probabilistic neural-network-based protection of power transformer

Probabilistic neural-network-based protectionof power transformer

M. Tripathy, R.P. Maheshwari and H.K. Verma

Abstract: An optimal probabilistic neural network (PNN) as a core classifier for fault detection andstatus indication of a power transformer has been presented. In this scheme, various operating con-ditions of a transformer are distinguished using signatures of the differential currents. The proposeddifferential protection scheme is implemented through two different structures of PNN, that is, onehaving one output and the other having five outputs. The developed algorithm is found to be stableagainst external fault, magnetising inrush, sympathetic inrush and over-excitation conditions forwhich relay operation is not required. For the test data of fault, it is found to operate successfully.The performance of proposed PNN and classical artificial neural network (ANN) has been com-pared. For evaluation of the developed algorithm, relaying signals for various operating conditionsof a transformer are obtained by modelling the transformer in PSCAD/EMTDC. The algorithmsare implemented using MATLAB. The results show the capability of PNN in terms of classificationaccuracy and speed in comparison to classical ANNs.

1 Introduction

Power transformers are vital links in the chain of com-ponents constituting a power system. They are very expens-ive and are an important component of power system whichfacilitates the transmission of electric power at highervoltage over long distances. The continuous monitoring ofpower transformers can provide early warning of electricalfailure and could prevent catastrophic losses as well asunscheduled outages of power supply. In view of this,avoiding damage to power transformers is vital; otherwise,continuity of power supply may be seriously disrupted.Furthermore, the repairing or replacing cost of apower transformer may be very high. Therefore, providingproper protection to power transformers is a crucialtask. Accordingly, high demands are imposed onpower-transformer-protective relays, that is (i) dependabil-ity (no missing operation), (ii) stability (no false tripping)and (iii) speed of operation (short fault clearing).Differential protection scheme is generally used as theprimary protection of medium- and large-sized power trans-formers, in which the value of differential current greaterthan no-load value indicates an internal fault. The magnetis-ing inrush occurs in transformers whenever polarity andmagnitude of residual flux do not agree with polarity andmagnitude of instantaneous value of flux. Whenever thereis a large and sudden change in the input terminal voltageof a transformer (either due to switching-in or due to recov-ery from external fault), large current is drawn by the trans-former from supply. Similar condition is encountered when atransformer is energised in parallel with another transformeralready in service, and this situation is known as ‘sympath-etic inrush’. This large current from the source results in the

# The Institution of Engineering and Technology 2007

doi:10.1049/iet-epa:20070009

Paper first received 4th January and in revised form 4th April 2007

The authors are with the Department of Electrical Engineering, Indian Instituteof Technology Roorkee, Roorkee 247667, Uttarakhand, India

E-mail: [email protected]

IET Electr. Power Appl., 2007, 1, (5), pp. 793–798

saturation of the transformer core. Peaks of magnetisinginrush current some time may rise very high to be of theorder of 10 times that of full load current [1]. This largecurrent from the source results in large differential current,which in turn causes the relay to operate undesirably.Owing to this reason, conventional differential relays areblocked for few initial cycles of energisation whichmakes the relay operation delayed on switching-in of thetransformer on faults. Therefore, discrimination betweenmagnetising inrush and internal fault condition is the keyto improve the security of the differential protectionscheme. Traditionally, two types of approaches are usedfor this purpose, that is, harmonic restraint (HR) andwaveform identification (WI) concepts [2]. The HR isbased on the fact that the second harmonic (sometimes thefifth) component of the magnetising inrush current isconsiderably larger than that in a typical fault current [1].The literature reveals the extensive use of the HR method[3–6]. However, the HR-based method fails to preventfalse tripping of relays because high second harmoniccomponents during internal faults and low second harmoniccomponents are generated during magnetising inrushfor transformers having modern core material [7–10].Therefore, the techniques based on detection of second/fifth harmonic component are not useful to discriminatebetween the magnetising inrush and internal fault conditionof modern power transformers.The second method consists of distinguishing magnetis-

ing inrush and over-excitation condition from internalfault condition on the basis of WI concept [11, 12]. Thedevelopment of advanced digital signal-processing tech-niques and recently introduced artificial neural network(ANN) provide an opportunity to improve the conventionalWI technique and facilitate faster, secured and dependableprotection for power transformers.As reported in literature, in recent years, different types

of ANNs were used for power transformer protectionbecause of its good generalisation ability and learning stab-ility with different topologies. Most of the ANNs were feedforward back-propagation neural network (FFBPNN) type

