04359249

52 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 1, JANUARY 2008

Advanced Coordination Method for OvercurrentProtection Relays Using Nonstandard

Tripping CharacteristicsTimo Keil and Johann Jger, Member, IEEE

AbstractThis paper describes an advanced coordinationmethod for an optimized protection time grading based on a newnonstandard tripping characteristic for overcurrent protectionrelays. The intention is the highest possible reduction of trippingtimes for a selective fault clearing in distribution networks pro-tected by overcurrent relays without communication links. Thenew nonstandard tripping characteristic will be described fromits basic idea to its constraints of the optimization problem. Theoptimization is solved by the method of Lagrange generalized withthe KarushKuhnTucker conditions and is aimed at selectivefault tripping with shorter tripping times as standard charac-teristics and conventional coordination methods. Overcurrentrelay coordination becomes a mathematical optimization task. Acomparison with the standard characteristics and conventionalcoordination methods shows a notable advancement regardingtheir average and maximum tripping times which can be achievedusing this new method.

Index TermsOptimization method, overcurrent protection,protection coordination, selectivity, tripping characteristic, trip-ping time.

I. INTRODUCTION

PROTECTION systems must react fast and be selectiveand reliable to faulty network conditions. Overcurrentprotection, one of the basic protective relaying principles, isthe common system for distribution networks. With respectto distance and differential protection systems, overcurrentprotection is more economical and, therefore, favored on adistribution level. Monetary constraints make it also beneficialto be applied in distribution networks with distributed-genera-tion (DG) networks requiring faster and selective fault clearingwithout the application of costly communication equipment forcomparison protection schemes.

However, in the majority of cases, selectivity can only beachieved by time grading. This results in high tripping times de-pending on the number of subunits belonging to the grading pathwhich can be expected numerously in extended distribution net-works or in DG networks (e.g., wind farms). In this paper, faultcurrent contributions of interinfeeds at the subunits will be ne-glected, assuming only converter-connected sources, which willbe switched off immediately in the case of a fault.

Manuscript received May 26, 2006; revised September 27, 2006. Paper no.TPWRD-00288-2006.

The authors are with the Department of Electrical Power Systems,Friedrich-Alexander-University of Erlangen-Nuremberg, Erlangen 91058, Ger-many (e-mail: [email protected]; [email protected]).

Digital Object Identifier 10.1109/TPWRD.2007.905337

Fig. 1. Typical network structure and grading path to be investigated: behaviorof (a) three-phase fault current, (b) effective definite tripping times, and (c) ef-fective inverse tripping time.

II. CONVENTIONAL OVERCURRENT CHARACTERISTICSFig. 1 shows a typical single-fed network structure repre-

senting the grading path and the effective tripping timesof the relays applied to the network. The behavior of the three-phase fault current and the effective tripping character-istic of each definite time overcurrent (DTOC) relay andeach inverse definite minimum time (IDMT) relay at stations1, 2, and 3, depending on downstream fault location is illus-trated below Fig. 1. The downstream path is directed from theinfeeding transformer to the dead-end feeder and the upstreampath vice-versa.

The fault current decreases for downstream fault locations.The degree of decline depends on the ratio between the sourceand the fault-loop impedance also called source impedance ratio(SIR). In case of DTOC relays in Fig. 1(b), the effective trip-ping characteristics are independent of the fault location. Thegrading time is constant for all downstream fault locationsand selectivity is ensured in any case. The grading time de-pends on the opening time of the circuit breaker, dropout time,and safety margins and is normally chosen according to typical

0885-8977/$25.00 2007 IEEE

KEIL AND JGER: ADVANCED COORDINATION METHOD FOR OVERCURRENT PROTECTION RELAYS 53

values [1]. As the fault moves upstream, the fault current in-creases [Fig. 1(a)], but the tripping time also increases caused bythe time grading. This is contradictory; the heaviest fault shouldbe cleared fastest.

