dynamic state estimation based protection of mutually...

6 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL. 2, NO. 4, DECEMBER 2016

Dynamic State Estimation Based Protection ofMutually Coupled Transmission Lines

Yu Liu, Student Member, IEEE, A. P. Meliopoulos, Fellow, IEEE, Liangyi Sun, Student Member, IEEE,and Rui Fan, Student Member, IEEE

Abstract—Mutually coupled lines create challenges for legacyprotection schemes. In this paper, a dynamic state estimationbased protection (EBP) method is proposed to address thesechallenges. The method requires GPS synchronized measure-ments at both ends of the line and a high fidelity model ofthe protected line. The paper presents the dynamic model ofthe protected line and its impact on the performance of theprotection scheme. Numerical simulations prove that the methodcan correctly identify faults, independent of position and type.The work also demonstrates the advantages of the proposedmethod versus legacy protection functions such as distanceprotection and line differential. These advantages include reliableand faster detection of internal low impedance faults, inter-circuitfaults, and high impedance faults, even in cases of 1) partiallycoupled lines and 2) lack of measurements in adjacent lines.

Index Terms—Estimation based protection (EBP), highimpedance faults, inter-circuit faults, mutually coupled lines,partial coupling.

I. INTRODUCTION

TRANSMISSION lines are important components of mod-ern power systems. With ever larger demand for power

transmission, transmission systems are evolving with morecomplexity. Because of limited right of ways, many transmis-sion circuits share the right of way creating mutually coupledlines [1]–[3]. The coupling can involve multiple circuits withdifferent lengths of coupling for each circuit.

The protection challenges for these lines are brought by themagnetic mutual coupling which affects voltages and currentsas seen at the terminals of the line under protection. Fig. 1shows an example mutually coupled transmission line system.The line under protection is line 2 (MN).

Known limitations in protection of lines, such as the oneshown in Fig. 1, are as follows.

1) Directional overcurrent protection and distance protec-tion at relay I may occasionally fail to detect fault F1.The measured voltage at relay I will be affected by

Manuscript received September 7, 2016; accepted September 23, 2016. Dateof publication December 30, 2016; date of current version October 12, 2016.This work was supported by the Electric Power Research Institute (EPRI) andthe Power Systems Engineering Research Center (PSERC).

Y. Liu, A. P. Meliopoulos, and L. Y. Sun (corresponding author, e-mail: [email protected]) are with the School of Electrical and ComputerEngineering, Georgia Institute of Technology, Atlanta, GA 30332 USA.

R. Fan is with Pacific Northwest National Laboratory, Richland, WA 99354USA.

DOI: 10.17775/CSEEJPES.2016.00043

I IIM

N

Mutual coupling

III

I0,1

I0,3F2

F1

Line 3

(protected line)Line 2

Line 1

Fig. 1. Mutually coupled transmission lines.

zero sequence current in lines 1 (I0,1) and 3 (I0,3). Itis possible that the directional element may not detectthe fault while the distance function may see the faultbeyond its zone setting [4].

2) Distance protection with compensation [5] is a promisingmethod to compensate for the effects of currents inadjacent lines. This method considers the zero sequencecurrent of adjacent lines (I0,1 and I0,3) as inputs tocalculate apparent impedance. The main disadvantagesare as follows:

a) The protected line may not be mutually coupledfor its entire length with the adjacent lines, asillustrated in Fig. 1. In this case the relay may beovercompensated.

b) Sometimes, measurement of the zero sequencecurrent of adjacent line may require telemeteringadding to the complexity of the scheme.

c) Distance protection may not accurately detect inter-circuit internal faults [6], especially when the twolines are operating at different rated voltage levels.

d) The induced voltage in the protected line is not onlyinfluenced by zero sequence current of the adjacentline, but also by positive and negative sequencecurrents as well (5%–7%) [6], [7]. Thus, evenin perfect conditions, the compensation methodis subject to systematic errors, which will furthercompromise protection effectiveness.

3) Directional comparison scheme will confront similarproblems as overcurrent directional element. The direc-tional calculation results may be affected by the zerosequence current in adjacent lines [8].

4) Line differential protection is one of the most effectiveprotection schemes for mutually coupled lines [9]. How-ever, there are limitations:

a) The capacitive current may desensitize the relay,especially for long lines.

2096-0042 c© 2016 CSEE

LIU et al.: DYNAMIC STATE ESTIMATION BASED PROTECTION OF MUTUALLY COUPLED TRANSMISSION LINES 7

b) High impedance faults are difficult to detect.In addition, most legacy protection functions are based

phasors, which adds a delay in detecting the onset of a fault.We present a protection method that is based on sampled

values, requires a high fidelity model of the protection zone,requires only a few settings, and most importantly, it does notrequire coordination with other protection functions. Specif-ically, the method is based on dynamic state estimation tomonitor the health of the protection zone and take protectiondecision based on the status of the protection zone. Themethod is called the dynamic state estimation based protection(EBP) (also known as setting-less protection) [10]–[13].

