Panel Session on Data for Modeling System Transients Insulated Cables

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1 Panel Session on Data for Modeling System Transients Insulated Cables Bjørn Gustavsen SINTEF Energy Researh N-7465 Trondheim, Norway Abstrat: The available EMTP-type programs have dediated support routines (Cable Constants) for alulating an eletri representation of able systems in terms of a series impedane matrix Z and a shunt admittane matrix Y, based on able data defined by geometry and material properties. Z and Y are then used as the basi input for the various able models applied in time domain transient simulations. This paper desribes neessary proedures for onverting the available able data into a new set of data whih an be used as input for Cable Constants. In partiular, the paper shows how to handle the semionduting sreens of single ore oaxial type ables. In situations where the able plays an important role in the transient simulation, the user should also onsider obtaining a speimen of the able in order to verify the geometrial data provided by the manufaturer. The reommendations in this paper are supported by field test results. Keywords: Eletromagneti Transients, Insulated Cables, Modeling, EMTP. I. INTRODUCTION The modeling of insulated ables for the simulation of eletromagneti transients requires ) Calulation of able parameters from geometrial data and material properties [],[]. ) Conversion of the able parameters into a new set of parameters for usage by the transmission line/able model. This paper deals with the first step in the proedure, namely the alulation of able parameters. All the ommonly used programs for simulation of eletromagneti transients (EMTP/ATP/EMTDC) have dediated support routines for this task. The routine(s) have very similar features and will in this presentation be given the ommon generi name Cable Constants (CC). Data onversion is often needed by the user in order to bring the available able data into a form whih an be used as input by CC. This onversion is needed beause ) The data an have alternative representations with CC only supporting one of the representations. ) The CC routine does not onsider ertain able features, suh as semionduting sreens and wire sreens. The situation is made further ompliated by the fat that the nominal thikness of the various layers (insulation, semionduting sreens) as stated by manufaturers an be smaller than the atual (design) thikness of the layers. Therefore, the information on geometrial data from the manufaturer an be inaurate from the viewpoint of able parameter alulations. This paper demonstrates the needed onversions for one real ase of a single ore oaxial able system, and proposes how to best use the available data to produe a reliable able model. The effet of inaurate data on a time domain simulation is also shown. The paper further disusses the shortoming of CC in taking into aount possible attenuation effets aused by the semionduting sreens. II. CABLE PARAMETERS The basi parameters used by transmission line/able models are the following: Z ( ω) = R( ω) + jωl ( ω) () Y ( ω) = G( ω) + jωc ( ω) () where R,L,G,C are the series resistane, series indutane, shunt ondutane and shunt apaitane per unit length of the able system. These quantities are n by n matries where n is the number of (parallel) ondutors of the able system. The variable ω reflets that these quantities are alulated as funtion of frequeny. Z and Y are alulated using CC based on the geometry and material properties of the system [],[]. III. ACTUAL CABLE VS. CABLE CONSTANTS REPRESENTATION A. Geometry In the following we onsider CC applied to systems of parallel single ore oaxial type ables (SC ables). The user must speify the following input data: The loation of eah able (x-y oordinates). The geometry of eah SC able. In general, CC represents eah SC able by a set of onentrially loated homogenous pipes, separated by insulating layers. Figure shows the representation whih would be used for a SC able without armour.

