An extreme learning machine based fast and accurate adaptive distance relaying scheme

Electrical Power and Energy Systems 73 (2015) 1002–1014

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

An extreme learning machine based fast and accurate adaptive distance relaying scheme Rahul Dubey a, S.R. Samantaray b,⇑, B.K. Panigrahi a a b

Department of Electrical Engineering, Indian Institute of Technology, Delhi, India Schools of Electrical Sciences, Indian Institute of Technology, Bhubaneswar, India

a r t i c l e

i n f o

Article history: Received 2 December 2014 Received in revised form 12 June 2015 Accepted 16 June 2015

Keywords: Adaptive distance relaying scheme (ADRS) Fast adaptive distance relaying scheme (FADRS) Power swing Artificial neural networks (ANNs) Extreme learning machine (ELM)

a b s t r a c t The ideal trip characteristics of the distance relay is greatly affected by pre-fault system conditions, ground fault resistance, shunt capacitance and mutual coupling of transmission network. This paper presents an extreme learning machine (ELM) based fast and accurate adaptive relaying scheme for stand-alone distance protection of transmission network. The proposed ELM based fast adaptive distance relaying scheme (FADRS) is extensively validated on the two terminal transmission lines with complex mutual coupling and shunt capacitance and, the performance is compared with the conventional artificial neural networks (ANNs) based adaptive distance relaying scheme (ADRS). The simulation results show significant improvement in the performance indices such as relay speed and selectivity. Further, the performance of proposed FADRS is tested for stressed condition such as power swing and found to be effective and reliable. Ó 2015 Elsevier Ltd. All rights reserved.

Introduction The mutual coupling between transmission lines is common in modern power systems network and has significant effect on behavior of the relay protection during faults involving ground. The positive and negative-sequence mutual impedances are negligible. However; the zero-sequence mutual coupling may be significant and should be considered for ground relays setting [1–4]. Initially, due to slow computer and communication technologies, overall integrated protection could not be put into practice. Still, digital relaying provided several advantages over conventional relaying (e.g., improved reliability, self-checking, functional flexibility, and adaptive relaying [5]). Adaptive relaying concepts provide another opportunity for improved performance [6,7]. In recent works [8,9], the adaptive relaying is conceptualized along with the detailed analyses of the apparent impedance as seen from the relaying point considering the mutual coupling, pre-fault condition, remote in-feed/out-feed and fault resistance. Further, single hidden layer feed-forward networks (SLFNs) have been discussed thoroughly by many researchers [10–13] for relaying applications. Two main architectures exist for SLFN, namely: (1) those with additive hidden nodes, and (2) those with radial basis function (RBF) hidden nodes. For many of the ⇑ Corresponding author. Tel.: +91 9437305131; fax: +91 6742301983. E-mail address: [email protected] (S.R. Samantaray). http://dx.doi.org/10.1016/j.ijepes.2015.06.024 0142-0615/Ó 2015 Elsevier Ltd. All rights reserved.

applications using SLFNs, training methods are usually of batch-learning type. Batch learning is usually a time consuming affair as it may involve many iterations during training. In most applications, this may take several minutes to several hours and further, the learning parameters (i.e. learning rate, number of learning epochs, stopping criteria, and other predefined parameters) must be properly chosen to ensure convergence. Also, whenever a new data is received, batch learning uses the past data together with the new data and performs retraining and thus, consuming a lot of time. Extreme learning machine (ELM) proposed by Huang et al. [14] is a new learning scheme for single hidden layer feed forward networks (SLFNs). Compared to those traditional computational intelligence techniques, ELM provides better generalization performance with a much faster learning speed on a number of benchmark problems and engineering applications in regression and classification areas [15–17]. None of the above works has considered mutual coupling and shunt capacitance influences in case of three source simultaneously, along with the variations in the pre-fault load-flow condition and fault resistance while measuring the apparent impedance seen by the distance relay placed on a two-terminal transmission network with three sources. On the other hand, it is also observed that the conventional adaptive distance relaying learning algorithm based on back propagation neural networks (BPNN) and RBFNN is too slow. This paper presents an ELM based comprehensive adaptive distance relaying scheme for stand-alone

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R. Dubey et al. / Electrical Power and Energy Systems 73 (2015) 1002–1014

Nomenclature Esm Esx Esn Z0L1 Z1L1 Z0L2 Z1L2 Z0L3 Z1L3 Z1sm Z0sm Z1sx

source-1 voltage source-2 voltage source-3 voltage zero sequence impedance of Line-1 positive sequence impedance of Line-1 zero sequence impedance of Line-2 positive sequence impedance of Line-2 zero sequence impedance of Line-3 positive sequence impedance of Line-3 positive sequence source-1 impedance zero sequence source-1 impedance positive sequence source-2 impedance

Z0sx Z1sn Z0sn Zc1 Zc2 Zc3 x Rf 0 1 2

zero sequence source-2 impedance positive sequence source-3 impedance zero sequence source-3 impedance shunt impedance of Line-1 shunt impedance of Line-2 shunt impedance of Line-3 fault location (0–80%) fault resistance (0–200 O) stands for zero sequence stands for positive sequence stands for negative sequence

distance protection of two-terminal transmission network with three equivalent source with a single-line-to-ground fault condition considering mutual coupling and shunt capacitance influences, simultaneously, along with the variations in the pre-fault load-flow condition and fault resistance. A mathematical model is developed and the analytical behavior of the relay considering the variations in fault resistance, fault position, and pre-fault power-flow conditions is studied using MATLAB/SIMULINK. The applicability of the adaptive concept for the transmission network protection during the single-line-to-ground fault is discussed. ELM with sigmoid activation function is used in developing the proposed scheme. Extensive test results are presented to investigating the influence of shunt capacitance on the ideal tripping region of an adaptive distance relay for a two-terminal transmission network. The proposed study focuses on building intelligent and adaptive relaying for zone-1 protection only. The rest of the line is protected by zone-2 and zone-3 back-up protection relay.