The main idea behind the EBP relay is to monitor theconsistency between the measurements and the dynamic modelof the protection zone. Consistency is expressed in terms ofprobabilistic and quantifiable measures such as confidencelevel. Here the dynamic model consists of the differentialand algebraic equations expressing the physical laws that theprotected device(s) must obey. The quantification of how wellthe measurements fit the dynamic model of the protection zoneis performed using dynamic state estimation. It is importantto note that the EBP uses instantaneous values as opposed tophasors of legacy protection, and therefore, can detect faultswithin one of a few samples after fault initiation. This makes ita faster detector of faulty conditions. The best implementationof the EBP relay is with merging units (MU) technology:sampled values are transmitted to the process bus where theEBP uses the sample values to perform the analytics.

In this paper, the EBP algorithm is proposed to protectmutually coupled lines. Standard application of the EBP [10]–[13] requires that measurements are available at all terminalsof the line(s) under protection. However, for mutually coupledlines, not all the terminal voltages and currents may beavailable, since some of the mutually coupled circuits mayterminate at different substations than the line under protec-tion. In this case, additional techniques such as introducingadditional states (e.g., currents in mutually coupled lines thatare not available as measurements) are necessary to ensureperformance of the EBP relay. This paper first introduces asystematic way to derive the model of protected lines. Next,the performance of EBP relay for mutually coupled lines underseveral scenarios is presented via numerical experiments.Finally, detection and correction for hidden failures, whichenhances the security and reliability of the EBP relay, isdiscussed.

II. EBP METHOD

The EBP method has been introduced in [10]–[13]. Inthis section, we provide a concise description of the EBPmethod. EBP utilizes dynamic state estimation (DSE), whichestimates states x(t, tm) (with length of mx) from availablemeasurements z(t, tm) (with length of mz > mx) and adynamic mathematical model of measurements expressed interms of an algebraic companion form. This section will bearranged as follows. First, the construction of the dynamicmathematical model of measurements in algebraic companion

form is introduced; next, the DSE procedure is described toprovide the estimated states x(t, tm); finally, the trip logic ofEBP is provided.

A. Dynamic Measurement Model in Algebraic CompanionForm

The measurement model is constructed in an object-orientedway. First, the device quadratized dynamic model (QDM) forany specific component is introduced; second, the device QDMis equivalently transformed into device algebraic quadraticcompanion form (AQCF); finally, the measurement definitionsare considered to obtain the measurement of the AQCF model.

The device QDM describes all physical laws that the specificcomponent should satisfy via a set of differential and algebraicequations. The device QDM is shown in the following format,

i(t) = Yeqx1x(t) + Deqxd1dx(t)

dt+ Ceqc1

0 = Yeqx2x(t) + Deqxd2dx(t)

dt+ Ceqc2 (1)

0 = Yeqx3x(t) +

...

x(t)T⟨F ieqxx3

⟩x(t)

...

+ Ceqc3

where x(t) and i(t) represent the state vector and the terminalcurrent vector of the model, respectively. Usually terminalvoltages are included in x(t).

Sometimes the protection zone consists of several compo-nents (protection unit). The overall protection zone deviceQDM can be derived by combining the device QDM ofeach individual component. This combination is achieved byobserving the fact that, for the shared nodes among thesecomponents, the voltages are the same and the currents shouldbe summed up to zero. Thereafter, the combined model hasthe same syntax as the device QDM, shown in (1).

Specifically, in this paper, the device QDM of a partiallymutually coupled line is constructed as follows. 1) The line isdivided into several segments where each segment representsa mutually coupled line (an example can be found in SectionIII). 2) For each mutually coupled line segment, a multi-section model is utilized, where each section is a short π-equivalent line. The reason to use the multi-section model isto ensure accuracy during numerical calculations. The numberof sections for the multi-section model is chosen such that thetraveling length of electromagnetic waves during one samplinginterval is comparable to the length of each section. Basedon this, the overall model can be generated by combining allsections and segments together. The device QDM of the π-equivalent mutually coupled line section is given in AppendixA.

The device algebraic quadratic companion form (AQCF) isobtained by quadratic integration [14] of device QDM. Thisprocess transforms device models into algebraic companionform equations that fully retain the dynamics of the model.The device AQCF has the syntax described below.

8 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL. 2, NO. 4, DECEMBER 2016i(t)00

i(tm)00

= Yeqxx(t, tm) +

...

x(t, tm)T⟨F ieqx

⟩x(t, tm)

...

+ b (t− 2∆t) (2)

b(t− 2∆t) = Neqxx(t− 2∆t) + Meqi(t− 2∆t) + Keq

where x(t, tm) = [x(t) x(tm)]T, tm = t − ∆t, ∆t isthe sampling interval, and all other matrices can be directlyderived from matrices in (1).

The measurement AQCF is formed by expressing eachmeasurement as a function of the protection zone state uti-lizing the protection zone AQCF. For example, consider themeasurement of a terminal current of phase A of the line attime t. The AQCF model of this measurement will be the firstequation of (2), which expresses the phase A current at timet as a function of the line states at time t and tm. In general,the measurement AQCF has the following syntax:

z(t, tm) = h(x(t, tm))

= Ym,xx(t, tm) +

...

x(t, tm)T⟨F im,x

⟩x(t, tm)

...