An IDMT relay overcomes this problem [2]. According tothe IEC or ANSI standard, the tripping characteristicsof IDMT relays are rational functions depending on the faultcurrent and result in effective tripping characteristicsdepending on the fault location consequently. The tripping timedecreases while the fault location moves upstream [Fig. 1(c)]and the fault current increases. On the other hand, the gradingtime must be checked at each relay location to be sufficient,ensuring selectivity [3]. Moreover, IDMT relays tend to havehigher maximum tripping times in regards to DTOC relays.

In addition to the IEC or ANSI standard characteristics, nu-merical relays provide the opportunity of user-defined trippingcharacteristics which are not subjected to any standards [4].In this respect, a new tripping characteristic, which joins thepros of IDMTreduced tripping time for higher currents andDTOCselectivity regardless of the current, is possibly real-ized. In this way, protection grading and coordination are theresult of a mathematical optimization task.

This paper presents the pros and cons of standard DTOC andIDMT relays, according to IEC or ANSI, more precisely. Thederivation of a new nonstandard tripping characteristic and ad-vanced time grading using the method of Lagrange generalizedwith the KarushKuhnTucker conditions will be described. Bymeans of characteristic values regarding speed and selectivity,the new coordination method will be compared with the con-ventional approach which has been used up to now.

III. CHARACTERISTIC VALUES AND DEFINITIONS

A. Tripping Time and SpeedTo evaluate tripping time quantities, characteristic values will

be introduced. The following restrictions and definitions havebeen stipulated. The current represents the scalar value ofthe fault current which is sensed by the protection relay duringa fault with

(1)where refers to the number of relays of one grading path. Thecurrent varies in accordance to the fault location causedby the impedance of cables, overhead lines etc.

(2)The tripping characteristic of the relay can be formulated

as considering currents exceeding the pickup currentof the relay . Generally, the effective tripping character-

istic is based on a combination of two functions asfollows:

(3)Thus, the tripping characteristic is determined by the fault

current, which is sensed by the relay and exceeds the pickupwhereas the effective tripping characteristic is determined

by the fault location . Only fault locations of the primary pro-

Fig. 2. Effective tripping characteristics t (l), grading timest (l),relay locations L , and primary tripping zones of the grading path of Fig. 1.

tection zone, that means no backup fault clearing, will be con-sidered. The primary protection zone for relay is bordered bythe relay locations and as shown in Fig. 2.

The maximum fault current sensed by the relay during afault at the location or is defined as

(4)

The effective average tripping time will be definedusing the areas . These are limited by the effective trip-ping characteristics above and by the -coordinate below and

, , respectively, as depicted in Fig. 2. is deter-mined as follows:

(5)

The effective average tripping time is now defined as

(6)

to evaluate the speed of a protection coordination method andits effective tripping characteristic.

B. Grading Time and SelectivityThe grading of two successive overcurrent relays and

must maintain dedicated grading times ensuring selec-tivity as described before. In practice, current measurement er-rors of relays and their transducers have to be considered. Fig. 3shows the ideal grading time without considering cur-rent measurement errors and the real grading time whileconsidering current measurement errors. This example assumesdifferent polarity of errors of both graded relays 1 and 2 and,thus, represents the best and worst case. The real grading time

may become less than sufficient due to selectivity, and theideal grading time must be increased [Fig. 3(b)].

In the followings, a typical composite current error of 5%will be regarded. This results in a tolerance band of 10%. Con-sidering this effect, the real grading time between relay and

can be formulated analytically as

(7)Proper grading times depend on the employed relay and cir-

cuit-breaker technology. Typical values range between 0.2 s to0.5 s. In the following, a grading time of 0.3 s is applied.


Fig. 3. Influence of current measurement errors on the grading timet . (a) Positive influence. (b) Negative influence.

Fig. 4. Effective DTOC tripping characteristics of the investigated gradingpath.

