Unsynchronized fault-location technique for two- and three-terminal transmission lines

Electric Power Systems Research 158 (2018) 228–239

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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr

Unsynchronized fault-location technique for two- and three-terminal transmission lines Mahmoud A. Elsadd a , Almoataz Y. Abdelaziz b,∗ a b

Department of Electrical Engineering, Faculty of Engineering, Menoufia University, 32511 Shebin El-Kom, Egypt Electrical Power and Machines Department, Faculty of Engineering, Ain Shams University, Cairo, Egypt

a r t i c l e

i n f o

Article history: Received 11 August 2017 Received in revised form 25 November 2017 Accepted 5 January 2018 Available online 3 February 2018 Keywords: Fault location Transmission lines Simulation MATLAB Symmetrical components Unsynchronized measurement

a b s t r a c t In this work, a novel fault-locator technique for two- and three-terminal power transmission lines is introduced. Unsynchronized three-phase current and voltage measurements of all line ends are processed for estimating the required synchronization angle/s and the fault location via exploiting the initial conditions of each fault type. To realize this target, the computations of the required synchronization angle/s are initially accomplished independent of the fault location via considering a lumped charging current at the reference terminal which is selected arbitrarily. Consequently, the initial fault location is determined via equating the deduced equations of the positive-sequence voltage at the faulty point from two sides of the faulted segment as a function of the measured data after their correction. The previous obtained fault location is, then, utilized as an input for the next iterative computations, where the distributed line model is used to update the charging current. This process is repeated until the change rate of the obtained fault location becomes negligible. The proposed technique has been examined and assessed under different fault scenarios simulated using MATLAB. The sample results of the assessment are declared and discussed. © 2018 Elsevier B.V. All rights reserved.

1. Introduction Power transmission system transfers electrical energy from the power plants to the substations near loads. Usually, the electrical power is transferred through overhead transmission lines. Conventional transmission lines have two terminals. Now, the use of three-terminal lines is growing for diverse economical and technical purposes [1]. Three terminal lines usually hold until installing new substation when the loads increase to a certain level [2]. Overhead transmission system suffers from occurrence of various faults. These faults usually are shunt faults triggered by lightning strokes, rain, birds, streamer, or insulators pollution. The malfunction of the transmission system leads to serious influences on highly electrified modern society. Therefore, various protection devices are installed on the transmission lines in order to isolate the faulted line. Also, it is very important to accurately locate the faulty point to quickly accomplish the necessary repair process, thus, reducing operating costs [3–7].

∗ Corresponding author. E-mail addresses: [email protected]fia.edu.eg (M.A. Elsadd), almoataz [email protected] (A.Y. Abdelaziz). https://doi.org/10.1016/j.epsr.2018.01.010 0378-7796/© 2018 Elsevier B.V. All rights reserved.

The difficulty of fault-location determination for transmission lines is due to that the measurements at transmission line terminals may be unsynchronized. This reason is related to using fault location algorithms based on two-terminal measurements recorded by the intelligent electronic devices (IEDs) with unsynchronized measurements. Earlier, the single-ended fault location techniques based on the Phasor estimation were used. However, they required necessary assumptions to remove the effect of fault impedance such as considering its value to be zero or purely resistive, or considering that the impedances behind line ends are constant and have known values [8]. Therefore, the synchronized two-terminal measurement-based fault location techniques were used after developing the phasor-measurement units (PMUs) based on the global positioning system (GPS) in the early 1980s [9–14]. In these techniques, the common time reference for recorded measurements was obtained by the GPS signal. However, practically now, the IEDs have been installed on most substations for protection purposes [15] instead of the GPS-based PMUs. Consequently, a synchronization factor (ej␦ ) is required in order to synchronize the recorded measurements. The angle ı is the required synchronization angle. Also, the procedures of fault location determination for three-terminal lines are more difficult than those of the traditional two-terminal ones due to the outfeed/infeed from the third terminal [16–18]. Consequently, fault location determination based on

