An optimal radial basis function neural

An optimal radial basis function neural network for fault location in a distribution network with high penetration of DG units Hadi Zayandehroodi a,⇑, Azah Mohamed a, Masoud Farhoodnea a, Marjan Mohammadjafari b a b Department of Electrical, Electronic and Systems Engineering, Universiti Kebangsaan Malaysia (UKM), Bangi 43600, Selangor, Malaysia 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 protection blinding This paper presents an automated and accurate fault location 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 compared 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 Introduction Typically, distribution systems are with radial configuration and have only one source from the main grid Distribution 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 ⇑ Corresponding author Tel.: +60 89216590, H/P: +60 173141329; fax: +60 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) will have unfavorable impact on the traditional fault location methods because the distribution 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 configuration 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 implemented to match the loads with the DG units generating capability in the island A method for finding the exact location of faults in a MV network with DG has been developed using software procedures which require a telecommunication 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 continuity.[6] Another fault location method is based on the estimates of the fault impedance by measuring current and voltage at a substation [7] In this method, the fault location performance is inaccurate when a DG is located upstream of the fault section where the impact is more severe for synchronous machine based DG Since, increasing the number of installed DG units and the amount of injected 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 artificial 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 connection 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 satisfy the desired speed and performance in the training process Therefore, there is a need to consider using an optimum learning algorithm to improve the accuracy and speed in training RBFNN Input X Weights To overcome the above-mentioned problem, this paper presents an automated and accurate fault location method for a distribution system equipped with distributed generation 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 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 values 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 For the training of the RBFNN and considering a k dimensional input vector, X, the computed scalar values can be expressed as, Radial basis functions Linear Weights W0 C1 W1 + Input X C2 W2 ∑ Output Y Wm Cm Input X k Input Layer Hidden Layer Fig A generic architecture of the RBFNN Output Layer Y ¼ f Xị ẳ W ỵ Start m X W i /Di ị 1ị iẳ1 Offline Process Step1: Obtain input data and target data from the simulation Step 2: Assemble and preprocess the training data for the RBFNN-OSD where W0 is the bias, Wi is 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 generalizing 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 given by uDi ị ẳ exp 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 ÀD2i ! ð2Þ r2 Here r is the radius of the cluster represented by the center node (Spread) and usually called width, Di is the distance between the input vector X and all the data centers The Euclidean norm is normally used to calculate the distance, Di which is given by vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u k uX Di ¼ t ðX j À C ji ị2 3ị jẳ1 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 expressed as, Step 5: Stored the trained network Y ẳ ẵyi ẳ W UT 4ị i ẳ 1; ; n Online Process Step 6: Preprocess the new input before they are subjected to the trained network to obtain required data Therefore, the error vector, E and its respective sum squared error, J, which should be minimized through the learning process, are defined as [14], E¼Y J¼ d ÀY ¼Y d À W UT EET ð5Þ It should be noted that in the conventional steepest descent algorithm, new weights are computed using the gradient of J in the W space as, End @J @1=2ịEET ị @Y @W UT ị ẳ ẳ Y d Yị ẳE @W @W @W @W ẳ EU OJ ¼ Fig The implementation procedures in the training of the RBFNN–OSD Actuating Input Determine Fault type Online Calculation Determine Fault distance from each source Offline Calculation • System Modeling • • Model distribution network Run load flow& short circuit Train RBFNN-OSD Identify the exact faulty line Fig Outline of the proposed fault location scheme using RBFNN–OSD method ð6Þ Fig Procedures of the RBFNN–OSD based fault location method DW ẳ OJ ẳ EU 7ị W new ẳ W old ỵ kDW 8ị where the coefcient l is called learning rate which remains 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: T JWị ỵ kDW ẳ Y d W ỵ kDWịUT ịY d W ỵ kDWịUT ị T ẳ E kDW UT ÞðE À kDW UT Þ 1 ¼ EET kEUDW T ỵ k2 DW UT UDW T 2 ẳ A ỵ Bk ỵ Ck2 9ị T T T @J @A ỵ Bk ỵ Ck2 ị ẳ ẳ B ỵ 2kC ẳ @k @k Hence, kmin ẳ B EUịEUịT ẳ 2C EUUT ịEUUT ịT 11ị This learning rate minimizes the J(k), and so OLR can be expressed as, kopt ẳ EUịEUịT T EUUT ịEUUT ị P0 ð12Þ Using the above equation, the optimum delta weight vector can be determined as, DW opt ¼ kopt DW ¼ ðEUÞðEUÞT EU T ð13Þ T ð14Þ ðEUUT ÞðEUUT Þ Hence, T where A = (1/2)EE , B = ÀEUDW and C = (1/2)DWU UDW are scalar constants Thus, J(W + kDW) is a quadratic function of k with constant coefficients A, B and C Therefore, J(k) defines a quadratic function of U with positive coefficients of the second-order term J(k) can be minimized by taking its derivation as, ð10Þ DW opt ẳ kopt DW ẳ EUịEUịT EU EUUT ịEUUT ị 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 in Fig Proposed fault location scheme phase short circuit current of main source and all DG units RBFNN-OSD 1,3,5,7 RBFNN-OSD 2,4,6,8 Fault distances from the main source and all DG units Faulty line Fig Description of inputs and outputs of the RBFNN–OSD 