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Simulation and Detection of Transients on a150 kV High Voltage AC Cable

Thomas Mathew Plackattu, s131641

Abstract—The aim of this thesis project is to model an existing underground High Voltage (150 kV) cable that was laid betweenWoensdrecht to Bergen op Zoom in 1970, and further use this model to study partial discharges and transients that occur on this cable,which in turn helps us understand the insulation degradation state of the cable. In this thesis, a cable modeling technique that has beenvalidated for low and high frequency transient studies has been used to model the cable. The project was done in collaboration withTenneT B.V. This paper is supplemented with a report under the same title. The Universal Line model (ULM) was used for modeling thecable. Substation terminating the cable is described as a lumped component, where bus bar, transformers and the connected overheadline are replaced by R,L,C components. By vector fitting, this model is incorporated in the ULM approach. Partial discharges occurringalong the cable are introduced as local current sources. Signal amplitude scales roughly inversely proportional to the traveled distance.Important for detection of partial discharge currents is a low load impedance e.g. from an overhead line connected to the substation.

Index Terms—Partial Discharge; Transients; Universal Line Modeling; High Voltage Cables; End Terminations.

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1 INTRODUCTION

The Netherlands has about 2,500 km of undergroundHigh Voltage cables in service, of which about 250 km isof the same type, External Gas Pressurized cable, as thecable that is studied in this project. The age of these cablesare between 20 and 45 years. The service age of powercables are in between 30 to 45 years, which substantiatesthe importance of having a systematic knowledge of thedegradation status of different cables in the network. Inview of the vital role of High Voltage cables in the electricitytransmission grid, the time needed to repair a high-voltageconnection must be reduced to a minimum. Experience hasshown that a cable circuit is out of operation for 2 to 20days after each disruption. This time lost can be significantlyreduced in terms of time spent in preparation and locatingthe faults, if we can predict or localize the location wherethe fault has occurred using On-Line Partial Discharge (PD)monitoring systems.

The aim of this thesis project is to model an existingunderground High Voltage (150 kV) cable that was laid be-tween Woensdrecht to Bergen op Zoom in 1970, and furtheruse this model to study partial discharges and transientsthat occur on this cable, which in turn helps us understandthe insulation degradation state of the cable. In this thesis, acable modeling technique that has been validated for lowfrequency and high frequency transient studies has beenused to model the cable.

2 PROBLEM FORMULATION

In order to achieve the goal, several sub-objectives were setas follows:

1) Model and simulate the HV cable (Woensdrecht toBergen op Zoom) using a proper modeling tech-nique.

2) Verify this model using an EMT based computersoftware.

3) Model proper end terminations to incorporate re-flections in the cable.

4) Simulate partial discharges in the cable model.5) Verify model with data obtained from site and cal-

culate PD locations.1

6) Improve model to obtain acceptable results.1

3 TRANSMISSION CABLES

Cables have been used in power transmission since the late19th century, and for high and extra high voltage since thebeginning of the 20th century. These cables are laid in ductsor may be buried in the ground. Unlike in overhead lines, airdoes not form part of the insulation, and the conductor mustbe completely insulated, thereby making it more costly thanoverhead lines. Cables can be divided into three categoriesbased on their construction and purposes, namely, fluidfilled cables (FF), gas filled cables (GF) and extruded cables,as shown in Figure 1 and further sub-categorized as inFigure 2.

Cables have a much lower inductance than overheadlines due to the lower spacing between conductor andearth, but have a correspondingly higher capacitance, andhence a much higher charging current. High voltage cablesare generally single cored, and hence have their separateinsulation and mechanical protection by sheaths, usually alead sheath [3].

The cable that is studied in this thesis is the HighPressure Gas Filled (HPGF) cable, and these types of cablesare sub categorized as shown in the Figure 2.

