Knowledge Based Approach for Transmission lineDistance Relay Coordination

Ravikumar B., Thukaram D. and H. P. KhinchaDepartment of Electrical Engineering

Indian Institute of ScienceBangalore, India 560012

Email: {ravi, dtram, hpk}@ee.iisc.ernet.in

Abstract—The protection of transmission lines is traditionallyperformed on-line, new pattern recognition techniques should beimplemented quickly and flexibly. In this paper, a new approachto enhance the Transmission system distance relay co-ordinationis presented. The approach depends on the apparent impedanceloci seen by the distance relay during all possible disturbances. Ina distance relay, the impedance loci seen at the relay location isobtained by extensive transient stability studies. Support VectorMachines (SVMs), a class of patterns classifiers are used indiscriminating zone settings (Zone-1, Zone-2 and Zone-3) usingthe signals to be used by the relay. Studies on a sample 9-busare presented for illustrating the proposed scheme.

I. INTRODUCTION

System-wide disturbances become a major concern in thepower industry again as a result of the Northeast blackout onAug 14, 2003. The blackout affected an estimated 50 millionpeople, and more than 61,800 MW of load was lost. Theblackout had several causes or contributory factors in commonwith the earlier outages, including inadequate coordination ofrelays and other protective devices or systems [1].Distance protection is widely used in the protection of EHVand UHV transmission lines in view of the fact that itcan provide fast fault clearance and system co-ordination. Itprovides both primary and backup protection by its zonalsettings correctly coordinated between distance relays. It isdesired that a distance relay cover most of the line in itsfirst zone of protection. Also, it must not operate for faultsbeyond the remote bus even for the most unfavorable systemconditions. The nominal reach of a non-pilot distance relay isset shorter than the protected line length to account for relayoverreach caused by system uncertainties. The usual practiceis to set the relay to cover 80% - 90% of the line length. Sincesystem uncertainties such as variations in system parameters,load current, charging current, metering errors, etc. are notusually considered in distance relay setting, the relay mayunexpectedly fail to operate for an internal fault or mal-operatefor an external fault under certain system conditions.Since protection of transmission lines is traditionally per-formed on-line, new pattern recognition techniques should beimplemented quickly and flexibly. Application of ArtificialNeural Networks (ANNs) for transmission line protection ispresented in literature [2-5]. ANN application as a patternclassifier works well for transmission line protection, and

consequently results in the improvement of conventional dig-ital relays. However, the algorithm used for adjusting theparameters of ANN does not produce robust classification.Recently, SVMs applications to transmission line protectionare examined in the literature [6-8].This paper presents an approach for estimating the coordinatedzonal setting of distance relays using SVMs. The trainingpatterns (feature vectors) consist of apparent impedance valuesobserved at a relay following disturbance. In this paper,apparent impedance values are simulated by creating 3-phasefaults. During the fault, the apparent impedance values aregenerated by using Transient Stability Program [9-10]. Thisprogram is extensively used for stability studies of severalIndia Power Networks. The time delay settings (TDS) of zone-2 and zone-3 have to be calculated such that all faults have tobe cleared with in a maximum allowable time delay.

II. PROPOSED SCHEME

Power system protection at the transmission level is basedon distance relaying. The apparent impedance seen by thedistance relay at substation on a transmission line connectingthe nodes i and j, and having flow Pij + jQij is given as

ZR =

[Pij

P 2

ij + Q2

ij

+ jQij

P 2

ij + Q2

ij

]|Vi|2 (1)

Where, all quantities refer to positive sequence values. Thus,the quadrant of ZR depends only on the direction of P and Qflows.Suppose a stable system at time t0 is subjected to fault ona transmission line at time t1. Conventional relay algorithmwill detect the fault, fault type, discriminate the zone settingsbased on preset reach values and TDSs and clear the faultat time t2. During this period, the possible events can beopening of the faulted line, and/or some generators mayfall in out-of synchronism and/or some load rejection canhappen. Transient stability program [9-10] is used to obtain theapparent impedance trajectory seen by different relays of thesystem. This program is extensively used for stability studiesof several India Power Networks. The program simulatesthe impedances seen during three time laps. First time lapT1 consists of impedances seen before occurrence of fault(T1 = t1−t0 Sec.). Second time lap T2 consists of impedances

