A combined adaptive network and fuzzy inference system (ANFIS) approach for overcurrent relay system

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Neurocomputing 71 (2008) 895–903 www.elsevier.com/locate/neucom

A combined adaptive network and fuzzy inference system (ANFIS) approach for overcurrent relay system M. Geethanjali, S. Mary Raja Slochanal Department of Electrical and Electronics Engineering, Thiagarajar College of Engineering, Madurai-625 015, Tamilnadu, India Received 3 May 2006; received in revised form 9 October 2006; accepted 26 February 2007 Communicated by A. Zobaa Available online 7 April 2007

Abstract Accurate models of overcurrent (OC) relays with inverse time relay characteristics play an important role for the coordination of power system protection schemes. Conventional OC relay modelling using techniques like system identification, parameter estimation, direct data storage and software gave only approximate models. Hence, in this paper a new method for modelling OC relay characteristics curves based on a combined adaptive network and fuzzy inference system (ANFIS) is proposed. In this method, OC relay modeling is done using ANFIS for two types of OC relays (RSA20 and CRP9 with different types and various numbers of membership functions to bring out the optimal design. The simulated results are compared with the published results of analytical method and fuzzy model systems. The results obtained are quite encouraging and will be useful as an effective tool for modelling OC relays. r 2007 Elsevier B.V. All rights reserved. Keywords: Fuzzy neural approach; Adaptive network fuzzy inference system (ANFIS); Overcurrent relay

1. Introduction Overcurrent relays (OC relays) sense fault current and also over-load currents. OC protection is that protection in which the relay picks when magnitude of current exceeds the pickup level. The basic element in OC protection is an OC relay. It is widely used for motor protection, transformer protection, line protection and protection of utility equipment. In OC relays there is a facility for selecting the plug setting and time setting such that the same relay can be used for a wide range of current, time and characteristics. Conventionally, the arrangement is such that the relay characteristics remain the same for various plug settings, for a given time setting. In the present day of higher degree of automation, it is necessary to provide appropriate protective relaying to protect the system against faults. In order to increase the reliability and flexibility of such protective relaying, highspeed digital relaying is used. Modern power systems using Corresponding author.

E-mail address: [email protected] (M. Geethanjali). 0925-2312/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.neucom.2007.02.015

digital relays are operated close to their design limits. Hence, it is necessary to model relays to realistic conditions [17]. Of the different methods for OC relay models time–current (TC) characteristics curves is one of the most familiar methods [12]. For OC relay modeling, conventional techniques like system identification and parameter estimation are used. These techniques require expensive equipments or accurate mathematical models. But practically to obtain them are very difficult because the OC relay characteristics remain the same for various plug settings for a given time setting. In the recent past, software models and direct data storage are two major methods of modeling an OC relay using digital computers [13]. A complete literature survey of software models of OC relays has been made in [3]. In Ref. [6], it is given that any digital relay abiding to the IEEE std. C37.112, does not require any mathematical representation than the equations provided in the standard. Also, the time dial setting (TDS) provided by the standard is linear. But, in both these methods the main problem is to store and use a large amount of data in the computer memory for different settings. Moreover, if the operating point is not matching with any set of the

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stored values, then to obtain the midpoints, interpolation is necessary to get good accuracy. Hence, to overcome the drawbacks with these conventional approaches a flexible approach is to be formulated. The fuzzy logic concept is used to solve complex and uncertainty problems [5,15]. The major benefit of fuzzy logic is that its knowledge representation is explicit, using simple IF-THEN relations. But this model uses the human-determined membership functions (MFs) that are fixed. Therefore, they are rarely optimal in terms of reproducing the desired outputs. Hence, recently many researchers use neural networks also to overcome most of the complex problems to adapt dynamically to the system operating conditions, and to make correct decisions, if the signals are uncertain [2,4,16]. The use of neural nets in applications is very sparse due to its implicit knowledge representation, the prohibitive computational effort and so on. But the integration of neural network into the fuzzy logic system makes it possible to learn from prior obtained data sets. [7–9,11,14,18]. A flexible approach based on fuzzy logic and neural networks for OC relay was presented by Karegar et al. [1,10]. In that paper, the results were obtained with analytical model, fuzzy model and neural network model for two types of OC relays (RSA20 and CRP9). But the recent advancements in digital protection necessitate obtaining still improved results. Therefore, a flexible approach based on fuzzy logic and artificial neural networks, namely adaptive network-based fuzzy inference system (ANFIS), is used to develop OC relay modeling in this paper. This developed model is trained and validated by applying it to the relay data quoted in Ref. [10] (i.e. sampled data of two types of OC relays). The results are compared with the results obtained for analytical model and fuzzy model published in [10].

