Power-Line Communication Channel Model for ... - IEEE Xplore

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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 24, NO. 1, JANUARY 2009

Power-Line Communication Channel Model for Interconnected Networks—Part I: Two-Conductor System Justinian Anatory, Member, IEEE, Nelson Theethayi, Member, IEEE, and Rajeev Thottappillil, Senior Member, IEEE

Abstract—This paper presents a generalized transmission-line approach to determine the transfer function of a power-line network of a two-conductor system (two parallel conductors) with distributed branches. The channel frequency responses are derived considering different terminal loads and branches. The model’s time-domain behavior is validated using commercial power system simulation software called Alternative Transients Program–Electromagnetic Transients Program (ATP–EMTP). The simulation results from the model for three different topologies considered have excellent agreement with corresponding ATP–EMTP results. Hence, the model can be considered as a tool to characterize any given power-line channel topology that involves the two-conductor system. In the companion paper (Part II), the proposed method is extended for a multiconductor power-line system. Index Terms—Branched network, communication channel model, multipath, power-line communication (PLC), transfer function.

I. INTRODUCTION OWER-LINE networks have been used for delivering broadband data access using indoor, low-voltage, and medium-voltage channel topologies. It involves interconnecting one municipality and others and to provide different information and communications technology (ICT) services in developed and developing countries. In addition, power-line communication (PLC) systems can be interconnected to wireless networks, such as wireless local-area network (WLAN), Wimax, and WiFi technologies, which make it convenient for use with fourth-generation systems. PLC is also used for narrowband services applications, such as automatic meter reading (AMR) [1]–[4]. For efficient communication using the power-line networks, the channel’s performance has to be evaluated to greater accuracy. This would later help in the suitable design of the communication equipment for the aforementioned efficient PLC systems. For this reason, researchers have attempted to come up with appropriate channel models. The earlier models

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Manuscript received June 18, 2008. Current version published December 24, 2008. Paper no. TPWRD-00472-2008. J. Anatory is with the School of Virtual Education, College of Informatics and Virtual Education, University of Dodoma, Dodoma, Tanzania (e-mail: [email protected]). (e-mail: [email protected]). N. Theethayi and R. Thottappillil are with the Division for Electricity, Uppsala University, Uppsala 75121, Sweden (e-mail: Nelson.Theethayi@ angstrom.uu.se; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRD.2008.2005679

were somewhat channel dependent, such as indoor applications by Banwell and Galli [5] and for low- and medium-voltage applications by Zimmermann and Dostert [6], Hensen and Schulz [7], Philipps [8], etc. Some of the low- and medium-voltage channel models were extended to the indoor applications too. Some indoor models have been derived from measurements (e.g., Canete [9], [10]). Generally, the modeling that is being used can be categorized as either time-domain models or frequency-domain models [11]. It is, however, to be noted that the channel’s performance can be more accurately assessed from the channel transfer functions. A simple channel model based on transmission and reflection factors in conjunction with the propagation constants was proposed by Anatory et al. [12]–[14] for a PLC network with two-conductor transmission-line (TL) systems (one phase conductor and one return conductor). The model was capable of handling TL systems with distributed branches (multiple TL branches at a given node on the TL connecting the sending and receiving ends or multiple TL branches distributed on the TL connecting the sending and receiving ends). This model though comprehensive, had some drawbacks as far as model accuracy is concerned. The main reason was that the model neglected the generalized transmission-line theory and considered only the transmission and reflection factors at nodes or junctions with an appropriate propagation factor similar to the multipath model [6]. Due to this in the time-domain response of the model, incorrect amplitudes at late times were found at different points along the TL network having multiple branches for a given pulse input at the sending end. This problem is now overcome as we adopt the generalized TL approach [15]–[17] for determining the channel responses. Hence, we call this model the generalized channel model based on TL theory. Therefore, better accuracy is obtained in the frequency response of the channel model. The advantage of this generalized channel model is that it can be used for multiconductor-coupled PLC networks as discussed in Part II. In this paper, first, the expressions for the transfer function based on the generalized channel model are derived. The responses of the model in the time domain are compared for validation with the ATP–EMTP [18] software, which also uses the TL theory for solving power systems involving transmission lines. II. NETWORK TRANSFER FUNCTION DERIVATIONS For any transmission-line system, the current and voltage at arbitrary line length are given by (1) and , , , and are (2), respectively [16]. In (1) and (2),

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ANATORY et al.: POWER-LINE COMMUNICATION CHANNEL MODEL FOR INTERCONNECTED NETWORKS—PART I

Fig. 1. Example of the power-line network terminated in another transmission line with one branch.

