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Multi Path Signal Propagation Modelfor the Power Line Channel in the High Frequency Range

Manfred Zimmermann, Klaus DostertInstitute of Industrial Information SystemsUniversity of KarlsruheHertzstrasse 16, D -76 187 Karlsruhe, GermanyPhone: +49 721 608 4419 , Fax: +49 721 608 4500e-mail: [email protected] karlsruhe.deKlaus.Dostert @ etec.uni-karlsruhe.de

BSTR CTFor the use of the mains networks as high speed datapath for Internet, voice and data services carrierfrequencies within the range from 50 0 kHz up to 20MHz must be considered. The development ofsuitable communication systems and the planning ofpower line communication networks requiresmeasurement-based models of the transfercharacteristics of the mains network in the above-mentioned frequency range.The heterogeneous structure of the mains networkwith numerous branches and impedance mismatchingcauses numerous reflections. Besides multi-pathpropagation w ith freque ncy-selec tive fading, typicalpower cables exhibit signal attenuation increasingwith lengtli and frequency. The complex transferfunction of pow er line link can be described by aparametric model in the considered frequency range.Measurements of amp litude and p hase response of asample network with well-known geometry approvethe validity of the model. Comparisons withmeasurements con ducted at ,,live6 mains networksprove the validity of the model also for real networktopologies.1 IntroductionDue to recent demands in the area of communicationnetworks the electrical power su pply system is on theway to migrate from a pure energy distribution

, network to a multi-purpose medium deliveringenergy, voice and various data services [Zimm98].Especially Internet access is in the focus of the effortsof various research activities.The power line network differs considerably intopology, structure and physical properties fromconventional telecommunication mediums liketwisted pair, coaxial or fibre optic cables. Thereforespecial communication systems, considering thehostile properties of power line channels, arerequired [Wald98]. For the design of appropriate

communication systems and for planning of powerline communication networks, models of the transfercharacteristic s of the low voltage m ains network arerequired.Several approaches for modelling the transfercharacteris tics of power lin es can be foun d inliterature. Most of these models represent bottom upapproaches describing the behaviour of a network bythe components using scattering parameter matrices[Thregl] or four pole impedance and admittancematrices [Barn98], [D alb97], [Kar197]. These modelsgenerally imply detailed knowlegde about thecompon ents of the network to determin e the elemen tsof the matrices. The main drawback of suchapproaches is the great number of parameters whichcannot be determined with sufficient precision. Onthe contrary to that, a top down approach byregarding the communication channel as a black boxand describing its transfer characteristics by atransfer function is the purpose of this pape r.

Noisen t)

Transmitter Channel Receiver

Figure : General channel modelFigur e 1 shows a general chann el model widely usedin communication engineering. The model presentedin this paper describes the transfer function H( f) by afew characteristic parameters in the frequency rangefrom 5OOkHz up to 20 MHz and is based on physicaleffects observed during a great number ofmeasurements. The goal of the model is thedescription of the transfer function by parameters


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derived from channel measurements in contrast topredictive modelling of a network by its geometricdimensions, structure or material properties. In thecase of a simp le topology (i.e. cable with one branch)the physical reasons for the observed results (cableloss, reflection and transmission factors) can beidentified. In the case of more complicated realnetwork topologies the back-tracing of the results tothe reasons is often not possible. However, thetransfer function may also in such casees bedescribed by the model. The parameters, however,can not be traced back to ph ysical dimension s of thenetwork.2 Topology of the rnains networkIn Europe the mains network is typically divided intothree sections with different voltage levels. The highvoltage, medium v oltage and the low vo ltage section.From a communication point of view not all parts ofthe mains distribution network are of equal interest.Espec ially the low v oltage distribution grid is of greatinterest as last-mile access network. Hence themodel pr esented in this paper foc uses on this section.~ b w e v e r, t can also be easily applied to othersections. The coinrnunication link from the substationto the 'backbone network can be im plemented byconventional communication links as fibre optics,radio relay links, broadband cables or even by usingthe medium voltage lines [Zimm98].The low voltage local loop access netwo rk betweenthe substation and the customer premises are oftenoperated in a star shaped structure. From acomm unication point of view they have a similarstructure as mob ile radio networks consisting of cells

