Inter national J our nal of Electrical and Computer Engineering (IJECE) V ol. 9, No. 5, October 2019, pp. 3891 3904 ISSN: 2088-8708, DOI: 10.11591/ijece.v9i5.pp3891-3904 r 3891 Multi-scale mor phological gradient algorithm based ultra-high-speed dir ectional transmission line pr otection f or inter nal and exter nal fault discrimination Elmahdi Khoudry 1 , Abdelaziz Belfqih 2 , T ay eb Ouaderhman 3 , J amal Boukher ouaa 4 , F aissal Elmariami 5 1,2,4,5 T eam of Electric Netw orks and Static Con v erters. Laboratory of Ener gy and Electrical Systems., National Higher School of Electricity and Mechanics (ENSEM). Hassan II Uni v ersity , Casablanca, Morocco 3 MA CS Laboratory . FSA C. Hassan 2 Uni v ersity . Casablanca. Morocco Article Inf o Article history: Recei v ed Jan 9, 2019 Re vised Apr 5, 2019 Accepted Apr 15, 2019 K eyw ords: Ultra-high-speed directional protection Internal and e xternal f ault discrimination Multi-scale morphological gradient algorithm T ra v eling w a v es F ault-induced transients ABSTRA CT This paper introduces an ultra-high-speed directional transmission line protection scheme based on multi-scale morphological gradient algorithm (MSMGA). The direc- tional protection scheme sets do wn the rules for determining the f ault position in rela- tion to the relaying point. The MSMGA is used to e xtract the f ault-induced transient characteristics contained in the v oltage and current signals. The associated signals are formed from these transient characteristics and the polarity of their local modulus maxima allo w the discrimination between internal and e xternal f aults. Copyright c 2019 Insitute of Advanced Engineeering and Science . All rights r eserved. Corresponding A uthor: Elmahdi Khoudry , Laboratory of Ener gy and Electrical Systems, National Higher School of Electricity and Mechanics, Road El Jadida, Km 7, BP: 8118, Oasis-Casablanca, Morocco, Email: e.khoudry@gmail.com 1. INTR ODUCTION Extra High V oltage (EHV) transmission lines constitute an essential part of the electrical po wer s ys- tem. Therefore, the y should rely on ef ficient protection schemes capable of remo ving f aults swiftly and se- lecti v ely to enhance the transient stability and ensuring the continuity of po wer supply . F or these reasons, ultra-high-speed directional protection (UHSDP) schemes ha v e started to be closely studied and broadly im- plemented in EHV po wer systems. Being one of the UHSDP schemes, tra v eling w a v e-based directi onal protection can quickly identi fy the direction of the f ault based on the tra v eling w a v e signal [1], [2], [3]. Not only that, b ut it is also sheltered from the impacts of po wer swings and current transformer saturation. Ne v ertheless, it is highly sensiti v e to the f ault inception angle. In f act, it is unable to detect f aults under lo w v oltage inception angle because the f ault-induced tra v eling w a v e is too damped. Artificial intelligence based directional protection schemes ha v e been put forw ard as an alternati v e t o the pre vious method [4], [5], [6], [7], [8]. These sc hemes are essentially based on artificial neural netw orks which remain a f ast and reliable tool when the directional protection is treated as a pattern recognition prob- J ournal homepage: http://iaescor e .com/journals/inde x.php/IJECE Evaluation Warning : The document was created with Spire.PDF for Python.