1. For this project, Universal Line Modeling is used. The reason forusing this method, is that, at the moment PD modeling is mostly donein the frequency domain, but according to literature the ULM can bemore generally applied. Steps 5 and 6 were anticipated, but could notbe completed, although a reasonable estimation of the site parametershas been done and used for this work. A detailed description of themodel is provided in the accompanying report [1]

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Fig. 1: Types of land and sea cables categorized based on insulationtype [2]

Fig. 2: Classification of gas filled cables [2]

The cable under study falls under the following cate-gory; Pipe type, external pressurized, self-contained withimpregnated paper insulation. The pipe is filled with Nitro-gen subjected to a pressure of 200 psi (about 16 bar). Themain insulation is paper tape impregnated with mineral oil.A typical HV AC underground power cable consists of fourkey layers, namely; Conductor, first Insulation, Screen andsecond Insulation. In addition to these layers, the cable alsohas semi conductive screens, swelling tapes and metal foil.

4 DESCRIPTION OF THE CABLE UNDER STUDY

The cable under study is a double circuit 150 kV AC cablethat transmits power from Woensdrecht to Bergen op Zoom.The basic construction of the cable is as shown in Figure 3.

Fig. 3: Topology of the cable under study; refer Table 1 for descriptionof layers

The cable was laid in the year 1970, and was manu-factured by the NKF/NKT cable manufacturers. The Oilused for impregnation was mineral oil. Although the rateddegeneration temperature for this oil was supplied as 70C,

TABLE 1: Cable Construction

1. Outer protection 7. Seamless Lead sheath2. Steel pipe 8. Carbon black paper3. Nitrogen 16bar 9. Metal foil4. Flat Steel Wires 10. Paper-oil insulation5. Cotton Layer 11. Carbon black paper6. AFM Steel layer 12. Copper Conductor

laboratory tests conducted in The Netherlands and Ger-many found that degeneration occurred as from 60C.The length of one cable circuit is 6.3 km. Since the cableconsists of three cores with individual insulations alongwith individual lead sheaths, it can be assumed that waveswill propagate along each core without interfering or bedisturbed by the waves traveling in the other phases. Henceeach phase can be considered as an individual cable forthe purpose of modeling. It is assumed that cable jointshave little effect on the waves in the frequency spectrum ofinterest as their length is significantly smaller than typicalwavelengths associated with the relevant frequencies, beingin the order of 10 MHz at most. Only TEM-modes will beconsidered.

5 EXISTING MODELING TECHNIQUES

The design and operation of power systems, as well as ofpower apparatuses, depends nowadays on accurate simu-lations of Electromagnetic Transients (EMTs). Essential tothis is the modeling of power transmission lines and cables.There are various modeling techniques that were developedthroughout the years. Among these, the most importantones are:

1) Constant Parameters Line model (CP)2) Distributed Parameter Modeling3) Frequency Dependent or J. Marti Line model (FD)4) Universal Line Model (ULM).

The CP Line model is the simplest and most efficient onefrom the computational point of view. Nevertheless, it tendsto overestimate the transient phenomena as it considersthat line parameters are constant.[4] The model is basedon lumped R, C and L parameters for the transmissionline/cable. The lumped parameters are simply multipliedby the cable length, thus not taking distribution of theparameters into account, hence named Constant Parametermodel.

In the Distributed Parameter model the R, L and C circuitelements are not lumped together, but are uniformly dis-tributed along the length of the line, in order to capturethe distributed nature of the circuit parameters along thetransmission system. The Bergeron model is an example ofthis type of modeling. This technique accurately representsthe system parameters at the fundamental frequency.

The FD Line model is a frequency dependent mode modelthat evaluates multiconductor line propagation in the modaldomain and takes into account effects due to frequencydependence of the line parameters. Frequency dependentmodels give a much more realistic current and voltage be-havior than models using lumped parameters. However, thetransformations between the modal and the phase domains

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are only real with constant matrices for cases with sufficientsymmetry, e.g. three-fold rotation symmetry for 3-phasecables in a triangular configuration [2][4]. Otherwise eachfrequency component has its own transformation matrixand numerical issues may arise (computation time, modehopping). Time-domain representation can be obtained viathe (Inverse) Fourier Transform.