the line characteristic impedance, propagation constant, and model currents representing the forward and backward waves, respectively (1) (2) In all of the transfer function derivations, the aforementioned general equations are used appropriately. The procedure for deriving the transfer function is explained by considering the example of a power-line network with one branch as shown in Fig. , , , , , , and are the source 1. In Fig. 1, voltage, source impedance, characteristic impedance of line 1, characteristic impedance of line 2, characteristic impedance of line 3, load impedance of line 2, and load impedance terminated are the line lengths as on line 3, respectively. , , and and include . In Fig. 1, shown in Fig. 1. Note that , using (1) and (2), the voltage and currents at point A, at that particular point are given by (3) and (4), respectively. at point A is given by (5) and substituting the reVoltage spective values from (3) and (4), the results are as in (6). Let and , then (6) can be represented by (7)

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Fig. 2. Example of the power-line network with branches concentrated at one node.

, and . Consider now at point E the current in the loads and , and (2),

and point C is where using

, (1) , ,

, and . Solving the linear simultaneous expressions so obtained at , , , , , and all nodes, the values for can be obtained for any frequency. The expression for transfer functions H(f) relating the voltage at node C to node A can be obtained. A. Branches Concentrated at one Node

(4) (5)

Consider the configuration as given in Fig. 2, with the line and load parameters as discussed in the previous section. Using the procedure discussed in the previous section for writing the boundary condition expressions at every node, the generalized transfer function between any load termination and the , sending end is given by (8a). In general, the parameters , , and are the characteristic impedance for line , load impedance for line , propagation constant for line , and length for line the which is the shortest distance measured from point A to any point at the load, respectively

(6)

(8a)

in (6), we get

(8b)

(3)

From (3)–(5), we obtain

Defining

, and

(7) (8c) , let , , and be the propagaConsider point B at tion constants for lines 1, line 2, and line 3, respectively. At and B, the voltage is continuous . Using the current is discontinuous , (1) and (2), and and for currents ,

(8d) (8e) (8f) (8g)

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Fig. 3. Example of the power-line network with distributed branches.

(8h) (8i) (8j) (8k) (8l) , In the equations just shown, , , , and . In (8c), is the total number of branches connected at node B.

Fig. 4. Simulation results for the case of nine distributed branches at single node as Fig. 2 using the generalized channel model based on TL theory developed in this paper.

B. Distributed Branches Along the Line Section Consider the power-line network as shown in Fig. 3. Note that the procedure for obtaining the transfer function is the same (i.e., writing the voltage and current boundary conditions at all of the nodes and solving for the unknown modal currents). The transfer function for the voltage between any load point and the sending end is given by (9a). In (9a), , , , , and are the characteristic impedance of line segment nm, terminal load impedance of line nm, propagation constant of line segment nm, shortest length of line segment nm, and shortest line length from the sending end to the node under consideration, respectively. Note that all parameters with mean the consideration is at the node

(9m) (9n) (9o) (9p) (9q) (9r) (9s) (9t) In (9a),

and

.

III. VALIDATION OF THE CHANNEL MODEL

(9a)

Note that the voltage at any load can be obtained from the transfer functions so obtained in the previous section as (10) (10)

(9b) (9c)

(9d) (9e) (9f) (9g) to node to load

(9h) (9i) (9j) (9k) (9l)

The corresponding time-domain response is obtained by the inverse Fourier transform of (10). A. Example of Branches at Single Node The configuration as shown in Fig. 2 is considered with nine branches excluding branch AB. All line segments were considered to be1 km long and have a transmission line per unit length and a capacitance of 7.843743 inductance of pF/m. The source impedance Zs and one of the loads were terminated in 656.95 , while other loads were terminated in 50 . The source was a rectangular pulse with pulse width 1 s and amplitude of 2 V. The pulse is shifted by 0.5 s. The voltage at the node terminated in 656.95 is shown in Fig. 4. The same configuration was implemented in ATP–EMTP software and the results are shown in Fig. 5. It can be observed that the results predicted by the channel model and that by ATP–EMTP software are identical.


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Fig. 8. Simulation results for the case of distributed branches per Fig. 6 using ATP–EMTP with all terminals terminated in 456 , including source and receiving points. Fig. 5. Simulation results for the case of nine distributed branches at single node per Fig. 2 using ATP–EMTP.

Fig. 6. Power-line network with four distributed branches between the transmitting and receiving ends.

