An optimal radial basis function neural

This paper presents an automated and accurate fault locaprotec-tion method for identifying the exact faulty line in the test distribution network with high penetration level of DG units

An optimal radial basis function neural network for fault

location in a distribution network with high penetration of DG

units

Hadi Zayandehroodia,⇑, Azah Mohameda, Masoud Farhoodneaa, Marjan Mohammadjafarib a

Department of Electrical, Electronic and Systems Engineering, Universiti Kebangsaan Malaysia (UKM), Bangi 43600, Selangor, Malaysia

b

Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Kerman, Iran

a r t i c l e i n f o

Keywords:

Protection

Fault location

RBFNN-OSD

Neural network

Distributed generation (DG)

Distribution network

Coordination

a b s t r a c t Due to environmental concerns and growing cost of fossil fuel, high levels of distributed generation (DG) units have been installed in power distribution systems However, with the installation of DG units in a distribution system, many problems may arise such as increase and decrease of short circuit levels, false tripping of protective devices and protec-tion blinding This paper presents an automated and accurate fault locaprotec-tion method for identifying the exact faulty line in the test distribution network with high penetration level

of DG units by using the Radial Basis Function Neural Network with Optimum Steepest Descent (RBFNN–OSD) learning algorithm In the proposed method, to determine the fault location, two RBFNN–OSD have been developed for various fault types The first RBFNN–OSD is used for predicting the fault distance from the source and all DG units while the second RBFNN is used for identifying the exact faulty line Several case studies have been simulated to verify the accuracy of the proposed method Furthermore, the results

of RBFNN–OSD and RBFNN with conventional steepest descent algorithm are also com-pared The results show that the proposed RBFNN–OSD can accurately determine the location of faults in a test given distribution system with several DG units

1 Introduction

Typically, distribution systems are with radial

configu-ration and have only one source from the main grid

Distri-bution systems are usually not designed to operate with

DG units connected to the system In recent years, the

installation DG units has increased significantly in the

power distribution systems due to economic and technical

benefits associated with DG unit such as higher efficiency,

reduced system losses and enhanced system reliability[1–

3] The presence of such DG units in a distribution system

will have unfavorable impact on the traditional fault loca-tion methods because the distribuloca-tion systems are usually not designed to operate with DG units connected to the system This is due to the fact that the present distribution system is designed as a passive and radial network config-uration and have only one source from the main grid[4] With the installation of DG units in a distribution system,

it brings about a change in the fault current level of the system and causes many problems in the system, such as increase and decrease in short-circuit levels, undesirable network islanding and out-of-synchronism reclosers Recently, several methods have been developed for automated fault location in distribution system with DG units A fault location algorithm has been developed by using current measurements in[5] In this method, after

a faulted segment is located, islands are formed involving groups of DG units and a load shedding scheme is

⇑Corresponding author Tel.: +60 3 89216590, H/P: +60 173141329;

fax: +60 3 89216146.

E-mail addresses: h.zayandehroodi@yahoo.com (H Zayandehroodi),

azah@eng.ukm.my (A Mohamed), farhoodnea_masoud@yahoo.com (M.

Farhoodnea), marjan_mohamadjafari@yahoo.com (M Mohammadjafari).

implemented to match the loads with the DG units

gener-ating capability in the island A method for finding the

ex-act location of faults in a MV network with DG has been

developed using software procedures which require a

tele-communication control system In this paper also proposed

a protection philosophy based on innovative technical

solutions to solve the problem of lack of protective devices

coordination in presence of DG to improve service

continu-ity.[6] Another fault location method is based on the

esti-mates of the fault impedance by measuring current and

voltage at a substation[7] In this method, the fault

loca-tion performance is inaccurate when a DG is located

up-stream of the fault section where the impact is more

severe for synchronous machine based DG Since,

increas-ing the number of installed DG units and the amount of

in-jected energy by the DG units raise the ratio of DG

penetration levels that can disturb coordination between

the protection devices, the proposed methods are not able

to determining correct fault location after connecting each

DG in such distribution systems[1]

