### Virtual Indicative Broadband over Power Lines Topologies for Respective Subclasses by Adjusting Channel Attenuation Statistical Distribution Parameters of Statistical Hybrid Models (Class Maps) – Part 1: Theory

#### Abstract

Based on a set of indicative overhead and underground medium voltage broadband over power lines (OV and UN MV BPL) topologies, initial statistical hybrid model (iSHM) and modified statistical hybrid model (mSHM) are statistical channel models suitable for the distribution BPL networks. Both iSHM and mSHM statistically process channel attenuation and capacity values of assumed indicative OV and UN MV BPL topologies by exploiting channel attenuation statistical distributions (CASDs). iSHM exploits a set of well-known CASDs (i.e., Gaussian, Lognormal, Wald, Weibull and Gumbel CASDs) while mSHM exploits the Empirical CASD. Each indicative OV and UN MV BPL topology acts as the representative one of a respective OV and UN MV BPL topology class (i.e., rural, suburban, urban and aggravated urban class) that consists of a number of respective statistically equivalent OV and UN MV BPL topologies. The contribution of this paper is the theoretical framework presentation of the creation of new virtual indicative OV and UN MV BPL topologies by appropriately adjusting the parameters of iSHM and mSHM CASDs. These new virtual indicative OV and UN MV BPL topologies will enrich the respective today’s OV and UN MV BPL topology classes with respective OV and UN MV BPL topology subclasses while each subclass will be enriched by a number of respective statistically equivalent OV and UN MV BPL topologies. The procedure of defining new virtual distribution BPL topologies by applying iSHM and mSHM will allow a better capacity study of OV and UN MV BPL topology classes. Apart from the definition procedure of the virtual indicative OV MV and UN MV BPL topologies and their respective virtual subclasses by adjusting CASD parameters of iSHM and mSHM, the contribution of this paper is the class map that analytically describes the taxonomy of distribution BPL topology classes and subclasses.

**Citation: **Lazaropoulos, A. G. (2019). Virtual Indicative Broadband over Power Lines Topologies for Respective Subclasses by Adjusting Channel Attenuation Statistical Distribution Parameters of Statistical Hybrid Models (Class Maps) – Part 1: Theory. Trends in Renewable Energy, 5, 237-257. DOI: 10.17737/tre.2019.5.3.0099

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A. G. Lazaropoulos, “Factors Influencing Broadband Transmission Characteristics of Underground Low-Voltage Distribution Networks,” IET Commun., vol. 6, no. 17, pp. 2886-2893, Nov. 2012.

F. Aalamifar and L. Lampe, “Optimized WiMAX profile configuration for smart grid communications,” IEEE Transactions on Smart Grid, vol. 8, no. 6, pp. 2723-2732, 2017.

A. G. Lazaropoulos, “Deployment Concepts for Overhead High Voltage Broadband over Power Lines Connections with Two-Hop Repeater System: Capacity Countermeasures against Aggravated Topologies and High Noise Environments,” Progress in Electromagnetics Research B, vol. 44, pp. 283-307, 2012. [Online]. Available: http://www.jpier.org/PIERB/pierb44/13.12081104.pdf

A. G. Lazaropoulos, “Towards Broadband over Power Lines Systems Integration: Transmission Characteristics of Underground Low-Voltage Distribution Power Lines,” Progress in Electromagnetics Research B, vol. 39, pp. 89-114, 2012. [Online]. Available: http://www.jpier.org/PIERB/pierb39/05.12012409.pdf

A. G. Lazaropoulos, “Broadband Performance Metrics and Regression Approximations of the New Coupling Schemes for Distribution Broadband over Power Lines (BPL) Networks,” Trends in Renewable Energy, vol. 4, no. 1, pp. 43-73, Jan. 2018. [Online]. Available: http://futureenergysp.com/index.php/tre/article/view/59/pdf

A. G. Lazaropoulos, “Wireless Sensor Network Design for Transmission Line Monitoring, Metering and Controlling Introducing Broadband over PowerLines-enhanced Network Model (BPLeNM),” ISRN Power Engineering, vol. 2014, Article ID 894628, 22 pages, 2014. doi:10.1155/2014/894628. [Online]. Available: http://www.hindawi.com/journals/isrn.power.engineering/2014/894628/

A. G. Lazaropoulos, “Improvement of Power Systems Stability by Applying Topology Identification Methodology (TIM) and Fault and Instability Identification Methodology (FIIM)–Study of the Overhead Medium-Voltage Broadband over Power Lines (OV MV BPL) Networks Case,” Trends in Renewable Energy, vol. 3, no. 2, pp. 102-128, Apr. 2017. [Online]. Available: http://futureenergysp.com/index.php/tre/article/view/34