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and others were radial basis neural network and evolvingneural network type [9, 10, 13–15]. However, theseANNs have two major drawbacks: the learning process istime-consuming and the networks’ architectures aredecided empirically. Furthermore, the FFBPNN suffersfrom network paralysis and trapping at local minima. Toget rid of these limitations of the conventional ANNs, appli-cability of another type of ANN called probabilistic neuralnetwork (PNN) is investigated, for power transformerprotection and classifying all possible operating conditions,such as normal, over-excitation, magnetising inrush/sympathetic inrush, external fault and internal fault. Thedifferential current is used as the input of the neuralnetwork.Modern protective relays used for the protection of power

transformers not only provide protection, but also use theinputs given to them for status monitoring of transformer.This could become possible because of the use of digitalsignal-processing and high-speed processors.Two algorithms using the PNN and FFBPNN having two

different structures for fault detection (FD) and status indi-cation of power transformers are implemented. The firstalgorithm has been developed around the theme of conven-tional differential protection of transformers. It makes use ofratio of the voltage-to-frequency and the amplitude ofdifferential current for the detection of the operating con-dition of the transformer. The second algorithm makes useof WI technique based on ANNs in power differential pro-tection scheme.

2 Probabilistic neural network

PNN is one of the members of feed-forward neural networkfamily. The original PNN structure [16] is a direct neuralnetwork implementation of Parzen non-parametric prob-ability density function (PDF) estimation [17] and Bayesclassification rule [18]. The standard training procedure ofthe PNN requires a single pass over all the patterns of thetraining set [16]. This characteristic renders PNN faster totrain, compared with FFBPNN [19, 20]. The only drawbackof PNN is the requirement of larger storage for exemplarpatterns. As the computer memory has become very cheapand effective, the cost and size of larger storage are nolonger concern these days.The typical PNN structure is shown in Fig. 1. It is a four-

layer feed-forward neural network that is capable of realis-ing or approximating the optimal classifier.When a Gaussian kernel function is adopted, the Parzen

PDF estimator is derived as follows [21].Let X [ Rd be a d-dimensional pattern vectors and its

associated class be i [ (S1, S2, S3, . . . , Sk), where k is thenumber of possible class. If a posteriori probability,

Fig. 1 Typical PNN structure

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Pr (Si/x) that is from class Si is by Bayes’ rule

Pr(Si=x) ¼Pr(x=Si)Pr(Si)

P(x)(1)

where Pr (x/Si), i ¼ 1, 2, 3, . . . , k is a priori PDF of thepattern in classes to be separated, Pr(Si), i ¼ 1, 2, 3, . . . ,k are the priori probabilities of the classes and P(x) isassumed to be constant.The decision rule is to select class Si for which Pr(Si/x) is

maximum. This will happen if for all j = i,

P(x=Si)Pr(Si) . P(x=Sj)Pr(Sj) (2)

It is assumed that the a priori probabilities Pr(Si) of theclasses are known and the priori PDF P(x/Si) is Gaussian,then the estimator for the priori PDF is

P̂(x=Si) ¼1

(2p)d=2s di jSij

Xnij¼1

exp�(x� x

ij)T(x� x

ij)

2s 2i

" #(3)

where xji is the jth exemplar pattern from class Si, jSij ¼ ni

the cardinality of the set patterns in class Si and si thesmoothing factor.The input layer has d units, to which the d-dimensional

input vector X [ Rd is applied. The first hidden layer hasone pattern unit for each pattern exemplar. Therefore eachsuch pattern unit may be associated with a generic termdepicted in the summation of (3) for the ith class. Thesecond hidden layer contains one summation unit for eachclass. The output layer is decision layer used for implement-ing the decision rule by selecting maximum posteriori prob-ability, Pr(Si/x) from outputs preceding summation layerfor each i. The network is constructed by setting weightvector to one of the pattern unit equal to each distinctpattern vector in the training set from a certain class andthen connecting the outputs of the pattern units to the appro-priate summation units for that class. The conventionaltrial-and-error method is used to obtain smoothing factor.The smoothing factor is given by (4) [21]. From thisequation, it is clear that it is very simple and does notrequire complex calculation.

si ¼ gdijavg (4)

where dji is the distance between the jth exemplar pattern

and nearest exemplar pattern in class i and g is a constantthat has been found experimentally.

