Single phase fault location in electrical distribution feeder using hybrid method

Energy 103 (2016) 356e368

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Single phase fault location in electrical distribution feeder using hybrid method Mohammad Daisy, Rahman Dashti* Electrical Engineering Department, Persian Gulf University, Bushehr 7516913817, Iran

a r t i c l e i n f o

a b s t r a c t

Article history: Received 14 April 2015 Received in revised form 11 January 2016 Accepted 16 February 2016

Restoration of electrical energy after each distribution feeder's outage can improve the reliability indices and its efficiency. Accurate fault locating can cause the Power distribution (PD) systems to restore rapidly. PD networks include many branches, laterals, sub-laterals and load taps. Thus, accurate fault locating is very complicated and important. In the present paper, a new combined method is proposed for locating the single-phase fault to earth in PD networks. An impedance-based fault-location algorithm is also used to find the possible fault locations. Then, the new method is proposed for determining the faulty section using voltage sag matching algorithm. In this method, after single-phase fault to ground, the possible locations of fault are determined by using the impedance-based fault-location algorithm. The same fault is simulated in possible locations, separately. The voltage, then, at the beginning of feeder is saved and amplitude and angle of the voltage differences are determined and online databank is generated. This databank is compared with the obtained and recorded amplitude and angle of the voltage differences for actual fault. The real location of fault is specified by the matching value of each possible fault location. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Power distribution network Impedance based fault location method Voltage sags

1. Introduction Power systems are composed of four sections: generation, transmission, sub-transmission and distribution. The reliability indices variation of Power Distribution (PD) and the consequences of service interruption depend on the number of interrupted customers, customer load type and size, occurrence time, frequency of outages, and the outage duration period [1]. Due to the serious fallout of system outages on customers and utilities, restoration of power supply to the healthy out-of-service loads in the least time is of profound importance. After occurring faults and interrupting PD feeder, locating fault should be applied to restore the maximum reenergized loads in minimum outage time duration for minimizing the energy rather supplying and satisfying the consumers [1e3]. Due to widespread geographical area covered by PD systems, determining the fault location in distribution networks feeders has several problems in terms of time, costs, and equipment [4]. Three types of methods are given for locating the faults in PD such as impedance method, traveling waves and intelligent methods. But, these methods still encounter some problems. Traveling wave-

* Corresponding author. E-mail addresses: [email protected] (M. Daisy), [email protected] (R. Dashti). http://dx.doi.org/10.1016/j.energy.2016.02.097 0360-5442/© 2016 Elsevier Ltd. All rights reserved.

based method may face problems such as high sampling frequency, complex structure and requirement for the databank [5]. The intelligent methods might be problematic due to the complex structure as well as the requirement for a large and precise databank [6,7]. Finally, the most recent important issue presents the impedance-based fault locating method [8e15]. In Refs. [11,12], fault locating equations of impedance-based methods are generalized for different types of two- and threephase faults either resistive or solidly. Results of variations in fault initial phase, fault resistance phase and load variations are presented. The results revealed that fault locating accounts for less than 10% error for most of simulated conditions except those associated with short circuits with resistance higher than 100 U. In this method, short-line model is considered to obtain accurate results; line parameters should be also accurate; inductor and capacitor should be taken into account in the line model. Also, for section detection, the neural network method is used. It can be specified that this method needs an offline databank while PD networks are changed continuously. Consequently, the accuracy of this method relies on this databank. In Ref. [13] a new equation for fault location in distribution network is introduced. In this method, p line model (medium line model) is considered for each section and a modified impedancebased method is presented improving the precision. The

M. Daisy, R. Dashti / Energy 103 (2016) 356e368

Nomenclature PD IBFLM DLM SLM pM SL CL FI CP Nn Pd V FBS XDV

Power distribution Impedance based fault location method distributed - parameter line model short line model. p model static load constant load fault indicator current pattern neural network Protective devices voltage magnitude forward backward sweep calculated fault distance from the obtained equation of the magnitude of voltage difference