Fig. 9. Example of the power-line configuration with tree structure.

was implemented in ATP–EMTP software and the results are shown in Fig. 8. It can be observed that the results predicted by the channel model and that by ATP–EMTP software are identical. C. Example of Power-Line Network With Tree Topology

Fig. 7. Simulation results for the case of distributed branches per Fig. 6 using the generalized channel model using TL theory with all terminals terminated in 456 , including source and receiving points.

B. Example of Power-Line Network With Distributed Branches Next, consider the configuration as in Fig. 6 which is an example of distributed branches. All line segments were 500 m, and a capaciwith a per unit length inductance of 1.64 tance of 7.84 pF/m. The source impedance Zs and all terminal loads are 456 . The network was excited by the same source as discussed in the previous section. The voltage simulated using the channel model at the node is shown in Fig. 7. The same configuration terminated in

To demonstrate that the channel model derivation can be extended to any TL network topology, consider the tree configuration as shown in Fig. 9. All of the transmission-line segments are 500 m. The source impedance Zs and the receiving end were terminated in 456 , while the other loads are terminated in 50 . All lines have per unit length inductance and capaciand 7.84 pF/m. The configuration tance was excited by the same rectangular pulse as discussed earlier. , based on the proposed channel model derivaThe voltage at tion, is shown in Fig. 10. The same case was simulated using the ATP–EMTP software and the result is shown in Fig. 11. Again, it is seen that the results are comparable. IV. CONCLUSION In this paper, the derivation of a power-line channel based on generalized transmission-line theory is presented in which there are minimal assumptions in the so obtained channel frequency

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Fig. 10. Simulation results for a case of tree topology per Fig. 9, using the generalized channel model based on TL theory when all terminal loads are terminated in 50 , while source Zs and receiving point Z are terminated at 456 .

[3] L. E. Brown, “Industrial control with power-line communication,” Control Eng., vol. 38, no. 13, p. 250, 1991. [4] S. T. Mark, “Twacs, a power-line communication technology for power distribution network control and monitoring,” IEEE Trans. Power Del., vol. 1, no. 1, pp. 66–72, Jan. 1986. [5] T. Banwell and S. Gali, “A novel approach to the modeling of the indoor powerline channel—Part I: Circuit analysis and companion model,” IEEE Trans. Power Del., vol. 20, no. 2, pt. 1, pp. 655–663, Apr. 2005. [6] M. Zimmermann and K. Dostert, “A multipath model for the powerline channel,” IEEE Trans. Commun., vol. 50, no. 4, pp. 553–559, Apr. 2002. [7] C. Hensen and W. Schulz, “Time dependence of the channel characteristics of low voltage power-lines and its effects on hardware implementation,” AEU Int. J. Electron. Commun., vol. 54, no. 1, pp. 23–32, Feb. 2000. [8] H. Philipps, “Modelling of powerline communication channels,” in Proc. 3rd Int. Symp. Power-Line Communications Applications, Lancaster, U.K., 1999, pp. 14–21. [9] F. J. Canete, L. Diez, J. A. Cortes, and J. T. Entrambasaguas, “Modelling and evaluation of the indoor powerline transmission medium,” in IEEE Commun. Mag., Apr. 2003, vol. 41, no. 4, pp. 41–47. [10] F. J. Canete, L. Diez, J. A. Cortes, and J. T. Entrambasaguas, “Broadband modeling of indoor power-line channels,” IEEE Trans. Consum. Electron., vol. 48, no. 1, pp. 175–183, Feb. 2002. [11] X. Ding and J. Meng, “Channel estimation and simulation of an indoor power-line network via a recursive time-domain solution,” IEEE Trans. Power Del., vol. 24, no. 1, pp. 144–152, Jan. 2009. [12] J. Anatory, M. M. Kissaka, and N. H. Mvungi, “Channel model for broadband powerline communication,” IEEE Trans. Power Del., vol. 22, no. 1, pp. 135–141, Jan. 2006. [13] J. Anatory and N. Theethayi, “On the efficacy of using ground return in the broadband power line communications—A transmission line analysis,” IEEE Trans. Power Del., vol. 23, pp. 132–139, Jan. 2008. [14] J. Anatory, N. Theethayi, R. Thottappillil, M. M. Kissaka, and N. H. Mvungi, “Broadband power line communications: The channel capacity analysis,” IEEE Trans. Power Del., vol. 23, no. 1, pp. 164–170, Jan. 2008. [15] Electromagnetic Field Interaction With Transmission Lines From Classical Theory to HF Radiation Effects, F. Rachidi and S. V. Tkachenko, Eds. Wessex, U.K.: WIT Press Publisher, 2008. [16] C. R. Paul, Analysis of Multiconductor Transmission Lnes. New York: Wiley, 1994. [17] F. M. Tesche, V. M. Ianoz, and T. Karlsson, EMC Analysis Methods and Computational Models. New York: Wiley, 1997. [18] H. W. Dommel, Electromagnetic Transients Program (EMTP Theory Book). Portland, OR: Bonneville Power Administration, 1988.