2. Adaptive-network-based fuzzy inference system (ANFIS) Functionally, there are almost no constraints on the node functions of an adaptive network except piecewise differentiability. Structurally, the only limitation of network configuration is that it should be of feed forward type. Owing to these minimal restrictions, the adaptive network’s applications are immediate and immense in various areas. The proposed architecture is referred to as ANFIS, standing for Adaptive-Network-based Fuzzy Inference System. The method of decomposition of the parameter set in order to apply the hybrid learning rule is described. 2.1. ANFIS architecture For simplicity, it is assumed that the fuzzy inference system under consideration has two inputs x and y and one output f. Suppose, if the rule base contains two fuzzy if-then rules such as Rule 1: If x is A1 and y is B1, then f1 ¼ p1x+q1y+r1. Rule 2: If x is A2 and y is B2, then f2 ¼ p2x+q2y+r2. Then the fuzzy reasoning is illustrated in Fig. 1(a), and the corresponding equivalent ANFIS architecture (ANFIS) is shown in Fig. 1(b). The node functions in the same layer are of the same function family as described below: Layer 1: Every node i in this layer is a square node with a node function O1i ¼ mAi ðxÞ,

(1)

where x is the input to node i and Ai the linguistic label (small, large, etc.) associated with this node function. Usually mAi (x) is selected to be bell shaped with maximum equal to 1 and minimum equal to 0, such as the generalized

Fig. 1. (a) Selected type of fuzzy reasoning; (b) equivalent ANFIS.

ARTICLE IN PRESS M. Geethanjali, S.M. Raja Slochanal / Neurocomputing 71 (2008) 895–903

bell function mAi ðxÞ ¼ 1þ



1

xci ai

2  bi

(2)

or the Gaussian function "   # x  ci 2 mAi ðxÞ ¼ exp  , ai

(3)

where {ai, bi, ci} is the parameter set. As the values of these parameters change, the bell-shaped functions vary accordingly, thus exhibiting various forms of MFs on linguistic label Ai. In fact, any continuous and piecewise differentiable functions, such as commonly used trapezoidal or triangular-shaped MFs, are also used for node functions in this layer. Parameters in this layer are referred to as premise parameters. Layer 2: Every node in this layer is a circle node labeled P, which multiplies the incoming signals and sends the product out. For instance, oi ¼ mAi ðxÞmBi ðyÞ

i ¼ 1; 2 . . . .

(4)

Each node output represents the firing strength of a rule. (In fact, other T-norm operators that performs generalized AND can be used as the node function in this layer.) Layer 3: Every node in this layer is a circle node labeled N. The ith node calculates the ratio of the ith rule’s firing strength to the sum of all rules’ firing strengths: oi oi ¼ ; i ¼ 1; 2 . . . . (5) o1 þ o2 For convenience, outputs of this layer will be called normalized firing strengths. Layer 4: Every node i in this layer is a square node with a node function O4i ¼ $i f i ¼ $i ðpi x þ qi y þ ri Þ,

(6)

Table 1 Two passes in the hybrid learning procedure for ANFIS

Premise parameters Consequent parameters Signals

Forward pass

Backward pass

Fixed Least squares estimate Node outputs

Gradient descent Fixed Error rates

897

where oi is the output of layer 3, and {pi, qi, ri} is the parameter set. Parameters in this layer will be referred to as consequent parameters. Layer 5: The single node in this layer is a circle node labeled S that computes the overall output as the summation of all incoming signals, i.e., P X oi f i O5i ¼ overalloutput ¼ $i f i ¼ Pi . (7) i oi i Thus an adaptive network has been constructed. The proposed ANFIS-based overcurrent relay system (AOCRS) is based upon Jang’s ANFIS [15], which is a fuzzy inference system implemented on the architecture of a five-layer feed forward network. Using a hybrid learning procedure, the AOCRS can construct an input–output mapping based on both human knowledge (in the form of if-then rules) and input–output data observations. In the hybrid learning algorithm, in the forward pass, the functional signals go forward till layer 4 and the consequent parameters are identified by the least squares estimate. In the backward pass, the error rates propagate backward and the premise parameters are updated by the gradient descent. The consequent parameters thus identified are optimal (in the consequent parameter space) under the condition that the premise parameters are fixed. Accordingly, the hybrid approach is much faster than the strict gradient descent. Table 1 summarizes the activities in each pass. A summary of the general specifications including the learning algorithm, required initial knowledge, domain partitioning, rule structuring and extracted knowledge type are given in Table 2. 3. Design and development of ANFIS based over current relay system (AOCRS) The conceptual diagram of the proposed over current relay system is shown in Fig. 2. The proposed AOCRS is developed using MATLAB 7.0 version. For this case the input variables are load current (IL) and TDS. By trial and error, initially, the system was developed with five numbers of different types of MFs such as Gaussian type, bell-shaped type and triangular types for each input variable. Suitable linguistic variables such as VERY LOW (VL), LOW (L), MEDIUM (M), HIGH (H) and VERY HIGH (VH), are assigned to fuzzy sets of Load current (IL) and TDS. The output variable was operating time (t). All the combinations of if-then-type fuzzy rules

