Communication Characteristics of Faulted Overhead High Voltage Power Lines at Low Radio Frequencies

Transcription

1 energies Artile Communiation Charateristis of Faulted Overhead High Voltage Power Lines at Low Radio Frequenies Nermin Suljanović, Aljo Mujčić and Matej Zaj 2, * ID Faulty of Eletrial Engineering, University of Tuzla, Franjevačka 2, Tuzla, Bosnia and Herzegovina; nermin.suljanovi@fet.ba (N.S.); aljo.muji@fet.ba (A.M.) 2 Faulty of Eletrial Engineering, University of Ljubljana, Trzaška 25, SI-000 Ljubljana, Slovenia * Correspondene: matej.zaj@fe.uni-lj.si; Tel.: Reeived: 9 September 207; Aepted: 6 November 207; Published: 8 November 207 Abstrat: This paper derives a model of high-voltage overhead power line under fault onditions at low radio frequenies. The derived model is essential for design of ommuniation systems to reliably transfer information over high voltage power lines. In addition, model an also benefit advaned systems for power-line fault detetion and lassifiation exploiting phenomenon of hanged onditions on faulted power line, resulting in hange of low radio frequeny signal propagation. The methodology used in paper is based on multiondutor system analysis and propagation of eletromagneti waves over power lines. The model for high voltage power line under normal operation is validated using atual measurements obtained on 400 kv power line. The proposed model of faulted power lines extends validated power-line model under normal operation. Simulation results are provided for typial power line faults and typial fault loations. Results learly indiate sensitivity of power-line frequeny response on different fault types. Keywords: high-voltage power-line; ommuniations; fault detetion; signal propagation; modelling; power line arrier (PLC). Introdution Eletriity grids are in transition from fossil-based towards a low-arbon senario, primarily based on renewable generation. This onept has led to evolution of eletrial grids to smart grids, dominantly foused on inorporation of renewable energy soures (RESs) into eletrial distribution grid and ability to enable harging of an arbitrary number of eletrial vehiles. This is a signifiant transition from traditional eletrial (power) systems in whih eletriity demand was met by fossil-based bulk generated energy and onveyed to loads through transmission and distribution grids. The smart grid onept requires ontinuous development of power grids, at transmission and distribution levels, developing new tehnologies and tehniques as well as repurposing existing ones. Transmission grids remain vital also in smart grids due to numerous reasons suh as to onvey energy from large renewable generation loations to demand sites, to link national markets and allow transfer of renewable eletriity surpluses, and to support intermittent renewable generation to operate more effiiently. The task is to ensure power flow by maintaining grid stability at required power quality levels. As investments are very high, great attention is devoted to monitoring and maintaining transmission lines. A transmission grid onsists of high-voltage (HV) power lines spread over a large geographi area. In alternating urrent (AC) grids, eletriity is transferred as three- voltages and urrents at 50/60 Hz, whih is usually denoted as power frequeny. Besides eletriity transfer, HV power lines have also being utilized for ommuniation purposes to transfer relevant operational data and Energies 207, 0, 80; doi:0.3390/en080

2 Energies 207, 0, 80 2 of 24 lines have also being utilized for ommuniation purposes to transfer relevant operational data and protetion protetion signals signals (Figure (Figure ). ). With With this this aim, aim, high-frequeny high-frequeny (HF) (HF) signals signals an an be be injeted injeted into into power power line line ondutors ondutors at at one one terminal terminal using using appropriate appropriate frequeny-seletive frequeny-seletive iruits iruits (filters) (filters) and and extrated extrated at at or or terminal, terminal, not not interfering interfering with with power-frequeny power-frequeny signals. signals. Information Information is superimposed is superimposed into HF into signals HF signals using using analog analog or digital or digital modulation. modulation. Figure. High voltage power line utilized for ommuniations. This teleommuniation tehnology founded on HF signal transmission over HV power lines This teleommuniation tehnology founded on HF signal transmission over HV power is known as power line arrier (PLC). Nowadays HV PLC doesn t provide throughput that an lines is known as power line arrier (PLC). Nowadays HV PLC doesn t provide throughput that ompete with optial fiber or fourth generation (4G) ellular systems, and its appliation is very an ompete with optial fiber or fourth generation (4G) ellular systems, and its appliation is very limited to speifi appliations in power systems. On or hand, knowledge gained in limited to speifi appliations in power systems. On or hand, knowledge gained in domain of HF signal transmission over HV power lines and phenomena aompanying it an be domain of HF signal transmission over HV power lines and phenomena aompanying it an be used for some or advaned appliations suh as fault detetion and loalization. Mamatial used for some or advaned appliations suh as fault detetion and loalization. Mamatial models primarily derived for PLC ommuniations are fundamental for design of suh advaned models primarily derived for PLC ommuniations are fundamental for design of suh advaned systems. Tehnology deployed in smart transmission grids an utilize se data as input for realtime monitoring of overhead power lines. systems. Tehnology deployed in smart transmission grids an utilize se data as input for real-time monitoring of overhead power lines. Eletrial grids are faing inorporation of intermittent renewable energy resoures and Eletrial grids are faing inorporation of intermittent renewable energy resoures and neessity for infrastruture reinforement []. Transmission system operators (TSOs) onsider neessity for infrastruture reinforement []. Transmission system operators (TSOs) onsider different power-line monitoring tehnologies to enhane operational effiieny of existing HV different power-line monitoring tehnologies to enhane operational effiieny of existing HV power lines, suh as Dynami Line Rating (DLR) [2,3]. DLR is sensor-based system that inreases power lines, suh as Dynami Line Rating (DLR) [2,3]. DLR is a sensor-based system that inreases transmission apaity by utilizing real-time data and information. These data inlude various transmission apaity by utilizing real-time data and information. These data inlude various fators that impat temperature of overhead ondutors. With suh an approah, power line fators that impat temperature of overhead ondutors. With suh an approah, power line transmission apaity an reah 0 30% of designed limits, under suitable wear onditions. transmission apaity an reah 0 30% of designed limits, under suitable wear onditions. Besides DLR sensors, information about temperature of overhead power line ondutors an be Besides DLR sensors, information about temperature of overhead power line ondutors an be extrated from knowledge about overhead line atenary. In partiular, power line sag is diretly extrated from knowledge about overhead line atenary. In partiular, power line sag is diretly related related to wear onditions and temperature of ondutors. In [4], authors proposed to wear onditions and temperature of ondutors. In [4], authors proposed appliation appliation of PLC signals for real-time sag monitoring of HV overhead power lines. The method of PLC signals for real-time sag monitoring of HV overhead power lines. The method determines determines average overhead ondutor height variations in real-time, orrelating mamatial average overhead ondutor height variations in real-time, orrelating mamatial models with models with proessed PLC signals aptured at power-line terminals. proessed PLC signals aptured at power-line terminals. Ie load an ause severe damage on overhead power lines. The number of iing disasters on Ie load an ause severe damage on overhead power lines. The number of iing disasters overhead power lines is inreasing due to prevailing marolimate, mirometeorologial, and on overhead power lines is inreasing due to prevailing marolimate, mirometeorologial, mirotopography onditions [5]. There are several omplex methods to obtain information about and mirotopography onditions [5]. There are several omplex methods to obtain information state of ie aretion based on real-time measurements with speifi sensor systems [6]. Anor about state of ie aretion based on real-time measurements with speifi sensor systems [6]. approah for iing thikness monitoring is based on image reognition algorithms [5]. Ie load on Anor approah for iing thikness monitoring is based on image reognition algorithms [5]. Ie load overhead line ondutors auses PLC signal propagation hanges, whih an be utilized for on overhead line ondutors auses PLC signal propagation hanges, whih an be utilized for detetion of ie loads [7]. In or words, ie load detetion an be implemented through proessing detetion of ie loads [7]. In or words, ie load detetion an be implemented through proessing of of PLC signals propagated over HV power line. PLC signals propagated over HV power line. Detetion and lassifiation of faults on HV power lines is ruial for stable and reliable power system operation. Various methods for detetion, lassifiation and loation of faults on HV power