+ bz (t− 2∆t) (3)

bz(t− 2∆t) = Nm,x · x(t− 2∆t) + Mm · i(t− 2∆t) + Km

Here the measurements z(t, tm) include: 1) actual mea-surements measured by VTs/CTs, with standard deviationsdetermined by meters; 2) virtual measurements representingphysical laws that must be obeyed by the protection zone, e.g.,KCL, KVL, etc., and a relatively small standard deviation isassigned; and 3) pseudo measurements representing physicalquantities, not directly measured, for which a typical value isexpected and a relatively large standard deviation is assigned.

B. Dynamic State Estimation (DSE) Procedure

The state vector x(t, tm) in (3) needs to be estimated. Wehave developed three dynamic state estimators. Here only oneof the solution methods (unconstraint weighted least square)is provided since the results are statistically similar with othermethods. For each DSE time step, the method first constructsan unconstrained optimization problem,

MinJ = (h(x(t, tm))−z(t, tm))TW (h(x(t, tm))−z(t, tm))

(4)where W = diag

1/σ2

1 , 1/σ22 , · · ·

, and σi is the standard

deviation of each measurement.Next, the best estimated state vector is provided by the

following iterative algorithm until convergence,

x(t, tm)ν+1 = x(t, tm)ν−(HTWH)−1HTW (h(x(t, tm)ν)

− z(t, tm)) (5)

where the Jacobian matrix H = ∂h(x)/∂x.

C. Trip Logic of EBP

After calculating the best estimated state vector x(t, tm),the health condition of the protection zone, or the confidencelevel [15] Pconf(t) is calculated as,

Pconf(t) = P(χ2 ≥ ζ(t)

)= 1− P (ζ(t),mv) (6)

ζ(t) = s(t, tm)Ts(t, tm) (7)

s(t, tm) =√W · r(t, tm) (8)

r(t, tm) = h(x(t, tm))− z(t, tm) (9)

where P (ζ(t),mv) is the probability of χ2 distribution givenχ2 ≤ ζ(t) with mv = mz −mx degree of freedom, r(t, tm)is the residual vector, and s(t, tm) is the normalized residualvector.

The confidence level acts as an indicator of the consistencybetween the measurements and the model. If the confidencelevel is high (near 100%), the system is healthy. If the con-fidence level is consistently low, there must be some internalfault inside the protection zone. To ensure dependability andsecurity of the EBP scheme, two settings (a user defined timedelay τdelay and a reset time τreset) are introduced to decidethe trip signal as below. The trip signal is issued only when theconfidence level remains consistently low for a user definedtime interval. The trip logic settings for the EBP relay areτreset and τdelay.

Tripvalue(t) =

∫ t

t−τreset(1− Pconf (t)) dt (10)

Trip(t) =

1, if Tripvalue(t) ≥ τdelay0, if Tripvalue(t) < τdelay

(11)

III. SIMULATION EXAMPLE: PARTIALLY MUTUALLYCOUPLED TRANSMISSION LINES

In this part, we demonstrate the performance of EBP onpartially mutually coupled lines. An example system is shownin Fig. 2. There are 9 voltage and 9 current measurements.Notice that the measurements at side M1 are easy to obtainsince line 1 and line 2 share the same substation M. Ourobjective is to protect line 2 (39 miles in total, 1.2 kA currentrating). The relative positions of these mutually coupled lines

Fiber optic

LEGEND

Breakers

M P QT

S

3-phase PTs 3-phase CTs

Side 1

Relay

I

Relay

II

Side 2Line 169 kVProtected line

M1

M2

Q1

Q2 S2 T2

S3Q3P3

P2

P1

230 kV Line 3

Line 2

115 kV

15 miles 10 miles 8 miles 6 miles

Fig. 2. Example test system: partially mutually coupled transmission lines.


are given in Fig. 3. The device model is built by combiningthe following four segments: MP (mutually coupled lines M1-P1, M2-P2), PQ (mutually coupled lines P1-Q1, P2-Q2, P3-Q3), QS (mutually coupled lines Q2-S2, Q3-S3) and ST (lineS2-T2). The model is a physically based, three phase, asym-metric, shields/grounds inclusive transmission line model. Thesampling rate is 4800 samples per second, as defined in IECstandards.

12

20

20

24

12 42 14 14 76 10 10 10 10

12

N1

A1

B1

C1

Line 1

A2

B2

C2

Line 2

N2

N3

N4

A3

B3

C3

Line 3

unit: ft

Fig. 3. Tower structures of the protected transmission lines, segment PQ.

A. State and Measurement Additions for EBP Relay

As shown in Fig. 2, there is a total of 6 terminals (M1, M2,P3, Q1, T2, S3); however, measurements are available onlyat 3 line terminals (M1, M2 and T2). While measurements atthe other terminals can be telemetered, we elect not to relayon these measurements to minimize the complexity of thescheme. Instead, we introduce additional states, such as virtualmeasurements and pseudo measurements to enable operationof the proposed EBP scheme.1) Additional States

Currents in mutually coupled lines are introduced as ad-ditional states to be estimated by the EBP algorithm. In theexample of Fig. 2, it will be the currents in lines 1 and 3.To ensure observability of the system, additional virtual andpseudo measurements are considered next.2) Additional Virtual Measurements

Additional virtual measurements describe the physical lawsinfluenced by the mutual coupling. Voltage drops between twoterminals of any line due to the currents through the adjacentlines are introduced as virtual measurements.3) Additional Pseudo Measurements

Pseudo measurements are introduced to augment the mea-surement set, provide redundancy, and ensure observability.