maximum fault for 34-node IEEE (Institute of Electrical and Electronics Engineer) network is reported as 1.58% which equals to 1551 m considering the total length of the network (98180 m). This method is presented only for determining the fault distance while in distribution network, section detection is very important. Another method is proposed in Ref. [14] which uses the distributed model of transmission line as well as voltage and current at the beginning of feeder. In this method, different fault location equations are presented based on the fault types which are a function of voltage and current at the beginning of the feeder. This method does not present any method for fault section estimation. An impedance-based fault location method presented in Ref. [15] uses the fault location utilizing voltage and current registered at the beginning of feeder. In this reference, three impedance indicators are introduced and fault distance is determined in various types of faults. Based on the results, it might be seen that the mentioned method is sensitive to fault resistance. Moreover, line capacitance is ignored in this method which causes the error to increase. In what follows, a new improved impedance-based fault location method is given which is used in accurate load model and distributed parameter line model [8]. Then a new fault section estimation method is suggested using the coordination among protection devices in distribution system [9]. In another research by these authors, a matching algorithm is proposed for faulty section detection using fast Fourier transform and impedance based method [10]. Impedance-based methods use the installed measurements at the beginning of feeder to determine the fault distance, while in practical system, current is only stored in a few cycles before and after fault in over-current relays and extra registers would also be needed to store the voltage. Thus, in Ref. [16] two methods are presented where current phasor and current amplitude are respectively used for determining the fault distance. The accuracy of this method reaches to 8%. Since most impedance-based methods determine fault location using the iterative algorithms, a technique proposed in Ref. [17] estimates the location of fault in less iteration. It exploits impedances of positive, negative and zero components as well as recorded voltage and current information at the beginning of the feeder. It is applied for looped feeders. In Ref. [18], the voltage and dip voltage of each node is determined using voltage and current data at the beginning of feeder and some other points of feeder during fault occurrence. This method assumes that fault can be occurred in each section and tries

357

i x

a section of equation which is employed distance d the matching index Dv i The magnitude difference of voltage Dqi The phase angle variation of voltage q phase variation x actual the real fault distance x calculated the calculated fault distance lt total length of feeder Xs calculated fault distance from the proposed improved IBFLM XDq calculated fault distance from the obtained equation of the phase variation of voltage Dq is the obtained distance derived from phase angle variation equation

to find the fault current in that section. The dip voltage of each node is calculated from recorded voltage and current data. Then, they are compared. If the values match, fault has occurred and the fault distance is determined utilizing the recorded voltage and current. In Ref. [7] dip voltage phase and amplitude, at first, are calculated for the simulated fault in each node and then are stored in offline databank. Then, dip voltage amplitude and phase are derived based on the fault voltage data and compared to generated offline databank which leads to the extraction of possible locations. Then, based on the calculated dip voltage amplitude and phase for each possible fault location, the desired points in the plane are specified and the distance between perpendicular line and straight lines are determined. Then the location whose perpendicular line is less distant from fault point is selected as the main fault location. The same method is executed in Ref. [6] but the mentioned algorithm is divided into two different planes; dip voltage amplitude-fault distance and dip voltage phase-fault distance. The drawback of the methods given in Refs. [6,7] is needed for databank while it is known that the distribution networks are changed continuously. Moreover, the important papers in this title are reviewed and some important details and characteristics of them are shown in Table 1. In this paper, a new combined method is proposed for determining the fault distance and faulty section in PD networks for single-phase to ground fault. In this article, initially, the possible locations of fault are determined using the improved impedancebased fault location method (IBFLM). In enhanced IBFLM, the distributed line model without any approximation is used for any part of PD network. Since IBFLM might be multi-response, consequently, the matching value is defined and supposed for determining the section of fault by using voltage sag data. Two new third-order algebraic equations are obtained for defining the amplitude and angle of voltage difference at the beginning of feeder relative to fault distance. When the fault is occurred, the possible locations are determined by the proposed improved IBFLM. Then, these voltage differences are determined from the recorded voltage at the beginning of feeder. Then, the same fault is simulated in the possible locations and online databank of magnitude difference and phase variations of voltage is generated. Now, the recorded voltage differences are compared with the simulation results and the matching one is the real location of fault. The modified IEEE 34 Node Test Feeder is selected for evaluating the proposed method. The simulation of test feeder and calculation of differences’ values are done in Simulink/Matlab in different types of fault, different fault inception algorithm, different fault distances and different

Table 1 Comparison of different PD fault-location methods.

Line model Load model Load estimation Non-homogeneity Unbalanced system Laterals Load taps Fault type Section detection Network type Smart grid Time domain Phase domain Sequence domain

Srinivasan and Girgis Zhu et al. et al. (1997) St-Jacques (1993) [23] (2003) [21] [22]

Aggarwal et al. (1997) [24]

Das et al. Saha et al. Choi et al. Jamali and Lee et al. Yang et al. Salim Nouri Salim (2009) (2009) (2011) (2008) (2004) Talavat (2004) (2002) (1995, [13] [31] [11] [30] [29] (2004) [27] [20] 2000) [28] [25,26]

DLMa SLd e e e e √ All e

SLM SL √ √ √ √ √ All e Radial e e √ e

DLM SL √ e √ e √ All Flf Radial e e e √

e e √

SLMb CLe e e √ √ √ All e Radial e e √ √

This table is completed of [9]. a DLM ¼ distributed - parameter line model. b SLM ¼ short line model. c pM ¼ p model. d SL ¼ static load. e CL ¼ constant load. f FI ¼ fault indicator. g CP ¼ current pattern. h Nn ¼ neural network. i Pd ¼ Protective devices.