3 Energies 207, 0, 80 3 of 24 Detetion and lassifiation of faults on HV power lines is ruial for stable and reliable power system operation. Various methods for detetion, lassifiation and loation of faults on HV power lines have been studied, taking advantage of digital signal proessing algorithms and mahine learning methods [8]. The ommon harateristi of all available approahes is to utilize measured voltage and urrent signals or fault-generated transient phenomena [9,0]. On or hand, faults on power lines have a signifiant impat on frequeny response. If a signal at PLC frequeny is onstantly injeted, faults an be lassified and loated by proessing reeived signal at line terminal. The authors of [] proposed a onept in whih faults in multiondutor overhead distribution networks are deteted using PLC devies. The method is based on deteting differenes between values of metris related to input impedane at frequenies utilized by PLC systems. The purpose of this work is to provide high-frequeny model of faulted HV power line, whih an be utilized for fault lassifiation and loalization purposes. This information is needed for future utilization of HV power lines for transmission of HF signals for various smart grid servies. Analytial model is derived for HV system under normal operation and evaluated with omputer simulations validated with real HV power line measurements. This model is furr extended for a faulted HV power-line and frequeny response is obtained with omputer simulations for different types of faults and deployed ouplings. Different ouplings are onsidered in order to determine oupling with H(f ) most sensitive to power-line faults. The researh presented in paper is foused on high-frequeny harateristis of HV power line under faulted operation. The main ontributions of paper are: Telegrapher s equations for multiondutor lines are extended with equations that provide harateristis for available ouplings onneting eletroni equipment to HV power-line ondutors. This approah has been validated with atual measurements on 400 kv power line and outer-to-middle oupling. The methodology for alulation of high-frequeny harateristis of faulted HV power lines is developed for series and shunt faults. The presented methodology is based on validated approah used for HV power line in normal operation. 2. From HV PLC Systems to Advaned Power-Line Monitoring Appliations Reliable ommuniations are fundamental omponent of modern power grids. The ability to utilize power lines for ommuniations has attrated researh ommunity for almost a entury. At transmission level, PLC presents one of first ommuniation tehnologies inside power systems. The range and quality of HV PLC ommuniations strongly depends on ommuniation harateristis of power lines (attenuation and noise), but also interferene with or systems. HV overhead power lines radiate energy at high frequenies and interfere with or systems operating at same frequenies. In Europe, frequeny range devoted to HV PLC system is from 30 khz to 500 khz [2 4]. HV PLC systems are not permitted to operate in broadband, but rar in frequeny range whih is a multiple of 4 khz bands to limit interferene. Therefore, HV PLC systems operate in a narrowband at arrier frequenies, whih are determined at deployment site to prevent interferene. Available data rates are low for this reason, even at high spetral effiient digital modulation tehniques (number of bits per Hz that hannel transfers). On or side, major advantages of HV PLC ommuniations are high reliability of se systems and apability to transfer information over long distanes, both ruial inside smart grid onept. HV PLC hannels are haraterized with very low attenuation, refore ommuniation signals an be transferred over very long distanes. The distane is limited by noise, generated by orona phenomena (disharges generated by rated high voltage) and interfering signals [2 4]. Even though orona noise intensity varies with power frequeny voltage, it doesn t make huge impat on ultra-narrow band systems. It means that ultra-narrow band ommuniation signals an be reliably used for ontrol and ommand signals, suh as trip signal for distant protetion of HV power lines. Consequently, for deades HV PLC systems have provided a ommuniation link to reah different

4 Energies 207, 0, 80 4 of 24 power system omponents for ontrol reasons and appliations that require high reliability, low delays, and small throughput. HV power lines employ three ondutors (usually denoted as A, B and C) for eletriity Energies 207, 0, 80 4 of 24 transfer and two shield wires for lightning protetion. Shemes that desribe how two terminals of ommuniation equipment are onneted to to ondutors are known as as ouplings. Shield wires are grounded at at eah power-line pole and annot be be used for for signal transmission. Coupling equipment bloks bloks power-frequeny voltages voltages and forwards and forwards HF ommuniation HF ommuniation signals. Communiation signals. Communiation signals are signals bloked are bloked from propagating from propagating towards towards transformers transformers at both at both power-line line terminals by frequeny-tuned by frequeny-tuned iruits iruits named named line trap line trap units units (LTUs). (LTUs). PLC PLC hannel hannel harateristis harateristis are terminals different are different for individual for individual ouplings ouplings shemes. shemes. High-frequeny High-frequeny signal signal transmission transmission over over three three ondutors ondutors is oupled is oupled refore refore three three ondutors ondutors annot be analyzed annot be as three analyzed independent as three hannels. independent Forhannels. this reason, For modal this reason, analysis modal is used analysis to deouple is used PLC to deouple hannel into PLC three hannel virtual into modal three hannels. virtual modal While hannels. modal hannels While modal are haraterized hannels are haraterized with differentwith attenuations, different attenuations, ir exitation ir is diretly exitation orrelated is diretly with orrelated seleted with oupling seleted sheme oupling [2 4]. sheme [2 4]. For advaned HV power-line monitoring appliations, a similar topology is used for HF signal injetion and and detetion (Figure (Figure 2). Eah 2). Eah individual individual appliation appliation defines defines shape and shape frequeny and frequeny ontent of ontent injeted of HF injeted signals HF atsignals transmitting at transmitting site as well site as as proessing well as proessing algorithms algorithms of apturedof signals aptured at signals reeiving at site. reeiving The ondition site. The ofondition HV powerof line HV ispower superimposed line is superimposed into its frequeny into response its frequeny H(f ). Complete response understanding H(f). Complete ofunderstanding H(f ) is ruial for of design H(f) is of advaned ruial for power-line design of monitoring advaned appliations power-line utilizing monitoring HFappliations signal propagation. utilizing HF signal propagation. I E( x)dx + rdx Ldx I + di V gdx Cdx J ( x)dx V + dv x dx l x Figure Figure Equivalent Equivalent iruit iruit representing representing one-ondutor one-ondutor transmission transmission line line lump. lump. 3. High-Voltage Overhead Power Line High Frequeny Charateristis in Operation 3. High-Voltage Overhead Power Line High Frequeny Charateristis in Operation Voltage and urrent propagation along a transmission line an be desribed with telegrapher s Voltage and urrent propagation along a transmission line an be desribed with telegrapher s equations. Sine HV power line is multiondutor line, telegrapher s equations take matrix form. equations. Sine HV power line is a multiondutor line, telegrapher s equations take a matrix form. Telegrapher s equations in matrix form are derived from Maxwell equations and an be simplified Telegrapher s equations in matrix form are derived from Maxwell equations and an be simplified for ase of sinusoidal voltages and urrents [5,6]. for ase of sinusoidal voltages and urrents [5,6]. In order to obtain frequeny response of a HV power line, we onsider propagation of timeharmoni voltages and urrents along power line. Our analysis uses two assumptions: In order to obtain frequeny response of a HV power line, we onsider propagation of time-harmoni voltages and urrents along power line. Our analysis uses two assumptions:. HV power line is a linear system.. 2. HV Only power stationary line isstates a linear are system. onsidered Only Transmission stationary line states is assumed are onsidered. to be infinitely long. 3. Transmission line is assumed to be infinitely long. Telegrapher s equations for ase of sinusoidal voltages and urrents are derived starting with equivalent Telegrapher s eletrial equations sheme for of infinitely ase of sinusoidal small line voltages lumps [7]. and urrents are derived starting with equivalent eletrial sheme of infinitely small line lumps [7]. 3.. Wave Propagation on Infinetely Long Homogoneous Multiondutor Transmission Line 3.. Wave Propagation on Infinetely Long Homogoneous Multiondutor Transmission Line In order to desribe wave propagation over a multiondutor transmission line, we use equivalent In order eletrial to desribe iruit wave of a propagation line lump [7]. over In a multiondutor first step, transmission line, line wewith use one equivalent ylindrial eletrial ondutor iruit parallel of with a line lump earth [7]. plane Inand harmoni first step, soures transmission at line line terminals with one are onsidered. Voltage and urrent at any arbitrary point on line are determined with onentrated harmoni soures at line terminal as well as distributed soures along line, toger with transmission line harateristis. This is modelled with an equivalent eletrial iruit of line lump with onentrated parameters as is shown in Figure 2 [7].