Z 1L2 ; Z 1L3 , and M 1 1 forms star and is converted into delta and new variable defined below,

Apparent impedance calculation in presence of shunt capacitance and mutual coupling

L4

The system studied is shown in Fig. 1. The lengths of all lines are equal and the Line-1 (i.e. ZL1) has mutual coupling with Line-2 (i.e. ZL2) up to 50% of length starting from relay location and rest 50% length of Line-1 has mutual coupling with Line-3 (i.e. ZL3) along with Line-2. The calculation of apparent impedance for phase-A to ground (A–G) fault is carried out as follows with the following the abbreviations defined in comprehensive section on nomenclature in the beginning of the paper. (i) Calculation for pre-fault voltage and current through line ZL1: All capacitances assumed to be on buses. The current can be calculated by superposition theorem. From Fig. 1.

Z c4 ¼

Z c1 Z c2 ; Z c1 þ Z c2

Z c5 ¼

Z c2 Z c3 ; Z c2 þ Z c3

Z c6 ¼

Z c1 Z c3 Z c1 þ Z c3

M1

1

¼

Z 1sx Z 1c2 Z 1c3 ; Z 1sx Z 1c2 þ Z 1c2 Z 1c3 þ Z 1sx Z 1c3

1

¼ Z 1L2 M 1

D1

1

¼

n1 1 ; M1 1

¼

L1 1 D2 1 ; L1 1 þ D2 1

L1

2

1

þ M 1 1 Z 1L3 þ Z 1L2 Z 1L3 D2

1

¼

R1

L3

1

M c1 ¼

Z 1cm Z 1cn Z 1cm þ Z 1cn

ð2Þ

2

¼

M3

L1 2 D1 1 ; þ D1 1 þ R1 2 2 R1 2 L 1 2 ¼ L1 2 þ D1 1 þ R1 2

¼ 1

L1

D3

1

¼

n1 1 Z 1L2

ð4Þ

R1 1 D 3 1 R1 1 þ D3 1

R3

1

¼

L1

ð5Þ 2

forms delta

R1 2 D1 1 ; þ D1 1 þ R1 2 2 ð6Þ

Further from study it is found out that:

¼ xZ 1L1 þ L3 1 ; R4 1 ¼ ð1  xÞZ 1L1 þ R3 1 ; L4 1 R4 1 ; M5 1 ¼ M4 1 þ M3 1 M4 1 ¼ L4 1 þ R4 1 1

M6

1

¼

ð7Þ

M 5 1 Mc1 ; Z positive ¼ M6 1 ; Z negative ¼ Z positive ; Z 2 ¼ Z 1 M5 1 þ M c1 ð8Þ

(ii) The zero sequence networks: The zero sequence networks for first 50% of Line-1 starting from relay location will be different for rest 50% of line as rest 50% is having mutual coupling with Line-2 as well as Line-3. The above diagram is applicable for fault occurring in first 50% section only. The detailed diagrams are shown in Fig. 5.

Z 0cm1 Z 0cm2 Z 0cm1 Z 0cmn ; Z 0c2 ¼ ; Z 0cm1 þ Z 0cm2 Z 0cm1 þ Z 0cmn Z 0cn1 Z 0cmn Z 0cn1 Z 0cn3 ¼ ; Z 0c4 ¼ Z 0cn1 þ Z 0cmn Z 0cn1 þ Z 0cn3

Z 0c1 ¼

Z 0cn3 Z 0cx3 ; Z 0cn3 þ Z 0cx3 Z 0cx2 Z 0cmx ¼ ; Z 0cx2 þ Z 0cmx

Z 0cx2 Z 0cx3 ; Z 0cx2 þ Z 0cx3 Z 0cm2 Z 0cmx ¼ Z 0cm2 þ Z 0cmx

Z 0c5 ¼

Z 0c6 ¼

Z 0c7

Z 0c8

Where,

ð1Þ

n1 1 ; Z 1L3

ð3Þ

From study it is observed that, D1 1 ; L1 2 , and R1 and is converted into star:-

Z 0c3

Z L1 ; Z L2 , and Z L3 forms a delta, this is converted into star is shown in Fig. 2. Fig. 3 shows the Sequence Schematic diagram for A–G fault. The positive sequence network reduced form shown in Fig. 4. Where new variable is defined below,

Z 1sm Z 1sm Z 1c2 L1 1 ¼ ; Z 1sm Z 1sm þ Z 1sm Z 1c2 þ Z 1sm Z 1c2 Z 1sn Z 1cn Z 1c3 R1 1 ¼ Z 1sn Z 1cn þ Z 1cn Z 1c3 þ Z 1sn Z 1c3

n1

Z ax ¼ Z 1L0 

Z 20mu12 Z 2L0

Z bx ¼ Z 2L0 

Z 20mu12 Z 1L0

Z 2L0 Z mx ¼ ZZ1L0  Z 0mu12 0mu12

Zs ¼ Z1 þ Z2 þ Z0

ð9Þ

ð10Þ

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R. Dubey et al. / Electrical Power and Energy Systems 73 (2015) 1002–1014

xZL1

(1-x) ZL1

Rf Zc1

M

ZL1

Zsm

N

Zc1

Zsn

Esn

Esm Zc2 ZL2

Zc2

Zc3

ZL3

X

Zc3

Zsx

Esx Fig. 1. Phase-A to ground fault model for three source equivalent system including shunt capacitance and mutual coupling.