Table 2 Summary of general specifications of the used architecture Adaptive FIS type

Adaptive architecture

Algorithmic learning structure

Partition of spaces

Required initial knowledge

Structural change

Extracted knowledge type

ANFIS

Multilayer feed forward network

Hybrid: supervised (gradient descent)

Adaptive fuzzy grid

Numerical data

No

If-then fuzzy rules

ARTICLE IN PRESS M. Geethanjali, S.M. Raja Slochanal / Neurocomputing 71 (2008) 895–903

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Over Current Relay System

Fuzzy Inference System ----------------------Fuzzification ----------------------Fuzzy inference Engine ----------- ---------Defuzzification

Error Measure Mechanism

Architectural Update Mechanism

Fig. 2. Conceptual diagram of the proposed ANFIS-based over current relay system.

were used. Similarly the system was developed with seven numbers of MFs of different types such as Gaussian type, bell-shaped type and triangular type for each input variable. Suitable linguistic variables such as VERY LOW (VL), LOW (L), MEDIUM LOW (ML), MEDIUM (M), MEDIUM HIGH (MH), HIGH (H) and VERY HIGH (VH), are assigned to fuzzy sets of Load current (IL) and TDS. The output variable was operating time (t). All the combinations of if-then-type fuzzy rules were used. It is to be noted that there is no analytical method to determine the optimal number of MFs. The optimal number of MFs is usually determined heuristically and verified experimentally. A smaller number yields lower complexity and shorter training time, but poor performance. On the other hand, greater number yields better performance but higher complexity and much longer training time [15]. Hence, the number of MFs and the type of MFs are selected in trial and error basis. ANFIS model development is summarized as follows: Type 1: The input variables: No. of MFs used: Type of MFs used: Linguistic variables: Output variable:

Load current (IL) and TDS. 5 Gaussian type, bell-shaped type and triangular type VERY LOW (VL), LOW (L), MEDIUM (M), HIGH (H) and VERY HIGH (VH) Operating time (t)

Linguistic variables:

VERY LOW (VL), LOW (L), MEDIUM LOW (ML), MEDIUM (M), MEDIUM HIGH (MH), HIGH (H) and VERY HIGH (VH). Operating time (t).

Output variable:

3.1. Case study Two types of OC relays were used for evaluating the proposed model. The first one was RSA 20, an electromechanical OC relay. Its TDS varies from 4 to 20. The second one was CRP9, a very inverse electromechanical OC relay. Its TDS varies from 4 to 10. For both the relays the sampled data obtained from [10] for doing modeling are tabulated in Appendix A. 3.2. Simulation results and analysis Using the sampled data given in Appendix A as inputs for training of ANFIS the system was developed with different numbers and types of MFs and each case was trained for 500 iterations with hybrid learning algorithm. The defuzzification method selected was weighted average method. The detailed simulated results obtained using the developed AOCRS in calculating operating time of the RSA20 OC relay corresponding to the respective load current and TDS for different cases are tabulated and given from Tables 3 to 6. 3.2.1. ANFIS model application for RSA20 OC relay

Type 2: The input variables: No. of MFs used: Type of MFs used:

Load current (IL) and TDS.

CASE CASE CASE CASE

1: 2: 3: 4:

TDS ¼ 4, TDS ¼ 8, TDS ¼ 14, TDS ¼ 20.

