Email this article From Vector-Level to Frequency-Wise Gaussian Mixture Modeling: A Footprint Analysis for Populating OV LV BPL Topology Class Maps
Abstract
In [1], the Gaussian Mixture Model (GMM) was introduced as an alternative population method for generating overhead low-voltage broadband over power lines (OV LV BPL) topologies, where a vector-level formulation was adopted to capture the joint statistical behavior of the channel attenuation error across the entire frequency range. This approach enabled the formation of clustered topology footprints on the OV LV BPL topology class maps, defined by the graphical combination of the average channel attenuation (ACA) and the standard deviation of the channel attenuation (SDCA).
Building upon this framework, the present short paper proposes a frequency-wise GMM population methodology, where the channel attenuation error is modeled independently at each frequency as a weighted sum of Normal Distributions (NDs). In contrast to the vector-level formulation, the proposed approach does not enforce a common latent component across frequencies, thus allowing increased flexibility in capturing frequency-dependent statistical variations.
The impact of the frequency-wise GMM parameters on the position, shape and dispersion of the resulting OV LV BPL topology footprints on the topology class maps is systematically investigated. The comparative assessment with the vector-level GMM of [1] is conducted through suitable Graphical Performance Indicators (GPIs), highlighting the fundamental trade-off between cross-frequency clustering and modeling flexibility. The results demonstrate that the frequency-wise GMM constitutes a versatile population mechanism, capable of approximating complex marginal distributions while altering the footprint structure on the topology class maps.
Citation: Lazaropoulos, A. (2026). From Vector-Level to Frequency-Wise Gaussian Mixture Modeling: A Footprint Analysis for Populating OV LV BPL Topology Class Maps. Trends in Renewable Energy, 12(2), 140-161. doi:http://dx.doi.org/10.17737/tre.2026.12.2.00202
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Lazaropoulos, A. (2026). Footprint Analysis of the Gaussian Mixture Model (GMM) for Populating Overhead Low Voltage Broadband over Power Lines (OV LV BPL) Topology Class Maps. Trends in Renewable Energy, 12(1), 33-65. doi:http://dx.doi.org/10.17737/tre.2026.12.1.00199
Lazaropoulos, A. G., & Leligou, H. C. (2022). Fiber optics and broadband over power lines in smart grid: a communications system architecture for overhead high-voltage, medium-voltage and low-voltage power grids. Progress in Electromagnetics Research B, 95, 185-205. doi: https://doi.org/10.2528/PIERB22062502
Lazaropoulos, A. G., & Leligou, H. C. (2024). Integration of LiFi, BPL, and Fiber Optic Technologies in Smart Grid Backbone Networks: A Proposal for Exploiting the LiFi LED Street Lighting Networks of Power Utilities and Smart Cities. Sustainability, 16(2), 686.
Kippke Salomón, M. A., Carou Álvarez, J. M., Suárez Ramón, L., & Arboleya, P. (2025). Self-Diagnostic Advanced Metering Infrastructure Based on Power-Line Communication: A Study Case in Spanish Low-Voltage Distribution Networks. Energies (19961073), 18(7).
Kalula, S. R., Dida, A. M., & Zaipuna, Y. O. (2024). Towards a low-cost sustainable broadband solution in rural areas of low and middle-income countries: Tanzania’s backhaul perspective. International Journal of Engineering, Science and Technology, 16(1), 20-34.
Fernandez, J. H., Jarouf, A., Omri, A., & Di Pietro, R. (2025). Leveraging Power Line Communications for Grid Intelligence: A Comprehensive Review of Signal-Based Techniques to Infer Grid Information. IEEE Access, 13, 118423-118437. DOI: 10.1109/ACCESS.2025.3586095
Goktas, P., & Ibrahim, S. (2025). Energy Management and Smart Grid Communication. AI and ML Techniques in IoT‐based Communication: A Path to Sustainable Development Goals, 179-212.