The Universal Line Model or Frequency dependent PhaseModel takes into account the full-frequency dependenceof line parameters. ULM works directly in phase domain,thus avoiding simplifying assumptions regarding modal tophase transformations [5][4]. As of yet, it is the most generalmodel, capable to accurately represent asymmetric aeriallines as well as underground cables, including situationsof non-linear loads. To this end, techniques have been de-veloped as fitting frequency domain parameters to rationalexpressions, which can be transformed in order to solvenumerically the time-domain Telegraphers equations.

The classification of modeling techniques is representedin Figure 4 with relation to its accuracy.

Fig. 4: Classification of modeling techniques

6 THE ULM MODEL

The description of the ULM model is based on the literaturefrom Morched, Gustavsen and Tartibi which is presented in[6]. Even though the modeling of transmission lines is mucheasier when the solution is formulated in the frequency-domain, for the study of a complete systems with switchingoperations, non-linear elements, and other phenomena, stepby step time-domain solutions are much more flexible andgeneral than frequency-domain formulations.

Since this model is the latest and most accurate for tran-sient simulations, it has been used for this thesis work. In thesoftware EMTDC/PSCAD, the model named ”FrequencyDependent Phase Model” is based on the universal linemodel theory.

The code that was modified for this project, and the briefdescription on the steps involved in the ULM technique, isreferred from the work of Octavio Ramos-Leaos, Jose LuisNaredo and Jose Alberto Gutierrez-Robles in [4]. A moredetailed explanation on how these models are formulated,the derivations involved to arrive at the final equations, andthe method of including time delays can be obtained fromtheir paper [4] .

When a transmission line, either an overhead line or anunderground cable, is represented, it can be characterizedby the propagation matrix H and the admittance matrixYc. As these matrices are frequency dependent, due to thefrequency dependent parameters of the cable. The frequencydomain is used only to calculate the discrete functions ofthe matrices. In order to obtain the time-domain values,a convolution of the matrices time-domain equivalents,obtained with inverse Fourier transformation, is used. Inorder to reduce computing time and simplify the calcula-tions, it is much more efficient to use frequency domainH and Yc where no convolution is necessary (convolutionin time-domain is equivalent with multiplication in the s-domain)[2].

6.1 Formulation

We first formulate the wave equations using the Telegra-phers equations, which in frequency domain can be ex-pressed as :

− dV

dx= ZI,−dI

dx= Y V (1)

where V is the vector of voltages, I is the vector of currents,Z and Y are the (N ×N) per unit length series impedanceand shunt admittance matrix of a given line with N con-ductors, respectively. Differentiating it with respect to x, andsubstituting to eliminate the vectors in the right hand side,we obtain:

d2I

dx2= Y ZI,

d2V

dx2= ZY V (2)

The solutions for these being :

I(x) = e−√Y ZxC1 + e+

√Y ZxC2 (3)

V (x) = −Y −1 dIdx

= Zc[e−√Y ZxC1 − e+

√Y ZxC2] (4)

Where C1 and C2 are vectors of integration constants de-termined by the line boundary conditions; that is, by theconnections at the two line ends, and Zc = Y −1

√Y Z is the

characteristic impedance and its inverse is the characteristicadmittance, Yc = Z−1c .

