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Abstract --The objective of optimal relay coordination ininterconnected power system is to achieve selectivity withoutsacrificing sensitivity & fast fault clearance time. This paperpresents the effect of fault location on the flow of currentdirection & optimal coordination of directional over currentrelay. In this coordination problem Time Dial Setting (TDS) &Pick up Current Setting (Ip) of all relays considered as optimalparameter & it will provide coordination for all kind of fault(LLL, LLG, LG). The problem is solved using optimizationtoolbox of MatLab for continuous value of TDS & Ip

Index Terms -- Power system protection, Optimal relaycoordination, Over current relay, LLL LLG LG faultcoordination.

I. I NTRODUCTION

HE problem of coordinating protective relay in electric power system consists of selecting suitable settings suchthat their fundamental protective function is met under the

requirements of sensitivity, selectivity, reliability and speed.These requirements must be met for a variety of systemconditions and configurations and can be translated intoconditions such as : (i) a variety of fault condition must bedetected by the appropriate relays, (ii) the relays located closer

to the fault should have priority of operation, (iii) if a primaryrelay fails , a backup relay should operate and (iv) theoperation of relay should be as fast as possible to preventequipment damage and must occur only in presence ofabnormal operating conditions which jeopardize the systemintegrity.[1]

In a system where there is a source at more than one of theline terminals, fault and load current can flow in eitherdirection. Relays protecting the line are therefore subject tofault currents flowing in both directions. If nondirectionalrelays were used in such systems, they would have tocoordinate with not only relays at the remote end of the line,

but also the relays behind them. Since directional relays

operate only when the fault current flows in the specifiedtripping direction, they avoid compromising line protection.[2]

Directional overcurrent relays have two types of settings:time dial setting (TDS) and pickup current setting (Ip). Thesettings should be designed for minimum relay time operation.On the other hand, the settings should also provide selectivityand reliability by providing backup protection. Each zone inthe system should be protected by a primary and backup relay.In other words, the settings should be chosen to minimize the

overall time of operation of relays while maintainingselectivity and reliability. Thus, the directional overcurrentrelay coordination problem involves optimization, where thesolution is the optimal settings of each relay. [3]The problem of determining the settings of the relays usingoptimization was first stated in [4,5,6,7]. In general, the

protective relay coordination problem was formulated in previous work either as a linear, nonlinear, or a mixed integernonlinear programming problem depending on the type ofvariables in the problem. The pickup current setting is thevariable that determines mainly the type of problem. If Ip isset fixed, the coordination problem becomes a LinearProgramming (LP) problem. For continuous Ip values, the

problem becomes a Nonlinear Programming (NLP) problem.Lastly, if the discrete values of Ip are taken into account, the

problem becomes a Mixed Integer Nonlinear Programming(MINLP) problem.

It was observed by authors that the same relay backups arenot functioning using optimal algorithm for various faultlocation. The backup relays are different for different faultlocation. One of the issue identified was that current direction

become opposite during fault condition when fault locationchanges. This leads to change in backup relay operations. This

problem has been dealt in this paper where we have added a

new constraint when the direction of current changes. Whenthe direction of current remains same in backup zone duringfault condition as original we have one identified backup relayfor every primary relay. The proposed approach determinesthe optimal solution to coordination problem for all kind offaults (LLL, LLG, LG) & what ever the fault location. Forsolving the optimal problem Medium Scale Algorithm ofoptimization toolbox of MatLab is used [11]. The paper isorganized as follows: Section II & III presents an overview onthe optimization theory and relay characteristic. Section IV &V presents the problem formulation & proposed algorithm.Simulation results are presented in section VI. Finally,conclusions are drawn in section VII.

II. OPTIMAL COORDINATION PROBLEM OFPROTECTIVE RELAY

The coordination problem of protective relay in powersystem is stated here as an optimization problem of thefollowing general form [1]:

min [ z (s, p) ] ..(1)s S

where z represents a suitable performance index, s representsthe protective device setting, S is the set of permissible settingand p represents the perturbation or fault conditions. This

Effect of Fault Location on OptimalCoordination of Directional over Current Relay

Chetan Aggarwal, H.A. Mangalvedekar and H.B. ChaudhariVJTI-Siemens-AICTE High Voltage Laboratory

Electrical Dept, VJTI

T

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coordination problem is very large dimensional problem,especially when a large number of perturbations are to beconsidered. One way of obtaining a solution to this problem is

by using the extended minimax approach proposed by meansof which the problem in eq. (1) is written as:

min [max z (s, p) ] ..(2)s S p P

where the sub problem [ max z (s, p) s.t. p P ] is assumedto have multiple local solutions pk * P * , k = 1,np.

