Optimum Coordination of Overcurrent Relays Using SADE Algorithm

8/13/2019 Optimum Coordination of Overcurrent Relays Using SADE Algorithm

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A l p _3075

mum u y g S DE g hm

M j b M se i, mi f m d,F M se ip u

Dep me f E e i E gi ee i g Is mi z d U ive si y f e m Im m se i83@ i m f m d@ i m f m I986 m

AbstractOne of t e impo ta t conside ations in

designing powe systems is designing theisecu ity systems. The most common fault in powe systems is the line to g ound one th tove cu ent elays a e used to p otect thes stem agai st it ( s ima y p otectio idist ibution systems and second y p otectionin t nsfe ing ones). The most impo t nt

issue in using ove cu ent el ys is theicoo dination. In today v st systems, using t aditional methods that a e o en based onmathem tic l elations such as g dient oexpe imental elations a e not e cient

nymo e nd the solution is to utilizeintelligent methods. In this text, Self-AdaptiveDiffe ential Evolutiona y algo it m (SADE)used fo Optimum Rel ys Coo dination p oblem (ORC) and its function on 1 and 30netwo ks of IEEE st nda d bus was tested,

nally a compa ison done between SADE andcommo m th ds o E, also wit theevolution y lgo it ms such as PSO and GA that shows the capability of SADE to solvenonline optimum p oblems with many localoptimums.

K ord : Powe system p otection,Coo dination, Ove cu en elay, DE

lgo it m, PSM, TDS

1. IntroductionToday one of the most impo tan issues in

indust y is systems cont olling and secu ity.

Basic indust y of elect icity not only is thesame s bove but lso it is mo e impo tant t n othe s because it is the inf ast uctu e of

ny count y economics.In powe systems, one of the instability

f cto s is t e occu ence of fault tha ifcontinues, it may lead to blackout o evenlosing of some system p ts. The efo e, p eventing the exp nsion of fault is an

essential task in cont olling of powe systemsand this would be p actical by p otectiveel ying.

Bec use mo e than 80% of powe systemfaults is single phase to g ound fault, ifg ounding of system done imp ope ly it willbe the most intensive one, so the mostimpo t nt and many of a powe system

el ying is ove cu ent one[ ].In elaying aspect, exp ess and accu ate

function without t e inte fe ence of elays is

of challenging cases bec use we need fob ck each e a s s assu a ce a d the efo e elays coo dination is a d p oblem in elaying .Since 60s dec de tillnow the e a e ttempts to solve the ORC p oblem th t e divided into t ee catego ies: t i l and e o methods [10, 11], topologyanalysis methods [1 ], and optimum methods.Op imum methods e mo e accept ble due to t ei high speed nd they a e divided into twog oups: p og amming methods nd intuitionmethods. Due to t e complexity of nonlinea

OptimumRelay Coordina tion


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optimum p og amming methods, theoptimum coo dination of ove cu ent elaysdone usually by linea p og amming methodwhich is including simplex, dual-phasesimplex, Duality simplex and some modemethods.

In [8] the issue of coo dination solved bylinea p og amming (dual-phase simplex)with one diffe ence that conside ing possibleva iations of netwo k load and topology, anadaptive algo ithm with suppo t of monito ing(SCADA) was used.In linea p og ming,one of the p oblems is low esponding speeddue to complexity of the p oblem that in [9] itis t ied to obtain optimum solutions withoutestablishing ta get function and just bysolving limitations equations. In this method,at st those limitations that make the p oblem impossible a e speci ed and then thecomplexity of the p oblem dec eased bydec easing the limitations. The dif culty of this method is to accomplish all emaininglimitations othe wise the p oblem will beunsolvable.

Using planning method which is based onmathematical and expe imental elations o enmay not lead to optimum solutions that couldbe due to incapability of these methods inmoving f om many di ections towa d theoptimum solution, and because thecoo dination issue has seve al minimum points, so these methods could not be ef cientenough and also whe eas they a e based on aninitial guess, they may get caught in localminimums; the efo e, the e need intelligentalgo it ms which a e capable of app oachingoptimum solution f om seve al di ections.Recently, due to high speed, PSO algo it m is

conside ed and applied fo coo dination issues[7] .PSO algo ithm is based on animals socialbehavio and pa icles theo y. Each pa ticle(solution) di ected by a speed depend on itsexpe iences and those of a ound it. Despite all the above, this algo ithm sometimes getcaught in local optimums.