M.A. Elsadd, A.Y. Abdelaziz / Electric Power Systems Research 158 (2018) 228–239

unsynchronized measurements for transmission lines represents a challenge for engineers due to these various problems. Set of the phasor based-algorithms have been presented for overcoming the aforementioned fault-location problems [19–28]. These algorithms can be categorized from number-of-lineterminals point of view into techniques presented for two-terminal transmission lines [19–23] and others presented for three-terminal transmission lines [24–28]. In Ref. [19], a fault location scheme was developed via equating the equation of the negative- or zero-sequence voltage at the faulty point from two sides as a function of measured currents only using the short-distance line model to locate phase-to-phase or earth faults, respectively. However, this scheme considered that the source impedance’s value is constant. In Ref. [20], a faultlocation algorithm was presented to find, unknown variables, the fault distance and the synchronization angle (ı). Relationship that combines the unknown variables was based on equating the positive-sequence voltage at the faulty point from two sides as a function of two-end unsynchronized measurements based on the distributed line model. These unknown variables are obtained via the Newton–Raphson method-based iterative calculations. The initial values for these variables are obtained via firstly solving the problem considering the short-distance line model to guarantee the convergence behavior. In Ref. [21], a numerical method was proposed to obtain ı value by a proposed equation exploiting that the estimated fault distance must be a real value only at the actual value of ı. The fault distance was estimated after correcting unsynchronized measurements by equating the positive-sequence voltage from two sides using the distributed line model. However, the estimated fault distance may also be a real value at a false ı value. Hence, three constraints were used to treat multiple-solution conditions and then single out the precise ı. The first constraint is that the estimated fault distance should be less than the total line length at the precise ı. The second constraint is that the fault distance obtained via using positive-sequence variables is very close to that obtained via using negative-sequence variables at the correct ı. The third constraint is that at the correct ı, the calculated fault impedance is almost real value. In Ref. [22], the algorithm is based on obtaining the fault impedance equation as a function of only an unknown variable which is the fault distance where its equation was independent of the ı value. Then, the fault distance is obtained via assuming that the fault impedance is purely resistive. However, this algorithm can not locate the faults associated with a fault impedance having an imaginary part as faults in electrical cables. In Ref. [23], an unsynchronized fault-location method is presented via equating only the magnitudes of the positive-sequence voltages at the faulty point computed form two sides. The equation was solved by assuming that the variations of the voltage magnitudes along the line length were linear. The slopes of the two straight lines were firstly assumed to be equal to that at line terminals. Hence, the precise solution was obtained by an iterative algorithm to update the slope of the two straight lines based on the past fault distance calculated via the intersection point of these two lines. Other algorithms were suggested to estimate the fault location in three-terminal transmission lines [24–28]. Some of these algorithms used synchronized measurements [24–26] and the others used the unsynchronized data [27,28]. In Ref. [24], the fault distance was estimated as a function of synchronized data measured only at two terminals. However, it is based on a pure resistance assumption for the fault impedance. In Ref. [25], the proposed formula is deduced based on the distributed line model. The suggested formula was solved via an iterative solving procedure. In Ref. [26], a fault-locator algorithm using only negative-sequence circuit was proposed to locate the unbalanced shunt faults. This method used the short-line model. The proposed formula is a func-

229

tion of negative-sequence currents and voltage at all line terminals. However, it is dependent of the negative-sequence impedance magnitude of the source. In Ref. [27], an unsynchronized faultlocator algorithm for two- and three-terminal lines based on equating the voltages at the faulty point from all terminals’ directions was introduced. The proposed formula having two unknown variables was derived based on the short line model. The unknown variables were estimated by an iterative solving process. However, the initialization of the calculation process was random based on the probability distribution of fault location. Hence, this process may give rise to a divergent solution. In Ref. [28], an unsynchronized fault-locator method using only the negative-sequence voltages magnitudes at three line ends was proposed using the short line model to locate the unbalanced shunt faults. The faulted section identification and then the fault distance determination were obtained as a function of the ratios between the negative-sequence voltages magnitudes measured at line terminals, line parameters, and negative-sequence reactances behind measuring points. However, this method is sensitive to source reactance variation. This paper presents an iterative unsynchronized fault-location technique for two- and three-terminal transmission lines. The paper concentrates on unbalanced faults. In the first iteration, the correction of the unsynchronized measurements is initially accomplished via assuming that the charging current is lumped at the reference terminal. Then, the initial fault distance is calculated. In order to cancel the error resulted from this assumption, other iterations are required. In the next iteration, the value of the charging current is updated based on the obtained fault distance from the previous iteration. Then, the synchronization angle and the fault distance values are also updated. This process is repeated until the change of the fault distance becomes insignificant. The proposed synchronization-angle calculation method and the fault-location algorithm are extended to be suitable for three-terminal transmission lines in conjunction with a faulty side identification method independent of the synchronization angle. The proposed algorithms are independent of both the fault and source impedances.

2. Proposed unsynchronized fault-locator scheme for transmission lines The proposed unsynchronized fault-locator scheme is iterative in order to be adequate to short and long transmission lines. The proposed synchronization-angle calculation method does not need the transmission line parameters in case of short transmission lines via neglecting the charging current. However, it needs the line parameters and the fault distance in case of long transmission lines. Therefore, the algorithm must be iterative. In the first iteration, the synchronization operator (ej␦ ) is estimated independently of the fault distance whether the line is two or three terminals.

2.1. First iteration 2.1.1. Proposed synchronization-angle calculation technique As aforementioned before, a synchronization factor (ej␦ ) is utilized to synchronize the recorded measurements. This factor should be applied on the phasors measured on all terminals except that arbitrarily considered the reference. The measured phasors at these selected terminals (Vj and Ij ) are corrected via applying the synchronization factor as in Eq. (1). If the start time of the recording phasors at j terminal lags the reference by an angle Ø, the required synchronization angle ı must compensate for this angle Ø in the counter

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direction with the same value. For example, if Ø is 10◦ lagging, then ı must be 10◦ leading, and vice versa. Vj (cor) = Vj · ejı



ICapi = VAi ·



yi

(4)

(1)

Ij (cor) = Ij · ejı

where j is the terminal (substation) symbol. The synchronization operator (ejı ) is obtained using the initial conditions according to the fault type. Under line-to-ground fault, the currents of two healthy phases at the faulty point equal zero as in Fig. 1a, whereas under phase-to-phase or phase-to-phase-toground faults, the current of the healthy phase at the faulty point equals zero as in Fig. 1b. Using the symmetric component transformation to decouple three-phase quantities as in Eq. (2), the relation between the sequence currents components at the faulty point is different according to the fault type as follows. Under line-toground fault, the zero-, positive-, and negative-sequence currents (IF0 , IF1 , and IF2 ) of the faulty phase at the faulty point are equal, whereas for phase-to-phase or phase-to-phase-to-ground faults, the summation of the existing sequence currents of the healthy phase at the faulty point equals zero. The exploiting of the initial conditions for three-terminal transmission lines is more complicated than that for two-terminal lines. Thus, the method is first presented for two-terminal lines.

