Multipath channel model of power lines

Transcription

1 VOL., O., JE 00 Multpath channel model of power lnes Petr Mlynek, Martn Koutny, Jr Msurec rno nversty of Technology, Faculty of Electrcal Engneerng and Communcaton, Department of Telecommuncatons Emal: {mlynek, koutnym, Abstrakt The paper s focused on realzaton of power lne model. The power lnes are modelled from transfer functon of multpath sgnal envronment. The paper descrbes the PLC communcaton model too. Ths model s necessary for testng and verfyng the correct functon of power lne model n communcaton strng. The power lne model was testng on sample topology wth one branch. Fnally the resultng applcaton s descrbes. Introducton Systems for communcaton over power lnes are referred to as PLC (Power Lne Communcaton). PLC systems do not requre any specfc cablng because the termnal equpment s connected drectly to the power network []. There are no dffcultes of buldng up a new communcatons network because we use an already exstng power network. Ths brngs manly savngs n fnancal costs and tme, whch we would otherwse spend on buldng up a new communcatons network. We can nterconnect a PLC network wth exstng communcatons networks, for example the LA computer network or drectly wth the Internet. PLC systems fall nto two areas: broadband PLC and narrowband PLC. roadband PLC acheves the characterstcs of broadband communcaton, enablng, for example, fast Internet access or mplementaton of small LA networks. arrowband PLC today seem to be a lttle n the background. Ths s, of course, gven only by the area of applcablty. Power networks can also be used for other applcatons, whch would be hard to mplement n practce through another type of communcaton. Specfc servces nclude central management of power consumpton, tarffng, remote meter readng, commandng, etc. Remote meter readng at customers on a large scale s hampered exactly by the communcaton paths. It s the swtched PST telephone lnes, GSM, and the Internet that are manly used today []. The possblty of usng the power network and systems of narrow-band PLC s a most recent development [3]. Each of the systems has ts specfc pros and cons and so t s approprate to consder all the systems that are potentally capable of provdng suffcent transmsson capacty al low costs. A problematc area of PLC s nterference. The nterference may affect servce relablty. Also, there s consderable attenuaton on the path towards the termnal equpment. From the vewpont of data transmsson, the power lne s always msmatched and thus there appear reflectons on the lne, and the lne propertes and parameters vary wth tme and place. Every electrc lne s characterzed by consderable sgnal attenuaton and dverse nterference and nose so that data transmsson exhbts a very hgh error rate when no error check mechansm s employed. Therefore ths artcle focuses on the realzatons of complex PLC communcaton system, whch contan error check mechansm and modelled power lne as multpath sgnal reflecton envronment. For the purpose of modellng, PLC communcaton system can be set up from follows components: PLC communcaton model Power lne model ose model OFDM model for PLC communcaton Computer smulaton of PLC systems wll enable a better understandng of the problematc of data transmsson over power lnes, t wll reveal the potentals of these systems, and the area of PLC applcablty wll be better defned. Suffcently precse computer models of PLC systems wll thus make the process of selectng and deployng new telemetry and management technologes markedly more effectve. A model wll be descrbed wth frequency dvson of spectrum usng the OFDM technque, where partcular carrer frequences are mapped wth 56-state, 64-state or 3-state QAM or QPSK and PSK modulaton [4] [5]. The resultng model s shown n Fg.. 48

2 VOL., O., JE 00 Transmtter P Sequence Generator npolar to polar Converter QAM Modulator ernoull nary ernoull nary Generator nary Input RS Encoder Random Interleaver t to Integer Converter General QAM Select Rows complex(0,0) Pad Shft for FFT IFFT IFFT Add Cyclc Prefx Concatenate Delay delay Fnd Delay sref sdel Tx Error Rate RxCalculaton Error Rate Calculaton ER Constellaton dagram before channel Power lne channel Constellaton dagram behnd channel nary Output RS Decoder nary-output RS Decoder Random Denterleaver Integer to t Converter General QAM General QAM Demodulator Termnal element Data sgnals Plot sgnals Select Rows Remove plot sgnals Remove zero To Frame Frame Status Converson FFT FFT Cyclc Prefx In Recever ser Fgure : OFDM model. Model descrpton [6]: A ernoull nary Generator s used as the data source n the proposed model. It s a generator whch generates random bnary numbers accordng the ernoull dstrbuton. In real systems, t allocaton (mappng) can be obtaned from ths equaton [7]: 3, () bn log SR n ER Q 4 where b n s number of bts at n-subchannel, SR n average sgnal to nose rato n part subchannel n, where Q - s defned as: y Q( x) e x dy Channel codng, realzed by the Reed-Solomon code (RS(5; )), was used to ensure data transfer n the communcaton channel. From the channel codng block we obtan a seral flow of data. Ths flow enters the mappng block. The bt sequences are converted to a symbol sequence n the block mappng. The () dstrbuton of symbols s the result of mappng. Ths symbols dstrbuton s dependent on the selected modulaton. The sub-band separaton of the useful sgnal s realzed n the Select Rows block. It s necessary to nsert the plot sgnals and mplement an estmate of transmsson channel n the case of coherent system detecton. Ths s realzed by the help of the P Sequence Generator. lock Complex(0,0) s used to generate the mddle carrer frequency. lock Concatenate s used to add up all the carrer frequences, whch enter ths block. The sze of the framework s then adjusted for IFFT n the Pad block and the sgnal s adjusted for IFFT n the Shft block. After that the sgnal undergoes the Fast Fourer transform, where data are converted from the frequency doman to the tme doman. To avod ntersymbol nterference (ISI) the OFDM protectve nterval s used. It s realzed by the Add Cyclc Prefx block. The blocks for calculatng of the bt error are used too. The blocks are connected nversely on the recever sde. The power lne channel block wll be descrbed n the next chapter. 49