A. G. Lazaropoulos, “Main Line Fault Localization Methodology in Smart Grid–Part 1: Extended TM2 Method for the Overhead Medium-Voltage Broadband over Power Lines Networks Case,” Trends in Renewable Energy, vol. 3, no. 3, pp. 2-25, Dec. 2017. [Online]. Available: http://futureenergysp.com/index.php/tre/article/view/36

A. G. Lazaropoulos, “Main Line Fault Localization Methodology in Smart Grid–Part 2: Extended TM2 Method, Measurement Differences and L1 Piecewise Monotonic Data Approximation for the Overhead Medium-Voltage Broadband over Power Lines Networks Case,” Trends in Renewable Energy, vol. 3, no. 3, pp. 26-61, Dec. 2017. [Online]. Available: http://futureenergysp.com/index.php/tre/article/view/37

A. G. Lazaropoulos, “Main Line Fault Localization Methodology in Smart Grid–Part 3: Main Line Fault Localization Methodology (MLFLM),” Trends in Renewable Energy, vol. 3, no. 3, pp. 62-81, Dec. 2017. [Online]. Available: http://futureenergysp.com/index.php/tre/article/view/38

A. G. Lazaropoulos, “Main Line Fault Localization Methodology (MLFLM) in Smart Grid–The Underground Medium- and Low-Voltage Broadband over Power Lines Networks Case,” Trends in Renewable Energy, vol. 4, no. 1, pp. 15-42, Dec. 2017. [Online]. Available: http://futureenergysp.com/index.php/tre/article/view/45

A. G. Lazaropoulos, “Smart Energy and Spectral Efficiency (SE) of Distribution Broadband over Power Lines (BPL) Networks – Part 1: The Impact of Measurement Differences on SE Metrics,” Trends in Renewable Energy, vol. 4, no. 2, pp. 125-184, Aug. 2018. [Online]. Available: http://futureenergysp.com/index.php/tre/article/view/76/pdf

A. G. Lazaropoulos, “Smart Energy and Spectral Efficiency (SE) of Distribution Broadband over Power Lines (BPL) Networks – Part 2: L1PMA, L2WPMA and L2CXCV for SE against Measurement Differences in Overhead Medium-Voltage BPL Networks,” Trends in Renewable Energy, vol. 4, no. 2, pp. 185-212, Aug. 2018. [Online]. Available: http://futureenergysp.com/index.php/tre/article/view/77/pdf

M. H. Rehmani, M. Reisslein, A. Rachedi, M. Erol-Kantarci, and M. Radenkovic, “Integrating renewable energy resources into the smart grid: recent developments in information and communication technologies,” IEEE Transactions on Industrial Informatics, vol. 14, no. 7, pp. 2814-2825, 2018.

F. R. Yu, P. Zhang, W. Xiao, and P. Choudhury, “Communication systems for grid integration of renewable energy resources,” IEEE Network, vol. 25, no. 5, pp. 22–29, Sep. 2011.

B. Heile, “Smart grids for green communications [industry perspectives],” IEEE Wireless Commun., vol. 17, no. 3, pp. 4–6, Jun. 2010.

A. G. Lazaropoulos, “Statistical Broadband over Power Lines Channel Modeling – Part 1: The Theory of the Statistical Hybrid Model,” Progress in Electromagnetics Research C, vol. 92, pp. 1-16, 2019. [Online]. Available: http://www.jpier.org/PIERC/pierc92/01.19012902.pdf

A. G. Lazaropoulos, “Statistical Broadband over Power Lines (BPL) Channel Modeling – Part 2: The Numerical Results of the Statistical Hybrid Model,” Progress in Electromagnetics Research C, vol. 92, pp. 17-30, 2019. [Online]. Available: http://www.jpier.org/PIERC/pierc92/02.19012903.pdf

A. G. Lazaropoulos, “Underground Distribution BPL Connections with (N + 1)-hop Repeater Systems: A Novel Capacity Mitigation Technique,” Elsevier Computers and Electrical Engineering, vol. 40, pp. 1813-1826, 2014.

A. G. Lazaropoulos, “Review and Progress towards the Capacity Boost of Overhead and Underground Medium-Voltage and Low-Voltage Broadband over Power Lines Networks: Cooperative Communications through Two- and Three-Hop Repeater Systems,” ISRN Electronics, vol. 2013, Article ID 472190, pp. 1-19, 2013. [Online]. Available: http://www.hindawi.com/isrn/electronics/aip/472190/

A. G. Lazaropoulos, “Broadband over Power Lines (BPL) Systems Convergence: Multiple-Input Multiple-Output (MIMO) Communications Analysis of Overhead and Underground Low-Voltage and Medium-Voltage BPL Networks (Invited Paper),” ISRN Power Engineering, vol. 2013, Article ID 517940, pp. 1-30, 2013. [Online]. Available: http://www.hindawi.com/isrn/power.engineering/2013/517940/

A. Nazem and M. R Arshad, “An Approach in Full Duplex Digital Multipoint Systems Using Large Signal Power Line Communication,” Bentham Recent Patents on Electrical & Electronic Engineering, vol. 6, no. 2, pp. 138-146, 2013.