A more recent fault location method for a distribution

network with DG units considers the application of

artifi-cial neural networks (ANNs)[8–10] However, considering

the structure and training algorithm of the radial basis

function neural network (RBFNN) in comparison with

other type of ANN, the speed of this method is suitable

for fast and accurate fault location[11,12] The training

of RBF networks is accomplished through the estimation

of three kinds of parameters, namely the centers and the

widths of the basis functions and finally, the neuron

con-nection weights [13] According to different applications

of RBFNN, there is a wide variety of learning strategies that

have been proposed in the literature for changing the

parameters of the RBFNN in the training process [14]

Therefore, using conventional learning algorithm while

employing RBFNN for real time applications, will not

sat-isfy the desired speed and performance in the training

pro-cess Therefore, there is a need to consider using an

optimum learning algorithm to improve the accuracy and

speed in training RBFNN

To overcome the above-mentioned problem, this paper presents an automated and accurate fault location method for a distribution system equipped with distributed gener-ation This fault location schemes are proposed by using the Radial Basis Function Neural Network with Optimum Steepest Descent learning algorithm (RBFNN–OSD) In this method is developed using two staged RBFNN–OSD in which the first RBFNN–OSD determines the fault distance from each source, while the second RBFNN–OSD identifies the exact faulty line The proposed method is different from the previous neural network based methods, in the fact that using RBFNN–OSD makes the proposed method able to accurately determine the exact faulty line with minimum error

2 Radial basis function neural network with optimum steepest descent learning algorithm

The RBFNN is a feed-forward neural network consisting

of three layers namely, an input layer which feeds the val-ues to each of the neurons in the hidden layer, a hidden layer which consists of neurons with radial basis activation functions and an output layer which contains neurons with linear activation function[15] The learning process for RBF neural networks is composed of initiating centers and widths for RBF units and computing weights for connectors

of these units Based on different applications of RBFNN, in the literature many learning strategies have been applied for changing the parameters of RBFNN during the training process The conventional learning algorithm applied for real time application cannot satisfy the desired speed and performance in the training process Hence, the optimum steepest descent learning algorithm is applied to improve the RBFNN training process with fewer epochs so as to make it faster and more accurate A generic topology of RBFNN with k input and m hidden neurons is shown in

Fig 1 For the training of the RBFNN and considering a k dimensional input vector, X, the computed scalar values can be expressed as,

Cm

∑

W0

W1

W2

Wm

+

Output Y

Radial basis functions Weights Linear Weights

Y ¼ f ðXÞ ¼ W0þX

i¼1

where W0is the bias, Wiis the weight parameter, m is the number of neurons in the hidden layer and (Di) is the RBF There are many basis functional choices possible for the RBF like spline, multi-quadratic, and Gaussian functions, but the most widely used one is the Gaussian function The Gaussian RBFNN is found not only suitable in general-izing a global mapping but also in refining local features without altering the already learned mapping[16] In this study, the Gaussian function is used as the RBF and it is gi-ven by

uðDiÞ ¼ exp D

2 i

r2

!

ð2Þ

Hereris the radius of the cluster represented by the cen-ter node (Spread) and usually called width, Diis the dis-tance between the input vector X and all the data centers The Euclidean norm is normally used to calculate the distance, Diwhich is given by

Di¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Xk j¼1

ðXj CjiÞ2

v u

ð3Þ

where C is a cluster center for any of the given neurons in the hidden layer[3]

In an RBFNN, the estimated output vector, Y can be ex-pressed as,

Y ¼ ½yi ¼ WUT

Therefore, the error vector, E and its respective sum squared error, J, which should be minimized through the learning process, are defined as[14],

E ¼ Y d Y ¼ Yd WUT

It should be noted that in the conventional steepest des-cent algorithm, new weights are computed using the gradi-ent of J in the W space as,

OJ ¼ @J

@ðð1=2ÞEETÞ

@Y

@W¼ E

@ðWUTÞ

@W

Online Process

Offline Process

Step1:

Obtain input data and target data from

the simulation

Step 2:

Assemble and preprocess the training

data for the RBFNN-OSD

Step 3:

Create the network object and train the

network until condition of network

setting parameters are reached

Step 4:

Test and conduct regression analysis

Step 5:

Stored the trained network

Step 6:

Preprocess the new input before they

are subjected to the trained network to

obtain required data Start

End

Fig 2 The implementation procedures in the training of the RBFNN–OSD.

