of reactive power limit of generatingches loading and voltages are within their admissible14 shows the distribution of voltage magnitude at alle 4 shows the optimized control variables, the corre-ate variables such as, active and reactive power transitshes are depicted in Table 5. As we can see all controld state variables are within their admissible limits.


Table 4Optimized control variables for IEEE 14-bus system: cases 4 and 5: PD = 414.4 MW.

Bold font with blue color has been used to indicate best results of the proposedstrategy.

Case 5: Vity maximiz

Voltage ering energsecurity limengineer. I0.0890 p.u.,point of brapower loss achieved wshows the othe correspotransits in atages at all b

Fig. 19. Distribution of optimized voltages at all buses: cases 4 and 5: Loading marginstability = 1.6 p.u.

show the repartition of power transit in branches, a comparativestudy in term of solution quality is depicted in Table 7. It is impor-tant to note that all security constraints are satised.

7.2. Test system 2: IEEE 30-Bus: without considering SVCcontroller

This second test system consists of 6 generating units locatedes: 1-12 d atl contor daximre giic pllti ompoe1: Me2: Me3: Me1: M

Table 5Active power t

Bold font witholtage deviation minimization and margin loading stabil-ationmagnitude is an important power quality index; deliv-y to consumer at critical situation within admissibleit is an important and difcult task for expert and

n this test case the voltage deviation minimized at the optimal reactive power injected by SVC at the mid-nch 13-14 is 4.92 MVAR, the corresponding total activeis 3.6594 MW. The maximum loading margin stabilityithout violation of security constraint is 1.6 p.u. Table 4ptimal control variables corresponding to this test case,nding state variables such as, active and reactive powerll branches are depicted in Table 6. The optimized vol-uses for cases 4 and 5 is shown in Fig. 19. Tables 5 and 6

at bus6-10, 4installenormageneraand munits adynamthe muthree i

CasCasCasCasransit in branches: case 4: PD = 414.4 MW/loading margin stability: LF = 1.6 p.u.

red color has been used to indicate the maximum limits of power transit in branches.-2-5-8-11-13, four transformers located at lines 6-9,and 28-27 and nine shunt VAR compensation buses

buses 10, 12, 15, 17, 20, 21, 23, 24 and 29 [51,52], atdition the total load demand to satisfy is 283.4 MW. Theata, the values of fuel cost coefcients, the minimumum limits for active and reactive power of generatingven in Table 8 and available in [55,56]. The proposedanning strategy based FFAPS has been applied to solvebjective OPF. In this study and for fair comparison onlyrtant cases are considered:inimization of total generation fuel costinimization of total power lossinimization of total voltage deviationinimization of total generation fuel cost


Table 6Active power transit in branches: case 5: PD = 414 MW/loading margin stability = 1.6 p.u.

Bold font with red color has been used to indicate the maximum limits of power transit in branches.

Table 7The best results for optimized objective functions: IEEE 14-Bus: PD = 414 MW: LF = 1.6 p.u.

Bold font with blue color has been used to indicate best results of the proposed strategy.

Table 8Technical admissible parameters of generators and the fuel cost coefcients: IEEE 30-Bus.

Bold font with red color has been used to indicate the limits of control variables.

Fig. 20. Convergence characteristic for fuel cost minimization at the rst stage: global search achieved using FFA.


Table 9Optimal setting of control variables: cases 13.

