### Enhancing the Statistical Hybrid Model Performance in Overhead and Underground Medium Voltage Broadband over Power Lines Channels by Adopting Empirical Channel Attenuation Statistical Distribution

#### Abstract

Statistical hybrid model is a statistical channel model suitable for the broadband over power lines (BPL) networks while it is based on the statistical processing of channel attenuation and capacity values of preassumed BPL topology classes. One of the key operation elements of the statistical hybrid model, which affects its results fidelity, is the selection of the appropriate channel attenuation statistical distribution among a set of well-known channel attenuation statistical distributions (i.e., such as Gaussian, Lognormal, Wald, Weibull and Gumbel distributions). The selection of the appropriate channel attenuation statistical distribution becomes a hard task since it depends on a number of factors such as the power grid type –either overhead (OV) or underground (UN) power grid–, the representative distribution BPL topology of the examined class, the applied electromagnetic interference (EMI) policies and the used coupling scheme type. The contribution of this paper is to identify the conditions whether the Empirical channel attenuation statistical distribution can act as the default distribution of statistical hybrid model (modified statistical hybrid model) thus replacing the required comparison analysis prior to the selection of the aforementioned distributions of the initial statistical hybrid model. The evaluation comparison is based on the already applied metrics of capacity percentage change and average absolute capacity percentage change.

**Citation:** Lazaropoulos, A. G. (2019). 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, 5, 181-217. DOI: 10.17737/tre.2019.5.2.0096

#### Keywords

#### Full Text:

FULL TEXT (PDF)#### References

F. Xia, L. T. Yang, L. Wang, and A. Vinel, “Internet of things,” International Journal of Communication Systems, vol. 25, no. 9, pp. 1101-1102, 2012.

L. Atzori, A. Iera, and G. Morabito, “The Internet of Things: A survey,” Elsevier Comput Netw., vol. 54, no. 15, pp. 2787–2805, 2010.

H. Farhangi, “The path of the smart grid,” IEEE Power and Energy Magazine, vol. 8, no. 1, pp. 18-28, 2010.

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, “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 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, “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 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. 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/

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

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.

FCC, “In the Matter of Amendment of Part 15 regarding new requirements and measurement guidelines for Access Broadband over Power Line Systems,” FCC 04-245 Report and Order, Jul. 2008.

A. Milioudis, G. Andreou, and D. Labridis, “Optimum transmitted power spectral distribution for broadband power line communication systems considering electromagnetic emissions,” Elsevier Electric Power Systems Research, vol. 140, pp. 958–964, 2016. DOI: 10.1016/j.epsr.2016.03.047

A. G. Lazaropoulos, “A Panacea to Inherent BPL Technology Deficiencies by Deploying Broadband over Power Lines (BPL) Connections with Multi-Hop Repeater Systems,” Bentham Recent Advances in Electrical & Electronic Engineering, vol. 10, no. 1, pp. 30-46, 2017.

http://matlabtricks.com/post-44/generate-random-numbers-with-a-given-distribution

http://www.av8n.com/physics/arbitrary-probability.htm

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. W. van der Vaart, Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, Cambridge, 1998. ISBN: 0-521-49603-9; 0-521-78450-6

N. Suljanović, A. Mujčić, M. Zajc, and J. F. Tasič, “Approximate computation of high-frequency characteristics for power line with horizontal disposition and middle-phase to ground coupling,” Elsevier Electr. Power Syst. Res., vol. 69, pp. 17-24, Jan. 2004.

OPERA1, D5: Pathloss as a function of frequency, distance and network topology for various LV and MV European powerline networks. IST Integrated Project No 507667, Apr. 2005.

N. Suljanović, A. Mujčić, M. Zajc, and J. F. Tasič, “High-frequency characteristics of high-voltage power line,” in Proc. IEEE Int. Conf. on Computer as a Tool, Ljubljana, Slovenia, Sep. 2003, pp. 310-314.

N. Suljanović, A. Mujčić, M. Zajc, and J. F. Tasič, “Power-line high-frequency characteristics: analytical formulation,” in Proc. Joint 1st Workshop on Mobile Future & Symposium on Trends in Communications, Bratislava, Slovakia, Oct. 2003, pp. 106-109.

W. Villiers, J. H. Cloete, and R. Herman, “The feasibility of ampacity control on HV transmission lines using the PLC system,” in Proc. IEEE Conf. Africon, George, South Africa, Oct. 2002, vol. 2, pp. 865-870.

P. Amirshahi, “Broadband access and home networking through powerline networks” Ph.D. dissertation, Pennsylvania State Univ., University Park, PA, May 2006.