3892 r ISSN: 2088-8708 lem. Nonetheless, neural netw orks need a lar ge amount of data to perform their supervised learning, which is sometimes not a v ailable. T o address the do wnsides of the tra v eling w a v e-based directional protection and of the artificial intel- ligence techniques, the transient-based protection scheme has been introduced [9], [10]. The implementation of this scheme depends on e xploiting the w a v e equations which links together the transient v oltage, the tran- sient current, time and distance. The e xploitation of the w a v e equation consists of e xtracting the transients (the superimposed quantities) generated by a f ault. F or this task, tw o classical me thods were proposed. The first one consists of using the F ourier T ransform, b ut this method gi v es access only to the frequenc y components of a signal o v er the period of time in which it e xists b ut does not pro vide an y information about the interv al of times at which these frequencies appear . As a result, the F ourier T ransform is not suitable to e xtract the tran- sient signals, which is a non-stationary signal, from the signals measured at dif ferent transmission line b usbars under the f ault condition. The second method is based on the W a v elet T ransform [11], [12],[13]. The W a v elet T ransform uses a short time windo w for the analysis of the high-frequenc y content of a signal and a long time windo w for lo w-frequenc y content. Therefore, the W a v elet T ransform pro vides an accurate time-frequenc y analysis of the signal. Ho we v er , the W a v elet T ransform algorithm is computationally demanding and sensible to noise. In this paper , we propose another approach to the ultra-high-speed directional protection based on the multi-scale morphological gradient algorithm. This approach is used for the purpose of discriminating between internal and e xternal f aults. It should also be noted, unlik e the F ourier T ransform and the W a v elet transform, that this method processes the signal in the time domain only . In addition to that, narro w sliding data windo ws suf fice to perform accurate, quick and simple computations. All these adv antages mak e this approach suitable to real-time applications. 2. MUL TI-SCALE MORPHOLOGICAL GRADIENT ALGORITHM (MSMGA) Before presenting the MSMGA, we will first start by introducing the dif ferent flat morphological functions that interv ene in the algorithm [14], [15], [16]. These functions are mathematically defined as follo ws: (a) Le v el s flat positi v e dilation: + s [ n ] = ( max 1 m l s f s 1 [ n + m ] g 1 n l x l s + 1 s 1 [ n ] l x l s + 2 n l x (1) (b) Le v el s flat positi v e erosion: " + s [ n ] = ( s 1 [ n ] 1 n l s 1 min 1 m l s f s 1 [ n + m ] g l s n l x (2) (c) Le v el s flat ne g ati v e dilation: s [ n ] = ( s 1 [ n ] 1 n l s 1 max 1 m l s f s 1 [ n + m ] g l s n l x (3) (d) Le v el s flat ne g ati v e erosion: " s [ n ] = ( min 1 m l s f s 1 [ n + m ] g 1 n l x l s + 1 s 1 [ n ] l x l s + 2 n l x (4) (e) Le v el s flat positi v e gradient: + s [ n ] = + s [ n ] " + s [ n ] (5) (f) Le v el s flat ne g ati v e gradient: s [ n ] = " s [ n ] s [ n ] (6) Int J Elec & Comp Eng, V ol. 9, No. 5, October 2019 : 3891 – 3904 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Elec & Comp Eng ISSN: 2088-8708 r 3893 (g) Le v el s flat gradient: s [ n ] = + s [ n ] + s [ n ] (7) Where - x [ n ] : A sampled input signal. - 0 [ n ] = x [ n ] - l 1 : The le v el 1 length of the operators max and min . - l s = 2 s 1 l 1 : The dyadic le v el s length of the operators max and min . - l x : The length of the discrete signal x [ n ] . T o notice the ef fects of these functions, let’ s, for instance, consider the signal of Figure 1(a) and restrict our analysis to le v el 1 flat morphological functions. As depicted in Figure 1(b), the flat positi v e dilation and the flat positi v e erosion af fect only the ascending edge of the signal. In f act, the ascending edge of the ramped-signal has been e xpanded to the left by l 1 1 samples using the function + s [ n ] (see the signal in red), whereas it has been compressed to the right by l 1 1 samples using the function " + s [ n ] (see the signal in blue). As illustrated in Figure 1(c), the flat ne g ati v e dilation and the flat ne g ati v e erosion af fect only the descending edge of the signal. In f act, the descending edge of the ramped-signal has been e xpanded to the right by l 1 1 samples using the function s [ n ] (see the signal in red), whereas it has been compressed to the left by l 1 1 samples using