2 air soil ρ g, µ g y x ables. This means that CC assumes a ylindrially symmetrial urrent distribution in all ondutors. The assumed ylindrial distribution also means that the helial winding effet of the wire sreen is not taken into aount. Insulation ore sheath r 4 r 3 ρ, µ r r ε ε IV. MODELING REQUIREMENTS VS. PHENOMENON For situations with straight sheaths (i.e. no rossbondings), high frequeny transients propagate mainly as unoupled oaxial waves within eah SC able. The earth harateristis have in this situation only a mild effet on the resulting phase voltages and phase urrents. In the following we shall therefore fous on the representation of the able within the protetive jaket (oversheath). Fig. CC representation of system of 3 SC ables Figure shows an atual XLPE single ore oaxial able. Clearly, this able design is different from the simple onfiguration assumed in Figure. In partiular, the user needs to deide how to represent The ore stranding The inner semionduting sreen The outer semionduting sreen The wire sreen (sheath) Core Insulation B. Material properties Fig. SC XLPE able The user must speify the following material onstants: The soil resistivity and relative permeability ρ g, µ g The ore resistivity and relative permeability ρ, µ The sheath resistivity and relative permeability ρ s, µ s The insulation relative permittivity ε r (In non-magneti materials the relative permeability equals..) The CC-routine assumes the relative permittivity ε r of eah insulating layer to be real ( ε = ) and frequeny independent, thereby negleting any relaxation phenomena in the insulation. This implies : Z ( ω) = R( ω) + jωl ( ω) (3) C. Eddy urrent effets ρ s, µ s Inner semiondutor Outer semiondutor Wire sreen Y ( ω ) = jωc (4) The CC-routine takes into aount the frequeny dependent skin effet in the ondutors, but neglets the proximity effet between parallel A. Core V. CONVERSION PROCEDURES The CC-routine requires the ore data to be given by the resistivity ρ and the radius r. However, the ore ondutor is often of the stranded design (Figure ), whereas CC assumes a homogenous (solid) ondutor. This makes it neessary to inrease the resistivity ρ of the ore material to take into aount the spae between strands: πr A ρ = ρ (5) where A is the effiient (nominal) ross setional area of the ore. The resistivity ρ for to be used for annealed opper and hard drawn aluminum at C is aording to IEC 8 and IEC 889: Copper:.74E-8 Ωm Aluminum.864E-8 Ωm If the manufaturer provides the DC resistane for the ore, the sought resistivity an alternatively be alulated as πr ρ = R DC (6) l B. Insulation and semionduting sreens Proedure The semionduting sreens an have a substantial effet on the propagation harateristis of a able in terms of veloity, surge impedane and possibly the attenuation [3],[4]. Unfortunately, CC does not allow expliit representation of the semionduting sreens, so an approximate data onversion proedure must be applied : ) Calulate r as r plus the sum of the thikness of the semionduting sreens and the main insulation. ) Calulate the relative permittivity ε r as ε C ln( r / r ) r = (7) πε where C is the able apaitane stated by the manufaturer and ε = 8.854E-. If C is unknown, ε r an instead be alulated based on the relative permittivity ε rins of the main insulation: ln( r / r ) ε r = ε r ins (8) ln( b / a) where a and b are the insulation inner and outer radius, respetively. For XLPE ε rins equals.3.

3 Justifiation The inner and outer semionduting sreens have a relative permittivity of the order of, due to the high arbon ontent used in the semionduting sreens. This implies that the apaitane of the sreens is muh higher than that of the insulation and will tend to at as a short iruit when alulating the shunt admittane between ore and sheath. A similar effet is aused by the ohmi ondutivity of the semionduting sreens, whih is required by norm to be higher than E-3 S/m. At the same time the ondutivity of the semionduting sreens is muh lower than that of the ore and the sheath ondutors, implying that the semionduting sreens do not ontribute to the longitudinal urrent ondution. This implies that when entering the geometrial data in CC, the user should let the XPLE insulation extend to the surfae of the ore ondutor and the sheath ondutor, and inrease the relative permittivity to leave the apaitane unaltered. Note that this modeling neglets the possible attenuation aused by the semionduting sreens. The attenuation ould have a strong impat on very high frequeny transients. This is disussed in Setion X. C. Wire sreen When the sheath ondutor onsists of a wire sreen, the most pratial proedure is to replae the sreen with a tubular ondutor having a ross setional area equal to the total wire area A s. With an inner sheath radius of r, the outer radius r 3 beomes A 3 = s + r r π VI. APPLICATION TO 66 kv CABLE A. Manufaturer s data The proedures outlined in the previous setions will be demonstrated for a 66 kv able similar to the one shown in Figure 3. For this able (manufatured in the 98 s), the following data were provided by the manufaturer: =mm A C =.4 nf/m R DC =.9E 5 Ù/m r = 9.5 mm Thikness of inner insulation sreen: Thikness of insulation: 4mm Thikness of outer insulation sreen: Wire sreen: A s = 5 mm B. Data onsisteny.8 mm.4 mm In Setion VB it was justified that the insulation sreens an be represented by short iruit when alulating the shunt admittane. This is equivalent to a apaitane between two ylindrial shells with radius : a = ( ) mm =.3mm b = a +4 mm = 34.3mm (9) πε ε C = r () ln( b / a) 3 With a relative permittivity of.3 for XLPE, this defines a apaitane of.44 nf/m whih is in agreement with the apaitane of.4 nf/m stated by the manufaturer. C. Data onversion Core From the manufaturer: r = 9.5 mm The resistivity is alulated by (6) : 8 ρ = Ù/m Insulation and insulation sreens r = r + ( ) = 34.7 mm ε.486 (by (7)) r = Wire sreen The outer radius is alulated using (9): r 3 = mm ρ =.78 E 8 Ù/m (opper) s VII. INACCURACY IN DATA FROM MANUFACTURER The relevant able norms (e.g. IEC 84, IEC 65) puts limitations on the minimum thikness of eah able layer (in relation to the nominal thikness), but not on the maximum thikness. Therefore, the manufaturer is free to use thiker layers than the nominal ones, e.g. to aount for dispersity in prodution and ageig effets. This situation is prevalent for both the main insulation, the oversheath, and the semionduting sreens. By measurement on a speimen of the 66 kv able it was found that the insulation and in partiular the semionduting sreens were thiker than stated in the data sheets : Thikness of inner insulation sreen:.5 mm Thikness of insulation: 4.7 mm Thikness of outer insulation sreen:. mm Separation between outer insulation sreen and entre of eah ondutor in wire sreen: mm This gives a modified model : r = 9.5 mm = r = r 37.8 mm ε. 856 (by (7))