M Zsm

Esm

S1

N

S3

Zsn

S2

Zc4

Esn

Zc6 X Zsx

Zc5

Esx Fig. 2. Pre-fault reduced model for three source equivalent system.

(iii) Fault current through faulted lines: Positive sequence

Positive Sequence

Negative Sequence

F1 1 ¼

M c1 ; F2 M 4 1 þ M 3 1 þ M c1

1

¼

3Rf

R3 1 þ ð1  xÞZ 1L1 ; I1 ¼ F 1 1 F 2 1 I1F R3 1 þ Z 1L1 þ L3 1 ð12Þ

Zero sequence

V1

Zero Sequence

0

¼ I0F Z bus ð2; 1Þ; V 2

0

¼ I0F Z bus ð2; 2Þ; I0 ¼ ðV 1 0  V 2 0 Þy1

2

ð13Þ V8

0

¼ I0F Z bus ð8; 2Þ; I0

2

¼ ðV 1

0

 V 8 0 Þy1

ð14Þ

8

Post-fault voltage

Fig. 3. Sequence Schematic diagram for A–G fault.

V postf ¼ ðI0F þ I1F þ I2F ÞRf þ ðIpref þ I0

Y bus ¼ matrix ½8  8

2

xZ 0mu12 þ I0 xZ L1

Z L1

þ I1 þ I2 Þ xZ L1

0

ð15Þ

0

Z bus ¼ Y 1 bus

Post fault current through the relay: From above study it can be seen that ð1  xÞZ 1L1 ; R1 1 , and Z 1L3 forms star and this is converted to delta,

Z 0 ¼ Z bus ð2; 2Þ

n2

1

¼ ð1  xÞZ 1L1 R1

D4

1

¼

I1F ¼

V pref ; I2F ¼ I1F ; I0F ¼ I1F Z s þ 3Rf

ð11Þ

n2 1 ; R1 1

D5

1

1

¼

þ Z 1L3 R1 n2 1 ; Z 1L3

1

D6

þ ð1  xÞZ 1L3 Z 1L1 1

¼

n2 1 ð1  xÞZ 1L1

ð16Þ ð17Þ

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R. Dubey et al. / Electrical Power and Energy Systems 73 (2015) 1002–1014

Z1cm

Z1cm

Z1cn

Z1cn

Esn

Esm Z1sm

Z1sn

(1-x)Z1L1

xZ1L1 F

Z1c2

Z1L2

Z1c3

Z1L3 Z1c3

Z1c2 Z1sx

Esx

Fig. 4. Equivalent positive sequence network diagram.

Z0cm1 M

Z0cm1 xZ0L1

Z0sm

Z0cmn

Z0cm2

Z0cm2

Z0cn1

Z0cn1 0.5Z0L1

(0.5-x)Z0L1

Z0mu12 xZ0L2

Z0cmn

Z0mu12

Z0sn

Zomu13

(0.5-x)Z0L2 Z0cmx

N

0.5Z0L3 Z0cmx

Z0cn3

Z0cn3

0.5Z0L2 Z0cx2

0.5Z0L3 Z0cx3

Z0mu23

X Z0cx2

Z0cx3

Z0sx

I0f

Fig. 5. Equivalent zero sequence network diagram.

From analysis it can be seen,

X 16 ¼

M 1 1 D6 1 ; M 1 1 þ D6 1

xZ 1L1 ; Z 1L2 , and D4

S1

1

S3

1

X 17 ¼ 1

M c1 D5 1 Mc1 þ D5 1

ð18Þ

X 18 ¼ S1

1

þ L1 1 ;

X 19 ¼ X 16 þ S3 1 ;

X 20 ¼

X 18 X 19 X 18 þ X 19

ð20Þ

forms delta and this is converted into star

xZ 1L1 Z 2L1 ; xZ 1L1 þ Z 2L1 þ D4 1 D4 1 Z 2L1 ¼ xZ 1L1 þ Z 2L1 þ D4 1 ¼

From above analysis it can be seen that,

S2

1

¼

X 17 X 19 ; F 12 ¼ ; X 17 þ X 20 þ S2 1 X 19 þ X 18 Z 1c2 Z 1sm F 13 ¼ ; F 14 ¼ Z 1c2 þ Z 1sm F 13 þ Z 1cm

F 11 ¼

xZ 1L1 D4 1 ; xZ 1L1 þ Z 2L1 þ D4 1 ð19Þ

F 13

ð21Þ

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Current through

Zero sequence voltages:

Z 1cm ; I1cm ¼ F 11 F 12 F 14 I1F Ir1

¼ I1  I1cm1 ; Ir2

postf

Similarly, Ir0

I0cm1 ¼

postf

V1

postf

¼ Ir1

I0

is:-

¼ Ir

pref

þ Ir1

postf

þ Ir2

postf

þ Ir0

2

¼ ðV 1 V6

V1 0 V1 0 ; I0cm2 ¼ ; Ir0 postf ¼ I0 I0cm1 ; I0 r2 ¼ I0 2 I0cm2 Z 0cm1 Z 0cm2

I0

postf

þ K:Ir0

postf

þ K0

Z 0L1  Z 1L1 ; Z 1L1

K0

12

¼

12 I 0 r2

¼ ðV 7

0

¼ I0

þ I0

3 1

 V 6 0 Þy6

ð28Þ

7

ð29Þ

3 2

Z L1

þ I1 þ I2 ÞxZ L1

1

þ I0 xZ 1

0

Iocm1 ¼ Ir0

K0

13

¼

Ir

postf

¼ I0

3

 I0cx3

ð31Þ

¼ Ir

pref

þ Ir0

postf

þ Ir1

postf

þ Ir2

ð32Þ

postf

V postf Ir

postf

þ KIr0

postf

þ ðK 0

12 I0 r2

0:5 Þ þ ðK 0 x

13 I 0 r3

x0:5 x

Þ

ð33Þ

3

2

4

Z0c3

Z0c2

0.5(Z0L1-Z0mu13)

x(Z0L1-Z0mu12) x(Z0L2-Z0mu12) 8

r3

Apparent impedance seen by relay:

Zr ¼

Z0c1

V1 0 V1 0 V6 0 ; Iocm2 ¼ ; Iocx3 ¼ ; Z 0cm1 Z 0cm2 Z 0cx3 postf ¼ I 0  I0cm1 ; I0 r2 ¼ I 0 2  I0cm2 ; I0

Relay current:

Z 0mu13 Z 1L1

1

ð30Þ

Zero sequence current through relay:

Z 0 ¼ Z bus ð3; 3Þ

xZ0mu12

3

ð27Þ

þ 0:5I0 2 Z 0mu12 þ ðx  0:5ÞI0 3 Z 0mu13 ð25Þ

postf

Similarly the circuit is being separately reduced for Fig. 6 and network analysis is carried out.

Z0sm

3 1

V postf ¼ ðI0F þ I1F þ I2F ÞRf þ ðIpref

ð26Þ

Z 0mu12 ; Z 1L1

¼ I0F Z bus ð8; 3Þ

¼ I0F Z bus ð7; 3Þ;

0

¼ I0F Z bus ð6; 3Þ; I0

¼ ðV 6 0 Þ=Z 0c6 ; I0

3 2

where

K¼

 V 8 0 Þy1 8 ; V 7

0

0

0

Post-fault voltage:

ð24Þ

V postf Ir

¼ I0F Z bus ð2; 3Þ;

ð23Þ

Apparent impedance seen by relay,

Zr ¼

0

I0 ¼ ðV 1 0  V 2 0 Þy1 2 ; V 8

Relay current, postf

¼  I0F Z bus ð1; 3Þ; V 2

ð22Þ

postf

V1 0 V1 0 I0cm1 ¼ ; I0cm2 ¼ ; Ir0 postf ¼ I0 I0cm1 ; I0 r2 ¼ I0 2 I0cm2 Z 0cm1 Z 0cm2 Ir

0

7

0.5Z0mu13

Z0sn

0.5(Z0L3-Z0mu13)

5

Z0c4

Z0c8

Z0c5 Z0c7

0.5(Z0L3-Z0mu23)

0.5(Z0L2-Z0mu23)

Z0c6 6 0.5Z0mu23

Z0sx

xZax I0f xZmx

-xZmx

-xZmx

xZmx

xZbx Fig. 6. Equivalent of mutual coupling lines for three sources equivalent system for A–G fault on first 50% of Line-1 having mutual coupling with Line-2 only as seen from relay location at substation M.

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R. Dubey et al. / Electrical Power and Energy Systems 73 (2015) 1002–1014

Hðw1 ; w2 ; . . . ; we ; b1 ; b2 ; . . . ; be ; x1 ; x2 ; . . . ; xN Þ N N 2 3 Gða1 ; b1 ; x1 Þ :: Gðae :be ; x1 Þ N N 6 7 : :: : ¼4 5 Gða1 :b1 ; xN Þ :: Gðae :be ; xN Þ e

Extreme learning machine (ELM) ELM is a single hidden-layer feed forward neural network (SLFN) and its learning speed is faster than the traditional feed-forward network learning algorithm like back propagation algorithm while obtaining better generalization performance. The structure of ELM model is given in Fig. 7. ELM randomly chooses and fixes the weights between input neurons and hidden neurons based on continuous probability density function, and then analytically determines the weights between hidden neurons and output neurons of the SLFN. Consider N arbitrary distinct samples ðxi ; t i Þ,

N

N

ð34Þ

i¼1

where ai ¼ ½ai1 ; ai2 ; . . . ; ain T is the weight vector connecting ith hid-

tT1

N N

3

6 : 7 6 7 & T¼6 7 4 : 5 t TN

N m

ð38Þ

Nm

^ ¼ Hy T b

den nodes and the input node, bi ¼ ½bi1 ; bi2 ; . . . ; bim T is the weight vector connecting the ith hidden node and the output nodes, and bi is the threshold of the ith hidden node. ai :xj denote the inner proe hidden nodes with duct of ai and xj . If the standard SLFNs with N

ð39Þ

where T is the target matrix, H is the hidden layer output matrix, Hy is the Moore–Penrose generalized inverse of the matrix H [17] and b is the hidden layer output matrix. By using the Moore–Penrose inverse method, ELM tends to obtain a good generalization performance with a radically increased learning speed.

activation function g(x) can approximate these N samples with zero error, then we have

e N X koj  t j k ¼ 0

N

H is called the hidden layer output matrix of the neural network; the ith column of H is the ith hidden node output with respect to inputs x1 ; x2 ; . . . ; xN . Unlike SLFN, in ELM, the input weights and hidden biases are randomly generated and do not require any tuning. The output weights linking the hidden layer to the output layer can be determined in a similar fashion as finding the least-square solution to the given linear system. The minimum norm least-square (LS) solution to the linear system (36) is

e hidden nodes and activaFor this data, a standard SLFN with N tion function G(x) can be mathematically modeled as [14].

i¼1

2

bT1 7 6 6 : 7 7 b¼6 6 : 7 5 4 bTe e

where xi ¼ ½xi1 ; xi2 ; . . . ; xin T 2 Rn and t i ¼ ½ti1 ; t i2 ; . . . ; tim T 2 Rm

e e N N X X bi Gi ðxj Þ ¼ bi Gðai :; bi ; xj Þ ¼ oj ; j ¼ 1; 2; . . . N

3

2

ð37Þ

ELM based fast adaptive relaying

ð35Þ

j¼1

(i) Ideal trip region

where oj is the actual output value of the SLFN. This implies the existence of bi ; ai and bi such that the above N equations can be written compactly as

Hb ¼ T

Adaptive protection requires an estimation of the actual power system condition before the fault. In this paper, an adaptive distance relaying concept is presented to calculate the appropriate tripping impedance under the simultaneous influence of the complex mutual coupling and shunt capacitances of a two-terminal parallel transmission line. To avoid the implantation of

ð36Þ

where

OJ

Output Nodes

β1

β2

β3

βn

βL

L-Hidden Nodes 1

2

x1

n

3

x2

xn

L

n-Input Nodes

Fig. 7. Architecture of the ELM based ADRS.