Bold font withBold font with

Fig. 21. Compintermediary s

The totaing total po1.9142 p.u. compared tcompared terature. To mechanismrepresentedstage the toout consideconsideringbased on neintermediarstage, the tovalue found blue color has been used to indicate best results of the proposed strategy. red color has been used to indicate the limits of control variables.

arison of convergence characteristic for fuel cost minimization attage.

l fuel cost achieved is 798.9857 $/h, the correspond-wer loss and voltage deviation are: 8.4855 MW, andrespectively. The fuel cost achieved is highly reducedo the base case (power ow solution), and also improvedo many recent optimization methods cited in the lit-illustrate the principle of the proposed new combined

search, the convergence characteristic of the fuel cost is in three stages as well shown in Figs. 2022, in the rsttal fuel cost optimized is 801.4326 $/h using FFA with-ring the brainstorming process, at specied trail and

the practical rules generated by brainstorming rulesw updated database, the total fuel cost achieved at thisy stage is reduced to 800.6193 $/h, nally at the lasttal fuel cost optimized is reduced to 798.9857 $/h, this

using local search based PS algorithm. It is important

Fig. 22. Convesearch achieve

to clarify thconstraintssecurity vaables foundoptimizatioother recenTable 10.

Case2: MThe tota

tive functiocorrespondacceptable.total activesumer withrgence characteristic for fuel cost minimization at nal stage: locald using PS.

at the optimal fuel cost achieved without violation of, all security state and control variables are within theirlues. Table 9 shows results of optimized control vari-

for three cases compared to the base case (withoutn). Comparison results of the proposed approach witht metaheuristic optimization methods are tabulated in

inimization of total power lossl cost and the total power losses are two conict objec-ns. In the rst case, the total power losses generateding to the minimization of total fuel cost may not be

There for the goal of this second case is to minimize the power loss by considering delivering energy to con-in the security limits. The convergence characteristic of


Table 10Comparison results of the proposed approach with other metaheuristic optimization methods: IEEE 30-Bus: cases 13.

Bold font with blue color has been used to indicate best results of the proposed strategy.Bold font with red color has been used to indicate infeasible results.


Fig. 23. Convenear global sea

Fig. 24. Convestage.

Fig. 25. Convesearch achieve

the total poFigs. 2325.from the in

The bestis 2.9162 Merences. Alssecurity conwith other Table 10.rgence characteristic for power loss minimization at the rst stage:rch achieved using FFA.

rgence characteristic for power loss minimization at intermediary

rgence characteristic for power loss minimization at nal stage: locald using PS.

wer loss is represented in three stages, as well shown in As we can see the total power loss optimized is reduceditial stage to the last stage.

total power loss achieved using the proposed strategyW which is better than many results cited in recent ref-o, the total power loss optimized without violation anystraints. Comparison results of the proposed approachmetaheuristic optimization methods are tabulated in

Fig. 26. Convestage: near glo

Fig. 27. Convediary stage.

Fig. 28. Convstage: local se

Case2: MVoltage

ideal value case is the iload buses bthe ideal de0.1114 p.u.,convergencsented in ththe total vorgence characteristic for voltage deviation minimization at the rstbal search achieved using FFA.

rgence characteristic for voltage deviation minimization at interme-

ergence characteristic for voltage deviation minimization at nalarch achieved using PS.

inimization of total voltage deviationproles at load buses must be within a desired value, theto be satised is 1 p.u. Therefore, the goal of this thirdmprovement of the distribution of voltage proles at ally minimizing the voltage deviation of PQ buses aroundsired value. The best total voltage deviation achieved is

which is better compared to other recent methods. Thee characteristic of the total voltage deviation is repre-ree stages, as well shown in Figs. 2628. As we can seeltage deviation optimized is improved during the search


Fig. 29. Distristability = 1 p.u

process. It ivoltage devWe can notimproved a

8. Verica

In the resolution qua category affect the foptimizatiopublished rtopology ofwell knownby injectingthe proposeNewtonRaactive powstraints of ctransformepensator anon details ocorrectionsin Table 10.

