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468 IEEE TRANSACTIONS ON SMART GRID, VOL. 2, NO. 3, SEPTEMBER 2011

A Fault Steady State Component-Based Wide AreaBackup Protection Algorithm

Jing Ma, Member, IEEE, Jinlong Li, James S. Thorp, Life Fellow, IEEE, Andrew J. Arana, Qixun Yang, andA. G. Phadke, Life Fellow, IEEE

AbstractA novel wide area backup protection algorithm toidentify fault branch based on the fault steady state component isproposed. Under normal conditions of the power system, subsetsof buses called protection correlation regions (PCRs) are formedon the basis of the network topology and phasor measurement unit(PMU) placement. After the fault occurs, by analyzing the faultsteady state component of differential current in each PCR, thefault correlation region is confirmed and then a fault correlationfactor (FCF), is calculated in real time to locate the fault branch.The simulation results for the 10-generator 39-bus system verifythat this method is able to easily identify fault branch with limitedmeasurement points.

Index TermsFault correlation factor (FCF), PMU, protectioncorrelation region (PCR), wide area backup protection.

Symbols

incidence matrix of buses with PMUs.

incidence matrix of buses without PMUs.

incidence matrix between the buses with and

without PMUs.

bus admittance matrix.branch admittance matrix.

bus-branch incidence matrix.

bus injection current vector.

fault transient state bus voltage vector.

fault state transient branch current vector.

postfault variation of injection current vector.

bus voltage vector in the fault steady state

network.

Manuscript received September 23, 2010; revised April 29, 2011; acceptedMay 25, 2011. Date of current version August 24, 2011. This work was sup-ported by the project of National Science Foundation of China (No. 50907021,50837002), the Fundamental Research Funds for the Central Universities(11MG01), and 111 project (B08013). Paper no. TSG-00136-2010.

J.Ma is with theSchoolof Electrical andElectronicEngineering,NorthChinaElectric Power University, Changping District, 102206 Beijing, China, and alsowith the Bradley Department of Electrical and Computer Engineering, VirginiaPolytechnic Institute and State University, Blacksburg, VA 24061 USA.

J. Li and Q. Yang are with the School of Electrical and Electronic Engi-neering, North China Electric Power University, Changping District, 102206Beijing, China.

J. S. Thorp , A. J. Arana,and A. G. Phadke arewith theBradleyDepartmentofElectrical and Computer Engineering, Virginia Polytechnic Institute and StateUniversity, Blacksburg, VA 24061 USA.

Digital Object Identifier 10.1109/TSG.2011.2158861

branch current vector in the fault steady state

network.

faulted bus voltage vector.

faulted branch current vector.

virtual branch voltage vector.

normal branch voltage vector.

employed as FCF to identify the fault branch.

the fault steady state component of differentialcurrent injecting into each PCR.

I. INTRODUCTION

BACKUP protection systems traditionally have been self-

contained, and in general do not depend upon wide area

measurement information. With only local measurements con-

ventional backup protection can misoperate when the system

is highly stressed. In todays competitive environment, trans-

mission grids are more tightly interconnected, and transmission

lines are operated close to their limits, in order to maximize

power transfers and take advantage of different energy costs[1], [2]. It is appropriate to review traditional backup protection

and consider changes to meet todays competitive challenges.

Recommended practice in the National Grid Company is that

backup protection relies on earth fault overcurrent protection

and overreaching zone 2 and zone 3 distance protection [3], [4].

It is required for Zone 2 elements to detect earth and phase faults

on the busbar at the remote end of the feeder. Zone 2 elements

operate in typically 0.5 s. if the fault had not been cleared by

primary busbar protection, Zone 3 elements are required to de-

termine earth and phase faults on any transmission line which is

connected to the remote end of the main protected line. Zone 3

elements operate in typically 1.0 s. However, this practice often

encountered the problem of Zone 3 elements tripping on over-load.