SLMb SL √ e √ √ √ All e Radial e e √ e

SLM CL e e e e √ SLG e Radial e e √ e

SLM CL e e √ e e All e Radial e e e √

DLM CL e √ e √ √ All e Radial e e √ e

SLM SL √ √ √ √ √ SLG CPg Radial e e √ e

DLM CL √ e e e √ SLG e Radial e e e √

SLM SL √ √ √ √ √ All Nnh Radial e e √ e

DLM CL e e e e e All e Radial e e e √

pMc SL √ √ √ √ √ All e Radial e e √ e

Nouri Dashti Yuan (2013) Liao et al. (2014) (2012) [9] [35] [32] DLM CL √ e e e e All e Radial e √ e e

DLM CL √ √ √ √ √ All √ Radial e e √ √

pM SL e e √ √ √ All √ loop e e √ e

D.S. Gazzana [2014] [34]

Proposed Liang Deng (2015) method Rui (2015) [33] [36]

pMc SL e √ √ √ √ All Pdi Radial e e √ e

pM CL e e e √ e All e Radial e √ e e

DLM CL e e e e √ SLG SVM loop √ e √ √

DLM SL √ √ √ √ √ SLG √ Radial e e √ √

M. Daisy, R. Dashti / Energy 103 (2016) 356e368

fault resistances. According to the results, accuracy of the proposed method is very high in comparison to the previous IBFLM and its sensitive on fault resistance is low (less than 0.42). Also, the faulty section is determined so accurately by using the proposed method. This paper is organized as follows. In Section 2, the improved IBFLM is presented. Section 3 presents the proposed method for determining the faulty section and its application on PD systems. Section 4 describes the simulation results for evaluating the accuracy of proposed method, and conclusions are finally drawn in Section 5.

2. The improved IBFLM The fault location is determined by using the presented impedance-based method in Ref. [9]. In this method, a fifth-order algebraic equations in regards to fault distance is derived for locating single-phase-to-ground fault by using the distributedparameter line model and symmetrical component, which are presented as follows:

h

 i i i h  h  * * * Im k5m IFm x5 þ Im k4m IFm x4 þ Im k3m IFm x3 i i h  i h  h  * * * x2 þ Im k1m IFm x þ Im k0m IFm þ Im k2m IFm ¼0

359

3. The proposed faulty section estimation method and its applying In the proposed method, considering the limitations associated with information of distribution systems, all possible fault points should initially be determined by using recorded voltages and currents at the beginning of feeder (method given in Section 2). From among these possible fault points, only one of them is the real location of fault. Thus, in this section, a new fault section estimation method is suggested to achieve the real fault point and faulty section. To achieve this goal, the same type of fault is simulated in the section of possible locations of fault with 0.1 km steps and the phase angle variation and magnitude difference of voltages at the beginning of feeder are calculated with respect to fault distance and then stored for each one. Therefore, the databanks are generated in online form. Now, the phase angle variation and magnitude difference of recorded voltage are shown on the new calculated curves (databanks). The nearest one is selected as the real fault point. In what follows, details of each part of the proposed method for determining the faulty section are explained as follows.

3.1. Databank generation

(1)

The calculated vectors k0 to k5 are given in Appendix A (Eq. (A1)). In this equation, determining the fault point current is very important and depends on both the load model and current. Thus, in this algorithm, the accurate model of load is used of which the value is calculated by the proposed method in Ref. [9]. Now, by solving these equations, five solutions are achieved. Selecting the correct solution is very important. Each solution should satisfy the following conditions to be selected as the correct solution [10]: _ it should be a real and positive number; and _ its value should be less than the length of given section. The flowchart of proposed IBFLM is shown in Fig. 1. According to this, firstly, it can be observed that the proposed algorithm for PD network and voltage and current data at the beginning of feeder is given as input data. Secondly, the status of network is determined whether it is healthy or faulty and if faulty, which type of fault occurres? Then, the algorithm is discussed for single-phase fault to ground. Now, the fault type is known and the equivalent load at the downstream of each section and the voltage and current at the beginning of each part and section should be determined with supposing the fault in the investigated section. After doing so, forward- backward sweep (FBS load flow) is run and load current of each section is determined. Thus, the fault current is determined by using calculated current at the beginning of section as well as load current from FBS load flow. The fault distance and fault resistance are determined by using the calculated voltage at the beginning of section and fault current. In this method, a fifth-order algebraic equation of fault distance is used to improve the accuracy of the possible fault location. This algorithm is run for each section of PD network. It is clear that sometimes impedance-based fault-location methods may estimate several distances and points of a fault in different sections due to its configuration (laterals, sub-laterals and load taps). These different locations are named as the possible points. Among them, distinguishing the actual location of fault is very important. Thus, in order to determine the actual fault location, it is necessary to have an algorithm for fault section estimation. In the next section, a new method is suggested for estimating the faulty section.