System Modeling

Offline Calculation

• Model distribution network

• Run load flow& short circuit

• Train RBFNN-OSD

Online Calculation

Determine Fault type

Determine Fault distance from each source

Identify the exact faulty line Actuating

Input

DW ¼ OJ ¼ EU ð7Þ

where the coefficient l is called learning rate which

re-mains constant throughout the learning process

Eq.(7)shows that the optimum direction of the delta

weight vector, in the sense of first-order estimation, does

not still specify the optimum length of J vector and the

optimum learning rate (OLR) To achieve the OLR, the

sum squared error of the new weights should be obtained

using Eqs.(4)–(8)as follows:

JðWÞ þ kDW ¼1

2ðYd ðW þ kDWÞU

T

ÞðYd ðW þ kDWÞUTÞT

¼1

2ðE  kDWU

T

ÞðE  kDWUTÞT

¼1

2EE

T

 kEUDWTþ1

2k

2

DWUTUDWT

where A = (1/2)EET, B = EUDWTand C = (1/2)DWUTUDWT

are scalar constants Thus, J(W + kDW) is a quadratic

func-tion of k with constant coefficients A, B and C Therefore,

J(k) defines a quadratic function of U with positive

coeffi-cients of the second-order term J(k) can be minimized by

taking its derivation as,

@J

@k¼@ðA þ Bk þ Ck

2Þ

Hence,

kmin¼  B

2C¼

ðEUÞðEUÞT

This learning rate minimizes the J(k), and so OLR can be expressed as,

kopt¼ ðEUÞðEUÞ

T

ðEUUTÞðEUUTÞT

Using the above equation, the optimum delta weight vector can be determined as,

DWopt¼ koptDW ¼ ðEUÞðEUÞ

T

EU

Hence,

DWopt¼ koptDW ¼ ðEUÞðEUÞ

T

EU

ðEUUT

ÞðEUUT

ÞT

ð14Þ

for which the initial value for W is set with a random value The implementation procedures in the training of the RBFNN–OSD are shows inFig 2

3 Proposed fault location scheme

In this work, through offline calculation, the two staged RBFNN–OSD are trained with the proper input data which

is generated by performing short circuit simulations con-sidering various fault locations and different fault types The trained RBFNN–OSD is then used in online mode for determining the fault type and location of fault Fig 3

shows the outline of the proposed fault location scheme using the RBFNN–OSD

In the initial implementation of the fault location

meth-od, to identify the various fault types, the three phase cur-rents of the main source or the feeding substation are used The fault type is determined based on the normalized three phase output current of the feeding substation After rec-ognizing the fault type, its location is determined by using the RBFNN–OSD.Fig 4shows the procedures of fault loca-tion method using the RBFNN–OSD From the figure, the RBFNN–OSD 1, 3, 5, 7 are used to determine fault distances from the main source and the DG units (DS, DDGs) and the RNFNN-OSD 2, 4, 6, 8 are used is for determining the faulty line for the respective fault types

According to the procedures in determining the fault location, for each fault type, firstly the three phase currents

