Abstract—This paper presents the development of the cross

differential relay. The new relay is suitable to double circuit HV transmission lines. Based on basic principle of cross differential relay, The paper introduces a Percentage Cross Differential Current elements used to improve sensitivity of cross differential relay. To improve stability of cross differential relay, voltage elements are used to distinguish between fault and open circuit condition, and phase selector elements are used to block healthy phase elements. EMTP simulations and Real Time Digital Simulator system (RTDS) tests prove that the cross differential protection is able to offer correct responses under various system and fault conditions.

Index Terms—cross differential relay, double transmission lines, non-communication protection.

I. INTRODUCTION

The parallel double transmission lines are more and more

widely used in modern power system to improve transmission capability and reliability. Many kinds of relaying protection can be used to protect parallel double transmission lines, such as over-current relay, distance relay and pilot relay[1]. Current relay and distance relay do not need communication channel but can not operate to trip at any point on the line without time-delay. Pilot relay can fast operate without time-delay but need communication channel[2]. The cross differential protection can operate without time-delay and does not need communication links. It is one of the most suitable ways to protect parallel double transmission lines[3][4].

A typical parallel double transmission line is shown in Fig.1. The terminals of both lines are connected to the same bus and they have same parameters. So the currents and voltages of double lines are related. The basic principle of the cross differential protection is based on comparing currents or directions of the double lines[5]. If no faults or external faults

This work was financed by NSFC (the National Natural Science Foundation

of China) under Grant numbers 50077011 and 50377019 and AREVA T&D Automation & Information Systems

Q P Wang is with the Electric Power Research Institute, China.

X Z Dong is with the Department of Electrical Engineering, Tsinghua University, China

Z Q Bo, B R J Caunce D Tholomier, and A Apostolov are with the AREVA T&D – Automation & Information Systems

.

occur, electric quantities of double lines are similar. When internal faults occur, balance will be destroyed from which internal or external fault can be distinguished.

Relay

CT

CT

VT

VT

Relay

CT

CT

VT

VT

Source

Source

Load

B1S B1R

B2S B2R

Line 1

Line 2

RS RR

Bus S Bus R

F

Fig.1 Parallel double lines system

This paper presents a scheme of cross differential relay for

double transmission lines. The currents of double lines and voltages are all used by cross differential relay[6]. Two basic principle of cross differential relay is introduced in this paper. Percentage cross differential current element is used to improve sensitivity of the cross differential relay. To improve stability of cross differential relay, voltage elements are used to distinguish fault or open circuit condition, and phase selector elements are used to block healthy phase. The relay includes percentage cross differential current element, voltage start element, phase selector element and block element. EMTP simulations and Real-Time Digital Simulator system (RTDS) tests are performed for different fault conditions, and the results prove that the presented scheme is able to offer fast and reliable operation without the need for communication links.

II. PERCENTAGE CROSS DIFFERENTIAL PRINCIPLE

The conventional principle of cross differential relay includes the current-balanced relay and the transverse differential directional relay.

Basic principle of current-balanced relay is based on comparing current-amplitudes of double lines. The criterions of current-balanced relay are

opIII >− 21

opIII >− 12 (1)

Where 1I and 2I are current amplitudes of double lines;

opI is operating value.

Basic principle of transverse differential directional relay is based on calculating amplitude of differential current to determine internal fault or external fault and selecting fault

Protection Scheme of Cross Differential Relay for Double Transmission Lines

Q.P. Wang, X.Z. Dong, Z.Q. Bo, B.R.J. Caunce, D. Tholomier, A. Apostolov

line by their directions. The criterions of transverse differential directional relay are

opIII >− 21

max12

min

)(arg θθ

φφ

θ

<⋅−<U

eII j

max21

min

)(arg θθ

φφ

θ

<⋅−<U

eII j

(2)

Where 1I and 2I are currents of double lines; opI is

operating value; φφU is phase-phase voltage; minθ and

maxθ are operating ranges.