Databank is generated from simulated fault in the part of possible fault point with 0.1 km steps when the fault occurs. This databank is composed of the phase angle variation and magnitude difference of voltages at the beginning of feeder. The databank is utilized for obtaining the general third-order algebraic equation of the phase angle variation and magnitude difference of voltage concerning the distance. The collected information for databank is shown in Table 2. The first column shows the different distance with 0.1 steps and the second and third columns are the phase angle variation and magnitude difference of voltage, respectively. According to the details of the database, it can be understood that the behavior of phase and voltage variations is non-linear with respect to the distance. Two third-order polynomial equations can be introduced with respect to the fault distance: 1 The phase angle variation of voltage (at the beginning of feeder) - fault distance. 2 The magnitude difference of voltage (at the beginning of feeder) - fault distance. The global equations are as follows:

Dvi ¼ a3 x3 þ a2 x2 þ a1 x þ a0

(2)

Dqi ¼ b3 x3 þ b2 x2 þ b1 x þ b0

(3)

V: voltage magnitude. q: phase variation. i: a section of equation which is employed. x: distance. Voltage magnitude coefficient in the equation: This coefficient is determined with curve fitting mathematic methods. These equations are obtained from the simulated fault on the possible faulty sections, when the real fault occurs in PD feeders. These equations can be constant, linear and nonlinear which depend on the coefficients. Therefore, a set of two equations is generated for each possible faulty section. The structure of these coefficients is shown in Fig. 2.

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Fig. 1. The flowchart of the proposed IBFLM.

Table 2 The structure of data base. Fault distance

Magnitude of voltage difference

Phase angle variation of voltage difference

0 0.1 0.2 . . . xij

Dv 1 Dv 2 Dv 3

Dq1 Dq2 Dq3

. . .

. . .

Dvij

Dqij

The first and second columns of databank are two adjacent buses. Third, fourth, fifth and sixth columns are the coefficients of Eqs. (2) and (3). 3.2. Matching algorithm and enhancing the accuracy of the determined fault distance In this part, an algorithm is suggested for determining the real faulty section among the determined possible fault sections from IBFLM results. Flowchart of the proposed fault section estimation method is shown in Fig. 3. In this algorithm, after fault occurrence and distinguishing it, the value of phase variation (Dq) and

magnitude differences (Dv) of recorded voltage are extracted and saved simultaneously, the possible fault locations are determined by using the improved IBFLM (Xs). Then, the same fault is simulated in each possible section by 0.1 km away and the online databank is created. According to each of phase variation (Dq) and magnitude differences (Dv) of recorded voltage, there is a cubic equation related to fault distance; so, the constant coefficients of these equations are determined by using this generated online databank for each possible fault section. Thus, two fault distances are determined as xDV and xDq in each possible section through the recorded actual Dv and Dq and calculating cubic equations for Dv and Dq. This is done for an obtained equation for each of determined possible fault sections from IBFLM. Now, the matching index is defined for determining the main faulty section. It is calculated with Eq. (4). It should be calculated for each possible fault section. This method has two important notes rather than the same methods: at first, the online databank generation and online fault section and fault distance detection and secondly, using two cubic equations for improving the accuracy of fault section estimation algorithm and enhancing the fault distance determination. According to this defined match index, ranking of the determined possible location of faults is carried out. Each of them with the minimum index is the real fault point. Matching value is derived from the following formula:

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and conductors number is 300 MCM; all loads, as spot loads, have information which could be found in Ref. [20]. Here, the Simulink toolbox of MATLAB (MathWorks, Natick, MA, USA) software is used for simulating the modified IEEE 34 Node Network which is used for distributed parameter line model. In this method, fault location is specified only by using three-phase voltages and currents at the beginning of feeder. The comparing index defines the error percentage of fault location which is calculated by following equation like other papers in this title:

Error% ¼

xactual  xcalculated  100 lt

(5)

where: x actual: the real fault distance. x calculated: the calculated fault distance. lt: the total length of feeder.

4.2. Performance evaluation

Fig. 2. Data arrangement for the phase variations and voltage magnitude difference equations.

d ¼ j xDV  xDq j

(4)

where:d is matching or mismatching value.DV is the obtained distance from voltage magnitude difference equation.Dq is the obtained distance derived from phase angle variation equation. If d z 0.0, then, the matching is complete. Ranking and priority of possible points are sorted based on matching value. The procedure is simplified by use of the following relations. The final result is a list of possible fault section or sections which are sorted based on the matching degree. Each one with the minimum value is the main faulty section. It can be understood better, if Fig. 4 is taken into account. This figure shows two curves that are obtained from simulating fault in determined possible fault section by IBFLM in step 0.1 km. This demonstrates the curve of voltage magnitude difference equation related to the distance (fDv (DV, x)) and phase angle variation related to the distance (fDq(Dq, x)). Both equations represent a voltage sag diagram along with two adjacent buses for each possible fault section. Therefore, the recorded magnitude difference and phase variation of voltage (actual values) are assigned on these figures and two distances xDV and xDq can be calculated as shown in Fig. 4. These distances close to each other for main faulty section which is known through matching index d. It is shown in this figure.