       IFa0   1 1 1   IFa         1  2  IFa1  = 3 ·  1 ˛ ˛  ·  IFb     1 ˛2 ˛    I  IFc Fa2

(2)

A. Two-terminal transmission lines As illustrated in Fig. 1, a single-line diagram of a simple twoterminal transmission line connecting between two substations A and B subjected to different fault types is used to illustrate the proposed algorithm for obtaining the synchronization angle. The total transmission line length between two substations A and B is L. The Thévenin equivalent circuits of rest of grid connected to the two substations A and B are ESA , ZSA , ESB , and ZSB . The measured phase currents on Busbars A and B are denoted by IA and IB , respectively. The transmission line is subjected to a fault at point F that is located at a distance x from substation A. The positive-, negative-, and zero-sequence currents at the faulty point are expressed as a function of the measured data as in Eq. (3).



ICapi = IAi + IBi · ejı



yi is the sumwhere VAi is ith sequence voltage of terminal A. mation of ith sequence line’s admittance of entire transmission line. The positive-, negative-, and zero-sequence currents at the terminal A after subtracting the summation of ith sequence line’s capacitors currents, respectively, are denoted by IA1 , IA2 , and IA0 . However, there may be errors associated with the calculation of Eq. (4). Those errors would be corrected by an iterative process proposed in this paper. For line-to-ground fault, the sequence currents components at the faulty point are equal because only one phase has a current through the fault path as illustrated in Fig. 1a. By equating the positive- and zero-sequence currents at the faulty point, Eq. (5) can be obtained: (IA1 − IA0 ) = (IB0 − IB1 ) · ejı

(3)

where subscript: i refers to the zero-, positive-, and negativesequence components. IAi and IBi  are the ith sequence currents at terminals A and B, respectively. ICapi is the summation of ith sequence line’s capacitors currents. The line’s capacitors current is not effective in earthed distribution system [29] due to low voltage level and short line lengths. On the other hand, the voltage level of the transmission lines is high. Thus, the line’s capacitors current can be only neglected irrespective of the value of fault impedance in case of short transmission lines such as that protected by differential relay as a primary protection. In case of long transmission lines, the capacitors current should be taken into consideration. This current is initially calculated as a function of both voltage of

(5)

The required synchronization angle under line-to-ground fault can be obtained using Eq. (6). ı = angle (IA1 − IA0 ) − angle (IB0 − IB1 )

(6)

For line-to-line-to-ground fault, the summation of the sequence currents components at the faulty point equals zero as in Eq. (7) due to the parallel connection of the sequence networks. IA1 + IA2 + IA0 = − (IB1 + IB2 + IB0 ) · ejı

where subscripts: 0, 1, and 2 refer to the zero-, positive- and negative-sequence components. Subscripts: a, b, and c refer to the phases. ˛ is ej2/3 . IFa , IFb , and IFc are the three-phase current at the faulty point.

IFi = IAi + IBi · ejı −

the reference terminal, terminal A, and line’s capacitors in order to be referred to the reference time as follows:

(7)

The required synchronization angle under line-to-line-toground fault can be obtained utilizing Eq. (8). ı = 180◦ + angle (IA1 + IA2 + IA0 ) − angle (IB1 + IB2 + IB0 )

(8)

For line-to-line fault, the positive- and negative-sequence currents at the faulty point are equal in the magnitude and opposite in the direction as in Eq. (9) due to the parallel connection of the positive- and negative-sequence networks and absence of the zerosequence component. IA1 + IA2 = − (IB1 + IB2 ) · ejı

(9)

The required synchronization angle under line-to-line fault can be obtained using Eq. (10). ı = 180◦ + angle(IA1 + IA2 ) − angle(IB1 + IB2 )

(10)

However, the calculation of the synchronization angle is based on the fault type. Hence, a fault classification method is required. Under line-to-line fault, the measured three-phase current have positive- and negative-sequence components but the zero-sequence component is, almost zero, lower than the normal unbalance zero-sequence current (I0n ). However, the discrimination between the line-to-ground fault and the line-toline-to-ground fault is more difficult. The presented algorithm can also identify the fault type using the calculated magnitude of the synchronization factor (|ejı |). The |ejı | is almost one if the considered fault type is the real fault type. The |ejı | can be obtained as follows: Under line-to-ground fault, the |ejı | can be obtained using Eq. (11).

 jı  |(IA2 − IA0 )| |(IA1 − IA0 )| e  = = |(IB0 − IB2 )|

|(IB0 − IB1 )|

(11)

If the fault type is line to ground, then two sides of Eq. (11) is almost equal to one. Otherwise, the fault type is line to line

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231

Fig. 1. A single line diagram of two-terminal transmission line under: (a) phase-to-ground fault and (b) phase-to-phase or phase-to-phase-to-ground faults.

to ground. Under line-to-line-to-ground fault, the |e jı| can be obtained using Eq. (12).

 jı  e  = |IA1 + IA2 + IA0 |

(12)

|(IB1 + IB2 + IB0 )|

As illustrated in Fig. 2, a single-line diagram of a simple threeterminal transmission line connecting between three substations A, B, and C is utilized to clarify the presented algorithm. The line lengths between each of substations A, B, and C and Busbar T are LAT , LBT , and LCT . The Thévenin equivalent circuits of the rest of grid connected to the three substations A, B, and C are ESA , ZSA , ESB , ZSB , ESC , and ZSC , respectively. The measured currents on Busbars A, B, and C are denoted by IA , IB , and IC , respectively. The transmission line is subjected to a fault at a distance x from Busbar A. The positive-, negative-, and zero-sequence currents at the faulty point are expressed as a function of the measured data as in Eq. (13):



