calculating the hf transmission line parameters of power cables

8/6/2019 Calculating the HF Transmission Line Parameters of Power Cables

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Calculating the high frequency transmission line parameters of power

cablesIAuthors: Dr. John Dickinson, Laboratory Services Manager, N0 WEBCommunications

I '

Mr. Peter J. Nicholson, Project Assignment Manager, NORWEB ~ommunicationsI

Introduction

In using electricity distribution networks for high frequency communications it would be of

significant value to be able to predict the way that the attenuation and phase vary as thefrequency of the communication signal is changed. Ifthis were possible then reference to acompany's records could quickly reveal the performance of any comm unication system thatwas to be installed. Hardware could be pre-programmed with a su itable algorithm that w ould

allow certain frequencies to be automatically avoided. T he four transmission line parametersof capacitance, resistance, inductance and conductance are required in order to start theprocess of network modelling. In cables designed primarily to carry HF signals thetransmission line parameters are a ll known and kept within strict tolerance levels duringmanufacture, this is not necessarily the case for power cables whose primary func tion is thedistribution of electrical energy. This paper describes the steps required in order to determine

the transmission line parameters for three phase distribution cables.I

II UK LV Networks

Practical testing on UK, low voltage electricity distribution networks has shown that for thefrequency range from 1 to 10 MHz the attenuation can be a s little as 30 dB or asmuch 90 dB

1 for a network length of 250 metres. This varia tion in attenuat ion is caused by reflectionscreated by impedance mismatches at the end of each spur and from any points on the cable

i where the cable's electrical parameters change.

i

,

A typical UK low voltage distribution spur comprises a three phase distributor running( geographically close to the premises to be supplied. Individual, single or three phase supplies

I are taken from the distributor to locations where an electricity supply is required. In the UK '

I there will be between 25 and 50 supplies from one distributor.

tIII Cable Architecture

II The feeder cable will reduce in size as the d istance from the substation increases. Typ icallybeing 185 mm2 on leaving the substation and reducing to 95 mm2 after some distance. Typical

Icable construction for two types of modem cable is shown in figure 1.

II

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!



Solid Aluminium Conductors

Figure 1, A

Solid Aluminium or StrandedCopper Conductor

Figure 1, B

Transmission line parameters for the cables shown in figure 1 can be calculated using the

equations given in the follow ing pages. This analysis assumes that the propagation is v ia the

TEM mode,



- . - .

Capacitance [Ref. 11

Figure 2

! There are two values of capacitance associated with the conductors of both types of 3 phasecables. These are shown schematically in figure 2.

Sector shaped conductors (Figure 1, A)

Core to core capacitance (C,) can be calculated by treating the conductors as two parallelplates separated by twice the thickness of the cable insulation of length one meter. Core toshield capacitance (C,) can be calculated by tak ing one third of the capacitance for twoparalle l concentric cylinders of length one meter. Equations are given below.

&a ~ X R X ECc=T C, =

b3 x l n -

a

By using finite element analysis for comparison with the above equations an error of between3% and 5% can be expected.

Ii

Circula r conductors (Figure 1,B)

Equations for the core to core (C,) and screen to core (C,) capacitance has been developed'I -I empirically using finite element and linear regression techniques. The following equations areonly valid fo r modern 3 phase cable where the conductor centre is 0 .536 of the screen radius

firom the centre o fth e cable. The figure of 0.536 is arrived at by placing 3 maximum sizedcircles within a larger circle.



Where r is the conductor radius and R is the screen internal radius. Accuracy of theseequations is expected to be better than 4%.

For older cables where conductor centre is not necessarily at 0.536 of the screen radius thefollowing two equations are needed.

Where: "a" is the conductor radius. I

"b" is the screen internal radius."d" s the distance fiom screen centre to conductor centre. '

These equations are less accurate than those given previously with an expected accuracy o fbetween 6% and 10% based on comparison with practical measurement fiom actual cables.

As these equations are on ly applicable to older types of cable the comparisons are not idealbecause the cable used had been reclaimed fiom fault sites or fiom sites where re-working of



Resistance [Ref. 11When alternating current flows within a conductor the self inductance within he conductorcauses more current to flow on the outside of the wire than towards the centre. Thisphenomenon is termed the skin effect [Ref 21. As the frequency increases this effect causes anincrease in the resistance of the cable. At the frequencies of interest this increase in resistancemust be accounted for in any calculations Though the current flow is still distributed .throughout the cable, when calculating the resistance it is n h a l o assume that All the current

flows within he "skindepth" of the cable. The skin depth (6) is a hnc tion of the &equencyand can be calculated using the equation below.

I1

I Figure 3. Slun effect in a round conductor.

If the conductor is of solid composition then by using the above method for calcu lating the

skin depth and knowing the radius of the conductor the effective cross sectional area of currentflow can be determined. However, if the conductor is stranded then the area of current flow isagain reduced because of the gaps left at the circumference of the conductor. See figure 4.

Figure 4. M ag die d diagram of outer surface of stranded core showing

approximate area of current flow

I13



An approximation to this current flow can be made as follows

Figure 5. Magdied diagram of outer surface of stranded core showing calculatedarea of current flow.

Figure 6. Single conductor of stranded core showing 6 as calculated from the tota lcross sectional area of all cores.

Rad - 8)a =Aces[' ]ad

Effective- rea = a x ad' - a ad - 6 ) ) \ I ~ a d- Rad - 8)'

(Rad - 6 )Asor[ ] x ~ a d ' - ( R a d - d ) h a d 2 - ( R a d - 6 ) '

Effective- area - RadRatio = -T otal- a re a 2 x R a d x S

132



A more accurate value for resistance can now be calculated using the ratio to mod* the cross

sectional area.

This ca lculation assumes the core diameter to be very large when compared to the coreconductor diameter. The larger this ratio, the more accurate will be the approximation. A

similar calculation can be applied to a stranded shield. On some stranded shield cables theconductors do not touch each other. In this case the distance between conductors qompared to

conductor radius must be measured and a decision made as to whether or not to account for a

reduction in effective area as shown.

Conductance and Inductance

The conductance for these types of cables is very high and will not normally affect the resultsof calculations. Lf equired then the equations given here for capacitance can be used to

calculate conductance by replacing E with o.

The contribution of the inductance to the propagation of signals on these cables is small. Inimplementing he transmission line equations the inductance was calculated using standard

equations for concentric cylinders and parallel conductors. The accuracy of results could beimproved by applying the same analysis to the inductance a s has been outlined here for thecapacitance.

Conclusion

Tfie methods described above provide a means of obtaining transmission line parameters forthree phase electricity distribution cables. These parameters can in turn be used to determinethe attenuation and phase characteristics of commuiication signals on complex tree andbranch type distribution networks. Transmission line ana lysis as applied to three phaseunderground distribution networks is highly complex [Ref 31 and not easily summarised in a

short paper however research work within NORWEB Comm unications has proved itsviability.

3. M. Riddle, S. Ardalan, J. Sue, "Derivation of voltage and cu rrent transfer functions for

multiconductor transmission lines", IEEE, ISCAS, 1989, PP 2219-2222.

References

1. J. Dickinson, "High frequency modelling of powerline distribution networks", Open

University, PhD thesis, 1996.

2. A H. Morton, "Advanced Electrical Engineering", Longman Scientific and Technical,

1966.

calculating the hf transmission line parameters of power cables

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