5 Energies 207, 0, 80 5 of 24 ylindrial ondutor parallel with earth plane and harmoni soures at line terminals are onsidered. Voltage and urrent at any arbitrary point on line are determined with onentrated harmoni soures at line terminal as well as distributed soures along line, toger with transmission line harateristis. This is modelled with an equivalent eletrial iruit of line lump with onentrated parameters as is shown in Figure 2 [7]. Distributed voltage and urrent soures exist due to different types of noise (e.g., Corona noise) appearing on transmission line. The line is haraterized with passive elements per unit length: r, L, g and C. Element r orresponds to line resistane per unit length while L is indutane per unit length. The shunt passive elements g and C represent a ondutane and a apaitane of transmission line per unit length. The analysis is redued to harmoni voltage and urrent propagation, presented as phasors rotating with angular frequeny f. Aording to Figure 2, inrement of voltage and urrent aross line lump an be written as [7]: dv = zi + E(x)dx di = yv + J(x)dx () where z = r + jωl is line impedane per unit length and y = g + jωc is shunt admittane per unit length. Separating variables in oupled Equation () and negleting term dv in omparison with V, equations desribing voltage and urrent along transmission line are obtained: d 2 V de(x) zyv = + zj(x) dx2 dx d 2 I dj(x) yzi = + ye(x) (2) dx2 dx These equations are also known as telegrapher s equations for transmission line with a single ondutor above ground. Equation (2) an be extended to multiondutor ase. A major differene with previous ase is existene of magneti and eletrostati ouplings between ondutors. The magneti oupling is modeled with distributed voltage soures per unit length E ij and E ji, and mutual impedanes z ij = z ji. Eletrostati oupling is represented with admittane y ij between ondutors. A number of equations inreases with a number of ondutors and refore it is appropriate to write Equation (2) in a matrix form [6,7]: dv dx = ZI + E(x) where Z and Y are square matries: di = YV + J(x) (3) dx Y(i, i) = Z(i, k) = z ik, i, k =,... n n y ij, Y(i, j) = y ij, i, k =,... n, i = k (4) j= and n is number of ondutors. Vetors V, I, E and J have all dimension n. Variable separation in Equation (3) derives matrix telegrapher s equations: d 2 V de(x) ZYV = + ZJ(x) dx2 dx

6 Energies 207, 0, 80 6 of 24 d 2 I dj(x) YZI = + YE(x) (5) dx2 dx In ase of a passive network, distributed soures are equal to zero and telegrapher s equations beome: d 2 V dx 2 ZYV = 0 d 2 I YZI = 0 (6) dx2 Matries Z and Y in Equation (3), also found in literature as primary parameters of a transmission line, define how harmoni voltage and urrent propagate over a multiondutor transmission line. The detailed alulation of HV overhead power line primary parameters is given in [2 4] Solution of Telegrapher's Equations The non-diagonal elements of matries Z and Y, orresponding to ouplings between s, make solution of telegrapher s equations diffiult. Therefore, let s replae produt of matries Z and Y with matrix Γ taking into aount that matries Z and Y are symmetrial [7]: Γ 2 = ZY (7) furrmore: ( Γ 2) T = (ZY) T = Y T Z T = YZ (8) In analogy with propagation onstant, we will denote this matrix as propagation matrix. Equation (6) an be rewritten as: d 2 V dx 2 Γ2 V = 0 d 2 I ( dx 2 Γ 2) T I = 0 (9) In ase that Γ 2 is a diagonal matrix, previous equation is equal to set of n independent differential equations. Therefore, we need to find an appropriate linear transformation that results in diagonal matrix Γ 2. This linear transformation is founded on matries S and Q, orrelating voltages and urrents in natural () oordinates V and I with voltages and urrents in modal oordinates V (m) and I (m) [6 8]: V = SV (m) I = QI (m) (0) Substituting expression for voltage and urrent vetors defined with Equation (0), Equation (9) beomes: d 2 V (m) dx 2 = S Γ 2 SV (m) d 2 I (m) dx 2 = Q ( Γ 2) T QI (m) The matrix S is determined to diagonalize produt [8,9]: { } S Γ 2 S = γ 2 = diag γ 2, γ γ2 n We onlude that elements of diagonal matrix γ 2 are eigenvalues of matrix Γ 2, where olumns of matrix S are ir orresponding eigenvetors [8,20,2]. () (2)

7 Energies 207, 0, 80 7 of 24 Matries ZY and YZ are similar sine: YZ = Z (ZY)Z (3) and refore produt YZ has same eigenvalues [8 20]. The olumns of matrix Q are eigenvetors of matrix Γ T = YZ, resulting in: { } Q YZQ = γ 2 = diag γ 2, γ γ2 n The presented analysis that deouples telegrapher s equations into 2 n ordinary differential equations is known as modal analysis. The modal analysis introdues deoupled modal hannels. Propagation of a modal voltage and urrent through modal hannel k is desribed by a modal propagation onstant γ k. The modal voltage and urrent in modal hannel k at arbitrary point x an be expressed as: V (k) (x) = V (k)+ e γ kx + V (k) e γ kx = V (k)+ (x) + V (k) (x) I (k) (x) = I (k)+ e γ kx I (k) e γx = I (k)+ (x) I (k) (x) (5) Constants I (k)+ and I (k) are alulated using boundary onditions at power-line terminal. A olumn vetor of matrix S defines distribution of modal voltage between ondutors. Distribution between power-line ondutors i and j is defined with ratio: (4) V(i) S(i, k) = V(j) S(j, k) (6) Matrix S is usually normalized with respet to first row that is multiplied with a transformation matrix in manner that elements in first row are all equal to one. We denote suh normalized matrix S with λ. Similar expressions an be derived for urrents: I(i) Q(i, k) = I(j) Q(j, k) (7) where matrix Q is normalized in respet to first row, denoted with δ Charateristi Impedane Matrix Voltage V (k) and urrent I (k) propagate through modal hannel k independently from or modal hannels. At an arbitrary point x on a power line, modal voltage and urrent are equal to sum of inident and refleted waves, as it is written in Equation (5). The modal harateristi impedane establishes a relation between modal inident voltage and urrent with modal refleted voltage and urrent: V (k)+ = Z (k) V (k) = Z (k) for k =,... n, or rewritten in a matrix form: where Z (m) V (m)+ (x) = Z (m) V (m) (x) = Z (m) I (k)+ = Z (k) I (k)+ e γ kx I (k) = Z (k) I (k) e γ kx I (m)+ (x) = Z (m) I (m)+ e γx (8) I (m) (x) = Z (m) I (m) e γx (9) is a diagonal matrix ontaining harateristi impedanes of modal hannels: Z (m) { = diag Z ()... Z (n) } (20)

8 Energies 207, 0, 80 8 of 24 Matrix e γx is a diagonal matrix defined as: e γx = diag{e γ x... e γ nx } (2) Modal voltages at an arbitrary point x equal to sum of inident and refleted waves: while orresponding modal urrents are: V (m) (x) = V (m)+ (x) + V (m) (x) = V (m)+ e γx + V (m) e γx (22) I (m) (x) = I (m)+ e γx I (m) e γx = Y (m) ( V (m)+ e γx V (m) e γx) (23) The boundary ondition at first line terminal determines onstants V (m)+ and V (m). Substituting modal voltage in modal telegrapher s Equation () with equations (22) and (23), modal harateristi impedane [7] is derived: Z (m) ( ) = S ZQ γ (24) The modal harateristi admittane matrix is defined by: Y (m) = Z (m) { = diag Y ()... Y () } (25) Voltage and urrent vetors in natural () oordinates are omputed from modal voltage and urrent vetors obtained as a solution of telegrapher s equation. Equations (0) and (9) also orrelate inident and refleted waves in natural oordinates with inident and refleted waves in modal oordinates: V + = SV (m)+ = SZ (m) I (m)+ = SZ (m) Q I + = Z I + V = SV (m) = SZ (m) I (m) = SZ (m) Q I = Z I (26) where V + and I + are inident voltage and urrent vetors in natural oordinates. Charateristi impedane matrix Z is omputed as: Z = SZ (m) Q (27) while harateristi admittane matrix is: Y = Z = QY (m) S (28) Substitution of modal voltage and urrent in Equation (0) with Equations (24) and (25) yields [9]: ( V(x) = SV (m) (x) = S e γx S V (m)+ + e γx S V (m)+ ) ( I(x) = QI (m) (x) = Y Se γx S SV (m)+ Se γx S SV (m) ) (29) We introdue exponential funtion: and denote: V + n Equation (29) an be rewritten in form: EXP(±Γx) = Se ±γx S (30) = SV(m)+, V = SV(m) (3) V(x) = EXP( Γx)V + + EXP(Γx)V

9 Energies 207, 0, 80 9 of 24 ( I(x) = Y EXP( Γx)V + EXP(Γx)V ) (32) Vetors V + and V are omputed from boundary onditions defined at power-line terminal. When boundary onditions are V(0) = V and I(0) = I, vetors V + and V are found to be: V + = 2 (V + Z I ), V = 2 (V Z I ) (33) Substitution of previous expressions into Equation (32) yields [7]: V(x) = 2 (EXP(Γx) + EXP( Γx))V 2 (EXP(Γx) EXP( Γx))Z I I(x) = 2 Y (EXP(Γx) EXP( Γx))V + 2 Y (EXP(Γx) + EXP( Γx))Z I (34) 3.4. Charateristis of HV Power Line Terminated with Impedane Communiation equipment an be onneted to a HV power line in different ouplings (to one, two or three ondutors), employing different power-line hannels for data transmission. Eah power-line hannel is haraterized with its own frequeny-dependent transfer funtion sine different ouplings exite different modes. There are two major approahes to HV power-line modeling based on modal analysis [6]. The first approah utilizes power-line multiport representation and redution of ports in respet to used oupling, without omputation of voltages and urrents. The seond approah omputes reeived voltages and urrents with known transmitted voltages and urrents for seleted oupling. This approah inorporates refletion oeffiient and it is usually denoted as a method of matrix refletion oeffiients [7,7,2]. If V and I are known harmoni voltage and urrent of an arbitrary frequeny f at power-line transmitting end and V 2 and I 2 are reeived voltages at or line end, frequeny-dependent power-line transfer funtion is defined with amplitude α and harateristi β: H(jω) = e α(ω)+jβ(ω) = Ae jβ(ω) (35) where: α = 2 ln V 2 I 2 V I [Np] or α = 0 log V 2 I 2 V I [db] { β = Im ln V } 2I 2 [rad] (36) V I Voltage Transfer Matrix The voltage and urrent at transmitting line terminal are interrelated through input admittane (or input impedane) matrix and at reeiving end with load admittane matrix: I = Y in V = Z in V I 2 = Y L V 2 = Z L V 2 (37) The voltage and urrent at line terminal is a sum of inident and refleted omponents: V 2 = V V 2 I 2 = I + 2 I 2 = Y ( V + 2 V ) 2 (38)