6.2 Line Modeling

Assume a multi conductor transmission line or cable oflength L, with x = 0 as the sending end and x = L asthe receiving end. I0, V0, IL and VL represent the injectedcurrent and voltages at the sending and receiving endsrespectively. Equations (3) and (4) become:

I0 = I(0) = C1 + C2 (5)

V0 = V (0) = Zc[C1 − C2] (6)

Leading to :

C1 =I0 + YcV0

2(7)

Similarly, the equations for line end L become:

IL = −I(L) = −e−√Y ZLC1 − e+

√Y ZLC2 (8)

VL = V (L) = Zc[e−√Y ZLC1 − e+

√Y ZLC2] (9)

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Multiplying (9) with Yc and subtracting from (8), we obtain

IL − YcVL = −2e−√Y ZLC1 (10)

Introducing (7) in (9) we get

IL − YcVL = −e−√Y ZL[I0 + YcV0] (11)

This equation establishes the relation between the volt-ages and currents at the terminals of a multi conductorline section. the term at its right hand side represents atraveling wave of currents leaving the line end at x = 0 andpropagating in the positive x direction, the left hand side isthe traveling wave of currents leaving the line end at x =L. Similarly, by exchanging the indices of equation (11), weobtain

I0 − YcV0 = −e−√Y ZL[IL + YcVL] (12)

Equations (11) and (12) are rewritten as

IL = Ish,L − Iaux,L (13)

I0 = Ish,0 − Iaux,0 (14)

At the far end Ish,L = YcVL is the shunt currentsvector produced at terminal L by injected voltages VL;Iaux,L = HIrfl,0 is the auxiliary currents vector consistingof the reflected currents at terminal 0; Irfl,0 = I0 + YCV0,and the transfer functions matrix H = e−

√Y ZL. Their coun-

terparts at the near end are: Ish,0 = YCV0 , Iaux,0 = HIrfl,Land Irfl,L = IL + YcVL .

Equations (13) and (14) constitute a traveling wave linemodel for the segment of length L. A schematic representa-tion of the complete model is shown in Figure 5:

Fig. 5: Frequency domain circuit representation of a multi-conductortransmission line

The line model defined by expressions (13) and (14) isin frequency domain. Power system transient simulationsrequire this model to be transformed to time domain. Forinstance, the transformation of (14) to the time domainyields:

i0 = ish,0 − iaux,0 (15)

where

ish,0 = yc ∗ v0 (16)

andiaux,0 = h ∗ irfl,L (17)

In equations (15)-(17) the lowercase variables representthe time domain images of their uppercase counterpartsin (14) and the symbol * represents convolution. Reflectedcurrents can be represented as:

irfl,L = 2ish,L − iaux,L (18)

Expressions (15)-(18) constitute a general traveling wavebased time-domain model for line end 0. The model cor-responding to the other end is obtained by interchanging0 and L in (15)-(18). Expressions (16) and (17) require theperformance of matrix to vector convolutions that are car-ried out by means of State Space methods in [7]. State Spaceequivalents of (16) and (17) arise naturally as Y c and H arerepresented by means of fitted rational functions [4].

6.3 Rational approximation of Yc

In 1982, Marti [8] proposed a rational model described bythe formula :

Yc = G0 +

Ny∑i=1

Gis− qi

(19)

where Ny is the fitting order, qi represents the ith fittingpole, Gi is the corresponding matrix of residues and G0

is a constant matrix obtained at the limit of Y c whens = jω tends to infinity. The rational approximation is doneusing the vector fitting toolbox proposed by Gustavsen andSemlyen, [9], and was made available in 1998 as a publicdomain MATLAB routine, vectfit.m. An overview of the VFprocedure and further information is to be found in [9].

6.4 Rational approximation of H

To attain an accurate and low order rational representationfor H, it is essential to factor out all terms involving timedelays [8]. The major difficulty here is that its elements couldinvolve a mix of up to N different delay terms due to themulti mode propagation on an N conductor line. Separationof matrix H into single-delay terms is obtained from thefollowing modal factorization [10]:

H = MHmM−1 (20)

where Hm is a diagonal matrix of the form

Hm = diag[e−γ1L, e−γ2L, ..., e−γNL] (21)

and γ =√Y Z is the propagation coefficient of a multi

conductor line. Equation (20) can be rewritten as follows:

H =N∑i=1

Die−γiL (22)

where Di is an idempotent matrix obtained by pre-multiplying the elements of M [11]. The derivation of theidempotent matrix is explained in detail by Marcano andMarti in [11]. Once the desired separation of H is obtainedas a sum of terms, each involving a single delay factor, themode delays that are identical, can be grouped together.Suppose a certain number Ng of groups can be formed, theequation can be rewritten as

H =

Ng∑k=1

Hke−sτk (23)

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where Ng is less or equal to N, and τk is the representativedelay for the kth group, and

Hk =Mk∑i=1

Die−γiLe−sτi (24)

where Mk is the number of modal terms in the kth group,and e−γiL is the minimum phase shift function [12]. Theexpression is then fitted as follows:

Hk =

Nh(k)∑i=1

Rk,is− pk,i

(25)

where Nh(k) is the fitting order for the kth term, ρk,irepresents its ith fitting pole and Rk,i is the correspondingmatrix of residues. Introducing (25) in (23), we obtain thefollowing rational form for the transfer matrix H.

H =

Ng∑k=1

e−sτkNh(k)∑i=1

Rk,is− pk,i

(26)

Vector fitting is applied throughout all these fitting tasksand detailed descriptions of these processes can be found in[9].

6.5 State space analysis

Based on the derivations described in the supplementaryreport [1], we can derive a representation of the model asshown in the Figure 6.

Fig. 6: Discrete time domain circuit representation of amulti-conductor line

The model consists of parallel arrangements of shuntconductance and auxiliary sources of currents comprisingof historic terms at ends 0 and L.

The various steps involved in the computation withreference to the equivalent circuit and the report, are sum-marized below, the procedure involves various quantitiesthat are not defined here, but are given in the accompanyingreport [1]):

1) State variable and historic current values are as-sumed to be known, either from initial conditionsor from previous simulation steps. These valuesare used by the nodal solver to determine line end(nodal) voltages v0 and vL.

2) Shunt current due to the characteristic admittanceof the line is calculated by:

ish,0 = Gv0 + iy−aux,0 (27)

3) Auxiliary current source value, due to the reflectedtraveling waves at the remote line end, are calcu-lated:

iaux,0 =

Ng∑k=1

Nh(k)∑i=1

xk,i (28)

4) Vector of reflected currents at the local line end(node) irfl,0 is calculated for the present time, mod-ified to suit line end 0:

irfl,0 = 2ish,0 − iaux,0 (29)

This vector is delivered to end L sub block througha delay buffer.

5) Internal states inside the line model are:

xk,i = ak,ixk,i + Rk,i[irfl,L(t− τk) + irfl,L(t− τk)];(30)

yi = aiyi + v0; i = 1, 2, ..., Ny (31)

6) The vector of history currents for end (node) 0 isupdated and delivered to the nodal-network solver.

Steps 1 to 6 are iterated Nt times until Nt × ∆t spans thetotal simulation time of interest.

The discrete time line model depicted in Figure 6 hasbeen programmed using the corresponding equations. Thisfunction consists of two sub blocks, one for each multi-conductor line end. This model is to be used with a nodalnetwork solver to solve each sub block, i.e. for line end 0 andline end L. A more detailed description on the nodal solvercan be found in [10] [13]. The code used in this project ismodified from the code provided in [4].

6.6 Cable parameter calculations

The cable parameters YC and H are given by equations:

Yc(ω) =√Y (ω).Z(ω)

−1Y (32)

H(ω) = e−γL = e−√Y (ω)Z(ω)L (33)

For calculating the cable parameters, the seriesimpedance matrix Z(ω) and the shunt admittance matrixY (ω) must be calculated.

6.6.1 Series impedance matrix of a single conductor cable

As described earlier, the cable under study is a pipe type ca-ble, and although the cable consists of 3 cores, each conduc-tor has a lead sheath which confines all signals within thesheath and the core, except for low frequencies. Having saidthat, we examine a simple situation of conductor-insulation-screen-insulation to calculate the cable parameters. Figure 7shows this model of a two layer cable.