the function " s [ n ] (see the signal in blue). (a) (b) (c) Figure 1. (a) A ramped-step signal, (b) The ramped-step signal (black), + s [ n ] (red) and " + s [ n ] (blue), (c) The ramped-step signal (black), s [ n ] (red) and " s [ n ] (blue) Finally , we deduce from Figures 2(a) and 2(b) that + 1 [ n ] and 1 [ n ] not only pro vide us with infor - mation about the moment of w a v eform changes, b ut also inform us about the polarities of these changes. The polarity is positi v e for ascending edges and ne g ati v e for descending edges. T o obtain the whole profile of the w a v eform changes, it suf fices to combine the flat positi v e gradient and the flat ne g ati v e gradient in one single flat gradient as sho wn in Figure 2(c). Hence the definition of le v el s flat gradient and the flo wchart of the MSMGA that is gi v en in Figure 3. (a) (b) (c) Figure 2. (a) + 1 [ n ] of the ramped-step signal, (b) 1 [ n ] of the ramped-step signal, (c) 1 [ n ] of the ramped-step signal Multi-scale morpholo gical gr adient algorithm based ultr a-high-speed... (Elmahdi Khoudry) Evaluation Warning : The document was created with Spire.PDF for Python.
3894 r ISSN: 2088-8708 Figure 3. MSMGA flo wchart 3. MSMGA B ASED UL TRA-HIGH-SPEED DIRECTION AL PR O TECTION (UHSDP) A lossless single-phase transmission line modeled by distrib uted parameters can be described mathe- matically by the so-called tele grapher equations: @ 2 ~ v ( x; t ) @ t 2 = 1 l c @ 2 ~ v ( x; t ) @ x 2 (8) @ 2 ~ i ( x; t ) @ t 2 = 1 l c @ 2 ~ i ( x; t ) @ x 2 (9) Where l and c are the per -unit-length inductance and capacitance respecti v ely , x = x i x j represents the distance from the source, x i is the abscissa of the point at which the v oltage is measured and x j is the source abscissa. Equations (8) and (9) are also called w a v e equations, and their general solutions were gi v en by D’Alembert as: ~ v ( x; t ) = ~ v + t x + ~ v t + x (10) Z ~ i ( x; t ) = ~ v + t x ~ v t + x (11) Where Z = p l =c is the sur ge impedance of the transmission line and = 1 = p l c is the w a v e v elocity of propag ation. The function ~ v ( t + x= ) describes a v oltage w a v e propag ating in the ne g ati v e x -direction, and it is called the backw ard v oltage v oltage w a v e. In contrast, the function ~ v + ( t x= ) describes a v oltage w a v e propag ating in the positi v e x -direction, and it is called the forw ard v oltage w a v e. As depicted in Figure 4, when a transmission line is e xposed to a f ault conditi on, the v oltage ~ v ( x; t ) and the current ~ i ( x; t ) at an y point of the line are subjected to tw o re gimes [17], [18]: the steady-state re gime v ( x; t ) and i ( x; t ) which is caused by the origi nal sources as sho wn in Figure 5(a), and the f ault inception re gime where the superimposed quantities v ( x; t ) and i ( x; t ) are caused by a fictitious source e x erted at the f ault location x F and at the f ault inception time t F = 0 . Therefore 8 t 0 ~ v ( x; t ) = v ( x; t ) + v ( x; t ) (12) ~ i ( x; t ) = i ( x; t ) + i ( x; t ) (13) W e deduce from the equations a bo v e that the f ault inception re gime can be modeled by a netw ork with all original sources short-circuited as sho wn in 5(b). W e also deduce, at the f ault point, that the v oltage of the fictitious superimposed source and the steady-state v oltage are equal in magnitude b ut of opposite sign. In f act, noting that v F ( t ) = v ( x F ; t ) and that we ha v e ~ v F ( t ) = ~ v ( x F ; t ) = 0 , we obtain then from equation (12) the follo wing relation : v F ( t ) = v F ( t ) (14) Int J Elec & Comp Eng, V ol. 9, No. 5, October 2019 : 3891 – 3904 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Elec & Comp Eng ISSN: 2088-8708 r 3895 Figure 4. A transmission line subjected to a f ault condition (a) (b) Figure 5. (a) The steady-state re gime, (b) The f ault inception re gime Considering that the superimposed quantities are directly related to to the f ault, the y should posses s