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seen during fault (T2 = t2 − t1 Sec). After the fault has beencleared and we are observing the system till time t3, then thethird time lap T3 consists of impedances seen during post-faulttime (T3 = t3−t2). The feature vector consists of the apparentimpedances seen by the relay located on a line during faulttime T2.Let a conventional fault detection algorithm detects the faultat time td (t1<td<t2), from td to next one or two cycles(te) fault data information will be captured to form a featurevector. The size of the feature vector now will depend on thesimulations time step during the gap te-td. In this paper, weare mainly concentrating on discriminating the zones basedon the available knowledge obtained from the simulationswhich is an important aspect of protecting a transmission line.Fig. 1(a), shows the collection of apparent impedances valuesobserved by the relay and Fig. 1(b), shows the training/testingof the SVM. Fig. 1(a) and Fig. 1(b) collectively show theimplementation of the proposed method at a relay location.Support Vector Machines are used to capture the underly-ing concept/model between reach of different zones and theimpedance swing trajectory characteristics. In this paper, thisinformation is intelligently utilized for identifying the differentzonal settings of a relay.

Feature Vector

R1

i j

1(a)

(R, X)

(R, X)

(R, X)

ZoneDiscrimination

(Zone−1 / Zone−2 / Zone−3)

Relay Observations

tk

t

SVM(during Fault)

td

e

(td< tk < te)

Feature Vector

1(b)

Fig. 1: (a) Collection of features from relay input to generate data forSVM; (b) Discrimination of feature data using SVM for identifyingthe zones.

III. BRIEF REVIEW ON SUPPORT VECTOR MACHINES

Support Vector Machines are a new learning-by-exampleparadigm spanning a broad range of classification, regression,and density estimation problems. They were first introduced

by Vapnik et. al [11-12] and are described in more detail byin B. Scholkopf et. al.[13-14] The roots of this approach,the so-called support vector (SV) methods of constructingthe optimal separating hyperplane for pattern recognition.The SV technique was generalized for nonlinear separatingsurfaces in [14], and it was further extended for constructingdecision rules in the non separable case. The training taskinvolves optimization of a convex cost function conveying toa technique without local minima.

A. Support Vector Classification

The problem of classification consists of estimating a func-tion f : RN → {±1} using l i.i.d input-output trainingdata (X1, Y1), ..., (Xl, Yl) ∈ RNx{±1} from a data set Dsuch that f classifies correctly on unobserved data (x, y)(i.e., f(x) = y for examples (x, y) generated from the someunderlying probability distribution P(x,y)). In other words, theloss function L can be defined by (2)

L(yi, f(xi)) = |1 − yif(xi)|+ (2)

Where |val|+

= max{0, val} val ∈ R A brief review ofsupport vector classification (SVC) [15-18] is presented in thissection; when data is linearly separable there exists a vectorw ∈ RN and a scalar b ∈ R such that yi (w.xi + b) ≥ 1for all patterns in the training set (i=1...l). The optimal hyperplane separates points lying on opposites classes yielding tothe maximum margin separation. A separating hyper planewhich generalizes well can be found by solving the followingquadratic programming (QP) problem for (i=1...l):

Minimize1

2‖ w ‖2

Subjected to yi (w.xi + b) ≥ 1 (3)

This constrained optimization problem is solved byconstructing a Lagrangian

λp(w, b, α) =1

2‖ w ‖2 −

l∑i=1

αi(yi (w.xi + b) − 1) (4)

The Lagrangian has to be minimized with respect to the primalvariables w and b and maximized with respect to the dualvariables αi. The Karush-Kuhn-Tucker (KKT) conditions leadto find the solution vector in terms of the training patternsw =

∑l

i=1αiyixi for some αi ≥ 0. Notice that αi �= 0 only

for a subset of the training patterns, precisely those few vectorsthat lie on the margin, called the support vectors (SVs). Undercertain conditions, a kernel function K(.,.) can be found suchthat K(xi, xj) = xi.xj . An SVM uses then the convolutionof the scalar product to build, in input space, the nonlineardecision function

f(x) = sgn(l∑

i=1

αiyiK(xi, xj) + b) (5)

