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Abstract— In this paper, the operation of Differential relay for

power transformer was presented using support vector machine. An SVM subroutine was used to discriminate internal faults from other situations, replacing the traditional Fourier method for harmonic restraint. The proposed methods was extensively tested and then compared to the traditional differential protection algorithm showing promising results. The application of the SVM tools is a new and important stage in the differential relay analysis methodology for power transformer protection. Index Terms—support vector machine (SVM), current transformer, saturation, differential protection, power transformers

I. INTRODUCTION

POWER transformers are devices that require special maintenance due to their importance to the electrical system to which they are connected. Generally, differential relays are used for the primary protection of large transformers. In such relays, differential currents are checked considering a percentage differential characteristic with operation and restraining zones, and in the case of an internal fault, the transformer should be disconnected from the rest of the system. However, a simple detection of a differential current is not sufficient to distinguish internal faults from other situations that also produce such a current. Some of these situations appear during transformer energization (inrush currents), current transformer (CT) saturation, among others, which can result in an incorrect trip .The correct and fast discrimination of internal faults from the other situations mentioned is one of the challenges for modern protection of power transformers. Concerning the identification of internal faults as opposed to inrush currents, the approach traditionally used is the aforementioned differential logic together with harmonic restraint. In this method, transformer inrush current due to energization is recognized on the basis of second and other harmonic components obtained by filters. However, the filtering method can sometimes delay the protection process. In addition to this, a second harmonic component can also be present during internal faults. New methods aiming at improved selectivity, sensibility, and operation of differential relays, such as neural networks, support vector machine and fuzzy logic has been studied recently. This paper presents an alternative approach using support vector machine (SVM) in

Vikramaditya Dave and Avdhesh Sharma are with, Department of Electrical

Engineering College of technology and Engg., Udaipur(Raj)-India

order to improve the performance of power transformer protection concerning the correct identification of internal faults as opposed to inrush currents and other situations, as described earlier. MATLAB 6.5.1is used to model the power transformer. This model is used to generate saturated and non-saturated data for the SVM training as well as for testing the proposed approach.

II. . DIFFERENTIAL PROTECTION

The diagram illustrating the differential logic used for the protection of large power transformers is shown in Fig. 1. The illustration also shows the connection of CTs coupled to the primary and secondary branches. Under normal conditions and external faults for a single-phase transformer, the currents i1s and i2s (secondary currents of CTs) are equal. However, in the case of internal faults, the difference between these currents becomes significant, causing the differential relay to trip. The differential current id=i1s-12s (1) gives a sensitive measure of the fault current. Considering the restraint current ir= (i1s+i2s)/2 , the relay will operate when

id > k.ir (2) where K is the slope of the differential characteristic. Fig. 2 shows a differential characteristic, including operation and restraint zones. Some adjustments for K are presented (15%, 25%, and 40%). CO’ is a threshold used when an over

Operation of Differential Relay for Power Transformer using Support Vector Machine

Vikramaditya Dave and Avdhesh Sharma

978-1-4244-1904-3/08/$25.00 ©2008 IEEE

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excitation situation is detected. As mentioned before, certain phenomena can cause a substantial differential current to flow when there is not any fault, and these false differential currents are generally sufficient to cause tripping. However, in these situations, the differential protection should not disconnect the system because an internal fault is not present. Magnetizing currents appear during transformer energization due to its core magnetization and saturation. The slope of the magnetization characteristic in the saturated area determines its magnitude. In modern transformers, large inrush currents can be reached. In transformer energization, as the secondary winding is opened, the differential current can reach sufficiently high values, causing a false relay operation. Some authors have studied the modeling of such a situation, showing the predominance of the second harmonic component. It must be emphasized that inrush currents can take place, even when the transformer is connected to a load. Some other phenomena that cause false differential currents are magnetizing inrush currents during an external fault removal, transformer over excitation, as well as CT saturation.