7 Gaussian type, bell shaped type and triangular type

From the results obtained for various cases it is inferred that for most of the cases of ANFIS model of RSA20 OC relay the error is getting decreased and the mean average

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Table 3 Simulation results of ANFIS model of RSA 20OC relay when TDS ¼ 4 IL

top

mf7-gbell

Er%

mf7-gauss

Er%

mf7-tri

Er%

mf5-gbell

Er%

mf5-gauss

Er %

mf5-tri

Er%

4 10 16 22 28 AV

4238 1240 1061 1010 1002

4224 1249 1063 1009 994

0.33 0.73 0.19 0.10 0.80 0.88

4238 1238 1059 1011 1002

0.00 0.16 0.19 0.10 0.00 0.15

4234 1235 1059 1011 1002

0.09 0.40 0.19 0.10 0.00 0.45

4219 1249 1068 1031 1015

0.45 0.73 0.66 2.08 1.30 1.31

4238 1227 1056 1011 1003

0.00 1.05 0.47 0.10 0.10 0.44

4235 1248 1060 1012 1002

0.07 0.65 0.09 0.20 0.00 0.57

IL, load current; top, actual operating time in milliseconds; mf7-gbell, operating time of the developed ANFIS with 7 number of bell-shaped membership functions; mf7-gauss, operating time of the developed ANFIS with 7 number of gauss-type membership functions; mf7-tri, operating time of the developed ANFIS with 7 number of triangular-type membership functions; mf5-gbell, operating time of the developed ANFIS with 5 number of bell-shaped membership functions; mf5-gauss, operating time of the developed ANFIS with 5 number of gauss-type membership functions; mf5-tri, operating time of the developed ANFIS with 5 number of triangular-type membership functions; Er%, % error value; AV, mean average error value in %.

Table 4 Simulation results of ANFIS model of RSA 20OC relay when TDS ¼ 8 IL

top

mf7-gbell

Er %

mf7gauss

Er %

mf7-tri

Er%

mf5-gbell

Er %

mf5-gauss

Er %

mf5-tri

Er %

4 10 16 22 28 AV

5690 1960 1754 1659 1603

5683 1969 1754 1660 1595

0.12 0.46 0.00 0.06 0.50 0.52

5690 1958 1752 1664 1603

0.00 0.10 0.11 0.30 0.00 0.15

5688 1955 1749 1663 1601

0.00 0.66 0.11 0.06 0.00 0.48

5678 1938 1740 1672 1610

0.21 1.12 0.80 0.78 0.44 0.85

5690 1947 1756 1660 1603

0.00 0.66 0.11 0.06 0.00 0.48

5693 1964 1752 1665 1602

0.05 0.20 0.11 0.36 0.06 0.44

For detailed explanation of the variables refer the legend to Table 3.

Table 5 Simulation results of ANFIS model of RSA 20OC relay when TDS ¼ 14 IL

top

mf7-gbell

Er %

mf7-gauss

Er %

mf7-tri

Er %

mf5-gbell

Er %

mf5-gauss

Er %

mf5-tri

Er %

4 10 16 22 28 AV

8840 3283 2993 2846 2734

8851 3275 2997 2838 2720

0.12 0.24 0.13 0.28 0.51 0.62

8840 3267 2988 2839 2730

0.00 0.49 0.17 0.25 0.15 0.16

8839 3265 2986 2840 2729

0.01 0.55 0.23 0.21 0.18 0.44

8824 3256 2985 2858 2744

0.18 0.82 0.27 0.42 0.37 0.76

8840 3252 2986 2836 2724

0.00 0.94 0.23 0.35 0.37 0.32

8842 3274 2986 2838 2725

0.02 0.27 0.23 0.28 0.33 0.47

For detailed explanation of the variables refer the legend to Table 3.

Table 6 Simulation results of ANFIS model of RSA 20OC relay when TDS ¼ 20 IL

top

mf7-gbell

Er %

mf7 gauss

Er %

mf7-tri

Er %

mf5-gbell

Er %

mf5-gauss

Er %

mf5-tri

Er %

4 10 16 22 28 AV

11975 4702 4264 4043 3915

11969 4705 4270 4037 3898

0.05 0.06 0.14 0.15 0.43 0.49

11975 4697 4259 4041 3915

0.00 0.11 0.12 0.05 0.00 0.12

11974 4696 4257 4042 3912

0.01 0.13 0.16 0.02 0.08 0.35

11949 4701 4265 4071 3935

0.22 0.02 0.02 0.69 0.51 0.66

11975 4684 4253 4035 3914

0.00 0.38 0.26 0.20 0.03 0.25

11973 4707 4256 4039 3912

0.02 0.11 0.19 0.10 0.08 0.39

For detailed explanation of the variables refer the legend to Table 3.

percentage error is in between 0.15% and 1% for all the cases except ANFIS model using five number of bellshaped MF case. For this case also, the average percentage error is 1.31%. This may be due to the insufficient number of MFs with the bell shape in ANFIS model. The lowest

mean average percentage error ie.0.15% is obtained for the ANFIS model using seven numbers of Gaussian-type MFs. The tuned MF parameters for ANFIS model using seven numbers of Gaussian-type MFs (since this is the most efficient case for RSA20 OC relay) are given in Table 7.