(IA0 − IA2 ) . (IB1 − IB2 ) + (IA2 − IA1 ) . (IB0 − IB2 ) (IC2 − IC1 ) . (IB2 − IB0 ) + (IC2 − IC0 ) . (IB1 − IB2 )

(13)

The sequence currents components at the faulty point are equal under line-to-ground fault. By equating the positive- and negativesequence currents at the faulty point, the first synchronization factor (ejı1 ) can be obtained as a function of the second synchronization factor (ejı2 ) as in Eq. (14): (IA2 − IA1 ) (IC2 − IC1 ) = + · ejı2 (IB1 − IB2 ) (IB1 − IB2 )

ejı1 =

(15)

(IA0 − IA2 ) . (IC2 − IC1 ) + (IA1 − IA2 ) . (IC0 − IC2 ) (IC2 − IC1 ) . (IB2 − IB0 ) + (IC2 − IC0 ) . (IB1 − IB2 )



[(IAi + IBi . ejı1 + ICi . ejı2 ) −



ICapi ] = 0.0

(17)

i=0,1,2

Then Eq. (18) can be obtained, as follows: IAa + IBa · ejı1 + ICa · ejı2 −



ICap1 −



ICap2 −



ICap0 (18)

where IAa , IBa , and ICa are the healthy phase current at the three terminals A, B, and C. Under consideration that the common time reference is the measured starting at Busbar A, the first and second synchronization angles (ı1, ı2) should modify the recorded angles of healthy phase current at terminals B and C denoted by  Ba and  Ca , respectively in order to be synchronized together. The summation of ı1 and  Ba is denoted by   Ba , while the summation of ı2 and  Ca is labeled as   Ca . Therefore, Eq. (18) can be rewritten as; |IAa | · ejAa + |IBa | · ej(ı1+Ba ) + |ICa | · ej(ı2+Ca ) = 0.0

(14)

(16)

For line-to-line or line-to-line-to-ground faults, the summation of the existing sequence currents components at the faulty point equals zero as in Eq. (17).

= IAa + IBa · ejı1 + ICa · ejı2 = 0.0

ICapi = IAi + IBi · ejı1

+ ICi · ejı2

ejı1

ejı2 =

Also, the first synchronization factor (ejı1 ) can be obtained as in Eq. (16) by substituting with Eq. (15) in Eq. (14).

• Three-terminal transmission lines

IFi = IAi + IBi · ejı1 + ICi · ejı2 −

The second synchronization factor (ejı2 ) can be obtained as in Eq. (15) by equating the negative- and zero-sequence currents at the faulty point and then substituting with Eq. (14).

|IAa | · ejAa + |IBa | · e

j( 

Ba )

+ |ICa | · e

j( 

Ca

)

= 0.0

(19) (20)

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Fig. 2. A single line diagram of a three-terminal transmission line under a fault on the section connected to terminal A.

where the healthy phase current magnitude at terminal A after subtracting summation of the three-sequence line’s capacitors currents referred to the reference time and its angle are |IAa |, and Aa , respectively. The formula presented in Eq. (20) has two unknown parameters (  Ba and   Ca ). The unknown parameters are very difficult to be obtained by using the real and imaginary parts of Eq. (20), because they would produce nonlinear equations. Thus, the phasor diagram of Eq. (20) is drawn in order to get the unknown angles as in Fig. 3. The presented phasor diagram is a triangle where all lengths of its sides are known but all its angles are unknown. Hence, the cosine rule can be directly applied to obtain the angles. The angle corresponding to side IBA , the current of the healthy phase at terminal B, can be obtained by Eq. (21) using cosine rule. Therefore, the second synchronization angle (ı2) is obtained as in Eq. (22). Cos(Aa − 



Ca

(|IAa |)2 + (|ICa |)2 − (|IBa |)2

+ ) =

2 . |IAa | . |ICa |

⎛ ı2 = Aa +  − Cos−1 ⎝

2

2

(|IAa |) + (|ICa |) −(|IBa |) 2 · |IAa | · |ICa |

2

(21)

⎞ ⎠ − Ca

(22)

Similarly, the angle corresponding to side ICA , the current of the healthy phase at terminal C, can be obtained and then the first synchronization angle (ı1) is obtained using Eq. (23).

ing the data form line terminals, the symmetrical components of the measured three-phase current and voltage from line terminals are first computed. Then, considering a time reference synchronized with measured data at Busbar A, the required synchronization factors (ejı ) of other terminals are calculated and, then, correcting measurements at the other terminal is conducted as introduced in Subsection 2.1.1. Finally, the fault distance is obtained via equating the equations of the positive-sequence voltage at the faulty point (Vf 1 ) as a function of the measured data at Busbars A and B as illustrated in Fig. 4. Hence, the Vf 1 can be represented as; Vf 1

= VA1 − x(0) · Z1 · (IA1 −

x(0) · y1 · VA1 ) 2 (L − x(0) ) · y1 · VB1 ) 2

= VB1 − (L − x(0) ) · Z1 · (IB1 −

where x(0) is the initial fault distance. VA1 and VB1 are the positivesequence voltages at terminals A and B, respectively. Z1 and Y1 are the positive-sequence impedance and admittance per unit length, respectively. L is total line length. Hence, the x(0) is calculated via using known second-order equation roots, where the coefficients of this equation are as follows: a=