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Fig. 7: Current loops in a single core cable

For this cable, there are two current loops: Conductor-screen loop and screen-ground loop. This is expressed as:[

VcsVsg

]=

[z11 z12z21 z22

] [IcsIsg

]

where z11 = Zcouter + Zcsinsul + Zsinner is the impedanceof the loop conductor-screen,z22 = Zsouter + Zsginsul + Zground is the impedance of theloop screen-ground, z12 = z21 = ZSm is the mutualimpedance of the loops conductor-screen andscreen-ground. These impedances are indicated in Figure 7.Referring to Figure 3 the impedances in z11 are related tothe individual phases. For the other matrix components thecommon ground layers are involved. These parameters canonly be estimated because of the complex cable design.However, main propagation of high frequency PD signalswill mainly occur within the phases, and therefore is notexpected to be much affected by the outside cable structure.

Each of the impedance parameter is calculated as describedin [1], and then used in the model.

6.6.2 Shunt Admittance matrix of a single conductor cableThe shunt admittance calculations are more direct than theseries impedance matrix. The equations for the admittancematrix are: [

IcsIsg

]=

[y1 00 y2

] [VcsVsg

]The admittance of a single conductor cable is calculated

from the insulation parameters.

yi = Gi + jωCi (34)

where Gi is the shunt conductance per unit length of theinsulator i, and Ci is the per unit length capacitance withpermittivity εi. Since this equation does not take into ac-count the semi-conductive layers, the permittivity used forcalculations must be modified to include the effects of theselayers. Hence the equivalent permittivity is obtained as:

ε = εisln(ri/r0)

ln(b/a)(35)

where ri is the inner radius of the screen and ro is the outerradius of the conductor, while ’b’ and ’a’ are the outer andinner radius of the insulation layers [2].

7 SIMULATION OF A TRANSMISSION CABLE

The next step is to modify and test the code to simulate thecable under study. The impedance and admittance matriceswere calculated as mentioned in the previous sections. Allparameters including the insulation and sheath character-istics were calculated and declared in the code. The lengthof the cable was set as 6.3 km and the voltage of 150 kVwas applied as per actual conditions. The simulations wereverified with PSCAD with the actual material properties andparameters. The cable parameters used for simulation areshown in Table 2 and the basic settings inserted in PSCADare chosen as shown in Figures 8 and 9.

Fig. 8: Cable section view.

Fig. 9: PSCAD settings

Figure 10 shows the sending end and receiving end volt-ages of a DC step excitation of 150 kV and the time and trendit takes to reach steady state both in MATLAB simulationand PSCAD. Similarly, Figure 11 shows the sending andreceiving end voltages upon AC excitation.

Fig. 10: Trend of DC excitation of a single core cable in MATLAB andPSCAD

Figure 11 shows the same cable excited with an ACvoltage of 50 Hz and compared with PSCAD simulation.

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Fig. 11: Trend of AC excitation of a single core cable in MATLAB andPSCAD

Both simulations show that the model is precise withminimum error, and hence can be used for further studiesin the project.

8 MODELING CABLE END TERMINATIONS

The reflection of a signal wave that occurs at the end termi-nation of a cable is subject to the impedance it faces at thecable end. Hence it is important to establish appropriate endimpedance which can perfectly imitate the site conditions atleast for our frequency range of interest. In this section anappropriate model is derived to simulate the end termina-tion of the cable under study. The cable is connected to anHV substation, where power is distributed to other feedersthrough HV/LV transformers. For this section, the studydone by Paul Wagenaars [5] on end termination modeling isused extensively.

8.1 Generic model of a substation

The model proposed by Paul Wagenaars, depicted in Figure12, shows a generic equivalent circuit of a substation. Theidea is to estimate the impedance that a PD would faceupon arriving at the cable terminations as a lumped circuitparameter. Each compartment has a load impedance ZL inseries with inductance Lc. The impedance ZL represents thecomponent that is connected to that compartment; it canbe a transformer or another cable. The inductance Lc is theinductance contribution of the loop from the connected com-ponent to the bus-bar. The inductance Lbb is the inductancecontribution of the loop between bus-bar and earth over thedistance of the width of one compartment [5].