4. The simulation results 4.1. Case study For evaluating the performance of the proposed method, the modified IEEE 34 Node Network is selected for simulation. This network is shown in Fig. 5 [19]. The general data of selected feeder are 98.18 km length which has eight laterals and sub-laterals and the voltage regulators are also removed. There is an assumption that the lines in modified IEEE 34 Node Network are three-phase

In this method, firstly, the possible locations of fault are determined by IBFLM. As an example, a single-phase fault occurred in section 808e810, 11.979148 km from the beginning of the feeder. Fault resistance is assumed to be zero U and the fault occurred at 0.3 s. The voltage and current waveforms of phase are shown in Fig. 6. Now, sections 808e810, 11.9780 km and 808e812, 12.0504 km are determined as the possible fault points by IBFLM. One of these sections is the real fault section. Therefore, for real faulty section detection, the same type of fault is simulated in each possible section of fault by step 0.1 km and the voltages obtained at the beginning of feeder are recorded. Then, voltage difference of pre-fault and past-fault is calculated for each simulated fault. Now through using recorded magnitude and phase variation of voltage difference, the coefficient of defined three-order polynomial equations are determined for magnitude and phase variation of voltage difference of phase a. The values of matching index d are calculated for two possible fault locations as 0.0086 for section 808e810 and 0.4283 for 808e812. From among them, the calculated index for fault in sections 808 and 810 at 11.9780 km is minimum. Consequently, based on the proposed method, the fault is located at 11.9780 km from the beginning of feeder in sections 808 and 810, of which the error is 0.0011%. It is run for some locations, as results show in Table 3. According to this table, it can be understood that the method is accurate for determining the faulty section and distance. In the following, effect of the influential parameters such as location of fault, fault inception angle have been considered in order to evaluate the accuracy of the proposed method. Case 1: Effect of different fault locations on the accuracy of the proposed method; in this part, single-phase fault in different locations is simulated to verify the accuracy of the method. The fault parameters are three fault distances in three sections (808e810, 11.979148 km, 862e838, 58.392614 km, 818e820, 34.301798 km)  and fault inception angle is 45 . The results are shown in Table 3. According to this table, it can be seen that the number of possible locations can be different. For example, the number of possible locations is two for fault in 808e810 and 818e820 while it is three for fault in 862e838. Also, it is one for fault in 802e806. Moreover, it can be understood that three fault distances is calculated for each possible fault point which is obtained by IBFLM (xIBFLM) and two cubic equations (xDv and xDq explained in part 3. B). These fault distances are sum of two integers that are actually the distances of

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Fig. 3. Flowchart of global steps of proposed method.

beginning bus of section to the beginning of the feeder and second one is distance of the beginning bus of investigated section to determined fault point. These three distances are close to each other. Also, according to this table, it is clear that the accuracy of the proposed method is significantly good for determining section and distance of fault. The maximum error is 0.42% (for 100 U fault resistance). Moreover, in this table, the calculated coefficients of the magnitude difference and phase variation of voltage that is threeorder algebraic equation are shown in column 3. Case 2: Effect of different fault resistance on the accuracy of proposed method; several tests are performed in which the parameters are fault inception angle: 45, single phase fault to ground at 11.9791 km. The obtained results are shown in Table 4. According to this table, it can be seen that the minimum and maximum errors are 0.0006% and 0.1623%, respectively, in these two locations of fault for different resistances. Also, as per the presented d (index of fault section estimation) values in this table, it can be found that the accuracy of the proposed method in fault section estimation is good and all real fault sections and location are determined precisely. As an example, the difference of d value in different locations and resistances is upper than 0.4; it means the minimum d can be determined clearly. Also, the minimum d is always calculated for real fault section. Meanwhile, according to the second selected location in Table 4, it can be seen that the number of possible

locations in 50 and 100 U fault resistances which is calculated with IBFLM are only one and it is real fault section and distance. Consequently, the proposed fault section estimation algorithm does not need them because it is should be applied when there are some possible locations. Case 3: Effect of fault inception angle on the accuracy of proposed method; a variety of simulations has been conducted for evaluating this condition. Parameters of simulations have been considered as follows:  Four distances of fault (6, 12.21, 42.3 and 60.41 km).  Five fault inception angles (0, 45, 90, 120, and 165). The results are shown in Table 5. According to this table, it can be pointed out that the errors’ differences are between 0 and 0.0017 for different fault inception angles. Therefore, on the basis of results, it can be observed that the accuracy of the given method is significantly high. Case study 4: Practical test in power system simulator; The new test feeder is simulated on power system simulator installed in central power system laboratory in Persian Gulf University. Single line diagram is shown in Fig. 7. This feeder has 8 nodes and 270 km line length. The load is distributed in this system. The line information is shown in Table 6. The actual simulation is shown in Fig. 8. According to this figure, it can be seen that the network starts from

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363

Fig. 6. Voltage and current of faulty phase at the beginning of feeder (faulty point is in sections 808 and 810, 11.979148 km).