Z1 · y1 Z · y1 .VA1 − · VB1 2 2

b = −Z1 · IA1 − Z1 · IB1 + L · y1 · Z1 · VB1 ı1 = Aa +  + Cos

−1

(

( |IAa |)2 + (|IBa |)2 − ( |ICa |)2 2 · |IAa | · |IBa |

) − Ba



(23)

Similarly, the fault classification can be carried out as in the previous subsection. The synchronization angles (ı1 and ı2 ) are used to correct the measured phasors at terminals B and C, respectively. Then, the corrected currents and voltages phasors are utilized to locate the faulty point as in the following subsection. 2.1.2. Presented fault-locator technique Unbalanced faults are the most frequent faults in the transmission lines. Such faults are divided into two main categories. The first category is series faults such as one open conductor. The second category is shunt faults which are balanced faults, three-phase faults, or unbalanced faults such as line-to-ground, line-to-line, and lineto-line-to-ground faults. This paper concentrates on locating the shunt unbalanced faults for transmission lines. Thus, a fault location function adequate to all shunt unbalanced faults is required. Consequently, the positive-sequence parameters are used to locate the faulty point. A. For two-terminal lines An example of a two-terminal transmission line subjected to a shunt fault is illustrated in Fig. 1. For locating a fault, after acquir-

(24)

c = VA1 − VB1 + L · Z1 IB1 −

L · y1 .VB1 2



(25)

• For three-terminal lines An example of a three-terminal network consisting of three sections AT, TB, and TC under a fault on the section AT is shown in Fig. 2. For locating a fault on the three-terminal transmission network, the faulty section must be firstly identified and, then, the fault-location procedure is applied. The faulty side is identified as follows: a. Faulty side identification The positive-sequence voltage at the junction point (Vjun1 ) is obtained three times as a function of the measured data at three terminals using the equivalent positive-sequence circuit illustrated in Fig. 5 assuming that the fault is on the junction point irrespective of the real fault point as: |

Vjun1 Ijun1

| = |

AjT 1

BjT 1

CjT 1

DjT 1

−1

|

.|

Vj1 Ij1

|

(26)

where AjT 1 , BjT 1 , CjT 1 , and DjT 1 are positive-sequence constants of the transmission line’s section connected to the terminal j; Vj1 and Ij1 are the positive-sequence voltage and current at terminal j. The

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233

Fig. 3. The phasor diagram of Eq. (20).

Fig. 4. The positive-sequence circuit of a two-terminal transmission line under a fault at x(0) distance from the terminal A.

Fig. 5. The positive-sequence circuit of a three-terminal transmission line under a fault on the section connected to the terminal A.

faulty side identification is based on the magnitude of the Vjun1 because the magnitude is not influenced by the error in the synchronization angle calculation. The faulty side can be identified as follows: • Under a healthy condition, the three calculated magnitudes of the Vjun1 from three sides are equal. • Under a faulty condition, only two calculated magnitudes of the Vjun1 from two sides are equal and the third magnitude is different and lower than the other values. Consequently, the faulty side is the side which results the different value. • Fault-location procedure After identifying the faulty section, the junction current feeding to the faulty section is a summation of the received positivesequence currents to the junction point from two healthy sections which are obtained using the measured data at the terminals of these sections and their parameters as in Eq. (26). Using the calculated phasors at the junction point and the measured phasors at the faulty section terminal, the fault distance can be estimated as presented in Eq. (25).

The obtained fault distance from the first iteration is not exactly the actual fault distance due to the assumption of the calculation of the summation of the ith sequence line’s capacitors currents line. In order ( ICapi ) especially in case of the long transmission  to accurately compute the value of the ICapi under a faulty condition, its formula must be a function of the fault distance.  Hence, ICapi . other iterations are required to update the value of the 2.2. Next iterations The updated value  of the summation of ith sequence line’s capacitors currents ( ICapi (1) ) can be calculated using equivalent ith sequence networks by dividing the faulty line into two sections based on the calculated distance from the previous iteration (x(0) ), as shown in Fig. 6. The first section is upstream the fault. The constants of ith sequence circuits of this section are Axi (0) , Bxi (0) , Cxi (0) , and Dxi (0) . The second section is downstream the fault and its con¯ ¯ ¯ ¯ stants are Axi(0) , Bxi(0) , Cxi(0) , and Dxi(0) . The ( ICapi (1) ) can be calculated as in Eq. (27).



ICapi (1) = IAi − IRi(x(0) ) + IBi − IRi(L−x(0) )

(27)

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Fig. 6. Equivalent ith sequence network of the faulty side considering the fault at the first calculated distance x(0) from terminal A.

Table 1 The transmission network parameters Component

Parameter Symbol

Value

Overhead transmission line

ZOH1 ZOH0 COH1 COH0

(0.3317 + j0.4082) /km (0.4817 + j1.4444) /km 0.008688 ␮F/km 0.004762 ␮F/km

Equivalent system at terminal A

MVASC X/R Angle of EMF

1250 10 0◦

Equivalent system at terminal B

MVASC X/R Angle of EMF

5250 10 −30◦

Equivalent system at terminal C

MVASC X/R Angle of EMF MVA MVA

5250 10 −20◦ 120 + j50 200 + j40

Load B Load C

where IRi(x) and IRi(L-x) are the ith sequence currents fed from the terminals A and B at the faulty point based on the calculated distance from the previous iteration (x(0) ) as shown in Fig. 4, respectively. These currents can be obtained as in Eq. (28). IR i (x(0) ) = −Cxi(0) · VAi − Axi(0) · IAi IR i (l−x(0) ) = −C xi(0) · VBi − Dxi(0) · IBi

