A Transmission Line Fault Classification Approach by ...

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9]; neural network and fuzzy logic [10, 11]; and neural. Corresponding .... Then the nonlinear classifier decision function is: ( ) sgn. i i i. SVs. f x yx b α. ⎛. ⎞. = +. ⎜.
Journal of Energy and Power Engineering 5 (2011) 268-274

A Transmission Line Fault Classification Approach by Support Vector Machines A.M. Ibrahim, A.Y. Abdelaziz, S.F. Mekhamer and M. Ramadan Electrical Power and Machines Department, Faculty of Engineering, Ain Shams University, Cairo, Egypt Received: May 08, 2010 / Accepted: August 23, 2010 / Published: March 31, 2011. Abstract: This paper presents an approach for shunt faults detection and classification in transmission line using Support Vector Machine (SVM). The paper compares between using three line post-fault current samples for one-half cycle and one-fourth cycle from the inception of the fault as inputs for SVM. Two SVMs are used, first SVMabc is used for faulty phase detection and second SVMg is used for ground detection. SVMs with polynomial kernel with different degrees are used to obtain the best classification score. The classification test results show that the proposed method is accurate and reliable. Key words: Transmission line protection, fault detection, fault classification, support vector machine.

1. Introduction Protecting transmission lines is very important to safeguard the power systems. Accurate, fast, reliable transmission line faults detection and classification is needed. On the one hand, correct information of the type of fault is readily needed for fault location algorithms. On the other hand, in digital distance protection schemes, for proper operation of the protection relays, correct determination of the fault type is prerequisite. Because of the above mentioned requirements, a significant amount of research work has been directed to address the problem of an accurate fault classification scheme. For transmission lines shunt faults classification, techniques such as kalman filter [1], neural network [2, 3], fuzzy logic [4], wavelet transform [5] and support vector machine [6, 7] are used. Furthermore, combined techniques have already been used, such as wavelet transform and fuzzy logic [8, 9]; neural network and fuzzy logic [10, 11]; and neural Corresponding author: A.Y. Abdelaziz, professor, research fields: the applications of artificial intelligence in power systems and protection and new optimization techniques in power systems planning and operation. E-mail: [email protected].

network and wavelet transform [12]. Since each branch has its own individual advantages /disadvantages, for any complex classification task, it is essential to compare all possible techniques and then choose the one most appropriate for solving a specific problem. For example, in the case of fault classification, apart from the accuracy requirements, speed is of the essence (typically 5-10 ms) [11]. Kalman filter has been proposed to classify shunt faults [1]. However, this technique is computationally time consuming and they require a number of different filters to accomplish the task. Many researchers have proposed different fault classification techniques using different types of neural networks [2, 3]. Although the neural-network-based approaches have been quite successful in determining the correct fault type, the main disadvantage of neural network is that it requires large amount of neurons a considerable amount of training effort for good performance. Moreover, another disadvantage of Neural Network based algorithms is that the training may not converge in some cases, as the starting point is chosen at random and can end up in a local minimum. Fuzzy logic based fault classifier uses magnitude and angle of

A Transmission Line Fault Classification Approach by Support Vector Machines

fundamental phasors [4]. However, the accuracy of fuzzy logic based schemes cannot be guaranteed for wide variations in the system conditions. Recently, wavelet transform [5] has been applied for fault classification for transmission line. This approach finds limitations as wavelet transform is highly prone to noise and provides erroneous results. SVM is considered as a new AI technique. SVM is a set of related supervised learning method which is used for classification. It is a linear classifier which seeks for maximum margin hyperplane separate between two classes very close to each other. This occurs through solving a quadratic programming (QP) problem. SVMs were developed to solve the classification problem, but recently they have been extended to the domain of regression problems [13, 14]. In a short period of time, SVM found numerous applications such as transformer fault diagnosis [15], power system disturbances [16-18], relay coordination [19] and transient stability of power system [20]. In addition, it is used for fault classification of transmission line [6, 7]. This is due to the advantages of SVM over traditional approaches such as neural networks. SVM has a good generalizetion performance; it can correctly classify a new object quite well. Moreover, it is efficient in terms of speed, complexity and robustness in high dimensions [14]. This paper presents an approach for faults classification in transmission lines using a support vector machine (SVM). The inputs to SVMs are the post fault current samples or healthy current samples at a sampling frequency 1.0 kHz (20 samples per cycle). A comparison between using one-half cycle current samples (10 ms) and one-fourth cycle current samples (5 ms) as inputs to SVM has been made. Also samples for healthy system are taken at any time as inputs to SVMs. Two SVMs are used SVMabc and SVMg. Both SVMs are trained with all the ten types of possible short circuit faults (e.g., a-g, b-g, c-g, a-b, b-c, c-a, a-b-g, b-c-g, c-a-g, a-b-c/a-b-c-g) in addition to normal state.

transmission line as shown in Fig. 1. The length of transmission line is 100 km. Transmission line sequence impedances are Z0 = 0.449 + j2.02 Ohm/km and Z1 = 0.041 + j0.528 Ohm/km respectively for zero and positive sequence. The source impedance is fixed at j20 Ohm. The relay is located at one end of transmission line as shown in Fig. 1. Simulations were performed using an electromagnetic transient program, EMTDC/PSCAD. Sampling frequency is 1.0 kHz at 50 Hz base frequency.