In cu ent pape , diffe ential-evolutiona y(DE) algo ithm conside ed fo the p oblem ofoptimum coo dination. DE function is basedon mathematical functions (sum, minus,

multiply) without using de ivation on vecto s that these vecto s a e the distance between a point in sea ching space and a speci ed o igin

[ ]. In compa ison with evolutiona yalgo ithms, DE like PSO has signi cantcha acte istics such as memo y andcoope ation between pa ticles that inc easesits speed and accu acy. Mo eove , it utilizesmutation which causes bette elease f om

local optimums in big p oblemscompa ison with PSO.Note that mutation may cause away f om

optimum solution and lead to dec ease inalgo ithm speed; in this pape , using feedbackan algo ithm suggested fo DE that is ef cientin big p oblems in compa ison with othe DE,GA and PSO algo ithms.

2. DE Algorithm

2.1. Algorithm review

DE sea ch algo ithm is one of thenewest sea ching methods. The theo y ofalgo it m imp ovement is eme ged f omKe neth V. P ice attempts in solving the p oblem of Chebyshev multi Adaptation andDE algo ithm we e int oduced in 1996.The lgo ithm functions like PS , that isacting on the position vecto and it hasmemo y the same as PSO; its main diffe ence

with PSO is its utilization of a dom vecto sdiffe entiation that is the int oduce ofmutation to some extent, and this causes it tobe an algo ithm mo e capable than PSO to pass f om local optimums.DE algo ithm function stages a e as follows[ ]:

a) Gene ating Initial Population: DEalgo ithm sta ted by gene ating initial population that contains NP ( umbe ofPopulation) ows and D (Dive se)c lumns.

b) Mutation: a newbo vecto p oduced foeach pa ent.

c) Mapping: if necessa y, newbo vectoshould be in (u in, u ).

d) C ossove : mutated vecto and initial population one p oduce testing vecto s.

e) Selection: the p oduced newbocompa ed with the pa ents and nextgene ation population engende . A e thestage of selection, calculation cycle in DE

Differential Evolutiona r


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continues until the convergence of allvectors or occurrence of stop criteria. The

owchart of differential-evolutionaryalgorit m shown in the following gure:

Genera e n al pop la on&e al a e ness

Ma n loop ( epea P mes):Mu a on Bounda y c eck n

3. C oss oveNo Selec on

Yes

F I c a DEa 1DE algorithm divided into various strategiesfrom the view point of mutation [ ] :

1) Best/rand strategy2) Old/ best/rand str tegy3) Best/rand/rand strategy

) Rand/rand strategy

) Ra d/rand/rand strategyIn the rst t ree methods future generation produced from the best parents and from thedifference of random vectors; in other twomethods the future generation produced justfrom the difference of random vectors.DE hasseveral reproducing methods. The followingmethod suggested by Price [ ]:It starts by NP solution vectors which wereselected randomly and for each belong to (1NP) the mutated vector calculated asfollows:

[ ] = U best[ ]+ x( [ ]-z [ ] 1

The Cro ov ragent on the mutated vector and intial population vector is done to

obtain test vectors ' . = = ' (2)- J J I I

For each part of this vector a number selected

between [0, 1] randomly and called randj IfCro ov r Ra 0< =CR


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= (U U( U U)

C / v g)(U U )Ur4d= (U U

=( d (U UU 3 _ -

UgJobaJ

Ur2

F 2 c SADE a c sIn the mentioned DE algorit ms, controlling the mutation is done by F and it causesintense dependency of the algorithm on this

parameter. In SADE, mutation vector controls the mutation effect adaptively usingfeedback, so a kind of self-regulationincreases the speed and exactness of thealgorit m. The F parameter also is for manualcontrolling of mutation.

3. The Problem FormulationOvercurrent relays are divided into g neralgroups:

1) Speci ed time2) Inverse of standard3) Much inverse

) Very much inverse (in nite inverse)Relays using in a feeder are better of one type.To describe the behavior of over currentrelays, time-current curves or mathematicalrelations can be used.In this article the following relations wereused:

PSM= c % X c (8

TDS = 3 XTMS /logPSM 9Where :TDS4: is a coe cient speci es time in whichhigh current relay functions.PSM5: is the initial current amount of thenetwork in proportion to amount of relay

Time Dial SettingPla y Setting Multiplier

4

regulatory current that is transferred toward the network. t : time of relay operationIsc : the least short circuit current in relayview scope% set : percentage of relay regulation