(28)



Using the value of the ICapi (1) , a new value for the required synchronization angle (ı(1) ) or angles (ı1(1) and ı2(1) ) can be obtained according to the network configuration and the fault type. Then, a new value for the fault distance (x(1) ) is obtained. This process is repeated until the change of the calculated fault distance becomes insignificant. Finally, the flowchart shown in Fig. 7 summarizes the steps of identifying the fault type and obtaining the fault distance for two-terminal transmission lines using unsynchronized data. However, in case of three-terminal transmission lines, an additional step which is the faulty side identification must be added as mentioned before. 3. Selected simulated systems To study the presented algorithm performance, the 220 kV twoand three-terminal transmission lines shown in Figs. 1 and 2 are simulated using MATLAB/SIMULINK. The two-terminal line length is 150 km. The three-terminal line consists of three sections; 50 km section AT, 150 km section TB, and 50 km section TC. Parameters of line sections are identical. All the line parameters are gathered in Table 1. The equivalent system behind the line ends (short circuit capacity (MVASC ), X/R ratio, and load angle) and loads’ values connected to the line terminals B and C are also listed in Table 1.

Various fault scenarios were investigated at different locations covering the whole line range. The evaluation results concern the unbalanced faults. After extracting the samples of the measured three-phase voltage and current at line terminals, they are fed into the Matlab environment. Recursive discrete Fourier transform (DFT) is utilized to estimate the fundamental frequency component of voltage and current phasors. In order to exclusively test the presented technique, the line parameters and the phasors at all transmission line terminals are considered completely correct as in the following. Although the DFT is widely used for phasor estimation, some errors may be encountered under existing exponential DC decaying components. Thus, the phasors are obtained under steady-state operation in order to avoid DC decaying components and exclusively test the presented technique precision. However, implementing the presented method under availability of insufficient samples after a fault occurrence needs using an advanced Fourier filter algorithm such as presented in Ref. [30]. An angle is added to the remote end phasors or two different angles are added to the remote ends phasors in case of two- or three-terminal lines, respectively, in order to test the proposed technique performance under unsynchronized data condition. Then, the mathematical core of the proposed technique is implemented in order to sequentially estimate the synchronization angle and the fault distance. Further, the error percentage of the calculated fault distance is obtained as,

% Error=|real fault distance (p.u.) − estimated fault distance (p.u.) | × 100

(29)

4. The presented algorithm assessment Various test scenarios were designed covering the whole range of lengths of the two- and three-terminal tested lines shown in Figs. 1 and 2 under different unbalanced faults. At first with respect to two-terminal line, the two-end measurements were collected with various unsynchronized angles. The obtained synchronization angles and the fault locations under line-to-ground, line-to-line, and line-to-line-to-ground faults occurred at different positions along the whole line length range and associated with 60  resistance with −30◦ unsynchronized shift angle are summarized in Table 2. The maximum error percentage was 0.0640%, 0.5380%, and 0.0640% under phase-to-ground, phase-to-phase, and phaseto-phase-to-ground faults along the test range, respectively. To check the presented algorithm reliability, its response is also evaluated with another unsynchronized angle value under different unbalanced faults and different fault distances as shown in Table 3. When Ø was −50◦ , the maximum error percentages were 0.3413%, 0.6553%, and 0.0480% under line-to-ground, line-to-line, and lineto-line-to-ground faults along the test range, respectively. The

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235

Fig. 7. The proposed unsynchronized faults-locator algorithm for two terminal transmission lines.

Table 2 Performance of the presented method against different fault types associated with 60  fault resistance and a −300 unsynchronization shift for measured data at remote end (B) of the two-terminal line. Fault type

Fault at (km)

Estimated distance (km)

Calculated ı

Error (km)

(%)

A-G

1 15 30 45 60 105 120 135

0.9217 14.9309 29.9334 44.915 59.920 104.911 119.916 134.938

0.0783 0.069 0.066 0.085 0.080 0.089 0.084 0.062

0.0522 0.0461 0.0444 0.0567 0.0533 0.0593 0.0560 0.0413

29.961 29.968 29.952 29.955 29.984 29.963 29.967 30.040

B-C

1 15 30 45 60 105 120 135

0.9304 14.9302 29.936 44.944 59.925 104.934 119.965 134.929

0.069 0.069 0.064 0.056 0.075 0.066 0.035 0.071

0.0464 0.0465 0.0427 0.0373 0.0500 0.0440 0.0233 0.0473

29.967 29.961 29.958 29.971 29.949 29.991 29.997 30.031

B-C-G

1 15 30 45 60 105 120 135

0.915 14.928 29.904 44.918 59.923 104.9304 119.912 134.917

0.085 0.072 0.096 0.082 0.077 0.069 0.088 0.083

0.0567 0.0480 0.0640 0.0547 0.0513 0.0464 0.0587 0.0553

29.944 29.958 29.960 29.964 29.973 29.987 30.015 30.018

results proved that the presented algorithm remarkably gives a satisfactory performance. Secondly, various fault cases were carried out covering the whole line length range of the three-terminal transmission lines shown in Fig. 2 with different unbalanced faults. The unsynchronized three-end measurements were collected with two unsynchronization shift angles −45◦ and −90◦ as in Table 4. All distances in Table 4 are referred to Busbar A. The maximum error percentage was 0.702% for the recorded data. The results testify to the efficacy of the proposed algorithms.

