algorithm for relay coordination

7/25/2019 algorithm for relay coordination

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Evolutionary Algorithm for Protection Relay Setting Coordination

K. K.

i,

C.

W .

So

Hong Kong Polytechnic U niversity

Abstract- The protection relay setting coordination manages

the protection relay operations to clear

a

sys tem fa d t

in

several

steps of contingence. Relays which are missoordinated will t r ip

out unnecessary circuits resulting in electric sup ply interruption.

The Time Coordination Method

TCM)

which formulates the

coordination of relay settings into a set of constraint equ ations

and objective function

is

developed

to

mana ge the relay settings.

The protection system coordination is a highly constrained

optimization problem and conventional methods fail

in

searching for the global optimum. This paper presents the

application of Evolutionary Algorithm EA) n optimizing the

protection relay setting coordination in comparison with other

intelligent methods. The result shows that Evolutionary

Algorithm is an effective tool to search the optimum protection

setting with ma ximum constraint satisfactions.

I.

INTRODUCTION

The protection relay setting coordination manages the

protection relay operations to clear a system fault in several

steps of contingence. Relays which are mis-coordinated will

trip out unnecessary circuits resulting in electric supply

interruption. The Time Coord ination Method TCM )

[l]

is

developed to manage the relay settings. It formulates the

coordination of relay settings

into a set of constraint

equations and ob jective function, which are optimize d by the

Evolutionary Algorithm EA). EA is a novel technique for

solving highly constrained discrete optimization problems

[2]

such as protection relay coordination. This problem is

difficult to be solved by co nvention al optimization technique

such as linear programming

or

steeper descend gradient

search

[2].

This

paper presents the application of

Evolutionary Algorithm on the protection relay setting

Coordination. The results show that EA effectively searches

for the optimum protection relay settings with maximum

constraint satisfactions.

11.

EVOLUTIONARY

LGORITHM

Evolutionary Algorithm EA) is one branch of the

Evolutionary Computation. It can search for the optimum

solution for a highly c onstrained problem. The

flow

chart for

EA is shown in Fig

1.

Initialization

I

Generation

Objective Value

Evaluation

4 Yes

End of EA

Fig. 1

Evolutionary A lgorithm Processes Flowing

Diagram

A. Initialization

The initialization process of EA is similar

to

all

Evolutionary Computational Methods such

as

Genetic

Algorithm and Evolutionary Programming. It provides

the

starting points for the EA to search fo r the optimized solution.

The greater number o f points to start, the higher is the chance

to search for the global optimum solution. The initialization

of

he TCM generates

a

set o f relay settings and formulated

a

column vectorX,as shown in equation

1).

X*=

Where

k

s the

j

setting in relay n.

(1)

Note

For example, if RI

is

Inverse

Definite Multiple Time Lag

IDMTL)

Overcurrent OC)

Relay, RI sl s the Current Setting

Multiplier CSM) and R I , is the

Time M ultiplier TM)

of

R,.

0-7803-6338-8/00/ 10.00(~)2000

EEE

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The dimension of X s the summation of all protection

relay settings in the TCM to be processed. Typically, EA

requires pure random initialization. It can broaden the se arch

area and increase the chance of searching out the global

optimum solution. Unfortunately, protection setting

coordination is a highly constrained problem. The pure

random generated relay settings very often fail due to

constraint violations [3]. For example, a random generated

relay settings may not satisfy the operation time margin

between upstream and downstream relays [l] under fault

conditions. Any insufficient relay operation time m argin may

cause unnecessary system supply interruption, which is

classified as a constraint violation case. Those initialized

relay settings with constraint violations will be discarded.

Another set of relay settings will be generated and it will be

tested against the c onstraint violations as before.

The successful rate of a pure random initialized

protection relay se ttings without a ny constraint violation may

be calculated in the equation

2).

N J U )

21

N = g m

Where

n is the number of relays in the powe r system,

m s the number of se ttings in relay n ,

N,(ij) is the number of setting step s of relay setting

j which satisfy the constraint violations,

N, ) is the number of settable steps of relay i

settingj

N

is the successfil rate of the protection relay

settin gs without constraint violations.

For example, if the total number of relays is 10. Each

relay has two settings with 100 steps in each setting range. If

the chance to

sat isfy

the constraints is only 10 in each

setting range, thus

N

=

(1

hOO 20 =

1

x

1

From equation

2,

if the number o f relays is increasing, the

successful rate of the initialized relay settings without

constraint violations will decre ase and approaches to zero. To

maximize the successful rate, the setting pusher technique is

developed [l] to push the random generated protection

settings from unfeasible solution region to feasible solution

region.