4 VIII. SENSITIVITY At high frequenies, the asymptoti (lossless) propagation veloity and surge impedane are given as v = / L C () Z = L / C () where µ L = ln( r / r ) (3) π with µ = 4π E 7 We will now ompare the asymptoti propagation harateristis as alulated by the following proedures: Case #: Negleting the semionduting sreens. Capaitane and indutane alulated using () and (3) with a=r =9.5 mm, b=r =33.5 mm, and ε r =.3. Case #: Taking the semionduting sreens into aount. Capaitane and geometrial data from the manufaturer: r =9.5 mm, r =34.7 mm, and ε r =.486. Case #3: Taking the semionduting sreens into aount. Capaitane from the manufaturer, geometrial data from able speimen: r =9.5 mm, r =37.8 mm, and ε r =.856. Using the indutane alulated from (), the veloity and harateristi impedane are alulated as: Table. Sensitivity of able propagation harateristis ase # ase # ase #3 v [m/µs] (-3.8%) 77.4 (-.3%)) Z [Ω].39.9 (+.4%) 3.49 (+9.8%) Thus, the able propagation harateristis are highly sensitive to the representation of the ore-sheath layers. IX. FIELD TEST AND TIME DOMAIN SIMULATION A field test was arried out on a 6.5 km length of the able. One ore ondutor was harged up to a 5 kv DC voltage and then shorted to ground. Thus, a negative step voltage was in effet applied to the able end (see Figure 3). ore sheath 3.85 km. km 5 m the surge admittane of the able ore-sheath loop, whih is the inverse of the surge impedane. The inrush urrent was also simulated using EMTDC v3 with a phase domain able model [5],[6]. The CC routine was applied for the three different ases defined in Setion VIII. It is seen that using the able representation in ase #3 gives a alulated response whih is in fairly lose agreement with the measured response. The two other representations have a muh larger disrepany. (The spike ourring at about 5 µs resulted beause of long leads onneting the two able setions). Fig. 4 Measured and simulated inrush urrent X. IMPROVED MODELING OF SEMICONDUCTING SCREENS Referene [3] suggests to model the admittane between the ore and the sheath using the iruit in Figure 5, in whih eah semionduting sreen is modeled by a ondutane in parallel with a apaitor. With omponent values obtained from measurements, they obtained a good agreement between measured attenuation and alulated attenuation in the range MHz 5 MHz. The attenuation effet of the semionduting sreens was strong. Referene [4] gives a systemati investigation of the effets of semionduting sreens on propagation harateristis. Y ore G C C Inner semionduting sreen Main insulation Negative step voltage G C Outer semionduting sreen Fig. 3 Cable test setup Figure 4 shows the measured initial inrush urrent flowing into the ore ondutor in p.u. of the DC-voltage. The initial urrent orresponds to 4 sheath Fig. 5 Improved model of insulation sreens [3] The ondutivity and permittivity of the semionduting sreens depends very muh on the amount of arbon added, the struture of