3 VOL., O., JE 00 3 Transmsson lne model In lterature the methods used to smulate and to study the transmsson lne behavor are dfferent [8] [0]. Most of them are obtaned from the tme dependent telegrapher s equatons whch are for the elementary lne transmsson cell, shown n Fg., the followng: ( + v( - R dx L dx C dx dx G dx (x+d + v(x+d Fgure : Elementary cell of a transmsson lne. v( ( R ( L 0 (3) x t ( v( G v( C 0 (4) x t In these equatons x denotes the longtudnal drecton of the lne and R, L, G and C are the per unt length resstance (Ω/m), nductance (H/m), conductance (S/m) and capactance (F/m) respectvely. The electrc quanttes are dependent by the geometrc and consttutve parameters. The parameters to descrbe a transmsson lne are the characterstc mpedance c and the propagaton constant γ: - plot dstrbuton network s known. 4. Transfer functon for multpath propagaton envronment Multple reflectons at mpedance dscontnutes are typcal for power lne channels, there are caused multpath propagaton. Ths behavor can be descrbed by a model of the channel n Fg. 3 []. Each transmtted sgnal arrves n the recever va dfferent paths. Each path s defned by a certan delay τ and a certan attenuaton factor C. The power lne channel can be descrbed by means of a dscrete-tme mpulse response h(. The mpulse response of the channel h( can be wrtten as a sum of the delayed and attenuated Drac pulses: h( jf C ( t ) H( f ) C e. (8) The transfer functon wth multpath sgnal propagaton can be wrtten: H( f ) jf g A( f, l ) e, (9) where g s a weghtng factor representng the reflecton and transmsson factors along the path and A(f,l ) s attenuaton factor derved from characterstcs of PLC transmsson cable, t can be found n []. The transfer functon ncludng the parameters of the attenuaton, mpedance fluctuatons and multpath effects. The nose model n Fg. 3 s added too. C R jl (5) G j C j ( R jl )( G jc ). (6) s( τ τ C ose r( The transfer functon of a lne wth the length l can be expressed as: H( f ) V ( x l) V ( x 0) l ( f ) l j ( f ) l e e e. (7) 4 Modellng of the power lne channel The power lne channel s requred to smulate PLC communcatons. There exst two possble methods for the modellng of power lne channels. The frst one apples the methods used for the modellng of rado channels. The power lne channel s assumed to be a multpath propagaton envronment. The second alternatve apples the methods used to model electrcty dstrbuton networks. The chan parameter matrces descrbng the relaton between nput and output voltage and current of two-port network can be appled for the modellng the transfer functon of a communcatons channel. The frst method has been chosen, because the topology of the τ Fgure 3: Multpath sgnal propagaton representng power lne channel model. 5 Model measurements 5. Sample network The smple dstrbuton network topology s shown n Fg. 4. The lnk has one branch and conssts of the segments (), () and (3) wth the lengths l, l a l 3 and the characterstc mpedance, C a C3. C 50