properties in relation to the directionality of the f ault [19],[20]. In order to e xhibit these properties, let’ s tak e for instance, as sho wn in Figure 6, a transmission system composed of tw o lines i n which a f ault is generated at point F at t F = 0 . According to equation (10), the forw ard v oltage w a v e, v + F ( t ( x x F ) = ) , generated by the fictitious generator , tra v els from the point F to the discontinuity point P along line 1 , the w a v e refracts to line 2 and the remaining reflects to line 1 . Consequently , v + F ( t ( x P x F ) = ) is the incident w a v e, v B ( t ) is the reflected w a v e and r v + F ( t ( x P x F ) = ) is the reflected w a v e, where r = ( Z 2 Z 1 ) = ( Z 2 + Z 1 ) is the coef ficient of reflection, Z 1 is the sur ge impedance of line 1 and Z 2 is the sur ge impedance of line 2 . Figure 6. The f ault inception re gime On Line 1, relay A measures a w a v e from the forw ard direction, namely r v + F ( t ( x P x F ) = ) , as well as one from the backw ard di rection, that is v + F ( t ( x P x F ) = ) . Thus, we ha v e ac cording to relay A reference direction of the current: v A ( t ) = (1 + r ) v + F t x P x F (15) Z 1 i A ( t ) = (1 r ) v + F t x P x F (16) Equations (14) and (15) imply the follo wing relations: v A ( t ) Z 1 i A ( t ) 6 = 0 (17) v A ( t ) + Z 1 i A ( t ) = r ( v A ( t ) Z 1 i A ( t )) (18) W e conclude that v A ( t ) and i A ( t ) are of dif ferent polarity . On line 2 , there is no w a v e from the forw ard direction, so relay B only measures a w a v e from the back- w ard direction. Thus, we obtain only , according to relay B reference direction of the current, the subsequent relation: v B ( t ) = Z 2 i B ( t ) (19) Multi-scale morpholo gical gr adient algorithm based ultr a-high-speed... (Elmahdi Khoudry) Evaluation Warning : The document was created with Spire.PDF for Python.
3896 r ISSN: 2088-8708 It follo ws from (19) that v B ( t ) and i B ( t ) ha v e the same polarity . This result in the follo wing directional detection criteria: (a) v ( x; t ) i ( x; t ) < 0 ) F orw ard f ault (b) v ( x; t ) i ( x; t ) > 0 ) Backw ard f ault Where v ( x; t ) and i ( x; t ) are the superim p os ed components measured at a certain discontinuity point. Since the superimposed quantities contain information about the f ault direction, as it has been sho wn earlier , the steady-state quantities must be remo v ed, hence the use of the MSMGA [16]. In f act, le v el s flat gradients ~ v A s [ n ] , ~ i A s [ n ] , ~ v B s [ n ] and ~ i B s [ n ] are e xtracted from the sampled signals ~ v A [ n ] , ~ i A [ n ] , ~ v B [ n ] and ~ i B [ n ] , respecti v ely . The y represent the superimposed (or transient) components, and replacing v A ( t ) , i A ( t ) , v B ( t ) and i B ( t ) in (17), (18) and (19), the f ault direction can be determined in practice according to the follo wing rules: (a) Rule 1: ~ v s [ k 0 ] ~ i s [ k 0 ] < s ) F orw ard f ault (b) Rule 2: ~ v s [ k 0 ] ~ i s [ k 0 ] > s ) Backw ard f ault (c) Rule 3: j ~ v s [ k 0 ] ~ i s [ k 0 ] j < s ) No-f ault Where ~ v [ n ] and ~ i [ n ] are, respecti v ely , the sampled v oltage signal and the sampled current signal measured by a gi v en relay at a certain discontinuity point. F or practical reasons, the threshold s > 0 should be predefined to determine the zero v alue of le v el s flat gradients. It should also be noted that k 0 is the sample inde x that corresponds to the local modulus maximum of the signal j ~ v s [ n ] ~ i s [ n ] j . It can be defined as follo ws: k 0 = arg max k i n k f fj ~ v s [ n ] ~ i s [ n ] jg (20) Where k i is the first sample inde x from which j ~ v s [ n ] ~ i s [ n ] j rises abo v e s , and k f is the sample inde x after which j ~ v s [ n ] ~ i s [ n ] j drops immediately under s . That is, j ~ v s [ n ] ~ i s [ n ] j s ; k i n k f 4. SIMULA TION RESUL TS AND DISCUSSION 4.1. Simulation model Figure 7 sho ws the (440 k V ; 60 H z ) transmission line system on which simulation studies