10 Energies 207, 0, 80 0 of 24 Solving set of Equation (38) per inident and refleted voltages, and taking into aount Equation (37), yields: V + 2 = 2 (I + Z Y L )V 2, V 2 = 2 (I Z Y L )V 2 (39) A refletion oeffiient represents a ratio between refleted and inident waves. Sine a power line is a multiondutor system, refletion oeffiient is a square matrix orrelating refleted and inident waves at different ports: V = K V +, V 2 = K 2V + 2 (40) Utilizing Equations (39) and (40), matrix refletion oeffiient at reeiving terminal is: K 2 = (I + Z Y L ) (I Z Y L ) (4) Similarly, voltage at transmitting line terminal is expressed in terms of inident wave and matrix refletion oeffiient K [7]: V = V + + V = (I + K )V + (42) Sine inident voltage at reeiving line end is determined by propagation funtion and power-line length: V + 2 = EXP( Γl)V+ (43) voltages at reeiving and sending line ends are interrelated with: V 2 = (I + K 2 )EXP( Γl)(I + K ) V = TV (44) where matrix T is voltage transfer matrix. The matrix refletion oeffiient is obtained by interrelating refleted and inident waves at transmitting line terminal [6,22]: K = EXP( Γl)K 2 EXP( Γl) (45) while input admittane is: Y in = Y ( K )( + K ) (46) If a refletion is onsidered in modal oordinates, we deal with modal inident and refleted waves are interrelated with modal refletion oeffiient. The relation between inident and refleted waves in (original) and modal oordinates is established with: V (m)+ x = SV + x, V (m) x = SV x (47) where index x is used to denote both line ends. The modal refletion oeffiient is n derived from Equations (40) and (47): K (m) x = S K x S (48) The transformation defined by Equation (48) results in a non-diagonal matrix, what auses power exhange between modes at termination points. A onlusion is that modal waves propagate along modal hannels without interating between eah or. However, interation ours at termination points. On or hand, any inhomogeneity on a power line produes refleted waves and power exhange between modes.

11 Energies 207, 0, 80 of 24 Energies 207, 0, 80 of Computation of High-Frequeny Power-Line Transfer Funtion for Different Couplings In this setion we we fous fous on two on two types types of oupling of oupling utilizing utilizing one or two one or two ondutors, ondutors, presented in presented Figure 3. in Figure 3. z eg z g + z z z g e g + z e g 2 + z g e g 2 + z g a) b) Figure Figure Prinipal Prinipal shemes shemes of of (a) (a) a a to to ground ground ouplingand, and, (b) (b) a a to to oupling. Voltages at transmitting and reeiving ends of HV power line are orrelated with voltage Voltages at transmitting and reeiving ends of a HV power line are orrelated with voltage transfer matrix T. Corresponding urrents are alulated using termination admittanes at both transfer matrix T. Corresponding urrents are alulated using termination admittanes at both power-line ends, denoted with matries Y power-line ends, denoted with matries Y g and Y L. g and Y L. When voltage voltage transfer transfer matrix matrix is determined, is determined, high-frequeny high-frequeny power-line hannel power-line harateristis hannel for harateristis different ouplings for different an be ouplings obtainedan with be two obtained approahes: with two approahes:. The first is to assume value of soure (voltage or urrent) and to ompute voltages and. The first is to assume a value of soure (voltage or urrent) and to ompute voltages and urrents at both line terminals. High-frequeny power-line hannel harateristis are n urrents at both line terminals. High-frequeny power-line hannel harateristis are n omputed from Equation (36). In ase of very long lines, suh approah an ause a omputed from Equation (36). In ase of very long lines, suh approah an ause a signifiant signifiant numerial inauray that inreases with frequeny. numerial inauray that inreases with frequeny. 2. In seond approah, high-frequeny power-line harateristis are omputed diretly 2. In seond approah, high-frequeny power-line harateristis are omputed diretly from from voltage transfer matrix, utilizing information of relations between voltages at voltage transfer matrix, utilizing information of relations between voltages at both both line ends ontained in matrix T. line ends ontained in matrix T. A problem that arises in suh formulae derivations is related to a multiondutor system, where voltages A problem of all output that arises ports in suh are interrelated formulae derivations with all voltages is relatedof toall a multiondutor input ports. In system, first where step, voltages frequeny ofresponse all output is alulated ports are interrelated for with to ground all voltages oupling. of all We input suppose ports. that In transmitter first step, frequeny is modeled response as voltage is alulated generator for E g and impedane to ground oupling. Z g. Sine We voltage supposesoure that impedane transmitter is is modeled as voltage generator E g and impedane Z g. Sine voltage soure impedane is z g, zg, expression that defines voltages of three s at transmitting line terminal is: expression that defines voltages of three s at transmitting line terminal is: V = YΣ I g = Yg + Yin ) E g = LE g (49) V = Y z Σ I g = ( ) Eg g Yg + Y z in = LE g (49) g I = Y in inv (50) Let s onsider aa transmitter onneted between between k andk and ground ground and a reeiver and a between reeiver between t and ground, t and as presented ground, in as Figure presented 3a. The in amplitude Figure 3a. and The amplitude harateristis and are omputed harateristis as: are omputed as: α = 20 log V 2 (t)i 2 (t) 2 () t I 2 () t α = 20 log V (k)i (k) [db] [db] { V( k ) I( k ) β = Im ln V } 2(t)I 2 (t) [rad] (5) V (k)i 2 () t I (k) 2 () t β = Im ln [rad] The k-th element in vetor E (5) g equals V e ( g k, ) Iwhile ( k ) or elements are zero. Equation (49) simplifies to: The k-th element in vetor E g equals V e g, while or elements are zero. Equation (49) = L k e g (52) simplifies to:

12 Energies 207, 0, 80 2 of 24 where L k is k-th olumn of matrix L. In next step all voltages should be expressed in term of one parameter. For instane, voltage of first port V () at sending end an be hosen as suh parameter. The ratio between voltage of i and voltage of is: V (i) V () L(i, k) =, i =,... n (53) L(, k) vetor L kr ontains elements defined by Equation (53). Now, vetor V is expressed in term of V () V = L kr V () (54) Furr we rewrite voltage at reeiving end in term of parameter V (): and voltage of t at reeiving end is found to be: V 2 = TL kr V () (55) V 2 (t) = T t L kr V () (56) where T t is a row t of matrix T. The urrent at sending end equals to: I 2 = Y L TL kr V () = FL kr V () (57) where F is auxiliary square matrix. If with Y k in we denote row k in input admittane matrix Y in and with F t row t in matrix F, n voltage of k at sending end and voltage of t at reeiving end equal to: I (k) = Y k in L krv () I 2 (t) = B t L R V () (58) Substituting expressions for both line ends in Equation (5) we derive: T t L α = 20 log R L kr (k) β = Im { ln T tl kr L kr (k) Y k in L kr B t L kr Y k in L kr B t L kr [db] } [rad] (59) Equation (59) defines high-frequeny power-line hannel harateristis for to ground oupling. A similar analysis an be onduted also for to oupling (Figure 3b). Let s assume oupling j to k at transmitting power-line terminal and s to t at reeiving terminal. The elements of voltage vetor E g equal zero, exept s-th and k-th elements that are: E g (j) = e g /2, E g (k) = e g /2 (60) If L j and L k denote j-th and k-th olumns of matrix L respetively, voltage at sending terminal is: V = ( ) e g L j L k 2 = L e g jk (6) 2 Likewise, to ground oupling, elements of voltage vetor V are expressed in term of voltage V () utilizing vetor olumn L jkr whose elements are: L jkr = V (i) V () = L jk(i) L(i, j) L(i, k) = L jk () L(, j) L(, k) (62)