IV. NETWORK CONFIGURATION

A. StructureThe fault current behavior depends on the network structures.

A radial feeder according to Fig. 1 is the basis of the followinginvestigations. It is a single-fed 10-kV system. The whole cablelength refers to 15 km. The resistive and reactive impedance is

and . The infeeding trans-former represents three-phase short-circuit power of 300 MVA.There are three substations located at 0, 5, and 12 km from theinfeeding transformer.

B. Simulated Fault CurrentsFirst, the three-phase fault behavior will be investigated. The

fault current decreases with downstream fault locations and eachrelay related to the fault loop senses the same fault current whichresults in

(8)

V. CONVENTIONAL COORDINATION METHODSOvercurrent relays for radial feeders will be normally time

graded. The grading starts from the last downstream relay to-ward the upstream relay. Fig. 4 depicts the effective DTOC trip-ping characteristics protecting the network structure shown inFig. 1.

The maximum tripping time is 0.61 s, whereas the effectiveaverage tripping time according to (6), results in 0.31 s. Thegrading time is constant equal to 0.3 s for any fault location.The protection relays are coordinated absolute selective. On the

Fig. 5. Thermal equivalents based on the DTOC tripping characteristic.

other hand, the maximum tripping time linearly increases de-pending on the number of stations of the grading path. It mustcomply with the maximum permissible thermal stresses of theprotected network equipment. The thermal equivalent isstated as follows:

(9)

Fig. 5 shows the resulting thermal equivalents of thegrading according to Fig. 4. It can be seen that the DTOC trip-ping characteristic leads to high thermal stresses of equipmentduring faults close to the infeed.

For an IDMT grading, the following IDMT tripping charac-teristic according to IEC60255-3 is considered [4]:

(10)

The tripping time depends on the following relay settings:pickup and time multiplier . In this case, the pickuphas been chosen to be equal for all relays as .

refers to the nominal current of the relay. The time mul-tiplier for relay can be calculated using the followingequation:

(11)

The formula (11) ensures selectivity under consideration ofthe current measurement error of 5%. The calculation pro-cedure starts with the time multiplier of the last down-stream relay of the considered grading path. should begiven by the further downstream network or if not, it can bechosen as the minimum adjustable setting of the relay.

Furthermore, the maximum fault current sensed by therelay during a fault at the location of the next down-stream relay determines the time multiplier according to(11).

This results in the effective tripping characteristics shown inFig. 6. The maximum tripping time referring to the primary


Fig. 6. Effective IDMT tripping characteristics of the investigated grading path(dashed line: speed up tripping with instantaneous elements).

Fig. 7. Grading times according to Fig. 6.

Fig. 8. Thermal equivalents based on IDMT tripping characteristic accordingto Fig. 6.

protection zone is 0.70 s. The effective average tripping timeaccording to (6) is 0.42 s. Fig. 7 shows that the grading times

and increase. But in relation to DTOC grading, theovercurrent grading using IDMT tripping characteristics leadsto lower thermal equivalents and lower stresses of the equip-ment in case of a fault that is close to the infeeding transformer.The maximum -value decreases from 182 to 163as seen in Fig. 8.

Tripping can be sped up using instantaneous elements alongwith IDMT elements (see the dashed lines in Figs. 68). Theinstantaneous element is set to reach the balance point as to bethe point causing the maximum fault current at the next down-stream relay. Here, the maximum fault current is a three-phasefault current along with an infinite slack bus. This definition isvery safe. The instantaneous elements cut the effective IDMTtripping characteristic (i.e., it leads to a faster effective average

tripping time of 0.32 s and to a decreased maximum -valueof 90 ). The maximum tripping time referring to the pri-mary protection zone is unchanged at 0.70 s.