1) Pseudo measurements at node Q1: Current and voltagemeasurements at side M, together with the model ofline 1 are utilized to estimate the approximate voltagesat side Q1. These voltages are introduced as pseudo-measurements.

2) Pseudo measurements at node P3 and S3: The best guessof the voltages at these nodes is selected as follows:Initially, the pseudo voltage instantaneous measurementsare calculated from phasors, where the rms values ofphasors are chosen as the nominal voltage, and the anglesof the phasors are chosen as the voltage angles at node

M1. In subsequent iterations, the estimated values areused to select the values of the pseudo measurements.

B. Settings of Relays

Line 2 is assumed to be protected with two legacy protectionfunctions: 1) distance protection with compensation method,and 2) line differential protection. It is also protected with anEBP relay. The settings of these protection functions are asfollows.1) Distance Protection Settings

The sequence parameters of the transmission line are com-puted and shown in Table I. The selected settings for thisrelay are shown in Table II, with zone 1, zone 2, andzone 3 chosen as 80%, 125%, and 260% of the positivesequence impedance of line 2. Here, the zero sequence self-compensation factor of line 2 is k(2)0 = (Z

(2)L0 − Z

(2)L1 )/Z

(2)L1 ,

the zero sequence mutual-compensation factor between line 2and line 1 is k

(2,1)M0 = Z

(2,1)M0 /Z

(2)L1 , and the zero sequence

mutual-compensation factor between line 2 and line 3 isk(2,3)M0 = Z

(2,3)M0 /Z

(2)L1 .

TABLE ISEQUENCE PARAMETERS OF THE PROTECTED LINE

Parameter (per mile) ValuePositive (negative) sequence impedance ofline 2 (Z(2)

L1 )0.72∠83.95 Ω/mile

Zero sequence impedance of line 2 (Z(2)L0 ) 2.40∠76.20 Ω/mile

Zero sequence mutual impedance betweenline 2, 1 (Z(2,1)

M0 )1.22∠67.12 Ω/mile

Zero sequence mutual impedance betweenline 2, 3 (Z(2,3)

M0 )1.06∠63.24 Ω/mile

TABLE IIDISTANCE RELAY SETTINGS

Function Settings

Line and grounddistance, zone 1

22.57∠83.95 Ω, 0.02 s delay, compensation factors:k(2)0 = 2.33∠− 11.06 k

(2,1)M0 = 1.69∠− 16.82

k(2,3)M0 = 1.47∠− 20.70



(2,1)M0 = 1.69∠− 16.82

k(2,3)M0 = 1.47∠− 20.70



(2,1)M0 = 1.69∠− 16.82

k(2,3)M0 = 1.47∠− 20.70

2) Line Differential Protection SettingsThe line differential relay uses the alpha-plane method [16].

The restraint region is between 1/6 to 6, with total angularextent of 195. The relay trip logic is activated when at leastone of the following thresholds is exceeded: 1) phase currentexceeds 1.44 kA, 2) zero sequence current exceeds 120 A, and3) negative sequence current exceeds 120 A. The relay willtrip when the trip logic is activated and the ratio falls outsidethe restraint region, with a delay of 0.02 s.3) EBP Relay Settings

For consistency, the intentional delay is also selected asτdelay = 0.02 s and the reset time is τreset = 0.04 s.


C. Event Studies

We compare the performance of the legacy protectionfunctions to the EBP relay performance via specific events.

Event 1: Bolt phase A to ground external fault in line 1, 1mile from side M1. A 0.01-ohm phase A to ground externalfault happens inside segment M1-P1 of line 1, at 1 mile fromthe side M1 and time 0.5 s. The results of available current andvoltage measurements are shown in Fig. 4. This is a severeexternal fault with large fault currents (see currents at sideM1) since the fault is near side M1.

Current_sideM1_C (A)

Current_sideM2_C (A)

Current_sideT2_C (A)

56.95 kV

89.26 kV

88.40 kV

77.57 kV

77.57 kV

0.450 s 0.550 sTime

7,871.3 A

8,347.2 A

793.8 A

793.5 A

800.0 A

800.3 A

56.65 kV

Current_sideM1_A (A)Current_sideM1_B (A)

Current_sideM2_A (A)Current_sideM2_B (A)

Current_sideT2_A (A)Current_sideT2_B (A)

Voltage_sideM1_A (V)Voltage_sideM1_B (V)Voltage_sideM1_C (V)


Voltage_sideT2_A (V)Voltage_sideT2_B (V)Voltage_sideT2_C (V)

Fig. 4. Current and voltage results of a bolt phase A to ground external faultin line 1.

For the distance protection relay, the trace of the impedance“seen” by the relay is shown in Fig. 5. We can observe thatthe impedance falls into zone 1 during the external fault andline 2 is wrongly tripped at 0.509 s + 0.02 s = 0.529 s. Thismis-operation is because the zero sequence current through thewhole length of line 1 is wrongly assumed as the measuredcurrent at side M1.