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Table 7 Tuned MF parameters for ANFIS model of RSA 20OC relay when seven numbers of Gaussian-type membership functions are used Tuned parameter, a

Tuned parameter, c

3.947 3.094 2.84 2.556 2.206 1.968 1.88

3.862 6.933 11.2 16.31 21.06 25.59 30

Input 2 (time dial setting) MF1 (VL) 1.133 MF2(L) 1.128 MF3(ML) 1.132 MF4(M) 1.122 MF5(MH) 1.134 MF6(H) 1.12 MF7(VH) 1.132

4 6.669 9.334 11.99 14.66 17.33 20

Input 1 (load current) MF1 (VL) MF2(L) MF3(ML) MF4(M) MF5(MH) MF6(H) MF7(VH)

3.2.2. ANFIS model application for CRP9 OC relay The detailed simulated results obtained using the developed AOCRS in calculating operating time of the CRP9 OC relay corresponding to the respective load current and TDS for different cases are tabulated and given from Tables 8 to 10. CASE 1: TDS ¼ 4, CASE 2: TDS ¼ 7, CASE 3: TDS ¼ 10. From the results obtained for various cases it is inferred that for most of the cases of ANFIS model of CRP9 OC relay the error for all the cases is getting decreased. The mean average percentage error is in between 0.61% and 1.8%. For this relay model when TDS ¼ 4 and the ANFIS model has seven number of Gaussian-type MFs the maximum mean error percentage value i.e. 1.8% is obtained. When When TDS ¼ 7 and the ANFIS model

Table 8 Simulation results of ANFIS model of CRP9 relay when TDS ¼ 4 IL

top

mf7-gbell

Er %

mf7-gauss

Er %

mf7 tri

Er %

mf5-gbell

Er %

mf5 -gauss

Er %

mf5-tri

Er %

4 8 12 16 20 AV

1352 605 459 375 358

1358 579 470 375 358

0.50 4.28 2.57 0.00 0.03 1.78

1346 .591 456 .383 356

0.47 2.28 0.65 2.11 0.56 1.80

1364 585 461 375 358

0.91 3.31 0.54 0.11 0.06 1.61

1356 629 450 372 355

0.33 4.05 1.90 0.75 0.70 1.66

1368 609 456 374 356

1.21 0.66 0.65 0.19 0.59 1.59

1309 582 451 372 357

3.17 3.69 1.68 0.59 0.22 1.54

For detailed explanation of the variables refer the legend to Table 3.

Table 9 Simulation results of ANFIS model of CRP9 relay when TDS ¼ 7 IL

top

mf7-gbell

Er %

mf7-gauss

Er %

mf7-tri

Er %

mf5-gbell

Er %

mf5-gauss

Er %

mf5 tri

Er %

4 8 12 16 20 AV

2459 1153 894 744 669

2570 1145 899 743 669

4.53 0.69 0.53 0.15 0.00 0.94

2564 1143 888 746 668

4.30 0.90 0.73 0.20 0.19 0.80

2572 1138 895 741 668

4.59 1.27 0.11 0.51 0.15 0.92

2550 1200 880 740 660

3.75 3.90 1.69 0.63 0.87 1.28

2570 1171 887 741 663

4.51 1.57 0.83 0.42 0.90 1.09

2477 1132 883 739 665

0.73 1.86 1.23 0.71 0.64 0.61

For detailed explanation of the variables refer the legend to Table 3.

Table 10 Simulation results of ANFIS model of CRP9 relay when TDS ¼ 10 IL

top

mf7-gbell

Er %

mf7-gauss

Er %

mf7-tri

Er %

mf5-gbell

Er %

mf5-gauss

Er %

mf5 tri

Er %

4 8 12 16 20 AV

3935 1754 1304 1123 1024

4049 1756 1304 1122 1024

2.90 0.13 0.04 0.06 0.00 0.69

4051 1754 1301 1123 1025

2.95 0.02 0.16 0.01 0.05 0.62

4050 1739 1305 1120 1025

2.93 0.85 0.12 0.25 0.14 0.66

3902 1761 1302 1129 1028

0.82 0.40 0.12 0.55 0.41 1.00

3968 1735 1300 1126 1026

0.83 1.07 0.33 0.23 0.18 0.99

3963 1738 1305 1124 1027

0.71 0.90 0.10 0.12 0.33 0.64

For detailed explanation of the variables refer the legend to Table 3.