The processing of EA introduce the continuous

improvement to relay settings in which some constraint

violation cases are corrected to w ithin th e constraint violation

limits. A small number of constraint violations is thus

allowed at initialization stage.

In

the TCM, the maximum

number of constraint violations is defmed.

It counts the

number of constraint violations for the initialized relay

setting during constraint checking. If the checked number of

constraint violations of the initialized relay settings is greater

than the pre-defined value, it will be discarded. Otherwise, it

will be put into the eligible pool for TCM process. The

number of constraint violations will be reflected on the

objective value. The initialization process will be terminated

after the pre-defined number re lay settings are initialized.

B.

Generation

The

EA

is

responsible for the generation of new relay

settings. It is carried out by mutation, which is different from

genetic algorithm [4] and evolutionary programming [5]. For

generation n of the relay settingsX f i ] , the n l generation

of elay settings

X,,+,F/

is generated by equation 3).

X, ,FI

=

X f i I + d w x f i I f l O Y 1 )

(3)

of i I=

}

onsinI =

JP

~.) xnrki)

where

/7 is the scale factor for EA mu tation.

is the offset for EP m utation.

@(XJk-n s the objective value o f the relay settingsXJk-1.

N(0,l) is the Gaussian normal distribution noise.

PmJk]

is a m utation e nablin g matrix.

a,@] is a step matrix.

The step matrix Jk] is calculated before mutation

process. This is generated from the objective value @(X,@J

of the protection setting X k] and each entry ,[RI is

independent of the others.

The mutation enabling matrix P m f i ] is designed to

decrease the number

of

relay settings alternation in each

mutation process. It is found that a larger number of relay

setting altemation will result in a larger number of constraint

violations. For the Genetic Algorithm, the single point

crossover operator [6] may provide smooth relay setting

alteration and introduce smaller number of constraint

violations, but the speed of searching for the optimum relay

setting is slow. If multi-point crossover operator is applied,

the relay setting altem ations in each generation is greater and

will caused larger number of constraint violations.

Consequently, the Genetic Algorithm fails in the Time

Coordination Method application.

At the end of gene ration, the new ge nerated relay settings

and the old relay settings will undergo a selection process to

select the better relay settings for the next generation. The

EA use s stochastic selection via a tournamen t [5]. Each new

generated relay settings face competition against a pre-

selected number of opponents and receives a

''win

if it is at

least as good as its opponent in each encounter. Selection

then eliminates those sets of relay settings with the least

wills.

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C. Objective Value Evaluation

The objective value evaluation is taking the key-roll in

the TCM. It generates all system constraints according to the

system configurations, fault types and fault locations

[

11. The

constraint checking is playing the important part in the

objective value evaluation. It checks the relay settings

satisfaction in all constraints and counts the number of

constraint violations. The number o f constraint violations s a

punishment to the relay settings as it is reflected in the

objective value. The larger number of constraint violations

scores higher objective value resulting in less chances to

survive in the next gen eration.

Systems Parameters

EA SurvivalSize

EA

Offsety

EA

Mutation Factor

EA ScaleFactor p

D . Termination

The termination of the EA process is sim ilar to the other

evolutionary computation methods, such as evolutionary

programming, by applying the fixed number of generations.

As EA introduce continuous improvement process, the

occurrence

of

the global optimum solution cannot be

predicted. Unlike Genetic Algorithm which generates

offspring mainly by crossover operator, EA generates relay

settings by mutation. It can get rid of the pre-mutual

dominance which is the solution trapped in the local

optimum. For some other optimization algorithms, the

termination is by monitoring the difference of the objective

values between two consecutive generations approaching to

the pre-defined value.

This

technique fails in the TCM

because the local optimum relay settings always last for

several number of generations which sa tisfies the termination

criteria but it is not the best optimum solution.

Values

10

0.9

0.1

111. SIMULATION

The control parameter

of

EA are as follows:

Number of generations- EA termination criteria.

Population size - The number of sets of relay settings in

each generation.

Mutation Probability -

To

generate the mutation

enabling matrix

h J k ] .

The TCM also has a set of control parameters to be set

and are described in [11.

To demonstrate the effectiveness of EA in Protection

Setting Coordination, a typical distribution network with 8

circuits and each circuit is protected by a IDMTL P hase Fault

/ Earth Fault Overcurrent Relay as shown in Fig. 2for study.

The circuit parameters are listed in Table 1.

Line L571

L67

-Bu B7

IDMTL Phase Fault / Earth Fault

Overcurrent Relay

Fig. 2

Typical distribution network

Table 1

Circuit Parameters

Note

:

All values are per-unit

@U

at IOOMVAbase and

all Lines are working at

1 1

kV.