13 Energies 207, 0, 80 3 of 24 The voltage at transmitting end is n: and for seleted oupling: V (j) V (k) = V = L jkr V () (63) ( ) L jkr (j) L jkr (k) V () (64) Voltage at reeiving end is orrelated to voltage at sending end with voltage transfer matrix: V 2 = TL jkr V () (65) and voltage at reeiver is: The urrents at power line terminals are: V 2 (s) V 2 (t) = (T s T t )L jkr V () (66) I = Y in L jkr V () I 2 = Y L TL jkr V () = FL jkr V () (67) When Y j in represents j-th row of matrix Y in and Fs orresponds to s-th row of matrix B, urrents at reeiver and at transmitter respetively are: I (j) = Y j in L jkrv () I 2 (s) = B s L jkr V () (68) The high-frequeny power-line hannel harateristis are n derived from Equations (64), (66) and (68) as: α = 20 log V 2 (s) V 2 (t) I 2 (s) (T s T t )L jkr B s L jkr V (j) V (k) I (j) = 20 log L jkr (j) L jkr (k) Y j in L [db] jkr { ( )} { ( )} V2 (s) V β = 2 (t) (Ts T t )L jkr Im ln = Im ln [rad] (69) V (j) V (k) L jkr (j) L jkr (k) 4. High-Frequeny Charateristis of Faulted HV Overhead Power Line In this setion we analyze high-frequeny response of HV power line under different fault onditions. For this purpose we start with previously derived model of a HV power line in normal operation, validated with atual measurements. Faulted HV power line model is derived for all known HV power line faults, whih are divided into two ategories [23,24]: shunt faults, series faults. The shunt faults refer to all types of short iruits that are furr ategorized as [25]: short iruit between one and ground ( to ground fault), short iruit between two s, with possibility of simultaneous grounding ( to fault and grounded to fault), short iruit of all three s (three fault).

14 Energies 207, 0, 80 4 of 24 short iruit between one and ground ( to ground fault), Energies short 207, iruit 0, 80 between two s, with possibility of simultaneous grounding ( to 4 of 24 fault and grounded to fault), short iruit of all three s (three fault). Short iruits are also denoted as permanent or temporary, depending on wher y still existsshort wheniruits power are linealso is not denoted rated byas apermanent high voltage. or The temporary, permanent depending faults are on aused wher by breaking y still exists when or shielding power ondutors line is not rated and short by a high iruiting voltage. with The permanent or faults ondutors are aused or by breaking ground. The temporary shielding short ondutors iruits exist and due short toiruiting ars and with disappear or after power ondutors line isor swithed ground. off. Temporary The temporary faults short aniruits be initiated exist by due to temporary ars and disappear insulationafter breakdown power due line to is short-duration swithed off. atmospheri Temporary faults disharges. an be Sine initiated a large by amount temporary of faults insulation are self-healing, breakdown due automati short-duration relosure proess atmospheri is utilized disharges. instead Sine of permanent a large amount power-line of swith faults are off. self-healing, Automati relosure automati attempts to relosure swith on proess power is utilized line until instead short-iruit of permanent pathpower-line is deionized. swith After off. predefined Automati number relosure of unsuessful attempts to attempts swith on (usually power up toline three until times) short-iruit power line path remains is deionized. swithedafter off [26]. predefined number of unsuessful The series attempts faults orrespond (usually up to to a three times) ondutors power breaking line without remains onnetion swithed off with [26]. or ondutors The series or faults ground. orrespond Toger, to a series and ondutors shunt faults breaking on two without sidesonnetion of fault loation with or on power ondutors line formor hybrid ground. type Toger, fault. The most series ommon and shunt faults faults are on totwo ground sides faults. of They fault ontribute loation on three power quarters line ofform all faults hybrid while type rarest fault. are The most threeommon faults faults [27]. are to ground faults. Next They weontribute derive three method quarters to ompute of all faults harateristis while rarest of are faulted three power line. faults It[27]. should be notied Next we that derive shor iruits method areto always ompute followed harateristis by of power faulted line trip power in order line. It toshould prevent be notied severe that damage short iruits of are equipment always followed due toby high power short-iruit line trip urrents. in order to Inprevent analysis severe we assume damage that of tripped equipment power due line to high is terminated short-iruit with urrents. modified In impedanes analysis we what assume auses that hanged tripped high-frequeny power line is harateristis. terminated with modified impedanes what auses hanged high-frequeny harateristis. 4.. Fault Modeling with Shunt Impedane 4.. Fault Modeling with Shunt Impedane The shunt impedane on HV power line is defined as an eletrial system that onsist of passive The elements shunt impedane onnetedon between HV power-line ( is defined or shield) as an eletrial ondutors system and that ground onsist or of between passive elements power-line onneted ondutors between only (Figure power-line 4). Inhomogeneity ( or shield) (fault ondutors loation) and is modelled ground withor a shunt between admittane power-line matrix ondutors Y sh. only (Figure 4). Inhomogeneity (fault loation) is modelled with a shunt There admittane are twomatrix approahes Ysh. to inorporate shunt impedane in derived high-frequeny power-line There are model. two approahes The first approah to inorporate utilized shunt method impedane of matrix in refletion derived high-frequeny oeffiients in ompliane power-line model. with The previous first approah setion. Itutilized is obvious that method a refleted of wave matrix appears refletion at oeffiients shunt point where ompliane impedane with previous hanges. setion. This phenomenon It is obvious that is inorporated a refleted wave in appears analysisat with shunt matrix point refletion where oeffiient impedane omputed hanges. as This [27]: phenomenon is inorporated in analysis with matrix refletion oeffiient omputed as [27]: K sh = ( ) ( ) I + Z Y eq I Z Y eq (70) K = ( I + Z Y ) ( I Z Y ) (70) sh where Y eq is admittane matrix terminating line setion before inhomogeneity and equals: where Y is admittane matrix terminating line setion before inhomogeneity and equals: eq eq eq Y eq = in2 (7) Y eq = Ysh + Yin2 (7) a b y 3 y2 y23 y0 y20 y30 Figure Figure HV HV overhead overhead power power line line fault fault modeled modeled with with shunt shunt impedane. impedane.

15 Energies 207, 0, 80 5 of 24 Energies 207, 0, 80 5 of 24 The admittane matrix Yin2 is input admittane of seond line setion Short Ciruits The admittane matrix Y in2 is input admittane of seond line setion. A short iruit represents a fault when a power line ondutor forms an eletrial ontat with 4.2. anor Shortondutor Ciruits or ground through some impedane. Suh fault is refore represented by shunt Aimpedane short iruit at represents fault loation. a fault when The faulted a power power-line ondutor high-frequeny forms anharateristis eletrial ontat are with n anor obtained ondutor as desribed or in Setion ground 4.. through some impedane. Suh fault is refore represented by shuntthe impedane fault analysis at is fault often loation. onduted The with faulted an power-line assumption high-frequeny that a fault impedane harateristis equals are zero. n It obtained implies that as desribed power-line Setion hannel 4.. attenuation with to oupling tends to infinity when The grounded fault analysis is to often onduted fault or three with an assumption fault ours. that However, a fault impedane it an be found equalsin zero. It literature implies that attenuation power-line introdued hannel attenuation by a short iruit with doesn t overreah to oupling 40 db to tends 50 db toand infinity that when redues grounded with frequeny to [7]. A magneti fault or oupling three between faulttwo ours. line setions However, separated it an be by found fault in an literature be represented that attenuation as indutive introdued reatane onneted by a shortat iruit fault doesn t loation. overreah The expressions 40 db to 50 that dbdefine and that redues fault impedanes with frequeny for different [7]. A magneti ouplings oupling are available between in [7,7,27]. two line setions separated by fault an be represented The fault impedane as indutive between reatane onneted ondutor at fault and loation. ground The (for expressions to ground that define fault) is fault omputed impedanes as [7,27]: for different ouplings are available in [7,7,27]. The fault impedane between Z ondutor and ground (for to ground fault) is f = rf + jωl fg (72) omputed as [7,27]: where r is sum of a grounding resistane Z f = r(between f + jωl f g 0 Ω and 20 Ω) and a ondutor aused (72) f where short iruit r f is (or sum ar). of Aording a grounding to [7,27], resistane L fg for (between to 0ground Ω and fault 20 Ω) is and omputed a ondutor as: aused short iruit (or ar). Aording to [7,27], L f g for to ground fault is omputed as: 7 2h L fg = 2 0 h( L f g = h ln 2h ln.06 ) (73) r0.06 (73) r where h and 0 r 0 are length and radius of grounding ondutor. The previous expression where holds when h and r 0 are distane length to and fault radius from of oupling grounding devie ondutor. is l f > 2The h [7]. previous expression holds when In distane ase of to a fault to from fault, oupling without devie grounding, is l f > 2h [7]. fault impedane is omputed as a short In iruit ase between of a two to parallel fault, lines. without The resistane grounding, is negleted, fault impedane while indutane is omputed equals as to a short [27]: iruit between two parallel lines. The resistane is negleted, while indutane equals to [27]: ( L f = S ) 7 S L f = 2 0 S (74) ln.06 (74) r0 The grounded to fault is a ombination of above defined impedanes. The short iruit is shematially represented in Figure 5. rf L fg L f L f L fg rf L f L f Phase to ground fault Phase to fault Grounded to fault Three fault Figure 5. Short-iruit types Series Series Faults Faults A series series fault fault ours ours when when one one of of ondutors ondutors breaks breaks without without any any onnetion onnetion between between s s or or between between a and and ground ground [23]. [23]. However, However, it it is is ommon ommon that that one one of of s s or or both both after after