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 considering 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 shows the outline of the proposed fault location scheme using the RBFNN–OSD In the initial implementation of the fault location method, to identify the various fault types, the three phase currents 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 recognizing the fault type, its location is determined by using the RBFNN–OSD Fig shows the procedures of fault location method using the RBFNN–OSD From the figure, the RBFNN–OSD 1, 3, 5, are used to determine fault distances from the main source and the DG units (DS, DDGs) and the RNFNN-OSD 2, 4, 6, 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 10 11 13 12 Line 10 Line 11 Line 12 BDG6 TDG6 DG4 G ~ Line ~ G DG6 BDG4 Line Line 14 Line 13 15 30 Line 29 BS Line S 14 TDG4 Line TS Line Line Line Line 18 TDG2 Line 19 17 31 32 BDG5 29 G ~ Line 17 Line 18 DG2 19 ~ G BDG2 Line 28 28 Line 16 16 TDG5 BDG1 Line 31 Line 27 Line 15 27 ~ G DG1 Line 30 Line 26 TDG1 Line DG5 20 21 22 Line 21 23 Line 22 24 Line 23 25 Line 24 26 Line 25 TDG3 BDG3 G ~ Line 20 DG3 Fig Single line diagram of the 32 bus test system 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 shows the description of the inputs and outputs of the developed RBFNNs Test system description and RBFNN–OSD results In this section, a modified 32-bus test system [1] shown in Fig is used to validate the performance and accuracy of the proposed RBFNN–OSD based fault location method implemented on a distribution network with high penetration of DG units The test system consists of a 20 kV distribution network with synchronous machines as DG units and 32 loads All DG units have the same characteristics with MW generation capacity for each DG, which are installed at six locations including buses B3, B4, B13, B19, B26 and B30 Table shows the parameters of all DG units applied in the simulations For each load, a three-step hourly load curve is considered as shown in Fig 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 km length and the technical information of the conductors is given in Table 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 considering 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 Table The DG units parameters Machine parameter Synchronous DG Rated MVA Rate output voltage Step up transformer (7 MVA) Synchronous reactance Xd Xq Transient reactance X 0d X 0q MVA 4.16 KV 0.074 p.u 1.305 p.u.Ã 0.474 p.u.Ã 0.202 p.u.Ã 0.243 p.u.Ã Subtransient reactance X 00d X 00q 0.15 p.u.Ã 0.18 p.u.Ã Per unit base Machine Transformer MVA, 4.16 kV 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 determining fault location in distribution network in the presence of DG units, as shown in Figs 8–11 From the figures, the mean square error (MSE) of the RBFNN–OSD method is significantly decreased and converged in less iteration in contrast with the conventional RBFNN method Comparing the conventional RBFNN and RBFNN–OSD training performances, it can be said that the RBFNN–OSD Fig Hourly load curve of the simulated feeder’s loads Table Technical data of distribution lines Conductor name HYENA Type ACSR A 126 mm2 Technical data R (X) X (X) R0 (X) X0 (X) In (A) 0.303 0.3383 0.4509 1.5866 250 Fig Training result of RBFNN–OSD and conventional RBFNN for 1ph-G fault Fig Training result of RBFNN–OSD and conventional RBFNN for 2ph fault Fig 10 Training result of RBFNN–OSD and conventional RBFNN for 2ph-G fault Fig 11 Training result of RBFNN–OSD and conventional RBFNN for 3ph fault Table Fault Location Results of the 32 Bus Test System Sample Method Fault distance from the main source and all DG units Faulty line no DS (m) DDG1 (m) DDG2 (m) DDG3 (m) DDG4 (m) DDG5 (m) DDG6 (m) Case RBFNN RBFNN–OSD Actual 371 380 380 1630 1619 1620 6612 6620.1 6620 10,613 10,621 10,620 4614 4619 4620 2611 2620 2620 6389 6381 6380 1.09 0.99 Case RBFNN RBFNN–OSD Actual 2420 2430 2430 423 429.5 430 5433 5431 5430 9438 9430 9430 2579 2570.6 2570 580 570.5 570 8422 8429 8430 2.91 3.01 Case RBFNN RBFNN–OSD Actual 3671 3681 3680 5677 5679 5680 9670 9680.1 9680 14,688 14,680 14,680 8685 8680.6 8680 6687 6681 6680 2330 2319.8 2320 10.09 10.01 10 Case RBFNN RBFNN–OSD Actual 6860 6871 6870 4875 4869 4870 131 130.1 130 5876 5870.4 5870 7880 7870.7 7870 5878 5871 5870 12,879 12,870 12,870 19.07 18.99 19 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 Case 2: Two phase (2ph) fault at 430 m of length of the line 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 show the outcome of the proposed RBFNN–OSD and the conventional RBFNN methods for locating faults in the 32 bus test system with DG units From Table 3, it is shown that the RBFNN–OSD give 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 m Since each distribution line section is km in length in the studied network, a deviation of 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 of Table After rounding to the nearest one, the detected faulty line is line The results in Table also show that the second RBFNN outputs give accurate prediction of the faulty lines when compared to the actual faulty lines Conclusion As high penetration of DG units into distribution systems would lead to conflicts with the conventional protection procedures operated in the present power distribution 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 exact 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 compared with the conventional RBFNN using the steepest descent learning algorithm The results showed that the proposed fault location method using the RBFNN–OSD can accurately determine the location of faults in a distribution 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 (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 LAMBERT Academic Publishing, Germany, 2012 [13] A.D Niros, G.E Tsekouras, A novel training algorithm for RBF neural 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 [15] H White, Artificial Neural Networks: Approximation and Learning 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