9. Discussi

The follospective of

The optimcorresponof solutio

The exibmodify thof the pro

The braingence andspecied search sppractical

The user cing the prmethods solved. It posed alg

also important to clarify that there are no parameters to adjust,which considered as an advantage, so the brainstorming processvery suitable to working on parallel and in coordination withone or more metaheuristic methods. The formulation of rules

nds to beis stution ct tom atropo

betwhancropo

orkin rela

nclu

ew pd PSto mion cned ads arn usng practitntroltly t

of pf cosstiga

loss y enng st4-Buserveic plowe

stabpracttionng pos valstra

wled

authbution of optimized voltages at all buses: cases 1-2-3: Loading margin.

s also important to note that minimization of the totaliation is achieved considering all security constraints.ice from Fig. 29, that the voltage prole has been greatlyround the desired value (1 p.u.).

tion of limit violations

cent literature many papers proposed to enhance theality of practical security OPF problems, unfortunatelyof results published recently are not well veried, thiseasibility, efciency and robustness of the proposedn methods. In this study the quality of some resultsecently are checked and veried considering the same

electrical network and their associated constraints. As, the verication methodology is simple and it consists

the optimal decision vector (vector control) found byd methods to the standard power ow program basedphson algorithm to determine all state variables, theer of slack generator and to verify the violation con-ontrol variables such as voltages of generating units, tapr, reactive power injected by conventional shunt com-d susceptance of specied SVC. In this section and basedptimal results given by in different papers, remarks and

regarding the quality of certain methods are presented

ons and perspectives

wings points summarize the particularity and the per-the proposed practical planning strategy:

ized results found for the two practical power system

depelem

In thdinasubjesyste

The ption to en

The pto wlems

10. Co

A nFFA anposed deviatcombimethosolutiostormiand prand coefcienin termterm ois invepowerstabilitplanniIEEE 1It is obdynamtotal pmarginposed applicaplannisuch athe con

Ackno

Theding to all objective functions are competitive in termn quality and convergence characteristic.ility of the proposed hybrid method allows expert toe algorithm based on the particularity and complexityblem.storm process proposed inspired from human intelli-

reasoning rules introduced to assist the FFA and PS atstages to exploit and explore new feasible region in theace, these rules are not generalized and depends on theproblems to be solved and experiences of users.an easily replicate the proposed algorithm by introduc-oposed rules in coordination with other metaheuristicconsidering the particularity of the problem to beis important to not that the user can improve the pro-orithm by introducing also his own practical rules. It is

editor and tand recommpaper. Real

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sion

ractical power system planning strategy based hybrid algorithm assisted with brainstorming rules is pro-inimize total fuel cost, total power losses and voltageonsidering loading margin stability. In this proposedpproach the performances of the standard FFA and PSe improved by adjusting dynamically their sub-optimaling interactive reasoning rules inspired from brain-ocess. The proposed planning strategy allows to expertioner specialized in power system planning, operation

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Security optimal power flow considering loading margin stability using hybrid FFAPS assisted with brainstorming rules1 Introduction2 Security optimal power flow2.1 Objective functions2.1.1 Minimization of total fuel cost2.1.2 Minimization of voltage deviation2.1.3 Minimization of power losses

2.2 Constraints2.2.1 Equality constraints2.2.2 Inequality constraints2.2.2.1 Generator constraints2.2.2.2 Transformer constraints2.2.2.3 FACTS controllers constraints2.2.2.4 Security limits

2.2.3 Constraints management

2.3 Loading margin stability2.4 Voltage stability index

3 Modeling of static VAR compensator (SVC)3.1 Optimal location strategy of SVC controllers

4 Overview of FFA5 Overview of pattern search (PS)6 The proposed dynamic power system planning strategy6.1 Methodology of the proposed combined algorithm6.2 Coordination based on brainstorming process6.2.1 Overview6.2.2 Brainstorm optimization algorithm6.2.3 Proposed brainstorming rules

7 Case studies and numerical results7.1 Test system 1: IEEE 14-Bus7.2 Test system 2: IEEE 30-Bus: without considering SVC controller

8 Verification of limit violations9 Discussions and perspectives10 ConclusionAcknowledgementReferences

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