Ict : nominal regulatory current of relay in proportion to initial side of the network.PSM and TDS quantities should be speci edfor coordination of over current relays inorder to obtain the time of relays operationfrom Eq.(2) .As said before, these timesshould obtained in a way that in addition tohaving no in-coordination between relays, weshould have the least time of operation inorder to have the least damage to the system.In this paper TDS and % set are reg ded as the variants. As the algorithm starts, TDS andPSM amounts are calculated in each stage andby using Eq.(2) the operation time of mainand backup relays are calculated. Then tobtained by following relation:L = ck p - m i -eTI (10)Where: tba ck up: operation time of backup relay

ma in : operation time of main relayCTI : coordination time intervalUsing L and m aimoperation of relays can bespeci ed. Negative L shows disorder infunction of main and backup relays; and highL shows that the cover of backup relay isinappropriate. High m aimshows much delay ofrelay in fault repulsion. The mentioned casesare undesirable situations that should be prevented and it is clear that the time shouldbe positive; thus, target function de ned indirection of realization of three goals:

1) Decrease of maim

2) Decrease of L3) Pos tiv b oL

) Positive being of the timesTherefore the following t get function wasused:OP= (( m i )+ ( m i -I m i ) )+ 2 (L + 3(L - IL I))(11)The owchart of solving the problem is asfollows:


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Tma n,Tbackup,

Dete mine pa amete s&Gene ate ini ialpopula ion

Evaluate ftness &dete mine he bests

No

4. S F g 3 c a s v gORCy SADETwo networks of 1 and 30 bus IEEEstandard system were used to dismount ORC problem. Considering network topology, 30relays were applied for 1 -bus network and67 relays for 30-bus network that are shownin Fig. ( ), Table (1) and Fig. (13), Table ( )respectively. Two variants of TDS and %setwere considered for each relay; totally, 60variants for 1 -bus network and 13 variantsfor 30-bus network were considered. Resultsof load ow and short circuit calculations arein Tables (2) and ( ). The ORC problem for

the mentioned networks also with mentionedDE algorithms and PSO and GA were solvedand nally a comparison done between allalgorit ms.

It is noticeable that SADE only has onecontrolling parameter (F) and this causes toregulate it simply. In this paper F considereddynamic.We speci ed the limitations of variants as0.0


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F g 4 s g - d ag a EEE14- s [13]

The average results of applying SADE during0 times implementation (NP= 0 and 100

iterations) on the above mentioned network isas follows:

4

Av rag B t ar A

4 it ra i 8

F g 5 av ag s s a 14- s

As seen in g.( ) average best so f ofSADE which shows the speed and exactnessof the algorithm moves toward the OPminimum quickly. Figures (6-8) show that thealgorithm managed to keep the time periodssmall and their differences positive to

possible range that is to realize the targetfunction.

5 5 2 25 3 35 Fig.6. a v a g tm n 14- s

0 r -

15 2 35e y n mbe

F g 7 av ag 14- s

1 5 15 2 3 35e y m e

F g 8 av ag A 14- s

a l h r sul s fapying O lgorithm 4 - us n wor%s

P P M %s P P Mlay M mai a u ay M tmai a unum num tOmai a u n p

Omai a ku n pr r

n p n p

o os - o.os 9 4o os 4 o.s 94o os o.os 4 9

4 o os 4 4 9 9 o.s 49o.sos I4 4 o.os o.sss 49

o.os 4 o.os 4 9 4 44 9 4 o.s 9 449o os 4 4 o.s 4 4 9 4

6


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90

1 2

41 5

0 . 1 5

.

9.

.

8 . 7 2

.1 2 . 9

49

4.94

4.

4

.4

.449494

4.4

.9

4

9

Notice: In the above table PSM de ned in form of Isc/In.

.

.

4.1. Application of SADE algorithm to IEEE 30-bus networkThe network data are in Tables ( ) and ( ).

Ta (4) T da a a a d ac ays 30- s

main

4

9

backup

4444

main backup main backup4

2 5

2 6

2 7

2 8

930 3 2

94

9

4449

4

4449

3 2 5 6 9

13

4

8

9

8

6 2

94

.4

.

9

9.4 4

4

944

44444 5

4

.4.4

9

.

3 2

44 2

44 0

4 5

442 6

9Table ( ). T da a I ad w and sh rt circuit f 30-bus netw rk

R laynum

4

9

1 3

4

91

main

9 .9

4 9.

994 4.99 .

99 .

9.9 44

.4 4

.4 .

4 44 .9 .9 .

bac ku p

. 99

94 .

4 9 4..

4 .94.

4.

.4

..

.44 .

.

Nominalrela y

curr n

9 .999

.4 4449

9 99. 49. 4

4 ..4 4.. 9

4449.

. 94 9

4 . 44.4

.9

Relaynum

2 4

2 5

2 7

29

30

3 1

32

33

34

3 5

37

3 8

3 9

40

4 1

4 2

43

44

44 6

main

.94

4 .4 9

4.

449. 4.

944 .

9. 44

..