16 Energies 207, 0, 80 6 of 24 Energies 207, 0, 80 6 of 24 breaking fall down on ground what auses a to ground fault. Suh ase is denoted as a hybrid fault. We onsider one break, with possibility that a ondutor at both sides an also be grounded (falling down on ground), presented in Figure a z fg z fg I = 0 z fg a y 2 y 32 y 0 b b y 20 I 2 y 23 Y in2 Fault loation (a) Y in2 I 3 (b) y 30 Figure Figure Shematially Shematially represented represented series series fault. fault. (a) (a) Priniple Priniple sheme; sheme; (b) (b) Termination Termination impedane impedane at at fault fault loation. loation. A fault divides line into two setions. In order to determine admittane terminating A fault divides line into two setions. In order to determine admittane terminating first line setion, let s assume that fault ours on first ondutor. We onsider two first line setion, let s assume that fault ours on first ondutor. We onsider two options: ondutor an be open-iruited or short-iruited via impedane zfg. The impedane options: ondutor an be open-iruited or short-iruited via impedane z zfg orresponds to to ground impedane, omputed in previous sub-setion. fg. The impedane The input z impedane fg orresponds to to ground impedane, omputed in previous sub-setion. The input of seond setion Yin2 is shematially represented in Figure 6b and an be determined impedane of seond setion Y for line termination admittane in2 is shematially represented in Figure 6b and an be determined Y. The interrelation between voltages and node urrents on L for line termination admittane Y L. The interrelation between voltages and node urrents on right side of fault loation (Figure 6) is established as: right side of fault loation (Figure 6) is established as: ( y + y) fg ) V + y2v + y3v = I (y + y f g V + y 2 V + y 3 V = I y = 2 V + y 22 V + y 23 V I 2 y 2 V + y 22 V + y 23 V = I 2 y y 3 V + y 32 V + y 33 V = I 3 (75) + (75) where I I, I and 2 I are node urrents. Admittane y 3 ij is an element (i, j) of matrix Y, I 2 and I 3 are node urrents. Admittane y ij is an element (i, j) of matrix Y in2 while in 2 ywhile f g = /z y fg f = g or / zy fg f g or = 0. y fg When = 0. When first first ondutor ondutor is faulted, is faulted, node urrent node urrent I equalsi zero equals and: zero and: V = (y y + y 2 V 2 + y 3 V 3 ) (76) f g V = ( y2v2 + y3v3 ) (76) y + y fg Substituting previous equation into Equation (75), a relation between two or voltages and nodesubstituting urrents anprevious be written equation in matrix into Equation form as: (75), a relation between two or voltages and node urrents an be written in ) matrix form as: ) y [ ] [ ] [ ] 22 y 2 y 2 / (y + y f g y y22 y2 y2 /( 23 y y + y fg ) 2 y 3 / (y + y ) y23 y2 y3 /( f g y + ) y V fg ) 2 V 2 = Y 2 I V p 2 I 2 = 2 (77) y 32 y 3 y 2 / = = ( ) ( ) Y p (77) y (y 32 y + y 3 f g 2 / y y + 33 y y 3 fg y y 3 33 / y (y 3 y + 3 / y f g V 3 V 3 I 3 + y fg 3 V3 I3 It is obvious that seond and third s of first line setion are terminated with seond line setion while while first first is eir is eir short-iruited short-iruited via fault via impedane fault impedane or open-iruited. or iruited. Therefore, admittane admittane terminating terminating first line setion first line is: setion is: Therefore, [ ] or fg Y f = 0 or y Y (78) f = f g 0 (78) p 0 Y p If termination admittane at fault loation is known n first-setion voltage transfer matrix T is determined, and voltages at sending line terminal and left-side fault loations an be alulated:

17 Energies 207, 0, 80 7 of 24 If termination admittane at fault loation is known n first-setion voltage transfer matrix T is determined, and voltages at sending line terminal and left-side fault loations an be alulated: V f L = T V (79) When line is terminated with load admittane Y L, seond-setion voltage transfer matrix is found in ompliane with analysis onduted in previous sub-setion. Voltage at line end equals to: V 2 = T 2 V f R (80) where V f R is voltage vetor at beginning of seond line setion. Furrmore, voltages at both sides of fault loation are interrelated with fault voltage transfer matrix: where T f is alulated taking into aount Equation (77) as: T f = ) 0 y 2 / (y + y f g V f R = T f V f L (8) ) y 3 / (y + y f g (82) The voltage transfer matrix is: T = T 2 T f T (83) Power-line high-frequeny harateristi are omputed from equations derived in sub-setion 3.4. Due to simpliity, expressions are derived for first while analogy is valid for faults of two or s. 5. Simulation Results with Disussion The methodology for high-frequeny harateristis omputation proposed in this paper is simulated and validated for a 52 km long 400 kv overhead power line with horizontal disposition of ondutors (Appendix A). Measurement methodology and results, with detailed desription of power line is available in [3]. Its harateristis are measured for middle to outer oupling when power line is in normal operation. The proposed omputation methodology is validated for normal power line operation. Charateristis of faulted power line are only simulated, sine re is no opportunity to measure harateristis of faulted power lines. The methodology for power lines under normal operation is extended also for faulted power lines with an assumption that simulation results are valid. 5.. Validation of Computation Methodology for 400 kv Overhead Powerline in Operation Due to high-frequeny harateristis of installed LTU, omputation of HV power-line amplitude harateristi and group delay is validated in frequeny range from 50 khz to 350 khz. The validation in this frequeny range also means possible extrapolation in wider high-frequeny range. The omparison of simulated high-frequeny PLC hannel harateristis with measured is arried out for ase of warm wear (measurements onduted in Marh with fair wear). Detailed measurement methodology and impat analysis of oupling equipment, LTU, impedane mismath and optial able used as return path for network analyzer, on measurements are given in [3]. In this setion we use measurements under fair wear onditions to validated model presented in Setion 3. Validation of models presented in paper for amplitude harateristis are given in Figure 7. The red line represents measurement while blak line orresponds to simulated harateristi. We assumed 6 m sag and ground resistane per unit length 50 Ωm (swampy ground). Sine

18 Energies 207, 0, 80 8 of 24 at both sides is onneted to HV transformer with large indutivity, non-operating is onsidered Energies 207, to0, be80 open iruited. 8 of 24-3 Amplitude harateristi [db] Amplitude harateristi [db] Frequeny [khz] (a) Frequeny [khz] (b) Amplitude harateristi [db] Amplitude harateristi [db] Amplitude harateristi [db] Frequeny [khz] () Frequeny [khz] (e) Amplitude harateristi [db] Frequeny [khz] (d) Frequeny [khz] (f) Figure Figure Comparison Comparison of of simulated simulated amplitude amplitude harateristi harateristi of of kv kv PLC PLC hannel hannel with with measured measured for for different different frequeny frequeny intervals intervals (a f): (a f): blak-simulated, blak-simulated, red-measured. red-measured. Osillations in measured and simulated amplitude harateristis are aused by refletion at Osillations in measured and simulated amplitude harateristis are aused by refletion at power-line terminals. Ehoes (refleted waves) on power line make ripples on amplitude power-line terminals. Ehoes (refleted waves) on power line make ripples on amplitude harateristi. Signifiant deviations between measured and simulated harateristis present in harateristi. Signifiant deviations between measured and simulated harateristis present in Figure 7a,d,e,f are aused by operating frequeny range of LTU. The apaity of oupling Figure 7a,d f are aused by operating frequeny range of LTU. The apaity of oupling apaitor apaitor is 4400 pf, while LTU has minimal resistane 600 Ω in frequeny range from 68 to is 4400 pf, while LTU has minimal resistane 600 Ω in frequeny range from 68 to 304 khz. 304 khz. Measurement equipment is onneted with oupling devie via a oaxial able. The Measurement equipment is onneted with oupling devie via a oaxial able. The estimated estimated length of oaxial able is 500 m and its attenuation varies linearly from 0.2 to 0.35 db/00 length of oaxial able is 500 m and its attenuation varies linearly from 0.2 to 0.35 db/00 m in m in frequeny range from 50 to 350 khz. frequeny range from 50 to 350 khz. The measurements proved existene of osillations in amplitude harateristi aused by The measurements proved existene of osillations in amplitude harateristi aused by refletion while period of osillations in measured and simulated harateristis math. The refletion while period of osillations in measured and simulated harateristis math. differene between measured and simulated harateristis in operational range is within db. The differene between measured and simulated harateristis in operational range is within This is aeptable beause we deal with estimated high-frequeny harateristis of oupling devies.