had been carried out. The system is composed of tw o Th ´ ev enin po wer system equi v alents and three identical transmission lines (Line 1 , Line 2 , Line 3 ) separated by tw o b uses R and S modeled as short transmission lines. Figure 7. Simulation model The data of the Th ´ ev enin po wer system equi v alents are listed in the T able 1, the distrib uted parameters of Line 1 , Line 2 and Line 3 are listed in T abl e 2, and The lumped parameters of the nominal- representation of b uses R and S are gi v en by the resistance, inductance and capacitance matrices. T able 1. Th ´ ev enin po wer system equi v alents data Generators V oltage ( k V ) Th ´ ev enin impedance Positi v e Seq. () Zero Seq. () G 1 462 19 : 45 \ 84 : 99 4 : 24 \ 85 : 25 G 2 418 20 : 47 \ 84 : 99 4 : 65 \ 85 Int J Elec & Comp Eng, V ol. 9, No. 5, October 2019 : 3891 – 3904 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Elec & Comp Eng ISSN: 2088-8708 r 3897 T able 2. T ransmission line data Impedance r ( =k m ) l ( mH =k m ) c ( F =k m ) Positi v e Sequence () 0 : 039 0 : 740 0 : 0157 Zero Sequence () 1 : 861 2 : 229 0 : 009 (a) Resistance matrix () : R = 0 @ 1 : 783 0 : 148 0 : 144 0 : 148 1 : 868 0 : 148 0 : 144 0 : 148 1 : 783 1 A (b) Inductance matrix ( mH ) : L = 0 @ 9 : 104 5 : 118 4 : 435 5 : 118 9 : 078 5 : 118 4 : 435 5 : 118 9 : 104 1 A (c) Capacitance matrix ( F ) : C = 0 @ 0 : 201 0 : 044 0 : 012 0 : 044 0 : 206 0 : 044 0 : 012 0 : 044 0 : 201 1 A 4.2. Inter nal and exter nal fault discrimination The analysis gi v en in section III for a single-phase transmission line can be e xtended to a t h r ee-phase transmission system using modal transformation. This transformation decomposes the v oltage phase sequence ( ~ v a ; ~ v b ; ~ v c ) and the current phase sequence ( ~ i a ; ~ i b ; ~ i c ) into three decoupled modes, namel y ground mode and aerial modes. In this scheme, the aerial mode , obtained from Clark e transformation, will be used: ~ v ( x; t ) = 2 3 ~ v a ( x; t ) 1 3 ~ v b ( x; t ) 1 3 ~ v c ( x; t ) (21) ~ i ( x; t ) = 2 3 ~ i a ( x; t ) 1 3 ~ i b ( x; t ) 1 3 ~ i c ( x; t ) (22) It is Line 2 which is the subject of the protection. Therefore, we desire to distinguish the f aults t hat occur outside this line from those that occur inside it. The criteria for e xternal and internal f ault discrimination, deduced from the rules established in the pre vious section, are presented in T able 3. T able 3. Rules for internal and e xternal f ault discrimination Bus R Bus S Exter nal to R ~ v R s [ k 0 ] ~ i R s [ k 0 ] > s ~ v S s [ k 0 ] ~ iS s [ k 0 ] < s Inter nal ~ v R s [ k 0 ] ~ iR s [ k 0 ] < s ~ v S s [ k 0 ] ~ iS s [ k 0 ] < s Exter nal to S ~ v R s [ k 0 ] ~ iR s [ k 0 ] < s ~ v S s [ k 0 ] ~ i S s [ k 0 ] > s The threshold s is defined by taking the maximum v alue of le v el s flat gradients in no-f ault conditi ons. 4.3. Simulation settings F or all case studies, the v oltage and current signals observ ed at relaying positions R and S are sam pled at the rate of 1 M H z and transformed into the aerial mode using relations (21) and (22). After that, le v el 2 flat gradients had been e xtracted from the aerial mode v oltage and current in order to carry out the simulation studies. It should also be indicated that the threshold had been set empirically at 2 = 1400 for le v el 2 flat gradients in no-f ault conditions. In the present simulation st ud y , a time-based sliding windo w with a length of 1200 s and a sliding interv al of 600 s is used, which is long enough to observ e the f ault-induced transients and short enough to a v oid the ef fects of the refle cted w a v es from the adjacent lines. This main windo w corresponds to the portions of the aerial mode v oltage and current signal to be processed in real-time by the MSMGA. In re g ards to the MSMGA, we consider l 1 = 8 , which is equi v alent to a sliding sub-windo w that co v ers a period of 8 s and mo v es continuously by one sample inside the main windo w . Multi-scale morpholo gical gr adient algorithm based ultr a-high-speed... (Elmahdi Khoudry) Evaluation Warning : The document was created with Spire.PDF for Python.