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Population No. of Objective

Simulation

Time per

Generation

for

Pentium

The optimum solution among these simulation cases

occurs in case 2 with the smallest objective value. The relay

settings are shown in Table 4.The optimum relay settings

can protect the system with fastest fault clearance time,

maximum operation time margin and minimum number of

constraint violations for all system conditions

[

13.

Table 4

Optimum Protection Relay Se ttings

Size

30

5

I00

Phase Fault Earth

Fault

Line

CSM I TM

CSM

I

TM

Generations Value

350MHz

500 0.000670 0.912 sec

500 0.000650 728 sec

500 0.000730 3.563 sec

The population size is the num ber of sets of relay settings

in each generation to be processed. Obviously, a larger

population size would use more computation power. Thus

case 1 is the fastest and the case

3

is the slowest. To examine

the

EA

performance, all trails are recorded

asshown

n Fig.

3,

4,

5

and

6.

Fig.3 shows

the

best, average and

m a x i

objective values recorded in each generation for the first 100

generations in case 1. From 21 to 93 generations , it is

found that the best objective values are improved

significantly. Beyond 93 generations, the improvements

become s less significant. When a ll individuals are improved,

the better relay settings is prepared by EA and stored in

several sets of relay settings. Eventually, the new best relay

settings are generated. This improvement is c arrying on for

the first 300 generationsas shown in Fig 4. In Fig 4 , s and 6,

the improveme nt becomes minimum, and the avera ge and the

best objective value become s almost constant for the la st 200

generations. Beyond 450 generations, the trend of

improvement for both average and best objective values

becomes flat. Typical effect also occurs in seve ral other trials

on the case. T herefore, 500 generations is selected to be the

tetmination criteria.

The Survival Size is controlled the tournament size and

10

is recomm ended by D.B. Foge l [SI. The Offset and Scale

Factor is set to 0 and 0.9 and they control the step matrix

a ]. The mutation enabling matrix Pm ] is c ontrolled by

the Mutation Fac tor 0.1.

The

PmJk] is generate

in

each

EA

generation by comparing the Mutation Factor and random

numbers.

The larger population size also allow more sets of

protection settings survives in. each generation and the

divergent effect is reflected on the maximum objective values

in Fig 3, 4, 5 and 6. The divergent effect should be limited

and specific to the problem. In case 2, the divergent effect is

the minimum.

V. CONCLUSION

The Ev olutionary Algorithm is successfully applied in the

Time Coordination Method for protection setting

coordination. The results show that the population size and

the number of generations should be pre-determhate by

several trials. The number of relays forms the problem

domain and imposes the divergent effect, which can be

suppressed by the selection of the correct population size.

The future work would be the development on a method to

find out the right population size and the number of

generations automatically.

VI. ACKNOWLEDGEMENTS

The authors would like to thank the Hong Kong

Polytechnic University for supporting the research and

publishing this work.

VII. REFERENCE

[11 C W

So,

K K L i, Time Coordination Method for Power

System Protection by Evolutionary Algorithm, 1999

IEEE Industry Application society Annual Meeting,

Phoe nix Arizona, U.S.A., 3-7 Octobe r 1999, Session 53,

paper no 53.4.

[ ]

R

Salomon, Evolutionary

Algorithms and

Gradient

Search Similarities and Differences, IEEE

Transactions on Evolutionary Computation, Volume 2,

[3]

C.W. So, K.K. Li, K.T. Lai, K.Y. Fung, Overcurrent

Relay G rading Coo rdination Using Gene tic Algorithm,

IEE APSCOM-97 Internation al Conference, Hong

Kong, Novem ber 11-14,1 997, Vol. 1, pp. 283-287.

[4] D.E. Goldberg, G ene tic Algorithm in Search,

optimization and Machine Learning, Addison-Wesley,

Reading

MA

1989

[5] D.B. Fogel, An analysis of evolutionary programming,

Proc. of the First Cod. on Evolutionary Programming,

Evolutionary Programm ing Society, La Jolla, CA, 1992,

pp 43-5 1 .

[6] C.W. So, K.K. Li, K.T. Lai, ICY. Fung, Application of

Genetic Algorithm for Overcurrent Relay

Coordination,IEE 6 Intemational Conference on

Developments in Power System Protection, Nottingham,

July 1998, pp 45-55.

UK, arch 19 97, pp. 66-69

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Fig

3

EA performance case

lin

the first

100

generations

Fig 5

EA performance

for

case 2

817

algorithm for relay coordination

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