With recent advances in communication, information, com-

puter networks and the significant development in phasor mea-

surement unit (PMU), technology today has the capability of ex-

panding the scope of the protection system [5][7]. The strategy

under investigation is the substitution of a PMU for the backup

relay, the system of PMUs must then provide all backup protec-

tion. Using the fault steady state component of PMU currents

and voltages, the problem of third zone relays tripping on over-

load can be overcome. Furthermore, the algorithm allows fast

operation compared with what is currently done, since it does

not need coordination between several protection zones. It is

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MA et al.: A FAULT STEADY STATE COMPONENT-BASED WIDE AREA BACKUP PROTECTION ALGORITHM 469

Fig. 1. Fault steady state network of a generalized PCR.

now feasible, and timely, to apply more sophisticated protec-

tion algorithms with a wider view of the protected network so

that the high standards of dependability and security inherent in

modern protection systems can be maintained.

In addition, the impact of a fault on the whole network can

be minimized by precisely locating the fault branch and trip-

ping the minimum number of circuit breakers to isolate the fault.

There are two ways to identify the fault branch. One is imple-

mented by judging the open/closed states of circuit breakers and

the operational response of conventional protection relays on the

network [8], [9]. The other is achieved by analyzing branch cur-

rents throughout the network [10][13].To employ wide area measurement information more suffi-

ciently and effectively, this paper proposes an algorithm to pre-

cisely locate the fault branch by utilizing the fault steady state

component of the currents and voltages. Before the fault occurs,

the protection correlation regions (PCRs) are formed by ana-

lyzing network topology and PMU placement. After the fault

occurs, if the primary protection fails to operate, the wide area

backup protection will take over. The steady state component

of the differential current in each PCR is used to determine the

PCR in which the fault exists. The fault correlation factor (FCF)

in this region is calculated in real time to locate the fault branch.

The simulation results validate the proposed method.

II. FORMATION OF PROTECTION CORRELATION REGION

A. PMU Placement Rules Under Fault Conditions

It is no longer sufficient to know the bus voltage and the

branch current to determine the voltage at the other end of the

branch for the faulted branch. Knowledge of the voltage at both

ends of a branch is also insufficient to determine the branch cur-

rent if the fault is on that branch. With a fault on the system,

the following 2 PMU placement rules are no longer valid, as the

fault location is unknown and the fault may occur on any branch.

If bus voltage and branch current at one end of a branch are

known, bus voltage at the other end of the branch can becalculated.

Fig. 2. Fault steady state expanded network of the generalized PCR.

If bus voltages at both the ends of a branch are known, the

branch current can be calculated.

Alternatively, the following rules are valid even in the pres-

ence of a fault [14], [15].

If there is a PMU at a bus, the bus voltage and currents of

all the branches connected to the bus can be measured.

If a zero injection bus has n branches connected to it and

of the currents are known then the remaining current

can be calculated.

If n nonzero injection buses with PMUs are adjacent to

a zero injection network (no circuit loop in the network),

voltages and currents in the network can be calculated. Ifthere is a loop in the network, a PMU is added on the loop

to make the system observable.

B. Formation of Protection Correlation Region

On the basis of network topology and PMU placement, the

protection correlation region (PCR) is formed as follows.

Step 1: Generate the bus-bus incidence matrix A of the whole

network in the order of buses with PMUs in the

former lines and columns, and buses without PMUs

in the latter

(1)

where is the incidence matrix of buses with

PMUs. is the incidence matrix of buses without

PMUs. is the incidence matrix between the

buses with and without PMUs.

Step 2: Any two connected buses where both have PMUs

(hence in ) are formed into a protection correla-

tion region, defined as a specialized PCR.

Step 3: Connected buses in along with the buses to

which they are connected in form a general-

ized PCR.

The calculation of PCRs in is straightforward. The inci-dence matrix is formed from the branch data with and

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if there is a branch connecting and . Spe-

cialized PCRs are formed from all off-diagonal entries in

which are not zero.

To find the generalized PCRs, the matrix is repeatedly

multiplied by itself [16]

(2)

until

(3)

The th entry of the th power of an incidence matrix is

known to give the number of different paths of length begin-

ning at and ending at [ ]. Multiply by a column of

ones, and then give a vector of integers indicating the connec-

tivity of the non-PMU buses

(4)

For the example in Section IV the resulting column has four

1s, two 2s, and six 6s. The interpretation is that four of the

non-PMU buses are not connected to any other non-PMU buses,

that 2 of the non-PMU buses are connected to each other, and

that the remaining 6 buses are connected to each other. The ma-

trix then gives the PMU buses that are connected to these

groups of non-PMU buses and defines the generalized PCRs.