5 the arbon, and the type of base polymer. Very high arbon onentrations are used (e.g. 35%). IEC 84 requires the resistivity to be lower than Ωm for the inner sreen, and below 5 Ωm for the outer sreen. One manufaturer stated that they use a muh lower resistivity, typially. Ωm Ωm. The relative permittivity is very high, typially of the order of. The permittivity and ondutivity an be strongly frequeny dependent. In order to investigate the possible attenuation effets of the insulation sreens of the able onsidered in this paper, a representation as in Figure 5 was employed assuming frequeny independent ondutanes and apaitanes. The omponent values were alulated as follows: C =.4 nf / m (from manufaturer) C = πε εr / ln( r / b) C = πε εr / ln( a / r ) G = πσ / ln( r / b) G = πσ / ln( a / ) r where a: Outer radius of inner semionduting sreen b: Inner radius of outer semionduting sreen ε r : Relative permittivity of semionduting sreens σ : Condutivity of semionduting sreens Figure 6 shows the attenuation per km, for a few ombinations of σ and ε r. The urves define to whih peak value a sinusoidal voltage of p.u. peak value deays to over a distane of km. (The signal deays exponentially as funtion of length). The model predits a signifiant ontribution from the semionduting sreens for a low value of both the relative permittivity (, ) and the ondutivity (.). With the high permittivity (), the apaitane tends to short out the ondutane, and no appreiable inrease of the attenuation is seen. The lowest value for the permittivity () is probably unrealisti. Fig. 6 Effet of semionduting sreens on attenuation XI. DISCUSSION This paper has foused on the importane of orretly modeling the semionduting sreens of single ore oaxial type ables. It is shown that a areless modeling tends to produe a model with a too low surge impedane and a too high propagation veloity. The importane of aurate modeling is strongly dependent on the type of transient study. If the able is part of a resonant overvoltage phenomenon, the aurate representation of the able the surge impedane and propagation veloity is ruial. XII. CONCLUSIONS This paper desribes neessary onversion proedures for the available able data for usage by Cable Constants type routines (CC), with fous on single ore (SC) oaxial type ables. The main onlusions are the following: CC does not diretly apply to SC ables with semionduting sreens, so a onversion proedure is needed before entering the able data into CC. This paper desribes the needed onversions and also desribes the onversions needed for handling the ore stranding and wire sreens. The nominal thikness of the various insulation and semionduting able sreens as stated by manufaturers an be smaller than those found in atual ables. This an result in a signifiant error for the propagation harateristis of the able model. CC has no means for taking into aount any additional attenuation at very high frequenies resulting from the semionduting sreens. XIII. REFERENCES [] L.M. Wedepohl and D.J. Wilox, Transient Analysis of Underground Power Transmission System ; System-Model and Wave Propagation Charateristis, Pro. IEE, vol., No., February 973, pp [] A. Ametani, A General Formulation of Impedane and Admittane of Cables, IEEE Trans. PAS, Vol. 99, No. 3, May/June 98, pp [3] G.C. Stone and S.A. Boggs, "Propagation of Partial Disharge Pulses in Shielded Power Cable, Proeedings of Conferene on Eletrial Insulation and Dieletri Phenomena, IEEE 8CH773-, Otober 98, pp [4] W.L. Weeks and Yi Min Diao, Wave Propagation in Underground Power Cable, IEEE Trans. PAS, Vol. 3, No., Otober 984, pp [5] A. Morhed, B. Gustavsen, and M. Tartibi, A Universal Line Model for Aurate Calulation of Eletromagneti Transients on Overhead Lines and Cables, IEEE trans. PWRD, vol. 4, no. 3, July 999, pp [6] B.Gustavsen, G. Irwin, R. Mangelrød, D. Brandt, and K. Kent, "Transmission Line Models for the Simulation of Interation Phenomena between Parallel AC and DC Overhead Lines", IPST'99 International Conferene on Power System Transients, Budapest, 999, pp XIV. BIOGRAPHY 5 Bjørn Gustavsen was born in Norway in 965. He reeived the M.S. degree in 989 and the Dr.-Ing. degree in 993, both from the

6 Norwegian Institute of Tehnology in Trondheim. Sine 994 he has been working at SINTEF Energy Researh (former EFI). His interests inlude simulation of eletromagneti transients and modeling of frequeny dependent effets. He spent 996 as a Visiting Researher at the University of Toronto, and the summer of 998 at the Manitoba HVDC Researh Centre, Winnipeg, Canada. APPENDIX DATA CONVERSION The following Matlab ode does the reommended data onversion for the ase desribed in Setion VI. All geometrial quantities are in meters. INPUT: C =.4e-9; %apaitane stated by manufaturer [F/m] Aore =e-6; %ore nominal ross setional area Asheath=5e-6; %sheath nominal ros setional area tins =4e-3; %thikness: main insulation tins =.8e-3; %thikness: inner insulation sreen tins =.4e-3; %thikness: outer insulation sreen r =9.5e-3; %ore radius RDC =.9e-5; %ore DC resistane [ohm/m] eps =8.854e-; %vauum permittivity OUTPUT: rho=rdc*pi*r^ %ore resistivity r=r+tins+tins+tins; %sheath inner radius r3=sqrt(asheath/pi+r^); %sheath outer radius epsr=c*log(r/r)/(*pi*eps); %effetive rel. permittivity %of ore sheath layer 6

Modes are solutions, of Maxwell s equation applied to a specific device.

Modes are solutions, of Maxwell s equation applied to a specific device. Mirowave Integrated Ciruits Prof. Jayanta Mukherjee Department of Eletrial Engineering Indian Institute of Tehnology, Bombay Mod 01, Le 06 Mirowave omponents Welome to another module of this NPTEL mok