P * = { p 1* ,.pnp

* } is the set of np worse or more relevant perturbations. This set, which might be determined with thehelp of system expertise, contains boundaries & other relevant

points of the perturbation space. The problem of determiningP* is not treated here and is assumed to have been solved

beforehand.

Each of the relevant perturbations, pk * P * , k =1,np

define a separate optimization problem with its own objective& constrain set, so that in essence the problem stated in eq. 2can be formulated as a multiple objective optimization

problem in terms of setting, as follows:

min [ z (s, p 1*

), .z (s, p np*

) ] (3) s.t. s S 1 ..s S np

where S k , k = 1, . np, represents the feasible set of settingfor the relevant perturbations or scenarios. Assuming oneobjective per perturbation, this problem can be formulated as amultiple criteria nonlinear optimization problem of the form:

min [ z 1(s , T) .z np (s, T) ]s.t. h (T) 0 ( coordination criteria )smin s smax ( bounds on the relay settings )Tmin T Tmax ( bounds on operation times )

T = f ( s ) (relay characteristic )The particularization of this general problem to the case of

directional overcurrent relay is presented below.

III. MODELING OF OVERCURRENT RELAY CHARECTERISTIC

Over-current relay generally include an instantaneous unitand inverse time equipment. The inverse time operationcharacteristic can be provided in terms of a family of curvesdepending on a parameter usually referred as the timemultiplier setting. The mathematical modelization of thisfamily of curves can be performed using multiple regressiontechniques in order to obtain an expression giving theoperating time in function of time multiplier and the currentflowing through the relay. In general, overcurrent relays

respond to a characteristic function of the type [2]:T = f (TDS, Ip, I) . (4)

where T is the operation time, TMS is time multiplier setting, I p is the pickup current and I is the current flowing through therelay. Under simplistic assumption, the above equation can beapproximated by the following equation:

T = K 13

K K Ip)/(ITDS

2 + ..(5)

where K 1, K 2 and K 3, are constants that depend upon thespecific device being considered. A more precise formula forapproximating the relay characteristics is as follows

T = P( TDS )P( Ip ) (6)

Where

P( TDS ) = K 10 + K 11TDS + K 12TDS2 + K 13TDS

3

4

4

3

3

2

21

0 )1()1()1()1()( +

+

+

+=

M

A

M

A

M

A

M

A

A Ip P

M is the ratio of relay current ( I ) to the pickup current ( I p)and K 10, K 11 , K 12, K 13, A0, A1, A2, A3, and A4 are scalarquantities which characterize the particular device beingsimulated. The calculation of two settings, TMS and I p, is theessence of the overcurrent relay coordination study. It is veryimportant to mention that in general these two parameters arediscrete. In this study, however, these parameters wereassumed to be continuous variables. The discrete solution areobtained by rounding-off the continuous solution to thenearest discrete values.

IV. PROBLEM FORMULATION The system in fig. 1 serves to explain how fault location

could lead to miscoordination of directional over current relay.In fig. 1 each protection zone corresponds with one of thetransmission line & each zone has two directional relays, oneoperates for clockwise & second for anticlockwise current.

As given in [1] assume a 3 phase fault occur at F1 in zone3. (This fault current direction is shown in fig. 1) Relay R 21 the only relay which may act as backup relay to main relayR 23. For relay R 13, R 12 is the only backup relay & normalcoordination constraints for both the main relays R 23, R 13 &

backup relays R 21, R 12 respectively, are given by:TR21 (F1) T R23 (F1) CI ..... (7)

TR12 (F1) T R13 (F1) CI . (8)Where:TR21 (F1) = Operating time of R 21 for a fault at F1TR23 (F1) = Operating time of R 23 for a fault at F1TR12 (F1) = Operating time of R 12 for a fault at F1TR13 (F1) = Operating time of R 13 for a fault at F1CI = Coordination Interval

Now if 3 phase fault occur at F2 (fig. 2) then the directionof current changes in zone 1 & zone 2 this leads to certaindifficulties in backup relay coordination shown in fig. 2

Fig. 1

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Fig. 2

From fig. 2 it is clear that relay R 21 will not provide backup to

main relay R 23 because backup relay R 21 operates only foranticlockwise current. So R 21 may not act as backup to R 23 &this leads to failure of backup protection.In order to overcome the above problem, the coordination

problem has been reformulated and additional constraintswere added.