3898 r ISSN: 2088-8708 4.4. Case studies The objecti v e behind these simulation studies is to see ho w the MS MGA based UHSDP relays at b uses R and S responds to the dif ferent critical cases that it ca n f ace: the ef fect of f ault inception angle near zero crossing and 90 [21], the ef fect of single phase-to-ground f ault resistance and the influence of f ault location and type. 4.4.1. An inter nal bolted fault Figure 8 sho ws the three-phase v oltages and currents observ ed at measurement points R and S for a bolted phase A-to-ground f ault with an inception angle close to 90 , at a distance of 50 k m from b us R. The modal v oltages and currents are depicted in Figure 9 and their associated signals, ~ v R 2 [ n ] ~ i R 2 [ n ] and ~ v S 2 [ n ] ~ i S 2 [ n ] , are depicted in Figures 10 and 11, respecti v ely . It can be observ ed from Figures 10 and 11 that the transient characteristics of f ault v oltage and current, represented by the product of their le v el 2 flat gradients, are well brought out by the MSMGA, whereas the steady-state components are lar gely depressed (the area delimited by the red dotted lines). Furthermore, both local modulus maxima v erify ~ v R 2 [ k 0 ] ~ i R 2 [ k 0 ] < 2 and ~ v S 2 [ k 0 ] ~ i S 2 [ k 0 ] < 2 (see the red points in the yello w areas of Fig.10 and Fig.11), which is consistent with the internal f ault detection rule gi v en in T able 3. Figure 8. Three-phase v oltages and currents measured at b uses R and S under an internal bolted phase A-to-ground f ault with a nearly 90 f ault inception angle at 50 k m from b us R Figure 9. Modal v oltages and currents measured at b uses R and S under an internal bolted phase A-to-ground f ault with a nearly 90 f ault inception angle at 50 k m from b us R Figure 10. The signal ~ v R 2 [ n ] ~ i R 2 [ n ] measured at b us R under an internal bolted phase A-to-ground f ault with a nearly 90 f ault inception angle at 50 k m from b us R Figure 11. The signal ~ v S 2 [ n ] ~ i S 2 [ n ] measured at b us S under an internal bolted phase A-to-ground f ault with a nearly 90 f ault inception angle at 50 k m from b us R 4.4.2. A high-gr ound r esistance inter nal fault Under the same f ault conditi ons as described in the pre vious case, the ground-f ault resistance is in- creased to 200 . The three-phase v oltages and currents observ ed at measurement points R and S are de- picted in Figure 12. The modal v oltages and currents are outlined in Figure 13 and thei r associated signals, ~ v R 2 [ n ] ~ i R 2 [ n ] and ~ v S 2 [ n ] ~ i S 2 [ n ] , are sho wn in Figures 14 and 15, respecti v ely . The obtained results indicate that the magnitude of the local m odulus maxima of the associated signals decrease with the increase of ground- f ault resistance. Indeed, in the pre vious case whe re the ground-resistance is near zero, the order of magnitude of the associated signals is about 10 8 , whereas it is about 10 7 in the present case. Ne v ertheless, the latter order Int J Elec & Comp Eng, V ol. 9, No. 5, October 2019 : 3891 – 3904 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Elec & Comp Eng ISSN: 2088-8708 r 3899 of magnitude is lar ge enough to enable the detection of an internal f ault (see the polarity of the red poi n t s in the yello w areas of Fig.14 and Fig.15). Figure 12. Three-phase v oltages and currents measured at b uses R and S under an internal phase A-to-ground f ault with ground-resistance 200 at 50 k m from b us R Figure 13. Modal v oltages and currents measured at b uses R and S under an internal phase A-to-ground f ault with ground-resistance 200 at 50 k m from b us R Figure 14. The signal ~ v R 2 [ n ] ~ i R 2 [ n ] measured at b us R under an internal phase A-to-ground f ault with ground-resistance 200 at 50 k m from b us R Figure 15. The signal ~ v S 2 [ n ] ~ i S 