Where b is found from the primal constraints and is computedby αi(yi (w.xi + b) − 1) = 0, i = 1...l such that αi �= 0.When the training data is not linearly separable, a separating

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hyper plane does not exist. Besides, when real data sets areused, SVMs can fit noise and outliers leading to poor general-ization. Thus, a hard margin classifier is no longer adequate.Introducing a soft margin, the learning task is essentially thesame as indicated in (3) except for the introduction of thepenalty term C and the slack variable ξ. The classifier triesthen to separate the data by minimizing the objective function

Minimize1

2‖ w ‖2 +

C

l

l∑i=1

ξi

Subjected to yi (w.xi + b) ≥ 1 − ξi, (6)

0 ≤ αi ≤ C/l, ξi ≥ 0

for i=1...l. In this sense, it acts by controlling the classifiercapacity and the number of training errors. In other words,the task is now to minimize the sum of errors

∑l

i=1ξi in

addition to ‖w‖2. Again this optimization problem can betransformed into a QP problem. The value of C can befound by experimentation in a validation set and cannot bedetermined from either the model or the data set. In thispaper “one-against-one” method is used for the extensionfrom the binary two-class problem to n classes for multi-class classification, because of its less training time over “one-against-all“.

B. Kernel Choice

The use of kernel methods [19] provides a powerful wayof obtaining nonlinear algorithms capable of handling non-separable data sets in the original input space. Different typesof kernels used for training the SVMs are Linear KernelQij = K(xi, xj) = xT

i .xj , Polynomial Kernel Qij =(γ(xi.xj) + r)Degree, Radial Basis Function (RBF) kernelQij = exp(−γ‖xi − xj‖2), where γ related with the kernelwidth and Sigmoidal Kernel Qij = tanh(γ(xi.xj) + r)where γ and r are kernel parameters. The RBF kernel hasless numerical difficulties. Moreover, we must note that thesigmoid kernel is not valid (i.e. not the inner product of twovectors) under some parameters [20]. In this paper we suggestthat RBF kernel is a reasonable first choice for SVM training.

C. SVM Model Selection:

In any predictive learning task, such as classification, anappropriate representation of examples as well as the modeland parameter estimation method should be selected to obtaina high level of performance of the learning machine. Underthe SVM’s approach, the usually parameters to be chosen arethe following:

1) The penalty term C which determines the trade-offbetween the complexity of the decision function and thenumber of training examples misclassified; and

2) Kernel function parameters

IV. SYSTEM STUDIES AND RESULTS

The single line diagram of the system considered for illus-trating the proposed scheme is shown in Fig. 2. The systemhas 3 generators, 3 transformers, 8 transmission lines and

loads are presented at busses 5, 6 and 7. Transient Stabilityprogram [9-10] is used to simulate the 3-ph fault on thesystem. The transient stability program is developed by consid-ereing IEEE standard models for representing the Turbines[21-22], Generators[23-24], Loads[25-26], and Excitation controlactions [27-28]. Unlike the rules developed for identifyingthe zone-1, zone-2 and zone-3 settings of the conventionalalgorithm, the proposed approach classifies the zones basedon the connectivity of the lines. Zone-1/Class-1 representsthe primary protection of its own line on which the relayof interest is located. Zone-2/Class-2 represents the lines thatare connected to the receiving end of the primary line. TheZone-3/Class-3 represents the lines that are next adjacent toprimary line. In this paper, the relay R13 at bus 6, mounted forprimarily protecting the line 6-9 is considered for applying theproposed scheme. This relay will be acting as a zone-2 backup for 9-8 line, 3-9 transformer and in its zone-3 backup, thelines 8-7(1) and 8-7(2) are covered.

R 1

~1

~2

~

3

R R

R

R

R

RR

R

R

15

3R

14

13

R 5

R 6

7

1112

16

10

2

R 44 5 7

8

6

9

R9R8

Fig. 2: Single line diagram of the sample system considered.