Different simulated fault cases are also accomplished under additional influences that are fault inception angles and fault impedances, when the recorded data are collected with unsynchronization angle equal to −15◦ . Fig. 8 illustrates the output of the presented method under various line-to-line fault inception angles when the fault occurs at 40 km from the substation A of the two-terminal line. As shown, the presented method is not influenced by the fault inception angles. Fig. 9 illustrates the error profile of the presented method as a function of both fault impedance and fault distance under phase-to-ground fault occurring at the

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Table 3 Performance of the presented method against different fault types associated with 60  fault resistance and a −500 unsynchronization shift for measured data at remote end (B) of the two-terminal line. Calculated ı

Error

Fault type

Fault at (km)

(km)

(%)

A-G

1 15 45 75 90 105 120 135

0.932 14.966 44.607 74.570 89.964 104.488 119.991 134.978

0.068 0.034 0.393 0.430 0.036 0.512 0.090 0.022

0.0453 0.0227 0.2620 0.2867 0.0240 0.3413 0.0060 0.0147

49.972 49.985 49.967 49.952 49.991 49.994 49.989 49.983

B-C

1 15 45 75 90 105 120 135

0.9524 14.950 44.952 74.941 89.668 104.865 119.912 134.017

0.047 0.050 0.048 0.059 0.332 0.135 0.088 0.983

0.0317 0.0333 0.0320 0.0393 0.2213 0.0900 0.0587 0.6553

49.951 49.957 49.960 49.976 49.981 49.993 49.996 50.014

1 15 45 75 90 105 120 135

0.9615 14.977 44.966 74.976 89.975 104.966 119.928 134.942

0.038 0.023 0.034 0.024 0.025 0.034 0.072 0.058

0.0257 0.0153 0.0227 0.0160 0.0167 0.0227 0.0480 0.0387

49.983 49.982 49.962 49.994 49.967 49.966 49.971 49.986

B-C-G

Estimated distance (km)

Fig. 9. The error profile of the presented algorithm as a function of the fault distance and the fault impedance.

Fig. 10. The error of the presented algorithm under 5% of the line parameters uncertainty.

Fig. 8. The presented algorithm output under different phase-to-phase faults occurred at 40 km from substation A.

two-terminal line, respectively. Fig. 9 confirms that the presented method is not influenced by the fault impedance. It is noteworthy that the electric power utility usually gives ideal line parameters without taking into consideration the history of the line running. The uncertainty of line parameters robustly affects the precision of most fault locator algorithms depending on the line parameters especially that solving the fault location problem utilizing one equation. Thus, the presented technique is evaluated considering that the given line impedance is deviated by 5% from its real value. Under simulating different fault positions of earth faults associated with 100  fault resistance, the obtained results show that the error of the proposed algorithm with the influence of such uncertainty reaches up to 4% as illustrated in Fig 10. The error of the presented technique still swings in a reasonable range by verifying the two presented equations. The first equation is deduced by exploiting the initial conditions of the fault. The second one is deduced via equating the deduced equations of the positivesequence voltage at the faulty point from two sides of the faulty segment. Table 5 illustrates the response of the presented algorithm versus three previously reported methods [19,22,28] under phaseto-ground fault associated with different conditions such as varying

the equivalent impedance behind the line terminals (Zs ), the unsynchronization angle (Ø), and the fault impedance (Zf ). It is noteworthy that these reported methods only calculate the fault distance regardless of the required synchronization angle. Firstly, the results prove that the output of Ref. [19] is very accurate whatever the fault impedance nature where the error percentage is lower than 0.2% as listed in Table 5. However, the results of Ref. [19] are unsatisfactory under either varying the Zs or largely unsynchronized data as declared via shaded cells with highlighting using dashed and solid ellipses in Table 5, respectively. Secondly, the error of Ref. [22] is lower than 0.6% whatever the Ø and the Zs values as declared in Table 5. However, the performance of Ref. [22] is completely wrong under faults associated with Zf having imaginary part as depicted via shaded cells with highlighting using dotted ellipse in Table 5. Thirdly, the algorithm reported in Ref. [28] concerning the three-terminal network is also tested under three different fault locations (25 km at section AT, 75 km at section TB, 150 km at section TC) where all listed lengths are referred to terminal A. The error of Ref. [28] is less than 0.5% whatever the Ø value as illustrated in Table 5. However, the output of Ref. [28] is unsatisfactory under varying the Zs value as depicted via shaded cells with highlighting using dashed ellipse in Table 5. Finally, the results of the presented algorithm are satisfactory under all these circumstances as shown in the right-handed column. Finally, Table 6 illustrates a comparative evaluation of the response of the presented algorithm and those obtained by diverse recent algorithms [19–23,5–28]. This table shows needed data, used line model in the mathematical algorithm, utilized Phasor

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Table 4 Performance of the presented method against different fault types associated with 10  fault resistance and a −20◦ and −40◦ unsynchronization shift for measured data at two remote ends (B and C) of the three-terminal line. Fault

Estimated distance (km)

Sec.