Fig. 12: Generic Model of a substation [5]

This model was verified by field measurements onvarious ring main units (RMUs) and substations. Currenttransfer functions and impedances were measured and themodel parameter were fitted to match the measured valuesby minimizing the mean absolute relative error between

model and measurement. It was observed that transformersmainly behaved as capacitances at the frequency rangefrom hundreds of kilohertz to several megahertz. Togetherwith the busbar inductance, it caused low MHz resonance,especially when there are no outgoing cables present. Withparallel cables, their characteristic impedances dominateand the resonance is less pronounced. The experiment isexplained in detail in [5].

8.2 The complete systemFigure 13 gives an overview of the complete cable systemunder study and helps to understand the impedance a trav-eling wave faces at the end of the cable section. The modelis simplified to eliminate the elements whose influence arenegligible in the frequency range of interest.

Fig. 13: A generic representation of the cable system

It can be deduced that apart from the impedance due tothe substation, there will be a mutual impedance from theinteraction of other phase cables at the ceramic insulators.The Bergen op Zoom substation has a total of six transform-ers and a transmission line and only three transformers areconnected to the busbar with the cable under study, at atime. The substation at Woensdrecht has three transformersand an overhead line. For modeling purposes, and the lackof experimental data, the transformer impedances are scaledby a factor of 10 from the work of Paul Wagenaars, toaccount for the different size of HV compared to MV substa-tions. Busbar inductances increase because of the larger dis-tances needed, capacitances increase because the capacitivecoupling between transformer windings and core/housingincreases. Scaling of resistance depends on the cause oflosses of high-frequency signals, a factor 10 is assumed aswell. The values used in the model are summarized in Table2.

TABLE 2: Model parameters chosen for substation

Transformer inductance Ltfr = 30 µHTransformer capacitance Ctfr = 30 nFConnection inductance Ltfr = 3.0 µHBusbarinductance Lbb = 1.5 µHOhmic losses Rtfr = 100 Ω

The impedance of the overhead line is taken as 75 Ω.This model is subject to certain assumption based on the fre-quency under study: 1) Signals arriving at the terminations

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are typically in the range of 50 kHz - 5 MHz. 2) Transformersoffer high impedance. 3) Transmission line effects on bus-barare not considered.

The modeling of the cable terminations, its interfacingwith the time domain analysis and its verification are de-scribed in the report [1].

9 MODELING OF PARTIAL DISCHARGES

To implement partial discharges in the system, we assumethat each PD is an independent current source. Therefore anumber of N PDs can be represented as N current sources.Assume a cable of length L, with a PD occurring at adistance x from the sending end, then we can form twotransfer functions [14] to represent the incident current atthe sending end k and the receiving end m as :

HPDk(s) = e−γx (36)

HPDm(s) = e−γ(L−x) (37)

To add the effect of PDs, the ULM model has to be mod-ified to include the new current source. For this purpose,equation (17) is modified as:

iaux,k(t) = h(t) ∗ irfl,k +1

2hPDk ∗ ipd(t) (38)

iaux,m(t) = h(t) ∗ irfl,m +1

2hPDk ∗ ipd(t) (39)

As each PD that occurs is another current source, toinclude multiple PDs, the corresponding current can beadded to the equation.

The arriving wave shapes of a 1 nC pulse injected at thestart of the cable was compared with PSCAD and is shownin Figure 14. The input pulse was modeled as a squarefunction with a width of 50 ns and an amplitude of 20 mA.

Fig. 14: Comparison of wave shape of arriving pulse at 6.3 km withPSCAD

There is a small deviation between the wave shapes. Thisis due to the different wave shape of the input signal used.A square pulse was simulated in MATLAB, while a surgewaveform was used in PSCAD to simulate the input signal.