3. Support Vector Machine Support vector machine [13, 14] was originally introduced by Vapnik and co-workers in the late 1990s. It is a computational learning method based on the statistical learning theory. While traditional statistical theory keeps to empirical risk minimization (ERM), SVM satisfies structural risk minimization (SRM) based on statistical learning theory (SLT), whose decision rule could still obtain small error to independent test sampling. SVM mainly has two classes of applications, classification and regression. In this paper, application of classification is discussed. The classification problem can be restricted to consideration of the two-class problem without loss of generality. In this problem, the goal is to separate the two classes by a function (a classifier), which is induced from available examples and work well on unseen examples, i.e., it generalizes well. There are many possible linear classifiers that can separate the data, but there is only one that maximizes the margin (maximizes the distance between it and the nearest data point of each class). This linear classifier is termed the optimal separating hyperplane. Intuitively, this boundary could be expected to generalize well as opposed to the other possible boundaries.

2. Power System under Study Two generation areas are connected by a 500 kV

269

Fig. 1 The power system for simulation.

270

A Transmission Line Fault Classification Approach by Support Vector Machines

Given a set of training data,

{x i , y i } ,

i = 1,..., n , y i ∈ {−1,1} , x i ∈ R d

(1)

d

Each xi is a d-dimensional real vector R . The points x which lie on the hyperplane satisfy: w . x +b = 0 (2) Where w is normal to the hyperplane, |b|/||w|| is the perpendicular distance from the hyperplane to the origin, and ||w|| is the Euclidean norm of w. For the linearly separable case, the support vector algorithm simply looks for the separating hyperplane with largest margin. This can be formulated as follows: suppose that all the training data satisfy the following constraints: xi . w + b ≥ +1 , for yi = +1 (3) (4) xi . w + b ≤ −1 , for yi = −1 These can be combined into one set of inequalities: yi ( xi . w + b) − 1 ≥ 0 , for all i (5) Now consider the points for which the equality in Eq. (3) holds. These points lie on the hyperplane H1: xi . w + b = 1 with normal w and perpendicular distance from the origin |1−b|/||w||. Similarly, the points for which the equality in Eq. (4) holds lie on the hyperplane H2: xi . w + b = −1, with normal again w, and perpendicular distance from the origin |−1−b|/||w||. It is noticed that H1 and H2 are parallel and the margin is simply 2/||w|| which is observed in Fig. 2. Training points for which the equality in Eq. (5) holds are called support vectors. The pair of hyperplanes which gives the maximum margin by minimizing ||w||, subject to constraints can be found. The optimization problem presented is difficult to solve because it depends on ||w|| which involves a square root. Fortunately it is possible to alter the equation by substituting ||w|| with 0.5||w||2 without changing the solution. Taking into account the noise with slack variable ξ and error penalty C, the optimal hyperplane can be found by solving the following convex quadratic programming (QP) problem: Minimize n 1 || w ||2 + C ∑ ξ i 2 i =1 Subject to y i (x i .w + b ) ≥ 1 − ξ i ,

Fig. 2 Maximum margin hyperplane and margins for a SVM trained with samples from two classes.

ξi ≥ 0, for i = 1,..., n

(6) Where ξi is measuring the degree of misclassification, the constant C > 0 determines the trade-off between margin maximization and training error minimization and n is the number of samples. In the present case, it will turn out that it is more convenient to deal with the dual. This can be done by converting the problem with the Karush-Kuhn-Tucker (KKT) conditions into Lagrange optimization dual problem: Maximize n

w(α ) = ∑ α i − i =1

1 n ∑ αiα j yi y j xi . x j 2 i , j =1

Subject to n

∑ yα i =1

i

i

= 0, 0 ≤ α ≤ C , i = 1,..., n

(7)

If αi > 0, then the corresponding xi is called a support vector. In general, support vectors are only a small part of the training samples. Finally, the optimal separating hyperplane is obtained as follows:

∑α y x . x i

i i

j

+b = 0

(8)

SVs

Where SVs stands for Support Vectors. Then the nonlinear classifier decision function is: ⎛ ⎞ (9) f ( x) = sgn ⎜ ∑ α i yi xi + b ⎟ ⎝ SVs ⎠

