Complexity reduction

Large grids analysed over many time steps can be slow and memory-hungry. eDisGo can reduce both the spatial size (number of buses) and the temporal size (number of time steps) of a problem.

Spatial complexity reduction

In plain terms

Spatial reduction merges nearby buses into a smaller set of representative buses, keeping the electrical behaviour as close as possible to the original grid. This shrinks the grid for faster power flow and optimisation.

../_images/spatial_complexity_reduction.png

Fig. 11 Spatial complexity reduction clusters buses along the grid into a smaller set of representative buses. Because the clusters are connected parts of the grid, the reduced grid stays radial — each reduced line aggregates real lines.

How it works

Call spatial_complexity_reduction(). The procedure has two steps: a busmap is built that maps every original bus to a clustered bus, and the eDisGo object is then reduced according to that busmap (lines are recalculated and sometimes merged). Parts of the method are based on the spatial clustering of [PyPSA].

All buses must have coordinates so that line lengths can be derived from the Euclidean distance and a detour factor. If your grid has no coordinates, set apply_pseudo_coordinates=True (the default) to compute coordinates from the radial grid topology.

Parameters:

  • mode — the clustering method:

    • "kmeans" — assign buses to K-Means cluster centres.

    • "kmeansdijkstra" — assign to the nearest cluster centre along the grid graph (Dijkstra distance).

    • "aggregate_to_main_feeder" — assign to the nearest node of the main feeder (the longest path in the feeder).

    • "equidistant_nodes" — place nodes equidistantly along the main feeder.

  • cluster_area — where clustering is applied: "grid", "feeder" or "main_feeder". Note that "aggregate_to_main_feeder" and "equidistant_nodes" only work with cluster_area="main_feeder".

  • reduction_factor — \(n_\text{buses} = k_\text{reduction}\cdot n_\text{buses, cluster area}\); a smaller factor means a stronger reduction.

  • reduction_factor_not_focused — reduce non-critical areas (no voltage or overloading problems in the worst case) more strongly than the focus areas.

For more control you can run the underlying functions directly:

from edisgo.tools.spatial_complexity_reduction import make_busmap, apply_busmap
from edisgo.tools.pseudo_coordinates import make_pseudo_coordinates

edisgo_obj = make_pseudo_coordinates(edisgo_obj)
busmap_df = make_busmap(
    edisgo_obj,
    mode="kmeans",
    cluster_area="feeder",
    reduction_factor=0.25,
)
edisgo_reduced, linemap_df = apply_busmap(edisgo_obj, busmap_df)

See [SCR] and [HoerschBrown] for the theory.

Temporal complexity reduction

The number of analysed time steps can be reduced by keeping only the grid-critical ones. reinforce() does this when called with reduced_analysis=True: it picks the most critical steps with get_most_critical_time_steps() (ranked by the worst voltage and line-loading issues, by default weighted by the estimated grid-expansion costs; whole worst-case intervals can be selected with get_most_critical_time_intervals()).

The flexibility optimisation uses a separate step selection in edisgo.opf.timeseries_reduction — get_steps_curtailment() and get_steps_storage() select and expand the critical time steps, while get_linked_steps() then groups them into representative steps for the OPF.

Memory

reduce_memory() downcasts the stored time-series, results, heat-pump and overlying-grid DataFrames to smaller dtypes (float32 by default), lowering memory use without changing the grid.

References

[SCR]

Malte Jahn, Analyse der Auswirkungen räumlicher Komplexitätsreduktion auf die Verteilnetzausbauplanung mit Flexibilitäten (in German; “Analysis of the effects of spatial complexity reduction on distribution grid expansion planning with flexibilities”), master’s thesis, Technische Universität Berlin (in cooperation with the Reiner Lemoine Institut), 2022. PDF The four clustering modes offered by spatial_complexity_reduction() ("kmeans", "kmeansdijkstra", "aggregate_to_main_feeder" and "equidistant_nodes") and the reduction_factor_not_focused option for reducing non-critical areas more strongly are developed and evaluated there.

[HoerschBrown]

Jonas Hörsch, Tom Brown: The role of spatial scale in joint optimisations of generation and transmission for European highly renewable scenarios, arXiv:1705.07617.