Type

At (km)

AT

A-G

15 30 45 15 30 45 15 30 45

B-C

B-C-G

TB

A-G

B-C

B-C-G

TC

A-G

B-C

B-C-G

75 100 125 75 100 125 75 100 125 65 80 95 65 80 95 65 80 95

Calculated ı1 & ı2

Error (km)

(%)

ı1

ı2

14.324 29.258 44.204 14.271 29.206 44.237 14.103 29.132 44.249

0.676 0.742 0.796 0.729 0.794 0.763 0.897 0.868 0.751

0.338 0.371 0.398 0.364 0.397 0.381 0.448 0.434 0.375

20.021 20.023 20.017 20.015 20.013 20.019 20.012 20.025 20.022

40.036 40.044 40.040 40.037 40.035 40.042 40.033 40.032 40.043

74.405 99.425 124.437 74.306 99.313 124.224 74.280 99.411 124.432

0.595 0.575 0.563 0.694 0.687 0.776 0.720 0.589 0.568

0.297 0.287 0.281 0.347 0.343 0.388 0.360 0.294 0.284

20.018 20.014 20.022 20.025 20.031 20.030 20.027 20.029 20.034

40.027 40.023 40.035 40.026 40.034 40.038 40.040 40.045 40.047

64.314 79.325 94.361 64.392 79.409 94.421 64.383 79.359 94.298

0.686 0.675 0.639 0.608 0.591 0.579 0.617 0.641 0.702

0.686 0.675 0.639 0.608 0.591 0.579 0.617 0.641 0.702

20.031 20.028 20.024 20.029 20.033 20.041 20.039 20.042 20.035

40.025 40.018 40.009 40.023 40.028 40.032 40.028 40.017 40.026

Note: Sec.: section. Table 5 The presented method versus other existing methods under phase-to-ground fault associated with different conditions.

Note: Term. no.: number of the network’s terminals; Per.: percentage; Unsynch.: unsynchronized; N-C: not covered; A: at terminal A; B: at terminal B; and C: at terminal C.

estimation method and number of samples per cycle, and algorithm type whether it is analytical or numerical for each reported method. Also, it shows whether the reported method is suitable under different conditions which are two-terminal transmission line, three-terminal transmission line, variation of the source impedance (Zs), fault impedance (Zf ) having imaginary part, and largely unsynchronized data. It is to be noted that from the view point of the used recorded devices cost, [19,28] need low cost, whereas they considered that the Zs is a constant value and they also neglected the capacitive charging current. The reported methods do not cover all the listed different conditions except Ref. [27]

as illustrated in Table 6. Although the iterative algorithm reported in Ref. [27] is suitable for the different conditions, the current of the capacitive charging is neglected and, also, constant initial values is considered for both the fault distance (middle of the total line length) and the required correction of the synchronization angle (ı = 0.0). On other hand, the proposed iterative method covers the listed different conditions taking into consideration the line’s capacitors currents. Further, the initial values of the unknown variables are obtained using the initial conditions of the current fault type.

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16 Non-iterat. No Yes No Yes Yes

32 Iterat. Yes Yes Yes Yes Yes

5. Conclusions and future works

Is Ref. suitable for

Two-terminal? Three-terminal? Zs variation? Zf having imag. Part? Largely unsynch. data?

N-R Non-iterat. Yes No No Yes No Samples/cycle Algorithm type Does Ref. cover

Note: Imag. imaginary; Unsynch.: unsynchronized; I: three-phase current; V: three-phase voltage; N-R: not reported; Iterat. iterative; Distr.: distributed; and Pres.: presented method.

N-R Non-iterat. Yes Yes No Yes No 32 Iterat. Yes No Yes Yes Yes 32 Non-iterat. Yes No Yes No Yes 16 Iterat. Yes No Yes Yes Yes

[25] I&V Distr. Not reported [20] I Short DFT [19] Required data Line model Used filter (Phasor estimation method)

Comparison items

Table 6 Performance comparison with recent reported methods.

Ref.

[21] I&V Distr. Full-cycle Fourier orthogonal 16 Iterat. Yes No Yes Yes Yes

[22] I&V Distr. Presented in Ref. [31]

[23] I&V Distr. Modified DFT [32]

[26] I&V Distr. Dynamic Phasor [33] algorithm 48 Iterat. Yes Yes Yes Yes No

[27] I&V Short Not reported

[28] I&V Short Kalman filtering algorithm N-R Iterat. Yes Yes Yes Yes Yes

Pres. V Short DFT

I&V Distr. DFT

238

In this paper, a new fault locator technique for electric power transmission lines utilizing the measurements of unsynchronized currents and voltages has been introduced. Two- and threeterminal transmission lines conditions have been treated. The technique does not only calculate the fault distance but also obtains the required synchronization angle/s via using the initial conditions of each fault type. The required variables are formulated as a function of the symmetrical components phasors via the proposed iterative manner. In the first iteration, the required synchronization angle/s is obtained via considering a lumped charging current at an arbitrary selected terminal. Consequently, the measured data is corrected and then the initial fault distance is estimated. In the next iterations, the line’s capacitors current is updated using the distributed line model based on the previous fault distance. Consequently, a new unsynchronization angle is obtained and then a new fault distance is estimated. This process is repeated until the estimated fault distance becomes almost constant. The simulated results confirmed satisfactory performance and high efficacy of the proposed fault-locator technique compared with other recent reported methods. The presented technique can be easily incorporated with the existing IEDs because all of the calculations are carried out using unsynchronized measurements. Further, the proposed unsynchronized fault-locator technique uses only the post fault data and does not need the source impedance value. Finally, the presented technique is represented as a faulty segment identifier and fault locator. However, it can not be applied under three-phase fault conditions due to absence of any healthy phase and then the synchronization operator expression cannot be obtained. Enhancing the proposed algorithm to be independent of the line parameters is the main future prospective of such work to ensure better response in aged power transmission lines.

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