In oppos ite to the telephone copper loop the powerline local loop access netwo rk does not consist ofpoint-to-point connections between substations andcustomer premises but represents a line bus with thedistributor cables and the house service cables.typical access network link between a substation anda customer (Figure 2) consists 'o f the distributorcable or a series connection of dis&ibutorcables withthe characteristic impedance ZLi and the branchinghouse connection cables with the characteristicimpedance ZLH The house service cable ends at ahouse connection box. The indoo r cabling follow s,which is modelled by a termination imped ance ZH(f).Each of the transitions at the connections betweencables along the propagation path represent changesof impedance and causes reflections.3 Physical Signal PropagationEffects3.1 Multi Path Signal PropagationDue to the structure of the low vo ltage mains networksignal propagation differs from matched lines.Numerous reflections are caused by the joints of thehouse service cables, house con nection boxes and thejoints at series connections of cables with differentcharacteristic impedance. Signal propagation doesnot only take place along a quasi ,,line of sight pathbetween the transmitter and the receiver, alsoadditional propagation paths (echoes) must becondidered. The result is multi-path signalpropagation with frequency selective fading.

and base stations.

Substation1no e f)

Figure : Signal propagation over the power linelocal loop access network

Figure 3: Multi path signal propagation; cablewith one tapMulti-path signal propagation is studied at a simpleexample which can be easily analysed (Figure 3).The link has one branch and consists of the segments( I ) , 2) and (3) with the lengths 11, 12, l and thecharacteristic impedance Z LI,ZL2,Z L ~ .


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Table : Signal Propagation paths of the examined sample networkPath Way of the signal path weighting factor gi length of path diNo.

A+B+C ~ I B 11 122 A+B+D+B+C tl~'r3D't3~ 1, 2 .1 ~ l2,

N A+B +D ~ B ) ~ - 'C ~ I B '3D. (r38' r 3 ~ ) ' ~ ' ~ )3B lI 2(N-1).13 l3

For a simplified consideration A and C arematched, which means ZA=ZLIand Zc=ZL2. The I s x ) ~ 9 It,xls1remaining points for reflections are ( B and ( ) j 1 2 3 , . X = A , B ,C ,D ... ( 8with the reflection factorsHence the weighting factor gi, a product of

( 1 ) transmission and reflection factors is also less orequal one.

and the transmission factors

With these assumptions the propag ation paths listedin Tab le are possible. Each path i has a weightingfactor gi, representing the product of the reflectionand transmission factors along the path. The d elayof a path

The more transitions and reflections occur along apath the smaller the weighting factor gi .,Due to thefact that longer paths have higher attenuation theycontribute less to the overall signal at the receivingpoint. It seems reasonable to choose the number ofdominant paths N no t to large.Signal propagation in more complicated networkswith more branches can be partitioned into paths ina similar way.3 2 Attenuation caused by cable lossesAs mentioned above the propagating signals areexposed to attenuation increasing with length andfrequency. This section presents a closer look at thelosses and derives a mathematical model for them.

4 Source Transmission Line ; ;SinkZ =- 6 )~ ;- r---

can be calculated from the length di and the phase b- m d x ~ ~velocity vp. The losses of real cables cause an . ,.- jattenuation A(f,d) increasing with length and xidx 1frequency . Th e signal compon ents of the paths haveto be added due to superposition and the transferfunction from A to C can be expressed as: Figure : Signal propagation over ajzafr transmission line~ ( f ) , - A ( f , d , ) . e 7 )

is Transmission line theory describes the voltage andAll reflection and transmission factors are generally current along a line ( Figure 4) as followsless or equal one. [Stein82]:


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The Parameters to describe a transmission line arethe characteristic impedance _Z and the propagationconstant y .

Considering a matched transmission line, which isequivalent to regarding only the wave propagatingfrom sou rce to destination, the transfer function of aline of the length can be expresse d as follows:

Figure 5 shows a cross section of a typical powerline cable with four conductors, widely used inGerman power distribution systems. When feedingsignals into two adjacent conductors, most of theelectric field is concentrated between these twoconductors. For a first estimate the electric andmagnetic field can be approximated by equationsdescribing a micro strip line. The parameters of thecable can be estimated by the geom etric dimensionsand som e material prope rties.