19 Energies 207, 0, 80 9 of 24 db. This is aeptable beause we deal with estimated high-frequeny harateristis of oupling devies. Energies 207, 0, 80 9 of Simulation of High-Frequeny Charaterstis of Faulted HV Power Line Energies 207, 0, 80 9 of 24 High-frequeny 5.2. Simulation of harateristis High-Frequeny Charaterstis are alulated of Faulted in MATLAB HV Power Line (R205a, MathWorks, Natik, MA, Energies 207, 0, 80 9 of 24 USA) for Simulation High-frequeny kv overhead of High-Frequeny power harateristis line Charaterstis for are different alulated of Faulted type in MATLAB of HV faults Power (R205a, and Line loations. MathWorks, Results Natik, are MA, presented in Figures 5.2. USA) 8. Simulation High-frequeny for 400 The kv of seleted overhead High-Frequeny harateristis frequeny power Charaterstis line are for range alulated different of isfaulted from type in MATLAB of HV 200 faults Power to 250 and (R205a, Line loations. khzmathworks, while Results we are assumed Natik, presented MA, that in Figures 8. The seleted frequeny range is from 200 to 250 khz while we assumed that fault fault ours USA) after High-frequeny for kV kmoverhead from harateristis power sending line are for point. alulated different Thetype in non-operating MATLAB of faults and (R205a, loations. s MathWorks, Results are terminated are Natik, presented MA, with 400 ours after 25 km from sending point. The non-operating s are terminated with 400 Ω Ω resistane USA) in Figures at for both kv line The overhead terminals seleted power frequeny for line afor range different is tofrom ground type 200 of to faults oupling 250 khz and while loations. andwe with assumed Results 600are that Ω presented for afault to ours resistane after at 25 both km line from terminals sending for a point. to The ground non-operating oupling and s with are 600 terminated Ω for a with to 400 Ω oupling. Figures 8. The seleted frequeny range is from 200 to 250 khz while we assumed that fault oupling. ours resistane after at 25 both km line from terminals sending for a point. to The ground non-operating oupling and s with are 600 terminated Ω for a with to 400 Ω resistane oupling. at both line terminals for 0 a to ground oupling and with 600 Ω for a to Faulted oupling. 0 Faulted 0 Faulted Frequeny [khz] Figure 8. Amplitude harateristis of faulted Frequeny power [khz] line. The middle to ground oupling. 0 Figure 8. Amplitude harateristis The broken middle 25 km 200 of away 205 from 20 faulted power sending end, 235 line. 240The with middle to ground oupling. Figure 8. Amplitude harateristis of faulted Frequeny power [khz] line. The middle middle to ground ondutor oupling. openiruited middle at both sides 25 km at away fault loation. from sending end, with middle ondutor The broken The broken middle 25 km away from sending end, with middle ondutor openiruited at both sides at fault loation. open-iruited Figure at 8. Amplitude both sides harateristis at fault of loation. faulted power line. The middle to ground oupling. The broken middle 25 km 0away from sending end, with middle ondutor openiruited at both sides at fault loation. Faulted 0 Faulted 0 Faulted Frequeny [khz] Figure 9. Amplitude harateristis of faulted Frequeny power [khz] line. The middle to ground oupling. The Figure broken 9. Amplitude middle harateristis 25 km 200 away 205 of from faulted 220 sending power end, line. with 245 The 250 middle middle to ground ondutor oupling. shortiruited Amplitude Frequeny [khz] Figure 9. The broken at harateristis middle left side and 25 open-iruited of faulted km away from at power sending right side line. end, at with The fault middle middle loation. to ground oupling. ondutor shortiruited middle at left side 25and kmopen-iruited away from Figure 9. Amplitude harateristis of faulted power line. The middle to ground oupling. The broken 0 at right sending side at end, fault withloation. middle ondutor The broken middle 25 km away from sending end, with middle ondutor shortiruited at left side and open-iruited 0 at right side at fault loation. short-iruited at left side and open-iruited at right Faulted side at fault loation. Faulted 0 Faulted Frequeny [khz] Figure 0. Amplitude harateristis of faulted Frequeny power [khz] line. The middle to ground oupling. The Figure broken 0. Amplitude middle harateristis 25 km 200 away 205 of from faulted 220 sending power end, line. with 245 The 250 middle middle to ground ondutor oupling. openiruited Frequeny [khz] The broken at middle left side and 25 short-iruited km away from at sending right side end, at with fault middle loation. ondutor openiruited Amplitude at left harateristis side and short-iruited of faulted at power right side line. at The fault middle loation. to ground oupling. Figure 0. Amplitude harateristis of faulted power line. The middle to ground oupling. Figure 0. The broken middle 25 km away from sending end, with middle ondutor openiruited middle at left side 25and kmshort-iruited away fromat right sending side at end, fault withloation. middle ondutor The broken open-iruited at left side and short-iruited at right side at fault loation. Amplitude Amplitude harateristi Amplitude harateristi harateristi [db] [db] [db] Amplitude Amplitude harateristi Amplitude harateristi harateristi [db] [db] [db] Amplitude Amplitude harateristi Amplitude harateristi harateristi [db] [db] [db]

20 Energies 207, 0, of 24 Energies 207, 0, 80 Energies 207, 0, of of 24 Amplitude harateristi [db] [db] Faulted Faulted Frequeny [kHz] Frequeny [khz] Figure. Amplitude harateristis of faulted power line. The middle to ground oupling. Figure.. Amplitude harateristis of of faulted faulted power power line. line. The middle The middle to ground to oupling. ground oupling. The broken outer 25 km away from sending end, with outer ondutor shortiruited at left side and open-iruited at right side at fault loation. at at left side left side and and open-iruited open-iruited at at right right side side at at fault fault loation. loation. The broken The outer broken outer25 km away 25 kmfrom away fromsending sending end, with end, withouter outer ondutor ondutor short- short-iruited HV power-line faults are lassified into two groups, short iruits and series faults. The short HV HV power-line faults faults are are lassified into into two two groups, groups, short short iruits iruits and and series series faults. faults. The The short short iruit shemes are given in Figure 5. Short-iruit impedanes are alulated using Equations (73) iruit iruit shemes shemes are are given given in Figure in Figure 5. Short-iruit 5. Short-iruit impedanes impedanes are alulated are alulated using using Equations Equations (73) (75). (73) (75). For to ground fault, we assumed grounding ondutor s length equals For (75). For to ground to fault, ground we assumed fault, we assumed grounding ondutor s grounding ondutor s length equals length equivalent equals equivalent ondutor s height 2.5 and radius mm. In our analysis, grounding equivalent ondutor s height ondutor s 2.5 m and height radius 2.5 m mm. and In our radius analysis, mm. grounding In our resistane analysis, isgrounding assumed resistane is assumed to be equal 0 Ω. The omputed fault indutane is Lfg H. In toresistane be equal 0 is assumed Ω. The omputed to be equal fault 0 indutane Ω. The omputed is L analysis of to fault, alulated fault fg = fault indutane 0 indutane between 5 H. is InLfg = analysis 0 of 5 H. In to s is Lf analysis fault, of alulated to fault fault, indutane alulated between fault indutane s is Lbetween H, for distane 0 m. In ase of series fault analysis, impedane f =.63 0s zfg orresponds 5 H, for is Lf distane =.63 S 0 = 5 to to 0H, m. for Indistane ase of S = series 0 m. fault In analysis, ase of impedane series fault zanalysis, ground indutane Lfg H. fg orresponds impedane to zfg orresponds to ground to indutane to L fg ground = indutane 0 The results 5 H. Lfg = H. presented in Figures 8 show distortion of power-line amplitude harateristi The The results results presented in in Figures Figures 8 8 show show distortion of of power-line amplitude harateristi aused by series faults. We onsidered breaking of operating ondutor as well as nonoperating for two ouplings: middle to ground and middle to outer. As aused aused by by series faults. We onsidered breaking of of operating ondutor ondutor as well as well as nonoperating for for two ouplings: two ouplings: middle middle to ground to ground and middle and middle to outer to. outer As as non-operating it was expeted, broken non-operating does not have signifiant influene on highfrequeny harateristis. In or words, small additional attenuation appears as refleted waves. it was Asexpeted, it was expeted, broken broken non-operating non-operating does not does have not a have signifiant a signifiant influene influene on high- on high-frequeny harateristis. harateristis. In or In or words, words, a small a small additional additional attenuation attenuation appears appears as refleted as refleted waves from fault loation distort high-frequeny harateristis. waves from from fault fault loation loation distort distort high-frequeny high-frequeny harateristis. harateristis. Influene of fault loation on amplitude harateristis is presented in Figure 2. We observe Influene of of fault fault loation loation on on amplitude amplitude harateristis harateristis presented is presented in Figure in Figure 2. We 2. observe We observe that that on suh short power line distane of fault loation from power line terminal does not onthat suh on short suh power short power line distane line distane of fault of loation fault loation from from power power line terminal line terminal does not does have not have ruial influene. When middle to ground oupling is used, middle a have ruial a influene. ruial influene. When When middle middle to groundto oupling ground is oupling used, is middle used, middle breaking breaking inreases attenuation about 0 db while osillations have higher amplitude levels. The series inreases breaking attenuation inreases attenuation about 0 db about while 0 osillations db while osillations have higher have amplitude higher amplitude levels. The levels. series The faults series faults that are loser to line terminal will inrease attenuation more than remote faults. that faults are that loser are toloser line to terminal line terminal will inrease will inrease attenuation attenuation more than more remote than faults. remote faults. 0 0 Fault 5 km Fault Fault 30 5 km km Fault 30 km Frequeny [kHz] Frequeny [khz] Figure 2. Amplitude harateristis of faulted power line for fault distane and 30 km from Figure Figure 2. Amplitude harateristis of faulted power line for fault distane 5 and 30 km from sending 2. terminal. Amplitude The harateristis middle of to ground faulted oupling. powerthe linebroken for fault middle distane 5 and ondutor 30 km from shortiruited sendingat terminal. left side The and middle open-iruited to ground at right oupling. side at The fault broken loation. middle ondutor sending terminal. The middle to ground oupling. The broken middle ondutor short- short-iruited at at left side left side and and open-iruited open-iruited at at right right side side at at fault fault loation. loation. Amplitude harateristi [db] [db] For ase of middle to outer oupling, series or hybrid fault ourrene also For ase of middle to outer oupling, a series or hybrid fault ourrene also degrades amplitude harateristi (Figures 3 and 4). The worst-ase degradation is middle degrades amplitude harateristi (Figures 3 and 4). The worst-ase degradation is middle break resulting in inreased attenuation for more than 0 db. The fault influene is smaller in break resulting in inreased attenuation for more than 0 db. The fault influene is smaller in