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R. Dubey et al. / Electrical Power and Energy Systems 73 (2015) 1002–1014

communication technology, only local measurements at the sending end are used to estimate the entire power system operating condition. From this estimate, the appropriate relay settings are calculated. The ideal operating region of a distance relay within the normal range of real and reactive power flows can be calculated off-line based on a given system configuration and pre-fault flows. With these assumptions, the typical operating characteristic of a distance relay is depicted in Fig. 8. In this figure, the four boundaries (1, 2, 3, 4) of the trip region in the R–X plane are defined as follows: boundary ‘‘1’’ represents the relay reach during the fault at 80% of the line length with various fault resistances ranging from 0 to 200 O, boundary ‘‘2’’ represents the relay reach during the 200 O-fault resistance with various fault locations ranging from 0% to 80% of the line length, boundary ‘‘3’’ represents the relay reach during the fault at the relay point with various fault resistances ranging from 0 to 200 O and boundary ‘‘4’’ represents the relay reach during the solid fault with various fault locations ranging from 0% to 80% of the line length.

(iii) Selection of activation function and number of hidden node for the proposed ELM based ADRS The relationship between performance of ELM and number of hidden neuron for four different trip boundaries (1, 2, 3 and 4) is shown in Fig. 9. In the proposed ELM based ADRS scheme, sigmoid activation function is chosen after rigorous testing. The relationships between the training accuracy and number of hidden neuron during training of the ELM method are as shown in Fig. 10. The number of hidden neuron chosen for proposed ELM based ADRS scheme is 12, which provide minimum root mean square error (RMSE). Results and analysis (i) Power system and parameter initialization Computer simulation for different conditions has been widely investigated for a typical 400 kV, 128 km, 60 Hz overhead transmission line. The trip boundaries are set for different operating conditions of the three sources connected with transmission network in presence of shunt capacitance. Initially, the values of voltage and impedances are chosen as follows for setting the trip boundaries,

(ii) Input feature selection for training ELM To incorporate the effect of pre-fault active and reactive power flows on the relay trip region, the change in active and reactive power flows (DP, DQ) with respect to a constant reference values is used as the one of the input parameters to train the ELM. To train the ELM to adapt boundary ‘‘1’’, the three input parameters are taken as DP, DQ and the various values of resistance R1 along the boundary ‘‘1’’ with X1 as the corresponding output parameter. Similarly, the three input parameters DP, DQ and the various values of resistance X2 along with the boundary ‘‘2’’ with R2 as the corresponding output parameter are considered. The procedure used to train the ELM, which adapts to the boundary ‘‘3’’ are the same as the procedure of boundary ‘‘1’’ with corresponding R3, X3 parameters. Further, training the ELM to adapt boundary ‘‘4’’, the input and output parameters are the same as that of the ELM for boundary ‘‘2’’ but with corresponding X4 and R4 values. The aforementioned four different ELM were trained individually and the corresponding outputs of trained ELM are used together to estimate the trip region for a given pre-fault condition. The training sample data is generated for various values of active power-flow (P) ranging from 800 to 1000 MW and for various values of reactive power (Q) flow ranging from 200 to 300 MVAR, and a total of 18 sets of different cases are considered. As observed from Table 1, there are 18 operating conditions considered in this study. For each operating condition, the distance relay will have the trip region that has four boundaries (non-linear) as shown in Fig. 8 and for each boundary, 81 training samples in normalized from are generated. Therefore, there are 18  4  81 = 5832 samples chosen for training the ELM based ADRS. To avoid training difficulties caused by the different units of input and output features. Normalized value of xi and oj is used.

Z 1L1 ¼ Z 1L2 ¼ Z 1L3 ¼ 38:359\85:529; Z 0L1 ¼ Z 0L2 ¼ Z 0L3 ¼ 139:846\69:17; Z 0mu12 ¼ Z 0mu13 ¼ Z 0mu23 ¼ 0:65  Z 0L1 ; Z 1sm ¼ Z 1sx ¼ 20\85; Z 0sm ¼ Z 0sx ¼ 30\85; Z 1sn ¼ 10\85; Z 0sn ¼ 20\85; Y sh1 ¼ ð0:00 þ j  0:10371Þ  102 =kmðp:uÞ; Y sh0 ¼ ð0:00 þ j  0:07083Þ  102 =kmðp:uÞ If the power system (Fig. 1) operating conditions, line impedance, and bus configuration of parallel lines do not change during normal operation, the error in measuring relay impedance may be compensated by selecting proper relay settings, such as changing the trip zone coverage settings or by changing the compensation factors [8,9] as shown in Fig. 11(a). It is observed from Fig. 11(b) that the trip boundary is affected by shunt capacitance. Even though for zero fault resistance, the apparent impedance will not be the actual line positive sequence impedance from the relaying point to the fault. For higher value of fault resistance, the effect of shunt capacitance influence is more pronounced. Computer simulation for different system conditions are investigated with and without shunt capacitance influences as shown in Fig. 11(b). The operating region of relay on the R–X plane for various load conditions under normal active and reactive power flows the studied have been carried out with such variation is as shown in Fig. 12(a) and (b). From these figures, it is found that the

50 Rf = 0-200 ohms, Length = 80% (Boundary-1)

X (Ohm)

40 30

Rf = 0 ohms, Length = 0-80% (Boundary-4)

Rf = 200 ohms, Length = 0-80% (Boundary-2)

20 10 0 -200

Rf = 0-200 ohms, Length = 0% (Boundary-3)

-150

-100

-50

0

50

100

150

200

R (Ohm) Fig. 8. Ideal operating regions of the distance relay.