3 Simulation and training cases

The training data set of a PNN should contain the necessaryinformation to generalise the problem. A 315 MVA, 400/220 kV, 3-phase transformer is modelled using PSCAD/EMTDC [22]. The parameters used for the modelling ofthis transformer through PSCAD/EMTDC were obtainedfrom M.P. State Electricity Board, Jabalpur, India. As themagnitude and the wave shape of inrush current dependon the switching angle, remanent flux in the core and theloading condition, the inrush condition is simulated withdifferent switching angles, and remanent flux varyingfrom 0 to 80% of the peak flux linkages generated at ratedvoltage with no load and full load condition of the transfor-mer. The training signals are obtained by varying theswitching angle from 08 to 3608 in step of 308, whereastesting signals are obtained by varying switching angle instep of 158. As transformers are not expected to be subjectedto more than 15% over-voltage, hence the over-excitationcondition is simulated by applying 115% of the rated

IET Electr. Power Appl., Vol. 1, No. 5, September 2007

voltage at full load. For internal faults, training andtesting data are obtained by simulating phase-to-phasefault from 1 to 99% of power transformer winding turns.Phase-to-ground faults are also simulated at differentlocations such as 5, 10, 15 and up to 50% of the windingas well as at transformer bushing. Some typical signals soacquired by simulating various operating conditions oftransformers are shown in Figs. 2–5.Digital relays decide their operation on parameters of

sampled measured quantity (differential current, in thiscase). The sampling rate and the data window size arechosen depending on the algorithm being used. PNN isbased on WI method; therefore to recognise the waveshape, a window of one cycle duration is suitable and it isused in this work. The simulation is performed at the rateof 12 samples per cycle of 50 Hz AC supply in view ofreported experience on different digital relay designs [23].The developed protection algorithms were implemented inMATLAB.

4 Implementation of PNN and results

The differential current is taken as input of neural network.It is represented in discrete form, as a set of 12 uniformlydistributed samples obtained over a data window of onecycle that is called a ‘pattern’. The sliding data window,consisting of one most recent and other of previouswindow, is fed to the neural network.

Fig. 3 Typical differential current waveform for ground faultoccurred at 0.055 s

Fig. 2 Typical input current waveform for normal condition

Fig. 4 Typical differential current waveform for magnetisinginrush, transformer switching - in at.055s


The two algorithms having two different structures ofPNN are considered: one is for the FD purpose and theother is for condition monitoring purpose.For the calculation of smoothing factor, a very simple

method is used given by (4). By trial-and-error method,the optimal value of multiplying factor (g) is obtained andtherefore optimal smoothing is achieved.In the FD model of PNN, the input layer has 12 neurons,

the first hidden layer has 777 neurons, the second hiddenlayer has two neurons and at the output layer only oneneuron is required. The numbers of neuron of the inputlayer are decided based on the dimension of the featurespace, that is, 12 samples per cycle. The numbers ofneuron of the first hidden layer are decided according tototal number of exemplar pattern set used to construct thePNN model. In exemplar pattern set, 444 patterns ofinrush (sympathetic inrush patterns are also included) and333 patterns of internal faults are applied. The secondhidden layer has two neurons as there are only twonumbers of classes to be discriminated, that is, inrush andinternal fault conditions. At the output, as binary decision(to trip or not) is required, only single output is sufficientand therefore the output layer consists of just one neuron.It is the decision layer which is used for selecting themaximum posteriori probability, from the outputs of thesummation layer.The flow chart given in Fig. 6 indicates the steps of the

first algorithm for FD of power transformers. Out of fiveoperating conditions as mentioned earlier, the two con-ditions namely magnetising inrush/sympathetic inrush andinternal fault are difficult to discriminate and most of thefalse operations of relays are reported for these conditions