4 VOL., O., JE 00 A () ranch () C Path o. Way of the path Weghtng factor g Length of path d A C t l +l Transmtter (3) Recever A D C t r 3D t 3D l +l 3 +l D A ( D ) - C t r 3D (r 3 r 3D ) (-) t 3D l +(- )l 3 +l Fgure 4: Topology of the sample network. R, L, G, C, c and γ parameter were obtan analytc from characterstc parameters of a cable M-J 3x.5. Table I shows the parameter of sample network. Table I: Sample network parameter. l 0 m l 30 m 0 m l 3 The transmtter and recever are mpedance matchng, whch means A =, C = C. The applance on the branch has dfferent mpedance than the cable, therefore the reflecton occur here. The parameters of the channel are acqured based on the topology of the dstrbuton network and on the bass of these parameters we can make a calculaton of characterstc mpedance and propagaton constant for each network segment. Of known characterstc mpedance of each segment we set the reflecton factors. The ponts for reflecton are and D wth the reflecton factor [3] [4]: C C3 C C3 r (0) C C3 r C3 D 3D () D r 3 C3 C3. () It s also necessary to calculate the transmsson factor [3] [4]: t r (3) t3 r3. (4) Each path has a weghtng factor g, representng the product of the reflecton and transmsson factors along the path. The delay τ of a path can be calculated from the length d, the speed of lght c 0 and the solaton relatve permttvty ε r : d r. (5) c 0 The sgnal components of the paths have to be added due to superposton and the transfer functon of sample network can be expressed as: H( f ) jf g A( f, d ) e. (6) Due to the fact that longer paths have hgher attenuaton they contrbute less to the overall sgnal at the recevng pont, therefore was chosen sx paths. 5. Smulaton results Fg. 5 shows the results of a smulaton of the multpath sgnal propagaton model based on transfer functon (6) wth sx paths. The reflectons at the open tap cause perodcal notches n the frequency response, whch can easly be seen n the Fg. 5. The parameter set s lsted n Table III, ths parameters are derved from parameters of sample topology, equatons (0) - (4) and characterstc parameters of a cable M-J 3x.5. Table III: Parameters of the sample network model. Path o. d g 00 0, , , , , ,000 The possble propagaton paths from transmtter to recever are shown n Table II. Table II: Propagaton paths. 5

5 H(f) [d] VOL., O., JE Frequency response lght dmmers and copers. They are bursts of nterference spkes wth repeatng of perod. Synchronous mpulse nose can be modelled by a source of whte nose wth a spectral colourng together wth a perodcal swtchng of rectangular wrap (Fg. 6) [5] f [Hz].5 x 0 7 Fgure 5: Smulaton of the sample network. Whte nose 5.4 PLC channel model Perodc rectangular sgnal Spectral colourng flter Fgure 6: Synchronous mpulsve nose. Synchronous mpulsve nose 5.3 ose n power lne channel ackground nose: t s every tme present n the network. It s caused by assemblng of multple sources of nose wth low power. It can be descrbed by a PSD (Power Spectral Densty) that t declnes wth a growly frequency. The background power nose densty can be descrbed wth equaton: 0 f f0 A( f ) A A e (7) The fnal model has been created from OFDM model and power lnes model together wth noses models n Matlab/Smulnk [6]. The coeffcents of the flter were calculated from the transfer functon of the mult path sgnal envronment (6). The power lne was modelled as flter together wth the sources of the nterference. More detaled nformaton about the sources of nterference can be found n []. Fg. 7 shows the resultng PLC channel. Ths PLC channel s used n OFDM model n Fg. and enables to smulate data communcaton over power lnes. where A s power densty for f,and A 0 s a dfferences between A( ) and A(0). Ths model enables modellng background nose as a whte nose process, whch gets a spectral colourng by a flter. In Dgtal Flter PLC channel Out arrow-band nose: ths nose prmary orgnates from the broadcastng statons that they transmt n a long, mddle a short wave range. The ampltude can be changed n dependence on tme and place. The narrow-band nose can be modelled as a sum of multple sne nose wth dfferent ampltude: n( A ( sn( f t ) (8) Impulsve nose Rcan ackground nose Addtve whte Gaussan nose Gaussan where s a number of waves of dfferencng frequences f, ampltude A ( and phase φ. The ampltude A ( s a constant n smplest case but t can be establshed from broadcast transmsson. The phase φ s randomly establshed from nterval [0;π]. arrowband nose 50 Hz DSP Asynchronous mpulsve nose: ths type of nose s characterzed by hgh and short spkes of voltage wth length 0 00 µs. These spkes can reach up to kv level. Ths nose s the cause of the swtchng equpments n the dstrbuton network. These knds of nose are consdered as a part of background nose. Synchronous mpulsve nose: s caused by thyrstors n 5.5 Resultng applcaton Fgure 7: PLC channel. The resultng smulaton applcaton (Fg. 8) contans selec- 5