Figure 15 shows the PD wave shape at the far endwith propagation distance. A 1 nC PD was simulated alongvarious lengths of the cable terminated by its characteristicimpedance. This impedance was added in order to preventreflected signals in the simulation. This situation occurs inpractice when a similar cable continues from the substa-tion, thereby terminating the cable with its characteristicimpedance. In Figure 15 we observe the attenuation anddispersion effects, as the PD travels longer distances.

Fig. 15: PD wave shape with distance traveled

Fig. 16: PD signal waveform with substation impedance

When the cable is terminated with the substationimpedance that was modeled from the parameters in Table2, we notice a change in the wave shape and amplitude.Figure 16 shows the effect of termination impedance ona PD that was ignited 3 km from the far end. The peakvalue is higher, as the load impedance is more than thecharacteristic impedance. It must be noted that, often withPD-detection systems the current transmitted to the sub-station is recorded, which will have a lower amplitudewith increasing impedance. In the simulated situation, the75 Ω overhead line dominates the load on the cable. If thisimpedance would be absent, the load impedance becomeshigher and a PD current will be hard to detect.

10 SITE CONFIGURATION

In this section, a description of the site configuration andthe possible sensor locations are described. The three corecable comes out of the ground into a junction box whichdirects the three core into three separate steel tubes (alsounder 16 bar pressure) as shown in Figure 17. The core alongwith the lead sheath is present within this pressurized steeltube. The steel tube then enters the insulator, where, thecore conductor continues into the substation while the leadsheath stops at this point. The construction drawings showthat the lead sheath is grounded at this point through thestructural support.

The location of the sensor is important to effectively cap-ture the partial discharge current signals. Ideally it should beat the last earth connection of the cable, depicted by location8 in Figure 18. But in the actual site configuration, the leadsheath is grounded at the insulator through its bottom platesupport . Considering this, two viable sensor location pointsarise as shown in Figure 19.

Location A arises from the fact that the lead sheathis grounded through the support structure, while location

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Fig. 17: Site configuration

Fig. 18: Possible sensor locations on the cable [15]

Fig. 19: Viable sensor locations A and B

B is the earthing point of the junction box. In case A,three separate sensors will be necessary for each cable core.Location B provides a point of observing PDs occurring inall three cores without the possibility of identifying whichcore could be faulty. Identifying signals at the latter locationpoint can be tricky due to the fact that it is not actuallythe last earthing point, and any PD signal will have to bereflected back from the insulator through the steel pipe. At

Fig. 20: Sensor installed at location B

the time of writing, the sensor was being installed at locationB as shown in Figure 20.

11 CONCLUSION

In this thesis, the cable between Woensdrecht and Bergenop Zoom was modeled using the ULM modeling tech-nique. The model was verified with PSCAD simulations.The model was later interfaced with end terminations inorder to incorporate end reflections. For this purpose, ra-tional models of the termination circuit was modeled andinterfaced with the cable model. The interface procedure isapplicable for models both in pole residue or state spaceform. Partial Discharges were included in the model, usingthe technique described in [14]. Partial Discharges that occurat various locations on the cable, with different chargesand inception time can be simulated with this model andtheir wave shape and magnitude can be compared andused to identify PDs and locating them. The model can beimproved by including noise in the model to imitate siteconditions. Further, the actual transformer model can beimplemented in the external circuit to obtain response ofsteady state conditions. At the time of writing, detectiondevices are being installed at the locations under study inthis thesis. This MATLAB model can be easily modifiedto represent any cable or transmission line system, withany configuration of end terminations to observe systemresponses. A more detailed description can be found in thereport [1]. Simulation results show that the PD signal ampli-tude approximately decrease inversely proportional to thetraveled distance. Note that the simulations were performedwith estimated parameter values. For detecting PD currents,a relatively low load impedance at the cable end is needed.In the simulations, the overhead line provided a dominant75 Ω load.

10

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