Fig. 5 Typical differential current waveform for over-excitation

Fig. 6 Flow chart of FD algorithm

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[24–26]. The external fault and normal operation are ruledout by comparing the two consecutive peaks of operatingsignal. The over-excitation condition is detected by compar-ing voltage-to-frequency ratio. If none of these conditionsexists, then inrush and internal fault conditions arechecked by PNN. The posteriori probabilities are calculatedby the summation layer of PNN. The decision layer selectsmaximum posteriori probability from the preceding sum-mation layer and on the basis of maximum posteriori prob-ability, the patterns are classified. Accordingly, the PNNgenerates tripping signal only if internal fault condition isdetected.Status monitoring is a technique which is adopted to

reduce unplanned outages and increasing availability ofpower supply. It is presented as an extension of the FDmethod which helps to improve the reliability of the protec-tion operation. In the second case of PNN model, 12neurons are considered in the input layer. In the firsthidden layer, 851 neurons are considered as exemplarpattern set consist of 444 inrush patterns (sympatheticinrush patterns are also included), 296 internal fault pat-terns, 37 over-excitation patterns, 37 external fault patternsand 37 patterns of normal condition. In the second hiddenlayer, five neurons are considered and five differentclasses are to be classified. At the output layer, oneneuron is considered and it is the decision layer which isused for selecting the maximum posteriori probability,from the outputs of the summation layer.The steps of the second algorithm are illustrated in Fig. 7.

All five operating conditions, such as normal operation,magnetising inrush/sympathetic inrush, over-excitation,external fault and internal fault, of a transformer are classi-fied but the relay will issue tripping signal in case of internalfault only.Fault currentmagnitude, remanent flux, load condition and

switching angle were varied to investigate their effects on theperformance of the PNN and FFBPNN models. As the waveshape of inrush current changes significantly with variationin switching-in instant of a transformer, it is variedbetween 08 and 3608. Similarly, due to remanence flux, themagnitude of inrush current may go as high as 2–5 timesof inrush current than that of inrush current without rema-nence effect although the wave shape remains the same. Itis found that the PNN-classifier-based relay is stable evenwith such high magnitude of inrush current caused by rema-nence flux, whereas the conventional HR-based relay maymaloperate due to such high magnitude of inrush current[24–26].After extensive experimentation on various FFBPNN

architectures, two different structures of FFBPNN wereselected to compare their performance with the PNNmodels. Single output is considered in the first case ofFFBPNN model, whereas five outputs are considered in

Fig. 7 Flow chart of condition monitoring algorithm

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the second case of FFBPNN model. From Fig. 8, it isclear that as the number of neurons in the hidden layerincreases, the error decreases but after certain number ofneurons, it increases again and in this case the minimumerror is obtained for 11 neurons in the hidden layer.Therefore the optimal numbers of neurons in the hiddenlayer for this application are 11. The FFBPNN is trainedby back-propagation algorithm [21]. Same data and algor-ithms were applied for the FFBPNN models as in thePNN models.Table 1 illustrates the parameters of the PNN and

FFBPNN that need to be set (tuned) by trial-and-errormethod to get satisfactory performance of neural network.The proposed PNN is faster and has good generalisationproperties than the FFBPNN because the detection accuracyof the PNN model with one and five outputs are 100% forthe test patterns in both cases as shown in Table 2. Itshows that the PNN has better classification capabilitythan the other classical ANNs. The training required forPNN is very different and much faster than that requiredfor FFBPNN. In PNN, the training process is one passwithout any iteration for the weight adaptation, as againsta large number of iteration (epochs) necessary in case ofFFBPNN. For example, 980 iterations are required for con-vergence in case of 12–11–1 structure of FFBPNN,whereas one iteration is required for PNN, thereby givinga ratio of about 980:1 in terms of the training time for thefirst case. In the second case, FFBPNN structure is 12–11–5 and epoch required to converge is 1000. Thereforethe PNN is free from the demerits such as trapping inlocal minima and slow convergence in training, empiricaldetermination of network structure and parameters. Thismakes it easy to design and simple in architecture thanthe classical ANNs.The first algorithm is made-up with the amalgamation of