Both of two principles use current differential elements. Based on the conventional cross differential relay, operating

value of current differential element opI must be above:

(i) Unbalance current for external fault (ii) Maximal load current in single line operation condition (iii) Differential current of healthy phase for phase-earth

fault in successive operation zone To meet condition (ii) and (iii), operating values are set to

very high. This will inevitably decrease sensitivity of cross differential relay, especially for heavy loaded transmission lines. The fast operation zone is reduced because of the high operating value and more faults will be cleared by successive operation. If successive operation zone is greater then 50% of the line length, there will be dead zone on the line where relays can operate when internal faults occur. Therefore, the conventional cross differential relay is not suitable to EHV transmission lines.

In this paper, a percentage cross differential element is used to improve conventional cross differential relay. The summary current of double lines is used as bias current. The criteria of percentage cross differential relay is

2121 IIkII +⋅>− (3)

Where 1I and 2I are currents of double lines; k is bias

coefficient. Bias current should be above unbalance current for external fault, as setting value (i).

When external fault occurs, currents of double line have the same phase angle and bias current is high enough to prevent operation incorrectly. When internal fault occurs, and bias current is low and relay can operate correctly. At the same time, when internal fault occurs, the summary current of double lines is the fault current.

When fault occurs near to bus R, the currents of double lines in relay R location are similar (show in Fig.2). Cross differential relay can not operate to trip breaker B1S. After

breaker on the other side opens, SI1 is short current and SI 2

is load current. Cross differential relay can successive operate to trip breaker B1S. The successive operation zone is calculated as follow.

Assuming l is the length of transmission line and l⋅α is the distance from fault point to the remote terminal of line.

The fault current is RSF III 11 += . Based on the

relationship of the voltages, we can obtain equation

SRS III 211)1( =−− αα (4)

and the differential current is FI⋅α :

FRSSS IIIII αα =+=− )( 1121 (5)

If differential current equates operation value opI , α can

be obtained. Fig.2 Calculation of successive operation zone

%1001 ×=F

op

I

Iα (6)

The reliable coefficient k is the percentage of successive

operation zone.

III. VOLTAGE START ELEMENT

The percentage cross differential relay can reduce successive zone and improve sensibility. But it also causes some problems. The criteria (3) has to be above the unbalance current. When open circuit occurs or remote side breaker trips, relay may operate incorrectly because of fault in successive operation zone.

In order to prevent relay operating incorrectly on condition of open circuit, voltage start element is used to increase reliability of cross differential relay. The voltage start element includes the negative over voltage element and the Phase-phase under voltage element.

(a) Negative over voltage element Negative over voltage element can pick up when

unsymmetrical fault occurs. The criterion of negative over voltage element is

2,2 opUU > (7)

Where 2U is negative voltage.

2,opU is operating value of the negative over voltage

element:

22, ⋅= umbrelop UKU (8)

Where 2⋅umbU is the maximal unbalanced negative voltage;

relK is reliable coefficient.

Cross differential relay will start when the equation (7) above is met and drop off when it is not met.

B1S

B2S

Line 1

Line 2

Bus S Bus R

F

SI1

SI2

RI1

RI2

l⋅α

FI

R S S

(b) Phase-phase under voltage element Phase-phase under voltage element is used for symmetrical

fault. The criterion of the phase-phase under voltage element is

popUU ,<φφ (9)

Where φφU is the phase-phase voltage: ABU , BCU and

CAU .

popU , is the operating value of phase-phase under voltage

element:

rel

epop K

UU

)95.09.0(,

→=

(10)

Where eU is the normal phase-phase voltage; relK is the

reliable coefficient. To prevent Phase-phase under voltage element from

starting under condition of power swing, the 1 cycle pre-fault (swing) voltage is used as normal phase-phase voltage.

Cross differential relay will start when the condition in equation (10) above is met, will drop off when it is not met.