Lazaropoulos, A.G. (2024). Virtual Topologies for Populating Overhead Low-Voltage Broadband over Powerlines Topology Classes by Exploiting Neural Network Topology Generator Methodology (NNTGM) - Part 1: Theory. Trends in Renewable Energy, 10(3), 301-314. doi: http://dx.doi.org/10.17737/tre.2024.10.3.00181
Lazaropoulos, A.G. (2024). Virtual Topologies for Populating Overhead Low-Voltage Broadband over Powerlines Topology Classes by Exploiting Neural Network Topology Generator Methodology (NNTGM) – Part 2: Numerical Results. Trends in Renewable Energy, 10(3), 315-334. doi: http://dx.doi.org/10.17737/tre.2024.10.3.00182
Lazaropoulos, A. G. (2025). The Impact of Operating Frequencies and Neural Network Training Program Properties on the Performance of Neural Network Topology Generator Methodology. Trends in Renewable Energy, 11(2), 237-254.
Lazaropoulos, A. G. (2020). Business Analytics and IT in Smart Grid - Part 1: The Impact of Measurement Differences on the iSHM Class Map Footprints of Overhead Low-Voltage Broadband over Power Lines Topologies. Trends in Renewable Energy, 6(2), 156-186. doi: http://dx.doi.org/10.17737/tre.2020.6.2.00117
Lazaropoulos, A. G. (2020). Business Analytics and IT in Smart Grid - Part 2: The Qualitative Mitigation Impact of Piecewise Monotonic Data Approximations on the iSHM Class Map Footprints of Overhead Low-Voltage Broadband over Power Lines Topologies Contaminated by Measurement Differences. Trends in Renewable Energy, 6(2), 187-213. doi: http://dx.doi.org/10.17737/tre.2020.6.2.00118
Lazaropoulos, A. G. (2016). Measurement Differences, Faults and Instabilities in Intelligent Energy Systems - Part 1: Identification of Overhead High-Voltage Broadband over Power Lines Network Topologies by Applying Topology Identification Methodology (TIM). Trends in Renewable Energy, 2, 85-112. doi: https://doi.org/10.17737/tre.2016.2.3.0026
Lazaropoulos, A. G. (2016). Best L1 piecewise monotonic data approximation in overhead and underground medium-voltage and low-voltage broadband over power lines networks: Theoretical and practical transfer function determination. Hindawi Journal of Computational Engineering, 2016, 6762390, 24 pp. doi: https://doi.org/10.1155/2016/6762390
Lazaropoulos, A. G., & Leligou, H. C. (2023). Artificial Intelligence, Machine Learning and Neural Networks for Tomography in Smart Grid – Performance Comparison between Topology Identification Methodology and Neural Network Identification Methodology for the Distribution Line and Branch Line Length Approximation of Overhead Low-Voltage Broadband over Power Lines Network Topologies. Trends in Renewable Energy, 9(1), 34-77. doi: http://dx.doi.org/10.17737/tre.2023.9.1.00149
Lazaropoulos, A. G. (2012). 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, 2012, 1-17. doi: https://doi.org/10.1155/2012/121628
Lazaropoulos, A. G. (2020). Business Analytics and IT in Smart Grid - Part 3: New Application Aspect and the Quantitative Mitigation Analysis of Piecewise Monotonic Data Approximations on the iSHM Class Map Footprints of Overhead Low-Voltage Broadband over Power Lines Topologies Contaminated by Measurement Differences. Trends in Renewable Energy, 6(2), 214-233. doi: http://dx.doi.org/10.17737/tre.2020.6.2.00119
DOI: http://dx.doi.org/10.17737/tre.2026.12.2.00202
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This work is licensed under a Creative Commons Attribution 4.0 License.Copyright @2014-2026 Trends in Renewable Energy (ISSN: 2376-2136, online ISSN: 2376-2144)