999

.49 . 4

ackup

.

.49

4 44 .

9 . 494 4

.9 . 49

4 4..4

4949 .

. 9994

. 4.

4 .

Nomina l

rela y cur rent

4.94

. 94

99.99. 9

.

.. 9

4 .444 .

.

.

.4 .4

Re ay.

47

4 8

4 9

5 0

5

5 2

53

54

5 5

5 6

57

5 8

5 9

6 0

61

6 2

63

64

6 5

mai

4 .99 9

4 .

4. 9

9 9.9 4

.

. 49 99 .4 49 .4

4 .4

.

.49

4 9

9

4

back p

4. 44 4

.9

49 4..49 4

4. 49

4 .9 94 .9

. 4

. 9. 9

4 9. 44

. 44

.449

9

2

4

N om ina l

rela yc ur e nt

.4

9.9

4 9 94 . 9

.4

.

.4

. 94 .4

4.44 .

49. 499

The average results of dismounting SADE during 0 times implementation ( P= 0 and 100iterations) on the above mentioned network are shown in gure (9).Fig.(9) the same as g.( ) shows that SADE algorithm has high convergence speed.

7


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65

4C

2

Av g st so f SADE

L = : = 6

i

O

o"u': oo .

Fig.9.average best so far of 30-bus network

Fig.II. average t c p of 30-bus network

[ W ND G TR SF ME QUY l fHANCk

12 F lO

6

O

L(B

0 0 0 0 0 0relay numberFig.I O. a vera ge tm n of 30-bus network

r lay num rFig.I2. average t of 30-bus network

Fig.I3. single-line diagram of EEE30-bus network[ 13]

8

70


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4.2. Comparing SADE resu ts with otheralgorithms

4.2.1. Comparing with mentioned DEalgorithms:In this section we compare SADE nctionwith DE , DE2 and DE3 algorithms.

8 ( SADE8 DE1 B DE8 8 DE

o . o w 0

i eration

Fig.14. average best so far of for 14-busnetwork comparing with

0

8 I

1

;; ;;

- averagebests far O. average bests far average bests far average bests far

\0 20

- 40 - nFig.IS. average best so far of for 30-bus

network comparing withAs seen in g. (14) and (15), in situations thatother DE algorithms trapped in localoptimums, SADE continues its movement by

x convergence speed. This shows that SADEis very capable to pass through localoptimums. The enlarged fo of g.(15) is in

g. (16) and 7).: ,

-

o

8 i

61

4

oo L 2- -O '6 S ;00i n

Fig.16. bigger view of Fig.( IS)

ao

r W

Fig.17. bigger view of Fig.( 16)

9

4.2.2. Comparing with PSO a gorithm:In this paper initial PSO algorithm was used that in [7] it used for ORC problem.

5Ii

g3\2 '\. ,." . _- .

4 0 1Fig.I . average best so far of for 14-bus

network comparing with algorith during SO times implementation.

' 6'- -- -'Fig.19. average best so far of for 30-bus

network comparing with algorithms during SO times implementation.

4.2.3. Comparing with GA a gorithm:

3J!22!!

iJ !

I . . _ 20 6 "8"

Fig.20. average best so far of for 14-busnetwork comparing with algorithm during SO times

implementation.

2 5 -205

f i0 .5\

-0 0 i so 100

i ion

Fig.2 . average best so far of for 30-busnetwork comparing with algorithm during SO times

implementation.

Fig. (18-21) are also have same results with(14) and (15) gures and especially it is vivid


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in g. ( 0) and ( 1) that GA trapped in a localoptimum quickly. Of course, in this part weapplied real GA with selecting SUS and onecut point mutation and other current methodsof GA also had no different results. As seen,

for bigger network (30) the SADE operationis more signi cant.

5.Conclusions

In this article for the problem of coordinationof over current relays, SADE algorit m wassuggested and it was tested on IEEE standard1 -bus and 30-bus networks and it showed that it is a noticeable algorit m. Incomparison with results from DE, PSO andGA algorithms, SADE algorit m can achievebetter solution with lower iteration; thisshows its speed and exactness in optimizationissues with big dimensions and several localoptimums (especially in 30-bus network that the differences were more vivid); alsoconsidering the its simplicity of crossover andselection, this algorit m needs lesser time toachieve optimum solu ion. DE is a ro ustalgorithm that is in several implementations,it has same results to some extent, and thiscase is more evident in SADE algorit m.

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protective relaying , Jo n Wiley&sons[ ] K. Price, R. Sto , J. Lampinen,

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[3] L Hewitson, M. Brown, B. Ramesh,

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Optimum Coordination of Overcurrent Relays Using SADE Algorithm

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