TABLE I: GENERATION OF TRAINING AND TEST PATTERNS

Zone/Class Fault distance from relay locationLine

label Training Testing

6-9 1

At distances of10%,20%...90%of their total linelength(Total 9)

At distancesof25%,45%,65%and 85% oftheir total linelength(Total 4)

9-8 2

8-7(1)8-7(2)

3 Faultresistancevalues variedover 0Ω, 2Ω, 5,10, 20, 25, 40,45, 50, 55, 65and 75Ω

Faultresistancevalues variedover 0Ω, 3Ω, 7,15, 30 and 60Ω

To illustrate the algorithm, only 3-phase faults are consideredin this paper. A normal operating system at time 0 secondsis subjected to 3-Ph fault on line time 0.1Sec and cleared thefault by isolating the line from operation at time 0.2 seconds.

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And the time of simulation is taken up to 1.0Sec after thefault is cleared. In this case, the time laps T1 is 0.1Sec, T2=(0.2-0.1) =0.1Sec and T3= (1.0-0.2) =0.8Sec. Fig.3 shows theobservations made by Relays R2, R14, R13 and R10 during T1,T2 and T3 for 3-ph faults on line 6-9 at 50% away from bus6.Fig. 4 shows the observations by relays at various locations ofthe system for 3-phase faults simulated at various locations onthe lines 6-9. Fig. 5 shows the apparent impedance movementobserved by the relay R13 located at 6 (on lines 6-9) during3-phase fault at various locations of the system. As such, Relayobservations for different fault conditions are different. AlsoFig. 3 to Fig. 5 contains the typical conventional zone-1, zone-2 and zone-3 reach settings of distance step protection modeledby mho characteristics [29-30]. Fig. 6 shows the observationsmade by relay R13 for variation in fault resistance value over0Ω, 10Ω, 20, 25, 40, 45 and 50Ω and fault location varied over10% to 90% in 10% distance variations. Fig.6 indicates that thefault resistance pull the loci away from the origin, which affectthe zone-1 settings of a conventional relay. From the figures3, 4 5 and 6, it is clearly observed that, a knowledgebase canbe developed based on the data available for various typesof faults, fault location, fault resistance and fault types. Inthis paper, we are concentrating only on 3-phase faults forgenerating the feature vectors, which can be further, extendedto various other types of faults.

A. SVM Training and Testing

Training patterns are generated by simulating the 3-ph faultsat different locations on the transmission lines. The faults arecreated at distances of 10% to 90% insteps of 10% of theiroverall transmission length. During the simulation, the faultresistance values are varied between the values 0Ω to 75Ω.Over all, the training patterns are generated 4 transmissionlines over 9 locations with varying 12 impedance values. Thenumber of training patterns is 5 X 9 X 12 = 432 patterns;The input patterns training and test patterns are normalizedto [-1, +1] before inputting to the SVMs. For the normalscaling method, if the maximum and minimum values of theith attributes are Mi and mi respectively, then, scaling to [-1,+1] means x1=2(x-mi)/(Mi-mi)-1.Test patterns are generated by creating at 25%, 45%, 65% and85% distances of their overall transmission line length. Faultresistance values are varied over the values 0Ω, 3Ω, 7, 15,30 and 60Ω. The number of test patterns is 4 lines X 6 faultresistances X 4 locations = 96 patterns per each fault type.The details of simulations carried for generating the trainingand test patterns are given in Table I.

B. SVM classifiers

SVMs training require selection of the cost function (C)and kernel function parameters, which influence the ensuringmodel performance. In our simulations, we have consideredradial basis function (RBF) as kernel function. RBF kernelis advantageous in complex non-separable classificationproblems due to its ability of nonlinear input mapping.So selecting a good RBF kernel required to select the

−1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4−2

−1.5

−1

−0.5

0

0.5

R (p.u) (a)

X (

p.u)

T1

T2

T3

R2

(a)

−1.4 −1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

R (p.u) (b)

X (

p.u)

T1

T2

T3

(b)

−0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

R (p.u)(c)

X (

p.u)

R13

T1

T2

T3

(c)

−1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

R (p.u)(d)

X (

p.u)

R10

T1

T2

T3

(d)

Fig. 3: (a − d) : Observations made by Relays R2, R14, R13

and R10 during Times T1, T2 and T3 for 3-ph faults on line6-9 at 50% away from bus6.