Fig. 4. Voltage magnitude and phase angle equation for a, b section.

Fig. 5. Single-line diagram of modified IEEE 34 Node Network.

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Table 3 Effect of different locations on the proposed fault section estimation method. Actual section

Possible locations

The coefficient of defined three order polynomial equations

d index

808e810, 11.21008 þ 0.7690 km

808e810 xIBFLM ¼ 11.21008 þ 0.7688 xDv ¼ 11.21008 þ 0.7704 km xDq ¼ 11.21008 þ 0.7618 km 808e812 xIBFLM ¼ 11.21008 þ 0.8403 xDv ¼ 11.21008 þ 0.8720 km xDq ¼ 11.21008 þ 0.4437 km 846e848 xIBFLM ¼ 58.099574 þ 0.6438 km xDv ¼ 58.099574 þ 0.2440 km xDq ¼ 58.099574 þ 0.2308 km 862e838 xIBFLM ¼ 57.822614 þ 0.6438 km xDv ¼ 57.822614 þ 0.5665 km xDq ¼ 57.822614 þ 0.5463 km 836e840 xIBFLM ¼ 57.822614 þ 0.3406 km xDv ¼ 57.822614 þ 0.5669 km xDq ¼ 57.822614 þ 0.5211 km 818e820 xIBFLM ¼ 32.301798 þ 2.0790 xDv ¼ 32.301798 þ 1.7059 xDq ¼ 32.301798 þ 2.0031 824e826 xIBFLM ¼ 34.813806 þ 0.1046 xDv ¼ 34.813806 þ 2.2586 xDq ¼ 34.813806 þ 0.4959 802e806 xIBFLM ¼ 0.786384 þ 0.3 xDv ¼ 0.786384 þ 0. 2956 xDq ¼ 0.786384 þ 0. 4722

a3 ¼ 5.4711, a2 ¼ 0, a1 ¼ 358.77, a0 ¼ 6685,b3 ¼ 0.0022627, b2 ¼ 0, b1 ¼ 0.01864, b0 ¼ 2.2344

0.0086 ok

a3 ¼ 0.3039, a2 ¼ 13.505, a1 ¼ 323.94, a0 ¼ 6683.1, b3 ¼ 4.0827e-6, b2 ¼ 0.0005179, b1 ¼ 0.034262, b0 ¼ 2.2343

0.4283

a3 ¼ 0, a2 ¼ 0, a1 ¼ 46.667, a0 ¼ 1965.1, b3 ¼ 0, b2 ¼ 0, b1 ¼ 0.00043333, b0 ¼ 1.5196

0.4748

a3 ¼ 0.37776, a2 ¼ 0, a1 ¼ 45.661, a0 ¼ 1980, b3 ¼ 0.00043519, b2 ¼ 0, b1 ¼ 0.0053616, b0 ¼ 1.5156

0.0202 ok

a3 ¼ 0, a2 ¼ 0, a1 ¼ 45.333, a0 ¼ 1979.9, b3 ¼ 0, b2 ¼ 0, b1 ¼ 0.0063333, b0 ¼ 1.5153

0.0458

a3 ¼ 5.3084e-005,a2 ¼ 0.0019807, a1 ¼ 0.0077968, a0 ¼ 1.7225 b3 ¼ 0.048022, b2 ¼ 2.9786, b1 ¼ 106.32, b0 ¼ 3303.8

0.2972 ok

a3 ¼ 0.0039232, a2 ¼ 0, a1 ¼ 0, a0 ¼ 1.6851, b3 ¼ 62.319, b2 ¼ 0, b1 ¼ 0, b0 ¼ 3094.8

2.7545

a3 ¼ 0.6373, a2 ¼ 9.4564, a1 ¼ 51.14, a0 ¼ 117.2, b3 ¼ 2.306e-008, b2 ¼ 0.00014, b1 ¼ 0.3581, b0 ¼ 342.3

ok

862e838 57.822614 þ 0.57 km

818e820 32.301798 þ 2 km

802e806 0.786384 þ 0.3 km

Table 4 Results of running the proposed algorithm at different locations. Actual fault location (km) 808e810 11.979148

Fault resistance (U) 0

20

50

100

818e820 42.3

0

20

50

100

Possible fault location (km)

Error %

d

808e810 11.9780 808e812 12.0504 808e810 11.9784 808e812 11.8629 808e810 11.9764 808e812 11.70614 808e810 11.9736 808e812 11.5714 818e820 42.387798 854e852 43.670306 854e856 43.378106 818e820 42.417098 854e852 42.646306 854e856 42.669406 818e820 42.459398