In proposed algorithm, main relay has been coordinatedwith two backup relays, one operates for clockwise current &other operates for anticlockwise current. Now whatever thefault location or current direction one of the backup relay willact as a backup relay to primary relay & only one backup relaywill operate at a time. So coordination constraints are given

by:TR21 (F1) T R23 (F1) CI .. (9)TR11 (F1) T R23 (F1) CI . (10)TR12 (F1) T R13 (F1) CI . (11)TR22 (F1) T R13 (F1) CI . (12)

Where

TR11 (F1) = Operating time of R 11 for a fault at F1TR22 (F1) = Operating time of R 22 for a fault at F1Equations (10) & (12) are the new constraints added.

V. PROPOSED ALGORITHM

A. Objective function

In the coordination problem, the main objective is tocalculate the TDS and Ip, which would minimize the time ofoperation of the relays [8-9]. The coordination problem ofdirectional overcurrent relays in a power system can be statedas follows:

Objective=min ' i ik W T . (13)where T ik indicates the operation time of relay Ri for a fault inzone k and W i is a coefficient and is usually set to 1. Theobjective is to minimize the time of operation of the relaysunder the following constraints.

B. Coordination Criteria

TR1k (F1) T Rij (F1) T (14)TR2k (F1) T Rij (F1) T (15)

Where

TRij (F1) operating time of primary relay R i of jth zone

TR1k (F1) operating time of first backup relay R1 of k th zone

TR2k (F1) operating time of second backup relay R2 of k th zone

T is the coordination time interval and is taken to be 0.2seconds.

C. Bounds on relay settings and operation times

min maxi iTDS TDS TDS .... (16)min maxi iIp Ip Ip . (17)min maxik ik ik T T T . (18)

D. Relay characteristicsAll relays were assumed identical and with characteristic

functions approximated by:T

ik =0.14

xTDS

i/ [(I

ik / Ip

i)0.04 1] .(19)

where I ik is the fault current passing through the relay for afault in zone k .

E. Transient Configuration EquationsFor the transient configuration that occurs when only one

relay of a zone has operated, the coordination criteria muststill assure a coordination operation, independently of atripping sequence, that is [10]:

TR1k (F1) T Rij (F1) T (20)TR2k (F1) T Rij (F1) T (21)

where the superscript ( ) indicates transient configuration

quantities.

VI. SIMULATION RESULTS

The system under study is shown in fig.1 was designed todemonstrate the calculation of the time dial settings and

pickup current settings of the directional overcurrent relayusing the proposed problem formulation .

Table 1Generator Data

G1 100 MVA 69 KV 20 %G2 25 MVA 69 KV 12 %

G3 50 MVA 69 KV 18 %

Table 2Line Data

LINE 12 50 KM Z = 5.5 + j 22.85LINE 23 40 KM Z = 4.4 + j 18LINE 31 60 KM Z = 7.6 + j 27

Table 3Backup Relay

Primary

Relay

Backup

Relay

Actual Backup

RelayR 11 R 13, R 23 R 13, R 23 R 12 R 11 , R 21 R 11 R 13 R 12, R 22 R 12, R 22 R 21 R 22, R 12 R 22 R 22 R 23, R 13 R 23 R 23 R 21, R 11 R 21, R 11

Table 4Relay setting

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Relays TDS Pickup CurrentR 11 0.2243 123.4501R 12 0.2657 60.0000R 13 0.2192 84.1039R 21 0.1900 123.5184R 22 0.2739 60.0000R 23 0.2475 84.7948

100 101 10210-1

100

101

X: 40.7Y: 0.4503

Priary relay R23 & backup relay R21 for fault F1

PSM

T i m e

X: 7.461Y: 0.6486

PC--R23

BC--R21

OT--R23

OT--R23

Fig. 3

100

101

102

10-1

100

101

Primary relay R23 and Back up Relay R11 for Fault F2

PSM

T i m e

PC--R23BC--R11

OT--R23data4

Fig. 4

Table 1 & Table 2 show generator data & line data of 3 bussystem in fig. 1. Table 3 shows backup relays & actual backuprelay (If current in backup zone does not change with changein fault location then we coordinate primary relay with onlyone backup relay according to current direction in backupzone) which is actually used in solving coordination problem.Simulation result of coordination problem has been shown inTable 4. Objective function value is 2.5425 sec . Fig 3 shows

primary relay R 23 & backup relay R 21 characteristic andoperating time for fault F1 in fig 1. Fig 4 shows relay R 11

providing backup to relay R 23 when fault location changes to point F2 in fig 2.In fig. 3 & 4 PC, BC and OT are Primary Characteristic,Backup Characteristic and Operating time respectively.