III. CT SATURATION CTs are employed to provide a reduction of the primary current as well as to supply galvanic insulation between the electric network and equipment connected to the CT secondary, including protective relays. Therefore, CTs are made to support fault currents and other phenomena for a few seconds, which can reach values of up to 50 times the magnitude of the load current. The current signals supplied on the secondary of a CT should be exact reproductions of the corresponding current signals on its primary. Although modern devices perform satisfactorily well in this condition for most cases, the protection design needs to take into account the possible errors eventually introduced by CTs, so that the relay performance in the presence of these errors can be enhanced. The CT performance under load current is not such a concern compared to the fault situation in which the relay should operate. When faults occur, the current values

can reach high levels. They can also contain a significant dc component as well as the remnant flux in the CT core. All these factors can lead to the saturation of the current transformer core and can produce significant distortion in the secondary current. In this case, the secondary current of a CT cannot represent its primary current exactly. Thus, relays that depend on this current to make their decision can easily operate incorrectly during this period, affecting the reliability of the protection. Fig. 3 shows an energization case where the saturation was not represented because an ideal CT was considered. Fig. 4 shows the same case where the distortions caused by saturation can be clearly observed. One can note the difference in the waveforms of the signals for the same analyzed situation. The signals were simulated in the MATLAB software. Figs. 3 and 4 show an internal fault case to the power transformer without and with the presence of CTs saturation, respectively. The possibility of CT saturation should then be carefully considered in a protection system design in terms of relay performance.

Fig 3 Internal Fault case without CT saturation

Fig 4 Internal Fault case with CT saturation

IV. SUPPORT VECTOR MACHINE Support vector machine is a new learning machine which implements the following idea: it maps the input vectors into some high dimensional feature space Z through some non-linear mapping chosen apriori .In this space a linear decision surface is constructed with special properties that ensure high generalization ability of the network .Two problems arise in this approach :one conceptual and one technical .The conceptual problem is how to find a separating hyper plane that will generalize well .The technical problem is how computationally to treat such high dimensional spaces.

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The conceptual part of this problem was solved by Vapnik (1965) by introducing the concept of optimal hyper planes for separable case .An optimal hyper plane is defined as linear decision function with maximal margin between the vectors of the two classes) The technical problem was solved by Boser and Vapnik (1992) by stating that the order of operations for constructing a decision function can be interchanged i.e. instead of making a non linear transformation of the input vectors followed by taking their dot product or some distance measure and then make a non linear transformation of the value of the result. The Optimal Hyper plane Algorithm The set of labeled training patterns

( 1y , 1x ),………….. ( ly , lx ), iy ε {-1, 1}

is said to be linearly separable if there exists a vector ‘w’ a scalar ‘b’ such that the inequalities

w. ix +b≥1 if y i =1

w. ix +b≤1 if y i =-1

are valid for all elements of the training set. The optimal hyper plane

w 0 .x+b 0 =0

Is the unique one which separates the training data with a maximal margin. This distance ρ (w, b) is given by

ρ (w 0 , b 0 ) =00.

2

ww

Thus to construct a optimal hyper plane, one has to minimize a functional Ф=w.w

Subject to constraints y .1).( ≥+ bwxii i=1,…….., l

To do this standard lagrangian optimization technique is used. The ultimate problem becomes Maximize function

W ( ΛΛ−Λ=Λ DTT

2

11)

With respect to ).....,.........( 1 lT αα=Λ

Subject to constraints

0

0

=Λ

≥Λ

YT

Where )....,,.........( 1 lT αα=Λ is the vector of

non-negative Lagrange multipliers

),,.........( 1 lT yyY =

D=Symmetric matrix with elements

jijiij xxyyD .=

The algorithm described above constructs hyperplane in the input space. To construct a hyperplane in a feature space one first has to transform the n-dimensional input vector x into an N dimensional feature vector. This can be done through functions called Kernel functions. Table 1 lists common types of Kernel function.

Table1 some common Kernel functions Type Kernel Function Polynomial classifier of degree p

K(x,y)=(x.y+1) p

Separating hyperplane K(x,y)=x.y Sigmoidal Perception classifiers

K(x,y)=tanh (x.y-δ )

V. POWER SYSTEM SIMULATED

Fig. 5 shows the representation of the electrical system simulated by the MATLAB software in order to generate data for ANN training and testing processes. The electrical system is composed of an 132-kV and 30-MVA generator, an 132:11-kV and 25-MVA three-phase power transformer, a transmission line of 5 km in length, and a 10-MVAload with an 0.92 inductive power factor.

Fig 5 Power system simulated The power transformer has a delta connection in the primary winding and a star connection in the secondary winding. Its model in MATLAB was implemented using three single-phase transformers [7].