250

300

350

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R. Dubey et al. / Electrical Power and Energy Systems 73 (2015) 1002–1014 Table 1 The system operating condition for creating training data set for ELM. Sl. no

Esm(real) (p.u)

Esn(img) (p.u)

Esn(real) (p.u)

Esn(img) (p.u)

Esx(real) (p.u)

Esx(img) (p.u)

P (MVA)

Q (MVA)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1.00925 1.0191 1.03916 1.01905 1.03909 1.02924 1.02931 1.03916 1.04915 1.01918 1.02937 1.03923 1.0191 0.99926 1.03916 1.01938 1.0093 1.03909

0.03877 0.04271 0.04173 0.04271 0.04355 0.03954 0.03774 0.04174 0.0403 0.04093 0.03595 0.03992 0.04271 0.03839 0.041737 0.035597 0.03877 0.04355

0.96513 0.94912 0.959 0.96003 0.96963 0.94706 0.96923 0.96799 0.96769 0.95694 0.95739 0.95617 0.95614 0.92381 0.95452 0.9561 0.93276 0.9527

0.16176 0.16899 0.15843 0.17582 0.16757 0.16885 0.18107 0.18226 0.17839 0.19697 0.18966 0.19069 0.21031 0.20822 0.20364 0.21509 0.21843 0.21654

0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995

0.16187 0.16187 0.16187 0.16187 0.16187 0.16187 0.16187 0.16187 0.16187 0.16187 0.16187 0.16187 0.16187 0.16187 0.16187 0.16187 0.16187 0.16187

550 550 550 600 600 600 650 650 650 700 700 700 750 750 750 800 800 800

150 200 250 150 200 250 150 200 250 150 200 250 150 200 250 150 200 250

1

0.15

Normalized RMSE

Normalized RMSE

0.2

Trip boundary-1

0.1 0.05 0

0

5

10

0.8

0.4 0.2 0

15

Trip boundary-2

0.6

0

Number of hidden neuron

10

15

0.015

0.06

Normalized RMSE

Normalized RMSE

0.08

Trip boundary-3

0.04 0.02 0

5

Number of hidden neuron

0

5

10

0.005

0

15

Trip boundary-4

0.01

0

Number of hidden neuron

5

10

15

Number of hidden neuron

Fig. 9. Normalized RMSE vs. number of hidden neuron for four different trip boundaries (1, 2, 3 and 4).

Training Accuracy (%)

1 0.9

ELM Training Accuracy

0.8 0.7 0.6 0.5 0.4 2

4

6

8

10

12

14

16

Number of Hidden Neurons Fig. 10. Relationships between the training accuracy and number of hidden neuron during training of the ELM.

boundaries 1, 2, 3 and 4 of the trip regions are non-linear in natures, which are different for different operating conditions as depicted in Table 1. (ii) Testing of ELM based FADRS

To test the performance accuracy of the ELM based ADRS, two test cases were generated for different values of P and Q power flows within the range of the training set which are listed in Table 1. Similarly, for the testing purpose, operating conditions as given in Table 2 are considered (for which 2  4  20 = 160

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R. Dubey et al. / Electrical Power and Energy Systems 73 (2015) 1002–1014 3

K0L with shunt capacitance only

Trip region with mutual coupling without shunt capacitance

60

OL

)

2.5 X(Ohm)

Compensation factor (K

50 2

K0L with mutual coupling

X (Ohm)

40

& shunt capacitance effect

1.5

1

30

20

0.5

0

R(Ohm)

10

0

0.2

0.4

0.6

0

0.8

Trip region with mutual coupling & shunt capacitance 0

25

50

75 100 125 150 175 200 225 250

(a) Fault Location (%)

(b) R (Ohm)

Fig. 11. (a) Variation of compensation factor with fault location. (b) Trip boundary with and without shunt capacitance.

80

60

Trip region with change in reactive power

Trip region with change in active power

70

50

data set-3

40

data set-1

30

data set-10

X (Ohm)

X (Ohm)

60

40

data set-2 30

data set-16

20

50

data set-1

20 10 0

10 0

100

200

0

300

0

100

200

300

(b) R (Ohm)

(a) R (Ohm)

Fig. 12. (a) Trip boundary of the distance relay during change in active power for data sets 1, 10, and 16. (b) Trip boundary of the distance relay during change in reactive power for data sets 1, 2, and 3.

Table 2 The system operating condition for creating testing data set for ELM. Test no.

Esm(real) (p.u)

Esn(img) (p.u)

Esn(real) (p.u)

Esn(img) (p.u)

Esx(real) (p.u)

Esx(img) (p.u)

P (MVA)

Q (MVA)

1 2

1.00926 1.01931

0.03877 0.03738

0.94216 0.94064

0.18419 0.19183

0.9995 0.9995

0.16187 0.16187

650 700

175 225

Substation Computer VBUS IBUS Central Computer

Status of Equipment

Pre-fault Measurement & Computation

P

ELM

Q

Fig. 13. Hierarchical structure of fast adaptive distance relay.