0

0

t =0.505s

Imag

inar

y P

art

of

the

Imped

ance

(ohm

)

20

80

60

40

20

40 20 20 40 60 80 100 120

Real Part of the Impedance (ohm)

t=0.50 s

t=0.505 s

t=0.51 s

t=0.515 s

Fig. 5. Trace of impedance during a phase A to ground external fault in line 1.

For the line differential protection relay, the phasor ratiotrace of phase A is shown in Fig. 6. The other phases are

not shown. Along the trace, the character “o” means thethresholds are not exceeded while the character “x” meansthe thresholds are exceeded. (The definitions can be appliedto all line differential relay figures.) The ratio stays near(−1, 0) both prior to the fault and during the fault, withno thresholds exceeded (with the character “o”). Thus, linedifferential protection relay correctly ignores this externalfault.

0 2 4

0

2

4

6

Imag

inar

y P

art

of

the

Phas

e A

Rat

io

Real Part of the Phase A Ratio

XO

Thresholds are exceededThresholds are not exceed

2

4

68 6 4 2

Fig. 6. Trace of the ratios during a phase A to ground external fault in line 1.

For the EBP relay, the results are depicted in Fig. 7.Here in the first two channels we show the residuals andnormalized residuals of three-phase currents of side M1. Also,the confidence level and the trip signal are given in the nexttwo channels. The confidence level stays low for a very shortperiod (around 2 ms) due to transients and then keeps a 100%confidence level during this external fault. Therefore, the EBPmethod also correctly ignores this external fault.

96.39 A

135.9 A

Residual_Current_sideM1_A (A)

Residual_Current_sideM1_B (A)

Residual_Current_sideM1_C (A)

27.26 p.u.

38.44 p.u.

100.00 % Confidence Level (%)

1.000 u

1.000 u

Trip

0.450 s 0.550 sTime

0.000 %

Normalized_Current_sideM1_A (p.u.)NormResidNormalized_Current_sideM1_B (p.u.)NormResidNormalized_Current_sideM1_C (p.u.)NormResid

Fig. 7. EBP results of a phase A to ground external fault in line 1.

In summary, for this external fault, the distance protectionrelay wrongly trips the line at 0.529 s; the line differential


protection relay correctly ignores this external fault; EBP relayalso correctly ignores this external fault.

Event 2: Bolt line 2 phase A to line 1 phase C internalinter-circuit fault. A 0.01-ohm line 2 phase A to line 1 phaseC internal fault happens inside segment P-Q at 5 miles fromside P and time 0.5 s. In line 2, the location of the fault (51%of the line) is within the instantaneous trip zone of the relay(80% of the line). The results of available current and voltagemeasurements are shown in Fig. 8.

Current_sideM1_A (A)Current_sideM1_B (A)Current_sideM1_C (A)


855.5 A

856.0 A

Current_sideT2_A (A)Current_sideT2_B (A)Current_sideT2_C (A)

55.74 kV

55.13 kV


96.50 kV

99.09 kV


84.25 kV

85.17 kV


0.450 s 0.550 sTime

2,649.1 A

3,149.3 A

2,828.5 A

2,308.4 A

Fig. 8. Current and voltage results of a bolt line 2 phase A to line 1 phaseC internal inter-circuit fault.

For the distance protection relay, the trace of the impedance“seen” by the relay is shown in Fig. 9. In the figure we canobserve that the impedance falls inside of zone 2 during theinternal fault. Therefore, the distance relay trips this fault withsome delay at 0.512 s + 0.15 s = 0.662 s. This trippingwith delay is because for distance relay it is hard to identifyinter-circuit faults, especially between lines with different ratedvoltage levels.

0

0

.


Imag

inar

y P

art

of

the

Imped

ance

(ohm

)

80

60

40

20

2040 20 20 40 60 80 100 120

t=0.50 st=0.515 s

t=0.51 s t=0.505 s

t=0.52 s

Fig. 9. Trace of impedance during a line 2 phase A to line 1 phase C internalinter-circuit fault.

For the line differential protection relay, the phasor ratiotrace of phase A is shown in Fig. 10. The other phases are notshown. Prior to the fault, the ratio of phase A is near (−1, 0),

and none of the thresholds are exceeded (with the character“o”). During the fault, the thresholds are gradually exceeded(from the character “o” to “x”) with the ratio entering thetripping zone. The differential protection relay correctly tripsthis fault at 0.519 s + 0.02 s = 0.539 s.

0 2 4

0

2

4

6

Imag

inar

y P

art

of

the

Phas

e A

Rat

io


2

4

68 6 4 2

t=0.51 st=0.52 s

t=0.50 s

XO

Thresholds are exceededThresholds are not exceed

Fig. 10. Trace of the ratios during a line 2 phase A to line 1 phase C internalinter-circuit fault.

For the EBP relay, the results are depicted in Fig. 11. Thefault is detected by the drop of the confidence level at 0.5002 sand the trip signal is triggered at 0.5202 s.

In summary, for this internal fault, the distance protectionrelay trips the line with delay at 0.662 s; the line differentialprotection relay correctly trips the line at 0.539 s; the EBPrelay correctly trips the line at 0.5202 s.