IV. PHASE SELECTOR AND BLOCK ELEMENT

The voltage start element can prevent operation incorrectly

when open circuit occurs. But when fault occurs in successive operation zone, the voltage start element will pick up. Because another side breaker will trip first, healthy phase relay of healthy line will operate incorrectly. To prevent that, phase selector element is used to block healthy phase. Its criteria is

}max{ ,2,1,2,1 iirelii IIKII +⋅<+ (11)

Where iI ,1 and iI ,2 are phase currents of double lines; relK

is reliable coefficient. Any phase meeting equation (11) is a healthy phase and should be blocked. After breakers open to clean faults, current of fault phase is zero and current of healthy line is the load current. Differential current of double lines will cause the cross differential relay to operate incorrectly and trip the health line. To prevent cross differential relay from operating incorrectly, percentage current differential element of the dead phase should be blocked. Percentage current differential elements of other phases still work. When one phase is opened, the differential current of healthy phase may be very high. The most serious operating conditions are I-AB & II-BC as show in Fig.3. The healthy phase current amplitudes of double lines are the same,

BB II ,2,1 = . But their angles are very different. Based on

Fig.3, voltage equation can be obtained

⎪⎪

⎩

⎪⎪

⎨

⎧

+=−+=−+=−+=−

CLBMCRCS

CMBLBRBS

BLBMBRBS

BMALARAS

IZIZUU

IZIZUU

IZIZUU

IZIZUU

,2,2,,

,2,2,,

,1,1,,

,1,1,,

(12) Where U is the bus voltage and I is the current of double

lines. LZ is self-resistance, MZ is mutual resistance.

Therefor,

2

10

10

10

10

,2

,1

21

21

aZZ

ZZ

aZZ

ZZ

I

I

B

B

+−

−

+−

−= (13)

When L

M

Z

Z is large, the differential current of healthy

phase will be very high. Cross differential relay will operate incorrectly to trip healthy phase. So all the cross differential elements need to be blocked when any switches of two different phases open.

I1,A

I1,B

I2,B

I2,C

US,B

US,A

US,C

UR,A

UR,B

UR,C

Fig.3 Connecting figure of I-AB & II-BC

When switches of bus open, double lines are disconnected.

Therefore, the whole cross differential relay should to be blocked under this condition. By using differential blocking element, the reliability of cross differential relay will be secured.

V. SCHEME OF CROSS DIFFERENTIAL RELAY

Cross differential relay is composed of voltage start element, percentage cross differential current element, phase selector element and other blocking elements.

The Logical map of voltage start element is shown in Fig.4. It is used to prevent cross differential relay from operating incorrectly on condition of open circuit. When voltage start element picks up, other elements can operate. Otherwise other elements will be blocked.

popAB UU ,<ABU

popU ,

popBC UU ,<BCU

popU ,

popCA UU ,<CAU

popU ,

+

2,2 opUU >2U

2,opU

+Start

Fig.4 Logical map of voltage start element

The Percentage cross differential current element is the

most important element in cross differential relay. It can distinguish internal and external fault and select the faulted line. Phase A is taken as example as show in Fig.5.

1,AI

2,AI

&

+ TripLine1

)( 2,1,1,2, AAAA IIkII +⋅>−

)( 2,1,2,1, AAAA IIkII +⋅>−

2,1,2,1, AAAA IIkII +⋅>−

oo 90)(

arg90 2,1, >−

⋅−<−

CB

jAA

UU

eII θ

oo 90)(

arg90 1,2, >−

⋅−<−

CB

jAA

UU

eII θ&

+ TripLine2

1,AI

2,AI

1,AI

2,AI

1,AI 2,AI

BU CU

1,AI 2,AI

BU CU

Fig.5 Logical map of percentage cross differential current element

In order to improve reliability of the cross differential relay,

phase selector and other blocking element are also used. These blocking element, voltage start element and percentage cross differential current element, which compose of the whole protection scheme, are shown in Fig.6.

&

Voltage start

Percentage crossdifferential

Phase selector

Block

&

&Trip

Fig.6 Logical map of cross differential relay

VI. RTDS TEST RESULTS

The presented cross differential relay has been implemented into the AREVA MiCOM P544 & P546 multifunction current differential relay. To demonstrate the performance of presented cross differential relay, a series of tests with respect to a 400km 500kV EHV transmission system have been conducted using RTDS (Real Time Digital Simulator). The structure of the simulated system is shown in Fig.7. The short circuit capacities of system at ends S and R are 1200MVA and 6000MVA respectively. Various typical faults and evolving faults are tested at a number of fault locations as shown in the figure.