OPERA1, D44: Report presenting the architecture of plc system, the electricity network topologies, the operating modes and the equipment over which PLC access system will be installed, IST Integr. Project No 507667, Dec. 2005.

J. Anatory, N. Theethayi, R. Thottappillil, M. M. Kissaka, and N. H. Mvungi, “The influence of load impedance, line length, and branches on underground cable Power-Line Communications (PLC) systems,” IEEE Trans. Power Del., vol. 23, no. 1, pp. 180-187, Jan. 2008.

J. Anatory, N. Theethayi, and R. Thottappillil, “Power-line communication channel model for interconnected networks-Part II: Multiconductor system,” IEEE Trans. Power Del., vol. 24, no. 1, pp. 124-128, Jan. 2009.

J. Anatory, N. Theethayi, R. Thottappillil, M. M. Kissaka, and N. H. Mvungi, “The effects of load impedance, line length, and branches in typical low-voltage channels of the BPLC systems of developing countries: transmission-line analyses,” IEEE Trans. Power Del., vol. 24, no. 2, pp. 621-629, Apr. 2009.

T. Banwell and S. Galli, “A novel approach to accurate modeling of the indoor power line channel—Part I: Circuit analysis and companion model,” IEEE Trans. Power Del., vol. 20, no. 2, pp. 655-663, Apr. 2005.

W. Villiers, J. H. Cloete, L. M. Wedepohl, and A. Burger, “Real-time sag monitoring system for high-voltage overhead transmission lines based on power-line carrier signal behavior,” IEEE Trans. Power Del., vol. 23, no. 1, pp. 389-395, Jan. 2008.

NTIA, “Potential interference from broadband over power line (BPL) systems to federal government radio communications at 1.7-80 MHz Phase 1 Study Vol. 1,” NTIA Rep. 04-413, Apr. 2004.

M. Gebhardt, F. Weinmann, and K. Dostert, “Physical and regulatory constraints for communication over the power supply grid,” IEEE Commun. Mag., vol. 41, no. 5, pp. 84-90, May 2003.

NATO, “HF Interference, Procedures and Tools (Interférences HF, procédures et outils) Final Report of NATO RTO Information Systems Technology,” RTO-TR-ISTR-050, Jun. 2007.

A. G. Lazaropoulos, “The Impact of Noise Models on Capacity Performance of Distribution Broadband over Power Lines Networks,” Hindawi Computer Networks and Communications, vol. 2016, Article ID 5680850, 14 pages, 2016. doi:10.1155/2016/5680850. [Online]. Available: http://www.hindawi.com/journals/jcnc/2016/5680850/

A. G. Lazaropoulos, “Capacity Performance of Overhead Transmission Multiple-Input Multiple-Output Broadband over Power Lines Networks: The Insidious Effect of Noise and the Role of Noise Models (Invited Paper),” Trends in Renewable Energy, vol. 2, no. 2, pp. 61-82, Jun. 2016. [Online]. Available: http://futureenergysp.com/index.php/tre/article/view/23

A. G. Lazaropoulos, “New Coupling Schemes for Distribution Broadband over Power Lines (BPL) Networks,” Progress in Electromagnetics Research B, vol. 71, pp. 39-54, 2016. [Online]. Available: http://www.jpier.org/PIERB/pierb71/02.16081503.pdf

A. G. Lazaropoulos, “Designing Broadband over Power Lines Networks Using the Techno-Economic Pedagogical (TEP) Method–Part I: Overhead High Voltage Networks and Their Capacity Characteristics (Invited Review Article),” Trends in Renewable Energy, vol. 1, no. 1, pp. 16-42, Mar. 2015. [Online]. Available: http://futureenergysp.com/index.php/tre/article/view/2

A. G. Lazaropoulos, “Overhead and Underground MIMO Low Voltage Broadband over Power Lines Networks and EMI Regulations: Towards Greener Capacity Performances,” Elsevier Computers and Electrical Engineering, vol. 39, pp. 2214-2230, 2013.

D. Fenton and P. Brown, “Some aspects of benchmarking high frequency radiated emissions from wireline communications systems in the near and far fields,” in Proc. IEEE Int. Symp. on Power Line Communications and its Applications, Malmö, Sweden, Apr. 2001, pp. 161-167.

DOI: http://dx.doi.org/10.17737/tre.2019.5.2.0096

### Refbacks

- There are currently no refbacks.

Copyright (c) 2019 Athanasios G. Lazaropoulos

This work is licensed under a Creative Commons Attribution 4.0 International License.

This work is licensed under a Creative Commons Attribution 4.0 License.

Copyright @2014-2020 Trends in Renewable Energy (ISSN: 2376-2136, online ISSN: 2376-2144)