VII. CONCLUSION

In this paper, an optimization methodology is presented tosolve the problem of coordinating directional overcurrentrelays in an interconnected power system. This paper

presented a new algorithm for coordinating directionalovercurrent relays. When change in fault location lead todirectional change in current. The new algorithm takes intoaccount the effect of fault location on current direction andoptimal solution of coordination problem. The coordination

problem is a nonlinear programming problem and i t is solvedusing optimization toolbox of MatLab.

VIII. ACKNOWLEDGMENT

The authors are gratefully acknowledges Mr. V.D.Vaidya,

General Manager, Electrical, Jacobs Engg. India Pvt Ltd. fortheir support and guidance in making this paper

IX. REFERENCES

[1] A. J. Urdaneta, R. Nadira, and L. G. Perez, OptimalCoordination of Directional Overcurrent Relays inInterconnected power Systems, IEEE Transactions on

Power Delivery , vol. 3, pp. 903-911, July 1988.[2] H. Zeineldin, E. F. El-Saadany, and M. A. Salama, A

Novel Problem Formulation for Directional OvercurrentRelay Coordination, power engineering, LESCOPE,2004.,pp.48-52, July2004.

[3] Javad Sadeh, Optimal Coordination of Overcurrent Relay

in an Interconnected Power System, 15th PSCC, Liege,22-26 August 2005.

[4] H. Zeineldin, E. F. El-Saadany, and M. A. Salama,Optimal Coordination of Directional Overcurrent RelayCoordination, Power Engineering society generalmeeting, IEEE, pp. 1101-1106, vol. 2, June 2005.

[5] A. J. Urdaneta, H. Restrepo, S. Marquez, and J. Sanchez,Coordination of Directional Overcurrent RelayTiming Using Linear Programming technique, IEEETransactions on Power Delivery , vol. 11, pp. 122-129,Jan. 1996.

[6] B. Chattopadhyay, M. S. Sachdev, and T. S. Sidhu, Anonline relay coordination algorithm for adaptive

protection using linear programming technique, IEEETransactions on Power Delivery, vol.11, pp. 165-173,Jan. 1996.

[7] L. Perez, and A. J. Urdaneta, Optimal Coordination ofDirectional Overcurrent Relays Considering DefiniteTime Backup Relaying , IEEETransactions on Power

Delivery , vol. 14, pp. 1276 1284, Oct. 1998.[8] C. W. So, and K. K. Li, Time Coordination Method for

Power System Protection by Evolutionary Algorithm, IEEE Transactions on Industry Applications , vol. 36, pp.1235- 240, Sept. 2000.

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[9] H. A. Abyaneh, M. Al-Dabbagh, H. K. Karegar, S. H. H.Sadeghi, and R. A. J. Khan, A new optimal approach forcoordination of overcurrent relays in interconnected

power systems, IEEE Transactions on Power Delivery,vol.18, pp. 430-435, April, 2003.

[10] A. J. Urdaneta, L. Perez, and H. Restrepo, OptimalCoordination of Directional Overcurrent RelaysConsidering Dynamic hanges in The Network Topology,

IEEE Transactions on Power Delivery , vol. 12, pp. 1458-1464, Oct. 1997.

[11] Matlab optimization toolbox user guide.

X. BIOGRAPHY

Aggarwal Chetan was born in Sriganganagar, Rajasthan,India, on December 15, 1983. He received his BachelorDegree in Electrical Engineering in 2005 from SKITManagement & Gramothan affiliated to Rajasthan University,Rajasthan, India and pursuing Master Degree in ElectricalEngineering with specialization in Power SystemsEngineering in 2008 from V. J. Tech. Institute Mumbai,India.(Email- chetanraj.aggarwal@gmail.com)

Harivittal. A. Mangalvedekar was born in Lalgudi,Tamilnadu, INDIA, on May 29, 1957. He finished hisBachelor Degree in 1979, Master Degree in 1984 andDoctorate in 1995 in Electrical Engg. from MumbaiUniversity. He is presently working as a professor in the dept.of Electrical Engineering at V. J. Tech. Institute. His areas ofinterest include Power Systems, High Voltage Engineeringand Pulsed Systems. He is a life member of ISTE and PowerBeam Society of INDIA .

Harish. B. Chaudhari was born in Jalgon, INDIA on April

24, 1967. He has finished his Bachelor Degree in ElectricalEngineering 1989 and Master Degree in ElectricalEngineering with specialization in Control Systems in 1992.He is presently working as a lecturer in the dept. of ElectricalEngg. at V. J. Tech Institute. His areas of interest include

power Electronics applications to Power Systems and HighVoltage Engineering. He is a life member of ISTE.