VI. NEW CHARACTERISTIC AND ADVANCED COORDINATION

A. New Tripping Characteristic and Its ObjectivesThe following three constraints are stipulated for joining the

pros of DTOC and IDMT gradings. The grading timeshould be constant and, therefore, independent of the fault loca-tion and fault current to ensure selectivity without any lossof tripping time like the DTOC characteristics. In addition, thecurrent measurement errors according to (7) should be consid-ered. It follows that:

s

(12)Furthermore, the new tripping characteristic should depend

on the fault currents such as the IDMT characteristic reducingthe tripping time as the fault moves closer to the source. Fromthis, it follows for the first derivative of that:

(13)

As the third constraint, the tripping time must have positivepolarity as

s (14)

The following new approach for a tripping characteristic isproposed:

(15)

It is based on the logarithmic function and the coefficients and. The coefficient is equal for all relays of one grading path

and is specific for each relay .Due to the fact that is equal for all relays, the grading time

(12) is independent of the fault location and the fault current. Applying the new tripping characteristic (15), the three con-

straints (12)(14) can be formulated as follows:

(16)(17)

(18)

where should be the maximum fault current during a faultat location of relay . In particular, the logarithmic approach(15) leads to selectivity independent of fault currents or loca-tion as constraint (16) shows. The constraints (16)(18) can befulfilled by choosing adequate coefficients and which willbe performed by the optimization task described in the next sec-tion. Thus, we have a proposal for a new tripping characteristic(15) with its constraints (16)(18) to determine the coefficients

and .


B. Advanced CoordinationThe optimization task is solved by the method of Lagrange

generalized with the KarushKuhnTucker condition. Forsolving optimization problems, the basic approach of Fermat is

(19)

Considering constraints such as

(20)the domain of results will be restricted because results of (19)may not be defined anymore. The basic approach (19) must beextended to

(21)

and are the so-called Lagrange multipliers. The re-sults , , and of (21) are only the minima, if theKarushKuhnTucker conditions

(22)

are fulfilled.The coordination of the new tripping characteristic (15)

should lead to optimized grading with respect to the trippingtime. Thus, the objective function to be minimized should bethe effective average tripping time (6). Using the mean valuetheorem, it can be shown that (6) is minimized if

(23)

with

and

(24)becomes minimal. The areas of the -diagram areupdown limited by the tripping characteristics and by the

-coordinate and , respectively.Applying the new tripping characteristic (15) to (24) and per-

forming the integration, the average tripping time (23) as theobjective function follows as:

(25)The objective function of optimization (25) as the average

tripping time is now formulated as a func-

Fig. 9. (a) New nonstandard tripping characteristic in comparison with (b) theIEC-standard IDTM tripping characteristic.

tion of the coefficients and which are also the coefficientsof the constraints (16)(18). The currents are maximumfault current values according to (4) and must be calculated inadvance of the optimization. In this way, the objective functionusing the new tripping time characteristic (15) and its constraintsis formulated for solving the optimization task.

C. Results of SimulationThe optimization method described before has been applied

to the grading path in Fig. 1. The calculations have been car-ried out using the MATLAB calculation tool box. The coeffi-cients resulting in , , , and

lead to the following three tripping characteristicsfor relays 13:

(26)to see in Fig. 9(a) in comparison with the IDTM tripping char-acteristic in Fig. 9(b).

Fig. 10 shows the corresponding effective tripping character-istics of the investigated grading path. The maximum trippingtime of the primary protection zone refers now to 0.42 s, whilethe effective average tripping time according to (6) is 0.18 s.That means a noticeable time reduction in relation to the DTOCand IDTM grading. The grading time is equally con-stant to 0.3 s. Thus, the grading is absolute selective at any faultlocation as can be seen in Fig. 11.

Furthermore, the thermal equivalents are strongly reduced.The maximum -value is decreased from 163 aswith an IDMT grading to 28 as with the new characteris-tics shown in Fig. 12. That means there is a strong minimizationof the thermal stresses on the power system equipment in caseof a fault.

D. Different Types of FaultsWith respect to overcurrent protection, different types

of faults, such as phase-to-phase, phase-to-earth faults, oradditional fault impedances, cause different ranges of faultcurrent values. This influences the tripping time of all cur-rent-depending characteristics and coordination methodstheconventional or the new one. But the new method is also selec-


Fig. 10. Optimized effective tripping characteristics of the investigated gradingpath.

