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Modeling medium and low voltage grids using population density

Emile Emery, Joseph Le Bihan, José Halloy

Abstract

The expansion of global electricity distribution systems necessitates the deployment of massive infrastructure. Assessing its implications from a spatial and material perspective requires an understanding of the core drivers of a distribution grid configuration. Our model samples substation locations using a non-linear relationship with population density and constructs the network applying the Kruskal algorithm. This streamlined approach generates realistic grid structures at the local scale and provides accurate estimates of the total network length at the national scale. Using highly granular population data, this local model reveals a profound connection between population spread and distribution grid, which appears to persist at the global level. Potentially driven by the emergent properties of population scaling laws, the full network characteristics appear to be well described by multivariate power laws on aggregated population and area. Validated across 35 countries, these results provide new multi-scale tools for characterizing electrical infrastructure and reveal key determinants of distribution grid extent.

Modeling medium and low voltage grids using population density

Abstract

The expansion of global electricity distribution systems necessitates the deployment of massive infrastructure. Assessing its implications from a spatial and material perspective requires an understanding of the core drivers of a distribution grid configuration. Our model samples substation locations using a non-linear relationship with population density and constructs the network applying the Kruskal algorithm. This streamlined approach generates realistic grid structures at the local scale and provides accurate estimates of the total network length at the national scale. Using highly granular population data, this local model reveals a profound connection between population spread and distribution grid, which appears to persist at the global level. Potentially driven by the emergent properties of population scaling laws, the full network characteristics appear to be well described by multivariate power laws on aggregated population and area. Validated across 35 countries, these results provide new multi-scale tools for characterizing electrical infrastructure and reveal key determinants of distribution grid extent.
Paper Structure (17 sections, 8 equations, 13 figures, 2 tables)

This paper contains 17 sections, 8 equations, 13 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Model
  3. Results
  4. Generating the French MV network from sole population density
  5. Visual comparison at the local scale
  6. Quantitative features at the country scale
  7. Results for other countries
  8. Macro-level indicators estimation
  9. Powerlaw-scaling of the number of substation - $N_{stat}$
  10. Powerlaw-scaling of the medium-voltage length - $L_{MV}$
  11. Powerlaw-scaling of the low-voltage length - $L_{LV}$
  12. Correlation between $L_{LV}$ and $L_{MV}$
  13. Material investment scaling with network length
  14. Discussion & Conclusion
  15. Voronoi slicing
  16. ...and 2 more sections

Figures (13)

  • Figure 1: Empirical relationship between the number of substation in a cell and the corresponding population density. Each point corresponds to the average number of substations per bin of density. The bin set is chosen such that each bin contains around 1000 data points. The threshold value is $\rho_0 \simeq 7.948$.
  • Figure 2: Histogram of the number of nodes in grid-cells.
  • Figure 3: Proportion of empty cells in the data for all population density values.
  • Figure 4: Node spatial distribution for the empirical dataset (top figure), and the model (bottom figure). The white holes in the top figures corresponds to area that are not managed by ENEDIS.
  • Figure 5: (a) Real population density data in France (orange) with simulated nodes (blue), minimum spanning tree edges (black), and computed Voronoi diagram (grey). (b) Real-world distribution grid layout in the corresponding area, with blue nodes representing MV/LV substations and black edges indicating MV lines.
  • ...and 8 more figures