For example if the six interconnected non-PMU buses are (5, 6,

10, 11, 13, 14) then all the PMU buses connected to these six

buses (4, 7, 8, 12, 15, 31, 32) combined with the six non-PMU

buses form a large generalized PCR. More details are in the ex-

ample in Section IV.

III. FAULT BRANCH LOCATION ALGORITHM

A. Basic Theory

When a fault occurs in the power system, the superposition

theorem [17], [18] allows us to consider the currents and volt-

ages as containing a prefault component, a fault transient com-

ponent and a fault steady state component.

Assume generators and loads to be current injection sources.

The bus voltage vector and branch current vector in the

prefault network are given by

(5)

where is bus admittance matrix, is branch admittance

matrix, is bus-branch incidence matrix, and is the bus

injection current vector.

The variation of the injection currents after the fault inception

results in the transient process. Therefore, the bus voltage vector

and branch current vector in the fault transient state

network are given by

(6)

where is postfault variation of injection current vector.

In the fault steady state network, the bus voltage vector

and branch current vector are given by

(7)

where is the faulted bus voltage vector, and is thefaulted branch current vector.

During normal conditions, the fault steady state compo-

nent of differential current injecting into each PCR is calculated

to monitor the system status. If a fault occurs somewhere in the

system, the primary protection should determine the fault within

typically 11.5 cycles. After this period plus breaker time, if the

fault still persists, indicated by in some PCR,

the decision-making unit will take over and perform its backup

function. Then a fault branch location mechanism based on fault

correlation factor (FCF) is activated in this PCR until the fault

branch is inferred.

B. Fault Correlation Factor

A fault steady state network of a generalized PCR, containing

interconnected non-PMU buses along with PMU buses, is

shown in Fig. 1.

The PMU buses are connected to the non-PMU buses

via branches. and are the branch impedance and

the ground admittance of the th branch respectively, where

. are voltages of the PMU buses.

are voltages of the non-PMU buses.

are branch currents flowing from the PMU

buses. are branch currents flowing into

the non-PMU buses. Assume a fault occurs on the branch ,

and the distance between fault point and bus accounts for

percent of the total branch length. The current injection from

fault point to the network is .

To determine the fault branch, the non-PMU buses and the

PMU buses are needed to be expanded to buses. As shown

in Fig. 2, the network has been changed by connecting the new

buses with original buses via virtual zero-impedance branches.

Consider as injection currents of the

non-PMU network (blocks in Figs. 1 and 2). The bus voltage

vector and branch current vector can be expressed as

(8)

where and constitute the partitioned bus

impedance matrix

......

...

... ... ...

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Fig. 3. Ten-generator 39-bus New England test system.

TABLE IPMU PLACEMENT RESULT

Injection currents corresponding to nonfault branches are

(9)

where , and .

The injection current corresponding to the fault branch is

- (10)

Substitute (9) and (10) into , and

voltage vector of buses can be expressed as

...

...

...

...

...

...

(11)

Assume the fault branch to be nonexistent and the injection

currents of all branches to be calculated as (9). Then the virtual

voltage vector of buses is obtained

...

...

...

.

..

(12)

TABLE IITOPOLOGY ANALYSIS OF THE SPECIALIZED PCRS

Also, the virtual branch voltage vector is calculated as

...

...

...

...

...

...

...

...

(13)

where .

Using (9), the normal branch voltage vector is given by

(14)

The difference between the virtual branch voltage vector

and the normal branch voltage vector is

...

...

...

...

(15)

Vector is defined as

...

...

...

...

(16)

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TABLE IIITOPOLOGY ANALYSIS OF THE GENERALIZED PCRS

Fig. 4. Fault steady state differential currents in different PCRs when a single-phase fault occurs.

where is a diagonal matrix and is formed by the th column

of . .

Let . Vector is

defined as

(17)

If ,

...

...

...

...

(18)

where

Fig. 5. Fault steady state differential currents in different PCRs when a three-phase fault occurs.

TABLE IVTHE CALCULATED FCFS OF BRANCHES 1 ; 2 AND 3

If ,

...

...

...

...