A. G. Lazaropoulos and P. G. Cottis, “Transmission characteristics of overhead medium voltage power line communication channels,” IEEE Trans. Power Del., vol. 24, no. 3, pp. 1164-1173, Jul. 2009.

A. G. Lazaropoulos and P. G. Cottis, “Capacity of overhead medium voltage power line communication channels,” IEEE Trans. Power Del., vol. 25, no. 2, pp. 723-733, Apr. 2010.

A. G. Lazaropoulos and P. G. Cottis, “Broadband transmission via underground medium-voltage power lines-Part I: transmission characteristics,” IEEE Trans. Power Del., vol. 25, no. 4, pp. 2414-2424, Oct. 2010.

A. G. Lazaropoulos and P. G. Cottis, “Broadband transmission via underground medium-voltage power lines-Part II: capacity,” IEEE Trans. Power Del., vol. 25, no. 4, pp. 2425-2434, Oct. 2010.

A. G. Lazaropoulos, “Broadband transmission and statistical performance properties of overhead high-voltage transmission networks,” Hindawi Journal of Computer Networks and Commun., 2012, article ID 875632, 2012. [Online]. Available: http://www.hindawi.com/journals/jcnc/aip/875632/

A. S. de Beer, A. Sheri, H. C. Ferreira, and A. H. Vinck, “Channel frequency response for a low voltage indoor cable up to 1GHz,” In Power Line Communications and its Applications (ISPLC), 2018 IEEE International Symposium on, pp. 1-6, 2018.

A. G. Lazaropoulos, “Enhancing the Statistical Hybrid Model Performance in Overhead and Underground Medium Voltage Broadband over Power Lines Channels by Adopting Empirical Channel Attenuation Statistical Distribution,” Trends in Renewable Energy, vol. 5, no. 2, pp. 181-217, 2019. [Online]. Available: http://futureenergysp.com/index.php/tre/article/view/96/pdf

A. G. Lazaropoulos, “Towards Modal Integration of Overhead and Underground Low-Voltage and Medium-Voltage Power Line Communication Channels in the Smart Grid Landscape: Model Expansion, Broadband Signal Transmission Characteristics, and Statistical Performance Metrics (Invited Paper),” ISRN Signal Processing, vol. 2012, Article ID 121628, pp. 1-17, 2012. [Online]. Available: http://www.hindawi.com/isrn/sp/2012/121628/

P. Amirshahi and M. Kavehrad, “High-frequency characteristics of overhead multiconductor power lines for broadband communications,” IEEE J. Sel. Areas Commun., vol. 24, no. 7, pp. 1292-1303, Jul. 2006.

T. Sartenaer, “Multiuser communications over frequency selective wired channels and applications to the powerline access network” Ph.D. dissertation, Univ. Catholique Louvain, Louvain-la-Neuve, Belgium, Sep. 2004.

T. Calliacoudas and F. Issa, ““Multiconductor transmission lines and cables solver,” An efficient simulation tool for plc channel networks development,” presented at the IEEE Int. Conf. Power Line Communications and Its Applications, Athens, Greece, Mar. 2002.

T. Sartenaer and P. Delogne, “Deterministic modelling of the (Shielded) outdoor powerline channel based on the multiconductor transmission line equations,” IEEE J. Sel. Areas Commun., vol. 24, no. 7, pp. 1277-1291, Jul. 2006.

A. G. Lazaropoulos, “Virtual Indicative Broadband over Power Lines Topologies for Respective Subclasses by Adjusting Channel Attenuation Statistical Distribution Parameters of Statistical Hybrid Models – Part 2: Numerical Results for the Overhead and Underground Medium-Voltage Power Grids,” Trends in Renewable Energy, vol. 5, no. 3, pp 258-281, Aug. 2019. DOI: 10.17737/tre.2019.5.3.00100

A. G. Lazaropoulos, “Virtual Indicative Broadband over Power Lines Topologies for Respective Subclasses by Adjusting Channel Attenuation Statistical Distribution Parameters of Statistical Hybrid Models – Part 3: The Case of Overhead Transmission Power Grids,” Trends in Renewable Energy, vol. 5, no. 3, pp 282-306, Aug. 2019. DOI: 10.17737/tre.2019.5.3.00101

Matlabtricks (2014) Generate random numbers with a given distribution, http://matlabtricks.com/post-44/generate-random-numbers-with-a-given-distribution (accessed on 8/14/2019)

J. Denker (2008) Randomly Generating Numbers with an Arbitrary Distribution http://www.av8n.com/physics/arbitrary-probability.htm (accessed on 8/14/2019)

DOI: http://dx.doi.org/10.17737/tre.2019.5.3.0099

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