A Transmission Line Fault Classification Approach by Support Vector Machines

271

The test data example “x” is classified as follows: ⎪⎧Class − 1, if f ( x) ≥ 0 x∈⎨ (10) ⎪⎩Class − 2, if f ( x) < 0 The original optimal hyperplane algorithm proposed by Vladimir Vapnik was a linear classifier. However, in 1992, Bernhard Boser, Isabelle Guyon and Vapnik suggested a way to create non-linear classifiers by applying the kernel trick to maximum-margin hyperplanes. The resulting algorithm is formally similar, except that every dot product is replaced by a non-linear kernel function.

k ( x, x′ ) = φ ( x), φ ( x′)

(11)

This allows the algorithm to fit the maximum-margin hyperplane in the transformed feature space. The transformation may be non-linear and the transformed space high dimensional; thus though the classifier is a hyperplane in the high-dimensional feature space, it may be non-linear in the original input space (Fig. 3). In this work, the polynomial kernel function with different degrees is used:

k ( x, x′ ) = ( x, x′ + 1)

n

(12)

Where n is the polynomial degree.

4. Support Vector Machine Training and Testing Fig. 4 shows the proposed protection scheme. It consists of four independent SVMs. SVMa, SVMb and SVMc are used for detection of the fault for phase a, b and c respectively. The fourth SVM, SVMg, is used for ground detection. 4.1 SVMs for Fault Classification A comparison between using one-half cycle current samples and one-fourth cycle current samples as inputs to SVM has been made. First one-half cycle current samples after the inception of the fault are used as inputs to SVMabc. SVMabc is trained with 420 data sets and tested with 108 data sets for all the 10 types of faults and normal conditions.

Fig. 3 Mapping the training data into a higher-dimensional feature space.

Training a SVM involves solving a constrained quadratic programming problem, which requires large memory and enormous amounts of training time for large scale problems. In contrast, the SVM decision function is fully determined by a small subset of the training data, called support vectors. Therefore, it is desirable to remove from the training set the data that is irrelevant to the final decision function [21], so we try to select data for fast SVM training by using margin data sets. The corresponding outputs for these training data are “1” for faults and “-1” for no faults (normal conditions) for each phase. Faults on the transmission line are simulated with different fault resistance Rf (10-200 Ω) at various locations for all the 10 types of faults and normal conditions. Different error penalty “C” values are used to get the most optimized value for the classification problem and a comparison between different kernel polynomial degrees has been made. Table 1 provides numbers of support vectors (SVs) and the percent of correct predictions for different error penalties “C” and different kernel polynomial degrees “n” for one-half cycle current samples inputs. Table 2 is similar to Table 1 but for one-fourth cycle current samples inputs. It is noticed that same kernel polynomial degrees are used with different error penalties “C” for one-half cycle current samples inputs and one-fourth cycle current samples inputs. The used kernel polynomial degrees are 2, 3 and 4 for both cases. 106, 108 and 1010 error penalties are used for one-half cycle current samples inputs. 108, 109 and 1010 error penalties are used for one-fourth cycle current samples inputs. The used values of error penalty are chosen to control the

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A Transmission Line Fault Classification Approach by Support Vector Machines

Fig. 4 The proposed protection scheme.

percent of correct predictions and to get the most optimized value for the classification problem. It is noticed from Table 1 that 100% correct predictions is reached with C = 108 for one-half cycle current samples inputs. From Table 2, 100% correct predictions is reached with C = 1010 for one-fourth cycle current samples inputs. The minimum percent of correct predictions for one-half cycle current samples inputs (94.44%) is obtained with C = 1010 and n = 3. Moreover for one-fourth cycle current samples inputs the minimum percent of correct predictions (97.22%) is obtained with C = 108 and n = 2 or 3. Table 3 and Table 4 summarize all false predictions which happened during the test of SVMabc for one-half cycle current samples inputs and one-fourth cycle current samples inputs respectively. The false predictions are highlighted in gray color. In comparison with the existing wavelet technique [5], the proposed approach has better generalization performance and higher detection speed. Overall accuracy of the wavelet-based approach is 99.53% for fault classification of transmission line. However, the proposed technique reached to 100% classification accuracy. 4.2 SVM for Ground Detection SVMg is trained with the peak value of the ground current as input “x”. Ground current is resulted from

Table 1 Testing of SVMabc for fault classification using one-half cycle current samples. Degree of kernel polynomial n=2

n=3

n=4

C Number of SVs Correct predictions (%) Number of SVs Correct predictions (%) Number of SVs Correct predictions (%)