0.0011

0.0086

0.0725

0.4283

0.0006

0.0029

0.1184

1.2985

0.0027

0.0014

0.2780

0.4967

0.0056

0.0058

0.4153

0.3987

0.0894

0.0754

1.3957

1.1514

1.0980

1.0348

0.1192

0.1254

0.3527

0.4710

0.3762

0.2061

0.1623

0.1425

e

e

e

e 818e820 42.6822

e

e

0.13515

0.1791

e

e

e

e

e

e

ok

ok

ok

ok

ok

ok

ok

ok

M. Daisy, R. Dashti / Energy 103 (2016) 356e368

365

Table 5 Results of running the proposed algorithm for fault inception angles. Actual fault location (km)

Fault inception angle (degrees) 0

45

90

120

165

1.4135e-6 3.0767e-5 0.1203 0.1181

0.8510e-5 6.8936e-4 0.1213 0.1181

6.3793e-4 12.0795e-4 0.1196 0.1181

8.0013e-4 6.9070e-4 0.1182 0.1181

Error % 6 12.21 42.3 60.41

7.1490e-4 6.8849e-4 0.1213 0.1181

the grid and reaches to the distribution feeder through one substation. All voltage and current data are gathered at the beginning of feeder by Krona-520 (Koha-520, Russian device) data loggers. Its sampling rate is set on 25 kHz (every 40 micro seconds, one data is recorded). The power system simulator consists of five parts namely the DG (distributed generator) and Grid cabinet, the substation (1.5 switch), transmission and distribution lines, subtransmission substation (double bus bar), constant and static loads. In this test, single-phase fault to ground occurs in 85 km from the beginning of feeder at node 7. The fault resistance is 12.5 U. The voltage and currents which are recorded at the beginning of feeder are shown in Fig. 9. This Krona-520 sends back the data as a text file which is entered into Matlab software and its figure is plotted. The magnitude difference and phase variation of voltage are calculated

Fig. 7. Single line diagram of test feeder 2.

Table 6 Simulated distribution feeder. Section

1e2

2e3

Distance (km) 15 15 Line type ACSR-118.5 ACSR-118.5 loads e e The voltage of PD system is 20 kV

2e4

4e5

4e6

2e7

7e8

15 ACSR-118.5 Constant, 315 kV A, 0.8 lag

15 ACSR-118.5 e

70 ACSR-226 Constant, 500 kVA, 0.8 lag

70 ACSR-226 Static 400 kV A, 0.8 lag

70 ACSR-226 Static 500 kV A, 0.85 lag

Fig. 8. Actual test on power system simulator in Central power system Laboratory in Persian Gulf University.

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M. Daisy, R. Dashti / Energy 103 (2016) 356e368

Fig. 9. Voltage and current at the beginning of feeder (output plot of Krona-520 in Matlab Software).

Table 7 Comparing the proposed method and other presented method in fault distance determination topic. Reference

[11,29]

[13]

[6,7]

[27]

The proposed method

Errors%

10.97%

1.58%

6.7%

8.15%

0.42%

and recorded. Then, the possible fault locations are calculated by IBFLM. It has two possible fault locations which are in section 2e7, 84.15 km (error ¼ 0.3148%) and section 4e6, 82.95 km (error ¼ 0.7592%). One location is the main place of fault. Now, the online databank is generated through simulating a similar fault in each possible fault section and extracting the cubic equation for magnitude difference and phase variation of voltage. Now, the recorded magnitude difference and phase variation of voltage for actual fault are set in these cubic equations and the xDV and x Dq are calculated. In this test, the d index is 0.1163 and 0.6382 for Sections 2e7 and 4e6, respectively. It is shown that the main location fault is in section 2e7 km from the beginning of feeder. Case 5: Comparing the proposed method accuracy to recent given methods: The proposed method is focused on fault distance determination and fault section estimation, thus, the comparative part with other methods should be investigated. At first, the accuracy of IBFLM is compared with other papers and it is presented in Table 7. All errors are calculated for 100-U fault resistance, whereas the

maximum error for the proposed method is 0.42%. According to this table, it can be concluded that the accuracy of the proposed improved IBFLM is higher than the other papers which is one of advantages of the suggested method. Secondly, the given fault section estimation methods are compared with the proposed method in them. Correct section estimation in different conditions is so important for comparing influence of operation services, upstream and downstream PD network development. Different conditions are investigated for some given methods and their results are reported as follows:  In Refs. [9] and [29], the faulted section is determined by protective devices one of which is cutout. This device is operating by melting the element and the mechanical moving. If the lubrication service of this device is not done in regular schedule, then, protection coordination is missed and estimating the faulty section is incorrect. Also, if the fuse link of this device is not selected commensurate with PD network, the performance of this device faces a mistake and the protection coordination is missed.  In Ref. [11], the neural network is used for determining the faulty section. According to the neural network, databank and learning are needed, thus it is not suitable for PD network; since, in accordance with different conditions, this network is changed. Consequently, its databank and learning set should be updated.