RBFNN-OSD

1,3,5,7

RBFNN-OSD 2,4,6,8

3 phase short circuit current of main source

and all DG units

Fault distances

from the main

source and all DG

of the main source and all the DG units are used as inputs

to the first RBFNN–OSD The outputs of the first RBFNN–

OSD which are the distances of fault from the main source

and the DG units are then used as inputs to the second

RBFNN–OSD Hence, the output of the second RBFNN–

OSD is the exact faulty line.Fig 5shows the description

of the inputs and outputs of the developed RBFNNs

4 Test system description and RBFNN–OSD results

In this section, a modified 32-bus test system[1]shown

of the proposed RBFNN–OSD based fault location method

implemented on a distribution network with high

penetra-tion of DG units The test system consists of a 20 kV

distri-bution network with 6 synchronous machines as DG units

and 32 loads All DG units have the same characteristics

with 6 MW generation capacity for each DG, which are

in-stalled at six locations including buses B3, B4, B13, B19,

B26 and B30.Table 1shows the parameters of all DG units

applied in the simulations

For each load, a three-step hourly load curve is

consid-ered as shown in Fig 7 The peak load for all loads is

1.5 MW and the power factor for all of them at each time

is assumed 0.92 lagging

All the distribution conductors are of HYENA type with

1 km length and the technical information of the

conduc-tors is given inTable 2

The DIgSILENT Power Factory 14.0.524 software was used to simulate the various types of faults created in each line of the test system Then the two-staged RBFNN–OSD is applied and implemented in MATLAB software to estimate the fault distance from each source and faulty line number, respectively The training data for the RBFNN–OSD was generated by simulating various fault situations consider-ing various type of faults, fault created at each 100 m of every line as a different location The target or output of the RBFNN–OSD is obtained from the simulations About

9486 training and testing data sets have been generated, from which 80% of the data sets are used for training the two RBFNN–OSD, and 20% are used for testing to evaluate

BS

BDG4

BDG3

BDG1

BDG5

DG6

DG5

S

DG1

DG2

DG3

DG4

8 7

32 31

6 5

4

26 3

25

23 22

10

2 1

20

29 28

27

16

30

TDG3 Line 23

TS

G

~

G ~

Line 19

TDG1

G

~

TDG2

TDG6

G ~

Line 5 Line 4

Line 2

Line 17

Line 9

Line 12 Line 11

Line 10

Line 7

Line 25 Line 24

Line 22 Line 21

Line 20

Line 1

Line 26

Line 3

Fig 6 Single line diagram of the 32 bus test system.

Table 1 The DG units parameters.

Transient reactance X 0

X 0

Transformer 7 MVA, 4.16 kV

its performance The results of the proposed RBFNN–OSD

based method are then compared with the RBFNN using

the conventional steepest descent algorithm for

determin-ing fault location in distribution network in the presence of

DG units, as shown inFigs 8–11 From the figures, the

mean square error (MSE) of the RBFNN–OSD method is sig-nificantly decreased and converged in less iteration in con-trast with the conventional RBFNN method

Comparing the conventional RBFNN and RBFNN–OSD training performances, it can be said that the RBFNN–OSD

Fig 7 Hourly load curve of the simulated feeder’s loads.

Table 2 Technical data of distribution lines.

Fig 10 Training result of RBFNN–OSD and conventional RBFNN for 2ph-G fault.

takes shorter time to achieve the required training

accuracy

Furthermore, to verify the accuracy and effectiveness of

the proposed fault location scheme at the time of fault

occurrence, the following scenarios are considered:

Case 1: Single phase to ground (1ph-G) fault at 380 m of

line 1

Case 2: Two phase (2ph) fault at 430 m of length of the

line 3

Case 3: Two phase to ground (2ph-G) fault at 680 m of

length of the line 10

Case 4: Three phase (3-ph) fault at 870 m of length of

the line 19

The results in Table 3 show the outcome of the proposed

RBFNN–OSD and the conventional RBFNN methods for

locating faults in the 32 bus test system with 6 DG units

accurate results in which the maximum error of the first

RBFNN–OSD which is the difference between the actual

and estimated distances of fault from the main source

and all DGs is about 1 m Since each distribution line

sec-tion is 1 km in length in the studied network, a deviasec-tion

of 1 m is acceptable The second RBFNN–OSD outputs after

rounding to the nearest one shows the exact number of

faulty lines For instance, when a single phase to ground

fault occurs at 380 m of line 1, the estimated output of

the second RBFNN-OSD is 0.99 as shown on the 1st row

and 4th column ofTable 3 After rounding to the nearest

one, the detected faulty line is line 1 The results inTable 3

also show that the second RBFNN outputs give accurate

prediction of the faulty lines when compared to the actual

faulty lines

5 Conclusion

As high penetration of DG units into distribution

sys-tems would lead to conflicts with the conventional

protec-tion procedures operated in the present power distribuprotec-tion

systems, effective fault location schemes are required to

ensure safe and selective protection relay coordination in

the system with DG units An automated and accurate fault

location method has been presented for identifying the ex-act faulty line in the test distribution network with high penetration level of DG units by using the RBFNN–OSD Several case studies have been used to verify the accuracy

of the method and the results of the RBFNN–OSD are com-pared with the conventional RBFNN using the steepest des-cent learning algorithm The results showed that the proposed fault location method using the RBFNN–OSD can accurately determine the location of faults in a distri-bution system with several DG units

References [1] H Zayandehroodi, A Mohamed, H Shareef, M Farhoodnea, A novel neural network and backtracking based protection coordination scheme for distribution system with distributed generation, Int J Electr Power Energy 43 (2012) 868–879

[2] H Zayandehroodi, A Mohamed, H Shareef, M Mohammadjafari, Distributed generator and their effects on distribution system protection performance, Aust J Basic Appl Sci 5 (2011) 398–405 [3] S Ghosh, S.P Ghoshal, S Ghosh, Optimal sizing and placement of distributed generation in a network system, Int J Electr Power Energy 32 (2010) 849–856

[4] H Zayandehroodi, A Mohamed, H Shareef, M Mohammadjafari, A comprehensive review of protection coordination methods in power distribution systems in the presence of DG, Prz Elektrotechniczny 87 (2011) 142–148

[5] G.-f Zhu, Y.-p Lu, Development of fault location algorithm for distribution networks with DG, in: IEEE International Conference on Sustainable Energy Technologies (ICSET 2008), 2008, pp 164–168 [6] S Conti, S Nicotra, Procedures for fault location and isolation to solve protection selectivity problems in MV distribution networks with dispersed generation, Electr Power Syst Res 79 (2009) 57–64 [7] T.H.M El-Fouly, C Abbey, On the compatibility of fault location approaches and distributed generation, in: Joint Symposium Integration of Wide-Scale Renewable Resources Into the Power Delivery, System (CIGRE2009), 2009, pp 1–5.

[8] H Zayandehroodi, A Mohamed, H Shareef, M Mohammadjafari, Automated fault location in a power system with distributed generations using radial basis function neural networks, J Appl Sci 10 (2010) 3032–3041

[9] A Bretas, L Pires, M Moreto, R Salim, A BP neural network based technique for HIF detection and location on distribution systems with distributed generation, Comput Intell (2006) 608–613 [10] L.X.L.Y.W Lianhe, New fault region location scheme in distribution system with DGs, Trans China Electrotech Soc 11 (2008) 023 [11] M Sanaye-Pasand, H Khorashadi-Zadeh, An extended ANN-based high speed accurate distance protection algorithm, Int J Electr Power Energy 28 (2006) 387–395

[12] H Zayandehroodi, A Mohamed, H Shareef, Power System Protection

an Coordination: In the Persence of Distributed Generator, LAP

Fault Location Results of the 32 Bus Test System.

D S (m) D DG1 (m) D DG2 (m) D DG3 (m) D DG4 (m) D DG5 (m) D DG6 (m)

network using a hybrid fuzzy clustering approach, Fuzzy Sets Syst.

193 (2012) 62–84

[14] G.A Montazer, R Sabzevari, F Ghorbani, Three-phase strategy for

the OSD learning method in RBF neural networks, Neurocomputing

72 (2009) 1797–1802

Theory, Blackwell Publishers, Inc., Cambridge, MA, USA, 1992 [16] M Joorabian, S Asl, R.K Aggarwal, Accurate fault locator for EHV transmission lines based on radial basis function neural networks, Electr Power Syst Res 71 (2004) 195–202