Figure 5: Cross section of a typical pow er linecable 4 conductors)The induc tance per unit length and capacity perunit length can be exp ressed as follows:

Considering frequencies in the MHz-range theresistance per unit length is dominated by the skin-effect and can be approximately expressed by

following a circular shaped conductor with thediameter r. The con ductan ce per unit lengthG =2i rcfC tanG -

c ( 1 8 )is mainly influenced by the dissipatian factor of thedielectric material (usually PVC).The result of using geometry and materialproperties in the above equations results inR L and G C in the frequencyrange of interest. Hence the cables can be regardedas weakly lossy and the ch aracteristic impe dance _Zand the propagation constant y can be determinedusing the following simplified expression s:

Summ arising the characteristic parameters of thecables into the constants kl and k 2 leads to the result

The real part of the propagation constant, theattenuation loss a i~.:reases with frequency. Th erelation between a and f with a special cable can beproportional to square root of f, proportional to f o rproportional to a mixture of both, either k l or k2dominates.Based on the derivations starting from physicalassumptions and extensive investigations ofmeasured frequency.responses the real part of thepropagation constant, the cable losses, can bedescribed as

With a suitable selection of the parameters ,ao, a land k the attenuation of a power line cable can becharacterised as


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4 The channel model4 1 A generalized m ulti-path-signalpropagation model of the transfer functionCombining the multi-path-propagation and thefrequency and length depending attenuation finallyleads to

H ( f ) = C g, f)Iq g i ( f ) e- q,+ci, f di j2n f z ie'=' T a f t e n ; u t i o ndeilryjilctor term termThe run time of a path is described by the delayterm. The low pass characteristic, the attenuationincreasing with length and frequency, areconsidered by the attenuation term. The weightingfactor gi comprises the reflection and transmissionfactors along a propagation path. Due to the factthat house impeda nces may exhibit complex,frequen cy dependent values this w eighting factor isfor a generalised case chosen complex andfrequency depend ent. The signal components of theN p aths add to gether at the receiving point.4 2 Simplified modelFortunately, in most practical cases the generalisedfrequency dep endent w eighting factors gi can besimplified to complex but not frequency dependingfactors. In heterogeneo us real world netwo rks oftenmore than one path with the sam e delay ~i exists, sothat it is very complicated to trace the weightingfactors gi back to their origins. In such cases theweighting factor simply describ es the weight of thepath.The relation between delay q ength of a path diand phase velocity vp is given by

with the speed of light in vacuum co and, thedielectric constant of the insulating material. Thisallows the substitute of the delay ci in (24). Theresulting model of the transfer function

fucto r term ternr

has been widely proved in practice. Table' 2explains the parameters of (26).

Table 2: Parameters of the m odel of the transferfunctionI Number of the path. The path with theshortest delay has the index i= lao,al attenuation parame tersk exponent of the attenuation factor(usual values between 0.2 and 1)gi Weighting factor for path i, in generalcomplex, can be physically interpreted as thereflection/transmission factors of that pathdi length of path iTi delay of path i

Equation 26 ) represents the basis of modelsdescribing the complex transfer function of typicalpower line channels. Using this model all thesubstantial effects of the transfer characteristics ofpower line channels in the frequency range from500kHz o 20 MHz can be modelled by a small setof parameters. Increasing the number of paths Nallows easy control of the precision of the model.5 Verification of the model bymeasurementsFor v erification the results of simu lations based onthe model (26) are compared with measurements.This was done on the one hand with a samplenetwork with well known topology and geometricdimensions and on the other hand with a real worldnetwork.5 1 Sample networkFigure 6 show s the topology of the samplenetwork. The signal transmitter was located atposition A the receiver at C. A and C were matchedwith the characteristic impedance of the cable andpoint D was left open leading to a reflection factor r= 1.