Protective Relay

Data Acquisition

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60

60

Test data set-1

50

40 X (Ohm)

40

X (Ohm)

Test data set-2

50

30

30 20

20

Ideal Predicted by ELM

10

10

Ideal Predicted by ELM

0

0 0

50

100

150

200

250

0

50

R (Ohm)

100

150

200

250

R (Ohm)

Fig. 14. ELM-based predicted trip region for test data sets 1 and 2.

Table 3 ELM predicted boundary outputs for test data set-1. Sl. no.

Trip boundary-1 Desired output (O)

ELM output (O)

% error

Desired output (O)

ELM output (O)

% error

Desired output (O)

ELM output (O)

% error

Desired output (O)

ELM output (O)

% error

1 2 3 4 5 6 7 8 9 10 11 12

30.96486 32.63283 34.26753 35.86315 37.4159 38.92355 40.38494 41.79975 43.16823 44.49106 45.76925 47.00398

30.87723 32.61331 34.27016 35.85469 37.37044 38.82019 40.20707 41.5346 42.80623 44.025 45.19356 46.31435

0.28 0.06 0.01 0.02 0.12 0.27 0.44 0.63 0.84 1.05 1.26 1.47

113.929 119.0701 124.6813 130.8283 137.5898 145.06 153.3533 162.6094 179.6656 183.5424 187.7921 192.4288

116.1153 121.1673 126.6756 132.7979 139.673 147.4151 156.1077 165.7943 179.1393 185.1336 191.4017 197.9392

1.92 1.76 1.60 1.51 1.51 1.62 1.80 1.96 0.29 0.87 1.92 2.86

1.336632 2.603768 3.840847 5.048925 6.229012 7.382068 8.509011 9.610719 10.68803 11.74175 12.77263 13.78142

1.368853 2.652008 3.902851 5.12207 6.309967 7.466882 8.593458 9.690717 10.75998 11.80269 12.82028 13.81403

2.41 1.85 1.61 1.45 1.30 1.15 0.99 0.83 0.67 0.52 0.37 0.24

0.300408 0.376123 0.452146 0.528509 0.605242 0.682372 0.759928 0.837935 0.916416 0.995391 1.074879 1.154891

0.297491 0.373667 0.450307 0.527393 0.604901 0.68281 0.761098 0.839742 0.918717 0.997998 1.077561 1.157379

0.97 0.65 0.41 0.21 0.06 0.06 0.15 0.22 0.25 0.26 0.25 0.22

Trip boundary-2

Trip boundary-3

Trip boundary-4

Table 4 ELM predicted boundary outputs for test data set-2. Sl. no.

Trip boundary-1 Desired output (O)

ELM output (O)

% error

Desired output (O)

Trip boundary-2 ELM output (O)

% error

Desired output (O)

Trip boundary-3 ELM output (O)

% error

Desired output (O)

ELM output (O)

% error

1 2 3 4 5 6 7 8 9 10 11 12 13

30.96384 32.55119 34.16985 35.79881 37.42265 39.03006 40.61286 42.16522 43.68307 45.16372 46.60545 48.00738 49.36915

30.89098 32.5222 34.16099 35.80188 37.42998 39.03301 40.60301 42.1352 43.62703 45.07736 46.48572 47.85194 49.17609

0.24 0.09 0.03 0.01 0.02 0.01 0.02 0.07 0.13 0.19 0.26 0.32 0.39

111.7571 116.6956 122.0773 127.9633 134.4257 141.5514 149.4448 158.2336 174.3567 178.0073 182.0053 186.3626 191.0964

111.8989 116.8891 122.2883 128.2112 134.7815 142.1313 150.3991 159.7281 171.1838 176.7754 182.6586 188.8379 195.3159

0.13 0.17 0.17 0.19 0.26 0.41 0.64 0.94 1.82 0.69 0.36 1.33 2.21

1.328684 2.592495 3.830518 5.043482 6.232094 7.397036 8.538967 9.658525 10.75633 11.83297 12.88903 13.92506 14.9416

1.36422 2.649871 3.907355 5.138332 6.344288 7.526311 8.685099 9.821067 10.93451 12.02574 13.09523 14.14364 15.1718

2.67 2.21 2.01 1.88 1.80 1.75 1.71 1.68 1.66 1.63 1.60 1.57 1.54

1.989332 2.068711 2.148185 2.227738 2.307347 2.386983 2.466605 0.300428 0.37615 0.452183 0.528556 0.605299 0.682442

1.992116 2.072041 2.151816 2.231409 2.310784 2.389904 2.468729 0.297904 0.373645 0.449898 0.526642 0.603858 0.681522

0.14 0.16 0.17 0.16 0.15 0.12 0.09 0.84 0.67 0.51 0.36 0.24 0.13

samples were generated for testing the ELM based ADRS). Total 120 different test samples were generated at regular intervals along the line, for different values of fault resistance (Rf) varies from 0 to 200 O. Fig. 13 shows hierarchical structure of fast adaptive distance relay. The generated test samples were different from the data samples considered to train the network. As an example, test results for the data set-1 and data set-2 operating condition listed in Table 2 for a required boundary are as depicted in Fig. 14. It is observed from Fig. 14 that testing results of the ELM-based network are able to give a successful prediction. For

Trip boundary-4

most cases, the ELM model is able to respond with negligible error. Therefore, the proposed ELM model performs accurately with high accuracy and enhances the performance of the distance relaying scheme under the influences of the mutual coupling and shunt capacitance effect of a two-terminal transmission line. The ELM module results for a few samples of test data set-1 and test data set-2 are presented in Tables 3 and 4. It is observed from Tables 3 and 4 that the trained ELM networks adapt to the operating conditions quite accurately. So based on the operating condition and the variation in the value of the proposed measured impedance

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Table 5 Comparative assessment. Trip boundary

Trip Trip Trip Trip

boundary-1 boundary-2 boundary-3 boundary-4

Training time response (s)