Fig.7 Test system configuration

As can be seen from the figure, the relay under test can be

installed at each end of the protected line. There are two operating modes of cross differential relay depending on fault locations. Here the relay at location R1 is taken as an example.

(1) Instant operation ( ‘F1’ and ‘F2’ as shown in Fig.7) The relay will instantly trip for near end and mid line faults. (2) Successive operation ( ‘F3’ as shown in Fig.7) The relay will trip successively for remote end fault. To test

this fault condition, the remote circuit breaker needs to be controlled to operate after fault inception (single pole tripping for single phase fault and three pole tripping for other faults), therefore enabling the relay to operate successively after the remote breaker operation. Various tests are given as follow,

Test 1 – Simple faults on line 1 Fault location: ‘F1’, ‘F2’ and ‘F3’. Fault Type: single phase, double phases, double phase to

earth, three phases. Test Results:

1). Single phase faults: trip faulted phase; Other faults: trip 3 phases.

2).Fault at point ‘F1’: Line1 fast trip, Line 2 no trip. Fault at point ‘F2’: Line1 fast trip, Line 2 no trip. Fault at point ‘F3’: Line1 successive trip, Line 2 no trip.

Test 2 – High resistance faults on line 1 Fault locations: ‘F1’, ‘F2’ and ‘F3’. Fault Type: single phase, double phases, double phase to

earth, three phases. Test Results:

1). Single phase faults: trip faulted phase; Other faults: trip 3 phases.

2). Fault at point ‘F1’: Line1 fast trip, Line 2 no trip. Fault at point ‘F2’: Line1 fast trip, Line 2 no trip. Fault at point ‘F3’: Line1 successive trip, Line 2 no trip.

G1

R

Line2

Line1

F4 F5

F1 F3

R1 R2

S

F2G2

Test 3 – Internal to External Evolving faults from line1 to line2 at various time intervals

Fault locations: ‘F1’ to ‘F4’ and ‘F3’ to ‘F5’. Fault Type: single phase. Test Results:

1). Trip faulted phase on both lines respectively after each fault inception. 2). ‘F1’ to ‘F4’: Line1 fast trip, Line2 fast trip.

‘F3’ to ‘F5’: Line1 successive trip, Line2 successive trip.

Test 4 – Internal to Internal Evolving faults from line1 to line1 at various time intervals Fault locations: ‘F1’ to ‘F1’ and ‘F3’ to ‘F3’. Fault Type: single phase evolving fault. Test Results: 1). Trip fault phase for the first fault, then trip 3 phases for the second fault. 2). ‘F1’ to ‘F1: Line1 fast trip, Line2 no trip.

‘F3’ to ‘F3: Line1 successive trip, Line2 no trip.

The RTDS results show that the presented cross differential relay is able to clean faults at any points on the lines by instant or successive operation. Cross differential relay can not only trip fast without communication channel, but also protect double line at the same time. Cross differential relay can reliably clean different kinds of simple faults, involving faults and high resistance faults.

VII. CONCLUSION

A new cross differential relay is presented for double transmission line protection. The relay including a Voltage start element, a percentage cross differential current element, a phase selector and other blocking element is able to clean faults by instant operating and successful operation without the need for communication channel. Results from extensive RTDS test have proved that the operation of the relay is fast and reliable.

.

VIII. REFERENCES

[1] Zhu Shengshi. “Theories and techniques of the protection in high voltage power system”. China electrical power, 1995

[2] AREVA, “MiCOM P540 current differential protection”, AREVA T&D Automation & Information Systems.

[3] NARI-Relays electric limited company. “ISA-258A digital transverse differential relaying protection”.

[4] Huang Yizhuang, Li Chunhui. “A new scheme of directional transverse differential relaying protection for parallel double transmission lines”. Proceedings of ISEDEM’93, 1993.1, pp421-425.