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has five number of triangular MFs the minimum mean error percentage value i.e. 0.61 has occurred. For the cases of TDS ¼ 7 the mean average percentage error is between 0.61 and 1.28. For the case of TDS ¼ 10, the mean error percentage is in the range of 0.62–1. The tuned MF parameters for ANFIS model using five numbers of triangular-type MFs (since this is the most efficient case for CRP9OC relay) are given in Table 11. The average (mean) error percentage for each case of RSA20 OC relay was calculated. The area chart illustrating the mean error percentage values of the ANFIS model with different MF cases are shown in Fig. 3. Similarly by calculating the average error percentage for each case of CRP9 OC relay, the area chart illustrating the mean error percentages of the ANFIS model with different cases are shown in Fig. 4. From Figs. 3 and 4, it is inferred that the error percentage of the ANFIS model decreases when the fault current increases. This is an important feature, because high fault currents can cause more damages to power system components. Comparing the average error percentage values of the analytical model, fuzzy model and ANFIS model it is very clear that ANFIS model gives more accurate results because the error is minimized in this model for different MF cases. Of all the cases for RSA20

Table 11 Tuned MF parameters for ANFIS model of CRP9OC relay when five numbers of triangular-type membership functions were used Tuned parameter, a

Tuned parameter, b

Tuned parameter, c

Input 1 (load current) MF1(VL) 1.25 MF2(L) 3.84 MF3(M) 7.297 MF4(H) 11.51 MF5(VH) 15.75

2.675 6.759 11.41 15.75 20

7.287 11.5 15.66 20 24.25

Input 2 (time dial setting) MF1(VL) 2.5 MF2(L) 4 MF3(M) 5.5 MF4(H) 7 MF5(VH) 8.5

4 5.5 7 8.5 10

5.5 7 8.5 10 11.5

Fig. 3. Average error percentage of ANFIS, fuzzy and analytical models for RSA20 OC relay.

901

Fig. 4. Average error percentage of ANFIS, fuzzy and analytical models for CRP9 OC relay.

OC relay ANFIS model with seven number of gauss-type MFs gave very minimum mean error percentage i.e. 0.15%. But for CRP9 OC relay ANFIS model with five number of triangular-type MFs gave very minimum mean error percentage i.e.0.61%. 3.3. Performance comparison of ANFIS model with conventional analytical and fuzzy models The performances of ANFIS model (AOCRS), analytical model and fuzzy model (FOCRS) for the two types (RSA20 and CRP9) OC relay system were evaluated in terms of accuracy in calculating operating time of the OC relay corresponding to the respective load current and TDS and extracted knowledge quality are discussed. 3.3.1. Accuracy AOCRS gave more accurate results. The output of ANFIS-based model was mostly matching the desired operating time values corresponding to the respective load current and TDS. This is because of the highly nonlinear mapping capability and self-adaptive nature of the finetuning of the MFs of ANFIS. Perhaps the results may get still improved if the membership-functions are altered. But the fuzzy model is rarely optimal in terms of reproducing the desired outputs because it uses the human-determined MFs that are not adaptive. Generally, OC relays are set and operate under a wide range of current multiplier setting/TDS. Therefore, each equation in the analytical model produces some errors when a relay operates in a section, which is different from the section of which data is sampled. ANFIS model does not have these sorts of errors. 3.3.2. Extracted knowledge A clear advantage of the FOCRS is that knowledge in terms of fuzzy if-then rules is transparent because they are formulated by human experience and knowledge about the system. But in the rules of AOCRS, the knowledge acquired is not as transparent as the FOCRS. In the rules of AOCRS, the estimate of function, which is the consequence part of the rules, is in the form of a weighted average, not a fuzzy proposition. Therefore, it is not clear how to extract heuristic fuzzy if-then rules from the AOCRS. After the initial training step of the AOCRS,