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−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1−1.5

−1

−0.5

0

0.5

1

1.5

R15R16R2R1R14R13R4R6R9R10R11R12

R (p.u)

X (p.u)

Fig. 4: Observations made by Relays at various locations on thesystem for 3-ph faults on line 6-9 at various location.

−1 −0.8 −0.6 −0.4 −0.2 0 0.2−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

4−5

4−6

5−7 (1)

6−9

7−8 (1)

8−9

R (p.u)

X (p.u)

Fig. 5: Impedance characteristics observed by relay R13 (at bus 6of 6-9 line) for 3-ph faults on various lines with varying distances .

−0.5 0 0.5 1 1.5 2−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0−ohms

10−ohms

20−ohms

25−ohms

40−ohms

45−ohms

50−ohms

R (p.u)

X (p.u)

Fig. 6: Relay R13 observations for faults on the line 6-9 with varyingfault locations and fault resistance values that are used for trainingin Table I.

γ(= 1/2σ2, σ : kernelwidth) is important parameter to bechosen. In this paper, LIBSVM [31-32] is used for trainingthe support vector machines in classification and regressionmodules.In a first series of experiments we run the classifier withseveral values of C and γ somehow trying to guess whichcombination of parameters might be the best for a ”good“model. Larger C corresponds to less number of SVs aswell as higher testing accuracy although over-fitting cannotthus be avoided. Further explanation is required for theseresults taking into account both C and γ parameters. Fornon-separable data, the penalty term C is able to reducethe training errors in the working data set. Therefore, themargin is an indicator of the generalization accuracy. In theabsence of a method to compute the best tradeoff betweenthe regularization term and the training errors, the balancesought by the SVM’s technique is hard to find. Thus, a largerC corresponds to assign a higher penalty of training errorsand clearly over-fitting occurs. On the other hand, when thekernel parameter γ becomes higher, the greater the variety ofthe decision boundaries that can be formed, originate a morecomplex model. The added flexibility decreases initially thegeneralization error as the model can better fit the data.

Fig. 7: SVM parameter selection using interactive grid search.

Choosing the best parameters can be timing consumingif a systematic approach is not used and/or the problemknowledge do not aid for proper selection. Therefore, aninteractive grid search model selection has been accomplishedfor SVM and the generalized accuracy evaluated on the traindata. Fig. 7 portrays the generalization graphic contours forthe SVM after a five-fold cross validation, thus, reducing thesearch space. The efficient heuristic way of searching pointsin that space with small generalization errors will lead to agood understanding of the hyper parameter space. We canthen do a refined search of the (C, γ) pairs for proper modelselection.Fig. 7 shows the parameter selection using interactive gridsearch for classifier SVM. The range of C chosen for trainingis [20, 220] and γ values ranges from [2−7, 27] are chosen.

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The highest cross validation accuracy resulted for SVM is97.22% on the training data with extracted model parametersof C=262144 and γ = 0.125. Once the SVM is learned withthese parameters, all parameters of the trained SVM havebeen frozen and then used in retrieval mode for testing thecapabilities of the system on the data not used in learning.The test data samples have been extracted using the transientstability program as explained earlier. The %testing accuracyis defined by No. of samples correctly classified*100 / totalnumber of samples presented. The obtained model parametersduring grid search are merit listed for selecting the bestparameters with highest testing accuracy.The parameters C= 262144 and γ=0.08839 has resultedhighest test accuracy of 97.91% with 94 patterns out of 96test patterns are correctly classified. The results obtainedchoosing the pair of parameters conveys to the learning modelwith the smallest capacity and, thus, the highest generalization.

V. CONCLUSION

The use of Support Vector Machines as a powerful tool forclassification and its application to distance relay coordinationis presented. Support Vector Machines with RBF kernel is ableto learn the underlying concepts between the reach settingsof different zones of protection and the apparent impedancemovement during the faulted condition. From the results,we conclude that an intelligent system can be useful fordiscriminating the zonal settings for backup protection oftransmission lines in an efficient way for varying conditionsof the power systems. This can further extended to topologicalchanges of the power network for adaptive control of thetransmission system.

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