House onneclion cable.about 7 Ohmo[ 17 rnA nergy islnbullon Cable NAWlSOBrspch 2 about 45 Ohm

Figure 6: Topology of the sample n etworkThe transmitted and ,the received s ignals were savedin a file using a Digital Storage Oscilloscope . Thecomplex transfer function and the group delay was


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computed off-line (Figure 7). Since the run time ofthe signal leads to large values in the phase plot,additiona lly a more detailed phase detail plot wasgenerated by su btracting the linear part of the phase.This plot gives a better impression of the frequencyranges with phase distortions.The reflections at the open tap cause periodicalnotches in the frequenc y response, which can easilybe seen in the plots (Figure 7). The same sectionsin the spectrum exhibit phase distortions andchanges in the group delay. Because of the nonideal matching at A and C additional small ripplesin the frequenc y response are visible.Figure 8 shows the results of a simulation of thetransfer characteristic with a model based onequation ( 26 ) with N=6 paths. The parameter set islisted in Table 3. It is obvious that the simulationand the measurement of the absolute value as wellas the phase differs only in some details. The mostimpo rtant conclusio n is that the model covers all theessential effects.Table 3: Parameters of the mod el of the samplenetworkPath No. 1 2 3 4 5 6Length di 200 221 242 259 266 530in mweighting 0,54 0,275 -0,15 0,08 -0,03 -0,02factor gi

Frequency Response Phase Response

....................... .;.. . . . .........

........ ........ . . . . . . . . .. . .. .0 5 10 15 20

Phase Details Group Delay" 1 ........


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Measurement Simulation with N=4 Paths [Karl971 Karl M.:. Mo glichk eiten der~ a c h r i c h t e n u b e r t r i ~ u n ~iber elektrische

. . . . . . . . ; Energieverteilnetze auf d er Grundlageeuropaischer Normen.Fortschrittsberichte VDI Reihe 10 Nr.500 VDI-Verlag Dusseldorf 19971 5 1 15 2 5 1 15 2 [Stein821 Steinbu ch K. Rupp recht W.:Frequency MHz Frequency MHz Nachrichtentechnik. S~ ing er-V erl agFigure 9: Power line link length 150mmeasurement and sim ulation

This example shows the applicability of the modelto real world networks. It is feasible to determine aset of parameters for a link and to describe its highfrequency signal propagation characteristics withoutdetailed knowledge of dimensions.Summary and conclusions

In this paper a model of the complex transferfunction of power line communication links in thefrequency range from 500 kHz to 20 M Hz has beenpresented. The model is derived based on physicaleffects namely multi-path signal propagation andcable losses. Measurement at a sam ple network withwell known dimensions proved good agreement ofthe simulation results with measurements.Furthe rmore the applicab ility of the model to realworld networks was demonstrated.

Auflage Berlin 1982[Thre9 11 Threin G Datenubertragung uberNiederspannungsnetze mitBandspreizverfahren. Fortschritt-Berichte VDI Reihe 10 Nr. 156 VDI-Verlag Dusseldorf 199[Wald98] Waldeck T. Zimmermann M. DostertK. : Kon zepte fur Pow erline-Kommunikationssysteme. FunkschauNo. 14 1998 pp. 40-43.[Zimm9 8] Zimmermann M. Dostert K. : Sprach eiiber die Stromleitung. Funkschau No.4

1998 pp. 22-27.

The presented models offers the possibility to carryout investigations in different network topologiesand study their effects on communication systemsby the means of sim ulation s. Based on a sufficientlylarge measurements database signal propagationmodels fbr planning power line communicationnetworks can be set up. Besides that referencemodels of typical channels can be defined forcomparison of the performance of differentmodulation and coding schemes and for futurestandardisation.7 References[Barn981 Barnes J : A Physical Multi-Path Modelfor Power Distribution NetworkPropagation. Proceedings of the 1998

International Symposium on Power LineCom mun ications and its ApplicationsTokyo 24.-26.Marz 19 98 pp. 76-89.[Dalb8 7] Dalby A.: Sig nal Transm ission on PowerLines Analysis of Power Line Circuits.Proceedings of the 1997 InternationalSymposium on Power LineCom mun ications and its ApplicationsEssen 2.-4.April 1998 pp. 37-44.

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