Fig. 11. Simulation results for a case of tree topology per Fig. 9, using ATP–EMTP when all terminal loads are terminated in 50 , while source Zs and receiving point Z are terminated in 456 .

response. The model derivation in the frequency domain is independent of network topology and terminal loads. The accuracy of the model has been validated using ATP–EMTP software, which is used for simulating power systems in the time domain. In this paper, a two-conductor system (one phase conductor and the other return conductor) is used. In Part II, the method is extended to the multiconductor case. REFERENCES [1] J. Anatory, M. M. Kissaka, and N. H. Mvungi, “Trends in telecommunication services provision: Power line network can provide alternative for access in developing countries,” in Proc. IEEE Africon, Gaborone, Botswana, Sep. 2004, pp. 601–606. [2] J. Newbury and K. T. Morris, “Power line carrier system for industrial control applications,” IEEE Trans. Power Del., vol. 14, no. 4, pp. 1191–1196, Oct. 1999.

Justinian Anatory (S’06–M’08) received the B.Sc. and M.Sc. degrees in electrical engineering and the Ph.D. degree in telecommunications engineering from the University of Dar es Salaam, Dar es Salaam, Tanzania, in 1998, 2003, and 2007, respectively. He was a Software and IT Engineer with Beta Communication Consulting Co. (T) Ltd., Dar es Salaam, before rejoining the University of Dar es Salaam in 2001. He was with the Faculty of Electrical and Computer Systems Engineering, University of Dar es Salaam, until 2008. Currently, he is a Senior Lecturer with the School of Virtual Education, College of Informatics and Virtual Education, University of Dodoma, Dodoma, Tanzania. He was a Visiting Researcher with the School of Electrical and Information Engineering, University of Witwatersrand, Johannesburg, South Africa, in 2002 and Visiting Researcher at the EMC Group of the Division for Electricity, Uppsala University, Uppsala, Sweden, in 2005 and 2006. In 2008, he was a Postdoctoral Researcher in the Division of Electricity at the University of Uppsala. His research interests include power-line communication, wireless communication, communication networks, and teletraffic engineering. Dr. Anatory is a member of the IEEE Power Engineering Society (PES), IEEE Computer Society, IEEE Communications Society, and IEEE Vehicular Technology Society. He is a Registered Engineer with the Engineers Registration Board (ERB) of Tanzania.


Nelson Theethayi (S’04–M’06) was born in India in 1975. He received the B.E. degree in electrical and electronics (Hons.) from the University of Mysore, Mysore, India, in 1996, the M.Sc. (Engineering) degree in high voltage engineering from the Indian Institute of Science, Bangalore, India, in 2001, and the Ph.D. degree in electricity with a specialization in electrical transients and discharges from Uppsala University, Uppsala, Sweden, in 2005. Currently, he is a Researcher at the EMC group of the Division for Electricity of Uppsala University. His research areas are electromagnetic compatibility, high voltage engineering, electrical power systems, lightning interaction, and lightning protection. Dr. Theethayi is a member of Subcommittee “Lightning” of the Technical Committee TC5 of the IEEE EMC Society, IEEE Dielectrics and Electrical Insulation Society (DEIS), the IEEE Power Engineering Society (PES), and the IEEE Industry Applications Society (IAS).

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Rajeev Thottappillil (S’88–M’92–SM’06) was born in India in 1958. He received the B.Sc. degree in electrical engineering from the University of Calicut, Calicut, India, in 1981, and the M.S. and Ph.D. degrees in electrical engineering from the University of Florida, Gainesville, in 1989 and 1992, respectively. He became an Associate Professor at Uppsala University, Uppsala, Sweden, in 1996 and was promoted to Full Professor in 2000. In 2008, he joined the Royal Institute of Technology, Stockholm, Sweden. His research interests are lightning phenomenon, electromagnetic interference, and electrical power systems. He has published many scientific articles, of them about 40 are in refereed journals. He has written a book chapter on lightning electromagnetic field computation. Prof. Thottappillil is the Chairman of the EU project COST action P18 "Physics of Lightning Flash and its Effects," in which groups from 23 countries are involved. He is also a member of SC 77C of SEK, IEC on High Power Transients, and the Technical Committee of Lightning (TC-5) of IEEE-EMC.