(19)

From (18) and (19), we can find that if branch is not the fault

branch, all entries in the vector are different from each other.

Or else, all entries in the vector are identical except the th

entry. The maximum absolute difference between entries in the

vector (except the th entry) is given by

(20)

is employed as FCF to identify the fault branch. If only

of some branch is less than a thresholdthe decision-making unit

determines that a fault occurs on that branch and trip the fault. If

of each branch is more than a threshold, the decision-making

unit determines that there is a fault in the non-PMU network. In

this case, voltages of buses and corresponding

branch currents are calculated by (9) and (14). Then, the above

procedure is executed repeatedly until fault branch is located.

IV. TESTING RESULTS AND ANALYSIS

The 10-generator 39-bus New England test system [19] is

used to demonstrate the effectiveness of proposed PCR forma-

tion method and wide area backup protection algorithm. The

system structure is shown in Fig. 3 and there is no circuit loop

in any zero-injection network.

By adopting three rules in Section II, PMUs are only needed

to be placed at the nonzero injection buses to make the system

observable. The result of PMU placement is shown in Table I.On the basis of power network topology and PMU placement

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result, bus-bus incidence matrix is obtained. and

are given in (21)(23), at the bottom of the page.

Any two connected buses where both have PMUs (hence in

) are formed into a specialized PCR, as shown in Table II.

(21)

(22)

(23)

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To find the generalized PCRs, the matrix is repeatedly

multiplied by itself. When . Multiply

by a column of ones, and then the vector of integers indicating

the connectivity of the non-PMU buses is as follows:

(24)

From (24), it can be found that non-PMU buses 9, 17, 19, and22 are not connected to any other non-PMU buses, non-PMU

buses 1 and 2 are connected to each other, and non-PMU buses

5, 6, 10, 11, 13, and 14 are connected to each other. The matrix

then gives PMU buses that are connected to these groups

of non-PMU buses and defines generalized PCRs as shown in

Table III.

A. Fault Correlation Region Determination

There are three branches in PCR 21: (16-19), (20-19)

and (33-19). A single-phase earth fault and a three-phase fault

were applied separately at branch (16-19) at the 5 cycle (0.1

s). The fault steady state components of the differential currents

of all PCRs in both cases are calculated and shown in Figs. 4

and 5, respectively.

In each case, the calculated steady state component of the dif-

ferential current of PCR 21 is very noticeable, whereas steady

state components of different currents in other PCRs are negli-

gible and only have little variation resulting from the measure-

ment and calculation errors. These results are in accordance with

the practical state of the power system and prove that the method

is effective to identify the fault correlation region no matter what

type of fault.

B. Fault Branch Location

Various types of faults with values of fault resistances 0 ohmsand 300 ohms are adopted to test the effectiveness and reliability

of the FCF. The calculated FCFs of branches and are

shown in Table IV. The values of FCFs of the faulted branch

are no more than 0.238, whereas the values of FCFs of nonfault

branches and are no less than 43.997. These results prove

that it is effective and sensitive to locate the fault at branch by

this method.

V. CONCLUSION

A fault steady state component-based method to precisely lo-

cate the fault branch is proposed. Before the fault occurs, the

protection correlation region (PCR) is formed by analyzing net-work topology and the PMU placement. After the fault occurs,

the fault correlation region is determined by calculating the fault

steady state component of the differential current in each PCR

and the fault correlation factor (FCF) in this region is calculated

in real time to locate the fault branch. The simulation results

validate the proposed methods and show that they are effective

for the identification of various types of faults. In the real world,

there may be many non-PMU buses which are connected only to

other non-PMU buses, but these connected non-PMU buses as

a network are finally surrounded by boundary PMU buses. If a

fault occurs in the non-PMU buses network, including the case

of a fault occurring between 2 non-PMU buses, the algorithm

first detects the fault between the boundary PMU buses and thenon-PMU buses connected to them. If no fault occurs between

these buses, the voltages of the non-PMU buses adjacent to the

boundary PMU buses and corresponding branch currents can be

calculated. Therefore, these non-PMU buses can be equivalent

to the PMU buses. Then, the fault branch location mechanism

is executed repeatedly until the fault branch is inferred.