Fig. 11. Grading times according to Fig. 10.

Fig. 12. Thermal equivalents based on the new tripping characteristicsaccording to Fig. 10.

tive independently of any kind of fault in contrast to the IDMTgrading with mutable grading times. That is why the advancedcoordination method using the new tripping characteristics isrobust against any fault current values and types.

VII. CONCLUSION

This paper presents a new nonstandard tripping characteristicfor overcurrent relays and its advanced method for optimizedcoordination. The characteristic is based on the logarithmicfunction and the optimization task has been solved using themethod of Lagrange generalized with the KarushKuhnTuckerconditions. This results in a noticeable reduction of the max-imum and effective average tripping time in relation to theconventional DTOC and IDTM grading. The thermal stresseson the power system devices as transformers or cables are

alleviated strongly. In our case study, the effective average trip-ping time could be reduced to 57% (43%) compared to IDMTgrading (with instantaneous elements) and 42% compared to aDTOC grading. In particular, the maximum thermal equivalentcould be reduced to 82% (69%) compared to an IDMT grading(with instantaneous elements) and 84% compared to a DTOCgrading. Along the way, the selectivity is maintained in anycase independent of any fault current, location, and line lengthor distance between the substations of the grading path.

An advantage can also be seen regarding motor startup. Here,the new nonstandard tripping characteristic fits very well withthe startup characteristic.

However, coordination with thermal overcurrent devices,such as fuses, poses a problem to be studied. Nevertheless,the new nonstandard tripping characteristic can be utilized incompletely new constructed networks (e.g., wind farms andauxiliary networks of power plants).

The favorable effects of the advanced coordination methodusing nonstandard tripping characteristics will become more ob-servable the higher the number of subunits is along the gradingpath. This can be expected in distribution networks with DG in-feeds preferably. With respect to that, this method is being ex-tended considering DG interinfeeds with a nonneglectable faultcurrent contribution which is under current investigations.

REFERENCES[1] E. O. Schweitzer and S. E. Zocholl, Aspects of overcurrent protection

for feeders and motors, presented at the PEA Relay Committee SpringMeeting, Matamoras, PA.

[2] Y. G. Paithankar, Transmission Network Protection. New York:Marcel Dekker, 1998.

[3] J. Jger and T. Keil, New protection co-ordination methods in the pres-ence of distributed generation, in Proc. 8th Inst. Elect. Eng. Int. Conf.Developments in Power System Protection, 2004, p. 319.

[4] Manual SIPROTEC Multi-Functional Protective Relay 7SJ62/63/642007 [Online]. Available: http://siemens.siprotec.de.

Timo Keil was born in Backnang, Germany, in 1976.He received the Dipl.-Ing. degree from the Univer-sity of Erlangen-Nuremberg, Nuremberg, Germany,in 2004.

In 2002, he joined the Fraunhofer Institute,Erlangen, Germany, and in 2003, the PowerTransmission and Distribution Group of SiemensCompany, Erlangen. Currently, he is with the Insti-tute for Electrical Power Systems at the University ofErlangen-Nuremberg, where he has been since 2004.His fields of interest are power system analysis,

protection systems and control, and distributed generation.

Johann Jger (M05) was born in Erlangen, Ger-many, in 1964. He received the Dipl.-Ing. and Dr.-Ing. degrees in electrical engineering and power sys-tems from the University of Erlangen, Erlangen, in1990 and 1996, respectively.

In 1990, he joined the Institute for Electrical PowerSystems at the University of Erlangen, working onthe analysis and calculation of FACTS devices. In1996, he was with the Power Transmission and Dis-tribution Group and the System Planning Departmentat Siemens AG, Erlangen, working in different fields

of network planning and protection in worldwide projects. Currently, he is incharge of a full professorship for power systems at the University of Erlangen.

Dr. Jger is a member of VDE/ETG and CIGRE as well as convenor ormember of several national and international working groups and task forces.

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