Event 3: High impedance phase A to ground internal faultin line 2. A 200-ohm phase A to ground internal fault happensinside segment P2-Q2 of line 2 at 5 miles from side P2

and time 0.5 s. The results of available current and voltagemeasurements are shown in Fig. 12.

0.550 sTime0.450 s

0.000

1.000

0.000%

Trip

100.00%

428.1 p.u.

352.4 p.u.

2,400.7 A

1,976.2 A

Confidence Level(%)

NormResid_Current_sideM2_A(p.u.)NormResid_Current_sideM2_B(p.u.)NormResid_Current_sideM2_C(p.u.)

Residual_Current_sideM2_A(A)

Residual_Current_sideM2_B(A)

Residual_Current_sideM2_C(A)

Fig. 11. EBP results of a line 2 phase A to line 1 phase C internal inter-circuitfault.


522.7 ACurrent_sideM1_A (A)Current_sideM1_B (A)Current_sideM1_C (A)


813.4 A

813.2 A

Current_sideT2_A (A)Current_sideT2_B (A)Current_sideT2_C (A)

60.21 kV

54.81 kV


93.16 kV

89.48 kV


81.20 kV

80.15 kV


0.450 s 0.550 sTime

522.8 A

1,070.2 A

1,071.7 A

Fig. 12. Current and voltage results of a high impedance phase A to groundinternal fault in line 2.

For the distance protection relay, the trace of the impedance“seen” by the relay is shown in Fig. 13. In the figure we canobserve that the impedance falls outside of the tripping zoneduring this internal fault. Therefore, the distance relay wronglyignores this internal fault. This refusal of operation is due tothe high fault impedance.

0

0

t=0.505 s

t=0.515 s

t=0.50 st=0.51 s

t=0.52 s

Imag

inar

y P

art

of

the

Imped

ance

(ohm

)


80

60

40

20

2040 20 20 40 60 80 100 120

Fig. 13. Trace of impedance during a high impedance phase A to groundinternal fault in line 2.

For the line differential protection relay, the phasor ratiotrace of phase A is shown in Fig. 14. The other phases arenot shown. The ratio of phase A stays inside the restraintregion with no thresholds exceeded (with the character “o”).Therefore, the line differential relay also wrongly ignores thisinternal fault due to high fault impedance.

For the EBP relay, the results are depicted in Fig. 15. Thefault is detected by the drop of the confidence level at 0.5002 sand the trip signal is triggered at 0.5202 s.

In summary, for this internal fault, the distance protectionrelay and line differential protection relay wrongly ignore thefault; the EBP relay correctly trips the line at 0.5202 s.

0 2 4

0

2

4

6

Imag

inar

y P

art

of

the

Phas

e A

Rat

io


2

4

68 6 4 2

X

O

Thresholds are exceeded

Thresholds are not exceed

11.21.4

0.2

0.2

0

t=0.52 s

t=0.51 st=0.50 s

Real Part of thePhase A Ratio

Imag

inar

y P

art

of

the

Phas

e A

Rat

io

Fig. 14. Trace of the ratios during a high impedance phase A to groundinternal fault in line 2.

0.450 s Time 0.550 s

Trip

0.000

1.000

0.000%

100.00%

40.21 p.u.

40.26 p.u.

225.5 A

225.7 A

Confidence_Level(%)

Residual_Current_sideM2_A(A)Residual_Current_sideM2_B(A)Residual_Current_sideM2_C(A)

NormResid_Current_sideM2_A(p.u.)NormResid_Current_sideM2_B(p.u.)NormResid_Current_sideM2_C(p.u.)

Fig. 15. EBP results of a high impedance phase A to ground internal faultin line 2.

IV. SUPERVISION OF DATA INTEGRITY AND CORRECTION

The effectiveness of the proposed EBP relay is based on theassumption that there are no hidden failures that deteriorate themeasurements. We can conclude from this method, therefore,that the inconsistency between the measurements and themodel is caused by internal faults of the protection zone.Thus, the detection of hidden failures and the correction ofcorresponding measurements are also essential to reliabilityand security of EBP relay.

There are mainly two approaches for detecting hiddenfailures:

1) The first approach is to estimate the fault related param-eters (location of the fault, fault admittance, etc.) duringinternal faults. This is achieved by altering the dynamicmodel of the protection zone to include fault related


parameters. If the measurements fit the faulted protectionzone model with a high confidence level, there exist nohidden failures; otherwise, there are hidden failures.

2) The second approach is to utilize redundant measure-ments. High measurement redundancy can be achievedby the use of data from the entire substation, alsoknown as the centralized substation protection (CSP)scheme [17]. Once the confidence level is low, the hy-pothesis test is applied to examine whether this is causedby internal faults or hidden failures. The hypothesis testeliminates any suspected measurements and performs theEBP procedure again until a high confidence level is ob-tained (hidden failures are detected), or all measurementsare covered (internal faults are detected).

After the detection of hidden failures, the proper correctionactions may differ according to different root causes. If theroot cause can be automatically corrected (e.g., a wrong CTratio), the values will be updated in the database. If the rootcause cannot be automatically corrected (e.g., a blown fuse),the bad data will be replaced with the estimated values andan alarm with the root cause will be sent to the control centerfor future maintenance.