VI. PATTERN RECOGNITION FOR CORRECT DISCRIMINATION OF INTERNAL FAULTS—THE

TRAINING PROCESS Initially, the training process using SVM for discriminating internal faults from other situations described will be considered. The simulated cases for this phase were the situations that involved a significant differential current. Capacitor bank energization and steady state were not included. A total of 2500 cases (7500 patterns, considering a moving window of three steps) were generated for the transformer of 25 MVA. It should be emphasized that no training was performed for the 6.25-MVA transformer and the same SVM trained will be used for the 6.25-MVA transformer. After simulating the data as described in the last section, the information was divided into training, validation, and test groups. A total of four serial samples of each phase for the differential currents were utilized for training at the sampling frequency of 1 kHz. A moving data window was then applied, generating three patterns for each case simulated

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by the matlab. The three moving windows for phase A are as follows:

Where K is the last read sample of the present data window,

and are the differential phase A current samples. The movement of one sample from one window to the next should be noted. The procedure is similar for phases B and C.For training and validation processes, 50% of the cases considered the saturation phenomenon caused by the current transformers. The architecture used in this paper is shown in Fig. 6.

The input signals are the differential current per phase and the output will indicate, if the case, the fault situation. The learning process converged in about 2000 training epochs using six support vectors. Sigmoidal perception is used as a kernel function. For this application in transformer protection, SVM outputs smaller than 0.5 consider that an internal fault is not present. On the other hand, outputs equal to or more than 0.5 were considered as an internal fault, and a trip signal should be sent to the circuit breakers.

VII. PROPOSED ALGORITHMS Fig. 7 illustrates the first algorithm implemented based on differential logic and utilizing SVM. In the algorithm, the first step is the calculation of the direct and differential currents using the sampled quantities. After that, the relay verifies if there is a significant differential current using a differential characteristic curve of the type shown in Fig. 2. In the case where you have a significant differential current, the SVM will discriminate a fault condition from the other situations mentioned earlier. This procedure would replace the conventional algorithm using harmonic restraint based on the Fourier technique. It must be emphasized that in this approach, no reconstruction action is implemented concerning the saturated signals mentioned before. The only precaution for this case is that in the training process, cases of differential current without saturation as well as some cases,

including the saturated condition, were used, as mentioned.

Fig 7: Proposed algorithm If a fault condition is detected, the fault counter is verified, and after confirmation, a trip signal will be sent.

VIII. PERFORMANCE OF THE PROPOSED ALGORITHMS BASED ON SVM

This section will illustrate the performance of the proposed SVM algorithms. The data used in this task were the same for the SVM approach, as well as for the traditional Fourier algorithm, to be presented in the next section. It is important to note that for generalization purposes, a power transformer of 25 MVA, as well as one of 6.25 MVA, was used in the tests.

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Table 2 illustrates the performance of the proposed algorithm using the 25-MVA-power transformer. Table 3 illustrates the performance of the proposed algorithm using the 6.25-MVA-power transformer.

TABLE: 2 Proposed Algorithm- 25 MVA Transformer

Test cases No of Patterns

Correct Answers

Errors

Energization 203 200 3 Internal fault 832 827 5 External fault 300 298 2 Fault Between Transformer and CT

160 158 2

Energization with Internal fault 142 141 1 Over excitation 84 83 1 Capacitor Energization 28 28 0 Load shedding 100 96 4 External fault Removal 642 639 3 Steady state stare 09 9 0 Total 2500 2479 21 Total (%) 100 99.16 .84 TABLE 3

Proposed Algorithm- 6.25 MVA Transformer Test cases No of

Patterns

Correct answers

Errors

Energization 203 196 7 Internal fault 832 824 8 External fault 300 293 7 Fault Between Transformer and CT

160 153 7

Energization with Internal fault 142 141 1 Over excitation 84 82 3 Capacitor Energization 28 26 3 Load shedding 100 93 8 External fault Removal 642 636 6 Steady state stare 09 09 0 Total 2500 2453 50 Total (%) 100 98.12 2

IX. PERFORMANCE OF THE TRADITIONAL

ALGORITHM BASED ON DFT

One important aspect at this stage of this paper is to compare the traditional approach to the proposed ones. Numerous algorithms have been proposed for traditional differential protection of power transformer. The one utilized used in this paper was inspired by reference [6], where the proposed algorithm consists of three modules: (1) the initialization module that is used for entering the settings, which are determined by the characteristics of the protected transformer; (2) the percentage differerential protection module that uses the differential characteristic curve of the type presented in fig 2 to determine whether the transformer

is operating under a normal or an external fault condition or an internal fault,inrush,or over excitation; and (3) the harmonic restraint module, which implements the discrete Fourier transform (DFT)- based harmonic restraint algorithm to distinguish amongst inrush,overexcitation, or internal conditions. The slope adjustment of the relay characteristic curve depends on many factors. In order to reach an appropriate number of possible slopes and to avoid possible errors on the curve adjustment, the algorithm was tested taking into account the 25%, 30%, and 40% slopes. Besides, the percentage of the second harmonic component, estimated by the DFT, in relation to the fundamental was varied during the tests Table 4 shows the results for the algorithm proposed using the conventional differential algorithm for the 25-MVA-power transformer. It illustrates the results for a 25% slope relay characteristic curve, and the content of the second harmonic component in relation to fundamental was adjusted to 20%.