21 Energies 207, 0, 80 2 of 24 For ase of middle to outer oupling, a series or hybrid fault ourrene also degrades Energies 207, amplitude 0, 80 harateristi (Figures 3 and 4). The worst-ase degradation is middle 2 of 24 Energies 207, 0, 80 2 of 24 break resulting in inreased attenuation for more than 0 db. The fault influene is smaller in senario senario of outer of outer break. break. This an This bean explained be explained by by fa that fat that middle middle partiipates partiipates in senario of outer break. This an be explained by fat that middle partiipates in mode with mode with smallest attenuation. smallest attenuation. The non-operating The non-operating break introdues break introdues a high-frequeny frequeny harateristis distortion aused distortion by refletion aused by at arefletion fault loation. fault Thisloation. distortionthis andistortion be negleted an inbe frequeny harateristis distortion aused by refletion at a fault loation. This distortion an be in mode with smallest attenuation. The non-operating break introdues a high- harateristis omparison negleted in with omparison faulted with operating faulted operating effets. effets. negleted in omparison with faulted operating effets. Amplitude harateristi [db] [db] Frequeny [kHz] Frequeny [khz] Figure Figure 3. Amplitude harateristis of faulted power line. The middle to outer Figure Amplitude harateristis of of faulted power power line. line. The The middle to to outer outer oupling. The The fault fault distane is is km km from from sending terminal. Legend: blak-normal, blue- C oupling. The fault distane is 25 km from sending terminal. Legend: blak-normal, blue- C broken, broken, red- B broken, broken, magenta- A broken. broken. broken, red- B broken, magenta- A broken Frequeny [kHz] Frequeny [khz] Figure 4. Amplitude harateristis of faulted power line for broken middle ondutor. Figure Figure 4. Amplitude harateristis of faulted power line for broken middle ondutor. The middle 4. Amplitude to harateristis outer of oupling. faulted Legend: power blue-5 line for km broken fault middle distane, red-30 ondutor. km fault The The middle to outer oupling. Legend: blue-5 km fault distane, red-30 km fault distane, middle blak-normal. to outer oupling. Legend: blue-5 km fault distane, red-30 km fault distane, distane, blak-normal. blak-normal. Amplitude harateristi [db] [db] The final onlusion based on presented simulations is that faulted operating auses The final onlusion based on presented simulations is that faulted operating auses signifiant The final onlusion attenuation based inrease on and presented group delay simulations distortion. thatthe faulted influene operating of faulted auses nonoperating attenuation an be inrease negleted andwhile group delay middle distortion. is The denoted influene as of most faulted sensitive non-operating to series a a signifiant attenuation inrease and group delay distortion. The influene of faulted nonoperating an be negleted while middle is denoted as most sensitive to series signifiant and hybrid an be negleted faults. The while presented middle analysis is is essential denotedfor as implementation most sensitiveof todifferent seriesalgorithms and hybridto and hybrid faults. The presented analysis is essential for implementation of different algorithms to faults. detet, The lassify presented and analysis loate faults is essential on HV for power implementation lines using ofhf different signals. algorithms Furrmore, to detet, obtained lassify detet, lassify and loate faults on HV power lines using HF signals. Furrmore, obtained and results loate show faults that on HV power lines using an provide HF signals. ommuniations Furrmore, using obtained PLC tehnology results show even that under HV results show that HV power lines an provide ommuniations using PLC tehnology even under power fault onditions. lines an provide ommuniations using PLC tehnology even under fault onditions. fault onditions Conlusions 5. Conlusions In In this this paper paper we we have have presented model model of of a faulted HV HV power-line in in low low radio radio frequeny In this paper we have presented model of a faulted HV power-line in low radio frequeny range. range. The The model is is derived from from multiondutor system system analysis and and eletromagneti wave wave range. The model is derived from multiondutor system analysis and eletromagneti wave propagation desribed by telegrapher s equations in matrix formulation. Analysis is done for propagation desribed by telegrapher s equations in a matrix formulation. Analysis is done for typial HV power line faults, short iruits and series faults. The developed model is validated for typial HV power line faults, short iruits and series faults. The developed model is validated for HV power line in normal operation using 400 kv HV power line measurements. The presented HV power line in normal operation using 400 kv HV power line measurements. The presented model is furr extended for HV power line under faulted onditions. model is furr extended for HV power line under faulted onditions.

22 Energies 207, 0, of 24 propagation desribed by telegrapher s equations in a matrix formulation. Analysis is done for typial HV power line faults, short iruits and series faults. The developed model is validated for HV Energies 207, 0, of 24 power line in normal operation using 400 kv HV power line measurements. The presented model is furr extended for HV power line under faulted onditions. The main fous is plaed on determination of HV power-line harateristis when one The main fous is plaed on determination of HV power-line harateristis when one ondutor is faulted for whih an adequate model is derived. The ondutor break-down ondutor is faulted for whih an adequate model is derived. The ondutor break-down (series (series or hybrid fault) is interesting for analysis sine handling suh faults is demanding and time or hybrid fault) is interesting for analysis sine handling suh faults is demanding and time onsuming onsuming while it is desired to maintain reliable ommuniations over HV power line. The while it is desired to maintain reliable ommuniations over HV power line. The onlusion is made onlusion is made that faulted operating auses serious degradation of power-line highfrequeny harateristis while fault on a non-operating an be negleted. Presented simulation that faulted operating auses serious degradation of power-line high-frequeny harateristis while fault on a non-operating an be negleted. Presented simulation results desribe results desribe impat of different faults on frequeny response of high voltage overhead impat of different faults on frequeny response of high voltage overhead power lines. Beside power lines. Beside design of PLC ommuniation systems resilient to power line faults, analysis design of PLC ommuniation systems resilient to power line faults, analysis presented in this paper presented in this paper is useful for design of smart systems for fault lassifiation and is useful for design of smart systems for fault lassifiation and loalization, utilizing low radio loalization, utilizing low radio frequeny signal propagation over power lines. frequeny signal propagation over power lines. Aknowledgments: This work was supported in part by ARRS under Sientifi Program P Aknowledgments: This work was supported in part by ARRS under Sientifi Program P Author Contributions: N.S., A.M. and M.Z. oneived and designed experiments; N.S. performed experiments; N.S. and M.Z. analyzed data; N.S. and A.M. onduted measurements; N.S. and M.Z. wrote paper. Conflits of of Interest: The authors delare no no onflit of of interest. Appendix Appendix A dx5 dx25 dx24 dx h 4 = h mm 2 3 dx2 dx23 h = h2 = h3 Figure Figure A. A kv kv power-line power-line pole. pole.

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