classical differential protection technique and WI techniquebased on neural network. Out of five operating conditionsof power transformers, three operating conditions (suchas over-excitation, normal and external fault condition)are ruled out by comparing the voltage-to-frequency ratioand consecutive picks of differential current. PNN/FFBPNN is used to discriminate between the inrush andinternal fault conditions only. In the second algorithm, allfive conditions are discriminated by PNN/FFBPNN.Therefore in the second algorithm, neural network willtake long processing time because more computation isto be performed when compared to the first algorithmand hence, the first algorithm is faster when compared tothe second algorithm.From the protection point of view, there is no need to

discriminate all operating conditions of power transfor-mers as relay has to operate only for internal fault.Therefore it is enough to identify the internal fault con-dition among operating conditions. Hence, the first algor-ithm seems to be more suitable from the protection pointof view.

Fig. 8 Effect of neurons (in the hidden layer) on the performanceof FFBPNN


Table 1: Parameters of PNN and FFBPNN architectures

Cases ANN topology Epochs Training error Learning rate Momentum factor Smoothing factor

I FFBPNN 12-11-1 980 0.0001 0.9 0.6 -

PNN 12-777-2-1 1 - - - 0.2

II FFBPNN 12-11-5 1000 0.0002 0.9 0.6 -

PNN 12-777-5-1 1 - - - 1.5

From Table 1, it is observed that more parameters need tobe set (tuned) in case of FFBPNN when compare with PNNand there is large difference between the epochs of PNN andFFBPNN, that makes the PNN faster and simple in design-ing for a particular application. The classification accuraciesare depicted in Table 2, and it is observed that when thePNN is evaluated with the testing and training patternsets, the performance is 100% in both cases, whereas theclassification accuracy of FFBPNN has 97.29 and96.13% with testing pattern sets in first and second cases,respectively.The proposed PNN recognises the different operating

conditions of power transformers quite accurately andwithin one cycle of the fault occurrence. It is successfullytested using relaying signals obtained from modelling thetransformer on PSCAD/EMTDC and simulating variousoperating conditions. This PNN-based relay provides fastand precise operation even in the presence of DC offsetbecause of saturation of current transformer core. It isobserved that the relay operation is independent of thedifferent harmonics presented in the operating signalswhich makes it simpler, fast and quite reliable than the con-ventional digital filtering algorithms.

5 Conclusion

This paper presents an approach for power transformeroperating status indication and protection based on thePNN model. The proposed PNN is utilised as core classifierfor differential protection scheme that works in principle ofWI technique. In this method, stability of differential relayis ensured during the magnetising inrush, sympatheticinrush, over-excitation and external fault conditions andgenerates trip signal only for internal fault condition. It per-forms quite accurately and reliably for a wide range of vari-ations in fault and magnetising inrush conditions, especiallyin case of modern power transformers, which use high-permeability low-coercion core materials. Although theconventional HR technique may fail to provide discrimi-nation between magnetising inrush and internal fault con-ditions, because high second harmonic components maybe generated during internal faults and low second harmoniccomponents during magnetising inrush with such corematerials, the PNN-based method is independent of the har-monic content of fault currents. The proposed PNN

Table 2: Performance evaluation of PNN and FFBPNNmodels

Cases ANN topology Classification accuracy in (%)

Testing sets Training sets

I FFBPNN 12-11-1 97.29 100

PNN 12-777-2-1 100 100

II FFBPNN 12-11-5 96.13 100

PNN 12-777-5-1 100 100


recognises the different operating conditions of power trans-formers within one cycle of the fault occurrence. A com-parison of PNN is made with FFBPNN. The structure ofPNN is not decided empirically like classical ANNs andis free from the demerits such as trapping in local minimaand slow convergence like FFBPNN. The PNN trainingprocess is one pass and without any iteration for weightadaptation, hence yielding great processing speed whencompare with FFBPNN and the network generalises to thenew incoming patterns without having to repeat the trainingprocess.

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