From the above detection and correction procedure, the EBPrelay can operate continuously, reliably and securely even withthe presence of hidden failures.

V. CONCLUSION

Mutually coupled lines bring not only benefits, but also pro-tection challenges. Legacy protection methods exhibit short-comings for mutually coupled lines. The paper proposes adynamic state estimation based protection (EBP) that promisesbetter protection for mutually coupled lines. The methodrequires the dynamic model of the line under protectionand measurements from both ends of the line. It uses adynamic state estimator to determine the goodness of fitbetween measurements and the line dynamic model. Internalfaults are detected by deviations between measurements andmodel. Numerical experiments were performed to comparetypical legacy protection systems (distance protection withcompensation method and line differential protection) to theEBP method. Results show the following advantages of theEBP method:

1) It performs well for lines that are partially coupled.2) It can dependably and securely operate even with limited

measurements in adjacent lines.3) It detects internal fault faster than legacy schemes.4) It can reliably detect inter-circuit faults.5) It can reliably detect high impedance faults.

APPENDIX

QDM of π-Equivalent Mutually Coupled Line Section

This appendix describes QDM of π-equivalent mutuallycoupled transmission line section. An example π-equivalentsection with 2 lines is provided in Fig. A1.

Side 1

i1(1)(t) i2

(1)(t)

iL

(2)(t)

iL

(1)(t)

i2(2)(t)

v2(1)(t)

L(1,2)

R(1,2)

C(1,2) C

(1,2)

v2(2)(t)

i1(2)(t)

v1(2)(t)

C(1)

C(2)

R(2)

R(1)

L(1)

L(2)

C(1)

C(2)

v1(1)(t)

Side 2

Line 1

Line 2(protected

line)

Fig. A1. π-equivalent mutually coupled line section (mutual inductances andcapacitances inside each line are not shown).

The standard format of QDM is given in (1). The QDMparameters of the mutually coupled line section are:

i(t) =[i(1)1 (t) i

(1)2 (t) i

(2)1 (t) i

(2)2 (t)

]T;

x(t) =[v(1)1 (t) v

(2)1 (t) v

(1)2 (t) v

(2)2 (t) i

(1)L (t) i

(2)L (t)

]T;

Yeqx1 =

[0 0 I0 0 −I

];Deqxd1 =

[C 0 00 C 0

];Ceqc1 = 0;

Yeqx2 =[−I I R

];Deqxd2 =

[0 0 L

];Ceqc2 = 0;

R =

[R(1) R(1,2)(

R(1,2))T

R(2)

];C =

[C(1) C(1,2)(

C(1,2))T

C(2)

];

L =

[L(1) L(1,2)(

L(1,2))T

L(2)

];

all other vectors and matrices are null; I is the identity ma-trix; R(1),L(1),C(1),R(2),L(2) and C(2) are the resistance,inductance and capacitance matrices of line 1 and line 2;R(1,2), L(1,2) and C(1,2) are the mutual resistance, inductanceand capacitance matrices between line 1 and line 2; i

(1)1 (t),

i(2)1 (t), i

(1)2 (t) and i

(2)2 (t) are current vectors of line 1 and

line 2 at each side; v(1)1 (t), v(2)

1 (t), v(1)2 (t) and v

(2)2 (t) are

voltage vectors of line 1 and line 2 at each side; i(1)L (t) andi(2)L (t) are the current vector of line 1 and line 2 through the

inductances.

REFERENCES

[1] C. S. Chen, C. W. Liu, and J. A. Jiang, “A new adaptive PMU basedprotection scheme for transposed/untransposed parallel transmissionlines,” IEEE Transactions on Power Delivery, vol. 17, no. 2, pp. 395–404, Apr. 2002.

[2] A. H. Osman and O. P. Malik, “Protection of parallel transmission linesusing wavelet transform,” IEEE Transactions on Power Delivery, vol.19, no. 1, pp. 49–55, Jan. 2004.

[3] B. R. Bhalja and R. P. Maheshwari, “High-resistance faults on twoterminal parallel transmission lines: analysis, simulation studies, andan adaptive distance relaying scheme,” IEEE Transactions on PowerDelivery, vol. 22, no. 2, pp. 801–812, Apr. 2007.

[4] B. Bhalja and R. P. Maheshwari, “Percentage differential protection ofdouble-circuit line using wavelet transform,” Electric Power Componentsand Systems, vol. 35, no. 8, pp. 945–954, May. 2007.

[5] Y. Hu, D. Novosel, M. M. Saha, and V. Leitloff, “An adaptive scheme forparallel-line distance protection,” IEEE Transactions on Power Delivery,vol. 17, no. 1, pp. 105–110, Jan. 2002.


[6] V. H. Makwana and B. Bhalja, “New adaptive digital distance relayingscheme for double infeed parallel transmission line during inter-circuitfaults,” IET Generation, Transmission & Distribution, vol. 5, no. 6, pp.667–673, Jun. 2011.

[7] V. H. Makwana and B. Bhalja, “A new adaptive distance relayingscheme for mutually coupled series-compensated parallel transmissionlines during intercircuit faults,” IEEE Transactions on Power Delivery,vol. 26, no. 4, pp. 2726–2734, Oct. 2011.