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902

which is the optimization of the consequence parameters, the system adapts such that the operating time estimate is significantly close to the actually calculated operating time of the OC relay. Therefore, in the backward pass, which uses gradient descent to adapt MF shapes, the network structure does not change significantly. Hence, the output error converges without a large change in the input membership mean and variance values. 4. Conclusion In this paper, for two different OC relays, namely RSA20 and CRP9 ANFIS model is designed and developed with various types of MFs. Both models calculate the operating time of the OC relays for different TDS i.e. When TDS ¼ 4, 8, 14 and 20 for RSA20 and TDS ¼ 4, 7, 10 for CRP9.The simulated results obtained are tabulated and analyzed. From the results, it is inferred that the ANFIS model using seven numbers of Gaussian-type MFs gave more accurate results (i.e. mean average error percentage is 0.15%). The ANFIS model using five numbers of triangular-type MFs gave more accurate results (i.e. mean average error percentage is 0.61%). The major drawback such as modeling error introduced in conventional nonlinear analytical model and fuzzy model were overcome in the proposed ANFIS model. For instance, when a relay operates in a particular range/ section, accurate characteristics shall be obtained using ANFIS model for that specific range with minimum modeling error. This advantage makes the OC relays to be set and operate under a wide range of current multiplier setting/TDS with minimum modeling error. In general modeling error is minimized when ANFIS model is used to develop a digital relay.

Also, the obtained results are compared with the published results obtained by analytical model and fuzzy model [10]. It is found that AOCRS gave more accurate results under varying load current and TDS values. However, the extracted knowledge in AOCRS is not as easy and straight forward as in the case of FOCRS due to utilization of the least-squares estimation in training. Therefore, the final knowledge extracted is not in the form of pure heuristic rules i.e., rules that can be expressed purely by linguistic terms. This reduces the effectiveness of this AOCRS, because it is hard to provide heuristic interpretation to the solution. An ideal NN/FZ scheme would combine the rule extraction power of FOCRS and the speed and accuracy of AOCRS. The proposed AOCRS gave more accurate results. The output of ANFIS-based model was mostly matching the desired operating time values corresponding to the respective load current and TDS. This is because of the highly nonlinear mapping capability and self-adaptive nature of the fine-tuning of the MFs of ANFIS. Perhaps the results may get still improved if the membership-functions are altered. Thus, with the combined synergy of fuzzy logic and neural networks, a better understanding of the heuristics underlying the OC fault relaying schemes can be achieved. Thus, the results obtained suggest new and promising research areas utilizing NN/FZ systems such as ANFIS in digital protective relaying area.

Acknowledgments The authors are thankful to the authorities of Thiagarajar College of Engineering, Madurai-625015, for providing all the facilities to do this research work.

Table A1 Operating time of RSA20 OC relay in ms when TDS ¼ 4,8,14,20 Load current (IL)

Operating time in milliseconds when TDS ¼ 4

Operating time in milliseconds when TDS ¼ 8

Operating time in milliseconds when TDS ¼ 14

Operating time in milliseconds when TDS ¼ 20

4 5.5 7 8.5 10 11.5 13 14.5 16 17.5 19 20.5 22 23.5 25 26.5 28 29.5

4238 2235 1648 1373 1240 1155 1112 1075 1061 1045 1028 1017 1010 1000 1006 1004 1002 1000

5690 3255 2412 2070 1960 1890 1825 1778 1754 1735 1714 1691 1659 1636 1626 1611 1603 1594

8840 5439 4012 3522 3283 3146 3076 3025 2993 2954 2911 2874 2846 2799 2771 2747 2734 2697

11,975 7516 5797 5035 4697 4507 4404 4332 4259 4186 4124 4079 4041 4001 3962 3933 3915 3894

ARTICLE IN PRESS M. Geethanjali, S.M. Raja Slochanal / Neurocomputing 71 (2008) 895–903

903

Table A2 Operating time of CRP9 OC relay when TDS ¼ 4, 6,7,10 Load current (IL)