106

108

1010

108

44

48

95.37

98.148

95.37

86

44

44

97.22

100

94.44

70

50

36

97.22

100

96.296

Table 2 Testing of SVMabc for fault classification using one-fourth cycle current samples. Degree of kernel polynomial n=2

n=3

n=4

C

108

109

1010

Number of SVs Correct predictions (%) Number of SVs Correct predictions (%) Number of SVs Correct predictions (%)

52

44

96

97.22

98.148

99.074

48

42

88

97.22

99.074 100

46

46

98.148

99.074 100

80

the summation of the three lines current Ia, Ib and Ic. The corresponding output “y” is “1” for the fault involving ground and “-1” for fault without ground. SVM is trained with 126 data sets. Different 72 data sets are used for testing SVM. The results are very accurate (100%) for both one-half cycle current samples inputs and one-fourth cycle current samples inputs with kernel polynomial degree n = 2 and error penalty C = 109.

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A Transmission Line Fault Classification Approach by Support Vector Machines

Table 3 False prediction samples for testing of one-half cycle current samples. Degree “n”

Error penalty “C” 6

10

108 n=2 1010

106 1010 n=3

106 1010

n=4

Fault

a

b

C

abc-g, Rf = 200 Ω, Fault at 60%

1

-1

1

abc-g, Rf = 200 Ω, Fault at 80%

-1

1

-1

ac-g, Rf =200 Ω, Fault at 80%

-1

-1

-1

ac-g, Rf =200 Ω, Fault at 80%

-1

-1

1

abc-g, Rf = 200 Ω, Fault at 80%

-1

1

1

abc, Rf = 200 Ω, Fault at 20%

1

1

-1

bc-g, Rf = 60 Ω, Fault at 20%

-1

1

-1

c-g, Rf = 150 Ω, Fault at 40%

-1

-1

-1

ab, Rf = 120 Ω, Fault at 40%

-1

-1

-1

ac-g, Rf = 200 Ω, Fault at 80%

-1

-1

-1

abc-g, Rf = 200 Ω Fault at 80%

-1

1

1

abc, Rf = 200 Ω, Fault at 20%

1

1

-1

bc-g, Rf = 60 Ω, Fault at 20%

-1

1

-1

c-g, Rf = 150 Ω, Fault at 40%

-1

-1

-1

ab, Rf = 120 Ω, Fault at 40%

-1

-1

-1

c-g, Rf = 50 Ω, Fault at 60%

-1

-1

-1

abc-g, Rf = 200 Ω, Fault at 80%

-1

1

1

ac-g, Rf = 200 Ω, Fault at 80%

-1

-1

-1

b-g, Rf = 10 Ω, Fault at 40%

-1

1

1

c-g, Rf = 150 Ω, Fault at 40%

-1

-1

-1

ab, Rf = 120 Ω, Fault at 40%

-1

-1

-1

b

c

Table 4 False prediction samples for testing of one-fourth cycle current samples. Degree “n”

n=2

Error penalty “C”

Fault

a

108

ac-g, Rf = 200 Ω, Fault at 80%

-1

-1

-1

abc-g, Rf = 200 Ω, Fault at 80%

-1

1

1

abc-g, Rf = 200 Ω, Fault at 80%

-1

1

1

ac-g, Rf = 200 Ω, Fault at 80%

-1

-1

1

abc-g, Rf = 200 Ω, Fault at 80%

-1

1

1

ac-g, Rf = 200 Ω, Fault at 80%

-1

-1

-1

abc-g, Rf = 200 Ω, Fault at 80%

-1

1

1

abc-g, Rf = 200 Ω, Fault at 80%

-1

1

1

abc-g, Rf = 200 Ω, Fault at 80%

-1

1

1

ac-g, Rf = 200 Ω, Fault at 80%

-1

-1

1

abc-g, Rf = 200 Ω, Fault at 80%

-1

1

1

109 1010 108

n=3 109 108 n=4 109

5. Conclusions This paper proposes a protection scheme of transmission line using SVM. Post-fault current samples are used as inputs for faulty phase detection SVMabc. The peak values of ground current are used as

inputs for ground detection SVMg. In this paper, kernel polynomial functions with different degrees are used. SVMs are trained with one-half cycle current samples and one-fourth cycle current samples respectively. The maximum errors for one-fourth cycle current samples and one-half cycle current samples are 2.78% and

274

A Transmission Line Fault Classification Approach by Support Vector Machines

5.56% respectively for the same training data. Both reached to 100% fault classification accuracy. It is found that SVMs have better generalization performance and higher classification speed (one-fourth cycle) compared to the existing neural network and wavelet techniques. The SVM-based technique proved to be a fast, accurate, and robust approach that would perform accurately for various system conditions.

References [1]

[2]

[3]

[4]

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[7]

[8]

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