M. Daisy, R. Dashti / Energy 103 (2016) 356e368

 In Ref. [37], the faulty section is determined through calculating the natural frequency from voltage waveform. The accuracy of this method depends on the fault resistance; since it can smooth the generated transient waveform and consequently determining the natural frequency might be impossible.  In Ref. [5], at first, the generated frequency is saved in databank for fault in each place and section. Then, when fault occurs, the faulty section is estimated through comparing the generated frequency in fault with the saved frequency in offline databank. Each one with the most overlap is presented as faulty section. This method is highly sensitive to fault resistance and databank, while the PD network spreads in different places and it changes in different conditions, regularly.  In the proposed method, the faulty section is estimated online without needing to offline databank. After determining the possible fault locations, the online databank is generated with the defined matching value and the faulty section is determined. The advantage of the proposed method is resistant against fault conditions. In accordance with the results in previous cases, it can be concluded that all faulty sections are estimated correctly.

367

5. Conclusion In the present paper, a new combined method is proposed for online locating fault in power distribution network. In this method, the possible fault locations are determined by the proposed impedance-based fault location method as well as the recorded voltage and current at the beginning of feeder. Then, the actual location of fault and faulty section are determined by a novel fault section estimation method. For applying this, firstly, the same fault type which should be simulated in each possible fault location and the voltage sags are recorded for each location. Then, the threeorder polynomial equation is determined for magnitude and phase variation of voltage difference which is recorded at the beginning of feeder for each possible faulty section. Finally, the real location of fault and faulty section are estimated through comparing the matching index (jxDV  xDqj). Each one with the minimum index is real fault location and section. Appendix A

32 3 2 Vsa 1 0 0 8 76 7 6 76 7 > k0 ¼ 6 > 4 0 1 0 54 Vsb 5 > > > > > Vsc 0 0 1 > > > 32 3 2 > > > Isa 1 1 1 > >   > 76 7 6 > 1 þ þ >   0 0 6 6 7 > k1 ¼  zc g þ zc g þ zc g 4 1 1 1 54 Isb 7 > 5 > 3 > > > > I 1 1 1 > sc > > > 2 3 > >        2  2    2  2  2 > 2 2 2 2 > þ  0 þ 2  0 þ  2 0 > > g g g g g þ g þ g þ a þ a g þ a g þ a 6 72 3 > > 6 7 Vsa > > 6 7 >  2  2  2  2  2  2  2  2 7 6 > 7 1 6  þ 2 > > 6 7 > k2 ¼ 6 gþ þ g þ g0 gþ þ a 2 g þ a g0 7 þ a g þ a2 g0 > 6 g 74 Vsb 5 > 6 > 6 7 > > 6  2 >  2  2  2  2  2 7  2  2  2 > 4 þ 5 Vsc > > > g gþ þ a g þ a2 g0 gþ þ g þ g0 þ a2 g þ a g0 > > > > > > 2 3 > >  3  3  3  3  3  3  3  3  3 > > þ  0 þ 2  0 þ  2 0 > > g g g g g þ g þ g þ a þ a g þ a g þ a 6 72 3 > < 6 7 Isa 6   3  3  3  3  3  3  3  3 7 6 76 7 3 1 þ > 6 7 k3 ¼  6 > gþ þ g þ g0 gþ þ a 2 g þ a g0 7 þ a g þ a2 g0 > 6 g 74 Isb 5 > 18 > 6 7 > > 6  3 >  3  3  3  3  3 7  3  3  3 > 4 þ 5 Isc > 2  0 þ  2 0 > g g g g gþ þ g þ g0 þ a þ a g þ a g þ a > > > > > > 2 3 > >  4  4  4  4  4  4  4  4  4 > > > þ  0 þ 2  0 þ  2 0 > g 6 72 g g g g þ g þ g þ a þ a g þ a g þ a 3 > > 6 7 Vsa > > 6  7 > >    4  4  4  4  4    4 7 6 7 > 1 6 > 6 6 gþ 4 þ a g 4 þ a2 g0 4 7 > > k4 ¼ gþ þ g þ g0 gþ þ a2 g þ a g0 7 6 74 Vsb 5 > > 72 > 6 7 > > 6  4  4  4  4  4  4 7  4  4  4 > > 4 þ 5 Vsc > 2  0 þ  2 0 þ  0 > g g g g g þ a þ a g þ a g þ a þ g þ g > > > > > > 2 3 > >  5  5  5  5  5  5  5  5  5 > > > þ  0 þ 2  0 þ  2 0 > g 6 72 3 g g þ g þ g þa g þa g þa g þa g > > 6 7 Isa > > 6  > >  5  5  5  5  5  5  5  5 7 6 76 7 > 5 1 > 6 7 6 gþ þ a g þ a2 g0 > k5 ¼  gþ þ g þ g0 gþ þ a2 g þ a g0 7 > 6 74 Isb 5 > 360 > 6 7 > : 6  5  5  5  5  5  5 7  5  5  5 4 þ 5 Isc g gþ þ a g þ a2 g0 gþ þ g þ g0 þ a2 g þ a g0

(A.1)

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