ACKNOWLEDGMENTMany faculty members and students contribute greatly to this

research. The authors would like to thank Dr. Yilu Liu.

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Jing Ma (S06M08) was born in Hebei Province,China, on February 25, 1981. He received the B.S.and Ph.D. degrees from North China Electric PowerUniversity, Beijing, in 2003 and 2008, respectively.

He is currently an Associate Professor in theSchool of Electrical and Electronic Engineering,North China Electric Power University. He wasa Visiting Scholar in the Bradley Department of

Electrical and Computer Engineering, VirginiaPolytechnic Institute and State University, from2008 to 2009. His major interests include wide-area

protection and control.

Jinlong Li received the B.S. degree from ZhengzhouUniversity in 2007. He is currently working towardthe M.S. degree in the School of Electrical and Elec-tronic Engineering, North China Electric Power Uni-versity, Beijing.

His interests mainly include wide area powersystem measurement, dynamic analysis, and backupprotection.

James S. Thorp (S58M63SM80F89LF03)received the B.E.E., M.S., and Ph.D. degrees fromCornell University, Ithaca, NY, in 1959, 1961, and1962, respectively.

He was the Charles N. Mellowes Professor in En-gineering at Cornell University from 1994 to 2004.He was the Director of the Cornell School of Elec-trical and Computer Engineering from 1994 to 2001,a Faculty Intern, American Electric Power ServiceCorporation in 19761977, and an Overseas Fellow,ChurchillCollege, CambridgeUniversityin 1988. He

is currently the Hugh P. and Ethel C. Kelley Professor of Electrical and Com-

puter Engineering and Department Headof the Bradley Department of Electricaland Computer Engineering, Virginia Polytechnic Institute and State University,Blacksburg.

Prof. Thorp was an Alfred P. Sloan Foundation National Scholar and waselected a Member of theNationalAcademyof Engineering in 1996. He receivedthe 2001 Power Engineering Society Career Service award, the 2006 IEEE Out-standing Power Engineering Educator Award, and shared the 2007 BenjaminFranklin Medal with A. G. Phadke.

Andrew J. Arana received the B.S. degree inelectrical engineering with the Sexton Distinctionfrom Dalhousie University, Halifax, NS, Canadain 2005 and the M.S. degree from Virginia Techin 2007. He is currently a Ph.D. candidate in theBradley Department of Electrical and ComputerEngineering at Virginia Polytechnic Institute andState University, Blacksburg.

His research interests include wide-area mon-itoring, analysis of electromechanical travellingwaves, relaying technology, and adaptive protection.

Qixun Yang was born in Shanghai, China, onOctober 30, 1937. He received the B.S. and Ph.D.degrees from Zhejiang University, China, and SouthWales University, Australia, in 1960 and 1982,respectively.

He is currently a Chinese academician of engi-neering and a Professor of North China ElectricPower University, Beijing. He is also the BoardChairman of Beijing Sifang Automation Co., Ltd.His research interests include power system protec-tion and control, and substation automation.

A. G. Phadke (M64SM97F80LF04) receivedthe B.Sc., B.Tech. (Hons.), M.S., and Ph.D. degreesfrom Agra University, IIT, Khargpur, IIT, Chicago,and the University of Wisconsin, Madison, in 1955,1959, 1961, and 1964 respectively.

He is a University Distinguished Professor (Emer-itus) at Virginia Polytechnique Institute and StateUniversity, Blacksburg. His primary research areais the microcomputer-based monitoring, protection,and control of power systems. He is a coauthorof two books on relaying: Computer Relaying for

Power Systems and Power System Relaying, and is the editor of and contributorto the bookHandbook of Electrical Engineering Computations.

Dr. Phadke was awarded the IEEE Third Millennium Medal in 2000, namedthe Outstanding Power Engineering Educator by the IEEE in 1991, and receivedthe Power Engineering Educator Award of the EEI in 1986. He received theIEEE Herman Halperin Transmission and Distribution award in 2000. He wasthe Chairman of the Technical Committee of USNC CIGRE, and Editor-In-Chief of IEEE TRANSACTIONS ON POWER DELIVERY. He was elected to the U.S.National Academy of Engineering in 1993. He was awarded Honorary Doc-torate by INP Grenoble, Grenoble, France in 2006.

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