Operating time in milliseconds when TDS ¼ 4

Operating time in milliseconds when TDS ¼ 6

Operating time in milliseconds when TDS ¼ 7

Operating time in milliseconds when TDS ¼ 10

3 4 5 6 7 8 9 10 12 14 16 18 20

2451 1352 953 .758 653 605 552 516 459 401 375 359 358

3521 2107 1527 1243 1054 934 836 742 658 634 618 608 585

4232 2459 1853 1517 1302 1153 1051 993 894 794 744 715 669

6495 3935 2734 2175 1927 1754 1621 1523 1304 1221 1123 1059 1024

Appendix A For both the relays (RSA 20 and CRP9), the sampled data obtained from [10] for doing modeling are tabulated in Tables A1 and A2. References [1] H. Askarian, K. Faez, H. Kazemi, A new method for overcurrent (OC) relay using neural network and fuzzy logic, in: Proceedings of IEEE Speech and Image Technologies for Telecommunications,TENCON’97, 1997, pp. 407–410. [2] A. Bernieri, D’apuzzo, L. Sansone, M. Savastano, A neural network approach for identification and fault diagnosis on dynamic systems, IEEE Trans. Instrum. Meas. 43 (1994) 867–873. [3] Computer representation of overcurrent relay characteristics—IEEE committee report, IEEE Trans. Power Delivery 4(3) (1989). [4] T. Dalstein, B. Kulicke, Neural network approach to fault classification for high speed protective relaying, IEEE Trans. Power Delivery 10 (2) (1995) 1002–1011. [5] A. Ferrero, S. Sangiovanni, E. Zappitelli, A fuzzy-sets approach to fault type identification in digital relaying, IEEE Trans. Power Delivery 10 (1) (1995) 169–175. [6] IEEE standard inverse-time characteristic equations for over-current relays, IEEE Std. C 37.112, 1996. [7] J.R. Jang, ANFIS: adaptive-network-based fuzzy inference system, IEEE Trans. Syst. Man Cybern. 23 (1993) 665–685. [8] J.R. Jang, C.T. Sun, Neuro-fuzzy modeling and control, Proc. IEEE 83 (1995) 378–406. [9] W.N. Sharp, M.-Y. Chow, S. Briggs, L. Windingland, Methodology using fuzzy logic to optimize feed forward artificial neural network configurations, IEEE Trans. Syst. Man Cybern. 24 (1994) 760–768. [10] H.K. Karegar, H.A. Abyaneh, M. Al-Dabbagh, A flexible approach for overcurrent relay characteristic simulation, Electr. Power Syst. Res. 66 (2003) 233–239. [11] S.M.C.H. Kim, et al., A novel approach for fault classification in transmission lines using a combined adaptive network and fuzzy inference system, Electr. Power Energy Syst. 25 (2003) 747–758. [12] P.G.K. Mclaren, G. Mustaohi, S.C. Hano Benmouyal, A. Giris, C. Henville, M. Kezunovic, L. Kojovic, R. Marttila, M. Meisinger, G. Michel, M.S. Sachdev, V. Skendzic, T.S. Sidhu, D. Tziouvaras, Software models for relays, IEEE Trans. Power Delivery 16 (2001) 238–245.

[13] M.S. Sachdev, T.S. Sidhu, Modelling relays for use in power system protection studies, in: Proceedings of IEE Development in Power System Protection, 2001, pp. 523–526. [14] J.-S.R. Jang, Self-learning fuzzy controllers based on temporal back propagation, IEEE Trans. Neural Networks 3 (5) (1992) 714–723. [15] R. Shekar, B.S. Savitha, H.N. Suresh, R.S. Janardhana Iyengar, Fuzzy logic based over current relay system, in: Proceedings of the Control Instrumentation System Conference (CISCON 2004), pp. 339–343. [16] T.S. Sidhu, H. Singh, M.S. Sachdev, Design implementation and testing of an ANN based fault direction discriminator for protecting transmission lines, IEEE Trans. Power Delivery 10 (2) (1995) 697–706. [17] T.S. Sidhu, M. Hfuda, M.S. Sachdev, A technique for generating computer models of microprocessor-based relays, in: Proceedings of IEEE Communications, Power and Computing, WESCANEX’ 97, 1997, pp. 191–196. [18] H. Wang, W.W.L. Keerthipala, Fuzzy-neuro approach to fault classification for transmission line protection, IEEE Trans. Power Delivery 13 (4) (1998) 1093–1104. M. Geethanjali obtained her BE degree in Electrical engineering in 1989 and Master’s degree in Power Systems Engineering in 1991 from Thiagarajar college of Engineering, Madurai, IndiayShe has been in teaching for the past 15 years. She is presently working as a Lecturer in Electrical Engineering in Thiagarajar college of Engineering, Madurai-625 015.She is now working towards her Ph.D. Her field of interest is Power system protection and control. S. Mary Raja Slochanal received the B.E degree in electrical engineering in 1981, the Master’s degree in power systems engineering (with distinction) in 1985, and the Ph.D degree in power systems in 1997,all from Thiagarajar College of engineering, Madurai, India. She has been involved in teaching for the past 20 years. She is currently a Professor of Electrical engineering at Thiagarajar College of Engineering. She has published 65 research papers. Her fields of interests are power system modeling, FACTS, reliability, and wind energy.