IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 24, NO. 2, APRIL 2009 621 The Effects of Load Impedance, Line Length, and Branches in Typical Low-Voltage Channels of the BPLC Systems of Developing Countries: Transmission-Line Analyses Justinian Anatory, Member, IEEE, Nelson Theethayi, Member, IEEE, Rajeev Thottappillil, Senior Member, IEEE, Mussa Kissaka, and Nerey Mvungi Abstract—This paper presents the influence of line length, number of branches (distributed and concentrated), and terminal impedances on the performance of a low-voltage broadband power-line communication channel. For analyses, the systems chosen are typical low-voltage power-line networks found in Tan- zania. The parameters varied were the network’s load impedances, direct line length (from transmitter to receiver), branched line lengths, and number of branches. From the frequency responses of the transfer functions (ratio of the received and transmitted signal), it is seen that the position of notches and peaks in the amplitude responses are affected by the aforementioned net- work parameters and topology. As a result, the time-domain responses are attenuated and distorted. Time-domain responses of power-line channels under various conditions are also investi- gated for a given pulse input at the transmitter. The observations presented in this paper could be useful for suitable power-line communication system design. Index Terms—Branched network, broadband power line, im- pulse response, interconnections, load impedance, low-voltage channel, multipath, transfer function. I. INTRODUCTION D UE to the advancements and increased demand in broad- band services, it is found that the power-line network can be used for connecting different cities and municipalities in developing countries such as Tanzania [1]. The Tanzanian network configuration is divided into three segments or chan- nels; namely, indoor voltage (within the buildings), outdoor low voltage, and medium voltage (MV). In this paper, we focus on the low-voltage networks (i.e., from distribution transformers to end users with a voltage level of 240 V). For low-voltage net- works, the typical line length from distribution transformers to far end users is about 1.2 km, with about 70 customers con- nected in urban and municipality areas and less in rural areas. Manuscript received November 26, 2007; revised February 07, 2008. First published May 07, 2008; current version published March 25, 2009. This work is a collaboration research between the Faculty of Electrical and Com- puter Systems Engineering, University of Dar es Salaam, Tanzania through SIDA/SAREC and the Division for Electricity and Lightning Research, Uppsala University, Sweden. Paper no. TPWRD-00736-2007. J. Anatory, M. M. Kissaka, and N. H. Mvungi are with the Faculty of Elec- trical and Computer Systems University of Dar es Salaam, Tanzania (e-mail: anatory@engineer.com; kissaka@ee.udsm.ac.tz; mvungi@ee.udsm.ac.tz). N. Theethayi and R. Thottappillil are with the Division for Elec- tricity and Lightning Research, Uppsala University, Sweden (e-mail: Nelson.Theethayi@angstrom.uu.se; Rajeev.Thottappillil@angstrom.uu.se). Digital Object Identifier 10.1109/TPWRD.2008.923395 The typical line length of branches that are either distributed or concentrated at a single node along the line is about 20 m and is not necessarily terminated in either characteristic impedance or a resistive load. The present study is essential for the following possible reasons. In some areas, customers who fail to settle electricity bills are disconnected from the network, causing an open-circuit termination. Also, there are situations where new customers need to be connected to the existing network that leads to either concentrated or distributed branches in the ex- isting system. To access the signal propagation characteristics, studies on the system response in frequency and time domain are presented. In the literature (e.g., [2]–[11]), the stochastic signal attenu- ation, notches distributions, load changes in the channel due to switching ON/OFF of equipment, etc., are presented. However, the authors still feel that only limited studies are available for typical low-voltage channels. For a more focused investigation, this paper attempts to address the following questions, which could benefit PLC system designers. • How much do the number of branches affect the signal response? • How do line lengths from the transmitter to the re- ceiver and branched line length affect the signal re- sponse? • How do the terminal load (infinite and low) impedances ( and ) affect the signal response? II. POWER-LINE CHANNEL MODEL For a transmission line with distributed branches (e.g., Fig. 1) the generalized transfer function can be represented by (1a) [12]–[16]. In (1a), is the total number of branches connected at a given node (e.g., see “node 1” in Fig. 1) and terminated in any arbitrary load. Let , , , , and represent any branch number, any referenced (terminated) load, number of reflections (with a total of number of reflections), transfer function between a given source point (transmitter) to a refer- enced load termination , and transmission factor with refer- ence to any load termination , respectively. With these, the signal contribution factor at referred node “ ” is given by (1b), where is the reflection factor at the referred node d between line to the referenced load , is the propaga- tion constant of line at referred node “d” that has line length . All terminal reflection factors in general are given by (1c), except at the source, where is the source 0885-8977/$25.00 © 2008 IEEE Authorized licensed use limited to: UNIVERSITY OF DAR ES SALAAM. Downloaded on May 12, 2009 at 13:11 from IEEE Xplore. Restrictions apply.