Maximum |% error|

ANN (BPNN, RBFNN) based ADRS [7–9]

ELM based FADRS

ANN (BPNN, RBFNN) based ADRS [7–9]

ELM based FADRS

20.5 7.3 12.74 3

0.314 0.2 0.30 0.157

1.49 2.86 3 0.9

1.49 2.86 2.67 1

60 Relay Output=Trip

50 Mho Relay

40

X (Ohm)

30 20

Impedance trajectory A-G fault (R f=20 Ohm) Impedance trajectory A-G-fault (R f=50 Ohm)

10 0 Proposed ELM ADRS schem

-10 -20 -30 -40 -50

0

50

100

150

200

250

R (Ohm) Fig. 15. Impedance trajectory during A–G fault.

considering the mutual coupling and shunt capacitance effects, the adaptive relay will be able to take more appropriate trip (or no-trip) action as demanded under a particular operating condition. Fig. 14 shows the testing accuracy of trip boundaries-1, 2, 3 and 4 for wide variations in fault resistance (Rf) 0–200 O with fault location ranging from 0% to 80% (of transmission line length). (iii) Performance assessment of proposed FADRS over conventional ADRS

comparing the performance of the proposed FADRS with the conventional relay such as MHO relay. The comparison with conventional relay such as MHO relay is given in Fig. 15 and it is observed that the MHO relay fails to operate in case of fault with high fault resistance (Rf = 20 O and 50 O) whereas the proposed relay succeeds. The proposed scheme provides wider margin of relay characteristics to accommodate the high resistance fault cases where the conventional MHO relay fails. (iv) Performance of proposed FADRS during stress condition

The adaptive distance relaying scheme (ADRS) for transmission networks with line-to-ground fault (a–g) situation is proposed and the impact of variations in operating conditions on the relay characteristics is studied. It is observed that the trip boundaries are significantly affected while the system configuration changes. Thus, the relay setting must be accordingly done to accommodate the changes in power system operating conditions during fault process. The conventional ANN (BPNN and RBFNN) based ADRS [8,9] uses batch learning process which is usually a time consuming process as it may involve many iterations during training. In most applications, this may take several minutes to several hours and further, the learning parameters (i.e. learning rate, number of learning epochs, stopping criteria, and other predefined parameters) must be properly chosen to ensure convergence. Also, whenever a new data is received, the batch learning uses the past data together with the new data and performs a retraining and thus, consumes a lot of time. Proposed extreme learning machine (ELM) based FADRS uses single hidden layer feed forward networks (SLFNs) [12–17]. Compared to those traditional computational intelligence (BPNN and RBFNN [7–9]) techniques, ELM provides better generalization performance with a much faster learning speed on a given problems. In case of ELM based FADRS, training time is much less compared to the conventional ANN based ADRS (Table 5). Further

The performance of the proposed ELM based FADRS are tested under stressed condition such as power swing [18–24]. Power swing is one of the major issues and the relay must perform accordingly. During power swing, the relay must not issue the tripping signal whereas the relay must issue the tripping signal for faults during power swing. Fig. 16(a) shows the apparent impedance trajectory seen by relay at bus M during the fast swing with a frequency of 5 Hz, whereas Fig. 16(b) shows the apparent impedance trajectory seen by relay at bus M for A–G fault during power swing. It is clearly observed that the impedance trajectory does not enter into the tripping zone for power swing case and enters into the tripping zone in the case of faults during power swing. This improves the reliability of the relay over the existing relays in distinguishing power swing and fault during power swing. Further, the apparent impedance is evaluated using the computed positive, negative and zero sequence components from the estimated phasors. The experimental validation is carried out on OPAL-RT eMEGAsim Real Time Simulator OP5600 platform. The simulator contains a powerful real time target computer equipped with up to 12, 3.3-GHz processor cores with a real-time operating system from QNX and Red Hat Linux. RT-LAB software is a distributed real time platform fully integrated with MATLAB/Simulink. It is the software that is used to conduct real time simulation of Simulink

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100 Relay Output=No Trip

X(Ohm)

50 0 Impedance trajectory during power swing

-50 Proposed ELM based FADRS scheme

-100 -150 0

50

100

150

200

250

300

(a) R(Ohm) 100 Relay Output=Trip

X(Ohm)

50 0

Fault created during power swing

-50 -100

Proposed ELM based FADRS scheme

-150 0

50

100

150

200

250

(b) R(Ohm)

(d) (c) Fig. 16. (a) Impedance trajectory during power swing. (b) Impedance trajectory fault during power swing. (c) Experimental setup. (d) Impedance trajectory during power swing validation in real time platform.

models in an OPAL-RT RTDS. Fig. 16(c) and (d) shows the experimental setup and impedance trajectory during power swing on real time platform, respectively.

Conclusion This paper presents an adaptive protection scheme based on ELM which addresses the problems experienced by conventional distance protection schemes for two terminal lines due to complex mutual coupling and shunt capacitance, under different power system conditions. Detailed modeling and analysis of apparent impedance seen from the relaying point are presented by considering the effect of complex mutual coupling situation, with and without shunt capacitance effect for the transmission line. The proposed approach uses local relaying end information for generating the tripping zone and found highly effective considering wide variations in operating parameters. The proposed ELM based ADRS is found suitable for relaying application subjected to changing power system environment which is more likely to occur in modern power transmission network. The test results indicate that the proposed adaptive technique is highly effective and reliable for adaptive protection of transmission lines including mutual coupling and shunt capacitive effects.

Acknowledgements The research work has been supported by Prime Minister’s Fellowship for Doctoral Research, being implemented jointly by Science & Engineering Research Board (SERB) and Confederation of Indian Industry (CII), with industry.

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