TABLE: 2 Proposed Algorithm- 25 MVA Transformer

Test cases No of Patterns

Correct answers

Errors

Energization 203 122 81 Internal fault 832 631 201 External fault 300 196 104 Fault Between Transformer and CT

160 101 59

Energization with Internal fault 142 125 17 Over excitation 84 70 14 Capacitor Energization 28 23 5 Load shedding 100 81 19 External fault Removal 642 601 41 Steady state stare 09 9 0 Total 2500 1959 541 Total (%) 100 78.36 21.64

X. COMPARISON AMONGST ALGORITHMS

This section will be dedicated to a global analysis concerning the performance of the studied algorithms, including an implementation of the conventional algorithm, which are as follows: traditional algorithm for differential protection of power transformers using harmonic restraint by Fourier transform; TABLE 4 25 MVA Transformer

SPEED ALGORITHIM

ACCURACY (%)

Samples per cycle

Response time(ms)

SVM 99.16 4 4.17 TRADITIONAL METHOD

78.76

16

16.67

XI. CONCLUSIONS

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This paper presented alternative approaches using SVM for the protection of power transformers. An SVM subroutine was used to discriminate internal faults from other situations, including inrush currents produced during the transformer operation. The best results showed the accuracy of 99.16% and 98.12% for power transformers of 25 MVA and 6.25 MVA, respectively. The time response was 1/4 of a cycle. The cases tested by SVM were then compared to the traditional differential protection algorithm, which presented inaccuracies. The application of the SVM tools is a new and important stage in the differential relay analysis methodology for the power transformer protection. REFERENCES

[1] S. H. Horowitz and A. G. Phadke, Power System Relaying, 2nd ed., New York: Wiley, 1992.

[2] J. Pihler, B. Grcar, and D. Dolinar, “Improved operation of power transformer protection using artificial neural network,” IEEE Trans on . Power Delivery., vol. 12, no. 3, pp. 1128–1136, Jul. 1997.

[3] L. G. Perez, A. J. Flechsig, J. L. Meador, and Z. Obradovic, “Training an artificial neural network to discriminate between magnetizing inrush and internal faults,” IEEE Trans. Power Del., vol. 9, no. 1, pp. 434–441, Jan. 1994.

[4] S. R. Kolla, “Digital protection of power transformers using artificial neural networks,” in Proc. Int. Conf. Advances Instrumentation Control, 1995, pp. 41–150.

[5] C.Cortes, V.Vapnik, Support vector Networks, Mach learning 20(3)(1995)273-295

[6] M.Habib and M.A. Marin, “a comparative analysis of digital relaying algorithms for the differential protection of three phase transformers,”IEEE Trans. Power syst.vol3, no.3, pp.1378-1384, aug.1998

[7] D.V.coury, P.G...Campos, ”Modelling a power transformer for investigation of digital protection schemes,” in proc. 8th Int. conf. harmonics Quality power, 1998, pp. 489-494

Vikramaditya Dave received the B.E.. (Electrical) from M.B.M. Engg college, Jodhpur, in 1999, M.E. (Control) from M.B.M. Engg college, Jodhpur, in 2004. He worked as Engineer in Rajasthan Electricity Board,,Rajasthan.. Presently, he is working as Assistant professor in Electrical Engineering Department CTAE, Maharana Pratap university of Agriculture and Technology. His research interests include Power System, power Quality, Artificial Neural Network, Fuzzy Logic Systems and Support Vector Machine

Avdhesh Sharma received the BSc.Engg. (Electrical) from D.E.I Engg. College, Dayalbagh, Agra, in 1983, M.Sc.Engg. (Instrumentation & Control) from AMU, Aligarh in 1987, M.Tech.(CSDP) from IIT,Kharagpur in 1992 and Ph.D.(Electrical Engineering) from Indian Institute of Technology, New Delhi in 2001. He worked as Assistant professor and Associate Professor at M.B.M. Engg. College, Jodhpur (Rajasthan). Presently,he is working as professor and Head Electrical Engineering department CTAE, Maharana Pratap university of

Agriculture and Technology. His research interests include Power System Stabilizers, unit commitment, power Quality, Artificial Neural Network and Fuzzy Logic Systems.