[8] D. A. Tziouvaras H. J. Altuve, and F. Calero, “Protecting mutuallycoupled transmission lines: challenges and solutions,” in Proceedingsof 67th Annual Conference Protective Relay Engineers, College Station,TX, 2014, pp. 30–49.

[9] S. V. Unde and S. S. Dambhare, “GPS synchronized current differentialprotection of mutually coupled line,” in International Conference onPower and Energy Systems (ICPS), Chennai, India, 2011, pp. 1–6.

[10] A. P. S. Meliopoulos, G. J. Cokkinides, Z. Y. Tan, S. Choi, Y. Lee,and P. Myrda, “Setting-less protection: feasibility study,” in Proceedingsof 2013 46th Hawaii International Conference on Systems Science(HICSS), Maui, HI, 2013, pp. 2345–2353.

[11] A. P. S. Meliopoulos, G. Cokkinides, Y. Liu, R. Fan, S. Choi, and P.Myrda, “Protection and control of systems with converter interfacedgeneration (CIG),” in Proceedings of 2016 49th Hawaii InternationalConference on Systems Science (HICSS), Koloa, HI, 2016, pp. 2481–2487.

[12] Y. Liu, A. P. Meliopoulos, R. Fan, and L. Y. Sun, “Dynamic stateestimation based protection of microgrid circuits,” in Proceedings ofIEEE Power and Energy Society (PES) General Meeting, Denver, CO,2015, pp. 1–5.

[13] R. Fan, A. P. S. Meliopoulos, G. J. Cokkinides, L. Y. Sun, and Y. Liu,“Dynamic state estimation-based protection of power transformers,” inProceedings of IEEE Power and Energy Society (PES) General Meeting,Denver, CO, 2015, pp. 1–5.

[14] A. P. S. Meliopoulos, G. J. Cokkinides, and G. K. Stefopoulos,“Quadratic integration method,” in Proceedings of 2005 InternationalPower Systems Transients Conference (IPST), Montreal, Canada, 2005,pp. 1–8.

[15] F. C. Schweppe and R. D. Masiello, “A tracking static state estimator,”IEEE Transactions on Power Application and Systems, vol. PAS-90, no.3, pp. 1025–1033, May. 1971.

[16] Schweitzer Engineering Laboratories, Inc. (2016, Jan.). SEL-387L relayinstruction manual. [Online]. Available: https://selinc.com/products/387/

[17] H. Albinali and A. P. S. Meliopoulos, “A centralized substation protec-tion scheme that detects hidden failures,” in Proceedings of IEEE Powerand Energy Society (PES) General Meeting, Boston, MA, 2016, pp. 1–5.

Yu Liu (S’13) received his B.S. and M.S. degreesin electric power engineering from Shanghai JiaoTong University, China, in 2011 and 2013; M.S.degree in electrical and computer engineering fromGeorgia Institute of Technology, U.S., in 2013. Heis currently a Ph.D. candidate in the Department ofElectrical and Computer Engineering, Georgia In-stitute of Technology. His research interests includepower system protection, parameter estimation, andcircuit fault locating.

A. P. Sakis Meliopoulos (M’76–SM’83–F’93) re-ceived the M.E. and E.E. diploma from the NationalTechnical University of Athens, Greece, in 1972; theM.S.E.E. and Ph.D. degrees from the Georgia Insti-tute of Technology in 1974 and 1976, respectively.In 1971, he worked for Western Electric in Atlanta,Georgia. In 1976, he joined the faculty of Elec-trical Engineering, Georgia Institute of Technology,where he is presently a Georgia Power DistinguishedProfessor. He is active in teaching and research inareas of modeling, analysis, and control of power

systems. He has made significant contributions to power system grounding,harmonics, and reliability assessment of power systems. He is the author ofthe books, Power Systems Grounding and Transients, Marcel Dekker, June1988, Lightning and Overvoltage Protection, Section 27, Standard Handbookfor Electrical Engineers, McGraw Hill, 1993. He holds three patents andhe has published over 300 technical papers. In 2005 he received the IEEERichard Kaufman Award and in 2010 received the George Montefiori Award.Dr. Meliopoulos is the Chairman of the Georgia Tech Protective RelayingConference, a Fellow of the IEEE, and a member of Sigma Xi.

Liangyi Sun (S’12) received his B.S. degree inelectrical power engineering from Shanghai JiaoTong University, China, in 2010 and the M.S. de-gree in electrical and computer engineering fromGeorgia Institute of Technology, U.S., in 2012.He is currently a Ph.D. candidate in Departmentof Electrical and Computer Engineering, GeorgiaInstitute of Technology. His research interests in-clude power system protection, transient stability,and wind power control.

Rui Fan (S’12) received his B.S. degree in electricalengineering from Huazhong University of Scienceand Technology, China in 2011, and M.S. andPh.D. degrees in ECE from the Georgia Instituteof Technology in 2012 and 2016, respectively. Heis currently working at the Pacific Northwest Na-tional Laboratory, U.S. His research interests includepower electronics, power system protection, reliabil-ity analysis, and microgrid autonomous operation.

dynamic state estimation based protection of mutually...

Documents