6 VOL., O., JE 00 ton of modulaton, channel model and nose model. Applcaton has the vew of frequency response of the selecton channel too. Fgure 8: Resultng applcaton. The smulaton can shown the constellaton dagram for dfferent modulatons, channel model and nose model. Through the constellaton dagram s possble to vew the effect of nose. 6 Concluson The progress n PLC technology has come about n the last decade. Remote data acquston s now necessary because t s gven by legal condtons. PLC technology s seemed as an alternatve data channel. The artcle deals wth desgn of the PLC communcaton system model. The model s composed of the OFDM communcaton model, the model of power lnes and nose model. The model of power lnes are modelled as an envronment of multpath sgnal propagaton. For the sample network topology was modelled power lnes and the resultng channel model was constructed consstng of a power lnes model and the sources of nterference. The work provdes computer apparatus for creatng models and modellng of power lnes for the smulaton of data transmsson over power lnes. The constructed power lne model offers possblty to carry out nvestgatons n dfferent network topologes and study ther effect on communcaton system. The complex PLC communcaton model can be used for comparson of the performance of dfferent modulaton and codng schemes and for future standardzaton. The results of smulatons based on the model wll be compared wth measurements of a real system n the future work. REFERECES [] Ferrera, H.C., Grove, H.M., Hoojen, O. Vnck, A.J.. Power lne communcatons: an overvew, Proc. of IEEE ISPLC, 996, pp [] Mlynek, P.; Msurec, J.; Koutny, M. The communcaton unt for remote data acquston va the Internet. In Proceedngs of the 7th WSEAS Internatonal Conference on Crcuts, systems, electroncs, control and sgnal processng (CSES'08). Puerto de La Cruz, Span: WSEAS Press, 008. s IS: [3] Msurec, J. The Data Acquston va PLC n Energetcs. In 3nd Internatonal Conference on Telecommuncatons and Sgnal Processng - TSP' s. -4. IS: [4] Krajsa, O.; Slhavy, P.; Koutny, M. Half- overlapped Fltered MultTone modulaton for PowerLne Communcaton systems. In Proceedngs of the 3th WSEAS Internatonal Conference on Systems. Rhodos: WSEAS Press, 009. s IS: [5] Krajsa, O.; Slhavy, P. Half-overlapped Fltered MultTone Modulaton, ts mplementaton and comparson wth non-overlapped Fltered Mult- Tone modulaton. In Proceedengs of The 7th WSEAS Internatonal Conference on CIRCITS, SSTEMS, ELECTROICS, COTROL & SIG- AL PROCESSIG.. Puerto De La Cruz, Span: WSEAS, 008. s IS: [6] Koutny, M.; Krajsa, O.; Mlynek, P. Modellng of PLC communcaton for supply networks. In Proceedngs of the 3th WSEAS Internatonal Conference on Communcaton. Rhodos: WSEAS Press, 009. s IS: [7] ngham, J.A.C. Multcarrer modulaton for data transmsson: An dea whose tme has Come. IEEE Communcaton Magazne, vl.5. no , pp.5-4. [8] Dostert, K. M. Power Lnes As Hgh Speed Data Transmsson Channels Modellng the Physcal Lmts, Proceedngs of the 5th IEEE Internatonal Symposum on Spread Spectrum Technques and Applcatons (ISSSTA 98), Sep. 998, pp [9] Hardy, M. E., Ardalan, S., O eal, J.., Gale, L. J., Shuey, K. C. A Model for Communcaton Sgnal Propagaton on Three Phase Power Dstrbuton Lnes. IEEE transactons on Power Delvery, Vol. 6, 3, July 99, pp [0] H. Meng, S. Chen, L. Guan, C. L. Law, P. L. So, E. Gunawan, T. T. Le. A Transmsson Lne Model for Hgh- Frequency Power Lne Communcaton Channel, IEEE Transactons, 000, pp [] HRASICA, H., HAIDIE, A., LEHERT, R. roadband Powerlne Communcatons etwork Desgn. [s.l.] : Wlley, c s. IS [] abc, M.; Hagenau, M.; Dostert, K.; ausch, J. Theoretcal postulaton of PLC channel model. Open PLC European Research Allance (OP- ERA). 005 [3] mmermann, M.; Dostert, K. A Mult-Path Sgnal Propagaton Model for the Power Lne Channel n the Hgh Frequency Range. Proceedngs of the 3rd Internatonal Symposum on Power-Lne Communcatons, Lancaster, K, 999, pp [4] mmermann, M; Dostert, K. A Multpath Model for the Powerlne Channel. IEEE Transactons on Communcatons. 00, VOL. 50, O. 4. [5] M. abc, M. Hagenau, K. Dostert, J. ausch, Theoretcal postulaton of PLC channel model. Open PLC European Research Allance (OPERA). 005 [6] The MathWorks [onlne]. 999 [ct ]. Onlne: < 53