[5] M M Eissa, O P Malik. “A New Digital Directional Transverse Differential Current Protection Technique.” IEEE Transactions on Power Delivery. Vol.11, No.3, 1996, pp1285-1291.

[6] Song Bin, Chen Yulan and Xu Qiulin. “Design of Microprocessor-based Transverse Differential Current Directional Protective Device. Automation of Electric Power System, Vol.27, No.10, 2003, pp85-89.

IX. BIOGRAPHY

Qingping Wang received his Bachelor’s degree in 1997, Master’s degree in 2000 and Ph.D. degree in 2002 from Department of Electrical Engineering, Tianjin University, China, respectively. He furthered his post-doctoral research in Electrical Engineering Department of Tsinghua University from 2002 to 2004. His interest research areas are relaying protection of power system. He has authored and presented more than 30 technical papers.

Xinzhou Dong received his BSc in 1983, MSc in 1991 and PhD in 1996 in the Department of Electrical Engineering, Xi’an Jiaotong University, China, respectively. He furthered his research work in the postdoctoral station of Tianjing University, China from 1997 to 1998. Presently, he is employed as the Associated Professor in Tsinghua University, China. His research interests are Protective Relaying, Fault Location and Application of Wavelet Transform in Power System.

Zhiqian Bo received his BSc degree from the Northeastern University, China in 1982 and PhD degree from The Queen's University of Belfast, UK in 1988 respectively. From 1989 to 1997, he worked at the Power Systems Group at the University of Bath. Presently, he is with AREVA T&D – Automation & Information Systems and responsible for new technology developments. His main research interests are power system protection and control.

Ben Caunce completed a student apprenticeship with the English Electric Company in 1973, graduating with a Stafford University degree. He was employed as a relay development engineer by GEC Measurements (now AREVA T&D – Automation & Information) before being appointed as a Project Leader in 1981. He was engaged in the development of one of the first microprocessor based distance relays for extra high voltage power transmission lines, and later on, other distance relays for sub-transmission and distribution lines. He was appointed to the position of Assistant Chief Engineer, Development in 1994. In 2000 he held the position as R&D Manager, Medium Voltage Development, for 2 years, giving him responsibility for all aspects of hardware and software design and validation testing of protection and control relays for medium voltage applications. In 2002 he was appointed as Certification Director - Protection Products.

Damien Tholomier received a BEng in Electrical and Automation Engineering in 1992 from the University of Marseilles, France (Ecole Polytechnique Universitaire de Marseille). Damien joined GEC ALSTHOM T&D GmbH (now AREVA T&D) in Stuttgart, Germany where he worked for 5 years in the Protection & Control department as Power System Application Engineer for medium and high voltage applications. In 1997 Damien moved as Marketing Manager, High Voltage Protection Business Unit with Alstom T&D Protection & Control in Lattes, France where he was engaged in the development of distance relays for sub- and extra high voltage power transmission as well as in the development of the numerical busbar protection (universal topology and CT saturation detection algorithms). From 1999-2001 he was appointed to the position of Sales & Service Director for Mediterranean Countries and Africa. From 2002, he is presently Marketing Products Director for AREVA T&D – Automation & Information. His main research interests are Protective Relays, Fault Location and Serial Communication to Non Conventional Instrument Transformers. Alexander Apostolov received his MS degree in Electrical Engineering, MS in Applied Mathematics and PhD from the Technical University in Sofia, Bulgaria. He is presently Principal Engineer for AREVA T&D EAI in Los Angeles, CA. He is a Senior Member of IEEE and member of the Power Systems Relaying Committee and Substations C0 Subcommittee. He is Vice-Chairman of the Relay Communications Subcommittee, and serves on many IEEE PES Working Groups.He is a member of IEC TC57 (leader of a Task Force on Power Quality Object Models in IEC 61850_ and CIGRE. He is Chairman of the Technical Publications Subcommittee of the UCA International Users Group. He holds three patents and has authored and presented more than 150 technical papers.