2 [ n ] measured at b us S under an internal phase A-to-ground f ault with ground-resistance 200 at 50 k m from b us R 4.4.3. Exter nal faults with lo w inception angle In this case, tw o simulations were carried out. One concerns a f ault e xternal t o b us R with an inception angle close to 0 at a distance 25 k m from b us R in Line 1 , and the other a f ault e xternal to b us S with an inception angle close to 0 at a distance 25 k m from b us S in Line 3 . Both f aults occur at 16 : 7 ms . Concerning the simulation case of a f ault e xternal to b us R, Figures 16 and 17 depict the three- phase v oltages and current measured at points R and S and their modal components, respecti v ely . As it can be observ ed, the f ault-induced transients are significantly damped. Figures 18 and 19 outline the modal components associated signals, ~ v R 2 [ n ] ~ i R 2 [ n ] and ~ v S 2 [ n ] ~ i S 2 [ n ] , respecti v ely . From these tw o figures, it can be noticed that the local modulus maxima are suf ficiently high to be detected. Furthermore, we ha v e ~ v R 2 [ k 0 ] ~ i R 2 [ k 0 ] > 2 and ~ v S 2 [ k 0 ] ~ i S 2 [ k 0 ] < 2 (see the red points in the yello w areas of Fig.18 and Fig.19), which is consistent with the detection rule of a f ault e xternal to b us R as indicated in T able 3. Figure 16. Three-phase v oltages and currents measured at b uses R and S under a phase A-to-ground f ault e xternal to b us R with an inception angle close to 0 Figure 17. Modal v oltages and currents measured at b uses R and S under a phase A-to-ground f ault e xternal to b us R with an inception angle close to 0 Multi-scale morpholo gical gr adient algorithm based ultr a-high-speed... (Elmahdi Khoudry) Evaluation Warning : The document was created with Spire.PDF for Python.
3900 r ISSN: 2088-8708 Figure 18. The signal ~ v R 2 [ n ] ~ i R 2 [ n ] measured at b us R under a phase A-to-ground f ault e xternal to b us R with an inception angle close to 0 Figure 19. The signal ~ v S 2 [ n ] ~ i S 2 [ n ] measured at b us S under a phase A-to-ground f ault e xternal to b us R with an inception angle close to 0 And re g arding the simulation case of a f ault e xternal to b us S, Figures 20 and 21 sho w the three- phase v oltages and currents measured at points R and S and their modal components, respecti v ely . As it can be noticed, the f ault-generated transients are significantly damped. Figures 22 and 23 outline the modal components associated signals, ~ v R 2 [ n ] ~ i R 2 [ n ] and ~ v S 2 [ n ] ~ i S 2 [ n ] , respecti v ely . From thes e tw o figures, it can be observ ed that the local modulus maxima are suf ficiently high to be detected. Furthermore, we ha v e ~ v R 2 [ k 0 ] ~ i R 2 [ k 0 ] < 2 and ~ v S 2 [ k 0 ] ~ i S 2 [ k 0 ] > 2 (see the red points in the yello w areas of Fig.22 and Fig.23), which is consistent with the detection rule of a f ault e xternal to b us S as indicated in T able 3. Figure 20. Three-phase v oltages and currents measured at b uses R and S under a phase A-to-ground f ault e xternal to b us S with an inception angle close to 0 Figure 21. Modal v oltages and currents measured at b uses R and S under a phase A-to-ground f ault e xternal to b us S with an inception angle close to 0 Figure 22. The signal ~ v R 2 [ n ] ~ i R 2 [ n ] measured at b us R under a phase A-to-ground f ault e xternal to b us S with an inception angle close to 0 Figure 23. The signal ~ v S 2 [ n ] ~ i S 2 [ n ] measured at b us S under a phase A-to-ground f ault e xternal to b us S with an inception angle close to 0 From the study of these tw o ca ses related to e xternal f aults with a f ault inception angle near zero crossing, it can be deduced that the MSMGA based UHSDP is highly sensiti v e to signal v ariation. That is, the MSMGA based UHSDP is capable of detecting lo w amplitude f ault-induced transients. Int J Elec & Comp Eng, V ol. 9, No. 5, October 2019 : 3891 – 3904 Evaluation Warning : The document was created with Spire.PDF for Python.